**Kepler KOI-774 (KIC-11656840) 1-(or more)-Planet(s)**

**TTVs are derived from Q1-Q16 Kepler data. x-axes: “Observed Tc” (Mid-Transit Time): EXOFAST’s best-fits from Kepler light flux vs. time data. y-axes: “(O – C)”: difference between Observed Tc and the Calculated Tc from the graphically obtained linear ephemeris. The plots are pictured in the order of orbital periods.**

**EXOFAST data were obtained using the recently (Aug'13) updated value for [Fe/H] of -0.308 as one of the Priors. Dual oscillations were found for KOI-774.01. The Lomb-Scargle Periodogram (LSP) of the TTV x-y data ((O-C) vs. Time) for KOI-774.01 showed two prominent periodicities both of which appeared to be highly credible due to their low P-values (i.e., "by-chance" probabilities):**

**LSP-Periodicity-A: 1504.66 days, Power: 16.15, P-value: 0.000171; and**

**LSP-Periodicity-B: 31.51 days, Power: 13.53; P-value: 0.00235;**

**the same data gave the following two sinusoidal "best-fit" curves:**

**Sinus.-A: 1720.35* ± 15.42 days, Average Amplitude: 0.57 ± 0.35 min.; and**

**Sinus.-B: 31.50 ± 0.01 days, Average Amplitude: 0.46 ± 0.10 min.**

**Residuals-of-Sinus.-A (differences between the initial set of data points and those calculated from the sinusoidal equation defining Sinus.-A) showed one prominent, highly credible LSP periodicity:**

**LSP-Periodicity-C: 31.48 days, Power: 16.69, P-value: 0.00000993;**

**along with the following sinusoidal "best-fit" curve:**

**Sinus.-C: 31.50 ± 0.01 days, Average Amplitude: 0.46 ± 0.09 min.**

**Note the close agreement between LSP-Periodicity-B & LSP-Periodicity-C, and between Sinus.-B & Sinus.-C.**

**An LSP of a (secondary) set of residuals determined from Sinus.-C showed no prominent periodicities at all. Also, Residuals-of-Sinus.-B (differences between the initial set of data points and those calculated from the sinusoidal equation defining Sinus.-B) showed one prominent, highly credible LSP periodicity:**

**LSP-Periodicity-D: 1504.66 days, Power: 19.18, P-value: 0.00000824;**

**along with the following sinusoidal "best-fit" curve:**

**Sinus.-D: 1753.79* ± 14.74 days, Average Amplitude: 0.59 ± 0.35 min.**

**Note the close agreement between LSP-Periodicity-A & LSP-Periodicity-D, and between Sinus.-A & Sinus.-D.**

**An LSP of a (secondary) set of residuals determined from Sinus.-D showed no prominent periodicities at all.**

*** These values are derived from the best-fit sinusoidal equations which, unfortunately, were mostly based upon a single very broad maximum. Based on a large number of other systems, better agreement with the Lomb-Scargle periodogram periodicities would be expected if more data were available to generate a more accurate sinusoidal equation.The results are graphically arrayed below in the same order they were discussed.**