Properties

Level $14$
Weight $0$
Character 14.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 14 = 2 \cdot 7 \)
Weight: \( 0 \)
Character: 14.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 7.8976039924 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.250627899\) \(a_{4}=+0.500000000\) \(a_{5}=+1.787072320\)
\(a_{6}=+0.884327468\) \(a_{7}=+0.377964473\) \(a_{8}=+0.353553391\) \(a_{9}=+0.564070141\) \(a_{10}=+1.263650956\)
\(a_{11}=-1.204314596\) \(a_{12}=+0.625313949\) \(a_{13}=-1.083018265\) \(a_{14}=+0.267261242\) \(a_{15}=+2.234962500\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.022441756\) \(a_{18}=+0.398857822\) \(a_{19}=-0.433761154\) \(a_{20}=+0.893536160\)
\(a_{21}=+0.472692915\) \(a_{22}=-0.851579018\) \(a_{23}=-0.117688185\) \(a_{24}=+0.442163734\) \(a_{25}=+2.193627475\)
\(a_{26}=-0.765809559\) \(a_{27}=-0.545186044\) \(a_{28}=+0.188982236\) \(a_{29}=+0.203529635\) \(a_{30}=+1.580357139\)
\(a_{31}=-0.783015572\) \(a_{32}=+0.176776695\) \(a_{33}=-1.506149433\) \(a_{34}=+0.722975499\) \(a_{35}=+0.675449848\)
\(a_{36}=+0.282035070\) \(a_{37}=+1.268886427\) \(a_{38}=-0.306715453\) \(a_{39}=-1.354452856\) \(a_{40}=+0.631825478\)
\(a_{41}=-1.701566877\) \(a_{42}=+0.334244365\) \(a_{43}=-0.892589190\) \(a_{44}=-0.602157297\) \(a_{45}=+1.008034134\)
\(a_{46}=-0.083218109\) \(a_{47}=+0.963108437\) \(a_{48}=+0.312656981\) \(a_{49}=+0.142857140\) \(a_{50}=+1.551128863\)
\(a_{51}=+1.278694199\) \(a_{52}=-0.541509158\) \(a_{53}=-0.519903720\) \(a_{54}=-0.385504788\) \(a_{55}=-2.152197201\)
\(a_{56}=+0.133630621\) \(a_{57}=-0.542473801\) \(a_{58}=+0.143917185\) \(a_{59}=+0.301360932\) \(a_{60}=+1.117481251\)
\(a_{61}=+0.195896207\) \(a_{62}=-0.553675621\) \(a_{63}=+0.213198472\) \(a_{64}=+0.125000000\) \(a_{65}=-1.935431960\)
\(a_{66}=-1.065008477\) \(a_{67}=+1.322938490\) \(a_{68}=+0.511220874\) \(a_{69}=-0.147184131\) \(a_{70}=+0.477615172\)
\(a_{71}=-0.819982425\) \(a_{72}=+0.199428913\) \(a_{73}=+0.095253085\) \(a_{74}=+0.897238193\) \(a_{75}=+2.743411725\)
\(a_{76}=-0.216880573\) \(a_{77}=-0.455188153\) \(a_{78}=-0.957742820\) \(a_{79}=+0.887235057\) \(a_{80}=+0.446768090\)
\(a_{81}=-1.245894946\) \(a_{82}=-1.203189623\) \(a_{83}=-1.281110609\) \(a_{84}=+0.236346332\) \(a_{85}=+1.827177361\)
\(a_{86}=-0.631155867\) \(a_{87}=+0.254539837\) \(a_{88}=-0.425789508\) \(a_{89}=-0.842390055\) \(a_{90}=+0.712787776\)
\(a_{91}=-0.409342433\) \(a_{92}=-0.058844095\) \(a_{93}=-0.979261118\) \(a_{94}=+0.681020523\) \(a_{95}=-0.775162562\)
\(a_{96}=+0.221081871\) \(a_{97}=-0.303808194\) \(a_{98}=+0.101015266\) \(a_{99}=-0.679317938\) \(a_{100}=+1.096813743\)

Showing 100 of 2000 available coefficients

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