Properties

Level $14$
Weight $0$
Character 14.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 14 = 2 \cdot 7 \)
Weight: \( 0 \)
Character: 14.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 6.49256560744 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.223827073\) \(a_{4}=+0.500000000\) \(a_{5}=-0.282481021\)
\(a_{6}=-0.865376422\) \(a_{7}=+0.377964473\) \(a_{8}=-0.353553391\) \(a_{9}=+0.497752705\) \(a_{10}=+0.199744246\)
\(a_{11}=+0.897948320\) \(a_{12}=+0.611913537\) \(a_{13}=+0.290030370\) \(a_{14}=-0.267261242\) \(a_{15}=-0.345707921\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.329176673\) \(a_{18}=-0.351964313\) \(a_{19}=+1.343504207\) \(a_{20}=-0.141240511\)
\(a_{21}=+0.462563155\) \(a_{22}=-0.634945346\) \(a_{23}=+0.604896604\) \(a_{24}=-0.432688211\) \(a_{25}=-0.920204473\)
\(a_{26}=-0.205082442\) \(a_{27}=-0.614663837\) \(a_{28}=+0.188982236\) \(a_{29}=+1.519007897\) \(a_{30}=+0.244452416\)
\(a_{31}=-0.568257131\) \(a_{32}=-0.176776695\) \(a_{33}=+1.098933464\) \(a_{34}=-0.939869839\) \(a_{35}=-0.106767790\)
\(a_{36}=+0.248876354\) \(a_{37}=+1.927109109\) \(a_{38}=-0.950000937\) \(a_{39}=+0.354947018\) \(a_{40}=+0.099872123\)
\(a_{41}=-0.596593674\) \(a_{42}=-0.327081542\) \(a_{43}=-1.774953234\) \(a_{44}=+0.448974156\) \(a_{45}=-0.140605695\)
\(a_{46}=-0.427726481\) \(a_{47}=-0.558547855\) \(a_{48}=+0.305956735\) \(a_{49}=+0.142857109\) \(a_{50}=+0.650682904\)
\(a_{51}=+1.626682378\) \(a_{52}=+0.145015200\) \(a_{53}=-0.192408742\) \(a_{54}=+0.434632968\) \(a_{55}=-0.253653359\)
\(a_{56}=-0.133630623\) \(a_{57}=+1.644216821\) \(a_{58}=-1.074100783\) \(a_{59}=-0.474329153\) \(a_{60}=-0.172853960\)
\(a_{61}=-1.326801984\) \(a_{62}=+0.401818466\) \(a_{63}=+0.188132839\) \(a_{64}=+0.125000009\) \(a_{65}=-0.081928068\)
\(a_{66}=-0.777063311\) \(a_{67}=-0.589081810\) \(a_{68}=+0.664588331\) \(a_{69}=+0.740288860\) \(a_{70}=+0.075496252\)
\(a_{71}=+0.425921956\) \(a_{72}=-0.175982198\) \(a_{73}=+0.765677251\) \(a_{74}=-1.362671887\) \(a_{75}=-1.126171030\)
\(a_{76}=+0.671752108\) \(a_{77}=+0.339392560\) \(a_{78}=-0.250985445\) \(a_{79}=-0.061774021\) \(a_{80}=-0.070620259\)
\(a_{81}=-1.249994946\) \(a_{82}=+0.421855435\) \(a_{83}=+1.433665740\) \(a_{84}=+0.231281587\) \(a_{85}=-0.375467189\)
\(a_{86}=+1.255081472\) \(a_{87}=+1.859002996\) \(a_{88}=-0.317472697\) \(a_{89}=-1.167120212\) \(a_{90}=+0.099423227\)
\(a_{91}=+0.109621157\) \(a_{92}=+0.302448363\) \(a_{93}=-0.695448520\) \(a_{94}=+0.394953019\) \(a_{95}=-0.379514430\)
\(a_{96}=-0.216344190\) \(a_{97}=-1.731362975\) \(a_{98}=-0.101015384\) \(a_{99}=+0.446956248\) \(a_{100}=-0.460102234\)

Showing 100 of 2000 available coefficients

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