Properties

Level $31$
Weight $0$
Character 31.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 1.83128343514 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.769069647\) \(a_{3}=+1.781276411\) \(a_{4}=-0.408531878\) \(a_{5}=-0.677411700\)
\(a_{6}=-1.369925621\) \(a_{7}=+0.495011114\) \(a_{8}=+1.083259114\) \(a_{9}=+2.172945652\) \(a_{10}=+0.520976777\)
\(a_{11}=-0.958864507\) \(a_{12}=-0.727708197\) \(a_{13}=+1.512149759\) \(a_{14}=-0.380698023\) \(a_{15}=-1.206657482\)
\(a_{16}=-0.424569827\) \(a_{17}=-0.848061213\) \(a_{18}=-1.671146546\) \(a_{19}=+0.221278283\) \(a_{20}=+0.276744274\)
\(a_{21}=+0.881751621\) \(a_{22}=+0.737433588\) \(a_{23}=-0.600015103\) \(a_{24}=+1.929583907\) \(a_{25}=-0.541113388\)
\(a_{26}=-1.162948481\) \(a_{27}=+2.089340422\) \(a_{28}=-0.202227820\) \(a_{29}=-0.493232031\) \(a_{30}=+0.928003644\)
\(a_{31}=-0.179605302\) \(a_{32}=-0.756735347\) \(a_{33}=-1.708002727\) \(a_{34}=+0.652218138\) \(a_{35}=-0.335326320\)
\(a_{36}=-0.887717568\) \(a_{37}=+1.725799631\) \(a_{38}=-0.170178411\) \(a_{39}=+2.693556695\) \(a_{40}=-0.733812398\)
\(a_{41}=+0.094854194\) \(a_{42}=-0.678128408\) \(a_{43}=-0.039563033\) \(a_{44}=+0.391726718\) \(a_{45}=-1.471978809\)
\(a_{46}=+0.461453404\) \(a_{47}=+0.684454542\) \(a_{48}=-0.756276217\) \(a_{49}=-0.754963997\) \(a_{50}=+0.416153883\)
\(a_{51}=-1.510631434\) \(a_{52}=-0.617761381\) \(a_{53}=+0.761729881\) \(a_{54}=-1.606848301\) \(a_{55}=+0.649546036\)
\(a_{56}=+0.536225301\) \(a_{57}=+0.394157787\) \(a_{58}=+0.379329784\) \(a_{59}=-0.458599708\) \(a_{60}=+0.492958047\)
\(a_{61}=-1.325686989\) \(a_{62}=+0.138128986\) \(a_{63}=+1.075632248\) \(a_{64}=+1.006552013\) \(a_{65}=-1.024347939\)
\(a_{66}=+1.313573054\) \(a_{67}=+0.195186691\) \(a_{68}=+0.346460040\) \(a_{69}=-1.068792750\) \(a_{70}=+0.257889295\)
\(a_{71}=+1.446950608\) \(a_{72}=+2.353863183\) \(a_{73}=+0.008810723\) \(a_{74}=-1.327260113\) \(a_{75}=-0.963872514\)
\(a_{76}=-0.090399233\) \(a_{77}=-0.474648588\) \(a_{78}=-2.071532697\) \(a_{79}=+0.613366087\) \(a_{80}=+0.287608568\)
\(a_{81}=+1.548747156\) \(a_{82}=-0.072949482\) \(a_{83}=-0.488481731\) \(a_{84}=-0.360223645\) \(a_{85}=+0.574486588\)
\(a_{86}=+0.030426728\) \(a_{87}=-0.878582583\) \(a_{88}=-1.038698716\) \(a_{89}=+0.672866502\) \(a_{90}=+1.132054223\)
\(a_{91}=+0.748530937\) \(a_{92}=+0.245125297\) \(a_{93}=-0.319926688\) \(a_{94}=-0.526393213\) \(a_{95}=-0.149896498\)
\(a_{96}=-1.347954824\) \(a_{97}=-0.638276004\) \(a_{98}=+0.580619895\) \(a_{99}=-2.083560461\) \(a_{100}=+0.221062069\)

Showing 100 of 546 available coefficients

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