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: \( 1.7546428498 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.159133046\) \(a_{3}=-0.347685898\) \(a_{4}=-0.974676674\) \(a_{5}=+1.769028235\)
\(a_{6}=-0.055328316\) \(a_{7}=+0.716573740\) \(a_{8}=-0.314236314\) \(a_{9}=-0.879114516\) \(a_{10}=+0.281510851\)
\(a_{11}=+1.271666943\) \(a_{12}=+0.338881335\) \(a_{13}=-0.554656293\) \(a_{14}=+0.114030562\) \(a_{15}=-0.615066170\)
\(a_{16}=+0.924671292\) \(a_{17}=-1.318426539\) \(a_{18}=-0.139896171\) \(a_{19}=+0.306257872\) \(a_{20}=-1.724230556\)
\(a_{21}=-0.249142584\) \(a_{22}=+0.202364234\) \(a_{23}=+0.035200668\) \(a_{24}=+0.109255535\) \(a_{25}=+2.129460896\)
\(a_{26}=-0.088264145\) \(a_{27}=+0.653341618\) \(a_{28}=-0.698427709\) \(a_{29}=-0.421564717\) \(a_{30}=-0.097877353\)
\(a_{31}=-0.179605302\) \(a_{32}=+0.461382073\) \(a_{33}=-0.442140663\) \(a_{34}=-0.209805231\) \(a_{35}=+1.267639178\)
\(a_{36}=+0.856852413\) \(a_{37}=+0.243190536\) \(a_{38}=+0.048735748\) \(a_{39}=+0.192846171\) \(a_{40}=-0.555892912\)
\(a_{41}=+0.721799999\) \(a_{42}=-0.039646818\) \(a_{43}=-0.142714162\) \(a_{44}=-1.239464106\) \(a_{45}=-1.555178401\)
\(a_{46}=+0.005601590\) \(a_{47}=-0.897378767\) \(a_{48}=-0.321495168\) \(a_{49}=-0.486522076\) \(a_{50}=+0.338867599\)
\(a_{51}=+0.458398315\) \(a_{52}=+0.540610551\) \(a_{53}=-1.480163606\) \(a_{54}=+0.103968242\) \(a_{55}=+2.249614728\)
\(a_{56}=-0.225173491\) \(a_{57}=-0.106481543\) \(a_{58}=-0.067084877\) \(a_{59}=+1.124646372\) \(a_{60}=+0.599490649\)
\(a_{61}=-0.458920329\) \(a_{62}=-0.028581139\) \(a_{63}=-0.629950376\) \(a_{64}=-0.851250157\) \(a_{65}=-0.981202643\)
\(a_{66}=-0.070359190\) \(a_{67}=+0.603856920\) \(a_{68}=+1.285039593\) \(a_{69}=-0.012238776\) \(a_{70}=+0.201723284\)
\(a_{71}=+0.683002947\) \(a_{72}=+0.276249705\) \(a_{73}=+0.437276527\) \(a_{74}=+0.038699651\) \(a_{75}=-0.740383524\)
\(a_{76}=-0.298502404\) \(a_{77}=+0.911243137\) \(a_{78}=+0.030688199\) \(a_{79}=-0.042606244\) \(a_{80}=+1.635769623\)
\(a_{81}=+0.651956849\) \(a_{82}=+0.114862232\) \(a_{83}=-1.788228873\) \(a_{84}=+0.242833465\) \(a_{85}=-2.332333773\)
\(a_{86}=-0.022710539\) \(a_{87}=+0.146572107\) \(a_{88}=-0.399603933\) \(a_{89}=-0.253409084\) \(a_{90}=-0.247480276\)
\(a_{91}=-0.397452134\) \(a_{92}=-0.034309270\) \(a_{93}=+0.062446231\) \(a_{94}=-0.142802617\) \(a_{95}=+0.541778823\)
\(a_{96}=-0.160416040\) \(a_{97}=+0.566446009\) \(a_{98}=-0.077421740\) \(a_{99}=-1.117940870\) \(a_{100}=-2.075535863\)

Showing 100 of 546 available coefficients

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