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: \( 3.74519506768 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.249602442\) \(a_{3}=-0.745440890\) \(a_{4}=+0.561506263\) \(a_{5}=-0.953394979\)
\(a_{6}=+0.931504757\) \(a_{7}=-1.460766192\) \(a_{8}=+0.547942844\) \(a_{9}=-0.444317879\) \(a_{10}=+1.191364694\)
\(a_{11}=+0.024276565\) \(a_{12}=-0.418569729\) \(a_{13}=+0.714247041\) \(a_{14}=+1.825377001\) \(a_{15}=+0.710699602\)
\(a_{16}=-1.246216980\) \(a_{17}=-1.059589362\) \(a_{18}=+0.555220706\) \(a_{19}=+0.945319411\) \(a_{20}=-0.535337252\)
\(a_{21}=+1.088914851\) \(a_{22}=-0.030336054\) \(a_{23}=-1.450679181\) \(a_{24}=-0.408459002\) \(a_{25}=-0.091038015\)
\(a_{26}=-0.892524847\) \(a_{27}=+1.076653606\) \(a_{28}=-0.820229366\) \(a_{29}=+1.036499716\) \(a_{30}=-0.888091958\)
\(a_{31}=-0.179605302\) \(a_{32}=+1.009332937\) \(a_{33}=-0.018096744\) \(a_{34}=+1.324065454\) \(a_{35}=+1.392687152\)
\(a_{36}=-0.249487272\) \(a_{37}=+0.383148949\) \(a_{38}=-1.181273445\) \(a_{39}=-0.532428950\) \(a_{40}=-0.522405956\)
\(a_{41}=-1.200781179\) \(a_{42}=-1.360710657\) \(a_{43}=+1.244629648\) \(a_{44}=+0.013631443\) \(a_{45}=+0.423610435\)
\(a_{46}=+1.812772248\) \(a_{47}=-1.300805593\) \(a_{48}=+0.928981095\) \(a_{49}=+1.133837868\) \(a_{50}=+0.113761326\)
\(a_{51}=+0.789861238\) \(a_{52}=+0.401054187\) \(a_{53}=-0.774257695\) \(a_{54}=-1.345388975\) \(a_{55}=-0.023145155\)
\(a_{56}=-0.800416382\) \(a_{57}=-0.704679744\) \(a_{58}=-1.295212577\) \(a_{59}=-0.302743512\) \(a_{60}=+0.399062278\)
\(a_{61}=+0.785468640\) \(a_{62}=+0.224435224\) \(a_{63}=+0.649044536\) \(a_{64}=-0.015047923\) \(a_{65}=-0.680959542\)
\(a_{66}=+0.022613735\) \(a_{67}=-0.759531033\) \(a_{68}=-0.594966063\) \(a_{69}=+1.081395581\) \(a_{70}=-1.740305267\)
\(a_{71}=+1.227287053\) \(a_{72}=-0.243460802\) \(a_{73}=+0.494988072\) \(a_{74}=-0.478783862\) \(a_{75}=+0.067863459\)
\(a_{76}=+0.530802770\) \(a_{77}=-0.035462385\) \(a_{78}=+0.665324516\) \(a_{79}=+1.840636966\) \(a_{80}=+1.188137011\)
\(a_{81}=-0.358263744\) \(a_{82}=+1.500499094\) \(a_{83}=-0.628516793\) \(a_{84}=+0.611432509\) \(a_{85}=+1.010207177\)
\(a_{86}=-1.555292247\) \(a_{87}=-0.772649271\) \(a_{88}=+0.013302170\) \(a_{89}=+0.669843206\) \(a_{90}=-0.529344634\)
\(a_{91}=-1.043347930\) \(a_{92}=-0.814565446\) \(a_{93}=+0.133885136\) \(a_{94}=+1.625489846\) \(a_{95}=-0.901262780\)
\(a_{96}=-0.752398043\) \(a_{97}=-0.359759693\) \(a_{98}=-1.416846568\) \(a_{99}=-0.010786512\) \(a_{100}=-0.051118415\)

Showing 100 of 546 available coefficients

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