Properties

Level $77$
Weight $0$
Character 77.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 77 = 7 \cdot 11 \)
Weight: \( 0 \)
Character: 77.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 3.31344205979 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.394323431\) \(a_{3}=-1.796498573\) \(a_{4}=+0.944137830\) \(a_{5}=-0.084375853\)
\(a_{6}=+2.504900054\) \(a_{7}=-0.377964473\) \(a_{8}=+0.077889932\) \(a_{9}=+2.227407124\) \(a_{10}=+0.117647229\)
\(a_{11}=-0.301511345\) \(a_{12}=-1.696142265\) \(a_{13}=-0.451974710\) \(a_{14}=+0.527004721\) \(a_{15}=+0.151581100\)
\(a_{16}=-1.052741588\) \(a_{17}=+0.261565911\) \(a_{18}=-3.105725943\) \(a_{19}=+1.903189558\) \(a_{20}=-0.079662435\)
\(a_{21}=+0.679012637\) \(a_{22}=+0.420404332\) \(a_{23}=+0.314125255\) \(a_{24}=-0.139929152\) \(a_{25}=-0.992880715\)
\(a_{26}=+0.630198928\) \(a_{27}=-2.205035147\) \(a_{28}=-0.356850557\) \(a_{29}=+0.614870434\) \(a_{30}=-0.211353079\)
\(a_{31}=+1.070217175\) \(a_{32}=+1.389972330\) \(a_{33}=+0.541664700\) \(a_{34}=-0.364707478\) \(a_{35}=+0.031891075\)
\(a_{36}=+2.102979329\) \(a_{37}=-0.262650113\) \(a_{38}=-2.653661794\) \(a_{39}=+0.811971921\) \(a_{40}=-0.006572029\)
\(a_{41}=-1.425621645\) \(a_{42}=-0.946763229\) \(a_{43}=+0.371549733\) \(a_{44}=-0.284668267\) \(a_{45}=-0.187939376\)
\(a_{46}=-0.437992203\) \(a_{47}=-0.201277372\) \(a_{48}=+1.891248761\) \(a_{49}=+0.142857143\) \(a_{50}=+1.384396846\)
\(a_{51}=-0.469902786\) \(a_{52}=-0.426726422\) \(a_{53}=-1.711430833\) \(a_{54}=+3.074532172\) \(a_{55}=+0.025440277\)
\(a_{56}=-0.029439627\) \(a_{57}=-3.419077325\) \(a_{58}=-0.857328253\) \(a_{59}=+0.735383745\) \(a_{60}=+0.143113451\)
\(a_{61}=+0.763858971\) \(a_{62}=-1.492228883\) \(a_{63}=-0.841880760\) \(a_{64}=-0.885329401\) \(a_{65}=+0.038135752\)
\(a_{66}=-0.755255783\) \(a_{67}=+0.562079591\) \(a_{68}=+0.246954271\) \(a_{69}=-0.564325572\) \(a_{70}=-0.044466473\)
\(a_{71}=-1.512556106\) \(a_{72}=+0.173492590\) \(a_{73}=+0.876104824\) \(a_{74}=+0.366219207\) \(a_{75}=+1.783708789\)
\(a_{76}=+1.796873259\) \(a_{77}=+0.113960576\) \(a_{78}=-1.132151475\) \(a_{79}=+1.936489394\) \(a_{80}=+0.088825970\)
\(a_{81}=+1.733935372\) \(a_{82}=+1.987777663\) \(a_{83}=-1.306727858\) \(a_{84}=+0.641081517\) \(a_{85}=-0.022069847\)
\(a_{86}=-0.518060499\) \(a_{87}=-1.104613857\) \(a_{88}=-0.023484698\) \(a_{89}=+1.420913687\) \(a_{90}=+0.262048276\)
\(a_{91}=+0.170830383\) \(a_{92}=+0.296577536\) \(a_{93}=-1.922643628\) \(a_{94}=+0.280645756\) \(a_{95}=-0.160583243\)
\(a_{96}=-2.497083308\) \(a_{97}=-0.429061930\) \(a_{98}=-0.199189062\) \(a_{99}=-0.671588517\) \(a_{100}=-0.937416244\)

Showing 100 of 672 available coefficients

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