Properties

Level $61$
Weight $0$
Character 61.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 61 \)
Weight: \( 0 \)
Character: 61.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 0.9880378241 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.728713716\) \(a_{3}=-1.596078658\) \(a_{4}=+1.988451112\) \(a_{5}=+0.878952736\)
\(a_{6}=+2.759163068\) \(a_{7}=+0.447382217\) \(a_{8}=-1.708748995\) \(a_{9}=+1.547467083\) \(a_{10}=-1.519457650\)
\(a_{11}=+0.627576979\) \(a_{12}=-3.173724382\) \(a_{13}=+0.045712952\) \(a_{14}=-0.773395775\) \(a_{15}=-1.402877703\)
\(a_{16}=+0.965486712\) \(a_{17}=+1.410842101\) \(a_{18}=-2.675127571\) \(a_{19}=+1.643683784\) \(a_{20}=+1.747754545\)
\(a_{21}=-0.714057209\) \(a_{22}=-1.084900931\) \(a_{23}=-1.067241622\) \(a_{24}=+2.727297802\) \(a_{25}=-0.227442088\)
\(a_{26}=-0.079024608\) \(a_{27}=-0.873800526\) \(a_{28}=+0.889597667\) \(a_{29}=+0.276994712\) \(a_{30}=+2.425173928\)
\(a_{31}=+0.984322762\) \(a_{32}=+0.039698872\) \(a_{33}=-1.001662222\) \(a_{34}=-2.438942091\) \(a_{35}=+0.393227824\)
\(a_{36}=+3.077062641\) \(a_{37}=+0.525472350\) \(a_{38}=-2.841458703\) \(a_{39}=-0.072961468\) \(a_{40}=-1.501909604\)
\(a_{41}=-0.903764396\) \(a_{42}=+1.234400491\) \(a_{43}=-0.393110655\) \(a_{44}=+1.247906142\) \(a_{45}=+1.360150426\)
\(a_{46}=+1.844955231\) \(a_{47}=+0.043592486\) \(a_{48}=-1.540992736\) \(a_{49}=-0.799849152\) \(a_{50}=+0.393182257\)
\(a_{51}=-2.251814967\) \(a_{52}=+0.090897971\) \(a_{53}=+0.962013454\) \(a_{54}=+1.510550955\) \(a_{55}=+0.551610503\)
\(a_{56}=-0.764463914\) \(a_{57}=-2.623448609\) \(a_{58}=-0.478844558\) \(a_{59}=-0.755992412\) \(a_{60}=-2.789553729\)
\(a_{61}=+0.128036880\) \(a_{62}=-1.701612260\) \(a_{63}=+0.692309255\) \(a_{64}=-1.034114697\) \(a_{65}=+0.040179525\)
\(a_{66}=+1.731587223\) \(a_{67}=+1.585514177\) \(a_{68}=+2.805390544\) \(a_{69}=+1.703401576\) \(a_{70}=-0.679778333\)
\(a_{71}=-0.216028416\) \(a_{72}=-2.644232822\) \(a_{73}=+1.730201578\) \(a_{74}=-0.908391258\) \(a_{75}=+0.363015462\)
\(a_{76}=+3.268384849\) \(a_{77}=+0.280766780\) \(a_{78}=+0.126129490\) \(a_{79}=-0.777286490\) \(a_{80}=+0.848617188\)
\(a_{81}=-0.152812711\) \(a_{82}=+1.562349907\) \(a_{83}=-0.618089916\) \(a_{84}=-1.419867851\) \(a_{85}=+1.240063525\)
\(a_{86}=+0.679575781\) \(a_{87}=-0.442105348\) \(a_{88}=-1.072371532\) \(a_{89}=-0.369067977\) \(a_{90}=-2.351310697\)
\(a_{91}=+0.020451162\) \(a_{92}=-2.122157790\) \(a_{93}=-1.571056553\) \(a_{94}=-0.075358928\) \(a_{95}=+1.444720359\)
\(a_{96}=-0.063362523\) \(a_{97}=-0.984473896\) \(a_{98}=+1.382710199\) \(a_{99}=+0.971154717\) \(a_{100}=-0.452257473\)

Showing 100 of 546 available coefficients

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