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: \( 3.3914645439 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.977509175\) \(a_{3}=+1.552807357\) \(a_{4}=-0.044475813\) \(a_{5}=+1.724144041\)
\(a_{6}=-1.517883438\) \(a_{7}=-0.989909763\) \(a_{8}=+1.020984690\) \(a_{9}=+1.411210686\) \(a_{10}=-1.685366619\)
\(a_{11}=+1.471112193\) \(a_{12}=-0.069062370\) \(a_{13}=+0.264765419\) \(a_{14}=+0.967645876\) \(a_{15}=+2.677263550\)
\(a_{16}=-0.953546089\) \(a_{17}=-0.515972130\) \(a_{18}=-1.379471394\) \(a_{19}=-0.485612367\) \(a_{20}=-0.076682708\)
\(a_{21}=-1.537139163\) \(a_{22}=-1.438025666\) \(a_{23}=+1.037248698\) \(a_{24}=+1.585392538\) \(a_{25}=+1.972672672\)
\(a_{26}=-0.258810626\) \(a_{27}=+0.638530979\) \(a_{28}=+0.044027041\) \(a_{29}=-0.424227199\) \(a_{30}=-2.617049683\)
\(a_{31}=-0.179605302\) \(a_{32}=-0.088884639\) \(a_{33}=+2.284353835\) \(a_{34}=+0.504367490\) \(a_{35}=-1.706747019\)
\(a_{36}=-0.062764742\) \(a_{37}=-0.941156415\) \(a_{38}=+0.474690545\) \(a_{39}=+0.411129690\) \(a_{40}=+1.760324668\)
\(a_{41}=-0.467130559\) \(a_{42}=+1.502567636\) \(a_{43}=-0.982215793\) \(a_{44}=-0.065428911\) \(a_{45}=+2.433130493\)
\(a_{46}=-1.013920120\) \(a_{47}=+0.210603035\) \(a_{48}=-1.480673379\) \(a_{49}=-0.020078660\) \(a_{50}=-1.928305640\)
\(a_{51}=-0.801205322\) \(a_{52}=-0.011775657\) \(a_{53}=+1.027328865\) \(a_{54}=-0.624169883\) \(a_{55}=+2.536409317\)
\(a_{56}=-1.010682724\) \(a_{57}=-0.754062465\) \(a_{58}=+0.414685985\) \(a_{59}=-0.297168070\) \(a_{60}=-0.119073463\)
\(a_{61}=-0.650376129\) \(a_{62}=+0.175565798\) \(a_{63}=-1.396971253\) \(a_{64}=+1.040431675\) \(a_{65}=+0.456493778\)
\(a_{66}=-2.232976827\) \(a_{67}=+0.303123733\) \(a_{68}=+0.022948202\) \(a_{69}=+1.610647428\) \(a_{70}=+1.668361002\)
\(a_{71}=-1.620058395\) \(a_{72}=+1.440824490\) \(a_{73}=-1.389009454\) \(a_{74}=+0.919988991\) \(a_{75}=+3.063180683\)
\(a_{76}=+0.021597994\) \(a_{77}=-1.456268342\) \(a_{78}=-0.401883019\) \(a_{79}=+1.316866739\) \(a_{80}=-1.644050791\)
\(a_{81}=-0.419695125\) \(a_{82}=+0.456624320\) \(a_{83}=+0.697018933\) \(a_{84}=+0.068365559\) \(a_{85}=-0.889610283\)
\(a_{86}=+0.960124969\) \(a_{87}=-0.658743133\) \(a_{88}=+1.501982999\) \(a_{89}=+0.674481736\) \(a_{90}=-2.378407406\)
\(a_{91}=-0.262093936\) \(a_{92}=-0.046132435\) \(a_{93}=-0.278892425\) \(a_{94}=-0.205866366\) \(a_{95}=-0.837265702\)
\(a_{96}=-0.138020791\) \(a_{97}=-0.053950266\) \(a_{98}=+0.019627086\) \(a_{99}=+2.076049236\) \(a_{100}=-0.087736209\)

Showing 100 of 1500 available coefficients

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