Properties

Level $65$
Weight $0$
Character 65.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 65 = 5 \cdot 13 \)
Weight: \( 0 \)
Character: 65.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 3.40497156843 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.181494208\) \(a_{3}=-0.595100640\) \(a_{4}=-0.967059853\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.108007319\) \(a_{7}=-0.084808820\) \(a_{8}=+0.357009970\) \(a_{9}=-0.645855229\) \(a_{10}=+0.081166677\)
\(a_{11}=+0.868811402\) \(a_{12}=+0.575497937\) \(a_{13}=-0.277350098\) \(a_{14}=+0.015392310\) \(a_{15}=+0.266137097\)
\(a_{16}=+0.902264611\) \(a_{17}=-1.603744701\) \(a_{18}=+0.117218983\) \(a_{19}=+0.152192408\) \(a_{20}=+0.432482314\)
\(a_{21}=+0.050469783\) \(a_{22}=-0.157684237\) \(a_{23}=+1.264984867\) \(a_{24}=-0.212456861\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.050337436\) \(a_{27}=+0.979449499\) \(a_{28}=+0.082015205\) \(a_{29}=+0.722416775\) \(a_{30}=-0.048302342\)
\(a_{31}=+0.294298251\) \(a_{32}=-0.520765771\) \(a_{33}=-0.517030221\) \(a_{34}=+0.291070374\) \(a_{35}=+0.037927657\)
\(a_{36}=+0.624580662\) \(a_{37}=+1.075963375\) \(a_{38}=-0.027622040\) \(a_{39}=+0.165051221\) \(a_{40}=-0.159659712\)
\(a_{41}=-1.815902110\) \(a_{42}=-0.009159973\) \(a_{43}=+0.887521512\) \(a_{44}=-0.840192626\) \(a_{45}=+0.288835239\)
\(a_{46}=-0.229587426\) \(a_{47}=-0.577161624\) \(a_{48}=-0.536938247\) \(a_{49}=-0.992807464\) \(a_{50}=-0.036298842\)
\(a_{51}=+0.954389497\) \(a_{52}=+0.268214145\) \(a_{53}=+1.155042644\) \(a_{54}=-0.177764411\) \(a_{55}=-0.388544271\)
\(a_{56}=-0.030277594\) \(a_{57}=-0.090569799\) \(a_{58}=-0.131114460\) \(a_{59}=-1.286897695\) \(a_{60}=-0.257370501\)
\(a_{61}=+0.569038869\) \(a_{62}=-0.053413428\) \(a_{63}=+0.054774220\) \(a_{64}=-0.807748640\) \(a_{65}=+0.124034735\)
\(a_{66}=+0.093837990\) \(a_{67}=+0.292228738\) \(a_{68}=+1.550917114\) \(a_{69}=-0.752793303\) \(a_{70}=-0.006883650\)
\(a_{71}=+1.867734781\) \(a_{72}=-0.230576756\) \(a_{73}=+0.594156528\) \(a_{74}=-0.195281120\) \(a_{75}=-0.119020128\)
\(a_{76}=-0.147179167\) \(a_{77}=-0.073682870\) \(a_{78}=-0.029955841\) \(a_{79}=+0.279689038\) \(a_{80}=-0.403505001\)
\(a_{81}=+0.062984205\) \(a_{82}=+0.329575715\) \(a_{83}=+0.636094068\) \(a_{84}=-0.048807301\) \(a_{85}=+0.717216434\)
\(a_{86}=-0.161080014\) \(a_{87}=-0.429910685\) \(a_{88}=+0.310174332\) \(a_{89}=+0.309487387\) \(a_{90}=-0.052421923\)
\(a_{91}=+0.023521735\) \(a_{92}=-1.223316079\) \(a_{93}=-0.175137077\) \(a_{94}=+0.104751492\) \(a_{95}=-0.068062514\)
\(a_{96}=+0.309908043\) \(a_{97}=-0.525359558\) \(a_{98}=+0.180188804\) \(a_{99}=-0.561126387\) \(a_{100}=-0.193411971\)

Showing 100 of 660 available coefficients

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