Properties

Level $10$
Weight $0$
Character 10.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 22.6900189031 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.066481935\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.754116608\) \(a_{7}=-1.900382421\) \(a_{8}=+0.353553391\) \(a_{9}=+0.137383718\) \(a_{10}=-0.316227766\)
\(a_{11}=+1.340281361\) \(a_{12}=+0.533240968\) \(a_{13}=+1.508165926\) \(a_{14}=-1.343773297\) \(a_{15}=-0.476945221\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.813548005\) \(a_{18}=+0.097144959\) \(a_{19}=+0.333503105\) \(a_{20}=-0.223606798\)
\(a_{21}=-2.026723522\) \(a_{22}=+0.947722039\) \(a_{23}=+0.059458007\) \(a_{24}=+0.377058304\) \(a_{25}=+0.199951172\)
\(a_{26}=+1.066434353\) \(a_{27}=-0.919964682\) \(a_{28}=-0.950191211\) \(a_{29}=-0.865072225\) \(a_{30}=-0.337251200\)
\(a_{31}=+0.733785347\) \(a_{32}=+0.176776695\) \(a_{33}=+1.429385859\) \(a_{34}=-0.575265311\) \(a_{35}=+0.849876855\)
\(a_{36}=+0.068691859\) \(a_{37}=+0.614171664\) \(a_{38}=+0.235822307\) \(a_{39}=+1.608431715\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.613424675\) \(a_{42}=-1.433109946\) \(a_{43}=-0.398361675\) \(a_{44}=+0.670140680\) \(a_{45}=-0.061439866\)
\(a_{46}=+0.042043160\) \(a_{47}=-0.124390448\) \(a_{48}=+0.266620484\) \(a_{49}=+2.611453348\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.867634251\) \(a_{52}=+0.754082963\) \(a_{53}=+0.763578307\) \(a_{54}=-0.650513265\) \(a_{55}=-0.599392046\)
\(a_{56}=-0.671886649\) \(a_{57}=+0.355675037\) \(a_{58}=-0.611698437\) \(a_{59}=+1.761399592\) \(a_{60}=-0.238472610\)
\(a_{61}=+0.827144406\) \(a_{62}=+0.518864595\) \(a_{63}=-0.261081602\) \(a_{64}=+0.125000000\) \(a_{65}=-0.674472306\)
\(a_{66}=+1.010728434\) \(a_{67}=+1.503636300\) \(a_{68}=-0.406774003\) \(a_{69}=+0.063410890\) \(a_{70}=+0.600953688\)
\(a_{71}=-0.573590661\) \(a_{72}=+0.048572479\) \(a_{73}=+1.759691370\) \(a_{74}=+0.434284949\) \(a_{75}=+0.213296387\)
\(a_{76}=+0.166751553\) \(a_{77}=-2.547047138\) \(a_{78}=+1.137332973\) \(a_{79}=+0.835828643\) \(a_{80}=-0.111803399\)
\(a_{81}=-1.118509432\) \(a_{82}=+0.433756747\) \(a_{83}=+0.267144692\) \(a_{84}=-1.013361761\) \(a_{85}=+0.363829729\)
\(a_{86}=-0.281684242\) \(a_{87}=-0.922583901\) \(a_{88}=+0.473861020\) \(a_{89}=-0.658207330\) \(a_{90}=-0.043444546\)
\(a_{91}=-2.866092013\) \(a_{92}=+0.029729003\) \(a_{93}=+0.782568817\) \(a_{94}=-0.087957329\) \(a_{95}=-0.149147123\)
\(a_{96}=+0.188529152\) \(a_{97}=+1.307548205\) \(a_{98}=+1.846576371\) \(a_{99}=+0.184132836\) \(a_{100}=+0.099975586\)

Showing 100 of 210 available coefficients

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