Properties

Level $10$
Weight $0$
Character 10.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 30.9513504138 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.387127413\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.980847200\) \(a_{7}=+1.492550128\) \(a_{8}=+0.353553391\) \(a_{9}=+0.924122461\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.689553369\) \(a_{12}=+0.693563707\) \(a_{13}=+0.549632306\) \(a_{14}=+1.055392317\) \(a_{15}=+0.620342238\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.750683087\) \(a_{18}=+0.653453259\) \(a_{19}=-0.662337919\) \(a_{20}=+0.223606798\)
\(a_{21}=+2.070357198\) \(a_{22}=+0.487587863\) \(a_{23}=-0.518555114\) \(a_{24}=+0.490423600\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.388648730\) \(a_{27}=-0.105251815\) \(a_{28}=+0.746275064\) \(a_{29}=+1.100220049\) \(a_{30}=+0.438648203\)
\(a_{31}=-0.768850509\) \(a_{32}=+0.176776695\) \(a_{33}=+0.956498381\) \(a_{34}=+1.237919883\) \(a_{35}=+0.667488709\)
\(a_{36}=+0.462061230\) \(a_{37}=+1.335541420\) \(a_{38}=-0.468343634\) \(a_{39}=+0.762410038\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.697623191\) \(a_{42}=+1.463963614\) \(a_{43}=-0.035937625\) \(a_{44}=+0.344776684\) \(a_{45}=+0.413280128\)
\(a_{46}=-0.366673838\) \(a_{47}=-1.365871394\) \(a_{48}=+0.346781853\) \(a_{49}=+1.227705884\) \(a_{50}=+0.141421356\)
\(a_{51}=+2.428420502\) \(a_{52}=+0.274816153\) \(a_{53}=-0.823192757\) \(a_{54}=-0.074424272\) \(a_{55}=+0.308377641\)
\(a_{56}=+0.527696158\) \(a_{57}=-0.918747084\) \(a_{58}=+0.777973058\) \(a_{59}=-1.816872308\) \(a_{60}=+0.310171119\)
\(a_{61}=-1.099049206\) \(a_{62}=-0.543659408\) \(a_{63}=+1.379299097\) \(a_{64}=+0.125000000\) \(a_{65}=+0.245803040\)
\(a_{66}=+0.676346491\) \(a_{67}=+0.007751018\) \(a_{68}=+0.875341544\) \(a_{69}=-0.719302014\) \(a_{70}=+0.471985793\)
\(a_{71}=+1.157795547\) \(a_{72}=+0.326726629\) \(a_{73}=+0.856333121\) \(a_{74}=+0.944370395\) \(a_{75}=+0.277425483\)
\(a_{76}=-0.331168959\) \(a_{77}=+1.029192969\) \(a_{78}=+0.539105308\) \(a_{79}=+1.500467487\) \(a_{80}=+0.111803399\)
\(a_{81}=-1.070120138\) \(a_{82}=-0.493294089\) \(a_{83}=-0.396622449\) \(a_{84}=+1.035178599\) \(a_{85}=+0.782929278\)
\(a_{86}=-0.025411738\) \(a_{87}=+1.526145391\) \(a_{88}=+0.243793932\) \(a_{89}=-1.067786899\) \(a_{90}=+0.292233181\)
\(a_{91}=+0.820353768\) \(a_{92}=-0.259277557\) \(a_{93}=-1.066493617\) \(a_{94}=-0.965816925\) \(a_{95}=-0.296206522\)
\(a_{96}=+0.245211800\) \(a_{97}=-1.956918836\) \(a_{98}=+0.868119156\) \(a_{99}=+0.637231756\) \(a_{100}=+0.099975586\)

Showing 100 of 250 available coefficients

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