Properties

Level $1$
Weight $0$
Character 1.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 46.4814024123 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.595010105\) \(a_{3}=+0.732309138\) \(a_{4}=-0.645962975\) \(a_{5}=-0.091775046\)
\(a_{6}=-0.435731337\) \(a_{7}=+1.784478322\) \(a_{8}=+0.979364603\) \(a_{9}=-0.463723326\) \(a_{10}=+0.054607080\)
\(a_{11}=+0.130229908\) \(a_{12}=-0.473044589\) \(a_{13}=-0.127989301\) \(a_{14}=-1.061782634\) \(a_{15}=-0.067207705\)
\(a_{16}=+0.063231139\) \(a_{17}=+1.365184203\) \(a_{18}=+0.275920065\) \(a_{19}=-0.296906068\) \(a_{20}=+0.059283281\)
\(a_{21}=+1.306789785\) \(a_{22}=-0.077488135\) \(a_{23}=-0.945384035\) \(a_{24}=+0.717197648\) \(a_{25}=-0.991577341\)
\(a_{26}=+0.076154927\) \(a_{27}=-1.071897967\) \(a_{28}=-1.152706925\) \(a_{29}=+0.870720972\) \(a_{30}=+0.039989263\)
\(a_{31}=+0.626110672\) \(a_{32}=-1.016987770\) \(a_{33}=+0.095368551\) \(a_{34}=-0.812298397\) \(a_{35}=-0.163770580\)
\(a_{36}=+0.299548099\) \(a_{37}=+1.375345389\) \(a_{38}=+0.176662111\) \(a_{39}=-0.093727735\) \(a_{40}=-0.089881231\)
\(a_{41}=-0.106766372\) \(a_{42}=-0.777553126\) \(a_{43}=-1.492780130\) \(a_{44}=-0.084123699\) \(a_{45}=+0.042558230\)
\(a_{46}=+0.562513054\) \(a_{47}=-0.197303294\) \(a_{48}=+0.046304741\) \(a_{49}=+2.184362883\) \(a_{50}=+0.589998538\)
\(a_{51}=+0.999736867\) \(a_{52}=+0.082676350\) \(a_{53}=+1.540158020\) \(a_{54}=+0.637790122\) \(a_{55}=-0.011951856\)
\(a_{56}=+1.747654903\) \(a_{57}=-0.217427027\) \(a_{58}=-0.518087777\) \(a_{59}=+0.848601046\) \(a_{60}=+0.043413689\)
\(a_{61}=+1.109213684\) \(a_{62}=-0.372542177\) \(a_{63}=-0.827504223\) \(a_{64}=+0.541886860\) \(a_{65}=+0.011746224\)
\(a_{66}=-0.056745249\) \(a_{67}=+1.301624069\) \(a_{68}=-0.881858433\) \(a_{69}=-0.692313376\) \(a_{70}=+0.097445094\)
\(a_{71}=+0.598188284\) \(a_{72}=-0.454154211\) \(a_{73}=+1.362310939\) \(a_{74}=-0.818344404\) \(a_{75}=-0.726141148\)
\(a_{76}=+0.191790327\) \(a_{77}=+0.232392447\) \(a_{78}=+0.055768949\) \(a_{79}=+0.322916215\) \(a_{80}=-0.005803041\)
\(a_{81}=-0.321237350\) \(a_{82}=+0.063527070\) \(a_{83}=+0.234757232\) \(a_{84}=-0.844137815\) \(a_{85}=-0.125289843\)
\(a_{86}=+0.888219262\) \(a_{87}=+0.637636924\) \(a_{88}=+0.127542562\) \(a_{89}=-1.409194796\) \(a_{90}=-0.025322577\)
\(a_{91}=-0.228394133\) \(a_{92}=+0.610683083\) \(a_{93}=+0.458506567\) \(a_{94}=+0.117397454\) \(a_{95}=+0.027248568\)
\(a_{96}=-0.744749437\) \(a_{97}=+0.781261168\) \(a_{98}=-1.299717989\) \(a_{99}=-0.060390646\) \(a_{100}=+0.640522249\)

Showing 100 of 5000 available coefficients

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