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: \( 12.9729966293 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.511027953\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+1.068458112\) \(a_{7}=-0.726788453\) \(a_{8}=+0.353553391\) \(a_{9}=+1.283205473\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.115581979\) \(a_{12}=+0.755513976\) \(a_{13}=+1.330254151\) \(a_{14}=-0.513917044\) \(a_{15}=+0.675752244\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.431904353\) \(a_{18}=+0.907363292\) \(a_{19}=+1.148602375\) \(a_{20}=+0.223606798\)
\(a_{21}=-1.098197668\) \(a_{22}=-0.081728801\) \(a_{23}=-1.421795010\) \(a_{24}=+0.534229056\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.940631731\) \(a_{27}=+0.427931387\) \(a_{28}=-0.363394226\) \(a_{29}=-1.406564863\) \(a_{30}=+0.477828994\)
\(a_{31}=+1.501103983\) \(a_{32}=+0.176776695\) \(a_{33}=-0.174647601\) \(a_{34}=+1.012509278\) \(a_{35}=-0.325029677\)
\(a_{36}=+0.641602737\) \(a_{37}=-0.122923531\) \(a_{38}=+0.812184528\) \(a_{39}=+2.010051206\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.996748626\) \(a_{42}=-0.776543018\) \(a_{43}=+0.299132152\) \(a_{44}=-0.057790990\) \(a_{45}=+0.573866933\)
\(a_{46}=-1.005360893\) \(a_{47}=+0.094804518\) \(a_{48}=+0.377756988\) \(a_{49}=-0.471778545\) \(a_{50}=+0.141421356\)
\(a_{51}=+2.163647503\) \(a_{52}=+0.665127076\) \(a_{53}=-1.086734823\) \(a_{54}=+0.302593185\) \(a_{55}=-0.051689832\)
\(a_{56}=-0.256958522\) \(a_{57}=+1.735570294\) \(a_{58}=-0.994591553\) \(a_{59}=-0.308370341\) \(a_{60}=+0.337876122\)
\(a_{61}=-1.590908086\) \(a_{62}=+1.061440806\) \(a_{63}=-0.932618921\) \(a_{64}=+0.125000000\) \(a_{65}=+0.594907742\)
\(a_{66}=-0.123494503\) \(a_{67}=+1.263279081\) \(a_{68}=+0.715952176\) \(a_{69}=-2.148372003\) \(a_{70}=-0.229830689\)
\(a_{71}=+0.552176949\) \(a_{72}=+0.453681646\) \(a_{73}=-0.961863362\) \(a_{74}=-0.086920062\) \(a_{75}=+0.302205591\)
\(a_{76}=+0.574301187\) \(a_{77}=+0.084003647\) \(a_{78}=+1.421320838\) \(a_{79}=+0.002092352\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.636589184\) \(a_{82}=+0.704807713\) \(a_{83}=-1.127277720\) \(a_{84}=-0.549098834\) \(a_{85}=+0.640367094\)
\(a_{86}=+0.211518373\) \(a_{87}=-2.125358815\) \(a_{88}=-0.040864401\) \(a_{89}=-0.340855480\) \(a_{90}=+0.405785200\)
\(a_{91}=-0.966813325\) \(a_{92}=-0.710897505\) \(a_{93}=+2.268210089\) \(a_{94}=+0.067036917\) \(a_{95}=+0.513670598\)
\(a_{96}=+0.267114528\) \(a_{97}=+1.556551883\) \(a_{98}=-0.333597808\) \(a_{99}=-0.148315469\) \(a_{100}=+0.099975586\)

Showing 100 of 165 available coefficients

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