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: \( 24.6001318362 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.030193836\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.021350266\) \(a_{7}=-0.963531428\) \(a_{8}=-0.353553391\) \(a_{9}=-0.999088332\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.052420388\) \(a_{12}=-0.015096918\) \(a_{13}=+0.798236515\) \(a_{14}=+0.681319607\) \(a_{15}=+0.013503094\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.984018665\) \(a_{18}=+0.706462135\) \(a_{19}=-0.871961820\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.029092710\) \(a_{22}=-0.744173593\) \(a_{23}=-0.136635968\) \(a_{24}=+0.010675133\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.564438453\) \(a_{27}=+0.060360145\) \(a_{28}=-0.481765714\) \(a_{29}=-1.100256367\) \(a_{30}=-0.009548129\)
\(a_{31}=+0.475305727\) \(a_{32}=-0.176776695\) \(a_{33}=-0.031776609\) \(a_{34}=+1.402913052\) \(a_{35}=+0.430904355\)
\(a_{36}=-0.499544166\) \(a_{37}=-0.362295770\) \(a_{38}=+0.616570116\) \(a_{39}=-0.024101822\) \(a_{40}=+0.158113883\)
\(a_{41}=-1.637767679\) \(a_{42}=-0.020571653\) \(a_{43}=+1.446181938\) \(a_{44}=+0.526210194\) \(a_{45}=+0.446805885\)
\(a_{46}=+0.096616220\) \(a_{47}=-1.465594288\) \(a_{48}=-0.007548459\) \(a_{49}=-0.071607186\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.059905134\) \(a_{52}=+0.399118257\) \(a_{53}=+0.963963310\) \(a_{54}=-0.042681068\) \(a_{55}=-0.470656706\)
\(a_{56}=+0.340659803\) \(a_{57}=+0.026327872\) \(a_{58}=+0.777998738\) \(a_{59}=+0.146752114\) \(a_{60}=+0.006751547\)
\(a_{61}=-1.374908231\) \(a_{62}=-0.336091902\) \(a_{63}=+0.962653008\) \(a_{64}=+0.125000000\) \(a_{65}=-0.356982222\)
\(a_{66}=+0.022469455\) \(a_{67}=-0.123274279\) \(a_{68}=-0.992009332\) \(a_{69}=+0.004125564\) \(a_{70}=-0.304695391\)
\(a_{71}=-1.586408243\) \(a_{72}=+0.353231067\) \(a_{73}=-1.903185958\) \(a_{74}=+0.256181796\) \(a_{75}=-0.006038767\)
\(a_{76}=-0.435980910\) \(a_{77}=-1.014040120\) \(a_{78}=+0.017042562\) \(a_{79}=+0.555692626\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.997265828\) \(a_{82}=+1.158076632\) \(a_{83}=+0.033108771\) \(a_{84}=+0.014546355\) \(a_{85}=+0.887280121\)
\(a_{86}=-1.022605055\) \(a_{87}=+0.033220960\) \(a_{88}=-0.372086797\) \(a_{89}=+0.249064109\) \(a_{90}=-0.315939471\)
\(a_{91}=-0.769125970\) \(a_{92}=-0.068317984\) \(a_{93}=-0.014351303\) \(a_{94}=+1.036331659\) \(a_{95}=+0.389953181\)
\(a_{96}=+0.005337567\) \(a_{97}=-0.338242856\) \(a_{98}=+0.050633927\) \(a_{99}=-1.051460931\) \(a_{100}=+0.099975586\)

Showing 100 of 222 available coefficients

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