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: \( 19.7128261759 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.567894421\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-1.108668777\) \(a_{7}=+1.237151574\) \(a_{8}=-0.353553391\) \(a_{9}=+1.458292915\) \(a_{10}=-0.316227766\)
\(a_{11}=+1.953337653\) \(a_{12}=+0.783947211\) \(a_{13}=-0.765874534\) \(a_{14}=-0.874798267\) \(a_{15}=+0.701183701\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.796873771\) \(a_{18}=-1.031168809\) \(a_{19}=-0.646821762\) \(a_{20}=+0.223606798\)
\(a_{21}=+1.939723050\) \(a_{22}=-1.381218300\) \(a_{23}=+0.255207924\) \(a_{24}=-0.554334389\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.541555077\) \(a_{27}=+0.718554905\) \(a_{28}=+0.618575787\) \(a_{29}=+1.670386896\) \(a_{30}=-0.495811750\)
\(a_{31}=+1.111261700\) \(a_{32}=-0.176776695\) \(a_{33}=+3.062627208\) \(a_{34}=-0.563474848\) \(a_{35}=+0.553271003\)
\(a_{36}=+0.729146458\) \(a_{37}=-0.896473669\) \(a_{38}=+0.457372054\) \(a_{39}=-1.200810409\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.536438605\) \(a_{42}=-1.371591322\) \(a_{43}=-1.638584864\) \(a_{44}=+0.976668826\) \(a_{45}=+0.652168418\)
\(a_{46}=-0.180459253\) \(a_{47}=-0.848513249\) \(a_{48}=+0.391973605\) \(a_{49}=+0.530544016\) \(a_{50}=-0.141421356\)
\(a_{51}=+1.249413940\) \(a_{52}=-0.382937267\) \(a_{53}=-0.782186616\) \(a_{54}=-0.508095046\) \(a_{55}=+0.873559155\)
\(a_{56}=-0.437399134\) \(a_{57}=-1.014148233\) \(a_{58}=-1.181141902\) \(a_{59}=+0.854848254\) \(a_{60}=+0.350591851\)
\(a_{61}=-1.257223229\) \(a_{62}=-0.785780684\) \(a_{63}=+1.804129375\) \(a_{64}=+0.125000000\) \(a_{65}=-0.342509504\)
\(a_{66}=-2.165604467\) \(a_{67}=-0.421110053\) \(a_{68}=+0.398436886\) \(a_{69}=+0.400139079\) \(a_{70}=-0.391221678\)
\(a_{71}=-0.408176556\) \(a_{72}=-0.515584405\) \(a_{73}=+0.020065642\) \(a_{74}=+0.633902610\) \(a_{75}=+0.313578884\)
\(a_{76}=-0.323410881\) \(a_{77}=+2.416574751\) \(a_{78}=+0.849101183\) \(a_{79}=-0.865509442\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.331674688\) \(a_{82}=-0.379319376\) \(a_{83}=+0.812471671\) \(a_{84}=+0.969861525\) \(a_{85}=+0.356372784\)
\(a_{86}=+1.158654469\) \(a_{87}=+2.618990296\) \(a_{88}=-0.690609150\) \(a_{89}=-0.555766522\) \(a_{90}=-0.461152711\)
\(a_{91}=-0.947502885\) \(a_{92}=+0.127603962\) \(a_{93}=+1.742341020\) \(a_{94}=+0.599989473\) \(a_{95}=-0.289267486\)
\(a_{96}=-0.277167194\) \(a_{97}=-0.066223612\) \(a_{98}=-0.375151272\) \(a_{99}=+2.848538461\) \(a_{100}=+0.099975586\)

Showing 100 of 190 available coefficients

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