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: \( 28.869142831 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.308683306\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.218272059\) \(a_{7}=-0.009151034\) \(a_{8}=-0.353553391\) \(a_{9}=-0.904714617\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.274532081\) \(a_{12}=-0.154341653\) \(a_{13}=+0.304822842\) \(a_{14}=+0.006470758\) \(a_{15}=+0.138047371\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.556714142\) \(a_{18}=+0.639729840\) \(a_{19}=+0.073201487\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.002824771\) \(a_{22}=-0.194123496\) \(a_{23}=+1.323334243\) \(a_{24}=+0.109136029\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.215542298\) \(a_{27}=+0.587953605\) \(a_{28}=-0.004575517\) \(a_{29}=+0.742119453\) \(a_{30}=-0.097614232\)
\(a_{31}=-1.721514516\) \(a_{32}=-0.176776695\) \(a_{33}=-0.084743470\) \(a_{34}=+1.100763126\) \(a_{35}=+0.004092467\)
\(a_{36}=-0.452357308\) \(a_{37}=+1.090609506\) \(a_{38}=-0.051761268\) \(a_{39}=-0.094093722\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.113816017\) \(a_{42}=-0.001997415\) \(a_{43}=+0.230838290\) \(a_{44}=+0.137266040\) \(a_{45}=+0.404600677\)
\(a_{46}=-0.935738617\) \(a_{47}=+0.886583800\) \(a_{48}=-0.077170826\) \(a_{49}=-0.999916259\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.480531668\) \(a_{52}=+0.152411421\) \(a_{53}=-1.715548478\) \(a_{54}=-0.415745981\) \(a_{55}=-0.122774479\)
\(a_{56}=+0.003235379\) \(a_{57}=-0.022596077\) \(a_{58}=-0.524757698\) \(a_{59}=+0.430605220\) \(a_{60}=+0.069023686\)
\(a_{61}=+1.512602469\) \(a_{62}=+1.217294588\) \(a_{63}=+0.008279074\) \(a_{64}=+0.125000000\) \(a_{65}=-0.136320919\)
\(a_{66}=+0.059922682\) \(a_{67}=-0.188448415\) \(a_{68}=-0.778357071\) \(a_{69}=-0.408491189\) \(a_{70}=-0.002893811\)
\(a_{71}=-0.147647700\) \(a_{72}=+0.319864920\) \(a_{73}=+0.194870638\) \(a_{74}=-0.771177377\) \(a_{75}=-0.061736661\)
\(a_{76}=+0.036600743\) \(a_{77}=-0.002512252\) \(a_{78}=+0.066534309\) \(a_{79}=+0.795665018\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.723223154\) \(a_{82}=+0.080480078\) \(a_{83}=-1.065476138\) \(a_{84}=+0.001412386\) \(a_{85}=+0.696183729\)
\(a_{86}=-0.163227320\) \(a_{87}=-0.229079886\) \(a_{88}=-0.097061748\) \(a_{89}=+0.610489773\) \(a_{90}=-0.286095882\)
\(a_{91}=-0.002789444\) \(a_{92}=+0.661667122\) \(a_{93}=+0.531402792\) \(a_{94}=-0.626909417\) \(a_{95}=-0.032736700\)
\(a_{96}=+0.054568015\) \(a_{97}=+0.374962701\) \(a_{98}=+0.707047567\) \(a_{99}=-0.248373186\) \(a_{100}=+0.099975586\)

Showing 100 of 240 available coefficients

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