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: \( 19.1774440783 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.116592991\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.082443695\) \(a_{7}=-0.700757475\) \(a_{8}=-0.353553391\) \(a_{9}=-0.986406074\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.973876495\) \(a_{12}=+0.058296495\) \(a_{13}=-1.382450421\) \(a_{14}=+0.495510363\) \(a_{15}=+0.052141971\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.480998410\) \(a_{18}=+0.697494424\) \(a_{19}=+1.571015064\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.081703410\) \(a_{22}=+0.688634674\) \(a_{23}=-1.379682230\) \(a_{24}=-0.041221847\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.977540067\) \(a_{27}=-0.231601025\) \(a_{28}=-0.350378738\) \(a_{29}=+1.482532414\) \(a_{30}=-0.036869941\)
\(a_{31}=+0.356169910\) \(a_{32}=-0.176776695\) \(a_{33}=-0.113547173\) \(a_{34}=+1.047224019\) \(a_{35}=-0.313388270\)
\(a_{36}=-0.493203037\) \(a_{37}=-0.565077959\) \(a_{38}=-1.110875405\) \(a_{39}=-0.161184029\) \(a_{40}=-0.158113883\)
\(a_{41}=-1.799966115\) \(a_{42}=+0.057773035\) \(a_{43}=+1.865925392\) \(a_{44}=-0.486938248\) \(a_{45}=-0.441134207\)
\(a_{46}=+0.975582661\) \(a_{47}=+0.127437881\) \(a_{48}=+0.029148248\) \(a_{49}=-0.508938961\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.172674034\) \(a_{52}=-0.691225211\) \(a_{53}=-0.354232040\) \(a_{54}=+0.163766656\) \(a_{55}=-0.435530809\)
\(a_{56}=+0.247755181\) \(a_{57}=+0.183169345\) \(a_{58}=-1.048308723\) \(a_{59}=-0.626632173\) \(a_{60}=+0.026070985\)
\(a_{61}=-0.658907035\) \(a_{62}=-0.251850158\) \(a_{63}=+0.691231430\) \(a_{64}=+0.125000000\) \(a_{65}=-0.618250623\)
\(a_{66}=+0.080289976\) \(a_{67}=-0.284652478\) \(a_{68}=-0.740499205\) \(a_{69}=-0.160861278\) \(a_{70}=+0.221598971\)
\(a_{71}=+1.046577886\) \(a_{72}=+0.348747212\) \(a_{73}=+0.143337450\) \(a_{74}=+0.399570457\) \(a_{75}=+0.023318598\)
\(a_{76}=+0.785507532\) \(a_{77}=+0.682451234\) \(a_{78}=+0.113974320\) \(a_{79}=+0.261907302\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.959403018\) \(a_{82}=+1.272768246\) \(a_{83}=+1.234788568\) \(a_{84}=-0.040851705\) \(a_{85}=-0.662322624\)
\(a_{86}=-1.319408498\) \(a_{87}=+0.172852888\) \(a_{88}=+0.344317337\) \(a_{89}=+1.536676534\) \(a_{90}=+0.311928989\)
\(a_{91}=+0.968762467\) \(a_{92}=-0.689841115\) \(a_{93}=+0.041526915\) \(a_{94}=-0.090112190\) \(a_{95}=+0.702579295\)
\(a_{96}=-0.020610924\) \(a_{97}=+1.144109062\) \(a_{98}=+0.359874191\) \(a_{99}=+0.960637690\) \(a_{100}=+0.099975586\)

Showing 100 of 190 available coefficients

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