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: \( 30.0062244986 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.203231380\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.143706287\) \(a_{7}=+1.498036549\) \(a_{8}=-0.353553391\) \(a_{9}=-0.958697006\) \(a_{10}=-0.316227766\)
\(a_{11}=+1.074232879\) \(a_{12}=+0.101615690\) \(a_{13}=+0.712116094\) \(a_{14}=-1.059271802\) \(a_{15}=+0.090887836\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.825611286\) \(a_{18}=+0.677901154\) \(a_{19}=+1.707059704\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.304448035\) \(a_{22}=-0.759597353\) \(a_{23}=-1.680136278\) \(a_{24}=-0.071853143\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.503542119\) \(a_{27}=-0.398068696\) \(a_{28}=+0.749018274\) \(a_{29}=+0.971625333\) \(a_{30}=-0.064267405\)
\(a_{31}=+0.137774763\) \(a_{32}=-0.176776695\) \(a_{33}=+0.218317830\) \(a_{34}=+0.583795339\) \(a_{35}=+0.669942311\)
\(a_{36}=-0.479348503\) \(a_{37}=+1.330004092\) \(a_{38}=-1.207073493\) \(a_{39}=+0.144724337\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.167913446\) \(a_{42}=-0.215277270\) \(a_{43}=+0.841501509\) \(a_{44}=+0.537116439\) \(a_{45}=-0.428742335\)
\(a_{46}=+1.188035755\) \(a_{47}=-0.818702134\) \(a_{48}=+0.050807845\) \(a_{49}=+1.244113501\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.167790121\) \(a_{52}=+0.356058047\) \(a_{53}=-0.800027416\) \(a_{54}=+0.281477074\) \(a_{55}=+0.480411548\)
\(a_{56}=-0.529635901\) \(a_{57}=+0.346928100\) \(a_{58}=-0.687042862\) \(a_{59}=+1.809656807\) \(a_{60}=+0.045443918\)
\(a_{61}=+1.812579329\) \(a_{62}=-0.097421469\) \(a_{63}=-1.436163154\) \(a_{64}=+0.125000000\) \(a_{65}=+0.318467999\)
\(a_{66}=-0.154374018\) \(a_{67}=-0.146496286\) \(a_{68}=-0.412805643\) \(a_{69}=-0.341456414\) \(a_{70}=-0.473720751\)
\(a_{71}=-0.599149472\) \(a_{72}=+0.338950577\) \(a_{73}=+1.372686916\) \(a_{74}=-0.940454912\) \(a_{75}=+0.040646276\)
\(a_{76}=+0.853529852\) \(a_{77}=+1.609240114\) \(a_{78}=-0.102335560\) \(a_{79}=-0.394319713\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.877796956\) \(a_{82}=+0.118732736\) \(a_{83}=+0.254412608\) \(a_{84}=+0.152224018\) \(a_{85}=-0.369224592\)
\(a_{86}=-0.595031423\) \(a_{87}=+0.197464757\) \(a_{88}=-0.379798677\) \(a_{89}=-1.112913295\) \(a_{90}=+0.303166613\)
\(a_{91}=+1.066775936\) \(a_{92}=-0.840068139\) \(a_{93}=+0.028000155\) \(a_{94}=+0.578909831\) \(a_{95}=+0.763420308\)
\(a_{96}=-0.035926572\) \(a_{97}=-0.756123091\) \(a_{98}=-0.879721093\) \(a_{99}=-1.029863845\) \(a_{100}=+0.099975586\)

Showing 100 of 240 available coefficients

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