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: \( 11.9357108569 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.150663367\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.106535088\) \(a_{7}=+0.822857299\) \(a_{8}=+0.353553391\) \(a_{9}=-0.977300550\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.018312919\) \(a_{12}=-0.075331683\) \(a_{13}=+1.203617376\) \(a_{14}=+0.581847976\) \(a_{15}=+0.067378706\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.292599073\) \(a_{18}=-0.691055846\) \(a_{19}=+1.138542757\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.123974451\) \(a_{22}=+0.012949189\) \(a_{23}=-0.623686592\) \(a_{24}=-0.053267544\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.851086009\) \(a_{27}=+0.297906758\) \(a_{28}=+0.411428650\) \(a_{29}=+1.533414039\) \(a_{30}=+0.047643940\)
\(a_{31}=+1.307613390\) \(a_{32}=+0.176776695\) \(a_{33}=-0.002759086\) \(a_{34}=-0.206898789\) \(a_{35}=-0.367992971\)
\(a_{36}=-0.488650275\) \(a_{37}=+1.534036928\) \(a_{38}=+0.805071304\) \(a_{39}=-0.181341046\) \(a_{40}=-0.158113883\)
\(a_{41}=+1.312425911\) \(a_{42}=-0.087663175\) \(a_{43}=+0.857752894\) \(a_{44}=+0.009156460\) \(a_{45}=+0.437062093\)
\(a_{46}=-0.441013019\) \(a_{47}=-1.099101489\) \(a_{48}=-0.037665842\) \(a_{49}=-0.322905865\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.044083961\) \(a_{52}=+0.601808688\) \(a_{53}=-0.126435883\) \(a_{54}=+0.210651888\) \(a_{55}=-0.008189786\)
\(a_{56}=+0.290923988\) \(a_{57}=-0.171536685\) \(a_{58}=+1.084287465\) \(a_{59}=-0.911429582\) \(a_{60}=+0.033689353\)
\(a_{61}=+0.073327029\) \(a_{62}=+0.924622295\) \(a_{63}=-0.804178891\) \(a_{64}=+0.125000000\) \(a_{65}=-0.538274054\)
\(a_{66}=-0.001950968\) \(a_{67}=+0.763819969\) \(a_{68}=-0.146299537\) \(a_{69}=+0.093966722\) \(a_{70}=-0.260210326\)
\(a_{71}=-0.918583441\) \(a_{72}=-0.345527923\) \(a_{73}=-0.839009043\) \(a_{74}=+1.084727914\) \(a_{75}=-0.030132673\)
\(a_{76}=+0.569271379\) \(a_{77}=+0.015068919\) \(a_{78}=-0.128227483\) \(a_{79}=+0.226776898\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.932416916\) \(a_{82}=+0.928025262\) \(a_{83}=-1.241491156\) \(a_{84}=-0.061987225\) \(a_{85}=+0.130854284\)
\(a_{86}=+0.606522888\) \(a_{87}=-0.231029323\) \(a_{88}=+0.006474595\) \(a_{89}=-1.131743914\) \(a_{90}=+0.309049570\)
\(a_{91}=+0.990405361\) \(a_{92}=-0.311843296\) \(a_{93}=-0.197009416\) \(a_{94}=-0.777182116\) \(a_{95}=-0.509171800\)
\(a_{96}=-0.026633772\) \(a_{97}=-1.239511814\) \(a_{98}=-0.228328927\) \(a_{99}=-0.017897099\) \(a_{100}=+0.099975586\)

Showing 100 of 162 available coefficients

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