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: \( 14.6341180002 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.167648796\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.118545601\) \(a_{7}=+0.015747270\) \(a_{8}=+0.353553391\) \(a_{9}=-0.971893881\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.259243269\) \(a_{12}=+0.083824398\) \(a_{13}=-1.679191976\) \(a_{14}=+0.011135001\) \(a_{15}=+0.074974821\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.692619073\) \(a_{18}=-0.687232754\) \(a_{19}=-1.293226864\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.002640011\) \(a_{22}=-0.183312674\) \(a_{23}=-1.522497483\) \(a_{24}=+0.059272800\) \(a_{25}=+0.199951172\)
\(a_{26}=-1.187368033\) \(a_{27}=-0.330585635\) \(a_{28}=+0.007873635\) \(a_{29}=+0.027315640\) \(a_{30}=+0.053015204\)
\(a_{31}=+1.111639401\) \(a_{32}=+0.176776695\) \(a_{33}=-0.043461822\) \(a_{34}=+1.196862425\) \(a_{35}=+0.007042393\)
\(a_{36}=-0.485946941\) \(a_{37}=-0.524752500\) \(a_{38}=-0.914449485\) \(a_{39}=-0.281514513\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.692198024\) \(a_{42}=+0.001866770\) \(a_{43}=+0.135997119\) \(a_{44}=-0.129621635\) \(a_{45}=-0.434644157\)
\(a_{46}=-1.076568295\) \(a_{47}=-0.553626219\) \(a_{48}=+0.041912199\) \(a_{49}=-0.999752023\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.283765550\) \(a_{52}=-0.839595988\) \(a_{53}=-1.363031660\) \(a_{54}=-0.233759345\) \(a_{55}=-0.115937115\)
\(a_{56}=+0.005567501\) \(a_{57}=-0.216807927\) \(a_{58}=+0.019315075\) \(a_{59}=-1.160292644\) \(a_{60}=+0.037487410\)
\(a_{61}=+0.159962460\) \(a_{62}=+0.786047759\) \(a_{63}=-0.015304675\) \(a_{64}=+0.125000000\) \(a_{65}=-0.750957481\)
\(a_{66}=-0.030732149\) \(a_{67}=-0.338900874\) \(a_{68}=+0.846309537\) \(a_{69}=-0.255244870\) \(a_{70}=+0.004979724\)
\(a_{71}=-1.006687845\) \(a_{72}=-0.343616377\) \(a_{73}=+0.250547830\) \(a_{74}=-0.371056051\) \(a_{75}=+0.033529759\)
\(a_{76}=-0.646613432\) \(a_{77}=-0.004082374\) \(a_{78}=-0.199060821\) \(a_{79}=+0.538553718\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.916471597\) \(a_{82}=-0.489457917\) \(a_{83}=+0.667094150\) \(a_{84}=+0.001320005\) \(a_{85}=+0.756962262\)
\(a_{86}=+0.096164485\) \(a_{87}=+0.004579435\) \(a_{88}=-0.091656337\) \(a_{89}=-0.526806189\) \(a_{90}=-0.307339831\)
\(a_{91}=-0.026442689\) \(a_{92}=-0.761248742\) \(a_{93}=+0.186365009\) \(a_{94}=-0.391472854\) \(a_{95}=-0.578348636\)
\(a_{96}=+0.029636400\) \(a_{97}=-0.393020355\) \(a_{98}=-0.706931435\) \(a_{99}=+0.251956946\) \(a_{100}=+0.099975586\)

Showing 100 of 172 available coefficients

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