Properties

Level $10$
Weight $0$
Character 10.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 31.0823425766 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.500875041\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.354172138\) \(a_{7}=+0.618686475\) \(a_{8}=+0.353553391\) \(a_{9}=-0.749124193\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.985378373\) \(a_{12}=+0.250437521\) \(a_{13}=+1.045493501\) \(a_{14}=+0.437477402\) \(a_{15}=-0.223998128\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.113318720\) \(a_{18}=-0.529710797\) \(a_{19}=+0.236069465\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.309884613\) \(a_{22}=-0.696767730\) \(a_{23}=+1.917735913\) \(a_{24}=+0.177086069\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.739275545\) \(a_{27}=-0.876092652\) \(a_{28}=+0.309343237\) \(a_{29}=+0.262601668\) \(a_{30}=-0.158390595\)
\(a_{31}=+0.236268057\) \(a_{32}=+0.176776695\) \(a_{33}=-0.493551433\) \(a_{34}=-0.787235217\) \(a_{35}=-0.276685003\)
\(a_{36}=-0.374562097\) \(a_{37}=-1.177315072\) \(a_{38}=+0.166926320\) \(a_{39}=+0.523661600\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.447522046\) \(a_{42}=+0.219121512\) \(a_{43}=-1.012728175\) \(a_{44}=-0.492689186\) \(a_{45}=+0.335018524\)
\(a_{46}=+1.356044069\) \(a_{47}=+1.102652762\) \(a_{48}=+0.125218760\) \(a_{49}=-0.617227046\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.557633560\) \(a_{52}=+0.522746751\) \(a_{53}=-1.703735065\) \(a_{54}=-0.619491055\) \(a_{55}=+0.440674605\)
\(a_{56}=+0.218738701\) \(a_{57}=+0.118241303\) \(a_{58}=+0.185687420\) \(a_{59}=-0.175722116\) \(a_{60}=-0.111999064\)
\(a_{61}=+1.035314736\) \(a_{62}=+0.167066746\) \(a_{63}=-0.463473006\) \(a_{64}=+0.125000000\) \(a_{65}=-0.467558908\)
\(a_{66}=-0.348993565\) \(a_{67}=-0.541534799\) \(a_{68}=-0.556659360\) \(a_{69}=+0.960546054\) \(a_{70}=-0.195645842\)
\(a_{71}=+0.544000438\) \(a_{72}=-0.264855398\) \(a_{73}=-1.580000405\) \(a_{74}=-0.832487471\) \(a_{75}=+0.100175008\)
\(a_{76}=+0.118034733\) \(a_{77}=-0.609640272\) \(a_{78}=+0.370284669\) \(a_{79}=-0.085848547\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.310311250\) \(a_{82}=+0.316445873\) \(a_{83}=-0.792198823\) \(a_{84}=+0.154942307\) \(a_{85}=+0.497891268\)
\(a_{86}=-0.716106960\) \(a_{87}=+0.131530621\) \(a_{88}=-0.348383865\) \(a_{89}=-1.563645078\) \(a_{90}=+0.236893870\)
\(a_{91}=+0.646832689\) \(a_{92}=+0.958867957\) \(a_{93}=+0.118340773\) \(a_{94}=+0.779693246\) \(a_{95}=-0.105573474\)
\(a_{96}=+0.088543035\) \(a_{97}=+1.264021678\) \(a_{98}=-0.436445430\) \(a_{99}=+0.738170779\) \(a_{100}=+0.099975586\)

Showing 100 of 250 available coefficients

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