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: \( 25.9030999676 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.047524141\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.740711424\) \(a_{7}=-1.364690413\) \(a_{8}=+0.353553391\) \(a_{9}=+0.097306826\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.162475180\) \(a_{12}=+0.523762071\) \(a_{13}=+0.171129133\) \(a_{14}=-0.964981845\) \(a_{15}=+0.468467038\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.281764176\) \(a_{18}=+0.068806317\) \(a_{19}=-0.479092547\) \(a_{20}=+0.223606798\)
\(a_{21}=-1.429546153\) \(a_{22}=-0.114887301\) \(a_{23}=-0.087915665\) \(a_{24}=+0.370355712\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.121006570\) \(a_{27}=-0.945592892\) \(a_{28}=-0.682345207\) \(a_{29}=+1.101218991\) \(a_{30}=+0.331256219\)
\(a_{31}=+0.662855904\) \(a_{32}=+0.176776695\) \(a_{33}=-0.170196673\) \(a_{34}=+0.906344141\) \(a_{35}=-0.610308106\)
\(a_{36}=+0.048653413\) \(a_{37}=+1.431608820\) \(a_{38}=-0.338769589\) \(a_{39}=+0.179261898\) \(a_{40}=+0.158113883\)
\(a_{41}=-1.312729642\) \(a_{42}=-1.010841779\) \(a_{43}=+1.336010606\) \(a_{44}=-0.081237590\) \(a_{45}=+0.043516936\)
\(a_{46}=-0.062165763\) \(a_{47}=+1.395072324\) \(a_{48}=+0.261881035\) \(a_{49}=+0.862379923\) \(a_{50}=+0.141421356\)
\(a_{51}=+1.342678918\) \(a_{52}=+0.085564566\) \(a_{53}=+1.765605930\) \(a_{54}=-0.668635146\) \(a_{55}=-0.072661109\)
\(a_{56}=-0.482490923\) \(a_{57}=-0.501861009\) \(a_{58}=+0.778679416\) \(a_{59}=-0.877291127\) \(a_{60}=+0.234233519\)
\(a_{61}=-0.181920024\) \(a_{62}=+0.468709905\) \(a_{63}=-0.132793693\) \(a_{64}=+0.125000000\) \(a_{65}=+0.076531275\)
\(a_{66}=-0.120347222\) \(a_{67}=+0.692946488\) \(a_{68}=+0.640882088\) \(a_{69}=-0.092093782\) \(a_{70}=-0.431553001\)
\(a_{71}=+1.158449146\) \(a_{72}=+0.034403158\) \(a_{73}=+0.892918373\) \(a_{74}=+1.012300305\) \(a_{75}=+0.209504828\)
\(a_{76}=-0.239546274\) \(a_{77}=+0.221728320\) \(a_{78}=+0.126757304\) \(a_{79}=-0.061265257\) \(a_{80}=+0.111803399\)
\(a_{81}=-1.087838208\) \(a_{82}=-0.928240032\) \(a_{83}=+0.544724121\) \(a_{84}=-0.714773076\) \(a_{85}=+0.573222366\)
\(a_{86}=+0.944702159\) \(a_{87}=+1.153553478\) \(a_{88}=-0.057443651\) \(a_{89}=+0.343210494\) \(a_{90}=+0.030771120\)
\(a_{91}=-0.233538287\) \(a_{92}=-0.043957833\) \(a_{93}=+0.694357562\) \(a_{94}=+0.986465101\) \(a_{95}=-0.214256701\)
\(a_{96}=+0.185177856\) \(a_{97}=+0.765928787\) \(a_{98}=+0.609794692\) \(a_{99}=-0.015809944\) \(a_{100}=+0.099975586\)

Showing 100 of 222 available coefficients

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