Properties

Level $2$
Weight $0$
Character 2.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 2 \)
Weight: \( 0 \)
Character: 2.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 29.6165214395 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.823455686\) \(a_{4}=+0.500000000\) \(a_{5}=+0.616912797\)
\(a_{6}=+0.582271099\) \(a_{7}=-0.496041370\) \(a_{8}=-0.353553391\) \(a_{9}=-0.321920734\) \(a_{10}=-0.436223222\)
\(a_{11}=-0.949002733\) \(a_{12}=-0.411727843\) \(a_{13}=+1.800322192\) \(a_{14}=+0.350754216\) \(a_{15}=-0.508000350\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.312678996\) \(a_{18}=+0.227632334\) \(a_{19}=+0.154522352\) \(a_{20}=+0.308456398\)
\(a_{21}=+0.408468086\) \(a_{22}=+0.671046268\) \(a_{23}=+1.254079932\) \(a_{24}=+0.291135550\) \(a_{25}=-0.619418601\)
\(a_{26}=-1.273020030\) \(a_{27}=+1.088543144\) \(a_{28}=-0.248020685\) \(a_{29}=-0.885674259\) \(a_{30}=+0.359210492\)
\(a_{31}=+1.949126824\) \(a_{32}=-0.176776695\) \(a_{33}=+0.781461697\) \(a_{34}=-0.221097438\) \(a_{35}=-0.306014269\)
\(a_{36}=-0.160960367\) \(a_{37}=-0.486988953\) \(a_{38}=-0.109263803\) \(a_{39}=-1.482485545\) \(a_{40}=-0.218111611\)
\(a_{41}=-1.752814374\) \(a_{42}=-0.288830554\) \(a_{43}=-0.305755913\) \(a_{44}=-0.474501367\) \(a_{45}=-0.198597020\)
\(a_{46}=-0.886768424\) \(a_{47}=-0.361869294\) \(a_{48}=-0.205863921\) \(a_{49}=-0.753942959\) \(a_{50}=+0.437995093\)
\(a_{51}=-0.257477297\) \(a_{52}=+0.900161096\) \(a_{53}=-0.363483854\) \(a_{54}=-0.769716239\) \(a_{55}=-0.585451931\)
\(a_{56}=+0.175377108\) \(a_{57}=-0.127242310\) \(a_{58}=+0.626266274\) \(a_{59}=+0.909754514\) \(a_{60}=-0.254000175\)
\(a_{61}=-0.283621100\) \(a_{62}=-1.378240795\) \(a_{63}=+0.159686002\) \(a_{64}=+0.125000000\) \(a_{65}=+1.110641799\)
\(a_{66}=-0.552576865\) \(a_{67}=+0.496253610\) \(a_{68}=+0.156339498\) \(a_{69}=-1.032679250\) \(a_{70}=+0.216384765\)
\(a_{71}=+0.676031783\) \(a_{72}=+0.113816167\) \(a_{73}=-1.610318814\) \(a_{74}=+0.344353191\) \(a_{75}=+0.510063769\)
\(a_{76}=+0.077261176\) \(a_{77}=+0.470744616\) \(a_{78}=+1.048275582\) \(a_{79}=-1.545537591\) \(a_{80}=+0.154228199\)
\(a_{81}=-0.574446308\) \(a_{82}=+1.239426930\) \(a_{83}=-1.557721000\) \(a_{84}=+0.204234043\) \(a_{85}=+0.192895674\)
\(a_{86}=+0.216202079\) \(a_{87}=+0.729313504\) \(a_{88}=+0.335523134\) \(a_{89}=-0.242687293\) \(a_{90}=+0.140429300\)
\(a_{91}=-0.893034287\) \(a_{92}=+0.627039966\) \(a_{93}=-1.605019566\) \(a_{94}=+0.255880232\) \(a_{95}=+0.095326817\)
\(a_{96}=+0.145567775\) \(a_{97}=+1.050038737\) \(a_{98}=+0.533118179\) \(a_{99}=+0.305503656\) \(a_{100}=-0.309709300\)

Showing 100 of 1228 available coefficients

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