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: \( 26.2206008714 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.987819760\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-1.405600832\) \(a_{7}=-0.711218692\) \(a_{8}=-0.353553391\) \(a_{9}=+2.951427400\) \(a_{10}=-0.316227766\)
\(a_{11}=-1.373733772\) \(a_{12}=+0.993909880\) \(a_{13}=-0.432589095\) \(a_{14}=+0.502907560\) \(a_{15}=+0.888980022\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.514558446\) \(a_{18}=-2.086974329\) \(a_{19}=+0.174389107\) \(a_{20}=+0.223606798\)
\(a_{21}=-1.413774570\) \(a_{22}=+0.971376465\) \(a_{23}=+0.437464156\) \(a_{24}=-0.702800416\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.305886683\) \(a_{27}=+3.879085947\) \(a_{28}=-0.355609346\) \(a_{29}=+0.155533732\) \(a_{30}=-0.628603802\)
\(a_{31}=+0.892494246\) \(a_{32}=-0.176776695\) \(a_{33}=-2.730735137\) \(a_{34}=+1.070954547\) \(a_{35}=-0.318066668\)
\(a_{36}=+1.475713700\) \(a_{37}=-0.167801200\) \(a_{38}=-0.123311720\) \(a_{39}=-0.859909152\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.865760921\) \(a_{42}=+0.999689586\) \(a_{43}=-1.217777648\) \(a_{44}=-0.686866886\) \(a_{45}=+1.319918459\)
\(a_{46}=-0.309333871\) \(a_{47}=-0.755743045\) \(a_{48}=+0.496954940\) \(a_{49}=-0.494167972\) \(a_{50}=-0.141421356\)
\(a_{51}=-3.010669207\) \(a_{52}=-0.216294548\) \(a_{53}=+0.212260130\) \(a_{54}=-2.742927978\) \(a_{55}=-0.614352419\)
\(a_{56}=+0.251453780\) \(a_{57}=+0.346654113\) \(a_{58}=-0.109978957\) \(a_{59}=-1.176289065\) \(a_{60}=+0.444490011\)
\(a_{61}=-1.394134085\) \(a_{62}=-0.631088734\) \(a_{63}=-2.099110335\) \(a_{64}=+0.125000000\) \(a_{65}=-0.193459725\)
\(a_{66}=+1.930921333\) \(a_{67}=+0.046159772\) \(a_{68}=-0.757279223\) \(a_{69}=+0.869599893\) \(a_{70}=+0.224907098\)
\(a_{71}=-1.046555508\) \(a_{72}=-1.043487164\) \(a_{73}=-0.672246730\) \(a_{74}=+0.118653367\) \(a_{75}=+0.397563952\)
\(a_{76}=+0.087194554\) \(a_{77}=+0.977025136\) \(a_{78}=+0.608047593\) \(a_{79}=-1.805998952\) \(a_{80}=+0.111803399\)
\(a_{81}=+4.759496298\) \(a_{82}=-0.612185418\) \(a_{83}=+1.806715811\) \(a_{84}=-0.706887285\) \(a_{85}=-0.677331128\)
\(a_{86}=+0.861098833\) \(a_{87}=+0.309173026\) \(a_{88}=+0.485688233\) \(a_{89}=-1.619979912\) \(a_{90}=-0.933323293\)
\(a_{91}=+0.307665451\) \(a_{92}=+0.218732078\) \(a_{93}=+1.774117699\) \(a_{94}=+0.534391032\) \(a_{95}=+0.077989180\)
\(a_{96}=-0.351400208\) \(a_{97}=+0.235451580\) \(a_{98}=+0.349429524\) \(a_{99}=-4.054475494\) \(a_{100}=+0.099975586\)

Showing 100 of 226 available coefficients

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