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: \( 28.9257946349 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.607269780\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+1.136511361\) \(a_{7}=-1.552627695\) \(a_{8}=+0.353553391\) \(a_{9}=+1.583316146\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.195717154\) \(a_{12}=+0.803634890\) \(a_{13}=+1.382717513\) \(a_{14}=-1.097873572\) \(a_{15}=-0.718792897\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.500571241\) \(a_{18}=+1.119573583\) \(a_{19}=+0.182629361\) \(a_{20}=-0.223606798\)
\(a_{21}=-2.495491574\) \(a_{22}=-0.138392927\) \(a_{23}=-1.493752105\) \(a_{24}=+0.568255680\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.977728930\) \(a_{27}=+0.937546413\) \(a_{28}=-0.776313848\) \(a_{29}=+1.337572685\) \(a_{30}=-0.508263332\)
\(a_{31}=-1.612602618\) \(a_{32}=+0.176776695\) \(a_{33}=-0.314570268\) \(a_{34}=-0.353957319\) \(a_{35}=+0.694356214\)
\(a_{36}=+0.791658073\) \(a_{37}=-1.002438736\) \(a_{38}=+0.129138460\) \(a_{39}=+2.222400073\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.893083803\) \(a_{42}=-1.764579015\) \(a_{43}=+0.394279379\) \(a_{44}=-0.097858577\) \(a_{45}=-0.708080506\)
\(a_{46}=-1.056242243\) \(a_{47}=+1.637248062\) \(a_{48}=+0.401817445\) \(a_{49}=+1.410652761\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.804553029\) \(a_{52}=+0.691358757\) \(a_{53}=-1.325773544\) \(a_{54}=+0.662945426\) \(a_{55}=+0.087527372\)
\(a_{56}=-0.548936786\) \(a_{57}=+0.293534653\) \(a_{58}=+0.945806716\) \(a_{59}=-1.652548230\) \(a_{60}=-0.359396449\)
\(a_{61}=+0.108841120\) \(a_{62}=-1.140282246\) \(a_{63}=-2.458300498\) \(a_{64}=+0.125000000\) \(a_{65}=-0.618370071\)
\(a_{66}=-0.222434769\) \(a_{67}=+0.255691557\) \(a_{68}=-0.250285621\) \(a_{69}=-2.400862617\) \(a_{70}=+0.490983988\)
\(a_{71}=-0.958783754\) \(a_{72}=+0.559786792\) \(a_{73}=-0.562692880\) \(a_{74}=-0.708831228\) \(a_{75}=+0.321453956\)
\(a_{76}=+0.091314681\) \(a_{77}=+0.303875874\) \(a_{78}=+1.571474162\) \(a_{79}=-0.812207749\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.076426129\) \(a_{82}=-0.631505613\) \(a_{83}=+0.953672372\) \(a_{84}=-1.247745787\) \(a_{85}=+0.223862265\)
\(a_{86}=+0.278797622\) \(a_{87}=+2.149840156\) \(a_{88}=-0.069196464\) \(a_{89}=-1.597107667\) \(a_{90}=-0.500688528\)
\(a_{91}=-2.146845506\) \(a_{92}=-0.746876052\) \(a_{93}=-2.591887455\) \(a_{94}=+1.157709207\) \(a_{95}=-0.081674333\)
\(a_{96}=+0.284127840\) \(a_{97}=-0.754183893\) \(a_{98}=+0.997482133\) \(a_{99}=-0.309882131\) \(a_{100}=+0.099975586\)

Showing 100 of 232 available coefficients

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