Properties

Level $10$
Weight $0$
Character 10.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 18.2714714374 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.544818788\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.385245059\) \(a_{7}=+1.316924380\) \(a_{8}=+0.353553391\) \(a_{9}=-0.703172488\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.743157544\) \(a_{12}=-0.272409394\) \(a_{13}=-0.594275198\) \(a_{14}=+0.931206160\) \(a_{15}=-0.243650369\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.543480682\) \(a_{18}=-0.497218035\) \(a_{19}=+0.047939635\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.717485145\) \(a_{22}=-0.525491739\) \(a_{23}=+1.386346641\) \(a_{24}=-0.192622530\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.420216022\) \(a_{27}=+0.927920371\) \(a_{28}=+0.658462190\) \(a_{29}=-0.729376869\) \(a_{30}=-0.172286828\)
\(a_{31}=+1.003138646\) \(a_{32}=+0.176776695\) \(a_{33}=+0.404886192\) \(a_{34}=-1.091405657\) \(a_{35}=+0.588946487\)
\(a_{36}=-0.351586244\) \(a_{37}=-1.239418245\) \(a_{38}=+0.033898441\) \(a_{39}=+0.323772293\) \(a_{40}=+0.158113883\)
\(a_{41}=-1.632664181\) \(a_{42}=-0.507338611\) \(a_{43}=-1.334186532\) \(a_{44}=-0.371578772\) \(a_{45}=-0.314468297\)
\(a_{46}=+0.980295111\) \(a_{47}=+0.393743336\) \(a_{48}=-0.136204697\) \(a_{49}=+0.734289824\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.840917274\) \(a_{52}=-0.297137599\) \(a_{53}=-0.331646297\) \(a_{54}=+0.656138787\) \(a_{55}=-0.332350157\)
\(a_{56}=+0.465603080\) \(a_{57}=-0.026118414\) \(a_{58}=-0.515747330\) \(a_{59}=+0.081961697\) \(a_{60}=-0.121825185\)
\(a_{61}=+0.804271454\) \(a_{62}=+0.709326139\) \(a_{63}=-0.926024994\) \(a_{64}=+0.125000000\) \(a_{65}=-0.265767948\)
\(a_{66}=+0.286297772\) \(a_{67}=-0.805660638\) \(a_{68}=-0.771740341\) \(a_{69}=-0.755307697\) \(a_{70}=+0.416448055\)
\(a_{71}=-0.707245373\) \(a_{72}=-0.248609017\) \(a_{73}=-1.805500129\) \(a_{74}=-0.876401046\) \(a_{75}=-0.108963758\)
\(a_{76}=+0.023969818\) \(a_{77}=-0.978682288\) \(a_{78}=+0.228941584\) \(a_{79}=+0.341476930\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.197624037\) \(a_{82}=-1.154467914\) \(a_{83}=+1.037569396\) \(a_{84}=-0.358742572\) \(a_{85}=-0.690265545\)
\(a_{86}=-0.943412344\) \(a_{87}=+0.397378222\) \(a_{88}=-0.262745869\) \(a_{89}=-1.698958813\) \(a_{90}=-0.222362665\)
\(a_{91}=-0.782615497\) \(a_{92}=+0.693173321\) \(a_{93}=-0.546528781\) \(a_{94}=+0.278418583\) \(a_{95}=+0.021439257\)
\(a_{96}=-0.096311265\) \(a_{97}=-1.627162105\) \(a_{98}=+0.519221314\) \(a_{99}=+0.522567941\) \(a_{100}=+0.099975586\)

Showing 100 of 180 available coefficients

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