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: \( 29.5432049025 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.617188222\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+1.143524758\) \(a_{7}=+0.338998680\) \(a_{8}=+0.353553391\) \(a_{9}=+1.615297744\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.945531785\) \(a_{12}=+0.808594111\) \(a_{13}=-0.456707436\) \(a_{14}=+0.239708265\) \(a_{15}=+0.723228559\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.914157395\) \(a_{18}=+1.142187988\) \(a_{19}=+0.521250057\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.548224672\) \(a_{22}=+0.668591937\) \(a_{23}=+1.480676180\) \(a_{24}=+0.571762379\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.322940925\) \(a_{27}=+0.995052264\) \(a_{28}=+0.169499340\) \(a_{29}=-1.219207609\) \(a_{30}=+0.511399819\)
\(a_{31}=+1.395634200\) \(a_{32}=+0.176776695\) \(a_{33}=+1.529102865\) \(a_{34}=-0.646406893\) \(a_{35}=+0.151604818\)
\(a_{36}=+0.807648872\) \(a_{37}=+0.619375850\) \(a_{38}=+0.368579450\) \(a_{39}=-0.738581885\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.726800379\) \(a_{42}=+0.387653383\) \(a_{43}=+0.995975538\) \(a_{44}=+0.472765892\) \(a_{45}=+0.722383112\)
\(a_{46}=+1.046996168\) \(a_{47}=+0.766916072\) \(a_{48}=+0.404297055\) \(a_{49}=-0.885079895\) \(a_{50}=+0.141421356\)
\(a_{51}=-1.478364572\) \(a_{52}=-0.228353718\) \(a_{53}=-0.823190435\) \(a_{54}=+0.703608204\) \(a_{55}=+0.422854669\)
\(a_{56}=+0.119854133\) \(a_{57}=+0.842959453\) \(a_{58}=-0.862109968\) \(a_{59}=-1.450921616\) \(a_{60}=+0.361614280\)
\(a_{61}=+1.824655045\) \(a_{62}=+0.986862407\) \(a_{63}=+0.547583802\) \(a_{64}=+0.125000000\) \(a_{65}=-0.204245774\)
\(a_{66}=+1.081239005\) \(a_{67}=+1.112373482\) \(a_{68}=-0.457078697\) \(a_{69}=+2.394532079\) \(a_{70}=+0.107200795\)
\(a_{71}=-0.267192309\) \(a_{72}=+0.571093994\) \(a_{73}=+0.827164512\) \(a_{74}=+0.437964864\) \(a_{75}=+0.323437644\)
\(a_{76}=+0.260625029\) \(a_{77}=+0.320534026\) \(a_{78}=-0.522256260\) \(a_{79}=-0.121391538\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.006110942\) \(a_{82}=-0.513925477\) \(a_{83}=+0.945434571\) \(a_{84}=+0.274112336\) \(a_{85}=-0.408823615\)
\(a_{86}=+0.704261057\) \(a_{87}=-1.971688186\) \(a_{88}=+0.334295968\) \(a_{89}=-1.656764570\) \(a_{90}=+0.510801997\)
\(a_{91}=-0.154823218\) \(a_{92}=+0.740338090\) \(a_{93}=+2.257003189\) \(a_{94}=+0.542291555\) \(a_{95}=+0.233110112\)
\(a_{96}=+0.285881189\) \(a_{97}=+1.358780285\) \(a_{98}=-0.625845996\) \(a_{99}=+1.527315359\) \(a_{100}=+0.099975586\)

Showing 100 of 247 available coefficients

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