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: \( 26.4536952758 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.684415559\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-1.191061664\) \(a_{7}=+0.657303325\) \(a_{8}=-0.353553391\) \(a_{9}=+1.837255776\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.242992369\) \(a_{12}=+0.842207780\) \(a_{13}=+0.123935206\) \(a_{14}=-0.464783639\) \(a_{15}=-0.753293539\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.311753118\) \(a_{18}=-1.299136018\) \(a_{19}=-1.263942562\) \(a_{20}=-0.223606798\)
\(a_{21}=+1.107171948\) \(a_{22}=-0.171821552\) \(a_{23}=-1.905507331\) \(a_{24}=-0.595530832\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.087635424\) \(a_{27}=+1.410286656\) \(a_{28}=+0.328651663\) \(a_{29}=+1.561436699\) \(a_{30}=+0.532658969\)
\(a_{31}=-0.983160076\) \(a_{32}=-0.176776695\) \(a_{33}=+0.409300128\) \(a_{34}=+0.220442744\) \(a_{35}=-0.293954983\)
\(a_{36}=+0.918627888\) \(a_{37}=-1.032938237\) \(a_{38}=+0.893742356\) \(a_{39}=+0.208758389\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.199373164\) \(a_{42}=-0.782888793\) \(a_{43}=+0.684691797\) \(a_{44}=+0.121496185\) \(a_{45}=-0.821645761\)
\(a_{46}=+1.347397156\) \(a_{47}=-1.606279507\) \(a_{48}=+0.421103890\) \(a_{49}=-0.567952338\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.525121802\) \(a_{52}=+0.061967603\) \(a_{53}=-1.172995887\) \(a_{54}=-0.997223258\) \(a_{55}=-0.108669491\)
\(a_{56}=-0.232391819\) \(a_{57}=-2.129004517\) \(a_{58}=-1.104102478\) \(a_{59}=-0.272676180\) \(a_{60}=-0.376646769\)
\(a_{61}=-1.009166997\) \(a_{62}=+0.695199157\) \(a_{63}=+1.207634331\) \(a_{64}=+0.125000000\) \(a_{65}=-0.055425509\)
\(a_{66}=-0.289418896\) \(a_{67}=-0.719273421\) \(a_{68}=-0.155876559\) \(a_{69}=-3.209666197\) \(a_{70}=+0.207857562\)
\(a_{71}=+0.672984542\) \(a_{72}=-0.649568009\) \(a_{73}=+1.594983598\) \(a_{74}=+0.730397632\) \(a_{75}=+0.336883112\)
\(a_{76}=-0.631971281\) \(a_{77}=+0.159719693\) \(a_{78}=-0.147614472\) \(a_{79}=+1.208717722\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.538253011\) \(a_{82}=-0.140978116\) \(a_{83}=-0.324918227\) \(a_{84}=+0.553585974\) \(a_{85}=+0.139420233\)
\(a_{86}=-0.484150213\) \(a_{87}=+2.630108270\) \(a_{88}=-0.085910776\) \(a_{89}=+1.633227995\) \(a_{90}=+0.580991290\)
\(a_{91}=+0.081463023\) \(a_{92}=-0.952753666\) \(a_{93}=-1.656050129\) \(a_{94}=+1.135811132\) \(a_{95}=+0.565252298\)
\(a_{96}=-0.297765416\) \(a_{97}=-1.786727191\) \(a_{98}=+0.401602950\) \(a_{99}=+0.446439134\) \(a_{100}=+0.099975586\)

Showing 100 of 228 available coefficients

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