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: \( 19.549801355 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.291858141\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.206374871\) \(a_{7}=+0.817698948\) \(a_{8}=+0.353553391\) \(a_{9}=-0.914818825\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.437902289\) \(a_{12}=+0.145929071\) \(a_{13}=-0.164021429\) \(a_{14}=+0.578200471\) \(a_{15}=+0.130522929\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.199969100\) \(a_{18}=-0.646874595\) \(a_{19}=-0.182150412\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.238652095\) \(a_{22}=+0.309643678\) \(a_{23}=+1.161258131\) \(a_{24}=+0.103187435\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.115980664\) \(a_{27}=-0.558855463\) \(a_{28}=+0.408849474\) \(a_{29}=+0.188202245\) \(a_{30}=+0.092293648\)
\(a_{31}=-0.242085918\) \(a_{32}=+0.176776695\) \(a_{33}=+0.127805348\) \(a_{34}=+0.848506288\) \(a_{35}=+0.365686086\)
\(a_{36}=-0.457409413\) \(a_{37}=-1.019450602\) \(a_{38}=-0.128799792\) \(a_{39}=-0.047870989\) \(a_{40}=+0.158113883\)
\(a_{41}=+1.065143286\) \(a_{42}=+0.168752515\) \(a_{43}=+0.705864728\) \(a_{44}=+0.218951145\) \(a_{45}=-0.409119416\)
\(a_{46}=+0.821133499\) \(a_{47}=+1.239396741\) \(a_{48}=+0.072964535\) \(a_{49}=-0.331368431\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.350220751\) \(a_{52}=-0.082010714\) \(a_{53}=+1.588328415\) \(a_{54}=-0.395170488\) \(a_{55}=+0.195835857\)
\(a_{56}=+0.289100235\) \(a_{57}=-0.053162081\) \(a_{58}=+0.133079084\) \(a_{59}=-1.046179307\) \(a_{60}=+0.065261464\)
\(a_{61}=-1.811725496\) \(a_{62}=-0.171180595\) \(a_{63}=-0.748046391\) \(a_{64}=+0.125000000\) \(a_{65}=-0.073352613\)
\(a_{66}=+0.090372028\) \(a_{67}=-0.369676170\) \(a_{68}=+0.599984550\) \(a_{69}=+0.338922640\) \(a_{70}=+0.258579112\)
\(a_{71}=+0.512904856\) \(a_{72}=-0.323437297\) \(a_{73}=+1.082951367\) \(a_{74}=-0.720860434\) \(a_{75}=+0.058371628\)
\(a_{76}=-0.091075206\) \(a_{77}=+0.358072241\) \(a_{78}=-0.033849901\) \(a_{79}=-0.490406146\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.751712308\) \(a_{82}=+0.753170041\) \(a_{83}=+1.560692866\) \(a_{84}=+0.119326048\) \(a_{85}=+0.536642496\)
\(a_{86}=+0.499121736\) \(a_{87}=+0.054928358\) \(a_{88}=+0.154821839\) \(a_{89}=+1.860370704\) \(a_{90}=-0.289291113\)
\(a_{91}=-0.134120150\) \(a_{92}=+0.580629066\) \(a_{93}=-0.070654746\) \(a_{94}=+0.876385840\) \(a_{95}=-0.081460141\)
\(a_{96}=+0.051593718\) \(a_{97}=+0.678840335\) \(a_{98}=-0.234312865\) \(a_{99}=-0.400601258\) \(a_{100}=+0.099975586\)

Showing 100 of 192 available coefficients

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