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: \( 27.0342235 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.375831701\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.972859925\) \(a_{7}=+0.875971955\) \(a_{8}=+0.353553391\) \(a_{9}=+0.892912869\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.880905239\) \(a_{12}=-0.687915850\) \(a_{13}=-0.124013288\) \(a_{14}=+0.619405709\) \(a_{15}=+0.615290642\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.034555101\) \(a_{18}=+0.631384745\) \(a_{19}=+0.264332439\) \(a_{20}=-0.223606798\)
\(a_{21}=-1.205189984\) \(a_{22}=-0.622894068\) \(a_{23}=-0.367801221\) \(a_{24}=-0.486429963\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.087690637\) \(a_{27}=+0.147333869\) \(a_{28}=+0.437985977\) \(a_{29}=-1.642060828\) \(a_{30}=+0.435076185\)
\(a_{31}=+1.289474897\) \(a_{32}=+0.176776695\) \(a_{33}=+1.211977353\) \(a_{34}=+0.024434146\) \(a_{35}=-0.391746567\)
\(a_{36}=+0.446456435\) \(a_{37}=+0.968802580\) \(a_{38}=+0.186911260\) \(a_{39}=+0.170621413\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.970413477\) \(a_{42}=-0.852198011\) \(a_{43}=-0.940419043\) \(a_{44}=-0.440452619\) \(a_{45}=-0.399322775\)
\(a_{46}=-0.260074738\) \(a_{47}=+1.675795047\) \(a_{48}=-0.343957925\) \(a_{49}=-0.232673134\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.047542003\) \(a_{52}=-0.062006644\) \(a_{53}=+1.443478072\) \(a_{54}=+0.104180778\) \(a_{55}=+0.393952799\)
\(a_{56}=+0.309702855\) \(a_{57}=-0.363676949\) \(a_{58}=-1.161112347\) \(a_{59}=+1.630930612\) \(a_{60}=+0.307645321\)
\(a_{61}=+0.867030668\) \(a_{62}=+0.911796444\) \(a_{63}=+0.782166631\) \(a_{64}=+0.125000000\) \(a_{65}=+0.055460428\)
\(a_{66}=+0.856997405\) \(a_{67}=+1.039737555\) \(a_{68}=+0.017277550\) \(a_{69}=+0.506032580\) \(a_{70}=-0.277006654\)
\(a_{71}=-0.357863195\) \(a_{72}=+0.315692372\) \(a_{73}=-0.551858440\) \(a_{74}=+0.685046874\) \(a_{75}=-0.275166340\)
\(a_{76}=+0.132166219\) \(a_{77}=-0.771648284\) \(a_{78}=+0.120647558\) \(a_{79}=-0.945824273\) \(a_{80}=-0.111803399\)
\(a_{81}=-1.095619477\) \(a_{82}=-0.686185950\) \(a_{83}=-0.485013256\) \(a_{84}=-0.602594992\) \(a_{85}=-0.015453511\)
\(a_{86}=-0.664976683\) \(a_{87}=+2.259199342\) \(a_{88}=-0.311447034\) \(a_{89}=+1.801407574\) \(a_{90}=-0.282363842\)
\(a_{91}=-0.108632162\) \(a_{92}=-0.183900611\) \(a_{93}=-1.774100441\) \(a_{94}=+1.184966042\) \(a_{95}=-0.118213060\)
\(a_{96}=-0.243214981\) \(a_{97}=-1.062893719\) \(a_{98}=-0.164524751\) \(a_{99}=-0.786571624\) \(a_{100}=+0.099975586\)

Showing 100 of 228 available coefficients

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