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: \( 29.9472580173 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.293975681\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.914978979\) \(a_{7}=+1.034965913\) \(a_{8}=+0.353553391\) \(a_{9}=+0.674373064\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.144678296\) \(a_{12}=-0.646987841\) \(a_{13}=-0.025706756\) \(a_{14}=+0.731831415\) \(a_{15}=+0.578683517\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.286829476\) \(a_{18}=+0.476853766\) \(a_{19}=+0.747927900\) \(a_{20}=-0.223606798\)
\(a_{21}=-1.339220722\) \(a_{22}=+0.102303004\) \(a_{23}=+1.095049275\) \(a_{24}=-0.457489489\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.018177422\) \(a_{27}=+0.421353337\) \(a_{28}=+0.517482956\) \(a_{29}=+1.452671634\) \(a_{30}=+0.409191039\)
\(a_{31}=+0.191957725\) \(a_{32}=+0.176776695\) \(a_{33}=-0.187210196\) \(a_{34}=-0.909925849\) \(a_{35}=-0.462850827\)
\(a_{36}=+0.337186532\) \(a_{37}=+0.258823569\) \(a_{38}=+0.528864890\) \(a_{39}=+0.033263917\) \(a_{40}=-0.158113883\)
\(a_{41}=-1.081325304\) \(a_{42}=-0.946972054\) \(a_{43}=-0.910621856\) \(a_{44}=+0.072339148\) \(a_{45}=-0.301588802\)
\(a_{46}=+0.774316768\) \(a_{47}=-0.958233924\) \(a_{48}=-0.323493920\) \(a_{49}=+0.071154441\) \(a_{50}=+0.141421356\)
\(a_{51}=+1.665126048\) \(a_{52}=-0.012853378\) \(a_{53}=+0.918811418\) \(a_{54}=+0.297941802\) \(a_{55}=-0.064702101\)
\(a_{56}=+0.365915708\) \(a_{57}=-0.967800514\) \(a_{58}=+1.027193963\) \(a_{59}=+0.000447802\) \(a_{60}=+0.289341758\)
\(a_{61}=-0.995426634\) \(a_{62}=+0.135734609\) \(a_{63}=+0.697953133\) \(a_{64}=+0.125000000\) \(a_{65}=+0.011496411\)
\(a_{66}=-0.132377599\) \(a_{67}=-1.551671839\) \(a_{68}=-0.643414738\) \(a_{69}=-1.416967131\) \(a_{70}=-0.327284958\)
\(a_{71}=-0.837322542\) \(a_{72}=+0.238426883\) \(a_{73}=+0.517542178\) \(a_{74}=+0.183015901\) \(a_{75}=-0.258795136\)
\(a_{76}=+0.373963950\) \(a_{77}=+0.149737104\) \(a_{78}=+0.023521142\) \(a_{79}=-1.899239041\) \(a_{80}=-0.111803399\)
\(a_{81}=-1.219594035\) \(a_{82}=-0.764612455\) \(a_{83}=+0.610795884\) \(a_{84}=-0.669610361\) \(a_{85}=+0.575487637\)
\(a_{86}=-0.643906889\) \(a_{87}=-1.879721767\) \(a_{88}=+0.051151502\) \(a_{89}=+1.511193552\) \(a_{90}=-0.213255487\)
\(a_{91}=-0.026605616\) \(a_{92}=+0.547524637\) \(a_{93}=-0.248388628\) \(a_{94}=-0.677573706\) \(a_{95}=-0.334483525\)
\(a_{96}=-0.228744745\) \(a_{97}=+1.821146145\) \(a_{98}=+0.050313787\) \(a_{99}=+0.097567146\) \(a_{100}=+0.099975586\)

Showing 100 of 249 available coefficients

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