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: \( 24.9063465366 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.062305851\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.044056890\) \(a_{7}=+0.089706777\) \(a_{8}=-0.353553391\) \(a_{9}=-0.996117981\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.842286813\) \(a_{12}=-0.031152926\) \(a_{13}=+0.506504380\) \(a_{14}=-0.063432270\) \(a_{15}=+0.027864024\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.251674183\) \(a_{18}=+0.704361779\) \(a_{19}=-0.504350613\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.005589257\) \(a_{22}=+0.595586717\) \(a_{23}=-0.437311788\) \(a_{24}=+0.022028445\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.358152682\) \(a_{27}=+0.124369830\) \(a_{28}=+0.044853388\) \(a_{29}=+1.507076765\) \(a_{30}=-0.019702840\)
\(a_{31}=+0.075239423\) \(a_{32}=-0.176776695\) \(a_{33}=+0.052479397\) \(a_{34}=-0.885067302\) \(a_{35}=-0.040118090\)
\(a_{36}=-0.498058990\) \(a_{37}=-0.137109171\) \(a_{38}=+0.356629739\) \(a_{39}=-0.031558187\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.910341781\) \(a_{42}=+0.003952202\) \(a_{43}=+0.976107422\) \(a_{44}=-0.421143406\) \(a_{45}=+0.445477504\)
\(a_{46}=+0.309226131\) \(a_{47}=-0.405160441\) \(a_{48}=-0.015576463\) \(a_{49}=-0.991952694\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.077986625\) \(a_{52}=+0.253252190\) \(a_{53}=+0.681208420\) \(a_{54}=-0.087942750\) \(a_{55}=+0.376682114\)
\(a_{56}=-0.031716135\) \(a_{57}=+0.031423994\) \(a_{58}=-1.065664200\) \(a_{59}=+0.302351787\) \(a_{60}=+0.013932012\)
\(a_{61}=-1.189067824\) \(a_{62}=-0.053202307\) \(a_{63}=-0.089358533\) \(a_{64}=+0.125000000\) \(a_{65}=-0.226515645\)
\(a_{66}=-0.037108537\) \(a_{67}=+1.948611052\) \(a_{68}=+0.625837091\) \(a_{69}=+0.027247083\) \(a_{70}=+0.028367774\)
\(a_{71}=+0.743907594\) \(a_{72}=+0.352180890\) \(a_{73}=+1.232092666\) \(a_{74}=+0.096950825\) \(a_{75}=-0.012461170\)
\(a_{76}=-0.252175307\) \(a_{77}=-0.075558835\) \(a_{78}=+0.022315008\) \(a_{79}=+0.200016373\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.988369013\) \(a_{82}=+0.643708847\) \(a_{83}=+0.612896804\) \(a_{84}=-0.002794629\) \(a_{85}=-0.559765712\)
\(a_{86}=-0.690212177\) \(a_{87}=-0.093899701\) \(a_{88}=+0.297793358\) \(a_{89}=-1.676602843\) \(a_{90}=-0.315000164\)
\(a_{91}=+0.045436875\) \(a_{92}=-0.218655894\) \(a_{93}=-0.004687856\) \(a_{94}=+0.286491695\) \(a_{95}=+0.225552451\)
\(a_{96}=+0.011014222\) \(a_{97}=-0.861840809\) \(a_{98}=+0.701416477\) \(a_{99}=+0.839017039\) \(a_{100}=+0.099975586\)

Showing 100 of 225 available coefficients

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