Properties

Level $971$
Weight $0$
Character 971.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 971 \)
Weight: \( 0 \)
Character: 971.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 0.3848752595 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.003009460\) \(a_{3}=+0.678015505\) \(a_{4}=+0.006025706\) \(a_{5}=+0.653741030\)
\(a_{6}=+0.680054093\) \(a_{7}=-1.583463664\) \(a_{8}=-0.996964665\) \(a_{9}=-0.540296881\) \(a_{10}=+0.655708437\)
\(a_{11}=+1.551492120\) \(a_{12}=+0.004085386\) \(a_{13}=-1.207390427\) \(a_{14}=-1.588227032\) \(a_{15}=+0.443246478\)
\(a_{16}=-1.005991096\) \(a_{17}=+1.910414267\) \(a_{18}=-0.541922971\) \(a_{19}=+0.068178257\) \(a_{20}=+0.003939985\)
\(a_{21}=-1.073610788\) \(a_{22}=+1.556160846\) \(a_{23}=-0.842124135\) \(a_{24}=-0.675956295\) \(a_{25}=-0.572622689\)
\(a_{26}=-1.211022869\) \(a_{27}=-1.044344154\) \(a_{28}=-0.009541916\) \(a_{29}=-0.972650929\) \(a_{30}=+0.444579664\)
\(a_{31}=-0.147617370\) \(a_{32}=-0.012051558\) \(a_{33}=+1.051934211\) \(a_{34}=+1.916161889\) \(a_{35}=-1.035175739\)
\(a_{36}=-0.003255341\) \(a_{37}=-0.118281046\) \(a_{38}=+0.068383331\) \(a_{39}=-0.818627723\) \(a_{40}=-0.651757339\)
\(a_{41}=-0.504652433\) \(a_{42}=-1.076840204\) \(a_{43}=+1.224469967\) \(a_{44}=+0.009349041\) \(a_{45}=-0.353214629\)
\(a_{46}=-0.844657263\) \(a_{47}=-0.803007183\) \(a_{48}=-0.682074936\) \(a_{49}=+1.507354151\) \(a_{50}=-0.574345875\)
\(a_{51}=+1.295287634\) \(a_{52}=-0.007275787\) \(a_{53}=-0.013878839\) \(a_{54}=-1.047485595\) \(a_{55}=+1.014274137\)
\(a_{56}=+1.578656501\) \(a_{57}=+0.046225896\) \(a_{58}=-0.975575585\) \(a_{59}=-0.023600356\) \(a_{60}=+0.002670168\)
\(a_{61}=+1.505954978\) \(a_{62}=-0.148061620\) \(a_{63}=+0.855540607\) \(a_{64}=+0.993902969\) \(a_{65}=-0.789320631\)
\(a_{66}=+1.055098354\) \(a_{67}=-0.340264688\) \(a_{68}=+0.011511881\) \(a_{69}=-0.570971074\) \(a_{70}=-1.038288994\)
\(a_{71}=+1.805656593\) \(a_{72}=+0.538656790\) \(a_{73}=+0.950131735\) \(a_{74}=-0.118637245\) \(a_{75}=-0.388246190\)
\(a_{76}=+0.000411716\) \(a_{77}=-2.456730443\) \(a_{78}=-0.821090839\) \(a_{79}=+0.983616988\) \(a_{80}=-0.657657331\)
\(a_{81}=-0.167782241\) \(a_{82}=-0.506170080\) \(a_{83}=-0.795346928\) \(a_{84}=-0.006470026\) \(a_{85}=+1.248916850\)
\(a_{86}=+1.228153412\) \(a_{87}=-0.659469608\) \(a_{88}=-1.546782360\) \(a_{89}=+0.722879351\) \(a_{90}=-0.354276942\)
\(a_{91}=+1.911857738\) \(a_{92}=-0.005074083\) \(a_{93}=-0.100085904\) \(a_{94}=-0.805423169\) \(a_{95}=+0.044570346\)
\(a_{96}=-0.008171721\) \(a_{97}=+0.194104865\) \(a_{98}=+1.511890061\) \(a_{99}=-0.838266392\) \(a_{100}=-0.003450264\)

Showing 100 of 2520 available coefficients

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