Properties

Level $7$
Weight $0$
Character 7.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 4.82800766847 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.111646056\) \(a_{3}=-0.392871433\) \(a_{4}=-0.987535158\) \(a_{5}=-0.464972300\)
\(a_{6}=+0.043862546\) \(a_{7}=+0.377964473\) \(a_{8}=+0.221900461\) \(a_{9}=-0.845652037\) \(a_{10}=+0.051912323\)
\(a_{11}=-0.510377703\) \(a_{12}=+0.387974353\) \(a_{13}=+0.339083983\) \(a_{14}=-0.042198243\) \(a_{15}=+0.182674334\)
\(a_{16}=+0.962760847\) \(a_{17}=-0.913591260\) \(a_{18}=+0.094413715\) \(a_{19}=-1.537288554\) \(a_{20}=+0.459176494\)
\(a_{21}=-0.148491444\) \(a_{22}=+0.056981658\) \(a_{23}=+1.704314179\) \(a_{24}=-0.087178352\) \(a_{25}=-0.783800760\)
\(a_{26}=-0.037857389\) \(a_{27}=+0.725103960\) \(a_{28}=-0.373253206\) \(a_{29}=+0.366688349\) \(a_{30}=-0.020394869\)
\(a_{31}=-1.467798948\) \(a_{32}=-0.329388913\) \(a_{33}=+0.200512820\) \(a_{34}=+0.101998861\) \(a_{35}=-0.175743010\)
\(a_{36}=+0.835111118\) \(a_{37}=+0.655169924\) \(a_{38}=+0.171632204\) \(a_{39}=-0.133216410\) \(a_{40}=-0.103177568\)
\(a_{41}=+0.361042394\) \(a_{42}=+0.016578484\) \(a_{43}=-1.011231546\) \(a_{44}=+0.504015926\) \(a_{45}=+0.393204773\)
\(a_{46}=-0.190279956\) \(a_{47}=-1.364471759\) \(a_{48}=-0.378241233\) \(a_{49}=+0.142857143\) \(a_{50}=+0.087508263\)
\(a_{51}=+0.358923907\) \(a_{52}=-0.334857355\) \(a_{53}=+1.070932776\) \(a_{54}=-0.080954997\) \(a_{55}=+0.237311495\)
\(a_{56}=+0.083870491\) \(a_{57}=+0.603956757\) \(a_{58}=-0.040939308\) \(a_{59}=-0.156035795\) \(a_{60}=-0.180397327\)
\(a_{61}=+0.325838567\) \(a_{62}=+0.163873963\) \(a_{63}=-0.319626427\) \(a_{64}=-0.925985874\) \(a_{65}=-0.157664659\)
\(a_{66}=-0.022386465\) \(a_{67}=-1.328232054\) \(a_{68}=+0.902203490\) \(a_{69}=-0.669576354\) \(a_{70}=+0.019621014\)
\(a_{71}=+1.150127617\) \(a_{72}=-0.187650577\) \(a_{73}=+0.082410793\) \(a_{74}=-0.073147138\) \(a_{75}=+0.307932928\)
\(a_{76}=+1.518126495\) \(a_{77}=-0.192904640\) \(a_{78}=+0.014873087\) \(a_{79}=-0.445786617\) \(a_{80}=-0.447657125\)
\(a_{81}=+0.560779405\) \(a_{82}=-0.040308959\) \(a_{83}=-0.891409017\) \(a_{84}=+0.146640522\) \(a_{85}=+0.424794630\)
\(a_{86}=+0.112900014\) \(a_{87}=-0.144061377\) \(a_{88}=-0.113253048\) \(a_{89}=-0.920472346\) \(a_{90}=-0.043899762\)
\(a_{91}=+0.128161699\) \(a_{92}=-1.683070173\) \(a_{93}=+0.576656276\) \(a_{94}=+0.152337890\) \(a_{95}=+0.714796595\)
\(a_{96}=+0.129407494\) \(a_{97}=-0.172602725\) \(a_{98}=-0.015949437\) \(a_{99}=+0.431601945\) \(a_{100}=+0.774030808\)

Showing 100 of 1228 available coefficients

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