Properties

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

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 6.33448316434 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.753588819\) \(a_{3}=-0.195919225\) \(a_{4}=+2.075073745\) \(a_{5}=+0.975948577\)
\(a_{6}=-0.343561762\) \(a_{7}=+0.377964473\) \(a_{8}=+1.885237299\) \(a_{9}=-0.961615657\) \(a_{10}=+1.711412513\)
\(a_{11}=-1.527141639\) \(a_{12}=-0.406546840\) \(a_{13}=+0.386520355\) \(a_{14}=+0.662794274\) \(a_{15}=-0.191207089\)
\(a_{16}=+1.230857303\) \(a_{17}=-1.000141772\) \(a_{18}=-1.686278465\) \(a_{19}=+1.094226126\) \(a_{20}=+2.025165269\)
\(a_{21}=-0.074050507\) \(a_{22}=-2.677978503\) \(a_{23}=+0.576826444\) \(a_{24}=-0.369354230\) \(a_{25}=-0.047524375\)
\(a_{26}=+0.677797772\) \(a_{27}=+0.384318219\) \(a_{28}=+0.784304155\) \(a_{29}=+0.220073090\) \(a_{30}=-0.335298613\)
\(a_{31}=-0.345334607\) \(a_{32}=+0.273180306\) \(a_{33}=+0.299196406\) \(a_{34}=-1.753837429\) \(a_{35}=+0.368873890\)
\(a_{36}=-1.995423404\) \(a_{37}=-0.239273466\) \(a_{38}=+1.918822700\) \(a_{39}=-0.075726768\) \(a_{40}=+1.839894660\)
\(a_{41}=+1.442916339\) \(a_{42}=-0.129854140\) \(a_{43}=+0.401621503\) \(a_{44}=-3.168931521\) \(a_{45}=-0.938487433\)
\(a_{46}=+1.011516403\) \(a_{47}=-0.125136269\) \(a_{48}=-0.241148609\) \(a_{49}=+0.142857143\) \(a_{50}=-0.083338212\)
\(a_{51}=+0.195947001\) \(a_{52}=+0.802058240\) \(a_{53}=-0.467502972\) \(a_{54}=+0.673936132\) \(a_{55}=-1.490411710\)
\(a_{56}=+0.712552722\) \(a_{57}=-0.214379935\) \(a_{58}=+0.385917710\) \(a_{59}=+0.712977074\) \(a_{60}=-0.396768810\)
\(a_{61}=+0.867527585\) \(a_{62}=-0.605574906\) \(a_{63}=-0.363456555\) \(a_{64}=-0.751811374\) \(a_{65}=+0.377223990\)
\(a_{66}=+0.524667473\) \(a_{67}=+1.772780243\) \(a_{68}=-2.075367933\) \(a_{69}=-0.113011390\) \(a_{70}=+0.646853128\)
\(a_{71}=+0.455718693\) \(a_{72}=-1.812873705\) \(a_{73}=-1.179804026\) \(a_{74}=-0.419587274\) \(a_{75}=+0.009310939\)
\(a_{76}=+2.270599906\) \(a_{77}=-0.577205285\) \(a_{78}=-0.132793614\) \(a_{79}=-0.510033369\) \(a_{80}=+1.201253434\)
\(a_{81}=+0.886320330\) \(a_{82}=+2.530281958\) \(a_{83}=-0.452292743\) \(a_{84}=-0.153660262\) \(a_{85}=-0.976086940\)
\(a_{86}=+0.704278978\) \(a_{87}=-0.043116549\) \(a_{88}=-2.879024379\) \(a_{89}=-0.598562267\) \(a_{90}=-1.645721068\)
\(a_{91}=+0.146090962\) \(a_{92}=+1.196957410\) \(a_{93}=+0.067657689\) \(a_{94}=-0.219437562\) \(a_{95}=+1.067908431\)
\(a_{96}=-0.053521274\) \(a_{97}=-0.477864181\) \(a_{98}=+0.250512688\) \(a_{99}=+1.468523311\) \(a_{100}=-0.098616582\)

Showing 100 of 1228 available coefficients

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