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: \( 3.19085876294 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.836259912\) \(a_{3}=-0.269846823\) \(a_{4}=-0.300669360\) \(a_{5}=+1.131273268\)
\(a_{6}=-0.225662080\) \(a_{7}=+0.377964473\) \(a_{8}=-1.087697644\) \(a_{9}=-0.927182692\) \(a_{10}=+0.946038483\)
\(a_{11}=+0.990723229\) \(a_{12}=+0.081134672\) \(a_{13}=-0.427866338\) \(a_{14}=+0.316076537\) \(a_{15}=-0.305270497\)
\(a_{16}=-0.608928575\) \(a_{17}=-0.111837647\) \(a_{18}=-0.775365716\) \(a_{19}=+1.445279910\) \(a_{20}=-0.340139210\)
\(a_{21}=-0.101992512\) \(a_{22}=+0.828502120\) \(a_{23}=-0.560696139\) \(a_{24}=+0.293511754\) \(a_{25}=+0.279779207\)
\(a_{26}=-0.357807466\) \(a_{27}=+0.520044127\) \(a_{28}=-0.113642336\) \(a_{29}=-1.189362591\) \(a_{30}=-0.255285479\)
\(a_{31}=-0.297756453\) \(a_{32}=+0.578475088\) \(a_{33}=-0.267343516\) \(a_{34}=-0.093525341\) \(a_{35}=+0.427581105\)
\(a_{36}=+0.278775427\) \(a_{37}=+1.021141296\) \(a_{38}=+1.208629650\) \(a_{39}=+0.115458372\) \(a_{40}=-1.230483269\)
\(a_{41}=-0.993435495\) \(a_{42}=-0.085292249\) \(a_{43}=+0.041820293\) \(a_{44}=-0.297880120\) \(a_{45}=-1.048896994\)
\(a_{46}=-0.468887703\) \(a_{47}=+1.287210122\) \(a_{48}=+0.164317441\) \(a_{49}=+0.142857143\) \(a_{50}=+0.233968135\)
\(a_{51}=+0.030179034\) \(a_{52}=+0.128646298\) \(a_{53}=+0.026897122\) \(a_{54}=+0.434892055\) \(a_{55}=+1.120778705\)
\(a_{56}=-0.411111067\) \(a_{57}=-0.390004192\) \(a_{58}=-0.994616256\) \(a_{59}=-0.025831873\) \(a_{60}=+0.091785485\)
\(a_{61}=+0.161147372\) \(a_{62}=-0.249001785\) \(a_{63}=-0.350442118\) \(a_{64}=+1.092684101\) \(a_{65}=-0.484033751\)
\(a_{66}=-0.223568665\) \(a_{67}=-1.088382879\) \(a_{68}=+0.033626154\) \(a_{69}=+0.151302072\) \(a_{70}=+0.357568937\)
\(a_{71}=-0.887865272\) \(a_{72}=+1.008494430\) \(a_{73}=+0.604132023\) \(a_{74}=+0.853939530\) \(a_{75}=-0.075497530\)
\(a_{76}=-0.434551386\) \(a_{77}=+0.374458183\) \(a_{78}=+0.096553208\) \(a_{79}=+0.581705200\) \(a_{80}=-0.688864619\)
\(a_{81}=+0.786850437\) \(a_{82}=-0.830770279\) \(a_{83}=-0.610997314\) \(a_{84}=+0.030666023\) \(a_{85}=-0.126518940\)
\(a_{86}=+0.034972635\) \(a_{87}=+0.320945717\) \(a_{88}=-1.077607322\) \(a_{89}=-0.740366821\) \(a_{90}=-0.877150508\)
\(a_{91}=-0.161718275\) \(a_{92}=+0.168584149\) \(a_{93}=+0.080348633\) \(a_{94}=+1.076442223\) \(a_{95}=+1.635006527\)
\(a_{96}=-0.156099665\) \(a_{97}=+1.690291104\) \(a_{98}=+0.119465702\) \(a_{99}=-0.918581430\) \(a_{100}=-0.084121035\)

Showing 100 of 1228 available coefficients

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