Properties

Level $51$
Weight $0$
Character 51.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 51 = 3 \cdot 17 \)
Weight: \( 0 \)
Character: 51.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 2.30240498094 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.018184739\) \(a_{3}=-0.577350269\) \(a_{4}=+0.036700163\) \(a_{5}=+0.939212390\)
\(a_{6}=+0.587849233\) \(a_{7}=+0.431085990\) \(a_{8}=+0.980817193\) \(a_{9}=+0.333333333\) \(a_{10}=-0.956291722\)
\(a_{11}=+0.481427128\) \(a_{12}=-0.021188849\) \(a_{13}=+0.223333000\) \(a_{14}=-0.438925176\) \(a_{15}=-0.542254526\)
\(a_{16}=-1.035353261\) \(a_{17}=+0.242535625\) \(a_{18}=-0.339394913\) \(a_{19}=+0.528012687\) \(a_{20}=+0.034469248\)
\(a_{21}=-0.248887612\) \(a_{22}=-0.490181755\) \(a_{23}=+1.357815336\) \(a_{24}=-0.566275071\) \(a_{25}=-0.117880086\)
\(a_{26}=-0.227394252\) \(a_{27}=-0.192450090\) \(a_{28}=+0.015820926\) \(a_{29}=+1.476706085\) \(a_{30}=+0.552115283\)
\(a_{31}=+1.336186970\) \(a_{32}=+0.073363697\) \(a_{33}=-0.277952082\) \(a_{34}=-0.246946072\) \(a_{35}=+0.404881303\)
\(a_{36}=+0.012233388\) \(a_{37}=-0.275829709\) \(a_{38}=-0.537614460\) \(a_{39}=-0.128941367\) \(a_{40}=+0.921195660\)
\(a_{41}=-1.093969136\) \(a_{42}=+0.253413569\) \(a_{43}=-1.131567769\) \(a_{44}=+0.017668454\) \(a_{45}=+0.313070797\)
\(a_{46}=-1.382506853\) \(a_{47}=+1.406767125\) \(a_{48}=+0.597761484\) \(a_{49}=-0.814164869\) \(a_{50}=+0.120023705\)
\(a_{51}=-0.140028008\) \(a_{52}=+0.008196357\) \(a_{53}=-1.801202202\) \(a_{54}=+0.195949744\) \(a_{55}=+0.452162324\)
\(a_{56}=+0.422816551\) \(a_{57}=-0.304848267\) \(a_{58}=-1.503559600\) \(a_{59}=+1.339704222\) \(a_{60}=-0.019900829\)
\(a_{61}=+0.876521510\) \(a_{62}=-1.360485182\) \(a_{63}=+0.143695330\) \(a_{64}=+0.960655465\) \(a_{65}=+0.209757120\)
\(a_{66}=+0.283006568\) \(a_{67}=+0.244816958\) \(a_{68}=+0.008901097\) \(a_{69}=-0.783935050\) \(a_{70}=-0.412243964\)
\(a_{71}=+1.078530069\) \(a_{72}=+0.326939064\) \(a_{73}=-0.966597123\) \(a_{74}=+0.280845601\) \(a_{75}=+0.068058100\)
\(a_{76}=+0.019378152\) \(a_{77}=+0.207536490\) \(a_{78}=+0.131286133\) \(a_{79}=+0.187015053\) \(a_{80}=-0.972416611\)
\(a_{81}=+0.111111111\) \(a_{82}=+1.113862679\) \(a_{83}=-0.537229718\) \(a_{84}=-0.009134216\) \(a_{85}=+0.227792464\)
\(a_{86}=+1.152145033\) \(a_{87}=-0.852576656\) \(a_{88}=+0.472192005\) \(a_{89}=+0.068536210\) \(a_{90}=-0.318763907\)
\(a_{91}=+0.096275727\) \(a_{92}=+0.049832044\) \(a_{93}=-0.771447907\) \(a_{94}=-1.432348819\) \(a_{95}=+0.495916058\)
\(a_{96}=-0.042356550\) \(a_{97}=+1.320647893\) \(a_{98}=+0.828970245\) \(a_{99}=+0.160475709\) \(a_{100}=-0.004326218\)

Showing 100 of 486 available coefficients

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