Properties

Level $51$
Weight $0$
Character 51.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 51 = 3 \cdot 17 \)
Weight: \( 0 \)
Character: 51.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 3.1505701599 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.670444161\) \(a_{3}=+0.577350269\) \(a_{4}=-0.550504627\) \(a_{5}=+1.406351531\)
\(a_{6}=-0.387081117\) \(a_{7}=+0.040423556\) \(a_{8}=+1.039526774\) \(a_{9}=+0.333333333\) \(a_{10}=-0.942880172\)
\(a_{11}=-0.389032865\) \(a_{12}=-0.317833995\) \(a_{13}=+0.758061240\) \(a_{14}=-0.027101737\) \(a_{15}=+0.811957435\)
\(a_{16}=-0.146440028\) \(a_{17}=+0.242535625\) \(a_{18}=-0.223481387\) \(a_{19}=+1.599200598\) \(a_{20}=-0.774203026\)
\(a_{21}=+0.023338551\) \(a_{22}=+0.260824813\) \(a_{23}=+1.395276750\) \(a_{24}=+0.600171063\) \(a_{25}=+0.977824629\)
\(a_{26}=-0.508237732\) \(a_{27}=+0.192450090\) \(a_{28}=-0.022253355\) \(a_{29}=-1.160647118\) \(a_{30}=-0.544372121\)
\(a_{31}=-1.083313426\) \(a_{32}=-0.941346912\) \(a_{33}=-0.224608229\) \(a_{34}=-0.162606594\) \(a_{35}=+0.056849730\)
\(a_{36}=-0.183501542\) \(a_{37}=+0.925869252\) \(a_{38}=-1.072174702\) \(a_{39}=+0.437666861\) \(a_{40}=+1.461940070\)
\(a_{41}=-0.636445490\) \(a_{42}=-0.015647195\) \(a_{43}=+1.561938489\) \(a_{44}=+0.214164392\) \(a_{45}=+0.468783844\)
\(a_{46}=-0.935455150\) \(a_{47}=+0.263370714\) \(a_{48}=-0.084547189\) \(a_{49}=-0.998365936\) \(a_{50}=-0.655576813\)
\(a_{51}=+0.140028008\) \(a_{52}=-0.417316221\) \(a_{53}=+0.938329665\) \(a_{54}=-0.129027039\) \(a_{55}=-0.547116965\)
\(a_{56}=+0.042021369\) \(a_{57}=+0.923298896\) \(a_{58}=+0.778149083\) \(a_{59}=-1.179200084\) \(a_{60}=-0.446986325\)
\(a_{61}=+0.004643295\) \(a_{62}=+0.726301161\) \(a_{63}=+0.013474519\) \(a_{64}=+0.777560568\) \(a_{65}=+1.066100586\)
\(a_{66}=+0.150587276\) \(a_{67}=-0.014520862\) \(a_{68}=-0.133516984\) \(a_{69}=+0.805563407\) \(a_{70}=-0.038114569\)
\(a_{71}=-0.023403470\) \(a_{72}=+0.346508925\) \(a_{73}=-0.888094518\) \(a_{74}=-0.620743633\) \(a_{75}=+0.564547313\)
\(a_{76}=-0.880367329\) \(a_{77}=-0.015726092\) \(a_{78}=-0.293431191\) \(a_{79}=-0.015552952\) \(a_{80}=-0.205946157\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.426701162\) \(a_{83}=-1.173899631\) \(a_{84}=-0.012847980\) \(a_{85}=+0.341090348\)
\(a_{86}=-1.047192539\) \(a_{87}=-0.670099926\) \(a_{88}=-0.404410079\) \(a_{89}=+1.630914802\) \(a_{90}=-0.314293391\)
\(a_{91}=+0.030643531\) \(a_{92}=-0.768106307\) \(a_{93}=-0.625451298\) \(a_{94}=-0.176575357\) \(a_{95}=+2.249038209\)
\(a_{96}=-0.543486893\) \(a_{97}=+0.478080635\) \(a_{98}=+0.669348612\) \(a_{99}=-0.129677622\) \(a_{100}=-0.538296983\)

Showing 100 of 420 available coefficients

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