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: \( 3.82710940564 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.740719752\) \(a_{3}=+0.577350269\) \(a_{4}=-0.451334249\) \(a_{5}=+0.189094374\)
\(a_{6}=-0.427654748\) \(a_{7}=+1.047721215\) \(a_{8}=+1.075031945\) \(a_{9}=+0.333333333\) \(a_{10}=-0.140065938\)
\(a_{11}=-1.795954973\) \(a_{12}=-0.260577950\) \(a_{13}=-0.814515034\) \(a_{14}=-0.776067799\) \(a_{15}=+0.109173688\)
\(a_{16}=-0.344963148\) \(a_{17}=+0.242535625\) \(a_{18}=-0.246906584\) \(a_{19}=-1.121609217\) \(a_{20}=-0.085344767\)
\(a_{21}=+0.604902126\) \(a_{22}=+1.330299323\) \(a_{23}=-0.557603746\) \(a_{24}=+0.620669983\) \(a_{25}=-0.964243318\)
\(a_{26}=+0.603327374\) \(a_{27}=+0.192450090\) \(a_{28}=-0.472872467\) \(a_{29}=+1.783001919\) \(a_{30}=-0.080867107\)
\(a_{31}=-1.591565824\) \(a_{32}=-0.819510928\) \(a_{33}=-1.036895087\) \(a_{34}=-0.179650928\) \(a_{35}=+0.198118187\)
\(a_{36}=-0.150444750\) \(a_{37}=-0.268788068\) \(a_{38}=+0.830798101\) \(a_{39}=-0.470260474\) \(a_{40}=+0.203282493\)
\(a_{41}=-0.350317973\) \(a_{42}=-0.448062953\) \(a_{43}=-0.114968712\) \(a_{44}=+0.810575988\) \(a_{45}=+0.063031458\)
\(a_{46}=+0.413028108\) \(a_{47}=-0.272356298\) \(a_{48}=-0.199164566\) \(a_{49}=+0.097719744\) \(a_{50}=+0.714234071\)
\(a_{51}=+0.140028008\) \(a_{52}=+0.367618531\) \(a_{53}=-1.933856426\) \(a_{54}=-0.142551583\) \(a_{55}=-0.339604981\)
\(a_{56}=+1.126333776\) \(a_{57}=-0.647561383\) \(a_{58}=-1.320704740\) \(a_{59}=+1.058287587\) \(a_{60}=-0.049273824\)
\(a_{61}=-0.852480850\) \(a_{62}=+1.178904243\) \(a_{63}=+0.349240405\) \(a_{64}=+0.951991079\) \(a_{65}=-0.154020210\)
\(a_{66}=+0.768048672\) \(a_{67}=-0.071604359\) \(a_{68}=-0.109464634\) \(a_{69}=-0.321932673\) \(a_{70}=-0.146750055\)
\(a_{71}=+1.135060671\) \(a_{72}=+0.358343982\) \(a_{73}=+0.552591027\) \(a_{74}=+0.199096631\) \(a_{75}=-0.556706139\)
\(a_{76}=+0.506220653\) \(a_{77}=-1.881660127\) \(a_{78}=+0.348331222\) \(a_{79}=-1.340079162\) \(a_{80}=-0.065230590\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.259487442\) \(a_{83}=+1.182839503\) \(a_{84}=-0.273013046\) \(a_{85}=+0.045862122\)
\(a_{86}=+0.085159596\) \(a_{87}=+1.029416638\) \(a_{88}=-1.930708968\) \(a_{89}=+0.819706225\) \(a_{90}=-0.046688646\)
\(a_{91}=-0.853384681\) \(a_{92}=+0.251665667\) \(a_{93}=-0.918890957\) \(a_{94}=+0.201739689\) \(a_{95}=-0.212089993\)
\(a_{96}=-0.473144855\) \(a_{97}=-0.503633919\) \(a_{98}=-0.072382945\) \(a_{99}=-0.598651658\) \(a_{100}=+0.435196033\)

Showing 100 of 546 available coefficients

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