Properties

Level $463$
Weight $0$
Character 463.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 463 \)
Weight: \( 0 \)
Character: 463.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 0.68820929233 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.209924395\) \(a_{3}=-1.469983880\) \(a_{4}=+0.463917090\) \(a_{5}=+0.986748228\)
\(a_{6}=-1.778569381\) \(a_{7}=+1.230942999\) \(a_{8}=-0.648619831\) \(a_{9}=+1.160852636\) \(a_{10}=+1.193890752\)
\(a_{11}=+0.654090177\) \(a_{12}=-0.681950635\) \(a_{13}=-1.828604148\) \(a_{14}=+1.489347963\) \(a_{15}=-1.450503990\)
\(a_{16}=-1.248698033\) \(a_{17}=+1.270180379\) \(a_{18}=+1.404543958\) \(a_{19}=-1.817183386\) \(a_{20}=+0.457769420\)
\(a_{21}=-1.809466374\) \(a_{22}=+0.791399723\) \(a_{23}=+1.048473330\) \(a_{24}=+0.953460651\) \(a_{25}=-0.026327966\)
\(a_{26}=-2.212472805\) \(a_{27}=-0.236450803\) \(a_{28}=+0.571055528\) \(a_{29}=-0.601095357\) \(a_{30}=-1.755000216\)
\(a_{31}=-1.384783291\) \(a_{32}=-0.862210482\) \(a_{33}=-0.961502063\) \(a_{34}=+1.536822240\) \(a_{35}=+1.214630817\)
\(a_{36}=+0.538539368\) \(a_{37}=-0.338063830\) \(a_{38}=-2.198654536\) \(a_{39}=+2.688018652\) \(a_{40}=-0.640024410\)
\(a_{41}=+0.206611885\) \(a_{42}=-2.189317551\) \(a_{43}=+0.797718799\) \(a_{44}=+0.303443611\) \(a_{45}=+1.145469269\)
\(a_{46}=+1.268573470\) \(a_{47}=+1.097064875\) \(a_{48}=+1.835566023\) \(a_{49}=+0.515220696\) \(a_{50}=-0.031854893\)
\(a_{51}=-1.867144683\) \(a_{52}=-0.848320731\) \(a_{53}=-0.145108323\) \(a_{54}=-0.286087579\) \(a_{55}=+0.645422323\)
\(a_{56}=-0.798414035\) \(a_{57}=+2.671230308\) \(a_{58}=-0.727279930\) \(a_{59}=+0.705640534\) \(a_{60}=-0.672913597\)
\(a_{61}=+0.532083026\) \(a_{62}=-1.675483123\) \(a_{63}=+1.428943415\) \(a_{64}=+0.205488548\) \(a_{65}=-1.804371897\)
\(a_{66}=-1.163344801\) \(a_{67}=+1.269446874\) \(a_{68}=+0.589258403\) \(a_{69}=-1.541238895\) \(a_{70}=+1.469611446\)
\(a_{71}=+0.745074875\) \(a_{72}=-0.752951996\) \(a_{73}=-0.357187569\) \(a_{74}=-0.409031676\) \(a_{75}=+0.038701697\)
\(a_{76}=-0.843022448\) \(a_{77}=+0.805147708\) \(a_{78}=+3.252299422\) \(a_{79}=+0.276574817\) \(a_{80}=-1.232150490\)
\(a_{81}=-0.813273760\) \(a_{82}=+0.249984790\) \(a_{83}=+0.609961311\) \(a_{84}=-0.839442384\) \(a_{85}=+1.253348207\)
\(a_{86}=+0.965179439\) \(a_{87}=+0.883600509\) \(a_{88}=-0.424255822\) \(a_{89}=-1.225806783\) \(a_{90}=+1.385931251\)
\(a_{91}=-2.250907484\) \(a_{92}=+0.486404698\) \(a_{93}=+2.035609147\) \(a_{94}=+1.327365544\) \(a_{95}=-1.793102500\)
\(a_{96}=+1.267435469\) \(a_{97}=-0.339140488\) \(a_{98}=+0.623378062\) \(a_{99}=+0.759302333\) \(a_{100}=-0.012213986\)

Showing 100 of 1432 available coefficients

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