Properties

Level $1$
Weight $0$
Character 1.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 29.5463881241 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.723160555\) \(a_{3}=-0.395636926\) \(a_{4}=+1.969282300\) \(a_{5}=-1.471689036\)
\(a_{6}=-0.681745946\) \(a_{7}=-0.128354332\) \(a_{8}=+1.670229026\) \(a_{9}=-0.843471422\) \(a_{10}=-2.535956497\)
\(a_{11}=-0.344420960\) \(a_{12}=-0.779120796\) \(a_{13}=-0.933186779\) \(a_{14}=-0.221175123\) \(a_{15}=+0.582254527\)
\(a_{16}=+0.908790475\) \(a_{17}=+0.358513912\) \(a_{18}=-1.453436685\) \(a_{19}=+0.636458064\) \(a_{20}=-2.898171169\)
\(a_{21}=+0.050781714\) \(a_{22}=-0.593492613\) \(a_{23}=-1.063423583\) \(a_{24}=-0.660804278\) \(a_{25}=+1.165868619\)
\(a_{26}=-1.608030649\) \(a_{27}=+0.729345367\) \(a_{28}=-0.252765915\) \(a_{29}=-0.378238764\) \(a_{30}=+1.003318034\)
\(a_{31}=-0.871747002\) \(a_{32}=-0.104237124\) \(a_{33}=+0.136265650\) \(a_{34}=+0.617777032\) \(a_{35}=+0.188897664\)
\(a_{36}=-1.661033343\) \(a_{37}=+0.609484812\) \(a_{38}=+1.096719431\) \(a_{39}=+0.369203149\) \(a_{40}=-2.458057745\)
\(a_{41}=+1.485771714\) \(a_{42}=+0.087505046\) \(a_{43}=+0.121111525\) \(a_{44}=-0.678262100\) \(a_{45}=+1.241327645\)
\(a_{46}=-1.832449572\) \(a_{47}=+1.375480969\) \(a_{48}=-0.359551071\) \(a_{49}=-0.983525165\) \(a_{50}=+2.008978817\)
\(a_{51}=-0.141841342\) \(a_{52}=-1.837708207\) \(a_{53}=-0.144223390\) \(a_{54}=+1.256779167\) \(a_{55}=+0.506880552\)
\(a_{56}=-0.214381131\) \(a_{57}=-0.251806317\) \(a_{58}=-0.651766108\) \(a_{59}=-0.831415280\) \(a_{60}=+1.146623517\)
\(a_{61}=+1.585315764\) \(a_{62}=-1.502160048\) \(a_{63}=+0.108263211\) \(a_{64}=-1.088407777\) \(a_{65}=+1.373360752\)
\(a_{66}=+0.234807593\) \(a_{67}=-1.523394860\) \(a_{68}=+0.706015101\) \(a_{69}=+0.420729638\) \(a_{70}=+0.325501003\)
\(a_{71}=+0.444148113\) \(a_{72}=-1.408790453\) \(a_{73}=-0.733919824\) \(a_{74}=+1.050240187\) \(a_{75}=-0.461260677\)
\(a_{76}=+1.253365600\) \(a_{77}=+0.044207922\) \(a_{78}=+0.636196303\) \(a_{79}=-1.779823471\) \(a_{80}=-1.337456980\)
\(a_{81}=+0.554915463\) \(a_{82}=+2.560223211\) \(a_{83}=-1.044068673\) \(a_{84}=+0.100003530\) \(a_{85}=-0.527620994\)
\(a_{86}=+0.208694603\) \(a_{87}=+0.149645222\) \(a_{88}=-0.575261884\) \(a_{89}=-1.006889132\) \(a_{90}=+2.139006833\)
\(a_{91}=+0.119778566\) \(a_{92}=-2.094181238\) \(a_{93}=+0.344895305\) \(a_{94}=+2.370174549\) \(a_{95}=-0.936668356\)
\(a_{96}=+0.041240060\) \(a_{97}=-0.813934412\) \(a_{98}=-1.694771779\) \(a_{99}=+0.290509245\) \(a_{100}=+2.295924444\)

Showing 100 of 5000 available coefficients

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