Properties

Level $23$
Weight $0$
Character 23.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 23 \)
Weight: \( 0 \)
Character: 23.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 2.49362378677 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.668074813\) \(a_{3}=-0.143445932\) \(a_{4}=-0.553676044\) \(a_{5}=-1.152212309\)
\(a_{6}=+0.095832615\) \(a_{7}=+1.201324089\) \(a_{8}=+1.037971833\) \(a_{9}=-0.979423264\) \(a_{10}=+0.769764024\)
\(a_{11}=-1.323457499\) \(a_{12}=+0.079422576\) \(a_{13}=+0.154736124\) \(a_{14}=-0.802574367\) \(a_{15}=+0.165280169\)
\(a_{16}=-0.139766795\) \(a_{17}=-1.076977983\) \(a_{18}=+0.654328015\) \(a_{19}=+0.124615291\) \(a_{20}=+0.637952353\)
\(a_{21}=-0.172325054\) \(a_{22}=+0.884168621\) \(a_{23}=-0.208514414\) \(a_{24}=-0.148892837\) \(a_{25}=+0.327593206\)
\(a_{26}=-0.103375307\) \(a_{27}=+0.283940216\) \(a_{28}=-0.665144369\) \(a_{29}=+1.378333107\) \(a_{30}=-0.110419518\)
\(a_{31}=-0.676118155\) \(a_{32}=-0.944597158\) \(a_{33}=+0.189844595\) \(a_{34}=+0.719501865\) \(a_{35}=-1.384180403\)
\(a_{36}=+0.542283198\) \(a_{37}=+1.239923515\) \(a_{38}=-0.083252337\) \(a_{39}=-0.022196268\) \(a_{40}=-1.195963923\)
\(a_{41}=-1.859338208\) \(a_{42}=+0.115126028\) \(a_{43}=-0.226942204\) \(a_{44}=+0.732766712\) \(a_{45}=+1.128503541\)
\(a_{46}=+0.139303228\) \(a_{47}=-0.279054776\) \(a_{48}=+0.020048978\) \(a_{49}=+0.443179567\) \(a_{50}=-0.218856770\)
\(a_{51}=+0.154488111\) \(a_{52}=-0.085673685\) \(a_{53}=-0.571090755\) \(a_{54}=-0.189693307\) \(a_{55}=+1.524904021\)
\(a_{56}=+1.246940567\) \(a_{57}=-0.017875557\) \(a_{58}=-0.920829633\) \(a_{59}=+1.082474182\) \(a_{60}=-0.091511670\)
\(a_{61}=-0.196907588\) \(a_{62}=+0.451697510\) \(a_{63}=-1.176604761\) \(a_{64}=+0.770828364\) \(a_{65}=-0.178288866\)
\(a_{66}=-0.126830392\) \(a_{67}=-1.437121858\) \(a_{68}=+0.596296909\) \(a_{69}=+0.029910545\) \(a_{70}=+0.924736064\)
\(a_{71}=-1.619512024\) \(a_{72}=-1.016613761\) \(a_{73}=-0.262011254\) \(a_{74}=-0.828361671\) \(a_{75}=-0.046991913\)
\(a_{76}=-0.068996501\) \(a_{77}=-1.589901374\) \(a_{78}=+0.014828767\) \(a_{79}=+0.898977340\) \(a_{80}=+0.161041021\)
\(a_{81}=+0.938693195\) \(a_{82}=+1.242177026\) \(a_{83}=+1.091739335\) \(a_{84}=+0.095412254\) \(a_{85}=+1.240907289\)
\(a_{86}=+0.151614370\) \(a_{87}=-0.197716278\) \(a_{88}=-1.373711606\) \(a_{89}=+0.179586563\) \(a_{90}=-0.753924793\)
\(a_{91}=+0.185888233\) \(a_{92}=+0.115449436\) \(a_{93}=+0.096986399\) \(a_{94}=+0.186429467\) \(a_{95}=-0.143583272\)
\(a_{96}=+0.135498620\) \(a_{97}=+0.641407002\) \(a_{98}=-0.296077107\) \(a_{99}=+1.296225064\) \(a_{100}=-0.181380510\)

Showing 100 of 546 available coefficients

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