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: \( 4.99908300143 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.675629232\) \(a_{3}=-0.827534229\) \(a_{4}=+1.807733322\) \(a_{5}=-1.651490830\)
\(a_{6}=-1.386640544\) \(a_{7}=+0.024414966\) \(a_{8}=+1.353461566\) \(a_{9}=-0.315187100\) \(a_{10}=-2.767286312\)
\(a_{11}=-1.159376948\) \(a_{12}=-1.495961201\) \(a_{13}=-0.016493148\) \(a_{14}=+0.040910430\) \(a_{15}=+1.366665191\)
\(a_{16}=+0.460166443\) \(a_{17}=+0.411294858\) \(a_{18}=-0.528136718\) \(a_{19}=+1.656645008\) \(a_{20}=-2.985455006\)
\(a_{21}=-0.020204220\) \(a_{22}=-1.942685905\) \(a_{23}=-0.208514414\) \(a_{24}=-1.120035774\) \(a_{25}=+1.727421963\)
\(a_{26}=-0.027636401\) \(a_{27}=+1.088362343\) \(a_{28}=+0.044135747\) \(a_{29}=-1.748159682\) \(a_{30}=+2.290024144\)
\(a_{31}=-0.934264620\) \(a_{32}=-0.582393224\) \(a_{33}=+0.959424109\) \(a_{34}=+0.689177687\) \(a_{35}=-0.040321092\)
\(a_{36}=-0.569774223\) \(a_{37}=-0.337411575\) \(a_{38}=+2.775922803\) \(a_{39}=+0.013648644\) \(a_{40}=-2.235229366\)
\(a_{41}=-0.779583818\) \(a_{42}=-0.033854782\) \(a_{43}=+1.428108444\) \(a_{44}=-2.095844342\) \(a_{45}=+0.520528605\)
\(a_{46}=-0.349392847\) \(a_{47}=-1.464158504\) \(a_{48}=-0.380803482\) \(a_{49}=-0.999403909\) \(a_{50}=+2.894518737\)
\(a_{51}=-0.340360573\) \(a_{52}=-0.029815213\) \(a_{53}=-0.130611695\) \(a_{54}=+1.823691756\) \(a_{55}=+1.914700399\)
\(a_{56}=+0.033044718\) \(a_{57}=-1.370930450\) \(a_{58}=-2.929267466\) \(a_{59}=+0.833885814\) \(a_{60}=+2.470566207\)
\(a_{61}=-0.194629314\) \(a_{62}=-1.565481107\) \(a_{63}=-0.007695282\) \(a_{64}=-1.436041553\) \(a_{65}=+0.027238282\)
\(a_{66}=+1.607639082\) \(a_{67}=-0.631667512\) \(a_{68}=+0.743511420\) \(a_{69}=+0.172552815\) \(a_{70}=-0.067563201\)
\(a_{71}=+0.411598463\) \(a_{72}=-0.426593626\) \(a_{73}=+1.043717603\) \(a_{74}=-0.565376698\) \(a_{75}=-1.429500803\)
\(a_{76}=+2.994772385\) \(a_{77}=-0.028306149\) \(a_{78}=+0.022870067\) \(a_{79}=-1.175977934\) \(a_{80}=-0.759960660\)
\(a_{81}=-0.585469992\) \(a_{82}=-1.306293435\) \(a_{83}=-0.262285538\) \(a_{84}=-0.036523842\) \(a_{85}=-0.679249686\)
\(a_{86}=+2.392980256\) \(a_{87}=+1.446661975\) \(a_{88}=-1.569172140\) \(a_{89}=-0.004922491\) \(a_{90}=+0.872212947\)
\(a_{91}=-0.000402680\) \(a_{92}=-0.376938455\) \(a_{93}=+0.773135952\) \(a_{94}=-2.453386789\) \(a_{95}=-2.735934041\)
\(a_{96}=+0.481950328\) \(a_{97}=+0.912680231\) \(a_{98}=-1.674630405\) \(a_{99}=+0.365420658\) \(a_{100}=+3.122718245\)

Showing 100 of 546 available coefficients

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