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: \( 3.5882850865 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.989746093\) \(a_{3}=-0.948950189\) \(a_{4}=-0.020402671\) \(a_{5}=-0.939718655\)
\(a_{6}=-0.939219742\) \(a_{7}=+0.545009731\) \(a_{8}=-1.009939557\) \(a_{9}=-0.099493539\) \(a_{10}=-0.930082868\)
\(a_{11}=+0.469358971\) \(a_{12}=+0.019361118\) \(a_{13}=+0.747491604\) \(a_{14}=+0.539421252\) \(a_{15}=+0.891746196\)
\(a_{16}=-0.979181060\) \(a_{17}=-1.300793405\) \(a_{18}=-0.098473341\) \(a_{19}=-1.192603343\) \(a_{20}=+0.019172770\)
\(a_{21}=-0.517187087\) \(a_{22}=+0.464546208\) \(a_{23}=-0.208514414\) \(a_{24}=+0.958382333\) \(a_{25}=-0.116928849\)
\(a_{26}=+0.739826894\) \(a_{27}=+1.043364602\) \(a_{28}=-0.011119654\) \(a_{29}=-0.956672041\) \(a_{30}=+0.882602313\)
\(a_{31}=+1.157347451\) \(a_{32}=+0.040798928\) \(a_{33}=-0.445398285\) \(a_{34}=-1.287455191\) \(a_{35}=-0.512155811\)
\(a_{36}=+0.002029934\) \(a_{37}=+0.297254602\) \(a_{38}=-1.180374500\) \(a_{39}=-0.709332298\) \(a_{40}=+0.949059042\)
\(a_{41}=+1.270884267\) \(a_{42}=-0.511883899\) \(a_{43}=-1.176074090\) \(a_{44}=-0.009576177\) \(a_{45}=+0.093495935\)
\(a_{46}=-0.206376327\) \(a_{47}=-0.514056453\) \(a_{48}=+0.929194052\) \(a_{49}=-0.702964393\) \(a_{50}=-0.115729871\)
\(a_{51}=+1.234388147\) \(a_{52}=-0.015250825\) \(a_{53}=+1.224544461\) \(a_{54}=+1.032666038\) \(a_{55}=-0.441065381\)
\(a_{56}=-0.550426886\) \(a_{57}=+1.131721168\) \(a_{58}=-0.946862415\) \(a_{59}=-1.886227451\) \(a_{60}=-0.018194004\)
\(a_{61}=+0.619696463\) \(a_{62}=+1.145480118\) \(a_{63}=-0.054224947\) \(a_{64}=+1.019561640\) \(a_{65}=-0.702431805\)
\(a_{66}=-0.440831212\) \(a_{67}=+0.386926239\) \(a_{68}=+0.026539659\) \(a_{69}=+0.197869793\) \(a_{70}=-0.506904214\)
\(a_{71}=-1.949141769\) \(a_{72}=+0.100482461\) \(a_{73}=-0.028149309\) \(a_{74}=+0.294206581\) \(a_{75}=+0.110959653\)
\(a_{76}=+0.024332293\) \(a_{77}=+0.255805207\) \(a_{78}=-0.702058871\) \(a_{79}=-0.512072035\) \(a_{80}=+0.920154709\)
\(a_{81}=-0.890607497\) \(a_{82}=+1.257852738\) \(a_{83}=-0.197137885\) \(a_{84}=+0.010551998\) \(a_{85}=+1.222379829\)
\(a_{86}=-1.164014736\) \(a_{87}=+0.907834114\) \(a_{88}=-0.474024192\) \(a_{89}=-0.894858130\) \(a_{90}=+0.092537236\)
\(a_{91}=+0.407390198\) \(a_{92}=+0.004254251\) \(a_{93}=-1.098265082\) \(a_{94}=-0.508785367\) \(a_{95}=+1.120711610\)
\(a_{96}=-0.038716150\) \(a_{97}=+0.336331943\) \(a_{98}=-0.695756262\) \(a_{99}=-0.046698185\) \(a_{100}=+0.002385661\)

Showing 100 of 546 available coefficients

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