Properties

Level $93$
Weight $0$
Character 93.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 93 = 3 \cdot 31 \)
Weight: \( 0 \)
Character: 93.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 1.68439149142 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.548715689\) \(a_{3}=+0.577350269\) \(a_{4}=-0.698911093\) \(a_{5}=+0.865561936\)
\(a_{6}=-0.316801150\) \(a_{7}=+0.905923242\) \(a_{8}=+0.932219170\) \(a_{9}=+0.333333333\) \(a_{10}=-0.474947414\)
\(a_{11}=+0.967761576\) \(a_{12}=-0.403516508\) \(a_{13}=+0.192163651\) \(a_{14}=-0.497094295\) \(a_{15}=+0.499732417\)
\(a_{16}=+0.187387809\) \(a_{17}=+0.835824651\) \(a_{18}=-0.182905230\) \(a_{19}=+0.123782010\) \(a_{20}=-0.604950839\)
\(a_{21}=+0.523035028\) \(a_{22}=-0.531025960\) \(a_{23}=-1.320906594\) \(a_{24}=+0.538216989\) \(a_{25}=-0.250802535\)
\(a_{26}=-0.105443210\) \(a_{27}=+0.192450090\) \(a_{28}=-0.633159803\) \(a_{29}=-0.341254265\) \(a_{30}=-0.274211017\)
\(a_{31}=-0.179605302\) \(a_{32}=-1.035041801\) \(a_{33}=+0.558737406\) \(a_{34}=-0.458630099\) \(a_{35}=+0.784132675\)
\(a_{36}=-0.232970364\) \(a_{37}=-0.721661708\) \(a_{38}=-0.067921131\) \(a_{39}=+0.110945736\) \(a_{40}=+0.806893430\)
\(a_{41}=+1.919315171\) \(a_{42}=-0.286997525\) \(a_{43}=-1.039105338\) \(a_{44}=-0.676379301\) \(a_{45}=+0.288520645\)
\(a_{46}=+0.724802171\) \(a_{47}=+0.978517703\) \(a_{48}=+0.108188402\) \(a_{49}=-0.179303080\) \(a_{50}=+0.137619286\)
\(a_{51}=+0.482563587\) \(a_{52}=-0.134305307\) \(a_{53}=+0.733737280\) \(a_{54}=-0.105600383\) \(a_{55}=+0.837657583\)
\(a_{56}=+0.844519013\) \(a_{57}=+0.071465577\) \(a_{58}=+0.187251569\) \(a_{59}=-0.813965336\) \(a_{60}=-0.349268530\)
\(a_{61}=+1.813724808\) \(a_{62}=+0.098552247\) \(a_{63}=+0.301974414\) \(a_{64}=+0.380555865\) \(a_{65}=+0.166329542\)
\(a_{66}=-0.306587981\) \(a_{67}=-0.772546116\) \(a_{68}=-0.584167121\) \(a_{69}=-0.762625778\) \(a_{70}=-0.430265901\)
\(a_{71}=-1.873604085\) \(a_{72}=+0.310739723\) \(a_{73}=-1.307023523\) \(a_{74}=+0.395987101\) \(a_{75}=-0.144800911\)
\(a_{76}=-0.086512620\) \(a_{77}=+0.876717704\) \(a_{78}=-0.060877666\) \(a_{79}=-1.238219929\) \(a_{80}=+0.162195755\)
\(a_{81}=+0.111111111\) \(a_{82}=-1.053158346\) \(a_{83}=-0.084015392\) \(a_{84}=-0.365554983\) \(a_{85}=+0.723458003\)
\(a_{86}=+0.570173401\) \(a_{87}=-0.197023242\) \(a_{88}=+0.902165894\) \(a_{89}=+0.487475332\) \(a_{90}=-0.158315805\)
\(a_{91}=+0.174085518\) \(a_{92}=+0.923196272\) \(a_{93}=-0.103695169\) \(a_{94}=-0.536928015\) \(a_{95}=+0.107140996\)
\(a_{96}=-0.597581662\) \(a_{97}=-0.508525705\) \(a_{98}=+0.098386413\) \(a_{99}=+0.322587192\) \(a_{100}=+0.175288674\)

Showing 100 of 786 available coefficients

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