Properties

Level $3$
Weight $0$
Character 3.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 26.4520989046 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.445269150\) \(a_{3}=-0.577350269\) \(a_{4}=-0.801735384\) \(a_{5}=+0.242679785\)
\(a_{6}=-0.257076264\) \(a_{7}=-1.682586364\) \(a_{8}=-0.802257183\) \(a_{9}=+0.333333333\) \(a_{10}=+0.108057822\)
\(a_{11}=-0.787759033\) \(a_{12}=+0.462882140\) \(a_{13}=-0.601580354\) \(a_{14}=-0.749203801\) \(a_{15}=-0.140111239\)
\(a_{16}=+0.444515010\) \(a_{17}=-1.246865342\) \(a_{18}=+0.148423050\) \(a_{19}=-1.178082308\) \(a_{20}=-0.194564971\)
\(a_{21}=+0.971441690\) \(a_{22}=-0.350764795\) \(a_{23}=+1.088230177\) \(a_{24}=+0.463183401\) \(a_{25}=-0.941106522\)
\(a_{26}=-0.267865173\) \(a_{27}=-0.192450090\) \(a_{28}=+1.348989025\) \(a_{29}=+0.534967418\) \(a_{30}=-0.062387212\)
\(a_{31}=-0.350004602\) \(a_{32}=+1.000186004\) \(a_{33}=+0.454812890\) \(a_{34}=-0.555190671\) \(a_{35}=-0.408329698\)
\(a_{36}=-0.267245128\) \(a_{37}=-1.334915381\) \(a_{38}=-0.524563708\) \(a_{39}=+0.347322579\) \(a_{40}=-0.194691601\)
\(a_{41}=+0.458642267\) \(a_{42}=+0.432553016\) \(a_{43}=-0.299452565\) \(a_{44}=+0.631574291\) \(a_{45}=+0.080893262\)
\(a_{46}=+0.484555326\) \(a_{47}=+1.950412880\) \(a_{48}=-0.256640861\) \(a_{49}=+1.831096874\) \(a_{50}=-0.419045701\)
\(a_{51}=+0.719878041\) \(a_{52}=+0.482308256\) \(a_{53}=+0.442664631\) \(a_{54}=-0.085692088\) \(a_{55}=-0.191173193\)
\(a_{56}=+1.349866997\) \(a_{57}=+0.680166138\) \(a_{58}=+0.238204488\) \(a_{59}=-0.395845599\) \(a_{60}=+0.112332138\)
\(a_{61}=+0.609904721\) \(a_{62}=-0.155846252\) \(a_{63}=-0.560862121\) \(a_{64}=+0.000836962\) \(a_{65}=-0.145991391\)
\(a_{66}=+0.202514149\) \(a_{67}=+0.755881181\) \(a_{68}=+0.999656064\) \(a_{69}=-0.628289986\) \(a_{70}=-0.181816617\)
\(a_{71}=+0.541532949\) \(a_{72}=-0.267419061\) \(a_{73}=-1.573510515\) \(a_{74}=-0.594396637\) \(a_{75}=+0.543348104\)
\(a_{76}=+0.944510271\) \(a_{77}=+1.325472607\) \(a_{78}=+0.154652030\) \(a_{79}=-1.443539467\) \(a_{80}=+0.107874807\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.204219252\) \(a_{83}=+0.382026006\) \(a_{84}=-0.778839177\) \(a_{85}=-0.302589014\)
\(a_{86}=-0.133336989\) \(a_{87}=-0.308863583\) \(a_{88}=+0.631985343\) \(a_{89}=+0.093517621\) \(a_{90}=+0.036019274\)
\(a_{91}=+1.012210901\) \(a_{92}=-0.872472639\) \(a_{93}=+0.202075251\) \(a_{94}=+0.868458686\) \(a_{95}=-0.285896762\)
\(a_{96}=-0.577457659\) \(a_{97}=-1.443917674\) \(a_{98}=+0.815330949\) \(a_{99}=-0.262586344\) \(a_{100}=+0.754518399\)

Showing 100 of 1228 available coefficients

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