Properties

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

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 21.6126500168 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.903799587\) \(a_{3}=-0.577350269\) \(a_{4}=+2.624452869\) \(a_{5}=+0.238602184\)
\(a_{6}=+1.099159204\) \(a_{7}=-1.315328267\) \(a_{8}=-3.092632701\) \(a_{9}=+0.333333333\) \(a_{10}=-0.454250739\)
\(a_{11}=+0.418709061\) \(a_{12}=-1.515228570\) \(a_{13}=-0.686051319\) \(a_{14}=+2.504121413\) \(a_{15}=-0.137757035\)
\(a_{16}=+3.263299991\) \(a_{17}=+0.533318171\) \(a_{18}=-0.634599862\) \(a_{19}=+0.688011039\) \(a_{20}=+0.626200186\)
\(a_{21}=+0.759405129\) \(a_{22}=-0.797138137\) \(a_{23}=+0.891490491\) \(a_{24}=+1.785532322\) \(a_{25}=-0.943068998\)
\(a_{26}=+1.306104218\) \(a_{27}=-0.192450090\) \(a_{28}=-3.452017045\) \(a_{29}=+1.268852556\) \(a_{30}=+0.262261786\)
\(a_{31}=+0.378715222\) \(a_{32}=-3.120036475\) \(a_{33}=-0.241741789\) \(a_{34}=-1.015330915\) \(a_{35}=-0.313840197\)
\(a_{36}=+0.874817623\) \(a_{37}=-0.432976603\) \(a_{38}=-1.309835132\) \(a_{39}=+0.396091914\) \(a_{40}=-0.737908916\)
\(a_{41}=+0.536626190\) \(a_{42}=-1.445755172\) \(a_{43}=+0.320461246\) \(a_{44}=+1.098882196\) \(a_{45}=+0.079534061\)
\(a_{46}=-1.697219228\) \(a_{47}=+1.623096736\) \(a_{48}=-1.884067128\) \(a_{49}=+0.730088451\) \(a_{50}=+1.795414369\)
\(a_{51}=-0.307911390\) \(a_{52}=-1.800509353\) \(a_{53}=-1.178504839\) \(a_{54}=+0.366386401\) \(a_{55}=+0.099904896\)
\(a_{56}=+4.067827212\) \(a_{57}=-0.397223359\) \(a_{58}=-2.415640973\) \(a_{59}=-0.185649580\) \(a_{60}=-0.361536846\)
\(a_{61}=+0.012349606\) \(a_{62}=-0.720997884\) \(a_{63}=-0.438442756\) \(a_{64}=+2.676624163\) \(a_{65}=-0.163693343\)
\(a_{66}=+0.460227918\) \(a_{67}=-1.670549427\) \(a_{68}=+1.399668405\) \(a_{69}=-0.514702275\) \(a_{70}=+0.597488838\)
\(a_{71}=-1.882510647\) \(a_{72}=-1.030877567\) \(a_{73}=+0.461156669\) \(a_{74}=+0.824300677\) \(a_{75}=+0.544481140\)
\(a_{76}=+1.805652545\) \(a_{77}=-0.550739864\) \(a_{78}=-0.754079622\) \(a_{79}=-1.169469599\) \(a_{80}=+0.778630504\)
\(a_{81}=+0.111111111\) \(a_{82}=-1.021628720\) \(a_{83}=-0.187513008\) \(a_{84}=+1.993022970\) \(a_{85}=+0.127250880\)
\(a_{86}=-0.610093989\) \(a_{87}=-0.732572365\) \(a_{88}=-1.294913334\) \(a_{89}=+0.565155453\) \(a_{90}=-0.151416913\)
\(a_{91}=+0.902382693\) \(a_{92}=+2.339674775\) \(a_{93}=-0.218651335\) \(a_{94}=-3.090050896\) \(a_{95}=+0.164160936\)
\(a_{96}=+1.801353899\) \(a_{97}=+1.293643579\) \(a_{98}=-1.389942092\) \(a_{99}=+0.139569687\) \(a_{100}=-2.475040137\)

Showing 100 of 1228 available coefficients

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