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: \( 26.8897729312 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.149778365\) \(a_{3}=+0.577350269\) \(a_{4}=+0.321990289\) \(a_{5}=+1.555920105\)
\(a_{6}=-0.663824849\) \(a_{7}=-0.131025716\) \(a_{8}=+0.779560897\) \(a_{9}=+0.333333333\) \(a_{10}=-1.788963275\)
\(a_{11}=-0.162727442\) \(a_{12}=+0.185901180\) \(a_{13}=-1.478015353\) \(a_{14}=+0.150650534\) \(a_{15}=+0.898310892\)
\(a_{16}=-1.218312543\) \(a_{17}=+0.091181241\) \(a_{18}=-0.383259455\) \(a_{19}=-1.596482053\) \(a_{20}=+0.500991165\)
\(a_{21}=-0.075647733\) \(a_{22}=+0.187100492\) \(a_{23}=-0.376955964\) \(a_{24}=+0.450079694\) \(a_{25}=+1.420887374\)
\(a_{26}=+1.699390076\) \(a_{27}=+0.192450090\) \(a_{28}=-0.042189008\) \(a_{29}=+1.783623195\) \(a_{30}=-1.032858428\)
\(a_{31}=-0.914975455\) \(a_{32}=+0.621228507\) \(a_{33}=-0.093950733\) \(a_{34}=-0.104838218\) \(a_{35}=-0.203865546\)
\(a_{36}=+0.107330096\) \(a_{37}=+0.652522725\) \(a_{38}=+1.835600525\) \(a_{39}=-0.853332562\) \(a_{40}=+1.212934473\)
\(a_{41}=-0.101179875\) \(a_{42}=+0.086978126\) \(a_{43}=-1.441987732\) \(a_{44}=-0.052396656\) \(a_{45}=+0.518640035\)
\(a_{46}=+0.433415812\) \(a_{47}=-1.470954530\) \(a_{48}=-0.703393075\) \(a_{49}=-0.982832262\) \(a_{50}=-1.633705562\)
\(a_{51}=+0.052643514\) \(a_{52}=-0.475906591\) \(a_{53}=-0.054709705\) \(a_{54}=-0.221274950\) \(a_{55}=-0.253190899\)
\(a_{56}=-0.102142525\) \(a_{57}=-0.921729343\) \(a_{58}=-2.050771361\) \(a_{59}=+0.558937487\) \(a_{60}=+0.289247384\)
\(a_{61}=-0.537651023\) \(a_{62}=+1.052018983\) \(a_{63}=-0.043675239\) \(a_{64}=+0.504037446\) \(a_{65}=-2.299673803\)
\(a_{66}=+0.108022520\) \(a_{67}=+0.786852482\) \(a_{68}=+0.029359474\) \(a_{69}=-0.217635627\) \(a_{70}=+0.234400194\)
\(a_{71}=-1.076419531\) \(a_{72}=+0.259853632\) \(a_{73}=+0.861236026\) \(a_{74}=-0.750256512\) \(a_{75}=+0.820349708\)
\(a_{76}=-0.514051718\) \(a_{77}=+0.021321480\) \(a_{78}=+0.981143318\) \(a_{79}=+0.203913505\) \(a_{80}=-1.895596980\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.116334431\) \(a_{83}=-0.532871122\) \(a_{84}=-0.024357835\) \(a_{85}=+0.141870726\)
\(a_{86}=+1.657966298\) \(a_{87}=+1.029775332\) \(a_{88}=-0.126855951\) \(a_{89}=-1.465670536\) \(a_{90}=-0.596321092\)
\(a_{91}=+0.193658020\) \(a_{92}=-0.121376160\) \(a_{93}=-0.528261325\) \(a_{94}=+1.691271694\) \(a_{95}=-2.483998523\)
\(a_{96}=+0.358666446\) \(a_{97}=+0.634230340\) \(a_{98}=+1.130039271\) \(a_{99}=-0.054242481\) \(a_{100}=+0.457511937\)

Showing 100 of 1228 available coefficients

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