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: \( 24.9310866374 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.346873039\) \(a_{3}=-0.577350269\) \(a_{4}=+0.814066983\) \(a_{5}=+1.136353593\)
\(a_{6}=-0.777617512\) \(a_{7}=-0.537118201\) \(a_{8}=-0.250428168\) \(a_{9}=+0.333333333\) \(a_{10}=+1.530524018\)
\(a_{11}=+0.283042804\) \(a_{12}=-0.470001792\) \(a_{13}=+1.830400051\) \(a_{14}=-0.723430023\) \(a_{15}=-0.656074053\)
\(a_{16}=-1.151361930\) \(a_{17}=-0.852342532\) \(a_{18}=+0.448957680\) \(a_{19}=+0.966493287\) \(a_{20}=+0.925067942\)
\(a_{21}=+0.310105338\) \(a_{22}=+0.381222721\) \(a_{23}=+0.804637437\) \(a_{24}=+0.144584770\) \(a_{25}=+0.291299489\)
\(a_{26}=+2.465316479\) \(a_{27}=-0.192450090\) \(a_{28}=-0.437250193\) \(a_{29}=+0.337701550\) \(a_{30}=-0.883648454\)
\(a_{31}=+1.165443539\) \(a_{32}=-1.300310174\) \(a_{33}=-0.163414839\) \(a_{34}=-1.147997177\) \(a_{35}=-0.610356198\)
\(a_{36}=+0.271355661\) \(a_{37}=+1.624212760\) \(a_{38}=+1.301743751\) \(a_{39}=-1.056781962\) \(a_{40}=-0.284574948\)
\(a_{41}=+1.259555537\) \(a_{42}=+0.417672519\) \(a_{43}=+1.816546386\) \(a_{44}=+0.230415801\) \(a_{45}=+0.378784531\)
\(a_{46}=+1.083744469\) \(a_{47}=-0.062548410\) \(a_{48}=+0.664739120\) \(a_{49}=-0.711504038\) \(a_{50}=+0.392343429\)
\(a_{51}=+0.492100190\) \(a_{52}=+1.490068247\) \(a_{53}=-0.420255253\) \(a_{54}=-0.259205837\) \(a_{55}=+0.321636707\)
\(a_{56}=+0.134509527\) \(a_{57}=-0.558005160\) \(a_{58}=+0.454841113\) \(a_{59}=+0.907165525\) \(a_{60}=-0.534088225\)
\(a_{61}=-1.704898192\) \(a_{62}=+1.569704482\) \(a_{63}=-0.179039400\) \(a_{64}=-0.599990786\) \(a_{65}=+2.079981675\)
\(a_{66}=-0.220099041\) \(a_{67}=-0.296007271\) \(a_{68}=-0.693863914\) \(a_{69}=-0.464557641\) \(a_{70}=-0.822072307\)
\(a_{71}=+0.630615106\) \(a_{72}=-0.083476056\) \(a_{73}=-0.532031723\) \(a_{74}=+2.187608376\) \(a_{75}=-0.168181839\)
\(a_{76}=+0.786790275\) \(a_{77}=-0.152027441\) \(a_{78}=-1.423351133\) \(a_{79}=-0.246977872\) \(a_{80}=-1.308354267\)
\(a_{81}=+0.111111111\) \(a_{82}=+1.696461394\) \(a_{83}=-0.608503976\) \(a_{84}=+0.252446517\) \(a_{85}=-0.968562499\)
\(a_{86}=+2.446657351\) \(a_{87}=-0.194972081\) \(a_{88}=-0.070881891\) \(a_{89}=-1.350346255\) \(a_{90}=+0.510174673\)
\(a_{91}=-0.983141182\) \(a_{92}=+0.655028770\) \(a_{93}=-0.672869141\) \(a_{94}=-0.084244766\) \(a_{95}=+1.098278120\)
\(a_{96}=+0.750734429\) \(a_{97}=-0.996946886\) \(a_{98}=-0.958305607\) \(a_{99}=+0.094347601\) \(a_{100}=+0.237137296\)

Showing 100 of 1228 available coefficients

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