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: \( 6.12057553309 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.671615596\) \(a_{3}=-0.577350269\) \(a_{4}=-0.548932491\) \(a_{5}=+0.325698715\)
\(a_{6}=+0.387757448\) \(a_{7}=-1.455716951\) \(a_{8}=+1.040287311\) \(a_{9}=+0.333332796\) \(a_{10}=-0.218741204\)
\(a_{11}=-0.685976506\) \(a_{12}=+0.317030100\) \(a_{13}=-0.333087355\) \(a_{14}=+0.977682198\) \(a_{15}=-0.188042241\)
\(a_{16}=-0.149740630\) \(a_{17}=-0.332036478\) \(a_{18}=-0.223871865\) \(a_{19}=+0.061836908\) \(a_{20}=-0.178786607\)
\(a_{21}=+0.840458565\) \(a_{22}=+0.460700302\) \(a_{23}=-0.154648770\) \(a_{24}=-0.600610106\) \(a_{25}=-0.893920347\)
\(a_{26}=+0.223706663\) \(a_{27}=-0.192450090\) \(a_{28}=+0.799090323\) \(a_{29}=+0.916654593\) \(a_{30}=+0.126292102\)
\(a_{31}=-0.676538286\) \(a_{32}=-0.939719076\) \(a_{33}=+0.396038217\) \(a_{34}=+0.223000877\) \(a_{35}=-0.474125135\)
\(a_{36}=-0.182977497\) \(a_{37}=+0.517000275\) \(a_{38}=-0.041530632\) \(a_{39}=+0.192308075\) \(a_{40}=+0.338820210\)
\(a_{41}=+1.003087522\) \(a_{42}=-0.564465080\) \(a_{43}=-1.575433008\) \(a_{44}=+0.376544807\) \(a_{45}=+0.108566235\)
\(a_{46}=+0.103864526\) \(a_{47}=-0.956108002\) \(a_{48}=+0.086452802\) \(a_{49}=+1.119111795\) \(a_{50}=+0.600370834\)
\(a_{51}=+0.191701353\) \(a_{52}=+0.182842467\) \(a_{53}=-0.577581529\) \(a_{54}=+0.129252418\) \(a_{55}=-0.223415742\)
\(a_{56}=-1.514363717\) \(a_{57}=-0.035701568\) \(a_{58}=-0.615639520\) \(a_{59}=+1.906738317\) \(a_{60}=+0.103222495\)
\(a_{61}=-0.168195259\) \(a_{62}=+0.454373665\) \(a_{63}=-0.485238977\) \(a_{64}=+0.780870618\) \(a_{65}=-0.108486126\)
\(a_{66}=-0.265985444\) \(a_{67}=-0.674443210\) \(a_{68}=+0.182265614\) \(a_{69}=+0.089286505\) \(a_{70}=+0.318429828\)
\(a_{71}=-1.235161027\) \(a_{72}=+0.346762418\) \(a_{73}=-0.075863754\) \(a_{74}=-0.347225466\) \(a_{75}=+0.516105139\)
\(a_{76}=-0.033944267\) \(a_{77}=+0.998561167\) \(a_{78}=-0.129157118\) \(a_{79}=+0.956007497\) \(a_{80}=-0.048770326\)
\(a_{81}=+0.111111210\) \(a_{82}=-0.673689175\) \(a_{83}=-1.359575291\) \(a_{84}=-0.461355167\) \(a_{85}=-0.108143682\)
\(a_{86}=+1.058085680\) \(a_{87}=-0.529230867\) \(a_{88}=-0.713594231\) \(a_{89}=+1.016832568\) \(a_{90}=-0.072913920\)
\(a_{91}=+0.484881430\) \(a_{92}=+0.084890696\) \(a_{93}=+0.390598018\) \(a_{94}=+0.642138186\) \(a_{95}=+0.020143115\)
\(a_{96}=+0.542547035\) \(a_{97}=-1.268672096\) \(a_{98}=-0.751612936\) \(a_{99}=-0.228652766\) \(a_{100}=+0.490701911\)

Showing 100 of 5000 available coefficients

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