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: \( 31.8222975293 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.761737526\) \(a_{3}=+0.577350269\) \(a_{4}=+2.103719111\) \(a_{5}=+0.571837405\)
\(a_{6}=-1.017139635\) \(a_{7}=+0.420334994\) \(a_{8}=-1.944463376\) \(a_{9}=+0.333333333\) \(a_{10}=-1.007427415\)
\(a_{11}=-0.937794332\) \(a_{12}=+1.214582795\) \(a_{13}=-1.639576928\) \(a_{14}=-0.740519932\) \(a_{15}=+0.330150480\)
\(a_{16}=+1.321914986\) \(a_{17}=+1.672834224\) \(a_{18}=-0.587245842\) \(a_{19}=+1.547733007\) \(a_{20}=+1.202985277\)
\(a_{21}=+0.242680522\) \(a_{22}=+1.652147467\) \(a_{23}=-0.686739051\) \(a_{24}=-1.122636453\) \(a_{25}=-0.673001982\)
\(a_{26}=+2.888504201\) \(a_{27}=+0.192450090\) \(a_{28}=+0.884266760\) \(a_{29}=+1.091371315\) \(a_{30}=-0.581638489\)
\(a_{31}=-0.403879822\) \(a_{32}=-0.384403862\) \(a_{33}=-0.541435810\) \(a_{34}=-2.947094827\) \(a_{35}=+0.240363272\)
\(a_{36}=+0.701239704\) \(a_{37}=-0.467135196\) \(a_{38}=-2.726699320\) \(a_{39}=-0.946610181\) \(a_{40}=-1.111916891\)
\(a_{41}=+0.025486844\) \(a_{42}=-0.427539382\) \(a_{43}=+0.861654552\) \(a_{44}=-1.972855859\) \(a_{45}=+0.190612468\)
\(a_{46}=+1.209853956\) \(a_{47}=+0.125187800\) \(a_{48}=+0.763207973\) \(a_{49}=-0.823318493\) \(a_{50}=+1.185652847\)
\(a_{51}=+0.965811290\) \(a_{52}=-3.449209317\) \(a_{53}=+1.189034049\) \(a_{54}=-0.339046545\) \(a_{55}=-0.536265878\)
\(a_{56}=-0.817326001\) \(a_{57}=+0.893584068\) \(a_{58}=-1.922709801\) \(a_{59}=-0.391536452\) \(a_{60}=+0.694543874\)
\(a_{61}=+0.383698138\) \(a_{62}=+0.711530239\) \(a_{63}=+0.140111665\) \(a_{64}=-0.644696278\) \(a_{65}=-0.937571416\)
\(a_{66}=+0.953867785\) \(a_{67}=+1.153287448\) \(a_{68}=+3.519173326\) \(a_{69}=-0.396488976\) \(a_{70}=-0.423456996\)
\(a_{71}=+1.028966690\) \(a_{72}=-0.648154459\) \(a_{73}=+0.077279275\) \(a_{74}=+0.822969605\) \(a_{75}=-0.388557876\)
\(a_{76}=+3.255995506\) \(a_{77}=-0.394187775\) \(a_{78}=+1.667678678\) \(a_{79}=-1.384625640\) \(a_{80}=+0.755920435\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.044901129\) \(a_{83}=-0.726034751\) \(a_{84}=+0.510531652\) \(a_{85}=+0.956589182\)
\(a_{86}=-1.518009159\) \(a_{87}=+0.630103523\) \(a_{88}=+1.823506733\) \(a_{89}=+1.242717878\) \(a_{90}=-0.335809138\)
\(a_{91}=-0.689171558\) \(a_{92}=-1.444706065\) \(a_{93}=-0.233180124\) \(a_{94}=-0.220548044\) \(a_{95}=+0.885051627\)
\(a_{96}=-0.221935673\) \(a_{97}=+0.633559595\) \(a_{98}=+1.450471085\) \(a_{99}=-0.312598111\) \(a_{100}=-1.415807131\)

Showing 100 of 1228 available coefficients

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