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: \( 10.5076073043 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.972678523\) \(a_{3}=-0.577350269\) \(a_{4}=-0.053896490\) \(a_{5}=-0.254073983\)
\(a_{6}=-0.561576207\) \(a_{7}=-1.155824568\) \(a_{8}=-1.025102481\) \(a_{9}=+0.333333331\) \(a_{10}=-0.247132297\)
\(a_{11}=-1.206388157\) \(a_{12}=+0.031117395\) \(a_{13}=+1.561090336\) \(a_{14}=-1.124239384\) \(a_{15}=+0.146657521\)
\(a_{16}=-0.943198678\) \(a_{17}=+0.872883006\) \(a_{18}=+0.324226174\) \(a_{19}=-0.379222462\) \(a_{20}=+0.013693696\)
\(a_{21}=+0.667315625\) \(a_{22}=-1.173427805\) \(a_{23}=+0.030480273\) \(a_{24}=+0.591843194\) \(a_{25}=-0.935446411\)
\(a_{26}=+1.518440250\) \(a_{27}=-0.192450090\) \(a_{28}=+0.062294887\) \(a_{29}=-0.733621187\) \(a_{30}=+0.142681904\)
\(a_{31}=-0.968893444\) \(a_{32}=+0.107673384\) \(a_{33}=+0.696508500\) \(a_{34}=+0.849034554\) \(a_{35}=+0.293664952\)
\(a_{36}=-0.017965497\) \(a_{37}=-0.852530760\) \(a_{38}=-0.368861545\) \(a_{39}=-0.901296642\) \(a_{40}=+0.260451870\)
\(a_{41}=+0.775750821\) \(a_{42}=+0.649083577\) \(a_{43}=-0.247334812\) \(a_{44}=+0.065020085\) \(a_{45}=-0.084691328\)
\(a_{46}=+0.029647507\) \(a_{47}=-0.514002935\) \(a_{48}=+0.544556015\) \(a_{49}=+0.335930430\) \(a_{50}=-0.909888637\)
\(a_{51}=-0.503959240\) \(a_{52}=-0.084137360\) \(a_{53}=+0.538057908\) \(a_{54}=-0.187192100\) \(a_{55}=+0.306511834\)
\(a_{56}=+1.184838599\) \(a_{57}=+0.218944250\) \(a_{58}=-0.713577447\) \(a_{59}=+0.114637532\) \(a_{60}=-0.007905924\)
\(a_{61}=-0.777495176\) \(a_{62}=-0.942421844\) \(a_{63}=-0.385274856\) \(a_{64}=+1.047930266\) \(a_{65}=-0.396632755\)
\(a_{66}=+0.677478859\) \(a_{67}=+0.815029247\) \(a_{68}=-0.047045330\) \(a_{69}=-0.017597795\) \(a_{70}=+0.285641590\)
\(a_{71}=+0.563744433\) \(a_{72}=-0.341700825\) \(a_{73}=-1.727656635\) \(a_{74}=-0.829238365\) \(a_{75}=+0.540080237\)
\(a_{76}=+0.020438766\) \(a_{77}=+1.394373019\) \(a_{78}=-0.876671894\) \(a_{79}=+0.083659258\) \(a_{80}=+0.239642249\)
\(a_{81}=+0.111111128\) \(a_{82}=+0.754556167\) \(a_{83}=-0.471588357\) \(a_{84}=-0.035965987\) \(a_{85}=-0.221776834\)
\(a_{86}=-0.240577219\) \(a_{87}=+0.423556367\) \(a_{88}=+1.236671363\) \(a_{89}=-0.833503797\) \(a_{90}=-0.082377303\)
\(a_{91}=-1.804347905\) \(a_{92}=-0.001642941\) \(a_{93}=+0.559390634\) \(a_{94}=-0.499959501\) \(a_{95}=+0.096351028\)
\(a_{96}=-0.062165167\) \(a_{97}=+1.796569038\) \(a_{98}=+0.326751823\) \(a_{99}=-0.402128538\) \(a_{100}=+0.050418396\)

Showing 100 of 5000 available coefficients

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