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: \( 31.4014761773 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.143289345\) \(a_{3}=-0.577350269\) \(a_{4}=-0.979468164\) \(a_{5}=+1.067875021\)
\(a_{6}=-0.082728142\) \(a_{7}=-0.969333830\) \(a_{8}=-0.283636697\) \(a_{9}=+0.333333333\) \(a_{10}=+0.153015113\)
\(a_{11}=+1.419543776\) \(a_{12}=+0.565496208\) \(a_{13}=-1.946559758\) \(a_{14}=-0.138895210\) \(a_{15}=-0.616537931\)
\(a_{16}=+0.938826047\) \(a_{17}=-0.341037130\) \(a_{18}=+0.047763115\) \(a_{19}=+1.606693148\) \(a_{20}=-1.045949586\)
\(a_{21}=+0.559645148\) \(a_{22}=+0.203405498\) \(a_{23}=+1.173998092\) \(a_{24}=+0.163757723\) \(a_{25}=+0.140357061\)
\(a_{26}=-0.278921273\) \(a_{27}=-0.192450090\) \(a_{28}=+0.949431627\) \(a_{29}=+0.042111763\) \(a_{30}=-0.088343316\)
\(a_{31}=+0.232659441\) \(a_{32}=+0.418160467\) \(a_{33}=-0.819573981\) \(a_{34}=-0.048866987\) \(a_{35}=-1.035127385\)
\(a_{36}=-0.326489388\) \(a_{37}=+0.692184619\) \(a_{38}=+0.230222009\) \(a_{39}=+1.123846801\) \(a_{40}=-0.302888544\)
\(a_{41}=-0.308704882\) \(a_{42}=+0.080191187\) \(a_{43}=+0.208098633\) \(a_{44}=-1.390397936\) \(a_{45}=+0.355958340\)
\(a_{46}=+0.168221418\) \(a_{47}=-0.825314414\) \(a_{48}=-0.542031471\) \(a_{49}=-0.060391925\) \(a_{50}=+0.020111671\)
\(a_{51}=+0.196897879\) \(a_{52}=+1.906593312\) \(a_{53}=-0.258572558\) \(a_{54}=-0.027576047\) \(a_{55}=+1.515895341\)
\(a_{56}=+0.274938646\) \(a_{57}=-0.927624722\) \(a_{58}=+0.006034167\) \(a_{59}=-0.015987056\) \(a_{60}=+0.603879275\)
\(a_{61}=-0.023282701\) \(a_{62}=+0.033337619\) \(a_{63}=-0.323111277\) \(a_{64}=-0.878908107\) \(a_{65}=-2.078682544\)
\(a_{66}=-0.117436219\) \(a_{67}=-0.742776239\) \(a_{68}=+0.334035011\) \(a_{69}=-0.677808115\) \(a_{70}=-0.148322725\)
\(a_{71}=-1.825825411\) \(a_{72}=-0.094545566\) \(a_{73}=-0.114141005\) \(a_{74}=+0.099182681\) \(a_{75}=-0.081035187\)
\(a_{76}=-1.573704787\) \(a_{77}=-1.376011806\) \(a_{78}=+0.161035272\) \(a_{79}=-0.487379100\) \(a_{80}=+1.002548885\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.044234120\) \(a_{83}=-0.225451962\) \(a_{84}=-0.548154605\) \(a_{85}=-0.364185032\)
\(a_{86}=+0.029818317\) \(a_{87}=-0.024313238\) \(a_{88}=-0.402634708\) \(a_{89}=-0.932023990\) \(a_{90}=+0.051005038\)
\(a_{91}=+1.886866227\) \(a_{92}=-1.149893755\) \(a_{93}=-0.134325991\) \(a_{94}=-0.118258762\) \(a_{95}=+1.715747480\)
\(a_{96}=-0.241425058\) \(a_{97}=-1.336715284\) \(a_{98}=-0.008653519\) \(a_{99}=+0.473181259\) \(a_{100}=-0.137475273\)

Showing 100 of 1228 available coefficients

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