Properties

Level $67$
Weight $0$
Character 67.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 67 \)
Weight: \( 0 \)
Character: 67.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 1.82731794986 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.743256020\) \(a_{3}=-0.381504749\) \(a_{4}=+2.038941553\) \(a_{5}=+1.103983405\)
\(a_{6}=-0.665060450\) \(a_{7}=-0.875338441\) \(a_{8}=+1.811141117\) \(a_{9}=-0.854454127\) \(a_{10}=+1.924525718\)
\(a_{11}=+1.106065488\) \(a_{12}=-0.777865885\) \(a_{13}=-1.031545596\) \(a_{14}=-1.525939007\) \(a_{15}=-0.421174912\)
\(a_{16}=+1.118341104\) \(a_{17}=-0.261611330\) \(a_{18}=-1.489532301\) \(a_{19}=-1.230200980\) \(a_{20}=+2.250957639\)
\(a_{21}=+0.333945772\) \(a_{22}=+1.928155321\) \(a_{23}=+1.375094530\) \(a_{24}=-0.690958937\) \(a_{25}=+0.218779359\)
\(a_{26}=-1.798248070\) \(a_{27}=+0.707483056\) \(a_{28}=-1.784763920\) \(a_{29}=+1.240314174\) \(a_{30}=-0.734215701\)
\(a_{31}=+1.249630650\) \(a_{32}=+0.138413745\) \(a_{33}=-0.421969236\) \(a_{34}=-0.456055526\) \(a_{35}=-0.966359113\)
\(a_{36}=-1.742182024\) \(a_{37}=+0.375729297\) \(a_{38}=-2.144555264\) \(a_{39}=+0.393539543\) \(a_{40}=+1.999469738\)
\(a_{41}=-0.828923594\) \(a_{42}=+0.582152977\) \(a_{43}=+1.065603481\) \(a_{44}=+2.255202884\) \(a_{45}=-0.943303176\)
\(a_{46}=+2.397141818\) \(a_{47}=+1.231552258\) \(a_{48}=-0.426652442\) \(a_{49}=-0.233782614\) \(a_{50}=+0.381388435\)
\(a_{51}=+0.099805965\) \(a_{52}=-2.103261179\) \(a_{53}=-0.436933139\) \(a_{54}=+1.233324096\) \(a_{55}=+1.221077944\)
\(a_{56}=-1.585361441\) \(a_{57}=+0.469327516\) \(a_{58}=+2.162185151\) \(a_{59}=-1.485418878\) \(a_{60}=-0.858751029\)
\(a_{61}=-1.682086979\) \(a_{62}=+2.178426154\) \(a_{63}=+0.747936543\) \(a_{64}=-0.877050510\) \(a_{65}=-1.138809219\)
\(a_{66}=-0.735600412\) \(a_{67}=+0.122169444\) \(a_{68}=-0.533410211\) \(a_{69}=-0.524605093\) \(a_{70}=-1.684611341\)
\(a_{71}=+1.549439355\) \(a_{72}=-1.547537002\) \(a_{73}=-0.336617856\) \(a_{74}=+0.654992359\) \(a_{75}=-0.083465364\)
\(a_{76}=-2.508307896\) \(a_{77}=-0.968181640\) \(a_{78}=+0.686040178\) \(a_{79}=-0.953822639\) \(a_{80}=+1.234630020\)
\(a_{81}=+0.584545981\) \(a_{82}=-1.445026046\) \(a_{83}=-0.826411936\) \(a_{84}=+0.680895911\) \(a_{85}=-0.288814567\)
\(a_{86}=+1.857619684\) \(a_{87}=-0.473185747\) \(a_{88}=+2.003240684\) \(a_{89}=+1.714695072\) \(a_{90}=-1.644418941\)
\(a_{91}=+0.902951513\) \(a_{92}=+2.803737376\) \(a_{93}=-0.476740027\) \(a_{94}=+2.146910889\) \(a_{95}=-1.358121467\)
\(a_{96}=-0.052805501\) \(a_{97}=+0.581950617\) \(a_{98}=-0.407542950\) \(a_{99}=-0.945082221\) \(a_{100}=+0.446078326\)

Showing 100 of 546 available coefficients

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