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: \( 20.8054689922 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.914159472\) \(a_{3}=+0.577350269\) \(a_{4}=+2.664006485\) \(a_{5}=+0.414542355\)
\(a_{6}=+1.105140486\) \(a_{7}=+0.539593973\) \(a_{8}=+3.185173774\) \(a_{9}=+0.333333333\) \(a_{10}=+0.793500175\)
\(a_{11}=-1.584340991\) \(a_{12}=+1.538064861\) \(a_{13}=+0.313528674\) \(a_{14}=+1.032868914\) \(a_{15}=+0.239336140\)
\(a_{16}=+3.432924065\) \(a_{17}=+0.142946521\) \(a_{18}=+0.638053157\) \(a_{19}=-0.564543745\) \(a_{20}=+1.104343521\)
\(a_{21}=+0.311534726\) \(a_{22}=-3.032681314\) \(a_{23}=+0.309555144\) \(a_{24}=+1.838960936\) \(a_{25}=-0.828154636\)
\(a_{26}=+0.600143881\) \(a_{27}=+0.192450090\) \(a_{28}=+1.437481843\) \(a_{29}=+0.637523820\) \(a_{30}=+0.458127540\)
\(a_{31}=-0.867820845\) \(a_{32}=+3.385990343\) \(a_{33}=-0.914719697\) \(a_{34}=+0.273622438\) \(a_{35}=+0.223684556\)
\(a_{36}=+0.888002162\) \(a_{37}=+0.054120475\) \(a_{38}=-1.080626758\) \(a_{39}=+0.181015864\) \(a_{40}=+1.320389437\)
\(a_{41}=+0.096709602\) \(a_{42}=+0.596327146\) \(a_{43}=+1.458222352\) \(a_{44}=-4.220694673\) \(a_{45}=+0.138180785\)
\(a_{46}=+0.592537911\) \(a_{47}=+1.235504942\) \(a_{48}=+1.981999633\) \(a_{49}=-0.708838344\) \(a_{50}=-1.585220041\)
\(a_{51}=+0.082530213\) \(a_{52}=+0.835242421\) \(a_{53}=-1.556265170\) \(a_{54}=+0.368380162\) \(a_{55}=-0.656776445\)
\(a_{56}=+1.718700571\) \(a_{57}=-0.325939483\) \(a_{58}=+1.220322258\) \(a_{59}=-1.119025947\) \(a_{60}=+0.637593029\)
\(a_{61}=-0.932805024\) \(a_{62}=-1.661147491\) \(a_{63}=+0.179864658\) \(a_{64}=+3.048401421\) \(a_{65}=+0.129970915\)
\(a_{66}=-1.750919373\) \(a_{67}=-0.970980728\) \(a_{68}=+0.380810460\) \(a_{69}=+0.178721746\) \(a_{70}=+0.428167912\)
\(a_{71}=-0.005940333\) \(a_{72}=+1.061724591\) \(a_{73}=+0.170716343\) \(a_{74}=+0.103595220\) \(a_{75}=-0.478135302\)
\(a_{76}=-1.503948198\) \(a_{77}=-0.854900850\) \(a_{78}=+0.346493231\) \(a_{79}=+0.164208934\) \(a_{80}=+1.423092426\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.185117601\) \(a_{83}=-1.304620769\) \(a_{84}=+0.829930529\) \(a_{85}=+0.059257388\)
\(a_{86}=+2.791270127\) \(a_{87}=+0.368074549\) \(a_{88}=-5.046401373\) \(a_{89}=-0.415814797\) \(a_{90}=+0.264500058\)
\(a_{91}=+0.169178183\) \(a_{92}=+0.824656910\) \(a_{93}=-0.501036599\) \(a_{94}=+2.364953488\) \(a_{95}=-0.234027294\)
\(a_{96}=+1.954902436\) \(a_{97}=-0.864565680\) \(a_{98}=-1.356829631\) \(a_{99}=-0.528113664\) \(a_{100}=-2.206209321\)

Showing 100 of 1228 available coefficients

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