Properties

Level $3$
Weight $0$
Character 3.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 29.4188261584 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.352558246\) \(a_{3}=+0.577350269\) \(a_{4}=-0.875702683\) \(a_{5}=+1.573719168\)
\(a_{6}=+0.203549599\) \(a_{7}=+0.607113276\) \(a_{8}=-0.661294449\) \(a_{9}=+0.333333333\) \(a_{10}=+0.554827670\)
\(a_{11}=-1.611803103\) \(a_{12}=-0.505587180\) \(a_{13}=-1.651885222\) \(a_{14}=+0.214042792\) \(a_{15}=+0.908587185\)
\(a_{16}=+0.642557872\) \(a_{17}=-0.187423507\) \(a_{18}=+0.117519415\) \(a_{19}=+0.374779454\) \(a_{20}=-1.378110098\)
\(a_{21}=+0.350517013\) \(a_{22}=-0.568254476\) \(a_{23}=-0.129523275\) \(a_{24}=-0.381798528\) \(a_{25}=+1.476592021\)
\(a_{26}=-0.582385757\) \(a_{27}=+0.192450090\) \(a_{28}=-0.531650724\) \(a_{29}=-1.755517979\) \(a_{30}=+0.320329905\)
\(a_{31}=+0.141274195\) \(a_{32}=+0.887833525\) \(a_{33}=-0.930574955\) \(a_{34}=-0.066077703\) \(a_{35}=+0.955425800\)
\(a_{36}=-0.291900894\) \(a_{37}=-0.544807335\) \(a_{38}=+0.132131587\) \(a_{39}=-0.953716378\) \(a_{40}=-1.040691750\)
\(a_{41}=+0.457246587\) \(a_{42}=+0.123577664\) \(a_{43}=-0.702637383\) \(a_{44}=+1.411460301\) \(a_{45}=+0.524573056\)
\(a_{46}=-0.045664499\) \(a_{47}=+0.815612643\) \(a_{48}=+0.370980960\) \(a_{49}=-0.631413470\) \(a_{50}=+0.520584694\)
\(a_{51}=-0.108209012\) \(a_{52}=+1.446560321\) \(a_{53}=-0.700352384\) \(a_{54}=+0.067849866\) \(a_{55}=-2.536525439\)
\(a_{56}=-0.401480639\) \(a_{57}=+0.216379019\) \(a_{58}=-0.618922341\) \(a_{59}=-0.345120858\) \(a_{60}=-0.795652236\)
\(a_{61}=-1.087027257\) \(a_{62}=+0.049807382\) \(a_{63}=+0.202371092\) \(a_{64}=-0.329544841\) \(a_{65}=-2.599603437\)
\(a_{66}=-0.328081874\) \(a_{67}=-0.133362053\) \(a_{68}=+0.164127268\) \(a_{69}=-0.074780298\) \(a_{70}=+0.336843245\)
\(a_{71}=+0.057920555\) \(a_{72}=-0.220431483\) \(a_{73}=-1.408990877\) \(a_{74}=-0.192076319\) \(a_{75}=+0.852510801\)
\(a_{76}=-0.328195373\) \(a_{77}=-0.978547062\) \(a_{78}=-0.336240574\) \(a_{79}=+0.178810197\) \(a_{80}=+1.011205639\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.161206055\) \(a_{83}=-0.078779528\) \(a_{84}=-0.306948689\) \(a_{85}=-0.294951965\)
\(a_{86}=-0.247720604\) \(a_{87}=-1.013548778\) \(a_{88}=+1.065876444\) \(a_{89}=+0.272629948\) \(a_{90}=+0.184942557\)
\(a_{91}=-1.002881448\) \(a_{92}=+0.113423880\) \(a_{93}=+0.081564694\) \(a_{94}=+0.287550963\) \(a_{95}=+0.589797610\)
\(a_{96}=+0.512590925\) \(a_{97}=+0.018443226\) \(a_{98}=-0.222610026\) \(a_{99}=-0.537267701\) \(a_{100}=-1.293055594\)

Showing 100 of 1228 available coefficients

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