Properties

Level $6$
Weight $0$
Character 6.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 6 = 2 \cdot 3 \)
Weight: \( 0 \)
Character: 6.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 3.84467228501 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=-1.190039215\)
\(a_{6}=+0.408248290\) \(a_{7}=+0.451582718\) \(a_{8}=+0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=-0.841484799\)
\(a_{11}=-1.038568825\) \(a_{12}=+0.288675135\) \(a_{13}=+1.078459868\) \(a_{14}=+0.319317202\) \(a_{15}=-0.687069461\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.134294617\) \(a_{18}=+0.235702261\) \(a_{19}=-0.409950251\) \(a_{20}=-0.595019611\)
\(a_{21}=+0.260721430\) \(a_{22}=-0.734379059\) \(a_{23}=+0.333646953\) \(a_{24}=+0.204124145\) \(a_{25}=+0.416193334\)
\(a_{26}=+0.762586286\) \(a_{27}=+0.192450090\) \(a_{28}=+0.225791359\) \(a_{29}=-0.769772408\) \(a_{30}=-0.485831475\)
\(a_{31}=-0.354272223\) \(a_{32}=+0.176776695\) \(a_{33}=-0.599617991\) \(a_{34}=+0.094960634\) \(a_{35}=-0.537401143\)
\(a_{36}=+0.166666667\) \(a_{37}=+1.684577363\) \(a_{38}=-0.289878600\) \(a_{39}=+0.622649095\) \(a_{40}=-0.420742400\)
\(a_{41}=+1.080765339\) \(a_{42}=+0.184357872\) \(a_{43}=-1.772260210\) \(a_{44}=-0.519284413\) \(a_{45}=-0.396679739\)
\(a_{46}=+0.235924023\) \(a_{47}=+0.493363606\) \(a_{48}=+0.144337568\) \(a_{49}=-0.796073049\) \(a_{50}=+0.294293128\)
\(a_{51}=+0.077535031\) \(a_{52}=+0.539229937\) \(a_{53}=-0.594724341\) \(a_{54}=+0.136082766\) \(a_{55}=+1.235937641\)
\(a_{56}=+0.159658594\) \(a_{57}=-0.236684994\) \(a_{58}=-0.544311468\) \(a_{59}=-0.082891907\) \(a_{60}=-0.343534798\)
\(a_{61}=+1.229912680\) \(a_{62}=-0.250507369\) \(a_{63}=+0.150528798\) \(a_{64}=+0.124997273\) \(a_{65}=-1.283409535\)
\(a_{66}=-0.423993947\) \(a_{67}=-1.220973426\) \(a_{68}=+0.067147308\) \(a_{69}=+0.192631158\) \(a_{70}=-0.379999992\)
\(a_{71}=+1.644668930\) \(a_{72}=+0.117851130\) \(a_{73}=+0.437738000\) \(a_{74}=+1.191176077\) \(a_{75}=+0.240289336\)
\(a_{76}=-0.204975124\) \(a_{77}=-0.468999735\) \(a_{78}=+0.440279396\) \(a_{79}=-1.004918483\) \(a_{80}=-0.297509802\)
\(a_{81}=+0.111111092\) \(a_{82}=+0.764216480\) \(a_{83}=-0.933170329\) \(a_{84}=+0.130360713\) \(a_{85}=-0.159815871\)
\(a_{86}=-1.253177185\) \(a_{87}=-0.444428260\) \(a_{88}=-0.367189365\) \(a_{89}=+1.411784943\) \(a_{90}=-0.280494889\)
\(a_{91}=+0.487013746\) \(a_{92}=+0.166823402\) \(a_{93}=-0.204539520\) \(a_{94}=+0.348861875\) \(a_{95}=+0.487855115\)
\(a_{96}=+0.102060149\) \(a_{97}=+1.063125057\) \(a_{98}=-0.562909235\) \(a_{99}=-0.346191238\) \(a_{100}=+0.208099947\)

Showing 100 of 1000 available coefficients

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