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: \( 12.8347409661 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=+1.340750995\)
\(a_{6}=+0.408248290\) \(a_{7}=-0.037147036\) \(a_{8}=+0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=+0.948054120\)
\(a_{11}=+1.185659794\) \(a_{12}=+0.288675135\) \(a_{13}=-1.674593206\) \(a_{14}=-0.026266921\) \(a_{15}=+0.774082948\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.241376111\) \(a_{18}=+0.235702260\) \(a_{19}=+0.561516632\) \(a_{20}=+0.670375497\)
\(a_{21}=-0.021446851\) \(a_{22}=+0.838388080\) \(a_{23}=+1.719984649\) \(a_{24}=+0.204124145\) \(a_{25}=+0.797613230\)
\(a_{26}=-1.184116212\) \(a_{27}=+0.192450090\) \(a_{28}=-0.018573518\) \(a_{29}=+1.067609652\) \(a_{30}=+0.547359302\)
\(a_{31}=-0.432656070\) \(a_{32}=+0.176776695\) \(a_{33}=+0.684541001\) \(a_{34}=-0.170678685\) \(a_{35}=-0.049804926\)
\(a_{36}=+0.166666667\) \(a_{37}=-0.779789806\) \(a_{38}=+0.397052219\) \(a_{39}=-0.966826838\) \(a_{40}=+0.474027060\)
\(a_{41}=+1.240023814\) \(a_{42}=-0.015165214\) \(a_{43}=-1.734231591\) \(a_{44}=+0.592829897\) \(a_{45}=+0.446916998\)
\(a_{46}=+1.216212809\) \(a_{47}=-0.369245066\) \(a_{48}=+0.144337567\) \(a_{49}=-0.998620098\) \(a_{50}=+0.563997724\)
\(a_{51}=-0.139358562\) \(a_{52}=-0.837296603\) \(a_{53}=-1.457014834\) \(a_{54}=+0.136082763\) \(a_{55}=+1.589674548\)
\(a_{56}=-0.013133461\) \(a_{57}=+0.324191779\) \(a_{58}=+0.754914024\) \(a_{59}=-0.336816210\) \(a_{60}=+0.387041474\)
\(a_{61}=+0.286056600\) \(a_{62}=-0.305934041\) \(a_{63}=-0.012382345\) \(a_{64}=+0.125000000\) \(a_{65}=-2.245212507\)
\(a_{66}=+0.484043584\) \(a_{67}=-0.471796000\) \(a_{68}=-0.120688055\) \(a_{69}=+0.993033600\) \(a_{70}=-0.035217401\)
\(a_{71}=+0.066156000\) \(a_{72}=+0.117851130\) \(a_{73}=+0.800750017\) \(a_{74}=-0.551394659\) \(a_{75}=+0.460502213\)
\(a_{76}=+0.280758316\) \(a_{77}=-0.044043747\) \(a_{78}=-0.683649814\) \(a_{79}=+0.171600103\) \(a_{80}=+0.335187749\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.876829248\) \(a_{83}=-1.702900000\) \(a_{84}=-0.010723426\) \(a_{85}=-0.323625260\)
\(a_{86}=-1.226286918\) \(a_{87}=+0.616384720\) \(a_{88}=+0.419194040\)

Showing all 88 available coefficients

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