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: \( 6.30636358623 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=+0.971929539\)
\(a_{6}=+0.408248290\) \(a_{7}=+0.448713332\) \(a_{8}=-0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=-0.687257968\)
\(a_{11}=+1.972156578\) \(a_{12}=-0.288675135\) \(a_{13}=-0.838006855\) \(a_{14}=-0.317288240\) \(a_{15}=-0.561143781\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.255315271\) \(a_{18}=-0.235702260\) \(a_{19}=+0.095769257\) \(a_{20}=+0.485964770\)
\(a_{21}=-0.259064763\) \(a_{22}=-1.394525290\) \(a_{23}=+0.132180232\) \(a_{24}=+0.204124145\) \(a_{25}=-0.055352970\)
\(a_{26}=+0.592560330\) \(a_{27}=-0.192450090\) \(a_{28}=+0.224356666\) \(a_{29}=-0.465918495\) \(a_{30}=+0.396788573\)
\(a_{31}=+1.327624348\) \(a_{32}=-0.176776695\) \(a_{33}=-1.138625131\) \(a_{34}=-0.887641941\) \(a_{35}=+0.436117742\)
\(a_{36}=+0.166666667\) \(a_{37}=-0.313236420\) \(a_{38}=-0.067719091\) \(a_{39}=+0.483823483\) \(a_{40}=-0.343628984\)
\(a_{41}=-0.183355666\) \(a_{42}=+0.183186451\) \(a_{43}=+0.594894574\) \(a_{44}=+0.986078289\) \(a_{45}=+0.323976513\)
\(a_{46}=-0.093465538\) \(a_{47}=-0.711461421\) \(a_{48}=-0.144337567\) \(a_{49}=-0.798656346\) \(a_{50}=+0.039140461\)
\(a_{51}=-0.724756610\) \(a_{52}=-0.419003427\) \(a_{53}=-0.409902100\) \(a_{54}=+0.136082763\) \(a_{55}=+1.916797235\)
\(a_{56}=-0.158644120\) \(a_{57}=-0.055292406\) \(a_{58}=+0.329454128\) \(a_{59}=+1.376839000\) \(a_{60}=-0.280571891\)
\(a_{61}=-0.463597660\) \(a_{62}=-0.938772180\) \(a_{63}=+0.149571111\) \(a_{64}=+0.125000000\) \(a_{65}=-0.814483616\)
\(a_{66}=+0.805129552\) \(a_{67}=-1.119600000\) \(a_{68}=+0.627657636\) \(a_{69}=-0.076314292\) \(a_{70}=-0.308381813\)
\(a_{71}=+0.172560000\) \(a_{72}=-0.117851130\) \(a_{73}=-0.354430001\) \(a_{74}=+0.221491597\) \(a_{75}=+0.031958052\)
\(a_{76}=+0.047884629\) \(a_{77}=+0.884932949\) \(a_{78}=-0.342114866\) \(a_{79}=+0.719970703\) \(a_{80}=+0.242982385\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.129652035\) \(a_{83}=-1.130000000\) \(a_{84}=-0.129532381\) \(a_{85}=+1.220077993\)
\(a_{86}=-0.420653987\) \(a_{87}=+0.268998169\) \(a_{88}=-0.697262645\)

Showing all 88 available coefficients

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