Properties

Level $6$
Weight $0$
Character 6.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 6 = 2 \cdot 3 \)
Weight: \( 0 \)
Character: 6.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 17.0365482074 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=-0.427554787\)
\(a_{6}=-0.408248290\) \(a_{7}=-1.843337787\) \(a_{8}=+0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=-0.302326889\)
\(a_{11}=+0.540472337\) \(a_{12}=-0.288675135\) \(a_{13}=-0.043588208\) \(a_{14}=-1.303436649\) \(a_{15}=+0.246848871\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.028377298\) \(a_{18}=+0.235702260\) \(a_{19}=+1.649395537\) \(a_{20}=-0.213777393\)
\(a_{21}=+1.064251568\) \(a_{22}=+0.382171655\) \(a_{23}=+0.569476698\) \(a_{24}=-0.204124145\) \(a_{25}=-0.817196904\)
\(a_{26}=-0.030821517\) \(a_{27}=-0.192450090\) \(a_{28}=-0.921668893\) \(a_{29}=-0.170685203\) \(a_{30}=+0.174548511\)
\(a_{31}=+1.194306307\) \(a_{32}=+0.176776695\) \(a_{33}=-0.312041849\) \(a_{34}=-0.727172561\) \(a_{35}=+0.788127894\)
\(a_{36}=+0.166666667\) \(a_{37}=+1.490057886\) \(a_{38}=+1.166298769\) \(a_{39}=+0.025165664\) \(a_{40}=-0.151163445\)
\(a_{41}=+1.630970929\) \(a_{42}=+0.752539500\) \(a_{43}=-0.484190170\) \(a_{44}=+0.270236168\) \(a_{45}=-0.142518262\)
\(a_{46}=+0.402680835\) \(a_{47}=-0.482526954\) \(a_{48}=-0.144337567\) \(a_{49}=+2.397894197\) \(a_{50}=-0.577845473\)
\(a_{51}=+0.593733910\) \(a_{52}=-0.021794104\) \(a_{53}=+0.857019780\) \(a_{54}=-0.136082763\) \(a_{55}=-0.231081535\)
\(a_{56}=-0.651718325\) \(a_{57}=-0.952278957\) \(a_{58}=-0.120692664\) \(a_{59}=+0.384475100\) \(a_{60}=+0.123424436\)
\(a_{61}=+0.827220200\) \(a_{62}=+0.844502088\) \(a_{63}=-0.614445929\) \(a_{64}=+0.125000000\) \(a_{65}=+0.018636347\)
\(a_{66}=-0.220646908\) \(a_{67}=+0.914054997\) \(a_{68}=-0.514188649\) \(a_{69}=-0.328787525\) \(a_{70}=+0.557290579\)
\(a_{71}=-1.164250001\) \(a_{72}=+0.117851130\) \(a_{73}=-1.120230004\) \(a_{74}=+1.053630036\) \(a_{75}=+0.471808853\)
\(a_{76}=+0.824697768\) \(a_{77}=-0.996273082\) \(a_{78}=+0.017794811\) \(a_{79}=-0.415870000\) \(a_{80}=-0.106888697\)
\(a_{81}=+0.111111111\) \(a_{82}=+1.153270604\) \(a_{83}=-0.527400017\) \(a_{84}=+0.532125784\) \(a_{85}=+0.439687636\)
\(a_{86}=-0.342374153\) \(a_{87}=+0.098545148\) \(a_{88}=+0.191085827\) \(a_{89}=-1.193800000\) \(a_{90}=-0.100775630\)
\(a_{91}=+0.080347791\) \(a_{92}=+0.284738349\) \(a_{93}=-0.689533068\) \(a_{94}=-0.341198081\) \(a_{95}=-0.705206957\)
\(a_{96}=-0.102062073\)

Showing all 96 available coefficients

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