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: \( 13.9018163092 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=+1.908052527\)
\(a_{6}=+0.408248290\) \(a_{7}=+1.153763238\) \(a_{8}=-0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=-1.349196881\)
\(a_{11}=+0.446298491\) \(a_{12}=-0.288675135\) \(a_{13}=+0.364562364\) \(a_{14}=-0.815833809\) \(a_{15}=-1.101614640\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.286345704\) \(a_{18}=-0.235702260\) \(a_{19}=+0.252542103\) \(a_{20}=+0.954026264\)
\(a_{21}=-0.666125516\) \(a_{22}=-0.315580689\) \(a_{23}=+0.845523226\) \(a_{24}=+0.204124145\) \(a_{25}=+2.640664447\)
\(a_{26}=-0.257784520\) \(a_{27}=-0.192450090\) \(a_{28}=+0.576881619\) \(a_{29}=+0.915372241\) \(a_{30}=+0.778959182\)
\(a_{31}=-1.042990270\) \(a_{32}=-0.176776694\) \(a_{33}=-0.257670555\) \(a_{34}=+0.909583768\) \(a_{35}=+2.201440866\)
\(a_{36}=+0.166666667\) \(a_{37}=-0.783792490\) \(a_{38}=-0.178574234\) \(a_{39}=-0.210480179\) \(a_{40}=-0.674598440\)
\(a_{41}=-0.254859817\) \(a_{42}=+0.471021869\) \(a_{43}=-0.019467692\) \(a_{44}=+0.223149246\) \(a_{45}=+0.636017509\)
\(a_{46}=-0.597875207\) \(a_{47}=+1.318829971\) \(a_{48}=-0.144337567\) \(a_{49}=+0.331169609\) \(a_{50}=-1.867231738\)
\(a_{51}=+0.742672039\) \(a_{52}=+0.182281182\) \(a_{53}=-0.856701770\) \(a_{54}=+0.136082763\) \(a_{55}=+0.851560964\)
\(a_{56}=-0.407916905\) \(a_{57}=-0.145805251\) \(a_{58}=-0.647265919\) \(a_{59}=+1.100332580\) \(a_{60}=-0.550807320\)
\(a_{61}=-0.421836331\) \(a_{62}=+0.737505493\) \(a_{63}=+0.384587746\) \(a_{64}=+0.125000000\) \(a_{65}=+0.695604141\)
\(a_{66}=+0.182200596\) \(a_{67}=-0.469424943\) \(a_{68}=-0.643172852\) \(a_{69}=-0.488163062\) \(a_{70}=-1.556653762\)
\(a_{71}=+1.144732378\) \(a_{72}=-0.117851131\) \(a_{73}=+0.624743971\) \(a_{74}=+0.554224986\) \(a_{75}=-1.524588332\)
\(a_{76}=+0.126271052\) \(a_{77}=+0.514922796\) \(a_{78}=+0.148831960\) \(a_{79}=+0.452357866\) \(a_{80}=+0.477013132\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.180213105\) \(a_{83}=+1.653503314\) \(a_{84}=-0.333062758\) \(a_{85}=-2.454415172\)
\(a_{86}=+0.013765737\) \(a_{87}=-0.528490410\) \(a_{88}=-0.157790345\) \(a_{89}=-0.030503093\) \(a_{90}=-0.449732294\)
\(a_{91}=+0.420618654\) \(a_{92}=+0.422761613\) \(a_{93}=+0.602170713\) \(a_{94}=-0.932553616\) \(a_{95}=+0.481863598\)
\(a_{96}=+0.102062073\) \(a_{97}=+0.117924908\) \(a_{98}=-0.234172276\) \(a_{99}=+0.148766164\) \(a_{100}=+1.320332224\)

Showing 100 of 1000 available coefficients

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