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: \( 8.81974775988 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=-1.563756278\)
\(a_{6}=-0.408248290\) \(a_{7}=+0.843138956\) \(a_{8}=-0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=+1.105742669\)
\(a_{11}=+0.702323597\) \(a_{12}=+0.288675135\) \(a_{13}=+1.118227658\) \(a_{14}=-0.596189273\) \(a_{15}=-0.902835108\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.603266665\) \(a_{18}=-0.235702260\) \(a_{19}=+0.381066715\) \(a_{20}=-0.781878139\)
\(a_{21}=+0.486786503\) \(a_{22}=-0.496617778\) \(a_{23}=-0.499148125\) \(a_{24}=-0.204124145\) \(a_{25}=+1.445333697\)
\(a_{26}=-0.790706360\) \(a_{27}=+0.192450091\) \(a_{28}=+0.421569473\) \(a_{29}=-0.797768598\) \(a_{30}=+0.638400827\)
\(a_{31}=+0.486966027\) \(a_{32}=-0.176776695\) \(a_{33}=+0.405486718\) \(a_{34}=-1.133680731\) \(a_{35}=-1.318463835\)
\(a_{36}=+0.166666667\) \(a_{37}=+0.991504751\) \(a_{38}=-0.269454858\) \(a_{39}=+0.645609040\) \(a_{40}=+0.552871334\)
\(a_{41}=+0.299112769\) \(a_{42}=-0.344210037\) \(a_{43}=+0.041784644\) \(a_{44}=+0.351161798\) \(a_{45}=-0.521252093\)
\(a_{46}=+0.352951024\) \(a_{47}=-1.618080380\) \(a_{48}=+0.144337567\) \(a_{49}=-0.289116701\) \(a_{50}=-1.022005259\)
\(a_{51}=+0.925646441\) \(a_{52}=+0.559113829\) \(a_{53}=+1.922533882\) \(a_{54}=-0.136082763\) \(a_{55}=-1.098262934\)
\(a_{56}=-0.298094637\) \(a_{57}=+0.220008971\) \(a_{58}=+0.564107585\) \(a_{59}=+0.727635418\) \(a_{60}=-0.451417554\)
\(a_{61}=-0.811728167\) \(a_{62}=-0.344336980\) \(a_{63}=+0.281046318\) \(a_{64}=+0.125000000\) \(a_{65}=-1.748635521\)
\(a_{66}=-0.286722410\) \(a_{67}=+0.893694319\) \(a_{68}=+0.801633333\) \(a_{69}=-0.288183310\) \(a_{70}=+0.932294721\)
\(a_{71}=+0.403997292\) \(a_{72}=-0.117851130\) \(a_{73}=-0.834253689\) \(a_{74}=-0.701099733\) \(a_{75}=+0.834463800\)
\(a_{76}=+0.190533358\) \(a_{77}=+0.592156384\) \(a_{78}=-0.456514530\) \(a_{79}=+0.542278507\) \(a_{80}=-0.390939070\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.211504668\) \(a_{83}=+0.448777703\) \(a_{84}=+0.243393252\) \(a_{85}=-2.507118313\)
\(a_{86}=-0.029546205\) \(a_{87}=-0.460591915\) \(a_{88}=-0.248308889\) \(a_{89}=+0.798985378\) \(a_{90}=+0.368580889\)
\(a_{91}=+0.942821300\) \(a_{92}=-0.249574062\) \(a_{93}=+0.281149967\) \(a_{94}=+1.144155609\) \(a_{95}=-0.595895468\)
\(a_{96}=-0.102062073\) \(a_{97}=+0.633178738\) \(a_{98}=+0.204436380\) \(a_{99}=+0.234107866\) \(a_{100}=+0.722666849\)

Showing 100 of 1000 available coefficients

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