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: \( 14.8720924008 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=+1.527615168\)
\(a_{6}=+0.408248290\) \(a_{7}=+1.311619671\) \(a_{8}=+0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=+1.080187044\)
\(a_{11}=-1.347579887\) \(a_{12}=+0.288675135\) \(a_{13}=+1.005270599\) \(a_{14}=+0.927455164\) \(a_{15}=+0.881969029\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.294603218\) \(a_{18}=+0.235702260\) \(a_{19}=-1.341838484\) \(a_{20}=+0.763807584\)
\(a_{21}=+0.757263970\) \(a_{22}=-0.952882876\) \(a_{23}=-0.888218197\) \(a_{24}=+0.204124145\) \(a_{25}=+1.333608102\)
\(a_{26}=+0.710833658\) \(a_{27}=+0.192450090\) \(a_{28}=+0.655809836\) \(a_{29}=+0.494018993\) \(a_{30}=+0.623646281\)
\(a_{31}=+1.107103509\) \(a_{32}=+0.176776695\) \(a_{33}=-0.778025611\) \(a_{34}=-0.208315933\) \(a_{35}=+2.003650106\)
\(a_{36}=+0.166666672\) \(a_{37}=+0.415344869\) \(a_{38}=-0.948823091\) \(a_{39}=+0.580393251\) \(a_{40}=+0.540093522\)
\(a_{41}=+0.806225577\) \(a_{42}=+0.535466489\) \(a_{43}=-1.256068524\) \(a_{44}=-0.673789944\) \(a_{45}=+0.509205056\)
\(a_{46}=-0.628065110\) \(a_{47}=-0.015157752\) \(a_{48}=+0.144337567\) \(a_{49}=+0.720346163\) \(a_{50}=+0.943003332\)
\(a_{51}=-0.170089247\) \(a_{52}=+0.502635300\) \(a_{53}=+0.140169037\) \(a_{54}=+0.136082763\) \(a_{55}=-2.058583476\)
\(a_{56}=+0.463727582\) \(a_{57}=-0.774710810\) \(a_{58}=+0.349324180\) \(a_{59}=-0.014891813\) \(a_{60}=+0.440984514\)
\(a_{61}=-0.876510218\) \(a_{62}=+0.782840398\) \(a_{63}=+0.437206557\) \(a_{64}=+0.125000000\) \(a_{65}=+1.535666615\)
\(a_{66}=-0.550147185\) \(a_{67}=-0.840122356\) \(a_{68}=-0.147301609\) \(a_{69}=-0.512813015\) \(a_{70}=+1.416794576\)
\(a_{71}=-1.864094162\) \(a_{72}=+0.117851131\) \(a_{73}=+0.279185195\) \(a_{74}=+0.293693181\) \(a_{75}=+0.769958997\)
\(a_{76}=-0.670919243\) \(a_{77}=-1.767512284\) \(a_{78}=+0.410399999\) \(a_{79}=+0.810633694\) \(a_{80}=+0.381903800\)
\(a_{81}=+0.111111120\) \(a_{82}=+0.570087561\) \(a_{83}=+0.589712526\) \(a_{84}=+0.378631985\) \(a_{85}=-0.450040344\)
\(a_{86}=-0.888174571\) \(a_{87}=+0.285221999\) \(a_{88}=-0.476441438\) \(a_{89}=-1.089951092\) \(a_{90}=+0.360062348\)
\(a_{91}=+1.318532693\) \(a_{92}=-0.444109098\) \(a_{93}=+0.639186509\) \(a_{94}=-0.010718150\) \(a_{95}=-2.049812821\)
\(a_{96}=+0.102062073\) \(a_{97}=+0.286167238\) \(a_{98}=+0.509361656\) \(a_{99}=-0.449193296\) \(a_{100}=+0.666804051\)

Showing 100 of 1000 available coefficients

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