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: \( 6.87436376055 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=-1.642577407\)
\(a_{6}=-0.408248290\) \(a_{7}=-1.069052682\) \(a_{8}=+0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=-1.161477623\)
\(a_{11}=-0.002160533\) \(a_{12}=-0.288675135\) \(a_{13}=+0.602986206\) \(a_{14}=-0.755934401\) \(a_{15}=+0.948342508\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.675711510\) \(a_{18}=+0.235702260\) \(a_{19}=-0.219204742\) \(a_{20}=-0.821288704\)
\(a_{21}=+0.617217854\) \(a_{22}=-0.001527728\) \(a_{23}=-0.361129342\) \(a_{24}=-0.204124147\) \(a_{25}=+1.698060541\)
\(a_{26}=+0.426375643\) \(a_{27}=-0.192450090\) \(a_{28}=-0.534526341\) \(a_{29}=-1.918005655\) \(a_{30}=+0.670579418\)
\(a_{31}=-0.194818090\) \(a_{32}=+0.176776695\) \(a_{33}=+0.001247384\) \(a_{34}=-0.477800191\) \(a_{35}=+1.756001782\)
\(a_{36}=+0.166666667\) \(a_{37}=+0.393109865\) \(a_{38}=-0.155001159\) \(a_{39}=-0.348134248\) \(a_{40}=-0.580738812\)
\(a_{41}=-1.421254613\) \(a_{42}=+0.436438930\) \(a_{43}=+1.238694905\) \(a_{44}=-0.001080267\) \(a_{45}=-0.547525802\)
\(a_{46}=-0.255357007\) \(a_{47}=-0.520823914\) \(a_{48}=-0.144337567\) \(a_{49}=+0.142873637\) \(a_{50}=+1.200710121\)
\(a_{51}=+0.390122222\) \(a_{52}=+0.301493103\) \(a_{53}=-0.125691968\) \(a_{54}=-0.136082764\) \(a_{55}=+0.003548843\)
\(a_{56}=-0.377967200\) \(a_{57}=+0.126557917\) \(a_{58}=-1.356234805\) \(a_{59}=+0.995386779\) \(a_{60}=+0.474171253\)
\(a_{61}=-0.904455540\) \(a_{62}=-0.137757193\) \(a_{63}=-0.356350892\) \(a_{64}=+0.125000001\) \(a_{65}=-0.990451517\)
\(a_{66}=+0.000882031\) \(a_{67}=+1.814502962\) \(a_{68}=-0.337855745\) \(a_{69}=+0.208498125\) \(a_{70}=+1.241680799\)
\(a_{71}=+0.641132131\) \(a_{72}=+0.117851130\) \(a_{73}=-1.141233164\) \(a_{74}=+0.277970651\) \(a_{75}=-0.980375709\)
\(a_{76}=-0.109602371\) \(a_{77}=+0.002309724\) \(a_{78}=-0.246168088\) \(a_{79}=-0.025202800\) \(a_{80}=-0.410644352\)
\(a_{81}=+0.111111111\) \(a_{82}=-1.004978774\) \(a_{83}=-0.844207889\) \(a_{84}=+0.308608927\) \(a_{85}=+1.109908460\)
\(a_{86}=+0.875889567\) \(a_{87}=+1.107361081\) \(a_{88}=-0.000763864\) \(a_{89}=+0.588452404\) \(a_{90}=-0.387159208\)
\(a_{91}=-0.644624020\) \(a_{92}=-0.180564672\) \(a_{93}=+0.112478276\) \(a_{94}=-0.368278121\) \(a_{95}=+0.360060755\)
\(a_{96}=-0.102062073\) \(a_{97}=-0.569038443\) \(a_{98}=+0.101026918\) \(a_{99}=-0.000720177\) \(a_{100}=+0.849030269\)

Showing 100 of 1000 available coefficients

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