Properties

Level $1$
Weight $0$
Character 1.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 36.6775529931 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.194052311\) \(a_{3}=-1.374957530\) \(a_{4}=+0.425760921\) \(a_{5}=+1.086391604\)
\(a_{6}=+1.641771217\) \(a_{7}=+0.454411027\) \(a_{8}=+0.685671499\) \(a_{9}=+0.890508211\) \(a_{10}=-1.297208405\)
\(a_{11}=-1.565364198\) \(a_{12}=-0.585403185\) \(a_{13}=+1.260712987\) \(a_{14}=-0.542590537\) \(a_{15}=-1.493742317\)
\(a_{16}=-1.244488559\) \(a_{17}=+0.238591949\) \(a_{18}=-1.063313386\) \(a_{19}=-1.019827484\) \(a_{20}=+0.462543090\)
\(a_{21}=-0.624795864\) \(a_{22}=+1.869126738\) \(a_{23}=-0.397372942\) \(a_{24}=-0.942769191\) \(a_{25}=+0.180246717\)
\(a_{26}=-1.505357255\) \(a_{27}=+0.150546560\) \(a_{28}=+0.193470458\) \(a_{29}=+0.449790711\) \(a_{30}=+1.783606465\)
\(a_{31}=+0.102398072\) \(a_{32}=+0.800312941\) \(a_{33}=+2.152309292\) \(a_{34}=-0.284891269\) \(a_{35}=+0.493668325\)
\(a_{36}=+0.379143596\) \(a_{37}=+0.465686977\) \(a_{38}=+1.217727357\) \(a_{39}=-1.733426815\) \(a_{40}=+0.744907759\)
\(a_{41}=+0.296022958\) \(a_{42}=+0.746038945\) \(a_{43}=-0.809303956\) \(a_{44}=-0.666470903\) \(a_{45}=+0.967440643\)
\(a_{46}=+0.474484079\) \(a_{47}=-1.572371672\) \(a_{48}=+1.711118916\) \(a_{49}=-0.793510618\) \(a_{50}=-0.215224008\)
\(a_{51}=-0.328053798\) \(a_{52}=+0.536762322\) \(a_{53}=+0.835920122\) \(a_{54}=-0.179760468\) \(a_{55}=-1.700598521\)
\(a_{56}=+0.311576690\) \(a_{57}=+1.402219470\) \(a_{58}=-0.537073638\) \(a_{59}=+0.452804431\) \(a_{60}=-0.635977105\)
\(a_{61}=-0.327338001\) \(a_{62}=-0.122268655\) \(a_{63}=+0.404656751\) \(a_{64}=+0.288873043\) \(a_{65}=+1.369628002\)
\(a_{66}=-2.569969876\) \(a_{67}=+0.752189490\) \(a_{68}=+0.101583128\) \(a_{69}=+0.546370918\) \(a_{70}=-0.589465804\)
\(a_{71}=-0.082464468\) \(a_{72}=+0.610596100\) \(a_{73}=+0.305338103\) \(a_{74}=-0.556054610\) \(a_{75}=-0.247831580\)
\(a_{76}=-0.434202686\) \(a_{77}=-0.711318754\) \(a_{78}=+2.069802294\) \(a_{79}=+0.974517566\) \(a_{80}=-1.352001922\)
\(a_{81}=-1.097503337\) \(a_{82}=-0.353466898\) \(a_{83}=+1.142950042\) \(a_{84}=-0.266013663\) \(a_{85}=+0.259204291\)
\(a_{86}=+0.966351259\) \(a_{87}=-0.618443125\) \(a_{88}=-1.073325616\) \(a_{89}=+1.125485331\) \(a_{90}=-1.155174735\)
\(a_{91}=+0.572881884\) \(a_{92}=-0.169185870\) \(a_{93}=-0.140793000\) \(a_{94}=+1.877494029\) \(a_{95}=-1.107932009\)
\(a_{96}=-1.100396305\) \(a_{97}=+0.706319584\) \(a_{98}=+0.947493187\) \(a_{99}=-1.393969671\) \(a_{100}=+0.076742008\)

Showing 100 of 5000 available coefficients

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