Properties

Level $2$
Weight $0$
Character 2.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 2 \)
Weight: \( 0 \)
Character: 2.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 27.7570459928 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.365098106\) \(a_{4}=+0.500000000\) \(a_{5}=+1.186975082\)
\(a_{6}=+0.258163346\) \(a_{7}=-0.986949047\) \(a_{8}=-0.353553391\) \(a_{9}=-0.866703373\) \(a_{10}=-0.839318130\)
\(a_{11}=+1.247837442\) \(a_{12}=-0.182549053\) \(a_{13}=-0.471495382\) \(a_{14}=+0.697878364\) \(a_{15}=-0.433362354\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.245386287\) \(a_{18}=+0.612851832\) \(a_{19}=+1.018475265\) \(a_{20}=+0.593487541\)
\(a_{21}=+0.360333228\) \(a_{22}=-0.882354317\) \(a_{23}=-0.543907963\) \(a_{24}=+0.129081673\) \(a_{25}=+0.408909846\)
\(a_{26}=+0.333397582\) \(a_{27}=+0.681529866\) \(a_{28}=-0.493474524\) \(a_{29}=+1.894502900\) \(a_{30}=+0.306433459\)
\(a_{31}=-1.895137871\) \(a_{32}=-0.176776695\) \(a_{33}=-0.455583087\) \(a_{34}=-0.173514308\) \(a_{35}=-1.171483926\)
\(a_{36}=-0.433351687\) \(a_{37}=-1.551644151\) \(a_{38}=-0.720170766\) \(a_{39}=+0.172142071\) \(a_{40}=-0.419659065\)
\(a_{41}=-0.227745035\) \(a_{42}=-0.254794069\) \(a_{43}=-1.052720178\) \(a_{44}=+0.623918721\) \(a_{45}=-1.028755307\)
\(a_{46}=+0.384601009\) \(a_{47}=+0.352143956\) \(a_{48}=-0.091274526\) \(a_{49}=-0.025931578\) \(a_{50}=-0.289142925\)
\(a_{51}=-0.089590069\) \(a_{52}=-0.235747691\) \(a_{53}=-0.113212631\) \(a_{54}=-0.481914390\) \(a_{55}=+1.481151950\)
\(a_{56}=+0.348939182\) \(a_{57}=-0.371843390\) \(a_{58}=-1.339615847\) \(a_{59}=+0.751118227\) \(a_{60}=-0.216681177\)
\(a_{61}=-1.252201665\) \(a_{62}=+1.340064840\) \(a_{63}=+0.855392068\) \(a_{64}=+0.125000000\) \(a_{65}=-0.559653269\)
\(a_{66}=+0.322145890\) \(a_{67}=-1.553349310\) \(a_{68}=+0.122693144\) \(a_{69}=+0.198579767\) \(a_{70}=+0.828364228\)
\(a_{71}=-0.055923410\) \(a_{72}=+0.306425916\) \(a_{73}=-1.110873744\) \(a_{74}=+1.097178101\) \(a_{75}=-0.149292210\)
\(a_{76}=+0.509237632\) \(a_{77}=-1.231551975\) \(a_{78}=-0.121722826\) \(a_{79}=-0.240181746\) \(a_{80}=+0.296743771\)
\(a_{81}=+0.617878110\) \(a_{82}=+0.161040059\) \(a_{83}=-0.433722941\) \(a_{84}=+0.180166614\) \(a_{85}=+0.291267409\)
\(a_{86}=+0.744385576\) \(a_{87}=-0.691679420\) \(a_{88}=-0.441177159\) \(a_{89}=-1.410925852\) \(a_{90}=+0.727439854\)
\(a_{91}=+0.465341918\) \(a_{92}=-0.271953982\) \(a_{93}=+0.691911247\) \(a_{94}=-0.249003379\) \(a_{95}=+1.208904761\)
\(a_{96}=+0.064540837\) \(a_{97}=-0.827653441\) \(a_{98}=+0.018336395\) \(a_{99}=-1.081504920\) \(a_{100}=+0.204454923\)

Showing 100 of 1228 available coefficients

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