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: \( 39.1680849679 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.585073932\) \(a_{3}=-1.702961588\) \(a_{4}=+1.512459371\) \(a_{5}=-0.678740779\)
\(a_{6}=+2.699320021\) \(a_{7}=+0.144356615\) \(a_{8}=-0.812285990\) \(a_{9}=+1.900078170\) \(a_{10}=+1.075854316\)
\(a_{11}=+0.410487903\) \(a_{12}=-2.575660212\) \(a_{13}=-1.239119880\) \(a_{14}=-0.228815907\) \(a_{15}=+1.155869475\)
\(a_{16}=-0.224926022\) \(a_{17}=-1.023843237\) \(a_{18}=-3.011764377\) \(a_{19}=+0.179127598\) \(a_{20}=-1.026567883\)
\(a_{21}=-0.245833770\) \(a_{22}=-0.650653674\) \(a_{23}=-1.268143304\) \(a_{24}=+1.383291840\) \(a_{25}=-0.539310955\)
\(a_{26}=+1.964096620\) \(a_{27}=-1.532798550\) \(a_{28}=+0.218333515\) \(a_{29}=-0.324542033\) \(a_{30}=-1.832138574\)
\(a_{31}=+0.113898396\) \(a_{32}=+1.168810365\) \(a_{33}=-0.699045131\) \(a_{34}=+1.622867226\) \(a_{35}=-0.097980721\)
\(a_{36}=+2.873791034\) \(a_{37}=-0.124969748\) \(a_{38}=-0.283930480\) \(a_{39}=+2.110173558\) \(a_{40}=+0.551331626\)
\(a_{41}=-0.404237466\) \(a_{42}=+0.389664701\) \(a_{43}=+0.353417620\) \(a_{44}=+0.620846275\) \(a_{45}=-1.289660538\)
\(a_{46}=+2.010100894\) \(a_{47}=-1.222784069\) \(a_{48}=+0.383040376\) \(a_{49}=-0.979161168\) \(a_{50}=+0.854847735\)
\(a_{51}=+1.743565704\) \(a_{52}=-1.874118473\) \(a_{53}=-1.588961897\) \(a_{54}=+2.429599024\) \(a_{55}=-0.278614879\)
\(a_{56}=-0.117258856\) \(a_{57}=-0.305047412\) \(a_{58}=+0.514423117\) \(a_{59}=-1.864451816\) \(a_{60}=+1.748205619\)
\(a_{61}=+0.098092230\) \(a_{62}=-0.180537378\) \(a_{63}=+0.274288852\) \(a_{64}=-1.627724818\) \(a_{65}=+0.841041192\)
\(a_{66}=+1.108038214\) \(a_{67}=-0.682665131\) \(a_{68}=-1.548521309\) \(a_{69}=+2.159599335\) \(a_{70}=+0.155306687\)
\(a_{71}=-0.701267038\) \(a_{72}=-1.543406878\) \(a_{73}=+0.916635130\) \(a_{74}=+0.198086289\) \(a_{75}=+0.918425840\)
\(a_{76}=+0.270923208\) \(a_{77}=+0.059256644\) \(a_{78}=-3.344781099\) \(a_{79}=+1.973955908\) \(a_{80}=+0.152666464\)
\(a_{81}=+0.710218882\) \(a_{82}=+0.640746269\) \(a_{83}=-1.356867255\) \(a_{84}=-0.371813589\) \(a_{85}=+0.694924156\)
\(a_{86}=-0.560193056\) \(a_{87}=+0.552682616\) \(a_{88}=-0.333433573\) \(a_{89}=-0.621416112\) \(a_{90}=+2.044207300\)
\(a_{91}=-0.178875151\) \(a_{92}=-1.918015224\) \(a_{93}=-0.193964593\) \(a_{94}=+1.938203152\) \(a_{95}=-0.121581203\)
\(a_{96}=-1.990439155\) \(a_{97}=+0.140992094\) \(a_{98}=+1.552042843\) \(a_{99}=+0.779959103\) \(a_{100}=-0.815685907\)

Showing 100 of 5000 available coefficients

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