Properties

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

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 27.2843840117 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.205623358\) \(a_{3}=+1.664570225\) \(a_{4}=+0.453527681\) \(a_{5}=-0.451284244\)
\(a_{6}=-2.006844744\) \(a_{7}=-0.796536199\) \(a_{8}=+0.658839792\) \(a_{9}=+1.770794034\) \(a_{10}=+0.544078826\)
\(a_{11}=-0.854052618\) \(a_{12}=+0.754928675\) \(a_{13}=+0.390665781\) \(a_{14}=+0.960322647\) \(a_{15}=-0.751194314\)
\(a_{16}=-1.247840324\) \(a_{17}=-0.236602401\) \(a_{18}=-2.134910649\) \(a_{19}=+0.018990770\) \(a_{20}=-0.204669897\)
\(a_{21}=-1.325890440\) \(a_{22}=+1.029665785\) \(a_{23}=-1.192333915\) \(a_{24}=+1.096685101\) \(a_{25}=-0.796342531\)
\(a_{26}=-0.470995791\) \(a_{27}=+1.283040798\) \(a_{28}=-0.361251215\) \(a_{29}=-1.064116290\) \(a_{30}=+0.905657413\)
\(a_{31}=-0.191447217\) \(a_{32}=+0.845585649\) \(a_{33}=-1.421630559\) \(a_{34}=+0.285253381\) \(a_{35}=+0.359464236\)
\(a_{36}=+0.803104112\) \(a_{37}=-1.183779191\) \(a_{38}=-0.022895716\) \(a_{39}=+0.650290627\) \(a_{40}=-0.297324017\)
\(a_{41}=-0.559372741\) \(a_{42}=+1.598524485\) \(a_{43}=-0.950172846\) \(a_{44}=-0.387336504\) \(a_{45}=-0.799131447\)
\(a_{46}=+1.437505618\) \(a_{47}=+1.306174266\) \(a_{48}=-2.077117848\) \(a_{49}=-0.365530083\) \(a_{50}=+0.960089157\)
\(a_{51}=-0.393841312\) \(a_{52}=+0.177177746\) \(a_{53}=+1.242079738\) \(a_{54}=-1.546863956\) \(a_{55}=+0.385420490\)
\(a_{56}=-0.524789743\) \(a_{57}=+0.031611470\) \(a_{58}=+1.282923456\) \(a_{59}=-0.741708067\) \(a_{60}=-0.340687419\)
\(a_{61}=+0.678642113\) \(a_{62}=+0.230813230\) \(a_{63}=-1.410501549\) \(a_{64}=+0.228382514\) \(a_{65}=-0.176301312\)
\(a_{66}=+1.713951008\) \(a_{67}=+0.000082486\) \(a_{68}=-0.107305738\) \(a_{69}=-1.984723533\) \(a_{70}=-0.433378480\)
\(a_{71}=+1.588767680\) \(a_{72}=+1.166669573\) \(a_{73}=-1.635206369\) \(a_{74}=+1.427191843\) \(a_{75}=-1.325568066\)
\(a_{76}=+0.008612840\) \(a_{77}=+0.680283826\) \(a_{78}=-0.784005569\) \(a_{79}=-0.216823462\) \(a_{80}=+0.563130677\)
\(a_{81}=+0.364917477\) \(a_{82}=+0.674392842\) \(a_{83}=-0.772414560\) \(a_{84}=-0.601328017\) \(a_{85}=+0.106774936\)
\(a_{86}=+1.145550578\) \(a_{87}=-1.771296292\) \(a_{88}=-0.562683849\) \(a_{89}=+1.801008658\) \(a_{90}=+0.963451538\)
\(a_{91}=-0.311179436\) \(a_{92}=-0.540756436\) \(a_{93}=-0.318677338\) \(a_{94}=-1.574754205\) \(a_{95}=-0.008570235\)
\(a_{96}=+1.407536694\) \(a_{97}=+1.032828248\) \(a_{98}=+0.440691606\) \(a_{99}=-1.512351279\) \(a_{100}=-0.361163382\)

Showing 100 of 5000 available coefficients

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