Properties

Level $449$
Weight $0$
Character 449.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 449 \)
Weight: \( 0 \)
Character: 449.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 0.237296691202 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.059997360\) \(a_{3}=-0.257854920\) \(a_{4}=+0.123594431\) \(a_{5}=-0.431540027\)
\(a_{6}=-0.273325534\) \(a_{7}=+0.479101681\) \(a_{8}=-0.928987607\) \(a_{9}=-0.933510844\) \(a_{10}=-0.457431294\)
\(a_{11}=-1.074321789\) \(a_{12}=-0.031869416\) \(a_{13}=+0.627770341\) \(a_{14}=+0.507846512\) \(a_{15}=+0.111274729\)
\(a_{16}=-1.108318836\) \(a_{17}=+0.783833193\) \(a_{18}=-0.989519044\) \(a_{19}=-0.614547874\) \(a_{20}=-0.053335941\)
\(a_{21}=-0.123538730\) \(a_{22}=-1.138778283\) \(a_{23}=-0.633623046\) \(a_{24}=+0.239544017\) \(a_{25}=-0.813773218\)
\(a_{26}=+0.665434929\) \(a_{27}=+0.498565290\) \(a_{28}=+0.059214297\) \(a_{29}=+1.342987664\) \(a_{30}=+0.117950910\)
\(a_{31}=+1.176385566\) \(a_{32}=-0.245827439\) \(a_{33}=+0.277019152\) \(a_{34}=+0.830861124\) \(a_{35}=-0.206751534\)
\(a_{36}=-0.115376753\) \(a_{37}=-0.531936683\) \(a_{38}=-0.651419128\) \(a_{39}=-0.161873660\) \(a_{40}=+0.400895320\)
\(a_{41}=-0.138707869\) \(a_{42}=-0.130950716\) \(a_{43}=-1.668709299\) \(a_{44}=-0.132780175\) \(a_{45}=+0.402847273\)
\(a_{46}=-0.671638780\) \(a_{47}=+0.986375483\) \(a_{48}=+0.285785478\) \(a_{49}=-0.770461583\) \(a_{50}=-0.862597456\)
\(a_{51}=-0.202115249\) \(a_{52}=+0.077588892\) \(a_{53}=+0.882850659\) \(a_{54}=+0.528477895\) \(a_{55}=+0.463612884\)
\(a_{56}=-0.445079535\) \(a_{57}=+0.158464160\) \(a_{58}=+1.423563400\) \(a_{59}=+1.149092822\) \(a_{60}=+0.013752941\)
\(a_{61}=-0.445443683\) \(a_{62}=+1.246965582\) \(a_{63}=-0.447246599\) \(a_{64}=+0.847742411\) \(a_{65}=-0.270908060\)
\(a_{66}=+0.293639578\) \(a_{67}=-0.708509205\) \(a_{68}=+0.096877382\) \(a_{69}=+0.163382815\) \(a_{70}=-0.219156072\)
\(a_{71}=+1.960404008\) \(a_{72}=+0.867220012\) \(a_{73}=+0.032306823\) \(a_{74}=-0.563851495\) \(a_{75}=+0.209835435\)
\(a_{76}=-0.075954680\) \(a_{77}=-0.514709364\) \(a_{78}=-0.171585662\) \(a_{79}=+0.914018434\) \(a_{80}=+0.478283921\)
\(a_{81}=+0.804953347\) \(a_{82}=-0.147029943\) \(a_{83}=-1.587153314\) \(a_{84}=-0.015268707\) \(a_{85}=-0.338255428\)
\(a_{86}=-1.768827441\) \(a_{87}=-0.346295960\) \(a_{88}=+0.998031617\) \(a_{89}=+0.652393401\) \(a_{90}=+0.427017061\)
\(a_{91}=+0.300765781\) \(a_{92}=-0.078312262\) \(a_{93}=-0.303336759\) \(a_{94}=+1.045555431\) \(a_{95}=+0.265202003\)
\(a_{96}=+0.063387795\) \(a_{97}=+0.270786806\) \(a_{98}=-0.816687185\) \(a_{99}=+1.002891013\) \(a_{100}=-0.100577855\)

Showing 100 of 1366 available coefficients

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