Properties

Level $53$
Weight $0$
Character 53.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 53 \)
Weight: \( 0 \)
Character: 53.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 1.49379571497 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.873757493\) \(a_{3}=-1.517468096\) \(a_{4}=+2.510967143\) \(a_{5}=-0.699542881\)
\(a_{6}=+2.843367215\) \(a_{7}=+0.679874331\) \(a_{8}=-2.831186006\) \(a_{9}=+1.302709422\) \(a_{10}=+1.310773715\)
\(a_{11}=-0.435107601\) \(a_{12}=-3.810312530\) \(a_{13}=-1.441399128\) \(a_{14}=-1.273919622\) \(a_{15}=+1.061534004\)
\(a_{16}=+2.793988850\) \(a_{17}=+0.978158237\) \(a_{18}=-2.440961542\) \(a_{19}=+0.536313595\) \(a_{20}=-1.756529190\)
\(a_{21}=-1.031687606\) \(a_{22}=+0.815286127\) \(a_{23}=-0.189488965\) \(a_{24}=+4.296234438\) \(a_{25}=-0.510639757\)
\(a_{26}=+2.700832416\) \(a_{27}=-0.459351891\) \(a_{28}=+1.707142106\) \(a_{29}=-1.381397419\) \(a_{30}=-1.989057294\)
\(a_{31}=+0.090152631\) \(a_{32}=-2.404071537\) \(a_{33}=+0.660261903\) \(a_{34}=-1.832831325\) \(a_{35}=-0.475601248\)
\(a_{36}=+3.271060556\) \(a_{37}=-0.517356006\) \(a_{38}=-1.004921617\) \(a_{39}=+2.187277190\) \(a_{40}=+1.980536016\)
\(a_{41}=-0.935130680\) \(a_{42}=+1.933132383\) \(a_{43}=+0.169211938\) \(a_{44}=-1.092540889\) \(a_{45}=-0.911301103\)
\(a_{46}=+0.355056369\) \(a_{47}=+0.713290105\) \(a_{48}=-4.239788940\) \(a_{49}=-0.537770894\) \(a_{50}=+0.956815072\)
\(a_{51}=-1.484323917\) \(a_{52}=-3.619305850\) \(a_{53}=+0.137360564\) \(a_{54}=+0.860714047\) \(a_{55}=+0.304376425\)
\(a_{56}=-1.924850691\) \(a_{57}=-0.813838770\) \(a_{58}=+2.588403765\) \(a_{59}=+1.598663330\) \(a_{60}=+2.665477005\)
\(a_{61}=-0.797932857\) \(a_{62}=-0.168924168\) \(a_{63}=+0.885678697\) \(a_{64}=+1.710658207\) \(a_{65}=+1.008320499\)
\(a_{66}=-1.237170687\) \(a_{67}=-1.373510760\) \(a_{68}=+2.456123193\) \(a_{69}=+0.287543460\) \(a_{70}=+0.891161403\)
\(a_{71}=+0.224770881\) \(a_{72}=-3.688212686\) \(a_{73}=+1.462569615\) \(a_{74}=+0.969399692\) \(a_{75}=+0.774879540\)
\(a_{76}=+1.346665815\) \(a_{77}=-0.295818489\) \(a_{78}=-4.098427025\) \(a_{79}=-0.184547752\) \(a_{80}=-1.954515010\)
\(a_{81}=-0.605657583\) \(a_{82}=+1.752208118\) \(a_{83}=-1.096439902\) \(a_{84}=-2.590533681\) \(a_{85}=-0.684263631\)
\(a_{86}=-0.317062137\) \(a_{87}=+2.096226511\) \(a_{88}=+1.231870550\) \(a_{89}=+0.964260391\) \(a_{90}=+1.707557270\)
\(a_{91}=-0.979970267\) \(a_{92}=-0.475800566\) \(a_{93}=-0.136803742\) \(a_{94}=-1.336532679\) \(a_{95}=-0.375174357\)
\(a_{96}=+3.648101859\) \(a_{97}=+0.078465708\) \(a_{98}=+1.007652243\) \(a_{99}=-0.566818771\) \(a_{100}=-1.282199653\)

Showing 100 of 546 available coefficients

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