Properties

Level $563$
Weight $0$
Character 563.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 563 \)
Weight: \( 0 \)
Character: 563.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 0.51442639183 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.173164436\) \(a_{3}=-1.065555689\) \(a_{4}=-0.970014080\) \(a_{5}=-1.375680073\)
\(a_{6}=-0.184516351\) \(a_{7}=+0.001266533\) \(a_{8}=-0.341136376\) \(a_{9}=+0.135408918\) \(a_{10}=-0.238218858\)
\(a_{11}=-0.468393067\) \(a_{12}=+1.033604025\) \(a_{13}=-1.496019732\) \(a_{14}=+0.000219317\) \(a_{15}=+1.465863728\)
\(a_{16}=+0.910941393\) \(a_{17}=-0.600913865\) \(a_{18}=+0.023448010\) \(a_{19}=+1.128138827\) \(a_{20}=+1.334429036\)
\(a_{21}=-0.001349562\) \(a_{22}=-0.081109030\) \(a_{23}=-0.088076511\) \(a_{24}=+0.363499807\) \(a_{25}=+0.892495653\)
\(a_{26}=-0.259057411\) \(a_{27}=+0.921269953\) \(a_{28}=-0.001228555\) \(a_{29}=-1.204878257\) \(a_{30}=+0.253835455\)
\(a_{31}=-0.337896542\) \(a_{32}=+0.498879027\) \(a_{33}=+0.499098892\) \(a_{34}=-0.104056917\) \(a_{35}=-0.001742348\)
\(a_{36}=-0.131348568\) \(a_{37}=+0.082503743\) \(a_{38}=+0.195353523\) \(a_{39}=+1.594092336\) \(a_{40}=+0.469294512\)
\(a_{41}=+1.944939990\) \(a_{42}=-0.000233691\) \(a_{43}=+0.162223648\) \(a_{44}=+0.454347884\) \(a_{45}=-0.186279363\)
\(a_{46}=-0.015251716\) \(a_{47}=-0.496923364\) \(a_{48}=-0.970658788\) \(a_{49}=-0.999998405\) \(a_{50}=+0.154548510\)
\(a_{51}=+0.640307197\) \(a_{52}=+1.451160214\) \(a_{53}=-1.091137813\) \(a_{54}=+0.159531190\) \(a_{55}=+0.644359016\)
\(a_{56}=-0.000432049\) \(a_{57}=-1.202094747\) \(a_{58}=-0.208642055\) \(a_{59}=-1.998221247\) \(a_{60}=-1.421908456\)
\(a_{61}=+0.943310781\) \(a_{62}=-0.058511658\) \(a_{63}=+0.000171515\) \(a_{64}=-0.824553300\) \(a_{65}=+2.058044525\)
\(a_{66}=+0.086426190\) \(a_{67}=-1.025826361\) \(a_{68}=+0.582894917\) \(a_{69}=+0.093850433\) \(a_{70}=-0.000301721\)
\(a_{71}=+0.559620243\) \(a_{72}=-0.046192928\) \(a_{73}=-1.686978784\) \(a_{74}=+0.014286716\) \(a_{75}=-0.951003809\)
\(a_{76}=-1.094310541\) \(a_{77}=-0.000593225\) \(a_{78}=+0.276040096\) \(a_{79}=+1.353896697\) \(a_{80}=-1.253163933\)
\(a_{81}=-1.117073373\) \(a_{82}=+0.336794428\) \(a_{83}=-1.487573840\) \(a_{84}=+0.001309086\) \(a_{85}=+0.826665239\)
\(a_{86}=+0.028091382\) \(a_{87}=+1.283864875\) \(a_{88}=+0.159785929\) \(a_{89}=-1.170269160\) \(a_{90}=-0.032256945\)
\(a_{91}=-0.001894776\) \(a_{92}=+0.085435441\) \(a_{93}=+0.360047610\) \(a_{94}=-0.086049453\) \(a_{95}=-1.551958076\)
\(a_{96}=-0.531583378\) \(a_{97}=+0.584217561\) \(a_{98}=-0.173164170\) \(a_{99}=-0.063424608\) \(a_{100}=-0.865733349\)

Showing 100 of 1708 available coefficients

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