Properties

Level $58$
Weight $0$
Character 58.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 58 = 2 \cdot 29 \)
Weight: \( 0 \)
Character: 58.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 2.8874500935 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.619168410\) \(a_{4}=+0.500000000\) \(a_{5}=+0.550293537\)
\(a_{6}=-0.437818182\) \(a_{7}=+1.948888952\) \(a_{8}=-0.353553391\) \(a_{9}=-0.616630480\) \(a_{10}=-0.389116292\)
\(a_{11}=+0.492922310\) \(a_{12}=+0.309584205\) \(a_{13}=-0.084006205\) \(a_{14}=-1.378072594\) \(a_{15}=+0.340724374\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.101014414\) \(a_{18}=+0.436023594\) \(a_{19}=+1.827318141\) \(a_{20}=+0.275146768\)
\(a_{21}=+1.206690474\) \(a_{22}=-0.348548708\) \(a_{23}=+0.637892870\) \(a_{24}=-0.218909091\) \(a_{25}=-0.697177023\)
\(a_{26}=+0.059401357\) \(a_{27}=-1.000966524\) \(a_{28}=+0.974444476\) \(a_{29}=-0.185695338\) \(a_{30}=-0.240928516\)
\(a_{31}=+0.257485238\) \(a_{32}=-0.176776695\) \(a_{33}=+0.305201923\) \(a_{34}=-0.071427977\) \(a_{35}=+1.072460995\)
\(a_{36}=-0.308315240\) \(a_{37}=-1.546540051\) \(a_{38}=-1.292109049\) \(a_{39}=-0.052013989\) \(a_{40}=-0.194558146\)
\(a_{41}=-0.342741844\) \(a_{42}=-0.853259017\) \(a_{43}=+1.180015497\) \(a_{44}=+0.246461155\) \(a_{45}=-0.339327768\)
\(a_{46}=-0.451058374\) \(a_{47}=-0.452664524\) \(a_{48}=+0.154792103\) \(a_{49}=+2.798168148\) \(a_{50}=+0.492978601\)
\(a_{51}=+0.062544934\) \(a_{52}=-0.042003103\) \(a_{53}=-1.453894620\) \(a_{54}=+0.707790217\) \(a_{55}=+0.271251962\)
\(a_{56}=-0.689036297\) \(a_{57}=+1.131417668\) \(a_{58}=+0.131306433\) \(a_{59}=-0.940165428\) \(a_{60}=+0.170362187\)
\(a_{61}=+0.860309999\) \(a_{62}=-0.182069557\) \(a_{63}=-1.201744330\) \(a_{64}=+0.125000000\) \(a_{65}=-0.046228072\)
\(a_{66}=-0.215810350\) \(a_{67}=-0.289047284\) \(a_{68}=+0.050507207\) \(a_{69}=+0.394963114\) \(a_{70}=-0.758344442\)
\(a_{71}=+0.346662119\) \(a_{72}=+0.218011797\) \(a_{73}=+1.296536413\) \(a_{74}=+1.093568958\) \(a_{75}=-0.431669989\)
\(a_{76}=+0.913659070\) \(a_{77}=+0.960650845\) \(a_{78}=+0.036779444\) \(a_{79}=-1.552453485\) \(a_{80}=+0.137573384\)
\(a_{81}=-0.003136371\) \(a_{82}=+0.242355082\) \(a_{83}=-1.079024831\) \(a_{84}=+0.603345237\) \(a_{85}=+0.055587579\)
\(a_{86}=-0.834396960\) \(a_{87}=-0.114976687\) \(a_{88}=-0.174274354\) \(a_{89}=-1.739559548\) \(a_{90}=+0.239940966\)
\(a_{91}=-0.163718765\) \(a_{92}=+0.318946435\) \(a_{93}=+0.159426725\) \(a_{94}=+0.320082154\) \(a_{95}=+1.005561363\)
\(a_{96}=-0.109454545\) \(a_{97}=+1.108280230\) \(a_{98}=-1.978603672\) \(a_{99}=-0.303950921\) \(a_{100}=-0.348588512\)

Showing 100 of 546 available coefficients

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