Properties

Level $98$
Weight $0$
Character 98.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 98 = 2 \cdot 7^{2} \)
Weight: \( 0 \)
Character: 98.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 1.93220145575 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.457682461\) \(a_{4}=+0.500000000\) \(a_{5}=+1.689223628\)
\(a_{6}=+0.323630372\) \(a_{7}=+0.000000000\) \(a_{8}=+0.353553391\) \(a_{9}=-0.790526765\) \(a_{10}=+1.194461482\)
\(a_{11}=-0.792131200\) \(a_{12}=+0.228841231\) \(a_{13}=-0.817670841\) \(a_{14}=+0.000000000\) \(a_{15}=+0.773128027\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.335295220\) \(a_{18}=-0.558986836\) \(a_{19}=+1.277120033\) \(a_{20}=+0.844611814\)
\(a_{21}=+0.000000000\) \(a_{22}=-0.560121343\) \(a_{23}=+0.246925252\) \(a_{24}=+0.161815186\) \(a_{25}=+1.853476465\)
\(a_{26}=-0.578180596\) \(a_{27}=-0.819492696\) \(a_{28}=+0.000000000\) \(a_{29}=-0.760220056\) \(a_{30}=+0.546684071\)
\(a_{31}=+0.244276667\) \(a_{32}=+0.176776695\) \(a_{33}=-0.362544557\) \(a_{34}=-0.237089524\) \(a_{35}=+0.000000000\)
\(a_{36}=-0.395263382\) \(a_{37}=+0.501108055\) \(a_{38}=+0.903060236\) \(a_{39}=-0.374233603\) \(a_{40}=+0.597230741\)
\(a_{41}=+1.014129839\) \(a_{42}=+0.000000000\) \(a_{43}=+0.167575428\) \(a_{44}=-0.396065600\) \(a_{45}=-1.335376490\)
\(a_{46}=+0.174602520\) \(a_{47}=+0.581185665\) \(a_{48}=+0.114420615\) \(a_{49}=+0.000000000\) \(a_{50}=+1.310605777\)
\(a_{51}=-0.153458741\) \(a_{52}=-0.408835420\) \(a_{53}=-1.607316804\) \(a_{54}=-0.579468843\) \(a_{55}=-1.338086739\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.584515440\) \(a_{58}=-0.537556757\) \(a_{59}=+1.460367201\) \(a_{60}=+0.386564014\)
\(a_{61}=-0.404057457\) \(a_{62}=+0.172729688\) \(a_{63}=+0.000000000\) \(a_{64}=+0.125000000\) \(a_{65}=-1.381228904\)
\(a_{66}=-0.256357715\) \(a_{67}=-0.888203310\) \(a_{68}=-0.167647610\) \(a_{69}=+0.113013357\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.997461284\) \(a_{72}=-0.279493418\) \(a_{73}=-0.563204395\) \(a_{74}=+0.354336904\) \(a_{75}=+0.848303670\)
\(a_{76}=+0.638560016\) \(a_{77}=+0.000000000\) \(a_{78}=-0.264623118\) \(a_{79}=+0.877120338\) \(a_{80}=+0.422305907\)
\(a_{81}=+0.415459331\) \(a_{82}=+0.717098086\) \(a_{83}=+1.182900613\) \(a_{84}=+0.000000000\) \(a_{85}=-0.566388608\)
\(a_{86}=+0.118493721\) \(a_{87}=-0.347939386\) \(a_{88}=-0.280060671\) \(a_{89}=-1.613289929\) \(a_{90}=-0.944253771\)
\(a_{91}=+0.000000000\) \(a_{92}=+0.123462626\) \(a_{93}=+0.111801146\) \(a_{94}=+0.410960325\) \(a_{95}=+2.157341335\)
\(a_{96}=+0.080907593\) \(a_{97}=-1.350767387\) \(a_{98}=+0.000000000\) \(a_{99}=+0.626200915\) \(a_{100}=+0.926738232\)

Showing 100 of 718 available coefficients

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