Properties

Level $23$
Weight $0$
Character 23.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 23 \)
Weight: \( 0 \)
Character: 23.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 4.16025275662 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.267143567\) \(a_{3}=-0.984761864\) \(a_{4}=+0.605652820\) \(a_{5}=-1.739706864\)
\(a_{6}=+1.247834662\) \(a_{7}=-1.120584298\) \(a_{8}=+0.499694492\) \(a_{9}=-0.030244070\) \(a_{10}=+2.204458361\)
\(a_{11}=-0.169642009\) \(a_{12}=-0.596423800\) \(a_{13}=-0.701420453\) \(a_{14}=+1.419941185\) \(a_{15}=+1.713196975\)
\(a_{16}=-1.238837482\) \(a_{17}=+0.188489143\) \(a_{18}=+0.038323579\) \(a_{19}=-1.686301706\) \(a_{20}=-1.053658368\)
\(a_{21}=+1.103508682\) \(a_{22}=+0.214960780\) \(a_{23}=-0.208514414\) \(a_{24}=-0.492080080\) \(a_{25}=+2.026579972\)
\(a_{26}=+0.888800414\) \(a_{27}=+1.014545072\) \(a_{28}=-0.678685040\) \(a_{29}=-1.013996053\) \(a_{30}=-2.170866526\)
\(a_{31}=-0.637497120\) \(a_{32}=+1.070090453\) \(a_{33}=+0.167056981\) \(a_{34}=-0.238842805\) \(a_{35}=+1.949488195\)
\(a_{36}=-0.018317407\) \(a_{37}=-0.399068704\) \(a_{38}=+2.136786359\) \(a_{39}=+0.690732113\) \(a_{40}=-0.869321938\)
\(a_{41}=-0.833665090\) \(a_{42}=-1.398303928\) \(a_{43}=-1.640716802\) \(a_{44}=-0.102744161\) \(a_{45}=+0.052615817\)
\(a_{46}=+0.264217698\) \(a_{47}=+0.795106770\) \(a_{48}=+1.219959909\) \(a_{49}=+0.255709170\) \(a_{50}=-2.567967775\)
\(a_{51}=-0.185616922\) \(a_{52}=-0.424817274\) \(a_{53}=+0.997936334\) \(a_{54}=-1.285574261\) \(a_{55}=+0.295127364\)
\(a_{56}=-0.559949805\) \(a_{57}=+1.660605617\) \(a_{58}=+1.284878582\) \(a_{59}=+0.721879741\) \(a_{60}=+1.037602568\)
\(a_{61}=-0.610143694\) \(a_{62}=+0.807800396\) \(a_{63}=+0.033891030\) \(a_{64}=-0.117120754\) \(a_{65}=+1.220265974\)
\(a_{66}=-0.211685177\) \(a_{67}=-0.691946705\) \(a_{68}=+0.114158983\) \(a_{69}=+0.205337036\) \(a_{70}=-2.470281431\)
\(a_{71}=+0.470072957\) \(a_{72}=-0.015112789\) \(a_{73}=-0.612301661\) \(a_{74}=+0.505677340\) \(a_{75}=-1.995698686\)
\(a_{76}=-1.021313398\) \(a_{77}=+0.190098179\) \(a_{78}=-0.875256712\) \(a_{79}=-0.250265996\) \(a_{80}=+2.155214032\)
\(a_{81}=-0.968841256\) \(a_{82}=+1.056373316\) \(a_{83}=-1.305014514\) \(a_{84}=+0.668343149\) \(a_{85}=-0.327915854\)
\(a_{86}=+2.079023738\) \(a_{87}=+0.998544644\) \(a_{88}=-0.084769177\) \(a_{89}=-1.811156355\) \(a_{90}=-0.066671801\)
\(a_{91}=+0.786000750\) \(a_{92}=-0.126287341\) \(a_{93}=+0.627782835\) \(a_{94}=-1.007514413\) \(a_{95}=+2.933670655\)
\(a_{96}=-1.053784274\) \(a_{97}=-0.254541936\) \(a_{98}=-0.324020244\) \(a_{99}=+0.005130683\) \(a_{100}=+1.227403802\)

Showing 100 of 1500 available coefficients

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