Properties

Level $65$
Weight $0$
Character 65.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 65 = 5 \cdot 13 \)
Weight: \( 0 \)
Character: 65.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 0.95822362039 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.373259225\) \(a_{3}=+0.646960373\) \(a_{4}=+0.885840898\) \(a_{5}=+0.447213596\)
\(a_{6}=-0.888444300\) \(a_{7}=-1.587550373\) \(a_{8}=+0.156770040\) \(a_{9}=-0.581442276\) \(a_{10}=-0.614140195\)
\(a_{11}=+0.247685919\) \(a_{12}=+0.573103958\) \(a_{13}=+0.277350098\) \(a_{14}=+2.180118194\) \(a_{15}=+0.289329475\)
\(a_{16}=-1.101126801\) \(a_{17}=+1.739818115\) \(a_{18}=+0.798470969\) \(a_{19}=+0.697215526\) \(a_{20}=+0.396160093\)
\(a_{21}=-1.027082181\) \(a_{22}=-0.340136973\) \(a_{23}=-0.407446171\) \(a_{24}=+0.101424003\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.380873581\) \(a_{27}=-1.023130485\) \(a_{28}=-1.406317048\) \(a_{29}=+0.168106592\) \(a_{30}=-0.397324370\)
\(a_{31}=+0.971978497\) \(a_{32}=+1.355362498\) \(a_{33}=+0.160242975\) \(a_{34}=-2.389221276\) \(a_{35}=-0.709974110\)
\(a_{36}=-0.515065348\) \(a_{37}=-1.066233442\) \(a_{38}=-0.957457652\) \(a_{39}=+0.179434523\) \(a_{40}=+0.070109693\)
\(a_{41}=+0.699502977\) \(a_{42}=+1.410450080\) \(a_{43}=+0.056033770\) \(a_{44}=+0.219410317\) \(a_{45}=-0.260028891\)
\(a_{46}=+0.559529212\) \(a_{47}=-0.192427710\) \(a_{48}=-0.712385406\) \(a_{49}=+1.520316187\) \(a_{50}=-0.274651845\)
\(a_{51}=+1.125593377\) \(a_{52}=+0.245688060\) \(a_{53}=+0.185029496\) \(a_{54}=+1.405023376\) \(a_{55}=+0.110768510\)
\(a_{56}=-0.248880335\) \(a_{57}=+0.451070816\) \(a_{58}=-0.230853928\) \(a_{59}=-1.028319116\) \(a_{60}=+0.256299882\)
\(a_{61}=+0.646545737\) \(a_{62}=-1.334778437\) \(a_{63}=+0.923068902\) \(a_{64}=-0.760137251\) \(a_{65}=+0.124034735\)
\(a_{66}=-0.220055143\) \(a_{67}=-1.579126352\) \(a_{68}=+1.541202042\) \(a_{69}=-0.263601526\) \(a_{70}=+0.974978496\)
\(a_{71}=-0.972576777\) \(a_{72}=-0.091152729\) \(a_{73}=-0.056144850\) \(a_{74}=+1.464214910\) \(a_{75}=+0.129392075\)
\(a_{76}=+0.617622027\) \(a_{77}=-0.393213873\) \(a_{78}=-0.246410114\) \(a_{79}=-1.660707002\) \(a_{80}=-0.492438876\)
\(a_{81}=-0.080482604\) \(a_{82}=-0.960598916\) \(a_{83}=+0.203132204\) \(a_{84}=-0.909831402\) \(a_{85}=+0.778070315\)
\(a_{86}=-0.076948892\) \(a_{87}=+0.108758303\) \(a_{88}=+0.038829731\) \(a_{89}=+1.156797643\) \(a_{90}=+0.357087073\)
\(a_{91}=-0.440307252\) \(a_{92}=-0.360932482\) \(a_{93}=+0.628831571\) \(a_{94}=+0.264253128\) \(a_{95}=+0.311804262\)
\(a_{96}=+0.876865827\) \(a_{97}=+1.323091289\) \(a_{98}=-2.087788228\) \(a_{99}=-0.144015064\) \(a_{100}=+0.177168180\)

Showing 100 of 418 available coefficients

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