Properties

Level $13$
Weight $0$
Character 13.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 13 \)
Weight: \( 0 \)
Character: 13.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 6.26632820327 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.369871617\) \(a_{3}=+1.220991218\) \(a_{4}=+0.876548248\) \(a_{5}=+0.477800889\)
\(a_{6}=+1.672601214\) \(a_{7}=+0.273233038\) \(a_{8}=-0.169113051\) \(a_{9}=+0.490819554\) \(a_{10}=+0.654525877\)
\(a_{11}=+1.529314301\) \(a_{12}=+1.070257713\) \(a_{13}=-0.277350098\) \(a_{14}=+0.374294184\) \(a_{15}=+0.583390690\)
\(a_{16}=-1.108211417\) \(a_{17}=-1.169083331\) \(a_{18}=+0.672359776\) \(a_{19}=+0.691780319\) \(a_{20}=+0.418815532\)
\(a_{21}=+0.333615140\) \(a_{22}=+2.094964256\) \(a_{23}=-1.047959667\) \(a_{24}=-0.206485550\) \(a_{25}=-0.771706310\)
\(a_{26}=-0.379934027\) \(a_{27}=-0.621704853\) \(a_{28}=+0.239501941\) \(a_{29}=+0.152822560\) \(a_{30}=+0.799170348\)
\(a_{31}=+0.540148664\) \(a_{32}=-1.348994315\) \(a_{33}=+1.867279331\) \(a_{34}=-1.601494073\) \(a_{35}=+0.130550989\)
\(a_{36}=+0.430227020\) \(a_{37}=-1.555647330\) \(a_{38}=+0.947650225\) \(a_{39}=-0.338642034\) \(a_{40}=-0.080802366\)
\(a_{41}=+0.144046491\) \(a_{42}=+0.457009911\) \(a_{43}=+1.082750963\) \(a_{44}=+1.340517772\) \(a_{45}=+0.234514019\)
\(a_{46}=-1.435570204\) \(a_{47}=+1.451450768\) \(a_{48}=-1.353116407\) \(a_{49}=-0.925343707\) \(a_{50}=-1.057138571\)
\(a_{51}=-1.427440480\) \(a_{52}=-0.243110743\) \(a_{53}=+1.768767162\) \(a_{54}=-0.851655833\) \(a_{55}=+0.730707733\)
\(a_{56}=-0.046207273\) \(a_{57}=+0.844657695\) \(a_{58}=+0.209347287\) \(a_{59}=-0.454471940\) \(a_{60}=+0.511370087\)
\(a_{61}=-0.722379205\) \(a_{62}=+0.739934323\) \(a_{63}=+0.134108118\) \(a_{64}=-0.739737607\) \(a_{65}=-0.132518124\)
\(a_{66}=+2.557932958\) \(a_{67}=+1.399596505\) \(a_{68}=-1.024757945\) \(a_{69}=-1.279549550\) \(a_{70}=+0.178838094\)
\(a_{71}=+0.770773219\) \(a_{72}=-0.083003992\) \(a_{73}=-1.347656019\) \(a_{74}=-2.131037125\) \(a_{75}=-0.942246627\)
\(a_{76}=+0.606378827\) \(a_{77}=+0.417859193\) \(a_{78}=-0.463896111\) \(a_{79}=+1.437359317\) \(a_{80}=-0.529504400\)
\(a_{81}=-1.249915719\) \(a_{82}=+0.197325200\) \(a_{83}=+1.198808407\) \(a_{84}=+0.292429766\) \(a_{85}=-0.558589055\)
\(a_{86}=+1.483229813\) \(a_{87}=+0.186595003\) \(a_{88}=-0.258627007\) \(a_{89}=+0.431112577\) \(a_{90}=+0.321254099\)
\(a_{91}=-0.075781210\) \(a_{92}=-0.918587210\) \(a_{93}=+0.659516775\) \(a_{94}=+1.988301211\) \(a_{95}=+0.330533252\)
\(a_{96}=-1.647110211\) \(a_{97}=+0.225809386\) \(a_{98}=-1.267602080\) \(a_{99}=+0.750617363\) \(a_{100}=-0.676437814\)

Showing 100 of 546 available coefficients

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