Properties

Level $3$
Weight $0$
Character 3.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 17.2883277697 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.152680359\) \(a_{3}=+0.577350269\) \(a_{4}=-0.976688708\) \(a_{5}=-1.634879497\)
\(a_{6}=+0.088150046\) \(a_{7}=+0.434482807\) \(a_{8}=-0.301801542\) \(a_{9}=+0.333333333\) \(a_{10}=-0.249613988\)
\(a_{11}=+1.636999897\) \(a_{12}=-0.563891488\) \(a_{13}=-0.822168208\) \(a_{14}=+0.066336991\) \(a_{15}=-0.943898118\)
\(a_{16}=+0.930609540\) \(a_{17}=-0.048303864\) \(a_{18}=+0.050893453\) \(a_{19}=+1.126706349\) \(a_{20}=+1.596768344\)
\(a_{21}=+0.250848765\) \(a_{22}=+0.249937732\) \(a_{23}=+0.328711721\) \(a_{24}=-0.174245201\) \(a_{25}=+1.672830970\)
\(a_{26}=-0.125528937\) \(a_{27}=+0.192450090\) \(a_{28}=-0.424354451\) \(a_{29}=+0.278642558\) \(a_{30}=-0.144114703\)
\(a_{31}=-0.358950308\) \(a_{32}=+0.443887340\) \(a_{33}=+0.945122331\) \(a_{34}=-0.007375051\) \(a_{35}=-0.710327032\)
\(a_{36}=-0.325562903\) \(a_{37}=+0.050091933\) \(a_{38}=+0.172025930\) \(a_{39}=-0.474679036\) \(a_{40}=+0.493409152\)
\(a_{41}=+0.361013574\) \(a_{42}=+0.038299680\) \(a_{43}=+1.162884449\) \(a_{44}=-1.598839314\) \(a_{45}=-0.544959832\)
\(a_{46}=+0.050187824\) \(a_{47}=+0.423837682\) \(a_{48}=+0.537287669\) \(a_{49}=-0.811224691\) \(a_{50}=+0.255408433\)
\(a_{51}=-0.027888249\) \(a_{52}=+0.803002404\) \(a_{53}=+0.962108453\) \(a_{54}=+0.029383349\) \(a_{55}=-2.676297568\)
\(a_{56}=-0.131127581\) \(a_{57}=+0.650504214\) \(a_{58}=+0.042543246\) \(a_{59}=+0.274653225\) \(a_{60}=+0.921894633\)
\(a_{61}=-0.259824083\) \(a_{62}=-0.054804662\) \(a_{63}=+0.144827602\) \(a_{64}=-0.862836662\) \(a_{65}=+1.344145946\)
\(a_{66}=+0.144301617\) \(a_{67}=-1.841139871\) \(a_{68}=+0.047177838\) \(a_{69}=+0.189781800\) \(a_{70}=-0.108452986\)
\(a_{71}=+0.276514776\) \(a_{72}=-0.100600514\) \(a_{73}=+0.682153541\) \(a_{74}=+0.007648054\) \(a_{75}=+0.965809411\)
\(a_{76}=-1.100441368\) \(a_{77}=+0.711248309\) \(a_{78}=-0.072474166\) \(a_{79}=-0.194450646\) \(a_{80}=-1.521434457\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.055119682\) \(a_{83}=+0.672541225\) \(a_{84}=-0.245001156\) \(a_{85}=+0.078970996\)
\(a_{86}=+0.177549615\) \(a_{87}=+0.160874356\) \(a_{88}=-0.494049092\) \(a_{89}=+1.722264994\) \(a_{90}=-0.083204663\)
\(a_{91}=-0.357217950\) \(a_{92}=-0.321049026\) \(a_{93}=-0.207240057\) \(a_{94}=+0.064711689\) \(a_{95}=-1.842029109\)
\(a_{96}=+0.256278475\) \(a_{97}=+1.044479427\) \(a_{98}=-0.123858077\) \(a_{99}=+0.545666632\) \(a_{100}=-1.633835118\)

Showing 100 of 1228 available coefficients

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