Properties

Level $199$
Weight $0$
Character 199.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 199 \)
Weight: \( 0 \)
Character: 199.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 0.5342378472 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.241431681\) \(a_{3}=-0.672969831\) \(a_{4}=-0.941710743\) \(a_{5}=+0.704594441\)
\(a_{6}=-0.162476237\) \(a_{7}=-0.649090466\) \(a_{8}=-0.468790489\) \(a_{9}=-0.547111607\) \(a_{10}=+0.170111420\)
\(a_{11}=-0.624425287\) \(a_{12}=+0.633742919\) \(a_{13}=-1.283415019\) \(a_{14}=-0.156711002\) \(a_{15}=-0.474170803\)
\(a_{16}=+0.828529866\) \(a_{17}=+0.346282837\) \(a_{18}=-0.132090077\) \(a_{19}=-1.096610412\) \(a_{20}=-0.663524155\)
\(a_{21}=+0.436818300\) \(a_{22}=-0.150756046\) \(a_{23}=+0.206639435\) \(a_{24}=+0.315481855\) \(a_{25}=-0.503546669\)
\(a_{26}=-0.309857048\) \(a_{27}=+1.041159436\) \(a_{28}=+0.611255466\) \(a_{29}=+1.748905929\) \(a_{30}=-0.114479852\)
\(a_{31}=-0.760443132\) \(a_{32}=+0.668823850\) \(a_{33}=+0.420219379\) \(a_{34}=+0.083603648\) \(a_{35}=-0.457345533\)
\(a_{36}=+0.515220877\) \(a_{37}=-0.727668063\) \(a_{38}=-0.264756493\) \(a_{39}=+0.863699585\) \(a_{40}=-0.330307169\)
\(a_{41}=+1.261979142\) \(a_{42}=+0.105461775\) \(a_{43}=+1.956781309\) \(a_{44}=+0.588028000\) \(a_{45}=-0.385491796\)
\(a_{46}=+0.049889308\) \(a_{47}=-1.026712552\) \(a_{48}=-0.557575604\) \(a_{49}=-0.578681567\) \(a_{50}=-0.121572122\)
\(a_{51}=-0.233037897\) \(a_{52}=+1.208605711\) \(a_{53}=-1.535095773\) \(a_{54}=+0.251368875\) \(a_{55}=-0.439966589\)
\(a_{56}=+0.304287434\) \(a_{57}=+0.737985728\) \(a_{58}=+0.422241301\) \(a_{59}=-1.179379783\) \(a_{60}=+0.446531744\)
\(a_{61}=-1.327954200\) \(a_{62}=-0.183595066\) \(a_{63}=+0.355124930\) \(a_{64}=-0.667054601\) \(a_{65}=-0.904287089\)
\(a_{66}=+0.101454268\) \(a_{67}=+0.968817735\) \(a_{68}=-0.326098268\) \(a_{69}=-0.139062106\) \(a_{70}=-0.110417697\)
\(a_{71}=+0.919174873\) \(a_{72}=+0.256480718\) \(a_{73}=+0.493765162\) \(a_{74}=-0.175682128\) \(a_{75}=+0.338871727\)
\(a_{76}=+1.032689799\) \(a_{77}=+0.405308503\) \(a_{78}=+0.208524446\) \(a_{79}=-0.581914470\) \(a_{80}=+0.583777547\)
\(a_{81}=-0.153557281\) \(a_{82}=+0.304681733\) \(a_{83}=-0.708248920\) \(a_{84}=-0.411356490\) \(a_{85}=+0.243988955\)
\(a_{86}=+0.472429009\) \(a_{87}=-1.176960931\) \(a_{88}=+0.292724629\) \(a_{89}=-0.712729391\) \(a_{90}=-0.093069932\)
\(a_{91}=+0.833052455\) \(a_{92}=-0.194594582\) \(a_{93}=+0.511755292\) \(a_{94}=-0.247880944\) \(a_{95}=-0.772665606\)
\(a_{96}=-0.450098263\) \(a_{97}=-0.731189453\) \(a_{98}=-0.139712058\) \(a_{99}=+0.341630311\) \(a_{100}=+0.474195317\)

Showing 100 of 646 available coefficients

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