Properties

Level $10$
Weight $0$
Character 10.1
Symmetry odd
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 20.1661566994 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.370989115\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.262328919\) \(a_{7}=-0.160619136\) \(a_{8}=-0.353553391\) \(a_{9}=-0.862367077\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.119386324\) \(a_{12}=-0.185494557\) \(a_{13}=-0.312623967\) \(a_{14}=+0.113574880\) \(a_{15}=+0.165911376\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.352270783\) \(a_{18}=+0.609785608\) \(a_{19}=+0.718801390\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.059587951\) \(a_{22}=-0.791525660\) \(a_{23}=-1.059709829\) \(a_{24}=+0.131164459\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.221058527\) \(a_{27}=+0.690917913\) \(a_{28}=-0.080309568\) \(a_{29}=+0.149689607\) \(a_{30}=-0.117317059\)
\(a_{31}=+0.084193542\) \(a_{32}=-0.176776695\) \(a_{33}=-0.415280142\) \(a_{34}=+0.249093059\) \(a_{35}=+0.071831061\)
\(a_{36}=-0.431183538\) \(a_{37}=-0.388010132\) \(a_{38}=-0.508269337\) \(a_{39}=+0.115980089\) \(a_{40}=+0.158113883\)
\(a_{41}=+1.921356200\) \(a_{42}=-0.042135044\) \(a_{43}=+0.778202025\) \(a_{44}=+0.559693162\) \(a_{45}=+0.385662281\)
\(a_{46}=+0.749328006\) \(a_{47}=-0.020917448\) \(a_{48}=-0.092747279\) \(a_{49}=-0.974201493\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.130688626\) \(a_{52}=-0.156311984\) \(a_{53}=+1.359795003\) \(a_{54}=-0.488552742\) \(a_{55}=-0.500604783\)
\(a_{56}=+0.056787440\) \(a_{57}=-0.266667492\) \(a_{58}=-0.105846536\) \(a_{59}=+0.586972867\) \(a_{60}=+0.082955688\)
\(a_{61}=+1.312105434\) \(a_{62}=-0.059533825\) \(a_{63}=+0.138512655\) \(a_{64}=+0.125000000\) \(a_{65}=+0.139809689\)
\(a_{66}=+0.293647404\) \(a_{67}=+0.530601644\) \(a_{68}=-0.176135391\) \(a_{69}=+0.393140811\) \(a_{70}=-0.050792230\)
\(a_{71}=-0.453792407\) \(a_{72}=+0.304892804\) \(a_{73}=+1.408753543\) \(a_{74}=+0.274364596\) \(a_{75}=-0.074197823\)
\(a_{76}=+0.359400695\) \(a_{77}=-0.179794864\) \(a_{78}=-0.082010307\) \(a_{79}=-1.266713840\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.606044051\) \(a_{82}=-1.358603998\) \(a_{83}=-1.580499801\) \(a_{84}=+0.029793976\) \(a_{85}=+0.157540283\)
\(a_{86}=-0.550271929\) \(a_{87}=-0.055533215\) \(a_{88}=-0.395762830\) \(a_{89}=-0.742770993\) \(a_{90}=-0.272704414\)
\(a_{91}=+0.050213392\) \(a_{92}=-0.529854914\) \(a_{93}=-0.031234888\) \(a_{94}=+0.014790869\) \(a_{95}=-0.321457754\)
\(a_{96}=+0.065582230\) \(a_{97}=-0.658441319\) \(a_{98}=+0.688864482\) \(a_{99}=-0.965321912\) \(a_{100}=+0.099975586\)

Showing 100 of 198 available coefficients

Rows: Cols: