Properties

Level $10$
Weight $0$
Character 10.1
Symmetry even
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 28.6669629702 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.384840761\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.979230293\) \(a_{7}=+0.377846806\) \(a_{8}=-0.353553391\) \(a_{9}=+0.917783932\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.594522498\) \(a_{12}=+0.692420380\) \(a_{13}=-0.370933265\) \(a_{14}=-0.267178039\) \(a_{15}=+0.619319616\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.049706857\) \(a_{18}=-0.648971242\) \(a_{19}=-0.021344576\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.523257658\) \(a_{22}=-0.420390890\) \(a_{23}=-1.130286017\) \(a_{24}=-0.489615146\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.262289427\) \(a_{27}=-0.113856162\) \(a_{28}=+0.188923403\) \(a_{29}=+0.107467285\) \(a_{30}=-0.437925100\)
\(a_{31}=+0.249310168\) \(a_{32}=-0.176776695\) \(a_{33}=+0.823318988\) \(a_{34}=+0.742254837\) \(a_{35}=+0.168978229\)
\(a_{36}=+0.458891966\) \(a_{37}=+0.514335304\) \(a_{38}=+0.015092894\) \(a_{39}=-0.513683505\) \(a_{40}=-0.158113883\)
\(a_{41}=-1.615076428\) \(a_{42}=-0.369999038\) \(a_{43}=-0.893277950\) \(a_{44}=+0.297261249\) \(a_{45}=+0.410445452\)
\(a_{46}=+0.799232907\) \(a_{47}=+1.344613619\) \(a_{48}=+0.346210190\) \(a_{49}=-0.857231791\) \(a_{50}=-0.141421356\)
\(a_{51}=-1.453676841\) \(a_{52}=-0.185466633\) \(a_{53}=+0.138110710\) \(a_{54}=+0.080508464\) \(a_{55}=+0.265878544\)
\(a_{56}=-0.133589019\) \(a_{57}=-0.029558839\) \(a_{58}=-0.075990846\) \(a_{59}=-0.809379759\) \(a_{60}=+0.309659808\)
\(a_{61}=-1.787853386\) \(a_{62}=-0.176288911\) \(a_{63}=+0.346781727\) \(a_{64}=+0.125000000\) \(a_{65}=-0.165886399\)
\(a_{66}=-0.582174440\) \(a_{67}=-0.996681221\) \(a_{68}=-0.524853428\) \(a_{69}=-1.565266147\) \(a_{70}=-0.119485651\)
\(a_{71}=-0.098994434\) \(a_{72}=-0.324485621\) \(a_{73}=-1.526874956\) \(a_{74}=-0.363689981\) \(a_{75}=+0.276968152\)
\(a_{76}=-0.010672288\) \(a_{77}=+0.224638427\) \(a_{78}=+0.363229090\) \(a_{79}=+0.377156312\) \(a_{80}=+0.111803399\)
\(a_{81}=-1.075456586\) \(a_{82}=+1.142031494\) \(a_{83}=-1.272820552\) \(a_{84}=+0.261628829\) \(a_{85}=-0.469443178\)
\(a_{86}=+0.631642896\) \(a_{87}=+0.148825076\) \(a_{88}=-0.210195445\) \(a_{89}=+1.182966506\) \(a_{90}=-0.290228762\)
\(a_{91}=-0.140155949\) \(a_{92}=-0.565143008\) \(a_{93}=+0.345254883\) \(a_{94}=-0.950785408\) \(a_{95}=-0.009545585\)
\(a_{96}=-0.244807573\) \(a_{97}=+1.296378073\) \(a_{98}=+0.606154413\) \(a_{99}=+0.545643196\) \(a_{100}=+0.099975586\)

Showing 100 of 226 available coefficients

Rows: Cols: