Properties

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

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 14.712382788 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.027229133\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.726360686\) \(a_{7}=+0.711730782\) \(a_{8}=-0.353553391\) \(a_{9}=+0.055199692\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.372980515\) \(a_{12}=+0.513614566\) \(a_{13}=-1.869077700\) \(a_{14}=-0.503269662\) \(a_{15}=-0.459390834\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.581135046\) \(a_{18}=-0.039032076\) \(a_{19}=+0.344200820\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.731110594\) \(a_{22}=-0.970843833\) \(a_{23}=+0.269596354\) \(a_{24}=-0.363180343\) \(a_{25}=+0.199951172\)
\(a_{26}=+1.321637517\) \(a_{27}=-0.970526402\) \(a_{28}=+0.355865391\) \(a_{29}=+0.956618098\) \(a_{30}=+0.324838374\)
\(a_{31}=-0.228936717\) \(a_{32}=-0.176776695\) \(a_{33}=+1.410365584\) \(a_{34}=+1.118031313\) \(a_{35}=-0.318295682\)
\(a_{36}=+0.027599846\) \(a_{37}=+1.070843377\) \(a_{38}=-0.243386734\) \(a_{39}=-1.919971066\) \(a_{40}=+0.158113883\)
\(a_{41}=-1.522617021\) \(a_{42}=-0.516973259\) \(a_{43}=+0.119772103\) \(a_{44}=+0.686490258\) \(a_{45}=-0.024686053\)
\(a_{46}=-0.190633410\) \(a_{47}=-0.796719156\) \(a_{48}=+0.256807283\) \(a_{49}=-0.493439294\) \(a_{50}=-0.141421356\)
\(a_{51}=-1.624187982\) \(a_{52}=-0.934538850\) \(a_{53}=-1.063261891\) \(a_{54}=+0.686265800\) \(a_{55}=-0.614015553\)
\(a_{56}=-0.251634831\) \(a_{57}=+0.353573110\) \(a_{58}=-0.676431144\) \(a_{59}=-0.163568747\) \(a_{60}=-0.229695417\)
\(a_{61}=+0.494094954\) \(a_{62}=+0.161882705\) \(a_{63}=+0.039287320\) \(a_{64}=+0.125000000\) \(a_{65}=+0.835876959\)
\(a_{66}=-0.997279069\) \(a_{67}=-0.877421973\) \(a_{68}=-0.790567523\) \(a_{69}=+0.276937228\) \(a_{70}=+0.225069035\)
\(a_{71}=+0.333325625\) \(a_{72}=-0.019516038\) \(a_{73}=-1.195995496\) \(a_{74}=-0.757200614\) \(a_{75}=+0.205445827\)
\(a_{76}=+0.172100410\) \(a_{77}=+0.977192495\) \(a_{78}=+1.357624560\) \(a_{79}=-1.422799375\) \(a_{80}=-0.111803399\)
\(a_{81}=-1.052152686\) \(a_{82}=+1.076652821\) \(a_{83}=+0.089979268\) \(a_{84}=+0.365555297\) \(a_{85}=+0.707105089\)
\(a_{86}=-0.084691666\) \(a_{87}=+0.982665979\) \(a_{88}=-0.485421916\) \(a_{89}=-0.989122191\) \(a_{90}=+0.017455675\)
\(a_{91}=-1.330280137\) \(a_{92}=+0.134798177\) \(a_{93}=-0.235170468\) \(a_{94}=+0.563365518\) \(a_{95}=-0.153931286\)
\(a_{96}=-0.181590171\) \(a_{97}=-0.327359974\) \(a_{98}=+0.348914271\) \(a_{99}=+0.075788082\) \(a_{100}=+0.099975586\)

Showing 100 of 172 available coefficients

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