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: \( 20.5489421376 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.800324234\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.565914693\) \(a_{7}=+0.541120350\) \(a_{8}=+0.353553391\) \(a_{9}=-0.359481121\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.191877683\) \(a_{12}=+0.400162117\) \(a_{13}=-1.855769790\) \(a_{14}=+0.382629869\) \(a_{15}=+0.357915878\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.483355168\) \(a_{18}=-0.254191538\) \(a_{19}=-1.091077625\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.433071729\) \(a_{22}=+0.135678011\) \(a_{23}=-0.529937682\) \(a_{24}=+0.282957346\) \(a_{25}=+0.199951172\)
\(a_{26}=-1.312227403\) \(a_{27}=-1.088025686\) \(a_{28}=+0.270560175\) \(a_{29}=+0.094593995\) \(a_{30}=+0.253084744\)
\(a_{31}=-1.178538064\) \(a_{32}=+0.176776695\) \(a_{33}=+0.153564360\) \(a_{34}=-1.048890498\) \(a_{35}=+0.241996377\)
\(a_{36}=-0.179740561\) \(a_{37}=+1.091991107\) \(a_{38}=-0.771508388\) \(a_{39}=-1.485217535\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.047133181\) \(a_{42}=+0.306227956\) \(a_{43}=-0.531263017\) \(a_{44}=+0.095938841\) \(a_{45}=-0.160764845\)
\(a_{46}=-0.374722528\) \(a_{47}=+1.049220410\) \(a_{48}=+0.200081058\) \(a_{49}=-0.707188767\) \(a_{50}=+0.141421356\)
\(a_{51}=-1.187165088\) \(a_{52}=-0.927884895\) \(a_{53}=-1.394808090\) \(a_{54}=-0.769350341\) \(a_{55}=+0.085810308\)
\(a_{56}=+0.191314934\) \(a_{57}=-0.873215864\) \(a_{58}=+0.066888055\) \(a_{59}=+1.251477919\) \(a_{60}=+0.178957939\)
\(a_{61}=+0.232043452\) \(a_{62}=-0.833352257\) \(a_{63}=-0.194522550\) \(a_{64}=+0.125000000\) \(a_{65}=-0.829925480\)
\(a_{66}=+0.108586400\) \(a_{67}=+1.917259236\) \(a_{68}=-0.741677584\) \(a_{69}=-0.424121969\) \(a_{70}=+0.171117279\)
\(a_{71}=+1.045273264\) \(a_{72}=-0.127095769\) \(a_{73}=+1.616461313\) \(a_{74}=+0.772154317\) \(a_{75}=+0.160064847\)
\(a_{76}=-0.545538813\) \(a_{77}=+0.103828919\) \(a_{78}=-1.050207391\) \(a_{79}=+0.205760527\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.511292202\) \(a_{82}=-0.033328192\) \(a_{83}=-0.826556686\) \(a_{84}=+0.216535865\) \(a_{85}=-0.663376598\)
\(a_{86}=-0.375659682\) \(a_{87}=+0.075705866\) \(a_{88}=+0.067839005\) \(a_{89}=-0.865985829\) \(a_{90}=-0.113677912\)
\(a_{91}=-1.004194798\) \(a_{92}=-0.264968841\) \(a_{93}=-0.943212572\) \(a_{94}=+0.741910867\) \(a_{95}=-0.487944748\)
\(a_{96}=+0.141478673\) \(a_{97}=-0.560749669\) \(a_{98}=-0.500057973\) \(a_{99}=-0.068976405\) \(a_{100}=+0.099975586\)

Showing 100 of 196 available coefficients

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