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: \( 27.5885331611 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.442613703\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.312975151\) \(a_{7}=+0.541428788\) \(a_{8}=+0.353553391\) \(a_{9}=-0.804093110\) \(a_{10}=+0.316227766\)
\(a_{11}=-1.723360596\) \(a_{12}=+0.221306851\) \(a_{13}=-0.628866795\) \(a_{14}=+0.382847968\) \(a_{15}=+0.197942865\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.083695569\) \(a_{18}=-0.568579691\) \(a_{19}=+1.559808355\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.239643801\) \(a_{22}=-1.218599964\) \(a_{23}=+0.608110313\) \(a_{24}=+0.156487575\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.444675975\) \(a_{27}=-0.798516332\) \(a_{28}=+0.270714394\) \(a_{29}=-0.862352624\) \(a_{30}=+0.139966742\)
\(a_{31}=-0.064616888\) \(a_{32}=+0.176776695\) \(a_{33}=-0.762783015\) \(a_{34}=+0.766288485\) \(a_{35}=+0.242134315\)
\(a_{36}=-0.402046555\) \(a_{37}=-1.970960678\) \(a_{38}=+1.102951065\) \(a_{39}=-0.278345061\) \(a_{40}=+0.158113883\)
\(a_{41}=-1.386450907\) \(a_{42}=+0.169453757\) \(a_{43}=+0.780765837\) \(a_{44}=-0.861680298\) \(a_{45}=-0.359601371\)
\(a_{46}=+0.429998926\) \(a_{47}=+0.078417553\) \(a_{48}=+0.110653426\) \(a_{49}=-0.706854867\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.479658508\) \(a_{52}=-0.314433398\) \(a_{53}=-0.084022609\) \(a_{54}=-0.564636313\) \(a_{55}=-0.770710288\)
\(a_{56}=+0.191423984\) \(a_{57}=+0.690392552\) \(a_{58}=-0.609775388\) \(a_{59}=-0.854548952\) \(a_{60}=+0.098971433\)
\(a_{61}=-1.065590746\) \(a_{62}=-0.045691040\) \(a_{63}=-0.435359158\) \(a_{64}=+0.125000000\) \(a_{65}=-0.281237781\)
\(a_{66}=-0.539369042\) \(a_{67}=+1.558208928\) \(a_{68}=+0.541847784\) \(a_{69}=+0.269157958\) \(a_{70}=+0.171214816\)
\(a_{71}=+1.574239293\) \(a_{72}=-0.284289845\) \(a_{73}=-0.021430457\) \(a_{74}=-1.393679661\) \(a_{75}=+0.088522741\)
\(a_{76}=+0.779904178\) \(a_{77}=-0.933077039\) \(a_{78}=-0.196819680\) \(a_{79}=-1.283299562\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.450658840\) \(a_{82}=-0.980368838\) \(a_{83}=-1.188707634\) \(a_{84}=+0.119821900\) \(a_{85}=+0.484643392\)
\(a_{86}=+0.552084818\) \(a_{87}=-0.381689088\) \(a_{88}=-0.609299982\) \(a_{89}=-0.889071739\) \(a_{90}=-0.254276568\)
\(a_{91}=-0.340486587\) \(a_{92}=+0.304055157\) \(a_{93}=-0.028600320\) \(a_{94}=+0.055449584\) \(a_{95}=+0.697567503\)
\(a_{96}=+0.078243788\) \(a_{97}=-1.444892300\) \(a_{98}=-0.499821870\) \(a_{99}=+1.385742381\) \(a_{100}=+0.099975586\)

Showing 100 of 228 available coefficients

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