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: \( 22.106362656 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.940314624\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.664902847\) \(a_{7}=+1.045275839\) \(a_{8}=-0.353553391\) \(a_{9}=-0.115808408\) \(a_{10}=-0.316227766\)
\(a_{11}=-1.286136928\) \(a_{12}=-0.470157312\) \(a_{13}=+0.328829515\) \(a_{14}=-0.739121634\) \(a_{15}=-0.420521484\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.689285137\) \(a_{18}=+0.081888910\) \(a_{19}=+0.566367216\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.982888157\) \(a_{22}=+0.909436143\) \(a_{23}=+0.293551675\) \(a_{24}=+0.332451424\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.232517580\) \(a_{27}=+1.049210963\) \(a_{28}=+0.522637919\) \(a_{29}=+1.644128917\) \(a_{30}=+0.297353593\)
\(a_{31}=-1.893336704\) \(a_{32}=-0.176776695\) \(a_{33}=+1.209373362\) \(a_{34}=-1.194504976\) \(a_{35}=+0.467461566\)
\(a_{36}=-0.057904204\) \(a_{37}=-1.514280728\) \(a_{38}=-0.400482099\) \(a_{39}=-0.309203202\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.112350610\) \(a_{42}=+0.695006881\) \(a_{43}=+0.785620364\) \(a_{44}=-0.643068464\) \(a_{45}=-0.051791094\)
\(a_{46}=-0.207572380\) \(a_{47}=+0.576810603\) \(a_{48}=-0.235078656\) \(a_{49}=+0.092601579\) \(a_{50}=-0.141421356\)
\(a_{51}=-1.588459519\) \(a_{52}=+0.164414758\) \(a_{53}=-0.520065443\) \(a_{54}=-0.741904187\) \(a_{55}=-0.575177920\)
\(a_{56}=-0.369560817\) \(a_{57}=-0.532563376\) \(a_{58}=-1.162574706\) \(a_{59}=+0.045649798\) \(a_{60}=-0.210260742\)
\(a_{61}=+0.817281355\) \(a_{62}=+1.338791223\) \(a_{63}=-0.121051730\) \(a_{64}=+0.125000000\) \(a_{65}=+0.147057030\)
\(a_{66}=-0.855156105\) \(a_{67}=-0.466410098\) \(a_{68}=+0.844642569\) \(a_{69}=-0.276030933\) \(a_{70}=-0.330545243\)
\(a_{71}=-1.171389230\) \(a_{72}=+0.040944455\) \(a_{73}=+1.002260467\) \(a_{74}=+1.070758171\) \(a_{75}=-0.188062925\)
\(a_{76}=+0.283183608\) \(a_{77}=-1.344367856\) \(a_{78}=+0.218639681\) \(a_{79}=-0.764971628\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.870780005\) \(a_{82}=+0.079443878\) \(a_{83}=-1.357200600\) \(a_{84}=-0.491444079\) \(a_{85}=+0.755471280\)
\(a_{86}=-0.555517487\) \(a_{87}=-1.545998465\) \(a_{88}=+0.454718072\) \(a_{89}=-0.197915386\) \(a_{90}=+0.036621834\)
\(a_{91}=+0.343717547\) \(a_{92}=+0.146775837\) \(a_{93}=+1.780332191\) \(a_{94}=-0.407866689\) \(a_{95}=+0.253287119\)
\(a_{96}=+0.166225712\) \(a_{97}=-0.126164771\) \(a_{98}=-0.065479204\) \(a_{99}=+0.148945470\) \(a_{100}=+0.099975586\)

Showing 100 of 210 available coefficients

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