Properties

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

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 23.4039248757 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.508738191\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.359732224\) \(a_{7}=+1.543283906\) \(a_{8}=+0.353553391\) \(a_{9}=-0.741185453\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.909538681\) \(a_{12}=-0.254369095\) \(a_{13}=-1.490485325\) \(a_{14}=+1.091266515\) \(a_{15}=-0.227514635\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.852819980\) \(a_{18}=-0.524097260\) \(a_{19}=+1.770909039\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.785127462\) \(a_{22}=+0.643140969\) \(a_{23}=+0.020955625\) \(a_{24}=-0.179866112\) \(a_{25}=+0.199951172\)
\(a_{26}=-1.053932281\) \(a_{27}=+0.885807537\) \(a_{28}=+0.771641953\) \(a_{29}=+1.321776948\) \(a_{30}=-0.160877141\)
\(a_{31}=-0.649452866\) \(a_{32}=+0.176776695\) \(a_{33}=-0.462717063\) \(a_{34}=+0.603034791\) \(a_{35}=+0.690177544\)
\(a_{36}=-0.370592727\) \(a_{37}=-0.035049557\) \(a_{38}=+1.252221790\) \(a_{39}=+0.758266807\) \(a_{40}=+0.158113883\)
\(a_{41}=-1.233519769\) \(a_{42}=-0.555168952\) \(a_{43}=-1.547544687\) \(a_{44}=+0.454769341\) \(a_{45}=-0.331468212\)
\(a_{46}=+0.014817864\) \(a_{47}=-1.448845750\) \(a_{48}=-0.127184548\) \(a_{49}=+1.381725214\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.433862094\) \(a_{52}=-0.745242662\) \(a_{53}=-0.037534815\) \(a_{54}=+0.626360516\) \(a_{55}=+0.406758064\)
\(a_{56}=+0.545633258\) \(a_{57}=-0.900929060\) \(a_{58}=+0.934637443\) \(a_{59}=+0.174361816\) \(a_{60}=-0.113757318\)
\(a_{61}=+1.693994847\) \(a_{62}=-0.459232526\) \(a_{63}=-1.143859582\) \(a_{64}=+0.125000000\) \(a_{65}=-0.666565301\)
\(a_{66}=-0.327190373\) \(a_{67}=+0.975944981\) \(a_{68}=+0.426409990\) \(a_{69}=-0.010660927\) \(a_{70}=+0.488029222\)
\(a_{71}=+1.317097172\) \(a_{72}=-0.262048630\) \(a_{73}=+0.606414931\) \(a_{74}=-0.024783779\) \(a_{75}=-0.101747638\)
\(a_{76}=+0.885454519\) \(a_{77}=+1.403676409\) \(a_{78}=+0.536175601\) \(a_{79}=-1.232649255\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.290541330\) \(a_{82}=-0.872230193\) \(a_{83}=+1.175426446\) \(a_{84}=-0.392563731\) \(a_{85}=+0.381392690\)
\(a_{86}=-1.094279343\) \(a_{87}=-0.672438413\) \(a_{88}=+0.321570485\) \(a_{89}=+1.075713061\) \(a_{90}=-0.234383420\)
\(a_{91}=-2.300242014\) \(a_{92}=+0.010477812\) \(a_{93}=+0.330401476\) \(a_{94}=-1.024488655\) \(a_{95}=+0.791974598\)
\(a_{96}=-0.089933056\) \(a_{97}=-0.235846392\) \(a_{98}=+0.977027269\) \(a_{99}=-0.674136840\) \(a_{100}=+0.099975586\)

Showing 100 of 217 available coefficients

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