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: \( 6.73532969117 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.626604979\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.443076629\) \(a_{7}=-1.825255500\) \(a_{8}=+0.353553390\) \(a_{9}=-0.607366200\) \(a_{10}=+0.316227765\)
\(a_{11}=-1.355624718\) \(a_{12}=-0.313302489\) \(a_{13}=+0.251544271\) \(a_{14}=-1.290650544\) \(a_{15}=-0.280226264\)
\(a_{16}=+0.249999999\) \(a_{17}=+0.872671510\) \(a_{18}=-0.429472756\) \(a_{19}=-0.222109790\) \(a_{20}=+0.223606795\)
\(a_{21}=+1.143714195\) \(a_{22}=-0.958571436\) \(a_{23}=-1.008662316\) \(a_{24}=-0.221538278\) \(a_{25}=+0.200000023\)
\(a_{26}=+0.177868536\) \(a_{27}=+1.007183707\) \(a_{28}=-0.912627471\) \(a_{29}=-0.326508634\) \(a_{30}=-0.198149893\)
\(a_{31}=+0.569947055\) \(a_{32}=+0.176776698\) \(a_{33}=+0.849441199\) \(a_{34}=+0.617071941\) \(a_{35}=-0.816279074\)
\(a_{36}=-0.303683101\) \(a_{37}=+0.135817981\) \(a_{38}=-0.157055333\) \(a_{39}=-0.157618884\) \(a_{40}=+0.158113874\)
\(a_{41}=-1.381462852\) \(a_{42}=+0.808728076\) \(a_{43}=-0.177454041\) \(a_{44}=-0.677812389\) \(a_{45}=-0.271622342\)
\(a_{46}=-0.713231950\) \(a_{47}=+1.590142916\) \(a_{48}=-0.156651144\) \(a_{49}=+2.331557649\) \(a_{50}=+0.141421152\)
\(a_{51}=-0.546820313\) \(a_{52}=+0.125772136\) \(a_{53}=-0.539420379\) \(a_{54}=+0.712186391\) \(a_{55}=-0.606253800\)
\(a_{56}=-0.645325255\) \(a_{57}=+0.139175086\) \(a_{58}=-0.230876249\) \(a_{59}=-1.402533145\) \(a_{60}=-0.140113150\)
\(a_{61}=-0.836142465\) \(a_{62}=+0.403013486\) \(a_{63}=+1.108598478\) \(a_{64}=+0.124999937\) \(a_{65}=+0.112494008\)
\(a_{66}=+0.600645680\) \(a_{67}=-0.164736564\) \(a_{68}=+0.436335677\) \(a_{69}=+0.632032958\) \(a_{70}=-0.577196315\)
\(a_{71}=-0.699660674\) \(a_{72}=-0.214736394\) \(a_{73}=+0.476022089\) \(a_{74}=+0.096037860\) \(a_{75}=-0.125320925\)
\(a_{76}=-0.111054909\) \(a_{77}=+2.474361521\) \(a_{78}=-0.111453315\) \(a_{79}=-1.617519874\) \(a_{80}=+0.111803253\)
\(a_{81}=-0.023739962\) \(a_{82}=-0.976841719\) \(a_{83}=-1.078679395\) \(a_{84}=+0.571856952\) \(a_{85}=+0.390270367\)
\(a_{86}=-0.125479069\) \(a_{87}=+0.204592014\) \(a_{88}=-0.479285652\) \(a_{89}=+0.575413047\) \(a_{90}=-0.192066097\)
\(a_{91}=-0.459132696\) \(a_{92}=-0.504331281\) \(a_{93}=-0.357131646\) \(a_{94}=+1.124401084\) \(a_{95}=-0.099330326\)
\(a_{96}=-0.110768999\) \(a_{97}=-0.401239615\) \(a_{98}=+1.648660142\) \(a_{99}=+0.823360574\) \(a_{100}=+0.099999966\)

Showing 100 of 2000 available coefficients

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