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: \( 20.3060013567 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.577895620\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+1.115740693\) \(a_{7}=-0.193904989\) \(a_{8}=+0.353553391\) \(a_{9}=+1.489754587\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.157108068\) \(a_{12}=+0.788947810\) \(a_{13}=+1.107617322\) \(a_{14}=-0.137111532\) \(a_{15}=-0.705656373\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.690776997\) \(a_{18}=+1.053415571\) \(a_{19}=-1.244859738\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.305961832\) \(a_{22}=+0.111092180\) \(a_{23}=-1.138872929\) \(a_{24}=+0.557870346\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.783203719\) \(a_{27}=+0.772781618\) \(a_{28}=-0.096952494\) \(a_{29}=+1.262460519\) \(a_{30}=-0.498974407\)
\(a_{31}=+1.034339427\) \(a_{32}=+0.176776695\) \(a_{33}=+0.247900132\) \(a_{34}=+1.195559880\) \(a_{35}=+0.086716947\)
\(a_{36}=+0.744877294\) \(a_{37}=-0.134814495\) \(a_{38}=-0.880248762\) \(a_{39}=+1.747704520\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.698619400\) \(a_{42}=-0.216347686\) \(a_{43}=+0.488973082\) \(a_{44}=+0.078554034\) \(a_{45}=-0.666238505\)
\(a_{46}=-0.805304771\) \(a_{47}=+1.469605081\) \(a_{48}=+0.394473905\) \(a_{49}=-0.962400855\) \(a_{50}=+0.141421356\)
\(a_{51}=+2.667869618\) \(a_{52}=+0.553808661\) \(a_{53}=+1.294662879\) \(a_{54}=+0.546439122\) \(a_{55}=-0.070260864\)
\(a_{56}=-0.068555766\) \(a_{57}=-1.964258727\) \(a_{58}=+0.892694394\) \(a_{59}=-0.433324174\) \(a_{60}=-0.352828187\)
\(a_{61}=+0.460180489\) \(a_{62}=+0.731388423\) \(a_{63}=-0.288870846\) \(a_{64}=+0.125000000\) \(a_{65}=-0.495341525\)
\(a_{66}=+0.175291865\) \(a_{67}=-0.135301650\) \(a_{68}=+0.845388499\) \(a_{69}=-1.797022606\) \(a_{70}=+0.061318141\)
\(a_{71}=-1.655753322\) \(a_{72}=+0.526707785\) \(a_{73}=-0.954304227\) \(a_{74}=-0.095328244\) \(a_{75}=+0.315579124\)
\(a_{76}=-0.622429869\) \(a_{77}=-0.030464038\) \(a_{78}=+1.235813718\) \(a_{79}=+1.880997194\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.270385857\) \(a_{82}=+0.493998515\) \(a_{83}=-0.146443046\) \(a_{84}=-0.152980916\) \(a_{85}=-0.756138460\)
\(a_{86}=+0.345756182\) \(a_{87}=+1.992030922\) \(a_{88}=+0.055546090\) \(a_{89}=+1.639588768\) \(a_{90}=-0.471101765\)
\(a_{91}=-0.214772524\) \(a_{92}=-0.569436464\) \(a_{93}=+1.632079651\) \(a_{94}=+1.039167718\) \(a_{95}=+0.556718199\)
\(a_{96}=+0.278935173\) \(a_{97}=-1.052460254\) \(a_{98}=-0.680520171\) \(a_{99}=+0.234052465\) \(a_{100}=+0.099975586\)

Showing 100 of 192 available coefficients

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