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: \( 28.3439938304 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.119514100\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.084509231\) \(a_{7}=-0.743662087\) \(a_{8}=+0.353553391\) \(a_{9}=-0.985716380\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.571398257\) \(a_{12}=+0.059757050\) \(a_{13}=-1.428195352\) \(a_{14}=-0.525848505\) \(a_{15}=-0.053448330\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.493006704\) \(a_{18}=-0.697006737\) \(a_{19}=+0.007855861\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.088878105\) \(a_{22}=-0.404039583\) \(a_{23}=-0.506285162\) \(a_{24}=+0.042254615\) \(a_{25}=+0.199951172\)
\(a_{26}=-1.009886618\) \(a_{27}=-0.237321106\) \(a_{28}=-0.371831044\) \(a_{29}=+0.584572779\) \(a_{30}=-0.037793677\)
\(a_{31}=+0.251416374\) \(a_{32}=+0.176776695\) \(a_{33}=-0.068290148\) \(a_{34}=-1.055715164\) \(a_{35}=+0.332575796\)
\(a_{36}=-0.492858190\) \(a_{37}=-0.758970165\) \(a_{38}=+0.005554933\) \(a_{39}=-0.170689482\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.947409236\) \(a_{42}=-0.062846311\) \(a_{43}=-0.261967120\) \(a_{44}=-0.285699129\) \(a_{45}=+0.440825766\)
\(a_{46}=-0.357997671\) \(a_{47}=+1.110544869\) \(a_{48}=+0.029878525\) \(a_{49}=-0.446966700\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.178435352\) \(a_{52}=-0.714097676\) \(a_{53}=+1.394648261\) \(a_{54}=-0.167811363\) \(a_{55}=+0.255537069\)
\(a_{56}=-0.262924252\) \(a_{57}=+0.000938886\) \(a_{58}=+0.413355376\) \(a_{59}=+0.294037718\) \(a_{60}=-0.026724165\)
\(a_{61}=-0.971232223\) \(a_{62}=+0.177778223\) \(a_{63}=+0.733039900\) \(a_{64}=+0.125000000\) \(a_{65}=+0.638708378\)
\(a_{66}=-0.048288427\) \(a_{67}=+1.481717348\) \(a_{68}=-0.746503352\) \(a_{69}=-0.060508215\) \(a_{70}=+0.235166600\)
\(a_{71}=-0.972286250\) \(a_{72}=-0.348503368\) \(a_{73}=-1.156019312\) \(a_{74}=-0.536672951\) \(a_{75}=+0.023902820\)
\(a_{76}=+0.003927931\) \(a_{77}=+0.424927221\) \(a_{78}=-0.120695690\) \(a_{79}=-1.361331396\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.957353162\) \(a_{82}=+0.669919495\) \(a_{83}=+1.299792922\) \(a_{84}=-0.044439053\) \(a_{85}=+0.667692896\)
\(a_{86}=-0.185238727\) \(a_{87}=+0.069864690\) \(a_{88}=-0.202019791\) \(a_{89}=+0.246715787\) \(a_{90}=+0.311710889\)
\(a_{91}=+1.062094736\) \(a_{92}=-0.253142581\) \(a_{93}=+0.030047802\) \(a_{94}=+0.785273808\) \(a_{95}=-0.003513248\)
\(a_{96}=+0.021127308\) \(a_{97}=+1.427680258\) \(a_{98}=-0.316053185\) \(a_{99}=+0.563236622\) \(a_{100}=+0.099975586\)

Showing 100 of 238 available coefficients

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