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: \( 13.8721865958 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.835362068\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.590690183\) \(a_{7}=+1.442301480\) \(a_{8}=-0.353553391\) \(a_{9}=-0.302170215\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.972345870\) \(a_{12}=+0.417681034\) \(a_{13}=+1.762608324\) \(a_{14}=-1.019861157\) \(a_{15}=+0.373585274\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.193182237\) \(a_{18}=+0.213666608\) \(a_{19}=-1.681027127\) \(a_{20}=+0.223606798\)
\(a_{21}=+1.204843947\) \(a_{22}=-0.687552358\) \(a_{23}=-0.307376327\) \(a_{24}=-0.295345091\) \(a_{25}=+0.199951172\)
\(a_{26}=-1.246352298\) \(a_{27}=-1.087783604\) \(a_{28}=+0.721150740\) \(a_{29}=-0.428235328\) \(a_{30}=-0.264164681\)
\(a_{31}=-0.794710951\) \(a_{32}=-0.176776695\) \(a_{33}=+0.812260857\) \(a_{34}=-0.843707251\) \(a_{35}=+0.645016831\)
\(a_{36}=-0.151085108\) \(a_{37}=+1.188805295\) \(a_{38}=+1.188665681\) \(a_{39}=+1.472416134\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.584888379\) \(a_{42}=-0.851953325\) \(a_{43}=+1.028181167\) \(a_{44}=+0.486172935\) \(a_{45}=-0.135134629\)
\(a_{46}=+0.217347885\) \(a_{47}=+1.142440766\) \(a_{48}=+0.208840517\) \(a_{49}=+1.080233560\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.996739181\) \(a_{52}=+0.881304162\) \(a_{53}=-0.873143218\) \(a_{54}=+0.769179163\) \(a_{55}=+0.434846293\)
\(a_{56}=-0.509930579\) \(a_{57}=-1.404266297\) \(a_{58}=+0.302808104\) \(a_{59}=-0.383693085\) \(a_{60}=+0.186792637\)
\(a_{61}=+0.499472345\) \(a_{62}=+0.561945502\) \(a_{63}=-0.435820549\) \(a_{64}=+0.125000000\) \(a_{65}=+0.788262406\)
\(a_{66}=-0.574355160\) \(a_{67}=+1.227128998\) \(a_{68}=+0.596591119\) \(a_{69}=-0.256770524\) \(a_{70}=-0.456095775\)
\(a_{71}=-0.197686541\) \(a_{72}=+0.106833304\) \(a_{73}=+0.509624246\) \(a_{74}=-0.840612285\) \(a_{75}=+0.167072414\)
\(a_{76}=-0.840513564\) \(a_{77}=+1.402415888\) \(a_{78}=-1.041155433\) \(a_{79}=-0.478993592\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.606522946\) \(a_{82}=+0.413578539\) \(a_{83}=+0.157741733\) \(a_{84}=+0.602421974\) \(a_{85}=+0.533607318\)
\(a_{86}=-0.727033876\) \(a_{87}=-0.357731549\) \(a_{88}=-0.343776179\) \(a_{89}=+0.742093672\) \(a_{90}=+0.095554612\)
\(a_{91}=+2.542212596\) \(a_{92}=-0.153688164\) \(a_{93}=-0.663871385\) \(a_{94}=-0.807827613\) \(a_{95}=-0.751778186\)
\(a_{96}=-0.147672546\) \(a_{97}=+0.718567615\) \(a_{98}=-0.763840476\) \(a_{99}=-0.293813951\) \(a_{100}=+0.099975586\)

Showing 100 of 169 available coefficients

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