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: \( 18.6257215488 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.894790618\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.632712514\) \(a_{7}=+0.999309404\) \(a_{8}=-0.353553391\) \(a_{9}=-0.199349749\) \(a_{10}=-0.316227766\)
\(a_{11}=+1.160800684\) \(a_{12}=-0.447395309\) \(a_{13}=+1.775657768\) \(a_{14}=-0.706618456\) \(a_{15}=-0.400162530\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.521847867\) \(a_{18}=+0.140961560\) \(a_{19}=+1.676118854\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.894172679\) \(a_{22}=-0.820810035\) \(a_{23}=-0.070070945\) \(a_{24}=+0.316356257\) \(a_{25}=+0.199951172\)
\(a_{26}=-1.255579649\) \(a_{27}=+1.073166904\) \(a_{28}=+0.499654702\) \(a_{29}=-1.399605145\) \(a_{30}=+0.282957638\)
\(a_{31}=+0.580834181\) \(a_{32}=-0.176776695\) \(a_{33}=-1.038673562\) \(a_{34}=-1.076108946\) \(a_{35}=+0.446904751\)
\(a_{36}=-0.099674875\) \(a_{37}=-0.324920446\) \(a_{38}=-1.185195008\) \(a_{39}=-1.588841912\) \(a_{40}=-0.158113883\)
\(a_{41}=+1.191757896\) \(a_{42}=+0.632275565\) \(a_{43}=+0.562282170\) \(a_{44}=+0.580400342\) \(a_{45}=-0.089151918\)
\(a_{46}=+0.049547640\) \(a_{47}=-1.831547553\) \(a_{48}=-0.223697655\) \(a_{49}=-0.001380716\) \(a_{50}=-0.141421356\)
\(a_{51}=-1.361735193\) \(a_{52}=+0.887828884\) \(a_{53}=+0.018005132\) \(a_{54}=-0.758843595\) \(a_{55}=+0.519125847\)
\(a_{56}=-0.353309228\) \(a_{57}=-1.499775426\) \(a_{58}=+0.989670289\) \(a_{59}=-0.530169566\) \(a_{60}=-0.200081265\)
\(a_{61}=-0.434567315\) \(a_{62}=-0.410711788\) \(a_{63}=-0.199212079\) \(a_{64}=+0.125000000\) \(a_{65}=+0.794098295\)
\(a_{66}=+0.734453119\) \(a_{67}=-0.632545672\) \(a_{68}=+0.760923933\) \(a_{69}=+0.062698824\) \(a_{70}=-0.316009380\)
\(a_{71}=+1.214298543\) \(a_{72}=+0.070480780\) \(a_{73}=+0.400421149\) \(a_{74}=+0.229753451\) \(a_{75}=-0.178958124\)
\(a_{76}=+0.838059427\) \(a_{77}=+1.159999039\) \(a_{78}=+1.123480890\) \(a_{79}=+1.342261878\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.760909928\) \(a_{82}=-0.842700090\) \(a_{83}=+0.923748590\) \(a_{84}=-0.447086340\) \(a_{85}=+0.680591056\)
\(a_{86}=-0.397593535\) \(a_{87}=+1.252353553\) \(a_{88}=-0.410405018\) \(a_{89}=-0.062096582\) \(a_{90}=+0.063039926\)
\(a_{91}=+1.774431505\) \(a_{92}=-0.035035472\) \(a_{93}=-0.519724976\) \(a_{94}=+1.295099695\) \(a_{95}=+0.749583139\)
\(a_{96}=+0.158178128\) \(a_{97}=+0.316505368\) \(a_{98}=+0.000976314\) \(a_{99}=-0.231405325\) \(a_{100}=+0.099975586\)

Showing 100 of 190 available coefficients

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