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: \( 23.6178443809 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.107082634\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.075718857\) \(a_{7}=-1.860505461\) \(a_{8}=-0.353553391\) \(a_{9}=-0.988533310\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.383613160\) \(a_{12}=-0.053541317\) \(a_{13}=-1.561609805\) \(a_{14}=+1.315576028\) \(a_{15}=+0.047888810\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.192318527\) \(a_{18}=+0.698998607\) \(a_{19}=+1.196147820\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.199227825\) \(a_{22}=-0.271255467\) \(a_{23}=+1.274990482\) \(a_{24}=+0.037859428\) \(a_{25}=+0.199951172\)
\(a_{26}=+1.104224883\) \(a_{27}=+0.212937384\) \(a_{28}=-0.930252731\) \(a_{29}=+0.114787185\) \(a_{30}=-0.033862502\)
\(a_{31}=-0.261505154\) \(a_{32}=-0.176776695\) \(a_{33}=-0.041078308\) \(a_{34}=-0.843096516\) \(a_{35}=+0.832043337\)
\(a_{36}=-0.494266655\) \(a_{37}=+0.754995881\) \(a_{38}=-0.845804235\) \(a_{39}=+0.167221291\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.292881290\) \(a_{42}=-0.140875346\) \(a_{43}=+0.757477617\) \(a_{44}=+0.191806580\) \(a_{45}=+0.442085536\)
\(a_{46}=-0.901554415\) \(a_{47}=-1.567525052\) \(a_{48}=-0.026770658\) \(a_{49}=+2.461480571\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.127676608\) \(a_{52}=-0.780804902\) \(a_{53}=-1.515676734\) \(a_{54}=-0.150569468\) \(a_{55}=-0.171557021\)
\(a_{56}=+0.657788014\) \(a_{57}=-0.128086659\) \(a_{58}=-0.081166797\) \(a_{59}=+1.029344738\) \(a_{60}=+0.023944405\)
\(a_{61}=+0.828792801\) \(a_{62}=+0.184912068\) \(a_{63}=+1.839171621\) \(a_{64}=+0.125000000\) \(a_{65}=+0.698373136\)
\(a_{66}=+0.029046750\) \(a_{67}=-0.303780239\) \(a_{68}=+0.596159264\) \(a_{69}=-0.136529339\) \(a_{70}=-0.588343486\)
\(a_{71}=-0.460341797\) \(a_{72}=+0.349499303\) \(a_{73}=+1.354839079\) \(a_{74}=-0.533862707\) \(a_{75}=-0.021416527\)
\(a_{76}=+0.598073910\) \(a_{77}=-0.713714379\) \(a_{78}=-0.118243309\) \(a_{79}=-0.667295787\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.965731414\) \(a_{82}=+0.207098346\) \(a_{83}=-0.997208760\) \(a_{84}=+0.099613912\) \(a_{85}=-0.533221055\)
\(a_{86}=-0.535617560\) \(a_{87}=-0.012291714\) \(a_{88}=-0.135627733\) \(a_{89}=+0.494488000\) \(a_{90}=-0.312601680\)
\(a_{91}=+2.905383570\) \(a_{92}=+0.637495241\) \(a_{93}=+0.028002661\) \(a_{94}=+1.108407594\) \(a_{95}=-0.534933568\)
\(a_{96}=+0.018929714\) \(a_{97}=+1.849355644\) \(a_{98}=-1.740529604\) \(a_{99}=-0.379214387\) \(a_{100}=+0.099975586\)

Showing 100 of 218 available coefficients

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