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: \( 29.9953210933 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.730632429\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.516635145\) \(a_{7}=-1.592100219\) \(a_{8}=+0.353553391\) \(a_{9}=-0.466176253\) \(a_{10}=-0.316227766\)
\(a_{11}=-1.267127800\) \(a_{12}=+0.365316215\) \(a_{13}=-0.372047891\) \(a_{14}=-1.125784861\) \(a_{15}=-0.326748756\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.200072999\) \(a_{18}=-0.329636390\) \(a_{19}=-1.010667697\) \(a_{20}=-0.223606798\)
\(a_{21}=-1.163240051\) \(a_{22}=-0.895994660\) \(a_{23}=+1.392481750\) \(a_{24}=+0.258317573\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.263077587\) \(a_{27}=-1.071235918\) \(a_{28}=-0.796050110\) \(a_{29}=-0.734860736\) \(a_{30}=-0.231046261\)
\(a_{31}=+0.152572868\) \(a_{32}=+0.176776695\) \(a_{33}=-0.925804662\) \(a_{34}=-0.141472974\) \(a_{35}=+0.712008863\)
\(a_{36}=-0.233088127\) \(a_{37}=+1.135511371\) \(a_{38}=-0.714649982\) \(a_{39}=-0.271830254\) \(a_{40}=-0.158113883\)
\(a_{41}=-1.251177736\) \(a_{42}=-0.822534928\) \(a_{43}=+1.305469310\) \(a_{44}=-0.633563900\) \(a_{45}=+0.208480358\)
\(a_{46}=+0.984633288\) \(a_{47}=-1.478656245\) \(a_{48}=+0.182658107\) \(a_{49}=+1.534783108\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.146179821\) \(a_{52}=-0.186023945\) \(a_{53}=+0.329144699\) \(a_{54}=-0.757478182\) \(a_{55}=+0.566676779\)
\(a_{56}=-0.562892431\) \(a_{57}=-0.738426595\) \(a_{58}=-0.519625010\) \(a_{59}=+0.517424514\) \(a_{60}=-0.163374378\)
\(a_{61}=+1.414560924\) \(a_{62}=+0.107885309\) \(a_{63}=+0.742199315\) \(a_{64}=+0.125000000\) \(a_{65}=+0.166384875\)
\(a_{66}=-0.654642755\) \(a_{67}=+0.555496833\) \(a_{68}=-0.100036499\) \(a_{69}=+1.017392324\) \(a_{70}=+0.503466296\)
\(a_{71}=-0.263513692\) \(a_{72}=-0.164818195\) \(a_{73}=+0.241470306\) \(a_{74}=+0.802927791\) \(a_{75}=+0.146126486\)
\(a_{76}=-0.505333849\) \(a_{77}=+2.017394448\) \(a_{78}=-0.192213016\) \(a_{79}=+1.013035292\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.316503447\) \(a_{82}=-0.884716262\) \(a_{83}=-1.596397286\) \(a_{84}=-0.581620025\) \(a_{85}=+0.089475365\)
\(a_{86}=+0.923106202\) \(a_{87}=-0.536913085\) \(a_{88}=-0.447997330\) \(a_{89}=+0.328097797\) \(a_{90}=+0.147417875\)
\(a_{91}=+0.592337528\) \(a_{92}=+0.696240875\) \(a_{93}=+0.111474685\) \(a_{94}=-1.045567858\) \(a_{95}=+0.451984335\)
\(a_{96}=+0.129158786\) \(a_{97}=-0.996303214\) \(a_{98}=+1.085255543\) \(a_{99}=+0.590704890\) \(a_{100}=+0.099975586\)

Showing 100 of 238 available coefficients

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