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: \( 22.6952412757 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.354673889\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.957899093\) \(a_{7}=+0.417536846\) \(a_{8}=-0.353553391\) \(a_{9}=+0.835141345\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.803108678\) \(a_{12}=+0.677336944\) \(a_{13}=-0.271753419\) \(a_{14}=-0.295243135\) \(a_{15}=-0.605828581\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.612031608\) \(a_{18}=-0.590534108\) \(a_{19}=+1.675355345\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.565626262\) \(a_{22}=+0.567883592\) \(a_{23}=+0.354869919\) \(a_{24}=-0.478949547\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.192158685\) \(a_{27}=-0.223329715\) \(a_{28}=+0.208768423\) \(a_{29}=+0.921447963\) \(a_{30}=+0.428385498\)
\(a_{31}=-0.380378450\) \(a_{32}=-0.176776695\) \(a_{33}=-1.087950355\) \(a_{34}=+0.432771700\) \(a_{35}=-0.186728154\)
\(a_{36}=+0.417570672\) \(a_{37}=-1.205116950\) \(a_{38}=-1.184655125\) \(a_{39}=-0.368137261\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.694139570\) \(a_{42}=-0.399958166\) \(a_{43}=-0.549539652\) \(a_{44}=-0.401554339\) \(a_{45}=-0.373486564\)
\(a_{46}=-0.250930926\) \(a_{47}=-1.252795835\) \(a_{48}=+0.338668472\) \(a_{49}=-0.825662983\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.829103238\) \(a_{52}=-0.135876709\) \(a_{53}=+1.438526248\) \(a_{54}=+0.157917956\) \(a_{55}=+0.359161119\)
\(a_{56}=-0.147621567\) \(a_{57}=+2.269560140\) \(a_{58}=-0.651562103\) \(a_{59}=+1.812516508\) \(a_{60}=-0.302914290\)
\(a_{61}=-0.717957665\) \(a_{62}=+0.268968181\) \(a_{63}=+0.348702283\) \(a_{64}=+0.125000000\) \(a_{65}=+0.121531823\)
\(a_{66}=+0.769297074\) \(a_{67}=-1.300591786\) \(a_{68}=-0.306015804\) \(a_{69}=+0.480733014\) \(a_{70}=+0.132036744\)
\(a_{71}=-0.664555192\) \(a_{72}=-0.295267054\) \(a_{73}=-0.293683339\) \(a_{74}=+0.852146367\) \(a_{75}=+0.270934778\)
\(a_{76}=+0.837677672\) \(a_{77}=-0.335327464\) \(a_{78}=+0.260312353\) \(a_{79}=-0.818699963\) \(a_{80}=-0.111803399\)
\(a_{81}=-1.137680279\) \(a_{82}=+0.490830797\) \(a_{83}=+0.719160830\) \(a_{84}=+0.282813131\) \(a_{85}=+0.273708856\)
\(a_{86}=+0.388583214\) \(a_{87}=+1.248261495\) \(a_{88}=+0.283941796\) \(a_{89}=+1.871303535\) \(a_{90}=+0.264094882\)
\(a_{91}=-0.113467065\) \(a_{92}=+0.177434960\) \(a_{93}=-0.515288754\) \(a_{94}=+0.885860430\) \(a_{95}=-0.749241687\)
\(a_{96}=-0.239474773\) \(a_{97}=-1.952698869\) \(a_{98}=+0.583831894\) \(a_{99}=-0.670709261\) \(a_{100}=+0.099975586\)

Showing 100 of 210 available coefficients

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