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: \( 19.9265889222 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.914236134\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+1.353569351\) \(a_{7}=-1.498127020\) \(a_{8}=-0.353553391\) \(a_{9}=+2.664299977\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.314084349\) \(a_{12}=-0.957118067\) \(a_{13}=+0.377109799\) \(a_{14}=+1.059335775\) \(a_{15}=-0.856072424\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.007182884\) \(a_{18}=-1.883944581\) \(a_{19}=+1.032422695\) \(a_{20}=+0.223606798\)
\(a_{21}=+2.867768876\) \(a_{22}=-0.222091173\) \(a_{23}=+0.508951509\) \(a_{24}=+0.676784676\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.266656896\) \(a_{27}=-3.185863154\) \(a_{28}=-0.749063510\) \(a_{29}=+0.887588837\) \(a_{30}=+0.605334616\)
\(a_{31}=-1.600120679\) \(a_{32}=-0.176776695\) \(a_{33}=-0.601231609\) \(a_{34}=-0.712185847\) \(a_{35}=-0.669982771\)
\(a_{36}=+1.332149989\) \(a_{37}=+0.342885964\) \(a_{38}=-0.730033089\) \(a_{39}=-0.721877203\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.544140889\) \(a_{42}=-2.027818819\) \(a_{43}=-1.910789558\) \(a_{44}=+0.157042174\) \(a_{45}=+1.191511172\)
\(a_{46}=-0.359883063\) \(a_{47}=+0.765212055\) \(a_{48}=-0.478559034\) \(a_{49}=+1.244384570\) \(a_{50}=-0.141421356\)
\(a_{51}=-1.927985871\) \(a_{52}=+0.188554899\) \(a_{53}=-1.035591821\) \(a_{54}=+2.252745440\) \(a_{55}=+0.140462791\)
\(a_{56}=+0.529667888\) \(a_{57}=-1.976300829\) \(a_{58}=-0.627620086\) \(a_{59}=+0.881338668\) \(a_{60}=-0.428036212\)
\(a_{61}=+0.148457706\) \(a_{62}=+1.131456183\) \(a_{63}=-3.991459786\) \(a_{64}=+0.125000000\) \(a_{65}=+0.168648629\)
\(a_{66}=+0.425134948\) \(a_{67}=+0.057082942\) \(a_{68}=+0.503591442\) \(a_{69}=-0.974253369\) \(a_{70}=+0.473749361\)
\(a_{71}=+0.649536280\) \(a_{72}=-0.941972290\) \(a_{73}=-0.944376762\) \(a_{74}=-0.242456990\) \(a_{75}=-0.382847227\)
\(a_{76}=+0.516211348\) \(a_{77}=-0.470538249\) \(a_{78}=+0.510444265\) \(a_{79}=+0.180315179\) \(a_{80}=+0.111803399\)
\(a_{81}=+3.434194391\) \(a_{82}=+0.384765712\) \(a_{83}=-0.853155174\) \(a_{84}=+1.433884438\) \(a_{85}=+0.450425879\)
\(a_{86}=+1.351132254\) \(a_{87}=-1.699054624\) \(a_{88}=-0.111045586\) \(a_{89}=+0.543451275\) \(a_{90}=-0.842525630\)
\(a_{91}=-0.564958379\) \(a_{92}=+0.254475755\) \(a_{93}=+3.063008823\) \(a_{94}=-0.541086633\) \(a_{95}=+0.461713466\)
\(a_{96}=+0.338392338\) \(a_{97}=+1.089535404\) \(a_{98}=-0.879912768\) \(a_{99}=+0.836814923\) \(a_{100}=+0.099975586\)

Showing 100 of 196 available coefficients

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