Properties

Level $10$
Weight $0$
Character 10.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 18.3951548888 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.476870948\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+1.044305462\) \(a_{7}=+0.264936689\) \(a_{8}=-0.353553391\) \(a_{9}=+1.181147797\) \(a_{10}=-0.316227766\)
\(a_{11}=-1.081170081\) \(a_{12}=-0.738435474\) \(a_{13}=+0.766203115\) \(a_{14}=-0.187338529\) \(a_{15}=-0.660476767\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.800760689\) \(a_{18}=-0.835197617\) \(a_{19}=-0.585196768\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.391277299\) \(a_{22}=+0.764502696\) \(a_{23}=+1.289460380\) \(a_{24}=+0.522152731\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.541787418\) \(a_{27}=-0.267531919\) \(a_{28}=+0.132468344\) \(a_{29}=+0.639704981\) \(a_{30}=+0.467027601\)
\(a_{31}=+0.277136754\) \(a_{32}=-0.176776695\) \(a_{33}=+1.596748682\) \(a_{34}=+1.273330095\) \(a_{35}=+0.118483289\)
\(a_{36}=+0.590573899\) \(a_{37}=-0.802214993\) \(a_{38}=+0.413796603\) \(a_{39}=-1.131583120\) \(a_{40}=-0.158113883\)
\(a_{41}=+1.307046450\) \(a_{42}=+0.276674831\) \(a_{43}=+1.043315957\) \(a_{44}=-0.540585040\) \(a_{45}=+0.528225353\)
\(a_{46}=-0.911786179\) \(a_{47}=+0.044934548\) \(a_{48}=-0.369217737\) \(a_{49}=-0.929808551\) \(a_{50}=-0.141421356\)
\(a_{51}=+2.659491146\) \(a_{52}=+0.383101557\) \(a_{53}=+1.453257155\) \(a_{54}=+0.189173634\) \(a_{55}=-0.483513959\)
\(a_{56}=-0.093669265\) \(a_{57}=+0.864260106\) \(a_{58}=-0.452339730\) \(a_{59}=+1.213608366\) \(a_{60}=-0.330238383\)
\(a_{61}=-1.590479029\) \(a_{62}=-0.195965278\) \(a_{63}=+0.312929386\) \(a_{64}=+0.125000000\) \(a_{65}=+0.342656450\)
\(a_{66}=-1.129071821\) \(a_{67}=+1.782617644\) \(a_{68}=-0.900380345\) \(a_{69}=-1.904366574\) \(a_{70}=-0.083780337\)
\(a_{71}=-0.252911104\) \(a_{72}=-0.417598808\) \(a_{73}=-1.264678953\) \(a_{74}=+0.567251661\) \(a_{75}=-0.295374190\)
\(a_{76}=-0.292598384\) \(a_{77}=-0.286441621\) \(a_{78}=+0.800150098\) \(a_{79}=-0.946883290\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.786037679\) \(a_{82}=-0.924221408\) \(a_{83}=-1.106041513\) \(a_{84}=-0.195638649\) \(a_{85}=-0.805324662\)
\(a_{86}=-0.737735788\) \(a_{87}=-0.944761702\) \(a_{88}=+0.382251348\) \(a_{89}=+1.161992430\) \(a_{90}=-0.373511729\)
\(a_{91}=+0.202995316\) \(a_{92}=+0.644730190\) \(a_{93}=-0.409295220\) \(a_{94}=-0.031773524\) \(a_{95}=-0.261707951\)
\(a_{96}=+0.261076366\) \(a_{97}=-0.138606508\) \(a_{98}=+0.657473931\) \(a_{99}=-1.277021659\) \(a_{100}=+0.099975586\)

Showing 100 of 190 available coefficients

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