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: \( 28.8519682703 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.942469602\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.666426647\) \(a_{7}=+1.191277825\) \(a_{8}=-0.353553391\) \(a_{9}=-0.111751048\) \(a_{10}=+0.316227766\)
\(a_{11}=-1.452646587\) \(a_{12}=-0.471234801\) \(a_{13}=+1.411580201\) \(a_{14}=-0.842360628\) \(a_{15}=+0.421485220\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.268924551\) \(a_{18}=+0.079019924\) \(a_{19}=+0.264181875\) \(a_{20}=-0.223606798\)
\(a_{21}=-1.122743138\) \(a_{22}=+1.027176252\) \(a_{23}=-1.512614824\) \(a_{24}=+0.333213323\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.998137933\) \(a_{27}=+1.047791569\) \(a_{28}=+0.595638913\) \(a_{29}=+0.881835843\) \(a_{30}=-0.298035057\)
\(a_{31}=+0.791215638\) \(a_{32}=-0.176776695\) \(a_{33}=+1.369075251\) \(a_{34}=+0.897265155\) \(a_{35}=-0.532755639\)
\(a_{36}=-0.055875524\) \(a_{37}=-0.252755346\) \(a_{38}=-0.186804795\) \(a_{39}=-1.330371431\) \(a_{40}=+0.158113883\)
\(a_{41}=+1.385808546\) \(a_{42}=+0.793899287\) \(a_{43}=-1.730033953\) \(a_{44}=-0.726323293\) \(a_{45}=+0.049976588\)
\(a_{46}=+1.069580199\) \(a_{47}=-0.288157176\) \(a_{48}=-0.235617401\) \(a_{49}=+0.419142857\) \(a_{50}=-0.141421356\)
\(a_{51}=+1.195922817\) \(a_{52}=+0.705790101\) \(a_{53}=+1.911019715\) \(a_{54}=-0.740900523\) \(a_{55}=+0.649643303\)
\(a_{56}=-0.421180314\) \(a_{57}=-0.248983387\) \(a_{58}=-0.623552105\) \(a_{59}=-1.102891977\) \(a_{60}=+0.210742610\)
\(a_{61}=-0.780806492\) \(a_{62}=-0.559473943\) \(a_{63}=-0.133126546\) \(a_{64}=+0.125000000\) \(a_{65}=-0.631277857\)
\(a_{66}=-0.968082394\) \(a_{67}=-0.434541376\) \(a_{68}=-0.634462276\) \(a_{69}=+1.425593492\) \(a_{70}=+0.376715125\)
\(a_{71}=-0.846754330\) \(a_{72}=+0.039509962\) \(a_{73}=+0.612598805\) \(a_{74}=+0.178725019\) \(a_{75}=-0.188493920\)
\(a_{76}=+0.132090938\) \(a_{77}=-1.730505666\) \(a_{78}=+0.940714661\) \(a_{79}=+1.159092514\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.875760655\) \(a_{82}=-0.979914621\) \(a_{83}=-0.953807286\) \(a_{84}=-0.561371569\) \(a_{85}=+0.567480311\)
\(a_{86}=+1.223318740\) \(a_{87}=-0.831103477\) \(a_{88}=+0.513588126\) \(a_{89}=-0.619859156\) \(a_{90}=-0.035338784\)
\(a_{91}=+1.681584192\) \(a_{92}=-0.756307412\) \(a_{93}=-0.745696688\) \(a_{94}=+0.203757893\) \(a_{95}=-0.118145726\)
\(a_{96}=+0.166606662\) \(a_{97}=-1.100287590\) \(a_{98}=-0.296378756\) \(a_{99}=+0.162334779\) \(a_{100}=+0.099975586\)

Showing 100 of 240 available coefficients

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