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: \( 23.4946353042 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.702512342\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+1.203858022\) \(a_{7}=+1.299627771\) \(a_{8}=+0.353553391\) \(a_{9}=+1.898548276\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.340368232\) \(a_{12}=+0.851256171\) \(a_{13}=+0.394954291\) \(a_{14}=+0.918975610\) \(a_{15}=-0.761386666\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.457145913\) \(a_{18}=+1.342476361\) \(a_{19}=+0.940889767\) \(a_{20}=-0.223606798\)
\(a_{21}=+2.212632322\) \(a_{22}=-0.240676685\) \(a_{23}=-1.019966227\) \(a_{24}=+0.601929011\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.279274857\) \(a_{27}=+1.529789531\) \(a_{28}=+0.649813886\) \(a_{29}=-0.994986495\) \(a_{30}=-0.538381675\)
\(a_{31}=-1.657590854\) \(a_{32}=+0.176776695\) \(a_{33}=-0.579481116\) \(a_{34}=+1.030357756\) \(a_{35}=-0.581211209\)
\(a_{36}=+0.949274138\) \(a_{37}=+0.662718927\) \(a_{38}=+0.665309535\) \(a_{39}=+0.672414554\) \(a_{40}=-0.158113883\)
\(a_{41}=+1.423147356\) \(a_{42}=+1.564567319\) \(a_{43}=+1.542504473\) \(a_{44}=-0.170184116\) \(a_{45}=-0.849056601\)
\(a_{46}=-0.721225036\) \(a_{47}=-0.704689143\) \(a_{48}=+0.425628086\) \(a_{49}=+0.689032344\) \(a_{50}=+0.141421356\)
\(a_{51}=+2.480808902\) \(a_{52}=+0.197477145\) \(a_{53}=-1.422844451\) \(a_{54}=+1.081724551\) \(a_{55}=+0.152217301\)
\(a_{56}=+0.459487805\) \(a_{57}=+1.601876442\) \(a_{58}=-0.703561698\) \(a_{59}=-0.486791090\) \(a_{60}=-0.380693333\)
\(a_{61}=+0.219282781\) \(a_{62}=-1.172093733\) \(a_{63}=+2.467406065\) \(a_{64}=+0.125000000\) \(a_{65}=-0.176628928\)
\(a_{66}=-0.409755026\) \(a_{67}=+0.554814676\) \(a_{68}=+0.728572957\) \(a_{69}=-1.736505091\) \(a_{70}=-0.410978387\)
\(a_{71}=+1.989727657\) \(a_{72}=+0.671238180\) \(a_{73}=+0.930138587\) \(a_{74}=+0.468613047\) \(a_{75}=+0.340502468\)
\(a_{76}=+0.470444884\) \(a_{77}=-0.442352007\) \(a_{78}=+0.475468891\) \(a_{79}=-1.761021599\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.705937281\) \(a_{82}=+1.006317146\) \(a_{83}=+0.619895283\) \(a_{84}=+1.106316161\) \(a_{85}=-0.651655463\)
\(a_{86}=+1.090715373\) \(a_{87}=-1.693976789\) \(a_{88}=-0.120338342\) \(a_{89}=+0.023395775\) \(a_{90}=-0.600373680\)
\(a_{91}=+0.513293565\) \(a_{92}=-0.509983114\) \(a_{93}=-2.822068888\) \(a_{94}=-0.498290472\) \(a_{95}=-0.420778696\)
\(a_{96}=+0.300964506\) \(a_{97}=+1.165951838\) \(a_{98}=+0.487219443\) \(a_{99}=-0.646205520\) \(a_{100}=+0.099975586\)

Showing 100 of 218 available coefficients

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