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: \( 28.8267168675 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.254881204\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.180228228\) \(a_{7}=-0.006971098\) \(a_{8}=-0.353553391\) \(a_{9}=-0.935035572\) \(a_{10}=-0.316227766\)
\(a_{11}=+1.497744748\) \(a_{12}=+0.127440602\) \(a_{13}=+0.306518404\) \(a_{14}=+0.004929310\) \(a_{15}=+0.113986340\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.641942050\) \(a_{18}=+0.661169994\) \(a_{19}=-0.582506763\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.001776802\) \(a_{22}=-1.059065468\) \(a_{23}=-0.044837678\) \(a_{24}=-0.090114114\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.216741242\) \(a_{27}=-0.493204196\) \(a_{28}=-0.003485549\) \(a_{29}=-1.021008432\) \(a_{30}=-0.080600514\)
\(a_{31}=+1.278039870\) \(a_{32}=-0.176776695\) \(a_{33}=+0.381746984\) \(a_{34}=-1.161028358\) \(a_{35}=-0.003117570\)
\(a_{36}=-0.467517786\) \(a_{37}=+0.097511960\) \(a_{38}=+0.411894482\) \(a_{39}=+0.078125780\) \(a_{40}=-0.158113883\)
\(a_{41}=+1.746507135\) \(a_{42}=+0.001256389\) \(a_{43}=-1.119625943\) \(a_{44}=+0.748872374\) \(a_{45}=-0.418160620\)
\(a_{46}=+0.031705026\) \(a_{47}=+1.184512512\) \(a_{48}=+0.063720301\) \(a_{49}=-0.999951404\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.418500167\) \(a_{52}=+0.153259202\) \(a_{53}=+1.057135575\) \(a_{54}=+0.348748032\) \(a_{55}=+0.669811814\)
\(a_{56}=+0.002464655\) \(a_{57}=-0.148470025\) \(a_{58}=+0.721961986\) \(a_{59}=-0.900153798\) \(a_{60}=+0.056993170\)
\(a_{61}=-0.657791148\) \(a_{62}=-0.903710659\) \(a_{63}=+0.006518224\) \(a_{64}=+0.125000000\) \(a_{65}=+0.137079197\)
\(a_{66}=-0.269935881\) \(a_{67}=+1.523390718\) \(a_{68}=+0.820971025\) \(a_{69}=-0.011428281\) \(a_{70}=+0.002204455\)
\(a_{71}=-0.015229336\) \(a_{72}=+0.330584997\) \(a_{73}=+0.701550541\) \(a_{74}=-0.068951368\) \(a_{75}=+0.050976241\)
\(a_{76}=-0.291253382\) \(a_{77}=-0.010440925\) \(a_{78}=-0.055243269\) \(a_{79}=+0.054895859\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.809327093\) \(a_{82}=-1.234967039\) \(a_{83}=-0.803920314\) \(a_{84}=-0.000888401\) \(a_{85}=+0.734298808\)
\(a_{86}=+0.791695097\) \(a_{87}=-0.260235858\) \(a_{88}=-0.529532734\) \(a_{89}=-0.215794080\) \(a_{90}=+0.295684210\)
\(a_{91}=-0.002136770\) \(a_{92}=-0.022418839\) \(a_{93}=+0.325748341\) \(a_{94}=-0.837576830\) \(a_{95}=-0.260504944\)
\(a_{96}=-0.045057057\) \(a_{97}=-1.136338751\) \(a_{98}=+0.707072418\) \(a_{99}=-1.400444617\) \(a_{100}=+0.099975586\)

Showing 100 of 238 available coefficients

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