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: \( 11.5198192086 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.604138286\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.427190278\) \(a_{7}=+1.381000738\) \(a_{8}=-0.353553391\) \(a_{9}=-0.635016932\) \(a_{10}=-0.316227766\)
\(a_{11}=+1.266202546\) \(a_{12}=-0.302069143\) \(a_{13}=-0.650177156\) \(a_{14}=-0.976514987\) \(a_{15}=-0.270178855\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.480686230\) \(a_{18}=+0.449024779\) \(a_{19}=-0.803110596\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.834315418\) \(a_{22}=-0.895340407\) \(a_{23}=+1.595947646\) \(a_{24}=+0.213595139\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.459744676\) \(a_{27}=+0.987776326\) \(a_{28}=+0.690500369\) \(a_{29}=+0.025848145\) \(a_{30}=+0.191045300\)
\(a_{31}=+1.236145979\) \(a_{32}=-0.176776695\) \(a_{33}=-0.764961436\) \(a_{34}=+1.047003274\) \(a_{35}=+0.617602306\)
\(a_{36}=-0.317508466\) \(a_{37}=+0.011155007\) \(a_{38}=+0.567884949\) \(a_{39}=+0.392796912\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.035127798\) \(a_{42}=+0.589950090\) \(a_{43}=+1.079777017\) \(a_{44}=+0.633101273\) \(a_{45}=-0.283988205\)
\(a_{46}=-1.128505403\) \(a_{47}=-1.261633312\) \(a_{48}=-0.151034571\) \(a_{49}=+0.907163039\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.894539240\) \(a_{52}=-0.325088578\) \(a_{53}=-0.027098671\) \(a_{54}=-0.698463338\) \(a_{55}=+0.566262993\)
\(a_{56}=-0.488257493\) \(a_{57}=+0.485189859\) \(a_{58}=-0.018277398\) \(a_{59}=+1.269389060\) \(a_{60}=-0.135089427\)
\(a_{61}=+1.390329383\) \(a_{62}=-0.874087204\) \(a_{63}=-0.876958852\) \(a_{64}=+0.125000000\) \(a_{65}=-0.290768064\)
\(a_{66}=+0.540909418\) \(a_{67}=-0.941792524\) \(a_{68}=-0.740343115\) \(a_{69}=-0.964173075\) \(a_{70}=-0.436710778\)
\(a_{71}=+1.016745089\) \(a_{72}=+0.224512389\) \(a_{73}=+0.668821295\) \(a_{74}=-0.007887781\) \(a_{75}=-0.120827657\)
\(a_{76}=-0.401555298\) \(a_{77}=+1.748626652\) \(a_{78}=-0.277749360\) \(a_{79}=+1.058447941\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.038263435\) \(a_{82}=+0.024839104\) \(a_{83}=-0.724710687\) \(a_{84}=-0.417157709\) \(a_{85}=-0.662183013\)
\(a_{86}=-0.763517651\) \(a_{87}=-0.015615851\) \(a_{88}=-0.447670203\) \(a_{89}=+0.897556971\) \(a_{90}=+0.200809986\)
\(a_{91}=-0.897895129\) \(a_{92}=+0.797973823\) \(a_{93}=-0.746803093\) \(a_{94}=+0.892109470\) \(a_{95}=-0.359161977\)
\(a_{96}=+0.106797570\) \(a_{97}=+0.750756029\) \(a_{98}=-0.641461137\) \(a_{99}=-0.804060080\) \(a_{100}=+0.099975586\)

Showing 100 of 156 available coefficients

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