Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,4,Mod(1,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(3.71712033036\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 21) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 63.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.00000 | 1.06066 | 0.530330 | − | 0.847791i | \(-0.322068\pi\) | ||||
0.530330 | + | 0.847791i | \(0.322068\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.125000 | ||||||||
\(5\) | 18.0000 | 1.60997 | 0.804984 | − | 0.593296i | \(-0.202174\pi\) | ||||
0.804984 | + | 0.593296i | \(0.202174\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | −21.0000 | −0.928078 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 54.0000 | 1.70763 | ||||||||
\(11\) | 36.0000 | 0.986764 | 0.493382 | − | 0.869813i | \(-0.335760\pi\) | ||||
0.493382 | + | 0.869813i | \(0.335760\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −34.0000 | −0.725377 | −0.362689 | − | 0.931910i | \(-0.618141\pi\) | ||||
−0.362689 | + | 0.931910i | \(0.618141\pi\) | |||||||
\(14\) | 21.0000 | 0.400892 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −71.0000 | −1.10938 | ||||||||
\(17\) | −42.0000 | −0.599206 | −0.299603 | − | 0.954064i | \(-0.596854\pi\) | ||||
−0.299603 | + | 0.954064i | \(0.596854\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −124.000 | −1.49724 | −0.748620 | − | 0.663000i | \(-0.769283\pi\) | ||||
−0.748620 | + | 0.663000i | \(0.769283\pi\) | |||||||
\(20\) | 18.0000 | 0.201246 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 108.000 | 1.04662 | ||||||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 199.000 | 1.59200 | ||||||||
\(26\) | −102.000 | −0.769379 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 7.00000 | 0.0472456 | ||||||||
\(29\) | −102.000 | −0.653135 | −0.326568 | − | 0.945174i | \(-0.605892\pi\) | ||||
−0.326568 | + | 0.945174i | \(0.605892\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −160.000 | −0.926995 | −0.463498 | − | 0.886098i | \(-0.653406\pi\) | ||||
−0.463498 | + | 0.886098i | \(0.653406\pi\) | |||||||
\(32\) | −45.0000 | −0.248592 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −126.000 | −0.635554 | ||||||||
\(35\) | 126.000 | 0.608511 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 398.000 | 1.76840 | 0.884200 | − | 0.467109i | \(-0.154704\pi\) | ||||
0.884200 | + | 0.467109i | \(0.154704\pi\) | |||||||
\(38\) | −372.000 | −1.58806 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −378.000 | −1.49418 | ||||||||
\(41\) | 318.000 | 1.21130 | 0.605649 | − | 0.795732i | \(-0.292913\pi\) | ||||
0.605649 | + | 0.795732i | \(0.292913\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −268.000 | −0.950456 | −0.475228 | − | 0.879863i | \(-0.657634\pi\) | ||||
−0.475228 | + | 0.879863i | \(0.657634\pi\) | |||||||
\(44\) | 36.0000 | 0.123346 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −240.000 | −0.744843 | −0.372421 | − | 0.928064i | \(-0.621472\pi\) | ||||
−0.372421 | + | 0.928064i | \(0.621472\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 597.000 | 1.68857 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −34.0000 | −0.0906721 | ||||||||
\(53\) | 498.000 | 1.29067 | 0.645335 | − | 0.763899i | \(-0.276718\pi\) | ||||
0.645335 | + | 0.763899i | \(0.276718\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 648.000 | 1.58866 | ||||||||
\(56\) | −147.000 | −0.350780 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −306.000 | −0.692755 | ||||||||
\(59\) | 132.000 | 0.291270 | 0.145635 | − | 0.989338i | \(-0.453477\pi\) | ||||
0.145635 | + | 0.989338i | \(0.453477\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 398.000 | 0.835388 | 0.417694 | − | 0.908588i | \(-0.362838\pi\) | ||||
0.417694 | + | 0.908588i | \(0.362838\pi\) | |||||||
\(62\) | −480.000 | −0.983227 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 433.000 | 0.845703 | ||||||||
\(65\) | −612.000 | −1.16783 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 92.0000 | 0.167755 | 0.0838775 | − | 0.996476i | \(-0.473270\pi\) | ||||
0.0838775 | + | 0.996476i | \(0.473270\pi\) | |||||||
\(68\) | −42.0000 | −0.0749007 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 378.000 | 0.645423 | ||||||||
\(71\) | 720.000 | 1.20350 | 0.601748 | − | 0.798686i | \(-0.294471\pi\) | ||||
0.601748 | + | 0.798686i | \(0.294471\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −502.000 | −0.804858 | −0.402429 | − | 0.915451i | \(-0.631834\pi\) | ||||
−0.402429 | + | 0.915451i | \(0.631834\pi\) | |||||||
\(74\) | 1194.00 | 1.87567 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −124.000 | −0.187155 | ||||||||
\(77\) | 252.000 | 0.372962 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1024.00 | −1.45834 | −0.729171 | − | 0.684332i | \(-0.760094\pi\) | ||||
−0.729171 | + | 0.684332i | \(0.760094\pi\) | |||||||
\(80\) | −1278.00 | −1.78606 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 954.000 | 1.28478 | ||||||||
\(83\) | 204.000 | 0.269782 | 0.134891 | − | 0.990860i | \(-0.456932\pi\) | ||||
0.134891 | + | 0.990860i | \(0.456932\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −756.000 | −0.964703 | ||||||||
\(86\) | −804.000 | −1.00811 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −756.000 | −0.915794 | ||||||||
\(89\) | −354.000 | −0.421617 | −0.210809 | − | 0.977527i | \(-0.567610\pi\) | ||||
−0.210809 | + | 0.977527i | \(0.567610\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −238.000 | −0.274167 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −720.000 | −0.790025 | ||||||||
\(95\) | −2232.00 | −2.41051 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −286.000 | −0.299370 | −0.149685 | − | 0.988734i | \(-0.547826\pi\) | ||||
−0.149685 | + | 0.988734i | \(0.547826\pi\) | |||||||
\(98\) | 147.000 | 0.151523 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 199.000 | 0.199000 | ||||||||
\(101\) | −414.000 | −0.407867 | −0.203933 | − | 0.978985i | \(-0.565373\pi\) | ||||
−0.203933 | + | 0.978985i | \(0.565373\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 56.0000 | 0.0535713 | 0.0267857 | − | 0.999641i | \(-0.491473\pi\) | ||||
0.0267857 | + | 0.999641i | \(0.491473\pi\) | |||||||
\(104\) | 714.000 | 0.673206 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1494.00 | 1.36896 | ||||||||
\(107\) | −12.0000 | −0.0108419 | −0.00542095 | − | 0.999985i | \(-0.501726\pi\) | ||||
−0.00542095 | + | 0.999985i | \(0.501726\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1478.00 | 1.29878 | 0.649389 | − | 0.760457i | \(-0.275025\pi\) | ||||
0.649389 | + | 0.760457i | \(0.275025\pi\) | |||||||
\(110\) | 1944.00 | 1.68503 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −497.000 | −0.419304 | ||||||||
\(113\) | −402.000 | −0.334664 | −0.167332 | − | 0.985901i | \(-0.553515\pi\) | ||||
−0.167332 | + | 0.985901i | \(0.553515\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −102.000 | −0.0816419 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 396.000 | 0.308939 | ||||||||
\(119\) | −294.000 | −0.226478 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −35.0000 | −0.0262960 | ||||||||
\(122\) | 1194.00 | 0.886063 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −160.000 | −0.115874 | ||||||||
\(125\) | 1332.00 | 0.953102 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1280.00 | 0.894344 | 0.447172 | − | 0.894448i | \(-0.352431\pi\) | ||||
0.447172 | + | 0.894448i | \(0.352431\pi\) | |||||||
\(128\) | 1659.00 | 1.14560 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1836.00 | −1.23868 | ||||||||
\(131\) | −1764.00 | −1.17650 | −0.588250 | − | 0.808679i | \(-0.700183\pi\) | ||||
−0.588250 | + | 0.808679i | \(0.700183\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −868.000 | −0.565903 | ||||||||
\(134\) | 276.000 | 0.177931 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 882.000 | 0.556109 | ||||||||
\(137\) | 2358.00 | 1.47049 | 0.735246 | − | 0.677800i | \(-0.237066\pi\) | ||||
0.735246 | + | 0.677800i | \(0.237066\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −52.0000 | −0.0317308 | −0.0158654 | − | 0.999874i | \(-0.505050\pi\) | ||||
−0.0158654 | + | 0.999874i | \(0.505050\pi\) | |||||||
\(140\) | 126.000 | 0.0760639 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2160.00 | 1.27650 | ||||||||
\(143\) | −1224.00 | −0.715776 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1836.00 | −1.05153 | ||||||||
\(146\) | −1506.00 | −0.853681 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 398.000 | 0.221050 | ||||||||
\(149\) | 1746.00 | 0.959986 | 0.479993 | − | 0.877272i | \(-0.340639\pi\) | ||||
0.479993 | + | 0.877272i | \(0.340639\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −232.000 | −0.125032 | −0.0625162 | − | 0.998044i | \(-0.519913\pi\) | ||||
−0.0625162 | + | 0.998044i | \(0.519913\pi\) | |||||||
\(152\) | 2604.00 | 1.38955 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 756.000 | 0.395586 | ||||||||
\(155\) | −2880.00 | −1.49243 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1694.00 | 0.861120 | 0.430560 | − | 0.902562i | \(-0.358316\pi\) | ||||
0.430560 | + | 0.902562i | \(0.358316\pi\) | |||||||
\(158\) | −3072.00 | −1.54681 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −810.000 | −0.400226 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2932.00 | −1.40891 | −0.704454 | − | 0.709750i | \(-0.748808\pi\) | ||||
−0.704454 | + | 0.709750i | \(0.748808\pi\) | |||||||
\(164\) | 318.000 | 0.151412 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 612.000 | 0.286147 | ||||||||
\(167\) | −1176.00 | −0.544920 | −0.272460 | − | 0.962167i | \(-0.587837\pi\) | ||||
−0.272460 | + | 0.962167i | \(0.587837\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1041.00 | −0.473828 | ||||||||
\(170\) | −2268.00 | −1.02322 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −268.000 | −0.118807 | ||||||||
\(173\) | −870.000 | −0.382340 | −0.191170 | − | 0.981557i | \(-0.561228\pi\) | ||||
−0.191170 | + | 0.981557i | \(0.561228\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1393.00 | 0.601719 | ||||||||
\(176\) | −2556.00 | −1.09469 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1062.00 | −0.447193 | ||||||||
\(179\) | 2316.00 | 0.967072 | 0.483536 | − | 0.875324i | \(-0.339352\pi\) | ||||
0.483536 | + | 0.875324i | \(0.339352\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −106.000 | −0.0435299 | −0.0217650 | − | 0.999763i | \(-0.506929\pi\) | ||||
−0.0217650 | + | 0.999763i | \(0.506929\pi\) | |||||||
\(182\) | −714.000 | −0.290798 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7164.00 | 2.84707 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1512.00 | −0.591275 | ||||||||
\(188\) | −240.000 | −0.0931053 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6696.00 | −2.55673 | ||||||||
\(191\) | 1128.00 | 0.427326 | 0.213663 | − | 0.976907i | \(-0.431461\pi\) | ||||
0.213663 | + | 0.976907i | \(0.431461\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4034.00 | 1.50453 | 0.752263 | − | 0.658862i | \(-0.228962\pi\) | ||||
0.752263 | + | 0.658862i | \(0.228962\pi\) | |||||||
\(194\) | −858.000 | −0.317530 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 49.0000 | 0.0178571 | ||||||||
\(197\) | 1314.00 | 0.475221 | 0.237611 | − | 0.971360i | \(-0.423636\pi\) | ||||
0.237611 | + | 0.971360i | \(0.423636\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5096.00 | 1.81531 | 0.907653 | − | 0.419722i | \(-0.137872\pi\) | ||||
0.907653 | + | 0.419722i | \(0.137872\pi\) | |||||||
\(200\) | −4179.00 | −1.47750 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1242.00 | −0.432608 | ||||||||
\(203\) | −714.000 | −0.246862 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5724.00 | 1.95015 | ||||||||
\(206\) | 168.000 | 0.0568209 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2414.00 | 0.804715 | ||||||||
\(209\) | −4464.00 | −1.47742 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3076.00 | −1.00360 | −0.501802 | − | 0.864982i | \(-0.667330\pi\) | ||||
−0.501802 | + | 0.864982i | \(0.667330\pi\) | |||||||
\(212\) | 498.000 | 0.161334 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −36.0000 | −0.0114996 | ||||||||
\(215\) | −4824.00 | −1.53020 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1120.00 | −0.350371 | ||||||||
\(218\) | 4434.00 | 1.37756 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 648.000 | 0.198583 | ||||||||
\(221\) | 1428.00 | 0.434650 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1888.00 | −0.566950 | −0.283475 | − | 0.958980i | \(-0.591487\pi\) | ||||
−0.283475 | + | 0.958980i | \(0.591487\pi\) | |||||||
\(224\) | −315.000 | −0.0939590 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1206.00 | −0.354964 | ||||||||
\(227\) | 4716.00 | 1.37891 | 0.689454 | − | 0.724330i | \(-0.257851\pi\) | ||||
0.689454 | + | 0.724330i | \(0.257851\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1690.00 | −0.487678 | −0.243839 | − | 0.969816i | \(-0.578407\pi\) | ||||
−0.243839 | + | 0.969816i | \(0.578407\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2142.00 | 0.606160 | ||||||||
\(233\) | −138.000 | −0.0388012 | −0.0194006 | − | 0.999812i | \(-0.506176\pi\) | ||||
−0.0194006 | + | 0.999812i | \(0.506176\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4320.00 | −1.19917 | ||||||||
\(236\) | 132.000 | 0.0364088 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −882.000 | −0.240217 | ||||||||
\(239\) | −1896.00 | −0.513147 | −0.256573 | − | 0.966525i | \(-0.582594\pi\) | ||||
−0.256573 | + | 0.966525i | \(0.582594\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3598.00 | −0.961691 | −0.480846 | − | 0.876805i | \(-0.659670\pi\) | ||||
−0.480846 | + | 0.876805i | \(0.659670\pi\) | |||||||
\(242\) | −105.000 | −0.0278911 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 398.000 | 0.104424 | ||||||||
\(245\) | 882.000 | 0.229996 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4216.00 | 1.08606 | ||||||||
\(248\) | 3360.00 | 0.860323 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3996.00 | 1.01092 | ||||||||
\(251\) | 3060.00 | 0.769504 | 0.384752 | − | 0.923020i | \(-0.374287\pi\) | ||||
0.384752 | + | 0.923020i | \(0.374287\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 3840.00 | 0.948595 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1513.00 | 0.369385 | ||||||||
\(257\) | 6822.00 | 1.65582 | 0.827908 | − | 0.560864i | \(-0.189531\pi\) | ||||
0.827908 | + | 0.560864i | \(0.189531\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2786.00 | 0.668392 | ||||||||
\(260\) | −612.000 | −0.145979 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5292.00 | −1.24787 | ||||||||
\(263\) | −2592.00 | −0.607717 | −0.303858 | − | 0.952717i | \(-0.598275\pi\) | ||||
−0.303858 | + | 0.952717i | \(0.598275\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8964.00 | 2.07794 | ||||||||
\(266\) | −2604.00 | −0.600231 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 92.0000 | 0.0209694 | ||||||||
\(269\) | −8214.00 | −1.86177 | −0.930886 | − | 0.365311i | \(-0.880963\pi\) | ||||
−0.930886 | + | 0.365311i | \(0.880963\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5344.00 | −1.19788 | −0.598939 | − | 0.800795i | \(-0.704411\pi\) | ||||
−0.598939 | + | 0.800795i | \(0.704411\pi\) | |||||||
\(272\) | 2982.00 | 0.664744 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7074.00 | 1.55969 | ||||||||
\(275\) | 7164.00 | 1.57093 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6514.00 | −1.41295 | −0.706477 | − | 0.707736i | \(-0.749717\pi\) | ||||
−0.706477 | + | 0.707736i | \(0.749717\pi\) | |||||||
\(278\) | −156.000 | −0.0336556 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2646.00 | −0.564746 | ||||||||
\(281\) | −6618.00 | −1.40497 | −0.702485 | − | 0.711698i | \(-0.747926\pi\) | ||||
−0.702485 | + | 0.711698i | \(0.747926\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3260.00 | 0.684759 | 0.342380 | − | 0.939562i | \(-0.388767\pi\) | ||||
0.342380 | + | 0.939562i | \(0.388767\pi\) | |||||||
\(284\) | 720.000 | 0.150437 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3672.00 | −0.759195 | ||||||||
\(287\) | 2226.00 | 0.457828 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3149.00 | −0.640953 | ||||||||
\(290\) | −5508.00 | −1.11531 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −502.000 | −0.100607 | ||||||||
\(293\) | −5118.00 | −1.02047 | −0.510233 | − | 0.860036i | \(-0.670441\pi\) | ||||
−0.510233 | + | 0.860036i | \(0.670441\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2376.00 | 0.468936 | ||||||||
\(296\) | −8358.00 | −1.64121 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5238.00 | 1.01822 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1876.00 | −0.359239 | ||||||||
\(302\) | −696.000 | −0.132617 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8804.00 | 1.66100 | ||||||||
\(305\) | 7164.00 | 1.34495 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 452.000 | 0.0840293 | 0.0420147 | − | 0.999117i | \(-0.486622\pi\) | ||||
0.0420147 | + | 0.999117i | \(0.486622\pi\) | |||||||
\(308\) | 252.000 | 0.0466202 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8640.00 | −1.58296 | ||||||||
\(311\) | −5016.00 | −0.914570 | −0.457285 | − | 0.889320i | \(-0.651178\pi\) | ||||
−0.457285 | + | 0.889320i | \(0.651178\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5402.00 | 0.975524 | 0.487762 | − | 0.872977i | \(-0.337813\pi\) | ||||
0.487762 | + | 0.872977i | \(0.337813\pi\) | |||||||
\(314\) | 5082.00 | 0.913356 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1024.00 | −0.182293 | ||||||||
\(317\) | −10086.0 | −1.78702 | −0.893511 | − | 0.449041i | \(-0.851766\pi\) | ||||
−0.893511 | + | 0.449041i | \(0.851766\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3672.00 | −0.644491 | ||||||||
\(320\) | 7794.00 | 1.36156 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5208.00 | 0.897154 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6766.00 | −1.15480 | ||||||||
\(326\) | −8796.00 | −1.49437 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6678.00 | −1.12418 | ||||||||
\(329\) | −1680.00 | −0.281524 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8044.00 | −1.33577 | −0.667883 | − | 0.744267i | \(-0.732799\pi\) | ||||
−0.667883 | + | 0.744267i | \(0.732799\pi\) | |||||||
\(332\) | 204.000 | 0.0337228 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3528.00 | −0.577975 | ||||||||
\(335\) | 1656.00 | 0.270080 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4178.00 | 0.675342 | 0.337671 | − | 0.941264i | \(-0.390361\pi\) | ||||
0.337671 | + | 0.941264i | \(0.390361\pi\) | |||||||
\(338\) | −3123.00 | −0.502570 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −756.000 | −0.120588 | ||||||||
\(341\) | −5760.00 | −0.914726 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 5628.00 | 0.882097 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2610.00 | −0.405533 | ||||||||
\(347\) | −156.000 | −0.0241341 | −0.0120670 | − | 0.999927i | \(-0.503841\pi\) | ||||
−0.0120670 | + | 0.999927i | \(0.503841\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12418.0 | −1.90464 | −0.952321 | − | 0.305097i | \(-0.901311\pi\) | ||||
−0.952321 | + | 0.305097i | \(0.901311\pi\) | |||||||
\(350\) | 4179.00 | 0.638220 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1620.00 | −0.245302 | ||||||||
\(353\) | 7830.00 | 1.18059 | 0.590296 | − | 0.807187i | \(-0.299011\pi\) | ||||
0.590296 | + | 0.807187i | \(0.299011\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12960.0 | 1.93759 | ||||||||
\(356\) | −354.000 | −0.0527021 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6948.00 | 1.02574 | ||||||||
\(359\) | 9312.00 | 1.36899 | 0.684497 | − | 0.729016i | \(-0.260022\pi\) | ||||
0.684497 | + | 0.729016i | \(0.260022\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8517.00 | 1.24173 | ||||||||
\(362\) | −318.000 | −0.0461705 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −238.000 | −0.0342709 | ||||||||
\(365\) | −9036.00 | −1.29580 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3760.00 | −0.534797 | −0.267398 | − | 0.963586i | \(-0.586164\pi\) | ||||
−0.267398 | + | 0.963586i | \(0.586164\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 21492.0 | 3.01977 | ||||||||
\(371\) | 3486.00 | 0.487828 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5870.00 | 0.814845 | 0.407422 | − | 0.913240i | \(-0.366428\pi\) | ||||
0.407422 | + | 0.913240i | \(0.366428\pi\) | |||||||
\(374\) | −4536.00 | −0.627142 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5040.00 | 0.691272 | ||||||||
\(377\) | 3468.00 | 0.473769 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1852.00 | −0.251005 | −0.125502 | − | 0.992093i | \(-0.540054\pi\) | ||||
−0.125502 | + | 0.992093i | \(0.540054\pi\) | |||||||
\(380\) | −2232.00 | −0.301314 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3384.00 | 0.453247 | ||||||||
\(383\) | −2160.00 | −0.288175 | −0.144087 | − | 0.989565i | \(-0.546025\pi\) | ||||
−0.144087 | + | 0.989565i | \(0.546025\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4536.00 | 0.600457 | ||||||||
\(386\) | 12102.0 | 1.59579 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −286.000 | −0.0374213 | ||||||||
\(389\) | 6786.00 | 0.884483 | 0.442241 | − | 0.896896i | \(-0.354183\pi\) | ||||
0.442241 | + | 0.896896i | \(0.354183\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −1029.00 | −0.132583 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3942.00 | 0.504048 | ||||||||
\(395\) | −18432.0 | −2.34788 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6514.00 | −0.823497 | −0.411748 | − | 0.911298i | \(-0.635082\pi\) | ||||
−0.411748 | + | 0.911298i | \(0.635082\pi\) | |||||||
\(398\) | 15288.0 | 1.92542 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −14129.0 | −1.76612 | ||||||||
\(401\) | −3330.00 | −0.414694 | −0.207347 | − | 0.978267i | \(-0.566483\pi\) | ||||
−0.207347 | + | 0.978267i | \(0.566483\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5440.00 | 0.672421 | ||||||||
\(404\) | −414.000 | −0.0509833 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2142.00 | −0.261837 | ||||||||
\(407\) | 14328.0 | 1.74499 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5398.00 | −0.652601 | −0.326301 | − | 0.945266i | \(-0.605802\pi\) | ||||
−0.326301 | + | 0.945266i | \(0.605802\pi\) | |||||||
\(410\) | 17172.0 | 2.06845 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 56.0000 | 0.00669641 | ||||||||
\(413\) | 924.000 | 0.110090 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3672.00 | 0.434341 | ||||||||
\(416\) | 1530.00 | 0.180323 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −13392.0 | −1.56704 | ||||||||
\(419\) | −13092.0 | −1.52646 | −0.763229 | − | 0.646128i | \(-0.776387\pi\) | ||||
−0.763229 | + | 0.646128i | \(0.776387\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −322.000 | −0.0372763 | −0.0186381 | − | 0.999826i | \(-0.505933\pi\) | ||||
−0.0186381 | + | 0.999826i | \(0.505933\pi\) | |||||||
\(422\) | −9228.00 | −1.06448 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −10458.0 | −1.19784 | ||||||||
\(425\) | −8358.00 | −0.953935 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2786.00 | 0.315747 | ||||||||
\(428\) | −12.0000 | −0.00135524 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −14472.0 | −1.62303 | ||||||||
\(431\) | −2616.00 | −0.292363 | −0.146181 | − | 0.989258i | \(-0.546698\pi\) | ||||
−0.146181 | + | 0.989258i | \(0.546698\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4322.00 | 0.479681 | 0.239841 | − | 0.970812i | \(-0.422905\pi\) | ||||
0.239841 | + | 0.970812i | \(0.422905\pi\) | |||||||
\(434\) | −3360.00 | −0.371625 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1478.00 | 0.162347 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9016.00 | −0.980205 | −0.490103 | − | 0.871665i | \(-0.663041\pi\) | ||||
−0.490103 | + | 0.871665i | \(0.663041\pi\) | |||||||
\(440\) | −13608.0 | −1.47440 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4284.00 | 0.461016 | ||||||||
\(443\) | 5268.00 | 0.564989 | 0.282495 | − | 0.959269i | \(-0.408838\pi\) | ||||
0.282495 | + | 0.959269i | \(0.408838\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6372.00 | −0.678790 | ||||||||
\(446\) | −5664.00 | −0.601341 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3031.00 | 0.319646 | ||||||||
\(449\) | 5310.00 | 0.558117 | 0.279058 | − | 0.960274i | \(-0.409978\pi\) | ||||
0.279058 | + | 0.960274i | \(0.409978\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11448.0 | 1.19527 | ||||||||
\(452\) | −402.000 | −0.0418329 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 14148.0 | 1.46255 | ||||||||
\(455\) | −4284.00 | −0.441400 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15770.0 | 1.61420 | 0.807100 | − | 0.590415i | \(-0.201036\pi\) | ||||
0.807100 | + | 0.590415i | \(0.201036\pi\) | |||||||
\(458\) | −5070.00 | −0.517261 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5370.00 | 0.542529 | 0.271264 | − | 0.962505i | \(-0.412558\pi\) | ||||
0.271264 | + | 0.962505i | \(0.412558\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3328.00 | −0.334050 | −0.167025 | − | 0.985953i | \(-0.553416\pi\) | ||||
−0.167025 | + | 0.985953i | \(0.553416\pi\) | |||||||
\(464\) | 7242.00 | 0.724572 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −414.000 | −0.0411549 | ||||||||
\(467\) | −4548.00 | −0.450656 | −0.225328 | − | 0.974283i | \(-0.572345\pi\) | ||||
−0.225328 | + | 0.974283i | \(0.572345\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 644.000 | 0.0634055 | ||||||||
\(470\) | −12960.0 | −1.27192 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2772.00 | −0.270321 | ||||||||
\(473\) | −9648.00 | −0.937876 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −24676.0 | −2.38361 | ||||||||
\(476\) | −294.000 | −0.0283098 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5688.00 | −0.544274 | ||||||||
\(479\) | 8064.00 | 0.769214 | 0.384607 | − | 0.923080i | \(-0.374337\pi\) | ||||
0.384607 | + | 0.923080i | \(0.374337\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13532.0 | −1.28276 | ||||||||
\(482\) | −10794.0 | −1.02003 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −35.0000 | −0.00328700 | ||||||||
\(485\) | −5148.00 | −0.481977 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16616.0 | 1.54608 | 0.773042 | − | 0.634355i | \(-0.218734\pi\) | ||||
0.773042 | + | 0.634355i | \(0.218734\pi\) | |||||||
\(488\) | −8358.00 | −0.775305 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2646.00 | 0.243947 | ||||||||
\(491\) | 7140.00 | 0.656260 | 0.328130 | − | 0.944633i | \(-0.393582\pi\) | ||||
0.328130 | + | 0.944633i | \(0.393582\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4284.00 | 0.391362 | ||||||||
\(494\) | 12648.0 | 1.15194 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 11360.0 | 1.02839 | ||||||||
\(497\) | 5040.00 | 0.454879 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9124.00 | −0.818530 | −0.409265 | − | 0.912416i | \(-0.634215\pi\) | ||||
−0.409265 | + | 0.912416i | \(0.634215\pi\) | |||||||
\(500\) | 1332.00 | 0.119138 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9180.00 | 0.816182 | ||||||||
\(503\) | 6552.00 | 0.580794 | 0.290397 | − | 0.956906i | \(-0.406213\pi\) | ||||
0.290397 | + | 0.956906i | \(0.406213\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7452.00 | −0.656653 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1280.00 | 0.111793 | ||||||||
\(509\) | −2790.00 | −0.242956 | −0.121478 | − | 0.992594i | \(-0.538763\pi\) | ||||
−0.121478 | + | 0.992594i | \(0.538763\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3514.00 | −0.304208 | ||||||||
\(512\) | −8733.00 | −0.753804 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 20466.0 | 1.75626 | ||||||||
\(515\) | 1008.00 | 0.0862481 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8640.00 | −0.734984 | ||||||||
\(518\) | 8358.00 | 0.708937 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 12852.0 | 1.08384 | ||||||||
\(521\) | 14862.0 | 1.24974 | 0.624871 | − | 0.780728i | \(-0.285151\pi\) | ||||
0.624871 | + | 0.780728i | \(0.285151\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17660.0 | 1.47652 | 0.738258 | − | 0.674518i | \(-0.235649\pi\) | ||||
0.738258 | + | 0.674518i | \(0.235649\pi\) | |||||||
\(524\) | −1764.00 | −0.147062 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7776.00 | −0.644581 | ||||||||
\(527\) | 6720.00 | 0.555461 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12167.0 | −1.00000 | ||||||||
\(530\) | 26892.0 | 2.20399 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −868.000 | −0.0707379 | ||||||||
\(533\) | −10812.0 | −0.878649 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −216.000 | −0.0174551 | ||||||||
\(536\) | −1932.00 | −0.155690 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −24642.0 | −1.97471 | ||||||||
\(539\) | 1764.00 | 0.140966 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19834.0 | −1.57621 | −0.788106 | − | 0.615540i | \(-0.788938\pi\) | ||||
−0.788106 | + | 0.615540i | \(0.788938\pi\) | |||||||
\(542\) | −16032.0 | −1.27054 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1890.00 | 0.148958 | ||||||||
\(545\) | 26604.0 | 2.09099 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20972.0 | 1.63930 | 0.819651 | − | 0.572863i | \(-0.194167\pi\) | ||||
0.819651 | + | 0.572863i | \(0.194167\pi\) | |||||||
\(548\) | 2358.00 | 0.183812 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 21492.0 | 1.66622 | ||||||||
\(551\) | 12648.0 | 0.977900 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7168.00 | −0.551201 | ||||||||
\(554\) | −19542.0 | −1.49866 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −52.0000 | −0.00396635 | ||||||||
\(557\) | −21174.0 | −1.61072 | −0.805360 | − | 0.592786i | \(-0.798028\pi\) | ||||
−0.805360 | + | 0.592786i | \(0.798028\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9112.00 | 0.689439 | ||||||||
\(560\) | −8946.00 | −0.675067 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −19854.0 | −1.49020 | ||||||||
\(563\) | 17772.0 | 1.33037 | 0.665187 | − | 0.746677i | \(-0.268352\pi\) | ||||
0.665187 | + | 0.746677i | \(0.268352\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7236.00 | −0.538798 | ||||||||
\(566\) | 9780.00 | 0.726297 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −15120.0 | −1.11694 | ||||||||
\(569\) | −8250.00 | −0.607835 | −0.303917 | − | 0.952698i | \(-0.598295\pi\) | ||||
−0.303917 | + | 0.952698i | \(0.598295\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20756.0 | 1.52121 | 0.760606 | − | 0.649214i | \(-0.224902\pi\) | ||||
0.760606 | + | 0.649214i | \(0.224902\pi\) | |||||||
\(572\) | −1224.00 | −0.0894720 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6678.00 | 0.485600 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.00000 | 0.000144300 0 | 7.21500e−5 | − | 1.00000i | \(-0.499977\pi\) | ||||
7.21500e−5 | 1.00000i | \(0.499977\pi\) | ||||||||
\(578\) | −9447.00 | −0.679833 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1836.00 | −0.131441 | ||||||||
\(581\) | 1428.00 | 0.101968 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17928.0 | 1.27359 | ||||||||
\(584\) | 10542.0 | 0.746971 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15354.0 | −1.08237 | ||||||||
\(587\) | −26364.0 | −1.85376 | −0.926881 | − | 0.375354i | \(-0.877521\pi\) | ||||
−0.926881 | + | 0.375354i | \(0.877521\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19840.0 | 1.38793 | ||||||||
\(590\) | 7128.00 | 0.497382 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −28258.0 | −1.96182 | ||||||||
\(593\) | −2298.00 | −0.159136 | −0.0795679 | − | 0.996829i | \(-0.525354\pi\) | ||||
−0.0795679 | + | 0.996829i | \(0.525354\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5292.00 | −0.364623 | ||||||||
\(596\) | 1746.00 | 0.119998 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3072.00 | −0.209547 | −0.104773 | − | 0.994496i | \(-0.533412\pi\) | ||||
−0.104773 | + | 0.994496i | \(0.533412\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24554.0 | 1.66652 | 0.833260 | − | 0.552881i | \(-0.186472\pi\) | ||||
0.833260 | + | 0.552881i | \(0.186472\pi\) | |||||||
\(602\) | −5628.00 | −0.381030 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −232.000 | −0.0156290 | ||||||||
\(605\) | −630.000 | −0.0423358 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16832.0 | 1.12552 | 0.562759 | − | 0.826621i | \(-0.309740\pi\) | ||||
0.562759 | + | 0.826621i | \(0.309740\pi\) | |||||||
\(608\) | 5580.00 | 0.372202 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 21492.0 | 1.42653 | ||||||||
\(611\) | 8160.00 | 0.540292 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2482.00 | −0.163535 | −0.0817676 | − | 0.996651i | \(-0.526057\pi\) | ||||
−0.0817676 | + | 0.996651i | \(0.526057\pi\) | |||||||
\(614\) | 1356.00 | 0.0891266 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5292.00 | −0.346138 | ||||||||
\(617\) | 15798.0 | 1.03080 | 0.515400 | − | 0.856950i | \(-0.327643\pi\) | ||||
0.515400 | + | 0.856950i | \(0.327643\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15460.0 | −1.00386 | −0.501930 | − | 0.864908i | \(-0.667377\pi\) | ||||
−0.501930 | + | 0.864908i | \(0.667377\pi\) | |||||||
\(620\) | −2880.00 | −0.186554 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −15048.0 | −0.970048 | ||||||||
\(623\) | −2478.00 | −0.159356 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −899.000 | −0.0575360 | ||||||||
\(626\) | 16206.0 | 1.03470 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1694.00 | 0.107640 | ||||||||
\(629\) | −16716.0 | −1.05964 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7720.00 | −0.487050 | −0.243525 | − | 0.969895i | \(-0.578304\pi\) | ||||
−0.243525 | + | 0.969895i | \(0.578304\pi\) | |||||||
\(632\) | 21504.0 | 1.35345 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −30258.0 | −1.89542 | ||||||||
\(635\) | 23040.0 | 1.43987 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1666.00 | −0.103625 | ||||||||
\(638\) | −11016.0 | −0.683586 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 29862.0 | 1.84437 | ||||||||
\(641\) | 17262.0 | 1.06366 | 0.531832 | − | 0.846850i | \(-0.321504\pi\) | ||||
0.531832 | + | 0.846850i | \(0.321504\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12220.0 | −0.749471 | −0.374735 | − | 0.927132i | \(-0.622266\pi\) | ||||
−0.374735 | + | 0.927132i | \(0.622266\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 15624.0 | 0.951576 | ||||||||
\(647\) | −13560.0 | −0.823955 | −0.411977 | − | 0.911194i | \(-0.635162\pi\) | ||||
−0.411977 | + | 0.911194i | \(0.635162\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4752.00 | 0.287415 | ||||||||
\(650\) | −20298.0 | −1.22485 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2932.00 | −0.176113 | ||||||||
\(653\) | −23094.0 | −1.38398 | −0.691989 | − | 0.721908i | \(-0.743265\pi\) | ||||
−0.691989 | + | 0.721908i | \(0.743265\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −31752.0 | −1.89413 | ||||||||
\(656\) | −22578.0 | −1.34378 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5040.00 | −0.298601 | ||||||||
\(659\) | −22548.0 | −1.33285 | −0.666423 | − | 0.745574i | \(-0.732175\pi\) | ||||
−0.666423 | + | 0.745574i | \(0.732175\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17462.0 | 1.02752 | 0.513762 | − | 0.857933i | \(-0.328252\pi\) | ||||
0.513762 | + | 0.857933i | \(0.328252\pi\) | |||||||
\(662\) | −24132.0 | −1.41679 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4284.00 | −0.250379 | ||||||||
\(665\) | −15624.0 | −0.911087 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −1176.00 | −0.0681150 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4968.00 | 0.286464 | ||||||||
\(671\) | 14328.0 | 0.824331 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22462.0 | −1.28655 | −0.643274 | − | 0.765636i | \(-0.722424\pi\) | ||||
−0.643274 | + | 0.765636i | \(0.722424\pi\) | |||||||
\(674\) | 12534.0 | 0.716308 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1041.00 | −0.0592285 | ||||||||
\(677\) | 25554.0 | 1.45069 | 0.725347 | − | 0.688383i | \(-0.241679\pi\) | ||||
0.725347 | + | 0.688383i | \(0.241679\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2002.00 | −0.113151 | ||||||||
\(680\) | 15876.0 | 0.895319 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −17280.0 | −0.970213 | ||||||||
\(683\) | −9276.00 | −0.519672 | −0.259836 | − | 0.965653i | \(-0.583669\pi\) | ||||
−0.259836 | + | 0.965653i | \(0.583669\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 42444.0 | 2.36745 | ||||||||
\(686\) | 1029.00 | 0.0572703 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 19028.0 | 1.05441 | ||||||||
\(689\) | −16932.0 | −0.936223 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27380.0 | 1.50736 | 0.753679 | − | 0.657243i | \(-0.228277\pi\) | ||||
0.753679 | + | 0.657243i | \(0.228277\pi\) | |||||||
\(692\) | −870.000 | −0.0477925 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −468.000 | −0.0255980 | ||||||||
\(695\) | −936.000 | −0.0510856 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13356.0 | −0.725817 | ||||||||
\(698\) | −37254.0 | −2.02018 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1393.00 | 0.0752149 | ||||||||
\(701\) | −25830.0 | −1.39171 | −0.695853 | − | 0.718184i | \(-0.744973\pi\) | ||||
−0.695853 | + | 0.718184i | \(0.744973\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −49352.0 | −2.64772 | ||||||||
\(704\) | 15588.0 | 0.834510 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 23490.0 | 1.25221 | ||||||||
\(707\) | −2898.00 | −0.154159 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6226.00 | −0.329792 | −0.164896 | − | 0.986311i | \(-0.552729\pi\) | ||||
−0.164896 | + | 0.986311i | \(0.552729\pi\) | |||||||
\(710\) | 38880.0 | 2.05513 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7434.00 | 0.391293 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −22032.0 | −1.15238 | ||||||||
\(716\) | 2316.00 | 0.120884 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 27936.0 | 1.45204 | ||||||||
\(719\) | 15072.0 | 0.781767 | 0.390884 | − | 0.920440i | \(-0.372169\pi\) | ||||
0.390884 | + | 0.920440i | \(0.372169\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 392.000 | 0.0202480 | ||||||||
\(722\) | 25551.0 | 1.31705 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −106.000 | −0.00544124 | ||||||||
\(725\) | −20298.0 | −1.03979 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32920.0 | −1.67942 | −0.839708 | − | 0.543038i | \(-0.817274\pi\) | ||||
−0.839708 | + | 0.543038i | \(0.817274\pi\) | |||||||
\(728\) | 4998.00 | 0.254448 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −27108.0 | −1.37440 | ||||||||
\(731\) | 11256.0 | 0.569519 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6946.00 | −0.350009 | −0.175004 | − | 0.984568i | \(-0.555994\pi\) | ||||
−0.175004 | + | 0.984568i | \(0.555994\pi\) | |||||||
\(734\) | −11280.0 | −0.567238 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3312.00 | 0.165535 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2356.00 | −0.117276 | −0.0586379 | − | 0.998279i | \(-0.518676\pi\) | ||||
−0.0586379 | + | 0.998279i | \(0.518676\pi\) | |||||||
\(740\) | 7164.00 | 0.355884 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 10458.0 | 0.517419 | ||||||||
\(743\) | 23520.0 | 1.16133 | 0.580663 | − | 0.814144i | \(-0.302793\pi\) | ||||
0.580663 | + | 0.814144i | \(0.302793\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 31428.0 | 1.54555 | ||||||||
\(746\) | 17610.0 | 0.864273 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1512.00 | −0.0739094 | ||||||||
\(749\) | −84.0000 | −0.00409785 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3008.00 | 0.146156 | 0.0730782 | − | 0.997326i | \(-0.476718\pi\) | ||||
0.0730782 | + | 0.997326i | \(0.476718\pi\) | |||||||
\(752\) | 17040.0 | 0.826310 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 10404.0 | 0.502508 | ||||||||
\(755\) | −4176.00 | −0.201298 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20770.0 | −0.997224 | −0.498612 | − | 0.866825i | \(-0.666157\pi\) | ||||
−0.498612 | + | 0.866825i | \(0.666157\pi\) | |||||||
\(758\) | −5556.00 | −0.266231 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 46872.0 | 2.23714 | ||||||||
\(761\) | −11538.0 | −0.549609 | −0.274804 | − | 0.961500i | \(-0.588613\pi\) | ||||
−0.274804 | + | 0.961500i | \(0.588613\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10346.0 | 0.490892 | ||||||||
\(764\) | 1128.00 | 0.0534157 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6480.00 | −0.305655 | ||||||||
\(767\) | −4488.00 | −0.211281 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8498.00 | 0.398499 | 0.199249 | − | 0.979949i | \(-0.436150\pi\) | ||||
0.199249 | + | 0.979949i | \(0.436150\pi\) | |||||||
\(770\) | 13608.0 | 0.636881 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4034.00 | 0.188066 | ||||||||
\(773\) | 32322.0 | 1.50393 | 0.751967 | − | 0.659200i | \(-0.229105\pi\) | ||||
0.751967 | + | 0.659200i | \(0.229105\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −31840.0 | −1.47578 | ||||||||
\(776\) | 6006.00 | 0.277839 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20358.0 | 0.938136 | ||||||||
\(779\) | −39432.0 | −1.81360 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25920.0 | 1.18757 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3479.00 | −0.158482 | ||||||||
\(785\) | 30492.0 | 1.38638 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26228.0 | 1.18796 | 0.593982 | − | 0.804479i | \(-0.297555\pi\) | ||||
0.593982 | + | 0.804479i | \(0.297555\pi\) | |||||||
\(788\) | 1314.00 | 0.0594027 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −55296.0 | −2.49031 | ||||||||
\(791\) | −2814.00 | −0.126491 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13532.0 | −0.605972 | ||||||||
\(794\) | −19542.0 | −0.873450 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5096.00 | 0.226913 | ||||||||
\(797\) | 43338.0 | 1.92611 | 0.963056 | − | 0.269302i | \(-0.0867931\pi\) | ||||
0.963056 | + | 0.269302i | \(0.0867931\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10080.0 | 0.446314 | ||||||||
\(800\) | −8955.00 | −0.395759 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9990.00 | −0.439849 | ||||||||
\(803\) | −18072.0 | −0.794206 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 16320.0 | 0.713210 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 8694.00 | 0.378532 | ||||||||
\(809\) | 28902.0 | 1.25604 | 0.628022 | − | 0.778195i | \(-0.283865\pi\) | ||||
0.628022 | + | 0.778195i | \(0.283865\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27164.0 | 1.17615 | 0.588075 | − | 0.808807i | \(-0.299886\pi\) | ||||
0.588075 | + | 0.808807i | \(0.299886\pi\) | |||||||
\(812\) | −714.000 | −0.0308577 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 42984.0 | 1.85085 | ||||||||
\(815\) | −52776.0 | −2.26830 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 33232.0 | 1.42306 | ||||||||
\(818\) | −16194.0 | −0.692188 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5724.00 | 0.243769 | ||||||||
\(821\) | 17202.0 | 0.731247 | 0.365624 | − | 0.930763i | \(-0.380856\pi\) | ||||
0.365624 | + | 0.930763i | \(0.380856\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5992.00 | −0.253789 | −0.126894 | − | 0.991916i | \(-0.540501\pi\) | ||||
−0.126894 | + | 0.991916i | \(0.540501\pi\) | |||||||
\(824\) | −1176.00 | −0.0497183 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2772.00 | 0.116768 | ||||||||
\(827\) | −25884.0 | −1.08836 | −0.544181 | − | 0.838968i | \(-0.683159\pi\) | ||||
−0.544181 | + | 0.838968i | \(0.683159\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1474.00 | −0.0617541 | −0.0308770 | − | 0.999523i | \(-0.509830\pi\) | ||||
−0.0308770 | + | 0.999523i | \(0.509830\pi\) | |||||||
\(830\) | 11016.0 | 0.460688 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −14722.0 | −0.613454 | ||||||||
\(833\) | −2058.00 | −0.0856008 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21168.0 | −0.877304 | ||||||||
\(836\) | −4464.00 | −0.184678 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −39276.0 | −1.61905 | ||||||||
\(839\) | −33528.0 | −1.37964 | −0.689818 | − | 0.723983i | \(-0.742310\pi\) | ||||
−0.689818 | + | 0.723983i | \(0.742310\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13985.0 | −0.573414 | ||||||||
\(842\) | −966.000 | −0.0395375 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3076.00 | −0.125451 | ||||||||
\(845\) | −18738.0 | −0.762848 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −245.000 | −0.00993896 | ||||||||
\(848\) | −35358.0 | −1.43184 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −25074.0 | −1.01180 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1190.00 | 0.0477665 | 0.0238832 | − | 0.999715i | \(-0.492397\pi\) | ||||
0.0238832 | + | 0.999715i | \(0.492397\pi\) | |||||||
\(854\) | 8358.00 | 0.334900 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 252.000 | 0.0100621 | ||||||||
\(857\) | −34578.0 | −1.37825 | −0.689126 | − | 0.724642i | \(-0.742005\pi\) | ||||
−0.689126 | + | 0.724642i | \(0.742005\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44404.0 | −1.76373 | −0.881865 | − | 0.471501i | \(-0.843712\pi\) | ||||
−0.881865 | + | 0.471501i | \(0.843712\pi\) | |||||||
\(860\) | −4824.00 | −0.191276 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7848.00 | −0.310097 | ||||||||
\(863\) | 38328.0 | 1.51182 | 0.755910 | − | 0.654676i | \(-0.227195\pi\) | ||||
0.755910 | + | 0.654676i | \(0.227195\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15660.0 | −0.615556 | ||||||||
\(866\) | 12966.0 | 0.508779 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1120.00 | −0.0437964 | ||||||||
\(869\) | −36864.0 | −1.43904 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3128.00 | −0.121686 | ||||||||
\(872\) | −31038.0 | −1.20537 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9324.00 | 0.360239 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −38842.0 | −1.49555 | −0.747777 | − | 0.663950i | \(-0.768879\pi\) | ||||
−0.747777 | + | 0.663950i | \(0.768879\pi\) | |||||||
\(878\) | −27048.0 | −1.03966 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −46008.0 | −1.76242 | ||||||||
\(881\) | 35046.0 | 1.34022 | 0.670108 | − | 0.742264i | \(-0.266248\pi\) | ||||
0.670108 | + | 0.742264i | \(0.266248\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14204.0 | 0.541339 | 0.270670 | − | 0.962672i | \(-0.412755\pi\) | ||||
0.270670 | + | 0.962672i | \(0.412755\pi\) | |||||||
\(884\) | 1428.00 | 0.0543313 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15804.0 | 0.599262 | ||||||||
\(887\) | 26136.0 | 0.989359 | 0.494679 | − | 0.869076i | \(-0.335286\pi\) | ||||
0.494679 | + | 0.869076i | \(0.335286\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8960.00 | 0.338030 | ||||||||
\(890\) | −19116.0 | −0.719966 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1888.00 | −0.0708687 | ||||||||
\(893\) | 29760.0 | 1.11521 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 41688.0 | 1.55696 | ||||||||
\(896\) | 11613.0 | 0.432995 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15930.0 | 0.591972 | ||||||||
\(899\) | 16320.0 | 0.605453 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20916.0 | −0.773377 | ||||||||
\(902\) | 34344.0 | 1.26777 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8442.00 | 0.310594 | ||||||||
\(905\) | −1908.00 | −0.0700818 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9052.00 | −0.331386 | −0.165693 | − | 0.986177i | \(-0.552986\pi\) | ||||
−0.165693 | + | 0.986177i | \(0.552986\pi\) | |||||||
\(908\) | 4716.00 | 0.172363 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −12852.0 | −0.468175 | ||||||||
\(911\) | −5016.00 | −0.182423 | −0.0912116 | − | 0.995832i | \(-0.529074\pi\) | ||||
−0.0912116 | + | 0.995832i | \(0.529074\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7344.00 | 0.266211 | ||||||||
\(914\) | 47310.0 | 1.71212 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1690.00 | −0.0609598 | ||||||||
\(917\) | −12348.0 | −0.444675 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44552.0 | 1.59917 | 0.799584 | − | 0.600555i | \(-0.205054\pi\) | ||||
0.799584 | + | 0.600555i | \(0.205054\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 16110.0 | 0.575439 | ||||||||
\(923\) | −24480.0 | −0.872989 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 79202.0 | 2.81529 | ||||||||
\(926\) | −9984.00 | −0.354314 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4590.00 | 0.162364 | ||||||||
\(929\) | −24234.0 | −0.855858 | −0.427929 | − | 0.903812i | \(-0.640757\pi\) | ||||
−0.427929 | + | 0.903812i | \(0.640757\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6076.00 | −0.213891 | ||||||||
\(932\) | −138.000 | −0.00485015 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −13644.0 | −0.477993 | ||||||||
\(935\) | −27216.0 | −0.951934 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13894.0 | −0.484415 | −0.242208 | − | 0.970224i | \(-0.577872\pi\) | ||||
−0.242208 | + | 0.970224i | \(0.577872\pi\) | |||||||
\(938\) | 1932.00 | 0.0672516 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4320.00 | −0.149897 | ||||||||
\(941\) | −46758.0 | −1.61984 | −0.809919 | − | 0.586542i | \(-0.800489\pi\) | ||||
−0.809919 | + | 0.586542i | \(0.800489\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −9372.00 | −0.323128 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −28944.0 | −0.994768 | ||||||||
\(947\) | −13812.0 | −0.473949 | −0.236974 | − | 0.971516i | \(-0.576156\pi\) | ||||
−0.236974 | + | 0.971516i | \(0.576156\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17068.0 | 0.583826 | ||||||||
\(950\) | −74028.0 | −2.52820 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6174.00 | 0.210190 | ||||||||
\(953\) | 58518.0 | 1.98907 | 0.994535 | − | 0.104402i | \(-0.0332930\pi\) | ||||
0.994535 | + | 0.104402i | \(0.0332930\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20304.0 | 0.687981 | ||||||||
\(956\) | −1896.00 | −0.0641433 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 24192.0 | 0.815875 | ||||||||
\(959\) | 16506.0 | 0.555794 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4191.00 | −0.140680 | ||||||||
\(962\) | −40596.0 | −1.36057 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3598.00 | −0.120211 | ||||||||
\(965\) | 72612.0 | 2.42224 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19640.0 | 0.653133 | 0.326567 | − | 0.945174i | \(-0.394108\pi\) | ||||
0.326567 | + | 0.945174i | \(0.394108\pi\) | |||||||
\(968\) | 735.000 | 0.0244047 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −15444.0 | −0.511213 | ||||||||
\(971\) | 58308.0 | 1.92708 | 0.963539 | − | 0.267568i | \(-0.0862200\pi\) | ||||
0.963539 | + | 0.267568i | \(0.0862200\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −364.000 | −0.0119931 | ||||||||
\(974\) | 49848.0 | 1.63987 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −28258.0 | −0.926759 | ||||||||
\(977\) | 23550.0 | 0.771168 | 0.385584 | − | 0.922673i | \(-0.374000\pi\) | ||||
0.385584 | + | 0.922673i | \(0.374000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12744.0 | −0.416037 | ||||||||
\(980\) | 882.000 | 0.0287494 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 21420.0 | 0.696069 | ||||||||
\(983\) | −15768.0 | −0.511619 | −0.255809 | − | 0.966727i | \(-0.582342\pi\) | ||||
−0.255809 | + | 0.966727i | \(0.582342\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 23652.0 | 0.765092 | ||||||||
\(986\) | 12852.0 | 0.415102 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4216.00 | 0.135758 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35264.0 | 1.13037 | 0.565186 | − | 0.824964i | \(-0.308805\pi\) | ||||
0.565186 | + | 0.824964i | \(0.308805\pi\) | |||||||
\(992\) | 7200.00 | 0.230444 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 15120.0 | 0.482472 | ||||||||
\(995\) | 91728.0 | 2.92259 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29338.0 | −0.931940 | −0.465970 | − | 0.884801i | \(-0.654294\pi\) | ||||
−0.465970 | + | 0.884801i | \(0.654294\pi\) | |||||||
\(998\) | −27372.0 | −0.868182 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 63.4.a.c.1.1 | 1 | ||
3.2 | odd | 2 | 21.4.a.a.1.1 | ✓ | 1 | ||
4.3 | odd | 2 | 1008.4.a.v.1.1 | 1 | |||
5.4 | even | 2 | 1575.4.a.b.1.1 | 1 | |||
7.2 | even | 3 | 441.4.e.b.361.1 | 2 | |||
7.3 | odd | 6 | 441.4.e.d.226.1 | 2 | |||
7.4 | even | 3 | 441.4.e.b.226.1 | 2 | |||
7.5 | odd | 6 | 441.4.e.d.361.1 | 2 | |||
7.6 | odd | 2 | 441.4.a.j.1.1 | 1 | |||
12.11 | even | 2 | 336.4.a.f.1.1 | 1 | |||
15.2 | even | 4 | 525.4.d.c.274.1 | 2 | |||
15.8 | even | 4 | 525.4.d.c.274.2 | 2 | |||
15.14 | odd | 2 | 525.4.a.g.1.1 | 1 | |||
21.2 | odd | 6 | 147.4.e.i.67.1 | 2 | |||
21.5 | even | 6 | 147.4.e.g.67.1 | 2 | |||
21.11 | odd | 6 | 147.4.e.i.79.1 | 2 | |||
21.17 | even | 6 | 147.4.e.g.79.1 | 2 | |||
21.20 | even | 2 | 147.4.a.c.1.1 | 1 | |||
24.5 | odd | 2 | 1344.4.a.ba.1.1 | 1 | |||
24.11 | even | 2 | 1344.4.a.n.1.1 | 1 | |||
84.83 | odd | 2 | 2352.4.a.r.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.4.a.a.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
63.4.a.c.1.1 | 1 | 1.1 | even | 1 | trivial | ||
147.4.a.c.1.1 | 1 | 21.20 | even | 2 | |||
147.4.e.g.67.1 | 2 | 21.5 | even | 6 | |||
147.4.e.g.79.1 | 2 | 21.17 | even | 6 | |||
147.4.e.i.67.1 | 2 | 21.2 | odd | 6 | |||
147.4.e.i.79.1 | 2 | 21.11 | odd | 6 | |||
336.4.a.f.1.1 | 1 | 12.11 | even | 2 | |||
441.4.a.j.1.1 | 1 | 7.6 | odd | 2 | |||
441.4.e.b.226.1 | 2 | 7.4 | even | 3 | |||
441.4.e.b.361.1 | 2 | 7.2 | even | 3 | |||
441.4.e.d.226.1 | 2 | 7.3 | odd | 6 | |||
441.4.e.d.361.1 | 2 | 7.5 | odd | 6 | |||
525.4.a.g.1.1 | 1 | 15.14 | odd | 2 | |||
525.4.d.c.274.1 | 2 | 15.2 | even | 4 | |||
525.4.d.c.274.2 | 2 | 15.8 | even | 4 | |||
1008.4.a.v.1.1 | 1 | 4.3 | odd | 2 | |||
1344.4.a.n.1.1 | 1 | 24.11 | even | 2 | |||
1344.4.a.ba.1.1 | 1 | 24.5 | odd | 2 | |||
1575.4.a.b.1.1 | 1 | 5.4 | even | 2 | |||
2352.4.a.r.1.1 | 1 | 84.83 | odd | 2 |