Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,4,Mod(1,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, 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("507.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.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: | \(29.9139683729\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 39) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 507.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.353553 | 0.176777 | − | 0.984251i | \(-0.443433\pi\) | ||||
0.176777 | + | 0.984251i | \(0.443433\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | −7.00000 | −0.875000 | ||||||||
\(5\) | −7.00000 | −0.626099 | −0.313050 | − | 0.949737i | \(-0.601351\pi\) | ||||
−0.313050 | + | 0.949737i | \(0.601351\pi\) | |||||||
\(6\) | 3.00000 | 0.204124 | ||||||||
\(7\) | 10.0000 | 0.539949 | 0.269975 | − | 0.962867i | \(-0.412985\pi\) | ||||
0.269975 | + | 0.962867i | \(0.412985\pi\) | |||||||
\(8\) | −15.0000 | −0.662913 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −7.00000 | −0.221359 | ||||||||
\(11\) | 22.0000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | −21.0000 | −0.505181 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 10.0000 | 0.190901 | ||||||||
\(15\) | −21.0000 | −0.361478 | ||||||||
\(16\) | 41.0000 | 0.640625 | ||||||||
\(17\) | 37.0000 | 0.527872 | 0.263936 | − | 0.964540i | \(-0.414979\pi\) | ||||
0.263936 | + | 0.964540i | \(0.414979\pi\) | |||||||
\(18\) | 9.00000 | 0.117851 | ||||||||
\(19\) | −30.0000 | −0.362235 | −0.181118 | − | 0.983461i | \(-0.557971\pi\) | ||||
−0.181118 | + | 0.983461i | \(0.557971\pi\) | |||||||
\(20\) | 49.0000 | 0.547837 | ||||||||
\(21\) | 30.0000 | 0.311740 | ||||||||
\(22\) | 22.0000 | 0.213201 | ||||||||
\(23\) | −162.000 | −1.46867 | −0.734333 | − | 0.678789i | \(-0.762505\pi\) | ||||
−0.734333 | + | 0.678789i | \(0.762505\pi\) | |||||||
\(24\) | −45.0000 | −0.382733 | ||||||||
\(25\) | −76.0000 | −0.608000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −70.0000 | −0.472456 | ||||||||
\(29\) | −113.000 | −0.723571 | −0.361786 | − | 0.932261i | \(-0.617833\pi\) | ||||
−0.361786 | + | 0.932261i | \(0.617833\pi\) | |||||||
\(30\) | −21.0000 | −0.127802 | ||||||||
\(31\) | −196.000 | −1.13557 | −0.567785 | − | 0.823177i | \(-0.692199\pi\) | ||||
−0.567785 | + | 0.823177i | \(0.692199\pi\) | |||||||
\(32\) | 161.000 | 0.889408 | ||||||||
\(33\) | 66.0000 | 0.348155 | ||||||||
\(34\) | 37.0000 | 0.186631 | ||||||||
\(35\) | −70.0000 | −0.338062 | ||||||||
\(36\) | −63.0000 | −0.291667 | ||||||||
\(37\) | −13.0000 | −0.0577618 | −0.0288809 | − | 0.999583i | \(-0.509194\pi\) | ||||
−0.0288809 | + | 0.999583i | \(0.509194\pi\) | |||||||
\(38\) | −30.0000 | −0.128070 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 105.000 | 0.415049 | ||||||||
\(41\) | −285.000 | −1.08560 | −0.542799 | − | 0.839863i | \(-0.682635\pi\) | ||||
−0.542799 | + | 0.839863i | \(0.682635\pi\) | |||||||
\(42\) | 30.0000 | 0.110217 | ||||||||
\(43\) | −246.000 | −0.872434 | −0.436217 | − | 0.899842i | \(-0.643682\pi\) | ||||
−0.436217 | + | 0.899842i | \(0.643682\pi\) | |||||||
\(44\) | −154.000 | −0.527645 | ||||||||
\(45\) | −63.0000 | −0.208700 | ||||||||
\(46\) | −162.000 | −0.519252 | ||||||||
\(47\) | 462.000 | 1.43382 | 0.716911 | − | 0.697165i | \(-0.245555\pi\) | ||||
0.716911 | + | 0.697165i | \(0.245555\pi\) | |||||||
\(48\) | 123.000 | 0.369865 | ||||||||
\(49\) | −243.000 | −0.708455 | ||||||||
\(50\) | −76.0000 | −0.214960 | ||||||||
\(51\) | 111.000 | 0.304767 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −537.000 | −1.39175 | −0.695874 | − | 0.718164i | \(-0.744983\pi\) | ||||
−0.695874 | + | 0.718164i | \(0.744983\pi\) | |||||||
\(54\) | 27.0000 | 0.0680414 | ||||||||
\(55\) | −154.000 | −0.377552 | ||||||||
\(56\) | −150.000 | −0.357939 | ||||||||
\(57\) | −90.0000 | −0.209137 | ||||||||
\(58\) | −113.000 | −0.255821 | ||||||||
\(59\) | −576.000 | −1.27100 | −0.635498 | − | 0.772102i | \(-0.719205\pi\) | ||||
−0.635498 | + | 0.772102i | \(0.719205\pi\) | |||||||
\(60\) | 147.000 | 0.316294 | ||||||||
\(61\) | −635.000 | −1.33284 | −0.666421 | − | 0.745575i | \(-0.732175\pi\) | ||||
−0.666421 | + | 0.745575i | \(0.732175\pi\) | |||||||
\(62\) | −196.000 | −0.401484 | ||||||||
\(63\) | 90.0000 | 0.179983 | ||||||||
\(64\) | −167.000 | −0.326172 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 66.0000 | 0.123091 | ||||||||
\(67\) | −202.000 | −0.368332 | −0.184166 | − | 0.982895i | \(-0.558958\pi\) | ||||
−0.184166 | + | 0.982895i | \(0.558958\pi\) | |||||||
\(68\) | −259.000 | −0.461888 | ||||||||
\(69\) | −486.000 | −0.847935 | ||||||||
\(70\) | −70.0000 | −0.119523 | ||||||||
\(71\) | 1086.00 | 1.81527 | 0.907637 | − | 0.419755i | \(-0.137884\pi\) | ||||
0.907637 | + | 0.419755i | \(0.137884\pi\) | |||||||
\(72\) | −135.000 | −0.220971 | ||||||||
\(73\) | 805.000 | 1.29066 | 0.645330 | − | 0.763904i | \(-0.276720\pi\) | ||||
0.645330 | + | 0.763904i | \(0.276720\pi\) | |||||||
\(74\) | −13.0000 | −0.0204219 | ||||||||
\(75\) | −228.000 | −0.351029 | ||||||||
\(76\) | 210.000 | 0.316956 | ||||||||
\(77\) | 220.000 | 0.325602 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 884.000 | 1.25896 | 0.629480 | − | 0.777017i | \(-0.283268\pi\) | ||||
0.629480 | + | 0.777017i | \(0.283268\pi\) | |||||||
\(80\) | −287.000 | −0.401095 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −285.000 | −0.383817 | ||||||||
\(83\) | −518.000 | −0.685035 | −0.342517 | − | 0.939511i | \(-0.611280\pi\) | ||||
−0.342517 | + | 0.939511i | \(0.611280\pi\) | |||||||
\(84\) | −210.000 | −0.272772 | ||||||||
\(85\) | −259.000 | −0.330500 | ||||||||
\(86\) | −246.000 | −0.308452 | ||||||||
\(87\) | −339.000 | −0.417754 | ||||||||
\(88\) | −330.000 | −0.399751 | ||||||||
\(89\) | −194.000 | −0.231056 | −0.115528 | − | 0.993304i | \(-0.536856\pi\) | ||||
−0.115528 | + | 0.993304i | \(0.536856\pi\) | |||||||
\(90\) | −63.0000 | −0.0737865 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1134.00 | 1.28508 | ||||||||
\(93\) | −588.000 | −0.655621 | ||||||||
\(94\) | 462.000 | 0.506933 | ||||||||
\(95\) | 210.000 | 0.226795 | ||||||||
\(96\) | 483.000 | 0.513500 | ||||||||
\(97\) | 1202.00 | 1.25819 | 0.629096 | − | 0.777328i | \(-0.283425\pi\) | ||||
0.629096 | + | 0.777328i | \(0.283425\pi\) | |||||||
\(98\) | −243.000 | −0.250477 | ||||||||
\(99\) | 198.000 | 0.201008 | ||||||||
\(100\) | 532.000 | 0.532000 | ||||||||
\(101\) | −429.000 | −0.422645 | −0.211322 | − | 0.977416i | \(-0.567777\pi\) | ||||
−0.211322 | + | 0.977416i | \(0.567777\pi\) | |||||||
\(102\) | 111.000 | 0.107751 | ||||||||
\(103\) | −1302.00 | −1.24553 | −0.622766 | − | 0.782408i | \(-0.713991\pi\) | ||||
−0.622766 | + | 0.782408i | \(0.713991\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −210.000 | −0.195180 | ||||||||
\(106\) | −537.000 | −0.492057 | ||||||||
\(107\) | −1338.00 | −1.20887 | −0.604436 | − | 0.796654i | \(-0.706602\pi\) | ||||
−0.604436 | + | 0.796654i | \(0.706602\pi\) | |||||||
\(108\) | −189.000 | −0.168394 | ||||||||
\(109\) | 1034.00 | 0.908617 | 0.454308 | − | 0.890844i | \(-0.349886\pi\) | ||||
0.454308 | + | 0.890844i | \(0.349886\pi\) | |||||||
\(110\) | −154.000 | −0.133485 | ||||||||
\(111\) | −39.0000 | −0.0333488 | ||||||||
\(112\) | 410.000 | 0.345905 | ||||||||
\(113\) | 1077.00 | 0.896599 | 0.448299 | − | 0.893884i | \(-0.352030\pi\) | ||||
0.448299 | + | 0.893884i | \(0.352030\pi\) | |||||||
\(114\) | −90.0000 | −0.0739410 | ||||||||
\(115\) | 1134.00 | 0.919531 | ||||||||
\(116\) | 791.000 | 0.633125 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −576.000 | −0.449365 | ||||||||
\(119\) | 370.000 | 0.285024 | ||||||||
\(120\) | 315.000 | 0.239629 | ||||||||
\(121\) | −847.000 | −0.636364 | ||||||||
\(122\) | −635.000 | −0.471231 | ||||||||
\(123\) | −855.000 | −0.626770 | ||||||||
\(124\) | 1372.00 | 0.993623 | ||||||||
\(125\) | 1407.00 | 1.00677 | ||||||||
\(126\) | 90.0000 | 0.0636336 | ||||||||
\(127\) | −988.000 | −0.690321 | −0.345161 | − | 0.938544i | \(-0.612176\pi\) | ||||
−0.345161 | + | 0.938544i | \(0.612176\pi\) | |||||||
\(128\) | −1455.00 | −1.00473 | ||||||||
\(129\) | −738.000 | −0.503700 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 560.000 | 0.373492 | 0.186746 | − | 0.982408i | \(-0.440206\pi\) | ||||
0.186746 | + | 0.982408i | \(0.440206\pi\) | |||||||
\(132\) | −462.000 | −0.304636 | ||||||||
\(133\) | −300.000 | −0.195589 | ||||||||
\(134\) | −202.000 | −0.130225 | ||||||||
\(135\) | −189.000 | −0.120493 | ||||||||
\(136\) | −555.000 | −0.349933 | ||||||||
\(137\) | 519.000 | 0.323658 | 0.161829 | − | 0.986819i | \(-0.448261\pi\) | ||||
0.161829 | + | 0.986819i | \(0.448261\pi\) | |||||||
\(138\) | −486.000 | −0.299790 | ||||||||
\(139\) | −348.000 | −0.212352 | −0.106176 | − | 0.994347i | \(-0.533861\pi\) | ||||
−0.106176 | + | 0.994347i | \(0.533861\pi\) | |||||||
\(140\) | 490.000 | 0.295804 | ||||||||
\(141\) | 1386.00 | 0.827817 | ||||||||
\(142\) | 1086.00 | 0.641796 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 369.000 | 0.213542 | ||||||||
\(145\) | 791.000 | 0.453027 | ||||||||
\(146\) | 805.000 | 0.456317 | ||||||||
\(147\) | −729.000 | −0.409027 | ||||||||
\(148\) | 91.0000 | 0.0505416 | ||||||||
\(149\) | 645.000 | 0.354634 | 0.177317 | − | 0.984154i | \(-0.443258\pi\) | ||||
0.177317 | + | 0.984154i | \(0.443258\pi\) | |||||||
\(150\) | −228.000 | −0.124107 | ||||||||
\(151\) | −2914.00 | −1.57045 | −0.785225 | − | 0.619211i | \(-0.787453\pi\) | ||||
−0.785225 | + | 0.619211i | \(0.787453\pi\) | |||||||
\(152\) | 450.000 | 0.240130 | ||||||||
\(153\) | 333.000 | 0.175957 | ||||||||
\(154\) | 220.000 | 0.115118 | ||||||||
\(155\) | 1372.00 | 0.710979 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2079.00 | −1.05683 | −0.528415 | − | 0.848986i | \(-0.677213\pi\) | ||||
−0.528415 | + | 0.848986i | \(0.677213\pi\) | |||||||
\(158\) | 884.000 | 0.445109 | ||||||||
\(159\) | −1611.00 | −0.803526 | ||||||||
\(160\) | −1127.00 | −0.556857 | ||||||||
\(161\) | −1620.00 | −0.793006 | ||||||||
\(162\) | 81.0000 | 0.0392837 | ||||||||
\(163\) | −1700.00 | −0.816897 | −0.408449 | − | 0.912781i | \(-0.633930\pi\) | ||||
−0.408449 | + | 0.912781i | \(0.633930\pi\) | |||||||
\(164\) | 1995.00 | 0.949898 | ||||||||
\(165\) | −462.000 | −0.217980 | ||||||||
\(166\) | −518.000 | −0.242196 | ||||||||
\(167\) | −3680.00 | −1.70519 | −0.852596 | − | 0.522571i | \(-0.824973\pi\) | ||||
−0.852596 | + | 0.522571i | \(0.824973\pi\) | |||||||
\(168\) | −450.000 | −0.206656 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −259.000 | −0.116849 | ||||||||
\(171\) | −270.000 | −0.120745 | ||||||||
\(172\) | 1722.00 | 0.763379 | ||||||||
\(173\) | 4146.00 | 1.82205 | 0.911025 | − | 0.412352i | \(-0.135293\pi\) | ||||
0.911025 | + | 0.412352i | \(0.135293\pi\) | |||||||
\(174\) | −339.000 | −0.147698 | ||||||||
\(175\) | −760.000 | −0.328289 | ||||||||
\(176\) | 902.000 | 0.386311 | ||||||||
\(177\) | −1728.00 | −0.733810 | ||||||||
\(178\) | −194.000 | −0.0816905 | ||||||||
\(179\) | 3674.00 | 1.53412 | 0.767060 | − | 0.641575i | \(-0.221719\pi\) | ||||
0.767060 | + | 0.641575i | \(0.221719\pi\) | |||||||
\(180\) | 441.000 | 0.182612 | ||||||||
\(181\) | −3283.00 | −1.34820 | −0.674098 | − | 0.738642i | \(-0.735467\pi\) | ||||
−0.674098 | + | 0.738642i | \(0.735467\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1905.00 | −0.769517 | ||||||||
\(184\) | 2430.00 | 0.973598 | ||||||||
\(185\) | 91.0000 | 0.0361646 | ||||||||
\(186\) | −588.000 | −0.231797 | ||||||||
\(187\) | 814.000 | 0.318319 | ||||||||
\(188\) | −3234.00 | −1.25459 | ||||||||
\(189\) | 270.000 | 0.103913 | ||||||||
\(190\) | 210.000 | 0.0801842 | ||||||||
\(191\) | −596.000 | −0.225786 | −0.112893 | − | 0.993607i | \(-0.536012\pi\) | ||||
−0.112893 | + | 0.993607i | \(0.536012\pi\) | |||||||
\(192\) | −501.000 | −0.188315 | ||||||||
\(193\) | 393.000 | 0.146574 | 0.0732869 | − | 0.997311i | \(-0.476651\pi\) | ||||
0.0732869 | + | 0.997311i | \(0.476651\pi\) | |||||||
\(194\) | 1202.00 | 0.444838 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1701.00 | 0.619898 | ||||||||
\(197\) | 3522.00 | 1.27377 | 0.636884 | − | 0.770960i | \(-0.280223\pi\) | ||||
0.636884 | + | 0.770960i | \(0.280223\pi\) | |||||||
\(198\) | 198.000 | 0.0710669 | ||||||||
\(199\) | 2018.00 | 0.718855 | 0.359428 | − | 0.933173i | \(-0.382972\pi\) | ||||
0.359428 | + | 0.933173i | \(0.382972\pi\) | |||||||
\(200\) | 1140.00 | 0.403051 | ||||||||
\(201\) | −606.000 | −0.212656 | ||||||||
\(202\) | −429.000 | −0.149427 | ||||||||
\(203\) | −1130.00 | −0.390692 | ||||||||
\(204\) | −777.000 | −0.266671 | ||||||||
\(205\) | 1995.00 | 0.679692 | ||||||||
\(206\) | −1302.00 | −0.440362 | ||||||||
\(207\) | −1458.00 | −0.489556 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −660.000 | −0.218436 | ||||||||
\(210\) | −210.000 | −0.0690066 | ||||||||
\(211\) | 160.000 | 0.0522031 | 0.0261016 | − | 0.999659i | \(-0.491691\pi\) | ||||
0.0261016 | + | 0.999659i | \(0.491691\pi\) | |||||||
\(212\) | 3759.00 | 1.21778 | ||||||||
\(213\) | 3258.00 | 1.04805 | ||||||||
\(214\) | −1338.00 | −0.427401 | ||||||||
\(215\) | 1722.00 | 0.546230 | ||||||||
\(216\) | −405.000 | −0.127578 | ||||||||
\(217\) | −1960.00 | −0.613150 | ||||||||
\(218\) | 1034.00 | 0.321245 | ||||||||
\(219\) | 2415.00 | 0.745162 | ||||||||
\(220\) | 1078.00 | 0.330358 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −39.0000 | −0.0117906 | ||||||||
\(223\) | −4072.00 | −1.22279 | −0.611393 | − | 0.791327i | \(-0.709391\pi\) | ||||
−0.611393 | + | 0.791327i | \(0.709391\pi\) | |||||||
\(224\) | 1610.00 | 0.480235 | ||||||||
\(225\) | −684.000 | −0.202667 | ||||||||
\(226\) | 1077.00 | 0.316995 | ||||||||
\(227\) | 5794.00 | 1.69410 | 0.847051 | − | 0.531511i | \(-0.178376\pi\) | ||||
0.847051 | + | 0.531511i | \(0.178376\pi\) | |||||||
\(228\) | 630.000 | 0.182995 | ||||||||
\(229\) | −6482.00 | −1.87049 | −0.935246 | − | 0.353999i | \(-0.884822\pi\) | ||||
−0.935246 | + | 0.353999i | \(0.884822\pi\) | |||||||
\(230\) | 1134.00 | 0.325103 | ||||||||
\(231\) | 660.000 | 0.187986 | ||||||||
\(232\) | 1695.00 | 0.479665 | ||||||||
\(233\) | 6890.00 | 1.93725 | 0.968624 | − | 0.248530i | \(-0.0799474\pi\) | ||||
0.968624 | + | 0.248530i | \(0.0799474\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3234.00 | −0.897714 | ||||||||
\(236\) | 4032.00 | 1.11212 | ||||||||
\(237\) | 2652.00 | 0.726860 | ||||||||
\(238\) | 370.000 | 0.100771 | ||||||||
\(239\) | −2466.00 | −0.667415 | −0.333708 | − | 0.942677i | \(-0.608300\pi\) | ||||
−0.333708 | + | 0.942677i | \(0.608300\pi\) | |||||||
\(240\) | −861.000 | −0.231572 | ||||||||
\(241\) | 3617.00 | 0.966770 | 0.483385 | − | 0.875408i | \(-0.339407\pi\) | ||||
0.483385 | + | 0.875408i | \(0.339407\pi\) | |||||||
\(242\) | −847.000 | −0.224989 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 4445.00 | 1.16624 | ||||||||
\(245\) | 1701.00 | 0.443563 | ||||||||
\(246\) | −855.000 | −0.221597 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2940.00 | 0.752783 | ||||||||
\(249\) | −1554.00 | −0.395505 | ||||||||
\(250\) | 1407.00 | 0.355946 | ||||||||
\(251\) | 4860.00 | 1.22215 | 0.611077 | − | 0.791571i | \(-0.290737\pi\) | ||||
0.611077 | + | 0.791571i | \(0.290737\pi\) | |||||||
\(252\) | −630.000 | −0.157485 | ||||||||
\(253\) | −3564.00 | −0.885639 | ||||||||
\(254\) | −988.000 | −0.244065 | ||||||||
\(255\) | −777.000 | −0.190814 | ||||||||
\(256\) | −119.000 | −0.0290527 | ||||||||
\(257\) | 565.000 | 0.137135 | 0.0685676 | − | 0.997646i | \(-0.478157\pi\) | ||||
0.0685676 | + | 0.997646i | \(0.478157\pi\) | |||||||
\(258\) | −738.000 | −0.178085 | ||||||||
\(259\) | −130.000 | −0.0311884 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1017.00 | −0.241190 | ||||||||
\(262\) | 560.000 | 0.132049 | ||||||||
\(263\) | −498.000 | −0.116760 | −0.0583802 | − | 0.998294i | \(-0.518594\pi\) | ||||
−0.0583802 | + | 0.998294i | \(0.518594\pi\) | |||||||
\(264\) | −990.000 | −0.230797 | ||||||||
\(265\) | 3759.00 | 0.871372 | ||||||||
\(266\) | −300.000 | −0.0691511 | ||||||||
\(267\) | −582.000 | −0.133400 | ||||||||
\(268\) | 1414.00 | 0.322290 | ||||||||
\(269\) | 5546.00 | 1.25705 | 0.628523 | − | 0.777791i | \(-0.283660\pi\) | ||||
0.628523 | + | 0.777791i | \(0.283660\pi\) | |||||||
\(270\) | −189.000 | −0.0426006 | ||||||||
\(271\) | 2256.00 | 0.505691 | 0.252845 | − | 0.967507i | \(-0.418634\pi\) | ||||
0.252845 | + | 0.967507i | \(0.418634\pi\) | |||||||
\(272\) | 1517.00 | 0.338168 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 519.000 | 0.114430 | ||||||||
\(275\) | −1672.00 | −0.366638 | ||||||||
\(276\) | 3402.00 | 0.741943 | ||||||||
\(277\) | 2309.00 | 0.500846 | 0.250423 | − | 0.968137i | \(-0.419430\pi\) | ||||
0.250423 | + | 0.968137i | \(0.419430\pi\) | |||||||
\(278\) | −348.000 | −0.0750779 | ||||||||
\(279\) | −1764.00 | −0.378523 | ||||||||
\(280\) | 1050.00 | 0.224105 | ||||||||
\(281\) | −5833.00 | −1.23832 | −0.619159 | − | 0.785265i | \(-0.712527\pi\) | ||||
−0.619159 | + | 0.785265i | \(0.712527\pi\) | |||||||
\(282\) | 1386.00 | 0.292678 | ||||||||
\(283\) | 1650.00 | 0.346581 | 0.173290 | − | 0.984871i | \(-0.444560\pi\) | ||||
0.173290 | + | 0.984871i | \(0.444560\pi\) | |||||||
\(284\) | −7602.00 | −1.58837 | ||||||||
\(285\) | 630.000 | 0.130940 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2850.00 | −0.586168 | ||||||||
\(288\) | 1449.00 | 0.296469 | ||||||||
\(289\) | −3544.00 | −0.721352 | ||||||||
\(290\) | 791.000 | 0.160169 | ||||||||
\(291\) | 3606.00 | 0.726417 | ||||||||
\(292\) | −5635.00 | −1.12933 | ||||||||
\(293\) | −2991.00 | −0.596369 | −0.298184 | − | 0.954508i | \(-0.596381\pi\) | ||||
−0.298184 | + | 0.954508i | \(0.596381\pi\) | |||||||
\(294\) | −729.000 | −0.144613 | ||||||||
\(295\) | 4032.00 | 0.795770 | ||||||||
\(296\) | 195.000 | 0.0382910 | ||||||||
\(297\) | 594.000 | 0.116052 | ||||||||
\(298\) | 645.000 | 0.125382 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1596.00 | 0.307150 | ||||||||
\(301\) | −2460.00 | −0.471070 | ||||||||
\(302\) | −2914.00 | −0.555238 | ||||||||
\(303\) | −1287.00 | −0.244014 | ||||||||
\(304\) | −1230.00 | −0.232057 | ||||||||
\(305\) | 4445.00 | 0.834492 | ||||||||
\(306\) | 333.000 | 0.0622103 | ||||||||
\(307\) | 2422.00 | 0.450263 | 0.225132 | − | 0.974328i | \(-0.427719\pi\) | ||||
0.225132 | + | 0.974328i | \(0.427719\pi\) | |||||||
\(308\) | −1540.00 | −0.284901 | ||||||||
\(309\) | −3906.00 | −0.719109 | ||||||||
\(310\) | 1372.00 | 0.251369 | ||||||||
\(311\) | −3402.00 | −0.620288 | −0.310144 | − | 0.950690i | \(-0.600377\pi\) | ||||
−0.310144 | + | 0.950690i | \(0.600377\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2310.00 | 0.417153 | 0.208577 | − | 0.978006i | \(-0.433117\pi\) | ||||
0.208577 | + | 0.978006i | \(0.433117\pi\) | |||||||
\(314\) | −2079.00 | −0.373646 | ||||||||
\(315\) | −630.000 | −0.112687 | ||||||||
\(316\) | −6188.00 | −1.10159 | ||||||||
\(317\) | 257.000 | 0.0455349 | 0.0227674 | − | 0.999741i | \(-0.492752\pi\) | ||||
0.0227674 | + | 0.999741i | \(0.492752\pi\) | |||||||
\(318\) | −1611.00 | −0.284089 | ||||||||
\(319\) | −2486.00 | −0.436330 | ||||||||
\(320\) | 1169.00 | 0.204216 | ||||||||
\(321\) | −4014.00 | −0.697943 | ||||||||
\(322\) | −1620.00 | −0.280370 | ||||||||
\(323\) | −1110.00 | −0.191214 | ||||||||
\(324\) | −567.000 | −0.0972222 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1700.00 | −0.288817 | ||||||||
\(327\) | 3102.00 | 0.524590 | ||||||||
\(328\) | 4275.00 | 0.719657 | ||||||||
\(329\) | 4620.00 | 0.774191 | ||||||||
\(330\) | −462.000 | −0.0770675 | ||||||||
\(331\) | −1028.00 | −0.170707 | −0.0853535 | − | 0.996351i | \(-0.527202\pi\) | ||||
−0.0853535 | + | 0.996351i | \(0.527202\pi\) | |||||||
\(332\) | 3626.00 | 0.599405 | ||||||||
\(333\) | −117.000 | −0.0192539 | ||||||||
\(334\) | −3680.00 | −0.602876 | ||||||||
\(335\) | 1414.00 | 0.230612 | ||||||||
\(336\) | 1230.00 | 0.199708 | ||||||||
\(337\) | 2487.00 | 0.402005 | 0.201002 | − | 0.979591i | \(-0.435580\pi\) | ||||
0.201002 | + | 0.979591i | \(0.435580\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3231.00 | 0.517651 | ||||||||
\(340\) | 1813.00 | 0.289187 | ||||||||
\(341\) | −4312.00 | −0.684774 | ||||||||
\(342\) | −270.000 | −0.0426898 | ||||||||
\(343\) | −5860.00 | −0.922479 | ||||||||
\(344\) | 3690.00 | 0.578347 | ||||||||
\(345\) | 3402.00 | 0.530891 | ||||||||
\(346\) | 4146.00 | 0.644192 | ||||||||
\(347\) | −2850.00 | −0.440911 | −0.220455 | − | 0.975397i | \(-0.570754\pi\) | ||||
−0.220455 | + | 0.975397i | \(0.570754\pi\) | |||||||
\(348\) | 2373.00 | 0.365535 | ||||||||
\(349\) | 2018.00 | 0.309516 | 0.154758 | − | 0.987952i | \(-0.450540\pi\) | ||||
0.154758 | + | 0.987952i | \(0.450540\pi\) | |||||||
\(350\) | −760.000 | −0.116068 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3542.00 | 0.536333 | ||||||||
\(353\) | 5287.00 | 0.797163 | 0.398582 | − | 0.917133i | \(-0.369503\pi\) | ||||
0.398582 | + | 0.917133i | \(0.369503\pi\) | |||||||
\(354\) | −1728.00 | −0.259441 | ||||||||
\(355\) | −7602.00 | −1.13654 | ||||||||
\(356\) | 1358.00 | 0.202174 | ||||||||
\(357\) | 1110.00 | 0.164559 | ||||||||
\(358\) | 3674.00 | 0.542394 | ||||||||
\(359\) | 7278.00 | 1.06997 | 0.534983 | − | 0.844863i | \(-0.320318\pi\) | ||||
0.534983 | + | 0.844863i | \(0.320318\pi\) | |||||||
\(360\) | 945.000 | 0.138350 | ||||||||
\(361\) | −5959.00 | −0.868786 | ||||||||
\(362\) | −3283.00 | −0.476659 | ||||||||
\(363\) | −2541.00 | −0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5635.00 | −0.808080 | ||||||||
\(366\) | −1905.00 | −0.272065 | ||||||||
\(367\) | −4202.00 | −0.597664 | −0.298832 | − | 0.954306i | \(-0.596597\pi\) | ||||
−0.298832 | + | 0.954306i | \(0.596597\pi\) | |||||||
\(368\) | −6642.00 | −0.940865 | ||||||||
\(369\) | −2565.00 | −0.361866 | ||||||||
\(370\) | 91.0000 | 0.0127861 | ||||||||
\(371\) | −5370.00 | −0.751473 | ||||||||
\(372\) | 4116.00 | 0.573668 | ||||||||
\(373\) | −1583.00 | −0.219744 | −0.109872 | − | 0.993946i | \(-0.535044\pi\) | ||||
−0.109872 | + | 0.993946i | \(0.535044\pi\) | |||||||
\(374\) | 814.000 | 0.112543 | ||||||||
\(375\) | 4221.00 | 0.581257 | ||||||||
\(376\) | −6930.00 | −0.950499 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 270.000 | 0.0367389 | ||||||||
\(379\) | 2052.00 | 0.278111 | 0.139056 | − | 0.990285i | \(-0.455593\pi\) | ||||
0.139056 | + | 0.990285i | \(0.455593\pi\) | |||||||
\(380\) | −1470.00 | −0.198446 | ||||||||
\(381\) | −2964.00 | −0.398557 | ||||||||
\(382\) | −596.000 | −0.0798273 | ||||||||
\(383\) | 6872.00 | 0.916822 | 0.458411 | − | 0.888740i | \(-0.348419\pi\) | ||||
0.458411 | + | 0.888740i | \(0.348419\pi\) | |||||||
\(384\) | −4365.00 | −0.580079 | ||||||||
\(385\) | −1540.00 | −0.203859 | ||||||||
\(386\) | 393.000 | 0.0518217 | ||||||||
\(387\) | −2214.00 | −0.290811 | ||||||||
\(388\) | −8414.00 | −1.10092 | ||||||||
\(389\) | −11653.0 | −1.51884 | −0.759422 | − | 0.650598i | \(-0.774518\pi\) | ||||
−0.759422 | + | 0.650598i | \(0.774518\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5994.00 | −0.775268 | ||||||||
\(392\) | 3645.00 | 0.469644 | ||||||||
\(393\) | 1680.00 | 0.215636 | ||||||||
\(394\) | 3522.00 | 0.450345 | ||||||||
\(395\) | −6188.00 | −0.788233 | ||||||||
\(396\) | −1386.00 | −0.175882 | ||||||||
\(397\) | −6134.00 | −0.775458 | −0.387729 | − | 0.921774i | \(-0.626740\pi\) | ||||
−0.387729 | + | 0.921774i | \(0.626740\pi\) | |||||||
\(398\) | 2018.00 | 0.254154 | ||||||||
\(399\) | −900.000 | −0.112923 | ||||||||
\(400\) | −3116.00 | −0.389500 | ||||||||
\(401\) | 10795.0 | 1.34433 | 0.672165 | − | 0.740401i | \(-0.265364\pi\) | ||||
0.672165 | + | 0.740401i | \(0.265364\pi\) | |||||||
\(402\) | −606.000 | −0.0751854 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 3003.00 | 0.369814 | ||||||||
\(405\) | −567.000 | −0.0695666 | ||||||||
\(406\) | −1130.00 | −0.138130 | ||||||||
\(407\) | −286.000 | −0.0348317 | ||||||||
\(408\) | −1665.00 | −0.202034 | ||||||||
\(409\) | 8489.00 | 1.02629 | 0.513147 | − | 0.858301i | \(-0.328480\pi\) | ||||
0.513147 | + | 0.858301i | \(0.328480\pi\) | |||||||
\(410\) | 1995.00 | 0.240307 | ||||||||
\(411\) | 1557.00 | 0.186864 | ||||||||
\(412\) | 9114.00 | 1.08984 | ||||||||
\(413\) | −5760.00 | −0.686274 | ||||||||
\(414\) | −1458.00 | −0.173084 | ||||||||
\(415\) | 3626.00 | 0.428900 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1044.00 | −0.122602 | ||||||||
\(418\) | −660.000 | −0.0772288 | ||||||||
\(419\) | 1496.00 | 0.174426 | 0.0872129 | − | 0.996190i | \(-0.472204\pi\) | ||||
0.0872129 | + | 0.996190i | \(0.472204\pi\) | |||||||
\(420\) | 1470.00 | 0.170783 | ||||||||
\(421\) | 11695.0 | 1.35387 | 0.676935 | − | 0.736043i | \(-0.263308\pi\) | ||||
0.676935 | + | 0.736043i | \(0.263308\pi\) | |||||||
\(422\) | 160.000 | 0.0184566 | ||||||||
\(423\) | 4158.00 | 0.477941 | ||||||||
\(424\) | 8055.00 | 0.922607 | ||||||||
\(425\) | −2812.00 | −0.320946 | ||||||||
\(426\) | 3258.00 | 0.370541 | ||||||||
\(427\) | −6350.00 | −0.719668 | ||||||||
\(428\) | 9366.00 | 1.05776 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1722.00 | 0.193121 | ||||||||
\(431\) | −10590.0 | −1.18353 | −0.591766 | − | 0.806110i | \(-0.701569\pi\) | ||||
−0.591766 | + | 0.806110i | \(0.701569\pi\) | |||||||
\(432\) | 1107.00 | 0.123288 | ||||||||
\(433\) | −13949.0 | −1.54814 | −0.774072 | − | 0.633098i | \(-0.781783\pi\) | ||||
−0.774072 | + | 0.633098i | \(0.781783\pi\) | |||||||
\(434\) | −1960.00 | −0.216781 | ||||||||
\(435\) | 2373.00 | 0.261555 | ||||||||
\(436\) | −7238.00 | −0.795040 | ||||||||
\(437\) | 4860.00 | 0.532003 | ||||||||
\(438\) | 2415.00 | 0.263455 | ||||||||
\(439\) | −10726.0 | −1.16611 | −0.583057 | − | 0.812431i | \(-0.698144\pi\) | ||||
−0.583057 | + | 0.812431i | \(0.698144\pi\) | |||||||
\(440\) | 2310.00 | 0.250284 | ||||||||
\(441\) | −2187.00 | −0.236152 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16228.0 | 1.74044 | 0.870221 | − | 0.492662i | \(-0.163976\pi\) | ||||
0.870221 | + | 0.492662i | \(0.163976\pi\) | |||||||
\(444\) | 273.000 | 0.0291802 | ||||||||
\(445\) | 1358.00 | 0.144664 | ||||||||
\(446\) | −4072.00 | −0.432320 | ||||||||
\(447\) | 1935.00 | 0.204748 | ||||||||
\(448\) | −1670.00 | −0.176116 | ||||||||
\(449\) | −7538.00 | −0.792294 | −0.396147 | − | 0.918187i | \(-0.629653\pi\) | ||||
−0.396147 | + | 0.918187i | \(0.629653\pi\) | |||||||
\(450\) | −684.000 | −0.0716535 | ||||||||
\(451\) | −6270.00 | −0.654640 | ||||||||
\(452\) | −7539.00 | −0.784524 | ||||||||
\(453\) | −8742.00 | −0.906700 | ||||||||
\(454\) | 5794.00 | 0.598956 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1350.00 | 0.138639 | ||||||||
\(457\) | −15539.0 | −1.59056 | −0.795278 | − | 0.606245i | \(-0.792675\pi\) | ||||
−0.795278 | + | 0.606245i | \(0.792675\pi\) | |||||||
\(458\) | −6482.00 | −0.661319 | ||||||||
\(459\) | 999.000 | 0.101589 | ||||||||
\(460\) | −7938.00 | −0.804589 | ||||||||
\(461\) | −4811.00 | −0.486053 | −0.243027 | − | 0.970020i | \(-0.578140\pi\) | ||||
−0.243027 | + | 0.970020i | \(0.578140\pi\) | |||||||
\(462\) | 660.000 | 0.0664632 | ||||||||
\(463\) | −562.000 | −0.0564111 | −0.0282056 | − | 0.999602i | \(-0.508979\pi\) | ||||
−0.0282056 | + | 0.999602i | \(0.508979\pi\) | |||||||
\(464\) | −4633.00 | −0.463538 | ||||||||
\(465\) | 4116.00 | 0.410484 | ||||||||
\(466\) | 6890.00 | 0.684921 | ||||||||
\(467\) | 4914.00 | 0.486922 | 0.243461 | − | 0.969911i | \(-0.421717\pi\) | ||||
0.243461 | + | 0.969911i | \(0.421717\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2020.00 | −0.198880 | ||||||||
\(470\) | −3234.00 | −0.317390 | ||||||||
\(471\) | −6237.00 | −0.610161 | ||||||||
\(472\) | 8640.00 | 0.842560 | ||||||||
\(473\) | −5412.00 | −0.526097 | ||||||||
\(474\) | 2652.00 | 0.256984 | ||||||||
\(475\) | 2280.00 | 0.220239 | ||||||||
\(476\) | −2590.00 | −0.249396 | ||||||||
\(477\) | −4833.00 | −0.463916 | ||||||||
\(478\) | −2466.00 | −0.235967 | ||||||||
\(479\) | 3600.00 | 0.343399 | 0.171700 | − | 0.985149i | \(-0.445074\pi\) | ||||
0.171700 | + | 0.985149i | \(0.445074\pi\) | |||||||
\(480\) | −3381.00 | −0.321502 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 3617.00 | 0.341805 | ||||||||
\(483\) | −4860.00 | −0.457842 | ||||||||
\(484\) | 5929.00 | 0.556818 | ||||||||
\(485\) | −8414.00 | −0.787753 | ||||||||
\(486\) | 243.000 | 0.0226805 | ||||||||
\(487\) | 17130.0 | 1.59391 | 0.796955 | − | 0.604038i | \(-0.206443\pi\) | ||||
0.796955 | + | 0.604038i | \(0.206443\pi\) | |||||||
\(488\) | 9525.00 | 0.883558 | ||||||||
\(489\) | −5100.00 | −0.471636 | ||||||||
\(490\) | 1701.00 | 0.156823 | ||||||||
\(491\) | −11838.0 | −1.08807 | −0.544034 | − | 0.839063i | \(-0.683104\pi\) | ||||
−0.544034 | + | 0.839063i | \(0.683104\pi\) | |||||||
\(492\) | 5985.00 | 0.548424 | ||||||||
\(493\) | −4181.00 | −0.381953 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1386.00 | −0.125851 | ||||||||
\(496\) | −8036.00 | −0.727474 | ||||||||
\(497\) | 10860.0 | 0.980156 | ||||||||
\(498\) | −1554.00 | −0.139832 | ||||||||
\(499\) | −8976.00 | −0.805252 | −0.402626 | − | 0.915364i | \(-0.631903\pi\) | ||||
−0.402626 | + | 0.915364i | \(0.631903\pi\) | |||||||
\(500\) | −9849.00 | −0.880921 | ||||||||
\(501\) | −11040.0 | −0.984493 | ||||||||
\(502\) | 4860.00 | 0.432096 | ||||||||
\(503\) | 1682.00 | 0.149099 | 0.0745494 | − | 0.997217i | \(-0.476248\pi\) | ||||
0.0745494 | + | 0.997217i | \(0.476248\pi\) | |||||||
\(504\) | −1350.00 | −0.119313 | ||||||||
\(505\) | 3003.00 | 0.264617 | ||||||||
\(506\) | −3564.00 | −0.313121 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6916.00 | 0.604031 | ||||||||
\(509\) | −15167.0 | −1.32076 | −0.660379 | − | 0.750933i | \(-0.729604\pi\) | ||||
−0.660379 | + | 0.750933i | \(0.729604\pi\) | |||||||
\(510\) | −777.000 | −0.0674630 | ||||||||
\(511\) | 8050.00 | 0.696890 | ||||||||
\(512\) | 11521.0 | 0.994455 | ||||||||
\(513\) | −810.000 | −0.0697122 | ||||||||
\(514\) | 565.000 | 0.0484846 | ||||||||
\(515\) | 9114.00 | 0.779827 | ||||||||
\(516\) | 5166.00 | 0.440737 | ||||||||
\(517\) | 10164.0 | 0.864627 | ||||||||
\(518\) | −130.000 | −0.0110268 | ||||||||
\(519\) | 12438.0 | 1.05196 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6783.00 | −0.570381 | −0.285191 | − | 0.958471i | \(-0.592057\pi\) | ||||
−0.285191 | + | 0.958471i | \(0.592057\pi\) | |||||||
\(522\) | −1017.00 | −0.0852737 | ||||||||
\(523\) | −13918.0 | −1.16366 | −0.581828 | − | 0.813312i | \(-0.697662\pi\) | ||||
−0.581828 | + | 0.813312i | \(0.697662\pi\) | |||||||
\(524\) | −3920.00 | −0.326805 | ||||||||
\(525\) | −2280.00 | −0.189538 | ||||||||
\(526\) | −498.000 | −0.0412810 | ||||||||
\(527\) | −7252.00 | −0.599435 | ||||||||
\(528\) | 2706.00 | 0.223037 | ||||||||
\(529\) | 14077.0 | 1.15698 | ||||||||
\(530\) | 3759.00 | 0.308076 | ||||||||
\(531\) | −5184.00 | −0.423666 | ||||||||
\(532\) | 2100.00 | 0.171140 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −582.000 | −0.0471641 | ||||||||
\(535\) | 9366.00 | 0.756874 | ||||||||
\(536\) | 3030.00 | 0.244172 | ||||||||
\(537\) | 11022.0 | 0.885725 | ||||||||
\(538\) | 5546.00 | 0.444433 | ||||||||
\(539\) | −5346.00 | −0.427214 | ||||||||
\(540\) | 1323.00 | 0.105431 | ||||||||
\(541\) | 1335.00 | 0.106093 | 0.0530463 | − | 0.998592i | \(-0.483107\pi\) | ||||
0.0530463 | + | 0.998592i | \(0.483107\pi\) | |||||||
\(542\) | 2256.00 | 0.178789 | ||||||||
\(543\) | −9849.00 | −0.778381 | ||||||||
\(544\) | 5957.00 | 0.469493 | ||||||||
\(545\) | −7238.00 | −0.568884 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3806.00 | −0.297501 | −0.148750 | − | 0.988875i | \(-0.547525\pi\) | ||||
−0.148750 | + | 0.988875i | \(0.547525\pi\) | |||||||
\(548\) | −3633.00 | −0.283201 | ||||||||
\(549\) | −5715.00 | −0.444281 | ||||||||
\(550\) | −1672.00 | −0.129626 | ||||||||
\(551\) | 3390.00 | 0.262103 | ||||||||
\(552\) | 7290.00 | 0.562107 | ||||||||
\(553\) | 8840.00 | 0.679774 | ||||||||
\(554\) | 2309.00 | 0.177076 | ||||||||
\(555\) | 273.000 | 0.0208796 | ||||||||
\(556\) | 2436.00 | 0.185808 | ||||||||
\(557\) | 1905.00 | 0.144915 | 0.0724573 | − | 0.997372i | \(-0.476916\pi\) | ||||
0.0724573 | + | 0.997372i | \(0.476916\pi\) | |||||||
\(558\) | −1764.00 | −0.133828 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2870.00 | −0.216571 | ||||||||
\(561\) | 2442.00 | 0.183781 | ||||||||
\(562\) | −5833.00 | −0.437812 | ||||||||
\(563\) | −4800.00 | −0.359318 | −0.179659 | − | 0.983729i | \(-0.557499\pi\) | ||||
−0.179659 | + | 0.983729i | \(0.557499\pi\) | |||||||
\(564\) | −9702.00 | −0.724340 | ||||||||
\(565\) | −7539.00 | −0.561359 | ||||||||
\(566\) | 1650.00 | 0.122535 | ||||||||
\(567\) | 810.000 | 0.0599944 | ||||||||
\(568\) | −16290.0 | −1.20337 | ||||||||
\(569\) | 14678.0 | 1.08143 | 0.540715 | − | 0.841206i | \(-0.318154\pi\) | ||||
0.540715 | + | 0.841206i | \(0.318154\pi\) | |||||||
\(570\) | 630.000 | 0.0462944 | ||||||||
\(571\) | −586.000 | −0.0429481 | −0.0214740 | − | 0.999769i | \(-0.506836\pi\) | ||||
−0.0214740 | + | 0.999769i | \(0.506836\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1788.00 | −0.130357 | ||||||||
\(574\) | −2850.00 | −0.207242 | ||||||||
\(575\) | 12312.0 | 0.892949 | ||||||||
\(576\) | −1503.00 | −0.108724 | ||||||||
\(577\) | −8939.00 | −0.644949 | −0.322474 | − | 0.946578i | \(-0.604515\pi\) | ||||
−0.322474 | + | 0.946578i | \(0.604515\pi\) | |||||||
\(578\) | −3544.00 | −0.255036 | ||||||||
\(579\) | 1179.00 | 0.0846245 | ||||||||
\(580\) | −5537.00 | −0.396399 | ||||||||
\(581\) | −5180.00 | −0.369884 | ||||||||
\(582\) | 3606.00 | 0.256827 | ||||||||
\(583\) | −11814.0 | −0.839255 | ||||||||
\(584\) | −12075.0 | −0.855594 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2991.00 | −0.210848 | ||||||||
\(587\) | 13792.0 | 0.969773 | 0.484887 | − | 0.874577i | \(-0.338861\pi\) | ||||
0.484887 | + | 0.874577i | \(0.338861\pi\) | |||||||
\(588\) | 5103.00 | 0.357898 | ||||||||
\(589\) | 5880.00 | 0.411343 | ||||||||
\(590\) | 4032.00 | 0.281347 | ||||||||
\(591\) | 10566.0 | 0.735410 | ||||||||
\(592\) | −533.000 | −0.0370037 | ||||||||
\(593\) | −9569.00 | −0.662650 | −0.331325 | − | 0.943517i | \(-0.607496\pi\) | ||||
−0.331325 | + | 0.943517i | \(0.607496\pi\) | |||||||
\(594\) | 594.000 | 0.0410305 | ||||||||
\(595\) | −2590.00 | −0.178453 | ||||||||
\(596\) | −4515.00 | −0.310305 | ||||||||
\(597\) | 6054.00 | 0.415031 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5192.00 | −0.354156 | −0.177078 | − | 0.984197i | \(-0.556664\pi\) | ||||
−0.177078 | + | 0.984197i | \(0.556664\pi\) | |||||||
\(600\) | 3420.00 | 0.232702 | ||||||||
\(601\) | −3677.00 | −0.249564 | −0.124782 | − | 0.992184i | \(-0.539823\pi\) | ||||
−0.124782 | + | 0.992184i | \(0.539823\pi\) | |||||||
\(602\) | −2460.00 | −0.166548 | ||||||||
\(603\) | −1818.00 | −0.122777 | ||||||||
\(604\) | 20398.0 | 1.37414 | ||||||||
\(605\) | 5929.00 | 0.398427 | ||||||||
\(606\) | −1287.00 | −0.0862719 | ||||||||
\(607\) | −10960.0 | −0.732871 | −0.366435 | − | 0.930443i | \(-0.619422\pi\) | ||||
−0.366435 | + | 0.930443i | \(0.619422\pi\) | |||||||
\(608\) | −4830.00 | −0.322175 | ||||||||
\(609\) | −3390.00 | −0.225566 | ||||||||
\(610\) | 4445.00 | 0.295037 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2331.00 | −0.153963 | ||||||||
\(613\) | 26027.0 | 1.71488 | 0.857439 | − | 0.514585i | \(-0.172054\pi\) | ||||
0.857439 | + | 0.514585i | \(0.172054\pi\) | |||||||
\(614\) | 2422.00 | 0.159192 | ||||||||
\(615\) | 5985.00 | 0.392420 | ||||||||
\(616\) | −3300.00 | −0.215845 | ||||||||
\(617\) | −17681.0 | −1.15366 | −0.576832 | − | 0.816863i | \(-0.695711\pi\) | ||||
−0.576832 | + | 0.816863i | \(0.695711\pi\) | |||||||
\(618\) | −3906.00 | −0.254243 | ||||||||
\(619\) | −3192.00 | −0.207265 | −0.103633 | − | 0.994616i | \(-0.533047\pi\) | ||||
−0.103633 | + | 0.994616i | \(0.533047\pi\) | |||||||
\(620\) | −9604.00 | −0.622106 | ||||||||
\(621\) | −4374.00 | −0.282645 | ||||||||
\(622\) | −3402.00 | −0.219305 | ||||||||
\(623\) | −1940.00 | −0.124758 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −349.000 | −0.0223360 | ||||||||
\(626\) | 2310.00 | 0.147486 | ||||||||
\(627\) | −1980.00 | −0.126114 | ||||||||
\(628\) | 14553.0 | 0.924726 | ||||||||
\(629\) | −481.000 | −0.0304908 | ||||||||
\(630\) | −630.000 | −0.0398410 | ||||||||
\(631\) | −7580.00 | −0.478217 | −0.239109 | − | 0.970993i | \(-0.576855\pi\) | ||||
−0.239109 | + | 0.970993i | \(0.576855\pi\) | |||||||
\(632\) | −13260.0 | −0.834580 | ||||||||
\(633\) | 480.000 | 0.0301395 | ||||||||
\(634\) | 257.000 | 0.0160990 | ||||||||
\(635\) | 6916.00 | 0.432210 | ||||||||
\(636\) | 11277.0 | 0.703085 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2486.00 | −0.154266 | ||||||||
\(639\) | 9774.00 | 0.605091 | ||||||||
\(640\) | 10185.0 | 0.629059 | ||||||||
\(641\) | −27707.0 | −1.70727 | −0.853635 | − | 0.520871i | \(-0.825607\pi\) | ||||
−0.853635 | + | 0.520871i | \(0.825607\pi\) | |||||||
\(642\) | −4014.00 | −0.246760 | ||||||||
\(643\) | −11216.0 | −0.687894 | −0.343947 | − | 0.938989i | \(-0.611764\pi\) | ||||
−0.343947 | + | 0.938989i | \(0.611764\pi\) | |||||||
\(644\) | 11340.0 | 0.693880 | ||||||||
\(645\) | 5166.00 | 0.315366 | ||||||||
\(646\) | −1110.00 | −0.0676043 | ||||||||
\(647\) | −2536.00 | −0.154097 | −0.0770483 | − | 0.997027i | \(-0.524550\pi\) | ||||
−0.0770483 | + | 0.997027i | \(0.524550\pi\) | |||||||
\(648\) | −1215.00 | −0.0736570 | ||||||||
\(649\) | −12672.0 | −0.766440 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5880.00 | −0.354002 | ||||||||
\(652\) | 11900.0 | 0.714785 | ||||||||
\(653\) | 17730.0 | 1.06252 | 0.531262 | − | 0.847207i | \(-0.321718\pi\) | ||||
0.531262 | + | 0.847207i | \(0.321718\pi\) | |||||||
\(654\) | 3102.00 | 0.185471 | ||||||||
\(655\) | −3920.00 | −0.233843 | ||||||||
\(656\) | −11685.0 | −0.695461 | ||||||||
\(657\) | 7245.00 | 0.430220 | ||||||||
\(658\) | 4620.00 | 0.273718 | ||||||||
\(659\) | 18920.0 | 1.11839 | 0.559195 | − | 0.829036i | \(-0.311110\pi\) | ||||
0.559195 | + | 0.829036i | \(0.311110\pi\) | |||||||
\(660\) | 3234.00 | 0.190732 | ||||||||
\(661\) | −5241.00 | −0.308398 | −0.154199 | − | 0.988040i | \(-0.549280\pi\) | ||||
−0.154199 | + | 0.988040i | \(0.549280\pi\) | |||||||
\(662\) | −1028.00 | −0.0603540 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7770.00 | 0.454118 | ||||||||
\(665\) | 2100.00 | 0.122458 | ||||||||
\(666\) | −117.000 | −0.00680729 | ||||||||
\(667\) | 18306.0 | 1.06269 | ||||||||
\(668\) | 25760.0 | 1.49204 | ||||||||
\(669\) | −12216.0 | −0.705976 | ||||||||
\(670\) | 1414.00 | 0.0815337 | ||||||||
\(671\) | −13970.0 | −0.803735 | ||||||||
\(672\) | 4830.00 | 0.277264 | ||||||||
\(673\) | 20467.0 | 1.17228 | 0.586140 | − | 0.810210i | \(-0.300647\pi\) | ||||
0.586140 | + | 0.810210i | \(0.300647\pi\) | |||||||
\(674\) | 2487.00 | 0.142130 | ||||||||
\(675\) | −2052.00 | −0.117010 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −70.0000 | −0.00397388 | −0.00198694 | − | 0.999998i | \(-0.500632\pi\) | ||||
−0.00198694 | + | 0.999998i | \(0.500632\pi\) | |||||||
\(678\) | 3231.00 | 0.183017 | ||||||||
\(679\) | 12020.0 | 0.679360 | ||||||||
\(680\) | 3885.00 | 0.219093 | ||||||||
\(681\) | 17382.0 | 0.978091 | ||||||||
\(682\) | −4312.00 | −0.242104 | ||||||||
\(683\) | −6432.00 | −0.360342 | −0.180171 | − | 0.983635i | \(-0.557665\pi\) | ||||
−0.180171 | + | 0.983635i | \(0.557665\pi\) | |||||||
\(684\) | 1890.00 | 0.105652 | ||||||||
\(685\) | −3633.00 | −0.202642 | ||||||||
\(686\) | −5860.00 | −0.326146 | ||||||||
\(687\) | −19446.0 | −1.07993 | ||||||||
\(688\) | −10086.0 | −0.558903 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 3402.00 | 0.187698 | ||||||||
\(691\) | 6666.00 | 0.366985 | 0.183492 | − | 0.983021i | \(-0.441260\pi\) | ||||
0.183492 | + | 0.983021i | \(0.441260\pi\) | |||||||
\(692\) | −29022.0 | −1.59429 | ||||||||
\(693\) | 1980.00 | 0.108534 | ||||||||
\(694\) | −2850.00 | −0.155885 | ||||||||
\(695\) | 2436.00 | 0.132954 | ||||||||
\(696\) | 5085.00 | 0.276935 | ||||||||
\(697\) | −10545.0 | −0.573056 | ||||||||
\(698\) | 2018.00 | 0.109430 | ||||||||
\(699\) | 20670.0 | 1.11847 | ||||||||
\(700\) | 5320.00 | 0.287253 | ||||||||
\(701\) | −14054.0 | −0.757221 | −0.378611 | − | 0.925556i | \(-0.623598\pi\) | ||||
−0.378611 | + | 0.925556i | \(0.623598\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 390.000 | 0.0209234 | ||||||||
\(704\) | −3674.00 | −0.196689 | ||||||||
\(705\) | −9702.00 | −0.518296 | ||||||||
\(706\) | 5287.00 | 0.281840 | ||||||||
\(707\) | −4290.00 | −0.228207 | ||||||||
\(708\) | 12096.0 | 0.642084 | ||||||||
\(709\) | 71.0000 | 0.00376088 | 0.00188044 | − | 0.999998i | \(-0.499401\pi\) | ||||
0.00188044 | + | 0.999998i | \(0.499401\pi\) | |||||||
\(710\) | −7602.00 | −0.401828 | ||||||||
\(711\) | 7956.00 | 0.419653 | ||||||||
\(712\) | 2910.00 | 0.153170 | ||||||||
\(713\) | 31752.0 | 1.66777 | ||||||||
\(714\) | 1110.00 | 0.0581803 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −25718.0 | −1.34236 | ||||||||
\(717\) | −7398.00 | −0.385332 | ||||||||
\(718\) | 7278.00 | 0.378290 | ||||||||
\(719\) | 3936.00 | 0.204156 | 0.102078 | − | 0.994776i | \(-0.467451\pi\) | ||||
0.102078 | + | 0.994776i | \(0.467451\pi\) | |||||||
\(720\) | −2583.00 | −0.133698 | ||||||||
\(721\) | −13020.0 | −0.672524 | ||||||||
\(722\) | −5959.00 | −0.307162 | ||||||||
\(723\) | 10851.0 | 0.558165 | ||||||||
\(724\) | 22981.0 | 1.17967 | ||||||||
\(725\) | 8588.00 | 0.439931 | ||||||||
\(726\) | −2541.00 | −0.129897 | ||||||||
\(727\) | 34202.0 | 1.74482 | 0.872409 | − | 0.488777i | \(-0.162557\pi\) | ||||
0.872409 | + | 0.488777i | \(0.162557\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −5635.00 | −0.285700 | ||||||||
\(731\) | −9102.00 | −0.460533 | ||||||||
\(732\) | 13335.0 | 0.673328 | ||||||||
\(733\) | 27363.0 | 1.37882 | 0.689410 | − | 0.724371i | \(-0.257870\pi\) | ||||
0.689410 | + | 0.724371i | \(0.257870\pi\) | |||||||
\(734\) | −4202.00 | −0.211306 | ||||||||
\(735\) | 5103.00 | 0.256091 | ||||||||
\(736\) | −26082.0 | −1.30624 | ||||||||
\(737\) | −4444.00 | −0.222112 | ||||||||
\(738\) | −2565.00 | −0.127939 | ||||||||
\(739\) | −21776.0 | −1.08396 | −0.541978 | − | 0.840393i | \(-0.682324\pi\) | ||||
−0.541978 | + | 0.840393i | \(0.682324\pi\) | |||||||
\(740\) | −637.000 | −0.0316440 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5370.00 | −0.265686 | ||||||||
\(743\) | −2484.00 | −0.122650 | −0.0613251 | − | 0.998118i | \(-0.519533\pi\) | ||||
−0.0613251 | + | 0.998118i | \(0.519533\pi\) | |||||||
\(744\) | 8820.00 | 0.434619 | ||||||||
\(745\) | −4515.00 | −0.222036 | ||||||||
\(746\) | −1583.00 | −0.0776914 | ||||||||
\(747\) | −4662.00 | −0.228345 | ||||||||
\(748\) | −5698.00 | −0.278529 | ||||||||
\(749\) | −13380.0 | −0.652730 | ||||||||
\(750\) | 4221.00 | 0.205506 | ||||||||
\(751\) | 32906.0 | 1.59888 | 0.799439 | − | 0.600748i | \(-0.205130\pi\) | ||||
0.799439 | + | 0.600748i | \(0.205130\pi\) | |||||||
\(752\) | 18942.0 | 0.918542 | ||||||||
\(753\) | 14580.0 | 0.705611 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20398.0 | 0.983257 | ||||||||
\(756\) | −1890.00 | −0.0909241 | ||||||||
\(757\) | −3914.00 | −0.187922 | −0.0939609 | − | 0.995576i | \(-0.529953\pi\) | ||||
−0.0939609 | + | 0.995576i | \(0.529953\pi\) | |||||||
\(758\) | 2052.00 | 0.0983272 | ||||||||
\(759\) | −10692.0 | −0.511324 | ||||||||
\(760\) | −3150.00 | −0.150345 | ||||||||
\(761\) | 33038.0 | 1.57375 | 0.786877 | − | 0.617110i | \(-0.211697\pi\) | ||||
0.786877 | + | 0.617110i | \(0.211697\pi\) | |||||||
\(762\) | −2964.00 | −0.140911 | ||||||||
\(763\) | 10340.0 | 0.490607 | ||||||||
\(764\) | 4172.00 | 0.197562 | ||||||||
\(765\) | −2331.00 | −0.110167 | ||||||||
\(766\) | 6872.00 | 0.324145 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −357.000 | −0.0167736 | ||||||||
\(769\) | 17586.0 | 0.824665 | 0.412332 | − | 0.911033i | \(-0.364714\pi\) | ||||
0.412332 | + | 0.911033i | \(0.364714\pi\) | |||||||
\(770\) | −1540.00 | −0.0720750 | ||||||||
\(771\) | 1695.00 | 0.0791750 | ||||||||
\(772\) | −2751.00 | −0.128252 | ||||||||
\(773\) | −18314.0 | −0.852146 | −0.426073 | − | 0.904689i | \(-0.640103\pi\) | ||||
−0.426073 | + | 0.904689i | \(0.640103\pi\) | |||||||
\(774\) | −2214.00 | −0.102817 | ||||||||
\(775\) | 14896.0 | 0.690426 | ||||||||
\(776\) | −18030.0 | −0.834071 | ||||||||
\(777\) | −390.000 | −0.0180067 | ||||||||
\(778\) | −11653.0 | −0.536993 | ||||||||
\(779\) | 8550.00 | 0.393242 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 23892.0 | 1.09465 | ||||||||
\(782\) | −5994.00 | −0.274098 | ||||||||
\(783\) | −3051.00 | −0.139251 | ||||||||
\(784\) | −9963.00 | −0.453854 | ||||||||
\(785\) | 14553.0 | 0.661680 | ||||||||
\(786\) | 1680.00 | 0.0762387 | ||||||||
\(787\) | 42068.0 | 1.90542 | 0.952708 | − | 0.303888i | \(-0.0982847\pi\) | ||||
0.952708 | + | 0.303888i | \(0.0982847\pi\) | |||||||
\(788\) | −24654.0 | −1.11455 | ||||||||
\(789\) | −1494.00 | −0.0674117 | ||||||||
\(790\) | −6188.00 | −0.278682 | ||||||||
\(791\) | 10770.0 | 0.484118 | ||||||||
\(792\) | −2970.00 | −0.133250 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −6134.00 | −0.274166 | ||||||||
\(795\) | 11277.0 | 0.503087 | ||||||||
\(796\) | −14126.0 | −0.628998 | ||||||||
\(797\) | −4282.00 | −0.190309 | −0.0951545 | − | 0.995463i | \(-0.530335\pi\) | ||||
−0.0951545 | + | 0.995463i | \(0.530335\pi\) | |||||||
\(798\) | −900.000 | −0.0399244 | ||||||||
\(799\) | 17094.0 | 0.756874 | ||||||||
\(800\) | −12236.0 | −0.540760 | ||||||||
\(801\) | −1746.00 | −0.0770186 | ||||||||
\(802\) | 10795.0 | 0.475293 | ||||||||
\(803\) | 17710.0 | 0.778297 | ||||||||
\(804\) | 4242.00 | 0.186074 | ||||||||
\(805\) | 11340.0 | 0.496500 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16638.0 | 0.725756 | ||||||||
\(808\) | 6435.00 | 0.280176 | ||||||||
\(809\) | 40221.0 | 1.74795 | 0.873977 | − | 0.485967i | \(-0.161532\pi\) | ||||
0.873977 | + | 0.485967i | \(0.161532\pi\) | |||||||
\(810\) | −567.000 | −0.0245955 | ||||||||
\(811\) | 7084.00 | 0.306724 | 0.153362 | − | 0.988170i | \(-0.450990\pi\) | ||||
0.153362 | + | 0.988170i | \(0.450990\pi\) | |||||||
\(812\) | 7910.00 | 0.341855 | ||||||||
\(813\) | 6768.00 | 0.291961 | ||||||||
\(814\) | −286.000 | −0.0123149 | ||||||||
\(815\) | 11900.0 | 0.511459 | ||||||||
\(816\) | 4551.00 | 0.195241 | ||||||||
\(817\) | 7380.00 | 0.316026 | ||||||||
\(818\) | 8489.00 | 0.362850 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −13965.0 | −0.594730 | ||||||||
\(821\) | −17338.0 | −0.737028 | −0.368514 | − | 0.929622i | \(-0.620133\pi\) | ||||
−0.368514 | + | 0.929622i | \(0.620133\pi\) | |||||||
\(822\) | 1557.00 | 0.0660664 | ||||||||
\(823\) | 35496.0 | 1.50342 | 0.751709 | − | 0.659495i | \(-0.229230\pi\) | ||||
0.751709 | + | 0.659495i | \(0.229230\pi\) | |||||||
\(824\) | 19530.0 | 0.825679 | ||||||||
\(825\) | −5016.00 | −0.211678 | ||||||||
\(826\) | −5760.00 | −0.242634 | ||||||||
\(827\) | 14992.0 | 0.630378 | 0.315189 | − | 0.949029i | \(-0.397932\pi\) | ||||
0.315189 | + | 0.949029i | \(0.397932\pi\) | |||||||
\(828\) | 10206.0 | 0.428361 | ||||||||
\(829\) | −20659.0 | −0.865521 | −0.432760 | − | 0.901509i | \(-0.642460\pi\) | ||||
−0.432760 | + | 0.901509i | \(0.642460\pi\) | |||||||
\(830\) | 3626.00 | 0.151639 | ||||||||
\(831\) | 6927.00 | 0.289164 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8991.00 | −0.373973 | ||||||||
\(834\) | −1044.00 | −0.0433462 | ||||||||
\(835\) | 25760.0 | 1.06762 | ||||||||
\(836\) | 4620.00 | 0.191132 | ||||||||
\(837\) | −5292.00 | −0.218540 | ||||||||
\(838\) | 1496.00 | 0.0616688 | ||||||||
\(839\) | −28716.0 | −1.18163 | −0.590814 | − | 0.806808i | \(-0.701193\pi\) | ||||
−0.590814 | + | 0.806808i | \(0.701193\pi\) | |||||||
\(840\) | 3150.00 | 0.129387 | ||||||||
\(841\) | −11620.0 | −0.476444 | ||||||||
\(842\) | 11695.0 | 0.478665 | ||||||||
\(843\) | −17499.0 | −0.714944 | ||||||||
\(844\) | −1120.00 | −0.0456777 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4158.00 | 0.168978 | ||||||||
\(847\) | −8470.00 | −0.343604 | ||||||||
\(848\) | −22017.0 | −0.891588 | ||||||||
\(849\) | 4950.00 | 0.200098 | ||||||||
\(850\) | −2812.00 | −0.113472 | ||||||||
\(851\) | 2106.00 | 0.0848328 | ||||||||
\(852\) | −22806.0 | −0.917043 | ||||||||
\(853\) | −13377.0 | −0.536952 | −0.268476 | − | 0.963286i | \(-0.586520\pi\) | ||||
−0.268476 | + | 0.963286i | \(0.586520\pi\) | |||||||
\(854\) | −6350.00 | −0.254441 | ||||||||
\(855\) | 1890.00 | 0.0755984 | ||||||||
\(856\) | 20070.0 | 0.801377 | ||||||||
\(857\) | −27419.0 | −1.09290 | −0.546450 | − | 0.837492i | \(-0.684021\pi\) | ||||
−0.546450 | + | 0.837492i | \(0.684021\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2422.00 | 0.0962021 | 0.0481010 | − | 0.998842i | \(-0.484683\pi\) | ||||
0.0481010 | + | 0.998842i | \(0.484683\pi\) | |||||||
\(860\) | −12054.0 | −0.477951 | ||||||||
\(861\) | −8550.00 | −0.338424 | ||||||||
\(862\) | −10590.0 | −0.418442 | ||||||||
\(863\) | 34522.0 | 1.36169 | 0.680847 | − | 0.732425i | \(-0.261612\pi\) | ||||
0.680847 | + | 0.732425i | \(0.261612\pi\) | |||||||
\(864\) | 4347.00 | 0.171167 | ||||||||
\(865\) | −29022.0 | −1.14078 | ||||||||
\(866\) | −13949.0 | −0.547351 | ||||||||
\(867\) | −10632.0 | −0.416472 | ||||||||
\(868\) | 13720.0 | 0.536506 | ||||||||
\(869\) | 19448.0 | 0.759181 | ||||||||
\(870\) | 2373.00 | 0.0924738 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −15510.0 | −0.602334 | ||||||||
\(873\) | 10818.0 | 0.419397 | ||||||||
\(874\) | 4860.00 | 0.188091 | ||||||||
\(875\) | 14070.0 | 0.543603 | ||||||||
\(876\) | −16905.0 | −0.652017 | ||||||||
\(877\) | −13733.0 | −0.528769 | −0.264385 | − | 0.964417i | \(-0.585169\pi\) | ||||
−0.264385 | + | 0.964417i | \(0.585169\pi\) | |||||||
\(878\) | −10726.0 | −0.412284 | ||||||||
\(879\) | −8973.00 | −0.344314 | ||||||||
\(880\) | −6314.00 | −0.241869 | ||||||||
\(881\) | −22759.0 | −0.870341 | −0.435170 | − | 0.900348i | \(-0.643312\pi\) | ||||
−0.435170 | + | 0.900348i | \(0.643312\pi\) | |||||||
\(882\) | −2187.00 | −0.0834922 | ||||||||
\(883\) | −2168.00 | −0.0826263 | −0.0413131 | − | 0.999146i | \(-0.513154\pi\) | ||||
−0.0413131 | + | 0.999146i | \(0.513154\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12096.0 | 0.459438 | ||||||||
\(886\) | 16228.0 | 0.615339 | ||||||||
\(887\) | 15888.0 | 0.601428 | 0.300714 | − | 0.953714i | \(-0.402775\pi\) | ||||
0.300714 | + | 0.953714i | \(0.402775\pi\) | |||||||
\(888\) | 585.000 | 0.0221073 | ||||||||
\(889\) | −9880.00 | −0.372739 | ||||||||
\(890\) | 1358.00 | 0.0511464 | ||||||||
\(891\) | 1782.00 | 0.0670025 | ||||||||
\(892\) | 28504.0 | 1.06994 | ||||||||
\(893\) | −13860.0 | −0.519381 | ||||||||
\(894\) | 1935.00 | 0.0723894 | ||||||||
\(895\) | −25718.0 | −0.960512 | ||||||||
\(896\) | −14550.0 | −0.542502 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7538.00 | −0.280118 | ||||||||
\(899\) | 22148.0 | 0.821665 | ||||||||
\(900\) | 4788.00 | 0.177333 | ||||||||
\(901\) | −19869.0 | −0.734664 | ||||||||
\(902\) | −6270.00 | −0.231450 | ||||||||
\(903\) | −7380.00 | −0.271972 | ||||||||
\(904\) | −16155.0 | −0.594366 | ||||||||
\(905\) | 22981.0 | 0.844104 | ||||||||
\(906\) | −8742.00 | −0.320567 | ||||||||
\(907\) | −11628.0 | −0.425691 | −0.212845 | − | 0.977086i | \(-0.568273\pi\) | ||||
−0.212845 | + | 0.977086i | \(0.568273\pi\) | |||||||
\(908\) | −40558.0 | −1.48234 | ||||||||
\(909\) | −3861.00 | −0.140882 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12584.0 | −0.457658 | −0.228829 | − | 0.973467i | \(-0.573490\pi\) | ||||
−0.228829 | + | 0.973467i | \(0.573490\pi\) | |||||||
\(912\) | −3690.00 | −0.133978 | ||||||||
\(913\) | −11396.0 | −0.413092 | ||||||||
\(914\) | −15539.0 | −0.562346 | ||||||||
\(915\) | 13335.0 | 0.481794 | ||||||||
\(916\) | 45374.0 | 1.63668 | ||||||||
\(917\) | 5600.00 | 0.201667 | ||||||||
\(918\) | 999.000 | 0.0359171 | ||||||||
\(919\) | 17184.0 | 0.616809 | 0.308405 | − | 0.951255i | \(-0.400205\pi\) | ||||
0.308405 | + | 0.951255i | \(0.400205\pi\) | |||||||
\(920\) | −17010.0 | −0.609569 | ||||||||
\(921\) | 7266.00 | 0.259960 | ||||||||
\(922\) | −4811.00 | −0.171846 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −4620.00 | −0.164488 | ||||||||
\(925\) | 988.000 | 0.0351192 | ||||||||
\(926\) | −562.000 | −0.0199443 | ||||||||
\(927\) | −11718.0 | −0.415178 | ||||||||
\(928\) | −18193.0 | −0.643550 | ||||||||
\(929\) | −12777.0 | −0.451238 | −0.225619 | − | 0.974216i | \(-0.572440\pi\) | ||||
−0.225619 | + | 0.974216i | \(0.572440\pi\) | |||||||
\(930\) | 4116.00 | 0.145128 | ||||||||
\(931\) | 7290.00 | 0.256627 | ||||||||
\(932\) | −48230.0 | −1.69509 | ||||||||
\(933\) | −10206.0 | −0.358124 | ||||||||
\(934\) | 4914.00 | 0.172153 | ||||||||
\(935\) | −5698.00 | −0.199299 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9191.00 | 0.320445 | 0.160222 | − | 0.987081i | \(-0.448779\pi\) | ||||
0.160222 | + | 0.987081i | \(0.448779\pi\) | |||||||
\(938\) | −2020.00 | −0.0703149 | ||||||||
\(939\) | 6930.00 | 0.240843 | ||||||||
\(940\) | 22638.0 | 0.785500 | ||||||||
\(941\) | −50498.0 | −1.74940 | −0.874701 | − | 0.484662i | \(-0.838942\pi\) | ||||
−0.874701 | + | 0.484662i | \(0.838942\pi\) | |||||||
\(942\) | −6237.00 | −0.215724 | ||||||||
\(943\) | 46170.0 | 1.59438 | ||||||||
\(944\) | −23616.0 | −0.814232 | ||||||||
\(945\) | −1890.00 | −0.0650600 | ||||||||
\(946\) | −5412.00 | −0.186003 | ||||||||
\(947\) | −1560.00 | −0.0535303 | −0.0267651 | − | 0.999642i | \(-0.508521\pi\) | ||||
−0.0267651 | + | 0.999642i | \(0.508521\pi\) | |||||||
\(948\) | −18564.0 | −0.636003 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 2280.00 | 0.0778663 | ||||||||
\(951\) | 771.000 | 0.0262896 | ||||||||
\(952\) | −5550.00 | −0.188946 | ||||||||
\(953\) | −21498.0 | −0.730733 | −0.365366 | − | 0.930864i | \(-0.619056\pi\) | ||||
−0.365366 | + | 0.930864i | \(0.619056\pi\) | |||||||
\(954\) | −4833.00 | −0.164019 | ||||||||
\(955\) | 4172.00 | 0.141364 | ||||||||
\(956\) | 17262.0 | 0.583988 | ||||||||
\(957\) | −7458.00 | −0.251915 | ||||||||
\(958\) | 3600.00 | 0.121410 | ||||||||
\(959\) | 5190.00 | 0.174759 | ||||||||
\(960\) | 3507.00 | 0.117904 | ||||||||
\(961\) | 8625.00 | 0.289517 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12042.0 | −0.402957 | ||||||||
\(964\) | −25319.0 | −0.845923 | ||||||||
\(965\) | −2751.00 | −0.0917698 | ||||||||
\(966\) | −4860.00 | −0.161872 | ||||||||
\(967\) | 418.000 | 0.0139007 | 0.00695035 | − | 0.999976i | \(-0.497788\pi\) | ||||
0.00695035 | + | 0.999976i | \(0.497788\pi\) | |||||||
\(968\) | 12705.0 | 0.421853 | ||||||||
\(969\) | −3330.00 | −0.110397 | ||||||||
\(970\) | −8414.00 | −0.278513 | ||||||||
\(971\) | 18132.0 | 0.599262 | 0.299631 | − | 0.954055i | \(-0.403136\pi\) | ||||
0.299631 | + | 0.954055i | \(0.403136\pi\) | |||||||
\(972\) | −1701.00 | −0.0561313 | ||||||||
\(973\) | −3480.00 | −0.114659 | ||||||||
\(974\) | 17130.0 | 0.563532 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −26035.0 | −0.853853 | ||||||||
\(977\) | −12501.0 | −0.409358 | −0.204679 | − | 0.978829i | \(-0.565615\pi\) | ||||
−0.204679 | + | 0.978829i | \(0.565615\pi\) | |||||||
\(978\) | −5100.00 | −0.166748 | ||||||||
\(979\) | −4268.00 | −0.139332 | ||||||||
\(980\) | −11907.0 | −0.388118 | ||||||||
\(981\) | 9306.00 | 0.302872 | ||||||||
\(982\) | −11838.0 | −0.384690 | ||||||||
\(983\) | 43708.0 | 1.41818 | 0.709089 | − | 0.705119i | \(-0.249106\pi\) | ||||
0.709089 | + | 0.705119i | \(0.249106\pi\) | |||||||
\(984\) | 12825.0 | 0.415494 | ||||||||
\(985\) | −24654.0 | −0.797504 | ||||||||
\(986\) | −4181.00 | −0.135041 | ||||||||
\(987\) | 13860.0 | 0.446979 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 39852.0 | 1.28131 | ||||||||
\(990\) | −1386.00 | −0.0444949 | ||||||||
\(991\) | −39614.0 | −1.26981 | −0.634904 | − | 0.772591i | \(-0.718960\pi\) | ||||
−0.634904 | + | 0.772591i | \(0.718960\pi\) | |||||||
\(992\) | −31556.0 | −1.00998 | ||||||||
\(993\) | −3084.00 | −0.0985577 | ||||||||
\(994\) | 10860.0 | 0.346538 | ||||||||
\(995\) | −14126.0 | −0.450075 | ||||||||
\(996\) | 10878.0 | 0.346067 | ||||||||
\(997\) | −36503.0 | −1.15954 | −0.579770 | − | 0.814780i | \(-0.696858\pi\) | ||||
−0.579770 | + | 0.814780i | \(0.696858\pi\) | |||||||
\(998\) | −8976.00 | −0.284700 | ||||||||
\(999\) | −351.000 | −0.0111163 |
(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 | 507.4.a.d.1.1 | 1 | ||
3.2 | odd | 2 | 1521.4.a.e.1.1 | 1 | |||
13.4 | even | 6 | 39.4.e.b.16.1 | ✓ | 2 | ||
13.5 | odd | 4 | 507.4.b.d.337.1 | 2 | |||
13.8 | odd | 4 | 507.4.b.d.337.2 | 2 | |||
13.10 | even | 6 | 39.4.e.b.22.1 | yes | 2 | ||
13.12 | even | 2 | 507.4.a.b.1.1 | 1 | |||
39.17 | odd | 6 | 117.4.g.a.55.1 | 2 | |||
39.23 | odd | 6 | 117.4.g.a.100.1 | 2 | |||
39.38 | odd | 2 | 1521.4.a.h.1.1 | 1 | |||
52.23 | odd | 6 | 624.4.q.c.529.1 | 2 | |||
52.43 | odd | 6 | 624.4.q.c.289.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.e.b.16.1 | ✓ | 2 | 13.4 | even | 6 | ||
39.4.e.b.22.1 | yes | 2 | 13.10 | even | 6 | ||
117.4.g.a.55.1 | 2 | 39.17 | odd | 6 | |||
117.4.g.a.100.1 | 2 | 39.23 | odd | 6 | |||
507.4.a.b.1.1 | 1 | 13.12 | even | 2 | |||
507.4.a.d.1.1 | 1 | 1.1 | even | 1 | trivial | ||
507.4.b.d.337.1 | 2 | 13.5 | odd | 4 | |||
507.4.b.d.337.2 | 2 | 13.8 | odd | 4 | |||
624.4.q.c.289.1 | 2 | 52.43 | odd | 6 | |||
624.4.q.c.529.1 | 2 | 52.23 | odd | 6 | |||
1521.4.a.e.1.1 | 1 | 3.2 | odd | 2 | |||
1521.4.a.h.1.1 | 1 | 39.38 | odd | 2 |