Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [19,8,Mod(1,19)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(19, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("19.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 19 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 19.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: | \(5.93531548420\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} - 540x^{4} + 610x^{3} + 80412x^{2} + 7680x - 2267712 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(5.78641\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 19.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 7.78641 | 0.688228 | 0.344114 | − | 0.938928i | \(-0.388179\pi\) | ||||
0.344114 | + | 0.938928i | \(0.388179\pi\) | |||||||
\(3\) | 37.1813 | 0.795061 | 0.397530 | − | 0.917589i | \(-0.369867\pi\) | ||||
0.397530 | + | 0.917589i | \(0.369867\pi\) | |||||||
\(4\) | −67.3719 | −0.526343 | ||||||||
\(5\) | 383.672 | 1.37267 | 0.686334 | − | 0.727287i | \(-0.259219\pi\) | ||||
0.686334 | + | 0.727287i | \(0.259219\pi\) | |||||||
\(6\) | 289.509 | 0.547183 | ||||||||
\(7\) | 1025.33 | 1.12985 | 0.564926 | − | 0.825141i | \(-0.308905\pi\) | ||||
0.564926 | + | 0.825141i | \(0.308905\pi\) | |||||||
\(8\) | −1521.24 | −1.05047 | ||||||||
\(9\) | −804.550 | −0.367878 | ||||||||
\(10\) | 2987.43 | 0.944707 | ||||||||
\(11\) | 7464.72 | 1.69098 | 0.845492 | − | 0.533989i | \(-0.179308\pi\) | ||||
0.845492 | + | 0.533989i | \(0.179308\pi\) | |||||||
\(12\) | −2504.97 | −0.418474 | ||||||||
\(13\) | −5468.73 | −0.690375 | −0.345187 | − | 0.938534i | \(-0.612185\pi\) | ||||
−0.345187 | + | 0.938534i | \(0.612185\pi\) | |||||||
\(14\) | 7983.66 | 0.777596 | ||||||||
\(15\) | 14265.4 | 1.09135 | ||||||||
\(16\) | −3221.44 | −0.196621 | ||||||||
\(17\) | −33272.0 | −1.64251 | −0.821255 | − | 0.570561i | \(-0.806726\pi\) | ||||
−0.821255 | + | 0.570561i | \(0.806726\pi\) | |||||||
\(18\) | −6264.56 | −0.253184 | ||||||||
\(19\) | −6859.00 | −0.229416 | ||||||||
\(20\) | −25848.7 | −0.722493 | ||||||||
\(21\) | 38123.2 | 0.898302 | ||||||||
\(22\) | 58123.4 | 1.16378 | ||||||||
\(23\) | −87483.9 | −1.49927 | −0.749636 | − | 0.661850i | \(-0.769772\pi\) | ||||
−0.749636 | + | 0.661850i | \(0.769772\pi\) | |||||||
\(24\) | −56561.9 | −0.835188 | ||||||||
\(25\) | 69079.3 | 0.884215 | ||||||||
\(26\) | −42581.8 | −0.475135 | ||||||||
\(27\) | −111230. | −1.08755 | ||||||||
\(28\) | −69078.6 | −0.594690 | ||||||||
\(29\) | −82018.1 | −0.624477 | −0.312239 | − | 0.950004i | \(-0.601079\pi\) | ||||
−0.312239 | + | 0.950004i | \(0.601079\pi\) | |||||||
\(30\) | 111076. | 0.751100 | ||||||||
\(31\) | 241441. | 1.45561 | 0.727805 | − | 0.685784i | \(-0.240540\pi\) | ||||
0.727805 | + | 0.685784i | \(0.240540\pi\) | |||||||
\(32\) | 169636. | 0.915151 | ||||||||
\(33\) | 277548. | 1.34443 | ||||||||
\(34\) | −259070. | −1.13042 | ||||||||
\(35\) | 393392. | 1.55091 | ||||||||
\(36\) | 54204.0 | 0.193630 | ||||||||
\(37\) | 60298.8 | 0.195705 | 0.0978526 | − | 0.995201i | \(-0.468803\pi\) | ||||
0.0978526 | + | 0.995201i | \(0.468803\pi\) | |||||||
\(38\) | −53407.0 | −0.157890 | ||||||||
\(39\) | −203335. | −0.548890 | ||||||||
\(40\) | −583659. | −1.44195 | ||||||||
\(41\) | 410651. | 0.930528 | 0.465264 | − | 0.885172i | \(-0.345959\pi\) | ||||
0.465264 | + | 0.885172i | \(0.345959\pi\) | |||||||
\(42\) | 296843. | 0.618236 | ||||||||
\(43\) | 83758.4 | 0.160653 | 0.0803265 | − | 0.996769i | \(-0.474404\pi\) | ||||
0.0803265 | + | 0.996769i | \(0.474404\pi\) | |||||||
\(44\) | −502912. | −0.890037 | ||||||||
\(45\) | −308683. | −0.504975 | ||||||||
\(46\) | −681185. | −1.03184 | ||||||||
\(47\) | −324050. | −0.455271 | −0.227636 | − | 0.973746i | \(-0.573099\pi\) | ||||
−0.227636 | + | 0.973746i | \(0.573099\pi\) | |||||||
\(48\) | −119777. | −0.156325 | ||||||||
\(49\) | 227765. | 0.276567 | ||||||||
\(50\) | 537879. | 0.608541 | ||||||||
\(51\) | −1.23710e6 | −1.30590 | ||||||||
\(52\) | 368439. | 0.363374 | ||||||||
\(53\) | 196659. | 0.181446 | 0.0907230 | − | 0.995876i | \(-0.471082\pi\) | ||||
0.0907230 | + | 0.995876i | \(0.471082\pi\) | |||||||
\(54\) | −866080. | −0.748480 | ||||||||
\(55\) | 2.86401e6 | 2.32116 | ||||||||
\(56\) | −1.55978e6 | −1.18688 | ||||||||
\(57\) | −255027. | −0.182399 | ||||||||
\(58\) | −638626. | −0.429783 | ||||||||
\(59\) | 2.37877e6 | 1.50789 | 0.753947 | − | 0.656935i | \(-0.228148\pi\) | ||||
0.753947 | + | 0.656935i | \(0.228148\pi\) | |||||||
\(60\) | −961089. | −0.574426 | ||||||||
\(61\) | −598880. | −0.337820 | −0.168910 | − | 0.985631i | \(-0.554025\pi\) | ||||
−0.168910 | + | 0.985631i | \(0.554025\pi\) | |||||||
\(62\) | 1.87996e6 | 1.00179 | ||||||||
\(63\) | −824932. | −0.415648 | ||||||||
\(64\) | 1.73320e6 | 0.826453 | ||||||||
\(65\) | −2.09820e6 | −0.947655 | ||||||||
\(66\) | 2.16110e6 | 0.925277 | ||||||||
\(67\) | −2.28946e6 | −0.929977 | −0.464988 | − | 0.885317i | \(-0.653941\pi\) | ||||
−0.464988 | + | 0.885317i | \(0.653941\pi\) | |||||||
\(68\) | 2.24160e6 | 0.864523 | ||||||||
\(69\) | −3.25277e6 | −1.19201 | ||||||||
\(70\) | 3.06311e6 | 1.06738 | ||||||||
\(71\) | −1.06076e6 | −0.351733 | −0.175866 | − | 0.984414i | \(-0.556273\pi\) | ||||
−0.175866 | + | 0.984414i | \(0.556273\pi\) | |||||||
\(72\) | 1.22392e6 | 0.386446 | ||||||||
\(73\) | −1.44824e6 | −0.435724 | −0.217862 | − | 0.975980i | \(-0.569908\pi\) | ||||
−0.217862 | + | 0.975980i | \(0.569908\pi\) | |||||||
\(74\) | 469511. | 0.134690 | ||||||||
\(75\) | 2.56846e6 | 0.703004 | ||||||||
\(76\) | 462104. | 0.120751 | ||||||||
\(77\) | 7.65383e6 | 1.91056 | ||||||||
\(78\) | −1.58325e6 | −0.377761 | ||||||||
\(79\) | −2.30738e6 | −0.526531 | −0.263265 | − | 0.964723i | \(-0.584799\pi\) | ||||
−0.263265 | + | 0.964723i | \(0.584799\pi\) | |||||||
\(80\) | −1.23597e6 | −0.269895 | ||||||||
\(81\) | −2.37612e6 | −0.496787 | ||||||||
\(82\) | 3.19749e6 | 0.640415 | ||||||||
\(83\) | 1.43685e6 | 0.275827 | 0.137914 | − | 0.990444i | \(-0.455960\pi\) | ||||
0.137914 | + | 0.990444i | \(0.455960\pi\) | |||||||
\(84\) | −2.56843e6 | −0.472814 | ||||||||
\(85\) | −1.27656e7 | −2.25462 | ||||||||
\(86\) | 652177. | 0.110566 | ||||||||
\(87\) | −3.04954e6 | −0.496497 | ||||||||
\(88\) | −1.13557e7 | −1.77633 | ||||||||
\(89\) | 7.41572e6 | 1.11503 | 0.557517 | − | 0.830165i | \(-0.311754\pi\) | ||||
0.557517 | + | 0.830165i | \(0.311754\pi\) | |||||||
\(90\) | −2.40354e6 | −0.347538 | ||||||||
\(91\) | −5.60727e6 | −0.780022 | ||||||||
\(92\) | 5.89395e6 | 0.789131 | ||||||||
\(93\) | 8.97710e6 | 1.15730 | ||||||||
\(94\) | −2.52319e6 | −0.313330 | ||||||||
\(95\) | −2.63161e6 | −0.314911 | ||||||||
\(96\) | 6.30729e6 | 0.727601 | ||||||||
\(97\) | 5.66811e6 | 0.630576 | 0.315288 | − | 0.948996i | \(-0.397899\pi\) | ||||
0.315288 | + | 0.948996i | \(0.397899\pi\) | |||||||
\(98\) | 1.77347e6 | 0.190341 | ||||||||
\(99\) | −6.00574e6 | −0.622076 | ||||||||
\(100\) | −4.65400e6 | −0.465400 | ||||||||
\(101\) | −1.06011e7 | −1.02382 | −0.511912 | − | 0.859038i | \(-0.671063\pi\) | ||||
−0.511912 | + | 0.859038i | \(0.671063\pi\) | |||||||
\(102\) | −9.63255e6 | −0.898754 | ||||||||
\(103\) | 1.80037e6 | 0.162342 | 0.0811711 | − | 0.996700i | \(-0.474134\pi\) | ||||
0.0811711 | + | 0.996700i | \(0.474134\pi\) | |||||||
\(104\) | 8.31928e6 | 0.725219 | ||||||||
\(105\) | 1.46268e7 | 1.23307 | ||||||||
\(106\) | 1.53126e6 | 0.124876 | ||||||||
\(107\) | 352539. | 0.0278204 | 0.0139102 | − | 0.999903i | \(-0.495572\pi\) | ||||
0.0139102 | + | 0.999903i | \(0.495572\pi\) | |||||||
\(108\) | 7.49375e6 | 0.572422 | ||||||||
\(109\) | 5.05631e6 | 0.373974 | 0.186987 | − | 0.982362i | \(-0.440128\pi\) | ||||
0.186987 | + | 0.982362i | \(0.440128\pi\) | |||||||
\(110\) | 2.23003e7 | 1.59748 | ||||||||
\(111\) | 2.24199e6 | 0.155597 | ||||||||
\(112\) | −3.30304e6 | −0.222153 | ||||||||
\(113\) | 2.23738e7 | 1.45870 | 0.729350 | − | 0.684141i | \(-0.239823\pi\) | ||||
0.729350 | + | 0.684141i | \(0.239823\pi\) | |||||||
\(114\) | −1.98574e6 | −0.125532 | ||||||||
\(115\) | −3.35651e7 | −2.05800 | ||||||||
\(116\) | 5.52571e6 | 0.328689 | ||||||||
\(117\) | 4.39987e6 | 0.253974 | ||||||||
\(118\) | 1.85221e7 | 1.03777 | ||||||||
\(119\) | −3.41149e7 | −1.85580 | ||||||||
\(120\) | −2.17012e7 | −1.14644 | ||||||||
\(121\) | 3.62349e7 | 1.85942 | ||||||||
\(122\) | −4.66312e6 | −0.232497 | ||||||||
\(123\) | 1.52685e7 | 0.739826 | ||||||||
\(124\) | −1.62663e7 | −0.766150 | ||||||||
\(125\) | −3.47059e6 | −0.158935 | ||||||||
\(126\) | −6.42326e6 | −0.286061 | ||||||||
\(127\) | −6.59897e6 | −0.285866 | −0.142933 | − | 0.989732i | \(-0.545653\pi\) | ||||
−0.142933 | + | 0.989732i | \(0.545653\pi\) | |||||||
\(128\) | −8.21801e6 | −0.346363 | ||||||||
\(129\) | 3.11425e6 | 0.127729 | ||||||||
\(130\) | −1.63374e7 | −0.652202 | ||||||||
\(131\) | 1.60434e7 | 0.623514 | 0.311757 | − | 0.950162i | \(-0.399082\pi\) | ||||
0.311757 | + | 0.950162i | \(0.399082\pi\) | |||||||
\(132\) | −1.86989e7 | −0.707633 | ||||||||
\(133\) | −7.03276e6 | −0.259206 | ||||||||
\(134\) | −1.78267e7 | −0.640036 | ||||||||
\(135\) | −4.26758e7 | −1.49284 | ||||||||
\(136\) | 5.06149e7 | 1.72541 | ||||||||
\(137\) | 4.34536e7 | 1.44379 | 0.721894 | − | 0.692004i | \(-0.243272\pi\) | ||||
0.721894 | + | 0.692004i | \(0.243272\pi\) | |||||||
\(138\) | −2.53274e7 | −0.820376 | ||||||||
\(139\) | 6.88324e6 | 0.217391 | 0.108695 | − | 0.994075i | \(-0.465333\pi\) | ||||
0.108695 | + | 0.994075i | \(0.465333\pi\) | |||||||
\(140\) | −2.65035e7 | −0.816311 | ||||||||
\(141\) | −1.20486e7 | −0.361968 | ||||||||
\(142\) | −8.25950e6 | −0.242072 | ||||||||
\(143\) | −4.08226e7 | −1.16741 | ||||||||
\(144\) | 2.59181e6 | 0.0723326 | ||||||||
\(145\) | −3.14681e7 | −0.857199 | ||||||||
\(146\) | −1.12766e7 | −0.299877 | ||||||||
\(147\) | 8.46860e6 | 0.219888 | ||||||||
\(148\) | −4.06244e6 | −0.103008 | ||||||||
\(149\) | 3.18926e7 | 0.789838 | 0.394919 | − | 0.918716i | \(-0.370773\pi\) | ||||
0.394919 | + | 0.918716i | \(0.370773\pi\) | |||||||
\(150\) | 1.99991e7 | 0.483827 | ||||||||
\(151\) | 5.55066e7 | 1.31197 | 0.655987 | − | 0.754772i | \(-0.272253\pi\) | ||||
0.655987 | + | 0.754772i | \(0.272253\pi\) | |||||||
\(152\) | 1.04342e7 | 0.240995 | ||||||||
\(153\) | 2.67690e7 | 0.604244 | ||||||||
\(154\) | 5.95958e7 | 1.31490 | ||||||||
\(155\) | 9.26342e7 | 1.99807 | ||||||||
\(156\) | 1.36990e7 | 0.288904 | ||||||||
\(157\) | −4.28079e7 | −0.882827 | −0.441413 | − | 0.897304i | \(-0.645523\pi\) | ||||
−0.441413 | + | 0.897304i | \(0.645523\pi\) | |||||||
\(158\) | −1.79662e7 | −0.362373 | ||||||||
\(159\) | 7.31202e6 | 0.144261 | ||||||||
\(160\) | 6.50846e7 | 1.25620 | ||||||||
\(161\) | −8.97001e7 | −1.69396 | ||||||||
\(162\) | −1.85014e7 | −0.341903 | ||||||||
\(163\) | −8.84360e7 | −1.59946 | −0.799728 | − | 0.600363i | \(-0.795023\pi\) | ||||
−0.799728 | + | 0.600363i | \(0.795023\pi\) | |||||||
\(164\) | −2.76663e7 | −0.489776 | ||||||||
\(165\) | 1.06487e8 | 1.84546 | ||||||||
\(166\) | 1.11879e7 | 0.189832 | ||||||||
\(167\) | 9.61510e7 | 1.59752 | 0.798759 | − | 0.601651i | \(-0.205490\pi\) | ||||
0.798759 | + | 0.601651i | \(0.205490\pi\) | |||||||
\(168\) | −5.79948e7 | −0.943640 | ||||||||
\(169\) | −3.28415e7 | −0.523383 | ||||||||
\(170\) | −9.93978e7 | −1.55169 | ||||||||
\(171\) | 5.51841e6 | 0.0843971 | ||||||||
\(172\) | −5.64296e6 | −0.0845585 | ||||||||
\(173\) | −7.19465e7 | −1.05645 | −0.528224 | − | 0.849105i | \(-0.677142\pi\) | ||||
−0.528224 | + | 0.849105i | \(0.677142\pi\) | |||||||
\(174\) | −2.37450e7 | −0.341703 | ||||||||
\(175\) | 7.08293e7 | 0.999033 | ||||||||
\(176\) | −2.40471e7 | −0.332483 | ||||||||
\(177\) | 8.84458e7 | 1.19887 | ||||||||
\(178\) | 5.77418e7 | 0.767398 | ||||||||
\(179\) | −1.45456e8 | −1.89560 | −0.947800 | − | 0.318866i | \(-0.896698\pi\) | ||||
−0.947800 | + | 0.318866i | \(0.896698\pi\) | |||||||
\(180\) | 2.07966e7 | 0.265790 | ||||||||
\(181\) | 1.37620e8 | 1.72507 | 0.862537 | − | 0.505994i | \(-0.168874\pi\) | ||||
0.862537 | + | 0.505994i | \(0.168874\pi\) | |||||||
\(182\) | −4.36605e7 | −0.536833 | ||||||||
\(183\) | −2.22671e7 | −0.268587 | ||||||||
\(184\) | 1.33084e8 | 1.57494 | ||||||||
\(185\) | 2.31349e7 | 0.268638 | ||||||||
\(186\) | 6.98993e7 | 0.796485 | ||||||||
\(187\) | −2.48367e8 | −2.77746 | ||||||||
\(188\) | 2.18319e7 | 0.239629 | ||||||||
\(189\) | −1.14048e8 | −1.22877 | ||||||||
\(190\) | −2.04908e7 | −0.216731 | ||||||||
\(191\) | 9.82018e7 | 1.01977 | 0.509885 | − | 0.860242i | \(-0.329688\pi\) | ||||
0.509885 | + | 0.860242i | \(0.329688\pi\) | |||||||
\(192\) | 6.44426e7 | 0.657081 | ||||||||
\(193\) | −3.27640e6 | −0.0328054 | −0.0164027 | − | 0.999865i | \(-0.505221\pi\) | ||||
−0.0164027 | + | 0.999865i | \(0.505221\pi\) | |||||||
\(194\) | 4.41342e7 | 0.433980 | ||||||||
\(195\) | −7.80138e7 | −0.753443 | ||||||||
\(196\) | −1.53450e7 | −0.145569 | ||||||||
\(197\) | −5.20058e7 | −0.484641 | −0.242321 | − | 0.970196i | \(-0.577909\pi\) | ||||
−0.242321 | + | 0.970196i | \(0.577909\pi\) | |||||||
\(198\) | −4.67632e7 | −0.428130 | ||||||||
\(199\) | −4.81956e7 | −0.433533 | −0.216766 | − | 0.976223i | \(-0.569551\pi\) | ||||
−0.216766 | + | 0.976223i | \(0.569551\pi\) | |||||||
\(200\) | −1.05087e8 | −0.928842 | ||||||||
\(201\) | −8.51253e7 | −0.739388 | ||||||||
\(202\) | −8.25444e7 | −0.704624 | ||||||||
\(203\) | −8.40959e7 | −0.705567 | ||||||||
\(204\) | 8.33456e7 | 0.687349 | ||||||||
\(205\) | 1.57555e8 | 1.27730 | ||||||||
\(206\) | 1.40184e7 | 0.111728 | ||||||||
\(207\) | 7.03852e7 | 0.551550 | ||||||||
\(208\) | 1.76172e7 | 0.135742 | ||||||||
\(209\) | −5.12005e7 | −0.387938 | ||||||||
\(210\) | 1.13890e8 | 0.848632 | ||||||||
\(211\) | −1.79146e8 | −1.31286 | −0.656431 | − | 0.754386i | \(-0.727935\pi\) | ||||
−0.656431 | + | 0.754386i | \(0.727935\pi\) | |||||||
\(212\) | −1.32493e7 | −0.0955028 | ||||||||
\(213\) | −3.94404e7 | −0.279649 | ||||||||
\(214\) | 2.74501e6 | 0.0191468 | ||||||||
\(215\) | 3.21358e7 | 0.220523 | ||||||||
\(216\) | 1.69208e8 | 1.14244 | ||||||||
\(217\) | 2.47558e8 | 1.64463 | ||||||||
\(218\) | 3.93705e7 | 0.257379 | ||||||||
\(219\) | −5.38476e7 | −0.346427 | ||||||||
\(220\) | −1.92953e8 | −1.22172 | ||||||||
\(221\) | 1.81956e8 | 1.13395 | ||||||||
\(222\) | 1.74570e7 | 0.107087 | ||||||||
\(223\) | −3.28725e7 | −0.198502 | −0.0992511 | − | 0.995062i | \(-0.531645\pi\) | ||||
−0.0992511 | + | 0.995062i | \(0.531645\pi\) | |||||||
\(224\) | 1.73933e8 | 1.03399 | ||||||||
\(225\) | −5.55777e7 | −0.325284 | ||||||||
\(226\) | 1.74212e8 | 1.00392 | ||||||||
\(227\) | 2.83590e7 | 0.160917 | 0.0804583 | − | 0.996758i | \(-0.474362\pi\) | ||||
0.0804583 | + | 0.996758i | \(0.474362\pi\) | |||||||
\(228\) | 1.71816e7 | 0.0960046 | ||||||||
\(229\) | 1.07307e8 | 0.590480 | 0.295240 | − | 0.955423i | \(-0.404600\pi\) | ||||
0.295240 | + | 0.955423i | \(0.404600\pi\) | |||||||
\(230\) | −2.61352e8 | −1.41637 | ||||||||
\(231\) | 2.84579e8 | 1.51901 | ||||||||
\(232\) | 1.24770e8 | 0.655995 | ||||||||
\(233\) | −8.52700e7 | −0.441622 | −0.220811 | − | 0.975317i | \(-0.570870\pi\) | ||||
−0.220811 | + | 0.975317i | \(0.570870\pi\) | |||||||
\(234\) | 3.42592e7 | 0.174792 | ||||||||
\(235\) | −1.24329e8 | −0.624936 | ||||||||
\(236\) | −1.60262e8 | −0.793669 | ||||||||
\(237\) | −8.57913e7 | −0.418624 | ||||||||
\(238\) | −2.65633e8 | −1.27721 | ||||||||
\(239\) | −5.42931e7 | −0.257248 | −0.128624 | − | 0.991693i | \(-0.541056\pi\) | ||||
−0.128624 | + | 0.991693i | \(0.541056\pi\) | |||||||
\(240\) | −4.59552e7 | −0.214583 | ||||||||
\(241\) | 1.20559e8 | 0.554806 | 0.277403 | − | 0.960754i | \(-0.410526\pi\) | ||||
0.277403 | + | 0.960754i | \(0.410526\pi\) | |||||||
\(242\) | 2.82140e8 | 1.27971 | ||||||||
\(243\) | 1.54912e8 | 0.692571 | ||||||||
\(244\) | 4.03476e7 | 0.177809 | ||||||||
\(245\) | 8.73871e7 | 0.379635 | ||||||||
\(246\) | 1.18887e8 | 0.509169 | ||||||||
\(247\) | 3.75100e7 | 0.158383 | ||||||||
\(248\) | −3.67291e8 | −1.52908 | ||||||||
\(249\) | 5.34239e7 | 0.219299 | ||||||||
\(250\) | −2.70234e7 | −0.109383 | ||||||||
\(251\) | 1.21294e8 | 0.484151 | 0.242075 | − | 0.970257i | \(-0.422172\pi\) | ||||
0.242075 | + | 0.970257i | \(0.422172\pi\) | |||||||
\(252\) | 5.55772e7 | 0.218774 | ||||||||
\(253\) | −6.53043e8 | −2.53525 | ||||||||
\(254\) | −5.13823e7 | −0.196741 | ||||||||
\(255\) | −4.74640e8 | −1.79256 | ||||||||
\(256\) | −2.85838e8 | −1.06483 | ||||||||
\(257\) | −3.14139e8 | −1.15440 | −0.577199 | − | 0.816604i | \(-0.695854\pi\) | ||||
−0.577199 | + | 0.816604i | \(0.695854\pi\) | |||||||
\(258\) | 2.42488e7 | 0.0879065 | ||||||||
\(259\) | 6.18263e7 | 0.221118 | ||||||||
\(260\) | 1.41360e8 | 0.498791 | ||||||||
\(261\) | 6.59877e7 | 0.229732 | ||||||||
\(262\) | 1.24920e8 | 0.429120 | ||||||||
\(263\) | 2.18127e7 | 0.0739375 | 0.0369687 | − | 0.999316i | \(-0.488230\pi\) | ||||
0.0369687 | + | 0.999316i | \(0.488230\pi\) | |||||||
\(264\) | −4.22219e8 | −1.41229 | ||||||||
\(265\) | 7.54524e7 | 0.249065 | ||||||||
\(266\) | −5.47599e7 | −0.178393 | ||||||||
\(267\) | 2.75726e8 | 0.886520 | ||||||||
\(268\) | 1.54245e8 | 0.489486 | ||||||||
\(269\) | 5.68573e8 | 1.78096 | 0.890479 | − | 0.455025i | \(-0.150370\pi\) | ||||
0.890479 | + | 0.455025i | \(0.150370\pi\) | |||||||
\(270\) | −3.32291e8 | −1.02741 | ||||||||
\(271\) | −1.18276e8 | −0.360998 | −0.180499 | − | 0.983575i | \(-0.557771\pi\) | ||||
−0.180499 | + | 0.983575i | \(0.557771\pi\) | |||||||
\(272\) | 1.07184e8 | 0.322952 | ||||||||
\(273\) | −2.08486e8 | −0.620165 | ||||||||
\(274\) | 3.38347e8 | 0.993655 | ||||||||
\(275\) | 5.15658e8 | 1.49519 | ||||||||
\(276\) | 2.19145e8 | 0.627407 | ||||||||
\(277\) | 5.18980e8 | 1.46714 | 0.733570 | − | 0.679614i | \(-0.237853\pi\) | ||||
0.733570 | + | 0.679614i | \(0.237853\pi\) | |||||||
\(278\) | 5.35957e7 | 0.149614 | ||||||||
\(279\) | −1.94251e8 | −0.535488 | ||||||||
\(280\) | −5.98445e8 | −1.62919 | ||||||||
\(281\) | −3.40465e8 | −0.915377 | −0.457689 | − | 0.889112i | \(-0.651323\pi\) | ||||
−0.457689 | + | 0.889112i | \(0.651323\pi\) | |||||||
\(282\) | −9.38154e7 | −0.249116 | ||||||||
\(283\) | −1.86257e8 | −0.488495 | −0.244247 | − | 0.969713i | \(-0.578541\pi\) | ||||
−0.244247 | + | 0.969713i | \(0.578541\pi\) | |||||||
\(284\) | 7.14653e7 | 0.185132 | ||||||||
\(285\) | −9.78466e7 | −0.250374 | ||||||||
\(286\) | −3.17861e8 | −0.803445 | ||||||||
\(287\) | 4.21054e8 | 1.05136 | ||||||||
\(288\) | −1.36481e8 | −0.336664 | ||||||||
\(289\) | 6.96690e8 | 1.69784 | ||||||||
\(290\) | −2.45023e8 | −0.589948 | ||||||||
\(291\) | 2.10748e8 | 0.501346 | ||||||||
\(292\) | 9.75708e7 | 0.229340 | ||||||||
\(293\) | 1.81719e8 | 0.422049 | 0.211024 | − | 0.977481i | \(-0.432320\pi\) | ||||
0.211024 | + | 0.977481i | \(0.432320\pi\) | |||||||
\(294\) | 6.59400e7 | 0.151333 | ||||||||
\(295\) | 9.12668e8 | 2.06984 | ||||||||
\(296\) | −9.17292e7 | −0.205583 | ||||||||
\(297\) | −8.30299e8 | −1.83902 | ||||||||
\(298\) | 2.48329e8 | 0.543589 | ||||||||
\(299\) | 4.78426e8 | 1.03506 | ||||||||
\(300\) | −1.73042e8 | −0.370021 | ||||||||
\(301\) | 8.58802e7 | 0.181514 | ||||||||
\(302\) | 4.32197e8 | 0.902937 | ||||||||
\(303\) | −3.94162e8 | −0.814003 | ||||||||
\(304\) | 2.20958e7 | 0.0451079 | ||||||||
\(305\) | −2.29773e8 | −0.463714 | ||||||||
\(306\) | 2.08435e8 | 0.415858 | ||||||||
\(307\) | −4.44144e8 | −0.876071 | −0.438035 | − | 0.898958i | \(-0.644326\pi\) | ||||
−0.438035 | + | 0.898958i | \(0.644326\pi\) | |||||||
\(308\) | −5.15653e8 | −1.00561 | ||||||||
\(309\) | 6.69401e7 | 0.129072 | ||||||||
\(310\) | 7.21288e8 | 1.37513 | ||||||||
\(311\) | 2.51879e8 | 0.474822 | 0.237411 | − | 0.971409i | \(-0.423701\pi\) | ||||
0.237411 | + | 0.971409i | \(0.423701\pi\) | |||||||
\(312\) | 3.09322e8 | 0.576593 | ||||||||
\(313\) | −4.05359e8 | −0.747196 | −0.373598 | − | 0.927591i | \(-0.621876\pi\) | ||||
−0.373598 | + | 0.927591i | \(0.621876\pi\) | |||||||
\(314\) | −3.33320e8 | −0.607586 | ||||||||
\(315\) | −3.16503e8 | −0.570547 | ||||||||
\(316\) | 1.55452e8 | 0.277136 | ||||||||
\(317\) | −5.80221e7 | −0.102302 | −0.0511512 | − | 0.998691i | \(-0.516289\pi\) | ||||
−0.0511512 | + | 0.998691i | \(0.516289\pi\) | |||||||
\(318\) | 5.69344e7 | 0.0992841 | ||||||||
\(319\) | −6.12242e8 | −1.05598 | ||||||||
\(320\) | 6.64980e8 | 1.13445 | ||||||||
\(321\) | 1.31078e7 | 0.0221189 | ||||||||
\(322\) | −6.98442e8 | −1.16583 | ||||||||
\(323\) | 2.28213e8 | 0.376818 | ||||||||
\(324\) | 1.60083e8 | 0.261480 | ||||||||
\(325\) | −3.77776e8 | −0.610440 | ||||||||
\(326\) | −6.88598e8 | −1.10079 | ||||||||
\(327\) | 1.88000e8 | 0.297332 | ||||||||
\(328\) | −6.24700e8 | −0.977492 | ||||||||
\(329\) | −3.32260e8 | −0.514389 | ||||||||
\(330\) | 8.29155e8 | 1.27010 | ||||||||
\(331\) | −4.47991e8 | −0.679002 | −0.339501 | − | 0.940606i | \(-0.610258\pi\) | ||||
−0.339501 | + | 0.940606i | \(0.610258\pi\) | |||||||
\(332\) | −9.68031e7 | −0.145180 | ||||||||
\(333\) | −4.85134e7 | −0.0719957 | ||||||||
\(334\) | 7.48671e8 | 1.09946 | ||||||||
\(335\) | −8.78404e8 | −1.27655 | ||||||||
\(336\) | −1.22812e8 | −0.176625 | ||||||||
\(337\) | −1.34379e9 | −1.91260 | −0.956302 | − | 0.292380i | \(-0.905553\pi\) | ||||
−0.956302 | + | 0.292380i | \(0.905553\pi\) | |||||||
\(338\) | −2.55717e8 | −0.360207 | ||||||||
\(339\) | 8.31889e8 | 1.15976 | ||||||||
\(340\) | 8.60039e8 | 1.18670 | ||||||||
\(341\) | 1.80229e9 | 2.46141 | ||||||||
\(342\) | 4.29686e7 | 0.0580844 | ||||||||
\(343\) | −6.10871e8 | −0.817372 | ||||||||
\(344\) | −1.27417e8 | −0.168761 | ||||||||
\(345\) | −1.24800e9 | −1.63624 | ||||||||
\(346\) | −5.60205e8 | −0.727077 | ||||||||
\(347\) | 9.19046e8 | 1.18082 | 0.590410 | − | 0.807103i | \(-0.298966\pi\) | ||||
0.590410 | + | 0.807103i | \(0.298966\pi\) | |||||||
\(348\) | 2.05453e8 | 0.261328 | ||||||||
\(349\) | −7.68598e8 | −0.967855 | −0.483928 | − | 0.875108i | \(-0.660790\pi\) | ||||
−0.483928 | + | 0.875108i | \(0.660790\pi\) | |||||||
\(350\) | 5.51506e8 | 0.687562 | ||||||||
\(351\) | 6.08286e8 | 0.750815 | ||||||||
\(352\) | 1.26629e9 | 1.54751 | ||||||||
\(353\) | −1.27917e8 | −0.154780 | −0.0773902 | − | 0.997001i | \(-0.524659\pi\) | ||||
−0.0773902 | + | 0.997001i | \(0.524659\pi\) | |||||||
\(354\) | 6.88675e8 | 0.825093 | ||||||||
\(355\) | −4.06984e8 | −0.482812 | ||||||||
\(356\) | −4.99611e8 | −0.586890 | ||||||||
\(357\) | −1.26844e9 | −1.47547 | ||||||||
\(358\) | −1.13258e9 | −1.30460 | ||||||||
\(359\) | −1.27530e8 | −0.145472 | −0.0727362 | − | 0.997351i | \(-0.523173\pi\) | ||||
−0.0727362 | + | 0.997351i | \(0.523173\pi\) | |||||||
\(360\) | 4.69583e8 | 0.530461 | ||||||||
\(361\) | 4.70459e7 | 0.0526316 | ||||||||
\(362\) | 1.07157e9 | 1.18724 | ||||||||
\(363\) | 1.34726e9 | 1.47836 | ||||||||
\(364\) | 3.77772e8 | 0.410559 | ||||||||
\(365\) | −5.55650e8 | −0.598104 | ||||||||
\(366\) | −1.73381e8 | −0.184849 | ||||||||
\(367\) | −3.41967e8 | −0.361121 | −0.180560 | − | 0.983564i | \(-0.557791\pi\) | ||||
−0.180560 | + | 0.983564i | \(0.557791\pi\) | |||||||
\(368\) | 2.81824e8 | 0.294788 | ||||||||
\(369\) | −3.30389e8 | −0.342321 | ||||||||
\(370\) | 1.80138e8 | 0.184884 | ||||||||
\(371\) | 2.01641e8 | 0.205007 | ||||||||
\(372\) | −6.04804e8 | −0.609136 | ||||||||
\(373\) | 1.48848e9 | 1.48512 | 0.742562 | − | 0.669777i | \(-0.233610\pi\) | ||||
0.742562 | + | 0.669777i | \(0.233610\pi\) | |||||||
\(374\) | −1.93388e9 | −1.91152 | ||||||||
\(375\) | −1.29041e8 | −0.126363 | ||||||||
\(376\) | 4.92960e8 | 0.478249 | ||||||||
\(377\) | 4.48535e8 | 0.431123 | ||||||||
\(378\) | −8.88021e8 | −0.845672 | ||||||||
\(379\) | −4.90803e8 | −0.463095 | −0.231548 | − | 0.972824i | \(-0.574379\pi\) | ||||
−0.231548 | + | 0.972824i | \(0.574379\pi\) | |||||||
\(380\) | 1.77296e8 | 0.165751 | ||||||||
\(381\) | −2.45358e8 | −0.227281 | ||||||||
\(382\) | 7.64639e8 | 0.701835 | ||||||||
\(383\) | 1.33842e9 | 1.21730 | 0.608649 | − | 0.793439i | \(-0.291712\pi\) | ||||
0.608649 | + | 0.793439i | \(0.291712\pi\) | |||||||
\(384\) | −3.05556e8 | −0.275380 | ||||||||
\(385\) | 2.93656e9 | 2.62257 | ||||||||
\(386\) | −2.55114e7 | −0.0225776 | ||||||||
\(387\) | −6.73878e7 | −0.0591008 | ||||||||
\(388\) | −3.81871e8 | −0.331899 | ||||||||
\(389\) | −5.84856e8 | −0.503762 | −0.251881 | − | 0.967758i | \(-0.581049\pi\) | ||||
−0.251881 | + | 0.967758i | \(0.581049\pi\) | |||||||
\(390\) | −6.07447e8 | −0.518540 | ||||||||
\(391\) | 2.91077e9 | 2.46257 | ||||||||
\(392\) | −3.46487e8 | −0.290526 | ||||||||
\(393\) | 5.96514e8 | 0.495732 | ||||||||
\(394\) | −4.04939e8 | −0.333543 | ||||||||
\(395\) | −8.85276e8 | −0.722752 | ||||||||
\(396\) | 4.04618e8 | 0.327425 | ||||||||
\(397\) | −9.73621e8 | −0.780950 | −0.390475 | − | 0.920613i | \(-0.627689\pi\) | ||||
−0.390475 | + | 0.920613i | \(0.627689\pi\) | |||||||
\(398\) | −3.75271e8 | −0.298369 | ||||||||
\(399\) | −2.61487e8 | −0.206085 | ||||||||
\(400\) | −2.22534e8 | −0.173855 | ||||||||
\(401\) | −1.16168e9 | −0.899669 | −0.449834 | − | 0.893112i | \(-0.648517\pi\) | ||||
−0.449834 | + | 0.893112i | \(0.648517\pi\) | |||||||
\(402\) | −6.62820e8 | −0.508867 | ||||||||
\(403\) | −1.32038e9 | −1.00492 | ||||||||
\(404\) | 7.14215e8 | 0.538882 | ||||||||
\(405\) | −9.11650e8 | −0.681923 | ||||||||
\(406\) | −6.54805e8 | −0.485591 | ||||||||
\(407\) | 4.50113e8 | 0.330934 | ||||||||
\(408\) | 1.88193e9 | 1.37181 | ||||||||
\(409\) | −2.15036e9 | −1.55410 | −0.777051 | − | 0.629438i | \(-0.783285\pi\) | ||||
−0.777051 | + | 0.629438i | \(0.783285\pi\) | |||||||
\(410\) | 1.22679e9 | 0.879076 | ||||||||
\(411\) | 1.61566e9 | 1.14790 | ||||||||
\(412\) | −1.21294e8 | −0.0854476 | ||||||||
\(413\) | 2.43903e9 | 1.70370 | ||||||||
\(414\) | 5.48048e8 | 0.379592 | ||||||||
\(415\) | 5.51278e8 | 0.378619 | ||||||||
\(416\) | −9.27693e8 | −0.631797 | ||||||||
\(417\) | 2.55928e8 | 0.172839 | ||||||||
\(418\) | −3.98668e8 | −0.266990 | ||||||||
\(419\) | −1.33670e9 | −0.887739 | −0.443870 | − | 0.896091i | \(-0.646395\pi\) | ||||
−0.443870 | + | 0.896091i | \(0.646395\pi\) | |||||||
\(420\) | −9.85436e8 | −0.649017 | ||||||||
\(421\) | −1.86476e9 | −1.21796 | −0.608982 | − | 0.793184i | \(-0.708422\pi\) | ||||
−0.608982 | + | 0.793184i | \(0.708422\pi\) | |||||||
\(422\) | −1.39491e9 | −0.903549 | ||||||||
\(423\) | 2.60715e8 | 0.167484 | ||||||||
\(424\) | −2.99166e8 | −0.190604 | ||||||||
\(425\) | −2.29841e9 | −1.45233 | ||||||||
\(426\) | −3.07099e8 | −0.192462 | ||||||||
\(427\) | −6.14051e8 | −0.381687 | ||||||||
\(428\) | −2.37512e7 | −0.0146431 | ||||||||
\(429\) | −1.51784e9 | −0.928164 | ||||||||
\(430\) | 2.50222e8 | 0.151770 | ||||||||
\(431\) | −3.55992e8 | −0.214175 | −0.107088 | − | 0.994250i | \(-0.534153\pi\) | ||||
−0.107088 | + | 0.994250i | \(0.534153\pi\) | |||||||
\(432\) | 3.58319e8 | 0.213834 | ||||||||
\(433\) | −6.11120e8 | −0.361758 | −0.180879 | − | 0.983505i | \(-0.557894\pi\) | ||||
−0.180879 | + | 0.983505i | \(0.557894\pi\) | |||||||
\(434\) | 1.92758e9 | 1.13188 | ||||||||
\(435\) | −1.17002e9 | −0.681526 | ||||||||
\(436\) | −3.40653e8 | −0.196838 | ||||||||
\(437\) | 6.00052e8 | 0.343957 | ||||||||
\(438\) | −4.19279e8 | −0.238421 | ||||||||
\(439\) | −8.62789e8 | −0.486720 | −0.243360 | − | 0.969936i | \(-0.578250\pi\) | ||||
−0.243360 | + | 0.969936i | \(0.578250\pi\) | |||||||
\(440\) | −4.35685e9 | −2.43831 | ||||||||
\(441\) | −1.83248e8 | −0.101743 | ||||||||
\(442\) | 1.41678e9 | 0.780414 | ||||||||
\(443\) | 1.69592e9 | 0.926815 | 0.463408 | − | 0.886145i | \(-0.346627\pi\) | ||||
0.463408 | + | 0.886145i | \(0.346627\pi\) | |||||||
\(444\) | −1.51047e8 | −0.0818976 | ||||||||
\(445\) | 2.84520e9 | 1.53057 | ||||||||
\(446\) | −2.55958e8 | −0.136615 | ||||||||
\(447\) | 1.18581e9 | 0.627969 | ||||||||
\(448\) | 1.77711e9 | 0.933771 | ||||||||
\(449\) | 2.75962e9 | 1.43876 | 0.719378 | − | 0.694619i | \(-0.244427\pi\) | ||||
0.719378 | + | 0.694619i | \(0.244427\pi\) | |||||||
\(450\) | −4.32751e8 | −0.223869 | ||||||||
\(451\) | 3.06539e9 | 1.57351 | ||||||||
\(452\) | −1.50737e9 | −0.767776 | ||||||||
\(453\) | 2.06381e9 | 1.04310 | ||||||||
\(454\) | 2.20815e8 | 0.110747 | ||||||||
\(455\) | −2.15135e9 | −1.07071 | ||||||||
\(456\) | 3.87958e8 | 0.191605 | ||||||||
\(457\) | 3.73353e9 | 1.82984 | 0.914921 | − | 0.403634i | \(-0.132253\pi\) | ||||
0.914921 | + | 0.403634i | \(0.132253\pi\) | |||||||
\(458\) | 8.35538e8 | 0.406385 | ||||||||
\(459\) | 3.70084e9 | 1.78631 | ||||||||
\(460\) | 2.26134e9 | 1.08321 | ||||||||
\(461\) | −1.77721e9 | −0.844860 | −0.422430 | − | 0.906396i | \(-0.638823\pi\) | ||||
−0.422430 | + | 0.906396i | \(0.638823\pi\) | |||||||
\(462\) | 2.21585e9 | 1.04543 | ||||||||
\(463\) | −2.11136e9 | −0.988621 | −0.494310 | − | 0.869285i | \(-0.664579\pi\) | ||||
−0.494310 | + | 0.869285i | \(0.664579\pi\) | |||||||
\(464\) | 2.64216e8 | 0.122785 | ||||||||
\(465\) | 3.44426e9 | 1.58859 | ||||||||
\(466\) | −6.63947e8 | −0.303936 | ||||||||
\(467\) | −3.13133e9 | −1.42272 | −0.711360 | − | 0.702828i | \(-0.751921\pi\) | ||||
−0.711360 | + | 0.702828i | \(0.751921\pi\) | |||||||
\(468\) | −2.96427e8 | −0.133677 | ||||||||
\(469\) | −2.34746e9 | −1.05074 | ||||||||
\(470\) | −9.68077e8 | −0.430098 | ||||||||
\(471\) | −1.59166e9 | −0.701901 | ||||||||
\(472\) | −3.61869e9 | −1.58400 | ||||||||
\(473\) | 6.25233e8 | 0.271661 | ||||||||
\(474\) | −6.68006e8 | −0.288109 | ||||||||
\(475\) | −4.73815e8 | −0.202853 | ||||||||
\(476\) | 2.29839e9 | 0.976784 | ||||||||
\(477\) | −1.58222e8 | −0.0667501 | ||||||||
\(478\) | −4.22748e8 | −0.177045 | ||||||||
\(479\) | −1.58968e9 | −0.660898 | −0.330449 | − | 0.943824i | \(-0.607200\pi\) | ||||
−0.330449 | + | 0.943824i | \(0.607200\pi\) | |||||||
\(480\) | 2.41993e9 | 0.998754 | ||||||||
\(481\) | −3.29758e8 | −0.135110 | ||||||||
\(482\) | 9.38724e8 | 0.381833 | ||||||||
\(483\) | −3.33517e9 | −1.34680 | ||||||||
\(484\) | −2.44121e9 | −0.978694 | ||||||||
\(485\) | 2.17470e9 | 0.865571 | ||||||||
\(486\) | 1.20621e9 | 0.476646 | ||||||||
\(487\) | 3.23424e9 | 1.26888 | 0.634440 | − | 0.772972i | \(-0.281231\pi\) | ||||
0.634440 | + | 0.772972i | \(0.281231\pi\) | |||||||
\(488\) | 9.11043e8 | 0.354870 | ||||||||
\(489\) | −3.28816e9 | −1.27166 | ||||||||
\(490\) | 6.80432e8 | 0.261275 | ||||||||
\(491\) | −2.17626e9 | −0.829709 | −0.414854 | − | 0.909888i | \(-0.636167\pi\) | ||||
−0.414854 | + | 0.909888i | \(0.636167\pi\) | |||||||
\(492\) | −1.02867e9 | −0.389402 | ||||||||
\(493\) | 2.72891e9 | 1.02571 | ||||||||
\(494\) | 2.92068e8 | 0.109003 | ||||||||
\(495\) | −2.30424e9 | −0.853904 | ||||||||
\(496\) | −7.77787e8 | −0.286203 | ||||||||
\(497\) | −1.08763e9 | −0.397406 | ||||||||
\(498\) | 4.15980e8 | 0.150928 | ||||||||
\(499\) | 2.86642e9 | 1.03273 | 0.516367 | − | 0.856367i | \(-0.327284\pi\) | ||||
0.516367 | + | 0.856367i | \(0.327284\pi\) | |||||||
\(500\) | 2.33820e8 | 0.0836540 | ||||||||
\(501\) | 3.57502e9 | 1.27012 | ||||||||
\(502\) | 9.44443e8 | 0.333206 | ||||||||
\(503\) | −5.65389e8 | −0.198089 | −0.0990443 | − | 0.995083i | \(-0.531579\pi\) | ||||
−0.0990443 | + | 0.995083i | \(0.531579\pi\) | |||||||
\(504\) | 1.25492e9 | 0.436627 | ||||||||
\(505\) | −4.06734e9 | −1.40537 | ||||||||
\(506\) | −5.08486e9 | −1.74483 | ||||||||
\(507\) | −1.22109e9 | −0.416121 | ||||||||
\(508\) | 4.44585e8 | 0.150464 | ||||||||
\(509\) | 3.87293e9 | 1.30175 | 0.650875 | − | 0.759185i | \(-0.274402\pi\) | ||||
0.650875 | + | 0.759185i | \(0.274402\pi\) | |||||||
\(510\) | −3.69574e9 | −1.23369 | ||||||||
\(511\) | −1.48493e9 | −0.492304 | ||||||||
\(512\) | −1.17375e9 | −0.386482 | ||||||||
\(513\) | 7.62925e8 | 0.249500 | ||||||||
\(514\) | −2.44601e9 | −0.794488 | ||||||||
\(515\) | 6.90752e8 | 0.222842 | ||||||||
\(516\) | −2.09813e8 | −0.0672291 | ||||||||
\(517\) | −2.41895e9 | −0.769856 | ||||||||
\(518\) | 4.81405e8 | 0.152180 | ||||||||
\(519\) | −2.67506e9 | −0.839941 | ||||||||
\(520\) | 3.19188e9 | 0.995484 | ||||||||
\(521\) | 3.30863e8 | 0.102498 | 0.0512491 | − | 0.998686i | \(-0.483680\pi\) | ||||
0.0512491 | + | 0.998686i | \(0.483680\pi\) | |||||||
\(522\) | 5.13807e8 | 0.158108 | ||||||||
\(523\) | 3.46760e9 | 1.05992 | 0.529960 | − | 0.848022i | \(-0.322207\pi\) | ||||
0.529960 | + | 0.848022i | \(0.322207\pi\) | |||||||
\(524\) | −1.08087e9 | −0.328182 | ||||||||
\(525\) | 2.63353e9 | 0.794292 | ||||||||
\(526\) | 1.69843e8 | 0.0508858 | ||||||||
\(527\) | −8.03324e9 | −2.39086 | ||||||||
\(528\) | −8.94104e8 | −0.264344 | ||||||||
\(529\) | 4.24861e9 | 1.24782 | ||||||||
\(530\) | 5.87503e8 | 0.171413 | ||||||||
\(531\) | −1.91384e9 | −0.554722 | ||||||||
\(532\) | 4.73810e8 | 0.136431 | ||||||||
\(533\) | −2.24574e9 | −0.642413 | ||||||||
\(534\) | 2.14692e9 | 0.610128 | ||||||||
\(535\) | 1.35259e8 | 0.0381882 | ||||||||
\(536\) | 3.48284e9 | 0.976914 | ||||||||
\(537\) | −5.40825e9 | −1.50712 | ||||||||
\(538\) | 4.42714e9 | 1.22570 | ||||||||
\(539\) | 1.70020e9 | 0.467671 | ||||||||
\(540\) | 2.87514e9 | 0.785745 | ||||||||
\(541\) | −2.72031e9 | −0.738631 | −0.369316 | − | 0.929304i | \(-0.620408\pi\) | ||||
−0.369316 | + | 0.929304i | \(0.620408\pi\) | |||||||
\(542\) | −9.20947e8 | −0.248449 | ||||||||
\(543\) | 5.11691e9 | 1.37154 | ||||||||
\(544\) | −5.64413e9 | −1.50315 | ||||||||
\(545\) | 1.93997e9 | 0.513342 | ||||||||
\(546\) | −1.62335e9 | −0.426815 | ||||||||
\(547\) | 1.16354e9 | 0.303965 | 0.151983 | − | 0.988383i | \(-0.451434\pi\) | ||||
0.151983 | + | 0.988383i | \(0.451434\pi\) | |||||||
\(548\) | −2.92755e9 | −0.759927 | ||||||||
\(549\) | 4.81829e8 | 0.124277 | ||||||||
\(550\) | 4.01512e9 | 1.02903 | ||||||||
\(551\) | 5.62562e8 | 0.143265 | ||||||||
\(552\) | 4.94825e9 | 1.25218 | ||||||||
\(553\) | −2.36583e9 | −0.594902 | ||||||||
\(554\) | 4.04099e9 | 1.00973 | ||||||||
\(555\) | 8.60188e8 | 0.213584 | ||||||||
\(556\) | −4.63736e8 | −0.114422 | ||||||||
\(557\) | 6.31126e9 | 1.54747 | 0.773737 | − | 0.633508i | \(-0.218385\pi\) | ||||
0.773737 | + | 0.633508i | \(0.218385\pi\) | |||||||
\(558\) | −1.51252e9 | −0.368538 | ||||||||
\(559\) | −4.58052e8 | −0.110911 | ||||||||
\(560\) | −1.26729e9 | −0.304942 | ||||||||
\(561\) | −9.23459e9 | −2.20825 | ||||||||
\(562\) | −2.65100e9 | −0.629988 | ||||||||
\(563\) | 2.16177e9 | 0.510540 | 0.255270 | − | 0.966870i | \(-0.417836\pi\) | ||||
0.255270 | + | 0.966870i | \(0.417836\pi\) | |||||||
\(564\) | 8.11738e8 | 0.190519 | ||||||||
\(565\) | 8.58422e9 | 2.00231 | ||||||||
\(566\) | −1.45027e9 | −0.336196 | ||||||||
\(567\) | −2.43631e9 | −0.561296 | ||||||||
\(568\) | 1.61367e9 | 0.369485 | ||||||||
\(569\) | −1.37473e8 | −0.0312842 | −0.0156421 | − | 0.999878i | \(-0.504979\pi\) | ||||
−0.0156421 | + | 0.999878i | \(0.504979\pi\) | |||||||
\(570\) | −7.61873e8 | −0.172314 | ||||||||
\(571\) | −8.08583e9 | −1.81760 | −0.908800 | − | 0.417233i | \(-0.863000\pi\) | ||||
−0.908800 | + | 0.417233i | \(0.863000\pi\) | |||||||
\(572\) | 2.75029e9 | 0.614459 | ||||||||
\(573\) | 3.65127e9 | 0.810780 | ||||||||
\(574\) | 3.27850e9 | 0.723574 | ||||||||
\(575\) | −6.04332e9 | −1.32568 | ||||||||
\(576\) | −1.39445e9 | −0.304034 | ||||||||
\(577\) | −5.12504e9 | −1.11066 | −0.555330 | − | 0.831630i | \(-0.687408\pi\) | ||||
−0.555330 | + | 0.831630i | \(0.687408\pi\) | |||||||
\(578\) | 5.42471e9 | 1.16850 | ||||||||
\(579\) | −1.21821e8 | −0.0260823 | ||||||||
\(580\) | 2.12006e9 | 0.451181 | ||||||||
\(581\) | 1.47325e9 | 0.311644 | ||||||||
\(582\) | 1.64097e9 | 0.345040 | ||||||||
\(583\) | 1.46800e9 | 0.306822 | ||||||||
\(584\) | 2.20313e9 | 0.457715 | ||||||||
\(585\) | 1.68811e9 | 0.348622 | ||||||||
\(586\) | 1.41493e9 | 0.290466 | ||||||||
\(587\) | 5.39273e9 | 1.10046 | 0.550231 | − | 0.835013i | \(-0.314540\pi\) | ||||
0.550231 | + | 0.835013i | \(0.314540\pi\) | |||||||
\(588\) | −5.70546e8 | −0.115736 | ||||||||
\(589\) | −1.65604e9 | −0.333940 | ||||||||
\(590\) | 7.10641e9 | 1.42452 | ||||||||
\(591\) | −1.93364e9 | −0.385319 | ||||||||
\(592\) | −1.94249e8 | −0.0384797 | ||||||||
\(593\) | 4.77369e9 | 0.940076 | 0.470038 | − | 0.882646i | \(-0.344240\pi\) | ||||
0.470038 | + | 0.882646i | \(0.344240\pi\) | |||||||
\(594\) | −6.46505e9 | −1.26567 | ||||||||
\(595\) | −1.30889e10 | −2.54739 | ||||||||
\(596\) | −2.14866e9 | −0.415726 | ||||||||
\(597\) | −1.79198e9 | −0.344685 | ||||||||
\(598\) | 3.72522e9 | 0.712357 | ||||||||
\(599\) | 2.74090e9 | 0.521074 | 0.260537 | − | 0.965464i | \(-0.416100\pi\) | ||||
0.260537 | + | 0.965464i | \(0.416100\pi\) | |||||||
\(600\) | −3.90725e9 | −0.738486 | ||||||||
\(601\) | −8.36025e9 | −1.57094 | −0.785468 | − | 0.618902i | \(-0.787578\pi\) | ||||
−0.785468 | + | 0.618902i | \(0.787578\pi\) | |||||||
\(602\) | 6.68699e8 | 0.124923 | ||||||||
\(603\) | 1.84199e9 | 0.342118 | ||||||||
\(604\) | −3.73958e9 | −0.690548 | ||||||||
\(605\) | 1.39023e10 | 2.55237 | ||||||||
\(606\) | −3.06911e9 | −0.560219 | ||||||||
\(607\) | 1.95759e9 | 0.355272 | 0.177636 | − | 0.984096i | \(-0.443155\pi\) | ||||
0.177636 | + | 0.984096i | \(0.443155\pi\) | |||||||
\(608\) | −1.16353e9 | −0.209950 | ||||||||
\(609\) | −3.12679e9 | −0.560969 | ||||||||
\(610\) | −1.78911e9 | −0.319141 | ||||||||
\(611\) | 1.77214e9 | 0.314308 | ||||||||
\(612\) | −1.80348e9 | −0.318040 | ||||||||
\(613\) | −7.62476e9 | −1.33695 | −0.668474 | − | 0.743736i | \(-0.733052\pi\) | ||||
−0.668474 | + | 0.743736i | \(0.733052\pi\) | |||||||
\(614\) | −3.45828e9 | −0.602936 | ||||||||
\(615\) | 5.85811e9 | 1.01553 | ||||||||
\(616\) | −1.16433e10 | −2.00699 | ||||||||
\(617\) | 2.39769e8 | 0.0410956 | 0.0205478 | − | 0.999789i | \(-0.493459\pi\) | ||||
0.0205478 | + | 0.999789i | \(0.493459\pi\) | |||||||
\(618\) | 5.21223e8 | 0.0888309 | ||||||||
\(619\) | 2.64242e9 | 0.447801 | 0.223900 | − | 0.974612i | \(-0.428121\pi\) | ||||
0.223900 | + | 0.974612i | \(0.428121\pi\) | |||||||
\(620\) | −6.24094e9 | −1.05167 | ||||||||
\(621\) | 9.73081e9 | 1.63053 | ||||||||
\(622\) | 1.96123e9 | 0.326786 | ||||||||
\(623\) | 7.60358e9 | 1.25982 | ||||||||
\(624\) | 6.55029e8 | 0.107923 | ||||||||
\(625\) | −6.72839e9 | −1.10238 | ||||||||
\(626\) | −3.15629e9 | −0.514241 | ||||||||
\(627\) | −1.90370e9 | −0.308434 | ||||||||
\(628\) | 2.88405e9 | 0.464669 | ||||||||
\(629\) | −2.00626e9 | −0.321448 | ||||||||
\(630\) | −2.46442e9 | −0.392666 | ||||||||
\(631\) | 5.19599e9 | 0.823315 | 0.411657 | − | 0.911339i | \(-0.364950\pi\) | ||||
0.411657 | + | 0.911339i | \(0.364950\pi\) | |||||||
\(632\) | 3.51009e9 | 0.553106 | ||||||||
\(633\) | −6.66090e9 | −1.04381 | ||||||||
\(634\) | −4.51783e8 | −0.0704073 | ||||||||
\(635\) | −2.53184e9 | −0.392399 | ||||||||
\(636\) | −4.92625e8 | −0.0759305 | ||||||||
\(637\) | −1.24559e9 | −0.190935 | ||||||||
\(638\) | −4.76717e9 | −0.726755 | ||||||||
\(639\) | 8.53434e8 | 0.129395 | ||||||||
\(640\) | −3.15302e9 | −0.475441 | ||||||||
\(641\) | 3.82179e9 | 0.573144 | 0.286572 | − | 0.958059i | \(-0.407484\pi\) | ||||
0.286572 | + | 0.958059i | \(0.407484\pi\) | |||||||
\(642\) | 1.02063e8 | 0.0152228 | ||||||||
\(643\) | −1.02626e10 | −1.52236 | −0.761180 | − | 0.648541i | \(-0.775379\pi\) | ||||
−0.761180 | + | 0.648541i | \(0.775379\pi\) | |||||||
\(644\) | 6.04326e9 | 0.891602 | ||||||||
\(645\) | 1.19485e9 | 0.175329 | ||||||||
\(646\) | 1.77696e9 | 0.259336 | ||||||||
\(647\) | −1.32728e10 | −1.92663 | −0.963316 | − | 0.268369i | \(-0.913515\pi\) | ||||
−0.963316 | + | 0.268369i | \(0.913515\pi\) | |||||||
\(648\) | 3.61466e9 | 0.521860 | ||||||||
\(649\) | 1.77569e10 | 2.54982 | ||||||||
\(650\) | −2.94152e9 | −0.420121 | ||||||||
\(651\) | 9.20451e9 | 1.30758 | ||||||||
\(652\) | 5.95809e9 | 0.841862 | ||||||||
\(653\) | −6.40674e9 | −0.900411 | −0.450206 | − | 0.892925i | \(-0.648649\pi\) | ||||
−0.450206 | + | 0.892925i | \(0.648649\pi\) | |||||||
\(654\) | 1.46385e9 | 0.204632 | ||||||||
\(655\) | 6.15540e9 | 0.855878 | ||||||||
\(656\) | −1.32289e9 | −0.182961 | ||||||||
\(657\) | 1.16518e9 | 0.160293 | ||||||||
\(658\) | −2.58711e9 | −0.354017 | ||||||||
\(659\) | 7.70810e9 | 1.04918 | 0.524588 | − | 0.851356i | \(-0.324219\pi\) | ||||
0.524588 | + | 0.851356i | \(0.324219\pi\) | |||||||
\(660\) | −7.17426e9 | −0.971345 | ||||||||
\(661\) | 5.64359e9 | 0.760064 | 0.380032 | − | 0.924973i | \(-0.375913\pi\) | ||||
0.380032 | + | 0.924973i | \(0.375913\pi\) | |||||||
\(662\) | −3.48824e9 | −0.467308 | ||||||||
\(663\) | 6.76536e9 | 0.901557 | ||||||||
\(664\) | −2.18580e9 | −0.289749 | ||||||||
\(665\) | −2.69827e9 | −0.355804 | ||||||||
\(666\) | −3.77745e8 | −0.0495494 | ||||||||
\(667\) | 7.17526e9 | 0.936262 | ||||||||
\(668\) | −6.47787e9 | −0.840842 | ||||||||
\(669\) | −1.22224e9 | −0.157821 | ||||||||
\(670\) | −6.83961e9 | −0.878556 | ||||||||
\(671\) | −4.47047e9 | −0.571248 | ||||||||
\(672\) | 6.46707e9 | 0.822082 | ||||||||
\(673\) | −1.00366e10 | −1.26922 | −0.634609 | − | 0.772834i | \(-0.718839\pi\) | ||||
−0.634609 | + | 0.772834i | \(0.718839\pi\) | |||||||
\(674\) | −1.04633e10 | −1.31631 | ||||||||
\(675\) | −7.68367e9 | −0.961625 | ||||||||
\(676\) | 2.21259e9 | 0.275479 | ||||||||
\(677\) | 3.49069e8 | 0.0432365 | 0.0216183 | − | 0.999766i | \(-0.493118\pi\) | ||||
0.0216183 | + | 0.999766i | \(0.493118\pi\) | |||||||
\(678\) | 6.47742e9 | 0.798176 | ||||||||
\(679\) | 5.81171e9 | 0.712458 | ||||||||
\(680\) | 1.94195e10 | 2.36841 | ||||||||
\(681\) | 1.05443e9 | 0.127938 | ||||||||
\(682\) | 1.40334e10 | 1.69401 | ||||||||
\(683\) | 6.73998e9 | 0.809442 | 0.404721 | − | 0.914440i | \(-0.367369\pi\) | ||||
0.404721 | + | 0.914440i | \(0.367369\pi\) | |||||||
\(684\) | −3.71785e8 | −0.0444218 | ||||||||
\(685\) | 1.66719e10 | 1.98184 | ||||||||
\(686\) | −4.75649e9 | −0.562538 | ||||||||
\(687\) | 3.98983e9 | 0.469467 | ||||||||
\(688\) | −2.69822e8 | −0.0315877 | ||||||||
\(689\) | −1.07547e9 | −0.125266 | ||||||||
\(690\) | −9.71740e9 | −1.12610 | ||||||||
\(691\) | 5.00817e9 | 0.577439 | 0.288720 | − | 0.957414i | \(-0.406770\pi\) | ||||
0.288720 | + | 0.957414i | \(0.406770\pi\) | |||||||
\(692\) | 4.84717e9 | 0.556054 | ||||||||
\(693\) | −6.15789e9 | −0.702855 | ||||||||
\(694\) | 7.15606e9 | 0.812673 | ||||||||
\(695\) | 2.64091e9 | 0.298405 | ||||||||
\(696\) | 4.63910e9 | 0.521556 | ||||||||
\(697\) | −1.36632e10 | −1.52840 | ||||||||
\(698\) | −5.98462e9 | −0.666105 | ||||||||
\(699\) | −3.17045e9 | −0.351116 | ||||||||
\(700\) | −4.77190e9 | −0.525833 | ||||||||
\(701\) | 1.26888e10 | 1.39126 | 0.695629 | − | 0.718402i | \(-0.255126\pi\) | ||||
0.695629 | + | 0.718402i | \(0.255126\pi\) | |||||||
\(702\) | 4.73636e9 | 0.516731 | ||||||||
\(703\) | −4.13589e8 | −0.0448978 | ||||||||
\(704\) | 1.29378e10 | 1.39752 | ||||||||
\(705\) | −4.62272e9 | −0.496862 | ||||||||
\(706\) | −9.96012e8 | −0.106524 | ||||||||
\(707\) | −1.08696e10 | −1.15677 | ||||||||
\(708\) | −5.95876e9 | −0.631015 | ||||||||
\(709\) | 1.38422e10 | 1.45863 | 0.729313 | − | 0.684181i | \(-0.239840\pi\) | ||||
0.729313 | + | 0.684181i | \(0.239840\pi\) | |||||||
\(710\) | −3.16894e9 | −0.332284 | ||||||||
\(711\) | 1.85640e9 | 0.193699 | ||||||||
\(712\) | −1.12811e10 | −1.17131 | ||||||||
\(713\) | −2.11222e10 | −2.18236 | ||||||||
\(714\) | −9.87657e9 | −1.01546 | ||||||||
\(715\) | −1.56625e10 | −1.60247 | ||||||||
\(716\) | 9.79965e9 | 0.997735 | ||||||||
\(717\) | −2.01869e9 | −0.204528 | ||||||||
\(718\) | −9.92998e8 | −0.100118 | ||||||||
\(719\) | −1.76297e10 | −1.76886 | −0.884429 | − | 0.466675i | \(-0.845452\pi\) | ||||
−0.884429 | + | 0.466675i | \(0.845452\pi\) | |||||||
\(720\) | 9.94404e8 | 0.0992885 | ||||||||
\(721\) | 1.84598e9 | 0.183423 | ||||||||
\(722\) | 3.66318e8 | 0.0362225 | ||||||||
\(723\) | 4.48255e9 | 0.441105 | ||||||||
\(724\) | −9.27174e9 | −0.907980 | ||||||||
\(725\) | −5.66575e9 | −0.552172 | ||||||||
\(726\) | 1.04903e10 | 1.01745 | ||||||||
\(727\) | −1.23993e10 | −1.19681 | −0.598406 | − | 0.801193i | \(-0.704199\pi\) | ||||
−0.598406 | + | 0.801193i | \(0.704199\pi\) | |||||||
\(728\) | 8.53003e9 | 0.819391 | ||||||||
\(729\) | 1.09564e10 | 1.04742 | ||||||||
\(730\) | −4.32652e9 | −0.411632 | ||||||||
\(731\) | −2.78681e9 | −0.263874 | ||||||||
\(732\) | 1.50018e9 | 0.141369 | ||||||||
\(733\) | 1.32362e9 | 0.124136 | 0.0620681 | − | 0.998072i | \(-0.480230\pi\) | ||||
0.0620681 | + | 0.998072i | \(0.480230\pi\) | |||||||
\(734\) | −2.66269e9 | −0.248533 | ||||||||
\(735\) | 3.24917e9 | 0.301833 | ||||||||
\(736\) | −1.48404e10 | −1.37206 | ||||||||
\(737\) | −1.70902e10 | −1.57258 | ||||||||
\(738\) | −2.57254e9 | −0.235595 | ||||||||
\(739\) | −9.34807e9 | −0.852052 | −0.426026 | − | 0.904711i | \(-0.640087\pi\) | ||||
−0.426026 | + | 0.904711i | \(0.640087\pi\) | |||||||
\(740\) | −1.55864e9 | −0.141396 | ||||||||
\(741\) | 1.39467e9 | 0.125924 | ||||||||
\(742\) | 1.57006e9 | 0.141092 | ||||||||
\(743\) | 1.03544e10 | 0.926116 | 0.463058 | − | 0.886328i | \(-0.346752\pi\) | ||||
0.463058 | + | 0.886328i | \(0.346752\pi\) | |||||||
\(744\) | −1.36564e10 | −1.21571 | ||||||||
\(745\) | 1.22363e10 | 1.08418 | ||||||||
\(746\) | 1.15899e10 | 1.02210 | ||||||||
\(747\) | −1.15602e9 | −0.101471 | ||||||||
\(748\) | 1.67329e10 | 1.46189 | ||||||||
\(749\) | 3.61470e8 | 0.0314330 | ||||||||
\(750\) | −1.00477e9 | −0.0869663 | ||||||||
\(751\) | 1.53227e9 | 0.132007 | 0.0660035 | − | 0.997819i | \(-0.478975\pi\) | ||||
0.0660035 | + | 0.997819i | \(0.478975\pi\) | |||||||
\(752\) | 1.04391e9 | 0.0895158 | ||||||||
\(753\) | 4.50986e9 | 0.384929 | ||||||||
\(754\) | 3.49248e9 | 0.296711 | ||||||||
\(755\) | 2.12963e10 | 1.80090 | ||||||||
\(756\) | 7.68360e9 | 0.646753 | ||||||||
\(757\) | 1.85063e10 | 1.55055 | 0.775273 | − | 0.631626i | \(-0.217612\pi\) | ||||
0.775273 | + | 0.631626i | \(0.217612\pi\) | |||||||
\(758\) | −3.82160e9 | −0.318715 | ||||||||
\(759\) | −2.42810e10 | −2.01567 | ||||||||
\(760\) | 4.00332e9 | 0.330805 | ||||||||
\(761\) | −2.01248e10 | −1.65533 | −0.827667 | − | 0.561219i | \(-0.810332\pi\) | ||||
−0.827667 | + | 0.561219i | \(0.810332\pi\) | |||||||
\(762\) | −1.91046e9 | −0.156421 | ||||||||
\(763\) | 5.18441e9 | 0.422535 | ||||||||
\(764\) | −6.61604e9 | −0.536749 | ||||||||
\(765\) | 1.02705e10 | 0.829426 | ||||||||
\(766\) | 1.04215e10 | 0.837779 | ||||||||
\(767\) | −1.30089e10 | −1.04101 | ||||||||
\(768\) | −1.06278e10 | −0.846605 | ||||||||
\(769\) | 5.91010e9 | 0.468654 | 0.234327 | − | 0.972158i | \(-0.424711\pi\) | ||||
0.234327 | + | 0.972158i | \(0.424711\pi\) | |||||||
\(770\) | 2.28653e10 | 1.80492 | ||||||||
\(771\) | −1.16801e10 | −0.917816 | ||||||||
\(772\) | 2.20737e8 | 0.0172669 | ||||||||
\(773\) | −4.28760e9 | −0.333876 | −0.166938 | − | 0.985967i | \(-0.553388\pi\) | ||||
−0.166938 | + | 0.985967i | \(0.553388\pi\) | |||||||
\(774\) | −5.24709e8 | −0.0406748 | ||||||||
\(775\) | 1.66786e10 | 1.28707 | ||||||||
\(776\) | −8.62259e9 | −0.662402 | ||||||||
\(777\) | 2.29878e9 | 0.175802 | ||||||||
\(778\) | −4.55393e9 | −0.346703 | ||||||||
\(779\) | −2.81665e9 | −0.213478 | ||||||||
\(780\) | 5.25594e9 | 0.396569 | ||||||||
\(781\) | −7.91827e9 | −0.594774 | ||||||||
\(782\) | 2.26644e10 | 1.69481 | ||||||||
\(783\) | 9.12285e9 | 0.679148 | ||||||||
\(784\) | −7.33731e8 | −0.0543789 | ||||||||
\(785\) | −1.64242e10 | −1.21183 | ||||||||
\(786\) | 4.64470e9 | 0.341176 | ||||||||
\(787\) | 1.19453e10 | 0.873546 | 0.436773 | − | 0.899572i | \(-0.356121\pi\) | ||||
0.436773 | + | 0.899572i | \(0.356121\pi\) | |||||||
\(788\) | 3.50373e9 | 0.255087 | ||||||||
\(789\) | 8.11026e8 | 0.0587848 | ||||||||
\(790\) | −6.89312e9 | −0.497418 | ||||||||
\(791\) | 2.29406e10 | 1.64812 | ||||||||
\(792\) | 9.13621e9 | 0.653473 | ||||||||
\(793\) | 3.27511e9 | 0.233222 | ||||||||
\(794\) | −7.58101e9 | −0.537472 | ||||||||
\(795\) | 2.80542e9 | 0.198022 | ||||||||
\(796\) | 3.24703e9 | 0.228187 | ||||||||
\(797\) | −1.59827e10 | −1.11827 | −0.559136 | − | 0.829076i | \(-0.688867\pi\) | ||||
−0.559136 | + | 0.829076i | \(0.688867\pi\) | |||||||
\(798\) | −2.03605e9 | −0.141833 | ||||||||
\(799\) | 1.07818e10 | 0.747788 | ||||||||
\(800\) | 1.17183e10 | 0.809190 | ||||||||
\(801\) | −5.96632e9 | −0.410197 | ||||||||
\(802\) | −9.04534e9 | −0.619177 | ||||||||
\(803\) | −1.08107e10 | −0.736802 | ||||||||
\(804\) | 5.73505e9 | 0.389171 | ||||||||
\(805\) | −3.44154e10 | −2.32524 | ||||||||
\(806\) | −1.02810e10 | −0.691612 | ||||||||
\(807\) | 2.11403e10 | 1.41597 | ||||||||
\(808\) | 1.61268e10 | 1.07550 | ||||||||
\(809\) | −5.48289e9 | −0.364074 | −0.182037 | − | 0.983292i | \(-0.558269\pi\) | ||||
−0.182037 | + | 0.983292i | \(0.558269\pi\) | |||||||
\(810\) | −7.09848e9 | −0.469318 | ||||||||
\(811\) | −1.87851e10 | −1.23663 | −0.618317 | − | 0.785929i | \(-0.712185\pi\) | ||||
−0.618317 | + | 0.785929i | \(0.712185\pi\) | |||||||
\(812\) | 5.66569e9 | 0.371370 | ||||||||
\(813\) | −4.39767e9 | −0.287015 | ||||||||
\(814\) | 3.50477e9 | 0.227758 | ||||||||
\(815\) | −3.39304e10 | −2.19552 | ||||||||
\(816\) | 3.98523e9 | 0.256766 | ||||||||
\(817\) | −5.74499e8 | −0.0368563 | ||||||||
\(818\) | −1.67436e10 | −1.06958 | ||||||||
\(819\) | 4.51133e9 | 0.286953 | ||||||||
\(820\) | −1.06148e10 | −0.672300 | ||||||||
\(821\) | 1.79451e10 | 1.13174 | 0.565869 | − | 0.824495i | \(-0.308541\pi\) | ||||
0.565869 | + | 0.824495i | \(0.308541\pi\) | |||||||
\(822\) | 1.25802e10 | 0.790016 | ||||||||
\(823\) | 1.52788e10 | 0.955411 | 0.477705 | − | 0.878520i | \(-0.341469\pi\) | ||||
0.477705 | + | 0.878520i | \(0.341469\pi\) | |||||||
\(824\) | −2.73880e9 | −0.170536 | ||||||||
\(825\) | 1.91728e10 | 1.18877 | ||||||||
\(826\) | 1.89913e10 | 1.17253 | ||||||||
\(827\) | −7.98240e9 | −0.490755 | −0.245377 | − | 0.969428i | \(-0.578912\pi\) | ||||
−0.245377 | + | 0.969428i | \(0.578912\pi\) | |||||||
\(828\) | −4.74198e9 | −0.290304 | ||||||||
\(829\) | −5.35359e9 | −0.326366 | −0.163183 | − | 0.986596i | \(-0.552176\pi\) | ||||
−0.163183 | + | 0.986596i | \(0.552176\pi\) | |||||||
\(830\) | 4.29248e9 | 0.260576 | ||||||||
\(831\) | 1.92964e10 | 1.16647 | ||||||||
\(832\) | −9.47840e9 | −0.570563 | ||||||||
\(833\) | −7.57821e9 | −0.454265 | ||||||||
\(834\) | 1.99276e9 | 0.118952 | ||||||||
\(835\) | 3.68904e10 | 2.19286 | ||||||||
\(836\) | 3.44948e9 | 0.204188 | ||||||||
\(837\) | −2.68554e10 | −1.58304 | ||||||||
\(838\) | −1.04081e10 | −0.610967 | ||||||||
\(839\) | 2.87985e10 | 1.68346 | 0.841730 | − | 0.539899i | \(-0.181537\pi\) | ||||
0.841730 | + | 0.539899i | \(0.181537\pi\) | |||||||
\(840\) | −2.22510e10 | −1.29530 | ||||||||
\(841\) | −1.05229e10 | −0.610028 | ||||||||
\(842\) | −1.45197e10 | −0.838237 | ||||||||
\(843\) | −1.26589e10 | −0.727781 | ||||||||
\(844\) | 1.20694e10 | 0.691016 | ||||||||
\(845\) | −1.26004e10 | −0.718430 | ||||||||
\(846\) | 2.03003e9 | 0.115267 | ||||||||
\(847\) | 3.71529e10 | 2.10088 | ||||||||
\(848\) | −6.33523e8 | −0.0356761 | ||||||||
\(849\) | −6.92528e9 | −0.388383 | ||||||||
\(850\) | −1.78963e10 | −0.999535 | ||||||||
\(851\) | −5.27517e9 | −0.293415 | ||||||||
\(852\) | 2.65717e9 | 0.147191 | ||||||||
\(853\) | −2.62772e10 | −1.44963 | −0.724814 | − | 0.688944i | \(-0.758075\pi\) | ||||
−0.724814 | + | 0.688944i | \(0.758075\pi\) | |||||||
\(854\) | −4.78125e9 | −0.262687 | ||||||||
\(855\) | 2.11726e9 | 0.115849 | ||||||||
\(856\) | −5.36298e8 | −0.0292245 | ||||||||
\(857\) | 2.40992e9 | 0.130788 | 0.0653942 | − | 0.997860i | \(-0.479170\pi\) | ||||
0.0653942 | + | 0.997860i | \(0.479170\pi\) | |||||||
\(858\) | −1.18185e10 | −0.638788 | ||||||||
\(859\) | 1.39166e10 | 0.749131 | 0.374566 | − | 0.927200i | \(-0.377792\pi\) | ||||
0.374566 | + | 0.927200i | \(0.377792\pi\) | |||||||
\(860\) | −2.16505e9 | −0.116071 | ||||||||
\(861\) | 1.56553e10 | 0.835894 | ||||||||
\(862\) | −2.77190e9 | −0.147401 | ||||||||
\(863\) | 1.83365e10 | 0.971133 | 0.485567 | − | 0.874200i | \(-0.338613\pi\) | ||||
0.485567 | + | 0.874200i | \(0.338613\pi\) | |||||||
\(864\) | −1.88686e10 | −0.995270 | ||||||||
\(865\) | −2.76039e10 | −1.45015 | ||||||||
\(866\) | −4.75843e9 | −0.248972 | ||||||||
\(867\) | 2.59038e10 | 1.34989 | ||||||||
\(868\) | −1.66784e10 | −0.865637 | ||||||||
\(869\) | −1.72239e10 | −0.890355 | ||||||||
\(870\) | −9.11028e9 | −0.469045 | ||||||||
\(871\) | 1.25205e10 | 0.642032 | ||||||||
\(872\) | −7.69189e9 | −0.392849 | ||||||||
\(873\) | −4.56028e9 | −0.231975 | ||||||||
\(874\) | 4.67225e9 | 0.236721 | ||||||||
\(875\) | −3.55851e9 | −0.179573 | ||||||||
\(876\) | 3.62781e9 | 0.182339 | ||||||||
\(877\) | −8.16310e9 | −0.408655 | −0.204327 | − | 0.978903i | \(-0.565501\pi\) | ||||
−0.204327 | + | 0.978903i | \(0.565501\pi\) | |||||||
\(878\) | −6.71803e9 | −0.334974 | ||||||||
\(879\) | 6.75654e9 | 0.335554 | ||||||||
\(880\) | −9.22621e9 | −0.456388 | ||||||||
\(881\) | 2.81568e10 | 1.38729 | 0.693646 | − | 0.720316i | \(-0.256003\pi\) | ||||
0.693646 | + | 0.720316i | \(0.256003\pi\) | |||||||
\(882\) | −1.42685e9 | −0.0700225 | ||||||||
\(883\) | 3.95427e8 | 0.0193287 | 0.00966437 | − | 0.999953i | \(-0.496924\pi\) | ||||
0.00966437 | + | 0.999953i | \(0.496924\pi\) | |||||||
\(884\) | −1.22587e10 | −0.596845 | ||||||||
\(885\) | 3.39342e10 | 1.64565 | ||||||||
\(886\) | 1.32052e10 | 0.637860 | ||||||||
\(887\) | −3.71978e10 | −1.78972 | −0.894858 | − | 0.446351i | \(-0.852723\pi\) | ||||
−0.894858 | + | 0.446351i | \(0.852723\pi\) | |||||||
\(888\) | −3.41061e9 | −0.163451 | ||||||||
\(889\) | −6.76614e9 | −0.322987 | ||||||||
\(890\) | 2.21539e10 | 1.05338 | ||||||||
\(891\) | −1.77371e10 | −0.840059 | ||||||||
\(892\) | 2.21468e9 | 0.104480 | ||||||||
\(893\) | 2.22266e9 | 0.104446 | ||||||||
\(894\) | 9.23319e9 | 0.432186 | ||||||||
\(895\) | −5.58075e10 | −2.60203 | ||||||||
\(896\) | −8.42620e9 | −0.391340 | ||||||||
\(897\) | 1.77885e10 | 0.822936 | ||||||||
\(898\) | 2.14875e10 | 0.990191 | ||||||||
\(899\) | −1.98025e10 | −0.908996 | ||||||||
\(900\) | 3.74438e9 | 0.171211 | ||||||||
\(901\) | −6.54323e9 | −0.298027 | ||||||||
\(902\) | 2.38684e10 | 1.08293 | ||||||||
\(903\) | 3.19314e9 | 0.144315 | ||||||||
\(904\) | −3.40361e10 | −1.53232 | ||||||||
\(905\) | 5.28011e10 | 2.36795 | ||||||||
\(906\) | 1.60696e10 | 0.717889 | ||||||||
\(907\) | 1.52026e10 | 0.676536 | 0.338268 | − | 0.941050i | \(-0.390159\pi\) | ||||
0.338268 | + | 0.941050i | \(0.390159\pi\) | |||||||
\(908\) | −1.91060e9 | −0.0846973 | ||||||||
\(909\) | 8.52910e9 | 0.376643 | ||||||||
\(910\) | −1.67513e10 | −0.736892 | ||||||||
\(911\) | 1.99899e10 | 0.875986 | 0.437993 | − | 0.898978i | \(-0.355690\pi\) | ||||
0.437993 | + | 0.898978i | \(0.355690\pi\) | |||||||
\(912\) | 8.21552e8 | 0.0358635 | ||||||||
\(913\) | 1.07257e10 | 0.466419 | ||||||||
\(914\) | 2.90708e10 | 1.25935 | ||||||||
\(915\) | −8.54328e9 | −0.368681 | ||||||||
\(916\) | −7.22949e9 | −0.310795 | ||||||||
\(917\) | 1.64498e10 | 0.704479 | ||||||||
\(918\) | 2.88163e10 | 1.22939 | ||||||||
\(919\) | 2.34855e10 | 0.998149 | 0.499075 | − | 0.866559i | \(-0.333673\pi\) | ||||
0.499075 | + | 0.866559i | \(0.333673\pi\) | |||||||
\(920\) | 5.10608e10 | 2.16187 | ||||||||
\(921\) | −1.65138e10 | −0.696529 | ||||||||
\(922\) | −1.38381e10 | −0.581456 | ||||||||
\(923\) | 5.80101e9 | 0.242827 | ||||||||
\(924\) | −1.91726e10 | −0.799521 | ||||||||
\(925\) | 4.16539e9 | 0.173045 | ||||||||
\(926\) | −1.64399e10 | −0.680396 | ||||||||
\(927\) | −1.44849e9 | −0.0597222 | ||||||||
\(928\) | −1.39132e10 | −0.571491 | ||||||||
\(929\) | 4.32545e10 | 1.77001 | 0.885006 | − | 0.465580i | \(-0.154154\pi\) | ||||
0.885006 | + | 0.465580i | \(0.154154\pi\) | |||||||
\(930\) | 2.68184e10 | 1.09331 | ||||||||
\(931\) | −1.56224e9 | −0.0634489 | ||||||||
\(932\) | 5.74480e9 | 0.232444 | ||||||||
\(933\) | 9.36519e9 | 0.377512 | ||||||||
\(934\) | −2.43818e10 | −0.979156 | ||||||||
\(935\) | −9.52913e10 | −3.81253 | ||||||||
\(936\) | −6.69328e9 | −0.266792 | ||||||||
\(937\) | −3.59091e9 | −0.142599 | −0.0712994 | − | 0.997455i | \(-0.522715\pi\) | ||||
−0.0712994 | + | 0.997455i | \(0.522715\pi\) | |||||||
\(938\) | −1.82783e10 | −0.723146 | ||||||||
\(939\) | −1.50718e10 | −0.594067 | ||||||||
\(940\) | 8.37628e9 | 0.328930 | ||||||||
\(941\) | 3.30778e10 | 1.29411 | 0.647057 | − | 0.762442i | \(-0.276000\pi\) | ||||
0.647057 | + | 0.762442i | \(0.276000\pi\) | |||||||
\(942\) | −1.23933e10 | −0.483068 | ||||||||
\(943\) | −3.59253e10 | −1.39511 | ||||||||
\(944\) | −7.66306e9 | −0.296483 | ||||||||
\(945\) | −4.37569e10 | −1.68669 | ||||||||
\(946\) | 4.86832e9 | 0.186965 | ||||||||
\(947\) | 2.41396e10 | 0.923644 | 0.461822 | − | 0.886973i | \(-0.347196\pi\) | ||||
0.461822 | + | 0.886973i | \(0.347196\pi\) | |||||||
\(948\) | 5.77992e9 | 0.220340 | ||||||||
\(949\) | 7.92005e9 | 0.300813 | ||||||||
\(950\) | −3.68932e9 | −0.139609 | ||||||||
\(951\) | −2.15734e9 | −0.0813366 | ||||||||
\(952\) | 5.18972e10 | 1.94946 | ||||||||
\(953\) | −1.20437e10 | −0.450750 | −0.225375 | − | 0.974272i | \(-0.572361\pi\) | ||||
−0.225375 | + | 0.974272i | \(0.572361\pi\) | |||||||
\(954\) | −1.23198e9 | −0.0459392 | ||||||||
\(955\) | 3.76773e10 | 1.39981 | ||||||||
\(956\) | 3.65783e9 | 0.135401 | ||||||||
\(957\) | −2.27640e10 | −0.839569 | ||||||||
\(958\) | −1.23779e10 | −0.454848 | ||||||||
\(959\) | 4.45544e10 | 1.63127 | ||||||||
\(960\) | 2.47248e10 | 0.901953 | ||||||||
\(961\) | 3.07812e10 | 1.11880 | ||||||||
\(962\) | −2.56763e9 | −0.0929864 | ||||||||
\(963\) | −2.83635e8 | −0.0102345 | ||||||||
\(964\) | −8.12231e9 | −0.292018 | ||||||||
\(965\) | −1.25706e9 | −0.0450310 | ||||||||
\(966\) | −2.59690e10 | −0.926904 | ||||||||
\(967\) | −7.77336e9 | −0.276450 | −0.138225 | − | 0.990401i | \(-0.544140\pi\) | ||||
−0.138225 | + | 0.990401i | \(0.544140\pi\) | |||||||
\(968\) | −5.51222e10 | −1.95327 | ||||||||
\(969\) | 8.48526e9 | 0.299593 | ||||||||
\(970\) | 1.69331e10 | 0.595710 | ||||||||
\(971\) | −5.46197e9 | −0.191462 | −0.0957308 | − | 0.995407i | \(-0.530519\pi\) | ||||
−0.0957308 | + | 0.995407i | \(0.530519\pi\) | |||||||
\(972\) | −1.04367e10 | −0.364529 | ||||||||
\(973\) | 7.05761e9 | 0.245619 | ||||||||
\(974\) | 2.51831e10 | 0.873278 | ||||||||
\(975\) | −1.40462e10 | −0.485336 | ||||||||
\(976\) | 1.92925e9 | 0.0664224 | ||||||||
\(977\) | −2.57357e10 | −0.882886 | −0.441443 | − | 0.897289i | \(-0.645533\pi\) | ||||
−0.441443 | + | 0.897289i | \(0.645533\pi\) | |||||||
\(978\) | −2.56030e10 | −0.875195 | ||||||||
\(979\) | 5.53563e10 | 1.88550 | ||||||||
\(980\) | −5.88743e9 | −0.199818 | ||||||||
\(981\) | −4.06806e9 | −0.137577 | ||||||||
\(982\) | −1.69453e10 | −0.571029 | ||||||||
\(983\) | 6.58381e9 | 0.221075 | 0.110538 | − | 0.993872i | \(-0.464743\pi\) | ||||
0.110538 | + | 0.993872i | \(0.464743\pi\) | |||||||
\(984\) | −2.32272e10 | −0.777166 | ||||||||
\(985\) | −1.99532e10 | −0.665251 | ||||||||
\(986\) | 2.12484e10 | 0.705922 | ||||||||
\(987\) | −1.23538e10 | −0.408971 | ||||||||
\(988\) | −2.52712e9 | −0.0833636 | ||||||||
\(989\) | −7.32751e9 | −0.240863 | ||||||||
\(990\) | −1.79417e10 | −0.587680 | ||||||||
\(991\) | −4.03603e10 | −1.31734 | −0.658668 | − | 0.752434i | \(-0.728880\pi\) | ||||
−0.658668 | + | 0.752434i | \(0.728880\pi\) | |||||||
\(992\) | 4.09571e10 | 1.33210 | ||||||||
\(993\) | −1.66569e10 | −0.539848 | ||||||||
\(994\) | −8.46874e9 | −0.273506 | ||||||||
\(995\) | −1.84913e10 | −0.595096 | ||||||||
\(996\) | −3.59927e9 | −0.115427 | ||||||||
\(997\) | −3.87439e9 | −0.123814 | −0.0619070 | − | 0.998082i | \(-0.519718\pi\) | ||||
−0.0619070 | + | 0.998082i | \(0.519718\pi\) | |||||||
\(998\) | 2.23191e10 | 0.710756 | ||||||||
\(999\) | −6.70702e9 | −0.212838 |
(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 | 19.8.a.b.1.4 | ✓ | 6 | |
3.2 | odd | 2 | 171.8.a.f.1.3 | 6 | |||
4.3 | odd | 2 | 304.8.a.h.1.3 | 6 | |||
5.4 | even | 2 | 475.8.a.b.1.3 | 6 | |||
19.18 | odd | 2 | 361.8.a.c.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
19.8.a.b.1.4 | ✓ | 6 | 1.1 | even | 1 | trivial | |
171.8.a.f.1.3 | 6 | 3.2 | odd | 2 | |||
304.8.a.h.1.3 | 6 | 4.3 | odd | 2 | |||
361.8.a.c.1.3 | 6 | 19.18 | odd | 2 | |||
475.8.a.b.1.3 | 6 | 5.4 | even | 2 |