Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8031,2,Mod(1,8031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8031, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8031 = 3 \cdot 2677 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8031.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: | \(64.1278578633\) |
Analytic rank: | \(1\) |
Dimension: | \(92\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 8031.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.66818 | −1.88669 | −0.943344 | − | 0.331817i | \(-0.892338\pi\) | ||||
−0.943344 | + | 0.331817i | \(0.892338\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 5.11918 | 2.55959 | ||||||||
\(5\) | 2.50193 | 1.11890 | 0.559448 | − | 0.828865i | \(-0.311013\pi\) | ||||
0.559448 | + | 0.828865i | \(0.311013\pi\) | |||||||
\(6\) | −2.66818 | −1.08928 | ||||||||
\(7\) | 2.17887 | 0.823535 | 0.411767 | − | 0.911289i | \(-0.364912\pi\) | ||||
0.411767 | + | 0.911289i | \(0.364912\pi\) | |||||||
\(8\) | −8.32253 | −2.94246 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −6.67559 | −2.11101 | ||||||||
\(11\) | 3.36263 | 1.01387 | 0.506936 | − | 0.861984i | \(-0.330778\pi\) | ||||
0.506936 | + | 0.861984i | \(0.330778\pi\) | |||||||
\(12\) | 5.11918 | 1.47778 | ||||||||
\(13\) | −0.728293 | −0.201992 | −0.100996 | − | 0.994887i | \(-0.532203\pi\) | ||||
−0.100996 | + | 0.994887i | \(0.532203\pi\) | |||||||
\(14\) | −5.81361 | −1.55375 | ||||||||
\(15\) | 2.50193 | 0.645995 | ||||||||
\(16\) | 11.9676 | 2.99191 | ||||||||
\(17\) | −1.01722 | −0.246713 | −0.123357 | − | 0.992362i | \(-0.539366\pi\) | ||||
−0.123357 | + | 0.992362i | \(0.539366\pi\) | |||||||
\(18\) | −2.66818 | −0.628896 | ||||||||
\(19\) | −8.14146 | −1.86778 | −0.933890 | − | 0.357561i | \(-0.883608\pi\) | ||||
−0.933890 | + | 0.357561i | \(0.883608\pi\) | |||||||
\(20\) | 12.8078 | 2.86392 | ||||||||
\(21\) | 2.17887 | 0.475468 | ||||||||
\(22\) | −8.97211 | −1.91286 | ||||||||
\(23\) | −8.21797 | −1.71357 | −0.856783 | − | 0.515677i | \(-0.827540\pi\) | ||||
−0.856783 | + | 0.515677i | \(0.827540\pi\) | |||||||
\(24\) | −8.32253 | −1.69883 | ||||||||
\(25\) | 1.25965 | 0.251929 | ||||||||
\(26\) | 1.94322 | 0.381096 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 11.1540 | 2.10791 | ||||||||
\(29\) | 1.36066 | 0.252669 | 0.126335 | − | 0.991988i | \(-0.459679\pi\) | ||||
0.126335 | + | 0.991988i | \(0.459679\pi\) | |||||||
\(30\) | −6.67559 | −1.21879 | ||||||||
\(31\) | −0.119992 | −0.0215512 | −0.0107756 | − | 0.999942i | \(-0.503430\pi\) | ||||
−0.0107756 | + | 0.999942i | \(0.503430\pi\) | |||||||
\(32\) | −15.2868 | −2.70234 | ||||||||
\(33\) | 3.36263 | 0.585359 | ||||||||
\(34\) | 2.71414 | 0.465470 | ||||||||
\(35\) | 5.45137 | 0.921450 | ||||||||
\(36\) | 5.11918 | 0.853197 | ||||||||
\(37\) | −6.71996 | −1.10476 | −0.552378 | − | 0.833594i | \(-0.686279\pi\) | ||||
−0.552378 | + | 0.833594i | \(0.686279\pi\) | |||||||
\(38\) | 21.7229 | 3.52392 | ||||||||
\(39\) | −0.728293 | −0.116620 | ||||||||
\(40\) | −20.8224 | −3.29231 | ||||||||
\(41\) | −1.65460 | −0.258405 | −0.129202 | − | 0.991618i | \(-0.541242\pi\) | ||||
−0.129202 | + | 0.991618i | \(0.541242\pi\) | |||||||
\(42\) | −5.81361 | −0.897060 | ||||||||
\(43\) | −8.77755 | −1.33856 | −0.669282 | − | 0.743009i | \(-0.733398\pi\) | ||||
−0.669282 | + | 0.743009i | \(0.733398\pi\) | |||||||
\(44\) | 17.2139 | 2.59510 | ||||||||
\(45\) | 2.50193 | 0.372965 | ||||||||
\(46\) | 21.9270 | 3.23296 | ||||||||
\(47\) | −8.23931 | −1.20183 | −0.600913 | − | 0.799314i | \(-0.705196\pi\) | ||||
−0.600913 | + | 0.799314i | \(0.705196\pi\) | |||||||
\(48\) | 11.9676 | 1.72738 | ||||||||
\(49\) | −2.25253 | −0.321790 | ||||||||
\(50\) | −3.36096 | −0.475312 | ||||||||
\(51\) | −1.01722 | −0.142440 | ||||||||
\(52\) | −3.72826 | −0.517017 | ||||||||
\(53\) | 9.36849 | 1.28686 | 0.643430 | − | 0.765505i | \(-0.277511\pi\) | ||||
0.643430 | + | 0.765505i | \(0.277511\pi\) | |||||||
\(54\) | −2.66818 | −0.363093 | ||||||||
\(55\) | 8.41307 | 1.13442 | ||||||||
\(56\) | −18.1337 | −2.42322 | ||||||||
\(57\) | −8.14146 | −1.07836 | ||||||||
\(58\) | −3.63050 | −0.476708 | ||||||||
\(59\) | −6.58197 | −0.856900 | −0.428450 | − | 0.903566i | \(-0.640940\pi\) | ||||
−0.428450 | + | 0.903566i | \(0.640940\pi\) | |||||||
\(60\) | 12.8078 | 1.65348 | ||||||||
\(61\) | −11.5200 | −1.47498 | −0.737490 | − | 0.675358i | \(-0.763989\pi\) | ||||
−0.737490 | + | 0.675358i | \(0.763989\pi\) | |||||||
\(62\) | 0.320160 | 0.0406604 | ||||||||
\(63\) | 2.17887 | 0.274512 | ||||||||
\(64\) | 16.8525 | 2.10657 | ||||||||
\(65\) | −1.82214 | −0.226008 | ||||||||
\(66\) | −8.97211 | −1.10439 | ||||||||
\(67\) | 0.965475 | 0.117951 | 0.0589757 | − | 0.998259i | \(-0.481217\pi\) | ||||
0.0589757 | + | 0.998259i | \(0.481217\pi\) | |||||||
\(68\) | −5.20735 | −0.631484 | ||||||||
\(69\) | −8.21797 | −0.989328 | ||||||||
\(70\) | −14.5452 | −1.73849 | ||||||||
\(71\) | 0.0597271 | 0.00708830 | 0.00354415 | − | 0.999994i | \(-0.498872\pi\) | ||||
0.00354415 | + | 0.999994i | \(0.498872\pi\) | |||||||
\(72\) | −8.32253 | −0.980820 | ||||||||
\(73\) | 4.87655 | 0.570756 | 0.285378 | − | 0.958415i | \(-0.407881\pi\) | ||||
0.285378 | + | 0.958415i | \(0.407881\pi\) | |||||||
\(74\) | 17.9301 | 2.08433 | ||||||||
\(75\) | 1.25965 | 0.145451 | ||||||||
\(76\) | −41.6776 | −4.78075 | ||||||||
\(77\) | 7.32674 | 0.834959 | ||||||||
\(78\) | 1.94322 | 0.220026 | ||||||||
\(79\) | −4.03279 | −0.453724 | −0.226862 | − | 0.973927i | \(-0.572847\pi\) | ||||
−0.226862 | + | 0.973927i | \(0.572847\pi\) | |||||||
\(80\) | 29.9422 | 3.34764 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.41476 | 0.487529 | ||||||||
\(83\) | 15.8058 | 1.73491 | 0.867457 | − | 0.497512i | \(-0.165753\pi\) | ||||
0.867457 | + | 0.497512i | \(0.165753\pi\) | |||||||
\(84\) | 11.1540 | 1.21700 | ||||||||
\(85\) | −2.54502 | −0.276046 | ||||||||
\(86\) | 23.4201 | 2.52545 | ||||||||
\(87\) | 1.36066 | 0.145879 | ||||||||
\(88\) | −27.9856 | −2.98328 | ||||||||
\(89\) | −3.83206 | −0.406197 | −0.203099 | − | 0.979158i | \(-0.565101\pi\) | ||||
−0.203099 | + | 0.979158i | \(0.565101\pi\) | |||||||
\(90\) | −6.67559 | −0.703669 | ||||||||
\(91\) | −1.58685 | −0.166348 | ||||||||
\(92\) | −42.0693 | −4.38603 | ||||||||
\(93\) | −0.119992 | −0.0124426 | ||||||||
\(94\) | 21.9840 | 2.26747 | ||||||||
\(95\) | −20.3694 | −2.08985 | ||||||||
\(96\) | −15.2868 | −1.56020 | ||||||||
\(97\) | −5.12282 | −0.520144 | −0.260072 | − | 0.965589i | \(-0.583746\pi\) | ||||
−0.260072 | + | 0.965589i | \(0.583746\pi\) | |||||||
\(98\) | 6.01016 | 0.607118 | ||||||||
\(99\) | 3.36263 | 0.337957 | ||||||||
\(100\) | 6.44835 | 0.644835 | ||||||||
\(101\) | −1.55509 | −0.154737 | −0.0773684 | − | 0.997003i | \(-0.524652\pi\) | ||||
−0.0773684 | + | 0.997003i | \(0.524652\pi\) | |||||||
\(102\) | 2.71414 | 0.268740 | ||||||||
\(103\) | 7.41047 | 0.730175 | 0.365087 | − | 0.930973i | \(-0.381039\pi\) | ||||
0.365087 | + | 0.930973i | \(0.381039\pi\) | |||||||
\(104\) | 6.06124 | 0.594354 | ||||||||
\(105\) | 5.45137 | 0.532000 | ||||||||
\(106\) | −24.9968 | −2.42790 | ||||||||
\(107\) | −8.52845 | −0.824476 | −0.412238 | − | 0.911076i | \(-0.635253\pi\) | ||||
−0.412238 | + | 0.911076i | \(0.635253\pi\) | |||||||
\(108\) | 5.11918 | 0.492593 | ||||||||
\(109\) | −18.9520 | −1.81528 | −0.907638 | − | 0.419755i | \(-0.862116\pi\) | ||||
−0.907638 | + | 0.419755i | \(0.862116\pi\) | |||||||
\(110\) | −22.4476 | −2.14029 | ||||||||
\(111\) | −6.71996 | −0.637831 | ||||||||
\(112\) | 26.0759 | 2.46394 | ||||||||
\(113\) | 0.530104 | 0.0498680 | 0.0249340 | − | 0.999689i | \(-0.492062\pi\) | ||||
0.0249340 | + | 0.999689i | \(0.492062\pi\) | |||||||
\(114\) | 21.7229 | 2.03453 | ||||||||
\(115\) | −20.5608 | −1.91730 | ||||||||
\(116\) | 6.96549 | 0.646729 | ||||||||
\(117\) | −0.728293 | −0.0673307 | ||||||||
\(118\) | 17.5619 | 1.61670 | ||||||||
\(119\) | −2.21640 | −0.203177 | ||||||||
\(120\) | −20.8224 | −1.90081 | ||||||||
\(121\) | 0.307304 | 0.0279367 | ||||||||
\(122\) | 30.7373 | 2.78283 | ||||||||
\(123\) | −1.65460 | −0.149190 | ||||||||
\(124\) | −0.614260 | −0.0551622 | ||||||||
\(125\) | −9.35810 | −0.837014 | ||||||||
\(126\) | −5.81361 | −0.517918 | ||||||||
\(127\) | 12.4958 | 1.10883 | 0.554413 | − | 0.832242i | \(-0.312943\pi\) | ||||
0.554413 | + | 0.832242i | \(0.312943\pi\) | |||||||
\(128\) | −14.3921 | −1.27209 | ||||||||
\(129\) | −8.77755 | −0.772820 | ||||||||
\(130\) | 4.86179 | 0.426407 | ||||||||
\(131\) | −9.15214 | −0.799626 | −0.399813 | − | 0.916597i | \(-0.630925\pi\) | ||||
−0.399813 | + | 0.916597i | \(0.630925\pi\) | |||||||
\(132\) | 17.2139 | 1.49828 | ||||||||
\(133\) | −17.7392 | −1.53818 | ||||||||
\(134\) | −2.57606 | −0.222538 | ||||||||
\(135\) | 2.50193 | 0.215332 | ||||||||
\(136\) | 8.46588 | 0.725943 | ||||||||
\(137\) | 5.72120 | 0.488795 | 0.244398 | − | 0.969675i | \(-0.421410\pi\) | ||||
0.244398 | + | 0.969675i | \(0.421410\pi\) | |||||||
\(138\) | 21.9270 | 1.86655 | ||||||||
\(139\) | 9.43803 | 0.800523 | 0.400261 | − | 0.916401i | \(-0.368919\pi\) | ||||
0.400261 | + | 0.916401i | \(0.368919\pi\) | |||||||
\(140\) | 27.9066 | 2.35854 | ||||||||
\(141\) | −8.23931 | −0.693875 | ||||||||
\(142\) | −0.159363 | −0.0133734 | ||||||||
\(143\) | −2.44898 | −0.204794 | ||||||||
\(144\) | 11.9676 | 0.997304 | ||||||||
\(145\) | 3.40428 | 0.282710 | ||||||||
\(146\) | −13.0115 | −1.07684 | ||||||||
\(147\) | −2.25253 | −0.185786 | ||||||||
\(148\) | −34.4007 | −2.82772 | ||||||||
\(149\) | 10.2856 | 0.842627 | 0.421313 | − | 0.906915i | \(-0.361569\pi\) | ||||
0.421313 | + | 0.906915i | \(0.361569\pi\) | |||||||
\(150\) | −3.36096 | −0.274421 | ||||||||
\(151\) | −21.2747 | −1.73131 | −0.865657 | − | 0.500638i | \(-0.833099\pi\) | ||||
−0.865657 | + | 0.500638i | \(0.833099\pi\) | |||||||
\(152\) | 67.7576 | 5.49587 | ||||||||
\(153\) | −1.01722 | −0.0822377 | ||||||||
\(154\) | −19.5490 | −1.57531 | ||||||||
\(155\) | −0.300211 | −0.0241135 | ||||||||
\(156\) | −3.72826 | −0.298500 | ||||||||
\(157\) | −4.19220 | −0.334574 | −0.167287 | − | 0.985908i | \(-0.553501\pi\) | ||||
−0.167287 | + | 0.985908i | \(0.553501\pi\) | |||||||
\(158\) | 10.7602 | 0.856035 | ||||||||
\(159\) | 9.36849 | 0.742969 | ||||||||
\(160\) | −38.2464 | −3.02364 | ||||||||
\(161\) | −17.9059 | −1.41118 | ||||||||
\(162\) | −2.66818 | −0.209632 | ||||||||
\(163\) | 13.3785 | 1.04788 | 0.523941 | − | 0.851755i | \(-0.324461\pi\) | ||||
0.523941 | + | 0.851755i | \(0.324461\pi\) | |||||||
\(164\) | −8.47018 | −0.661410 | ||||||||
\(165\) | 8.41307 | 0.654956 | ||||||||
\(166\) | −42.1728 | −3.27324 | ||||||||
\(167\) | 24.3499 | 1.88425 | 0.942125 | − | 0.335262i | \(-0.108825\pi\) | ||||
0.942125 | + | 0.335262i | \(0.108825\pi\) | |||||||
\(168\) | −18.1337 | −1.39905 | ||||||||
\(169\) | −12.4696 | −0.959199 | ||||||||
\(170\) | 6.79057 | 0.520813 | ||||||||
\(171\) | −8.14146 | −0.622593 | ||||||||
\(172\) | −44.9339 | −3.42617 | ||||||||
\(173\) | 10.6996 | 0.813474 | 0.406737 | − | 0.913545i | \(-0.366667\pi\) | ||||
0.406737 | + | 0.913545i | \(0.366667\pi\) | |||||||
\(174\) | −3.63050 | −0.275227 | ||||||||
\(175\) | 2.74460 | 0.207472 | ||||||||
\(176\) | 40.2428 | 3.03342 | ||||||||
\(177\) | −6.58197 | −0.494731 | ||||||||
\(178\) | 10.2246 | 0.766368 | ||||||||
\(179\) | 15.2684 | 1.14121 | 0.570606 | − | 0.821224i | \(-0.306708\pi\) | ||||
0.570606 | + | 0.821224i | \(0.306708\pi\) | |||||||
\(180\) | 12.8078 | 0.954639 | ||||||||
\(181\) | −5.91757 | −0.439850 | −0.219925 | − | 0.975517i | \(-0.570581\pi\) | ||||
−0.219925 | + | 0.975517i | \(0.570581\pi\) | |||||||
\(182\) | 4.23401 | 0.313846 | ||||||||
\(183\) | −11.5200 | −0.851581 | ||||||||
\(184\) | 68.3944 | 5.04210 | ||||||||
\(185\) | −16.8129 | −1.23611 | ||||||||
\(186\) | 0.320160 | 0.0234753 | ||||||||
\(187\) | −3.42055 | −0.250135 | ||||||||
\(188\) | −42.1785 | −3.07618 | ||||||||
\(189\) | 2.17887 | 0.158489 | ||||||||
\(190\) | 54.3491 | 3.94290 | ||||||||
\(191\) | −14.3070 | −1.03522 | −0.517608 | − | 0.855618i | \(-0.673177\pi\) | ||||
−0.517608 | + | 0.855618i | \(0.673177\pi\) | |||||||
\(192\) | 16.8525 | 1.21623 | ||||||||
\(193\) | −26.2676 | −1.89078 | −0.945390 | − | 0.325940i | \(-0.894319\pi\) | ||||
−0.945390 | + | 0.325940i | \(0.894319\pi\) | |||||||
\(194\) | 13.6686 | 0.981349 | ||||||||
\(195\) | −1.82214 | −0.130486 | ||||||||
\(196\) | −11.5311 | −0.823651 | ||||||||
\(197\) | −23.8132 | −1.69662 | −0.848311 | − | 0.529498i | \(-0.822380\pi\) | ||||
−0.848311 | + | 0.529498i | \(0.822380\pi\) | |||||||
\(198\) | −8.97211 | −0.637620 | ||||||||
\(199\) | −0.780516 | −0.0553293 | −0.0276647 | − | 0.999617i | \(-0.508807\pi\) | ||||
−0.0276647 | + | 0.999617i | \(0.508807\pi\) | |||||||
\(200\) | −10.4834 | −0.741291 | ||||||||
\(201\) | 0.965475 | 0.0680993 | ||||||||
\(202\) | 4.14925 | 0.291940 | ||||||||
\(203\) | 2.96471 | 0.208082 | ||||||||
\(204\) | −5.20735 | −0.364588 | ||||||||
\(205\) | −4.13968 | −0.289128 | ||||||||
\(206\) | −19.7724 | −1.37761 | ||||||||
\(207\) | −8.21797 | −0.571189 | ||||||||
\(208\) | −8.71595 | −0.604343 | ||||||||
\(209\) | −27.3768 | −1.89369 | ||||||||
\(210\) | −14.5452 | −1.00372 | ||||||||
\(211\) | −17.4775 | −1.20320 | −0.601599 | − | 0.798798i | \(-0.705470\pi\) | ||||
−0.601599 | + | 0.798798i | \(0.705470\pi\) | |||||||
\(212\) | 47.9590 | 3.29384 | ||||||||
\(213\) | 0.0597271 | 0.00409243 | ||||||||
\(214\) | 22.7554 | 1.55553 | ||||||||
\(215\) | −21.9608 | −1.49771 | ||||||||
\(216\) | −8.32253 | −0.566277 | ||||||||
\(217\) | −0.261447 | −0.0177482 | ||||||||
\(218\) | 50.5674 | 3.42486 | ||||||||
\(219\) | 4.87655 | 0.329526 | ||||||||
\(220\) | 43.0680 | 2.90365 | ||||||||
\(221\) | 0.740837 | 0.0498341 | ||||||||
\(222\) | 17.9301 | 1.20339 | ||||||||
\(223\) | 23.8007 | 1.59381 | 0.796906 | − | 0.604103i | \(-0.206469\pi\) | ||||
0.796906 | + | 0.604103i | \(0.206469\pi\) | |||||||
\(224\) | −33.3079 | −2.22547 | ||||||||
\(225\) | 1.25965 | 0.0839764 | ||||||||
\(226\) | −1.41441 | −0.0940854 | ||||||||
\(227\) | −2.96344 | −0.196690 | −0.0983452 | − | 0.995152i | \(-0.531355\pi\) | ||||
−0.0983452 | + | 0.995152i | \(0.531355\pi\) | |||||||
\(228\) | −41.6776 | −2.76017 | ||||||||
\(229\) | 18.7987 | 1.24225 | 0.621127 | − | 0.783710i | \(-0.286675\pi\) | ||||
0.621127 | + | 0.783710i | \(0.286675\pi\) | |||||||
\(230\) | 54.8599 | 3.61735 | ||||||||
\(231\) | 7.32674 | 0.482064 | ||||||||
\(232\) | −11.3242 | −0.743468 | ||||||||
\(233\) | 11.2917 | 0.739745 | 0.369872 | − | 0.929083i | \(-0.379401\pi\) | ||||
0.369872 | + | 0.929083i | \(0.379401\pi\) | |||||||
\(234\) | 1.94322 | 0.127032 | ||||||||
\(235\) | −20.6142 | −1.34472 | ||||||||
\(236\) | −33.6943 | −2.19331 | ||||||||
\(237\) | −4.03279 | −0.261958 | ||||||||
\(238\) | 5.91375 | 0.383331 | ||||||||
\(239\) | −16.1382 | −1.04389 | −0.521947 | − | 0.852978i | \(-0.674794\pi\) | ||||
−0.521947 | + | 0.852978i | \(0.674794\pi\) | |||||||
\(240\) | 29.9422 | 1.93276 | ||||||||
\(241\) | −15.1276 | −0.974455 | −0.487227 | − | 0.873275i | \(-0.661992\pi\) | ||||
−0.487227 | + | 0.873275i | \(0.661992\pi\) | |||||||
\(242\) | −0.819941 | −0.0527078 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −58.9728 | −3.77535 | ||||||||
\(245\) | −5.63567 | −0.360050 | ||||||||
\(246\) | 4.41476 | 0.281475 | ||||||||
\(247\) | 5.92937 | 0.377277 | ||||||||
\(248\) | 0.998637 | 0.0634135 | ||||||||
\(249\) | 15.8058 | 1.00165 | ||||||||
\(250\) | 24.9691 | 1.57918 | ||||||||
\(251\) | −15.4459 | −0.974934 | −0.487467 | − | 0.873141i | \(-0.662079\pi\) | ||||
−0.487467 | + | 0.873141i | \(0.662079\pi\) | |||||||
\(252\) | 11.1540 | 0.702637 | ||||||||
\(253\) | −27.6340 | −1.73734 | ||||||||
\(254\) | −33.3411 | −2.09201 | ||||||||
\(255\) | −2.54502 | −0.159375 | ||||||||
\(256\) | 4.69552 | 0.293470 | ||||||||
\(257\) | −0.0223687 | −0.00139532 | −0.000697660 | − | 1.00000i | \(-0.500222\pi\) | ||||
−0.000697660 | 1.00000i | \(0.500222\pi\) | ||||||||
\(258\) | 23.4201 | 1.45807 | ||||||||
\(259\) | −14.6419 | −0.909804 | ||||||||
\(260\) | −9.32784 | −0.578488 | ||||||||
\(261\) | 1.36066 | 0.0842230 | ||||||||
\(262\) | 24.4196 | 1.50865 | ||||||||
\(263\) | −1.11182 | −0.0685577 | −0.0342788 | − | 0.999412i | \(-0.510913\pi\) | ||||
−0.0342788 | + | 0.999412i | \(0.510913\pi\) | |||||||
\(264\) | −27.9856 | −1.72240 | ||||||||
\(265\) | 23.4393 | 1.43986 | ||||||||
\(266\) | 47.3313 | 2.90207 | ||||||||
\(267\) | −3.83206 | −0.234518 | ||||||||
\(268\) | 4.94244 | 0.301908 | ||||||||
\(269\) | 14.1411 | 0.862201 | 0.431100 | − | 0.902304i | \(-0.358125\pi\) | ||||
0.431100 | + | 0.902304i | \(0.358125\pi\) | |||||||
\(270\) | −6.67559 | −0.406264 | ||||||||
\(271\) | 17.2975 | 1.05075 | 0.525373 | − | 0.850872i | \(-0.323926\pi\) | ||||
0.525373 | + | 0.850872i | \(0.323926\pi\) | |||||||
\(272\) | −12.1738 | −0.738144 | ||||||||
\(273\) | −1.58685 | −0.0960408 | ||||||||
\(274\) | −15.2652 | −0.922204 | ||||||||
\(275\) | 4.23573 | 0.255424 | ||||||||
\(276\) | −42.0693 | −2.53227 | ||||||||
\(277\) | −26.8386 | −1.61257 | −0.806287 | − | 0.591525i | \(-0.798526\pi\) | ||||
−0.806287 | + | 0.591525i | \(0.798526\pi\) | |||||||
\(278\) | −25.1823 | −1.51034 | ||||||||
\(279\) | −0.119992 | −0.00718373 | ||||||||
\(280\) | −45.3692 | −2.71133 | ||||||||
\(281\) | −3.89982 | −0.232644 | −0.116322 | − | 0.993212i | \(-0.537110\pi\) | ||||
−0.116322 | + | 0.993212i | \(0.537110\pi\) | |||||||
\(282\) | 21.9840 | 1.30913 | ||||||||
\(283\) | 2.85301 | 0.169594 | 0.0847970 | − | 0.996398i | \(-0.472976\pi\) | ||||
0.0847970 | + | 0.996398i | \(0.472976\pi\) | |||||||
\(284\) | 0.305754 | 0.0181431 | ||||||||
\(285\) | −20.3694 | −1.20658 | ||||||||
\(286\) | 6.53432 | 0.386383 | ||||||||
\(287\) | −3.60515 | −0.212805 | ||||||||
\(288\) | −15.2868 | −0.900781 | ||||||||
\(289\) | −15.9653 | −0.939133 | ||||||||
\(290\) | −9.08324 | −0.533386 | ||||||||
\(291\) | −5.12282 | −0.300305 | ||||||||
\(292\) | 24.9639 | 1.46090 | ||||||||
\(293\) | −7.32108 | −0.427702 | −0.213851 | − | 0.976866i | \(-0.568601\pi\) | ||||
−0.213851 | + | 0.976866i | \(0.568601\pi\) | |||||||
\(294\) | 6.01016 | 0.350520 | ||||||||
\(295\) | −16.4676 | −0.958782 | ||||||||
\(296\) | 55.9271 | 3.25070 | ||||||||
\(297\) | 3.36263 | 0.195120 | ||||||||
\(298\) | −27.4437 | −1.58977 | ||||||||
\(299\) | 5.98509 | 0.346127 | ||||||||
\(300\) | 6.44835 | 0.372296 | ||||||||
\(301\) | −19.1251 | −1.10235 | ||||||||
\(302\) | 56.7648 | 3.26645 | ||||||||
\(303\) | −1.55509 | −0.0893374 | ||||||||
\(304\) | −97.4342 | −5.58823 | ||||||||
\(305\) | −28.8221 | −1.65035 | ||||||||
\(306\) | 2.71414 | 0.155157 | ||||||||
\(307\) | −28.1823 | −1.60845 | −0.804225 | − | 0.594324i | \(-0.797420\pi\) | ||||
−0.804225 | + | 0.594324i | \(0.797420\pi\) | |||||||
\(308\) | 37.5069 | 2.13715 | ||||||||
\(309\) | 7.41047 | 0.421567 | ||||||||
\(310\) | 0.801017 | 0.0454947 | ||||||||
\(311\) | 2.09340 | 0.118706 | 0.0593530 | − | 0.998237i | \(-0.481096\pi\) | ||||
0.0593530 | + | 0.998237i | \(0.481096\pi\) | |||||||
\(312\) | 6.06124 | 0.343150 | ||||||||
\(313\) | −11.9799 | −0.677144 | −0.338572 | − | 0.940940i | \(-0.609944\pi\) | ||||
−0.338572 | + | 0.940940i | \(0.609944\pi\) | |||||||
\(314\) | 11.1855 | 0.631237 | ||||||||
\(315\) | 5.45137 | 0.307150 | ||||||||
\(316\) | −20.6446 | −1.16135 | ||||||||
\(317\) | 22.1655 | 1.24494 | 0.622470 | − | 0.782644i | \(-0.286129\pi\) | ||||
0.622470 | + | 0.782644i | \(0.286129\pi\) | |||||||
\(318\) | −24.9968 | −1.40175 | ||||||||
\(319\) | 4.57542 | 0.256174 | ||||||||
\(320\) | 42.1638 | 2.35703 | ||||||||
\(321\) | −8.52845 | −0.476011 | ||||||||
\(322\) | 47.7761 | 2.66246 | ||||||||
\(323\) | 8.28169 | 0.460806 | ||||||||
\(324\) | 5.11918 | 0.284399 | ||||||||
\(325\) | −0.917391 | −0.0508877 | ||||||||
\(326\) | −35.6961 | −1.97702 | ||||||||
\(327\) | −18.9520 | −1.04805 | ||||||||
\(328\) | 13.7704 | 0.760345 | ||||||||
\(329\) | −17.9524 | −0.989746 | ||||||||
\(330\) | −22.4476 | −1.23570 | ||||||||
\(331\) | 17.7872 | 0.977675 | 0.488838 | − | 0.872375i | \(-0.337421\pi\) | ||||
0.488838 | + | 0.872375i | \(0.337421\pi\) | |||||||
\(332\) | 80.9128 | 4.44067 | ||||||||
\(333\) | −6.71996 | −0.368252 | ||||||||
\(334\) | −64.9698 | −3.55499 | ||||||||
\(335\) | 2.41555 | 0.131976 | ||||||||
\(336\) | 26.0759 | 1.42256 | ||||||||
\(337\) | 13.3148 | 0.725306 | 0.362653 | − | 0.931924i | \(-0.381871\pi\) | ||||
0.362653 | + | 0.931924i | \(0.381871\pi\) | |||||||
\(338\) | 33.2711 | 1.80971 | ||||||||
\(339\) | 0.530104 | 0.0287913 | ||||||||
\(340\) | −13.0284 | −0.706566 | ||||||||
\(341\) | −0.403489 | −0.0218502 | ||||||||
\(342\) | 21.7229 | 1.17464 | ||||||||
\(343\) | −20.1601 | −1.08854 | ||||||||
\(344\) | 73.0514 | 3.93867 | ||||||||
\(345\) | −20.5608 | −1.10696 | ||||||||
\(346\) | −28.5484 | −1.53477 | ||||||||
\(347\) | 21.8646 | 1.17375 | 0.586876 | − | 0.809677i | \(-0.300358\pi\) | ||||
0.586876 | + | 0.809677i | \(0.300358\pi\) | |||||||
\(348\) | 6.96549 | 0.373389 | ||||||||
\(349\) | 4.10810 | 0.219902 | 0.109951 | − | 0.993937i | \(-0.464931\pi\) | ||||
0.109951 | + | 0.993937i | \(0.464931\pi\) | |||||||
\(350\) | −7.32309 | −0.391436 | ||||||||
\(351\) | −0.728293 | −0.0388734 | ||||||||
\(352\) | −51.4038 | −2.73983 | ||||||||
\(353\) | 17.4549 | 0.929032 | 0.464516 | − | 0.885565i | \(-0.346228\pi\) | ||||
0.464516 | + | 0.885565i | \(0.346228\pi\) | |||||||
\(354\) | 17.5619 | 0.933403 | ||||||||
\(355\) | 0.149433 | 0.00793107 | ||||||||
\(356\) | −19.6170 | −1.03970 | ||||||||
\(357\) | −2.21640 | −0.117304 | ||||||||
\(358\) | −40.7387 | −2.15311 | ||||||||
\(359\) | −32.5122 | −1.71593 | −0.857965 | − | 0.513708i | \(-0.828271\pi\) | ||||
−0.857965 | + | 0.513708i | \(0.828271\pi\) | |||||||
\(360\) | −20.8224 | −1.09744 | ||||||||
\(361\) | 47.2834 | 2.48860 | ||||||||
\(362\) | 15.7891 | 0.829859 | ||||||||
\(363\) | 0.307304 | 0.0161293 | ||||||||
\(364\) | −8.12339 | −0.425781 | ||||||||
\(365\) | 12.2008 | 0.638617 | ||||||||
\(366\) | 30.7373 | 1.60667 | ||||||||
\(367\) | 23.0488 | 1.20314 | 0.601569 | − | 0.798821i | \(-0.294543\pi\) | ||||
0.601569 | + | 0.798821i | \(0.294543\pi\) | |||||||
\(368\) | −98.3498 | −5.12684 | ||||||||
\(369\) | −1.65460 | −0.0861349 | ||||||||
\(370\) | 44.8597 | 2.33215 | ||||||||
\(371\) | 20.4127 | 1.05977 | ||||||||
\(372\) | −0.614260 | −0.0318479 | ||||||||
\(373\) | 21.3192 | 1.10387 | 0.551934 | − | 0.833888i | \(-0.313890\pi\) | ||||
0.551934 | + | 0.833888i | \(0.313890\pi\) | |||||||
\(374\) | 9.12664 | 0.471928 | ||||||||
\(375\) | −9.35810 | −0.483250 | ||||||||
\(376\) | 68.5719 | 3.53633 | ||||||||
\(377\) | −0.990962 | −0.0510371 | ||||||||
\(378\) | −5.81361 | −0.299020 | ||||||||
\(379\) | 35.3028 | 1.81338 | 0.906691 | − | 0.421796i | \(-0.138600\pi\) | ||||
0.906691 | + | 0.421796i | \(0.138600\pi\) | |||||||
\(380\) | −104.274 | −5.34916 | ||||||||
\(381\) | 12.4958 | 0.640180 | ||||||||
\(382\) | 38.1735 | 1.95313 | ||||||||
\(383\) | 13.0399 | 0.666308 | 0.333154 | − | 0.942872i | \(-0.391887\pi\) | ||||
0.333154 | + | 0.942872i | \(0.391887\pi\) | |||||||
\(384\) | −14.3921 | −0.734442 | ||||||||
\(385\) | 18.3310 | 0.934233 | ||||||||
\(386\) | 70.0866 | 3.56731 | ||||||||
\(387\) | −8.77755 | −0.446188 | ||||||||
\(388\) | −26.2247 | −1.33136 | ||||||||
\(389\) | 12.9689 | 0.657552 | 0.328776 | − | 0.944408i | \(-0.393364\pi\) | ||||
0.328776 | + | 0.944408i | \(0.393364\pi\) | |||||||
\(390\) | 4.86179 | 0.246186 | ||||||||
\(391\) | 8.35952 | 0.422759 | ||||||||
\(392\) | 18.7468 | 0.946855 | ||||||||
\(393\) | −9.15214 | −0.461665 | ||||||||
\(394\) | 63.5380 | 3.20100 | ||||||||
\(395\) | −10.0897 | −0.507670 | ||||||||
\(396\) | 17.2139 | 0.865032 | ||||||||
\(397\) | 27.6360 | 1.38701 | 0.693506 | − | 0.720451i | \(-0.256065\pi\) | ||||
0.693506 | + | 0.720451i | \(0.256065\pi\) | |||||||
\(398\) | 2.08256 | 0.104389 | ||||||||
\(399\) | −17.7392 | −0.888070 | ||||||||
\(400\) | 15.0750 | 0.753750 | ||||||||
\(401\) | 21.8747 | 1.09237 | 0.546186 | − | 0.837664i | \(-0.316079\pi\) | ||||
0.546186 | + | 0.837664i | \(0.316079\pi\) | |||||||
\(402\) | −2.57606 | −0.128482 | ||||||||
\(403\) | 0.0873893 | 0.00435317 | ||||||||
\(404\) | −7.96077 | −0.396063 | ||||||||
\(405\) | 2.50193 | 0.124322 | ||||||||
\(406\) | −7.91037 | −0.392585 | ||||||||
\(407\) | −22.5968 | −1.12008 | ||||||||
\(408\) | 8.46588 | 0.419124 | ||||||||
\(409\) | 2.50714 | 0.123970 | 0.0619849 | − | 0.998077i | \(-0.480257\pi\) | ||||
0.0619849 | + | 0.998077i | \(0.480257\pi\) | |||||||
\(410\) | 11.0454 | 0.545494 | ||||||||
\(411\) | 5.72120 | 0.282206 | ||||||||
\(412\) | 37.9355 | 1.86895 | ||||||||
\(413\) | −14.3412 | −0.705687 | ||||||||
\(414\) | 21.9270 | 1.07765 | ||||||||
\(415\) | 39.5450 | 1.94119 | ||||||||
\(416\) | 11.1332 | 0.545852 | ||||||||
\(417\) | 9.43803 | 0.462182 | ||||||||
\(418\) | 73.0461 | 3.57280 | ||||||||
\(419\) | 17.9077 | 0.874850 | 0.437425 | − | 0.899255i | \(-0.355891\pi\) | ||||
0.437425 | + | 0.899255i | \(0.355891\pi\) | |||||||
\(420\) | 27.9066 | 1.36170 | ||||||||
\(421\) | −36.3205 | −1.77015 | −0.885076 | − | 0.465446i | \(-0.845894\pi\) | ||||
−0.885076 | + | 0.465446i | \(0.845894\pi\) | |||||||
\(422\) | 46.6330 | 2.27006 | ||||||||
\(423\) | −8.23931 | −0.400609 | ||||||||
\(424\) | −77.9696 | −3.78654 | ||||||||
\(425\) | −1.28134 | −0.0621542 | ||||||||
\(426\) | −0.159363 | −0.00772114 | ||||||||
\(427\) | −25.1005 | −1.21470 | ||||||||
\(428\) | −43.6587 | −2.11032 | ||||||||
\(429\) | −2.44898 | −0.118238 | ||||||||
\(430\) | 58.5953 | 2.82572 | ||||||||
\(431\) | 20.2500 | 0.975408 | 0.487704 | − | 0.873009i | \(-0.337835\pi\) | ||||
0.487704 | + | 0.873009i | \(0.337835\pi\) | |||||||
\(432\) | 11.9676 | 0.575794 | ||||||||
\(433\) | 15.8477 | 0.761592 | 0.380796 | − | 0.924659i | \(-0.375650\pi\) | ||||
0.380796 | + | 0.924659i | \(0.375650\pi\) | |||||||
\(434\) | 0.697587 | 0.0334852 | ||||||||
\(435\) | 3.40428 | 0.163223 | ||||||||
\(436\) | −97.0189 | −4.64636 | ||||||||
\(437\) | 66.9063 | 3.20056 | ||||||||
\(438\) | −13.0115 | −0.621713 | ||||||||
\(439\) | 36.0011 | 1.71824 | 0.859119 | − | 0.511777i | \(-0.171012\pi\) | ||||
0.859119 | + | 0.511777i | \(0.171012\pi\) | |||||||
\(440\) | −70.0180 | −3.33798 | ||||||||
\(441\) | −2.25253 | −0.107263 | ||||||||
\(442\) | −1.97669 | −0.0940213 | ||||||||
\(443\) | −30.2718 | −1.43826 | −0.719129 | − | 0.694876i | \(-0.755459\pi\) | ||||
−0.719129 | + | 0.694876i | \(0.755459\pi\) | |||||||
\(444\) | −34.4007 | −1.63259 | ||||||||
\(445\) | −9.58754 | −0.454493 | ||||||||
\(446\) | −63.5045 | −3.00703 | ||||||||
\(447\) | 10.2856 | 0.486491 | ||||||||
\(448\) | 36.7195 | 1.73483 | ||||||||
\(449\) | 5.21495 | 0.246109 | 0.123054 | − | 0.992400i | \(-0.460731\pi\) | ||||
0.123054 | + | 0.992400i | \(0.460731\pi\) | |||||||
\(450\) | −3.36096 | −0.158437 | ||||||||
\(451\) | −5.56380 | −0.261989 | ||||||||
\(452\) | 2.71370 | 0.127642 | ||||||||
\(453\) | −21.2747 | −0.999574 | ||||||||
\(454\) | 7.90699 | 0.371093 | ||||||||
\(455\) | −3.97020 | −0.186126 | ||||||||
\(456\) | 67.7576 | 3.17304 | ||||||||
\(457\) | −6.89838 | −0.322693 | −0.161346 | − | 0.986898i | \(-0.551584\pi\) | ||||
−0.161346 | + | 0.986898i | \(0.551584\pi\) | |||||||
\(458\) | −50.1583 | −2.34374 | ||||||||
\(459\) | −1.01722 | −0.0474800 | ||||||||
\(460\) | −105.254 | −4.90751 | ||||||||
\(461\) | 20.2748 | 0.944290 | 0.472145 | − | 0.881521i | \(-0.343480\pi\) | ||||
0.472145 | + | 0.881521i | \(0.343480\pi\) | |||||||
\(462\) | −19.5490 | −0.909504 | ||||||||
\(463\) | −2.87152 | −0.133451 | −0.0667255 | − | 0.997771i | \(-0.521255\pi\) | ||||
−0.0667255 | + | 0.997771i | \(0.521255\pi\) | |||||||
\(464\) | 16.2840 | 0.755964 | ||||||||
\(465\) | −0.300211 | −0.0139220 | ||||||||
\(466\) | −30.1283 | −1.39567 | ||||||||
\(467\) | 31.8861 | 1.47551 | 0.737756 | − | 0.675068i | \(-0.235886\pi\) | ||||
0.737756 | + | 0.675068i | \(0.235886\pi\) | |||||||
\(468\) | −3.72826 | −0.172339 | ||||||||
\(469\) | 2.10364 | 0.0971372 | ||||||||
\(470\) | 55.0023 | 2.53707 | ||||||||
\(471\) | −4.19220 | −0.193166 | ||||||||
\(472\) | 54.7787 | 2.52139 | ||||||||
\(473\) | −29.5157 | −1.35713 | ||||||||
\(474\) | 10.7602 | 0.494232 | ||||||||
\(475\) | −10.2554 | −0.470548 | ||||||||
\(476\) | −11.3461 | −0.520049 | ||||||||
\(477\) | 9.36849 | 0.428954 | ||||||||
\(478\) | 43.0597 | 1.96950 | ||||||||
\(479\) | 36.0218 | 1.64588 | 0.822940 | − | 0.568128i | \(-0.192332\pi\) | ||||
0.822940 | + | 0.568128i | \(0.192332\pi\) | |||||||
\(480\) | −38.2464 | −1.74570 | ||||||||
\(481\) | 4.89410 | 0.223152 | ||||||||
\(482\) | 40.3632 | 1.83849 | ||||||||
\(483\) | −17.9059 | −0.814746 | ||||||||
\(484\) | 1.57314 | 0.0715065 | ||||||||
\(485\) | −12.8169 | −0.581987 | ||||||||
\(486\) | −2.66818 | −0.121031 | ||||||||
\(487\) | 3.61926 | 0.164004 | 0.0820022 | − | 0.996632i | \(-0.473869\pi\) | ||||
0.0820022 | + | 0.996632i | \(0.473869\pi\) | |||||||
\(488\) | 95.8753 | 4.34007 | ||||||||
\(489\) | 13.3785 | 0.604994 | ||||||||
\(490\) | 15.0370 | 0.679302 | ||||||||
\(491\) | 4.61584 | 0.208310 | 0.104155 | − | 0.994561i | \(-0.466786\pi\) | ||||
0.104155 | + | 0.994561i | \(0.466786\pi\) | |||||||
\(492\) | −8.47018 | −0.381865 | ||||||||
\(493\) | −1.38410 | −0.0623368 | ||||||||
\(494\) | −15.8206 | −0.711803 | ||||||||
\(495\) | 8.41307 | 0.378139 | ||||||||
\(496\) | −1.43602 | −0.0644793 | ||||||||
\(497\) | 0.130137 | 0.00583746 | ||||||||
\(498\) | −42.1728 | −1.88981 | ||||||||
\(499\) | 32.1791 | 1.44054 | 0.720268 | − | 0.693696i | \(-0.244019\pi\) | ||||
0.720268 | + | 0.693696i | \(0.244019\pi\) | |||||||
\(500\) | −47.9058 | −2.14241 | ||||||||
\(501\) | 24.3499 | 1.08787 | ||||||||
\(502\) | 41.2123 | 1.83940 | ||||||||
\(503\) | −10.9719 | −0.489215 | −0.244607 | − | 0.969622i | \(-0.578659\pi\) | ||||
−0.244607 | + | 0.969622i | \(0.578659\pi\) | |||||||
\(504\) | −18.1337 | −0.807739 | ||||||||
\(505\) | −3.89071 | −0.173134 | ||||||||
\(506\) | 73.7326 | 3.27781 | ||||||||
\(507\) | −12.4696 | −0.553794 | ||||||||
\(508\) | 63.9684 | 2.83814 | ||||||||
\(509\) | −24.6477 | −1.09249 | −0.546245 | − | 0.837626i | \(-0.683943\pi\) | ||||
−0.546245 | + | 0.837626i | \(0.683943\pi\) | |||||||
\(510\) | 6.79057 | 0.300692 | ||||||||
\(511\) | 10.6254 | 0.470038 | ||||||||
\(512\) | 16.2556 | 0.718405 | ||||||||
\(513\) | −8.14146 | −0.359454 | ||||||||
\(514\) | 0.0596837 | 0.00263253 | ||||||||
\(515\) | 18.5405 | 0.816990 | ||||||||
\(516\) | −44.9339 | −1.97810 | ||||||||
\(517\) | −27.7058 | −1.21850 | ||||||||
\(518\) | 39.0673 | 1.71652 | ||||||||
\(519\) | 10.6996 | 0.469659 | ||||||||
\(520\) | 15.1648 | 0.665020 | ||||||||
\(521\) | −2.87732 | −0.126058 | −0.0630288 | − | 0.998012i | \(-0.520076\pi\) | ||||
−0.0630288 | + | 0.998012i | \(0.520076\pi\) | |||||||
\(522\) | −3.63050 | −0.158903 | ||||||||
\(523\) | −2.26922 | −0.0992262 | −0.0496131 | − | 0.998769i | \(-0.515799\pi\) | ||||
−0.0496131 | + | 0.998769i | \(0.515799\pi\) | |||||||
\(524\) | −46.8515 | −2.04672 | ||||||||
\(525\) | 2.74460 | 0.119784 | ||||||||
\(526\) | 2.96653 | 0.129347 | ||||||||
\(527\) | 0.122059 | 0.00531696 | ||||||||
\(528\) | 40.2428 | 1.75134 | ||||||||
\(529\) | 44.5351 | 1.93631 | ||||||||
\(530\) | −62.5402 | −2.71657 | ||||||||
\(531\) | −6.58197 | −0.285633 | ||||||||
\(532\) | −90.8100 | −3.93711 | ||||||||
\(533\) | 1.20503 | 0.0521957 | ||||||||
\(534\) | 10.2246 | 0.442463 | ||||||||
\(535\) | −21.3376 | −0.922503 | ||||||||
\(536\) | −8.03519 | −0.347068 | ||||||||
\(537\) | 15.2684 | 0.658879 | ||||||||
\(538\) | −37.7311 | −1.62670 | ||||||||
\(539\) | −7.57444 | −0.326254 | ||||||||
\(540\) | 12.8078 | 0.551161 | ||||||||
\(541\) | −14.8440 | −0.638193 | −0.319096 | − | 0.947722i | \(-0.603379\pi\) | ||||
−0.319096 | + | 0.947722i | \(0.603379\pi\) | |||||||
\(542\) | −46.1527 | −1.98243 | ||||||||
\(543\) | −5.91757 | −0.253947 | ||||||||
\(544\) | 15.5501 | 0.666704 | ||||||||
\(545\) | −47.4166 | −2.03111 | ||||||||
\(546\) | 4.23401 | 0.181199 | ||||||||
\(547\) | −0.245704 | −0.0105056 | −0.00525278 | − | 0.999986i | \(-0.501672\pi\) | ||||
−0.00525278 | + | 0.999986i | \(0.501672\pi\) | |||||||
\(548\) | 29.2879 | 1.25112 | ||||||||
\(549\) | −11.5200 | −0.491660 | ||||||||
\(550\) | −11.3017 | −0.481905 | ||||||||
\(551\) | −11.0778 | −0.471930 | ||||||||
\(552\) | 68.3944 | 2.91106 | ||||||||
\(553\) | −8.78691 | −0.373657 | ||||||||
\(554\) | 71.6101 | 3.04242 | ||||||||
\(555\) | −16.8129 | −0.713667 | ||||||||
\(556\) | 48.3150 | 2.04901 | ||||||||
\(557\) | −7.85104 | −0.332659 | −0.166330 | − | 0.986070i | \(-0.553192\pi\) | ||||
−0.166330 | + | 0.986070i | \(0.553192\pi\) | |||||||
\(558\) | 0.320160 | 0.0135535 | ||||||||
\(559\) | 6.39262 | 0.270379 | ||||||||
\(560\) | 65.2401 | 2.75690 | ||||||||
\(561\) | −3.42055 | −0.144416 | ||||||||
\(562\) | 10.4054 | 0.438927 | ||||||||
\(563\) | 3.67086 | 0.154708 | 0.0773542 | − | 0.997004i | \(-0.475353\pi\) | ||||
0.0773542 | + | 0.997004i | \(0.475353\pi\) | |||||||
\(564\) | −42.1785 | −1.77604 | ||||||||
\(565\) | 1.32628 | 0.0557971 | ||||||||
\(566\) | −7.61235 | −0.319971 | ||||||||
\(567\) | 2.17887 | 0.0915039 | ||||||||
\(568\) | −0.497081 | −0.0208570 | ||||||||
\(569\) | 14.7247 | 0.617290 | 0.308645 | − | 0.951177i | \(-0.400125\pi\) | ||||
0.308645 | + | 0.951177i | \(0.400125\pi\) | |||||||
\(570\) | 54.3491 | 2.27643 | ||||||||
\(571\) | 15.2220 | 0.637022 | 0.318511 | − | 0.947919i | \(-0.396817\pi\) | ||||
0.318511 | + | 0.947919i | \(0.396817\pi\) | |||||||
\(572\) | −12.5368 | −0.524189 | ||||||||
\(573\) | −14.3070 | −0.597682 | ||||||||
\(574\) | 9.61918 | 0.401497 | ||||||||
\(575\) | −10.3517 | −0.431697 | ||||||||
\(576\) | 16.8525 | 0.702189 | ||||||||
\(577\) | −4.54156 | −0.189068 | −0.0945338 | − | 0.995522i | \(-0.530136\pi\) | ||||
−0.0945338 | + | 0.995522i | \(0.530136\pi\) | |||||||
\(578\) | 42.5982 | 1.77185 | ||||||||
\(579\) | −26.2676 | −1.09164 | ||||||||
\(580\) | 17.4271 | 0.723623 | ||||||||
\(581\) | 34.4388 | 1.42876 | ||||||||
\(582\) | 13.6686 | 0.566582 | ||||||||
\(583\) | 31.5028 | 1.30471 | ||||||||
\(584\) | −40.5852 | −1.67943 | ||||||||
\(585\) | −1.82214 | −0.0753361 | ||||||||
\(586\) | 19.5339 | 0.806940 | ||||||||
\(587\) | −6.42545 | −0.265207 | −0.132603 | − | 0.991169i | \(-0.542334\pi\) | ||||
−0.132603 | + | 0.991169i | \(0.542334\pi\) | |||||||
\(588\) | −11.5311 | −0.475535 | ||||||||
\(589\) | 0.976910 | 0.0402529 | ||||||||
\(590\) | 43.9386 | 1.80892 | ||||||||
\(591\) | −23.8132 | −0.979545 | ||||||||
\(592\) | −80.4222 | −3.30533 | ||||||||
\(593\) | −7.90780 | −0.324734 | −0.162367 | − | 0.986730i | \(-0.551913\pi\) | ||||
−0.162367 | + | 0.986730i | \(0.551913\pi\) | |||||||
\(594\) | −8.97211 | −0.368130 | ||||||||
\(595\) | −5.54527 | −0.227334 | ||||||||
\(596\) | 52.6537 | 2.15678 | ||||||||
\(597\) | −0.780516 | −0.0319444 | ||||||||
\(598\) | −15.9693 | −0.653033 | ||||||||
\(599\) | 26.9505 | 1.10117 | 0.550584 | − | 0.834780i | \(-0.314405\pi\) | ||||
0.550584 | + | 0.834780i | \(0.314405\pi\) | |||||||
\(600\) | −10.4834 | −0.427985 | ||||||||
\(601\) | −5.73354 | −0.233876 | −0.116938 | − | 0.993139i | \(-0.537308\pi\) | ||||
−0.116938 | + | 0.993139i | \(0.537308\pi\) | |||||||
\(602\) | 51.0293 | 2.07980 | ||||||||
\(603\) | 0.965475 | 0.0393172 | ||||||||
\(604\) | −108.909 | −4.43145 | ||||||||
\(605\) | 0.768851 | 0.0312583 | ||||||||
\(606\) | 4.14925 | 0.168552 | ||||||||
\(607\) | −23.0467 | −0.935436 | −0.467718 | − | 0.883878i | \(-0.654924\pi\) | ||||
−0.467718 | + | 0.883878i | \(0.654924\pi\) | |||||||
\(608\) | 124.457 | 5.04738 | ||||||||
\(609\) | 2.96471 | 0.120136 | ||||||||
\(610\) | 76.9026 | 3.11370 | ||||||||
\(611\) | 6.00063 | 0.242759 | ||||||||
\(612\) | −5.20735 | −0.210495 | ||||||||
\(613\) | −35.8613 | −1.44843 | −0.724213 | − | 0.689577i | \(-0.757797\pi\) | ||||
−0.724213 | + | 0.689577i | \(0.757797\pi\) | |||||||
\(614\) | 75.1955 | 3.03464 | ||||||||
\(615\) | −4.13968 | −0.166928 | ||||||||
\(616\) | −60.9770 | −2.45683 | ||||||||
\(617\) | −6.29245 | −0.253325 | −0.126662 | − | 0.991946i | \(-0.540426\pi\) | ||||
−0.126662 | + | 0.991946i | \(0.540426\pi\) | |||||||
\(618\) | −19.7724 | −0.795365 | ||||||||
\(619\) | −1.90810 | −0.0766929 | −0.0383465 | − | 0.999265i | \(-0.512209\pi\) | ||||
−0.0383465 | + | 0.999265i | \(0.512209\pi\) | |||||||
\(620\) | −1.53684 | −0.0617208 | ||||||||
\(621\) | −8.21797 | −0.329776 | ||||||||
\(622\) | −5.58557 | −0.223961 | ||||||||
\(623\) | −8.34955 | −0.334518 | ||||||||
\(624\) | −8.71595 | −0.348917 | ||||||||
\(625\) | −29.7115 | −1.18846 | ||||||||
\(626\) | 31.9645 | 1.27756 | ||||||||
\(627\) | −27.3768 | −1.09332 | ||||||||
\(628\) | −21.4606 | −0.856373 | ||||||||
\(629\) | 6.83571 | 0.272558 | ||||||||
\(630\) | −14.5452 | −0.579496 | ||||||||
\(631\) | −33.7143 | −1.34214 | −0.671072 | − | 0.741392i | \(-0.734166\pi\) | ||||
−0.671072 | + | 0.741392i | \(0.734166\pi\) | |||||||
\(632\) | 33.5630 | 1.33506 | ||||||||
\(633\) | −17.4775 | −0.694667 | ||||||||
\(634\) | −59.1416 | −2.34881 | ||||||||
\(635\) | 31.2637 | 1.24066 | ||||||||
\(636\) | 47.9590 | 1.90170 | ||||||||
\(637\) | 1.64050 | 0.0649991 | ||||||||
\(638\) | −12.2080 | −0.483320 | ||||||||
\(639\) | 0.0597271 | 0.00236277 | ||||||||
\(640\) | −36.0079 | −1.42334 | ||||||||
\(641\) | 17.8889 | 0.706570 | 0.353285 | − | 0.935516i | \(-0.385065\pi\) | ||||
0.353285 | + | 0.935516i | \(0.385065\pi\) | |||||||
\(642\) | 22.7554 | 0.898085 | ||||||||
\(643\) | 27.6338 | 1.08977 | 0.544885 | − | 0.838511i | \(-0.316573\pi\) | ||||
0.544885 | + | 0.838511i | \(0.316573\pi\) | |||||||
\(644\) | −91.6635 | −3.61205 | ||||||||
\(645\) | −21.9608 | −0.864706 | ||||||||
\(646\) | −22.0970 | −0.869396 | ||||||||
\(647\) | 3.53161 | 0.138842 | 0.0694210 | − | 0.997587i | \(-0.477885\pi\) | ||||
0.0694210 | + | 0.997587i | \(0.477885\pi\) | |||||||
\(648\) | −8.32253 | −0.326940 | ||||||||
\(649\) | −22.1328 | −0.868787 | ||||||||
\(650\) | 2.44776 | 0.0960092 | ||||||||
\(651\) | −0.261447 | −0.0102469 | ||||||||
\(652\) | 68.4867 | 2.68215 | ||||||||
\(653\) | 19.5680 | 0.765756 | 0.382878 | − | 0.923799i | \(-0.374933\pi\) | ||||
0.382878 | + | 0.923799i | \(0.374933\pi\) | |||||||
\(654\) | 50.5674 | 1.97734 | ||||||||
\(655\) | −22.8980 | −0.894699 | ||||||||
\(656\) | −19.8016 | −0.773124 | ||||||||
\(657\) | 4.87655 | 0.190252 | ||||||||
\(658\) | 47.9001 | 1.86734 | ||||||||
\(659\) | −30.2620 | −1.17884 | −0.589420 | − | 0.807827i | \(-0.700644\pi\) | ||||
−0.589420 | + | 0.807827i | \(0.700644\pi\) | |||||||
\(660\) | 43.0680 | 1.67642 | ||||||||
\(661\) | 29.2882 | 1.13918 | 0.569590 | − | 0.821929i | \(-0.307102\pi\) | ||||
0.569590 | + | 0.821929i | \(0.307102\pi\) | |||||||
\(662\) | −47.4596 | −1.84457 | ||||||||
\(663\) | 0.740837 | 0.0287717 | ||||||||
\(664\) | −131.544 | −5.10491 | ||||||||
\(665\) | −44.3821 | −1.72107 | ||||||||
\(666\) | 17.9301 | 0.694776 | ||||||||
\(667\) | −11.1819 | −0.432965 | ||||||||
\(668\) | 124.651 | 4.82291 | ||||||||
\(669\) | 23.8007 | 0.920188 | ||||||||
\(670\) | −6.44512 | −0.248997 | ||||||||
\(671\) | −38.7374 | −1.49544 | ||||||||
\(672\) | −33.3079 | −1.28488 | ||||||||
\(673\) | 43.4808 | 1.67606 | 0.838031 | − | 0.545623i | \(-0.183707\pi\) | ||||
0.838031 | + | 0.545623i | \(0.183707\pi\) | |||||||
\(674\) | −35.5264 | −1.36843 | ||||||||
\(675\) | 1.25965 | 0.0484838 | ||||||||
\(676\) | −63.8341 | −2.45516 | ||||||||
\(677\) | −33.9151 | −1.30346 | −0.651731 | − | 0.758450i | \(-0.725957\pi\) | ||||
−0.651731 | + | 0.758450i | \(0.725957\pi\) | |||||||
\(678\) | −1.41441 | −0.0543202 | ||||||||
\(679\) | −11.1620 | −0.428357 | ||||||||
\(680\) | 21.1810 | 0.812255 | ||||||||
\(681\) | −2.96344 | −0.113559 | ||||||||
\(682\) | 1.07658 | 0.0412244 | ||||||||
\(683\) | −29.8612 | −1.14261 | −0.571304 | − | 0.820738i | \(-0.693562\pi\) | ||||
−0.571304 | + | 0.820738i | \(0.693562\pi\) | |||||||
\(684\) | −41.6776 | −1.59358 | ||||||||
\(685\) | 14.3140 | 0.546911 | ||||||||
\(686\) | 53.7906 | 2.05374 | ||||||||
\(687\) | 18.7987 | 0.717216 | ||||||||
\(688\) | −105.047 | −4.00487 | ||||||||
\(689\) | −6.82300 | −0.259936 | ||||||||
\(690\) | 54.8599 | 2.08848 | ||||||||
\(691\) | 5.56571 | 0.211730 | 0.105865 | − | 0.994381i | \(-0.466239\pi\) | ||||
0.105865 | + | 0.994381i | \(0.466239\pi\) | |||||||
\(692\) | 54.7731 | 2.08216 | ||||||||
\(693\) | 7.32674 | 0.278320 | ||||||||
\(694\) | −58.3386 | −2.21450 | ||||||||
\(695\) | 23.6133 | 0.895702 | ||||||||
\(696\) | −11.3242 | −0.429242 | ||||||||
\(697\) | 1.68310 | 0.0637518 | ||||||||
\(698\) | −10.9611 | −0.414886 | ||||||||
\(699\) | 11.2917 | 0.427092 | ||||||||
\(700\) | 14.0501 | 0.531044 | ||||||||
\(701\) | 13.5895 | 0.513270 | 0.256635 | − | 0.966508i | \(-0.417386\pi\) | ||||
0.256635 | + | 0.966508i | \(0.417386\pi\) | |||||||
\(702\) | 1.94322 | 0.0733419 | ||||||||
\(703\) | 54.7103 | 2.06344 | ||||||||
\(704\) | 56.6689 | 2.13579 | ||||||||
\(705\) | −20.6142 | −0.776374 | ||||||||
\(706\) | −46.5729 | −1.75279 | ||||||||
\(707\) | −3.38833 | −0.127431 | ||||||||
\(708\) | −33.6943 | −1.26631 | ||||||||
\(709\) | −8.68500 | −0.326172 | −0.163086 | − | 0.986612i | \(-0.552145\pi\) | ||||
−0.163086 | + | 0.986612i | \(0.552145\pi\) | |||||||
\(710\) | −0.398714 | −0.0149635 | ||||||||
\(711\) | −4.03279 | −0.151241 | ||||||||
\(712\) | 31.8924 | 1.19522 | ||||||||
\(713\) | 0.986091 | 0.0369294 | ||||||||
\(714\) | 5.91375 | 0.221316 | ||||||||
\(715\) | −6.12718 | −0.229143 | ||||||||
\(716\) | 78.1615 | 2.92103 | ||||||||
\(717\) | −16.1382 | −0.602693 | ||||||||
\(718\) | 86.7485 | 3.23742 | ||||||||
\(719\) | 0.633393 | 0.0236216 | 0.0118108 | − | 0.999930i | \(-0.496240\pi\) | ||||
0.0118108 | + | 0.999930i | \(0.496240\pi\) | |||||||
\(720\) | 29.9422 | 1.11588 | ||||||||
\(721\) | 16.1464 | 0.601324 | ||||||||
\(722\) | −126.161 | −4.69521 | ||||||||
\(723\) | −15.1276 | −0.562602 | ||||||||
\(724\) | −30.2931 | −1.12583 | ||||||||
\(725\) | 1.71396 | 0.0636547 | ||||||||
\(726\) | −0.819941 | −0.0304309 | ||||||||
\(727\) | −11.4686 | −0.425348 | −0.212674 | − | 0.977123i | \(-0.568217\pi\) | ||||
−0.212674 | + | 0.977123i | \(0.568217\pi\) | |||||||
\(728\) | 13.2066 | 0.489471 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −32.5538 | −1.20487 | ||||||||
\(731\) | 8.92873 | 0.330241 | ||||||||
\(732\) | −58.9728 | −2.17970 | ||||||||
\(733\) | 5.46114 | 0.201712 | 0.100856 | − | 0.994901i | \(-0.467842\pi\) | ||||
0.100856 | + | 0.994901i | \(0.467842\pi\) | |||||||
\(734\) | −61.4983 | −2.26994 | ||||||||
\(735\) | −5.63567 | −0.207875 | ||||||||
\(736\) | 125.626 | 4.63065 | ||||||||
\(737\) | 3.24654 | 0.119588 | ||||||||
\(738\) | 4.41476 | 0.162510 | ||||||||
\(739\) | −25.5997 | −0.941700 | −0.470850 | − | 0.882213i | \(-0.656053\pi\) | ||||
−0.470850 | + | 0.882213i | \(0.656053\pi\) | |||||||
\(740\) | −86.0681 | −3.16393 | ||||||||
\(741\) | 5.92937 | 0.217821 | ||||||||
\(742\) | −54.4647 | −1.99946 | ||||||||
\(743\) | 0.163146 | 0.00598523 | 0.00299262 | − | 0.999996i | \(-0.499047\pi\) | ||||
0.00299262 | + | 0.999996i | \(0.499047\pi\) | |||||||
\(744\) | 0.998637 | 0.0366118 | ||||||||
\(745\) | 25.7338 | 0.942812 | ||||||||
\(746\) | −56.8836 | −2.08266 | ||||||||
\(747\) | 15.8058 | 0.578305 | ||||||||
\(748\) | −17.5104 | −0.640244 | ||||||||
\(749\) | −18.5824 | −0.678985 | ||||||||
\(750\) | 24.9691 | 0.911742 | ||||||||
\(751\) | −15.6592 | −0.571412 | −0.285706 | − | 0.958317i | \(-0.592228\pi\) | ||||
−0.285706 | + | 0.958317i | \(0.592228\pi\) | |||||||
\(752\) | −98.6052 | −3.59576 | ||||||||
\(753\) | −15.4459 | −0.562879 | ||||||||
\(754\) | 2.64406 | 0.0962911 | ||||||||
\(755\) | −53.2279 | −1.93716 | ||||||||
\(756\) | 11.1540 | 0.405668 | ||||||||
\(757\) | 39.3740 | 1.43107 | 0.715536 | − | 0.698576i | \(-0.246182\pi\) | ||||
0.715536 | + | 0.698576i | \(0.246182\pi\) | |||||||
\(758\) | −94.1941 | −3.42129 | ||||||||
\(759\) | −27.6340 | −1.00305 | ||||||||
\(760\) | 169.525 | 6.14931 | ||||||||
\(761\) | −16.6844 | −0.604809 | −0.302405 | − | 0.953180i | \(-0.597789\pi\) | ||||
−0.302405 | + | 0.953180i | \(0.597789\pi\) | |||||||
\(762\) | −33.3411 | −1.20782 | ||||||||
\(763\) | −41.2940 | −1.49494 | ||||||||
\(764\) | −73.2399 | −2.64973 | ||||||||
\(765\) | −2.54502 | −0.0920155 | ||||||||
\(766\) | −34.7928 | −1.25711 | ||||||||
\(767\) | 4.79360 | 0.173087 | ||||||||
\(768\) | 4.69552 | 0.169435 | ||||||||
\(769\) | −22.4474 | −0.809473 | −0.404736 | − | 0.914433i | \(-0.632637\pi\) | ||||
−0.404736 | + | 0.914433i | \(0.632637\pi\) | |||||||
\(770\) | −48.9103 | −1.76261 | ||||||||
\(771\) | −0.0223687 | −0.000805589 0 | ||||||||
\(772\) | −134.468 | −4.83962 | ||||||||
\(773\) | 48.3274 | 1.73821 | 0.869107 | − | 0.494623i | \(-0.164694\pi\) | ||||
0.869107 | + | 0.494623i | \(0.164694\pi\) | |||||||
\(774\) | 23.4201 | 0.841817 | ||||||||
\(775\) | −0.151147 | −0.00542937 | ||||||||
\(776\) | 42.6349 | 1.53050 | ||||||||
\(777\) | −14.6419 | −0.525276 | ||||||||
\(778\) | −34.6035 | −1.24059 | ||||||||
\(779\) | 13.4708 | 0.482643 | ||||||||
\(780\) | −9.32784 | −0.333990 | ||||||||
\(781\) | 0.200840 | 0.00718663 | ||||||||
\(782\) | −22.3047 | −0.797614 | ||||||||
\(783\) | 1.36066 | 0.0486262 | ||||||||
\(784\) | −26.9575 | −0.962769 | ||||||||
\(785\) | −10.4886 | −0.374354 | ||||||||
\(786\) | 24.4196 | 0.871017 | ||||||||
\(787\) | 51.4259 | 1.83314 | 0.916568 | − | 0.399880i | \(-0.130948\pi\) | ||||
0.916568 | + | 0.399880i | \(0.130948\pi\) | |||||||
\(788\) | −121.904 | −4.34266 | ||||||||
\(789\) | −1.11182 | −0.0395818 | ||||||||
\(790\) | 26.9212 | 0.957815 | ||||||||
\(791\) | 1.15503 | 0.0410680 | ||||||||
\(792\) | −27.9856 | −0.994426 | ||||||||
\(793\) | 8.38991 | 0.297934 | ||||||||
\(794\) | −73.7378 | −2.61686 | ||||||||
\(795\) | 23.4393 | 0.831306 | ||||||||
\(796\) | −3.99560 | −0.141620 | ||||||||
\(797\) | −29.4307 | −1.04249 | −0.521245 | − | 0.853407i | \(-0.674532\pi\) | ||||
−0.521245 | + | 0.853407i | \(0.674532\pi\) | |||||||
\(798\) | 47.3313 | 1.67551 | ||||||||
\(799\) | 8.38122 | 0.296506 | ||||||||
\(800\) | −19.2559 | −0.680799 | ||||||||
\(801\) | −3.83206 | −0.135399 | ||||||||
\(802\) | −58.3657 | −2.06096 | ||||||||
\(803\) | 16.3980 | 0.578674 | ||||||||
\(804\) | 4.94244 | 0.174306 | ||||||||
\(805\) | −44.7992 | −1.57897 | ||||||||
\(806\) | −0.233170 | −0.00821307 | ||||||||
\(807\) | 14.1411 | 0.497792 | ||||||||
\(808\) | 12.9423 | 0.455307 | ||||||||
\(809\) | 12.6464 | 0.444625 | 0.222312 | − | 0.974976i | \(-0.428640\pi\) | ||||
0.222312 | + | 0.974976i | \(0.428640\pi\) | |||||||
\(810\) | −6.67559 | −0.234556 | ||||||||
\(811\) | −44.3397 | −1.55698 | −0.778489 | − | 0.627658i | \(-0.784014\pi\) | ||||
−0.778489 | + | 0.627658i | \(0.784014\pi\) | |||||||
\(812\) | 15.1769 | 0.532604 | ||||||||
\(813\) | 17.2975 | 0.606648 | ||||||||
\(814\) | 60.2922 | 2.11324 | ||||||||
\(815\) | 33.4719 | 1.17247 | ||||||||
\(816\) | −12.1738 | −0.426168 | ||||||||
\(817\) | 71.4621 | 2.50014 | ||||||||
\(818\) | −6.68949 | −0.233892 | ||||||||
\(819\) | −1.58685 | −0.0554492 | ||||||||
\(820\) | −21.1918 | −0.740049 | ||||||||
\(821\) | −25.3121 | −0.883399 | −0.441699 | − | 0.897163i | \(-0.645624\pi\) | ||||
−0.441699 | + | 0.897163i | \(0.645624\pi\) | |||||||
\(822\) | −15.2652 | −0.532435 | ||||||||
\(823\) | −56.6988 | −1.97639 | −0.988197 | − | 0.153185i | \(-0.951047\pi\) | ||||
−0.988197 | + | 0.153185i | \(0.951047\pi\) | |||||||
\(824\) | −61.6738 | −2.14851 | ||||||||
\(825\) | 4.23573 | 0.147469 | ||||||||
\(826\) | 38.2650 | 1.33141 | ||||||||
\(827\) | 17.3079 | 0.601856 | 0.300928 | − | 0.953647i | \(-0.402704\pi\) | ||||
0.300928 | + | 0.953647i | \(0.402704\pi\) | |||||||
\(828\) | −42.0693 | −1.46201 | ||||||||
\(829\) | 0.913024 | 0.0317106 | 0.0158553 | − | 0.999874i | \(-0.494953\pi\) | ||||
0.0158553 | + | 0.999874i | \(0.494953\pi\) | |||||||
\(830\) | −105.513 | −3.66242 | ||||||||
\(831\) | −26.8386 | −0.931020 | ||||||||
\(832\) | −12.2736 | −0.425510 | ||||||||
\(833\) | 2.29133 | 0.0793899 | ||||||||
\(834\) | −25.1823 | −0.871993 | ||||||||
\(835\) | 60.9216 | 2.10828 | ||||||||
\(836\) | −140.147 | −4.84707 | ||||||||
\(837\) | −0.119992 | −0.00414753 | ||||||||
\(838\) | −47.7810 | −1.65057 | ||||||||
\(839\) | 32.9728 | 1.13835 | 0.569173 | − | 0.822218i | \(-0.307263\pi\) | ||||
0.569173 | + | 0.822218i | \(0.307263\pi\) | |||||||
\(840\) | −45.3692 | −1.56539 | ||||||||
\(841\) | −27.1486 | −0.936158 | ||||||||
\(842\) | 96.9096 | 3.33972 | ||||||||
\(843\) | −3.89982 | −0.134317 | ||||||||
\(844\) | −89.4703 | −3.07969 | ||||||||
\(845\) | −31.1980 | −1.07324 | ||||||||
\(846\) | 21.9840 | 0.755824 | ||||||||
\(847\) | 0.669574 | 0.0230068 | ||||||||
\(848\) | 112.119 | 3.85017 | ||||||||
\(849\) | 2.85301 | 0.0979152 | ||||||||
\(850\) | 3.41885 | 0.117266 | ||||||||
\(851\) | 55.2245 | 1.89307 | ||||||||
\(852\) | 0.305754 | 0.0104749 | ||||||||
\(853\) | 6.78292 | 0.232243 | 0.116121 | − | 0.993235i | \(-0.462954\pi\) | ||||
0.116121 | + | 0.993235i | \(0.462954\pi\) | |||||||
\(854\) | 66.9726 | 2.29176 | ||||||||
\(855\) | −20.3694 | −0.696617 | ||||||||
\(856\) | 70.9783 | 2.42599 | ||||||||
\(857\) | −20.9229 | −0.714712 | −0.357356 | − | 0.933968i | \(-0.616322\pi\) | ||||
−0.357356 | + | 0.933968i | \(0.616322\pi\) | |||||||
\(858\) | 6.53432 | 0.223078 | ||||||||
\(859\) | −10.4406 | −0.356229 | −0.178115 | − | 0.984010i | \(-0.557000\pi\) | ||||
−0.178115 | + | 0.984010i | \(0.557000\pi\) | |||||||
\(860\) | −112.421 | −3.83353 | ||||||||
\(861\) | −3.60515 | −0.122863 | ||||||||
\(862\) | −54.0306 | −1.84029 | ||||||||
\(863\) | −6.60187 | −0.224730 | −0.112365 | − | 0.993667i | \(-0.535843\pi\) | ||||
−0.112365 | + | 0.993667i | \(0.535843\pi\) | |||||||
\(864\) | −15.2868 | −0.520066 | ||||||||
\(865\) | 26.7696 | 0.910193 | ||||||||
\(866\) | −42.2845 | −1.43689 | ||||||||
\(867\) | −15.9653 | −0.542208 | ||||||||
\(868\) | −1.33839 | −0.0454280 | ||||||||
\(869\) | −13.5608 | −0.460018 | ||||||||
\(870\) | −9.08324 | −0.307951 | ||||||||
\(871\) | −0.703148 | −0.0238253 | ||||||||
\(872\) | 157.729 | 5.34137 | ||||||||
\(873\) | −5.12282 | −0.173381 | ||||||||
\(874\) | −178.518 | −6.03846 | ||||||||
\(875\) | −20.3901 | −0.689310 | ||||||||
\(876\) | 24.9639 | 0.843453 | ||||||||
\(877\) | 13.9169 | 0.469940 | 0.234970 | − | 0.972003i | \(-0.424501\pi\) | ||||
0.234970 | + | 0.972003i | \(0.424501\pi\) | |||||||
\(878\) | −96.0573 | −3.24178 | ||||||||
\(879\) | −7.32108 | −0.246934 | ||||||||
\(880\) | 100.685 | 3.39408 | ||||||||
\(881\) | 9.87846 | 0.332814 | 0.166407 | − | 0.986057i | \(-0.446783\pi\) | ||||
0.166407 | + | 0.986057i | \(0.446783\pi\) | |||||||
\(882\) | 6.01016 | 0.202373 | ||||||||
\(883\) | 18.8888 | 0.635659 | 0.317829 | − | 0.948148i | \(-0.397046\pi\) | ||||
0.317829 | + | 0.948148i | \(0.397046\pi\) | |||||||
\(884\) | 3.79248 | 0.127555 | ||||||||
\(885\) | −16.4676 | −0.553553 | ||||||||
\(886\) | 80.7707 | 2.71354 | ||||||||
\(887\) | −23.2220 | −0.779719 | −0.389859 | − | 0.920874i | \(-0.627476\pi\) | ||||
−0.389859 | + | 0.920874i | \(0.627476\pi\) | |||||||
\(888\) | 55.9271 | 1.87679 | ||||||||
\(889\) | 27.2268 | 0.913156 | ||||||||
\(890\) | 25.5813 | 0.857486 | ||||||||
\(891\) | 3.36263 | 0.112652 | ||||||||
\(892\) | 121.840 | 4.07951 | ||||||||
\(893\) | 67.0800 | 2.24475 | ||||||||
\(894\) | −27.4437 | −0.917856 | ||||||||
\(895\) | 38.2004 | 1.27690 | ||||||||
\(896\) | −31.3584 | −1.04761 | ||||||||
\(897\) | 5.98509 | 0.199836 | ||||||||
\(898\) | −13.9144 | −0.464330 | ||||||||
\(899\) | −0.163269 | −0.00544532 | ||||||||
\(900\) | 6.44835 | 0.214945 | ||||||||
\(901\) | −9.52985 | −0.317485 | ||||||||
\(902\) | 14.8452 | 0.494292 | ||||||||
\(903\) | −19.1251 | −0.636444 | ||||||||
\(904\) | −4.41181 | −0.146735 | ||||||||
\(905\) | −14.8053 | −0.492146 | ||||||||
\(906\) | 56.7648 | 1.88588 | ||||||||
\(907\) | −29.1180 | −0.966848 | −0.483424 | − | 0.875386i | \(-0.660607\pi\) | ||||
−0.483424 | + | 0.875386i | \(0.660607\pi\) | |||||||
\(908\) | −15.1704 | −0.503447 | ||||||||
\(909\) | −1.55509 | −0.0515789 | ||||||||
\(910\) | 10.5932 | 0.351161 | ||||||||
\(911\) | −23.7607 | −0.787227 | −0.393613 | − | 0.919276i | \(-0.628775\pi\) | ||||
−0.393613 | + | 0.919276i | \(0.628775\pi\) | |||||||
\(912\) | −97.4342 | −3.22637 | ||||||||
\(913\) | 53.1492 | 1.75898 | ||||||||
\(914\) | 18.4061 | 0.608820 | ||||||||
\(915\) | −28.8221 | −0.952831 | ||||||||
\(916\) | 96.2340 | 3.17966 | ||||||||
\(917\) | −19.9413 | −0.658520 | ||||||||
\(918\) | 2.71414 | 0.0895798 | ||||||||
\(919\) | −36.7641 | −1.21274 | −0.606368 | − | 0.795184i | \(-0.707374\pi\) | ||||
−0.606368 | + | 0.795184i | \(0.707374\pi\) | |||||||
\(920\) | 171.118 | 5.64159 | ||||||||
\(921\) | −28.1823 | −0.928640 | ||||||||
\(922\) | −54.0967 | −1.78158 | ||||||||
\(923\) | −0.0434988 | −0.00143178 | ||||||||
\(924\) | 37.5069 | 1.23389 | ||||||||
\(925\) | −8.46477 | −0.278320 | ||||||||
\(926\) | 7.66174 | 0.251780 | ||||||||
\(927\) | 7.41047 | 0.243392 | ||||||||
\(928\) | −20.8002 | −0.682799 | ||||||||
\(929\) | −54.6011 | −1.79140 | −0.895701 | − | 0.444656i | \(-0.853326\pi\) | ||||
−0.895701 | + | 0.444656i | \(0.853326\pi\) | |||||||
\(930\) | 0.801017 | 0.0262664 | ||||||||
\(931\) | 18.3389 | 0.601033 | ||||||||
\(932\) | 57.8043 | 1.89344 | ||||||||
\(933\) | 2.09340 | 0.0685349 | ||||||||
\(934\) | −85.0778 | −2.78383 | ||||||||
\(935\) | −8.55797 | −0.279876 | ||||||||
\(936\) | 6.06124 | 0.198118 | ||||||||
\(937\) | −18.3872 | −0.600685 | −0.300343 | − | 0.953831i | \(-0.597101\pi\) | ||||
−0.300343 | + | 0.953831i | \(0.597101\pi\) | |||||||
\(938\) | −5.61289 | −0.183267 | ||||||||
\(939\) | −11.9799 | −0.390949 | ||||||||
\(940\) | −105.528 | −3.44193 | ||||||||
\(941\) | −32.5337 | −1.06057 | −0.530285 | − | 0.847820i | \(-0.677915\pi\) | ||||
−0.530285 | + | 0.847820i | \(0.677915\pi\) | |||||||
\(942\) | 11.1855 | 0.364445 | ||||||||
\(943\) | 13.5974 | 0.442793 | ||||||||
\(944\) | −78.7707 | −2.56377 | ||||||||
\(945\) | 5.45137 | 0.177333 | ||||||||
\(946\) | 78.7531 | 2.56048 | ||||||||
\(947\) | −46.7308 | −1.51855 | −0.759273 | − | 0.650772i | \(-0.774445\pi\) | ||||
−0.759273 | + | 0.650772i | \(0.774445\pi\) | |||||||
\(948\) | −20.6446 | −0.670504 | ||||||||
\(949\) | −3.55155 | −0.115288 | ||||||||
\(950\) | 27.3631 | 0.887777 | ||||||||
\(951\) | 22.1655 | 0.718766 | ||||||||
\(952\) | 18.4460 | 0.597840 | ||||||||
\(953\) | −10.0674 | −0.326114 | −0.163057 | − | 0.986617i | \(-0.552135\pi\) | ||||
−0.163057 | + | 0.986617i | \(0.552135\pi\) | |||||||
\(954\) | −24.9968 | −0.809301 | ||||||||
\(955\) | −35.7950 | −1.15830 | ||||||||
\(956\) | −82.6145 | −2.67194 | ||||||||
\(957\) | 4.57542 | 0.147902 | ||||||||
\(958\) | −96.1127 | −3.10526 | ||||||||
\(959\) | 12.4657 | 0.402540 | ||||||||
\(960\) | 42.1638 | 1.36083 | ||||||||
\(961\) | −30.9856 | −0.999536 | ||||||||
\(962\) | −13.0583 | −0.421018 | ||||||||
\(963\) | −8.52845 | −0.274825 | ||||||||
\(964\) | −77.4410 | −2.49421 | ||||||||
\(965\) | −65.7196 | −2.11559 | ||||||||
\(966\) | 47.7761 | 1.53717 | ||||||||
\(967\) | −2.61734 | −0.0841681 | −0.0420840 | − | 0.999114i | \(-0.513400\pi\) | ||||
−0.0420840 | + | 0.999114i | \(0.513400\pi\) | |||||||
\(968\) | −2.55754 | −0.0822026 | ||||||||
\(969\) | 8.28169 | 0.266046 | ||||||||
\(970\) | 34.1979 | 1.09803 | ||||||||
\(971\) | −33.5130 | −1.07548 | −0.537742 | − | 0.843109i | \(-0.680723\pi\) | ||||
−0.537742 | + | 0.843109i | \(0.680723\pi\) | |||||||
\(972\) | 5.11918 | 0.164198 | ||||||||
\(973\) | 20.5642 | 0.659258 | ||||||||
\(974\) | −9.65684 | −0.309425 | ||||||||
\(975\) | −0.917391 | −0.0293800 | ||||||||
\(976\) | −137.867 | −4.41301 | ||||||||
\(977\) | −9.85589 | −0.315318 | −0.157659 | − | 0.987494i | \(-0.550395\pi\) | ||||
−0.157659 | + | 0.987494i | \(0.550395\pi\) | |||||||
\(978\) | −35.6961 | −1.14144 | ||||||||
\(979\) | −12.8858 | −0.411832 | ||||||||
\(980\) | −28.8500 | −0.921581 | ||||||||
\(981\) | −18.9520 | −0.605092 | ||||||||
\(982\) | −12.3159 | −0.393016 | ||||||||
\(983\) | 11.8088 | 0.376641 | 0.188320 | − | 0.982108i | \(-0.439696\pi\) | ||||
0.188320 | + | 0.982108i | \(0.439696\pi\) | |||||||
\(984\) | 13.7704 | 0.438986 | ||||||||
\(985\) | −59.5790 | −1.89834 | ||||||||
\(986\) | 3.69303 | 0.117610 | ||||||||
\(987\) | −17.9524 | −0.571430 | ||||||||
\(988\) | 30.3535 | 0.965674 | ||||||||
\(989\) | 72.1337 | 2.29372 | ||||||||
\(990\) | −22.4476 | −0.713431 | ||||||||
\(991\) | 51.5702 | 1.63818 | 0.819091 | − | 0.573664i | \(-0.194478\pi\) | ||||
0.819091 | + | 0.573664i | \(0.194478\pi\) | |||||||
\(992\) | 1.83429 | 0.0582387 | ||||||||
\(993\) | 17.7872 | 0.564461 | ||||||||
\(994\) | −0.347230 | −0.0110135 | ||||||||
\(995\) | −1.95280 | −0.0619078 | ||||||||
\(996\) | 80.9128 | 2.56382 | ||||||||
\(997\) | 35.5520 | 1.12594 | 0.562972 | − | 0.826476i | \(-0.309658\pi\) | ||||
0.562972 | + | 0.826476i | \(0.309658\pi\) | |||||||
\(998\) | −85.8597 | −2.71784 | ||||||||
\(999\) | −6.71996 | −0.212610 |
(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 | 8031.2.a.a.1.3 | ✓ | 92 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8031.2.a.a.1.3 | ✓ | 92 | 1.1 | even | 1 | trivial |