Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8035,2,Mod(1,8035)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8035, 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("8035.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8035 = 5 \cdot 1607 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8035.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: | \(64.1597980241\) |
Analytic rank: | \(0\) |
Dimension: | \(127\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 8035.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.33324 | −1.64985 | −0.824925 | − | 0.565242i | \(-0.808783\pi\) | ||||
−0.824925 | + | 0.565242i | \(0.808783\pi\) | |||||||
\(3\) | −1.40461 | −0.810955 | −0.405477 | − | 0.914105i | \(-0.632895\pi\) | ||||
−0.405477 | + | 0.914105i | \(0.632895\pi\) | |||||||
\(4\) | 3.44401 | 1.72200 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 3.27730 | 1.33795 | ||||||||
\(7\) | −3.84799 | −1.45440 | −0.727202 | − | 0.686423i | \(-0.759180\pi\) | ||||
−0.727202 | + | 0.686423i | \(0.759180\pi\) | |||||||
\(8\) | −3.36922 | −1.19120 | ||||||||
\(9\) | −1.02706 | −0.342352 | ||||||||
\(10\) | 2.33324 | 0.737835 | ||||||||
\(11\) | 0.0531881 | 0.0160368 | 0.00801841 | − | 0.999968i | \(-0.497448\pi\) | ||||
0.00801841 | + | 0.999968i | \(0.497448\pi\) | |||||||
\(12\) | −4.83751 | −1.39647 | ||||||||
\(13\) | 4.09428 | 1.13555 | 0.567774 | − | 0.823184i | \(-0.307805\pi\) | ||||
0.567774 | + | 0.823184i | \(0.307805\pi\) | |||||||
\(14\) | 8.97829 | 2.39955 | ||||||||
\(15\) | 1.40461 | 0.362670 | ||||||||
\(16\) | 0.973182 | 0.243295 | ||||||||
\(17\) | 6.43239 | 1.56008 | 0.780042 | − | 0.625727i | \(-0.215198\pi\) | ||||
0.780042 | + | 0.625727i | \(0.215198\pi\) | |||||||
\(18\) | 2.39637 | 0.564830 | ||||||||
\(19\) | 3.86078 | 0.885723 | 0.442862 | − | 0.896590i | \(-0.353963\pi\) | ||||
0.442862 | + | 0.896590i | \(0.353963\pi\) | |||||||
\(20\) | −3.44401 | −0.770104 | ||||||||
\(21\) | 5.40495 | 1.17946 | ||||||||
\(22\) | −0.124101 | −0.0264584 | ||||||||
\(23\) | −1.52544 | −0.318076 | −0.159038 | − | 0.987272i | \(-0.550839\pi\) | ||||
−0.159038 | + | 0.987272i | \(0.550839\pi\) | |||||||
\(24\) | 4.73246 | 0.966009 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −9.55294 | −1.87348 | ||||||||
\(27\) | 5.65646 | 1.08859 | ||||||||
\(28\) | −13.2525 | −2.50449 | ||||||||
\(29\) | 0.386636 | 0.0717964 | 0.0358982 | − | 0.999355i | \(-0.488571\pi\) | ||||
0.0358982 | + | 0.999355i | \(0.488571\pi\) | |||||||
\(30\) | −3.27730 | −0.598351 | ||||||||
\(31\) | −5.73040 | −1.02921 | −0.514605 | − | 0.857427i | \(-0.672061\pi\) | ||||
−0.514605 | + | 0.857427i | \(0.672061\pi\) | |||||||
\(32\) | 4.46777 | 0.789798 | ||||||||
\(33\) | −0.0747088 | −0.0130051 | ||||||||
\(34\) | −15.0083 | −2.57390 | ||||||||
\(35\) | 3.84799 | 0.650430 | ||||||||
\(36\) | −3.53719 | −0.589532 | ||||||||
\(37\) | 7.40755 | 1.21779 | 0.608897 | − | 0.793249i | \(-0.291612\pi\) | ||||
0.608897 | + | 0.793249i | \(0.291612\pi\) | |||||||
\(38\) | −9.00812 | −1.46131 | ||||||||
\(39\) | −5.75089 | −0.920879 | ||||||||
\(40\) | 3.36922 | 0.532721 | ||||||||
\(41\) | 1.71601 | 0.267996 | 0.133998 | − | 0.990982i | \(-0.457218\pi\) | ||||
0.133998 | + | 0.990982i | \(0.457218\pi\) | |||||||
\(42\) | −12.6110 | −1.94593 | ||||||||
\(43\) | 8.69101 | 1.32537 | 0.662684 | − | 0.748900i | \(-0.269417\pi\) | ||||
0.662684 | + | 0.748900i | \(0.269417\pi\) | |||||||
\(44\) | 0.183180 | 0.0276155 | ||||||||
\(45\) | 1.02706 | 0.153105 | ||||||||
\(46\) | 3.55921 | 0.524778 | ||||||||
\(47\) | 3.60357 | 0.525635 | 0.262817 | − | 0.964846i | \(-0.415348\pi\) | ||||
0.262817 | + | 0.964846i | \(0.415348\pi\) | |||||||
\(48\) | −1.36695 | −0.197302 | ||||||||
\(49\) | 7.80706 | 1.11529 | ||||||||
\(50\) | −2.33324 | −0.329970 | ||||||||
\(51\) | −9.03503 | −1.26516 | ||||||||
\(52\) | 14.1007 | 1.95542 | ||||||||
\(53\) | 13.1394 | 1.80483 | 0.902415 | − | 0.430868i | \(-0.141793\pi\) | ||||
0.902415 | + | 0.430868i | \(0.141793\pi\) | |||||||
\(54\) | −13.1979 | −1.79601 | ||||||||
\(55\) | −0.0531881 | −0.00717189 | ||||||||
\(56\) | 12.9647 | 1.73249 | ||||||||
\(57\) | −5.42291 | −0.718281 | ||||||||
\(58\) | −0.902114 | −0.118453 | ||||||||
\(59\) | 5.87507 | 0.764869 | 0.382434 | − | 0.923983i | \(-0.375086\pi\) | ||||
0.382434 | + | 0.923983i | \(0.375086\pi\) | |||||||
\(60\) | 4.83751 | 0.624519 | ||||||||
\(61\) | 14.8116 | 1.89643 | 0.948213 | − | 0.317635i | \(-0.102889\pi\) | ||||
0.948213 | + | 0.317635i | \(0.102889\pi\) | |||||||
\(62\) | 13.3704 | 1.69804 | ||||||||
\(63\) | 3.95211 | 0.497919 | ||||||||
\(64\) | −12.3708 | −1.54634 | ||||||||
\(65\) | −4.09428 | −0.507833 | ||||||||
\(66\) | 0.174314 | 0.0214565 | ||||||||
\(67\) | −11.5574 | −1.41196 | −0.705978 | − | 0.708233i | \(-0.749492\pi\) | ||||
−0.705978 | + | 0.708233i | \(0.749492\pi\) | |||||||
\(68\) | 22.1532 | 2.68647 | ||||||||
\(69\) | 2.14265 | 0.257945 | ||||||||
\(70\) | −8.97829 | −1.07311 | ||||||||
\(71\) | −6.81391 | −0.808663 | −0.404331 | − | 0.914613i | \(-0.632496\pi\) | ||||
−0.404331 | + | 0.914613i | \(0.632496\pi\) | |||||||
\(72\) | 3.46038 | 0.407810 | ||||||||
\(73\) | 7.77783 | 0.910326 | 0.455163 | − | 0.890408i | \(-0.349581\pi\) | ||||
0.455163 | + | 0.890408i | \(0.349581\pi\) | |||||||
\(74\) | −17.2836 | −2.00918 | ||||||||
\(75\) | −1.40461 | −0.162191 | ||||||||
\(76\) | 13.2966 | 1.52522 | ||||||||
\(77\) | −0.204668 | −0.0233240 | ||||||||
\(78\) | 13.4182 | 1.51931 | ||||||||
\(79\) | 4.31554 | 0.485536 | 0.242768 | − | 0.970084i | \(-0.421945\pi\) | ||||
0.242768 | + | 0.970084i | \(0.421945\pi\) | |||||||
\(80\) | −0.973182 | −0.108805 | ||||||||
\(81\) | −4.86398 | −0.540442 | ||||||||
\(82\) | −4.00387 | −0.442153 | ||||||||
\(83\) | −7.65175 | −0.839889 | −0.419945 | − | 0.907550i | \(-0.637950\pi\) | ||||
−0.419945 | + | 0.907550i | \(0.637950\pi\) | |||||||
\(84\) | 18.6147 | 2.03103 | ||||||||
\(85\) | −6.43239 | −0.697691 | ||||||||
\(86\) | −20.2782 | −2.18666 | ||||||||
\(87\) | −0.543074 | −0.0582237 | ||||||||
\(88\) | −0.179203 | −0.0191031 | ||||||||
\(89\) | 9.33077 | 0.989059 | 0.494530 | − | 0.869161i | \(-0.335340\pi\) | ||||
0.494530 | + | 0.869161i | \(0.335340\pi\) | |||||||
\(90\) | −2.39637 | −0.252600 | ||||||||
\(91\) | −15.7548 | −1.65155 | ||||||||
\(92\) | −5.25363 | −0.547728 | ||||||||
\(93\) | 8.04900 | 0.834643 | ||||||||
\(94\) | −8.40800 | −0.867219 | ||||||||
\(95\) | −3.86078 | −0.396107 | ||||||||
\(96\) | −6.27550 | −0.640491 | ||||||||
\(97\) | −0.304722 | −0.0309398 | −0.0154699 | − | 0.999880i | \(-0.504924\pi\) | ||||
−0.0154699 | + | 0.999880i | \(0.504924\pi\) | |||||||
\(98\) | −18.2157 | −1.84007 | ||||||||
\(99\) | −0.0546273 | −0.00549025 | ||||||||
\(100\) | 3.44401 | 0.344401 | ||||||||
\(101\) | −16.0684 | −1.59887 | −0.799434 | − | 0.600754i | \(-0.794867\pi\) | ||||
−0.799434 | + | 0.600754i | \(0.794867\pi\) | |||||||
\(102\) | 21.0809 | 2.08732 | ||||||||
\(103\) | −3.48132 | −0.343024 | −0.171512 | − | 0.985182i | \(-0.554865\pi\) | ||||
−0.171512 | + | 0.985182i | \(0.554865\pi\) | |||||||
\(104\) | −13.7945 | −1.35266 | ||||||||
\(105\) | −5.40495 | −0.527469 | ||||||||
\(106\) | −30.6573 | −2.97770 | ||||||||
\(107\) | −10.6835 | −1.03281 | −0.516406 | − | 0.856344i | \(-0.672730\pi\) | ||||
−0.516406 | + | 0.856344i | \(0.672730\pi\) | |||||||
\(108\) | 19.4809 | 1.87455 | ||||||||
\(109\) | −1.66031 | −0.159029 | −0.0795143 | − | 0.996834i | \(-0.525337\pi\) | ||||
−0.0795143 | + | 0.996834i | \(0.525337\pi\) | |||||||
\(110\) | 0.124101 | 0.0118325 | ||||||||
\(111\) | −10.4048 | −0.987575 | ||||||||
\(112\) | −3.74480 | −0.353850 | ||||||||
\(113\) | 11.4399 | 1.07618 | 0.538089 | − | 0.842888i | \(-0.319146\pi\) | ||||
0.538089 | + | 0.842888i | \(0.319146\pi\) | |||||||
\(114\) | 12.6529 | 1.18506 | ||||||||
\(115\) | 1.52544 | 0.142248 | ||||||||
\(116\) | 1.33158 | 0.123634 | ||||||||
\(117\) | −4.20506 | −0.388758 | ||||||||
\(118\) | −13.7079 | −1.26192 | ||||||||
\(119\) | −24.7518 | −2.26899 | ||||||||
\(120\) | −4.73246 | −0.432012 | ||||||||
\(121\) | −10.9972 | −0.999743 | ||||||||
\(122\) | −34.5589 | −3.12882 | ||||||||
\(123\) | −2.41033 | −0.217333 | ||||||||
\(124\) | −19.7355 | −1.77230 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −9.22122 | −0.821492 | ||||||||
\(127\) | 4.87444 | 0.432536 | 0.216268 | − | 0.976334i | \(-0.430611\pi\) | ||||
0.216268 | + | 0.976334i | \(0.430611\pi\) | |||||||
\(128\) | 19.9284 | 1.76144 | ||||||||
\(129\) | −12.2075 | −1.07481 | ||||||||
\(130\) | 9.55294 | 0.837848 | ||||||||
\(131\) | 6.94772 | 0.607025 | 0.303513 | − | 0.952827i | \(-0.401841\pi\) | ||||
0.303513 | + | 0.952827i | \(0.401841\pi\) | |||||||
\(132\) | −0.257298 | −0.0223949 | ||||||||
\(133\) | −14.8562 | −1.28820 | ||||||||
\(134\) | 26.9661 | 2.32952 | ||||||||
\(135\) | −5.65646 | −0.486831 | ||||||||
\(136\) | −21.6721 | −1.85837 | ||||||||
\(137\) | 3.53942 | 0.302393 | 0.151196 | − | 0.988504i | \(-0.451687\pi\) | ||||
0.151196 | + | 0.988504i | \(0.451687\pi\) | |||||||
\(138\) | −4.99933 | −0.425571 | ||||||||
\(139\) | −5.60196 | −0.475152 | −0.237576 | − | 0.971369i | \(-0.576353\pi\) | ||||
−0.237576 | + | 0.971369i | \(0.576353\pi\) | |||||||
\(140\) | 13.2525 | 1.12004 | ||||||||
\(141\) | −5.06163 | −0.426266 | ||||||||
\(142\) | 15.8985 | 1.33417 | ||||||||
\(143\) | 0.217767 | 0.0182106 | ||||||||
\(144\) | −0.999514 | −0.0832928 | ||||||||
\(145\) | −0.386636 | −0.0321083 | ||||||||
\(146\) | −18.1475 | −1.50190 | ||||||||
\(147\) | −10.9659 | −0.904453 | ||||||||
\(148\) | 25.5117 | 2.09705 | ||||||||
\(149\) | −3.55897 | −0.291563 | −0.145781 | − | 0.989317i | \(-0.546570\pi\) | ||||
−0.145781 | + | 0.989317i | \(0.546570\pi\) | |||||||
\(150\) | 3.27730 | 0.267591 | ||||||||
\(151\) | 12.7853 | 1.04045 | 0.520227 | − | 0.854028i | \(-0.325847\pi\) | ||||
0.520227 | + | 0.854028i | \(0.325847\pi\) | |||||||
\(152\) | −13.0078 | −1.05507 | ||||||||
\(153\) | −6.60643 | −0.534099 | ||||||||
\(154\) | 0.477539 | 0.0384812 | ||||||||
\(155\) | 5.73040 | 0.460277 | ||||||||
\(156\) | −19.8061 | −1.58576 | ||||||||
\(157\) | 20.3533 | 1.62437 | 0.812186 | − | 0.583398i | \(-0.198277\pi\) | ||||
0.812186 | + | 0.583398i | \(0.198277\pi\) | |||||||
\(158\) | −10.0692 | −0.801062 | ||||||||
\(159\) | −18.4557 | −1.46364 | ||||||||
\(160\) | −4.46777 | −0.353209 | ||||||||
\(161\) | 5.86988 | 0.462611 | ||||||||
\(162\) | 11.3488 | 0.891649 | ||||||||
\(163\) | 8.28586 | 0.648999 | 0.324499 | − | 0.945886i | \(-0.394804\pi\) | ||||
0.324499 | + | 0.945886i | \(0.394804\pi\) | |||||||
\(164\) | 5.90996 | 0.461490 | ||||||||
\(165\) | 0.0747088 | 0.00581607 | ||||||||
\(166\) | 17.8534 | 1.38569 | ||||||||
\(167\) | 18.8878 | 1.46158 | 0.730791 | − | 0.682602i | \(-0.239152\pi\) | ||||
0.730791 | + | 0.682602i | \(0.239152\pi\) | |||||||
\(168\) | −18.2105 | −1.40497 | ||||||||
\(169\) | 3.76312 | 0.289471 | ||||||||
\(170\) | 15.0083 | 1.15109 | ||||||||
\(171\) | −3.96524 | −0.303229 | ||||||||
\(172\) | 29.9319 | 2.28229 | ||||||||
\(173\) | 13.1948 | 1.00318 | 0.501592 | − | 0.865104i | \(-0.332748\pi\) | ||||
0.501592 | + | 0.865104i | \(0.332748\pi\) | |||||||
\(174\) | 1.26712 | 0.0960603 | ||||||||
\(175\) | −3.84799 | −0.290881 | ||||||||
\(176\) | 0.0517617 | 0.00390169 | ||||||||
\(177\) | −8.25221 | −0.620274 | ||||||||
\(178\) | −21.7709 | −1.63180 | ||||||||
\(179\) | 7.98969 | 0.597178 | 0.298589 | − | 0.954382i | \(-0.403484\pi\) | ||||
0.298589 | + | 0.954382i | \(0.403484\pi\) | |||||||
\(180\) | 3.53719 | 0.263647 | ||||||||
\(181\) | 2.65337 | 0.197223 | 0.0986117 | − | 0.995126i | \(-0.468560\pi\) | ||||
0.0986117 | + | 0.995126i | \(0.468560\pi\) | |||||||
\(182\) | 36.7596 | 2.72481 | ||||||||
\(183\) | −20.8045 | −1.53792 | ||||||||
\(184\) | 5.13954 | 0.378892 | ||||||||
\(185\) | −7.40755 | −0.544614 | ||||||||
\(186\) | −18.7803 | −1.37704 | ||||||||
\(187\) | 0.342127 | 0.0250188 | ||||||||
\(188\) | 12.4107 | 0.905146 | ||||||||
\(189\) | −21.7660 | −1.58325 | ||||||||
\(190\) | 9.00812 | 0.653518 | ||||||||
\(191\) | −12.1539 | −0.879424 | −0.439712 | − | 0.898139i | \(-0.644919\pi\) | ||||
−0.439712 | + | 0.898139i | \(0.644919\pi\) | |||||||
\(192\) | 17.3761 | 1.25402 | ||||||||
\(193\) | −18.9896 | −1.36690 | −0.683452 | − | 0.729996i | \(-0.739522\pi\) | ||||
−0.683452 | + | 0.729996i | \(0.739522\pi\) | |||||||
\(194\) | 0.710989 | 0.0510461 | ||||||||
\(195\) | 5.75089 | 0.411829 | ||||||||
\(196\) | 26.8876 | 1.92054 | ||||||||
\(197\) | −8.51495 | −0.606665 | −0.303333 | − | 0.952885i | \(-0.598099\pi\) | ||||
−0.303333 | + | 0.952885i | \(0.598099\pi\) | |||||||
\(198\) | 0.127458 | 0.00905808 | ||||||||
\(199\) | 0.501648 | 0.0355609 | 0.0177804 | − | 0.999842i | \(-0.494340\pi\) | ||||
0.0177804 | + | 0.999842i | \(0.494340\pi\) | |||||||
\(200\) | −3.36922 | −0.238240 | ||||||||
\(201\) | 16.2336 | 1.14503 | ||||||||
\(202\) | 37.4915 | 2.63789 | ||||||||
\(203\) | −1.48777 | −0.104421 | ||||||||
\(204\) | −31.1167 | −2.17861 | ||||||||
\(205\) | −1.71601 | −0.119851 | ||||||||
\(206\) | 8.12274 | 0.565938 | ||||||||
\(207\) | 1.56671 | 0.108894 | ||||||||
\(208\) | 3.98448 | 0.276274 | ||||||||
\(209\) | 0.205348 | 0.0142042 | ||||||||
\(210\) | 12.6110 | 0.870245 | ||||||||
\(211\) | −24.1263 | −1.66092 | −0.830462 | − | 0.557075i | \(-0.811923\pi\) | ||||
−0.830462 | + | 0.557075i | \(0.811923\pi\) | |||||||
\(212\) | 45.2521 | 3.10793 | ||||||||
\(213\) | 9.57092 | 0.655789 | ||||||||
\(214\) | 24.9271 | 1.70398 | ||||||||
\(215\) | −8.69101 | −0.592722 | ||||||||
\(216\) | −19.0579 | −1.29672 | ||||||||
\(217\) | 22.0505 | 1.49689 | ||||||||
\(218\) | 3.87390 | 0.262373 | ||||||||
\(219\) | −10.9249 | −0.738233 | ||||||||
\(220\) | −0.183180 | −0.0123500 | ||||||||
\(221\) | 26.3360 | 1.77155 | ||||||||
\(222\) | 24.2768 | 1.62935 | ||||||||
\(223\) | −20.6011 | −1.37955 | −0.689775 | − | 0.724024i | \(-0.742291\pi\) | ||||
−0.689775 | + | 0.724024i | \(0.742291\pi\) | |||||||
\(224\) | −17.1920 | −1.14869 | ||||||||
\(225\) | −1.02706 | −0.0684705 | ||||||||
\(226\) | −26.6921 | −1.77553 | ||||||||
\(227\) | 15.1957 | 1.00857 | 0.504286 | − | 0.863536i | \(-0.331756\pi\) | ||||
0.504286 | + | 0.863536i | \(0.331756\pi\) | |||||||
\(228\) | −18.6765 | −1.23688 | ||||||||
\(229\) | −12.8564 | −0.849573 | −0.424786 | − | 0.905294i | \(-0.639651\pi\) | ||||
−0.424786 | + | 0.905294i | \(0.639651\pi\) | |||||||
\(230\) | −3.55921 | −0.234688 | ||||||||
\(231\) | 0.287479 | 0.0189147 | ||||||||
\(232\) | −1.30266 | −0.0855239 | ||||||||
\(233\) | 7.59265 | 0.497411 | 0.248706 | − | 0.968579i | \(-0.419995\pi\) | ||||
0.248706 | + | 0.968579i | \(0.419995\pi\) | |||||||
\(234\) | 9.81141 | 0.641392 | ||||||||
\(235\) | −3.60357 | −0.235071 | ||||||||
\(236\) | 20.2338 | 1.31711 | ||||||||
\(237\) | −6.06167 | −0.393748 | ||||||||
\(238\) | 57.7519 | 3.74350 | ||||||||
\(239\) | 4.62598 | 0.299230 | 0.149615 | − | 0.988744i | \(-0.452197\pi\) | ||||
0.149615 | + | 0.988744i | \(0.452197\pi\) | |||||||
\(240\) | 1.36695 | 0.0882360 | ||||||||
\(241\) | −15.9888 | −1.02993 | −0.514964 | − | 0.857212i | \(-0.672195\pi\) | ||||
−0.514964 | + | 0.857212i | \(0.672195\pi\) | |||||||
\(242\) | 25.6590 | 1.64943 | ||||||||
\(243\) | −10.1374 | −0.650313 | ||||||||
\(244\) | 51.0112 | 3.26566 | ||||||||
\(245\) | −7.80706 | −0.498775 | ||||||||
\(246\) | 5.62389 | 0.358566 | ||||||||
\(247\) | 15.8071 | 1.00578 | ||||||||
\(248\) | 19.3070 | 1.22599 | ||||||||
\(249\) | 10.7478 | 0.681112 | ||||||||
\(250\) | 2.33324 | 0.147567 | ||||||||
\(251\) | −0.581135 | −0.0366809 | −0.0183405 | − | 0.999832i | \(-0.505838\pi\) | ||||
−0.0183405 | + | 0.999832i | \(0.505838\pi\) | |||||||
\(252\) | 13.6111 | 0.857419 | ||||||||
\(253\) | −0.0811352 | −0.00510093 | ||||||||
\(254\) | −11.3732 | −0.713620 | ||||||||
\(255\) | 9.03503 | 0.565796 | ||||||||
\(256\) | −21.7562 | −1.35976 | ||||||||
\(257\) | 16.8480 | 1.05095 | 0.525474 | − | 0.850810i | \(-0.323888\pi\) | ||||
0.525474 | + | 0.850810i | \(0.323888\pi\) | |||||||
\(258\) | 28.4831 | 1.77328 | ||||||||
\(259\) | −28.5042 | −1.77116 | ||||||||
\(260\) | −14.1007 | −0.874491 | ||||||||
\(261\) | −0.397097 | −0.0245797 | ||||||||
\(262\) | −16.2107 | −1.00150 | ||||||||
\(263\) | −7.42969 | −0.458134 | −0.229067 | − | 0.973411i | \(-0.573568\pi\) | ||||
−0.229067 | + | 0.973411i | \(0.573568\pi\) | |||||||
\(264\) | 0.251711 | 0.0154917 | ||||||||
\(265\) | −13.1394 | −0.807144 | ||||||||
\(266\) | 34.6632 | 2.12534 | ||||||||
\(267\) | −13.1061 | −0.802082 | ||||||||
\(268\) | −39.8037 | −2.43140 | ||||||||
\(269\) | −7.18438 | −0.438040 | −0.219020 | − | 0.975720i | \(-0.570286\pi\) | ||||
−0.219020 | + | 0.975720i | \(0.570286\pi\) | |||||||
\(270\) | 13.1979 | 0.803198 | ||||||||
\(271\) | 12.1383 | 0.737348 | 0.368674 | − | 0.929559i | \(-0.379812\pi\) | ||||
0.368674 | + | 0.929559i | \(0.379812\pi\) | |||||||
\(272\) | 6.25989 | 0.379561 | ||||||||
\(273\) | 22.1294 | 1.33933 | ||||||||
\(274\) | −8.25831 | −0.498903 | ||||||||
\(275\) | 0.0531881 | 0.00320736 | ||||||||
\(276\) | 7.37932 | 0.444183 | ||||||||
\(277\) | −19.3545 | −1.16290 | −0.581449 | − | 0.813583i | \(-0.697514\pi\) | ||||
−0.581449 | + | 0.813583i | \(0.697514\pi\) | |||||||
\(278\) | 13.0707 | 0.783929 | ||||||||
\(279\) | 5.88545 | 0.352352 | ||||||||
\(280\) | −12.9647 | −0.774791 | ||||||||
\(281\) | 33.3153 | 1.98742 | 0.993711 | − | 0.111972i | \(-0.0357166\pi\) | ||||
0.993711 | + | 0.111972i | \(0.0357166\pi\) | |||||||
\(282\) | 11.8100 | 0.703275 | ||||||||
\(283\) | −9.55179 | −0.567795 | −0.283897 | − | 0.958855i | \(-0.591628\pi\) | ||||
−0.283897 | + | 0.958855i | \(0.591628\pi\) | |||||||
\(284\) | −23.4672 | −1.39252 | ||||||||
\(285\) | 5.42291 | 0.321225 | ||||||||
\(286\) | −0.508103 | −0.0300447 | ||||||||
\(287\) | −6.60320 | −0.389775 | ||||||||
\(288\) | −4.58866 | −0.270389 | ||||||||
\(289\) | 24.3757 | 1.43386 | ||||||||
\(290\) | 0.902114 | 0.0529739 | ||||||||
\(291\) | 0.428017 | 0.0250908 | ||||||||
\(292\) | 26.7869 | 1.56759 | ||||||||
\(293\) | −21.2837 | −1.24341 | −0.621703 | − | 0.783253i | \(-0.713559\pi\) | ||||
−0.621703 | + | 0.783253i | \(0.713559\pi\) | |||||||
\(294\) | 25.5861 | 1.49221 | ||||||||
\(295\) | −5.87507 | −0.342060 | ||||||||
\(296\) | −24.9577 | −1.45063 | ||||||||
\(297\) | 0.300857 | 0.0174575 | ||||||||
\(298\) | 8.30394 | 0.481034 | ||||||||
\(299\) | −6.24557 | −0.361191 | ||||||||
\(300\) | −4.83751 | −0.279294 | ||||||||
\(301\) | −33.4430 | −1.92762 | ||||||||
\(302\) | −29.8312 | −1.71659 | ||||||||
\(303\) | 22.5700 | 1.29661 | ||||||||
\(304\) | 3.75724 | 0.215492 | ||||||||
\(305\) | −14.8116 | −0.848108 | ||||||||
\(306\) | 15.4144 | 0.881182 | ||||||||
\(307\) | −25.7525 | −1.46977 | −0.734887 | − | 0.678190i | \(-0.762765\pi\) | ||||
−0.734887 | + | 0.678190i | \(0.762765\pi\) | |||||||
\(308\) | −0.704877 | −0.0401641 | ||||||||
\(309\) | 4.88991 | 0.278177 | ||||||||
\(310\) | −13.3704 | −0.759387 | ||||||||
\(311\) | 33.7565 | 1.91416 | 0.957079 | − | 0.289827i | \(-0.0935979\pi\) | ||||
0.957079 | + | 0.289827i | \(0.0935979\pi\) | |||||||
\(312\) | 19.3760 | 1.09695 | ||||||||
\(313\) | 14.3243 | 0.809658 | 0.404829 | − | 0.914392i | \(-0.367331\pi\) | ||||
0.404829 | + | 0.914392i | \(0.367331\pi\) | |||||||
\(314\) | −47.4892 | −2.67997 | ||||||||
\(315\) | −3.95211 | −0.222676 | ||||||||
\(316\) | 14.8628 | 0.836095 | ||||||||
\(317\) | 32.1227 | 1.80419 | 0.902095 | − | 0.431537i | \(-0.142029\pi\) | ||||
0.902095 | + | 0.431537i | \(0.142029\pi\) | |||||||
\(318\) | 43.0617 | 2.41478 | ||||||||
\(319\) | 0.0205644 | 0.00115139 | ||||||||
\(320\) | 12.3708 | 0.691546 | ||||||||
\(321\) | 15.0062 | 0.837564 | ||||||||
\(322\) | −13.6958 | −0.763239 | ||||||||
\(323\) | 24.8340 | 1.38180 | ||||||||
\(324\) | −16.7516 | −0.930644 | ||||||||
\(325\) | 4.09428 | 0.227110 | ||||||||
\(326\) | −19.3329 | −1.07075 | ||||||||
\(327\) | 2.33209 | 0.128965 | ||||||||
\(328\) | −5.78162 | −0.319237 | ||||||||
\(329\) | −13.8665 | −0.764486 | ||||||||
\(330\) | −0.174314 | −0.00959565 | ||||||||
\(331\) | −25.9993 | −1.42905 | −0.714525 | − | 0.699610i | \(-0.753357\pi\) | ||||
−0.714525 | + | 0.699610i | \(0.753357\pi\) | |||||||
\(332\) | −26.3527 | −1.44629 | ||||||||
\(333\) | −7.60798 | −0.416915 | ||||||||
\(334\) | −44.0698 | −2.41139 | ||||||||
\(335\) | 11.5574 | 0.631446 | ||||||||
\(336\) | 5.26000 | 0.286956 | ||||||||
\(337\) | −4.58480 | −0.249750 | −0.124875 | − | 0.992172i | \(-0.539853\pi\) | ||||
−0.124875 | + | 0.992172i | \(0.539853\pi\) | |||||||
\(338\) | −8.78027 | −0.477584 | ||||||||
\(339\) | −16.0687 | −0.872732 | ||||||||
\(340\) | −22.1532 | −1.20143 | ||||||||
\(341\) | −0.304789 | −0.0165053 | ||||||||
\(342\) | 9.25186 | 0.500283 | ||||||||
\(343\) | −3.10555 | −0.167684 | ||||||||
\(344\) | −29.2819 | −1.57878 | ||||||||
\(345\) | −2.14265 | −0.115357 | ||||||||
\(346\) | −30.7867 | −1.65510 | ||||||||
\(347\) | −15.5934 | −0.837096 | −0.418548 | − | 0.908195i | \(-0.637461\pi\) | ||||
−0.418548 | + | 0.908195i | \(0.637461\pi\) | |||||||
\(348\) | −1.87035 | −0.100261 | ||||||||
\(349\) | −35.0544 | −1.87642 | −0.938210 | − | 0.346067i | \(-0.887517\pi\) | ||||
−0.938210 | + | 0.346067i | \(0.887517\pi\) | |||||||
\(350\) | 8.97829 | 0.479910 | ||||||||
\(351\) | 23.1591 | 1.23614 | ||||||||
\(352\) | 0.237633 | 0.0126659 | ||||||||
\(353\) | −4.71655 | −0.251037 | −0.125518 | − | 0.992091i | \(-0.540059\pi\) | ||||
−0.125518 | + | 0.992091i | \(0.540059\pi\) | |||||||
\(354\) | 19.2544 | 1.02336 | ||||||||
\(355\) | 6.81391 | 0.361645 | ||||||||
\(356\) | 32.1352 | 1.70316 | ||||||||
\(357\) | 34.7667 | 1.84005 | ||||||||
\(358\) | −18.6419 | −0.985254 | ||||||||
\(359\) | −2.33013 | −0.122980 | −0.0614899 | − | 0.998108i | \(-0.519585\pi\) | ||||
−0.0614899 | + | 0.998108i | \(0.519585\pi\) | |||||||
\(360\) | −3.46038 | −0.182378 | ||||||||
\(361\) | −4.09440 | −0.215495 | ||||||||
\(362\) | −6.19095 | −0.325389 | ||||||||
\(363\) | 15.4468 | 0.810746 | ||||||||
\(364\) | −54.2595 | −2.84397 | ||||||||
\(365\) | −7.77783 | −0.407110 | ||||||||
\(366\) | 48.5420 | 2.53733 | ||||||||
\(367\) | 34.8477 | 1.81904 | 0.909518 | − | 0.415664i | \(-0.136451\pi\) | ||||
0.909518 | + | 0.415664i | \(0.136451\pi\) | |||||||
\(368\) | −1.48453 | −0.0773864 | ||||||||
\(369\) | −1.76244 | −0.0917490 | ||||||||
\(370\) | 17.2836 | 0.898531 | ||||||||
\(371\) | −50.5602 | −2.62495 | ||||||||
\(372\) | 27.7208 | 1.43726 | ||||||||
\(373\) | −7.35432 | −0.380792 | −0.190396 | − | 0.981707i | \(-0.560977\pi\) | ||||
−0.190396 | + | 0.981707i | \(0.560977\pi\) | |||||||
\(374\) | −0.798264 | −0.0412773 | ||||||||
\(375\) | 1.40461 | 0.0725340 | ||||||||
\(376\) | −12.1412 | −0.626136 | ||||||||
\(377\) | 1.58299 | 0.0815283 | ||||||||
\(378\) | 50.7854 | 2.61212 | ||||||||
\(379\) | 1.83124 | 0.0940644 | 0.0470322 | − | 0.998893i | \(-0.485024\pi\) | ||||
0.0470322 | + | 0.998893i | \(0.485024\pi\) | |||||||
\(380\) | −13.2966 | −0.682099 | ||||||||
\(381\) | −6.84670 | −0.350767 | ||||||||
\(382\) | 28.3579 | 1.45092 | ||||||||
\(383\) | −22.4259 | −1.14591 | −0.572954 | − | 0.819588i | \(-0.694203\pi\) | ||||
−0.572954 | + | 0.819588i | \(0.694203\pi\) | |||||||
\(384\) | −27.9917 | −1.42845 | ||||||||
\(385\) | 0.204668 | 0.0104308 | ||||||||
\(386\) | 44.3074 | 2.25519 | ||||||||
\(387\) | −8.92617 | −0.453743 | ||||||||
\(388\) | −1.04947 | −0.0532785 | ||||||||
\(389\) | 4.27589 | 0.216796 | 0.108398 | − | 0.994108i | \(-0.465428\pi\) | ||||
0.108398 | + | 0.994108i | \(0.465428\pi\) | |||||||
\(390\) | −13.4182 | −0.679457 | ||||||||
\(391\) | −9.81222 | −0.496225 | ||||||||
\(392\) | −26.3037 | −1.32854 | ||||||||
\(393\) | −9.75887 | −0.492270 | ||||||||
\(394\) | 19.8674 | 1.00091 | ||||||||
\(395\) | −4.31554 | −0.217138 | ||||||||
\(396\) | −0.188137 | −0.00945423 | ||||||||
\(397\) | 2.89010 | 0.145050 | 0.0725249 | − | 0.997367i | \(-0.476894\pi\) | ||||
0.0725249 | + | 0.997367i | \(0.476894\pi\) | |||||||
\(398\) | −1.17047 | −0.0586701 | ||||||||
\(399\) | 20.8673 | 1.04467 | ||||||||
\(400\) | 0.973182 | 0.0486591 | ||||||||
\(401\) | −6.62421 | −0.330797 | −0.165399 | − | 0.986227i | \(-0.552891\pi\) | ||||
−0.165399 | + | 0.986227i | \(0.552891\pi\) | |||||||
\(402\) | −37.8770 | −1.88913 | ||||||||
\(403\) | −23.4619 | −1.16872 | ||||||||
\(404\) | −55.3398 | −2.75326 | ||||||||
\(405\) | 4.86398 | 0.241693 | ||||||||
\(406\) | 3.47133 | 0.172279 | ||||||||
\(407\) | 0.393994 | 0.0195295 | ||||||||
\(408\) | 30.4410 | 1.50705 | ||||||||
\(409\) | −10.6685 | −0.527525 | −0.263763 | − | 0.964588i | \(-0.584964\pi\) | ||||
−0.263763 | + | 0.964588i | \(0.584964\pi\) | |||||||
\(410\) | 4.00387 | 0.197737 | ||||||||
\(411\) | −4.97152 | −0.245227 | ||||||||
\(412\) | −11.9897 | −0.590689 | ||||||||
\(413\) | −22.6072 | −1.11243 | ||||||||
\(414\) | −3.65552 | −0.179659 | ||||||||
\(415\) | 7.65175 | 0.375610 | ||||||||
\(416\) | 18.2923 | 0.896855 | ||||||||
\(417\) | 7.86859 | 0.385327 | ||||||||
\(418\) | −0.479125 | −0.0234348 | ||||||||
\(419\) | 9.04484 | 0.441869 | 0.220935 | − | 0.975289i | \(-0.429089\pi\) | ||||
0.220935 | + | 0.975289i | \(0.429089\pi\) | |||||||
\(420\) | −18.6147 | −0.908304 | ||||||||
\(421\) | −6.50841 | −0.317201 | −0.158600 | − | 0.987343i | \(-0.550698\pi\) | ||||
−0.158600 | + | 0.987343i | \(0.550698\pi\) | |||||||
\(422\) | 56.2925 | 2.74028 | ||||||||
\(423\) | −3.70107 | −0.179952 | ||||||||
\(424\) | −44.2694 | −2.14991 | ||||||||
\(425\) | 6.43239 | 0.312017 | ||||||||
\(426\) | −22.3313 | −1.08195 | ||||||||
\(427\) | −56.9948 | −2.75817 | ||||||||
\(428\) | −36.7940 | −1.77851 | ||||||||
\(429\) | −0.305879 | −0.0147680 | ||||||||
\(430\) | 20.2782 | 0.977903 | ||||||||
\(431\) | 6.92237 | 0.333439 | 0.166720 | − | 0.986004i | \(-0.446683\pi\) | ||||
0.166720 | + | 0.986004i | \(0.446683\pi\) | |||||||
\(432\) | 5.50477 | 0.264848 | ||||||||
\(433\) | −23.2515 | −1.11739 | −0.558697 | − | 0.829372i | \(-0.688698\pi\) | ||||
−0.558697 | + | 0.829372i | \(0.688698\pi\) | |||||||
\(434\) | −51.4492 | −2.46964 | ||||||||
\(435\) | 0.543074 | 0.0260384 | ||||||||
\(436\) | −5.71812 | −0.273848 | ||||||||
\(437\) | −5.88938 | −0.281727 | ||||||||
\(438\) | 25.4903 | 1.21797 | ||||||||
\(439\) | 25.8361 | 1.23309 | 0.616545 | − | 0.787319i | \(-0.288532\pi\) | ||||
0.616545 | + | 0.787319i | \(0.288532\pi\) | |||||||
\(440\) | 0.179203 | 0.00854315 | ||||||||
\(441\) | −8.01829 | −0.381824 | ||||||||
\(442\) | −61.4482 | −2.92279 | ||||||||
\(443\) | −0.285867 | −0.0135820 | −0.00679098 | − | 0.999977i | \(-0.502162\pi\) | ||||
−0.00679098 | + | 0.999977i | \(0.502162\pi\) | |||||||
\(444\) | −35.8341 | −1.70061 | ||||||||
\(445\) | −9.33077 | −0.442321 | ||||||||
\(446\) | 48.0673 | 2.27605 | ||||||||
\(447\) | 4.99899 | 0.236444 | ||||||||
\(448\) | 47.6026 | 2.24901 | ||||||||
\(449\) | −12.7000 | −0.599348 | −0.299674 | − | 0.954042i | \(-0.596878\pi\) | ||||
−0.299674 | + | 0.954042i | \(0.596878\pi\) | |||||||
\(450\) | 2.39637 | 0.112966 | ||||||||
\(451\) | 0.0912714 | 0.00429780 | ||||||||
\(452\) | 39.3993 | 1.85318 | ||||||||
\(453\) | −17.9584 | −0.843761 | ||||||||
\(454\) | −35.4552 | −1.66399 | ||||||||
\(455\) | 15.7548 | 0.738595 | ||||||||
\(456\) | 18.2710 | 0.855616 | ||||||||
\(457\) | 34.5110 | 1.61436 | 0.807178 | − | 0.590307i | \(-0.200994\pi\) | ||||
0.807178 | + | 0.590307i | \(0.200994\pi\) | |||||||
\(458\) | 29.9970 | 1.40167 | ||||||||
\(459\) | 36.3846 | 1.69829 | ||||||||
\(460\) | 5.25363 | 0.244952 | ||||||||
\(461\) | −1.31095 | −0.0610571 | −0.0305285 | − | 0.999534i | \(-0.509719\pi\) | ||||
−0.0305285 | + | 0.999534i | \(0.509719\pi\) | |||||||
\(462\) | −0.670758 | −0.0312065 | ||||||||
\(463\) | 8.97271 | 0.416997 | 0.208499 | − | 0.978023i | \(-0.433142\pi\) | ||||
0.208499 | + | 0.978023i | \(0.433142\pi\) | |||||||
\(464\) | 0.376267 | 0.0174677 | ||||||||
\(465\) | −8.04900 | −0.373264 | ||||||||
\(466\) | −17.7155 | −0.820654 | ||||||||
\(467\) | 31.5143 | 1.45831 | 0.729154 | − | 0.684350i | \(-0.239914\pi\) | ||||
0.729154 | + | 0.684350i | \(0.239914\pi\) | |||||||
\(468\) | −14.4823 | −0.669443 | ||||||||
\(469\) | 44.4727 | 2.05356 | ||||||||
\(470\) | 8.40800 | 0.387832 | ||||||||
\(471\) | −28.5886 | −1.31729 | ||||||||
\(472\) | −19.7944 | −0.911111 | ||||||||
\(473\) | 0.462259 | 0.0212547 | ||||||||
\(474\) | 14.1433 | 0.649625 | ||||||||
\(475\) | 3.86078 | 0.177145 | ||||||||
\(476\) | −85.2454 | −3.90722 | ||||||||
\(477\) | −13.4949 | −0.617888 | ||||||||
\(478\) | −10.7935 | −0.493684 | ||||||||
\(479\) | 23.6211 | 1.07927 | 0.539637 | − | 0.841898i | \(-0.318561\pi\) | ||||
0.539637 | + | 0.841898i | \(0.318561\pi\) | |||||||
\(480\) | 6.27550 | 0.286436 | ||||||||
\(481\) | 30.3286 | 1.38286 | ||||||||
\(482\) | 37.3057 | 1.69923 | ||||||||
\(483\) | −8.24492 | −0.375157 | ||||||||
\(484\) | −37.8744 | −1.72156 | ||||||||
\(485\) | 0.304722 | 0.0138367 | ||||||||
\(486\) | 23.6529 | 1.07292 | ||||||||
\(487\) | 38.7504 | 1.75595 | 0.877975 | − | 0.478707i | \(-0.158894\pi\) | ||||
0.877975 | + | 0.478707i | \(0.158894\pi\) | |||||||
\(488\) | −49.9034 | −2.25902 | ||||||||
\(489\) | −11.6384 | −0.526308 | ||||||||
\(490\) | 18.2157 | 0.822903 | ||||||||
\(491\) | 13.3406 | 0.602055 | 0.301027 | − | 0.953615i | \(-0.402670\pi\) | ||||
0.301027 | + | 0.953615i | \(0.402670\pi\) | |||||||
\(492\) | −8.30121 | −0.374248 | ||||||||
\(493\) | 2.48699 | 0.112008 | ||||||||
\(494\) | −36.8818 | −1.65939 | ||||||||
\(495\) | 0.0546273 | 0.00245531 | ||||||||
\(496\) | −5.57672 | −0.250402 | ||||||||
\(497\) | 26.2199 | 1.17612 | ||||||||
\(498\) | −25.0771 | −1.12373 | ||||||||
\(499\) | −9.83177 | −0.440130 | −0.220065 | − | 0.975485i | \(-0.570627\pi\) | ||||
−0.220065 | + | 0.975485i | \(0.570627\pi\) | |||||||
\(500\) | −3.44401 | −0.154021 | ||||||||
\(501\) | −26.5301 | −1.18528 | ||||||||
\(502\) | 1.35593 | 0.0605180 | ||||||||
\(503\) | −22.0632 | −0.983748 | −0.491874 | − | 0.870666i | \(-0.663688\pi\) | ||||
−0.491874 | + | 0.870666i | \(0.663688\pi\) | |||||||
\(504\) | −13.3155 | −0.593121 | ||||||||
\(505\) | 16.0684 | 0.715036 | ||||||||
\(506\) | 0.189308 | 0.00841577 | ||||||||
\(507\) | −5.28574 | −0.234748 | ||||||||
\(508\) | 16.7876 | 0.744829 | ||||||||
\(509\) | 31.2126 | 1.38348 | 0.691738 | − | 0.722149i | \(-0.256845\pi\) | ||||
0.691738 | + | 0.722149i | \(0.256845\pi\) | |||||||
\(510\) | −21.0809 | −0.933478 | ||||||||
\(511\) | −29.9290 | −1.32398 | ||||||||
\(512\) | 10.9057 | 0.481968 | ||||||||
\(513\) | 21.8384 | 0.964187 | ||||||||
\(514\) | −39.3104 | −1.73391 | ||||||||
\(515\) | 3.48132 | 0.153405 | ||||||||
\(516\) | −42.0428 | −1.85083 | ||||||||
\(517\) | 0.191667 | 0.00842951 | ||||||||
\(518\) | 66.5071 | 2.92216 | ||||||||
\(519\) | −18.5336 | −0.813536 | ||||||||
\(520\) | 13.7945 | 0.604930 | ||||||||
\(521\) | 27.4114 | 1.20091 | 0.600457 | − | 0.799657i | \(-0.294986\pi\) | ||||
0.600457 | + | 0.799657i | \(0.294986\pi\) | |||||||
\(522\) | 0.926522 | 0.0405528 | ||||||||
\(523\) | −17.2473 | −0.754173 | −0.377086 | − | 0.926178i | \(-0.623074\pi\) | ||||
−0.377086 | + | 0.926178i | \(0.623074\pi\) | |||||||
\(524\) | 23.9280 | 1.04530 | ||||||||
\(525\) | 5.40495 | 0.235891 | ||||||||
\(526\) | 17.3353 | 0.755853 | ||||||||
\(527\) | −36.8602 | −1.60565 | ||||||||
\(528\) | −0.0727053 | −0.00316409 | ||||||||
\(529\) | −20.6730 | −0.898828 | ||||||||
\(530\) | 30.6573 | 1.33167 | ||||||||
\(531\) | −6.03403 | −0.261855 | ||||||||
\(532\) | −51.1651 | −2.21829 | ||||||||
\(533\) | 7.02583 | 0.304322 | ||||||||
\(534\) | 30.5798 | 1.32332 | ||||||||
\(535\) | 10.6835 | 0.461888 | ||||||||
\(536\) | 38.9393 | 1.68192 | ||||||||
\(537\) | −11.2224 | −0.484284 | ||||||||
\(538\) | 16.7629 | 0.722700 | ||||||||
\(539\) | 0.415243 | 0.0178858 | ||||||||
\(540\) | −19.4809 | −0.838325 | ||||||||
\(541\) | −7.60227 | −0.326847 | −0.163424 | − | 0.986556i | \(-0.552254\pi\) | ||||
−0.163424 | + | 0.986556i | \(0.552254\pi\) | |||||||
\(542\) | −28.3215 | −1.21651 | ||||||||
\(543\) | −3.72696 | −0.159939 | ||||||||
\(544\) | 28.7385 | 1.23215 | ||||||||
\(545\) | 1.66031 | 0.0711198 | ||||||||
\(546\) | −51.6331 | −2.20969 | ||||||||
\(547\) | 12.1411 | 0.519115 | 0.259558 | − | 0.965728i | \(-0.416423\pi\) | ||||
0.259558 | + | 0.965728i | \(0.416423\pi\) | |||||||
\(548\) | 12.1898 | 0.520722 | ||||||||
\(549\) | −15.2123 | −0.649246 | ||||||||
\(550\) | −0.124101 | −0.00529167 | ||||||||
\(551\) | 1.49271 | 0.0635918 | ||||||||
\(552\) | −7.21907 | −0.307264 | ||||||||
\(553\) | −16.6062 | −0.706166 | ||||||||
\(554\) | 45.1587 | 1.91861 | ||||||||
\(555\) | 10.4048 | 0.441657 | ||||||||
\(556\) | −19.2932 | −0.818214 | ||||||||
\(557\) | −22.6142 | −0.958196 | −0.479098 | − | 0.877761i | \(-0.659036\pi\) | ||||
−0.479098 | + | 0.877761i | \(0.659036\pi\) | |||||||
\(558\) | −13.7322 | −0.581329 | ||||||||
\(559\) | 35.5834 | 1.50502 | ||||||||
\(560\) | 3.74480 | 0.158247 | ||||||||
\(561\) | −0.480556 | −0.0202891 | ||||||||
\(562\) | −77.7325 | −3.27895 | ||||||||
\(563\) | 41.2958 | 1.74041 | 0.870206 | − | 0.492689i | \(-0.163986\pi\) | ||||
0.870206 | + | 0.492689i | \(0.163986\pi\) | |||||||
\(564\) | −17.4323 | −0.734032 | ||||||||
\(565\) | −11.4399 | −0.481282 | ||||||||
\(566\) | 22.2866 | 0.936776 | ||||||||
\(567\) | 18.7166 | 0.786022 | ||||||||
\(568\) | 22.9576 | 0.963278 | ||||||||
\(569\) | −18.1614 | −0.761365 | −0.380683 | − | 0.924706i | \(-0.624311\pi\) | ||||
−0.380683 | + | 0.924706i | \(0.624311\pi\) | |||||||
\(570\) | −12.6529 | −0.529973 | ||||||||
\(571\) | 36.1298 | 1.51198 | 0.755992 | − | 0.654581i | \(-0.227155\pi\) | ||||
0.755992 | + | 0.654581i | \(0.227155\pi\) | |||||||
\(572\) | 0.749992 | 0.0313587 | ||||||||
\(573\) | 17.0715 | 0.713173 | ||||||||
\(574\) | 15.4068 | 0.643069 | ||||||||
\(575\) | −1.52544 | −0.0636152 | ||||||||
\(576\) | 12.7055 | 0.529395 | ||||||||
\(577\) | 10.0358 | 0.417794 | 0.208897 | − | 0.977938i | \(-0.433013\pi\) | ||||
0.208897 | + | 0.977938i | \(0.433013\pi\) | |||||||
\(578\) | −56.8743 | −2.36566 | ||||||||
\(579\) | 26.6731 | 1.10850 | ||||||||
\(580\) | −1.33158 | −0.0552907 | ||||||||
\(581\) | 29.4439 | 1.22154 | ||||||||
\(582\) | −0.998666 | −0.0413961 | ||||||||
\(583\) | 0.698858 | 0.0289437 | ||||||||
\(584\) | −26.2052 | −1.08438 | ||||||||
\(585\) | 4.20506 | 0.173858 | ||||||||
\(586\) | 49.6599 | 2.05143 | ||||||||
\(587\) | −22.2221 | −0.917206 | −0.458603 | − | 0.888641i | \(-0.651650\pi\) | ||||
−0.458603 | + | 0.888641i | \(0.651650\pi\) | |||||||
\(588\) | −37.7667 | −1.55747 | ||||||||
\(589\) | −22.1238 | −0.911595 | ||||||||
\(590\) | 13.7079 | 0.564347 | ||||||||
\(591\) | 11.9602 | 0.491978 | ||||||||
\(592\) | 7.20889 | 0.296284 | ||||||||
\(593\) | 20.6748 | 0.849013 | 0.424507 | − | 0.905425i | \(-0.360448\pi\) | ||||
0.424507 | + | 0.905425i | \(0.360448\pi\) | |||||||
\(594\) | −0.701971 | −0.0288022 | ||||||||
\(595\) | 24.7518 | 1.01472 | ||||||||
\(596\) | −12.2571 | −0.502072 | ||||||||
\(597\) | −0.704622 | −0.0288383 | ||||||||
\(598\) | 14.5724 | 0.595911 | ||||||||
\(599\) | 20.2471 | 0.827275 | 0.413638 | − | 0.910442i | \(-0.364258\pi\) | ||||
0.413638 | + | 0.910442i | \(0.364258\pi\) | |||||||
\(600\) | 4.73246 | 0.193202 | ||||||||
\(601\) | 10.9073 | 0.444917 | 0.222458 | − | 0.974942i | \(-0.428592\pi\) | ||||
0.222458 | + | 0.974942i | \(0.428592\pi\) | |||||||
\(602\) | 78.0305 | 3.18028 | ||||||||
\(603\) | 11.8701 | 0.483387 | ||||||||
\(604\) | 44.0327 | 1.79167 | ||||||||
\(605\) | 10.9972 | 0.447099 | ||||||||
\(606\) | −52.6611 | −2.13921 | ||||||||
\(607\) | −1.26576 | −0.0513755 | −0.0256877 | − | 0.999670i | \(-0.508178\pi\) | ||||
−0.0256877 | + | 0.999670i | \(0.508178\pi\) | |||||||
\(608\) | 17.2491 | 0.699543 | ||||||||
\(609\) | 2.08975 | 0.0846808 | ||||||||
\(610\) | 34.5589 | 1.39925 | ||||||||
\(611\) | 14.7540 | 0.596884 | ||||||||
\(612\) | −22.7526 | −0.919720 | ||||||||
\(613\) | 8.15339 | 0.329312 | 0.164656 | − | 0.986351i | \(-0.447349\pi\) | ||||
0.164656 | + | 0.986351i | \(0.447349\pi\) | |||||||
\(614\) | 60.0868 | 2.42491 | ||||||||
\(615\) | 2.41033 | 0.0971941 | ||||||||
\(616\) | 0.689570 | 0.0277836 | ||||||||
\(617\) | 6.83241 | 0.275063 | 0.137531 | − | 0.990497i | \(-0.456083\pi\) | ||||
0.137531 | + | 0.990497i | \(0.456083\pi\) | |||||||
\(618\) | −11.4093 | −0.458950 | ||||||||
\(619\) | −18.0731 | −0.726419 | −0.363209 | − | 0.931708i | \(-0.618319\pi\) | ||||
−0.363209 | + | 0.931708i | \(0.618319\pi\) | |||||||
\(620\) | 19.7355 | 0.792599 | ||||||||
\(621\) | −8.62859 | −0.346253 | ||||||||
\(622\) | −78.7621 | −3.15807 | ||||||||
\(623\) | −35.9047 | −1.43849 | ||||||||
\(624\) | −5.59666 | −0.224046 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −33.4221 | −1.33581 | ||||||||
\(627\) | −0.288434 | −0.0115190 | ||||||||
\(628\) | 70.0971 | 2.79718 | ||||||||
\(629\) | 47.6482 | 1.89986 | ||||||||
\(630\) | 9.22122 | 0.367382 | ||||||||
\(631\) | −34.8105 | −1.38579 | −0.692893 | − | 0.721041i | \(-0.743664\pi\) | ||||
−0.692893 | + | 0.721041i | \(0.743664\pi\) | |||||||
\(632\) | −14.5400 | −0.578370 | ||||||||
\(633\) | 33.8882 | 1.34693 | ||||||||
\(634\) | −74.9500 | −2.97664 | ||||||||
\(635\) | −4.87444 | −0.193436 | ||||||||
\(636\) | −63.5617 | −2.52039 | ||||||||
\(637\) | 31.9643 | 1.26647 | ||||||||
\(638\) | −0.0479817 | −0.00189962 | ||||||||
\(639\) | 6.99828 | 0.276848 | ||||||||
\(640\) | −19.9284 | −0.787739 | ||||||||
\(641\) | −12.3625 | −0.488289 | −0.244144 | − | 0.969739i | \(-0.578507\pi\) | ||||
−0.244144 | + | 0.969739i | \(0.578507\pi\) | |||||||
\(642\) | −35.0130 | −1.38185 | ||||||||
\(643\) | −24.1796 | −0.953550 | −0.476775 | − | 0.879025i | \(-0.658194\pi\) | ||||
−0.476775 | + | 0.879025i | \(0.658194\pi\) | |||||||
\(644\) | 20.2159 | 0.796619 | ||||||||
\(645\) | 12.2075 | 0.480671 | ||||||||
\(646\) | −57.9438 | −2.27977 | ||||||||
\(647\) | −8.62444 | −0.339062 | −0.169531 | − | 0.985525i | \(-0.554225\pi\) | ||||
−0.169531 | + | 0.985525i | \(0.554225\pi\) | |||||||
\(648\) | 16.3878 | 0.643775 | ||||||||
\(649\) | 0.312484 | 0.0122661 | ||||||||
\(650\) | −9.55294 | −0.374697 | ||||||||
\(651\) | −30.9725 | −1.21391 | ||||||||
\(652\) | 28.5366 | 1.11758 | ||||||||
\(653\) | −29.4156 | −1.15112 | −0.575561 | − | 0.817759i | \(-0.695216\pi\) | ||||
−0.575561 | + | 0.817759i | \(0.695216\pi\) | |||||||
\(654\) | −5.44133 | −0.212773 | ||||||||
\(655\) | −6.94772 | −0.271470 | ||||||||
\(656\) | 1.66999 | 0.0652022 | ||||||||
\(657\) | −7.98827 | −0.311652 | ||||||||
\(658\) | 32.3539 | 1.26129 | ||||||||
\(659\) | −20.7071 | −0.806634 | −0.403317 | − | 0.915060i | \(-0.632143\pi\) | ||||
−0.403317 | + | 0.915060i | \(0.632143\pi\) | |||||||
\(660\) | 0.257298 | 0.0100153 | ||||||||
\(661\) | 27.3892 | 1.06532 | 0.532658 | − | 0.846331i | \(-0.321193\pi\) | ||||
0.532658 | + | 0.846331i | \(0.321193\pi\) | |||||||
\(662\) | 60.6625 | 2.35772 | ||||||||
\(663\) | −36.9919 | −1.43665 | ||||||||
\(664\) | 25.7804 | 1.00048 | ||||||||
\(665\) | 14.8562 | 0.576101 | ||||||||
\(666\) | 17.7512 | 0.687846 | ||||||||
\(667\) | −0.589789 | −0.0228367 | ||||||||
\(668\) | 65.0497 | 2.51685 | ||||||||
\(669\) | 28.9366 | 1.11875 | ||||||||
\(670\) | −26.9661 | −1.04179 | ||||||||
\(671\) | 0.787799 | 0.0304127 | ||||||||
\(672\) | 24.1481 | 0.931533 | ||||||||
\(673\) | −31.3578 | −1.20875 | −0.604377 | − | 0.796698i | \(-0.706578\pi\) | ||||
−0.604377 | + | 0.796698i | \(0.706578\pi\) | |||||||
\(674\) | 10.6974 | 0.412050 | ||||||||
\(675\) | 5.65646 | 0.217717 | ||||||||
\(676\) | 12.9602 | 0.498470 | ||||||||
\(677\) | −48.4275 | −1.86122 | −0.930611 | − | 0.366011i | \(-0.880723\pi\) | ||||
−0.930611 | + | 0.366011i | \(0.880723\pi\) | |||||||
\(678\) | 37.4921 | 1.43988 | ||||||||
\(679\) | 1.17257 | 0.0449990 | ||||||||
\(680\) | 21.6721 | 0.831089 | ||||||||
\(681\) | −21.3441 | −0.817907 | ||||||||
\(682\) | 0.711146 | 0.0272312 | ||||||||
\(683\) | 0.565404 | 0.0216346 | 0.0108173 | − | 0.999941i | \(-0.496557\pi\) | ||||
0.0108173 | + | 0.999941i | \(0.496557\pi\) | |||||||
\(684\) | −13.6563 | −0.522163 | ||||||||
\(685\) | −3.53942 | −0.135234 | ||||||||
\(686\) | 7.24599 | 0.276653 | ||||||||
\(687\) | 18.0582 | 0.688965 | ||||||||
\(688\) | 8.45794 | 0.322456 | ||||||||
\(689\) | 53.7962 | 2.04947 | ||||||||
\(690\) | 4.99933 | 0.190321 | ||||||||
\(691\) | 21.7559 | 0.827634 | 0.413817 | − | 0.910360i | \(-0.364195\pi\) | ||||
0.413817 | + | 0.910360i | \(0.364195\pi\) | |||||||
\(692\) | 45.4431 | 1.72749 | ||||||||
\(693\) | 0.210205 | 0.00798504 | ||||||||
\(694\) | 36.3831 | 1.38108 | ||||||||
\(695\) | 5.60196 | 0.212494 | ||||||||
\(696\) | 1.82974 | 0.0693560 | ||||||||
\(697\) | 11.0381 | 0.418096 | ||||||||
\(698\) | 81.7904 | 3.09581 | ||||||||
\(699\) | −10.6647 | −0.403378 | ||||||||
\(700\) | −13.2525 | −0.500898 | ||||||||
\(701\) | 3.07596 | 0.116177 | 0.0580887 | − | 0.998311i | \(-0.481499\pi\) | ||||
0.0580887 | + | 0.998311i | \(0.481499\pi\) | |||||||
\(702\) | −54.0358 | −2.03945 | ||||||||
\(703\) | 28.5989 | 1.07863 | ||||||||
\(704\) | −0.657977 | −0.0247984 | ||||||||
\(705\) | 5.06163 | 0.190632 | ||||||||
\(706\) | 11.0048 | 0.414173 | ||||||||
\(707\) | 61.8312 | 2.32540 | ||||||||
\(708\) | −28.4207 | −1.06811 | ||||||||
\(709\) | 37.1833 | 1.39645 | 0.698223 | − | 0.715880i | \(-0.253974\pi\) | ||||
0.698223 | + | 0.715880i | \(0.253974\pi\) | |||||||
\(710\) | −15.8985 | −0.596660 | ||||||||
\(711\) | −4.43231 | −0.166224 | ||||||||
\(712\) | −31.4374 | −1.17817 | ||||||||
\(713\) | 8.74137 | 0.327367 | ||||||||
\(714\) | −81.1192 | −3.03581 | ||||||||
\(715\) | −0.217767 | −0.00814403 | ||||||||
\(716\) | 27.5166 | 1.02834 | ||||||||
\(717\) | −6.49772 | −0.242662 | ||||||||
\(718\) | 5.43676 | 0.202898 | ||||||||
\(719\) | 21.9924 | 0.820178 | 0.410089 | − | 0.912045i | \(-0.365498\pi\) | ||||
0.410089 | + | 0.912045i | \(0.365498\pi\) | |||||||
\(720\) | 0.999514 | 0.0372497 | ||||||||
\(721\) | 13.3961 | 0.498896 | ||||||||
\(722\) | 9.55321 | 0.355534 | ||||||||
\(723\) | 22.4581 | 0.835225 | ||||||||
\(724\) | 9.13823 | 0.339619 | ||||||||
\(725\) | 0.386636 | 0.0143593 | ||||||||
\(726\) | −36.0411 | −1.33761 | ||||||||
\(727\) | 51.8150 | 1.92171 | 0.960855 | − | 0.277051i | \(-0.0893572\pi\) | ||||
0.960855 | + | 0.277051i | \(0.0893572\pi\) | |||||||
\(728\) | 53.0813 | 1.96732 | ||||||||
\(729\) | 28.8310 | 1.06782 | ||||||||
\(730\) | 18.1475 | 0.671670 | ||||||||
\(731\) | 55.9040 | 2.06768 | ||||||||
\(732\) | −71.6510 | −2.64830 | ||||||||
\(733\) | −4.51528 | −0.166776 | −0.0833878 | − | 0.996517i | \(-0.526574\pi\) | ||||
−0.0833878 | + | 0.996517i | \(0.526574\pi\) | |||||||
\(734\) | −81.3081 | −3.00114 | ||||||||
\(735\) | 10.9659 | 0.404484 | ||||||||
\(736\) | −6.81532 | −0.251216 | ||||||||
\(737\) | −0.614714 | −0.0226433 | ||||||||
\(738\) | 4.11220 | 0.151372 | ||||||||
\(739\) | −18.9263 | −0.696217 | −0.348108 | − | 0.937454i | \(-0.613176\pi\) | ||||
−0.348108 | + | 0.937454i | \(0.613176\pi\) | |||||||
\(740\) | −25.5117 | −0.937828 | ||||||||
\(741\) | −22.2029 | −0.815643 | ||||||||
\(742\) | 117.969 | 4.33078 | ||||||||
\(743\) | −44.9459 | −1.64890 | −0.824452 | − | 0.565932i | \(-0.808516\pi\) | ||||
−0.824452 | + | 0.565932i | \(0.808516\pi\) | |||||||
\(744\) | −27.1189 | −0.994226 | ||||||||
\(745\) | 3.55897 | 0.130391 | ||||||||
\(746\) | 17.1594 | 0.628250 | ||||||||
\(747\) | 7.85879 | 0.287538 | ||||||||
\(748\) | 1.17829 | 0.0430825 | ||||||||
\(749\) | 41.1100 | 1.50213 | ||||||||
\(750\) | −3.27730 | −0.119670 | ||||||||
\(751\) | −46.7124 | −1.70456 | −0.852281 | − | 0.523085i | \(-0.824781\pi\) | ||||
−0.852281 | + | 0.523085i | \(0.824781\pi\) | |||||||
\(752\) | 3.50693 | 0.127885 | ||||||||
\(753\) | 0.816271 | 0.0297466 | ||||||||
\(754\) | −3.69351 | −0.134510 | ||||||||
\(755\) | −12.7853 | −0.465305 | ||||||||
\(756\) | −74.9624 | −2.72636 | ||||||||
\(757\) | −23.7932 | −0.864777 | −0.432388 | − | 0.901687i | \(-0.642329\pi\) | ||||
−0.432388 | + | 0.901687i | \(0.642329\pi\) | |||||||
\(758\) | −4.27272 | −0.155192 | ||||||||
\(759\) | 0.113964 | 0.00413662 | ||||||||
\(760\) | 13.0078 | 0.471843 | ||||||||
\(761\) | 19.6816 | 0.713457 | 0.356729 | − | 0.934208i | \(-0.383892\pi\) | ||||
0.356729 | + | 0.934208i | \(0.383892\pi\) | |||||||
\(762\) | 15.9750 | 0.578713 | ||||||||
\(763\) | 6.38886 | 0.231292 | ||||||||
\(764\) | −41.8581 | −1.51437 | ||||||||
\(765\) | 6.60643 | 0.238856 | ||||||||
\(766\) | 52.3249 | 1.89058 | ||||||||
\(767\) | 24.0542 | 0.868546 | ||||||||
\(768\) | 30.5591 | 1.10271 | ||||||||
\(769\) | 14.5815 | 0.525821 | 0.262911 | − | 0.964820i | \(-0.415318\pi\) | ||||
0.262911 | + | 0.964820i | \(0.415318\pi\) | |||||||
\(770\) | −0.477539 | −0.0172093 | ||||||||
\(771\) | −23.6649 | −0.852272 | ||||||||
\(772\) | −65.4004 | −2.35381 | ||||||||
\(773\) | 41.1355 | 1.47954 | 0.739770 | − | 0.672860i | \(-0.234934\pi\) | ||||
0.739770 | + | 0.672860i | \(0.234934\pi\) | |||||||
\(774\) | 20.8269 | 0.748607 | ||||||||
\(775\) | −5.73040 | −0.205842 | ||||||||
\(776\) | 1.02668 | 0.0368555 | ||||||||
\(777\) | 40.0374 | 1.43633 | ||||||||
\(778\) | −9.97668 | −0.357681 | ||||||||
\(779\) | 6.62514 | 0.237370 | ||||||||
\(780\) | 19.8061 | 0.709172 | ||||||||
\(781\) | −0.362419 | −0.0129684 | ||||||||
\(782\) | 22.8943 | 0.818697 | ||||||||
\(783\) | 2.18699 | 0.0781567 | ||||||||
\(784\) | 7.59769 | 0.271346 | ||||||||
\(785\) | −20.3533 | −0.726442 | ||||||||
\(786\) | 22.7698 | 0.812171 | ||||||||
\(787\) | 30.7943 | 1.09770 | 0.548850 | − | 0.835921i | \(-0.315066\pi\) | ||||
0.548850 | + | 0.835921i | \(0.315066\pi\) | |||||||
\(788\) | −29.3256 | −1.04468 | ||||||||
\(789\) | 10.4359 | 0.371526 | ||||||||
\(790\) | 10.0692 | 0.358246 | ||||||||
\(791\) | −44.0208 | −1.56520 | ||||||||
\(792\) | 0.184051 | 0.00653998 | ||||||||
\(793\) | 60.6427 | 2.15348 | ||||||||
\(794\) | −6.74329 | −0.239310 | ||||||||
\(795\) | 18.4557 | 0.654558 | ||||||||
\(796\) | 1.72768 | 0.0612360 | ||||||||
\(797\) | 21.4084 | 0.758323 | 0.379162 | − | 0.925330i | \(-0.376212\pi\) | ||||
0.379162 | + | 0.925330i | \(0.376212\pi\) | |||||||
\(798\) | −48.6884 | −1.72355 | ||||||||
\(799\) | 23.1796 | 0.820035 | ||||||||
\(800\) | 4.46777 | 0.157960 | ||||||||
\(801\) | −9.58323 | −0.338607 | ||||||||
\(802\) | 15.4559 | 0.545766 | ||||||||
\(803\) | 0.413688 | 0.0145987 | ||||||||
\(804\) | 55.9088 | 1.97175 | ||||||||
\(805\) | −5.86988 | −0.206886 | ||||||||
\(806\) | 54.7421 | 1.92821 | ||||||||
\(807\) | 10.0913 | 0.355230 | ||||||||
\(808\) | 54.1381 | 1.90457 | ||||||||
\(809\) | −32.3824 | −1.13850 | −0.569252 | − | 0.822163i | \(-0.692767\pi\) | ||||
−0.569252 | + | 0.822163i | \(0.692767\pi\) | |||||||
\(810\) | −11.3488 | −0.398757 | ||||||||
\(811\) | −10.0458 | −0.352755 | −0.176378 | − | 0.984323i | \(-0.556438\pi\) | ||||
−0.176378 | + | 0.984323i | \(0.556438\pi\) | |||||||
\(812\) | −5.12390 | −0.179814 | ||||||||
\(813\) | −17.0496 | −0.597956 | ||||||||
\(814\) | −0.919282 | −0.0322208 | ||||||||
\(815\) | −8.28586 | −0.290241 | ||||||||
\(816\) | −8.79273 | −0.307807 | ||||||||
\(817\) | 33.5541 | 1.17391 | ||||||||
\(818\) | 24.8923 | 0.870337 | ||||||||
\(819\) | 16.1810 | 0.565411 | ||||||||
\(820\) | −5.90996 | −0.206385 | ||||||||
\(821\) | 38.0383 | 1.32755 | 0.663773 | − | 0.747934i | \(-0.268954\pi\) | ||||
0.663773 | + | 0.747934i | \(0.268954\pi\) | |||||||
\(822\) | 11.5998 | 0.404588 | ||||||||
\(823\) | −47.9458 | −1.67128 | −0.835642 | − | 0.549274i | \(-0.814904\pi\) | ||||
−0.835642 | + | 0.549274i | \(0.814904\pi\) | |||||||
\(824\) | 11.7293 | 0.408610 | ||||||||
\(825\) | −0.0747088 | −0.00260103 | ||||||||
\(826\) | 52.7481 | 1.83534 | ||||||||
\(827\) | −14.4004 | −0.500750 | −0.250375 | − | 0.968149i | \(-0.580554\pi\) | ||||
−0.250375 | + | 0.968149i | \(0.580554\pi\) | |||||||
\(828\) | 5.39577 | 0.187516 | ||||||||
\(829\) | 12.2891 | 0.426819 | 0.213410 | − | 0.976963i | \(-0.431543\pi\) | ||||
0.213410 | + | 0.976963i | \(0.431543\pi\) | |||||||
\(830\) | −17.8534 | −0.619700 | ||||||||
\(831\) | 27.1856 | 0.943058 | ||||||||
\(832\) | −50.6493 | −1.75595 | ||||||||
\(833\) | 50.2180 | 1.73995 | ||||||||
\(834\) | −18.3593 | −0.635731 | ||||||||
\(835\) | −18.8878 | −0.653639 | ||||||||
\(836\) | 0.707219 | 0.0244597 | ||||||||
\(837\) | −32.4138 | −1.12038 | ||||||||
\(838\) | −21.1038 | −0.729018 | ||||||||
\(839\) | −41.1144 | −1.41943 | −0.709713 | − | 0.704491i | \(-0.751175\pi\) | ||||
−0.709713 | + | 0.704491i | \(0.751175\pi\) | |||||||
\(840\) | 18.2105 | 0.628321 | ||||||||
\(841\) | −28.8505 | −0.994845 | ||||||||
\(842\) | 15.1857 | 0.523334 | ||||||||
\(843\) | −46.7951 | −1.61171 | ||||||||
\(844\) | −83.0913 | −2.86012 | ||||||||
\(845\) | −3.76312 | −0.129455 | ||||||||
\(846\) | 8.63549 | 0.296894 | ||||||||
\(847\) | 42.3170 | 1.45403 | ||||||||
\(848\) | 12.7870 | 0.439107 | ||||||||
\(849\) | 13.4166 | 0.460456 | ||||||||
\(850\) | −15.0083 | −0.514781 | ||||||||
\(851\) | −11.2998 | −0.387351 | ||||||||
\(852\) | 32.9623 | 1.12927 | ||||||||
\(853\) | −18.8087 | −0.643996 | −0.321998 | − | 0.946740i | \(-0.604355\pi\) | ||||
−0.321998 | + | 0.946740i | \(0.604355\pi\) | |||||||
\(854\) | 132.983 | 4.55057 | ||||||||
\(855\) | 3.96524 | 0.135608 | ||||||||
\(856\) | 35.9950 | 1.23029 | ||||||||
\(857\) | −1.16400 | −0.0397616 | −0.0198808 | − | 0.999802i | \(-0.506329\pi\) | ||||
−0.0198808 | + | 0.999802i | \(0.506329\pi\) | |||||||
\(858\) | 0.713689 | 0.0243649 | ||||||||
\(859\) | 12.3624 | 0.421800 | 0.210900 | − | 0.977508i | \(-0.432360\pi\) | ||||
0.210900 | + | 0.977508i | \(0.432360\pi\) | |||||||
\(860\) | −29.9319 | −1.02067 | ||||||||
\(861\) | 9.27495 | 0.316090 | ||||||||
\(862\) | −16.1516 | −0.550124 | ||||||||
\(863\) | −5.47739 | −0.186453 | −0.0932263 | − | 0.995645i | \(-0.529718\pi\) | ||||
−0.0932263 | + | 0.995645i | \(0.529718\pi\) | |||||||
\(864\) | 25.2718 | 0.859764 | ||||||||
\(865\) | −13.1948 | −0.448637 | ||||||||
\(866\) | 54.2512 | 1.84353 | ||||||||
\(867\) | −34.2384 | −1.16280 | ||||||||
\(868\) | 75.9423 | 2.57765 | ||||||||
\(869\) | 0.229535 | 0.00778646 | ||||||||
\(870\) | −1.26712 | −0.0429595 | ||||||||
\(871\) | −47.3191 | −1.60335 | ||||||||
\(872\) | 5.59394 | 0.189435 | ||||||||
\(873\) | 0.312967 | 0.0105923 | ||||||||
\(874\) | 13.7413 | 0.464808 | ||||||||
\(875\) | 3.84799 | 0.130086 | ||||||||
\(876\) | −37.6253 | −1.27124 | ||||||||
\(877\) | −13.9132 | −0.469817 | −0.234908 | − | 0.972018i | \(-0.575479\pi\) | ||||
−0.234908 | + | 0.972018i | \(0.575479\pi\) | |||||||
\(878\) | −60.2819 | −2.03441 | ||||||||
\(879\) | 29.8954 | 1.00835 | ||||||||
\(880\) | −0.0517617 | −0.00174489 | ||||||||
\(881\) | 28.8897 | 0.973319 | 0.486660 | − | 0.873592i | \(-0.338215\pi\) | ||||
0.486660 | + | 0.873592i | \(0.338215\pi\) | |||||||
\(882\) | 18.7086 | 0.629952 | ||||||||
\(883\) | −6.75278 | −0.227249 | −0.113625 | − | 0.993524i | \(-0.536246\pi\) | ||||
−0.113625 | + | 0.993524i | \(0.536246\pi\) | |||||||
\(884\) | 90.7014 | 3.05062 | ||||||||
\(885\) | 8.25221 | 0.277395 | ||||||||
\(886\) | 0.666997 | 0.0224082 | ||||||||
\(887\) | 3.28827 | 0.110409 | 0.0552046 | − | 0.998475i | \(-0.482419\pi\) | ||||
0.0552046 | + | 0.998475i | \(0.482419\pi\) | |||||||
\(888\) | 35.0559 | 1.17640 | ||||||||
\(889\) | −18.7568 | −0.629083 | ||||||||
\(890\) | 21.7709 | 0.729763 | ||||||||
\(891\) | −0.258706 | −0.00866698 | ||||||||
\(892\) | −70.9503 | −2.37559 | ||||||||
\(893\) | 13.9126 | 0.465567 | ||||||||
\(894\) | −11.6638 | −0.390097 | ||||||||
\(895\) | −7.98969 | −0.267066 | ||||||||
\(896\) | −76.6843 | −2.56184 | ||||||||
\(897\) | 8.77262 | 0.292909 | ||||||||
\(898\) | 29.6321 | 0.988835 | ||||||||
\(899\) | −2.21558 | −0.0738936 | ||||||||
\(900\) | −3.53719 | −0.117906 | ||||||||
\(901\) | 84.5175 | 2.81569 | ||||||||
\(902\) | −0.212958 | −0.00709073 | ||||||||
\(903\) | 46.9745 | 1.56321 | ||||||||
\(904\) | −38.5437 | −1.28194 | ||||||||
\(905\) | −2.65337 | −0.0882009 | ||||||||
\(906\) | 41.9013 | 1.39208 | ||||||||
\(907\) | −3.33682 | −0.110797 | −0.0553986 | − | 0.998464i | \(-0.517643\pi\) | ||||
−0.0553986 | + | 0.998464i | \(0.517643\pi\) | |||||||
\(908\) | 52.3341 | 1.73677 | ||||||||
\(909\) | 16.5032 | 0.547376 | ||||||||
\(910\) | −36.7596 | −1.21857 | ||||||||
\(911\) | 24.7103 | 0.818688 | 0.409344 | − | 0.912380i | \(-0.365758\pi\) | ||||
0.409344 | + | 0.912380i | \(0.365758\pi\) | |||||||
\(912\) | −5.27747 | −0.174755 | ||||||||
\(913\) | −0.406982 | −0.0134692 | ||||||||
\(914\) | −80.5225 | −2.66345 | ||||||||
\(915\) | 20.8045 | 0.687777 | ||||||||
\(916\) | −44.2775 | −1.46297 | ||||||||
\(917\) | −26.7348 | −0.882860 | ||||||||
\(918\) | −84.8940 | −2.80192 | ||||||||
\(919\) | 51.9195 | 1.71267 | 0.856333 | − | 0.516425i | \(-0.172737\pi\) | ||||
0.856333 | + | 0.516425i | \(0.172737\pi\) | |||||||
\(920\) | −5.13954 | −0.169446 | ||||||||
\(921\) | 36.1724 | 1.19192 | ||||||||
\(922\) | 3.05876 | 0.100735 | ||||||||
\(923\) | −27.8981 | −0.918276 | ||||||||
\(924\) | 0.990081 | 0.0325713 | ||||||||
\(925\) | 7.40755 | 0.243559 | ||||||||
\(926\) | −20.9355 | −0.687983 | ||||||||
\(927\) | 3.57551 | 0.117435 | ||||||||
\(928\) | 1.72740 | 0.0567047 | ||||||||
\(929\) | −4.14538 | −0.136005 | −0.0680027 | − | 0.997685i | \(-0.521663\pi\) | ||||
−0.0680027 | + | 0.997685i | \(0.521663\pi\) | |||||||
\(930\) | 18.7803 | 0.615829 | ||||||||
\(931\) | 30.1413 | 0.987842 | ||||||||
\(932\) | 26.1492 | 0.856544 | ||||||||
\(933\) | −47.4149 | −1.55230 | ||||||||
\(934\) | −73.5304 | −2.40599 | ||||||||
\(935\) | −0.342127 | −0.0111887 | ||||||||
\(936\) | 14.1678 | 0.463088 | ||||||||
\(937\) | 20.3672 | 0.665367 | 0.332684 | − | 0.943038i | \(-0.392046\pi\) | ||||
0.332684 | + | 0.943038i | \(0.392046\pi\) | |||||||
\(938\) | −103.765 | −3.38806 | ||||||||
\(939\) | −20.1201 | −0.656596 | ||||||||
\(940\) | −12.4107 | −0.404793 | ||||||||
\(941\) | 44.4236 | 1.44817 | 0.724084 | − | 0.689712i | \(-0.242263\pi\) | ||||
0.724084 | + | 0.689712i | \(0.242263\pi\) | |||||||
\(942\) | 66.7040 | 2.17334 | ||||||||
\(943\) | −2.61767 | −0.0852430 | ||||||||
\(944\) | 5.71751 | 0.186089 | ||||||||
\(945\) | 21.7660 | 0.708049 | ||||||||
\(946\) | −1.07856 | −0.0350670 | ||||||||
\(947\) | 31.9869 | 1.03943 | 0.519717 | − | 0.854339i | \(-0.326037\pi\) | ||||
0.519717 | + | 0.854339i | \(0.326037\pi\) | |||||||
\(948\) | −20.8764 | −0.678036 | ||||||||
\(949\) | 31.8446 | 1.03372 | ||||||||
\(950\) | −9.00812 | −0.292262 | ||||||||
\(951\) | −45.1200 | −1.46312 | ||||||||
\(952\) | 83.3943 | 2.70282 | ||||||||
\(953\) | 33.2877 | 1.07830 | 0.539148 | − | 0.842211i | \(-0.318747\pi\) | ||||
0.539148 | + | 0.842211i | \(0.318747\pi\) | |||||||
\(954\) | 31.4868 | 1.01942 | ||||||||
\(955\) | 12.1539 | 0.393290 | ||||||||
\(956\) | 15.9319 | 0.515275 | ||||||||
\(957\) | −0.0288851 | −0.000933722 0 | ||||||||
\(958\) | −55.1136 | −1.78064 | ||||||||
\(959\) | −13.6197 | −0.439802 | ||||||||
\(960\) | −17.3761 | −0.560813 | ||||||||
\(961\) | 1.83746 | 0.0592730 | ||||||||
\(962\) | −70.7638 | −2.28152 | ||||||||
\(963\) | 10.9726 | 0.353586 | ||||||||
\(964\) | −55.0655 | −1.77354 | ||||||||
\(965\) | 18.9896 | 0.611298 | ||||||||
\(966\) | 19.2374 | 0.618952 | ||||||||
\(967\) | −43.1904 | −1.38891 | −0.694455 | − | 0.719536i | \(-0.744355\pi\) | ||||
−0.694455 | + | 0.719536i | \(0.744355\pi\) | |||||||
\(968\) | 37.0519 | 1.19089 | ||||||||
\(969\) | −34.8822 | −1.12058 | ||||||||
\(970\) | −0.710989 | −0.0228285 | ||||||||
\(971\) | 33.0915 | 1.06196 | 0.530978 | − | 0.847386i | \(-0.321825\pi\) | ||||
0.530978 | + | 0.847386i | \(0.321825\pi\) | |||||||
\(972\) | −34.9132 | −1.11984 | ||||||||
\(973\) | 21.5563 | 0.691063 | ||||||||
\(974\) | −90.4140 | −2.89705 | ||||||||
\(975\) | −5.75089 | −0.184176 | ||||||||
\(976\) | 14.4143 | 0.461392 | ||||||||
\(977\) | −7.34002 | −0.234828 | −0.117414 | − | 0.993083i | \(-0.537460\pi\) | ||||
−0.117414 | + | 0.993083i | \(0.537460\pi\) | |||||||
\(978\) | 27.1553 | 0.868330 | ||||||||
\(979\) | 0.496286 | 0.0158614 | ||||||||
\(980\) | −26.8876 | −0.858892 | ||||||||
\(981\) | 1.70523 | 0.0544439 | ||||||||
\(982\) | −31.1269 | −0.993300 | ||||||||
\(983\) | 19.1746 | 0.611575 | 0.305787 | − | 0.952100i | \(-0.401080\pi\) | ||||
0.305787 | + | 0.952100i | \(0.401080\pi\) | |||||||
\(984\) | 8.12095 | 0.258886 | ||||||||
\(985\) | 8.51495 | 0.271309 | ||||||||
\(986\) | −5.80275 | −0.184797 | ||||||||
\(987\) | 19.4771 | 0.619964 | ||||||||
\(988\) | 54.4398 | 1.73196 | ||||||||
\(989\) | −13.2576 | −0.421567 | ||||||||
\(990\) | −0.127458 | −0.00405090 | ||||||||
\(991\) | −29.6556 | −0.942042 | −0.471021 | − | 0.882122i | \(-0.656114\pi\) | ||||
−0.471021 | + | 0.882122i | \(0.656114\pi\) | |||||||
\(992\) | −25.6021 | −0.812868 | ||||||||
\(993\) | 36.5190 | 1.15889 | ||||||||
\(994\) | −61.1773 | −1.94043 | ||||||||
\(995\) | −0.501648 | −0.0159033 | ||||||||
\(996\) | 37.0154 | 1.17288 | ||||||||
\(997\) | 27.9012 | 0.883641 | 0.441820 | − | 0.897104i | \(-0.354333\pi\) | ||||
0.441820 | + | 0.897104i | \(0.354333\pi\) | |||||||
\(998\) | 22.9399 | 0.726149 | ||||||||
\(999\) | 41.9005 | 1.32567 |
(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 | 8035.2.a.c.1.11 | ✓ | 127 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8035.2.a.c.1.11 | ✓ | 127 | 1.1 | even | 1 | trivial |