Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,3,Mod(7,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.7");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.g (of order \(6\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(2.07085000914\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 11.12 | ||
Character | \(\chi\) | \(=\) | 76.11 |
Dual form | 76.3.g.c.7.12 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.19692 | − | 1.60230i | 0.598462 | − | 0.801151i | ||||
\(3\) | 3.65809 | + | 2.11200i | 1.21936 | + | 0.703999i | 0.964782 | − | 0.263052i | \(-0.0847291\pi\) |
0.254581 | + | 0.967051i | \(0.418062\pi\) | |||||||
\(4\) | −1.13475 | − | 3.83567i | −0.283687 | − | 0.958917i | ||||
\(5\) | −1.06722 | + | 1.84849i | −0.213445 | + | 0.369698i | −0.952790 | − | 0.303629i | \(-0.901802\pi\) |
0.739345 | + | 0.673326i | \(0.235135\pi\) | |||||||
\(6\) | 7.76251 | − | 3.33347i | 1.29375 | − | 0.555578i | ||||
\(7\) | − | 1.82388i | − | 0.260555i | −0.991478 | − | 0.130277i | \(-0.958413\pi\) | ||
0.991478 | − | 0.130277i | \(-0.0415868\pi\) | |||||||
\(8\) | −7.50411 | − | 2.77279i | −0.938014 | − | 0.346599i | ||||
\(9\) | 4.42107 | + | 7.65753i | 0.491231 | + | 0.850836i | ||||
\(10\) | 1.68445 | + | 3.92252i | 0.168445 | + | 0.392252i | ||||
\(11\) | 13.8522i | 1.25929i | 0.776882 | + | 0.629647i | \(0.216800\pi\) | ||||
−0.776882 | + | 0.629647i | \(0.783200\pi\) | |||||||
\(12\) | 3.94991 | − | 16.4278i | 0.329159 | − | 1.36898i | ||||
\(13\) | −9.95291 | − | 17.2389i | −0.765608 | − | 1.32607i | −0.939924 | − | 0.341383i | \(-0.889105\pi\) |
0.174316 | − | 0.984690i | \(-0.444229\pi\) | |||||||
\(14\) | −2.92241 | − | 2.18305i | −0.208744 | − | 0.155932i | ||||
\(15\) | −7.80801 | + | 4.50795i | −0.520534 | + | 0.300530i | ||||
\(16\) | −13.4247 | + | 8.70504i | −0.839043 | + | 0.544065i | ||||
\(17\) | 3.83013 | − | 6.63399i | 0.225302 | − | 0.390235i | −0.731108 | − | 0.682262i | \(-0.760996\pi\) |
0.956410 | + | 0.292027i | \(0.0943298\pi\) | |||||||
\(18\) | 17.5614 | + | 2.08157i | 0.975631 | + | 0.115643i | ||||
\(19\) | −16.7080 | + | 9.04663i | −0.879370 | + | 0.476138i | ||||
\(20\) | 8.30122 | + | 1.99595i | 0.415061 | + | 0.0997975i | ||||
\(21\) | 3.85204 | − | 6.67193i | 0.183430 | − | 0.317711i | ||||
\(22\) | 22.1955 | + | 16.5801i | 1.00888 | + | 0.753639i | ||||
\(23\) | 9.14824 | − | 5.28174i | 0.397749 | − | 0.229641i | −0.287763 | − | 0.957702i | \(-0.592912\pi\) |
0.685512 | + | 0.728061i | \(0.259578\pi\) | |||||||
\(24\) | −21.5946 | − | 25.9918i | −0.899774 | − | 1.08299i | ||||
\(25\) | 10.2221 | + | 17.7051i | 0.408882 | + | 0.708205i | ||||
\(26\) | −39.5349 | − | 4.68612i | −1.52057 | − | 0.180235i | ||||
\(27\) | − | 0.666761i | − | 0.0246949i | ||||||
\(28\) | −6.99581 | + | 2.06965i | −0.249850 | + | 0.0739160i | ||||
\(29\) | −0.0147659 | − | 0.0255754i | −0.000509170 | − | 0.000881909i | 0.865771 | − | 0.500441i | \(-0.166829\pi\) |
−0.866280 | + | 0.499559i | \(0.833495\pi\) | |||||||
\(30\) | −2.12248 | + | 17.9065i | −0.0707492 | + | 0.596882i | ||||
\(31\) | 42.2313i | 1.36230i | 0.732143 | + | 0.681150i | \(0.238520\pi\) | ||||
−0.732143 | + | 0.681150i | \(0.761480\pi\) | |||||||
\(32\) | −2.12022 | + | 31.9297i | −0.0662570 | + | 0.997803i | ||||
\(33\) | −29.2559 | + | 50.6727i | −0.886542 | + | 1.53554i | ||||
\(34\) | −6.04528 | − | 14.0774i | −0.177802 | − | 0.414042i | ||||
\(35\) | 3.37143 | + | 1.94649i | 0.0963264 | + | 0.0556141i | ||||
\(36\) | 24.3549 | − | 25.6471i | 0.676525 | − | 0.712421i | ||||
\(37\) | 19.5805 | 0.529202 | 0.264601 | − | 0.964358i | \(-0.414760\pi\) | ||||
0.264601 | + | 0.964358i | \(0.414760\pi\) | |||||||
\(38\) | −5.50280 | + | 37.5995i | −0.144811 | + | 0.989459i | ||||
\(39\) | − | 84.0821i | − | 2.15595i | ||||||
\(40\) | 13.1340 | − | 10.9121i | 0.328351 | − | 0.272802i | ||||
\(41\) | 15.7368 | − | 27.2570i | 0.383825 | − | 0.664805i | −0.607780 | − | 0.794105i | \(-0.707940\pi\) |
0.991605 | + | 0.129300i | \(0.0412732\pi\) | |||||||
\(42\) | −6.07985 | − | 14.1579i | −0.144758 | − | 0.337093i | ||||
\(43\) | −51.3500 | − | 29.6469i | −1.19418 | − | 0.689463i | −0.234932 | − | 0.972012i | \(-0.575487\pi\) |
−0.959253 | + | 0.282549i | \(0.908820\pi\) | |||||||
\(44\) | 53.1325 | − | 15.7188i | 1.20756 | − | 0.357245i | ||||
\(45\) | −18.8731 | −0.419403 | ||||||||
\(46\) | 2.48680 | − | 20.9801i | 0.0540608 | − | 0.456089i | ||||
\(47\) | 77.5317 | − | 44.7629i | 1.64961 | − | 0.952403i | 0.672384 | − | 0.740202i | \(-0.265270\pi\) |
0.977226 | − | 0.212201i | \(-0.0680631\pi\) | |||||||
\(48\) | −67.4937 | + | 3.49087i | −1.40612 | + | 0.0727264i | ||||
\(49\) | 45.6735 | 0.932111 | ||||||||
\(50\) | 40.6040 | + | 4.81285i | 0.812080 | + | 0.0962569i | ||||
\(51\) | 28.0219 | − | 16.1785i | 0.549450 | − | 0.317225i | ||||
\(52\) | −54.8288 | + | 57.7379i | −1.05440 | + | 1.11034i | ||||
\(53\) | −29.8268 | − | 51.6616i | −0.562770 | − | 0.974747i | −0.997253 | − | 0.0740668i | \(-0.976402\pi\) |
0.434483 | − | 0.900680i | \(-0.356931\pi\) | |||||||
\(54\) | −1.06835 | − | 0.798062i | −0.0197843 | − | 0.0147789i | ||||
\(55\) | −25.6057 | − | 14.7834i | −0.465558 | − | 0.268790i | ||||
\(56\) | −5.05724 | + | 13.6866i | −0.0903079 | + | 0.244404i | ||||
\(57\) | −80.2259 | − | 2.19398i | −1.40747 | − | 0.0384909i | ||||
\(58\) | −0.0586532 | − | 0.00695224i | −0.00101126 | − | 0.000119866i | ||||
\(59\) | 63.9584 | + | 36.9264i | 1.08404 | + | 0.625871i | 0.931984 | − | 0.362500i | \(-0.118077\pi\) |
0.152057 | + | 0.988372i | \(0.451410\pi\) | |||||||
\(60\) | 26.1511 | + | 24.8335i | 0.435852 | + | 0.413892i | ||||
\(61\) | −23.6620 | − | 40.9837i | −0.387901 | − | 0.671864i | 0.604266 | − | 0.796783i | \(-0.293466\pi\) |
−0.992167 | + | 0.124919i | \(0.960133\pi\) | |||||||
\(62\) | 67.6674 | + | 50.5477i | 1.09141 | + | 0.815285i | ||||
\(63\) | 13.9664 | − | 8.06352i | 0.221689 | − | 0.127992i | ||||
\(64\) | 48.6233 | + | 41.6146i | 0.759739 | + | 0.650229i | ||||
\(65\) | 42.4880 | 0.653661 | ||||||||
\(66\) | 46.1759 | + | 107.528i | 0.699635 | + | 1.62921i | ||||
\(67\) | 5.77732 | − | 3.33554i | 0.0862287 | − | 0.0497842i | −0.456266 | − | 0.889844i | \(-0.650813\pi\) |
0.542494 | + | 0.840059i | \(0.317480\pi\) | |||||||
\(68\) | −29.7920 | − | 7.16321i | −0.438118 | − | 0.105341i | ||||
\(69\) | 44.6201 | 0.646668 | ||||||||
\(70\) | 7.15421 | − | 3.07224i | 0.102203 | − | 0.0438892i | ||||
\(71\) | −24.1399 | − | 13.9372i | −0.339999 | − | 0.196298i | 0.320273 | − | 0.947325i | \(-0.396225\pi\) |
−0.660272 | + | 0.751027i | \(0.729559\pi\) | |||||||
\(72\) | −11.9435 | − | 69.7216i | −0.165882 | − | 0.968356i | ||||
\(73\) | −46.2611 | + | 80.1266i | −0.633714 | + | 1.09762i | 0.353072 | + | 0.935596i | \(0.385137\pi\) |
−0.986786 | + | 0.162028i | \(0.948196\pi\) | |||||||
\(74\) | 23.4363 | − | 31.3738i | 0.316707 | − | 0.423971i | ||||
\(75\) | 86.3559i | 1.15141i | ||||||||
\(76\) | 53.6593 | + | 53.8208i | 0.706043 | + | 0.708169i | ||||
\(77\) | 25.2648 | 0.328115 | ||||||||
\(78\) | −134.725 | − | 100.640i | −1.72724 | − | 1.29025i | ||||
\(79\) | −110.683 | − | 63.9027i | −1.40105 | − | 0.808895i | −0.406547 | − | 0.913630i | \(-0.633267\pi\) |
−0.994500 | + | 0.104735i | \(0.966601\pi\) | |||||||
\(80\) | −1.76399 | − | 34.1056i | −0.0220499 | − | 0.426320i | ||||
\(81\) | 41.1979 | − | 71.3568i | 0.508616 | − | 0.880948i | ||||
\(82\) | −24.8382 | − | 57.8397i | −0.302905 | − | 0.705362i | ||||
\(83\) | 88.9093i | 1.07120i | 0.844473 | + | 0.535598i | \(0.179914\pi\) | ||||
−0.844473 | + | 0.535598i | \(0.820086\pi\) | |||||||
\(84\) | −29.9624 | − | 7.20418i | −0.356695 | − | 0.0857640i | ||||
\(85\) | 8.17523 | + | 14.1599i | 0.0961792 | + | 0.166587i | ||||
\(86\) | −108.965 | + | 46.7931i | −1.26704 | + | 0.544106i | ||||
\(87\) | − | 0.124743i | − | 0.00143382i | ||||||
\(88\) | 38.4093 | − | 103.949i | 0.436469 | − | 1.18123i | ||||
\(89\) | 31.2173 | + | 54.0700i | 0.350756 | + | 0.607528i | 0.986382 | − | 0.164469i | \(-0.0525912\pi\) |
−0.635626 | + | 0.771997i | \(0.719258\pi\) | |||||||
\(90\) | −22.5897 | + | 30.2405i | −0.250996 | + | 0.336005i | ||||
\(91\) | −31.4418 | + | 18.1529i | −0.345514 | + | 0.199483i | ||||
\(92\) | −30.6399 | − | 29.0962i | −0.333043 | − | 0.316263i | ||||
\(93\) | −89.1925 | + | 154.486i | −0.959059 | + | 1.66114i | ||||
\(94\) | 21.0757 | − | 177.807i | 0.224210 | − | 1.89156i | ||||
\(95\) | 1.10865 | − | 40.5394i | 0.0116700 | − | 0.426730i | ||||
\(96\) | −75.1914 | + | 112.324i | −0.783244 | + | 1.17004i | ||||
\(97\) | 64.8024 | − | 112.241i | 0.668066 | − | 1.15712i | −0.310378 | − | 0.950613i | \(-0.600456\pi\) |
0.978444 | − | 0.206511i | \(-0.0662109\pi\) | |||||||
\(98\) | 54.6676 | − | 73.1827i | 0.557833 | − | 0.746762i | ||||
\(99\) | −106.074 | + | 61.2417i | −1.07145 | + | 0.618603i | ||||
\(100\) | 56.3115 | − | 59.2993i | 0.563115 | − | 0.592993i | ||||
\(101\) | 45.6483 | + | 79.0651i | 0.451963 | + | 0.782823i | 0.998508 | − | 0.0546069i | \(-0.0173906\pi\) |
−0.546545 | + | 0.837430i | \(0.684057\pi\) | |||||||
\(102\) | 7.61730 | − | 64.2640i | 0.0746794 | − | 0.630040i | ||||
\(103\) | 67.8160i | 0.658408i | 0.944259 | + | 0.329204i | \(0.106780\pi\) | ||||
−0.944259 | + | 0.329204i | \(0.893220\pi\) | |||||||
\(104\) | 26.8877 | + | 156.960i | 0.258536 | + | 1.50923i | ||||
\(105\) | 8.22198 | + | 14.2409i | 0.0783046 | + | 0.135628i | ||||
\(106\) | −118.478 | − | 14.0433i | −1.11772 | − | 0.132484i | ||||
\(107\) | 95.8811i | 0.896085i | 0.894012 | + | 0.448043i | \(0.147879\pi\) | ||||
−0.894012 | + | 0.448043i | \(0.852121\pi\) | |||||||
\(108\) | −2.55747 | + | 0.756606i | −0.0236803 | + | 0.00700561i | ||||
\(109\) | −30.9046 | + | 53.5283i | −0.283528 | + | 0.491085i | −0.972251 | − | 0.233939i | \(-0.924838\pi\) |
0.688723 | + | 0.725025i | \(0.258172\pi\) | |||||||
\(110\) | −54.3356 | + | 23.3334i | −0.493960 | + | 0.212122i | ||||
\(111\) | 71.6271 | + | 41.3539i | 0.645289 | + | 0.372558i | ||||
\(112\) | 15.8770 | + | 24.4851i | 0.141759 | + | 0.218617i | ||||
\(113\) | −33.7438 | −0.298618 | −0.149309 | − | 0.988791i | \(-0.547705\pi\) | ||||
−0.149309 | + | 0.988791i | \(0.547705\pi\) | |||||||
\(114\) | −99.5397 | + | 125.920i | −0.873156 | + | 1.10456i | ||||
\(115\) | 22.5472i | 0.196063i | ||||||||
\(116\) | −0.0813430 | + | 0.0856589i | −0.000701232 | + | 0.000738438i | ||||
\(117\) | 88.0051 | − | 152.429i | 0.752180 | − | 1.30281i | ||||
\(118\) | 135.721 | − | 58.2827i | 1.15017 | − | 0.493921i | ||||
\(119\) | −12.0996 | − | 6.98572i | −0.101677 | − | 0.0587035i | ||||
\(120\) | 71.0917 | − | 12.1782i | 0.592431 | − | 0.101485i | ||||
\(121\) | −70.8842 | −0.585820 | ||||||||
\(122\) | −93.9898 | − | 11.1407i | −0.770409 | − | 0.0913176i | ||||
\(123\) | 115.133 | − | 66.4724i | 0.936045 | − | 0.540426i | ||||
\(124\) | 161.985 | − | 47.9219i | 1.30633 | − | 0.386467i | ||||
\(125\) | −96.9982 | −0.775986 | ||||||||
\(126\) | 3.79654 | − | 32.0299i | 0.0301313 | − | 0.254205i | ||||
\(127\) | 28.8460 | − | 16.6543i | 0.227134 | − | 0.131136i | −0.382115 | − | 0.924115i | \(-0.624804\pi\) |
0.609249 | + | 0.792979i | \(0.291471\pi\) | |||||||
\(128\) | 124.878 | − | 28.0997i | 0.975606 | − | 0.219529i | ||||
\(129\) | −125.228 | − | 216.902i | −0.970763 | − | 1.68141i | ||||
\(130\) | 50.8548 | − | 68.0786i | 0.391191 | − | 0.523681i | ||||
\(131\) | 11.8573 | + | 6.84581i | 0.0905136 | + | 0.0522581i | 0.544574 | − | 0.838713i | \(-0.316691\pi\) |
−0.454060 | + | 0.890971i | \(0.650025\pi\) | |||||||
\(132\) | 227.562 | + | 54.7151i | 1.72395 | + | 0.414508i | ||||
\(133\) | 16.5000 | + | 30.4735i | 0.124060 | + | 0.229124i | ||||
\(134\) | 1.57047 | − | 13.2494i | 0.0117199 | − | 0.0988762i | ||||
\(135\) | 1.23250 | + | 0.711584i | 0.00912963 | + | 0.00527099i | ||||
\(136\) | −47.1364 | + | 39.1620i | −0.346591 | + | 0.287956i | ||||
\(137\) | −66.7629 | − | 115.637i | −0.487320 | − | 0.844063i | 0.512574 | − | 0.858643i | \(-0.328692\pi\) |
−0.999894 | + | 0.0145800i | \(0.995359\pi\) | |||||||
\(138\) | 53.4068 | − | 71.4949i | 0.387006 | − | 0.518079i | ||||
\(139\) | −192.509 | + | 111.145i | −1.38496 | + | 0.799606i | −0.992741 | − | 0.120268i | \(-0.961625\pi\) |
−0.392216 | + | 0.919873i | \(0.628291\pi\) | |||||||
\(140\) | 3.64038 | − | 15.1404i | 0.0260027 | − | 0.108146i | ||||
\(141\) | 378.157 | 2.68196 | ||||||||
\(142\) | −51.2252 | + | 21.9977i | −0.360741 | + | 0.154913i | ||||
\(143\) | 238.798 | − | 137.870i | 1.66991 | − | 0.964125i | ||||
\(144\) | −126.011 | − | 64.3143i | −0.875074 | − | 0.446627i | ||||
\(145\) | 0.0630343 | 0.000434719 | ||||||||
\(146\) | 73.0160 | + | 170.030i | 0.500110 | + | 1.16459i | ||||
\(147\) | 167.078 | + | 96.4623i | 1.13658 | + | 0.656206i | ||||
\(148\) | −22.2189 | − | 75.1042i | −0.150128 | − | 0.507461i | ||||
\(149\) | −11.8549 | + | 20.5333i | −0.0795632 | + | 0.137808i | −0.903062 | − | 0.429511i | \(-0.858686\pi\) |
0.823498 | + | 0.567319i | \(0.192019\pi\) | |||||||
\(150\) | 138.368 | + | 103.361i | 0.922456 | + | 0.689076i | ||||
\(151\) | − | 77.7402i | − | 0.514836i | −0.966300 | − | 0.257418i | \(-0.917128\pi\) | ||
0.966300 | − | 0.257418i | \(-0.0828717\pi\) | |||||||
\(152\) | 150.463 | − | 21.5590i | 0.989890 | − | 0.141836i | ||||
\(153\) | 67.7332 | 0.442701 | ||||||||
\(154\) | 30.2401 | − | 40.4819i | 0.196364 | − | 0.262870i | ||||
\(155\) | −78.0641 | − | 45.0703i | −0.503639 | − | 0.290776i | ||||
\(156\) | −322.511 | + | 95.4121i | −2.06738 | + | 0.611616i | ||||
\(157\) | −126.399 | + | 218.929i | −0.805087 | + | 1.39445i | 0.111146 | + | 0.993804i | \(0.464548\pi\) |
−0.916233 | + | 0.400647i | \(0.868785\pi\) | |||||||
\(158\) | −234.870 | + | 100.861i | −1.48652 | + | 0.638358i | ||||
\(159\) | − | 251.977i | − | 1.58476i | ||||||
\(160\) | −56.7589 | − | 37.9954i | −0.354743 | − | 0.237471i | ||||
\(161\) | −9.63327 | − | 16.6853i | −0.0598340 | − | 0.103636i | ||||
\(162\) | −65.0245 | − | 151.420i | −0.401386 | − | 0.934692i | ||||
\(163\) | − | 58.1739i | − | 0.356895i | −0.983949 | − | 0.178448i | \(-0.942893\pi\) | ||
0.983949 | − | 0.178448i | \(-0.0571075\pi\) | |||||||
\(164\) | −122.406 | − | 29.4314i | −0.746379 | − | 0.179460i | ||||
\(165\) | −62.4452 | − | 108.158i | −0.378456 | − | 0.655505i | ||||
\(166\) | 142.460 | + | 106.418i | 0.858191 | + | 0.641070i | ||||
\(167\) | −139.337 | + | 80.4465i | −0.834356 | + | 0.481716i | −0.855342 | − | 0.518064i | \(-0.826653\pi\) |
0.0209856 | + | 0.999780i | \(0.493320\pi\) | |||||||
\(168\) | −47.4060 | + | 39.3860i | −0.282178 | + | 0.234440i | ||||
\(169\) | −113.621 | + | 196.797i | −0.672312 | + | 1.16448i | ||||
\(170\) | 32.4736 | + | 3.84914i | 0.191021 | + | 0.0226420i | ||||
\(171\) | −143.142 | − | 87.9464i | −0.837089 | − | 0.514306i | ||||
\(172\) | −55.4464 | + | 230.603i | −0.322363 | + | 1.34072i | ||||
\(173\) | −123.372 | + | 213.686i | −0.713132 | + | 1.23518i | 0.250544 | + | 0.968105i | \(0.419391\pi\) |
−0.963676 | + | 0.267075i | \(0.913943\pi\) | |||||||
\(174\) | −0.199875 | − | 0.149307i | −0.00114871 | − | 0.000858088i | ||||
\(175\) | 32.2921 | − | 18.6438i | 0.184526 | − | 0.106536i | ||||
\(176\) | −120.584 | − | 185.962i | −0.685137 | − | 1.05660i | ||||
\(177\) | 155.977 | + | 270.160i | 0.881226 | + | 1.52633i | ||||
\(178\) | 124.001 | + | 14.6980i | 0.696636 | + | 0.0825732i | ||||
\(179\) | − | 129.378i | − | 0.722780i | −0.932415 | − | 0.361390i | \(-0.882302\pi\) | ||
0.932415 | − | 0.361390i | \(-0.117698\pi\) | |||||||
\(180\) | 21.4162 | + | 72.3910i | 0.118979 | + | 0.402172i | ||||
\(181\) | −96.1456 | − | 166.529i | −0.531191 | − | 0.920051i | −0.999337 | − | 0.0363994i | \(-0.988411\pi\) |
0.468146 | − | 0.883651i | \(-0.344922\pi\) | |||||||
\(182\) | −8.54694 | + | 72.1070i | −0.0469612 | + | 0.396192i | ||||
\(183\) | − | 199.896i | − | 1.09233i | ||||||
\(184\) | −83.2945 | + | 14.2686i | −0.452688 | + | 0.0775467i | ||||
\(185\) | −20.8968 | + | 36.1943i | −0.112955 | + | 0.195645i | ||||
\(186\) | 140.777 | + | 327.821i | 0.756864 | + | 1.76248i | ||||
\(187\) | 91.8955 | + | 53.0559i | 0.491420 | + | 0.283721i | ||||
\(188\) | −259.675 | − | 246.591i | −1.38125 | − | 1.31165i | ||||
\(189\) | −1.21609 | −0.00643436 | ||||||||
\(190\) | −63.6294 | − | 50.2989i | −0.334892 | − | 0.264731i | ||||
\(191\) | − | 1.29081i | − | 0.00675816i | −0.999994 | − | 0.00337908i | \(-0.998924\pi\) | ||
0.999994 | − | 0.00337908i | \(-0.00107560\pi\) | |||||||
\(192\) | 89.9782 | + | 254.922i | 0.468637 | + | 1.32772i | ||||
\(193\) | 186.582 | − | 323.169i | 0.966744 | − | 1.67445i | 0.261889 | − | 0.965098i | \(-0.415655\pi\) |
0.704855 | − | 0.709351i | \(-0.251012\pi\) | |||||||
\(194\) | −102.281 | − | 238.177i | −0.527220 | − | 1.22772i | ||||
\(195\) | 155.425 | + | 89.7345i | 0.797050 | + | 0.460177i | ||||
\(196\) | −51.8279 | − | 175.188i | −0.264428 | − | 0.893817i | ||||
\(197\) | 191.769 | 0.973448 | 0.486724 | − | 0.873556i | \(-0.338192\pi\) | ||||
0.486724 | + | 0.873556i | \(0.338192\pi\) | |||||||
\(198\) | −28.8344 | + | 243.264i | −0.145628 | + | 1.22861i | ||||
\(199\) | −285.397 | + | 164.774i | −1.43415 | + | 0.828009i | −0.997434 | − | 0.0715885i | \(-0.977193\pi\) |
−0.436720 | + | 0.899598i | \(0.643860\pi\) | |||||||
\(200\) | −27.6149 | − | 161.205i | −0.138074 | − | 0.806024i | ||||
\(201\) | 28.1786 | 0.140192 | ||||||||
\(202\) | 181.324 | + | 21.4925i | 0.897642 | + | 0.106399i | ||||
\(203\) | −0.0466465 | + | 0.0269314i | −0.000229786 | + | 0.000132667i | ||||
\(204\) | −93.8531 | − | 89.1244i | −0.460064 | − | 0.436884i | ||||
\(205\) | 33.5895 | + | 58.1787i | 0.163851 | + | 0.283799i | ||||
\(206\) | 108.662 | + | 81.1706i | 0.527485 | + | 0.394032i | ||||
\(207\) | 80.8901 | + | 46.7019i | 0.390773 | + | 0.225613i | ||||
\(208\) | 283.680 | + | 144.787i | 1.36385 | + | 0.696092i | ||||
\(209\) | −125.316 | − | 231.444i | −0.599598 | − | 1.10739i | ||||
\(210\) | 32.6593 | + | 3.87115i | 0.155520 | + | 0.0184341i | ||||
\(211\) | −48.2556 | − | 27.8604i | −0.228700 | − | 0.132040i | 0.381272 | − | 0.924463i | \(-0.375486\pi\) |
−0.609972 | + | 0.792423i | \(0.708819\pi\) | |||||||
\(212\) | −164.311 | + | 173.029i | −0.775050 | + | 0.816173i | ||||
\(213\) | −58.8706 | − | 101.967i | −0.276388 | − | 0.478718i | ||||
\(214\) | 153.631 | + | 114.762i | 0.717900 | + | 0.536273i | ||||
\(215\) | 109.604 | − | 63.2798i | 0.509785 | − | 0.294325i | ||||
\(216\) | −1.84879 | + | 5.00345i | −0.00855920 | + | 0.0231641i | ||||
\(217\) | 77.0250 | 0.354954 | ||||||||
\(218\) | 48.7781 | + | 113.588i | 0.223753 | + | 0.521045i | ||||
\(219\) | −338.454 | + | 195.407i | −1.54545 | + | 0.892268i | ||||
\(220\) | −27.6484 | + | 114.990i | −0.125674 | + | 0.522683i | ||||
\(221\) | −152.484 | −0.689973 | ||||||||
\(222\) | 151.994 | − | 65.2708i | 0.684656 | − | 0.294013i | ||||
\(223\) | −35.7192 | − | 20.6225i | −0.160176 | − | 0.0924774i | 0.417770 | − | 0.908553i | \(-0.362812\pi\) |
−0.577945 | + | 0.816076i | \(0.696145\pi\) | |||||||
\(224\) | 58.2360 | + | 3.86704i | 0.259982 | + | 0.0172636i | ||||
\(225\) | −90.3850 | + | 156.551i | −0.401711 | + | 0.695784i | ||||
\(226\) | −40.3888 | + | 54.0679i | −0.178711 | + | 0.239238i | ||||
\(227\) | − | 277.068i | − | 1.22057i | −0.792184 | − | 0.610283i | \(-0.791056\pi\) | ||
0.792184 | − | 0.610283i | \(-0.208944\pi\) | |||||||
\(228\) | 82.6209 | + | 310.210i | 0.362372 | + | 1.36057i | ||||
\(229\) | 141.178 | 0.616496 | 0.308248 | − | 0.951306i | \(-0.400257\pi\) | ||||
0.308248 | + | 0.951306i | \(0.400257\pi\) | |||||||
\(230\) | 36.1274 | + | 26.9873i | 0.157076 | + | 0.117336i | ||||
\(231\) | 92.4210 | + | 53.3593i | 0.400091 | + | 0.230993i | ||||
\(232\) | 0.0398901 | + | 0.232863i | 0.000171940 | + | 0.00100372i | ||||
\(233\) | 44.5846 | − | 77.2228i | 0.191350 | − | 0.331428i | −0.754348 | − | 0.656475i | \(-0.772047\pi\) |
0.945698 | + | 0.325047i | \(0.105380\pi\) | |||||||
\(234\) | −138.903 | − | 323.457i | −0.593601 | − | 1.38230i | ||||
\(235\) | 191.088i | 0.813143i | ||||||||
\(236\) | 69.0607 | − | 287.225i | 0.292630 | − | 1.21706i | ||||
\(237\) | −269.925 | − | 467.523i | −1.13892 | − | 1.97267i | ||||
\(238\) | −25.6756 | + | 11.0259i | −0.107880 | + | 0.0463272i | ||||
\(239\) | 82.2938i | 0.344325i | 0.985069 | + | 0.172163i | \(0.0550755\pi\) | ||||
−0.985069 | + | 0.172163i | \(0.944925\pi\) | |||||||
\(240\) | 65.5782 | − | 128.487i | 0.273242 | − | 0.535362i | ||||
\(241\) | −22.2946 | − | 38.6154i | −0.0925088 | − | 0.160230i | 0.816057 | − | 0.577971i | \(-0.196155\pi\) |
−0.908566 | + | 0.417741i | \(0.862822\pi\) | |||||||
\(242\) | −84.8429 | + | 113.578i | −0.350591 | + | 0.469330i | ||||
\(243\) | 296.214 | − | 171.019i | 1.21899 | − | 0.703783i | ||||
\(244\) | −130.349 | + | 137.266i | −0.534219 | + | 0.562564i | ||||
\(245\) | −48.7438 | + | 84.4268i | −0.198954 | + | 0.344599i | ||||
\(246\) | 31.2971 | − | 264.041i | 0.127224 | − | 1.07334i | ||||
\(247\) | 322.248 | + | 197.989i | 1.30465 | + | 0.801573i | ||||
\(248\) | 117.099 | − | 316.908i | 0.472172 | − | 1.27786i | ||||
\(249\) | −187.776 | + | 325.238i | −0.754122 | + | 1.30618i | ||||
\(250\) | −116.099 | + | 155.420i | −0.464398 | + | 0.621682i | ||||
\(251\) | 94.8716 | − | 54.7741i | 0.377974 | − | 0.218224i | −0.298962 | − | 0.954265i | \(-0.596640\pi\) |
0.676937 | + | 0.736041i | \(0.263307\pi\) | |||||||
\(252\) | −46.7774 | − | 44.4205i | −0.185625 | − | 0.176272i | ||||
\(253\) | 73.1638 | + | 126.723i | 0.289185 | + | 0.500883i | ||||
\(254\) | 7.84132 | − | 66.1540i | 0.0308713 | − | 0.260449i | ||||
\(255\) | 69.0643i | 0.270840i | ||||||||
\(256\) | 104.445 | − | 233.725i | 0.407987 | − | 0.912988i | ||||
\(257\) | 224.002 | + | 387.982i | 0.871602 | + | 1.50966i | 0.860339 | + | 0.509722i | \(0.170252\pi\) |
0.0112627 | + | 0.999937i | \(0.496415\pi\) | |||||||
\(258\) | −497.432 | − | 58.9612i | −1.92803 | − | 0.228532i | ||||
\(259\) | − | 35.7125i | − | 0.137886i | ||||||
\(260\) | −48.2132 | − | 162.970i | −0.185435 | − | 0.626807i | ||||
\(261\) | 0.130563 | − | 0.226141i | 0.000500240 | − | 0.000866441i | ||||
\(262\) | 25.1613 | − | 10.8051i | 0.0960355 | − | 0.0412407i | ||||
\(263\) | −272.533 | − | 157.347i | −1.03625 | − | 0.598277i | −0.117478 | − | 0.993075i | \(-0.537481\pi\) |
−0.918768 | + | 0.394798i | \(0.870814\pi\) | |||||||
\(264\) | 360.044 | − | 299.133i | 1.36380 | − | 1.13308i | ||||
\(265\) | 127.328 | 0.480482 | ||||||||
\(266\) | 68.5770 | + | 10.0365i | 0.257808 | + | 0.0377311i | ||||
\(267\) | 263.724i | 0.987730i | ||||||||
\(268\) | −19.3498 | − | 18.3749i | −0.0722009 | − | 0.0685630i | ||||
\(269\) | 145.563 | − | 252.123i | 0.541128 | − | 0.937261i | −0.457712 | − | 0.889101i | \(-0.651331\pi\) |
0.998840 | − | 0.0481601i | \(-0.0153358\pi\) | |||||||
\(270\) | 2.61538 | − | 1.12313i | 0.00968659 | − | 0.00415973i | ||||
\(271\) | 111.647 | + | 64.4596i | 0.411983 | + | 0.237858i | 0.691641 | − | 0.722241i | \(-0.256888\pi\) |
−0.279659 | + | 0.960100i | \(0.590221\pi\) | |||||||
\(272\) | 6.33073 | + | 122.401i | 0.0232748 | + | 0.450003i | ||||
\(273\) | −153.356 | −0.561743 | ||||||||
\(274\) | −265.195 | − | 31.4339i | −0.967865 | − | 0.114722i | ||||
\(275\) | −245.255 | + | 141.598i | −0.891838 | + | 0.514903i | ||||
\(276\) | −50.6326 | − | 171.148i | −0.183451 | − | 0.620101i | ||||
\(277\) | 23.1010 | 0.0833971 | 0.0416986 | − | 0.999130i | \(-0.486723\pi\) | ||||
0.0416986 | + | 0.999130i | \(0.486723\pi\) | |||||||
\(278\) | −52.3304 | + | 441.490i | −0.188239 | + | 1.58809i | ||||
\(279\) | −323.387 | + | 186.708i | −1.15909 | + | 0.669204i | ||||
\(280\) | −19.9023 | − | 23.9549i | −0.0710797 | − | 0.0855534i | ||||
\(281\) | 33.2086 | + | 57.5190i | 0.118180 | + | 0.204694i | 0.919046 | − | 0.394149i | \(-0.128961\pi\) |
−0.800866 | + | 0.598843i | \(0.795627\pi\) | |||||||
\(282\) | 452.625 | − | 605.922i | 1.60505 | − | 2.14866i | ||||
\(283\) | 84.3920 | + | 48.7237i | 0.298205 | + | 0.172169i | 0.641636 | − | 0.767009i | \(-0.278256\pi\) |
−0.343431 | + | 0.939178i | \(0.611589\pi\) | |||||||
\(284\) | −26.0657 | + | 108.408i | −0.0917806 | + | 0.381718i | ||||
\(285\) | 89.6747 | − | 145.955i | 0.314648 | − | 0.512123i | ||||
\(286\) | 64.9132 | − | 547.646i | 0.226969 | − | 1.91485i | ||||
\(287\) | −49.7136 | − | 28.7022i | −0.173218 | − | 0.100007i | ||||
\(288\) | −253.876 | + | 124.928i | −0.881514 | + | 0.433777i | ||||
\(289\) | 115.160 | + | 199.463i | 0.398478 | + | 0.690184i | ||||
\(290\) | 0.0754473 | − | 0.101000i | 0.000260163 | − | 0.000348276i | ||||
\(291\) | 474.106 | − | 273.725i | 1.62923 | − | 0.940636i | ||||
\(292\) | 359.834 | + | 86.5187i | 1.23231 | + | 0.296297i | ||||
\(293\) | 263.379 | 0.898903 | 0.449451 | − | 0.893305i | \(-0.351619\pi\) | ||||
0.449451 | + | 0.893305i | \(0.351619\pi\) | |||||||
\(294\) | 354.541 | − | 152.251i | 1.20592 | − | 0.517860i | ||||
\(295\) | −136.516 | + | 78.8176i | −0.462766 | + | 0.267178i | ||||
\(296\) | −146.934 | − | 54.2925i | −0.496399 | − | 0.183421i | ||||
\(297\) | 9.23612 | 0.0310981 | ||||||||
\(298\) | 18.7112 | + | 43.5720i | 0.0627892 | + | 0.146215i | ||||
\(299\) | −182.103 | − | 105.137i | −0.609041 | − | 0.351630i | ||||
\(300\) | 331.233 | − | 97.9923i | 1.10411 | − | 0.326641i | ||||
\(301\) | −54.0725 | + | 93.6563i | −0.179643 | + | 0.311151i | ||||
\(302\) | −124.563 | − | 93.0491i | −0.412462 | − | 0.308110i | ||||
\(303\) | 385.636i | 1.27273i | ||||||||
\(304\) | 145.549 | − | 266.892i | 0.478780 | − | 0.877935i | ||||
\(305\) | 101.010 | 0.331182 | ||||||||
\(306\) | 81.0715 | − | 108.529i | 0.264940 | − | 0.354670i | ||||
\(307\) | 245.559 | + | 141.774i | 0.799866 | + | 0.461803i | 0.843424 | − | 0.537248i | \(-0.180536\pi\) |
−0.0435580 | + | 0.999051i | \(0.513869\pi\) | |||||||
\(308\) | −28.6692 | − | 96.9075i | −0.0930820 | − | 0.314635i | ||||
\(309\) | −143.227 | + | 248.077i | −0.463519 | + | 0.802838i | ||||
\(310\) | −165.653 | + | 71.1366i | −0.534365 | + | 0.229473i | ||||
\(311\) | 254.508i | 0.818352i | 0.912455 | + | 0.409176i | \(0.134184\pi\) | ||||
−0.912455 | + | 0.409176i | \(0.865816\pi\) | |||||||
\(312\) | −233.142 | + | 630.961i | −0.747250 | + | 2.02231i | ||||
\(313\) | −167.705 | − | 290.473i | −0.535798 | − | 0.928029i | −0.999124 | − | 0.0418410i | \(-0.986678\pi\) |
0.463327 | − | 0.886188i | \(-0.346656\pi\) | |||||||
\(314\) | 199.501 | + | 464.570i | 0.635353 | + | 1.47952i | ||||
\(315\) | 34.4224i | 0.109277i | ||||||||
\(316\) | −119.512 | + | 497.056i | −0.378204 | + | 1.57296i | ||||
\(317\) | −132.064 | − | 228.741i | −0.416605 | − | 0.721580i | 0.578991 | − | 0.815334i | \(-0.303447\pi\) |
−0.995595 | + | 0.0937538i | \(0.970113\pi\) | |||||||
\(318\) | −403.743 | − | 301.597i | −1.26963 | − | 0.948418i | ||||
\(319\) | 0.354276 | − | 0.204541i | 0.00111058 | − | 0.000641195i | ||||
\(320\) | −128.816 | + | 45.4674i | −0.402550 | + | 0.142086i | ||||
\(321\) | −202.501 | + | 350.742i | −0.630844 | + | 1.09265i | ||||
\(322\) | −38.2652 | − | 4.53563i | −0.118836 | − | 0.0140858i | ||||
\(323\) | −3.97881 | + | 145.491i | −0.0123183 | + | 0.450436i | ||||
\(324\) | −320.450 | − | 77.0493i | −0.989044 | − | 0.237806i | ||||
\(325\) | 203.479 | − | 352.435i | 0.626088 | − | 1.08442i | ||||
\(326\) | −93.2122 | − | 69.6297i | −0.285927 | − | 0.213588i | ||||
\(327\) | −226.103 | + | 130.541i | −0.691448 | + | 0.399208i | ||||
\(328\) | −193.669 | + | 160.905i | −0.590454 | + | 0.490563i | ||||
\(329\) | −81.6424 | − | 141.409i | −0.248153 | − | 0.429814i | ||||
\(330\) | −248.044 | − | 29.4010i | −0.751650 | − | 0.0890940i | ||||
\(331\) | − | 611.200i | − | 1.84653i | −0.384170 | − | 0.923263i | \(-0.625512\pi\) | ||
0.384170 | − | 0.923263i | \(-0.374488\pi\) | |||||||
\(332\) | 341.027 | − | 100.890i | 1.02719 | − | 0.303885i | ||||
\(333\) | 86.5667 | + | 149.938i | 0.259960 | + | 0.450264i | ||||
\(334\) | −37.8766 | + | 319.549i | −0.113403 | + | 0.956734i | ||||
\(335\) | 14.2391i | 0.0425047i | ||||||||
\(336\) | 6.36694 | + | 123.101i | 0.0189492 | + | 0.366371i | ||||
\(337\) | 34.4295 | − | 59.6337i | 0.102165 | − | 0.176955i | −0.810412 | − | 0.585861i | \(-0.800756\pi\) |
0.912576 | + | 0.408906i | \(0.134090\pi\) | |||||||
\(338\) | 179.333 | + | 417.606i | 0.530571 | + | 1.23552i | ||||
\(339\) | −123.438 | − | 71.2669i | −0.364124 | − | 0.210227i | ||||
\(340\) | 45.0359 | − | 47.4254i | 0.132458 | − | 0.139486i | ||||
\(341\) | −584.998 | −1.71554 | ||||||||
\(342\) | −312.247 | + | 124.092i | −0.913003 | + | 0.362843i | ||||
\(343\) | − | 172.673i | − | 0.503421i | ||||||
\(344\) | 303.131 | + | 364.856i | 0.881195 | + | 1.06063i | ||||
\(345\) | −47.6197 | + | 82.4797i | −0.138028 | + | 0.239072i | ||||
\(346\) | 194.723 | + | 453.445i | 0.562785 | + | 1.31053i | ||||
\(347\) | −426.970 | − | 246.511i | −1.23046 | − | 0.710407i | −0.263336 | − | 0.964704i | \(-0.584823\pi\) |
−0.967126 | + | 0.254297i | \(0.918156\pi\) | |||||||
\(348\) | −0.478471 | + | 0.141551i | −0.00137492 | + | 0.000406757i | ||||
\(349\) | −180.545 | −0.517320 | −0.258660 | − | 0.965968i | \(-0.583281\pi\) | ||||
−0.258660 | + | 0.965968i | \(0.583281\pi\) | |||||||
\(350\) | 8.77807 | − | 74.0570i | 0.0250802 | − | 0.211591i | ||||
\(351\) | −11.4943 | + | 6.63621i | −0.0327472 | + | 0.0189066i | ||||
\(352\) | −442.297 | − | 29.3698i | −1.25653 | − | 0.0834369i | ||||
\(353\) | 441.313 | 1.25018 | 0.625089 | − | 0.780553i | \(-0.285063\pi\) | ||||
0.625089 | + | 0.780553i | \(0.285063\pi\) | |||||||
\(354\) | 619.571 | + | 73.4386i | 1.75020 | + | 0.207454i | ||||
\(355\) | 51.5254 | − | 29.7482i | 0.145142 | − | 0.0837978i | ||||
\(356\) | 171.971 | − | 181.095i | 0.483064 | − | 0.508694i | ||||
\(357\) | −29.5077 | − | 51.1088i | −0.0826545 | − | 0.143162i | ||||
\(358\) | −207.302 | − | 154.855i | −0.579056 | − | 0.432556i | ||||
\(359\) | 119.997 | + | 69.2800i | 0.334252 | + | 0.192981i | 0.657727 | − | 0.753256i | \(-0.271518\pi\) |
−0.323475 | + | 0.946237i | \(0.604851\pi\) | |||||||
\(360\) | 141.626 | + | 52.3312i | 0.393405 | + | 0.145364i | ||||
\(361\) | 197.317 | − | 302.303i | 0.546585 | − | 0.837404i | ||||
\(362\) | −381.909 | − | 45.2682i | −1.05500 | − | 0.125050i | ||||
\(363\) | −259.301 | − | 149.707i | −0.714327 | − | 0.412417i | ||||
\(364\) | 105.307 | + | 100.001i | 0.289306 | + | 0.274729i | ||||
\(365\) | −98.7420 | − | 171.026i | −0.270526 | − | 0.468565i | ||||
\(366\) | −320.294 | − | 239.260i | −0.875120 | − | 0.653716i | ||||
\(367\) | 304.552 | − | 175.833i | 0.829841 | − | 0.479109i | −0.0239571 | − | 0.999713i | \(-0.507627\pi\) |
0.853798 | + | 0.520604i | \(0.174293\pi\) | |||||||
\(368\) | −76.8345 | + | 150.541i | −0.208790 | + | 0.409080i | ||||
\(369\) | 278.295 | 0.754187 | ||||||||
\(370\) | 32.9823 | + | 76.8047i | 0.0891415 | + | 0.207580i | ||||
\(371\) | −94.2247 | + | 54.4006i | −0.253975 | + | 0.146632i | ||||
\(372\) | 693.768 | + | 166.810i | 1.86497 | + | 0.448414i | ||||
\(373\) | −196.793 | −0.527594 | −0.263797 | − | 0.964578i | \(-0.584975\pi\) | ||||
−0.263797 | + | 0.964578i | \(0.584975\pi\) | |||||||
\(374\) | 195.003 | − | 83.7406i | 0.521400 | − | 0.223905i | ||||
\(375\) | −354.828 | − | 204.860i | −0.946208 | − | 0.546293i | ||||
\(376\) | −705.924 | + | 120.927i | −1.87746 | + | 0.321614i | ||||
\(377\) | −0.293928 | + | 0.509099i | −0.000779650 | + | 0.00135039i | ||||
\(378\) | −1.45557 | + | 1.94855i | −0.00385072 | + | 0.00515490i | ||||
\(379\) | − | 169.249i | − | 0.446566i | −0.974754 | − | 0.223283i | \(-0.928323\pi\) | ||
0.974754 | − | 0.223283i | \(-0.0716774\pi\) | |||||||
\(380\) | −156.754 | + | 41.7496i | −0.412510 | + | 0.109867i | ||||
\(381\) | 140.695 | 0.369279 | ||||||||
\(382\) | −2.06827 | − | 1.54500i | −0.00541431 | − | 0.00404450i | ||||
\(383\) | 343.442 | + | 198.286i | 0.896715 | + | 0.517718i | 0.876133 | − | 0.482070i | \(-0.160115\pi\) |
0.0205817 | + | 0.999788i | \(0.493448\pi\) | |||||||
\(384\) | 516.160 | + | 160.950i | 1.34417 | + | 0.419141i | ||||
\(385\) | −26.9633 | + | 46.7017i | −0.0700345 | + | 0.121303i | ||||
\(386\) | −294.490 | − | 685.768i | −0.762928 | − | 1.77660i | ||||
\(387\) | − | 524.285i | − | 1.35474i | ||||||
\(388\) | −504.054 | − | 121.195i | −1.29911 | − | 0.312358i | ||||
\(389\) | 192.573 | + | 333.547i | 0.495047 | + | 0.857447i | 0.999984 | − | 0.00570929i | \(-0.00181733\pi\) |
−0.504936 | + | 0.863157i | \(0.668484\pi\) | |||||||
\(390\) | 329.813 | − | 141.632i | 0.845675 | − | 0.363159i | ||||
\(391\) | − | 80.9191i | − | 0.206954i | ||||||
\(392\) | −342.739 | − | 126.643i | −0.874333 | − | 0.323069i | ||||
\(393\) | 28.9167 | + | 50.0851i | 0.0735793 | + | 0.127443i | ||||
\(394\) | 229.533 | − | 307.273i | 0.582572 | − | 0.779880i | ||||
\(395\) | 236.247 | − | 136.397i | 0.598093 | − | 0.345309i | ||||
\(396\) | 355.270 | + | 337.370i | 0.897146 | + | 0.851944i | ||||
\(397\) | −141.267 | + | 244.682i | −0.355837 | + | 0.616328i | −0.987261 | − | 0.159110i | \(-0.949138\pi\) |
0.631424 | + | 0.775438i | \(0.282471\pi\) | |||||||
\(398\) | −77.5804 | + | 654.513i | −0.194926 | + | 1.64451i | ||||
\(399\) | −4.00157 | + | 146.323i | −0.0100290 | + | 0.366724i | ||||
\(400\) | −291.352 | − | 148.702i | −0.728380 | − | 0.371756i | ||||
\(401\) | −4.00500 | + | 6.93686i | −0.00998753 | + | 0.0172989i | −0.870976 | − | 0.491326i | \(-0.836513\pi\) |
0.860988 | + | 0.508625i | \(0.169846\pi\) | |||||||
\(402\) | 33.7276 | − | 45.1507i | 0.0838996 | − | 0.112315i | ||||
\(403\) | 728.023 | − | 420.325i | 1.80651 | − | 1.04299i | ||||
\(404\) | 251.468 | − | 264.811i | 0.622446 | − | 0.655472i | ||||
\(405\) | 87.9348 | + | 152.308i | 0.217123 | + | 0.376068i | ||||
\(406\) | −0.0126801 | + | 0.106977i | −3.12317e−5 | + | 0.000263489i | ||||
\(407\) | 271.233i | 0.666421i | ||||||||
\(408\) | −255.139 | + | 43.7061i | −0.625341 | + | 0.107123i | ||||
\(409\) | −77.6731 | − | 134.534i | −0.189910 | − | 0.328933i | 0.755310 | − | 0.655367i | \(-0.227486\pi\) |
−0.945220 | + | 0.326434i | \(0.894153\pi\) | |||||||
\(410\) | 133.424 | + | 15.8149i | 0.325424 | + | 0.0385730i | ||||
\(411\) | − | 564.012i | − | 1.37229i | ||||||
\(412\) | 260.120 | − | 76.9541i | 0.631359 | − | 0.186782i | ||||
\(413\) | 67.3495 | − | 116.653i | 0.163074 | − | 0.282452i | ||||
\(414\) | 171.650 | − | 73.7118i | 0.414613 | − | 0.178048i | ||||
\(415\) | −164.348 | − | 94.8862i | −0.396019 | − | 0.228642i | ||||
\(416\) | 571.536 | − | 281.243i | 1.37389 | − | 0.676064i | ||||
\(417\) | −938.954 | −2.25169 | ||||||||
\(418\) | −520.836 | − | 76.2261i | −1.24602 | − | 0.182359i | ||||
\(419\) | 402.751i | 0.961220i | 0.876934 | + | 0.480610i | \(0.159585\pi\) | ||||
−0.876934 | + | 0.480610i | \(0.840415\pi\) | |||||||
\(420\) | 45.2934 | − | 47.6966i | 0.107842 | − | 0.113563i | ||||
\(421\) | −227.604 | + | 394.222i | −0.540628 | + | 0.936395i | 0.458240 | + | 0.888828i | \(0.348480\pi\) |
−0.998868 | + | 0.0475667i | \(0.984853\pi\) | |||||||
\(422\) | −102.399 | + | 43.9734i | −0.242652 | + | 0.104202i | ||||
\(423\) | 685.547 | + | 395.801i | 1.62068 | + | 0.935699i | ||||
\(424\) | 80.5770 | + | 470.378i | 0.190040 | + | 1.10938i | ||||
\(425\) | 156.608 | 0.368488 | ||||||||
\(426\) | −233.846 | − | 27.7180i | −0.548933 | − | 0.0650658i | ||||
\(427\) | −74.7495 | + | 43.1566i | −0.175057 | + | 0.101069i | ||||
\(428\) | 367.768 | − | 108.801i | 0.859271 | − | 0.254208i | ||||
\(429\) | 1164.72 | 2.71498 | ||||||||
\(430\) | 29.7940 | − | 251.360i | 0.0692884 | − | 0.584557i | ||||
\(431\) | 427.854 | − | 247.021i | 0.992700 | − | 0.573135i | 0.0866195 | − | 0.996241i | \(-0.472394\pi\) |
0.906080 | + | 0.423106i | \(0.139060\pi\) | |||||||
\(432\) | 5.80418 | + | 8.95106i | 0.0134356 | + | 0.0207200i | ||||
\(433\) | −127.503 | − | 220.842i | −0.294465 | − | 0.510029i | 0.680395 | − | 0.732845i | \(-0.261808\pi\) |
−0.974860 | + | 0.222817i | \(0.928475\pi\) | |||||||
\(434\) | 92.1930 | − | 123.417i | 0.212426 | − | 0.284372i | ||||
\(435\) | 0.230585 | + | 0.133128i | 0.000530081 | + | 0.000306042i | ||||
\(436\) | 240.386 | + | 57.7985i | 0.551343 | + | 0.132565i | ||||
\(437\) | −105.067 | + | 171.008i | −0.240428 | + | 0.391323i | ||||
\(438\) | −92.0032 | + | 776.193i | −0.210053 | + | 1.77213i | ||||
\(439\) | −80.1980 | − | 46.3023i | −0.182683 | − | 0.105472i | 0.405869 | − | 0.913931i | \(-0.366969\pi\) |
−0.588553 | + | 0.808459i | \(0.700302\pi\) | |||||||
\(440\) | 151.156 | + | 181.936i | 0.343537 | + | 0.413490i | ||||
\(441\) | 201.926 | + | 349.746i | 0.457881 | + | 0.793074i | ||||
\(442\) | −182.512 | + | 244.325i | −0.412922 | + | 0.552772i | ||||
\(443\) | −319.754 | + | 184.610i | −0.721792 | + | 0.416727i | −0.815412 | − | 0.578881i | \(-0.803489\pi\) |
0.0936200 | + | 0.995608i | \(0.470156\pi\) | |||||||
\(444\) | 77.3412 | − | 321.664i | 0.174192 | − | 0.724469i | ||||
\(445\) | −133.264 | −0.299469 | ||||||||
\(446\) | −75.7965 | + | 32.5494i | −0.169947 | + | 0.0729807i | ||||
\(447\) | −86.7327 | + | 50.0751i | −0.194033 | + | 0.112025i | ||||
\(448\) | 75.9002 | − | 88.6832i | 0.169420 | − | 0.197954i | ||||
\(449\) | −457.229 | −1.01833 | −0.509163 | − | 0.860670i | \(-0.670045\pi\) | ||||
−0.509163 | + | 0.860670i | \(0.670045\pi\) | |||||||
\(450\) | 142.659 | + | 332.204i | 0.317020 | + | 0.738232i | ||||
\(451\) | 377.570 | + | 217.990i | 0.837184 | + | 0.483349i | ||||
\(452\) | 38.2908 | + | 129.430i | 0.0847141 | + | 0.286350i | ||||
\(453\) | 164.187 | − | 284.381i | 0.362444 | − | 0.627772i | ||||
\(454\) | −443.948 | − | 331.630i | −0.977858 | − | 0.730462i | ||||
\(455\) | − | 77.4931i | − | 0.170314i | ||||||
\(456\) | 595.941 | + | 238.914i | 1.30689 | + | 0.523933i | ||||
\(457\) | 83.5243 | 0.182767 | 0.0913833 | − | 0.995816i | \(-0.470871\pi\) | ||||
0.0913833 | + | 0.995816i | \(0.470871\pi\) | |||||||
\(458\) | 168.979 | − | 226.209i | 0.368949 | − | 0.493907i | ||||
\(459\) | −4.42328 | − | 2.55378i | −0.00963679 | − | 0.00556380i | ||||
\(460\) | 86.4836 | − | 25.5854i | 0.188008 | − | 0.0556205i | ||||
\(461\) | −120.895 | + | 209.396i | −0.262245 | + | 0.454221i | −0.966838 | − | 0.255390i | \(-0.917796\pi\) |
0.704593 | + | 0.709611i | \(0.251129\pi\) | |||||||
\(462\) | 196.119 | − | 84.2195i | 0.424499 | − | 0.182293i | ||||
\(463\) | − | 159.241i | − | 0.343934i | −0.985103 | − | 0.171967i | \(-0.944988\pi\) | ||
0.985103 | − | 0.171967i | \(-0.0550123\pi\) | |||||||
\(464\) | 0.420863 | + | 0.214803i | 0.000907032 | + | 0.000462938i | ||||
\(465\) | −190.377 | − | 329.742i | −0.409413 | − | 0.709124i | ||||
\(466\) | −70.3700 | − | 163.868i | −0.151009 | − | 0.351648i | ||||
\(467\) | − | 17.6334i | − | 0.0377588i | −0.999822 | − | 0.0188794i | \(-0.993990\pi\) | ||
0.999822 | − | 0.0188794i | \(-0.00600986\pi\) | |||||||
\(468\) | −684.532 | − | 164.589i | −1.46267 | − | 0.351687i | ||||
\(469\) | −6.08363 | − | 10.5372i | −0.0129715 | − | 0.0224673i | ||||
\(470\) | 306.182 | + | 228.718i | 0.651450 | + | 0.486635i | ||||
\(471\) | −924.755 | + | 533.907i | −1.96339 | + | 1.13356i | ||||
\(472\) | −377.562 | − | 454.443i | −0.799919 | − | 0.962803i | ||||
\(473\) | 410.676 | − | 711.311i | 0.868236 | − | 1.50383i | ||||
\(474\) | −1072.19 | − | 127.089i | −2.26201 | − | 0.268119i | ||||
\(475\) | −330.962 | − | 203.343i | −0.696763 | − | 0.428090i | ||||
\(476\) | −13.0649 | + | 54.3371i | −0.0274472 | + | 0.114154i | ||||
\(477\) | 263.733 | − | 456.799i | 0.552900 | − | 0.957651i | ||||
\(478\) | 131.860 | + | 98.4993i | 0.275857 | + | 0.206066i | ||||
\(479\) | −164.704 | + | 95.0917i | −0.343849 | + | 0.198521i | −0.661973 | − | 0.749528i | \(-0.730281\pi\) |
0.318124 | + | 0.948049i | \(0.396947\pi\) | |||||||
\(480\) | −127.383 | − | 258.865i | −0.265381 | − | 0.539302i | ||||
\(481\) | −194.883 | − | 337.547i | −0.405161 | − | 0.701760i | ||||
\(482\) | −88.5585 | − | 10.4970i | −0.183731 | − | 0.0217779i | ||||
\(483\) | − | 81.3818i | − | 0.168492i | ||||||
\(484\) | 80.4357 | + | 271.888i | 0.166190 | + | 0.561752i | ||||
\(485\) | 138.317 | + | 239.573i | 0.285191 | + | 0.493965i | ||||
\(486\) | 80.5209 | − | 679.322i | 0.165681 | − | 1.39778i | ||||
\(487\) | 421.853i | 0.866228i | 0.901339 | + | 0.433114i | \(0.142585\pi\) | ||||
−0.901339 | + | 0.433114i | \(0.857415\pi\) | |||||||
\(488\) | 63.9227 | + | 373.156i | 0.130989 | + | 0.764663i | ||||
\(489\) | 122.863 | − | 212.805i | 0.251254 | − | 0.435185i | ||||
\(490\) | 76.9347 | + | 179.155i | 0.157010 | + | 0.365622i | ||||
\(491\) | 707.298 | + | 408.359i | 1.44053 | + | 0.831688i | 0.997885 | − | 0.0650112i | \(-0.0207083\pi\) |
0.442641 | + | 0.896699i | \(0.354042\pi\) | |||||||
\(492\) | −385.613 | − | 366.184i | −0.783767 | − | 0.744277i | ||||
\(493\) | −0.226222 | −0.000458869 | ||||||||
\(494\) | 702.944 | − | 279.361i | 1.42296 | − | 0.565509i | ||||
\(495\) | − | 261.435i | − | 0.528151i | ||||||
\(496\) | −367.625 | − | 566.943i | −0.741180 | − | 1.14303i | ||||
\(497\) | −25.4198 | + | 44.0284i | −0.0511465 | + | 0.0885883i | ||||
\(498\) | 296.376 | + | 690.160i | 0.595133 | + | 1.38586i | ||||
\(499\) | −446.851 | − | 257.989i | −0.895492 | − | 0.517013i | −0.0197574 | − | 0.999805i | \(-0.506289\pi\) |
−0.875735 | + | 0.482792i | \(0.839623\pi\) | |||||||
\(500\) | 110.069 | + | 372.053i | 0.220137 | + | 0.744106i | ||||
\(501\) | −679.612 | −1.35651 | ||||||||
\(502\) | 25.7893 | − | 217.573i | 0.0513730 | − | 0.433413i | ||||
\(503\) | −328.542 | + | 189.684i | −0.653165 | + | 0.377105i | −0.789668 | − | 0.613535i | \(-0.789747\pi\) |
0.136503 | + | 0.990640i | \(0.456414\pi\) | |||||||
\(504\) | −127.164 | + | 21.7836i | −0.252310 | + | 0.0432214i | ||||
\(505\) | −194.868 | −0.385877 | ||||||||
\(506\) | 290.621 | + | 34.4477i | 0.574350 | + | 0.0680784i | ||||
\(507\) | −831.270 | + | 479.934i | −1.63959 | + | 0.946615i | ||||
\(508\) | −96.6132 | − | 91.7454i | −0.190184 | − | 0.180601i | ||||
\(509\) | 56.0386 | + | 97.0617i | 0.110096 | + | 0.190691i | 0.915809 | − | 0.401615i | \(-0.131551\pi\) |
−0.805713 | + | 0.592306i | \(0.798218\pi\) | |||||||
\(510\) | 110.662 | + | 82.6647i | 0.216984 | + | 0.162088i | ||||
\(511\) | 146.141 | + | 84.3748i | 0.285991 | + | 0.165117i | ||||
\(512\) | −249.486 | − | 447.103i | −0.487277 | − | 0.873248i | ||||
\(513\) | 6.03194 | + | 11.1403i | 0.0117582 | + | 0.0217159i | ||||
\(514\) | 889.778 | + | 105.467i | 1.73109 | + | 0.205188i | ||||
\(515\) | −125.357 | − | 72.3749i | −0.243412 | − | 0.140534i | ||||
\(516\) | −689.861 | + | 726.464i | −1.33694 | + | 1.40788i | ||||
\(517\) | 620.066 | + | 1073.99i | 1.19935 | + | 2.07734i | ||||
\(518\) | −57.2222 | − | 42.7451i | −0.110468 | − | 0.0825195i | ||||
\(519\) | −902.610 | + | 521.122i | −1.73913 | + | 1.00409i | ||||
\(520\) | −318.834 | − | 117.810i | −0.613143 | − | 0.226558i | ||||
\(521\) | −269.639 | −0.517542 | −0.258771 | − | 0.965939i | \(-0.583317\pi\) | ||||
−0.258771 | + | 0.965939i | \(0.583317\pi\) | |||||||
\(522\) | −0.206073 | − | 0.479875i | −0.000394776 | − | 0.000919300i | ||||
\(523\) | 416.867 | − | 240.678i | 0.797068 | − | 0.460188i | −0.0453767 | − | 0.998970i | \(-0.514449\pi\) |
0.842445 | + | 0.538782i | \(0.181115\pi\) | |||||||
\(524\) | 12.8032 | − | 53.2489i | 0.0244336 | − | 0.101620i | ||||
\(525\) | 157.503 | 0.300006 | ||||||||
\(526\) | −578.318 | + | 248.348i | −1.09946 | + | 0.472144i | ||||
\(527\) | 280.162 | + | 161.752i | 0.531617 | + | 0.306929i | ||||
\(528\) | −48.3563 | − | 934.938i | −0.0915839 | − | 1.77072i | ||||
\(529\) | −208.706 | + | 361.490i | −0.394530 | + | 0.683346i | ||||
\(530\) | 152.402 | − | 204.018i | 0.287550 | − | 0.384939i | ||||
\(531\) | 653.018i | 1.22979i | ||||||||
\(532\) | 98.1629 | − | 97.8683i | 0.184517 | − | 0.183963i | ||||
\(533\) | −626.509 | −1.17544 | ||||||||
\(534\) | 422.565 | + | 315.657i | 0.791321 | + | 0.591118i | ||||
\(535\) | −177.235 | − | 102.327i | −0.331281 | − | 0.191265i | ||||
\(536\) | −52.6024 | + | 9.01095i | −0.0981388 | + | 0.0168115i | ||||
\(537\) | 273.245 | − | 473.275i | 0.508837 | − | 0.881331i | ||||
\(538\) | −229.749 | − | 535.009i | −0.427043 | − | 0.994440i | ||||
\(539\) | 632.679i | 1.17380i | ||||||||
\(540\) | 1.33082 | − | 5.53493i | 0.00246449 | − | 0.0102499i | ||||
\(541\) | 52.7461 | + | 91.3589i | 0.0974974 | + | 0.168870i | 0.910648 | − | 0.413183i | \(-0.135583\pi\) |
−0.813151 | + | 0.582053i | \(0.802250\pi\) | |||||||
\(542\) | 236.917 | − | 101.740i | 0.437116 | − | 0.187711i | ||||
\(543\) | − | 812.238i | − | 1.49583i | ||||||
\(544\) | 203.700 | + | 136.361i | 0.374449 | + | 0.250663i | ||||
\(545\) | −65.9643 | − | 114.253i | −0.121035 | − | 0.209639i | ||||
\(546\) | −183.555 | + | 245.723i | −0.336182 | + | 0.450041i | ||||
\(547\) | 547.959 | − | 316.364i | 1.00175 | − | 0.578363i | 0.0929871 | − | 0.995667i | \(-0.470358\pi\) |
0.908767 | + | 0.417304i | \(0.137025\pi\) | |||||||
\(548\) | −367.785 | + | 387.299i | −0.671140 | + | 0.706749i | ||||
\(549\) | 209.223 | − | 362.384i | 0.381097 | − | 0.660080i | ||||
\(550\) | −66.6687 | + | 562.456i | −0.121216 | + | 1.02265i | ||||
\(551\) | 0.478081 | + | 0.293732i | 0.000867660 | + | 0.000533089i | ||||
\(552\) | −334.834 | − | 123.722i | −0.606583 | − | 0.224134i | ||||
\(553\) | −116.551 | + | 201.872i | −0.210761 | + | 0.365049i | ||||
\(554\) | 27.6501 | − | 37.0148i | 0.0499100 | − | 0.0668137i | ||||
\(555\) | −152.884 | + | 88.2679i | −0.275467 | + | 0.159041i | ||||
\(556\) | 644.765 | + | 612.279i | 1.15965 | + | 1.10122i | ||||
\(557\) | 526.047 | + | 911.140i | 0.944429 | + | 1.63580i | 0.756891 | + | 0.653541i | \(0.226717\pi\) |
0.187538 | + | 0.982257i | \(0.439949\pi\) | |||||||
\(558\) | −87.9075 | + | 741.640i | −0.157540 | + | 1.32910i | ||||
\(559\) | 1180.29i | 2.11143i | ||||||||
\(560\) | −62.2046 | + | 3.21731i | −0.111080 | + | 0.00574520i | ||||
\(561\) | 224.108 | + | 388.166i | 0.399479 | + | 0.691919i | ||||
\(562\) | 131.911 | + | 15.6356i | 0.234717 | + | 0.0278213i | ||||
\(563\) | 619.106i | 1.09966i | 0.835278 | + | 0.549828i | \(0.185307\pi\) | ||||
−0.835278 | + | 0.549828i | \(0.814693\pi\) | |||||||
\(564\) | −429.113 | − | 1450.48i | −0.760839 | − | 2.57178i | ||||
\(565\) | 36.0123 | − | 62.3751i | 0.0637385 | − | 0.110398i | ||||
\(566\) | 179.081 | − | 76.9029i | 0.316397 | − | 0.135871i | ||||
\(567\) | −130.146 | − | 75.1401i | −0.229535 | − | 0.132522i | ||||
\(568\) | 142.504 | + | 171.521i | 0.250887 | + | 0.301974i | ||||
\(569\) | 246.403 | 0.433046 | 0.216523 | − | 0.976277i | \(-0.430528\pi\) | ||||
0.216523 | + | 0.976277i | \(0.430528\pi\) | |||||||
\(570\) | −126.531 | − | 318.383i | −0.221984 | − | 0.558567i | ||||
\(571\) | 88.9193i | 0.155726i | 0.996964 | + | 0.0778628i | \(0.0248096\pi\) | ||||
−0.996964 | + | 0.0778628i | \(0.975190\pi\) | |||||||
\(572\) | −799.799 | − | 759.501i | −1.39825 | − | 1.32780i | ||||
\(573\) | 2.72619 | − | 4.72189i | 0.00475774 | − | 0.00824065i | ||||
\(574\) | −105.493 | + | 45.3019i | −0.183786 | + | 0.0789232i | ||||
\(575\) | 187.028 | + | 107.981i | 0.325266 | + | 0.187792i | ||||
\(576\) | −103.698 | + | 556.315i | −0.180031 | + | 0.965825i | ||||
\(577\) | 659.532 | 1.14304 | 0.571518 | − | 0.820589i | \(-0.306355\pi\) | ||||
0.571518 | + | 0.820589i | \(0.306355\pi\) | |||||||
\(578\) | 457.438 | + | 54.2208i | 0.791416 | + | 0.0938076i | ||||
\(579\) | 1365.06 | − | 788.120i | 2.35762 | − | 1.36117i | ||||
\(580\) | −0.0715281 | − | 0.241779i | −0.000123324 | − | 0.000416860i | ||||
\(581\) | 162.160 | 0.279105 | ||||||||
\(582\) | 128.878 | − | 1087.29i | 0.221440 | − | 1.86819i | ||||
\(583\) | 715.628 | − | 413.168i | 1.22749 | − | 0.708693i | ||||
\(584\) | 569.322 | − | 473.006i | 0.974867 | − | 0.809942i | ||||
\(585\) | 187.842 | + | 325.353i | 0.321098 | + | 0.556158i | ||||
\(586\) | 315.244 | − | 422.012i | 0.537959 | − | 0.720157i | ||||
\(587\) | −847.759 | − | 489.454i | −1.44422 | − | 0.833822i | −0.446095 | − | 0.894986i | \(-0.647186\pi\) |
−0.998128 | + | 0.0611631i | \(0.980519\pi\) | |||||||
\(588\) | 180.406 | − | 750.314i | 0.306813 | − | 1.27604i | ||||
\(589\) | −382.051 | − | 705.603i | −0.648644 | − | 1.19797i | ||||
\(590\) | −37.1096 | + | 313.079i | −0.0628977 | + | 0.530642i | ||||
\(591\) | 701.509 | + | 405.017i | 1.18699 | + | 0.685307i | ||||
\(592\) | −262.862 | + | 170.449i | −0.444023 | + | 0.287920i | ||||
\(593\) | −102.396 | − | 177.355i | −0.172675 | − | 0.299081i | 0.766679 | − | 0.642030i | \(-0.221908\pi\) |
−0.939354 | + | 0.342949i | \(0.888574\pi\) | |||||||
\(594\) | 11.0549 | − | 14.7991i | 0.0186110 | − | 0.0249143i | ||||
\(595\) | 25.8260 | − | 14.9107i | 0.0434051 | − | 0.0250599i | ||||
\(596\) | 92.2114 | + | 22.1714i | 0.154717 | + | 0.0372003i | ||||
\(597\) | −1392.01 | −2.33167 | ||||||||
\(598\) | −386.425 | + | 165.943i | −0.646196 | + | 0.277497i | ||||
\(599\) | 844.006 | − | 487.287i | 1.40903 | − | 0.813501i | 0.413731 | − | 0.910399i | \(-0.364225\pi\) |
0.995294 | + | 0.0968983i | \(0.0308922\pi\) | |||||||
\(600\) | 239.447 | − | 648.024i | 0.399078 | − | 1.08004i | ||||
\(601\) | 371.313 | 0.617825 | 0.308913 | − | 0.951090i | \(-0.400035\pi\) | ||||
0.308913 | + | 0.951090i | \(0.400035\pi\) | |||||||
\(602\) | 85.3451 | + | 198.740i | 0.141769 | + | 0.330133i | ||||
\(603\) | 51.0840 | + | 29.4933i | 0.0847164 | + | 0.0489110i | ||||
\(604\) | −298.186 | + | 88.2156i | −0.493685 | + | 0.146052i | ||||
\(605\) | 75.6494 | − | 131.029i | 0.125040 | − | 0.216576i | ||||
\(606\) | 617.906 | + | 461.577i | 1.01965 | + | 0.761678i | ||||
\(607\) | − | 692.679i | − | 1.14115i | −0.821245 | − | 0.570576i | \(-0.806720\pi\) | ||
0.821245 | − | 0.570576i | \(-0.193280\pi\) | |||||||
\(608\) | −253.431 | − | 552.663i | −0.416828 | − | 0.908986i | ||||
\(609\) | −0.227516 | −0.000373589 | ||||||||
\(610\) | 120.902 | − | 161.849i | 0.198200 | − | 0.265327i | ||||
\(611\) | −1543.33 | − | 891.043i | −2.52591 | − | 1.45834i | ||||
\(612\) | −76.8602 | − | 259.802i | −0.125589 | − | 0.424513i | ||||
\(613\) | 257.281 | − | 445.624i | 0.419708 | − | 0.726955i | −0.576202 | − | 0.817307i | \(-0.695466\pi\) |
0.995910 | + | 0.0903521i | \(0.0287992\pi\) | |||||||
\(614\) | 521.079 | − | 223.768i | 0.848664 | − | 0.364443i | ||||
\(615\) | 283.764i | 0.461404i | ||||||||
\(616\) | −189.590 | − | 70.0541i | −0.307776 | − | 0.113724i | ||||
\(617\) | 10.0069 | + | 17.3324i | 0.0162186 | + | 0.0280915i | 0.874021 | − | 0.485888i | \(-0.161504\pi\) |
−0.857802 | + | 0.513980i | \(0.828171\pi\) | |||||||
\(618\) | 226.062 | + | 526.423i | 0.365797 | + | 0.851817i | ||||
\(619\) | 266.861i | 0.431117i | 0.976491 | + | 0.215558i | \(0.0691572\pi\) | ||||
−0.976491 | + | 0.215558i | \(0.930843\pi\) | |||||||
\(620\) | −84.2917 | + | 350.571i | −0.135954 | + | 0.565438i | ||||
\(621\) | −3.52166 | − | 6.09969i | −0.00567094 | − | 0.00982236i | ||||
\(622\) | 407.798 | + | 304.626i | 0.655624 | + | 0.489753i | ||||
\(623\) | 98.6174 | − | 56.9368i | 0.158294 | − | 0.0913913i | ||||
\(624\) | 731.938 | + | 1128.78i | 1.17298 | + | 1.80894i | ||||
\(625\) | −152.033 | + | 263.328i | −0.243252 | + | 0.421325i | ||||
\(626\) | −666.155 | − | 78.9603i | −1.06415 | − | 0.126135i | ||||
\(627\) | 30.3915 | − | 1111.31i | 0.0484713 | − | 1.77242i | ||||
\(628\) | 983.169 | + | 236.394i | 1.56556 | + | 0.376423i | ||||
\(629\) | 74.9959 | − | 129.897i | 0.119230 | − | 0.206513i | ||||
\(630\) | 55.1551 | + | 41.2009i | 0.0875477 | + | 0.0653983i | ||||
\(631\) | −707.959 | + | 408.740i | −1.12196 | + | 0.647766i | −0.941901 | − | 0.335890i | \(-0.890963\pi\) |
−0.180062 | + | 0.983655i | \(0.557630\pi\) | |||||||
\(632\) | 653.386 | + | 786.433i | 1.03384 | + | 1.24436i | ||||
\(633\) | −117.682 | − | 203.832i | −0.185912 | − | 0.322009i | ||||
\(634\) | −524.582 | − | 62.1794i | −0.827417 | − | 0.0980748i | ||||
\(635\) | 71.0954i | 0.111961i | ||||||||
\(636\) | −966.499 | + | 285.930i | −1.51965 | + | 0.449576i | ||||
\(637\) | −454.584 | − | 787.362i | −0.713632 | − | 1.23605i | ||||
\(638\) | 0.0963040 | − | 0.812477i | 0.000150947 | − | 0.00127348i | ||||
\(639\) | − | 246.469i | − | 0.385711i | ||||||
\(640\) | −81.3305 | + | 260.823i | −0.127079 | + | 0.407536i | ||||
\(641\) | 118.269 | − | 204.847i | 0.184506 | − | 0.319574i | −0.758904 | − | 0.651203i | \(-0.774265\pi\) |
0.943410 | + | 0.331628i | \(0.107598\pi\) | |||||||
\(642\) | 319.616 | + | 744.279i | 0.497845 | + | 1.15931i | ||||
\(643\) | 364.648 | + | 210.529i | 0.567103 | + | 0.327417i | 0.755992 | − | 0.654581i | \(-0.227155\pi\) |
−0.188888 | + | 0.981999i | \(0.560488\pi\) | |||||||
\(644\) | −53.0680 | + | 55.8837i | −0.0824037 | + | 0.0867759i | ||||
\(645\) | 534.588 | 0.828818 | ||||||||
\(646\) | 228.358 | + | 180.517i | 0.353495 | + | 0.279437i | ||||
\(647\) | − | 633.110i | − | 0.978532i | −0.872135 | − | 0.489266i | \(-0.837265\pi\) | ||
0.872135 | − | 0.489266i | \(-0.162735\pi\) | |||||||
\(648\) | −507.011 | + | 421.236i | −0.782424 | + | 0.650056i | ||||
\(649\) | −511.513 | + | 885.967i | −0.788156 | + | 1.36513i | ||||
\(650\) | −321.160 | − | 747.872i | −0.494092 | − | 1.15057i | ||||
\(651\) | 281.764 | + | 162.677i | 0.432818 | + | 0.249887i | ||||
\(652\) | −223.136 | + | 66.0127i | −0.342233 | + | 0.101247i | ||||
\(653\) | −763.077 | −1.16857 | −0.584286 | − | 0.811548i | \(-0.698625\pi\) | ||||
−0.584286 | + | 0.811548i | \(0.698625\pi\) | |||||||
\(654\) | −61.4625 | + | 518.534i | −0.0939793 | + | 0.792865i | ||||
\(655\) | −25.3088 | + | 14.6120i | −0.0386393 | + | 0.0223084i | ||||
\(656\) | 26.0110 | + | 502.907i | 0.0396509 | + | 0.766626i | ||||
\(657\) | −818.095 | −1.24520 | ||||||||
\(658\) | −324.299 | − | 38.4396i | −0.492856 | − | 0.0584189i | ||||
\(659\) | 308.832 | − | 178.304i | 0.468637 | − | 0.270568i | −0.247032 | − | 0.969007i | \(-0.579455\pi\) |
0.715669 | + | 0.698440i | \(0.246122\pi\) | |||||||
\(660\) | −344.000 | + | 362.251i | −0.521211 | + | 0.548866i | ||||
\(661\) | 131.256 | + | 227.342i | 0.198572 | + | 0.343937i | 0.948066 | − | 0.318075i | \(-0.103036\pi\) |
−0.749494 | + | 0.662011i | \(0.769703\pi\) | |||||||
\(662\) | −979.327 | − | 731.559i | −1.47935 | − | 1.10507i | ||||
\(663\) | −557.800 | − | 322.046i | −0.841327 | − | 0.485740i | ||||
\(664\) | 246.527 | − | 667.185i | 0.371275 | − | 1.00480i | ||||
\(665\) | −73.9391 | − | 2.02205i | −0.111187 | − | 0.00304068i | ||||
\(666\) | 343.860 | + | 40.7582i | 0.516306 | + | 0.0611984i | ||||
\(667\) | −0.270165 | − | 0.155980i | −0.000405045 | − | 0.000233853i | ||||
\(668\) | 466.679 | + | 443.166i | 0.698622 | + | 0.663422i | ||||
\(669\) | −87.1092 | − | 150.878i | −0.130208 | − | 0.225527i | ||||
\(670\) | 22.8153 | + | 17.0431i | 0.0340527 | + | 0.0254374i | ||||
\(671\) | 567.716 | − | 327.771i | 0.846074 | − | 0.488481i | ||||
\(672\) | 204.865 | + | 137.140i | 0.304859 | + | 0.204078i | ||||
\(673\) | 776.136 | 1.15325 | 0.576624 | − | 0.817010i | \(-0.304370\pi\) | ||||
0.576624 | + | 0.817010i | \(0.304370\pi\) | |||||||
\(674\) | −54.3417 | − | 126.544i | −0.0806257 | − | 0.187750i | ||||
\(675\) | 11.8051 | − | 6.81567i | 0.0174890 | − | 0.0100973i | ||||
\(676\) | 883.779 | + | 212.496i | 1.30737 | + | 0.314344i | ||||
\(677\) | 114.432 | 0.169029 | 0.0845144 | − | 0.996422i | \(-0.473066\pi\) | ||||
0.0845144 | + | 0.996422i | \(0.473066\pi\) | |||||||
\(678\) | −261.937 | + | 112.484i | −0.386338 | + | 0.165905i | ||||
\(679\) | −204.715 | − | 118.192i | −0.301494 | − | 0.174068i | ||||
\(680\) | −22.0853 | − | 128.926i | −0.0324785 | − | 0.189597i | ||||
\(681\) | 585.168 | − | 1013.54i | 0.859278 | − | 1.48831i | ||||
\(682\) | −700.198 | + | 937.344i | −1.02668 | + | 1.37440i | ||||
\(683\) | 614.331i | 0.899460i | 0.893164 | + | 0.449730i | \(0.148480\pi\) | ||||
−0.893164 | + | 0.449730i | \(0.851520\pi\) | |||||||
\(684\) | −174.903 | + | 648.843i | −0.255706 | + | 0.948601i | ||||
\(685\) | 285.004 | 0.416064 | ||||||||
\(686\) | −276.675 | − | 206.677i | −0.403316 | − | 0.301278i | ||||
\(687\) | 516.440 | + | 298.167i | 0.751733 | + | 0.434013i | ||||
\(688\) | 947.435 | − | 49.0026i | 1.37709 | − | 0.0712247i | ||||
\(689\) | −593.727 | + | 1028.37i | −0.861723 | + | 1.49255i | ||||
\(690\) | 75.1603 | + | 175.023i | 0.108928 | + | 0.253656i | ||||
\(691\) | 388.024i | 0.561540i | 0.959775 | + | 0.280770i | \(0.0905898\pi\) | ||||
−0.959775 | + | 0.280770i | \(0.909410\pi\) | |||||||
\(692\) | 959.625 | + | 230.733i | 1.38674 | + | 0.333429i | ||||
\(693\) | 111.698 | + | 193.466i | 0.161180 | + | 0.279172i | ||||
\(694\) | −906.037 | + | 389.080i | −1.30553 | + | 0.560635i | ||||
\(695\) | − | 474.468i | − | 0.682687i | ||||||
\(696\) | −0.345885 | + | 0.936082i | −0.000496961 | + | 0.00134495i | ||||
\(697\) | −120.548 | − | 208.796i | −0.172953 | − | 0.299564i | ||||
\(698\) | −216.098 | + | 289.287i | −0.309596 | + | 0.414452i | ||||
\(699\) | 326.189 | − | 188.325i | 0.466651 | − | 0.269421i | ||||
\(700\) | −108.155 | − | 102.706i | −0.154507 | − | 0.146722i | ||||
\(701\) | 630.359 | − | 1091.81i | 0.899229 | − | 1.55751i | 0.0707461 | − | 0.997494i | \(-0.477462\pi\) |
0.828482 | − | 0.560015i | \(-0.189205\pi\) | |||||||
\(702\) | −3.12452 | + | 26.3603i | −0.00445089 | + | 0.0375503i | ||||
\(703\) | −327.151 | + | 177.137i | −0.465365 | + | 0.251973i | ||||
\(704\) | −576.455 | + | 673.541i | −0.818828 | + | 0.956734i | ||||
\(705\) | −403.579 | + | 699.019i | −0.572452 | + | 0.991516i | ||||
\(706\) | 528.218 | − | 707.117i | 0.748184 | − | 1.00158i | ||||
\(707\) | 144.206 | − | 83.2571i | 0.203968 | − | 0.117761i | ||||
\(708\) | 859.250 | − | 904.840i | 1.21363 | − | 1.27802i | ||||
\(709\) | −644.880 | − | 1116.97i | −0.909563 | − | 1.57541i | −0.814672 | − | 0.579921i | \(-0.803083\pi\) |
−0.0948904 | − | 0.995488i | \(-0.530250\pi\) | |||||||
\(710\) | 14.0063 | − | 118.166i | 0.0197272 | − | 0.166431i | ||||
\(711\) | − | 1130.07i | − | 1.58942i | ||||||
\(712\) | −84.3335 | − | 492.306i | −0.118446 | − | 0.691441i | ||||
\(713\) | 223.055 | + | 386.342i | 0.312840 | + | 0.541854i | ||||
\(714\) | −117.210 | − | 13.8931i | −0.164160 | − | 0.0194581i | ||||
\(715\) | 588.553i | 0.823151i | ||||||||
\(716\) | −496.250 | + | 146.811i | −0.693086 | + | 0.205043i | ||||
\(717\) | −173.804 | + | 301.038i | −0.242405 | + | 0.419858i | ||||
\(718\) | 254.634 | − | 109.348i | 0.354644 | − | 0.152295i | ||||
\(719\) | −826.687 | − | 477.288i | −1.14977 | − | 0.663822i | −0.200942 | − | 0.979603i | \(-0.564400\pi\) |
−0.948832 | + | 0.315781i | \(0.897734\pi\) | |||||||
\(720\) | 253.366 | − | 164.291i | 0.351897 | − | 0.228182i | ||||
\(721\) | 123.689 | 0.171551 | ||||||||
\(722\) | −248.207 | − | 677.995i | −0.343777 | − | 0.939051i | ||||
\(723\) | − | 188.345i | − | 0.260504i | ||||||
\(724\) | −529.649 | + | 557.751i | −0.731560 | + | 0.770375i | ||||
\(725\) | 0.301877 | − | 0.522866i | 0.000416382 | − | 0.000721194i | ||||
\(726\) | −550.239 | + | 236.290i | −0.757905 | + | 0.325468i | ||||
\(727\) | −882.411 | − | 509.460i | −1.21377 | − | 0.700771i | −0.250192 | − | 0.968196i | \(-0.580494\pi\) |
−0.963578 | + | 0.267426i | \(0.913827\pi\) | |||||||
\(728\) | 286.277 | − | 49.0401i | 0.393238 | − | 0.0673628i | ||||
\(729\) | 703.208 | 0.964620 | ||||||||
\(730\) | −392.222 | − | 46.4906i | −0.537291 | − | 0.0636858i | ||||
\(731\) | −393.354 | + | 227.103i | −0.538105 | + | 0.310675i | ||||
\(732\) | −766.735 | + | 226.832i | −1.04745 | + | 0.309879i | ||||
\(733\) | −442.473 | −0.603647 | −0.301823 | − | 0.953364i | \(-0.597595\pi\) | ||||
−0.301823 | + | 0.953364i | \(0.597595\pi\) | |||||||
\(734\) | 82.7874 | − | 698.443i | 0.112789 | − | 0.951557i | ||||
\(735\) | −356.619 | + | 205.894i | −0.485195 | + | 0.280128i | ||||
\(736\) | 149.248 | + | 303.299i | 0.202782 | + | 0.412091i | ||||
\(737\) | 46.2046 | + | 80.0288i | 0.0626929 | + | 0.108587i | ||||
\(738\) | 333.098 | − | 445.913i | 0.451352 | − | 0.604218i | ||||
\(739\) | 396.012 | + | 228.638i | 0.535876 | + | 0.309388i | 0.743406 | − | 0.668841i | \(-0.233209\pi\) |
−0.207530 | + | 0.978229i | \(0.566542\pi\) | |||||||
\(740\) | 162.542 | + | 39.0817i | 0.219651 | + | 0.0528131i | ||||
\(741\) | 760.660 | + | 1404.85i | 1.02653 | + | 1.89588i | ||||
\(742\) | −25.6134 | + | 216.090i | −0.0345194 | + | 0.291226i | ||||
\(743\) | 1040.55 | + | 600.759i | 1.40046 | + | 0.808559i | 0.994440 | − | 0.105303i | \(-0.0335813\pi\) |
0.406025 | + | 0.913862i | \(0.366915\pi\) | |||||||
\(744\) | 1097.67 | − | 911.967i | 1.47536 | − | 1.22576i | ||||
\(745\) | −25.3037 | − | 43.8273i | −0.0339647 | − | 0.0588287i | ||||
\(746\) | −235.546 | + | 315.321i | −0.315745 | + | 0.422683i | ||||
\(747\) | −680.825 | + | 393.075i | −0.911413 | + | 0.526204i | ||||
\(748\) | 99.2265 | − | 412.686i | 0.132656 | − | 0.551719i | ||||
\(749\) | 174.876 | 0.233479 | ||||||||
\(750\) | −752.950 | + | 323.340i | −1.00393 | + | 0.431120i | ||||
\(751\) | 257.509 | − | 148.673i | 0.342888 | − | 0.197967i | −0.318660 | − | 0.947869i | \(-0.603233\pi\) |
0.661548 | + | 0.749902i | \(0.269900\pi\) | |||||||
\(752\) | −651.176 | + | 1275.84i | −0.865925 | + | 1.69660i | ||||
\(753\) | 462.731 | 0.614517 | ||||||||
\(754\) | 0.463920 | + | 1.08031i | 0.000615279 | + | 0.00143278i | ||||
\(755\) | 143.702 | + | 82.9663i | 0.190334 | + | 0.109889i | ||||
\(756\) | 1.37996 | + | 4.66453i | 0.00182535 | + | 0.00617002i | ||||
\(757\) | −153.556 | + | 265.967i | −0.202848 | + | 0.351344i | −0.949445 | − | 0.313933i | \(-0.898353\pi\) |
0.746597 | + | 0.665277i | \(0.231687\pi\) | |||||||
\(758\) | −271.187 | − | 202.578i | −0.357767 | − | 0.267253i | ||||
\(759\) | 618.088i | 0.814345i | ||||||||
\(760\) | −120.727 | + | 301.138i | −0.158851 | + | 0.396234i | ||||
\(761\) | −198.836 | −0.261283 | −0.130641 | − | 0.991430i | \(-0.541704\pi\) | ||||
−0.130641 | + | 0.991430i | \(0.541704\pi\) | |||||||
\(762\) | 168.401 | − | 225.436i | 0.220999 | − | 0.295848i | ||||
\(763\) | 97.6294 | + | 56.3664i | 0.127955 | + | 0.0738746i | ||||
\(764\) | −4.95111 | + | 1.46474i | −0.00648052 | + | 0.00191720i | ||||
\(765\) | −72.2866 | + | 125.204i | −0.0944923 | + | 0.163665i | ||||
\(766\) | 728.788 | − | 312.964i | 0.951420 | − | 0.408569i | ||||
\(767\) | − | 1470.10i | − | 1.91669i | ||||||
\(768\) | 875.694 | − | 634.399i | 1.14023 | − | 0.826041i | ||||
\(769\) | 360.826 | + | 624.969i | 0.469214 | + | 0.812703i | 0.999381 | − | 0.0351906i | \(-0.0112038\pi\) |
−0.530166 | + | 0.847894i | \(0.677870\pi\) | |||||||
\(770\) | 42.5574 | + | 99.1017i | 0.0552693 | + | 0.128704i | ||||
\(771\) | 1892.36i | 2.45443i | ||||||||
\(772\) | −1451.29 | − | 348.950i | −1.87991 | − | 0.452007i | ||||
\(773\) | 593.625 | + | 1028.19i | 0.767950 | + | 1.33013i | 0.938673 | + | 0.344810i | \(0.112056\pi\) |
−0.170723 | + | 0.985319i | \(0.554610\pi\) | |||||||
\(774\) | −840.063 | − | 627.529i | −1.08535 | − | 0.810761i | ||||
\(775\) | −747.711 | + | 431.691i | −0.964789 | + | 0.557021i | ||||
\(776\) | −797.505 | + | 662.585i | −1.02771 | + | 0.853847i | ||||
\(777\) | 75.4247 | − | 130.639i | 0.0970717 | − | 0.168133i | ||||
\(778\) | 764.939 | + | 90.6692i | 0.983212 | + | 0.116541i | ||||
\(779\) | −16.3477 | + | 597.776i | −0.0209855 | + | 0.767364i | ||||
\(780\) | 167.824 | − | 697.984i | 0.215159 | − | 0.894851i | ||||
\(781\) | 193.061 | − | 334.392i | 0.247197 | − | 0.428158i | ||||
\(782\) | −129.657 | − | 96.8539i | −0.165802 | − | 0.123854i | ||||
\(783\) | −0.0170527 | + | 0.00984536i | −2.17786e−5 | + | 1.25739e-5i | ||||
\(784\) | −613.152 | + | 397.589i | −0.782082 | + | 0.507129i | ||||
\(785\) | −269.791 | − | 467.292i | −0.343683 | − | 0.595277i | ||||
\(786\) | 114.863 | + | 13.6148i | 0.146136 | + | 0.0173216i | ||||
\(787\) | 701.705i | 0.891620i | 0.895128 | + | 0.445810i | \(0.147084\pi\) | ||||
−0.895128 | + | 0.445810i | \(0.852916\pi\) | |||||||
\(788\) | −217.610 | − | 735.563i | −0.276155 | − | 0.933456i | ||||
\(789\) | −664.633 | − | 1151.18i | −0.842373 | − | 1.45903i | ||||
\(790\) | 64.2198 | − | 541.796i | 0.0812908 | − | 0.685817i | ||||
\(791\) | 61.5448i | 0.0778064i | ||||||||
\(792\) | 965.800 | − | 165.444i | 1.21944 | − | 0.208894i | ||||
\(793\) | −471.010 | + | 815.814i | −0.593960 | + | 1.02877i | ||||
\(794\) | 222.969 | + | 519.219i | 0.280817 | + | 0.653928i | ||||
\(795\) | 465.776 | + | 268.916i | 0.585882 | + | 0.338259i | ||||
\(796\) | 955.871 | + | 907.710i | 1.20084 | + | 1.14034i | ||||
\(797\) | 262.955 | 0.329930 | 0.164965 | − | 0.986299i | \(-0.447249\pi\) | ||||
0.164965 | + | 0.986299i | \(0.447249\pi\) | |||||||
\(798\) | 229.664 | + | 181.549i | 0.287799 | + | 0.227505i | ||||
\(799\) | − | 685.792i | − | 0.858313i | ||||||
\(800\) | −586.992 | + | 288.848i | −0.733740 | + | 0.361060i | ||||
\(801\) | −276.028 | + | 478.095i | −0.344605 | + | 0.596873i | ||||
\(802\) | 6.32128 | + | 14.7201i | 0.00788189 | + | 0.0183543i | ||||
\(803\) | −1109.93 | − | 640.819i | −1.38223 | − | 0.798031i | ||||
\(804\) | −31.9756 | − | 108.084i | −0.0397707 | − | 0.134433i | ||||
\(805\) | 41.1235 | 0.0510851 | ||||||||
\(806\) | 197.901 | − | 1669.61i | 0.245535 | − | 2.07148i | ||||
\(807\) | 1064.97 | − | 614.859i | 1.31966 | − | 0.761907i | ||||
\(808\) | −123.319 | − | 719.886i | −0.152622 | − | 0.890948i | ||||
\(809\) | −1368.29 | −1.69134 | −0.845669 | − | 0.533708i | \(-0.820798\pi\) | ||||
−0.845669 | + | 0.533708i | \(0.820798\pi\) | |||||||
\(810\) | 349.294 | + | 41.4023i | 0.431227 | + | 0.0511139i | ||||
\(811\) | 219.521 | − | 126.740i | 0.270679 | − | 0.156277i | −0.358517 | − | 0.933523i | \(-0.616717\pi\) |
0.629196 | + | 0.777246i | \(0.283384\pi\) | |||||||
\(812\) | 0.156232 | + | 0.148360i | 0.000192404 | + | 0.000182709i | ||||
\(813\) | 272.277 | + | 471.598i | 0.334904 | + | 0.580071i | ||||
\(814\) | 434.598 | + | 324.645i | 0.533904 | + | 0.398827i | ||||
\(815\) | 107.534 | + | 62.0846i | 0.131943 | + | 0.0761774i | ||||
\(816\) | −235.352 | + | 461.123i | −0.288421 | + | 0.565102i | ||||
\(817\) | 1126.16 | + | 30.7977i | 1.37841 | + | 0.0376961i | ||||
\(818\) | −308.532 | − | 36.5708i | −0.377179 | − | 0.0447075i | ||||
\(819\) | −278.013 | − | 160.511i | −0.339455 | − | 0.195984i | ||||
\(820\) | 185.039 | − | 194.856i | 0.225657 | − | 0.237630i | ||||
\(821\) | −772.109 | − | 1337.33i | −0.940450 | − | 1.62891i | −0.764615 | − | 0.644487i | \(-0.777071\pi\) |
−0.175835 | − | 0.984420i | \(-0.556263\pi\) | |||||||
\(822\) | −903.718 | − | 675.079i | −1.09941 | − | 0.821265i | ||||
\(823\) | −394.293 | + | 227.645i | −0.479093 | + | 0.276604i | −0.720038 | − | 0.693934i | \(-0.755876\pi\) |
0.240946 | + | 0.970539i | \(0.422542\pi\) | |||||||
\(824\) | 188.040 | − | 508.899i | 0.228203 | − | 0.617596i | ||||
\(825\) | −1196.22 | −1.44997 | ||||||||
\(826\) | −106.301 | − | 247.539i | −0.128693 | − | 0.299683i | ||||
\(827\) | −961.939 | + | 555.376i | −1.16317 | + | 0.671555i | −0.952061 | − | 0.305909i | \(-0.901040\pi\) |
−0.211106 | + | 0.977463i | \(0.567706\pi\) | |||||||
\(828\) | 87.3431 | − | 363.262i | 0.105487 | − | 0.438723i | ||||
\(829\) | 200.976 | 0.242432 | 0.121216 | − | 0.992626i | \(-0.461321\pi\) | ||||
0.121216 | + | 0.992626i | \(0.461321\pi\) | |||||||
\(830\) | −348.748 | + | 149.763i | −0.420178 | + | 0.180438i | ||||
\(831\) | 84.5055 | + | 48.7893i | 0.101691 | + | 0.0587115i | ||||
\(832\) | 233.449 | − | 1252.40i | 0.280588 | − | 1.50529i | ||||
\(833\) | 174.935 | − | 302.997i | 0.210007 | − | 0.363742i | ||||
\(834\) | −1123.86 | + | 1504.49i | −1.34755 | + | 1.80394i | ||||
\(835\) | − | 343.418i | − | 0.411279i | ||||||
\(836\) | −745.538 | + | 743.301i | −0.891792 | + | 0.889115i | ||||
\(837\) | 28.1582 | 0.0336418 | ||||||||
\(838\) | 645.329 | + | 482.062i | 0.770083 | + | 0.575253i | ||||
\(839\) | 671.461 | + | 387.668i | 0.800311 | + | 0.462060i | 0.843580 | − | 0.537004i | \(-0.180444\pi\) |
−0.0432688 | + | 0.999063i | \(0.513777\pi\) | |||||||
\(840\) | −22.2116 | − | 129.663i | −0.0264424 | − | 0.154361i | ||||
\(841\) | 420.500 | − | 728.327i | 0.499999 | − | 0.866025i | ||||
\(842\) | 359.239 | + | 836.545i | 0.426649 | + | 0.993521i | ||||
\(843\) | 280.546i | 0.332795i | ||||||||
\(844\) | −52.1052 | + | 216.707i | −0.0617360 | + | 0.256762i | ||||
\(845\) | −242.518 | − | 420.053i | −0.287003 | − | 0.497104i | ||||
\(846\) | 1454.74 | − | 624.711i | 1.71955 | − | 0.738428i | ||||
\(847\) | 129.284i | 0.152638i | ||||||||
\(848\) | 850.132 | + | 433.897i | 1.00251 | + | 0.511671i | ||||
\(849\) | 205.809 | + | 356.471i | 0.242413 | + | 0.419872i | ||||
\(850\) | 187.447 | − | 250.933i | 0.220526 | − | 0.295215i | ||||
\(851\) | 179.127 | − | 103.419i | 0.210490 | − | 0.121526i | ||||
\(852\) | −324.308 | + | 341.515i | −0.380643 | + | 0.400839i | ||||
\(853\) | −328.774 | + | 569.453i | −0.385432 | + | 0.667588i | −0.991829 | − | 0.127574i | \(-0.959281\pi\) |
0.606397 | + | 0.795162i | \(0.292614\pi\) | |||||||
\(854\) | −20.3194 | + | 171.426i | −0.0237932 | + | 0.200734i | ||||
\(855\) | 315.333 | − | 170.738i | 0.368810 | − | 0.199694i | ||||
\(856\) | 265.858 | − | 719.502i | 0.310582 | − | 0.840540i | ||||
\(857\) | 325.821 | − | 564.338i | 0.380187 | − | 0.658504i | −0.610901 | − | 0.791707i | \(-0.709193\pi\) |
0.991089 | + | 0.133203i | \(0.0425262\pi\) | |||||||
\(858\) | 1394.09 | − | 1866.24i | 1.62481 | − | 2.17511i | ||||
\(859\) | 746.478 | − | 430.979i | 0.869008 | − | 0.501722i | 0.00198969 | − | 0.999998i | \(-0.499367\pi\) |
0.867019 | + | 0.498276i | \(0.166033\pi\) | |||||||
\(860\) | −367.093 | − | 348.597i | −0.426853 | − | 0.405346i | ||||
\(861\) | −121.238 | − | 209.990i | −0.140810 | − | 0.243891i | ||||
\(862\) | 116.305 | − | 981.217i | 0.134925 | − | 1.13830i | ||||
\(863\) | 658.610i | 0.763163i | 0.924335 | + | 0.381582i | \(0.124620\pi\) | ||||
−0.924335 | + | 0.381582i | \(0.875380\pi\) | |||||||
\(864\) | 21.2895 | + | 1.41368i | 0.0246406 | + | 0.00163621i | ||||
\(865\) | −263.331 | − | 456.103i | −0.304429 | − | 0.527286i | ||||
\(866\) | −506.468 | − | 60.0323i | −0.584836 | − | 0.0693214i | ||||
\(867\) | 972.872i | 1.12211i | ||||||||
\(868\) | −87.4040 | − | 295.442i | −0.100696 | − | 0.340371i | ||||
\(869\) | 885.195 | − | 1533.20i | 1.01864 | − | 1.76433i | ||||
\(870\) | 0.489305 | − | 0.210123i | 0.000562419 | − | 0.000241520i | ||||
\(871\) | −115.002 | − | 66.3966i | −0.132035 | − | 0.0762304i | ||||
\(872\) | 380.334 | − | 315.990i | 0.436163 | − | 0.362374i | ||||
\(873\) | 1145.98 | 1.31270 | ||||||||
\(874\) | 148.250 | + | 373.033i | 0.169622 | + | 0.426811i | ||||
\(875\) | 176.913i | 0.202187i | ||||||||
\(876\) | 1133.58 | + | 1076.46i | 1.29404 | + | 1.22884i | ||||
\(877\) | 571.800 | − | 990.387i | 0.651996 | − | 1.12929i | −0.330642 | − | 0.943756i | \(-0.607265\pi\) |
0.982638 | − | 0.185534i | \(-0.0594014\pi\) | |||||||
\(878\) | −170.181 | + | 73.0811i | −0.193828 | + | 0.0832359i | ||||
\(879\) | 963.462 | + | 556.255i | 1.09609 | + | 0.632827i | ||||
\(880\) | 472.439 | − | 24.4352i | 0.536862 | − | 0.0277672i | ||||
\(881\) | 1399.10 | 1.58808 | 0.794041 | − | 0.607864i | \(-0.207973\pi\) | ||||
0.794041 | + | 0.607864i | \(0.207973\pi\) | |||||||
\(882\) | 802.088 | + | 95.0726i | 0.909397 | + | 0.107792i | ||||
\(883\) | −347.651 | + | 200.716i | −0.393716 | + | 0.227312i | −0.683769 | − | 0.729699i | \(-0.739660\pi\) |
0.290053 | + | 0.957011i | \(0.406327\pi\) | |||||||
\(884\) | 173.031 | + | 584.878i | 0.195736 | + | 0.661626i | ||||
\(885\) | −665.850 | −0.752373 | ||||||||
\(886\) | −86.9198 | + | 733.306i | −0.0981036 | + | 0.827660i | ||||
\(887\) | 782.180 | − | 451.592i | 0.881826 | − | 0.509123i | 0.0105662 | − | 0.999944i | \(-0.496637\pi\) |
0.871260 | + | 0.490821i | \(0.163303\pi\) | |||||||
\(888\) | −422.832 | − | 508.931i | −0.476162 | − | 0.573121i | ||||
\(889\) | −30.3754 | − | 52.6118i | −0.0341681 | − | 0.0591809i | ||||
\(890\) | −159.506 | + | 213.529i | −0.179221 | + | 0.239920i | ||||
\(891\) | 988.451 | + | 570.682i | 1.10937 | + | 0.640496i | ||||
\(892\) | −38.5687 | + | 160.408i | −0.0432384 | + | 0.179830i | ||||
\(893\) | −890.449 | + | 1449.30i | −0.997143 | + | 1.62296i | ||||
\(894\) | −23.5769 | + | 198.908i | −0.0263723 | + | 0.222492i | ||||
\(895\) | 239.153 | + | 138.075i | 0.267210 | + | 0.154274i | ||||
\(896\) | −51.2506 | − | 227.762i | −0.0571993 | − | 0.254199i | ||||
\(897\) | −444.100 | − | 769.203i | −0.495094 | − | 0.857529i | ||||
\(898\) | −547.268 | + | 732.619i | −0.609429 | + | 0.815834i | ||||
\(899\) | 1.08008 | − | 0.623585i | 0.00120143 | − | 0.000693643i | ||||
\(900\) | 703.043 | + | 169.040i | 0.781159 | + | 0.187823i | ||||
\(901\) | −456.963 | −0.507173 | ||||||||
\(902\) | 801.209 | − | 344.064i | 0.888258 | − | 0.381446i | ||||
\(903\) | −395.604 | + | 228.402i | −0.438100 | + | 0.252937i | ||||
\(904\) | 253.217 | + | 93.5646i | 0.280108 | + | 0.103501i | ||||
\(905\) | 410.436 | 0.453521 | ||||||||
\(906\) | −259.144 | − | 603.460i | −0.286031 | − | 0.666070i | ||||
\(907\) | −1216.26 | − | 702.209i | −1.34097 | − | 0.774211i | −0.354023 | − | 0.935237i | \(-0.615186\pi\) |
−0.986950 | + | 0.161026i | \(0.948520\pi\) | |||||||
\(908\) | −1062.74 | + | 314.403i | −1.17042 | + | 0.346259i | ||||
\(909\) | −403.629 | + | 699.105i | −0.444036 | + | 0.769093i | ||||
\(910\) | −124.167 | − | 92.7533i | −0.136448 | − | 0.101927i | ||||
\(911\) | − | 584.988i | − | 0.642138i | −0.947056 | − | 0.321069i | \(-0.895958\pi\) | ||
0.947056 | − | 0.321069i | \(-0.104042\pi\) | |||||||
\(912\) | 1096.11 | − | 668.916i | 1.20187 | − | 0.733461i | ||||
\(913\) | −1231.59 | −1.34895 | ||||||||
\(914\) | 99.9722 | − | 133.831i | 0.109379 | − | 0.146424i | ||||
\(915\) | 369.505 | + | 213.334i | 0.403831 | + | 0.233152i | ||||
\(916\) | −160.201 | − | 541.511i | −0.174892 | − | 0.591169i | ||||
\(917\) | 12.4859 | − | 21.6263i | 0.0136161 | − | 0.0235837i | ||||
\(918\) | −9.38627 | + | 4.03076i | −0.0102247 | + | 0.00439080i | ||||
\(919\) | 299.511i | 0.325909i | 0.986634 | + | 0.162955i | \(0.0521025\pi\) | ||||
−0.986634 | + | 0.162955i | \(0.947898\pi\) | |||||||
\(920\) | 62.5187 | − | 169.197i | 0.0679551 | − | 0.183909i | ||||
\(921\) | 598.851 | + | 1037.24i | 0.650218 | + | 1.12621i | ||||
\(922\) | 190.814 | + | 444.341i | 0.206957 | + | 0.481932i | ||||
\(923\) | 554.862i | 0.601151i | ||||||||
\(924\) | 99.7939 | − | 415.046i | 0.108002 | − | 0.449184i | ||||
\(925\) | 200.153 | + | 346.675i | 0.216381 | + | 0.374784i | ||||
\(926\) | −255.153 | − | 190.600i | −0.275543 | − | 0.205831i | ||||
\(927\) | −519.303 | + | 299.820i | −0.560197 | + | 0.323430i | ||||
\(928\) | 0.847920 | − | 0.417246i | 0.000913707 | − | 0.000449619i | ||||
\(929\) | −119.560 | + | 207.084i | −0.128697 | + | 0.222910i | −0.923172 | − | 0.384387i | \(-0.874413\pi\) |
0.794475 | + | 0.607297i | \(0.207746\pi\) | |||||||
\(930\) | −756.214 | − | 89.6350i | −0.813133 | − | 0.0963818i | ||||
\(931\) | −763.114 | + | 413.191i | −0.819671 | + | 0.443814i | ||||
\(932\) | −346.793 | − | 83.3833i | −0.372096 | − | 0.0894670i | ||||
\(933\) | −537.520 | + | 931.011i | −0.576120 | + | 0.997869i | ||||
\(934\) | −28.2540 | − | 21.1058i | −0.0302506 | − | 0.0225972i | ||||
\(935\) | −196.146 | + | 113.245i | −0.209782 | + | 0.121118i | ||||
\(936\) | −1083.05 | + | 899.826i | −1.15711 | + | 0.961353i | ||||
\(937\) | −472.094 | − | 817.691i | −0.503836 | − | 0.872669i | −0.999990 | − | 0.00443477i | \(-0.998588\pi\) |
0.496154 | − | 0.868234i | \(-0.334745\pi\) | |||||||
\(938\) | −24.1654 | − | 2.86435i | −0.0257627 | − | 0.00305368i | ||||
\(939\) | − | 1416.77i | − | 1.50880i | ||||||
\(940\) | 732.952 | − | 216.837i | 0.779736 | − | 0.230678i | ||||
\(941\) | 490.567 | + | 849.688i | 0.521326 | + | 0.902963i | 0.999692 | + | 0.0248024i | \(0.00789565\pi\) |
−0.478367 | + | 0.878160i | \(0.658771\pi\) | |||||||
\(942\) | −251.379 | + | 2120.78i | −0.266857 | + | 2.25136i | ||||
\(943\) | − | 332.471i | − | 0.352568i | ||||||
\(944\) | −1180.07 | + | 61.0347i | −1.25007 | + | 0.0646554i | ||||
\(945\) | 1.29785 | − | 2.24794i | 0.00137338 | − | 0.00237877i | ||||
\(946\) | −648.188 | − | 1509.41i | −0.685189 | − | 1.59557i | ||||
\(947\) | 780.522 | + | 450.635i | 0.824205 | + | 0.475855i | 0.851864 | − | 0.523762i | \(-0.175472\pi\) |
−0.0276593 | + | 0.999617i | \(0.508805\pi\) | |||||||
\(948\) | −1486.97 | + | 1565.86i | −1.56853 | + | 1.65175i | ||||
\(949\) | 1841.73 | 1.94071 | ||||||||
\(950\) | −721.953 | + | 286.916i | −0.759951 | + | 0.302017i | ||||
\(951\) | − | 1115.67i | − | 1.17316i | ||||||
\(952\) | 71.4269 | + | 85.9713i | 0.0750283 | + | 0.0903060i | ||||
\(953\) | −596.943 | + | 1033.94i | −0.626383 | + | 1.08493i | 0.361889 | + | 0.932221i | \(0.382132\pi\) |
−0.988272 | + | 0.152706i | \(0.951201\pi\) | |||||||
\(954\) | −416.262 | − | 969.334i | −0.436334 | − | 1.01607i | ||||
\(955\) | 2.38604 | + | 1.37758i | 0.00249848 | + | 0.00144250i | ||||
\(956\) | 315.652 | − | 93.3827i | 0.330179 | − | 0.0976807i | ||||
\(957\) | 1.72796 | 0.00180560 | ||||||||
\(958\) | −44.7720 | + | 377.723i | −0.0467348 | + | 0.394282i | ||||
\(959\) | −210.908 | + | 121.768i | −0.219925 | + | 0.126974i | ||||
\(960\) | −567.248 | − | 105.736i | −0.590883 | − | 0.110141i | ||||
\(961\) | −822.485 | −0.855864 | ||||||||
\(962\) | −774.112 | − | 91.7565i | −0.804690 | − | 0.0953810i | ||||
\(963\) | −734.212 | + | 423.898i | −0.762422 | + | 0.440184i | ||||
\(964\) | −122.817 | + | 129.333i | −0.127404 | + | 0.134163i | ||||
\(965\) | 398.249 | + | 689.787i | 0.412693 | + | 0.714806i | ||||
\(966\) | −130.398 | − | 97.4078i | −0.134988 | − | 0.100836i | ||||
\(967\) | 18.5798 | + | 10.7271i | 0.0192139 | + | 0.0110931i | 0.509576 | − | 0.860426i | \(-0.329802\pi\) |
−0.490362 | + | 0.871519i | \(0.663136\pi\) | |||||||
\(968\) | 531.923 | + | 196.547i | 0.549507 | + | 0.203044i | ||||
\(969\) | −321.831 | + | 523.815i | −0.332127 | + | 0.540572i | ||||
\(970\) | 549.424 | + | 65.1239i | 0.566416 | + | 0.0671381i | ||||
\(971\) | −1084.55 | − | 626.166i | −1.11694 | − | 0.644867i | −0.176324 | − | 0.984332i | \(-0.556420\pi\) |
−0.940619 | + | 0.339465i | \(0.889754\pi\) | |||||||
\(972\) | −992.101 | − | 942.115i | −1.02068 | − | 0.969254i | ||||
\(973\) | 202.716 | + | 351.114i | 0.208341 | + | 0.360857i | ||||
\(974\) | 675.937 | + | 504.926i | 0.693980 | + | 0.518405i | ||||
\(975\) | 1488.68 | − | 859.493i | 1.52686 | − | 0.881531i | ||||
\(976\) | 674.419 | + | 344.215i | 0.691003 | + | 0.352680i | ||||
\(977\) | 692.289 | 0.708586 | 0.354293 | − | 0.935134i | \(-0.384722\pi\) | ||||
0.354293 | + | 0.935134i | \(0.384722\pi\) | |||||||
\(978\) | −193.921 | − | 451.576i | −0.198283 | − | 0.461734i | ||||
\(979\) | −748.990 | + | 432.430i | −0.765056 | + | 0.441705i | ||||
\(980\) | 379.145 | + | 91.1620i | 0.386883 | + | 0.0930224i | ||||
\(981\) | −546.526 | −0.557111 | ||||||||
\(982\) | 1500.90 | − | 644.531i | 1.52841 | − | 0.656346i | ||||
\(983\) | −980.241 | − | 565.942i | −0.997193 | − | 0.575730i | −0.0897765 | − | 0.995962i | \(-0.528615\pi\) |
−0.907417 | + | 0.420232i | \(0.861949\pi\) | |||||||
\(984\) | −1048.29 | + | 179.575i | −1.06533 | + | 0.182495i | ||||
\(985\) | −204.661 | + | 354.483i | −0.207778 | + | 0.359881i | ||||
\(986\) | −0.270771 | + | 0.362476i | −0.000274615 | + | 0.000367623i | ||||
\(987\) | − | 689.714i | − | 0.698799i | ||||||
\(988\) | 393.748 | − | 1460.70i | 0.398531 | − | 1.47844i | ||||
\(989\) | −626.349 | −0.633315 | ||||||||
\(990\) | −418.898 | − | 312.917i | −0.423129 | − | 0.316078i | ||||
\(991\) | −1188.45 | − | 686.153i | −1.19924 | − | 0.692384i | −0.238857 | − | 0.971055i | \(-0.576773\pi\) |
−0.960387 | + | 0.278671i | \(0.910106\pi\) | |||||||
\(992\) | −1348.43 | − | 89.5398i | −1.35931 | − | 0.0902619i | ||||
\(993\) | 1290.85 | − | 2235.82i | 1.29995 | − | 2.25158i | ||||
\(994\) | 40.1213 | + | 93.4288i | 0.0403634 | + | 0.0939928i | ||||
\(995\) | − | 703.403i | − | 0.706938i | ||||||
\(996\) | 1460.58 | + | 351.184i | 1.46645 | + | 0.352594i | ||||
\(997\) | 658.351 | + | 1140.30i | 0.660332 | + | 1.14373i | 0.980528 | + | 0.196377i | \(0.0629176\pi\) |
−0.320197 | + | 0.947351i | \(0.603749\pi\) | |||||||
\(998\) | −948.223 | + | 407.197i | −0.950123 | + | 0.408013i | ||||
\(999\) | − | 13.0555i | − | 0.0130686i |
(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 | 76.3.g.c.11.12 | yes | 28 | |
4.3 | odd | 2 | inner | 76.3.g.c.11.10 | yes | 28 | |
19.7 | even | 3 | inner | 76.3.g.c.7.10 | ✓ | 28 | |
76.7 | odd | 6 | inner | 76.3.g.c.7.12 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.3.g.c.7.10 | ✓ | 28 | 19.7 | even | 3 | inner | |
76.3.g.c.7.12 | yes | 28 | 76.7 | odd | 6 | inner | |
76.3.g.c.11.10 | yes | 28 | 4.3 | odd | 2 | inner | |
76.3.g.c.11.12 | yes | 28 | 1.1 | even | 1 | trivial |