Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [143,4,Mod(32,143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(143, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("143.32");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 143 = 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 143.o (of order \(12\), degree \(4\), 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: | \(8.43727313082\) |
Analytic rank: | \(0\) |
Dimension: | \(160\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 32.10 | ||
Character | \(\chi\) | \(=\) | 143.32 |
Dual form | 143.4.o.a.76.10 |
$q$-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 \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) |
\(\chi(n)\) | \(e\left(\frac{5}{12}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.10849 | + | 0.832916i | −1.09902 | + | 0.294480i | −0.762364 | − | 0.647149i | \(-0.775961\pi\) |
−0.336652 | + | 0.941629i | \(0.609295\pi\) | |||||||
\(3\) | −2.01807 | + | 3.49539i | −0.388377 | + | 0.672689i | −0.992231 | − | 0.124406i | \(-0.960297\pi\) |
0.603854 | + | 0.797095i | \(0.293631\pi\) | |||||||
\(4\) | 2.04073 | − | 1.17821i | 0.255091 | − | 0.147277i | ||||
\(5\) | −2.38665 | + | 2.38665i | −0.213469 | + | 0.213469i | −0.805739 | − | 0.592271i | \(-0.798232\pi\) |
0.592271 | + | 0.805739i | \(0.298232\pi\) | |||||||
\(6\) | 3.36176 | − | 12.5463i | 0.228739 | − | 0.853665i | ||||
\(7\) | 25.0107 | + | 6.70161i | 1.35045 | + | 0.361853i | 0.860302 | − | 0.509785i | \(-0.170275\pi\) |
0.490151 | + | 0.871638i | \(0.336942\pi\) | |||||||
\(8\) | 12.8423 | − | 12.8423i | 0.567556 | − | 0.567556i | ||||
\(9\) | 5.35482 | + | 9.27482i | 0.198327 | + | 0.343512i | ||||
\(10\) | 5.43099 | − | 9.40675i | 0.171743 | − | 0.297468i | ||||
\(11\) | 6.74689 | + | 35.8536i | 0.184933 | + | 0.982751i | ||||
\(12\) | 9.51086i | 0.228796i | ||||||||
\(13\) | 45.6359 | + | 10.6941i | 0.973625 | + | 0.228155i | ||||
\(14\) | −83.3274 | −1.59073 | ||||||||
\(15\) | −3.52587 | − | 13.1587i | −0.0606916 | − | 0.226504i | ||||
\(16\) | −38.6493 | + | 66.9426i | −0.603896 | + | 1.04598i | ||||
\(17\) | −41.8500 | − | 72.4863i | −0.597065 | − | 1.03415i | −0.993252 | − | 0.115978i | \(-0.963000\pi\) |
0.396186 | − | 0.918170i | \(-0.370333\pi\) | |||||||
\(18\) | −24.3705 | − | 24.3705i | −0.319122 | − | 0.319122i | ||||
\(19\) | −3.43769 | + | 12.8296i | −0.0415084 | + | 0.154911i | −0.983569 | − | 0.180530i | \(-0.942219\pi\) |
0.942061 | + | 0.335441i | \(0.108885\pi\) | |||||||
\(20\) | −2.05852 | + | 7.68250i | −0.0230149 | + | 0.0858929i | ||||
\(21\) | −73.8981 | + | 73.8981i | −0.767899 | + | 0.767899i | ||||
\(22\) | −50.8356 | − | 105.831i | −0.492645 | − | 1.02560i | ||||
\(23\) | 39.0245 | + | 22.5308i | 0.353790 | + | 0.204261i | 0.666353 | − | 0.745636i | \(-0.267854\pi\) |
−0.312563 | + | 0.949897i | \(0.601188\pi\) | |||||||
\(24\) | 18.9723 | + | 70.8057i | 0.161363 | + | 0.602215i | ||||
\(25\) | 113.608i | 0.908862i | ||||||||
\(26\) | −150.766 | + | 4.76832i | −1.13722 | + | 0.0359671i | ||||
\(27\) | −152.201 | −1.08486 | ||||||||
\(28\) | 58.9360 | − | 15.7919i | 0.397781 | − | 0.106585i | ||||
\(29\) | −36.6188 | − | 21.1419i | −0.234481 | − | 0.135378i | 0.378157 | − | 0.925742i | \(-0.376558\pi\) |
−0.612638 | + | 0.790364i | \(0.709891\pi\) | |||||||
\(30\) | 21.9202 | + | 37.9669i | 0.133402 | + | 0.231059i | ||||
\(31\) | −11.5908 | + | 11.5908i | −0.0671539 | + | 0.0671539i | −0.739886 | − | 0.672732i | \(-0.765121\pi\) |
0.672732 | + | 0.739886i | \(0.265121\pi\) | |||||||
\(32\) | 26.7783 | − | 99.9381i | 0.147931 | − | 0.552085i | ||||
\(33\) | −138.938 | − | 48.7719i | −0.732909 | − | 0.257276i | ||||
\(34\) | 190.465 | + | 190.465i | 0.960720 | + | 0.960720i | ||||
\(35\) | −75.6863 | + | 43.6975i | −0.365524 | + | 0.211035i | ||||
\(36\) | 21.8555 | + | 12.6183i | 0.101183 | + | 0.0584178i | ||||
\(37\) | −99.8493 | + | 26.7545i | −0.443652 | + | 0.118876i | −0.473728 | − | 0.880671i | \(-0.657092\pi\) |
0.0300755 | + | 0.999548i | \(0.490425\pi\) | |||||||
\(38\) | − | 42.7440i | − | 0.182473i | ||||||
\(39\) | −129.476 | + | 137.934i | −0.531611 | + | 0.566336i | ||||
\(40\) | 61.3004i | 0.242311i | ||||||||
\(41\) | −219.612 | + | 58.8449i | −0.836528 | + | 0.224147i | −0.651560 | − | 0.758597i | \(-0.725885\pi\) |
−0.184968 | + | 0.982744i | \(0.559218\pi\) | |||||||
\(42\) | 168.160 | − | 291.262i | 0.617802 | − | 1.07006i | ||||
\(43\) | 50.6613 | + | 87.7479i | 0.179669 | + | 0.311196i | 0.941767 | − | 0.336265i | \(-0.109164\pi\) |
−0.762098 | + | 0.647462i | \(0.775831\pi\) | |||||||
\(44\) | 56.0118 | + | 65.2181i | 0.191911 | + | 0.223455i | ||||
\(45\) | −34.9159 | − | 9.35568i | −0.115666 | − | 0.0309925i | ||||
\(46\) | −140.073 | − | 37.5325i | −0.448971 | − | 0.120302i | ||||
\(47\) | 372.861 | + | 372.861i | 1.15718 | + | 1.15718i | 0.985080 | + | 0.172097i | \(0.0550541\pi\) |
0.172097 | + | 0.985080i | \(0.444946\pi\) | |||||||
\(48\) | −155.994 | − | 270.189i | −0.469079 | − | 0.812468i | ||||
\(49\) | 283.579 | + | 163.724i | 0.826760 | + | 0.477330i | ||||
\(50\) | −94.6257 | − | 353.148i | −0.267642 | − | 0.998854i | ||||
\(51\) | 337.824 | 0.927546 | ||||||||
\(52\) | 105.730 | − | 31.9451i | 0.281965 | − | 0.0851920i | ||||
\(53\) | −228.175 | −0.591362 | −0.295681 | − | 0.955287i | \(-0.595547\pi\) | ||||
−0.295681 | + | 0.955287i | \(0.595547\pi\) | |||||||
\(54\) | 473.115 | − | 126.771i | 1.19227 | − | 0.319469i | ||||
\(55\) | −101.673 | − | 69.4676i | −0.249264 | − | 0.170309i | ||||
\(56\) | 407.260 | − | 235.132i | 0.971830 | − | 0.561086i | ||||
\(57\) | −37.9071 | − | 37.9071i | −0.0880862 | − | 0.0880862i | ||||
\(58\) | 131.439 | + | 35.2189i | 0.297564 | + | 0.0797321i | ||||
\(59\) | 157.628 | − | 588.275i | 0.347820 | − | 1.29808i | −0.541462 | − | 0.840725i | \(-0.682129\pi\) |
0.889282 | − | 0.457358i | \(-0.151204\pi\) | |||||||
\(60\) | −22.6991 | − | 22.6991i | −0.0488407 | − | 0.0488407i | ||||
\(61\) | 721.596 | − | 416.614i | 1.51460 | − | 0.874458i | 0.514751 | − | 0.857339i | \(-0.327884\pi\) |
0.999853 | − | 0.0171181i | \(-0.00544914\pi\) | |||||||
\(62\) | 26.3757 | − | 45.6841i | 0.0540277 | − | 0.0935787i | ||||
\(63\) | 71.7718 | + | 267.856i | 0.143530 | + | 0.535662i | ||||
\(64\) | − | 285.429i | − | 0.557479i | ||||||
\(65\) | −134.440 | + | 83.3939i | −0.256542 | + | 0.159134i | ||||
\(66\) | 472.510 | + | 35.8830i | 0.881241 | + | 0.0669225i | ||||
\(67\) | 52.4039 | + | 195.574i | 0.0955545 | + | 0.356614i | 0.997103 | − | 0.0760638i | \(-0.0242353\pi\) |
−0.901548 | + | 0.432678i | \(0.857569\pi\) | |||||||
\(68\) | −170.809 | − | 98.6165i | −0.304612 | − | 0.175868i | ||||
\(69\) | −157.508 | + | 90.9373i | −0.274808 | + | 0.158660i | ||||
\(70\) | 198.873 | − | 198.873i | 0.339570 | − | 0.339570i | ||||
\(71\) | −643.820 | − | 172.511i | −1.07616 | − | 0.288356i | −0.323138 | − | 0.946352i | \(-0.604738\pi\) |
−0.753022 | + | 0.657996i | \(0.771405\pi\) | |||||||
\(72\) | 187.879 | + | 50.3420i | 0.307524 | + | 0.0824008i | ||||
\(73\) | −159.599 | + | 159.599i | −0.255885 | + | 0.255885i | −0.823378 | − | 0.567493i | \(-0.807913\pi\) |
0.567493 | + | 0.823378i | \(0.307913\pi\) | |||||||
\(74\) | 288.096 | − | 166.332i | 0.452574 | − | 0.261294i | ||||
\(75\) | −397.104 | − | 229.268i | −0.611381 | − | 0.352981i | ||||
\(76\) | 8.10066 | + | 30.2321i | 0.0122264 | + | 0.0456297i | ||||
\(77\) | −71.5320 | + | 941.939i | −0.105868 | + | 1.39408i | ||||
\(78\) | 287.588 | − | 536.609i | 0.417474 | − | 0.778961i | ||||
\(79\) | 1104.62i | 1.57315i | 0.617492 | + | 0.786577i | \(0.288149\pi\) | ||||
−0.617492 | + | 0.786577i | \(0.711851\pi\) | |||||||
\(80\) | −67.5262 | − | 252.011i | −0.0943708 | − | 0.352196i | ||||
\(81\) | 162.572 | − | 281.582i | 0.223006 | − | 0.386258i | ||||
\(82\) | 633.648 | − | 365.837i | 0.853350 | − | 0.492682i | ||||
\(83\) | −757.803 | − | 757.803i | −1.00216 | − | 1.00216i | −0.999998 | − | 0.00216706i | \(-0.999310\pi\) |
−0.00216706 | − | 0.999998i | \(-0.500690\pi\) | |||||||
\(84\) | −63.7380 | + | 237.874i | −0.0827903 | + | 0.308978i | ||||
\(85\) | 272.881 | + | 73.1182i | 0.348213 | + | 0.0933034i | ||||
\(86\) | −230.567 | − | 230.567i | −0.289100 | − | 0.289100i | ||||
\(87\) | 147.798 | − | 85.3315i | 0.182134 | − | 0.105155i | ||||
\(88\) | 547.090 | + | 373.798i | 0.662727 | + | 0.452807i | ||||
\(89\) | −1081.56 | + | 289.804i | −1.28815 | + | 0.345159i | −0.836958 | − | 0.547267i | \(-0.815668\pi\) |
−0.451193 | + | 0.892426i | \(0.649001\pi\) | |||||||
\(90\) | 116.328 | 0.136245 | ||||||||
\(91\) | 1069.72 | + | 573.302i | 1.23228 | + | 0.660422i | ||||
\(92\) | 106.184 | 0.120331 | ||||||||
\(93\) | −17.1234 | − | 63.9055i | −0.0190926 | − | 0.0712547i | ||||
\(94\) | −1469.59 | − | 848.470i | −1.61252 | − | 0.930989i | ||||
\(95\) | −22.4153 | − | 38.8244i | −0.0242080 | − | 0.0419295i | ||||
\(96\) | 295.283 | + | 295.283i | 0.313929 | + | 0.313929i | ||||
\(97\) | −441.945 | − | 118.419i | −0.462605 | − | 0.123955i | 0.0199862 | − | 0.999800i | \(-0.493638\pi\) |
−0.482592 | + | 0.875846i | \(0.660304\pi\) | |||||||
\(98\) | −1017.87 | − | 272.737i | −1.04919 | − | 0.281128i | ||||
\(99\) | −296.407 | + | 254.566i | −0.300910 | + | 0.258432i | ||||
\(100\) | 133.854 | + | 231.843i | 0.133854 | + | 0.231843i | ||||
\(101\) | 350.297 | − | 606.731i | 0.345107 | − | 0.597743i | −0.640266 | − | 0.768153i | \(-0.721176\pi\) |
0.985373 | + | 0.170410i | \(0.0545093\pi\) | |||||||
\(102\) | −1050.12 | + | 281.379i | −1.01939 | + | 0.273144i | ||||
\(103\) | 1457.16i | 1.39397i | 0.717087 | + | 0.696983i | \(0.245475\pi\) | ||||
−0.717087 | + | 0.696983i | \(0.754525\pi\) | |||||||
\(104\) | 723.409 | − | 448.734i | 0.682078 | − | 0.423096i | ||||
\(105\) | − | 352.738i | − | 0.327845i | ||||||
\(106\) | 709.277 | − | 190.050i | 0.649916 | − | 0.174144i | ||||
\(107\) | 105.787 | + | 61.0764i | 0.0955781 | + | 0.0551820i | 0.547027 | − | 0.837115i | \(-0.315759\pi\) |
−0.451449 | + | 0.892297i | \(0.649093\pi\) | |||||||
\(108\) | −310.601 | + | 179.326i | −0.276737 | + | 0.159774i | ||||
\(109\) | 388.435 | + | 388.435i | 0.341333 | + | 0.341333i | 0.856868 | − | 0.515535i | \(-0.172407\pi\) |
−0.515535 | + | 0.856868i | \(0.672407\pi\) | |||||||
\(110\) | 373.908 | + | 131.254i | 0.324098 | + | 0.113769i | ||||
\(111\) | 107.985 | − | 403.005i | 0.0923376 | − | 0.344609i | ||||
\(112\) | −1415.27 | + | 1415.27i | −1.19402 | + | 1.19402i | ||||
\(113\) | 668.440 | + | 1157.77i | 0.556474 | + | 0.963842i | 0.997787 | + | 0.0664884i | \(0.0211795\pi\) |
−0.441313 | + | 0.897353i | \(0.645487\pi\) | |||||||
\(114\) | 149.407 | + | 86.2602i | 0.122748 | + | 0.0708685i | ||||
\(115\) | −146.911 | + | 39.3647i | −0.119126 | + | 0.0319198i | ||||
\(116\) | −99.6388 | −0.0797520 | ||||||||
\(117\) | 145.186 | + | 480.530i | 0.114722 | + | 0.379701i | ||||
\(118\) | 1959.94i | 1.52904i | ||||||||
\(119\) | −560.924 | − | 2093.40i | −0.432099 | − | 1.61262i | ||||
\(120\) | −214.269 | − | 123.708i | −0.163000 | − | 0.0941080i | ||||
\(121\) | −1239.96 | + | 483.800i | −0.931600 | + | 0.363486i | ||||
\(122\) | −1896.07 | + | 1896.07i | −1.40706 | + | 1.40706i | ||||
\(123\) | 237.506 | − | 886.383i | 0.174107 | − | 0.649776i | ||||
\(124\) | −9.99723 | + | 37.3102i | −0.00724014 | + | 0.0270206i | ||||
\(125\) | −569.474 | − | 569.474i | −0.407482 | − | 0.407482i | ||||
\(126\) | −446.203 | − | 772.846i | −0.315484 | − | 0.546434i | ||||
\(127\) | 278.594 | − | 482.539i | 0.194655 | − | 0.337153i | −0.752132 | − | 0.659012i | \(-0.770975\pi\) |
0.946787 | + | 0.321860i | \(0.104308\pi\) | |||||||
\(128\) | 451.965 | + | 1686.76i | 0.312097 | + | 1.16476i | ||||
\(129\) | −408.951 | −0.279117 | ||||||||
\(130\) | 348.445 | − | 371.206i | 0.235082 | − | 0.250438i | ||||
\(131\) | − | 1746.14i | − | 1.16459i | −0.812977 | − | 0.582295i | \(-0.802155\pi\) | ||
0.812977 | − | 0.582295i | \(-0.197845\pi\) | |||||||
\(132\) | −340.998 | + | 64.1687i | −0.224849 | + | 0.0423119i | ||||
\(133\) | −171.958 | + | 297.840i | −0.112110 | + | 0.194181i | ||||
\(134\) | −325.793 | − | 564.291i | −0.210032 | − | 0.363786i | ||||
\(135\) | 363.251 | − | 363.251i | 0.231583 | − | 0.231583i | ||||
\(136\) | −1468.34 | − | 393.442i | −0.925805 | − | 0.248069i | ||||
\(137\) | −291.452 | + | 1087.71i | −0.181755 | + | 0.678319i | 0.813547 | + | 0.581499i | \(0.197534\pi\) |
−0.995302 | + | 0.0968198i | \(0.969133\pi\) | |||||||
\(138\) | 413.868 | − | 413.868i | 0.255296 | − | 0.255296i | ||||
\(139\) | 1229.20 | − | 709.677i | 0.750066 | − | 0.433051i | −0.0756520 | − | 0.997134i | \(-0.524104\pi\) |
0.825718 | + | 0.564084i | \(0.190770\pi\) | |||||||
\(140\) | −102.970 | + | 178.349i | −0.0621612 | + | 0.107666i | ||||
\(141\) | −2055.75 | + | 550.837i | −1.22784 | + | 0.328999i | ||||
\(142\) | 2144.99 | 1.26763 | ||||||||
\(143\) | −75.5228 | + | 1708.36i | −0.0441646 | + | 0.999024i | ||||
\(144\) | −827.841 | −0.479075 | ||||||||
\(145\) | 137.855 | − | 36.9381i | 0.0789532 | − | 0.0211555i | ||||
\(146\) | 363.178 | − | 629.043i | 0.205869 | − | 0.356575i | ||||
\(147\) | −1144.56 | + | 660.812i | −0.642189 | + | 0.370768i | ||||
\(148\) | −172.243 | + | 172.243i | −0.0956639 | + | 0.0956639i | ||||
\(149\) | −402.553 | + | 1502.35i | −0.221332 | + | 0.826021i | 0.762509 | + | 0.646977i | \(0.223967\pi\) |
−0.983841 | + | 0.179044i | \(0.942700\pi\) | |||||||
\(150\) | 1425.35 | + | 381.922i | 0.775864 | + | 0.207892i | ||||
\(151\) | 1199.02 | − | 1199.02i | 0.646191 | − | 0.646191i | −0.305879 | − | 0.952070i | \(-0.598950\pi\) |
0.952070 | + | 0.305879i | \(0.0989504\pi\) | |||||||
\(152\) | 120.614 | + | 208.910i | 0.0643626 | + | 0.111479i | ||||
\(153\) | 448.198 | − | 776.302i | 0.236828 | − | 0.410198i | ||||
\(154\) | −562.200 | − | 2987.58i | −0.294178 | − | 1.56329i | ||||
\(155\) | − | 55.3265i | − | 0.0286705i | ||||||
\(156\) | −101.710 | + | 434.037i | −0.0522010 | + | 0.222761i | ||||
\(157\) | 1139.05 | 0.579019 | 0.289509 | − | 0.957175i | \(-0.406508\pi\) | ||||
0.289509 | + | 0.957175i | \(0.406508\pi\) | |||||||
\(158\) | −920.054 | − | 3433.69i | −0.463263 | − | 1.72892i | ||||
\(159\) | 460.471 | − | 797.560i | 0.229671 | − | 0.397802i | ||||
\(160\) | 174.607 | + | 302.428i | 0.0862743 | + | 0.149432i | ||||
\(161\) | 825.039 | + | 825.039i | 0.403864 | + | 0.403864i | ||||
\(162\) | −270.817 | + | 1010.70i | −0.131342 | + | 0.490175i | ||||
\(163\) | 984.142 | − | 3672.87i | 0.472908 | − | 1.76492i | −0.156333 | − | 0.987704i | \(-0.549967\pi\) |
0.629240 | − | 0.777211i | \(-0.283366\pi\) | |||||||
\(164\) | −378.837 | + | 378.837i | −0.180379 | + | 0.180379i | ||||
\(165\) | 447.998 | − | 215.195i | 0.211373 | − | 0.101533i | ||||
\(166\) | 2986.81 | + | 1724.43i | 1.39651 | + | 0.806277i | ||||
\(167\) | −924.483 | − | 3450.22i | −0.428375 | − | 1.59872i | −0.756441 | − | 0.654062i | \(-0.773063\pi\) |
0.328065 | − | 0.944655i | \(-0.393603\pi\) | |||||||
\(168\) | 1898.05i | 0.871652i | ||||||||
\(169\) | 1968.27 | + | 976.073i | 0.895890 | + | 0.444275i | ||||
\(170\) | −909.148 | −0.410167 | ||||||||
\(171\) | −137.401 | + | 36.8164i | −0.0614461 | + | 0.0164644i | ||||
\(172\) | 206.772 | + | 119.380i | 0.0916640 | + | 0.0529222i | ||||
\(173\) | 2203.00 | + | 3815.71i | 0.968158 | + | 1.67690i | 0.700880 | + | 0.713279i | \(0.252791\pi\) |
0.267277 | + | 0.963620i | \(0.413876\pi\) | |||||||
\(174\) | −388.355 | + | 388.355i | −0.169202 | + | 0.169202i | ||||
\(175\) | −761.355 | + | 2841.41i | −0.328874 | + | 1.22738i | ||||
\(176\) | −2660.90 | − | 934.063i | −1.13962 | − | 0.400044i | ||||
\(177\) | 1738.15 | + | 1738.15i | 0.738121 | + | 0.738121i | ||||
\(178\) | 3120.64 | − | 1801.70i | 1.31406 | − | 0.758670i | ||||
\(179\) | 1187.91 | + | 685.842i | 0.496027 | + | 0.286381i | 0.727071 | − | 0.686562i | \(-0.240881\pi\) |
−0.231045 | + | 0.972943i | \(0.574214\pi\) | |||||||
\(180\) | −82.2768 | + | 22.0460i | −0.0340697 | + | 0.00912895i | ||||
\(181\) | 1375.63i | 0.564914i | 0.959280 | + | 0.282457i | \(0.0911495\pi\) | ||||
−0.959280 | + | 0.282457i | \(0.908850\pi\) | |||||||
\(182\) | −3802.72 | − | 891.114i | −1.54877 | − | 0.362933i | ||||
\(183\) | 3363.02i | 1.35848i | ||||||||
\(184\) | 790.514 | − | 211.817i | 0.316725 | − | 0.0848663i | ||||
\(185\) | 174.452 | − | 302.159i | 0.0693295 | − | 0.120082i | ||||
\(186\) | 106.456 | + | 184.387i | 0.0419662 | + | 0.0726877i | ||||
\(187\) | 2316.54 | − | 1989.53i | 0.905893 | − | 0.778015i | ||||
\(188\) | 1200.22 | + | 321.597i | 0.465611 | + | 0.124760i | ||||
\(189\) | −3806.66 | − | 1019.99i | −1.46505 | − | 0.392558i | ||||
\(190\) | 102.015 | + | 102.015i | 0.0389524 | + | 0.0389524i | ||||
\(191\) | −1731.80 | − | 2999.56i | −0.656065 | − | 1.13634i | −0.981626 | − | 0.190817i | \(-0.938886\pi\) |
0.325561 | − | 0.945521i | \(-0.394447\pi\) | |||||||
\(192\) | 997.687 | + | 576.015i | 0.375010 | + | 0.216512i | ||||
\(193\) | −85.3228 | − | 318.429i | −0.0318221 | − | 0.118762i | 0.948188 | − | 0.317710i | \(-0.102914\pi\) |
−0.980010 | + | 0.198949i | \(0.936247\pi\) | |||||||
\(194\) | 1472.41 | 0.544913 | ||||||||
\(195\) | −20.1851 | − | 638.216i | −0.00741273 | − | 0.234377i | ||||
\(196\) | 771.609 | 0.281199 | ||||||||
\(197\) | 126.769 | − | 33.9676i | 0.0458472 | − | 0.0122847i | −0.235823 | − | 0.971796i | \(-0.575778\pi\) |
0.281670 | + | 0.959511i | \(0.409112\pi\) | |||||||
\(198\) | 709.346 | − | 1038.20i | 0.254601 | − | 0.372633i | ||||
\(199\) | 4437.07 | − | 2561.74i | 1.58058 | − | 0.912548i | 0.585806 | − | 0.810452i | \(-0.300778\pi\) |
0.994774 | − | 0.102097i | \(-0.0325552\pi\) | |||||||
\(200\) | 1458.99 | + | 1458.99i | 0.515831 | + | 0.515831i | ||||
\(201\) | −789.362 | − | 211.509i | −0.277002 | − | 0.0742224i | ||||
\(202\) | −583.535 | + | 2177.78i | −0.203254 | + | 0.758556i | ||||
\(203\) | −774.179 | − | 774.179i | −0.267669 | − | 0.267669i | ||||
\(204\) | 689.407 | − | 398.029i | 0.236609 | − | 0.136606i | ||||
\(205\) | 383.695 | − | 664.580i | 0.130724 | − | 0.226421i | ||||
\(206\) | −1213.69 | − | 4529.57i | −0.410496 | − | 1.53199i | ||||
\(207\) | 482.593i | 0.162041i | ||||||||
\(208\) | −2479.69 | + | 2641.67i | −0.826614 | + | 0.880608i | ||||
\(209\) | −483.181 | − | 36.6934i | −0.159916 | − | 0.0121442i | ||||
\(210\) | 293.801 | + | 1096.48i | 0.0965438 | + | 0.360306i | ||||
\(211\) | −3920.65 | − | 2263.59i | −1.27919 | − | 0.738539i | −0.302488 | − | 0.953153i | \(-0.597817\pi\) |
−0.976699 | + | 0.214614i | \(0.931151\pi\) | |||||||
\(212\) | −465.642 | + | 268.839i | −0.150851 | + | 0.0870939i | ||||
\(213\) | 1902.26 | − | 1902.26i | 0.611930 | − | 0.611930i | ||||
\(214\) | −379.710 | − | 101.743i | −0.121292 | − | 0.0325000i | ||||
\(215\) | −330.335 | − | 88.5129i | −0.104784 | − | 0.0280769i | ||||
\(216\) | −1954.62 | + | 1954.62i | −0.615717 | + | 0.615717i | ||||
\(217\) | −367.572 | + | 212.218i | −0.114988 | + | 0.0663884i | ||||
\(218\) | −1530.98 | − | 883.911i | −0.475646 | − | 0.274615i | ||||
\(219\) | −235.779 | − | 879.941i | −0.0727511 | − | 0.271511i | ||||
\(220\) | −289.334 | − | 21.9724i | −0.0886676 | − | 0.00673353i | ||||
\(221\) | −1134.68 | − | 3755.53i | −0.345371 | − | 1.14310i | ||||
\(222\) | 1342.68i | 0.405922i | ||||||||
\(223\) | 644.429 | + | 2405.04i | 0.193516 | + | 0.722213i | 0.992646 | + | 0.121054i | \(0.0386274\pi\) |
−0.799130 | + | 0.601159i | \(0.794706\pi\) | |||||||
\(224\) | 1339.49 | − | 2320.07i | 0.399547 | − | 0.692036i | ||||
\(225\) | −1053.69 | + | 608.349i | −0.312205 | + | 0.180252i | ||||
\(226\) | −3042.17 | − | 3042.17i | −0.895406 | − | 0.895406i | ||||
\(227\) | −598.196 | + | 2232.50i | −0.174906 | + | 0.652758i | 0.821662 | + | 0.569975i | \(0.193047\pi\) |
−0.996568 | + | 0.0827823i | \(0.973619\pi\) | |||||||
\(228\) | −122.021 | − | 32.6953i | −0.0354431 | − | 0.00949694i | ||||
\(229\) | 3796.17 | + | 3796.17i | 1.09545 | + | 1.09545i | 0.994936 | + | 0.100514i | \(0.0320488\pi\) |
0.100514 | + | 0.994936i | \(0.467951\pi\) | |||||||
\(230\) | 423.883 | − | 244.729i | 0.121522 | − | 0.0701607i | ||||
\(231\) | −3148.09 | − | 2150.93i | −0.896663 | − | 0.612644i | ||||
\(232\) | −741.783 | + | 198.760i | −0.209916 | + | 0.0562467i | ||||
\(233\) | 1947.13 | 0.547470 | 0.273735 | − | 0.961805i | \(-0.411741\pi\) | ||||
0.273735 | + | 0.961805i | \(0.411741\pi\) | |||||||
\(234\) | −851.549 | − | 1372.79i | −0.237895 | − | 0.383514i | ||||
\(235\) | −1779.78 | −0.494042 | ||||||||
\(236\) | −371.439 | − | 1386.23i | −0.102452 | − | 0.382355i | ||||
\(237\) | −3861.07 | − | 2229.19i | −1.05824 | − | 0.610977i | ||||
\(238\) | 3487.25 | + | 6040.09i | 0.949768 | + | 1.64505i | ||||
\(239\) | 3724.72 | + | 3724.72i | 1.00808 | + | 1.00808i | 0.999967 | + | 0.00811746i | \(0.00258390\pi\) |
0.00811746 | + | 0.999967i | \(0.497416\pi\) | |||||||
\(240\) | 1017.15 | + | 272.545i | 0.273570 | + | 0.0733029i | ||||
\(241\) | −2608.09 | − | 698.835i | −0.697103 | − | 0.186788i | −0.107170 | − | 0.994241i | \(-0.534179\pi\) |
−0.589932 | + | 0.807453i | \(0.700846\pi\) | |||||||
\(242\) | 3451.43 | − | 2536.67i | 0.916803 | − | 0.673815i | ||||
\(243\) | −1398.55 | − | 2422.37i | −0.369207 | − | 0.639485i | ||||
\(244\) | 981.721 | − | 1700.39i | 0.257575 | − | 0.446132i | ||||
\(245\) | −1067.56 | + | 286.051i | −0.278382 | + | 0.0745923i | ||||
\(246\) | 2953.13i | 0.765385i | ||||||||
\(247\) | −294.084 | + | 548.728i | −0.0757574 | + | 0.141355i | ||||
\(248\) | 297.706i | 0.0762273i | ||||||||
\(249\) | 4178.11 | − | 1119.52i | 1.06336 | − | 0.284927i | ||||
\(250\) | 2244.52 | + | 1295.88i | 0.567825 | + | 0.327834i | ||||
\(251\) | 4213.65 | − | 2432.75i | 1.05961 | − | 0.611769i | 0.134289 | − | 0.990942i | \(-0.457125\pi\) |
0.925326 | + | 0.379173i | \(0.123792\pi\) | |||||||
\(252\) | 462.058 | + | 462.058i | 0.115504 | + | 0.115504i | ||||
\(253\) | −544.516 | + | 1551.18i | −0.135310 | + | 0.385462i | ||||
\(254\) | −464.091 | + | 1732.01i | −0.114644 | + | 0.427858i | ||||
\(255\) | −806.269 | + | 806.269i | −0.198002 | + | 0.198002i | ||||
\(256\) | −1668.14 | − | 2889.30i | −0.407260 | − | 0.705395i | ||||
\(257\) | 2758.87 | + | 1592.84i | 0.669625 | + | 0.386608i | 0.795935 | − | 0.605383i | \(-0.206980\pi\) |
−0.126309 | + | 0.991991i | \(0.540313\pi\) | |||||||
\(258\) | 1271.22 | − | 340.622i | 0.306754 | − | 0.0821946i | ||||
\(259\) | −2676.60 | −0.642147 | ||||||||
\(260\) | −176.100 | + | 328.584i | −0.0420048 | + | 0.0783765i | ||||
\(261\) | − | 452.844i | − | 0.107396i | ||||||
\(262\) | 1454.39 | + | 5427.86i | 0.342949 | + | 1.27990i | ||||
\(263\) | 5840.35 | + | 3371.93i | 1.36932 | + | 0.790578i | 0.990841 | − | 0.135032i | \(-0.0431137\pi\) |
0.378479 | + | 0.925610i | \(0.376447\pi\) | |||||||
\(264\) | −2410.63 | + | 1157.94i | −0.561986 | + | 0.269949i | ||||
\(265\) | 544.573 | − | 544.573i | 0.126237 | − | 0.126237i | ||||
\(266\) | 286.453 | − | 1069.06i | 0.0660285 | − | 0.246422i | ||||
\(267\) | 1169.69 | − | 4365.33i | 0.268104 | − | 1.00058i | ||||
\(268\) | 337.370 | + | 337.370i | 0.0768961 | + | 0.0768961i | ||||
\(269\) | 162.455 | + | 281.381i | 0.0368219 | + | 0.0637773i | 0.883849 | − | 0.467772i | \(-0.154943\pi\) |
−0.847027 | + | 0.531550i | \(0.821610\pi\) | |||||||
\(270\) | −826.603 | + | 1431.72i | −0.186316 | + | 0.322710i | ||||
\(271\) | −110.934 | − | 414.010i | −0.0248662 | − | 0.0928019i | 0.952378 | − | 0.304921i | \(-0.0986301\pi\) |
−0.977244 | + | 0.212119i | \(0.931963\pi\) | |||||||
\(272\) | 6469.90 | 1.44226 | ||||||||
\(273\) | −4162.68 | + | 2582.13i | −0.922846 | + | 0.572445i | ||||
\(274\) | − | 3623.90i | − | 0.799007i | ||||||
\(275\) | −4073.25 | + | 766.499i | −0.893185 | + | 0.168079i | ||||
\(276\) | −214.287 | + | 371.156i | −0.0467340 | + | 0.0809456i | ||||
\(277\) | −3267.90 | − | 5660.16i | −0.708840 | − | 1.22775i | −0.965288 | − | 0.261189i | \(-0.915885\pi\) |
0.256447 | − | 0.966558i | \(-0.417448\pi\) | |||||||
\(278\) | −3229.84 | + | 3229.84i | −0.696809 | + | 0.696809i | ||||
\(279\) | −169.569 | − | 45.4360i | −0.0363866 | − | 0.00974976i | ||||
\(280\) | −410.811 | + | 1533.17i | −0.0876809 | + | 0.327230i | ||||
\(281\) | 1601.55 | − | 1601.55i | 0.340002 | − | 0.340002i | −0.516366 | − | 0.856368i | \(-0.672716\pi\) |
0.856368 | + | 0.516366i | \(0.172716\pi\) | |||||||
\(282\) | 5931.47 | − | 3424.54i | 1.25253 | − | 0.723150i | ||||
\(283\) | −1744.01 | + | 3020.71i | −0.366327 | + | 0.634497i | −0.988988 | − | 0.147994i | \(-0.952718\pi\) |
0.622661 | + | 0.782492i | \(0.286052\pi\) | |||||||
\(284\) | −1517.12 | + | 406.510i | −0.316987 | + | 0.0849364i | ||||
\(285\) | 180.942 | 0.0376073 | ||||||||
\(286\) | −1188.16 | − | 5373.32i | −0.245655 | − | 1.11095i | ||||
\(287\) | −5887.01 | −1.21080 | ||||||||
\(288\) | 1070.30 | − | 286.786i | 0.218987 | − | 0.0586773i | ||||
\(289\) | −1046.34 | + | 1812.32i | −0.212974 | + | 0.368882i | ||||
\(290\) | −397.753 | + | 229.643i | −0.0805410 | + | 0.0465003i | ||||
\(291\) | 1305.79 | − | 1305.79i | 0.263048 | − | 0.263048i | ||||
\(292\) | −137.656 | + | 513.739i | −0.0275880 | + | 0.102960i | ||||
\(293\) | 270.052 | + | 72.3603i | 0.0538452 | + | 0.0144278i | 0.285641 | − | 0.958337i | \(-0.407793\pi\) |
−0.231796 | + | 0.972764i | \(0.574460\pi\) | |||||||
\(294\) | 3007.45 | − | 3007.45i | 0.596592 | − | 0.596592i | ||||
\(295\) | 1027.81 | + | 1780.21i | 0.202851 | + | 0.351349i | ||||
\(296\) | −938.708 | + | 1625.89i | −0.184329 | + | 0.319267i | ||||
\(297\) | −1026.88 | − | 5456.95i | −0.200626 | − | 1.06614i | ||||
\(298\) | − | 5005.32i | − | 0.972988i | ||||||
\(299\) | 1539.97 | + | 1445.55i | 0.297855 | + | 0.279592i | ||||
\(300\) | −1080.51 | −0.207944 | ||||||||
\(301\) | 679.024 | + | 2534.15i | 0.130028 | + | 0.485269i | ||||
\(302\) | −2728.45 | + | 4725.82i | −0.519883 | + | 0.900464i | ||||
\(303\) | 1413.84 | + | 2448.85i | 0.268063 | + | 0.464299i | ||||
\(304\) | −725.984 | − | 725.984i | −0.136967 | − | 0.136967i | ||||
\(305\) | −727.887 | + | 2716.51i | −0.136651 | + | 0.509990i | ||||
\(306\) | −746.623 | + | 2786.44i | −0.139482 | + | 0.520555i | ||||
\(307\) | 550.112 | − | 550.112i | 0.102269 | − | 0.102269i | −0.654121 | − | 0.756390i | \(-0.726961\pi\) |
0.756390 | + | 0.654121i | \(0.226961\pi\) | |||||||
\(308\) | 963.829 | + | 2006.52i | 0.178309 | + | 0.371208i | ||||
\(309\) | −5093.36 | − | 2940.65i | −0.937706 | − | 0.541385i | ||||
\(310\) | 46.0823 | + | 171.982i | 0.00844291 | + | 0.0315094i | ||||
\(311\) | − | 3858.82i | − | 0.703581i | −0.936079 | − | 0.351791i | \(-0.885573\pi\) | ||
0.936079 | − | 0.351791i | \(-0.114427\pi\) | |||||||
\(312\) | 108.614 | + | 3434.17i | 0.0197085 | + | 0.623147i | ||||
\(313\) | 7171.08 | 1.29499 | 0.647497 | − | 0.762068i | \(-0.275816\pi\) | ||||
0.647497 | + | 0.762068i | \(0.275816\pi\) | |||||||
\(314\) | −3540.71 | + | 948.731i | −0.636350 | + | 0.170510i | ||||
\(315\) | −810.573 | − | 467.985i | −0.144986 | − | 0.0837078i | ||||
\(316\) | 1301.48 | + | 2254.22i | 0.231689 | + | 0.401297i | ||||
\(317\) | −2845.97 | + | 2845.97i | −0.504244 | + | 0.504244i | −0.912754 | − | 0.408510i | \(-0.866049\pi\) |
0.408510 | + | 0.912754i | \(0.366049\pi\) | |||||||
\(318\) | −767.068 | + | 2862.74i | −0.135267 | + | 0.504825i | ||||
\(319\) | 510.950 | − | 1455.56i | 0.0896793 | − | 0.255472i | ||||
\(320\) | 681.220 | + | 681.220i | 0.119004 | + | 0.119004i | ||||
\(321\) | −426.972 | + | 246.512i | −0.0742407 | + | 0.0428629i | ||||
\(322\) | −3251.81 | − | 1877.43i | −0.562783 | − | 0.324923i | ||||
\(323\) | 1073.84 | − | 287.734i | 0.184984 | − | 0.0495664i | ||||
\(324\) | − | 766.177i | − | 0.131375i | ||||||
\(325\) | −1214.94 | + | 5184.59i | −0.207362 | + | 0.884891i | ||||
\(326\) | 12236.8i | 2.07893i | ||||||||
\(327\) | −2141.62 | + | 573.845i | −0.362177 | + | 0.0970450i | ||||
\(328\) | −2064.63 | + | 3576.04i | −0.347561 | + | 0.601993i | ||||
\(329\) | 6826.75 | + | 11824.3i | 1.14398 | + | 1.98144i | ||||
\(330\) | −1213.36 | + | 1042.08i | −0.202403 | + | 0.173832i | ||||
\(331\) | −9646.98 | − | 2584.90i | −1.60195 | − | 0.429242i | −0.656320 | − | 0.754483i | \(-0.727888\pi\) |
−0.945631 | + | 0.325241i | \(0.894555\pi\) | |||||||
\(332\) | −2439.32 | − | 653.615i | −0.403239 | − | 0.108048i | ||||
\(333\) | −782.819 | − | 782.819i | −0.128823 | − | 0.128823i | ||||
\(334\) | 5747.48 | + | 9954.93i | 0.941582 | + | 1.63087i | ||||
\(335\) | −591.837 | − | 341.697i | −0.0965239 | − | 0.0557281i | ||||
\(336\) | −2090.82 | − | 7803.04i | −0.339475 | − | 1.26694i | ||||
\(337\) | −3330.67 | −0.538377 | −0.269189 | − | 0.963088i | \(-0.586755\pi\) | ||||
−0.269189 | + | 0.963088i | \(0.586755\pi\) | |||||||
\(338\) | −6931.33 | − | 1394.70i | −1.11543 | − | 0.224443i | ||||
\(339\) | −5395.83 | −0.864487 | ||||||||
\(340\) | 643.025 | − | 172.298i | 0.102567 | − | 0.0274828i | ||||
\(341\) | −493.774 | − | 337.370i | −0.0784146 | − | 0.0535766i | ||||
\(342\) | 396.443 | − | 228.886i | 0.0626818 | − | 0.0361893i | ||||
\(343\) | −284.739 | − | 284.739i | −0.0448234 | − | 0.0448234i | ||||
\(344\) | 1777.50 | + | 476.279i | 0.278594 | + | 0.0746490i | ||||
\(345\) | 158.881 | − | 592.952i | 0.0247938 | − | 0.0925318i | ||||
\(346\) | −10026.2 | − | 10026.2i | −1.55783 | − | 1.55783i | ||||
\(347\) | 6880.80 | − | 3972.63i | 1.06450 | − | 0.614588i | 0.137824 | − | 0.990457i | \(-0.455989\pi\) |
0.926673 | + | 0.375869i | \(0.122656\pi\) | |||||||
\(348\) | 201.078 | − | 348.277i | 0.0309738 | − | 0.0536482i | ||||
\(349\) | −1680.46 | − | 6271.57i | −0.257745 | − | 0.961918i | −0.966543 | − | 0.256506i | \(-0.917429\pi\) |
0.708798 | − | 0.705412i | \(-0.249238\pi\) | |||||||
\(350\) | − | 9466.64i | − | 1.44575i | ||||||
\(351\) | −6945.83 | − | 1627.66i | −1.05624 | − | 0.247516i | ||||
\(352\) | 3763.81 | + | 285.828i | 0.569920 | + | 0.0432804i | ||||
\(353\) | 1290.33 | + | 4815.59i | 0.194554 | + | 0.726085i | 0.992382 | + | 0.123200i | \(0.0393156\pi\) |
−0.797828 | + | 0.602885i | \(0.794018\pi\) | |||||||
\(354\) | −6850.75 | − | 3955.28i | −1.02857 | − | 0.593844i | ||||
\(355\) | 1948.30 | − | 1124.85i | 0.291281 | − | 0.168171i | ||||
\(356\) | −1865.72 | + | 1865.72i | −0.277762 | + | 0.277762i | ||||
\(357\) | 8449.23 | + | 2263.96i | 1.25261 | + | 0.335635i | ||||
\(358\) | −4263.86 | − | 1142.50i | −0.629474 | − | 0.168667i | ||||
\(359\) | 2680.85 | − | 2680.85i | 0.394121 | − | 0.394121i | −0.482032 | − | 0.876154i | \(-0.660101\pi\) |
0.876154 | + | 0.482032i | \(0.160101\pi\) | |||||||
\(360\) | −568.550 | + | 328.252i | −0.0832367 | + | 0.0480567i | ||||
\(361\) | 5787.29 | + | 3341.29i | 0.843751 | + | 0.487140i | ||||
\(362\) | −1145.78 | − | 4276.11i | −0.166356 | − | 0.620850i | ||||
\(363\) | 811.248 | − | 5310.48i | 0.117299 | − | 0.767846i | ||||
\(364\) | 2858.48 | − | 90.4060i | 0.411607 | − | 0.0130180i | ||||
\(365\) | − | 761.813i | − | 0.109247i | ||||||
\(366\) | −2801.11 | − | 10453.9i | −0.400045 | − | 1.49299i | ||||
\(367\) | −3487.15 | + | 6039.91i | −0.495988 | + | 0.859076i | −0.999989 | − | 0.00462668i | \(-0.998527\pi\) |
0.504001 | + | 0.863703i | \(0.331861\pi\) | |||||||
\(368\) | −3016.54 | + | 1741.60i | −0.427305 | + | 0.246704i | ||||
\(369\) | −1721.76 | − | 1721.76i | −0.242903 | − | 0.242903i | ||||
\(370\) | −290.607 | + | 1084.56i | −0.0408323 | + | 0.152388i | ||||
\(371\) | −5706.81 | − | 1529.14i | −0.798606 | − | 0.213986i | ||||
\(372\) | −110.239 | − | 110.239i | −0.0153645 | − | 0.0153645i | ||||
\(373\) | 4077.79 | − | 2354.31i | 0.566059 | − | 0.326814i | −0.189515 | − | 0.981878i | \(-0.560691\pi\) |
0.755574 | + | 0.655063i | \(0.227358\pi\) | |||||||
\(374\) | −5543.81 | + | 8113.90i | −0.766480 | + | 1.12182i | ||||
\(375\) | 3139.77 | − | 841.299i | 0.432365 | − | 0.115852i | ||||
\(376\) | 9576.80 | 1.31353 | ||||||||
\(377\) | −1445.04 | − | 1356.44i | −0.197409 | − | 0.185305i | ||||
\(378\) | 12682.5 | 1.72571 | ||||||||
\(379\) | 309.042 | + | 1153.36i | 0.0418851 | + | 0.156317i | 0.983701 | − | 0.179812i | \(-0.0575489\pi\) |
−0.941816 | + | 0.336129i | \(0.890882\pi\) | |||||||
\(380\) | −91.4870 | − | 52.8200i | −0.0123505 | − | 0.00713055i | ||||
\(381\) | 1124.44 | + | 1947.59i | 0.151199 | + | 0.261885i | ||||
\(382\) | 7881.65 | + | 7881.65i | 1.05565 | + | 1.05565i | ||||
\(383\) | 6952.30 | + | 1862.86i | 0.927535 | + | 0.248532i | 0.690803 | − | 0.723043i | \(-0.257257\pi\) |
0.236732 | + | 0.971575i | \(0.423924\pi\) | |||||||
\(384\) | −6807.97 | − | 1824.19i | −0.904734 | − | 0.242423i | ||||
\(385\) | −2077.36 | − | 2418.80i | −0.274992 | − | 0.320191i | ||||
\(386\) | 530.449 | + | 918.765i | 0.0699460 | + | 0.121150i | ||||
\(387\) | −542.564 | + | 939.749i | −0.0712664 | + | 0.123437i | ||||
\(388\) | −1041.41 | + | 279.046i | −0.136262 | + | 0.0365113i | ||||
\(389\) | − | 2904.83i | − | 0.378613i | −0.981918 | − | 0.189307i | \(-0.939376\pi\) | ||
0.981918 | − | 0.189307i | \(-0.0606240\pi\) | |||||||
\(390\) | 594.325 | + | 1967.07i | 0.0771662 | + | 0.255401i | ||||
\(391\) | − | 3771.65i | − | 0.487828i | ||||||
\(392\) | 5744.41 | − | 1539.21i | 0.740144 | − | 0.198321i | ||||
\(393\) | 6103.46 | + | 3523.83i | 0.783407 | + | 0.452300i | ||||
\(394\) | −365.767 | + | 211.175i | −0.0467692 | + | 0.0270022i | ||||
\(395\) | −2636.34 | − | 2636.34i | −0.335819 | − | 0.335819i | ||||
\(396\) | −304.953 | + | 868.730i | −0.0386982 | + | 0.110241i | ||||
\(397\) | −1256.38 | + | 4688.88i | −0.158831 | + | 0.592766i | 0.839916 | + | 0.542717i | \(0.182604\pi\) |
−0.998747 | + | 0.0500488i | \(0.984062\pi\) | |||||||
\(398\) | −11658.8 | + | 11658.8i | −1.46835 | + | 1.46835i | ||||
\(399\) | −694.046 | − | 1202.12i | −0.0870820 | − | 0.150831i | ||||
\(400\) | −7605.20 | − | 4390.87i | −0.950650 | − | 0.548858i | ||||
\(401\) | 9212.81 | − | 2468.56i | 1.14730 | − | 0.307417i | 0.365415 | − | 0.930845i | \(-0.380927\pi\) |
0.781881 | + | 0.623428i | \(0.214260\pi\) | |||||||
\(402\) | 2629.89 | 0.326286 | ||||||||
\(403\) | −652.911 | + | 405.004i | −0.0807043 | + | 0.0500612i | ||||
\(404\) | − | 1650.90i | − | 0.203305i | ||||||
\(405\) | 284.037 | + | 1060.04i | 0.0348492 | + | 0.130059i | ||||
\(406\) | 3051.35 | + | 1761.70i | 0.372995 | + | 0.215349i | ||||
\(407\) | −1632.92 | − | 3399.45i | −0.198872 | − | 0.414015i | ||||
\(408\) | 4338.45 | − | 4338.45i | 0.526435 | − | 0.526435i | ||||
\(409\) | −460.562 | + | 1718.84i | −0.0556805 | + | 0.207802i | −0.988162 | − | 0.153416i | \(-0.950972\pi\) |
0.932481 | + | 0.361219i | \(0.117639\pi\) | |||||||
\(410\) | −639.172 | + | 2385.42i | −0.0769914 | + | 0.287336i | ||||
\(411\) | −3213.82 | − | 3213.82i | −0.385708 | − | 0.385708i | ||||
\(412\) | 1716.85 | + | 2973.67i | 0.205299 | + | 0.355588i | ||||
\(413\) | 7884.78 | − | 13656.8i | 0.939430 | − | 1.62714i | ||||
\(414\) | −401.960 | − | 1500.13i | −0.0477180 | − | 0.178086i | ||||
\(415\) | 3617.22 | 0.427862 | ||||||||
\(416\) | 2290.81 | − | 4274.40i | 0.269990 | − | 0.503773i | ||||
\(417\) | 5728.70i | 0.672748i | ||||||||
\(418\) | 1532.53 | − | 288.389i | 0.179326 | − | 0.0337453i | ||||
\(419\) | −1476.39 | + | 2557.19i | −0.172140 | + | 0.298155i | −0.939168 | − | 0.343459i | \(-0.888401\pi\) |
0.767028 | + | 0.641614i | \(0.221735\pi\) | |||||||
\(420\) | −415.601 | − | 719.842i | −0.0482839 | − | 0.0836302i | ||||
\(421\) | 6412.85 | − | 6412.85i | 0.742383 | − | 0.742383i | −0.230653 | − | 0.973036i | \(-0.574086\pi\) |
0.973036 | + | 0.230653i | \(0.0740863\pi\) | |||||||
\(422\) | 14072.6 | + | 3770.75i | 1.62333 | + | 0.434970i | ||||
\(423\) | −1461.61 | + | 5454.82i | −0.168005 | + | 0.627003i | ||||
\(424\) | −2930.29 | + | 2930.29i | −0.335631 | + | 0.335631i | ||||
\(425\) | 8235.01 | − | 4754.48i | 0.939898 | − | 0.542650i | ||||
\(426\) | −4328.73 | + | 7497.59i | −0.492319 | + | 0.852721i | ||||
\(427\) | 20839.6 | − | 5583.96i | 2.36183 | − | 0.632850i | ||||
\(428\) | 287.844 | 0.0325081 | ||||||||
\(429\) | −5818.99 | − | 3711.57i | −0.654880 | − | 0.417707i | ||||
\(430\) | 1100.56 | 0.123428 | ||||||||
\(431\) | 13386.3 | − | 3586.84i | 1.49604 | − | 0.400864i | 0.584271 | − | 0.811559i | \(-0.301381\pi\) |
0.911773 | + | 0.410695i | \(0.134714\pi\) | |||||||
\(432\) | 5882.47 | − | 10188.7i | 0.655140 | − | 1.13474i | ||||
\(433\) | −4957.55 | + | 2862.24i | −0.550219 | + | 0.317669i | −0.749210 | − | 0.662332i | \(-0.769567\pi\) |
0.198992 | + | 0.980001i | \(0.436233\pi\) | |||||||
\(434\) | 965.832 | − | 965.832i | 0.106824 | − | 0.106824i | ||||
\(435\) | −149.087 | + | 556.400i | −0.0164326 | + | 0.0613272i | ||||
\(436\) | 1250.35 | + | 335.030i | 0.137342 | + | 0.0368005i | ||||
\(437\) | −423.215 | + | 423.215i | −0.0463276 | + | 0.0463276i | ||||
\(438\) | 1465.83 | + | 2538.90i | 0.159909 | + | 0.276971i | ||||
\(439\) | 7555.01 | − | 13085.7i | 0.821368 | − | 1.42265i | −0.0832949 | − | 0.996525i | \(-0.526544\pi\) |
0.904663 | − | 0.426127i | \(-0.140122\pi\) | |||||||
\(440\) | −2197.84 | + | 413.587i | −0.238131 | + | 0.0448113i | ||||
\(441\) | 3506.85i | 0.378669i | ||||||||
\(442\) | 6655.19 | + | 10728.9i | 0.716188 | + | 1.15457i | ||||
\(443\) | 5032.80 | 0.539764 | 0.269882 | − | 0.962893i | \(-0.413015\pi\) | ||||
0.269882 | + | 0.962893i | \(0.413015\pi\) | |||||||
\(444\) | −254.459 | − | 949.653i | −0.0271984 | − | 0.101506i | ||||
\(445\) | 1889.65 | − | 3272.98i | 0.201299 | − | 0.348660i | ||||
\(446\) | −4006.39 | − | 6939.28i | −0.425355 | − | 0.736736i | ||||
\(447\) | −4438.92 | − | 4438.92i | −0.469695 | − | 0.469695i | ||||
\(448\) | 1912.83 | − | 7138.79i | 0.201725 | − | 0.752849i | ||||
\(449\) | −4482.05 | + | 16727.2i | −0.471094 | + | 1.75815i | 0.164758 | + | 0.986334i | \(0.447316\pi\) |
−0.635851 | + | 0.771811i | \(0.719351\pi\) | |||||||
\(450\) | 2768.68 | − | 2768.68i | 0.290038 | − | 0.290038i | ||||
\(451\) | −3591.50 | − | 7476.86i | −0.374982 | − | 0.780647i | ||||
\(452\) | 2728.21 | + | 1575.13i | 0.283903 | + | 0.163912i | ||||
\(453\) | 1771.34 | + | 6610.74i | 0.183720 | + | 0.685651i | ||||
\(454\) | − | 7437.93i | − | 0.768897i | ||||||
\(455\) | −3921.32 | + | 1184.78i | −0.404032 | + | 0.122073i | ||||
\(456\) | −973.631 | −0.0999878 | ||||||||
\(457\) | −12391.8 | + | 3320.37i | −1.26841 | + | 0.339869i | −0.829421 | − | 0.558623i | \(-0.811330\pi\) |
−0.438988 | + | 0.898493i | \(0.644663\pi\) | |||||||
\(458\) | −14962.2 | − | 8638.45i | −1.52650 | − | 0.881328i | ||||
\(459\) | 6369.61 | + | 11032.5i | 0.647730 | + | 1.12190i | ||||
\(460\) | −253.425 | + | 253.425i | −0.0256870 | + | 0.0256870i | ||||
\(461\) | 1264.38 | − | 4718.73i | 0.127740 | − | 0.476731i | −0.872183 | − | 0.489180i | \(-0.837296\pi\) |
0.999923 | + | 0.0124491i | \(0.00396278\pi\) | |||||||
\(462\) | 11577.3 | + | 4064.03i | 1.16586 | + | 0.409255i | ||||
\(463\) | −7285.39 | − | 7285.39i | −0.731276 | − | 0.731276i | 0.239596 | − | 0.970873i | \(-0.422985\pi\) |
−0.970873 | + | 0.239596i | \(0.922985\pi\) | |||||||
\(464\) | 2830.59 | − | 1634.24i | 0.283204 | − | 0.163508i | ||||
\(465\) | 193.388 | + | 111.653i | 0.0192863 | + | 0.0111350i | ||||
\(466\) | −6052.62 | + | 1621.79i | −0.601678 | + | 0.161219i | ||||
\(467\) | 867.762i | 0.0859855i | 0.999075 | + | 0.0429928i | \(0.0136892\pi\) | ||||
−0.999075 | + | 0.0429928i | \(0.986311\pi\) | |||||||
\(468\) | 862.452 | + | 809.571i | 0.0851856 | + | 0.0799624i | ||||
\(469\) | 5242.64i | 0.516168i | ||||||||
\(470\) | 5532.41 | − | 1482.41i | 0.542960 | − | 0.145486i | ||||
\(471\) | −2298.67 | + | 3981.42i | −0.224877 | + | 0.389499i | ||||
\(472\) | −5530.52 | − | 9579.14i | −0.539328 | − | 0.934143i | ||||
\(473\) | −2804.27 | + | 2408.41i | −0.272602 | + | 0.234121i | ||||
\(474\) | 13858.8 | + | 3713.46i | 1.34295 | + | 0.359841i | ||||
\(475\) | −1457.54 | − | 390.548i | −0.140793 | − | 0.0377254i | ||||
\(476\) | −3611.17 | − | 3611.17i | −0.347726 | − | 0.347726i | ||||
\(477\) | −1221.83 | − | 2116.28i | −0.117283 | − | 0.203140i | ||||
\(478\) | −14680.6 | − | 8475.86i | −1.40476 | − | 0.811039i | ||||
\(479\) | 2539.31 | + | 9476.83i | 0.242221 | + | 0.903982i | 0.974760 | + | 0.223257i | \(0.0716688\pi\) |
−0.732538 | + | 0.680726i | \(0.761665\pi\) | |||||||
\(480\) | −1409.47 | −0.134028 | ||||||||
\(481\) | −4842.83 | + | 153.166i | −0.459073 | + | 0.0145192i | ||||
\(482\) | 8689.27 | 0.821132 | ||||||||
\(483\) | −4548.82 | + | 1218.85i | −0.428526 | + | 0.114823i | ||||
\(484\) | −1960.40 | + | 2448.24i | −0.184110 | + | 0.229925i | ||||
\(485\) | 1337.39 | − | 772.145i | 0.125212 | − | 0.0722913i | ||||
\(486\) | 6365.01 | + | 6365.01i | 0.594080 | + | 0.594080i | ||||
\(487\) | −9103.97 | − | 2439.40i | −0.847105 | − | 0.226981i | −0.190943 | − | 0.981601i | \(-0.561155\pi\) |
−0.656162 | + | 0.754620i | \(0.727821\pi\) | |||||||
\(488\) | 3916.69 | − | 14617.3i | 0.363320 | − | 1.35593i | ||||
\(489\) | 10852.1 | + | 10852.1i | 1.00357 | + | 1.00357i | ||||
\(490\) | 3080.23 | − | 1778.37i | 0.283980 | − | 0.163956i | ||||
\(491\) | 4432.94 | − | 7678.07i | 0.407445 | − | 0.705716i | −0.587157 | − | 0.809473i | \(-0.699753\pi\) |
0.994603 | + | 0.103757i | \(0.0330864\pi\) | |||||||
\(492\) | −559.665 | − | 2088.70i | −0.0512839 | − | 0.191394i | ||||
\(493\) | 3539.15i | 0.323317i | ||||||||
\(494\) | 457.110 | − | 1950.66i | 0.0416323 | − | 0.177661i | ||||
\(495\) | 99.8612 | − | 1314.98i | 0.00906753 | − | 0.119402i | ||||
\(496\) | −327.942 | − | 1223.90i | −0.0296876 | − | 0.110796i | ||||
\(497\) | −14946.3 | − | 8629.25i | −1.34896 | − | 0.778823i | ||||
\(498\) | −12055.1 | + | 6960.04i | −1.08475 | + | 0.626279i | ||||
\(499\) | −285.291 | + | 285.291i | −0.0255939 | + | 0.0255939i | −0.719788 | − | 0.694194i | \(-0.755761\pi\) |
0.694194 | + | 0.719788i | \(0.255761\pi\) | |||||||
\(500\) | −1833.10 | − | 491.179i | −0.163958 | − | 0.0439323i | ||||
\(501\) | 13925.5 | + | 3731.33i | 1.24181 | + | 0.332742i | ||||
\(502\) | −11071.8 | + | 11071.8i | −0.984379 | + | 0.984379i | ||||
\(503\) | −16006.5 | + | 9241.35i | −1.41888 | + | 0.819188i | −0.996200 | − | 0.0870930i | \(-0.972242\pi\) |
−0.422675 | + | 0.906281i | \(0.638909\pi\) | |||||||
\(504\) | 4361.61 | + | 2518.18i | 0.385480 | + | 0.222557i | ||||
\(505\) | 612.021 | + | 2284.09i | 0.0539298 | + | 0.201269i | ||||
\(506\) | 400.617 | − | 5275.36i | 0.0351969 | − | 0.463475i | ||||
\(507\) | −7383.86 | + | 4910.10i | −0.646802 | + | 0.430109i | ||||
\(508\) | − | 1312.97i | − | 0.114673i | ||||||
\(509\) | 4989.51 | + | 18621.1i | 0.434491 | + | 1.62154i | 0.742281 | + | 0.670089i | \(0.233744\pi\) |
−0.307790 | + | 0.951454i | \(0.599589\pi\) | |||||||
\(510\) | 1834.72 | − | 3177.83i | 0.159300 | − | 0.275915i | ||||
\(511\) | −5061.25 | + | 2922.11i | −0.438154 | + | 0.252968i | ||||
\(512\) | −2286.41 | − | 2286.41i | −0.197355 | − | 0.197355i | ||||
\(513\) | 523.220 | − | 1952.68i | 0.0450306 | − | 0.168057i | ||||
\(514\) | −9902.61 | − | 2653.40i | −0.849777 | − | 0.227697i | ||||
\(515\) | −3477.74 | − | 3477.74i | −0.297568 | − | 0.297568i | ||||
\(516\) | −834.558 | + | 481.832i | −0.0712003 | + | 0.0411075i | ||||
\(517\) | −10852.7 | + | 15884.0i | −0.923217 | + | 1.35122i | ||||
\(518\) | 8320.18 | − | 2229.39i | 0.705729 | − | 0.189100i | ||||
\(519\) | −17783.2 | −1.50404 | ||||||||
\(520\) | −655.554 | + | 2797.50i | −0.0552845 | + | 0.235920i | ||||
\(521\) | −16928.4 | −1.42351 | −0.711753 | − | 0.702429i | \(-0.752099\pi\) | ||||
−0.711753 | + | 0.702429i | \(0.752099\pi\) | |||||||
\(522\) | 377.181 | + | 1407.66i | 0.0316260 | + | 0.118030i | ||||
\(523\) | 12567.6 | + | 7255.92i | 1.05075 | + | 0.606653i | 0.922860 | − | 0.385135i | \(-0.125845\pi\) |
0.127893 | + | 0.991788i | \(0.459179\pi\) | |||||||
\(524\) | −2057.33 | − | 3563.40i | −0.171517 | − | 0.297076i | ||||
\(525\) | −8395.39 | − | 8395.39i | −0.697914 | − | 0.697914i | ||||
\(526\) | −20963.2 | − | 5617.06i | −1.73771 | − | 0.465619i | ||||
\(527\) | 1325.25 | + | 355.100i | 0.109542 | + | 0.0293518i | ||||
\(528\) | 8634.78 | − | 7415.87i | 0.711706 | − | 0.611240i | ||||
\(529\) | −5068.23 | − | 8778.43i | −0.416555 | − | 0.721495i | ||||
\(530\) | −1239.21 | + | 2146.38i | −0.101562 | + | 0.175911i | ||||
\(531\) | 6300.22 | − | 1688.14i | 0.514889 | − | 0.137964i | ||||
\(532\) | 810.414i | 0.0660449i | ||||||||
\(533\) | −10651.5 | + | 336.878i | −0.865605 | + | 0.0273768i | ||||
\(534\) | 14543.8i | 1.17860i | ||||||||
\(535\) | −398.246 | + | 106.710i | −0.0321826 | + | 0.00862329i | ||||
\(536\) | 3184.62 | + | 1838.64i | 0.256631 | + | 0.148166i | ||||
\(537\) | −4794.57 | + | 2768.15i | −0.385291 | + | 0.222448i | ||||
\(538\) | −739.357 | − | 739.357i | −0.0592490 | − | 0.0592490i | ||||
\(539\) | −3956.83 | + | 11271.9i | −0.316201 | + | 0.900773i | ||||
\(540\) | 313.309 | − | 1169.28i | 0.0249679 | − | 0.0931814i | ||||
\(541\) | −7145.93 | + | 7145.93i | −0.567888 | + | 0.567888i | −0.931536 | − | 0.363648i | \(-0.881531\pi\) |
0.363648 | + | 0.931536i | \(0.381531\pi\) | |||||||
\(542\) | 689.671 | + | 1194.55i | 0.0546567 | + | 0.0946682i | ||||
\(543\) | −4808.35 | − | 2776.10i | −0.380011 | − | 0.219400i | ||||
\(544\) | −8364.82 | + | 2241.35i | −0.659262 | + | 0.176649i | ||||
\(545\) | −1854.12 | −0.145728 | ||||||||
\(546\) | 10788.9 | − | 11493.7i | 0.845648 | − | 0.900886i | ||||
\(547\) | − | 8606.06i | − | 0.672703i | −0.941737 | − | 0.336352i | \(-0.890807\pi\) | ||
0.941737 | − | 0.336352i | \(-0.109193\pi\) | |||||||
\(548\) | 686.787 | + | 2563.12i | 0.0535366 | + | 0.199801i | ||||
\(549\) | 7728.03 | + | 4461.78i | 0.600773 | + | 0.346856i | ||||
\(550\) | 12023.2 | − | 5775.32i | 0.932129 | − | 0.447746i | ||||
\(551\) | 397.127 | − | 397.127i | 0.0307045 | − | 0.0307045i | ||||
\(552\) | −854.923 | + | 3190.62i | −0.0659202 | + | 0.246018i | ||||
\(553\) | −7402.71 | + | 27627.3i | −0.569250 | + | 2.12447i | ||||
\(554\) | 14872.6 | + | 14872.6i | 1.14057 | + | 1.14057i | ||||
\(555\) | 704.111 | + | 1219.56i | 0.0538519 | + | 0.0932743i | ||||
\(556\) | 1672.30 | − | 2896.52i | 0.127557 | − | 0.220935i | ||||
\(557\) | 2542.54 | + | 9488.88i | 0.193413 | + | 0.721826i | 0.992672 | + | 0.120839i | \(0.0385586\pi\) |
−0.799259 | + | 0.600986i | \(0.794775\pi\) | |||||||
\(558\) | 564.949 | 0.0428605 | ||||||||
\(559\) | 1373.59 | + | 4546.23i | 0.103929 | + | 0.343981i | ||||
\(560\) | − | 6755.52i | − | 0.509773i | ||||||
\(561\) | 2279.26 | + | 12112.2i | 0.171534 | + | 0.911547i | ||||
\(562\) | −3644.44 | + | 6312.35i | −0.273543 | + | 0.473791i | ||||
\(563\) | −4334.39 | − | 7507.39i | −0.324463 | − | 0.561987i | 0.656940 | − | 0.753943i | \(-0.271850\pi\) |
−0.981404 | + | 0.191956i | \(0.938517\pi\) | |||||||
\(564\) | −3546.22 | + | 3546.22i | −0.264757 | + | 0.264757i | ||||
\(565\) | −4358.54 | − | 1167.87i | −0.324540 | − | 0.0869602i | ||||
\(566\) | 2905.23 | − | 10842.5i | 0.215752 | − | 0.805199i | ||||
\(567\) | 5953.09 | − | 5953.09i | 0.440928 | − | 0.440928i | ||||
\(568\) | −10483.6 | + | 6052.71i | −0.774440 | + | 0.447123i | ||||
\(569\) | 6981.61 | − | 12092.5i | 0.514384 | − | 0.890938i | −0.485477 | − | 0.874249i | \(-0.661354\pi\) |
0.999861 | − | 0.0166891i | \(-0.00531255\pi\) | |||||||
\(570\) | −562.456 | + | 150.710i | −0.0413310 | + | 0.0110746i | ||||
\(571\) | 3023.61 | 0.221601 | 0.110801 | − | 0.993843i | \(-0.464659\pi\) | ||||
0.110801 | + | 0.993843i | \(0.464659\pi\) | |||||||
\(572\) | 1858.70 | + | 3575.29i | 0.135867 | + | 0.261346i | ||||
\(573\) | 13979.5 | 1.01920 | ||||||||
\(574\) | 18299.7 | − | 4903.39i | 1.33069 | − | 0.356557i | ||||
\(575\) | −2559.67 | + | 4433.49i | −0.185645 | + | 0.321546i | ||||
\(576\) | 2647.30 | − | 1528.42i | 0.191501 | − | 0.110563i | ||||
\(577\) | 9374.86 | − | 9374.86i | 0.676396 | − | 0.676396i | −0.282787 | − | 0.959183i | \(-0.591259\pi\) |
0.959183 | + | 0.282787i | \(0.0912588\pi\) | |||||||
\(578\) | 1743.03 | − | 6505.08i | 0.125433 | − | 0.468124i | ||||
\(579\) | 1285.22 | + | 344.374i | 0.0922487 | + | 0.0247180i | ||||
\(580\) | 237.803 | − | 237.803i | 0.0170245 | − | 0.0170245i | ||||
\(581\) | −13874.7 | − | 24031.7i | −0.990740 | − | 1.71601i | ||||
\(582\) | −2971.43 | + | 5146.66i | −0.211632 | + | 0.366557i | ||||
\(583\) | −1539.47 | − | 8180.88i | −0.109362 | − | 0.581162i | ||||
\(584\) | 4099.24i | 0.290459i | ||||||||
\(585\) | −1493.37 | − | 800.350i | −0.105544 | − | 0.0565648i | ||||
\(586\) | −899.724 | −0.0634253 | ||||||||
\(587\) | −378.243 | − | 1411.62i | −0.0265959 | − | 0.0992571i | 0.951352 | − | 0.308106i | \(-0.0996951\pi\) |
−0.977948 | + | 0.208849i | \(0.933028\pi\) | |||||||
\(588\) | −1557.16 | + | 2697.08i | −0.109211 | + | 0.189159i | ||||
\(589\) | −108.860 | − | 188.551i | −0.00761546 | − | 0.0131904i | ||||
\(590\) | −4677.69 | − | 4677.69i | −0.326402 | − | 0.326402i | ||||
\(591\) | −137.098 | + | 511.655i | −0.00954221 | + | 0.0356120i | ||||
\(592\) | 2068.09 | − | 7718.22i | 0.143578 | − | 0.535839i | ||||
\(593\) | −1624.76 | + | 1624.76i | −0.112514 | + | 0.112514i | −0.761122 | − | 0.648608i | \(-0.775351\pi\) |
0.648608 | + | 0.761122i | \(0.275351\pi\) | |||||||
\(594\) | 7737.24 | + | 16107.6i | 0.534449 | + | 1.11263i | ||||
\(595\) | 6334.94 | + | 3657.48i | 0.436483 | + | 0.252004i | ||||
\(596\) | 948.588 | + | 3540.18i | 0.0651941 | + | 0.243308i | ||||
\(597\) | 20679.1i | 1.41765i | ||||||||
\(598\) | −5990.99 | − | 3210.79i | −0.409682 | − | 0.219564i | ||||
\(599\) | −22915.4 | −1.56310 | −0.781550 | − | 0.623842i | \(-0.785571\pi\) | ||||
−0.781550 | + | 0.623842i | \(0.785571\pi\) | |||||||
\(600\) | −8044.08 | + | 2155.40i | −0.547330 | + | 0.146657i | ||||
\(601\) | −8010.26 | − | 4624.73i | −0.543670 | − | 0.313888i | 0.202895 | − | 0.979200i | \(-0.434965\pi\) |
−0.746565 | + | 0.665313i | \(0.768298\pi\) | |||||||
\(602\) | −4221.47 | − | 7311.80i | −0.285805 | − | 0.495028i | ||||
\(603\) | −1533.30 | + | 1533.30i | −0.103550 | + | 0.103550i | ||||
\(604\) | 1034.17 | − | 3859.57i | 0.0696685 | − | 0.260006i | ||||
\(605\) | 1804.69 | − | 4114.01i | 0.121274 | − | 0.276460i | ||||
\(606\) | −6434.59 | − | 6434.59i | −0.431333 | − | 0.431333i | ||||
\(607\) | 4055.57 | − | 2341.48i | 0.271187 | − | 0.156570i | −0.358240 | − | 0.933630i | \(-0.616623\pi\) |
0.629427 | + | 0.777060i | \(0.283290\pi\) | |||||||
\(608\) | 1190.11 | + | 687.112i | 0.0793840 | + | 0.0458323i | ||||
\(609\) | 4268.41 | − | 1143.72i | 0.284014 | − | 0.0761013i | ||||
\(610\) | − | 9050.50i | − | 0.600728i | ||||||
\(611\) | 13028.4 | + | 21003.2i | 0.862640 | + | 1.39067i | ||||
\(612\) | − | 2112.29i | − | 0.139517i | ||||||
\(613\) | 10219.6 | − | 2738.35i | 0.673357 | − | 0.180425i | 0.0940902 | − | 0.995564i | \(-0.470006\pi\) |
0.579266 | + | 0.815138i | \(0.303339\pi\) | |||||||
\(614\) | −1251.82 | + | 2168.21i | −0.0822789 | + | 0.142511i | ||||
\(615\) | 1548.65 | + | 2682.33i | 0.101541 | + | 0.175873i | ||||
\(616\) | 11178.1 | + | 13015.3i | 0.731131 | + | 0.851304i | ||||
\(617\) | −8367.47 | − | 2242.06i | −0.545967 | − | 0.146291i | −0.0247156 | − | 0.999695i | \(-0.507868\pi\) |
−0.521252 | + | 0.853403i | \(0.674535\pi\) | |||||||
\(618\) | 18281.9 | + | 4898.63i | 1.18998 | + | 0.318854i | ||||
\(619\) | 567.451 | + | 567.451i | 0.0368461 | + | 0.0368461i | 0.725290 | − | 0.688444i | \(-0.241706\pi\) |
−0.688444 | + | 0.725290i | \(0.741706\pi\) | |||||||
\(620\) | −65.1865 | − | 112.906i | −0.00422250 | − | 0.00731359i | ||||
\(621\) | −5939.57 | − | 3429.21i | −0.383811 | − | 0.221593i | ||||
\(622\) | 3214.08 | + | 11995.1i | 0.207191 | + | 0.773247i | ||||
\(623\) | −28992.8 | −1.86448 | ||||||||
\(624\) | −4229.48 | − | 13998.5i | −0.271338 | − | 0.898062i | ||||
\(625\) | −11482.7 | −0.734893 | ||||||||
\(626\) | −22291.2 | + | 5972.91i | −1.42322 | + | 0.381350i | ||||
\(627\) | 1103.35 | − | 1614.86i | 0.0702768 | − | 0.102857i | ||||
\(628\) | 2324.49 | − | 1342.04i | 0.147702 | − | 0.0852760i | ||||
\(629\) | 6118.03 | + | 6118.03i | 0.387825 | + | 0.387825i | ||||
\(630\) | 2909.45 | + | 779.584i | 0.183992 | + | 0.0493006i | ||||
\(631\) | 3924.84 | − | 14647.7i | 0.247615 | − | 0.924113i | −0.724435 | − | 0.689343i | \(-0.757899\pi\) |
0.972051 | − | 0.234771i | \(-0.0754339\pi\) | |||||||
\(632\) | 14185.9 | + | 14185.9i | 0.892854 | + | 0.892854i | ||||
\(633\) | 15824.2 | − | 9136.13i | 0.993613 | − | 0.573663i | ||||
\(634\) | 6476.19 | − | 11217.1i | 0.405682 | − | 0.702662i | ||||
\(635\) | 486.746 | + | 1816.56i | 0.0304188 | + | 0.113524i | ||||
\(636\) | − | 2170.14i | − | 0.135301i | ||||||
\(637\) | 11190.5 | + | 10504.3i | 0.696048 | + | 0.653370i | ||||
\(638\) | −375.921 | + | 4950.16i | −0.0233274 | + | 0.307177i | ||||
\(639\) | −1847.53 | − | 6895.08i | −0.114377 | − | 0.426862i | ||||
\(640\) | −5104.39 | − | 2947.02i | −0.315263 | − | 0.182017i | ||||
\(641\) | 16357.7 | − | 9444.14i | 1.00794 | − | 0.581936i | 0.0973543 | − | 0.995250i | \(-0.468962\pi\) |
0.910589 | + | 0.413314i | \(0.135629\pi\) | |||||||
\(642\) | 1121.91 | − | 1121.91i | 0.0689694 | − | 0.0689694i | ||||
\(643\) | 27570.8 | + | 7387.59i | 1.69096 | + | 0.453092i | 0.970638 | − | 0.240547i | \(-0.0773267\pi\) |
0.720324 | + | 0.693638i | \(0.243993\pi\) | |||||||
\(644\) | 2655.75 | + | 711.606i | 0.162502 | + | 0.0435423i | ||||
\(645\) | 976.025 | − | 976.025i | 0.0595828 | − | 0.0595828i | ||||
\(646\) | −3098.35 | + | 1788.84i | −0.188704 | + | 0.108949i | ||||
\(647\) | 16461.1 | + | 9503.84i | 1.00024 | + | 0.577488i | 0.908319 | − | 0.418279i | \(-0.137367\pi\) |
0.0919192 | + | 0.995766i | \(0.470700\pi\) | |||||||
\(648\) | −1528.38 | − | 5703.98i | −0.0926547 | − | 0.345792i | ||||
\(649\) | 22155.3 | + | 1682.50i | 1.34002 | + | 0.101763i | ||||
\(650\) | −541.718 | − | 17128.2i | −0.0326891 | − | 1.03357i | ||||
\(651\) | − | 1713.08i | − | 0.103135i | ||||||
\(652\) | −2319.06 | − | 8654.85i | −0.139297 | − | 0.519862i | ||||
\(653\) | −84.5439 | + | 146.434i | −0.00506655 | + | 0.00877553i | −0.868548 | − | 0.495606i | \(-0.834946\pi\) |
0.863481 | + | 0.504381i | \(0.168279\pi\) | |||||||
\(654\) | 6179.23 | − | 3567.58i | 0.369460 | − | 0.213308i | ||||
\(655\) | 4167.44 | + | 4167.44i | 0.248604 | + | 0.248604i | ||||
\(656\) | 4548.63 | − | 16975.7i | 0.270723 | − | 1.01035i | ||||
\(657\) | −2334.87 | − | 625.627i | −0.138648 | − | 0.0371507i | ||||
\(658\) | −31069.5 | − | 31069.5i | −1.84075 | − | 1.84075i | ||||
\(659\) | −6253.62 | + | 3610.53i | −0.369661 | + | 0.213424i | −0.673310 | − | 0.739360i | \(-0.735128\pi\) |
0.303649 | + | 0.952784i | \(0.401795\pi\) | |||||||
\(660\) | 660.696 | − | 966.993i | 0.0389660 | − | 0.0570305i | ||||
\(661\) | −12232.5 | + | 3277.70i | −0.719804 | + | 0.192871i | −0.600084 | − | 0.799937i | \(-0.704866\pi\) |
−0.119720 | + | 0.992808i | \(0.538200\pi\) | |||||||
\(662\) | 32140.5 | 1.88697 | ||||||||
\(663\) | 15416.9 | + | 3612.74i | 0.903082 | + | 0.211625i | ||||
\(664\) | −19463.9 | −1.13757 | ||||||||
\(665\) | −300.437 | − | 1121.25i | −0.0175195 | − | 0.0653835i | ||||
\(666\) | 3085.40 | + | 1781.36i | 0.179515 | + | 0.103643i | ||||
\(667\) | −952.688 | − | 1650.10i | −0.0553047 | − | 0.0957905i | ||||
\(668\) | −5951.71 | − | 5951.71i | −0.344729 | − | 0.344729i | ||||
\(669\) | −9707.06 | − | 2601.00i | −0.560982 | − | 0.150315i | ||||
\(670\) | 2124.32 | + | 569.210i | 0.122492 | + | 0.0328217i | ||||
\(671\) | 19805.6 | + | 23061.0i | 1.13947 | + | 1.32676i | ||||
\(672\) | 5406.37 | + | 9364.10i | 0.310350 | + | 0.537542i | ||||
\(673\) | 3013.58 | − | 5219.68i | 0.172608 | − | 0.298966i | −0.766723 | − | 0.641978i | \(-0.778114\pi\) |
0.939331 | + | 0.343012i | \(0.111447\pi\) | |||||||
\(674\) | 10353.3 | − | 2774.17i | 0.591685 | − | 0.158541i | ||||
\(675\) | − | 17291.2i | − | 0.985985i | ||||||
\(676\) | 5166.73 | − | 327.147i | 0.293965 | − | 0.0186133i | ||||
\(677\) | − | 13615.1i | − | 0.772924i | −0.922305 | − | 0.386462i | \(-0.873697\pi\) | ||
0.922305 | − | 0.386462i | \(-0.126303\pi\) | |||||||
\(678\) | 16772.9 | − | 4494.27i | 0.950085 | − | 0.254574i | ||||
\(679\) | −10259.8 | − | 5923.48i | −0.579873 | − | 0.334790i | ||||
\(680\) | 4443.44 | − | 2565.42i | 0.250585 | − | 0.144676i | ||||
\(681\) | −6596.25 | − | 6596.25i | −0.371173 | − | 0.371173i | ||||
\(682\) | 1815.89 | + | 637.438i | 0.101956 | + | 0.0357900i | ||||
\(683\) | −564.463 | + | 2106.61i | −0.0316231 | + | 0.118019i | −0.979933 | − | 0.199326i | \(-0.936125\pi\) |
0.948310 | + | 0.317345i | \(0.102791\pi\) | |||||||
\(684\) | −237.020 | + | 237.020i | −0.0132495 | + | 0.0132495i | ||||
\(685\) | −1900.40 | − | 3291.59i | −0.106001 | − | 0.183599i | ||||
\(686\) | 1122.27 | + | 647.942i | 0.0624613 | + | 0.0360620i | ||||
\(687\) | −20930.0 | + | 5608.18i | −1.16234 | + | 0.311449i | ||||
\(688\) | −7832.10 | −0.434006 | ||||||||
\(689\) | −10413.0 | − | 2440.13i | −0.575765 | − | 0.134922i | ||||
\(690\) | 1975.52i | 0.108995i | ||||||||
\(691\) | −8621.98 | − | 32177.7i | −0.474668 | − | 1.77148i | −0.622656 | − | 0.782496i | \(-0.713946\pi\) |
0.147988 | − | 0.988989i | \(-0.452720\pi\) | |||||||
\(692\) | 8991.46 | + | 5191.22i | 0.493937 | + | 0.285174i | ||||
\(693\) | −9119.36 | + | 4380.47i | −0.499879 | + | 0.240116i | ||||
\(694\) | −18080.0 | + | 18080.0i | −0.988915 | + | 0.988915i | ||||
\(695\) | −1239.91 | + | 4627.42i | −0.0676728 | + | 0.252558i | ||||
\(696\) | 802.222 | − | 2993.93i | 0.0436899 | − | 0.163053i | ||||
\(697\) | 13456.2 | + | 13456.2i | 0.731263 | + | 0.731263i | ||||
\(698\) | 10447.4 | + | 18095.4i | 0.566532 | + | 0.981262i | ||||
\(699\) | −3929.43 | + | 6805.97i | −0.212625 | + | 0.368277i | ||||
\(700\) | 1794.08 | + | 6695.59i | 0.0968711 | + | 0.361528i | ||||
\(701\) | −23379.8 | −1.25969 | −0.629845 | − | 0.776721i | \(-0.716882\pi\) | ||||
−0.629845 | + | 0.776721i | \(0.716882\pi\) | |||||||
\(702\) | 22946.7 | − | 725.743i | 1.23372 | − | 0.0390191i | ||||
\(703\) | − | 1373.00i | − | 0.0736611i | ||||||
\(704\) | 10233.7 | − | 1925.76i | 0.547863 | − | 0.103096i | ||||
\(705\) | 3591.71 | − | 6221.02i | 0.191875 | − | 0.332336i | ||||
\(706\) | −8021.96 | − | 13894.4i | −0.427635 | − | 0.740686i | ||||
\(707\) | 12827.2 | − | 12827.2i | 0.682345 | − | 0.682345i | ||||
\(708\) | 5595.00 | + | 1499.18i | 0.296996 | + | 0.0795798i | ||||
\(709\) | 8325.55 | − | 31071.4i | 0.441005 | − | 1.64585i | −0.285268 | − | 0.958448i | \(-0.592083\pi\) |
0.726273 | − | 0.687406i | \(-0.241251\pi\) | |||||||
\(710\) | −5119.35 | + | 5119.35i | −0.270600 | + | 0.270600i | ||||
\(711\) | −10245.1 | + | 5915.03i | −0.540397 | + | 0.311998i | ||||
\(712\) | −10168.0 | + | 17611.5i | −0.535201 | + | 0.926995i | ||||
\(713\) | −713.476 | + | 191.175i | −0.0374753 | + | 0.0100415i | ||||
\(714\) | −28150.0 | −1.47547 | ||||||||
\(715\) | −3897.02 | − | 4257.51i | −0.203833 | − | 0.222688i | ||||
\(716\) | 3232.27 | 0.168709 | ||||||||
\(717\) | −20536.1 | + | 5502.63i | −1.06964 | + | 0.286610i | ||||
\(718\) | −6100.45 | + | 10566.3i | −0.317085 | + | 0.549207i | ||||
\(719\) | 32494.6 | − | 18760.8i | 1.68546 | − | 0.973100i | 0.727537 | − | 0.686068i | \(-0.240665\pi\) |
0.957921 | − | 0.287032i | \(-0.0926685\pi\) | |||||||
\(720\) | 1975.77 | − | 1975.77i | 0.102267 | − | 0.102267i | ||||
\(721\) | −9765.33 | + | 36444.7i | −0.504411 | + | 1.88249i | ||||
\(722\) | −20772.7 | − | 5566.03i | −1.07075 | − | 0.286906i | ||||
\(723\) | 7706.00 | − | 7706.00i | 0.396389 | − | 0.396389i | ||||
\(724\) | 1620.78 | + | 2807.28i | 0.0831988 | + | 0.144105i | ||||
\(725\) | 2401.88 | − | 4160.19i | 0.123040 | − | 0.213111i | ||||
\(726\) | 1901.44 | + | 17183.3i | 0.0972023 | + | 0.878417i | ||||
\(727\) | 16139.3i | 0.823348i | 0.911331 | + | 0.411674i | \(0.135056\pi\) | ||||
−0.911331 | + | 0.411674i | \(0.864944\pi\) | |||||||
\(728\) | 21100.2 | − | 6375.16i | 1.07421 | − | 0.324559i | ||||
\(729\) | 20068.4 | 1.01958 | ||||||||
\(730\) | 634.527 | + | 2368.09i | 0.0321711 | + | 0.120064i | ||||
\(731\) | 4240.35 | − | 7344.50i | 0.214549 | − | 0.371609i | ||||
\(732\) | 3962.35 | + | 6863.00i | 0.200072 | + | 0.346535i | ||||
\(733\) | −12081.0 | − | 12081.0i | −0.608763 | − | 0.608763i | 0.333860 | − | 0.942623i | \(-0.391649\pi\) |
−0.942623 | + | 0.333860i | \(0.891649\pi\) | |||||||
\(734\) | 5809.00 | − | 21679.5i | 0.292117 | − | 1.09020i | ||||
\(735\) | 1154.54 | − | 4308.80i | 0.0579399 | − | 0.216235i | ||||
\(736\) | 3296.70 | − | 3296.70i | 0.165106 | − | 0.165106i | ||||
\(737\) | −6658.47 | + | 3198.38i | −0.332792 | + | 0.159856i | ||||
\(738\) | 6786.14 | + | 3917.98i | 0.338484 | + | 0.195424i | ||||
\(739\) | 5265.53 | + | 19651.2i | 0.262105 | + | 0.978189i | 0.963999 | + | 0.265907i | \(0.0856714\pi\) |
−0.701894 | + | 0.712282i | \(0.747662\pi\) | |||||||
\(740\) | − | 822.167i | − | 0.0408425i | ||||||
\(741\) | −1324.54 | − | 2135.31i | −0.0656656 | − | 0.105860i | ||||
\(742\) | 19013.2 | 0.940695 | ||||||||
\(743\) | −18704.0 | + | 5011.71i | −0.923528 | + | 0.247459i | −0.689093 | − | 0.724673i | \(-0.741991\pi\) |
−0.234435 | + | 0.972132i | \(0.575324\pi\) | |||||||
\(744\) | −1040.60 | − | 600.791i | −0.0512772 | − | 0.0296049i | ||||
\(745\) | −2624.83 | − | 4546.34i | −0.129082 | − | 0.223577i | ||||
\(746\) | −10714.8 | + | 10714.8i | −0.525867 | + | 0.525867i | ||||
\(747\) | 2970.59 | − | 11086.4i | 0.145499 | − | 0.543011i | ||||
\(748\) | 2383.33 | − | 6789.46i | 0.116501 | − | 0.331882i | ||||
\(749\) | 2236.51 | + | 2236.51i | 0.109106 | + | 0.109106i | ||||
\(750\) | −9059.20 | + | 5230.33i | −0.441060 | + | 0.254646i | ||||
\(751\) | 22274.1 | + | 12859.9i | 1.08228 | + | 0.624855i | 0.931511 | − | 0.363714i | \(-0.118491\pi\) |
0.150770 | + | 0.988569i | \(0.451825\pi\) | |||||||
\(752\) | −39371.1 | + | 10549.4i | −1.90920 | + | 0.511568i | ||||
\(753\) | 19637.8i | 0.950388i | ||||||||
\(754\) | 5621.68 | + | 3012.87i | 0.271525 | + | 0.145520i | ||||
\(755\) | 5723.29i | 0.275883i | ||||||||
\(756\) | −8970.13 | + | 2403.54i | −0.431535 | + | 0.115629i | ||||
\(757\) | 12094.4 | − | 20948.1i | 0.580686 | − | 1.00578i | −0.414713 | − | 0.909952i | \(-0.636118\pi\) |
0.995398 | − | 0.0958246i | \(-0.0305488\pi\) | |||||||
\(758\) | −1921.31 | − | 3327.80i | −0.0920647 | − | 0.159461i | ||||
\(759\) | −4323.12 | − | 5033.68i | −0.206745 | − | 0.240726i | ||||
\(760\) | −786.461 | − | 210.731i | −0.0375367 | − | 0.0100579i | ||||
\(761\) | −2151.19 | − | 576.409i | −0.102471 | − | 0.0274570i | 0.207219 | − | 0.978295i | \(-0.433559\pi\) |
−0.309690 | + | 0.950838i | \(0.600225\pi\) | |||||||
\(762\) | −5117.49 | − | 5117.49i | −0.243290 | − | 0.243290i | ||||
\(763\) | 7111.91 | + | 12318.2i | 0.337442 | + | 0.584467i | ||||
\(764\) | −7068.25 | − | 4080.86i | −0.334712 | − | 0.193246i | ||||
\(765\) | 783.070 | + | 2922.46i | 0.0370091 | + | 0.138120i | ||||
\(766\) | −23162.7 | −1.09256 | ||||||||
\(767\) | 13484.6 | − | 25160.8i | 0.634811 | − | 1.18449i | ||||
\(768\) | 13465.7 | 0.632682 | ||||||||
\(769\) | 8221.79 | − | 2203.02i | 0.385547 | − | 0.103307i | −0.0608390 | − | 0.998148i | \(-0.519378\pi\) |
0.446386 | + | 0.894841i | \(0.352711\pi\) | |||||||
\(770\) | 8472.10 | + | 5788.55i | 0.396511 | + | 0.270915i | ||||
\(771\) | −11135.2 | + | 6428.89i | −0.520134 | + | 0.300300i | ||||
\(772\) | −549.298 | − | 549.298i | −0.0256084 | − | 0.0256084i | ||||
\(773\) | −26636.0 | − | 7137.10i | −1.23937 | − | 0.332087i | −0.421147 | − | 0.906992i | \(-0.638372\pi\) |
−0.818220 | + | 0.574905i | \(0.805039\pi\) | |||||||
\(774\) | 903.821 | − | 3373.11i | 0.0419731 | − | 0.156646i | ||||
\(775\) | −1316.81 | − | 1316.81i | −0.0610337 | − | 0.0610337i | ||||
\(776\) | −7196.38 | + | 4154.83i | −0.332906 | + | 0.192203i | ||||
\(777\) | 5401.56 | − | 9355.78i | 0.249395 | − | 0.431965i | ||||
\(778\) | 2419.48 | + | 9029.62i | 0.111494 | + | 0.416102i | ||||
\(779\) | − | 3019.83i | − | 0.138892i | ||||||
\(780\) | −793.147 | − | 1278.64i | −0.0364093 | − | 0.0586958i | ||||
\(781\) | 1841.36 | − | 24247.2i | 0.0843649 | − | 1.11092i | ||||
\(782\) | 3141.47 | + | 11724.1i | 0.143656 | + | 0.536131i | ||||
\(783\) | 5573.43 | + | 3217.82i | 0.254378 | + | 0.146865i | ||||
\(784\) | −21920.2 | + | 12655.7i | −0.998553 | + | 0.576515i | ||||
\(785\) | −2718.51 | + | 2718.51i | −0.123602 | + | 0.123602i | ||||
\(786\) | −21907.6 | − | 5870.12i | −0.994170 | − | 0.266387i | ||||
\(787\) | 42172.7 | + | 11300.2i | 1.91016 | + | 0.511826i | 0.993757 | + | 0.111569i | \(0.0355876\pi\) |
0.916403 | + | 0.400257i | \(0.131079\pi\) | |||||||
\(788\) | 218.679 | − | 218.679i | 0.00988595 | − | 0.00988595i | ||||
\(789\) | −23572.4 | + | 13609.5i | −1.06363 | + | 0.614084i | ||||
\(790\) | 10390.9 | + | 5999.17i | 0.467963 | + | 0.270178i | ||||
\(791\) | 8959.25 | + | 33436.4i | 0.402723 | + | 1.50298i | ||||
\(792\) | −537.343 | + | 7075.78i | −0.0241082 | + | 0.317458i | ||||
\(793\) | 37386.0 | − | 11295.7i | 1.67417 | − | 0.505828i | ||||
\(794\) | − | 15621.8i | − | 0.698231i | ||||||
\(795\) | 804.513 | + | 3002.48i | 0.0358907 | + | 0.133946i | ||||
\(796\) | 6036.57 | − | 10455.6i | 0.268794 | − | 0.465566i | ||||
\(797\) | −1848.77 | + | 1067.39i | −0.0821665 | + | 0.0474388i | −0.540520 | − | 0.841331i | \(-0.681773\pi\) |
0.458354 | + | 0.888770i | \(0.348439\pi\) | |||||||
\(798\) | 3158.70 | + | 3158.70i | 0.140121 | + | 0.140121i | ||||
\(799\) | 11423.1 | − | 42631.5i | 0.505781 | − | 1.88760i | ||||
\(800\) | 11353.8 | + | 3042.23i | 0.501770 | + | 0.134449i | ||||
\(801\) | −8479.45 | − | 8479.45i | −0.374041 | − | 0.374041i | ||||
\(802\) | −26581.8 | + | 15347.0i | −1.17037 | + | 0.675712i | ||||
\(803\) | −6798.98 | − | 4645.39i | −0.298793 | − | 0.204150i | ||||
\(804\) | −1860.08 | + | 498.406i | −0.0815919 | + | 0.0218625i | ||||
\(805\) | −3938.16 | −0.172425 | ||||||||
\(806\) | 1692.23 | − | 1802.77i | 0.0739532 | − | 0.0787839i | ||||
\(807\) | −1311.38 | −0.0572031 | ||||||||
\(808\) | −3293.22 | − | 12290.5i | −0.143385 | − | 0.535120i | ||||
\(809\) | 29654.6 | + | 17121.1i | 1.28875 | + | 0.744062i | 0.978432 | − | 0.206570i | \(-0.0662301\pi\) |
0.310321 | + | 0.950632i | \(0.399563\pi\) | |||||||
\(810\) | −1765.85 | − | 3058.54i | −0.0765996 | − | 0.132674i | ||||
\(811\) | −7610.42 | − | 7610.42i | −0.329517 | − | 0.329517i | 0.522886 | − | 0.852403i | \(-0.324855\pi\) |
−0.852403 | + | 0.522886i | \(0.824855\pi\) | |||||||
\(812\) | −2492.04 | − | 667.740i | −0.107701 | − | 0.0288585i | ||||
\(813\) | 1671.00 | + | 447.743i | 0.0720843 | + | 0.0193149i | ||||
\(814\) | 7907.36 | + | 9207.04i | 0.340482 | + | 0.396446i | ||||
\(815\) | 6417.05 | + | 11114.7i | 0.275803 | + | 0.477705i | ||||
\(816\) | −13056.7 | + | 22614.8i | −0.560141 | + | 0.970193i | ||||
\(817\) | −1299.93 | + | 348.315i | −0.0556656 | + | 0.0149156i | ||||
\(818\) | − | 5726.60i | − | 0.244775i | ||||||
\(819\) | 410.883 | + | 12991.4i | 0.0175304 | + | 0.554280i | ||||
\(820\) | − | 1808.30i | − | 0.0770106i | ||||||
\(821\) | 7912.57 | − | 2120.17i | 0.336359 | − | 0.0901271i | −0.0866864 | − | 0.996236i | \(-0.527628\pi\) |
0.423045 | + | 0.906109i | \(0.360961\pi\) | |||||||
\(822\) | 12667.0 | + | 7313.27i | 0.537483 | + | 0.310316i | ||||
\(823\) | −17371.0 | + | 10029.2i | −0.735742 | + | 0.424781i | −0.820519 | − | 0.571619i | \(-0.806316\pi\) |
0.0847770 | + | 0.996400i | \(0.472982\pi\) | |||||||
\(824\) | 18713.4 | + | 18713.4i | 0.791155 | + | 0.791155i | ||||
\(825\) | 5540.87 | − | 15784.4i | 0.233828 | − | 0.666114i | ||||
\(826\) | −13134.7 | + | 49019.4i | −0.553287 | + | 2.06490i | ||||
\(827\) | 24922.4 | − | 24922.4i | 1.04793 | − | 1.04793i | 0.0491360 | − | 0.998792i | \(-0.484353\pi\) |
0.998792 | − | 0.0491360i | \(-0.0156468\pi\) | |||||||
\(828\) | 568.599 | + | 984.842i | 0.0238649 | + | 0.0413353i | ||||
\(829\) | −21834.8 | − | 12606.4i | −0.914783 | − | 0.528150i | −0.0328163 | − | 0.999461i | \(-0.510448\pi\) |
−0.881967 | + | 0.471311i | \(0.843781\pi\) | |||||||
\(830\) | −11244.1 | + | 3012.84i | −0.470226 | + | 0.125997i | ||||
\(831\) | 26379.3 | 1.10119 | ||||||||
\(832\) | 3052.42 | − | 13025.8i | 0.127192 | − | 0.542775i | ||||
\(833\) | − | 27407.4i | − | 1.13999i | ||||||
\(834\) | −4771.53 | − | 17807.6i | −0.198111 | − | 0.739360i | ||||
\(835\) | 10440.9 | + | 6028.05i | 0.432721 | + | 0.249831i | ||||
\(836\) | −1029.27 | + | 494.410i | −0.0425816 | + | 0.0204540i | ||||
\(837\) | 1764.13 | − | 1764.13i | 0.0728524 | − | 0.0728524i | ||||
\(838\) | 2459.43 | − | 9178.70i | 0.101384 | − | 0.378369i | ||||
\(839\) | 6734.64 | − | 25134.0i | 0.277122 | − | 1.03423i | −0.677283 | − | 0.735722i | \(-0.736843\pi\) |
0.954406 | − | 0.298512i | \(-0.0964904\pi\) | |||||||
\(840\) | −4529.98 | − | 4529.98i | −0.186070 | − | 0.186070i | ||||
\(841\) | −11300.5 | − | 19573.1i | −0.463346 | − | 0.802538i | ||||
\(842\) | −14592.9 | + | 25275.6i | −0.597273 | + | 1.03451i | ||||
\(843\) | 2366.01 | + | 8830.09i | 0.0966665 | + | 0.360764i | ||||
\(844\) | −10668.0 | −0.435079 | ||||||||
\(845\) | −7027.13 | + | 2368.03i | −0.286083 | + | 0.0964057i | ||||
\(846\) | − | 18173.6i | − | 0.738560i | ||||||
\(847\) | −34254.5 | + | 3790.48i | −1.38961 | + | 0.153769i | ||||
\(848\) | 8818.79 | − | 15274.6i | 0.357121 | − | 0.618552i | ||||
\(849\) | −7039.05 | − | 12192.0i | −0.284546 | − | 0.492848i | ||||
\(850\) | −21638.3 | + | 21638.3i | −0.873162 | + | 0.873162i | ||||
\(851\) | −4499.37 | − | 1205.60i | −0.181241 | − | 0.0485635i | ||||
\(852\) | 1640.73 | − | 6123.28i | 0.0659747 | − | 0.246221i | ||||
\(853\) | 13596.6 | − | 13596.6i | 0.545766 | − | 0.545766i | −0.379448 | − | 0.925213i | \(-0.623886\pi\) |
0.925213 | + | 0.379448i | \(0.123886\pi\) | |||||||
\(854\) | −60128.7 | + | 34715.3i | −2.40932 | + | 1.39102i | ||||
\(855\) | 240.060 | − | 415.795i | 0.00960218 | − | 0.0166315i | ||||
\(856\) | 2142.92 | − | 574.194i | 0.0855649 | − | 0.0229270i | ||||
\(857\) | 18617.4 | 0.742074 | 0.371037 | − | 0.928618i | \(-0.379002\pi\) | ||||
0.371037 | + | 0.928618i | \(0.379002\pi\) | |||||||
\(858\) | 21179.7 | + | 6690.63i | 0.842729 | + | 0.266217i | ||||
\(859\) | −16309.7 | −0.647823 | −0.323912 | − | 0.946087i | \(-0.604998\pi\) | ||||
−0.323912 | + | 0.946087i | \(0.604998\pi\) | |||||||
\(860\) | −778.410 | + | 208.574i | −0.0308646 | + | 0.00827015i | ||||
\(861\) | 11880.4 | − | 20577.4i | 0.470247 | − | 0.814491i | ||||
\(862\) | −38623.5 | + | 22299.3i | −1.52613 | + | 0.881111i | ||||
\(863\) | −13244.7 | + | 13244.7i | −0.522426 | + | 0.522426i | −0.918303 | − | 0.395878i | \(-0.870440\pi\) |
0.395878 | + | 0.918303i | \(0.370440\pi\) | |||||||
\(864\) | −4075.69 | + | 15210.7i | −0.160484 | + | 0.598933i | ||||
\(865\) | −14364.6 | − | 3848.98i | −0.564637 | − | 0.151294i | ||||
\(866\) | 13026.5 | − | 13026.5i | 0.511152 | − | 0.511152i | ||||
\(867\) | −4223.18 | − | 7314.75i | −0.165429 | − | 0.286531i | ||||
\(868\) | −500.076 | + | 866.157i | −0.0195549 | + | 0.0338702i | ||||
\(869\) | −39604.5 | + | 7452.73i | −1.54602 | + | 0.290928i | ||||
\(870\) | − | 1853.74i | − | 0.0722387i | ||||||
\(871\) | 300.004 | + | 9485.61i | 0.0116708 | + | 0.369010i | ||||
\(872\) | 9976.83 | 0.387452 | ||||||||
\(873\) | −1268.22 | − | 4733.07i | −0.0491670 | − | 0.183494i | ||||
\(874\) | 963.056 | − | 1668.06i | 0.0372721 | − | 0.0645573i | ||||
\(875\) | −10426.6 | − | 18059.3i | −0.402837 | − | 0.697734i | ||||
\(876\) | −1517.92 | − | 1517.92i | −0.0585454 | − | 0.0585454i | ||||
\(877\) | 2079.87 | − | 7762.18i | 0.0800824 | − | 0.298871i | −0.914255 | − | 0.405139i | \(-0.867223\pi\) |
0.994338 | + | 0.106267i | \(0.0338899\pi\) | |||||||
\(878\) | −12585.4 | + | 46969.2i | −0.483754 | + | 1.80539i | ||||
\(879\) | −797.911 | + | 797.911i | −0.0306176 | + | 0.0306176i | ||||
\(880\) | 8579.92 | − | 4121.35i | 0.328669 | − | 0.157876i | ||||
\(881\) | 7395.80 | + | 4269.97i | 0.282827 | + | 0.163290i | 0.634703 | − | 0.772756i | \(-0.281123\pi\) |
−0.351875 | + | 0.936047i | \(0.614456\pi\) | |||||||
\(882\) | −2920.91 | − | 10901.0i | −0.111511 | − | 0.416163i | ||||
\(883\) | 40320.5i | 1.53669i | 0.640038 | + | 0.768343i | \(0.278918\pi\) | ||||
−0.640038 | + | 0.768343i | \(0.721082\pi\) | |||||||
\(884\) | −6740.40 | − | 6327.11i | −0.256453 | − | 0.240728i | ||||
\(885\) | −8296.72 | −0.315131 | ||||||||
\(886\) | −15644.4 | + | 4191.90i | −0.593209 | + | 0.158950i | ||||
\(887\) | 40913.3 | + | 23621.3i | 1.54874 | + | 0.894166i | 0.998238 | + | 0.0593337i | \(0.0188976\pi\) |
0.550504 | + | 0.834833i | \(0.314436\pi\) | |||||||
\(888\) | −3788.75 | − | 6562.30i | −0.143178 | − | 0.247992i | ||||
\(889\) | 10201.6 | − | 10201.6i | 0.384872 | − | 0.384872i | ||||
\(890\) | −3147.85 | + | 11747.9i | −0.118557 | + | 0.442462i | ||||
\(891\) | 11192.6 | + | 3928.97i | 0.420837 | + | 0.147728i | ||||
\(892\) | 4148.76 | + | 4148.76i | 0.155729 | + | 0.155729i | ||||
\(893\) | −6065.44 | + | 3501.88i | −0.227292 | + | 0.131227i | ||||
\(894\) | 17495.6 | + | 10101.1i | 0.654518 | + | 0.377886i | ||||
\(895\) | −4472.00 | + | 1198.27i | −0.167020 | + | 0.0447527i | ||||
\(896\) | 45215.9i | 1.68589i | ||||||||
\(897\) | −8160.51 | + | 2465.59i | −0.303759 | + | 0.0917768i | ||||
\(898\) | − | 55729.6i | − | 2.07096i | ||||||
\(899\) | 669.494 | − | 179.390i | 0.0248375 | − | 0.00665518i | ||||
\(900\) | −1433.53 | + | 2482.95i | −0.0530938 | + | 0.0919611i | ||||
\(901\) | 9549.10 | + | 16539.5i | 0.353082 | + | 0.611556i | ||||
\(902\) | 17391.7 | + | 20250.3i | 0.641996 | + | 0.747518i | ||||
\(903\) | −10228.2 | − | 2740.63i | −0.376935 | − | 0.100999i | ||||
\(904\) | 23452.8 | + | 6284.17i | 0.862865 | + | 0.231204i | ||||
\(905\) | −3283.14 | − | 3283.14i | −0.120592 | − | 0.120592i | ||||
\(906\) | −11012.4 | − | 19074.0i | −0.403821 | − | 0.699439i | ||||
\(907\) | 17689.9 | + | 10213.3i | 0.647612 | + | 0.373899i | 0.787541 | − | 0.616262i | \(-0.211354\pi\) |
−0.139928 | + | 0.990162i | \(0.544687\pi\) | |||||||
\(908\) | 1409.61 | + | 5260.72i | 0.0515192 | + | 0.192272i | ||||
\(909\) | 7503.10 | 0.273776 | ||||||||
\(910\) | 11202.5 | − | 6948.99i | 0.408089 | − | 0.253139i | ||||
\(911\) | −23581.1 | −0.857604 | −0.428802 | − | 0.903398i | \(-0.641064\pi\) | ||||
−0.428802 | + | 0.903398i | \(0.641064\pi\) | |||||||
\(912\) | 4002.68 | − | 1072.52i | 0.145331 | − | 0.0389414i | ||||
\(913\) | 22057.1 | − | 32282.8i | 0.799545 | − | 1.17021i | ||||
\(914\) | 35754.1 | − | 20642.6i | 1.29392 | − | 0.747043i | ||||
\(915\) | −8026.35 | − | 8026.35i | −0.289992 | − | 0.289992i | ||||
\(916\) | 12219.7 | + | 3274.25i | 0.440774 | + | 0.118105i | ||||
\(917\) | 11702.0 | − | 43672.3i | 0.421410 | − | 1.57272i | ||||
\(918\) | −28989.0 | − | 28989.0i | −1.04224 | − | 1.04224i | ||||
\(919\) | 16382.8 | − | 9458.61i | 0.588051 | − | 0.339511i | −0.176276 | − | 0.984341i | \(-0.556405\pi\) |
0.764326 | + | 0.644830i | \(0.223072\pi\) | |||||||
\(920\) | −1381.15 | + | 2392.22i | −0.0494946 | + | 0.0857272i | ||||
\(921\) | 812.695 | + | 3033.02i | 0.0290763 | + | 0.108514i | ||||
\(922\) | 15721.2i | 0.561551i | ||||||||
\(923\) | −27536.4 | − | 14757.8i | −0.981986 | − | 0.526282i | ||||
\(924\) | −8958.65 | − | 680.331i | −0.318959 | − | 0.0242221i | ||||
\(925\) | −3039.52 | − | 11343.7i | −0.108042 | − | 0.403219i | ||||
\(926\) | 28714.7 | + | 16578.4i | 1.01903 | + | 0.588337i | ||||
\(927\) | −13514.9 | + | 7802.85i | −0.478844 | + | 0.276461i | ||||
\(928\) | −3093.47 | + | 3093.47i | −0.109427 | + | 0.109427i | ||||
\(929\) | −5354.35 | − | 1434.69i | −0.189096 | − | 0.0506682i | 0.163028 | − | 0.986621i | \(-0.447874\pi\) |
−0.352124 | + | 0.935953i | \(0.614541\pi\) | |||||||
\(930\) | −694.140 | − | 185.994i | −0.0244750 | − | 0.00655806i | ||||
\(931\) | −3075.37 | + | 3075.37i | −0.108261 | + | 0.108261i | ||||
\(932\) | 3973.56 | − | 2294.13i | 0.139655 | − | 0.0806297i | ||||
\(933\) | 13488.1 | + | 7787.36i | 0.473291 | + | 0.273255i | ||||
\(934\) | −722.773 | − | 2697.43i | −0.0253210 | − | 0.0944994i | ||||
\(935\) | −780.454 | + | 10277.1i | −0.0272979 | + | 0.359461i | ||||
\(936\) | 8035.65 | + | 4306.60i | 0.280613 | + | 0.150391i | ||||
\(937\) | 28049.3i | 0.977940i | 0.872301 | + | 0.488970i | \(0.162627\pi\) | ||||
−0.872301 | + | 0.488970i | \(0.837373\pi\) | |||||||
\(938\) | −4366.68 | − | 16296.7i | −0.152001 | − | 0.567276i | ||||
\(939\) | −14471.7 | + | 25065.7i | −0.502946 | + | 0.871128i | ||||
\(940\) | −3632.04 | + | 2096.96i | −0.126026 | + | 0.0727609i | ||||
\(941\) | −3918.47 | − | 3918.47i | −0.135748 | − | 0.135748i | 0.635968 | − | 0.771715i | \(-0.280601\pi\) |
−0.771715 | + | 0.635968i | \(0.780601\pi\) | |||||||
\(942\) | 3829.20 | − | 14290.8i | 0.132444 | − | 0.494288i | ||||
\(943\) | −9896.07 | − | 2651.64i | −0.341740 | − | 0.0915689i | ||||
\(944\) | 33288.5 | + | 33288.5i | 1.14772 | + | 1.14772i | ||||
\(945\) | 11519.5 | − | 6650.81i | 0.396540 | − | 0.228943i | ||||
\(946\) | 6711.03 | − | 9822.24i | 0.230650 | − | 0.337578i | ||||
\(947\) | 9793.81 | − | 2624.24i | 0.336068 | − | 0.0900490i | −0.0868389 | − | 0.996222i | \(-0.527677\pi\) |
0.422906 | + | 0.906173i | \(0.361010\pi\) | |||||||
\(948\) | −10505.9 | −0.359931 | ||||||||
\(949\) | −8990.20 | + | 5576.66i | −0.307518 | + | 0.190755i | ||||
\(950\) | 4856.05 | 0.165843 | ||||||||
\(951\) | −4204.42 | − | 15691.1i | −0.143362 | − | 0.535036i | ||||
\(952\) | −34087.7 | − | 19680.5i | −1.16049 | − | 0.670010i | ||||
\(953\) | 21987.1 | + | 38082.8i | 0.747357 | + | 1.29446i | 0.949085 | + | 0.315020i | \(0.102011\pi\) |
−0.201728 | + | 0.979442i | \(0.564656\pi\) | |||||||
\(954\) | 5560.73 | + | 5560.73i | 0.188716 | + | 0.188716i | ||||
\(955\) | 11292.1 | + | 3025.71i | 0.382622 | + | 0.102523i | ||||
\(956\) | 11989.7 | + | 3212.62i | 0.405621 | + | 0.108686i | ||||
\(957\) | 4056.62 | + | 4723.38i | 0.137024 | + | 0.159546i | ||||
\(958\) | −15786.8 | − | 27343.6i | −0.532410 | − | 0.922161i | ||||
\(959\) | −14578.9 | + | 25251.3i | −0.490903 | + | 0.850269i | ||||
\(960\) | −3755.88 | + | 1006.38i | −0.126271 | + | 0.0338343i | ||||
\(961\) | 29522.3i | 0.990981i | ||||||||
\(962\) | 14926.3 | − | 4509.78i | 0.500253 | − | 0.151145i | ||||
\(963\) | 1308.21i | 0.0437763i | ||||||||
\(964\) | −6145.78 | + | 1646.76i | −0.205334 | + | 0.0550191i | ||||
\(965\) | 963.615 | + | 556.343i | 0.0321449 | + | 0.0185589i | ||||
\(966\) | 13124.7 | − | 7577.56i | 0.437144 | − | 0.252385i | ||||
\(967\) | −34333.1 | − | 34333.1i | −1.14176 | − | 1.14176i | −0.988129 | − | 0.153626i | \(-0.950905\pi\) |
−0.153626 | − | 0.988129i | \(-0.549095\pi\) | |||||||
\(968\) | −9710.85 | + | 22137.1i | −0.322436 | + | 0.735034i | ||||
\(969\) | −1161.33 | + | 4334.15i | −0.0385009 | + | 0.143687i | ||||
\(970\) | −3514.14 | + | 3514.14i | −0.116322 | + | 0.116322i | ||||
\(971\) | −2808.36 | − | 4864.23i | −0.0928164 | − | 0.160763i | 0.815879 | − | 0.578223i | \(-0.196254\pi\) |
−0.908695 | + | 0.417460i | \(0.862920\pi\) | |||||||
\(972\) | −5708.13 | − | 3295.59i | −0.188363 | − | 0.108751i | ||||
\(973\) | 35499.1 | − | 9511.95i | 1.16963 | − | 0.313401i | ||||
\(974\) | 30331.4 | 0.997823 | ||||||||
\(975\) | −15670.4 | − | 14709.5i | −0.514721 | − | 0.483161i | ||||
\(976\) | 64407.4i | 2.11233i | ||||||||
\(977\) | 8620.69 | + | 32172.9i | 0.282293 | + | 1.05353i | 0.950795 | + | 0.309822i | \(0.100269\pi\) |
−0.668502 | + | 0.743711i | \(0.733064\pi\) | |||||||
\(978\) | −42772.3 | − | 24694.6i | −1.39847 | − | 0.807409i | ||||
\(979\) | −17687.7 | − | 36822.6i | −0.577427 | − | 1.20210i | ||||
\(980\) | −1841.56 | + | 1841.56i | −0.0600271 | + | 0.0600271i | ||||
\(981\) | −1522.67 | + | 5682.66i | −0.0495565 | + | 0.184948i | ||||
\(982\) | −7384.53 | + | 27559.4i | −0.239969 | + | 0.895577i | ||||
\(983\) | 15478.7 | + | 15478.7i | 0.502230 | + | 0.502230i | 0.912130 | − | 0.409900i | \(-0.134436\pi\) |
−0.409900 | + | 0.912130i | \(0.634436\pi\) | |||||||
\(984\) | −8333.10 | − | 14433.4i | −0.269969 | − | 0.467600i | ||||
\(985\) | −221.484 | + | 383.622i | −0.00716454 | + | 0.0124093i | ||||
\(986\) | −2947.82 | − | 11001.4i | −0.0952106 | − | 0.355331i | ||||
\(987\) | −55107.3 | −1.77719 | ||||||||
\(988\) | 46.3751 | + | 1466.30i | 0.00149331 | + | 0.0472158i | ||||
\(989\) | 4565.76i | 0.146797i | ||||||||
\(990\) | 784.851 | + | 4170.77i | 0.0251962 | + | 0.133895i | ||||
\(991\) | −2900.34 | + | 5023.54i | −0.0929691 | + | 0.161027i | −0.908759 | − | 0.417321i | \(-0.862969\pi\) |
0.815790 | + | 0.578348i | \(0.196302\pi\) | |||||||
\(992\) | 847.982 | + | 1468.75i | 0.0271406 | + | 0.0470089i | ||||
\(993\) | 28503.5 | − | 28503.5i | 0.910907 | − | 0.910907i | ||||
\(994\) | 53647.8 | + | 14374.9i | 1.71188 | + | 0.458696i | ||||
\(995\) | −4475.75 | + | 16703.7i | −0.142604 | + | 0.532205i | ||||
\(996\) | 7207.36 | − | 7207.36i | 0.229291 | − | 0.229291i | ||||
\(997\) | −7517.26 | + | 4340.09i | −0.238791 | + | 0.137866i | −0.614621 | − | 0.788823i | \(-0.710691\pi\) |
0.375830 | + | 0.926689i | \(0.377358\pi\) | |||||||
\(998\) | 649.199 | − | 1124.45i | 0.0205912 | − | 0.0356651i | ||||
\(999\) | 15197.2 | − | 4072.07i | 0.481299 | − | 0.128964i |
(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 | 143.4.o.a.32.10 | ✓ | 160 | |
11.10 | odd | 2 | inner | 143.4.o.a.32.31 | yes | 160 | |
13.11 | odd | 12 | inner | 143.4.o.a.76.31 | yes | 160 | |
143.76 | even | 12 | inner | 143.4.o.a.76.10 | yes | 160 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
143.4.o.a.32.10 | ✓ | 160 | 1.1 | even | 1 | trivial | |
143.4.o.a.32.31 | yes | 160 | 11.10 | odd | 2 | inner | |
143.4.o.a.76.10 | yes | 160 | 143.76 | even | 12 | inner | |
143.4.o.a.76.31 | yes | 160 | 13.11 | odd | 12 | inner |