Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1350,3,Mod(251,1350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1350, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1350.251");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.i (of order \(6\), degree \(2\), not 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: | \(36.7848356886\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 18) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1151.1 | ||
Root | \(1.22474 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1350.1151 |
Dual form | 1350.3.i.b.251.1 |
$q$-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 \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1027\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22474 | + | 0.707107i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | − | 1.73205i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.17423 | + | 5.49794i | 0.453462 | + | 0.785419i | 0.998598 | − | 0.0529281i | \(-0.0168554\pi\) |
−0.545136 | + | 0.838347i | \(0.683522\pi\) | |||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8.17423 | + | 4.71940i | −0.743112 | + | 0.429036i | −0.823200 | − | 0.567752i | \(-0.807813\pi\) |
0.0800876 | + | 0.996788i | \(0.474480\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 9.84847 | − | 17.0580i | 0.757575 | − | 1.31216i | −0.186510 | − | 0.982453i | \(-0.559718\pi\) |
0.944084 | − | 0.329704i | \(-0.106949\pi\) | |||||||
\(14\) | −7.77526 | − | 4.48905i | −0.555375 | − | 0.320646i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | − | 3.46410i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.90702i | 0.112178i | 0.998426 | + | 0.0560889i | \(0.0178630\pi\) | ||||
−0.998426 | + | 0.0560889i | \(0.982137\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.69694 | 0.247207 | 0.123604 | − | 0.992332i | \(-0.460555\pi\) | ||||
0.123604 | + | 0.992332i | \(0.460555\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.67423 | − | 11.5601i | 0.303374 | − | 0.525460i | ||||
\(23\) | 8.17423 | + | 4.71940i | 0.355402 | + | 0.205191i | 0.667062 | − | 0.745002i | \(-0.267552\pi\) |
−0.311660 | + | 0.950194i | \(0.600885\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 27.8557i | 1.07137i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 12.6969 | 0.453462 | ||||||||
\(29\) | 2.84847 | − | 1.64456i | 0.0982231 | − | 0.0567091i | −0.450084 | − | 0.892986i | \(-0.648606\pi\) |
0.548307 | + | 0.836277i | \(0.315273\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 20.5227 | − | 35.5464i | 0.662023 | − | 1.14666i | −0.318061 | − | 0.948070i | \(-0.603032\pi\) |
0.980083 | − | 0.198587i | \(-0.0636351\pi\) | |||||||
\(32\) | 4.89898 | + | 2.82843i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.34847 | − | 2.33562i | −0.0396609 | − | 0.0686946i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −17.3031 | −0.467650 | −0.233825 | − | 0.972279i | \(-0.575124\pi\) | ||||
−0.233825 | + | 0.972279i | \(0.575124\pi\) | |||||||
\(38\) | −5.75255 | + | 3.32124i | −0.151383 | + | 0.0874010i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 53.5454 | + | 30.9145i | 1.30599 | + | 0.754011i | 0.981424 | − | 0.191853i | \(-0.0614498\pi\) |
0.324562 | + | 0.945864i | \(0.394783\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.477296 | + | 0.826701i | 0.0110999 | + | 0.0192256i | 0.871522 | − | 0.490356i | \(-0.163133\pi\) |
−0.860422 | + | 0.509582i | \(0.829800\pi\) | |||||||
\(44\) | 18.8776i | 0.429036i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −13.3485 | −0.290184 | ||||||||
\(47\) | −12.2196 | + | 7.05501i | −0.259992 | + | 0.150107i | −0.624331 | − | 0.781160i | \(-0.714628\pi\) |
0.364339 | + | 0.931267i | \(0.381295\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.34847 | − | 7.53177i | 0.0887443 | − | 0.153710i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −19.6969 | − | 34.1161i | −0.378787 | − | 0.656079i | ||||
\(53\) | 9.53512i | 0.179908i | 0.995946 | + | 0.0899539i | \(0.0286720\pi\) | ||||
−0.995946 | + | 0.0899539i | \(0.971328\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −15.5505 | + | 8.97809i | −0.277688 | + | 0.160323i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.32577 | + | 4.02834i | −0.0400994 | + | 0.0694542i | ||||
\(59\) | −79.2650 | − | 45.7637i | −1.34348 | − | 0.775656i | −0.356160 | − | 0.934425i | \(-0.615914\pi\) |
−0.987316 | + | 0.158769i | \(0.949247\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 37.5454 | + | 65.0306i | 0.615498 | + | 1.06607i | 0.990297 | + | 0.138968i | \(0.0443786\pi\) |
−0.374798 | + | 0.927106i | \(0.622288\pi\) | |||||||
\(62\) | 58.0470i | 0.936241i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.4773 | − | 26.8075i | 0.231004 | − | 0.400111i | −0.727100 | − | 0.686532i | \(-0.759132\pi\) |
0.958104 | + | 0.286421i | \(0.0924655\pi\) | |||||||
\(68\) | 3.30306 | + | 1.90702i | 0.0485744 | + | 0.0280445i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 85.9026i | 1.20990i | 0.796265 | + | 0.604948i | \(0.206806\pi\) | ||||
−0.796265 | + | 0.604948i | \(0.793194\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 96.0908 | 1.31631 | 0.658156 | − | 0.752881i | \(-0.271337\pi\) | ||||
0.658156 | + | 0.752881i | \(0.271337\pi\) | |||||||
\(74\) | 21.1918 | − | 12.2351i | 0.286376 | − | 0.165339i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.69694 | − | 8.13534i | 0.0618018 | − | 0.107044i | ||||
\(77\) | −51.8939 | − | 29.9609i | −0.673946 | − | 0.389103i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.8712 | − | 25.7576i | −0.188243 | − | 0.326046i | 0.756422 | − | 0.654084i | \(-0.226946\pi\) |
−0.944664 | + | 0.328038i | \(0.893612\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −87.4393 | −1.06633 | ||||||||
\(83\) | −76.1288 | + | 43.9530i | −0.917215 | + | 0.529554i | −0.882745 | − | 0.469852i | \(-0.844307\pi\) |
−0.0344693 | + | 0.999406i | \(0.510974\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.16913 | − | 0.674999i | −0.0135946 | − | 0.00784882i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −13.3485 | − | 23.1202i | −0.151687 | − | 0.262730i | ||||
\(89\) | − | 41.3766i | − | 0.464905i | −0.972608 | − | 0.232453i | \(-0.925325\pi\) | ||
0.972608 | − | 0.232453i | \(-0.0746751\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 125.045 | 1.37413 | ||||||||
\(92\) | 16.3485 | − | 9.43879i | 0.177701 | − | 0.102596i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.97730 | − | 17.2812i | 0.106141 | − | 0.183842i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 47.9393 | + | 83.0333i | 0.494219 | + | 0.856013i | 0.999978 | − | 0.00666202i | \(-0.00212060\pi\) |
−0.505758 | + | 0.862675i | \(0.668787\pi\) | |||||||
\(98\) | 12.2993i | 0.125503i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 136.772 | − | 78.9656i | 1.35418 | − | 0.781838i | 0.365350 | − | 0.930870i | \(-0.380949\pi\) |
0.988832 | + | 0.149032i | \(0.0476159\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.5681 | − | 25.2327i | 0.141438 | − | 0.244978i | −0.786600 | − | 0.617462i | \(-0.788161\pi\) |
0.928038 | + | 0.372485i | \(0.121494\pi\) | |||||||
\(104\) | 48.2474 | + | 27.8557i | 0.463918 | + | 0.267843i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.74235 | − | 11.6781i | −0.0636070 | − | 0.110171i | ||||
\(107\) | − | 171.805i | − | 1.60566i | −0.596210 | − | 0.802829i | \(-0.703327\pi\) | ||
0.596210 | − | 0.802829i | \(-0.296673\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 116.272 | 1.06672 | 0.533360 | − | 0.845888i | \(-0.320929\pi\) | ||||
0.533360 | + | 0.845888i | \(0.320929\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 12.6969 | − | 21.9917i | 0.113366 | − | 0.196355i | ||||
\(113\) | 175.166 | + | 101.132i | 1.55014 | + | 0.894976i | 0.998129 | + | 0.0611424i | \(0.0194744\pi\) |
0.552015 | + | 0.833834i | \(0.313859\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 6.57826i | − | 0.0567091i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 129.439 | 1.09694 | ||||||||
\(119\) | −10.4847 | + | 6.05334i | −0.0881067 | + | 0.0508684i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −15.9546 | + | 27.6342i | −0.131856 | + | 0.228382i | ||||
\(122\) | −91.9671 | − | 53.0972i | −0.753829 | − | 0.435223i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −41.0454 | − | 71.0927i | −0.331011 | − | 0.573328i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.0908 | −0.0794552 | −0.0397276 | − | 0.999211i | \(-0.512649\pi\) | ||||
−0.0397276 | + | 0.999211i | \(0.512649\pi\) | |||||||
\(128\) | 9.79796 | − | 5.65685i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.29567 | − | 2.48010i | −0.0327913 | − | 0.0189321i | 0.483515 | − | 0.875336i | \(-0.339360\pi\) |
−0.516306 | + | 0.856404i | \(0.672693\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.9092 | + | 25.8235i | 0.112099 | + | 0.194161i | ||||
\(134\) | 43.7764i | 0.326690i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.39388 | −0.0396609 | ||||||||
\(137\) | 203.242 | − | 117.342i | 1.48352 | − | 0.856511i | 0.483696 | − | 0.875236i | \(-0.339294\pi\) |
0.999825 | + | 0.0187249i | \(0.00596067\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −53.2650 | + | 92.2578i | −0.383202 | + | 0.663725i | −0.991518 | − | 0.129970i | \(-0.958512\pi\) |
0.608316 | + | 0.793695i | \(0.291845\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −60.7423 | − | 105.209i | −0.427763 | − | 0.740907i | ||||
\(143\) | 185.915i | 1.30011i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −117.687 | + | 67.9465i | −0.806074 | + | 0.465387i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −17.3031 | + | 29.9698i | −0.116913 | + | 0.202499i | ||||
\(149\) | 91.0301 | + | 52.5563i | 0.610940 | + | 0.352727i | 0.773333 | − | 0.634000i | \(-0.218588\pi\) |
−0.162393 | + | 0.986726i | \(0.551921\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 142.614 | + | 247.014i | 0.944460 | + | 1.63585i | 0.756828 | + | 0.653614i | \(0.226748\pi\) |
0.187632 | + | 0.982239i | \(0.439919\pi\) | |||||||
\(152\) | 13.2849i | 0.0874010i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 84.7423 | 0.550275 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −98.5908 | + | 170.764i | −0.627967 | + | 1.08767i | 0.359992 | + | 0.932955i | \(0.382779\pi\) |
−0.987959 | + | 0.154715i | \(0.950554\pi\) | |||||||
\(158\) | 36.4268 | + | 21.0310i | 0.230549 | + | 0.133108i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 59.9219i | 0.372186i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 249.060 | 1.52798 | 0.763988 | − | 0.645230i | \(-0.223238\pi\) | ||||
0.763988 | + | 0.645230i | \(0.223238\pi\) | |||||||
\(164\) | 107.091 | − | 61.8289i | 0.652993 | − | 0.377006i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 62.1589 | − | 107.662i | 0.374451 | − | 0.648569i | ||||
\(167\) | −41.9472 | − | 24.2182i | −0.251181 | − | 0.145019i | 0.369124 | − | 0.929380i | \(-0.379658\pi\) |
−0.620305 | + | 0.784361i | \(0.712991\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −109.485 | − | 189.633i | −0.647838 | − | 1.12209i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.90918 | 0.0110999 | ||||||||
\(173\) | 86.9847 | − | 50.2206i | 0.502802 | − | 0.290293i | −0.227068 | − | 0.973879i | \(-0.572914\pi\) |
0.729870 | + | 0.683586i | \(0.239581\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 32.6969 | + | 18.8776i | 0.185778 | + | 0.107259i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 29.2577 | + | 50.6757i | 0.164369 | + | 0.284695i | ||||
\(179\) | 285.071i | 1.59257i | 0.604919 | + | 0.796287i | \(0.293206\pi\) | ||||
−0.604919 | + | 0.796287i | \(0.706794\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 37.1214 | 0.205091 | 0.102545 | − | 0.994728i | \(-0.467301\pi\) | ||||
0.102545 | + | 0.994728i | \(0.467301\pi\) | |||||||
\(182\) | −153.149 | + | 88.4205i | −0.841476 | + | 0.485827i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −13.3485 | + | 23.1202i | −0.0725460 | + | 0.125653i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.00000 | − | 15.5885i | −0.0481283 | − | 0.0833607i | ||||
\(188\) | 28.2201i | 0.150107i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.5227 | − | 8.96204i | 0.0812707 | − | 0.0469217i | −0.458814 | − | 0.888532i | \(-0.651726\pi\) |
0.540085 | + | 0.841611i | \(0.318392\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −47.7270 | + | 82.6657i | −0.247290 | + | 0.428319i | −0.962773 | − | 0.270311i | \(-0.912873\pi\) |
0.715483 | + | 0.698630i | \(0.246207\pi\) | |||||||
\(194\) | −117.427 | − | 67.7964i | −0.605293 | − | 0.349466i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.69694 | − | 15.0635i | −0.0443721 | − | 0.0768548i | ||||
\(197\) | 160.363i | 0.814026i | 0.913422 | + | 0.407013i | \(0.133430\pi\) | ||||
−0.913422 | + | 0.407013i | \(0.866570\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.51531 | 0.0327402 | 0.0163701 | − | 0.999866i | \(-0.494789\pi\) | ||||
0.0163701 | + | 0.999866i | \(0.494789\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −111.674 | + | 193.425i | −0.552843 | + | 0.957552i | ||||
\(203\) | 18.0834 | + | 10.4405i | 0.0890809 | + | 0.0514309i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 41.2048i | 0.200024i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −78.7878 | −0.378787 | ||||||||
\(209\) | −38.3939 | + | 22.1667i | −0.183703 | + | 0.106061i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 77.2196 | − | 133.748i | 0.365970 | − | 0.633878i | −0.622961 | − | 0.782253i | \(-0.714071\pi\) |
0.988931 | + | 0.148374i | \(0.0474040\pi\) | |||||||
\(212\) | 16.5153 | + | 9.53512i | 0.0779024 | + | 0.0449770i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 121.485 | + | 210.418i | 0.567685 | + | 0.983260i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 260.576 | 1.20081 | ||||||||
\(218\) | −142.404 | + | 82.2170i | −0.653230 | + | 0.377142i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 32.5301 | + | 18.7813i | 0.147195 | + | 0.0849831i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 46.3865 | + | 80.3437i | 0.208011 | + | 0.360286i | 0.951088 | − | 0.308920i | \(-0.0999676\pi\) |
−0.743077 | + | 0.669206i | \(0.766634\pi\) | |||||||
\(224\) | 35.9124i | 0.160323i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −286.045 | −1.26569 | ||||||||
\(227\) | 147.053 | − | 84.9010i | 0.647810 | − | 0.374013i | −0.139807 | − | 0.990179i | \(-0.544648\pi\) |
0.787617 | + | 0.616166i | \(0.211315\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −203.772 | + | 352.944i | −0.889836 | + | 1.54124i | −0.0497675 | + | 0.998761i | \(0.515848\pi\) |
−0.840068 | + | 0.542480i | \(0.817485\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.65153 | + | 8.05669i | 0.0200497 | + | 0.0347271i | ||||
\(233\) | 15.2562i | 0.0654772i | 0.999464 | + | 0.0327386i | \(0.0104229\pi\) | ||||
−0.999464 | + | 0.0327386i | \(0.989577\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −158.530 | + | 91.5274i | −0.671738 | + | 0.387828i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 8.56072 | − | 14.8276i | 0.0359694 | − | 0.0623008i | ||||
\(239\) | −48.9620 | − | 28.2682i | −0.204862 | − | 0.118277i | 0.394059 | − | 0.919085i | \(-0.371070\pi\) |
−0.598921 | + | 0.800808i | \(0.704404\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −42.1061 | − | 72.9299i | −0.174714 | − | 0.302614i | 0.765348 | − | 0.643617i | \(-0.222567\pi\) |
−0.940062 | + | 0.341003i | \(0.889233\pi\) | |||||||
\(242\) | − | 45.1264i | − | 0.186473i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 150.182 | 0.615498 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 46.2577 | − | 80.1206i | 0.187278 | − | 0.324375i | ||||
\(248\) | 100.540 | + | 58.0470i | 0.405404 | + | 0.234060i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 218.903i | − | 0.872123i | −0.899917 | − | 0.436062i | \(-0.856373\pi\) | ||
0.899917 | − | 0.436062i | \(-0.143627\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −89.0908 | −0.352138 | ||||||||
\(254\) | 12.3587 | − | 7.13528i | 0.0486562 | − | 0.0280917i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −11.1061 | − | 6.41212i | −0.0432145 | − | 0.0249499i | 0.478237 | − | 0.878231i | \(-0.341276\pi\) |
−0.521452 | + | 0.853281i | \(0.674609\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −54.9240 | − | 95.1311i | −0.212062 | − | 0.367302i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.01479 | 0.0267740 | ||||||||
\(263\) | 291.386 | − | 168.232i | 1.10793 | − | 0.639666i | 0.169640 | − | 0.985506i | \(-0.445739\pi\) |
0.938293 | + | 0.345840i | \(0.112406\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −36.5199 | − | 21.0848i | −0.137293 | − | 0.0792661i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −30.9546 | − | 53.6149i | −0.115502 | − | 0.200056i | ||||
\(269\) | − | 60.4468i | − | 0.224709i | −0.993668 | − | 0.112355i | \(-0.964161\pi\) | ||
0.993668 | − | 0.112355i | \(-0.0358393\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 274.636 | 1.01342 | 0.506708 | − | 0.862118i | \(-0.330862\pi\) | ||||
0.506708 | + | 0.862118i | \(0.330862\pi\) | |||||||
\(272\) | 6.60612 | − | 3.81405i | 0.0242872 | − | 0.0140222i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −165.947 | + | 287.428i | −0.605645 | + | 1.04901i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.5000 | − | 42.4352i | −0.0884477 | − | 0.153196i | 0.818407 | − | 0.574638i | \(-0.194857\pi\) |
−0.906855 | + | 0.421442i | \(0.861524\pi\) | |||||||
\(278\) | − | 150.656i | − | 0.541929i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 297.121 | − | 171.543i | 1.05737 | − | 0.610473i | 0.132666 | − | 0.991161i | \(-0.457646\pi\) |
0.924704 | + | 0.380688i | \(0.124313\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −171.704 | + | 297.401i | −0.606729 | + | 1.05089i | 0.385047 | + | 0.922897i | \(0.374185\pi\) |
−0.991776 | + | 0.127988i | \(0.959148\pi\) | |||||||
\(284\) | 148.788 | + | 85.9026i | 0.523901 | + | 0.302474i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −131.462 | − | 227.699i | −0.459657 | − | 0.796150i | ||||
\(287\) | 392.519i | 1.36766i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 285.363 | 0.987416 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 96.0908 | − | 166.434i | 0.329078 | − | 0.569980i | ||||
\(293\) | −248.076 | − | 143.226i | −0.846674 | − | 0.488828i | 0.0128532 | − | 0.999917i | \(-0.495909\pi\) |
−0.859527 | + | 0.511090i | \(0.829242\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 48.9404i | − | 0.165339i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −148.652 | −0.498831 | ||||||||
\(299\) | 161.007 | − | 92.9577i | 0.538486 | − | 0.310895i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.03010 | + | 5.24829i | −0.0100668 | + | 0.0174362i | ||||
\(302\) | −349.330 | − | 201.686i | −1.15672 | − | 0.667834i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −9.39388 | − | 16.2707i | −0.0309009 | − | 0.0535219i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −154.091 | −0.501924 | −0.250962 | − | 0.967997i | \(-0.580747\pi\) | ||||
−0.250962 | + | 0.967997i | \(0.580747\pi\) | |||||||
\(308\) | −103.788 | + | 59.9219i | −0.336973 | + | 0.194552i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 62.3411 | + | 35.9926i | 0.200454 | + | 0.115732i | 0.596867 | − | 0.802340i | \(-0.296412\pi\) |
−0.396413 | + | 0.918072i | \(0.629745\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −183.803 | − | 318.356i | −0.587230 | − | 1.01711i | −0.994593 | − | 0.103846i | \(-0.966885\pi\) |
0.407363 | − | 0.913266i | \(-0.366448\pi\) | |||||||
\(314\) | − | 278.857i | − | 0.888079i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −59.4847 | −0.188243 | ||||||||
\(317\) | −93.1821 | + | 53.7987i | −0.293950 | + | 0.169712i | −0.639722 | − | 0.768607i | \(-0.720950\pi\) |
0.345772 | + | 0.938319i | \(0.387617\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.5227 | + | 26.8861i | −0.0486605 | + | 0.0842825i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −42.3712 | − | 73.3890i | −0.131587 | − | 0.227916i | ||||
\(323\) | 8.95717i | 0.0277312i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −305.035 | + | 176.112i | −0.935691 | + | 0.540221i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −87.4393 | + | 151.449i | −0.266583 | + | 0.461736i | ||||
\(329\) | −77.5760 | − | 44.7885i | −0.235793 | − | 0.136135i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.59873 | − | 14.8934i | −0.0259780 | − | 0.0449953i | 0.852744 | − | 0.522329i | \(-0.174937\pi\) |
−0.878722 | + | 0.477334i | \(0.841603\pi\) | |||||||
\(332\) | 175.812i | 0.529554i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 68.4995 | 0.205088 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 182.197 | − | 315.574i | 0.540644 | − | 0.936422i | −0.458223 | − | 0.888837i | \(-0.651514\pi\) |
0.998867 | − | 0.0475854i | \(-0.0151526\pi\) | |||||||
\(338\) | 268.182 | + | 154.835i | 0.793437 | + | 0.458091i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 387.419i | 1.13613i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 366.287 | 1.06789 | ||||||||
\(344\) | −2.33826 | + | 1.35000i | −0.00679728 | + | 0.00392441i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −71.0227 | + | 123.015i | −0.205268 | + | 0.355534i | ||||
\(347\) | 505.234 | + | 291.697i | 1.45601 | + | 0.840626i | 0.998811 | − | 0.0487402i | \(-0.0155206\pi\) |
0.457196 | + | 0.889366i | \(0.348854\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −156.379 | − | 270.856i | −0.448076 | − | 0.776091i | 0.550185 | − | 0.835043i | \(-0.314557\pi\) |
−0.998261 | + | 0.0589524i | \(0.981224\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −53.3939 | −0.151687 | ||||||||
\(353\) | −32.5760 | + | 18.8078i | −0.0922834 | + | 0.0532798i | −0.545431 | − | 0.838155i | \(-0.683634\pi\) |
0.453148 | + | 0.891435i | \(0.350301\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −71.6663 | − | 41.3766i | −0.201310 | − | 0.116226i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −201.576 | − | 349.139i | −0.563060 | − | 0.975249i | ||||
\(359\) | 294.028i | 0.819019i | 0.912306 | + | 0.409510i | \(0.134300\pi\) | ||||
−0.912306 | + | 0.409510i | \(0.865700\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −338.939 | −0.938889 | ||||||||
\(362\) | −45.4643 | + | 26.2488i | −0.125592 | + | 0.0725105i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 125.045 | − | 216.585i | 0.343531 | − | 0.595014i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.6135 | − | 28.7755i | −0.0452684 | − | 0.0784072i | 0.842503 | − | 0.538691i | \(-0.181081\pi\) |
−0.887772 | + | 0.460284i | \(0.847748\pi\) | |||||||
\(368\) | − | 37.7552i | − | 0.102596i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −52.4235 | + | 30.2667i | −0.141303 | + | 0.0815814i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −112.515 | + | 194.881i | −0.301648 | + | 0.522470i | −0.976509 | − | 0.215475i | \(-0.930870\pi\) |
0.674861 | + | 0.737945i | \(0.264203\pi\) | |||||||
\(374\) | 22.0454 | + | 12.7279i | 0.0589449 | + | 0.0340319i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −19.9546 | − | 34.5624i | −0.0530707 | − | 0.0919212i | ||||
\(377\) | − | 64.7858i | − | 0.171846i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −166.334 | −0.438875 | −0.219438 | − | 0.975627i | \(-0.570422\pi\) | ||||
−0.219438 | + | 0.975627i | \(0.570422\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −12.6742 | + | 21.9524i | −0.0331786 | + | 0.0574671i | ||||
\(383\) | −638.249 | − | 368.493i | −1.66645 | − | 0.962124i | −0.969530 | − | 0.244972i | \(-0.921221\pi\) |
−0.696917 | − | 0.717152i | \(-0.745445\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 134.992i | − | 0.349721i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 191.757 | 0.494219 | ||||||||
\(389\) | 146.682 | − | 84.6867i | 0.377074 | − | 0.217704i | −0.299471 | − | 0.954106i | \(-0.596810\pi\) |
0.676544 | + | 0.736402i | \(0.263477\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.00000 | + | 15.5885i | −0.0230179 | + | 0.0398682i | ||||
\(392\) | 21.3031 | + | 12.2993i | 0.0543445 | + | 0.0313758i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −113.394 | − | 196.404i | −0.287802 | − | 0.498487i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 256.272 | 0.645523 | 0.322761 | − | 0.946480i | \(-0.395389\pi\) | ||||
0.322761 | + | 0.946480i | \(0.395389\pi\) | |||||||
\(398\) | −7.97959 | + | 4.60702i | −0.0200492 | + | 0.0115754i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −226.364 | − | 130.691i | −0.564498 | − | 0.325913i | 0.190451 | − | 0.981697i | \(-0.439005\pi\) |
−0.754949 | + | 0.655784i | \(0.772338\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −404.234 | − | 700.155i | −1.00306 | − | 1.73736i | ||||
\(404\) | − | 315.862i | − | 0.781838i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −29.5301 | −0.0727342 | ||||||||
\(407\) | 141.439 | − | 81.6600i | 0.347517 | − | 0.200639i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 221.894 | − | 384.331i | 0.542528 | − | 0.939686i | −0.456230 | − | 0.889862i | \(-0.650801\pi\) |
0.998758 | − | 0.0498240i | \(-0.0158660\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −29.1362 | − | 50.4654i | −0.0707190 | − | 0.122489i | ||||
\(413\) | − | 581.059i | − | 1.40692i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 96.4949 | − | 55.7114i | 0.231959 | − | 0.133922i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 31.3485 | − | 54.2971i | 0.0749963 | − | 0.129897i | ||||
\(419\) | −9.32525 | − | 5.38394i | −0.0222560 | − | 0.0128495i | 0.488831 | − | 0.872379i | \(-0.337424\pi\) |
−0.511087 | + | 0.859529i | \(0.670757\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −127.152 | − | 220.233i | −0.302023 | − | 0.523119i | 0.674571 | − | 0.738210i | \(-0.264328\pi\) |
−0.976594 | + | 0.215091i | \(0.930995\pi\) | |||||||
\(422\) | 218.410i | 0.517560i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −26.9694 | −0.0636070 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −238.356 | + | 412.844i | −0.558210 | + | 0.966849i | ||||
\(428\) | −297.576 | − | 171.805i | −0.695270 | − | 0.401414i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 698.663i | − | 1.62103i | −0.585719 | − | 0.810514i | \(-0.699188\pi\) | ||
0.585719 | − | 0.810514i | \(-0.300812\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −211.728 | −0.488978 | −0.244489 | − | 0.969652i | \(-0.578620\pi\) | ||||
−0.244489 | + | 0.969652i | \(0.578620\pi\) | |||||||
\(434\) | −319.139 | + | 184.255i | −0.735342 | + | 0.424550i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 116.272 | − | 201.390i | 0.266680 | − | 0.461903i | ||||
\(437\) | 38.3939 | + | 22.1667i | 0.0878578 | + | 0.0507247i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −139.931 | − | 242.368i | −0.318750 | − | 0.552092i | 0.661477 | − | 0.749965i | \(-0.269930\pi\) |
−0.980228 | + | 0.197874i | \(0.936596\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −53.1214 | −0.120184 | ||||||||
\(443\) | −477.400 | + | 275.627i | −1.07765 | + | 0.622183i | −0.930262 | − | 0.366895i | \(-0.880421\pi\) |
−0.147391 | + | 0.989078i | \(0.547087\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −113.623 | − | 65.6004i | −0.254761 | − | 0.147086i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −25.3939 | − | 43.9835i | −0.0566828 | − | 0.0981774i | ||||
\(449\) | − | 542.865i | − | 1.20905i | −0.796585 | − | 0.604527i | \(-0.793362\pi\) | ||
0.796585 | − | 0.604527i | \(-0.206638\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −583.590 | −1.29399 | ||||||||
\(452\) | 350.333 | − | 202.265i | 0.775072 | − | 0.447488i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −120.068 | + | 207.964i | −0.264467 | + | 0.458071i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 46.1821 | + | 79.9898i | 0.101055 | + | 0.175032i | 0.912120 | − | 0.409924i | \(-0.134445\pi\) |
−0.811065 | + | 0.584957i | \(0.801112\pi\) | |||||||
\(458\) | − | 576.356i | − | 1.25842i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 199.030 | − | 114.910i | 0.431736 | − | 0.249263i | −0.268350 | − | 0.963321i | \(-0.586478\pi\) |
0.700086 | + | 0.714059i | \(0.253145\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −255.401 | + | 442.368i | −0.551623 | + | 0.955438i | 0.446535 | + | 0.894766i | \(0.352658\pi\) |
−0.998158 | + | 0.0606723i | \(0.980676\pi\) | |||||||
\(464\) | −11.3939 | − | 6.57826i | −0.0245558 | − | 0.0141773i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.7878 | − | 18.6849i | −0.0231497 | − | 0.0400964i | ||||
\(467\) | − | 833.657i | − | 1.78513i | −0.450915 | − | 0.892567i | \(-0.648902\pi\) | ||
0.450915 | − | 0.892567i | \(-0.351098\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 196.514 | 0.419007 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 129.439 | − | 224.195i | 0.274236 | − | 0.474990i | ||||
\(473\) | −7.80306 | − | 4.50510i | −0.0164970 | − | 0.00952452i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 24.2134i | 0.0508684i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 79.9546 | 0.167269 | ||||||||
\(479\) | −569.144 | + | 328.595i | −1.18819 | + | 0.686003i | −0.957895 | − | 0.287118i | \(-0.907303\pi\) |
−0.230296 | + | 0.973121i | \(0.573969\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −170.409 | + | 295.156i | −0.354280 | + | 0.613631i | ||||
\(482\) | 103.139 | + | 59.5471i | 0.213980 | + | 0.123542i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 31.9092 | + | 55.2683i | 0.0659281 | + | 0.114191i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 351.666 | 0.722107 | 0.361054 | − | 0.932545i | \(-0.382417\pi\) | ||||
0.361054 | + | 0.932545i | \(0.382417\pi\) | |||||||
\(488\) | −183.934 | + | 106.194i | −0.376914 | + | 0.217612i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −212.539 | − | 122.709i | −0.432869 | − | 0.249917i | 0.267699 | − | 0.963503i | \(-0.413737\pi\) |
−0.700568 | + | 0.713586i | \(0.747070\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.13622 | + | 5.43210i | 0.00636151 | + | 0.0110185i | ||||
\(494\) | 130.836i | 0.264851i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −164.182 | −0.331011 | ||||||||
\(497\) | −472.287 | + | 272.675i | −0.950276 | + | 0.548642i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −315.113 | + | 545.792i | −0.631489 | + | 1.09377i | 0.355758 | + | 0.934578i | \(0.384223\pi\) |
−0.987247 | + | 0.159193i | \(0.949111\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 154.788 | + | 268.100i | 0.308342 | + | 0.534064i | ||||
\(503\) | 286.891i | 0.570360i | 0.958474 | + | 0.285180i | \(0.0920534\pi\) | ||||
−0.958474 | + | 0.285180i | \(0.907947\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 109.114 | − | 62.9967i | 0.215639 | − | 0.124499i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −10.0908 | + | 17.4778i | −0.0198638 | + | 0.0344051i | ||||
\(509\) | −755.454 | − | 436.161i | −1.48419 | − | 0.856898i | −0.484353 | − | 0.874873i | \(-0.660945\pi\) |
−0.999838 | + | 0.0179741i | \(0.994278\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 305.015 | + | 528.301i | 0.596898 | + | 1.03386i | ||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 18.1362 | 0.0352845 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 66.5908 | − | 115.339i | 0.128802 | − | 0.223092i | ||||
\(518\) | 134.536 | + | 77.6742i | 0.259721 | + | 0.149950i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 206.132i | − | 0.395646i | −0.980238 | − | 0.197823i | \(-0.936613\pi\) | ||
0.980238 | − | 0.197823i | \(-0.0633872\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −884.817 | −1.69181 | −0.845906 | − | 0.533333i | \(-0.820939\pi\) | ||||
−0.845906 | + | 0.533333i | \(0.820939\pi\) | |||||||
\(524\) | −8.59133 | + | 4.96021i | −0.0163957 | + | 0.00946604i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −237.916 | + | 412.083i | −0.452312 | + | 0.783427i | ||||
\(527\) | 67.7878 | + | 39.1373i | 0.128630 | + | 0.0742643i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −219.955 | − | 380.973i | −0.415793 | − | 0.720175i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 59.6367 | 0.112099 | ||||||||
\(533\) | 1054.68 | − | 608.920i | 1.97876 | − | 1.14244i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 75.8230 | + | 43.7764i | 0.141461 | + | 0.0816724i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 42.7423 | + | 74.0319i | 0.0794467 | + | 0.137606i | ||||
\(539\) | 82.0886i | 0.152298i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −509.151 | −0.941129 | −0.470565 | − | 0.882365i | \(-0.655950\pi\) | ||||
−0.470565 | + | 0.882365i | \(0.655950\pi\) | |||||||
\(542\) | −336.359 | + | 194.197i | −0.620588 | + | 0.358297i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.39388 | + | 9.34247i | −0.00991521 | + | 0.0171737i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 274.022 | + | 474.620i | 0.500955 | + | 0.867679i | 0.999999 | + | 0.00110267i | \(0.000350992\pi\) |
−0.499045 | + | 0.866576i | \(0.666316\pi\) | |||||||
\(548\) | − | 469.368i | − | 0.856511i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.3791 | − | 7.72442i | 0.0242815 | − | 0.0140189i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 94.4092 | − | 163.522i | 0.170722 | − | 0.295699i | ||||
\(554\) | 60.0125 | + | 34.6482i | 0.108326 | + | 0.0625419i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 106.530 | + | 184.516i | 0.191601 | + | 0.331862i | ||||
\(557\) | − | 406.542i | − | 0.729879i | −0.931031 | − | 0.364939i | \(-0.881090\pi\) | ||
0.931031 | − | 0.364939i | \(-0.118910\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18.8025 | 0.0336360 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −242.598 | + | 420.192i | −0.431669 | + | 0.747673i | ||||
\(563\) | −525.220 | − | 303.236i | −0.932895 | − | 0.538607i | −0.0451687 | − | 0.998979i | \(-0.514383\pi\) |
−0.887726 | + | 0.460372i | \(0.847716\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 485.653i | − | 0.858045i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −242.969 | −0.427763 | ||||||||
\(569\) | 224.954 | − | 129.877i | 0.395350 | − | 0.228255i | −0.289126 | − | 0.957291i | \(-0.593365\pi\) |
0.684476 | + | 0.729036i | \(0.260031\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 43.9166 | − | 76.0657i | 0.0769117 | − | 0.133215i | −0.825004 | − | 0.565126i | \(-0.808827\pi\) |
0.901916 | + | 0.431911i | \(0.142161\pi\) | |||||||
\(572\) | 322.015 | + | 185.915i | 0.562963 | + | 0.325027i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −277.553 | − | 480.736i | −0.483541 | − | 0.837518i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 132.091 | 0.228927 | 0.114463 | − | 0.993427i | \(-0.463485\pi\) | ||||
0.114463 | + | 0.993427i | \(0.463485\pi\) | |||||||
\(578\) | −349.497 | + | 201.782i | −0.604666 | + | 0.349104i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −483.302 | − | 279.034i | −0.831844 | − | 0.480266i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −45.0000 | − | 77.9423i | −0.0771870 | − | 0.133692i | ||||
\(584\) | 271.786i | 0.465387i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 405.106 | 0.691306 | ||||||||
\(587\) | −491.614 | + | 283.833i | −0.837502 | + | 0.483532i | −0.856414 | − | 0.516289i | \(-0.827313\pi\) |
0.0189125 | + | 0.999821i | \(0.493980\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 96.3939 | − | 166.959i | 0.163657 | − | 0.283462i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 34.6061 | + | 59.9396i | 0.0584563 | + | 0.101249i | ||||
\(593\) | − | 77.0321i | − | 0.129902i | −0.997888 | − | 0.0649512i | \(-0.979311\pi\) | ||
0.997888 | − | 0.0649512i | \(-0.0206892\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 182.060 | − | 105.113i | 0.305470 | − | 0.176363i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −131.462 | + | 227.699i | −0.219836 | + | 0.380767i | ||||
\(599\) | 764.917 | + | 441.625i | 1.27699 | + | 0.737270i | 0.976294 | − | 0.216450i | \(-0.0694479\pi\) |
0.300696 | + | 0.953720i | \(0.402781\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 397.545 | + | 688.569i | 0.661473 | + | 1.14571i | 0.980229 | + | 0.197868i | \(0.0634018\pi\) |
−0.318755 | + | 0.947837i | \(0.603265\pi\) | |||||||
\(602\) | − | 8.57042i | − | 0.0142366i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 570.454 | 0.944460 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −148.372 | + | 256.987i | −0.244434 | + | 0.423373i | −0.961972 | − | 0.273147i | \(-0.911936\pi\) |
0.717538 | + | 0.696519i | \(0.245269\pi\) | |||||||
\(608\) | 23.0102 | + | 13.2849i | 0.0378457 | + | 0.0218502i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 277.924i | 0.454868i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 517.181 | 0.843688 | 0.421844 | − | 0.906668i | \(-0.361383\pi\) | ||||
0.421844 | + | 0.906668i | \(0.361383\pi\) | |||||||
\(614\) | 188.722 | − | 108.959i | 0.307365 | − | 0.177457i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 84.7423 | − | 146.778i | 0.137569 | − | 0.238276i | ||||
\(617\) | −229.909 | − | 132.738i | −0.372623 | − | 0.215134i | 0.301981 | − | 0.953314i | \(-0.402352\pi\) |
−0.674604 | + | 0.738180i | \(0.735686\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 98.5227 | + | 170.646i | 0.159164 | + | 0.275681i | 0.934568 | − | 0.355786i | \(-0.115787\pi\) |
−0.775403 | + | 0.631466i | \(0.782453\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −101.803 | −0.163670 | ||||||||
\(623\) | 227.486 | − | 131.339i | 0.365146 | − | 0.210817i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 450.224 | + | 259.937i | 0.719207 | + | 0.415234i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 197.182 | + | 341.529i | 0.313983 | + | 0.543835i | ||||
\(629\) | − | 32.9973i | − | 0.0524600i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −160.879 | −0.254958 | −0.127479 | − | 0.991841i | \(-0.540689\pi\) | ||||
−0.127479 | + | 0.991841i | \(0.540689\pi\) | |||||||
\(632\) | 72.8536 | − | 42.0620i | 0.115275 | − | 0.0665538i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 76.0829 | − | 131.779i | 0.120005 | − | 0.207854i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −85.6515 | − | 148.353i | −0.134461 | − | 0.232893i | ||||
\(638\) | − | 43.9048i | − | 0.0688164i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 267.894 | − | 154.669i | 0.417931 | − | 0.241293i | −0.276261 | − | 0.961083i | \(-0.589095\pi\) |
0.694192 | + | 0.719790i | \(0.255762\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 197.296 | − | 341.726i | 0.306836 | − | 0.531456i | −0.670832 | − | 0.741609i | \(-0.734063\pi\) |
0.977668 | + | 0.210153i | \(0.0673963\pi\) | |||||||
\(644\) | 103.788 | + | 59.9219i | 0.161161 | + | 0.0930464i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.33368 | − | 10.9703i | −0.00980445 | − | 0.0169818i | ||||
\(647\) | 418.736i | 0.647196i | 0.946195 | + | 0.323598i | \(0.104892\pi\) | ||||
−0.946195 | + | 0.323598i | \(0.895108\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 863.908 | 1.33114 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 249.060 | − | 431.385i | 0.381994 | − | 0.661633i | ||||
\(653\) | −459.621 | − | 265.363i | −0.703861 | − | 0.406375i | 0.104923 | − | 0.994480i | \(-0.466540\pi\) |
−0.808784 | + | 0.588106i | \(0.799874\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 247.316i | − | 0.377006i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 126.681 | 0.192524 | ||||||||
\(659\) | −310.204 | + | 179.096i | −0.470719 | + | 0.271770i | −0.716541 | − | 0.697545i | \(-0.754276\pi\) |
0.245822 | + | 0.969315i | \(0.420942\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 111.136 | − | 192.493i | 0.168133 | − | 0.291214i | −0.769631 | − | 0.638489i | \(-0.779560\pi\) |
0.937763 | + | 0.347275i | \(0.112893\pi\) | |||||||
\(662\) | 21.0625 | + | 12.1604i | 0.0318165 | + | 0.0183692i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −124.318 | − | 215.325i | −0.187226 | − | 0.324284i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31.0454 | 0.0465448 | ||||||||
\(668\) | −83.8944 | + | 48.4365i | −0.125590 | + | 0.0725097i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −613.810 | − | 354.383i | −0.914769 | − | 0.528142i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −144.606 | − | 250.464i | −0.214867 | − | 0.372161i | 0.738364 | − | 0.674402i | \(-0.235599\pi\) |
−0.953231 | + | 0.302241i | \(0.902265\pi\) | |||||||
\(674\) | 515.331i | 0.764586i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −437.939 | −0.647838 | ||||||||
\(677\) | 402.227 | − | 232.226i | 0.594131 | − | 0.343022i | −0.172598 | − | 0.984992i | \(-0.555216\pi\) |
0.766729 | + | 0.641971i | \(0.221883\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −304.341 | + | 527.134i | −0.448220 | + | 0.776339i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −273.947 | − | 474.490i | −0.401681 | − | 0.695733i | ||||
\(683\) | 1126.36i | 1.64913i | 0.565767 | + | 0.824565i | \(0.308580\pi\) | ||||
−0.565767 | + | 0.824565i | \(0.691420\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −448.608 | + | 259.004i | −0.653948 | + | 0.377557i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.90918 | − | 3.30680i | 0.00277498 | − | 0.00480640i | ||||
\(689\) | 162.650 | + | 93.9063i | 0.236067 | + | 0.136294i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −518.841 | − | 898.658i | −0.750855 | − | 1.30052i | −0.947409 | − | 0.320025i | \(-0.896309\pi\) |
0.196554 | − | 0.980493i | \(-0.437025\pi\) | |||||||
\(692\) | − | 200.883i | − | 0.290293i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −825.044 | −1.18882 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −58.9546 | + | 102.112i | −0.0845833 | + | 0.146503i | ||||
\(698\) | 383.048 | + | 221.153i | 0.548779 | + | 0.316838i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 778.180i | 1.11010i | 0.831817 | + | 0.555050i | \(0.187301\pi\) | ||||
−0.831817 | + | 0.555050i | \(0.812699\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −81.2714 | −0.115607 | ||||||||
\(704\) | 65.3939 | − | 37.7552i | 0.0928890 | − | 0.0536295i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 26.5982 | − | 46.0695i | 0.0376745 | − | 0.0652542i | ||||
\(707\) | 868.296 | + | 501.311i | 1.22814 | + | 0.709068i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 586.014 | + | 1015.01i | 0.826536 | + | 1.43160i | 0.900739 | + | 0.434360i | \(0.143025\pi\) |
−0.0742031 | + | 0.997243i | \(0.523641\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 117.031 | 0.164369 | ||||||||
\(713\) | 335.515 | − | 193.710i | 0.470568 | − | 0.271682i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 493.757 | + | 285.071i | 0.689605 | + | 0.398144i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −207.909 | − | 360.109i | −0.289567 | − | 0.501545i | ||||
\(719\) | − | 515.416i | − | 0.716851i | −0.933558 | − | 0.358426i | \(-0.883314\pi\) | ||
0.933558 | − | 0.358426i | \(-0.116686\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 184.970 | 0.256547 | ||||||||
\(722\) | 415.114 | − | 239.666i | 0.574949 | − | 0.331947i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 37.1214 | − | 64.2962i | 0.0512727 | − | 0.0888069i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −420.704 | − | 728.681i | −0.578685 | − | 1.00231i | −0.995630 | − | 0.0933809i | \(-0.970233\pi\) |
0.416945 | − | 0.908932i | \(-0.363101\pi\) | |||||||
\(728\) | 353.682i | 0.485827i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.57654 | + | 0.910215i | −0.00215669 | + | 0.00124516i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 303.181 | − | 525.125i | 0.413617 | − | 0.716405i | −0.581665 | − | 0.813428i | \(-0.697599\pi\) |
0.995282 | + | 0.0970229i | \(0.0309320\pi\) | |||||||
\(734\) | 40.6946 | + | 23.4951i | 0.0554423 | + | 0.0320096i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 26.6969 | + | 46.2405i | 0.0362730 | + | 0.0628267i | ||||
\(737\) | 292.174i | 0.396437i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −389.362 | −0.526877 | −0.263439 | − | 0.964676i | \(-0.584857\pi\) | ||||
−0.263439 | + | 0.964676i | \(0.584857\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 42.8036 | − | 74.1380i | 0.0576868 | − | 0.0999164i | ||||
\(743\) | 904.779 | + | 522.375i | 1.21774 | + | 0.703061i | 0.964434 | − | 0.264325i | \(-0.0851492\pi\) |
0.253304 | + | 0.967387i | \(0.418483\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 318.240i | − | 0.426595i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −36.0000 | −0.0481283 | ||||||||
\(749\) | 944.574 | − | 545.350i | 1.26111 | − | 0.728105i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 645.916 | − | 1118.76i | 0.860074 | − | 1.48969i | −0.0117826 | − | 0.999931i | \(-0.503751\pi\) |
0.871857 | − | 0.489761i | \(-0.162916\pi\) | |||||||
\(752\) | 48.8786 | + | 28.2201i | 0.0649981 | + | 0.0375267i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 45.8105 | + | 79.3460i | 0.0607566 | + | 0.105233i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1042.36 | −1.37697 | −0.688483 | − | 0.725252i | \(-0.741723\pi\) | ||||
−0.688483 | + | 0.725252i | \(0.741723\pi\) | |||||||
\(758\) | 203.716 | − | 117.616i | 0.268755 | − | 0.155166i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 281.607 | + | 162.586i | 0.370048 | + | 0.213647i | 0.673479 | − | 0.739206i | \(-0.264799\pi\) |
−0.303431 | + | 0.952853i | \(0.598132\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 369.076 | + | 639.258i | 0.483717 | + | 0.837822i | ||||
\(764\) | − | 35.8481i | − | 0.0469217i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1042.26 | 1.36065 | ||||||||
\(767\) | −1561.28 | + | 901.405i | −2.03557 | + | 1.17523i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −171.348 | + | 296.783i | −0.222819 | + | 0.385934i | −0.955663 | − | 0.294463i | \(-0.904859\pi\) |
0.732844 | + | 0.680397i | \(0.238193\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 95.4541 | + | 165.331i | 0.123645 | + | 0.214160i | ||||
\(773\) | 532.579i | 0.688977i | 0.938791 | + | 0.344488i | \(0.111948\pi\) | ||||
−0.938791 | + | 0.344488i | \(0.888052\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −234.854 | + | 135.593i | −0.302646 | + | 0.174733i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −119.765 | + | 207.439i | −0.153940 | + | 0.266631i | ||||
\(779\) | 251.499 | + | 145.203i | 0.322849 | + | 0.186397i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −405.409 | − | 702.188i | −0.519089 | − | 0.899089i | ||||
\(782\) | − | 25.4558i | − | 0.0325522i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −34.7878 | −0.0443721 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −51.9768 | + | 90.0264i | −0.0660442 | + | 0.114392i | −0.897157 | − | 0.441712i | \(-0.854371\pi\) |
0.831113 | + | 0.556104i | \(0.187704\pi\) | |||||||
\(788\) | 277.757 | + | 160.363i | 0.352484 | + | 0.203507i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1284.07i | 1.62335i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1479.06 | 1.86514 | ||||||||
\(794\) | −313.868 | + | 181.212i | −0.395300 | + | 0.228227i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.51531 | − | 11.2848i | 0.00818506 | − | 0.0141769i | ||||
\(797\) | −956.331 | − | 552.138i | −1.19991 | − | 0.692770i | −0.239378 | − | 0.970927i | \(-0.576943\pi\) |
−0.960536 | + | 0.278156i | \(0.910277\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.4541 | − | 23.3031i | −0.0168386 | − | 0.0291654i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 369.650 | 0.460911 | ||||||||
\(803\) | −785.469 | + | 453.491i | −0.978168 | + | 0.564746i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 990.168 | + | 571.674i | 1.22850 | + | 0.709273i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 223.348 | + | 386.851i | 0.276421 | + | 0.478776i | ||||
\(809\) | − | 256.465i | − | 0.317015i | −0.987358 | − | 0.158508i | \(-0.949332\pi\) | ||
0.987358 | − | 0.158508i | \(-0.0506683\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 735.362 | 0.906735 | 0.453368 | − | 0.891324i | \(-0.350222\pi\) | ||||
0.453368 | + | 0.891324i | \(0.350222\pi\) | |||||||
\(812\) | 36.1668 | − | 20.8809i | 0.0445404 | − | 0.0257154i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −115.485 | + | 200.025i | −0.141873 | + | 0.245731i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.24183 | + | 3.88296i | 0.00274398 | + | 0.00475271i | ||||
\(818\) | 627.611i | 0.767250i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1078.45 | + | 622.645i | −1.31358 | + | 0.758398i | −0.982688 | − | 0.185269i | \(-0.940684\pi\) |
−0.330896 | + | 0.943667i | \(0.607351\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −771.129 | + | 1335.63i | −0.936973 | + | 1.62288i | −0.165896 | + | 0.986143i | \(0.553052\pi\) |
−0.771077 | + | 0.636742i | \(0.780282\pi\) | |||||||
\(824\) | 71.3689 | + | 41.2048i | 0.0866127 | + | 0.0500059i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 410.871 | + | 711.649i | 0.497422 | + | 0.861560i | ||||
\(827\) | − | 955.707i | − | 1.15563i | −0.816167 | − | 0.577815i | \(-0.803905\pi\) | ||
0.816167 | − | 0.577815i | \(-0.196095\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1082.88 | 1.30625 | 0.653123 | − | 0.757252i | \(-0.273458\pi\) | ||||
0.653123 | + | 0.757252i | \(0.273458\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −78.7878 | + | 136.464i | −0.0946968 | + | 0.164020i | ||||
\(833\) | 14.3633 | + | 8.29263i | 0.0172428 | + | 0.00995514i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 88.6669i | 0.106061i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 15.2281 | 0.0181719 | ||||||||
\(839\) | −903.778 | + | 521.797i | −1.07721 | + | 0.621927i | −0.930142 | − | 0.367200i | \(-0.880317\pi\) |
−0.147067 | + | 0.989127i | \(0.546983\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −415.091 | + | 718.958i | −0.493568 | + | 0.854885i | ||||
\(842\) | 311.456 | + | 179.819i | 0.369901 | + | 0.213562i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −154.439 | − | 267.497i | −0.182985 | − | 0.316939i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −202.574 | −0.239167 | ||||||||
\(848\) | 33.0306 | − | 19.0702i | 0.0389512 | − | 0.0224885i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −141.439 | − | 81.6600i | −0.166204 | − | 0.0959577i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 236.909 | + | 410.338i | 0.277736 | + | 0.481053i | 0.970822 | − | 0.239802i | \(-0.0770827\pi\) |
−0.693086 | + | 0.720855i | \(0.743749\pi\) | |||||||
\(854\) | − | 674.172i | − | 0.789429i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 485.939 | 0.567685 | ||||||||
\(857\) | 793.939 | − | 458.381i | 0.926417 | − | 0.534867i | 0.0407403 | − | 0.999170i | \(-0.487028\pi\) |
0.885677 | + | 0.464303i | \(0.153695\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −478.901 | + | 829.480i | −0.557510 | + | 0.965635i | 0.440194 | + | 0.897903i | \(0.354910\pi\) |
−0.997704 | + | 0.0677322i | \(0.978424\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 494.030 | + | 855.684i | 0.573120 | + | 0.992673i | ||||
\(863\) | 524.200i | 0.607416i | 0.952765 | + | 0.303708i | \(0.0982247\pi\) | ||||
−0.952765 | + | 0.303708i | \(0.901775\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 259.312 | − | 149.714i | 0.299437 | − | 0.172880i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 260.576 | − | 451.330i | 0.300202 | − | 0.519965i | ||||
\(869\) | 243.121 | + | 140.366i | 0.279771 | + | 0.161526i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −304.855 | − | 528.025i | −0.350006 | − | 0.606228i | ||||
\(872\) | 328.868i | 0.377142i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −62.6969 | −0.0717356 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 503.878 | − | 872.742i | 0.574547 | − | 0.995145i | −0.421543 | − | 0.906808i | \(-0.638511\pi\) |
0.996091 | − | 0.0883370i | \(-0.0281552\pi\) | |||||||
\(878\) | 342.760 | + | 197.893i | 0.390388 | + | 0.225390i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1536.71i | 1.74428i | 0.489254 | + | 0.872141i | \(0.337269\pi\) | ||||
−0.489254 | + | 0.872141i | \(0.662731\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 294.213 | 0.333197 | 0.166599 | − | 0.986025i | \(-0.446722\pi\) | ||||
0.166599 | + | 0.986025i | \(0.446722\pi\) | |||||||
\(884\) | 65.0602 | − | 37.5625i | 0.0735975 | − | 0.0424915i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 389.796 | − | 675.146i | 0.439950 | − | 0.762016i | ||||
\(887\) | −497.794 | − | 287.402i | −0.561211 | − | 0.324015i | 0.192420 | − | 0.981313i | \(-0.438366\pi\) |
−0.753631 | + | 0.657297i | \(0.771700\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −32.0306 | − | 55.4787i | −0.0360299 | − | 0.0624057i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 185.546 | 0.208011 | ||||||||
\(893\) | −57.3949 | + | 33.1370i | −0.0642720 | + | 0.0371075i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 62.2020 | + | 35.9124i | 0.0694219 | + | 0.0400808i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 383.864 | + | 664.872i | 0.427465 | + | 0.740391i | ||||
\(899\) | − | 135.004i | − | 0.150171i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.1837 | −0.0201817 | ||||||||
\(902\) | 714.749 | − | 412.661i | 0.792405 | − | 0.457495i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −286.045 | + | 495.445i | −0.316422 | + | 0.548059i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −255.037 | − | 441.737i | −0.281187 | − | 0.487031i | 0.690490 | − | 0.723342i | \(-0.257395\pi\) |
−0.971677 | + | 0.236311i | \(0.924062\pi\) | |||||||
\(908\) | − | 339.604i | − | 0.374013i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 803.127 | − | 463.685i | 0.881588 | − | 0.508985i | 0.0104064 | − | 0.999946i | \(-0.496687\pi\) |
0.871182 | + | 0.490961i | \(0.163354\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 414.863 | − | 718.564i | 0.454396 | − | 0.787036i | ||||
\(914\) | −113.123 | − | 65.3114i | −0.123767 | − | 0.0714567i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 407.545 | + | 705.888i | 0.444918 | + | 0.770621i | ||||
\(917\) | − | 31.4897i | − | 0.0343399i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1240.63 | −1.34998 | −0.674991 | − | 0.737826i | \(-0.735853\pi\) | ||||
−0.674991 | + | 0.737826i | \(0.735853\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −162.507 | + | 281.471i | −0.176255 | + | 0.305283i | ||||
\(923\) | 1465.33 | + | 846.010i | 1.58757 | + | 0.916587i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 722.384i | − | 0.780112i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 18.6061 | 0.0200497 | ||||||||
\(929\) | −293.576 | + | 169.496i | −0.316013 | + | 0.182450i | −0.649614 | − | 0.760264i | \(-0.725069\pi\) |
0.333601 | + | 0.942714i | \(0.391736\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.4245 | − | 35.3763i | 0.0219382 | − | 0.0379981i | ||||
\(932\) | 26.4245 | + | 15.2562i | 0.0283525 | + | 0.0163693i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 589.485 | + | 1021.02i | 0.631140 | + | 1.09317i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1322.21 | −1.41111 | −0.705556 | − | 0.708655i | \(-0.749302\pi\) | ||||
−0.705556 | + | 0.708655i | \(0.749302\pi\) | |||||||
\(938\) | −240.680 | + | 138.957i | −0.256588 | + | 0.148141i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 310.984 | + | 179.547i | 0.330482 | + | 0.190804i | 0.656055 | − | 0.754713i | \(-0.272224\pi\) |
−0.325573 | + | 0.945517i | \(0.605557\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 291.795 | + | 505.404i | 0.309433 | + | 0.535953i | ||||
\(944\) | 366.110i | 0.387828i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.7423 | 0.0134697 | ||||||||
\(947\) | −671.855 | + | 387.896i | −0.709457 | + | 0.409605i | −0.810860 | − | 0.585240i | \(-0.801000\pi\) |
0.101403 | + | 0.994845i | \(0.467667\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 946.347 | − | 1639.12i | 0.997205 | − | 1.72721i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −17.1214 | − | 29.6552i | −0.0179847 | − | 0.0311504i | ||||
\(953\) | 465.082i | 0.488019i | 0.969773 | + | 0.244010i | \(0.0784628\pi\) | ||||
−0.969773 | + | 0.244010i | \(0.921537\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −97.9240 | + | 56.5364i | −0.102431 | + | 0.0591385i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 464.704 | − | 804.891i | 0.485077 | − | 0.840178i | ||||
\(959\) | 1290.28 | + | 744.942i | 1.34544 | + | 0.776791i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −361.863 | − | 626.765i | −0.376548 | − | 0.652200i | ||||
\(962\) | − | 481.989i | − | 0.501028i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −168.424 | −0.174714 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 612.113 | − | 1060.21i | 0.633002 | − | 1.09639i | −0.353933 | − | 0.935271i | \(-0.615156\pi\) |
0.986935 | − | 0.161121i | \(-0.0515109\pi\) | |||||||
\(968\) | −78.1612 | − | 45.1264i | −0.0807451 | − | 0.0466182i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 658.702i | − | 0.678375i | −0.940719 | − | 0.339188i | \(-0.889848\pi\) | ||
0.940719 | − | 0.339188i | \(-0.110152\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −676.303 | −0.695070 | ||||||||
\(974\) | −430.702 | + | 248.666i | −0.442199 | + | 0.255304i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 150.182 | − | 260.122i | 0.153875 | − | 0.266519i | ||||
\(977\) | 1314.92 | + | 759.170i | 1.34588 | + | 0.777042i | 0.987663 | − | 0.156597i | \(-0.0500525\pi\) |
0.358214 | + | 0.933639i | \(0.383386\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 195.272 | + | 338.222i | 0.199461 | + | 0.345477i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 347.074 | 0.353436 | ||||||||
\(983\) | 716.930 | − | 413.920i | 0.729329 | − | 0.421078i | −0.0888477 | − | 0.996045i | \(-0.528318\pi\) |
0.818177 | + | 0.574967i | \(0.194985\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −7.68215 | − | 4.43529i | −0.00779122 | − | 0.00449826i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −92.5153 | − | 160.241i | −0.0936390 | − | 0.162187i | ||||
\(989\) | 9.01020i | 0.00911041i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 429.546 | 0.433447 | 0.216723 | − | 0.976233i | \(-0.430463\pi\) | ||||
0.216723 | + | 0.976233i | \(0.430463\pi\) | |||||||
\(992\) | 201.081 | − | 116.094i | 0.202702 | − | 0.117030i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 385.621 | − | 667.915i | 0.387949 | − | 0.671947i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −347.499 | − | 601.886i | −0.348545 | − | 0.603697i | 0.637447 | − | 0.770495i | \(-0.279991\pi\) |
−0.985991 | + | 0.166798i | \(0.946657\pi\) | |||||||
\(998\) | − | 891.274i | − | 0.893060i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))