Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,3,Mod(65,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("576.65");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.q (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: | \(15.6948632272\) |
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: | \( 3 \) |
Twist minimal: | no (minimal twist has level 18) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 65.1 | ||
Root | \(-1.22474 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 576.65 |
Dual form | 576.3.q.f.257.1 |
$q$-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 \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(325\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.44949 | + | 1.73205i | −0.816497 | + | 0.577350i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.50000 | − | 2.59808i | 0.900000 | − | 0.519615i | 0.0227998 | − | 0.999740i | \(-0.492742\pi\) |
0.877200 | + | 0.480125i | \(0.159409\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.17423 | + | 5.49794i | −0.453462 | + | 0.785419i | −0.998598 | − | 0.0529281i | \(-0.983145\pi\) |
0.545136 | + | 0.838347i | \(0.316478\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000 | − | 8.48528i | 0.333333 | − | 0.942809i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8.17423 | − | 4.71940i | −0.743112 | − | 0.429036i | 0.0800876 | − | 0.996788i | \(-0.474480\pi\) |
−0.823200 | + | 0.567752i | \(0.807813\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 9.84847 | + | 17.0580i | 0.757575 | + | 1.31216i | 0.944084 | + | 0.329704i | \(0.106949\pi\) |
−0.186510 | + | 0.982453i | \(0.559718\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.52270 | + | 14.1582i | −0.434847 | + | 0.943879i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.90702i | − | 0.112178i | −0.998426 | − | 0.0560889i | \(-0.982137\pi\) | ||
0.998426 | − | 0.0560889i | \(-0.0178630\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.69694 | −0.247207 | −0.123604 | − | 0.992332i | \(-0.539445\pi\) | ||||
−0.123604 | + | 0.992332i | \(0.539445\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.74745 | − | 18.9651i | −0.0832118 | − | 0.903099i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.17423 | − | 4.71940i | 0.355402 | − | 0.205191i | −0.311660 | − | 0.950194i | \(-0.600885\pi\) |
0.667062 | + | 0.745002i | \(0.267552\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | − | 1.73205i | 0.0400000 | − | 0.0692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 7.34847 | + | 25.9808i | 0.272166 | + | 0.962250i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.84847 | + | 1.64456i | 0.0982231 | + | 0.0567091i | 0.548307 | − | 0.836277i | \(-0.315273\pi\) |
−0.450084 | + | 0.892986i | \(0.648606\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 20.5227 | + | 35.5464i | 0.662023 | + | 1.14666i | 0.980083 | + | 0.198587i | \(0.0636351\pi\) |
−0.318061 | + | 0.948070i | \(0.603032\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 28.1969 | − | 2.59808i | 0.854453 | − | 0.0787296i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 32.9876i | 0.942503i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −17.3031 | −0.467650 | −0.233825 | − | 0.972279i | \(-0.575124\pi\) | ||||
−0.233825 | + | 0.972279i | \(0.575124\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −53.6691 | − | 24.7255i | −1.37613 | − | 0.633986i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −53.5454 | + | 30.9145i | −1.30599 | + | 0.754011i | −0.981424 | − | 0.191853i | \(-0.938550\pi\) |
−0.324562 | + | 0.945864i | \(0.605217\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.477296 | − | 0.826701i | 0.0110999 | − | 0.0192256i | −0.860422 | − | 0.509582i | \(-0.829800\pi\) |
0.871522 | + | 0.490356i | \(0.163133\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −8.54541 | − | 45.9780i | −0.189898 | − | 1.02173i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.2196 | − | 7.05501i | −0.259992 | − | 0.150107i | 0.364339 | − | 0.931267i | \(-0.381295\pi\) |
−0.624331 | + | 0.781160i | \(0.714628\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.34847 | + | 7.53177i | 0.0887443 | + | 0.153710i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.30306 | + | 4.67123i | 0.0647659 | + | 0.0915928i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.53512i | 0.179908i | 0.995946 | + | 0.0899539i | \(0.0286720\pi\) | ||||
−0.995946 | + | 0.0899539i | \(0.971328\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −49.0454 | −0.891735 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.5051 | − | 8.13534i | 0.201844 | − | 0.142725i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −79.2650 | + | 45.7637i | −1.34348 | + | 0.775656i | −0.987316 | − | 0.158769i | \(-0.949247\pi\) |
−0.356160 | + | 0.934425i | \(0.615914\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −37.5454 | + | 65.0306i | −0.615498 | + | 1.06607i | 0.374798 | + | 0.927106i | \(0.377712\pi\) |
−0.990297 | + | 0.138968i | \(0.955621\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 37.1288 | + | 43.4281i | 0.589346 | + | 0.689335i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 88.6362 | + | 51.1741i | 1.36363 | + | 0.787295i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.4773 | + | 26.8075i | 0.231004 | + | 0.400111i | 0.958104 | − | 0.286421i | \(-0.0924655\pi\) |
−0.727100 | + | 0.686532i | \(0.759132\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −11.8485 | + | 25.7183i | −0.171717 | + | 0.372729i | ||||
\(70\) | 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 | \(-0.728663\pi\) | ||||
−0.658156 | + | 0.752881i | \(0.728663\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.550510 | + | 5.97469i | 0.00734014 | + | 0.0796626i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 51.8939 | − | 29.9609i | 0.673946 | − | 0.389103i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.8712 | + | 25.7576i | −0.188243 | + | 0.326046i | −0.944664 | − | 0.328038i | \(-0.893612\pi\) |
0.756422 | + | 0.654084i | \(0.226946\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −63.0000 | − | 50.9117i | −0.777778 | − | 0.628539i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 76.1288 | + | 43.9530i | 0.917215 | + | 0.529554i | 0.882745 | − | 0.469852i | \(-0.155693\pi\) |
0.0344693 | + | 0.999406i | \(0.489026\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.95459 | − | 8.58161i | −0.0582893 | − | 0.100960i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.82577 | + | 0.905350i | −0.112940 | + | 0.0104063i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 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 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −111.838 | − | 51.5241i | −1.20256 | − | 0.554023i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −21.1362 | + | 12.2030i | −0.222487 | + | 0.128453i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −47.9393 | + | 83.0333i | −0.494219 | + | 0.856013i | −0.999978 | − | 0.00666202i | \(-0.997879\pi\) |
0.505758 | + | 0.862675i | \(0.331213\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −64.5681 | + | 55.2025i | −0.652203 | + | 0.557601i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 136.772 | + | 78.9656i | 1.35418 | + | 0.781838i | 0.988832 | − | 0.149032i | \(-0.0476159\pi\) |
0.365350 | + | 0.930870i | \(0.380949\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.5681 | − | 25.2327i | −0.141438 | − | 0.244978i | 0.786600 | − | 0.617462i | \(-0.211839\pi\) |
−0.928038 | + | 0.372485i | \(0.878506\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −57.1362 | − | 80.8028i | −0.544155 | − | 0.769551i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 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 | \(-0.679071\pi\) | ||||
−0.533360 | + | 0.845888i | \(0.679071\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 42.3837 | − | 29.9698i | 0.381835 | − | 0.269998i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 175.166 | − | 101.132i | 1.55014 | − | 0.894976i | 0.552015 | − | 0.833834i | \(-0.313859\pi\) |
0.998129 | − | 0.0611424i | \(-0.0194744\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 24.5227 | − | 42.4746i | 0.213241 | − | 0.369344i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 174.288 | − | 32.3929i | 1.48964 | − | 0.276862i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.4847 | + | 6.05334i | 0.0881067 | + | 0.0508684i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −15.9546 | − | 27.6342i | −0.131856 | − | 0.228382i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 77.6135 | − | 168.468i | 0.631004 | − | 1.36966i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 119.512i | 0.956092i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.0908 | 0.0794552 | 0.0397276 | − | 0.999211i | \(-0.487351\pi\) | ||||
0.0397276 | + | 0.999211i | \(0.487351\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.262756 | + | 2.85170i | 0.00203687 | + | 0.0221062i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.29567 | + | 2.48010i | −0.0327913 | + | 0.0189321i | −0.516306 | − | 0.856404i | \(-0.672693\pi\) |
0.483515 | + | 0.875336i | \(0.339360\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.9092 | − | 25.8235i | 0.112099 | − | 0.194161i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 100.568 | + | 97.8215i | 0.744949 | + | 0.724604i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 203.242 | + | 117.342i | 1.48352 | + | 0.856511i | 0.999825 | − | 0.0187249i | \(-0.00596067\pi\) |
0.483696 | + | 0.875236i | \(0.339294\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 53.2650 | + | 92.2578i | 0.383202 | + | 0.663725i | 0.991518 | − | 0.129970i | \(-0.0414881\pi\) |
−0.608316 | + | 0.793695i | \(0.708155\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 42.1515 | − | 3.88386i | 0.298947 | − | 0.0275451i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 185.915i | − | 1.30011i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 17.0908 | 0.117868 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −23.6969 | − | 10.9172i | −0.161204 | − | 0.0742668i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 91.0301 | − | 52.5563i | 0.610940 | − | 0.352727i | −0.162393 | − | 0.986726i | \(-0.551921\pi\) |
0.773333 | + | 0.634000i | \(0.218588\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 142.614 | − | 247.014i | 0.944460 | − | 1.63585i | 0.187632 | − | 0.982239i | \(-0.439919\pi\) |
0.756828 | − | 0.653614i | \(-0.226748\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −16.1816 | − | 5.72107i | −0.105762 | − | 0.0373926i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 184.704 | + | 106.639i | 1.19164 | + | 0.687994i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −98.5908 | − | 170.764i | −0.627967 | − | 1.08767i | −0.987959 | − | 0.154715i | \(-0.950554\pi\) |
0.359992 | − | 0.932955i | \(-0.382779\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −16.5153 | − | 23.3562i | −0.103870 | − | 0.146894i | ||||
\(160\) | 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 | \(0.223238\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 120.136 | − | 84.9491i | 0.728098 | − | 0.514843i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −41.9472 | + | 24.2182i | −0.251181 | + | 0.145019i | −0.620305 | − | 0.784361i | \(-0.712991\pi\) |
0.369124 | + | 0.929380i | \(0.379658\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −109.485 | + | 189.633i | −0.647838 | + | 1.12209i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −14.0908 | + | 39.8548i | −0.0824024 | + | 0.233069i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −86.9847 | − | 50.2206i | −0.502802 | − | 0.290293i | 0.227068 | − | 0.973879i | \(-0.427086\pi\) |
−0.729870 | + | 0.683586i | \(0.760419\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.34847 | + | 10.9959i | 0.0362770 | + | 0.0628336i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 114.894 | − | 249.389i | 0.649118 | − | 1.40898i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 285.071i | − | 1.59257i | −0.604919 | − | 0.796287i | \(-0.706794\pi\) | ||
0.604919 | − | 0.796287i | \(-0.293206\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −37.1214 | −0.205091 | −0.102545 | − | 0.994728i | \(-0.532699\pi\) | ||||
−0.102545 | + | 0.994728i | \(0.532699\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −20.6691 | − | 224.322i | −0.112946 | − | 1.22580i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −77.8638 | + | 44.9547i | −0.420885 | + | 0.242998i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.00000 | + | 15.5885i | −0.0481283 | + | 0.0833607i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −166.166 | − | 42.0676i | −0.879187 | − | 0.222580i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.5227 | − | 8.96204i | −0.0812707 | − | 0.0469217i | 0.458814 | − | 0.888532i | \(-0.348274\pi\) |
−0.540085 | + | 0.841611i | \(0.681608\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 47.7270 | + | 82.6657i | 0.247290 | + | 0.428319i | 0.962773 | − | 0.270311i | \(-0.0871265\pi\) |
−0.715483 | + | 0.698630i | \(0.753793\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −305.750 | + | 28.1719i | −1.56795 | + | 0.144471i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 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 | ||||||||
\(201\) | −84.3434 | − | 38.8571i | −0.419619 | − | 0.193319i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −18.0834 | + | 10.4405i | −0.0890809 | + | 0.0514309i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −160.636 | + | 278.230i | −0.783591 | + | 1.35722i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −15.5227 | − | 83.5189i | −0.0749889 | − | 0.403473i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 38.3939 | + | 22.1667i | 0.183703 | + | 0.106061i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −77.2196 | − | 133.748i | −0.365970 | − | 0.633878i | 0.622961 | − | 0.782253i | \(-0.285929\pi\) |
−0.988931 | + | 0.148374i | \(0.952596\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −148.788 | − | 210.418i | −0.698534 | − | 0.987876i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 4.96021i | − | 0.0230707i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −260.576 | −1.20081 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 235.373 | − | 166.434i | 1.07476 | − | 0.759973i | ||||
\(220\) | 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 | \(-0.900032\pi\) |
0.743077 | + | 0.669206i | \(0.233366\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.6969 | − | 13.6814i | −0.0519864 | − | 0.0608064i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −147.053 | − | 84.9010i | −0.647810 | − | 0.374013i | 0.139807 | − | 0.990179i | \(-0.455352\pi\) |
−0.787617 | + | 0.616166i | \(0.788685\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 203.772 | + | 352.944i | 0.889836 | + | 1.54124i | 0.840068 | + | 0.542480i | \(0.182515\pi\) |
0.0497675 | + | 0.998761i | \(0.484152\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −75.2196 | + | 163.272i | −0.325626 | + | 0.706805i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 15.2562i | − | 0.0654772i | −0.999464 | − | 0.0327386i | \(-0.989577\pi\) | ||
0.999464 | − | 0.0327386i | \(-0.0104229\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −73.3179 | −0.311991 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.18673 | − | 88.8507i | −0.0345432 | − | 0.374897i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 48.9620 | − | 28.2682i | 0.204862 | − | 0.118277i | −0.394059 | − | 0.919085i | \(-0.628930\pi\) |
0.598921 | + | 0.800808i | \(0.295596\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −42.1061 | + | 72.9299i | −0.174714 | + | 0.302614i | −0.940062 | − | 0.341003i | \(-0.889233\pi\) |
0.765348 | + | 0.643617i | \(0.222567\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 242.499 | + | 15.5885i | 0.997940 | + | 0.0641500i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 39.1362 | + | 22.5953i | 0.159740 | + | 0.0922258i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −46.2577 | − | 80.1206i | −0.187278 | − | 0.324375i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −262.606 | + | 24.1966i | −1.05464 | + | 0.0971750i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 218.903i | 0.872123i | 0.899917 | + | 0.436062i | \(0.143627\pi\) | ||||
−0.899917 | + | 0.436062i | \(0.856373\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −89.0908 | −0.352138 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 27.0000 | + | 12.4389i | 0.105882 | + | 0.0487802i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.1061 | + | 6.41212i | −0.0432145 | + | 0.0249499i | −0.521452 | − | 0.853281i | \(-0.674609\pi\) |
0.478237 | + | 0.878231i | \(0.341276\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 54.9240 | − | 95.1311i | 0.212062 | − | 0.367302i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 22.5000 | − | 19.2364i | 0.0862069 | − | 0.0737026i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 291.386 | + | 168.232i | 1.10793 | + | 0.639666i | 0.938293 | − | 0.345840i | \(-0.112406\pi\) |
0.169640 | + | 0.985506i | \(0.445739\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 24.7730 | + | 42.9080i | 0.0934829 | + | 0.161917i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 71.6663 | + | 101.351i | 0.268413 | + | 0.379594i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 60.4468i | 0.224709i | 0.993668 | + | 0.112355i | \(0.0358393\pi\) | ||||
−0.993668 | + | 0.112355i | \(0.964161\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 274.636 | 1.01342 | 0.506708 | − | 0.862118i | \(-0.330862\pi\) | ||||
0.506708 | + | 0.862118i | \(0.330862\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 306.297 | − | 216.585i | 1.12197 | − | 0.793352i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −16.3485 | + | 9.43879i | −0.0594490 | + | 0.0343229i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.5000 | + | 42.4352i | −0.0884477 | + | 0.153196i | −0.906855 | − | 0.421442i | \(-0.861524\pi\) |
0.818407 | + | 0.574638i | \(0.194857\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 363.189 | − | 67.5018i | 1.30175 | − | 0.241942i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −297.121 | − | 171.543i | −1.05737 | − | 0.610473i | −0.132666 | − | 0.991161i | \(-0.542354\pi\) |
−0.924704 | + | 0.380688i | \(0.875687\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −171.704 | − | 297.401i | −0.606729 | − | 1.05089i | −0.991776 | − | 0.127988i | \(-0.959148\pi\) |
0.385047 | − | 0.922897i | \(-0.374185\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 30.6367 | − | 66.5001i | 0.107497 | − | 0.233334i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 392.519i | − | 1.36766i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 285.363 | 0.987416 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −26.3911 | − | 286.422i | −0.0906910 | − | 0.984270i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 248.076 | − | 143.226i | 0.846674 | − | 0.488828i | −0.0128532 | − | 0.999917i | \(-0.504091\pi\) |
0.859527 | + | 0.511090i | \(0.170758\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −237.795 | + | 411.873i | −0.806085 | + | 1.39618i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 62.5454 | − | 247.053i | 0.210591 | − | 0.831829i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 161.007 | + | 92.9577i | 0.538486 | + | 0.310895i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.03010 | + | 5.24829i | 0.0100668 | + | 0.0174362i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −471.795 | + | 43.4714i | −1.55708 | + | 0.143470i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 390.183i | 1.27929i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −154.091 | −0.501924 | −0.250962 | − | 0.967997i | \(-0.580747\pi\) | ||||
−0.250962 | + | 0.967997i | \(0.580747\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 79.3888 | + | 36.5746i | 0.256922 | + | 0.118364i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −62.3411 | + | 35.9926i | −0.200454 | + | 0.115732i | −0.596867 | − | 0.802340i | \(-0.703588\pi\) |
0.396413 | + | 0.918072i | \(0.370255\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 183.803 | − | 318.356i | 0.587230 | − | 1.01711i | −0.407363 | − | 0.913266i | \(-0.633552\pi\) |
0.994593 | − | 0.103846i | \(-0.0331150\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 279.909 | + | 98.9628i | 0.888601 | + | 0.314168i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 93.1821 | + | 53.7987i | 0.293950 | + | 0.169712i | 0.639722 | − | 0.768607i | \(-0.279050\pi\) |
−0.345772 | + | 0.938319i | \(0.612383\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.5227 | − | 26.8861i | −0.0486605 | − | 0.0842825i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 297.576 | + | 420.835i | 0.927027 | + | 1.31101i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.95717i | 0.0277312i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 39.3939 | 0.121212 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 284.808 | − | 201.390i | 0.870973 | − | 0.615871i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 77.5760 | − | 44.7885i | 0.235793 | − | 0.136135i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.59873 | − | 14.8934i | 0.0259780 | − | 0.0449953i | −0.852744 | − | 0.522329i | \(-0.825063\pi\) |
0.878722 | + | 0.477334i | \(0.158397\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −51.9092 | + | 146.821i | −0.155883 | + | 0.440905i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 139.296 | + | 80.4224i | 0.415808 | + | 0.240067i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −182.197 | − | 315.574i | −0.540644 | − | 0.936422i | −0.998867 | − | 0.0475854i | \(-0.984847\pi\) |
0.458223 | − | 0.888837i | \(-0.348486\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −253.902 | + | 551.120i | −0.748973 | + | 1.62572i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 387.419i | − | 1.13613i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −366.287 | −1.06789 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 13.5000 | + | 146.516i | 0.0391304 | + | 0.424683i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −505.234 | + | 291.697i | −1.45601 | + | 0.840626i | −0.998811 | − | 0.0487402i | \(-0.984479\pi\) |
−0.457196 | + | 0.889366i | \(0.651146\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 156.379 | − | 270.856i | 0.448076 | − | 0.776091i | −0.550185 | − | 0.835043i | \(-0.685443\pi\) |
0.998261 | + | 0.0589524i | \(0.0187760\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −370.810 | + | 381.221i | −1.05644 | + | 1.08610i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −32.5760 | − | 18.8078i | −0.0922834 | − | 0.0532798i | 0.453148 | − | 0.891435i | \(-0.350301\pi\) |
−0.545431 | + | 0.838155i | \(0.683634\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 223.182 | + | 386.562i | 0.628681 | + | 1.08891i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −36.1668 | + | 3.33243i | −0.101308 | + | 0.00933453i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 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 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 86.9444 | + | 40.0554i | 0.239516 | + | 0.110346i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −432.409 | + | 249.651i | −1.18468 | + | 0.683976i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.6135 | − | 28.7755i | 0.0452684 | − | 0.0784072i | −0.842503 | − | 0.538691i | \(-0.818919\pi\) |
0.887772 | + | 0.460284i | \(0.152252\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 101.682 | + | 547.091i | 0.275560 | + | 1.48263i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −52.4235 | − | 30.2667i | −0.141303 | − | 0.0815814i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −112.515 | − | 194.881i | −0.301648 | − | 0.522470i | 0.674861 | − | 0.737945i | \(-0.264203\pi\) |
−0.976509 | + | 0.215475i | \(0.930870\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −207.000 | − | 292.742i | −0.552000 | − | 0.780646i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 64.7858i | 0.171846i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 166.334 | 0.438875 | 0.219438 | − | 0.975627i | \(-0.429578\pi\) | ||||
0.219438 | + | 0.975627i | \(0.429578\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −24.7173 | + | 17.4778i | −0.0648749 | + | 0.0458735i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −638.249 | + | 368.493i | −1.66645 | + | 0.962124i | −0.696917 | + | 0.717152i | \(0.745445\pi\) |
−0.969530 | + | 0.244972i | \(0.921221\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 155.682 | − | 269.648i | 0.404368 | − | 0.700386i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.58290 | − | 6.53010i | −0.0144261 | − | 0.0168736i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 146.682 | + | 84.6867i | 0.377074 | + | 0.217704i | 0.676544 | − | 0.736402i | \(-0.263477\pi\) |
−0.299471 | + | 0.954106i | \(0.596810\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.00000 | − | 15.5885i | −0.0230179 | − | 0.0398682i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.22652 | − | 13.5153i | 0.0158436 | − | 0.0343901i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 154.546i | 0.391255i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 256.272 | 0.645523 | 0.322761 | − | 0.946480i | \(-0.395389\pi\) | ||||
0.322761 | + | 0.946480i | \(0.395389\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.20766 | + | 89.0778i | 0.0205706 | + | 0.223253i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 226.364 | − | 130.691i | 0.564498 | − | 0.325913i | −0.190451 | − | 0.981697i | \(-0.560995\pi\) |
0.754949 | + | 0.655784i | \(0.227662\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −404.234 | + | 700.155i | −1.00306 | + | 1.73736i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −415.772 | − | 65.4238i | −1.02660 | − | 0.161540i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 141.439 | + | 81.6600i | 0.347517 | + | 0.200639i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 221.894 | + | 384.331i | 0.542528 | + | 0.939686i | 0.998758 | + | 0.0498240i | \(0.0158660\pi\) |
−0.456230 | + | 0.889862i | \(0.650801\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −701.082 | + | 64.5980i | −1.70580 | + | 0.157173i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 581.059i | − | 1.40692i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 456.773 | 1.10066 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −290.267 | − | 133.727i | −0.696085 | − | 0.320688i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.32525 | + | 5.38394i | −0.0222560 | + | 0.0128495i | −0.511087 | − | 0.859529i | \(-0.670757\pi\) |
0.488831 | + | 0.872379i | \(0.337424\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 127.152 | − | 220.233i | 0.302023 | − | 0.523119i | −0.674571 | − | 0.738210i | \(-0.735672\pi\) |
0.976594 | + | 0.215091i | \(0.0690048\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −96.5227 | + | 82.5221i | −0.228186 | + | 0.195088i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.30306 | − | 1.90702i | −0.00777191 | − | 0.00448711i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −238.356 | − | 412.844i | −0.558210 | − | 0.966849i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 322.015 | + | 455.398i | 0.750617 | + | 1.06153i | ||||
\(430\) | 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 | \(-0.421380\pi\) | ||||
0.244489 | + | 0.969652i | \(0.421380\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −41.8638 | + | 29.6022i | −0.0962386 | + | 0.0680509i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −38.3939 | + | 22.1667i | −0.0878578 | + | 0.0507247i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −139.931 | + | 242.368i | −0.318750 | + | 0.552092i | −0.980228 | − | 0.197874i | \(-0.936596\pi\) |
0.661477 | + | 0.749965i | \(0.269930\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 76.9546 | − | 14.3027i | 0.174500 | − | 0.0324324i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 477.400 | + | 275.627i | 1.07765 | + | 0.622183i | 0.930262 | − | 0.366895i | \(-0.119579\pi\) |
0.147391 | + | 0.989078i | \(0.452913\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −107.499 | − | 186.195i | −0.241572 | − | 0.418415i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −131.947 | + | 286.405i | −0.295184 | + | 0.640727i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 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 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 78.5102 | + | 852.072i | 0.173312 | + | 1.88095i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −562.704 | + | 324.877i | −1.23671 | + | 0.714016i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −46.1821 | + | 79.9898i | −0.101055 | + | 0.175032i | −0.912120 | − | 0.409924i | \(-0.865555\pi\) |
0.811065 | + | 0.584957i | \(0.198888\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 49.5459 | − | 14.0137i | 0.107943 | − | 0.0305309i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 199.030 | + | 114.910i | 0.431736 | + | 0.249263i | 0.700086 | − | 0.714059i | \(-0.253145\pi\) |
−0.268350 | + | 0.963321i | \(0.586478\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 255.401 | + | 442.368i | 0.551623 | + | 0.955438i | 0.998158 | + | 0.0606723i | \(0.0193245\pi\) |
−0.446535 | + | 0.894766i | \(0.647342\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −637.136 | + | 58.7059i | −1.37018 | + | 0.126249i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 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 | ||||||||
\(471\) | 537.270 | + | 247.521i | 1.14070 | + | 0.525523i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.80306 | + | 4.50510i | −0.0164970 | + | 0.00952452i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.69694 | + | 8.13534i | −0.00988829 | + | 0.0171270i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 80.9082 | + | 28.6054i | 0.169619 | + | 0.0599693i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 569.144 | + | 328.595i | 1.18819 | + | 0.686003i | 0.957895 | − | 0.287118i | \(-0.0926972\pi\) |
0.230296 | + | 0.973121i | \(0.426031\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −170.409 | − | 295.156i | −0.354280 | − | 0.613631i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −103.788 | − | 146.778i | −0.214881 | − | 0.303888i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 498.200i | 1.02722i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −351.666 | −0.722107 | −0.361054 | − | 0.932545i | \(-0.617583\pi\) | ||||
−0.361054 | + | 0.932545i | \(0.617583\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −610.070 | + | 431.385i | −1.24759 | + | 0.882178i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −212.539 | + | 122.709i | −0.432869 | + | 0.249917i | −0.700568 | − | 0.713586i | \(-0.747070\pi\) |
0.267699 | + | 0.963503i | \(0.413737\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.13622 | − | 5.43210i | 0.00636151 | − | 0.0110185i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −147.136 | + | 416.164i | −0.297245 | + | 0.840736i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −472.287 | − | 272.675i | −0.950276 | − | 0.548642i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 315.113 | + | 545.792i | 0.631489 | + | 1.09377i | 0.987247 | + | 0.159193i | \(0.0508892\pi\) |
−0.355758 | + | 0.934578i | \(0.615777\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 60.8020 | − | 131.977i | 0.121361 | − | 0.263427i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 286.891i | − | 0.570360i | −0.958474 | − | 0.285180i | \(-0.907947\pi\) | ||
0.958474 | − | 0.285180i | \(-0.0920534\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 820.635 | 1.62502 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −60.2724 | − | 654.137i | −0.118881 | − | 1.29021i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −755.454 | + | 436.161i | −1.48419 | + | 0.856898i | −0.999838 | − | 0.0179741i | \(-0.994278\pi\) |
−0.484353 | + | 0.874873i | \(0.660945\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 305.015 | − | 528.301i | 0.596898 | − | 1.03386i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −34.5153 | − | 122.030i | −0.0672813 | − | 0.237875i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −131.113 | − | 75.6981i | −0.254588 | − | 0.146987i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 66.5908 | + | 115.339i | 0.128802 | + | 0.223092i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 300.053 | − | 27.6470i | 0.578136 | − | 0.0532697i | ||||
\(520\) | 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 | \(0.820939\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −34.5959 | − | 15.9384i | −0.0658970 | − | 0.0303589i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 67.7878 | − | 39.1373i | 0.128630 | − | 0.0742643i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −219.955 | + | 380.973i | −0.415793 | + | 0.720175i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 150.523 | + | 809.877i | 0.283470 | + | 1.52519i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1054.68 | − | 608.920i | −1.97876 | − | 1.14244i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −446.363 | − | 773.124i | −0.834324 | − | 1.44509i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 493.757 | + | 698.278i | 0.919473 | + | 1.30033i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 82.0886i | − | 0.152298i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 509.151 | 0.941129 | 0.470565 | − | 0.882365i | \(-0.344050\pi\) | ||||
0.470565 | + | 0.882365i | \(0.344050\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 90.9286 | − | 64.2962i | 0.167456 | − | 0.118409i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −523.226 | + | 302.085i | −0.960048 | + | 0.554284i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 274.022 | − | 474.620i | 0.500955 | − | 0.867679i | −0.499045 | − | 0.866576i | \(-0.666316\pi\) |
0.999999 | − | 0.00110267i | \(-0.000350992\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 439.166 | + | 513.675i | 0.799939 | + | 0.935656i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.3791 | − | 7.72442i | −0.0242815 | − | 0.0140189i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −94.4092 | − | 163.522i | −0.170722 | − | 0.295699i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 112.863 | − | 244.980i | 0.203356 | − | 0.441405i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 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 | ||||||||
\(561\) | −4.95459 | − | 53.7722i | −0.00883172 | − | 0.0958507i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 525.220 | − | 303.236i | 0.932895 | − | 0.538607i | 0.0451687 | − | 0.998979i | \(-0.485617\pi\) |
0.887726 | + | 0.460372i | \(0.152284\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 525.499 | − | 910.191i | 0.930087 | − | 1.61096i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 479.886 | − | 184.764i | 0.846360 | − | 0.325863i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −224.954 | − | 129.877i | −0.395350 | − | 0.228255i | 0.289126 | − | 0.957291i | \(-0.406635\pi\) |
−0.684476 | + | 0.729036i | \(0.739969\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −43.9166 | − | 76.0657i | −0.0769117 | − | 0.133215i | 0.825004 | − | 0.565126i | \(-0.191173\pi\) |
−0.901916 | + | 0.431911i | \(0.857839\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 53.5454 | − | 4.93369i | 0.0934475 | − | 0.00861029i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 18.8776i | − | 0.0328306i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −132.091 | −0.228927 | −0.114463 | − | 0.993427i | \(-0.536515\pi\) | ||||
−0.114463 | + | 0.993427i | \(0.536515\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −260.088 | − | 119.823i | −0.449202 | − | 0.206948i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −483.302 | + | 279.034i | −0.831844 | + | 0.480266i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 45.0000 | − | 77.9423i | 0.0771870 | − | 0.133692i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 700.136 | − | 598.581i | 1.19681 | − | 1.02322i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 491.614 | + | 283.833i | 0.837502 | + | 0.483532i | 0.856414 | − | 0.516289i | \(-0.172687\pi\) |
−0.0189125 | + | 0.999821i | \(0.506020\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −96.3939 | − | 166.959i | −0.163657 | − | 0.283462i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −277.757 | − | 392.808i | −0.469978 | − | 0.664650i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 77.0321i | 0.129902i | 0.997888 | + | 0.0649512i | \(0.0206892\pi\) | ||||
−0.997888 | + | 0.0649512i | \(0.979311\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 62.9082 | 0.105728 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −15.9592 | + | 11.2848i | −0.0267323 | + | 0.0189026i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −764.917 | + | 441.625i | −1.27699 | + | 0.737270i | −0.976294 | − | 0.216450i | \(-0.930552\pi\) |
−0.300696 | + | 0.953720i | \(0.597219\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 397.545 | − | 688.569i | 0.661473 | − | 1.14571i | −0.318755 | − | 0.947837i | \(-0.603265\pi\) |
0.980229 | − | 0.197868i | \(-0.0634018\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 273.901 | − | 50.9068i | 0.454230 | − | 0.0844226i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −143.591 | − | 82.9025i | −0.237341 | − | 0.137029i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 148.372 | + | 256.987i | 0.244434 | + | 0.423373i | 0.961972 | − | 0.273147i | \(-0.0880644\pi\) |
−0.717538 | + | 0.696519i | \(0.754731\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 26.2117 | − | 56.8952i | 0.0430406 | − | 0.0934240i | ||||
\(610\) | 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 | \(0.361383\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −88.4319 | − | 959.752i | −0.143792 | − | 1.56057i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −229.909 | + | 132.738i | −0.372623 | + | 0.215134i | −0.674604 | − | 0.738180i | \(-0.735686\pi\) |
0.301981 | + | 0.953314i | \(0.402352\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −98.5227 | + | 170.646i | −0.159164 | + | 0.275681i | −0.934568 | − | 0.355786i | \(-0.884213\pi\) |
0.775403 | + | 0.631466i | \(0.217547\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 182.682 | + | 177.693i | 0.294173 | + | 0.286139i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 227.486 | + | 131.339i | 0.365146 | + | 0.210817i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 335.500 | + | 581.103i | 0.536800 | + | 0.929765i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −132.439 | + | 12.2030i | −0.211227 | + | 0.0194625i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 32.9973i | 0.0524600i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −160.879 | −0.254958 | −0.127479 | − | 0.991841i | \(-0.540689\pi\) | ||||
−0.127479 | + | 0.991841i | \(0.540689\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 420.808 | + | 193.867i | 0.664783 | + | 0.306267i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 45.4087 | − | 26.2167i | 0.0715097 | − | 0.0412862i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −85.6515 | + | 148.353i | −0.134461 | + | 0.232893i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 728.908 | + | 257.708i | 1.14070 | + | 0.403299i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −267.894 | − | 154.669i | −0.417931 | − | 0.241293i | 0.276261 | − | 0.961083i | \(-0.410905\pi\) |
−0.694192 | + | 0.719790i | \(0.744238\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 197.296 | + | 341.726i | 0.306836 | + | 0.531456i | 0.977668 | − | 0.210153i | \(-0.0673963\pi\) |
−0.670832 | + | 0.741609i | \(0.734063\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.59133 | + | 12.1500i | 0.0133199 | + | 0.0188372i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 418.736i | − | 0.647196i | −0.946195 | − | 0.323598i | \(-0.895108\pi\) | ||
0.946195 | − | 0.323598i | \(-0.104892\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 863.908 | 1.33114 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 638.277 | − | 451.330i | 0.980456 | − | 0.693287i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 459.621 | − | 265.363i | 0.703861 | − | 0.406375i | −0.104923 | − | 0.994480i | \(-0.533460\pi\) |
0.808784 | + | 0.588106i | \(0.200126\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.8870 | + | 22.3209i | −0.0196748 | + | 0.0340778i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −288.272 | + | 815.358i | −0.438771 | + | 1.24103i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −310.204 | − | 179.096i | −0.470719 | − | 0.271770i | 0.245822 | − | 0.969315i | \(-0.420942\pi\) |
−0.716541 | + | 0.697545i | \(0.754276\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −111.136 | − | 192.493i | −0.168133 | − | 0.291214i | 0.769631 | − | 0.638489i | \(-0.220440\pi\) |
−0.937763 | + | 0.347275i | \(0.887107\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −47.1520 | + | 102.348i | −0.0711192 | + | 0.154371i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 154.941i | − | 0.232994i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31.0454 | 0.0465448 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −25.5362 | − | 277.145i | −0.0381708 | − | 0.414267i | ||||
\(670\) | 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 | \(-0.764401\pi\) |
0.953231 | + | 0.302241i | \(0.0977348\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 52.3485 | + | 13.2528i | 0.0775533 | + | 0.0196338i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −402.227 | − | 232.226i | −0.594131 | − | 0.343022i | 0.172598 | − | 0.984992i | \(-0.444784\pi\) |
−0.766729 | + | 0.641971i | \(0.778117\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −304.341 | − | 527.134i | −0.448220 | − | 0.776339i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 507.257 | − | 46.7389i | 0.744871 | − | 0.0686327i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1126.36i | 1.64913i | 0.565767 | + | 0.824565i | \(0.308580\pi\) | ||||
−0.565767 | + | 0.824565i | \(0.691420\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1219.45 | 1.78022 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1110.46 | − | 511.589i | −1.61638 | − | 0.744671i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −162.650 | + | 93.9063i | −0.236067 | + | 0.136294i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 518.841 | − | 898.658i | 0.750855 | − | 1.30052i | −0.196554 | − | 0.980493i | \(-0.562975\pi\) |
0.947409 | − | 0.320025i | \(-0.103691\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −98.5454 | − | 530.217i | −0.142201 | − | 0.765104i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 479.385 | + | 276.773i | 0.689763 | + | 0.398235i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 58.9546 | + | 102.112i | 0.0845833 | + | 0.146503i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 26.4245 | + | 37.3699i | 0.0378033 | + | 0.0534619i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 778.180i | − | 1.11010i | −0.831817 | − | 0.555050i | \(-0.812699\pi\) | ||
0.831817 | − | 0.555050i | \(-0.187301\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 81.2714 | 0.115607 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 179.591 | − | 126.990i | 0.254739 | − | 0.180128i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −868.296 | + | 501.311i | −1.22814 | + | 0.709068i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −586.014 | + | 1015.01i | −0.826536 | + | 1.43160i | 0.0742031 | + | 0.997243i | \(0.476359\pi\) |
−0.900739 | + | 0.434360i | \(0.856975\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 173.947 | + | 203.459i | 0.244651 | + | 0.286159i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 335.515 | + | 193.710i | 0.470568 | + | 0.271682i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −483.022 | − | 836.619i | −0.675556 | − | 1.17010i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −70.9699 | + | 154.047i | −0.0989817 | + | 0.214850i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 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 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −23.1799 | − | 251.571i | −0.0320607 | − | 0.347954i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.69694 | − | 3.28913i | 0.00785785 | − | 0.00453673i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 420.704 | − | 728.681i | 0.578685 | − | 1.00231i | −0.416945 | − | 0.908932i | \(-0.636899\pi\) |
0.995630 | − | 0.0933809i | \(-0.0297674\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −621.000 | + | 381.838i | −0.851852 | + | 0.523783i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.57654 | − | 0.910215i | −0.00215669 | − | 0.00124516i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 303.181 | + | 525.125i | 0.413617 | + | 0.716405i | 0.995282 | − | 0.0970229i | \(-0.0309320\pi\) |
−0.581665 | + | 0.813428i | \(0.697599\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −135.000 | + | 12.4389i | −0.183673 | + | 0.0169237i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 292.174i | − | 0.396437i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 389.362 | 0.526877 | 0.263439 | − | 0.964676i | \(-0.415143\pi\) | ||||
0.263439 | + | 0.964676i | \(0.415143\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 252.081 | + | 116.134i | 0.340190 | + | 0.156726i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 904.779 | − | 522.375i | 1.21774 | − | 0.703061i | 0.253304 | − | 0.967387i | \(-0.418483\pi\) |
0.964434 | + | 0.264325i | \(0.0851492\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 273.090 | − | 473.006i | 0.366564 | − | 0.634908i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 601.340 | − | 514.116i | 0.805007 | − | 0.688240i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 944.574 | + | 545.350i | 1.26111 | + | 0.728105i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 645.916 | + | 1118.76i | 0.860074 | + | 1.48969i | 0.871857 | + | 0.489761i | \(0.162916\pi\) |
−0.0117826 | + | 0.999931i | \(0.503751\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −379.151 | − | 536.201i | −0.503521 | − | 0.712086i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 1482.08i | − | 1.96302i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1042.36 | −1.37697 | −0.688483 | − | 0.725252i | \(-0.741723\pi\) | ||||
−0.688483 | + | 0.725252i | \(0.741723\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 218.227 | − | 154.310i | 0.287519 | − | 0.203307i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −281.607 | + | 162.586i | −0.370048 | + | 0.213647i | −0.673479 | − | 0.739206i | \(-0.735201\pi\) |
0.303431 | + | 0.952853i | \(0.401868\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 369.076 | − | 639.258i | 0.483717 | − | 0.837822i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −87.6811 | + | 16.2963i | −0.114616 | + | 0.0213023i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1561.28 | − | 901.405i | −2.03557 | − | 1.17523i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −171.348 | − | 296.783i | −0.222819 | − | 0.385934i | 0.732844 | − | 0.680397i | \(-0.238193\pi\) |
−0.955663 | + | 0.294463i | \(0.904859\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.0982 | − | 34.9428i | 0.0208797 | − | 0.0453214i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 532.579i | 0.688977i | 0.938791 | + | 0.344488i | \(0.111948\pi\) | ||||
−0.938791 | + | 0.344488i | \(0.888052\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 82.0908 | 0.105924 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 30.2362 | + | 328.154i | 0.0389140 | + | 0.422334i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 251.499 | − | 145.203i | 0.322849 | − | 0.186397i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 405.409 | − | 702.188i | 0.519089 | − | 0.899089i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −21.7951 | + | 86.0904i | −0.0278354 | + | 0.109949i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −887.317 | − | 512.293i | −1.13034 | − | 0.652602i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −51.9768 | − | 90.0264i | −0.0660442 | − | 0.114392i | 0.831113 | − | 0.556104i | \(-0.187704\pi\) |
−0.897157 | + | 0.441712i | \(0.854371\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1005.13 | + | 92.6135i | −1.27393 | + | 0.117381i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1284.07i | 1.62335i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1479.06 | −1.86514 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −135.000 | − | 62.1947i | −0.169811 | − | 0.0782324i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 956.331 | − | 552.138i | 1.19991 | − | 0.692770i | 0.239378 | − | 0.970927i | \(-0.423057\pi\) |
0.960536 | + | 0.278156i | \(0.0897233\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.4541 | + | 23.3031i | −0.0168386 | + | 0.0291654i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −351.092 | − | 124.130i | −0.438317 | − | 0.154968i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 785.469 | + | 453.491i | 0.978168 | + | 0.564746i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 155.682 | + | 269.648i | 0.193393 | + | 0.334967i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −104.697 | − | 148.064i | −0.129736 | − | 0.183474i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 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 | \(-0.649778\pi\) | ||||
−0.453368 | + | 0.891324i | \(0.649778\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −672.717 | + | 475.683i | −0.827451 | + | 0.585096i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1120.77 | − | 647.077i | 1.37518 | − | 0.793960i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.24183 | + | 3.88296i | −0.00274398 | + | 0.00475271i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −375.136 | + | 1061.05i | −0.458042 | + | 1.29554i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1078.45 | − | 622.645i | −1.31358 | − | 0.758398i | −0.330896 | − | 0.943667i | \(-0.607351\pi\) |
−0.982688 | + | 0.185269i | \(0.940684\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 771.129 | + | 1335.63i | 0.936973 | + | 1.62288i | 0.771077 | + | 0.636742i | \(0.219718\pi\) |
0.165896 | + | 0.986143i | \(0.446948\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 23.6969 | − | 51.4366i | 0.0287236 | − | 0.0623474i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 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 | \(-0.726542\pi\) | ||||
−0.653123 | + | 0.757252i | \(0.726542\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.4875 | − | 146.380i | −0.0162304 | − | 0.176149i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.3633 | − | 8.29263i | 0.0172428 | − | 0.00995514i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −125.842 | + | 217.964i | −0.150708 | + | 0.261035i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −772.711 | + | 794.407i | −0.923191 | + | 0.949112i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 903.778 | + | 521.797i | 1.07721 | + | 0.621927i | 0.930142 | − | 0.367200i | \(-0.119683\pi\) |
0.147067 | + | 0.989127i | \(0.453017\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −415.091 | − | 718.958i | −0.493568 | − | 0.854885i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1024.92 | − | 94.4361i | 1.21580 | − | 0.112024i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1137.80i | 1.34651i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 202.574 | 0.239167 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 935.701 | + | 431.079i | 1.10212 | + | 0.507749i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −141.439 | + | 81.6600i | −0.166204 | + | 0.0959577i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 236.909 | − | 410.338i | 0.277736 | − | 0.481053i | −0.693086 | − | 0.720855i | \(-0.743749\pi\) |
0.970822 | + | 0.239802i | \(0.0770827\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 40.1373 | + | 215.956i | 0.0469442 | + | 0.252580i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 793.939 | + | 458.381i | 0.926417 | + | 0.534867i | 0.885677 | − | 0.464303i | \(-0.153695\pi\) |
0.0407403 | + | 0.999170i | \(0.487028\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 478.901 | + | 829.480i | 0.557510 | + | 0.965635i | 0.997704 | + | 0.0677322i | \(0.0215764\pi\) |
−0.440194 | + | 0.897903i | \(0.645090\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 679.863 | + | 961.471i | 0.789620 | + | 1.11669i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 524.200i | − | 0.607416i | −0.952765 | − | 0.303708i | \(-0.901775\pi\) | ||
0.952765 | − | 0.303708i | \(-0.0982247\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −521.908 | −0.603362 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −698.994 | + | 494.264i | −0.806222 | + | 0.570085i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 243.121 | − | 140.366i | 0.279771 | − | 0.161526i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −304.855 | + | 528.025i | −0.350006 | + | 0.606228i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 560.743 | + | 655.878i | 0.642317 | + | 0.751292i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −657.067 | − | 379.358i | −0.750933 | − | 0.433551i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 503.878 | + | 872.742i | 0.574547 | + | 0.995145i | 0.996091 | + | 0.0883370i | \(0.0281552\pi\) |
−0.421543 | + | 0.906808i | \(0.638511\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −359.583 | + | 780.511i | −0.409082 | + | 0.887954i | ||||
\(880\) | 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 | \(0.446722\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −130.909 | − | 1420.75i | −0.147919 | − | 1.60537i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −497.794 | + | 287.402i | −0.561211 | + | 0.324015i | −0.753631 | − | 0.657297i | \(-0.771700\pi\) |
0.192420 | + | 0.981313i | \(0.438366\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −32.0306 | + | 55.4787i | −0.0360299 | + | 0.0624057i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 274.704 | + | 713.486i | 0.308310 | + | 0.800770i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 57.3949 | + | 33.1370i | 0.0642720 | + | 0.0371075i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −740.636 | − | 1282.82i | −0.827526 | − | 1.43332i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −555.393 | + | 51.1741i | −0.619168 | + | 0.0570503i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 135.004i | 0.150171i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.1837 | 0.0201817 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −16.5125 | − | 7.60734i | −0.0182863 | − | 0.00842452i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −167.046 | + | 96.4443i | −0.184582 | + | 0.106568i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −255.037 | + | 441.737i | −0.281187 | + | 0.487031i | −0.971677 | − | 0.236311i | \(-0.924062\pi\) |
0.690490 | + | 0.723342i | \(0.257395\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1080.36 | − | 923.656i | 1.18852 | − | 1.01612i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −803.127 | − | 463.685i | −0.881588 | − | 0.508985i | −0.0104064 | − | 0.999946i | \(-0.503313\pi\) |
−0.871182 | + | 0.490961i | \(0.836646\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −414.863 | − | 718.564i | −0.454396 | − | 0.787036i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −675.817 | − | 955.750i | −0.738598 | − | 1.04454i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 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 | ||||||||
\(921\) | 377.444 | − | 266.893i | 0.409820 | − | 0.289786i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1465.33 | + | 846.010i | −1.58757 | + | 0.916587i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.3031 | + | 29.9698i | −0.0187060 | + | 0.0323998i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −257.811 | + | 47.9164i | −0.278113 | + | 0.0516897i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 293.576 | + | 169.496i | 0.316013 | + | 0.182450i | 0.649614 | − | 0.760264i | \(-0.274931\pi\) |
−0.333601 | + | 0.942714i | \(0.608264\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.4245 | − | 35.3763i | −0.0219382 | − | 0.0379981i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 90.3627 | − | 196.141i | 0.0968518 | − | 0.210227i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 93.5307i | 0.100033i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1322.21 | 1.41111 | 0.705556 | − | 0.708655i | \(-0.250698\pi\) | ||||
0.705556 | + | 0.708655i | \(0.250698\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 101.185 | + | 1098.17i | 0.107759 | + | 1.16951i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 310.984 | − | 179.547i | 0.330482 | − | 0.190804i | −0.325573 | − | 0.945517i | \(-0.605557\pi\) |
0.656055 | + | 0.754713i | \(0.272224\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −291.795 | + | 505.404i | −0.309433 | + | 0.535953i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −857.043 | + | 242.408i | −0.906924 | + | 0.256517i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 671.855 | + | 387.896i | 0.709457 | + | 0.409605i | 0.810860 | − | 0.585240i | \(-0.199000\pi\) |
−0.101403 | + | 0.994845i | \(0.532333\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −946.347 | − | 1639.12i | −0.997205 | − | 1.72721i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −321.431 | + | 29.6168i | −0.337992 | + | 0.0311428i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 465.082i | − | 0.488019i | −0.969773 | − | 0.244010i | \(-0.921537\pi\) | ||
0.969773 | − | 0.244010i | \(-0.0784628\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −93.1362 | −0.0975248 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 84.5908 | + | 38.9711i | 0.0883917 | + | 0.0407222i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1290.28 | + | 744.942i | −1.34544 | + | 0.776791i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −361.863 | + | 626.765i | −0.376548 | + | 0.652200i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1457.82 | − | 515.416i | −1.51383 | − | 0.535219i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 429.543 | + | 247.997i | 0.445123 | + | 0.256992i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −612.113 | − | 1060.21i | −0.633002 | − | 1.09639i | −0.986935 | − | 0.161121i | \(-0.948489\pi\) |
0.353933 | − | 0.935271i | \(-0.384844\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −15.5143 | − | 21.9405i | −0.0160106 | − | 0.0226424i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 658.702i | 0.678375i | 0.940719 | + | 0.339188i | \(0.110152\pi\) | ||||
−0.940719 | + | 0.339188i | \(0.889848\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −676.303 | −0.695070 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −96.4949 | + | 68.2322i | −0.0989691 | + | 0.0699817i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1314.92 | − | 759.170i | 1.34588 | − | 0.777042i | 0.358214 | − | 0.933639i | \(-0.383386\pi\) |
0.987663 | + | 0.156597i | \(0.0500525\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −195.272 | + | 338.222i | −0.199461 | + | 0.345477i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −348.817 | + | 986.604i | −0.355573 | + | 1.00571i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 716.930 | + | 413.920i | 0.729329 | + | 0.421078i | 0.818177 | − | 0.574967i | \(-0.194985\pi\) |
−0.0888477 | + | 0.996045i | \(0.528318\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 416.636 | + | 721.634i | 0.422980 | + | 0.732624i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −112.446 | + | 244.075i | −0.113927 | + | 0.247289i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 9.01020i | − | 0.00911041i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 429.546 | 0.433447 | 0.216723 | − | 0.976233i | \(-0.430463\pi\) | ||||
0.216723 | + | 0.976233i | \(0.430463\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.73369 | + | 51.3747i | 0.00476706 | + | 0.0517369i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 29.3189 | − | 16.9273i | 0.0294662 | − | 0.0170123i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −347.499 | + | 601.886i | −0.348545 | + | 0.603697i | −0.985991 | − | 0.166798i | \(-0.946657\pi\) |
0.637447 | + | 0.770495i | \(0.279991\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −127.151 | − | 449.547i | −0.127278 | − | 0.449997i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))