Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1350,3,Mod(449,1350)]
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([5, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1350.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.k (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: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 18) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 899.3 | ||
Root | \(-0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1350.899 |
Dual form | 1350.3.k.a.449.3 |
$q$-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 \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1027\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 1.22474i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | − | 1.73205i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.49794 | + | 3.17423i | 0.785419 | + | 0.453462i | 0.838347 | − | 0.545136i | \(-0.183522\pi\) |
−0.0529281 | + | 0.998598i | \(0.516855\pi\) | |||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 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 | ||||||||
\(13\) | 17.0580 | − | 9.84847i | 1.31216 | − | 0.757575i | 0.329704 | − | 0.944084i | \(-0.393051\pi\) |
0.982453 | + | 0.186510i | \(0.0597176\pi\) | |||||||
\(14\) | 7.77526 | − | 4.48905i | 0.555375 | − | 0.320646i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.90702 | 0.112178 | 0.0560889 | − | 0.998426i | \(-0.482137\pi\) | ||||
0.0560889 | + | 0.998426i | \(0.482137\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.69694 | −0.247207 | −0.123604 | − | 0.992332i | \(-0.539445\pi\) | ||||
−0.123604 | + | 0.992332i | \(0.539445\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −11.5601 | + | 6.67423i | −0.525460 | + | 0.303374i | ||||
\(23\) | −4.71940 | − | 8.17423i | −0.205191 | − | 0.355402i | 0.745002 | − | 0.667062i | \(-0.232448\pi\) |
−0.950194 | + | 0.311660i | \(0.899115\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 27.8557i | − | 1.07137i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 12.6969i | − | 0.453462i | ||||||
\(29\) | −2.84847 | − | 1.64456i | −0.0982231 | − | 0.0567091i | 0.450084 | − | 0.892986i | \(-0.351394\pi\) |
−0.548307 | + | 0.836277i | \(0.684727\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 20.5227 | + | 35.5464i | 0.662023 | + | 1.14666i | 0.980083 | + | 0.198587i | \(0.0636351\pi\) |
−0.318061 | + | 0.948070i | \(0.603032\pi\) | |||||||
\(32\) | 2.82843 | + | 4.89898i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.34847 | − | 2.33562i | 0.0396609 | − | 0.0686946i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 17.3031i | − | 0.467650i | −0.972279 | − | 0.233825i | \(-0.924876\pi\) | ||
0.972279 | − | 0.233825i | \(-0.0751243\pi\) | |||||||
\(38\) | −3.32124 | + | 5.75255i | −0.0874010 | + | 0.151383i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 53.5454 | − | 30.9145i | 1.30599 | − | 0.754011i | 0.324562 | − | 0.945864i | \(-0.394783\pi\) |
0.981424 | + | 0.191853i | \(0.0614498\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.826701 | − | 0.477296i | −0.0192256 | − | 0.0110999i | 0.490356 | − | 0.871522i | \(-0.336867\pi\) |
−0.509582 | + | 0.860422i | \(0.670200\pi\) | |||||||
\(44\) | 18.8776i | 0.429036i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −13.3485 | −0.290184 | ||||||||
\(47\) | 7.05501 | − | 12.2196i | 0.150107 | − | 0.259992i | −0.781160 | − | 0.624331i | \(-0.785372\pi\) |
0.931267 | + | 0.364339i | \(0.118705\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.34847 | − | 7.53177i | −0.0887443 | − | 0.153710i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −34.1161 | − | 19.6969i | −0.656079 | − | 0.378787i | ||||
\(53\) | −9.53512 | −0.179908 | −0.0899539 | − | 0.995946i | \(-0.528672\pi\) | ||||
−0.0899539 | + | 0.995946i | \(0.528672\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −15.5505 | − | 8.97809i | −0.277688 | − | 0.160323i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.02834 | + | 2.32577i | −0.0694542 | + | 0.0400994i | ||||
\(59\) | 79.2650 | − | 45.7637i | 1.34348 | − | 0.775656i | 0.356160 | − | 0.934425i | \(-0.384086\pi\) |
0.987316 | + | 0.158769i | \(0.0507526\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 37.5454 | − | 65.0306i | 0.615498 | − | 1.06607i | −0.374798 | − | 0.927106i | \(-0.622288\pi\) |
0.990297 | − | 0.138968i | \(-0.0443786\pi\) | |||||||
\(62\) | 58.0470 | 0.936241 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −26.8075 | + | 15.4773i | −0.400111 | + | 0.231004i | −0.686532 | − | 0.727100i | \(-0.740868\pi\) |
0.286421 | + | 0.958104i | \(0.407535\pi\) | |||||||
\(68\) | −1.90702 | − | 3.30306i | −0.0280445 | − | 0.0485744i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 85.9026i | − | 1.20990i | −0.796265 | − | 0.604948i | \(-0.793194\pi\) | ||
0.796265 | − | 0.604948i | \(-0.206806\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 96.0908i | − | 1.31631i | −0.752881 | − | 0.658156i | \(-0.771337\pi\) | ||
0.752881 | − | 0.658156i | \(-0.228663\pi\) | |||||||
\(74\) | −21.1918 | − | 12.2351i | −0.286376 | − | 0.165339i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.69694 | + | 8.13534i | 0.0618018 | + | 0.107044i | ||||
\(77\) | −29.9609 | − | 51.8939i | −0.389103 | − | 0.673946i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.8712 | − | 25.7576i | 0.188243 | − | 0.326046i | −0.756422 | − | 0.654084i | \(-0.773054\pi\) |
0.944664 | + | 0.328038i | \(0.106388\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 87.4393i | − | 1.06633i | ||||||
\(83\) | −43.9530 | + | 76.1288i | −0.529554 | + | 0.917215i | 0.469852 | + | 0.882745i | \(0.344307\pi\) |
−0.999406 | + | 0.0344693i | \(0.989026\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.16913 | + | 0.674999i | −0.0135946 | + | 0.00784882i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 23.1202 | + | 13.3485i | 0.262730 | + | 0.151687i | ||||
\(89\) | − | 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 | ||||||||
\(92\) | −9.43879 | + | 16.3485i | −0.102596 | + | 0.177701i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.97730 | − | 17.2812i | −0.106141 | − | 0.183842i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 83.0333 | + | 47.9393i | 0.856013 | + | 0.494219i | 0.862675 | − | 0.505758i | \(-0.168787\pi\) |
−0.00666202 | + | 0.999978i | \(0.502121\pi\) | |||||||
\(98\) | −12.2993 | −0.125503 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 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 | ||||||||
\(103\) | 25.2327 | − | 14.5681i | 0.244978 | − | 0.141438i | −0.372485 | − | 0.928038i | \(-0.621494\pi\) |
0.617462 | + | 0.786600i | \(0.288161\pi\) | |||||||
\(104\) | −48.2474 | + | 27.8557i | −0.463918 | + | 0.267843i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.74235 | + | 11.6781i | −0.0636070 | + | 0.110171i | ||||
\(107\) | −171.805 | −1.60566 | −0.802829 | − | 0.596210i | \(-0.796673\pi\) | ||||
−0.802829 | + | 0.596210i | \(0.796673\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −116.272 | −1.06672 | −0.533360 | − | 0.845888i | \(-0.679071\pi\) | ||||
−0.533360 | + | 0.845888i | \(0.679071\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −21.9917 | + | 12.6969i | −0.196355 | + | 0.113366i | ||||
\(113\) | −101.132 | − | 175.166i | −0.894976 | − | 1.55014i | −0.833834 | − | 0.552015i | \(-0.813859\pi\) |
−0.0611424 | − | 0.998129i | \(-0.519474\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.57826i | 0.0567091i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 129.439i | − | 1.09694i | ||||||
\(119\) | 10.4847 | + | 6.05334i | 0.0881067 | + | 0.0508684i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −15.9546 | − | 27.6342i | −0.131856 | − | 0.228382i | ||||
\(122\) | −53.0972 | − | 91.9671i | −0.435223 | − | 0.753829i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 41.0454 | − | 71.0927i | 0.331011 | − | 0.573328i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 10.0908i | − | 0.0794552i | −0.999211 | − | 0.0397276i | \(-0.987351\pi\) | ||
0.999211 | − | 0.0397276i | \(-0.0126490\pi\) | |||||||
\(128\) | 5.65685 | − | 9.79796i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 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 | ||||||||
\(133\) | −25.8235 | − | 14.9092i | −0.194161 | − | 0.112099i | ||||
\(134\) | 43.7764i | 0.326690i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.39388 | −0.0396609 | ||||||||
\(137\) | −117.342 | + | 203.242i | −0.856511 | + | 1.48352i | 0.0187249 | + | 0.999825i | \(0.494039\pi\) |
−0.875236 | + | 0.483696i | \(0.839294\pi\) | |||||||
\(138\) | 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 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −105.209 | − | 60.7423i | −0.740907 | − | 0.427763i | ||||
\(143\) | −185.915 | −1.30011 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −117.687 | − | 67.9465i | −0.806074 | − | 0.465387i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −29.9698 | + | 17.3031i | −0.202499 | + | 0.116913i | ||||
\(149\) | −91.0301 | + | 52.5563i | −0.610940 | + | 0.352727i | −0.773333 | − | 0.634000i | \(-0.781412\pi\) |
0.162393 | + | 0.986726i | \(0.448079\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 142.614 | − | 247.014i | 0.944460 | − | 1.63585i | 0.187632 | − | 0.982239i | \(-0.439919\pi\) |
0.756828 | − | 0.653614i | \(-0.226748\pi\) | |||||||
\(152\) | 13.2849 | 0.0874010 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −84.7423 | −0.550275 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 170.764 | − | 98.5908i | 1.08767 | − | 0.627967i | 0.154715 | − | 0.987959i | \(-0.450554\pi\) |
0.932955 | + | 0.359992i | \(0.117221\pi\) | |||||||
\(158\) | −21.0310 | − | 36.4268i | −0.133108 | − | 0.230549i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 59.9219i | − | 0.372186i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 249.060i | − | 1.52798i | −0.645230 | − | 0.763988i | \(-0.723238\pi\) | ||
0.645230 | − | 0.763988i | \(-0.276762\pi\) | |||||||
\(164\) | −107.091 | − | 61.8289i | −0.652993 | − | 0.377006i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 62.1589 | + | 107.662i | 0.374451 | + | 0.648569i | ||||
\(167\) | −24.2182 | − | 41.9472i | −0.145019 | − | 0.251181i | 0.784361 | − | 0.620305i | \(-0.212991\pi\) |
−0.929380 | + | 0.369124i | \(0.879658\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 109.485 | − | 189.633i | 0.647838 | − | 1.12209i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.90918i | 0.0110999i | ||||||||
\(173\) | 50.2206 | − | 86.9847i | 0.290293 | − | 0.502802i | −0.683586 | − | 0.729870i | \(-0.739581\pi\) |
0.973879 | + | 0.227068i | \(0.0729140\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 32.6969 | − | 18.8776i | 0.185778 | − | 0.107259i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −50.6757 | − | 29.2577i | −0.284695 | − | 0.164369i | ||||
\(179\) | 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 | \(0.467301\pi\) | |||||||
\(182\) | 88.4205 | − | 153.149i | 0.485827 | − | 0.841476i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 13.3485 | + | 23.1202i | 0.0725460 | + | 0.125653i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.5885 | − | 9.00000i | −0.0833607 | − | 0.0481283i | ||||
\(188\) | −28.2201 | −0.150107 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.5227 | + | 8.96204i | 0.0812707 | + | 0.0469217i | 0.540085 | − | 0.841611i | \(-0.318392\pi\) |
−0.458814 | + | 0.888532i | \(0.651726\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −82.6657 | + | 47.7270i | −0.428319 | + | 0.247290i | −0.698630 | − | 0.715483i | \(-0.746207\pi\) |
0.270311 | + | 0.962773i | \(0.412873\pi\) | |||||||
\(194\) | 117.427 | − | 67.7964i | 0.605293 | − | 0.349466i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.69694 | + | 15.0635i | −0.0443721 | + | 0.0768548i | ||||
\(197\) | 160.363 | 0.814026 | 0.407013 | − | 0.913422i | \(-0.366570\pi\) | ||||
0.407013 | + | 0.913422i | \(0.366570\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.51531 | −0.0327402 | −0.0163701 | − | 0.999866i | \(-0.505211\pi\) | ||||
−0.0163701 | + | 0.999866i | \(0.505211\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 193.425 | − | 111.674i | 0.957552 | − | 0.552843i | ||||
\(203\) | −10.4405 | − | 18.0834i | −0.0514309 | − | 0.0890809i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 41.2048i | − | 0.200024i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 78.7878i | 0.378787i | ||||||||
\(209\) | 38.3939 | + | 22.1667i | 0.183703 | + | 0.106061i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 77.2196 | + | 133.748i | 0.365970 | + | 0.633878i | 0.988931 | − | 0.148374i | \(-0.0474040\pi\) |
−0.622961 | + | 0.782253i | \(0.714071\pi\) | |||||||
\(212\) | 9.53512 | + | 16.5153i | 0.0449770 | + | 0.0779024i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −121.485 | + | 210.418i | −0.567685 | + | 0.983260i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 260.576i | 1.20081i | ||||||||
\(218\) | −82.2170 | + | 142.404i | −0.377142 | + | 0.653230i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 32.5301 | − | 18.7813i | 0.147195 | − | 0.0849831i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −80.3437 | − | 46.3865i | −0.360286 | − | 0.208011i | 0.308920 | − | 0.951088i | \(-0.400032\pi\) |
−0.669206 | + | 0.743077i | \(0.733366\pi\) | |||||||
\(224\) | 35.9124i | 0.160323i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −286.045 | −1.26569 | ||||||||
\(227\) | −84.9010 | + | 147.053i | −0.374013 | + | 0.647810i | −0.990179 | − | 0.139807i | \(-0.955352\pi\) |
0.616166 | + | 0.787617i | \(0.288685\pi\) | |||||||
\(228\) | 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 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.05669 | + | 4.65153i | 0.0347271 | + | 0.0200497i | ||||
\(233\) | −15.2562 | −0.0654772 | −0.0327386 | − | 0.999464i | \(-0.510423\pi\) | ||||
−0.0327386 | + | 0.999464i | \(0.510423\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −158.530 | − | 91.5274i | −0.671738 | − | 0.387828i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 14.8276 | − | 8.56072i | 0.0623008 | − | 0.0359694i | ||||
\(239\) | 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 | \(0.222567\pi\) | |||||||
\(242\) | −45.1264 | −0.186473 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −150.182 | −0.615498 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −80.1206 | + | 46.2577i | −0.324375 | + | 0.187278i | ||||
\(248\) | −58.0470 | − | 100.540i | −0.234060 | − | 0.405404i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 218.903i | 0.872123i | 0.899917 | + | 0.436062i | \(0.143627\pi\) | ||||
−0.899917 | + | 0.436062i | \(0.856373\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 89.0908i | 0.352138i | ||||||||
\(254\) | −12.3587 | − | 7.13528i | −0.0486562 | − | 0.0280917i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −6.41212 | − | 11.1061i | −0.0249499 | − | 0.0432145i | 0.853281 | − | 0.521452i | \(-0.174609\pi\) |
−0.878231 | + | 0.478237i | \(0.841276\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 54.9240 | − | 95.1311i | 0.212062 | − | 0.367302i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.01479i | 0.0267740i | ||||||||
\(263\) | 168.232 | − | 291.386i | 0.639666 | − | 1.10793i | −0.345840 | − | 0.938293i | \(-0.612406\pi\) |
0.985506 | − | 0.169640i | \(-0.0542605\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −36.5199 | + | 21.0848i | −0.137293 | + | 0.0792661i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 53.6149 | + | 30.9546i | 0.200056 | + | 0.115502i | ||||
\(269\) | − | 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 | \(0.330862\pi\) | |||||||
\(272\) | −3.81405 | + | 6.60612i | −0.0140222 | + | 0.0242872i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 165.947 | + | 287.428i | 0.605645 | + | 1.04901i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −42.4352 | − | 24.5000i | −0.153196 | − | 0.0884477i | 0.421442 | − | 0.906855i | \(-0.361524\pi\) |
−0.574638 | + | 0.818407i | \(0.694857\pi\) | |||||||
\(278\) | 150.656 | 0.541929 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 297.121 | + | 171.543i | 1.05737 | + | 0.610473i | 0.924704 | − | 0.380688i | \(-0.124313\pi\) |
0.132666 | + | 0.991161i | \(0.457646\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −297.401 | + | 171.704i | −1.05089 | + | 0.606729i | −0.922897 | − | 0.385047i | \(-0.874185\pi\) |
−0.127988 | + | 0.991776i | \(0.540852\pi\) | |||||||
\(284\) | −148.788 | + | 85.9026i | −0.523901 | + | 0.302474i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −131.462 | + | 227.699i | −0.459657 | + | 0.796150i | ||||
\(287\) | 392.519 | 1.36766 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −285.363 | −0.987416 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −166.434 | + | 96.0908i | −0.569980 | + | 0.329078i | ||||
\(293\) | 143.226 | + | 248.076i | 0.488828 | + | 0.846674i | 0.999917 | − | 0.0128532i | \(-0.00409141\pi\) |
−0.511090 | + | 0.859527i | \(0.670758\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 48.9404i | 0.165339i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 148.652i | 0.498831i | ||||||||
\(299\) | −161.007 | − | 92.9577i | −0.538486 | − | 0.310895i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.03010 | − | 5.24829i | −0.0100668 | − | 0.0174362i | ||||
\(302\) | −201.686 | − | 349.330i | −0.667834 | − | 1.15672i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 9.39388 | − | 16.2707i | 0.0309009 | − | 0.0535219i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 154.091i | − | 0.501924i | −0.967997 | − | 0.250962i | \(-0.919253\pi\) | ||
0.967997 | − | 0.250962i | \(-0.0807470\pi\) | |||||||
\(308\) | −59.9219 | + | 103.788i | −0.194552 | + | 0.336973i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 62.3411 | − | 35.9926i | 0.200454 | − | 0.115732i | −0.396413 | − | 0.918072i | \(-0.629745\pi\) |
0.596867 | + | 0.802340i | \(0.296412\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 318.356 | + | 183.803i | 1.01711 | + | 0.587230i | 0.913266 | − | 0.407363i | \(-0.133552\pi\) |
0.103846 | + | 0.994593i | \(0.466885\pi\) | |||||||
\(314\) | − | 278.857i | − | 0.888079i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −59.4847 | −0.188243 | ||||||||
\(317\) | 53.7987 | − | 93.1821i | 0.169712 | − | 0.293950i | −0.768607 | − | 0.639722i | \(-0.779050\pi\) |
0.938319 | + | 0.345772i | \(0.112383\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.5227 | + | 26.8861i | 0.0486605 | + | 0.0842825i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −73.3890 | − | 42.3712i | −0.227916 | − | 0.131587i | ||||
\(323\) | −8.95717 | −0.0277312 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −305.035 | − | 176.112i | −0.935691 | − | 0.540221i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −151.449 | + | 87.4393i | −0.461736 | + | 0.266583i | ||||
\(329\) | 77.5760 | − | 44.7885i | 0.235793 | − | 0.136135i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.59873 | + | 14.8934i | −0.0259780 | + | 0.0449953i | −0.878722 | − | 0.477334i | \(-0.841603\pi\) |
0.852744 | + | 0.522329i | \(0.174937\pi\) | |||||||
\(332\) | 175.812 | 0.529554 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −68.4995 | −0.205088 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −315.574 | + | 182.197i | −0.936422 | + | 0.540644i | −0.888837 | − | 0.458223i | \(-0.848486\pi\) |
−0.0475854 | + | 0.998867i | \(0.515153\pi\) | |||||||
\(338\) | −154.835 | − | 268.182i | −0.458091 | − | 0.793437i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 387.419i | − | 1.13613i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 366.287i | − | 1.06789i | ||||||
\(344\) | 2.33826 | + | 1.35000i | 0.00679728 | + | 0.00392441i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −71.0227 | − | 123.015i | −0.205268 | − | 0.355534i | ||||
\(347\) | 291.697 | + | 505.234i | 0.840626 | + | 1.45601i | 0.889366 | + | 0.457196i | \(0.151146\pi\) |
−0.0487402 | + | 0.998811i | \(0.515521\pi\) | |||||||
\(348\) | 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 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 53.3939i | − | 0.151687i | ||||||
\(353\) | −18.8078 | + | 32.5760i | −0.0532798 | + | 0.0922834i | −0.891435 | − | 0.453148i | \(-0.850301\pi\) |
0.838155 | + | 0.545431i | \(0.183634\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −71.6663 | + | 41.3766i | −0.201310 | + | 0.116226i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 349.139 | + | 201.576i | 0.975249 | + | 0.563060i | ||||
\(359\) | 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 | ||||||||
\(362\) | 26.2488 | − | 45.4643i | 0.0725105 | − | 0.125592i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −125.045 | − | 216.585i | −0.343531 | − | 0.595014i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.7755 | − | 16.6135i | −0.0784072 | − | 0.0452684i | 0.460284 | − | 0.887772i | \(-0.347748\pi\) |
−0.538691 | + | 0.842503i | \(0.681081\pi\) | |||||||
\(368\) | 37.7552 | 0.102596 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −52.4235 | − | 30.2667i | −0.141303 | − | 0.0815814i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −194.881 | + | 112.515i | −0.522470 | + | 0.301648i | −0.737945 | − | 0.674861i | \(-0.764203\pi\) |
0.215475 | + | 0.976509i | \(0.430870\pi\) | |||||||
\(374\) | −22.0454 | + | 12.7279i | −0.0589449 | + | 0.0340319i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −19.9546 | + | 34.5624i | −0.0530707 | + | 0.0919212i | ||||
\(377\) | −64.7858 | −0.171846 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 166.334 | 0.438875 | 0.219438 | − | 0.975627i | \(-0.429578\pi\) | ||||
0.219438 | + | 0.975627i | \(0.429578\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 21.9524 | − | 12.6742i | 0.0574671 | − | 0.0331786i | ||||
\(383\) | 368.493 | + | 638.249i | 0.962124 | + | 1.66645i | 0.717152 | + | 0.696917i | \(0.245445\pi\) |
0.244972 | + | 0.969530i | \(0.421221\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 134.992i | 0.349721i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 191.757i | − | 0.494219i | ||||||
\(389\) | −146.682 | − | 84.6867i | −0.377074 | − | 0.217704i | 0.299471 | − | 0.954106i | \(-0.403190\pi\) |
−0.676544 | + | 0.736402i | \(0.736523\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.00000 | − | 15.5885i | −0.0230179 | − | 0.0398682i | ||||
\(392\) | 12.2993 | + | 21.3031i | 0.0313758 | + | 0.0543445i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 113.394 | − | 196.404i | 0.287802 | − | 0.498487i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 256.272i | 0.645523i | 0.946480 | + | 0.322761i | \(0.104611\pi\) | ||||
−0.946480 | + | 0.322761i | \(0.895389\pi\) | |||||||
\(398\) | −4.60702 | + | 7.97959i | −0.0115754 | + | 0.0200492i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −226.364 | + | 130.691i | −0.564498 | + | 0.325913i | −0.754949 | − | 0.655784i | \(-0.772338\pi\) |
0.190451 | + | 0.981697i | \(0.439005\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 700.155 | + | 404.234i | 1.73736 | + | 1.00306i | ||||
\(404\) | − | 315.862i | − | 0.781838i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −29.5301 | −0.0727342 | ||||||||
\(407\) | −81.6600 | + | 141.439i | −0.200639 | + | 0.347517i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −221.894 | − | 384.331i | −0.542528 | − | 0.939686i | −0.998758 | − | 0.0498240i | \(-0.984134\pi\) |
0.456230 | − | 0.889862i | \(-0.349199\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −50.4654 | − | 29.1362i | −0.122489 | − | 0.0707190i | ||||
\(413\) | 581.059 | 1.40692 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 96.4949 | + | 55.7114i | 0.231959 | + | 0.133922i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 54.2971 | − | 31.3485i | 0.129897 | − | 0.0749963i | ||||
\(419\) | 9.32525 | − | 5.38394i | 0.0222560 | − | 0.0128495i | −0.488831 | − | 0.872379i | \(-0.662576\pi\) |
0.511087 | + | 0.859529i | \(0.329243\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −127.152 | + | 220.233i | −0.302023 | + | 0.523119i | −0.976594 | − | 0.215091i | \(-0.930995\pi\) |
0.674571 | + | 0.738210i | \(0.264328\pi\) | |||||||
\(422\) | 218.410 | 0.517560 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 26.9694 | 0.0636070 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 412.844 | − | 238.356i | 0.966849 | − | 0.558210i | ||||
\(428\) | 171.805 | + | 297.576i | 0.401414 | + | 0.695270i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 698.663i | 1.62103i | 0.585719 | + | 0.810514i | \(0.300812\pi\) | ||||
−0.585719 | + | 0.810514i | \(0.699188\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 211.728i | 0.488978i | 0.969652 | + | 0.244489i | \(0.0786202\pi\) | ||||
−0.969652 | + | 0.244489i | \(0.921380\pi\) | |||||||
\(434\) | 319.139 | + | 184.255i | 0.735342 | + | 0.424550i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 116.272 | + | 201.390i | 0.266680 | + | 0.461903i | ||||
\(437\) | 22.1667 | + | 38.3939i | 0.0507247 | + | 0.0878578i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 139.931 | − | 242.368i | 0.318750 | − | 0.552092i | −0.661477 | − | 0.749965i | \(-0.730070\pi\) |
0.980228 | + | 0.197874i | \(0.0634035\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 53.1214i | − | 0.120184i | ||||||
\(443\) | −275.627 | + | 477.400i | −0.622183 | + | 1.07765i | 0.366895 | + | 0.930262i | \(0.380421\pi\) |
−0.989078 | + | 0.147391i | \(0.952913\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −113.623 | + | 65.6004i | −0.254761 | + | 0.147086i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 43.9835 | + | 25.3939i | 0.0981774 | + | 0.0566828i | ||||
\(449\) | − | 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 | ||||||||
\(452\) | −202.265 | + | 350.333i | −0.447488 | + | 0.775072i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 120.068 | + | 207.964i | 0.264467 | + | 0.458071i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 79.9898 | + | 46.1821i | 0.175032 | + | 0.101055i | 0.584957 | − | 0.811065i | \(-0.301112\pi\) |
−0.409924 | + | 0.912120i | \(0.634445\pi\) | |||||||
\(458\) | 576.356 | 1.25842 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 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 | ||||||||
\(463\) | −442.368 | + | 255.401i | −0.955438 | + | 0.551623i | −0.894766 | − | 0.446535i | \(-0.852658\pi\) |
−0.0606723 | + | 0.998158i | \(0.519324\pi\) | |||||||
\(464\) | 11.3939 | − | 6.57826i | 0.0245558 | − | 0.0141773i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.7878 | + | 18.6849i | −0.0231497 | + | 0.0400964i | ||||
\(467\) | −833.657 | −1.78513 | −0.892567 | − | 0.450915i | \(-0.851098\pi\) | ||||
−0.892567 | + | 0.450915i | \(0.851098\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −196.514 | −0.419007 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −224.195 | + | 129.439i | −0.474990 | + | 0.274236i | ||||
\(473\) | 4.50510 | + | 7.80306i | 0.00952452 | + | 0.0164970i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 24.2134i | − | 0.0508684i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 79.9546i | − | 0.167269i | ||||||
\(479\) | 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 | ||||
\(482\) | 59.5471 | + | 103.139i | 0.123542 | + | 0.213980i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −31.9092 | + | 55.2683i | −0.0659281 | + | 0.114191i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 351.666i | 0.722107i | 0.932545 | + | 0.361054i | \(0.117583\pi\) | ||||
−0.932545 | + | 0.361054i | \(0.882417\pi\) | |||||||
\(488\) | −106.194 | + | 183.934i | −0.217612 | + | 0.376914i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 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 | ||||||||
\(493\) | −5.43210 | − | 3.13622i | −0.0110185 | − | 0.00636151i | ||||
\(494\) | 130.836i | 0.264851i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −164.182 | −0.331011 | ||||||||
\(497\) | 272.675 | − | 472.287i | 0.548642 | − | 0.950276i | ||||
\(498\) | 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 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 268.100 | + | 154.788i | 0.534064 | + | 0.308342i | ||||
\(503\) | −286.891 | −0.570360 | −0.285180 | − | 0.958474i | \(-0.592053\pi\) | ||||
−0.285180 | + | 0.958474i | \(0.592053\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 109.114 | + | 62.9967i | 0.215639 | + | 0.124499i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −17.4778 | + | 10.0908i | −0.0344051 | + | 0.0198638i | ||||
\(509\) | 755.454 | − | 436.161i | 1.48419 | − | 0.856898i | 0.484353 | − | 0.874873i | \(-0.339055\pi\) |
0.999838 | + | 0.0179741i | \(0.00572163\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 305.015 | − | 528.301i | 0.596898 | − | 1.03386i | ||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −18.1362 | −0.0352845 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −115.339 | + | 66.5908i | −0.223092 | + | 0.128802i | ||||
\(518\) | −77.6742 | − | 134.536i | −0.149950 | − | 0.259721i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 206.132i | 0.395646i | 0.980238 | + | 0.197823i | \(0.0633872\pi\) | ||||
−0.980238 | + | 0.197823i | \(0.936613\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 884.817i | 1.69181i | 0.533333 | + | 0.845906i | \(0.320939\pi\) | ||||
−0.533333 | + | 0.845906i | \(0.679061\pi\) | |||||||
\(524\) | 8.59133 | + | 4.96021i | 0.0163957 | + | 0.00946604i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −237.916 | − | 412.083i | −0.452312 | − | 0.783427i | ||||
\(527\) | 39.1373 | + | 67.7878i | 0.0742643 | + | 0.128630i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 219.955 | − | 380.973i | 0.415793 | − | 0.720175i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 59.6367i | 0.112099i | ||||||||
\(533\) | 608.920 | − | 1054.68i | 1.14244 | − | 1.97876i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 75.8230 | − | 43.7764i | 0.141461 | − | 0.0816724i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −74.0319 | − | 42.7423i | −0.137606 | − | 0.0794467i | ||||
\(539\) | 82.0886i | 0.152298i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −509.151 | −0.941129 | −0.470565 | − | 0.882365i | \(-0.655950\pi\) | ||||
−0.470565 | + | 0.882365i | \(0.655950\pi\) | |||||||
\(542\) | 194.197 | − | 336.359i | 0.358297 | − | 0.620588i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.39388 | + | 9.34247i | 0.00991521 | + | 0.0171737i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 474.620 | + | 274.022i | 0.867679 | + | 0.500955i | 0.866576 | − | 0.499045i | \(-0.166316\pi\) |
0.00110267 | + | 0.999999i | \(0.499649\pi\) | |||||||
\(548\) | 469.368 | 0.856511 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.3791 | + | 7.72442i | 0.0242815 | + | 0.0140189i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 163.522 | − | 94.4092i | 0.295699 | − | 0.170722i | ||||
\(554\) | −60.0125 | + | 34.6482i | −0.108326 | + | 0.0625419i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 106.530 | − | 184.516i | 0.191601 | − | 0.331862i | ||||
\(557\) | −406.542 | −0.729879 | −0.364939 | − | 0.931031i | \(-0.618910\pi\) | ||||
−0.364939 | + | 0.931031i | \(0.618910\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.8025 | −0.0336360 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 420.192 | − | 242.598i | 0.747673 | − | 0.431669i | ||||
\(563\) | 303.236 | + | 525.220i | 0.538607 | + | 0.932895i | 0.998979 | + | 0.0451687i | \(0.0143825\pi\) |
−0.460372 | + | 0.887726i | \(0.652284\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 485.653i | 0.858045i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 242.969i | 0.427763i | ||||||||
\(569\) | −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 | 0.901916 | − | 0.431911i | \(-0.142161\pi\) |
−0.825004 | + | 0.565126i | \(0.808827\pi\) | |||||||
\(572\) | 185.915 | + | 322.015i | 0.325027 | + | 0.562963i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 277.553 | − | 480.736i | 0.483541 | − | 0.837518i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 132.091i | 0.228927i | 0.993427 | + | 0.114463i | \(0.0365149\pi\) | ||||
−0.993427 | + | 0.114463i | \(0.963485\pi\) | |||||||
\(578\) | −201.782 | + | 349.497i | −0.349104 | + | 0.604666i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −483.302 | + | 279.034i | −0.831844 | + | 0.480266i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 77.9423 | + | 45.0000i | 0.133692 | + | 0.0771870i | ||||
\(584\) | 271.786i | 0.465387i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 405.106 | 0.691306 | ||||||||
\(587\) | 283.833 | − | 491.614i | 0.483532 | − | 0.837502i | −0.516289 | − | 0.856414i | \(-0.672687\pi\) |
0.999821 | + | 0.0189125i | \(0.00602040\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −96.3939 | − | 166.959i | −0.163657 | − | 0.283462i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 59.9396 | + | 34.6061i | 0.101249 | + | 0.0584563i | ||||
\(593\) | 77.0321 | 0.129902 | 0.0649512 | − | 0.997888i | \(-0.479311\pi\) | ||||
0.0649512 | + | 0.997888i | \(0.479311\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 182.060 | + | 105.113i | 0.305470 | + | 0.176363i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −227.699 | + | 131.462i | −0.380767 | + | 0.219836i | ||||
\(599\) | −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 | \(-0.0634018\pi\) | |||||||
\(602\) | −8.57042 | −0.0142366 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −570.454 | −0.944460 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 256.987 | − | 148.372i | 0.423373 | − | 0.244434i | −0.273147 | − | 0.961972i | \(-0.588064\pi\) |
0.696519 | + | 0.717538i | \(0.254731\pi\) | |||||||
\(608\) | −13.2849 | − | 23.0102i | −0.0218502 | − | 0.0378457i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 277.924i | − | 0.454868i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 517.181i | − | 0.843688i | −0.906668 | − | 0.421844i | \(-0.861383\pi\) | ||
0.906668 | − | 0.421844i | \(-0.138617\pi\) | |||||||
\(614\) | −188.722 | − | 108.959i | −0.307365 | − | 0.177457i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 84.7423 | + | 146.778i | 0.137569 | + | 0.238276i | ||||
\(617\) | −132.738 | − | 229.909i | −0.215134 | − | 0.372623i | 0.738180 | − | 0.674604i | \(-0.235686\pi\) |
−0.953314 | + | 0.301981i | \(0.902352\pi\) | |||||||
\(618\) | 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 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 101.803i | − | 0.163670i | ||||||
\(623\) | 131.339 | − | 227.486i | 0.210817 | − | 0.365146i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 450.224 | − | 259.937i | 0.719207 | − | 0.415234i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −341.529 | − | 197.182i | −0.543835 | − | 0.313983i | ||||
\(629\) | − | 32.9973i | − | 0.0524600i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −160.879 | −0.254958 | −0.127479 | − | 0.991841i | \(-0.540689\pi\) | ||||
−0.127479 | + | 0.991841i | \(0.540689\pi\) | |||||||
\(632\) | −42.0620 | + | 72.8536i | −0.0665538 | + | 0.115275i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −76.0829 | − | 131.779i | −0.120005 | − | 0.207854i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −148.353 | − | 85.6515i | −0.232893 | − | 0.134461i | ||||
\(638\) | 43.9048 | 0.0688164 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 267.894 | + | 154.669i | 0.417931 | + | 0.241293i | 0.694192 | − | 0.719790i | \(-0.255762\pi\) |
−0.276261 | + | 0.961083i | \(0.589095\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 341.726 | − | 197.296i | 0.531456 | − | 0.306836i | −0.210153 | − | 0.977668i | \(-0.567396\pi\) |
0.741609 | + | 0.670832i | \(0.234063\pi\) | |||||||
\(644\) | −103.788 | + | 59.9219i | −0.161161 | + | 0.0930464i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.33368 | + | 10.9703i | −0.00980445 | + | 0.0169818i | ||||
\(647\) | 418.736 | 0.647196 | 0.323598 | − | 0.946195i | \(-0.395108\pi\) | ||||
0.323598 | + | 0.946195i | \(0.395108\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −863.908 | −1.33114 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −431.385 | + | 249.060i | −0.661633 | + | 0.381994i | ||||
\(653\) | 265.363 | + | 459.621i | 0.406375 | + | 0.703861i | 0.994480 | − | 0.104923i | \(-0.0334595\pi\) |
−0.588106 | + | 0.808784i | \(0.700126\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 247.316i | 0.377006i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 126.681i | − | 0.192524i | ||||||
\(659\) | 310.204 | + | 179.096i | 0.470719 | + | 0.271770i | 0.716541 | − | 0.697545i | \(-0.245724\pi\) |
−0.245822 | + | 0.969315i | \(0.579058\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 111.136 | + | 192.493i | 0.168133 | + | 0.291214i | 0.937763 | − | 0.347275i | \(-0.112893\pi\) |
−0.769631 | + | 0.638489i | \(0.779560\pi\) | |||||||
\(662\) | 12.1604 | + | 21.0625i | 0.0183692 | + | 0.0318165i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 124.318 | − | 215.325i | 0.187226 | − | 0.324284i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31.0454i | 0.0465448i | ||||||||
\(668\) | −48.4365 | + | 83.8944i | −0.0725097 | + | 0.125590i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −613.810 | + | 354.383i | −0.914769 | + | 0.528142i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 250.464 | + | 144.606i | 0.372161 | + | 0.214867i | 0.674402 | − | 0.738364i | \(-0.264401\pi\) |
−0.302241 | + | 0.953231i | \(0.597735\pi\) | |||||||
\(674\) | 515.331i | 0.764586i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −437.939 | −0.647838 | ||||||||
\(677\) | −232.226 | + | 402.227i | −0.343022 | + | 0.594131i | −0.984992 | − | 0.172598i | \(-0.944784\pi\) |
0.641971 | + | 0.766729i | \(0.278117\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 304.341 | + | 527.134i | 0.448220 | + | 0.776339i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −474.490 | − | 273.947i | −0.695733 | − | 0.401681i | ||||
\(683\) | −1126.36 | −1.64913 | −0.824565 | − | 0.565767i | \(-0.808580\pi\) | ||||
−0.824565 | + | 0.565767i | \(0.808580\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −448.608 | − | 259.004i | −0.653948 | − | 0.377557i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.30680 | − | 1.90918i | 0.00480640 | − | 0.00277498i | ||||
\(689\) | −162.650 | + | 93.9063i | −0.236067 | + | 0.136294i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −518.841 | + | 898.658i | −0.750855 | + | 1.30052i | 0.196554 | + | 0.980493i | \(0.437025\pi\) |
−0.947409 | + | 0.320025i | \(0.896309\pi\) | |||||||
\(692\) | −200.883 | −0.290293 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 825.044 | 1.18882 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 102.112 | − | 58.9546i | 0.146503 | − | 0.0845833i | ||||
\(698\) | −221.153 | − | 383.048i | −0.316838 | − | 0.548779i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 778.180i | − | 1.11010i | −0.831817 | − | 0.555050i | \(-0.812699\pi\) | ||
0.831817 | − | 0.555050i | \(-0.187301\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 81.2714i | 0.115607i | ||||||||
\(704\) | −65.3939 | − | 37.7552i | −0.0928890 | − | 0.0536295i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 26.5982 | + | 46.0695i | 0.0376745 | + | 0.0652542i | ||||
\(707\) | 501.311 | + | 868.296i | 0.709068 | + | 1.22814i | ||||
\(708\) | 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 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 117.031i | 0.164369i | ||||||||
\(713\) | 193.710 | − | 335.515i | 0.271682 | − | 0.470568i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 493.757 | − | 285.071i | 0.689605 | − | 0.398144i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 360.109 | + | 207.909i | 0.501545 | + | 0.289567i | ||||
\(719\) | − | 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 | ||||||||
\(722\) | −239.666 | + | 415.114i | −0.331947 | + | 0.574949i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −37.1214 | − | 64.2962i | −0.0512727 | − | 0.0888069i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −728.681 | − | 420.704i | −1.00231 | − | 0.578685i | −0.0933809 | − | 0.995630i | \(-0.529767\pi\) |
−0.908932 | + | 0.416945i | \(0.863101\pi\) | |||||||
\(728\) | −353.682 | −0.485827 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.57654 | − | 0.910215i | −0.00215669 | − | 0.00124516i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 525.125 | − | 303.181i | 0.716405 | − | 0.413617i | −0.0970229 | − | 0.995282i | \(-0.530932\pi\) |
0.813428 | + | 0.581665i | \(0.197599\pi\) | |||||||
\(734\) | −40.6946 | + | 23.4951i | −0.0554423 | + | 0.0320096i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 26.6969 | − | 46.2405i | 0.0362730 | − | 0.0628267i | ||||
\(737\) | 292.174 | 0.396437 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 389.362 | 0.526877 | 0.263439 | − | 0.964676i | \(-0.415143\pi\) | ||||
0.263439 | + | 0.964676i | \(0.415143\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −74.1380 | + | 42.8036i | −0.0999164 | + | 0.0576868i | ||||
\(743\) | −522.375 | − | 904.779i | −0.703061 | − | 1.21774i | −0.967387 | − | 0.253304i | \(-0.918483\pi\) |
0.264325 | − | 0.964434i | \(-0.414851\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 318.240i | 0.426595i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 36.0000i | 0.0481283i | ||||||||
\(749\) | −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 | \(0.503751\pi\) | |||||||
\(752\) | 28.2201 | + | 48.8786i | 0.0375267 | + | 0.0649981i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −45.8105 | + | 79.3460i | −0.0607566 | + | 0.105233i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1042.36i | − | 1.37697i | −0.725252 | − | 0.688483i | \(-0.758277\pi\) | ||
0.725252 | − | 0.688483i | \(-0.241723\pi\) | |||||||
\(758\) | 117.616 | − | 203.716i | 0.155166 | − | 0.268755i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 281.607 | − | 162.586i | 0.370048 | − | 0.213647i | −0.303431 | − | 0.952853i | \(-0.598132\pi\) |
0.673479 | + | 0.739206i | \(0.264799\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −639.258 | − | 369.076i | −0.837822 | − | 0.483717i | ||||
\(764\) | − | 35.8481i | − | 0.0469217i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1042.26 | 1.36065 | ||||||||
\(767\) | 901.405 | − | 1561.28i | 1.17523 | − | 2.03557i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 171.348 | + | 296.783i | 0.222819 | + | 0.385934i | 0.955663 | − | 0.294463i | \(-0.0951407\pi\) |
−0.732844 | + | 0.680397i | \(0.761807\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 165.331 | + | 95.4541i | 0.214160 | + | 0.123645i | ||||
\(773\) | −532.579 | −0.688977 | −0.344488 | − | 0.938791i | \(-0.611948\pi\) | ||||
−0.344488 | + | 0.938791i | \(0.611948\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −234.854 | − | 135.593i | −0.302646 | − | 0.174733i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −207.439 | + | 119.765i | −0.266631 | + | 0.153940i | ||||
\(779\) | −251.499 | + | 145.203i | −0.322849 | + | 0.186397i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −405.409 | + | 702.188i | −0.519089 | + | 0.899089i | ||||
\(782\) | −25.4558 | −0.0325522 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 34.7878 | 0.0443721 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 90.0264 | − | 51.9768i | 0.114392 | − | 0.0660442i | −0.441712 | − | 0.897157i | \(-0.645629\pi\) |
0.556104 | + | 0.831113i | \(0.312296\pi\) | |||||||
\(788\) | −160.363 | − | 277.757i | −0.203507 | − | 0.352484i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1284.07i | − | 1.62335i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 1479.06i | − | 1.86514i | ||||||
\(794\) | 313.868 | + | 181.212i | 0.395300 | + | 0.228227i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.51531 | + | 11.2848i | 0.00818506 | + | 0.0141769i | ||||
\(797\) | −552.138 | − | 956.331i | −0.692770 | − | 1.19991i | −0.970927 | − | 0.239378i | \(-0.923057\pi\) |
0.278156 | − | 0.960536i | \(-0.410277\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.4541 | − | 23.3031i | 0.0168386 | − | 0.0291654i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 369.650i | 0.460911i | ||||||||
\(803\) | −453.491 | + | 785.469i | −0.564746 | + | 0.978168i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 990.168 | − | 571.674i | 1.22850 | − | 0.709273i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −386.851 | − | 223.348i | −0.478776 | − | 0.276421i | ||||
\(809\) | − | 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 | \(0.350222\pi\) | |||||||
\(812\) | −20.8809 | + | 36.1668i | −0.0257154 | + | 0.0445404i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 115.485 | + | 200.025i | 0.141873 | + | 0.245731i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.88296 | + | 2.24183i | 0.00475271 | + | 0.00274398i | ||||
\(818\) | −627.611 | −0.767250 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 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 | ||||||||
\(823\) | −1335.63 | + | 771.129i | −1.62288 | + | 0.936973i | −0.636742 | + | 0.771077i | \(0.719718\pi\) |
−0.986143 | + | 0.165896i | \(0.946948\pi\) | |||||||
\(824\) | −71.3689 | + | 41.2048i | −0.0866127 | + | 0.0500059i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 410.871 | − | 711.649i | 0.497422 | − | 0.861560i | ||||
\(827\) | −955.707 | −1.15563 | −0.577815 | − | 0.816167i | \(-0.696095\pi\) | ||||
−0.577815 | + | 0.816167i | \(0.696095\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1082.88 | −1.30625 | −0.653123 | − | 0.757252i | \(-0.726542\pi\) | ||||
−0.653123 | + | 0.757252i | \(0.726542\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 136.464 | − | 78.7878i | 0.164020 | − | 0.0946968i | ||||
\(833\) | −8.29263 | − | 14.3633i | −0.00995514 | − | 0.0172428i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 88.6669i | − | 0.106061i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 15.2281i | − | 0.0181719i | ||||||
\(839\) | 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 | ||||
\(842\) | 179.819 | + | 311.456i | 0.213562 | + | 0.369901i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 154.439 | − | 267.497i | 0.182985 | − | 0.316939i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 202.574i | − | 0.239167i | ||||||
\(848\) | 19.0702 | − | 33.0306i | 0.0224885 | − | 0.0389512i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −141.439 | + | 81.6600i | −0.166204 | + | 0.0959577i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −410.338 | − | 236.909i | −0.481053 | − | 0.277736i | 0.239802 | − | 0.970822i | \(-0.422917\pi\) |
−0.720855 | + | 0.693086i | \(0.756251\pi\) | |||||||
\(854\) | − | 674.172i | − | 0.789429i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 485.939 | 0.567685 | ||||||||
\(857\) | −458.381 | + | 793.939i | −0.534867 | + | 0.926417i | 0.464303 | + | 0.885677i | \(0.346305\pi\) |
−0.999170 | + | 0.0407403i | \(0.987028\pi\) | |||||||
\(858\) | 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 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 855.684 | + | 494.030i | 0.992673 | + | 0.573120i | ||||
\(863\) | −524.200 | −0.607416 | −0.303708 | − | 0.952765i | \(-0.598225\pi\) | ||||
−0.303708 | + | 0.952765i | \(0.598225\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 259.312 | + | 149.714i | 0.299437 | + | 0.172880i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 451.330 | − | 260.576i | 0.519965 | − | 0.300202i | ||||
\(869\) | −243.121 | + | 140.366i | −0.279771 | + | 0.161526i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −304.855 | + | 528.025i | −0.350006 | + | 0.606228i | ||||
\(872\) | 328.868 | 0.377142 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 62.6969 | 0.0717356 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −872.742 | + | 503.878i | −0.995145 | + | 0.574547i | −0.906808 | − | 0.421543i | \(-0.861489\pi\) |
−0.0883370 | + | 0.996091i | \(0.528155\pi\) | |||||||
\(878\) | −197.893 | − | 342.760i | −0.225390 | − | 0.390388i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1536.71i | − | 1.74428i | −0.489254 | − | 0.872141i | \(-0.662731\pi\) | ||
0.489254 | − | 0.872141i | \(-0.337269\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 294.213i | − | 0.333197i | −0.986025 | − | 0.166599i | \(-0.946722\pi\) | ||
0.986025 | − | 0.166599i | \(-0.0532784\pi\) | |||||||
\(884\) | −65.0602 | − | 37.5625i | −0.0735975 | − | 0.0424915i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 389.796 | + | 675.146i | 0.439950 | + | 0.762016i | ||||
\(887\) | −287.402 | − | 497.794i | −0.324015 | − | 0.561211i | 0.657297 | − | 0.753631i | \(-0.271700\pi\) |
−0.981313 | + | 0.192420i | \(0.938366\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 32.0306 | − | 55.4787i | 0.0360299 | − | 0.0624057i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 185.546i | 0.208011i | ||||||||
\(893\) | −33.1370 | + | 57.3949i | −0.0371075 | + | 0.0642720i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 62.2020 | − | 35.9124i | 0.0694219 | − | 0.0400808i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −664.872 | − | 383.864i | −0.740391 | − | 0.427465i | ||||
\(899\) | − | 135.004i | − | 0.150171i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.1837 | −0.0201817 | ||||||||
\(902\) | −412.661 | + | 714.749i | −0.457495 | + | 0.792405i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 286.045 | + | 495.445i | 0.316422 | + | 0.548059i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −441.737 | − | 255.037i | −0.487031 | − | 0.281187i | 0.236311 | − | 0.971677i | \(-0.424062\pi\) |
−0.723342 | + | 0.690490i | \(0.757395\pi\) | |||||||
\(908\) | 339.604 | 0.374013 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 803.127 | + | 463.685i | 0.881588 | + | 0.508985i | 0.871182 | − | 0.490961i | \(-0.163354\pi\) |
0.0104064 | + | 0.999946i | \(0.496687\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 718.564 | − | 414.863i | 0.787036 | − | 0.454396i | ||||
\(914\) | 113.123 | − | 65.3114i | 0.123767 | − | 0.0714567i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 407.545 | − | 705.888i | 0.444918 | − | 0.770621i | ||||
\(917\) | −31.4897 | −0.0343399 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1240.63 | 1.34998 | 0.674991 | − | 0.737826i | \(-0.264147\pi\) | ||||
0.674991 | + | 0.737826i | \(0.264147\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 281.471 | − | 162.507i | 0.305283 | − | 0.176255i | ||||
\(923\) | −846.010 | − | 1465.33i | −0.916587 | − | 1.58757i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 722.384i | 0.780112i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 18.6061i | − | 0.0200497i | ||||||
\(929\) | 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 | ||||
\(932\) | 15.2562 | + | 26.4245i | 0.0163693 | + | 0.0283525i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −589.485 | + | 1021.02i | −0.631140 | + | 1.09317i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1322.21i | − | 1.41111i | −0.708655 | − | 0.705556i | \(-0.750698\pi\) | ||
0.708655 | − | 0.705556i | \(-0.249302\pi\) | |||||||
\(938\) | −138.957 | + | 240.680i | −0.148141 | + | 0.256588i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 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 | ||||||||
\(943\) | −505.404 | − | 291.795i | −0.535953 | − | 0.309433i | ||||
\(944\) | 366.110i | 0.387828i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.7423 | 0.0134697 | ||||||||
\(947\) | 387.896 | − | 671.855i | 0.409605 | − | 0.709457i | −0.585240 | − | 0.810860i | \(-0.699000\pi\) |
0.994845 | + | 0.101403i | \(0.0323332\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −946.347 | − | 1639.12i | −0.997205 | − | 1.72721i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −29.6552 | − | 17.1214i | −0.0311504 | − | 0.0179847i | ||||
\(953\) | −465.082 | −0.488019 | −0.244010 | − | 0.969773i | \(-0.578463\pi\) | ||||
−0.244010 | + | 0.969773i | \(0.578463\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −97.9240 | − | 56.5364i | −0.102431 | − | 0.0591385i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 804.891 | − | 464.704i | 0.840178 | − | 0.485077i | ||||
\(959\) | −1290.28 | + | 744.942i | −1.34544 | + | 0.776791i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −361.863 | + | 626.765i | −0.376548 | + | 0.652200i | ||||
\(962\) | −481.989 | −0.501028 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 168.424 | 0.174714 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1060.21 | + | 612.113i | −1.09639 | + | 0.633002i | −0.935271 | − | 0.353933i | \(-0.884844\pi\) |
−0.161121 | + | 0.986935i | \(0.551511\pi\) | |||||||
\(968\) | 45.1264 | + | 78.1612i | 0.0466182 | + | 0.0807451i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 658.702i | 0.678375i | 0.940719 | + | 0.339188i | \(0.110152\pi\) | ||||
−0.940719 | + | 0.339188i | \(0.889848\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 676.303i | 0.695070i | ||||||||
\(974\) | 430.702 | + | 248.666i | 0.442199 | + | 0.255304i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 150.182 | + | 260.122i | 0.153875 | + | 0.266519i | ||||
\(977\) | 759.170 | + | 1314.92i | 0.777042 | + | 1.34588i | 0.933639 | + | 0.358214i | \(0.116614\pi\) |
−0.156597 | + | 0.987663i | \(0.550052\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −195.272 | + | 338.222i | −0.199461 | + | 0.345477i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 347.074i | 0.353436i | ||||||||
\(983\) | 413.920 | − | 716.930i | 0.421078 | − | 0.729329i | −0.574967 | − | 0.818177i | \(-0.694985\pi\) |
0.996045 | + | 0.0888477i | \(0.0283184\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −7.68215 | + | 4.43529i | −0.00779122 | + | 0.00449826i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 160.241 | + | 92.5153i | 0.162187 | + | 0.0936390i | ||||
\(989\) | 9.01020i | 0.00911041i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 429.546 | 0.433447 | 0.216723 | − | 0.976233i | \(-0.430463\pi\) | ||||
0.216723 | + | 0.976233i | \(0.430463\pi\) | |||||||
\(992\) | −116.094 | + | 201.081i | −0.117030 | + | 0.202702i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −385.621 | − | 667.915i | −0.387949 | − | 0.671947i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −601.886 | − | 347.499i | −0.603697 | − | 0.348545i | 0.166798 | − | 0.985991i | \(-0.446657\pi\) |
−0.770495 | + | 0.637447i | \(0.779991\pi\) | |||||||
\(998\) | 891.274 | 0.893060 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))