Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1143,3,Mod(890,1143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1143, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1143.890");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1143 = 3^{2} \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1143.b (of order \(2\), degree \(1\), 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: | \(31.1444942164\) |
Analytic rank: | \(0\) |
Dimension: | \(84\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 890.1 | ||
Character | \(\chi\) | \(=\) | 1143.890 |
Dual form | 1143.3.b.a.890.84 |
$q$-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 \(\left(\mathbb{Z}/1143\mathbb{Z}\right)^\times\).
\(n\) | \(128\) | \(892\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 3.88526i | − 1.94263i | −0.237796 | − | 0.971315i | \(-0.576425\pi\) | ||||
0.237796 | − | 0.971315i | \(-0.423575\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −11.0952 | −2.77381 | ||||||||
\(5\) | 2.03195i | 0.406389i | 0.979138 | + | 0.203195i | \(0.0651324\pi\) | ||||
−0.979138 | + | 0.203195i | \(0.934868\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.71279 | −0.816113 | −0.408057 | − | 0.912957i | \(-0.633793\pi\) | ||||
−0.408057 | + | 0.912957i | \(0.633793\pi\) | |||||||
\(8\) | 27.5669i | 3.44586i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 7.89464 | 0.789464 | ||||||||
\(11\) | − 7.97333i | − 0.724848i | −0.932013 | − | 0.362424i | \(-0.881949\pi\) | ||||
0.932013 | − | 0.362424i | \(-0.118051\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −22.6045 | −1.73881 | −0.869405 | − | 0.494100i | \(-0.835498\pi\) | ||||
−0.869405 | + | 0.494100i | \(0.835498\pi\) | |||||||
\(14\) | 22.1957i | 1.58541i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 62.7235 | 3.92022 | ||||||||
\(17\) | 24.8287i | 1.46051i | 0.683172 | + | 0.730257i | \(0.260600\pi\) | ||||
−0.683172 | + | 0.730257i | \(0.739400\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 15.9522 | 0.839590 | 0.419795 | − | 0.907619i | \(-0.362102\pi\) | ||||
0.419795 | + | 0.907619i | \(0.362102\pi\) | |||||||
\(20\) | − 22.5449i | − 1.12725i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −30.9785 | −1.40811 | ||||||||
\(23\) | − 13.4635i | − 0.585369i | −0.956209 | − | 0.292684i | \(-0.905452\pi\) | ||||
0.956209 | − | 0.292684i | \(-0.0945485\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 20.8712 | 0.834848 | ||||||||
\(26\) | 87.8245i | 3.37787i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 63.3848 | 2.26374 | ||||||||
\(29\) | 22.5281i | 0.776829i | 0.921485 | + | 0.388415i | \(0.126977\pi\) | ||||
−0.921485 | + | 0.388415i | \(0.873023\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.55815 | −0.0502629 | −0.0251315 | − | 0.999684i | \(-0.508000\pi\) | ||||
−0.0251315 | + | 0.999684i | \(0.508000\pi\) | |||||||
\(32\) | − 133.430i | − 4.16968i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 96.4661 | 2.83724 | ||||||||
\(35\) | − 11.6081i | − 0.331660i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.12185 | 0.0843744 | 0.0421872 | − | 0.999110i | \(-0.486567\pi\) | ||||
0.0421872 | + | 0.999110i | \(0.486567\pi\) | |||||||
\(38\) | − 61.9785i | − 1.63101i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −56.0144 | −1.40036 | ||||||||
\(41\) | 4.15270i | 0.101285i | 0.998717 | + | 0.0506427i | \(0.0161270\pi\) | ||||
−0.998717 | + | 0.0506427i | \(0.983873\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.89437 | 0.230102 | 0.115051 | − | 0.993360i | \(-0.463297\pi\) | ||||
0.115051 | + | 0.993360i | \(0.463297\pi\) | |||||||
\(44\) | 88.4661i | 2.01059i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −52.3091 | −1.13715 | ||||||||
\(47\) | − 35.6762i | − 0.759067i | −0.925178 | − | 0.379534i | \(-0.876084\pi\) | ||||
0.925178 | − | 0.379534i | \(-0.123916\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −16.3640 | −0.333959 | ||||||||
\(50\) | − 81.0900i | − 1.62180i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 250.803 | 4.82313 | ||||||||
\(53\) | − 98.5702i | − 1.85982i | −0.367793 | − | 0.929908i | \(-0.619886\pi\) | ||||
0.367793 | − | 0.929908i | \(-0.380114\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 16.2014 | 0.294571 | ||||||||
\(56\) | − 157.484i | − 2.81221i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 87.5273 | 1.50909 | ||||||||
\(59\) | 70.4093i | 1.19338i | 0.802472 | + | 0.596689i | \(0.203517\pi\) | ||||
−0.802472 | + | 0.596689i | \(0.796483\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 37.5028 | 0.614801 | 0.307400 | − | 0.951580i | \(-0.400541\pi\) | ||||
0.307400 | + | 0.951580i | \(0.400541\pi\) | |||||||
\(62\) | 6.05382i | 0.0976423i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −267.515 | −4.17992 | ||||||||
\(65\) | − 45.9312i | − 0.706634i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 102.001 | 1.52240 | 0.761198 | − | 0.648519i | \(-0.224611\pi\) | ||||
0.761198 | + | 0.648519i | \(0.224611\pi\) | |||||||
\(68\) | − 275.481i | − 4.05119i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −45.1004 | −0.644292 | ||||||||
\(71\) | − 140.711i | − 1.98185i | −0.134410 | − | 0.990926i | \(-0.542914\pi\) | ||||
0.134410 | − | 0.990926i | \(-0.457086\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −37.1066 | −0.508310 | −0.254155 | − | 0.967163i | \(-0.581797\pi\) | ||||
−0.254155 | + | 0.967163i | \(0.581797\pi\) | |||||||
\(74\) | − 12.1292i | − 0.163908i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −176.994 | −2.32886 | ||||||||
\(77\) | 45.5500i | 0.591558i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −69.2564 | −0.876663 | −0.438331 | − | 0.898813i | \(-0.644430\pi\) | ||||
−0.438331 | + | 0.898813i | \(0.644430\pi\) | |||||||
\(80\) | 127.451i | 1.59313i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 16.1343 | 0.196760 | ||||||||
\(83\) | − 82.8101i | − 0.997712i | −0.866685 | − | 0.498856i | \(-0.833754\pi\) | ||||
0.866685 | − | 0.498856i | \(-0.166246\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −50.4507 | −0.593537 | ||||||||
\(86\) | − 38.4422i | − 0.447002i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 219.800 | 2.49773 | ||||||||
\(89\) | 148.742i | 1.67125i | 0.549298 | + | 0.835627i | \(0.314895\pi\) | ||||
−0.549298 | + | 0.835627i | \(0.685105\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 129.135 | 1.41907 | ||||||||
\(92\) | 149.381i | 1.62370i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −138.611 | −1.47459 | ||||||||
\(95\) | 32.4140i | 0.341200i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 25.7301 | 0.265258 | 0.132629 | − | 0.991166i | \(-0.457658\pi\) | ||||
0.132629 | + | 0.991166i | \(0.457658\pi\) | |||||||
\(98\) | 63.5784i | 0.648760i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −231.571 | −2.31571 | ||||||||
\(101\) | 80.0970i | 0.793040i | 0.918026 | + | 0.396520i | \(0.129782\pi\) | ||||
−0.918026 | + | 0.396520i | \(0.870218\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 89.2829 | 0.866824 | 0.433412 | − | 0.901196i | \(-0.357309\pi\) | ||||
0.433412 | + | 0.901196i | \(0.357309\pi\) | |||||||
\(104\) | − 623.137i | − 5.99170i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −382.971 | −3.61293 | ||||||||
\(107\) | − 2.37443i | − 0.0221910i | −0.999938 | − | 0.0110955i | \(-0.996468\pi\) | ||||
0.999938 | − | 0.0110955i | \(-0.00353188\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.17902 | 0.0199910 | 0.00999551 | − | 0.999950i | \(-0.496818\pi\) | ||||
0.00999551 | + | 0.999950i | \(0.496818\pi\) | |||||||
\(110\) | − 62.9466i | − 0.572242i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −358.326 | −3.19934 | ||||||||
\(113\) | − 116.498i | − 1.03096i | −0.856902 | − | 0.515480i | \(-0.827614\pi\) | ||||
0.856902 | − | 0.515480i | \(-0.172386\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 27.3571 | 0.237887 | ||||||||
\(116\) | − 249.954i | − 2.15478i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 273.559 | 2.31829 | ||||||||
\(119\) | − 141.841i | − 1.19195i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 57.4260 | 0.474595 | ||||||||
\(122\) | − 145.708i | − 1.19433i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 17.2881 | 0.139420 | ||||||||
\(125\) | 93.2078i | 0.745662i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.2694 | −0.0887357 | ||||||||
\(128\) | 505.646i | 3.95036i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −178.455 | −1.37273 | ||||||||
\(131\) | − 78.9935i | − 0.603004i | −0.953466 | − | 0.301502i | \(-0.902512\pi\) | ||||
0.953466 | − | 0.301502i | \(-0.0974879\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −91.1316 | −0.685200 | ||||||||
\(134\) | − 396.299i | − 2.95745i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −684.451 | −5.03273 | ||||||||
\(137\) | 87.1459i | 0.636102i | 0.948074 | + | 0.318051i | \(0.103028\pi\) | ||||
−0.948074 | + | 0.318051i | \(0.896972\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 232.830 | 1.67504 | 0.837519 | − | 0.546408i | \(-0.184005\pi\) | ||||
0.837519 | + | 0.546408i | \(0.184005\pi\) | |||||||
\(140\) | 128.795i | 0.919961i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −546.701 | −3.85000 | ||||||||
\(143\) | 180.233i | 1.26037i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −45.7758 | −0.315695 | ||||||||
\(146\) | 144.169i | 0.987459i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −34.6377 | −0.234039 | ||||||||
\(149\) | 285.179i | 1.91395i | 0.290164 | + | 0.956977i | \(0.406290\pi\) | ||||
−0.290164 | + | 0.956977i | \(0.593710\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 123.029 | 0.814759 | 0.407380 | − | 0.913259i | \(-0.366443\pi\) | ||||
0.407380 | + | 0.913259i | \(0.366443\pi\) | |||||||
\(152\) | 439.753i | 2.89311i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 176.974 | 1.14918 | ||||||||
\(155\) | − 3.16608i | − 0.0204263i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 209.967 | 1.33737 | 0.668685 | − | 0.743546i | \(-0.266858\pi\) | ||||
0.668685 | + | 0.743546i | \(0.266858\pi\) | |||||||
\(158\) | 269.079i | 1.70303i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 271.122 | 1.69451 | ||||||||
\(161\) | 76.9140i | 0.477727i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 222.316 | 1.36390 | 0.681952 | − | 0.731397i | \(-0.261131\pi\) | ||||
0.681952 | + | 0.731397i | \(0.261131\pi\) | |||||||
\(164\) | − 46.0753i | − 0.280947i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −321.739 | −1.93819 | ||||||||
\(167\) | 172.780i | 1.03461i | 0.855801 | + | 0.517306i | \(0.173065\pi\) | ||||
−0.855801 | + | 0.517306i | \(0.826935\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 341.965 | 2.02346 | ||||||||
\(170\) | 196.014i | 1.15302i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −109.780 | −0.638259 | ||||||||
\(173\) | − 252.077i | − 1.45709i | −0.684996 | − | 0.728547i | \(-0.740196\pi\) | ||||
0.684996 | − | 0.728547i | \(-0.259804\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −119.233 | −0.681330 | ||||||||
\(176\) | − 500.115i | − 2.84156i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 577.899 | 3.24663 | ||||||||
\(179\) | − 26.4932i | − 0.148007i | −0.997258 | − | 0.0740034i | \(-0.976422\pi\) | ||||
0.997258 | − | 0.0740034i | \(-0.0235776\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −63.2787 | −0.349606 | −0.174803 | − | 0.984603i | \(-0.555929\pi\) | ||||
−0.174803 | + | 0.984603i | \(0.555929\pi\) | |||||||
\(182\) | − 501.723i | − 2.75672i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 371.146 | 2.01710 | ||||||||
\(185\) | 6.34344i | 0.0342888i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 197.968 | 1.05865 | ||||||||
\(188\) | 395.836i | 2.10551i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 125.937 | 0.662826 | ||||||||
\(191\) | − 143.322i | − 0.750379i | −0.926948 | − | 0.375189i | \(-0.877578\pi\) | ||||
0.926948 | − | 0.375189i | \(-0.122422\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 364.106 | 1.88656 | 0.943279 | − | 0.332002i | \(-0.107724\pi\) | ||||
0.943279 | + | 0.332002i | \(0.107724\pi\) | |||||||
\(194\) | − 99.9680i | − 0.515299i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 181.563 | 0.926340 | ||||||||
\(197\) | 236.066i | 1.19830i | 0.800635 | + | 0.599152i | \(0.204495\pi\) | ||||
−0.800635 | + | 0.599152i | \(0.795505\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 278.694 | 1.40047 | 0.700236 | − | 0.713912i | \(-0.253078\pi\) | ||||
0.700236 | + | 0.713912i | \(0.253078\pi\) | |||||||
\(200\) | 575.354i | 2.87677i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 311.198 | 1.54058 | ||||||||
\(203\) | − 128.698i | − 0.633981i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.43807 | −0.0411613 | ||||||||
\(206\) | − 346.887i | − 1.68392i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1417.84 | −6.81652 | ||||||||
\(209\) | − 127.192i | − 0.608575i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −386.586 | −1.83216 | −0.916080 | − | 0.400996i | \(-0.868664\pi\) | ||||
−0.916080 | + | 0.400996i | \(0.868664\pi\) | |||||||
\(212\) | 1093.66i | 5.15878i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −9.22530 | −0.0431089 | ||||||||
\(215\) | 20.1048i | 0.0935108i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.90139 | 0.0410202 | ||||||||
\(218\) | − 8.46606i | − 0.0388352i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −179.758 | −0.817083 | ||||||||
\(221\) | − 561.242i | − 2.53956i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.23993 | 0.0324660 | 0.0162330 | − | 0.999868i | \(-0.494833\pi\) | ||||
0.0162330 | + | 0.999868i | \(0.494833\pi\) | |||||||
\(224\) | 762.256i | 3.40293i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −452.627 | −2.00277 | ||||||||
\(227\) | 298.177i | 1.31356i | 0.754084 | + | 0.656778i | \(0.228081\pi\) | ||||
−0.754084 | + | 0.656778i | \(0.771919\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −156.233 | −0.682241 | −0.341121 | − | 0.940019i | \(-0.610806\pi\) | ||||
−0.341121 | + | 0.940019i | \(0.610806\pi\) | |||||||
\(230\) | − 106.289i | − 0.462127i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −621.028 | −2.67684 | ||||||||
\(233\) | 101.771i | 0.436784i | 0.975861 | + | 0.218392i | \(0.0700811\pi\) | ||||
−0.975861 | + | 0.218392i | \(0.929919\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 72.4920 | 0.308477 | ||||||||
\(236\) | − 781.209i | − 3.31021i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −551.091 | −2.31551 | ||||||||
\(239\) | 122.338i | 0.511875i | 0.966693 | + | 0.255937i | \(0.0823841\pi\) | ||||
−0.966693 | + | 0.255937i | \(0.917616\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.637189 | 0.00264394 | 0.00132197 | − | 0.999999i | \(-0.499579\pi\) | ||||
0.00132197 | + | 0.999999i | \(0.499579\pi\) | |||||||
\(242\) | − 223.115i | − 0.921962i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −416.103 | −1.70534 | ||||||||
\(245\) | − 33.2508i | − 0.135717i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −360.592 | −1.45989 | ||||||||
\(248\) | − 42.9534i | − 0.173199i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 362.137 | 1.44855 | ||||||||
\(251\) | 135.183i | 0.538577i | 0.963060 | + | 0.269289i | \(0.0867886\pi\) | ||||
−0.963060 | + | 0.269289i | \(0.913211\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −107.349 | −0.424303 | ||||||||
\(254\) | 43.7847i | 0.172381i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 894.507 | 3.49417 | ||||||||
\(257\) | − 109.808i | − 0.427267i | −0.976914 | − | 0.213633i | \(-0.931470\pi\) | ||||
0.976914 | − | 0.213633i | \(-0.0685298\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17.8345 | −0.0688591 | ||||||||
\(260\) | 509.618i | 1.96007i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −306.910 | −1.17141 | ||||||||
\(263\) | − 266.392i | − 1.01290i | −0.862270 | − | 0.506448i | \(-0.830958\pi\) | ||||
0.862270 | − | 0.506448i | \(-0.169042\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 200.289 | 0.755809 | ||||||||
\(266\) | 354.070i | 1.33109i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1131.72 | −4.22284 | ||||||||
\(269\) | 79.5758i | 0.295821i | 0.989001 | + | 0.147910i | \(0.0472547\pi\) | ||||
−0.989001 | + | 0.147910i | \(0.952745\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 193.955 | 0.715700 | 0.357850 | − | 0.933779i | \(-0.383510\pi\) | ||||
0.357850 | + | 0.933779i | \(0.383510\pi\) | |||||||
\(272\) | 1557.35i | 5.72554i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 338.585 | 1.23571 | ||||||||
\(275\) | − 166.413i | − 0.605138i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 118.474 | 0.427702 | 0.213851 | − | 0.976866i | \(-0.431399\pi\) | ||||
0.213851 | + | 0.976866i | \(0.431399\pi\) | |||||||
\(278\) | − 904.607i | − 3.25398i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 319.999 | 1.14285 | ||||||||
\(281\) | − 57.3404i | − 0.204058i | −0.994781 | − | 0.102029i | \(-0.967467\pi\) | ||||
0.994781 | − | 0.102029i | \(-0.0325335\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −179.085 | −0.632810 | −0.316405 | − | 0.948624i | \(-0.602476\pi\) | ||||
−0.316405 | + | 0.948624i | \(0.602476\pi\) | |||||||
\(284\) | 1561.23i | 5.49728i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 700.254 | 2.44844 | ||||||||
\(287\) | − 23.7235i | − 0.0826604i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −327.467 | −1.13310 | ||||||||
\(290\) | 177.851i | 0.613279i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 411.707 | 1.40996 | ||||||||
\(293\) | − 423.884i | − 1.44670i | −0.690481 | − | 0.723351i | \(-0.742601\pi\) | ||||
0.690481 | − | 0.723351i | \(-0.257399\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −143.068 | −0.484976 | ||||||||
\(296\) | 86.0597i | 0.290742i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1108.00 | 3.71810 | ||||||||
\(299\) | 304.336i | 1.01784i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −56.5245 | −0.187789 | ||||||||
\(302\) | − 477.998i | − 1.58278i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1000.58 | 3.29138 | ||||||||
\(305\) | 76.2037i | 0.249848i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −474.504 | −1.54561 | −0.772807 | − | 0.634641i | \(-0.781148\pi\) | ||||
−0.772807 | + | 0.634641i | \(0.781148\pi\) | |||||||
\(308\) | − 505.388i | − 1.64087i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −12.3010 | −0.0396808 | ||||||||
\(311\) | 206.584i | 0.664257i | 0.943234 | + | 0.332128i | \(0.107767\pi\) | ||||
−0.943234 | + | 0.332128i | \(0.892233\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 112.876 | 0.360626 | 0.180313 | − | 0.983609i | \(-0.442289\pi\) | ||||
0.180313 | + | 0.983609i | \(0.442289\pi\) | |||||||
\(314\) | − 815.776i | − 2.59801i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 768.416 | 2.43170 | ||||||||
\(317\) | − 434.770i | − 1.37151i | −0.727831 | − | 0.685756i | \(-0.759472\pi\) | ||||
0.727831 | − | 0.685756i | \(-0.240528\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 179.624 | 0.563084 | ||||||||
\(320\) | − 543.576i | − 1.69867i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 298.831 | 0.928047 | ||||||||
\(323\) | 396.073i | 1.22623i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −471.784 | −1.45164 | ||||||||
\(326\) | − 863.757i | − 2.64956i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −114.477 | −0.349016 | ||||||||
\(329\) | 203.810i | 0.619485i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 261.919 | 0.791295 | 0.395647 | − | 0.918402i | \(-0.370520\pi\) | ||||
0.395647 | + | 0.918402i | \(0.370520\pi\) | |||||||
\(332\) | 918.799i | 2.76747i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 671.296 | 2.00987 | ||||||||
\(335\) | 207.260i | 0.618685i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 364.685 | 1.08215 | 0.541076 | − | 0.840974i | \(-0.318017\pi\) | ||||
0.541076 | + | 0.840974i | \(0.318017\pi\) | |||||||
\(338\) | − 1328.62i | − 3.93084i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 559.763 | 1.64636 | ||||||||
\(341\) | 12.4237i | 0.0364330i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 373.411 | 1.08866 | ||||||||
\(344\) | 272.757i | 0.792898i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −979.385 | −2.83059 | ||||||||
\(347\) | 149.497i | 0.430828i | 0.976523 | + | 0.215414i | \(0.0691101\pi\) | ||||
−0.976523 | + | 0.215414i | \(0.930890\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −463.218 | −1.32727 | −0.663636 | − | 0.748056i | \(-0.730988\pi\) | ||||
−0.663636 | + | 0.748056i | \(0.730988\pi\) | |||||||
\(350\) | 463.250i | 1.32357i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1063.88 | −3.02238 | ||||||||
\(353\) | 419.892i | 1.18950i | 0.803912 | + | 0.594748i | \(0.202748\pi\) | ||||
−0.803912 | + | 0.594748i | \(0.797252\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 285.918 | 0.805403 | ||||||||
\(356\) | − 1650.32i | − 4.63574i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −102.933 | −0.287523 | ||||||||
\(359\) | 78.8625i | 0.219673i | 0.993950 | + | 0.109836i | \(0.0350327\pi\) | ||||
−0.993950 | + | 0.109836i | \(0.964967\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −106.527 | −0.295089 | ||||||||
\(362\) | 245.854i | 0.679155i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1432.78 | −3.93622 | ||||||||
\(365\) | − 75.3987i | − 0.206572i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 584.688 | 1.59316 | 0.796578 | − | 0.604536i | \(-0.206642\pi\) | ||||
0.796578 | + | 0.604536i | \(0.206642\pi\) | |||||||
\(368\) | − 844.476i | − 2.29477i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 24.6459 | 0.0666105 | ||||||||
\(371\) | 563.111i | 1.51782i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.0162 | 0.0643866 | 0.0321933 | − | 0.999482i | \(-0.489751\pi\) | ||||
0.0321933 | + | 0.999482i | \(0.489751\pi\) | |||||||
\(374\) | − 769.157i | − 2.05657i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 983.480 | 2.61564 | ||||||||
\(377\) | − 509.236i | − 1.35076i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 609.893 | 1.60922 | 0.804609 | − | 0.593806i | \(-0.202375\pi\) | ||||
0.804609 | + | 0.593806i | \(0.202375\pi\) | |||||||
\(380\) | − 359.642i | − 0.946425i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −556.845 | −1.45771 | ||||||||
\(383\) | − 545.175i | − 1.42343i | −0.702467 | − | 0.711716i | \(-0.747918\pi\) | ||||
0.702467 | − | 0.711716i | \(-0.252082\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −92.5551 | −0.240403 | ||||||||
\(386\) | − 1414.64i | − 3.66488i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −285.481 | −0.735777 | ||||||||
\(389\) | 106.310i | 0.273291i | 0.990620 | + | 0.136646i | \(0.0436322\pi\) | ||||
−0.990620 | + | 0.136646i | \(0.956368\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 334.281 | 0.854939 | ||||||||
\(392\) | − 451.105i | − 1.15078i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 917.177 | 2.32786 | ||||||||
\(395\) | − 140.725i | − 0.356266i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 710.850 | 1.79056 | 0.895278 | − | 0.445509i | \(-0.146977\pi\) | ||||
0.895278 | + | 0.445509i | \(0.146977\pi\) | |||||||
\(398\) | − 1082.80i | − 2.72060i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1309.11 | 3.27279 | ||||||||
\(401\) | 208.003i | 0.518711i | 0.965782 | + | 0.259356i | \(0.0835102\pi\) | ||||
−0.965782 | + | 0.259356i | \(0.916490\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 35.2213 | 0.0873977 | ||||||||
\(404\) | − 888.696i | − 2.19974i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −500.025 | −1.23159 | ||||||||
\(407\) | − 24.8916i | − 0.0611587i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −655.639 | −1.60303 | −0.801515 | − | 0.597974i | \(-0.795972\pi\) | ||||
−0.801515 | + | 0.597974i | \(0.795972\pi\) | |||||||
\(410\) | 32.7841i | 0.0799612i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −990.616 | −2.40441 | ||||||||
\(413\) | − 402.234i | − 0.973932i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 168.266 | 0.405460 | ||||||||
\(416\) | 3016.12i | 7.25028i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −494.175 | −1.18224 | ||||||||
\(419\) | 69.6645i | 0.166264i | 0.996539 | + | 0.0831318i | \(0.0264923\pi\) | ||||
−0.996539 | + | 0.0831318i | \(0.973508\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 280.499 | 0.666268 | 0.333134 | − | 0.942880i | \(-0.391894\pi\) | ||||
0.333134 | + | 0.942880i | \(0.391894\pi\) | |||||||
\(422\) | 1501.99i | 3.55921i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2717.27 | 6.40866 | ||||||||
\(425\) | 518.206i | 1.21931i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −214.246 | −0.501747 | ||||||||
\(428\) | 26.3449i | 0.0615536i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 78.1125 | 0.181657 | ||||||||
\(431\) | − 507.000i | − 1.17633i | −0.808740 | − | 0.588167i | \(-0.799850\pi\) | ||||
0.808740 | − | 0.588167i | \(-0.200150\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 221.867 | 0.512396 | 0.256198 | − | 0.966624i | \(-0.417530\pi\) | ||||
0.256198 | + | 0.966624i | \(0.417530\pi\) | |||||||
\(434\) | − 34.5842i | − 0.0796872i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −24.1768 | −0.0554513 | ||||||||
\(437\) | − 214.772i | − 0.491470i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −243.190 | −0.553964 | −0.276982 | − | 0.960875i | \(-0.589334\pi\) | ||||
−0.276982 | + | 0.960875i | \(0.589334\pi\) | |||||||
\(440\) | 446.621i | 1.01505i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2180.57 | −4.93342 | ||||||||
\(443\) | − 317.504i | − 0.716714i | −0.933585 | − | 0.358357i | \(-0.883337\pi\) | ||||
0.933585 | − | 0.358357i | \(-0.116663\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −302.235 | −0.679179 | ||||||||
\(446\) | − 28.1290i | − 0.0630695i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1528.26 | 3.41129 | ||||||||
\(449\) | − 706.223i | − 1.57288i | −0.617666 | − | 0.786440i | \(-0.711922\pi\) | ||||
0.617666 | − | 0.786440i | \(-0.288078\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 33.1109 | 0.0734166 | ||||||||
\(452\) | 1292.58i | 2.85969i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1158.50 | 2.55175 | ||||||||
\(455\) | 262.395i | 0.576693i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 657.374 | 1.43846 | 0.719228 | − | 0.694774i | \(-0.244496\pi\) | ||||
0.719228 | + | 0.694774i | \(0.244496\pi\) | |||||||
\(458\) | 607.007i | 1.32534i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −303.533 | −0.659855 | ||||||||
\(461\) | − 558.636i | − 1.21179i | −0.795544 | − | 0.605896i | \(-0.792815\pi\) | ||||
0.795544 | − | 0.605896i | \(-0.207185\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 248.378 | 0.536454 | 0.268227 | − | 0.963356i | \(-0.413562\pi\) | ||||
0.268227 | + | 0.963356i | \(0.413562\pi\) | |||||||
\(464\) | 1413.04i | 3.04534i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 395.405 | 0.848510 | ||||||||
\(467\) | 449.563i | 0.962662i | 0.876539 | + | 0.481331i | \(0.159847\pi\) | ||||
−0.876539 | + | 0.481331i | \(0.840153\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −582.708 | −1.24245 | ||||||||
\(470\) | − 281.650i | − 0.599256i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1940.97 | −4.11221 | ||||||||
\(473\) | − 78.8911i | − 0.166789i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 332.942 | 0.700930 | ||||||||
\(476\) | 1573.77i | 3.30623i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 475.315 | 0.994383 | ||||||||
\(479\) | 581.495i | 1.21398i | 0.794711 | + | 0.606988i | \(0.207622\pi\) | ||||
−0.794711 | + | 0.606988i | \(0.792378\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −70.5680 | −0.146711 | ||||||||
\(482\) | − 2.47564i | − 0.00513619i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −637.155 | −1.31644 | ||||||||
\(485\) | 52.2821i | 0.107798i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 117.988 | 0.242276 | 0.121138 | − | 0.992636i | \(-0.461346\pi\) | ||||
0.121138 | + | 0.992636i | \(0.461346\pi\) | |||||||
\(488\) | 1033.84i | 2.11852i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −129.188 | −0.263649 | ||||||||
\(491\) | 536.142i | 1.09194i | 0.837805 | + | 0.545969i | \(0.183838\pi\) | ||||
−0.837805 | + | 0.545969i | \(0.816162\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −559.343 | −1.13457 | ||||||||
\(494\) | 1400.99i | 2.83602i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −97.7327 | −0.197042 | ||||||||
\(497\) | 803.855i | 1.61741i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 162.152 | 0.324954 | 0.162477 | − | 0.986712i | \(-0.448052\pi\) | ||||
0.162477 | + | 0.986712i | \(0.448052\pi\) | |||||||
\(500\) | − 1034.16i | − 2.06833i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 525.221 | 1.04626 | ||||||||
\(503\) | 80.4958i | 0.160031i | 0.996794 | + | 0.0800157i | \(0.0254970\pi\) | ||||
−0.996794 | + | 0.0800157i | \(0.974503\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −162.753 | −0.322283 | ||||||||
\(506\) | 417.078i | 0.824265i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 125.037 | 0.246136 | ||||||||
\(509\) | − 662.979i | − 1.30251i | −0.758858 | − | 0.651256i | \(-0.774242\pi\) | ||||
0.758858 | − | 0.651256i | \(-0.225758\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 211.983 | 0.414839 | ||||||||
\(512\) | − 1452.81i | − 2.83752i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −426.631 | −0.830021 | ||||||||
\(515\) | 181.418i | 0.352268i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −284.458 | −0.550209 | ||||||||
\(518\) | 69.2917i | 0.133768i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1266.18 | 2.43496 | ||||||||
\(521\) | 619.817i | 1.18967i | 0.803848 | + | 0.594834i | \(0.202782\pi\) | ||||
−0.803848 | + | 0.594834i | \(0.797218\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 114.109 | 0.218182 | 0.109091 | − | 0.994032i | \(-0.465206\pi\) | ||||
0.109091 | + | 0.994032i | \(0.465206\pi\) | |||||||
\(524\) | 876.452i | 1.67262i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1035.00 | −1.96768 | ||||||||
\(527\) | − 38.6869i | − 0.0734098i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 347.735 | 0.657344 | ||||||||
\(530\) | − 778.176i | − 1.46826i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1011.13 | 1.90062 | ||||||||
\(533\) | − 93.8700i | − 0.176116i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.82472 | 0.00901817 | ||||||||
\(536\) | 2811.84i | 5.24596i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 309.173 | 0.574670 | ||||||||
\(539\) | 130.476i | 0.242070i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.1841 | 0.0336120 | 0.0168060 | − | 0.999859i | \(-0.494650\pi\) | ||||
0.0168060 | + | 0.999859i | \(0.494650\pi\) | |||||||
\(542\) | − 753.565i | − 1.39034i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3312.89 | 6.08987 | ||||||||
\(545\) | 4.42765i | 0.00812413i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −946.157 | −1.72972 | −0.864860 | − | 0.502013i | \(-0.832593\pi\) | ||||
−0.864860 | + | 0.502013i | \(0.832593\pi\) | |||||||
\(548\) | − 966.906i | − 1.76443i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −646.558 | −1.17556 | ||||||||
\(551\) | 359.372i | 0.652218i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 395.647 | 0.715456 | ||||||||
\(554\) | − 460.301i | − 0.830868i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2583.31 | −4.64624 | ||||||||
\(557\) | 226.354i | 0.406380i | 0.979139 | + | 0.203190i | \(0.0651309\pi\) | ||||
−0.979139 | + | 0.203190i | \(0.934869\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −223.658 | −0.400103 | ||||||||
\(560\) | − 728.100i | − 1.30018i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −222.782 | −0.396410 | ||||||||
\(563\) | 813.544i | 1.44502i | 0.691363 | + | 0.722508i | \(0.257011\pi\) | ||||
−0.691363 | + | 0.722508i | \(0.742989\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 236.719 | 0.418971 | ||||||||
\(566\) | 695.793i | 1.22932i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3878.98 | 6.82918 | ||||||||
\(569\) | − 672.821i | − 1.18246i | −0.806502 | − | 0.591231i | \(-0.798642\pi\) | ||||
0.806502 | − | 0.591231i | \(-0.201358\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 335.830 | 0.588144 | 0.294072 | − | 0.955783i | \(-0.404989\pi\) | ||||
0.294072 | + | 0.955783i | \(0.404989\pi\) | |||||||
\(572\) | − 1999.73i | − 3.49604i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −92.1721 | −0.160579 | ||||||||
\(575\) | − 280.999i | − 0.488694i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −124.392 | −0.215584 | −0.107792 | − | 0.994173i | \(-0.534378\pi\) | ||||
−0.107792 | + | 0.994173i | \(0.534378\pi\) | |||||||
\(578\) | 1272.29i | 2.20120i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 507.894 | 0.875679 | ||||||||
\(581\) | 473.077i | 0.814246i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −785.933 | −1.34808 | ||||||||
\(584\) | − 1022.91i | − 1.75157i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1646.90 | −2.81041 | ||||||||
\(587\) | 170.171i | 0.289899i | 0.989439 | + | 0.144950i | \(0.0463020\pi\) | ||||
−0.989439 | + | 0.144950i | \(0.953698\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.8560 | −0.0422003 | ||||||||
\(590\) | 555.856i | 0.942129i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 195.814 | 0.330766 | ||||||||
\(593\) | − 233.420i | − 0.393625i | −0.980441 | − | 0.196812i | \(-0.936941\pi\) | ||||
0.980441 | − | 0.196812i | \(-0.0630590\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 288.214 | 0.484394 | ||||||||
\(596\) | − 3164.13i | − 5.30895i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1182.42 | 1.97730 | ||||||||
\(599\) | 876.407i | 1.46312i | 0.681779 | + | 0.731559i | \(0.261207\pi\) | ||||
−0.681779 | + | 0.731559i | \(0.738793\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −821.070 | −1.36617 | −0.683087 | − | 0.730337i | \(-0.739363\pi\) | ||||
−0.683087 | + | 0.730337i | \(0.739363\pi\) | |||||||
\(602\) | 219.612i | 0.364805i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1365.03 | −2.25999 | ||||||||
\(605\) | 116.686i | 0.192870i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −243.151 | −0.400579 | −0.200289 | − | 0.979737i | \(-0.564188\pi\) | ||||
−0.200289 | + | 0.979737i | \(0.564188\pi\) | |||||||
\(608\) | − 2128.50i | − 3.50082i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 296.071 | 0.485363 | ||||||||
\(611\) | 806.443i | 1.31987i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −496.958 | −0.810698 | −0.405349 | − | 0.914162i | \(-0.632850\pi\) | ||||
−0.405349 | + | 0.914162i | \(0.632850\pi\) | |||||||
\(614\) | 1843.57i | 3.00256i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1255.67 | −2.03843 | ||||||||
\(617\) | − 866.834i | − 1.40492i | −0.711724 | − | 0.702459i | \(-0.752086\pi\) | ||||
0.711724 | − | 0.702459i | \(-0.247914\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −766.155 | −1.23773 | −0.618866 | − | 0.785497i | \(-0.712407\pi\) | ||||
−0.618866 | + | 0.785497i | \(0.712407\pi\) | |||||||
\(620\) | 35.1284i | 0.0566588i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 802.632 | 1.29041 | ||||||||
\(623\) | − 849.729i | − 1.36393i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 332.387 | 0.531819 | ||||||||
\(626\) | − 438.553i | − 0.700564i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2329.64 | −3.70961 | ||||||||
\(629\) | 77.5117i | 0.123230i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −878.466 | −1.39218 | −0.696090 | − | 0.717954i | \(-0.745079\pi\) | ||||
−0.696090 | + | 0.717954i | \(0.745079\pi\) | |||||||
\(632\) | − 1909.18i | − 3.02086i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1689.19 | −2.66434 | ||||||||
\(635\) | − 22.8989i | − 0.0360612i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 369.901 | 0.580692 | ||||||||
\(638\) | − 697.885i | − 1.09386i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1027.45 | −1.60538 | ||||||||
\(641\) | 901.514i | 1.40642i | 0.710983 | + | 0.703209i | \(0.248250\pi\) | ||||
−0.710983 | + | 0.703209i | \(0.751750\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −96.0218 | −0.149334 | −0.0746671 | − | 0.997209i | \(-0.523789\pi\) | ||||
−0.0746671 | + | 0.997209i | \(0.523789\pi\) | |||||||
\(644\) | − 853.380i | − 1.32512i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1538.85 | 2.38212 | ||||||||
\(647\) | 932.456i | 1.44120i | 0.693351 | + | 0.720600i | \(0.256134\pi\) | ||||
−0.693351 | + | 0.720600i | \(0.743866\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 561.397 | 0.865018 | ||||||||
\(650\) | 1833.00i | 2.82000i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2466.66 | −3.78321 | ||||||||
\(653\) | 75.4491i | 0.115542i | 0.998330 | + | 0.0577711i | \(0.0183994\pi\) | ||||
−0.998330 | + | 0.0577711i | \(0.981601\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 160.510 | 0.245054 | ||||||||
\(656\) | 260.472i | 0.397061i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 791.857 | 1.20343 | ||||||||
\(659\) | 383.689i | 0.582229i | 0.956688 | + | 0.291114i | \(0.0940260\pi\) | ||||
−0.956688 | + | 0.291114i | \(0.905974\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 134.541 | 0.203542 | 0.101771 | − | 0.994808i | \(-0.467549\pi\) | ||||
0.101771 | + | 0.994808i | \(0.467549\pi\) | |||||||
\(662\) | − 1017.62i | − 1.53719i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2282.82 | 3.43798 | ||||||||
\(665\) | − 185.175i | − 0.278458i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 303.306 | 0.454731 | ||||||||
\(668\) | − 1917.04i | − 2.86982i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 805.257 | 1.20188 | ||||||||
\(671\) | − 299.023i | − 0.445637i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.81088 | 0.0130920 | 0.00654598 | − | 0.999979i | \(-0.497916\pi\) | ||||
0.00654598 | + | 0.999979i | \(0.497916\pi\) | |||||||
\(674\) | − 1416.90i | − 2.10222i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3794.19 | −5.61270 | ||||||||
\(677\) | − 1222.18i | − 1.80529i | −0.430388 | − | 0.902644i | \(-0.641623\pi\) | ||||
0.430388 | − | 0.902644i | \(-0.358377\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −146.990 | −0.216481 | ||||||||
\(680\) | − 1390.77i | − 2.04525i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 48.2691 | 0.0707759 | ||||||||
\(683\) | − 650.368i | − 0.952222i | −0.879385 | − | 0.476111i | \(-0.842046\pi\) | ||||
0.879385 | − | 0.476111i | \(-0.157954\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −177.076 | −0.258505 | ||||||||
\(686\) | − 1450.80i | − 2.11487i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 620.610 | 0.902049 | ||||||||
\(689\) | 2228.13i | 3.23387i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 709.417 | 1.02665 | 0.513326 | − | 0.858194i | \(-0.328413\pi\) | ||||
0.513326 | + | 0.858194i | \(0.328413\pi\) | |||||||
\(692\) | 2796.86i | 4.04170i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 580.836 | 0.836939 | ||||||||
\(695\) | 473.099i | 0.680718i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −103.106 | −0.147929 | ||||||||
\(698\) | 1799.72i | 2.57840i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1322.92 | 1.88988 | ||||||||
\(701\) | 850.556i | 1.21335i | 0.794951 | + | 0.606673i | \(0.207496\pi\) | ||||
−0.794951 | + | 0.606673i | \(0.792504\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 49.8005 | 0.0708399 | ||||||||
\(704\) | 2132.98i | 3.02981i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1631.39 | 2.31075 | ||||||||
\(707\) | − 457.578i | − 0.647210i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1199.05 | −1.69118 | −0.845591 | − | 0.533831i | \(-0.820752\pi\) | ||||
−0.845591 | + | 0.533831i | \(0.820752\pi\) | |||||||
\(710\) | − 1110.87i | − 1.56460i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4100.34 | −5.75890 | ||||||||
\(713\) | 20.9781i | 0.0294223i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −366.225 | −0.512202 | ||||||||
\(716\) | 293.949i | 0.410543i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 306.401 | 0.426743 | ||||||||
\(719\) | − 255.580i | − 0.355466i | −0.984079 | − | 0.177733i | \(-0.943124\pi\) | ||||
0.984079 | − | 0.177733i | \(-0.0568763\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −510.055 | −0.707427 | ||||||||
\(722\) | 413.885i | 0.573248i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 702.093 | 0.969741 | ||||||||
\(725\) | 470.187i | 0.648534i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −481.234 | −0.661945 | −0.330972 | − | 0.943640i | \(-0.607377\pi\) | ||||
−0.330972 | + | 0.943640i | \(0.607377\pi\) | |||||||
\(728\) | 3559.85i | 4.88990i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −292.944 | −0.401293 | ||||||||
\(731\) | 245.665i | 0.336067i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −245.297 | −0.334648 | −0.167324 | − | 0.985902i | \(-0.553513\pi\) | ||||
−0.167324 | + | 0.985902i | \(0.553513\pi\) | |||||||
\(734\) | − 2271.67i | − 3.09491i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1796.43 | −2.44080 | ||||||||
\(737\) | − 813.284i | − 1.10351i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −761.537 | −1.03050 | −0.515248 | − | 0.857041i | \(-0.672300\pi\) | ||||
−0.515248 | + | 0.857041i | \(0.672300\pi\) | |||||||
\(740\) | − 70.3820i | − 0.0951108i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2187.83 | 2.94856 | ||||||||
\(743\) | − 1378.21i | − 1.85493i | −0.373912 | − | 0.927464i | \(-0.621984\pi\) | ||||
0.373912 | − | 0.927464i | \(-0.378016\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −579.469 | −0.777810 | ||||||||
\(746\) | − 93.3092i | − 0.125079i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2196.50 | −2.93650 | ||||||||
\(749\) | 13.5647i | 0.0181103i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −85.4470 | −0.113778 | −0.0568888 | − | 0.998381i | \(-0.518118\pi\) | ||||
−0.0568888 | + | 0.998381i | \(0.518118\pi\) | |||||||
\(752\) | − 2237.73i | − 2.97571i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1978.52 | −2.62403 | ||||||||
\(755\) | 249.988i | 0.331109i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 89.9427 | 0.118815 | 0.0594074 | − | 0.998234i | \(-0.481079\pi\) | ||||
0.0594074 | + | 0.998234i | \(0.481079\pi\) | |||||||
\(758\) | − 2369.59i | − 3.12611i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −893.554 | −1.17573 | ||||||||
\(761\) | 1194.58i | 1.56975i | 0.619653 | + | 0.784876i | \(0.287273\pi\) | ||||
−0.619653 | + | 0.784876i | \(0.712727\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.4483 | −0.0163149 | ||||||||
\(764\) | 1590.20i | 2.08141i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2118.15 | −2.76520 | ||||||||
\(767\) | − 1591.57i | − 2.07506i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1240.46 | 1.61308 | 0.806542 | − | 0.591177i | \(-0.201337\pi\) | ||||
0.806542 | + | 0.591177i | \(0.201337\pi\) | |||||||
\(770\) | 359.601i | 0.467014i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4039.84 | −5.23295 | ||||||||
\(773\) | 1146.78i | 1.48354i | 0.670655 | + | 0.741770i | \(0.266013\pi\) | ||||
−0.670655 | + | 0.741770i | \(0.733987\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −32.5205 | −0.0419619 | ||||||||
\(776\) | 709.297i | 0.914043i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 413.044 | 0.530904 | ||||||||
\(779\) | 66.2448i | 0.0850383i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1121.94 | −1.43654 | ||||||||
\(782\) | − 1298.77i | − 1.66083i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1026.41 | −1.30919 | ||||||||
\(785\) | 426.642i | 0.543492i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1153.33 | 1.46548 | 0.732740 | − | 0.680509i | \(-0.238241\pi\) | ||||
0.732740 | + | 0.680509i | \(0.238241\pi\) | |||||||
\(788\) | − 2619.21i | − 3.32387i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −546.754 | −0.692094 | ||||||||
\(791\) | 665.532i | 0.841380i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −847.734 | −1.06902 | ||||||||
\(794\) | − 2761.84i | − 3.47839i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3092.18 | −3.88464 | ||||||||
\(797\) | 934.090i | 1.17201i | 0.810308 | + | 0.586004i | \(0.199300\pi\) | ||||
−0.810308 | + | 0.586004i | \(0.800700\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 885.794 | 1.10863 | ||||||||
\(800\) | − 2784.84i | − 3.48104i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 808.147 | 1.00766 | ||||||||
\(803\) | 295.864i | 0.368448i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −156.285 | −0.194143 | ||||||||
\(806\) | − 136.844i | − 0.169781i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2208.03 | −2.73270 | ||||||||
\(809\) | − 10.3335i | − 0.0127732i | −0.999980 | − | 0.00638658i | \(-0.997967\pi\) | ||||
0.999980 | − | 0.00638658i | \(-0.00203293\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1442.35 | 1.77848 | 0.889240 | − | 0.457440i | \(-0.151234\pi\) | ||||
0.889240 | + | 0.457440i | \(0.151234\pi\) | |||||||
\(812\) | 1427.94i | 1.75854i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −96.7102 | −0.118809 | ||||||||
\(815\) | 451.735i | 0.554276i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 157.837 | 0.193191 | ||||||||
\(818\) | 2547.33i | 3.11410i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 93.6225 | 0.114174 | ||||||||
\(821\) | − 1546.21i | − 1.88333i | −0.336552 | − | 0.941665i | \(-0.609261\pi\) | ||||
0.336552 | − | 0.941665i | \(-0.390739\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1582.02 | 1.92226 | 0.961129 | − | 0.276100i | \(-0.0890421\pi\) | ||||
0.961129 | + | 0.276100i | \(0.0890421\pi\) | |||||||
\(824\) | 2461.25i | 2.98695i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1562.78 | −1.89199 | ||||||||
\(827\) | − 58.0629i | − 0.0702091i | −0.999384 | − | 0.0351045i | \(-0.988824\pi\) | ||||
0.999384 | − | 0.0351045i | \(-0.0111764\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −279.841 | −0.337565 | −0.168783 | − | 0.985653i | \(-0.553984\pi\) | ||||
−0.168783 | + | 0.985653i | \(0.553984\pi\) | |||||||
\(830\) | − 653.756i | − 0.787658i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6047.05 | 7.26809 | ||||||||
\(833\) | − 406.298i | − 0.487753i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −351.080 | −0.420455 | ||||||||
\(836\) | 1411.23i | 1.68807i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 270.665 | 0.322989 | ||||||||
\(839\) | 611.537i | 0.728888i | 0.931225 | + | 0.364444i | \(0.118741\pi\) | ||||
−0.931225 | + | 0.364444i | \(0.881259\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 333.487 | 0.396536 | ||||||||
\(842\) | − 1089.81i | − 1.29431i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4289.26 | 5.08207 | ||||||||
\(845\) | 694.855i | 0.822313i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −328.063 | −0.387323 | ||||||||
\(848\) | − 6182.67i | − 7.29088i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2013.36 | 2.36866 | ||||||||
\(851\) | − 42.0310i | − 0.0493901i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −780.661 | −0.915195 | −0.457597 | − | 0.889159i | \(-0.651290\pi\) | ||||
−0.457597 | + | 0.889159i | \(0.651290\pi\) | |||||||
\(854\) | 832.401i | 0.974708i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 65.4558 | 0.0764670 | ||||||||
\(857\) | − 91.5738i | − 0.106854i | −0.998572 | − | 0.0534269i | \(-0.982986\pi\) | ||||
0.998572 | − | 0.0534269i | \(-0.0170144\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −976.219 | −1.13646 | −0.568230 | − | 0.822870i | \(-0.692372\pi\) | ||||
−0.568230 | + | 0.822870i | \(0.692372\pi\) | |||||||
\(860\) | − 223.068i | − 0.259381i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1969.83 | −2.28518 | ||||||||
\(863\) | − 514.017i | − 0.595616i | −0.954626 | − | 0.297808i | \(-0.903744\pi\) | ||||
0.954626 | − | 0.297808i | \(-0.0962555\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 512.207 | 0.592147 | ||||||||
\(866\) | − 862.012i | − 0.995395i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −98.7631 | −0.113782 | ||||||||
\(869\) | 552.204i | 0.635448i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2305.68 | −2.64716 | ||||||||
\(872\) | 60.0688i | 0.0688862i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −834.446 | −0.954743 | ||||||||
\(875\) | − 532.477i | − 0.608545i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 609.520 | 0.695006 | 0.347503 | − | 0.937679i | \(-0.387030\pi\) | ||||
0.347503 | + | 0.937679i | \(0.387030\pi\) | |||||||
\(878\) | 944.858i | 1.07615i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1016.21 | 1.15478 | ||||||||
\(881\) | − 981.132i | − 1.11366i | −0.830628 | − | 0.556828i | \(-0.812018\pi\) | ||||
0.830628 | − | 0.556828i | \(-0.187982\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 549.991 | 0.622867 | 0.311433 | − | 0.950268i | \(-0.399191\pi\) | ||||
0.311433 | + | 0.950268i | \(0.399191\pi\) | |||||||
\(884\) | 6227.12i | 7.04426i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1233.59 | −1.39231 | ||||||||
\(887\) | − 381.280i | − 0.429853i | −0.976630 | − | 0.214927i | \(-0.931049\pi\) | ||||
0.976630 | − | 0.214927i | \(-0.0689512\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 64.3799 | 0.0724183 | ||||||||
\(890\) | 1174.26i | 1.31939i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −80.3288 | −0.0900547 | ||||||||
\(893\) | − 569.114i | − 0.637305i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 53.8328 | 0.0601484 | ||||||||
\(896\) | − 2888.65i | − 3.22394i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2743.86 | −3.05553 | ||||||||
\(899\) | − 35.1021i | − 0.0390457i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2447.38 | 2.71629 | ||||||||
\(902\) | − 128.644i | − 0.142621i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3211.50 | 3.55254 | ||||||||
\(905\) | − 128.579i | − 0.142076i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −701.779 | −0.773737 | −0.386869 | − | 0.922135i | \(-0.626443\pi\) | ||||
−0.386869 | + | 0.922135i | \(0.626443\pi\) | |||||||
\(908\) | − 3308.35i | − 3.64356i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1019.47 | 1.12030 | ||||||||
\(911\) | 514.496i | 0.564760i | 0.959303 | + | 0.282380i | \(0.0911239\pi\) | ||||
−0.959303 | + | 0.282380i | \(0.908876\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −660.273 | −0.723190 | ||||||||
\(914\) | − 2554.07i | − 2.79439i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1733.45 | 1.89241 | ||||||||
\(917\) | 451.273i | 0.492119i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 753.168 | 0.819551 | 0.409776 | − | 0.912186i | \(-0.365607\pi\) | ||||
0.409776 | + | 0.912186i | \(0.365607\pi\) | |||||||
\(920\) | 754.149i | 0.819727i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2170.45 | −2.35406 | ||||||||
\(923\) | 3180.72i | 3.44606i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 65.1568 | 0.0704398 | ||||||||
\(926\) | − 965.015i | − 1.04213i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3005.91 | 3.23913 | ||||||||
\(929\) | 646.826i | 0.696261i | 0.937446 | + | 0.348130i | \(0.113183\pi\) | ||||
−0.937446 | + | 0.348130i | \(0.886817\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −261.042 | −0.280389 | ||||||||
\(932\) | − 1129.17i | − 1.21156i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1746.67 | 1.87010 | ||||||||
\(935\) | 402.260i | 0.430225i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1059.11 | 1.13032 | 0.565160 | − | 0.824981i | \(-0.308814\pi\) | ||||
0.565160 | + | 0.824981i | \(0.308814\pi\) | |||||||
\(938\) | 2263.97i | 2.41362i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −804.317 | −0.855656 | ||||||||
\(941\) | 66.0163i | 0.0701555i | 0.999385 | + | 0.0350777i | \(0.0111679\pi\) | ||||
−0.999385 | + | 0.0350777i | \(0.988832\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 55.9098 | 0.0592893 | ||||||||
\(944\) | 4416.32i | 4.67830i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −306.512 | −0.324009 | ||||||||
\(947\) | − 1136.85i | − 1.20048i | −0.799821 | − | 0.600238i | \(-0.795073\pi\) | ||||
0.799821 | − | 0.600238i | \(-0.204927\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 838.778 | 0.883855 | ||||||||
\(950\) | − 1293.57i | − 1.36165i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3910.13 | 4.10728 | ||||||||
\(953\) | 35.9360i | 0.0377083i | 0.999822 | + | 0.0188542i | \(0.00600182\pi\) | ||||
−0.999822 | + | 0.0188542i | \(0.993998\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 291.223 | 0.304946 | ||||||||
\(956\) | − 1357.37i | − 1.41984i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2259.26 | 2.35831 | ||||||||
\(959\) | − 497.847i | − 0.519131i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −958.572 | −0.997474 | ||||||||
\(962\) | 274.175i | 0.285005i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7.06977 | −0.00733378 | ||||||||
\(965\) | 739.843i | 0.766676i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −773.061 | −0.799443 | −0.399721 | − | 0.916637i | \(-0.630893\pi\) | ||||
−0.399721 | + | 0.916637i | \(0.630893\pi\) | |||||||
\(968\) | 1583.05i | 1.63539i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 203.129 | 0.209412 | ||||||||
\(971\) | 745.333i | 0.767593i | 0.923418 | + | 0.383796i | \(0.125384\pi\) | ||||
−0.923418 | + | 0.383796i | \(0.874616\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1330.11 | −1.36702 | ||||||||
\(974\) | − 458.415i | − 0.470652i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2352.31 | 2.41015 | ||||||||
\(977\) | 187.891i | 0.192314i | 0.995366 | + | 0.0961572i | \(0.0306551\pi\) | ||||
−0.995366 | + | 0.0961572i | \(0.969345\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1185.97 | 1.21141 | ||||||||
\(980\) | 368.926i | 0.376455i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2083.05 | 2.12123 | ||||||||
\(983\) | 970.266i | 0.987046i | 0.869733 | + | 0.493523i | \(0.164291\pi\) | ||||
−0.869733 | + | 0.493523i | \(0.835709\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −479.673 | −0.486978 | ||||||||
\(986\) | 2173.19i | 2.20405i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4000.86 | 4.04945 | ||||||||
\(989\) | − 133.213i | − 0.134694i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 654.491 | 0.660435 | 0.330218 | − | 0.943905i | \(-0.392878\pi\) | ||||
0.330218 | + | 0.943905i | \(0.392878\pi\) | |||||||
\(992\) | 207.904i | 0.209580i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3123.19 | 3.14204 | ||||||||
\(995\) | 566.291i | 0.569137i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1089.23 | 1.09251 | 0.546253 | − | 0.837620i | \(-0.316054\pi\) | ||||
0.546253 | + | 0.837620i | \(0.316054\pi\) | |||||||
\(998\) | − 630.003i | − 0.631266i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1143.3.b.a.890.1 | ✓ | 84 | |
3.2 | odd | 2 | inner | 1143.3.b.a.890.84 | yes | 84 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1143.3.b.a.890.1 | ✓ | 84 | 1.1 | even | 1 | trivial | |
1143.3.b.a.890.84 | yes | 84 | 3.2 | odd | 2 | inner |