Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [403,2,Mod(311,403)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(403, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("403.311");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 403 = 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 403.c (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: | \(3.21797120146\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 311.20 | ||
Character | \(\chi\) | \(=\) | 403.311 |
Dual form | 403.2.c.b.311.13 |
$q$-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 \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).
\(n\) | \(249\) | \(313\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.937316i | 0.662783i | 0.943493 | + | 0.331391i | \(0.107518\pi\) | ||||
−0.943493 | + | 0.331391i | \(0.892482\pi\) | |||||||
\(3\) | 1.68575 | 0.973268 | 0.486634 | − | 0.873606i | \(-0.338225\pi\) | ||||
0.486634 | + | 0.873606i | \(0.338225\pi\) | |||||||
\(4\) | 1.12144 | 0.560719 | ||||||||
\(5\) | − | 0.290760i | − | 0.130032i | −0.997884 | − | 0.0650159i | \(-0.979290\pi\) | ||
0.997884 | − | 0.0650159i | \(-0.0207098\pi\) | |||||||
\(6\) | 1.58008i | 0.645065i | ||||||||
\(7\) | − | 3.85549i | − | 1.45724i | −0.684918 | − | 0.728620i | \(-0.740162\pi\) | ||
0.684918 | − | 0.728620i | \(-0.259838\pi\) | |||||||
\(8\) | 2.92577i | 1.03442i | ||||||||
\(9\) | −0.158249 | −0.0527496 | ||||||||
\(10\) | 0.272534 | 0.0861828 | ||||||||
\(11\) | 2.09645i | 0.632104i | 0.948742 | + | 0.316052i | \(0.102357\pi\) | ||||
−0.948742 | + | 0.316052i | \(0.897643\pi\) | |||||||
\(12\) | 1.89046 | 0.545730 | ||||||||
\(13\) | 2.07708 | + | 2.94716i | 0.576077 | + | 0.817395i | ||||
\(14\) | 3.61382 | 0.965833 | ||||||||
\(15\) | − | 0.490148i | − | 0.126556i | ||||||
\(16\) | −0.499499 | −0.124875 | ||||||||
\(17\) | 5.29143 | 1.28336 | 0.641680 | − | 0.766972i | \(-0.278238\pi\) | ||||
0.641680 | + | 0.766972i | \(0.278238\pi\) | |||||||
\(18\) | − | 0.148329i | − | 0.0349615i | ||||||
\(19\) | − | 3.22555i | − | 0.739991i | −0.929034 | − | 0.369996i | \(-0.879359\pi\) | ||
0.929034 | − | 0.369996i | \(-0.120641\pi\) | |||||||
\(20\) | − | 0.326069i | − | 0.0729113i | ||||||
\(21\) | − | 6.49940i | − | 1.41828i | ||||||
\(22\) | −1.96504 | −0.418947 | ||||||||
\(23\) | −6.80143 | −1.41820 | −0.709098 | − | 0.705110i | \(-0.750898\pi\) | ||||
−0.709098 | + | 0.705110i | \(0.750898\pi\) | |||||||
\(24\) | 4.93212i | 1.00677i | ||||||||
\(25\) | 4.91546 | 0.983092 | ||||||||
\(26\) | −2.76242 | + | 1.94688i | −0.541755 | + | 0.381814i | ||||
\(27\) | −5.32402 | −1.02461 | ||||||||
\(28\) | − | 4.32370i | − | 0.817102i | ||||||
\(29\) | −4.52320 | −0.839938 | −0.419969 | − | 0.907539i | \(-0.637959\pi\) | ||||
−0.419969 | + | 0.907539i | \(0.637959\pi\) | |||||||
\(30\) | 0.459424 | 0.0838789 | ||||||||
\(31\) | 1.00000i | 0.179605i | ||||||||
\(32\) | 5.38336i | 0.951653i | ||||||||
\(33\) | 3.53409i | 0.615206i | ||||||||
\(34\) | 4.95974i | 0.850589i | ||||||||
\(35\) | −1.12102 | −0.189487 | ||||||||
\(36\) | −0.177466 | −0.0295777 | ||||||||
\(37\) | − | 4.81693i | − | 0.791899i | −0.918272 | − | 0.395950i | \(-0.870416\pi\) | ||
0.918272 | − | 0.395950i | \(-0.129584\pi\) | |||||||
\(38\) | 3.02336 | 0.490453 | ||||||||
\(39\) | 3.50143 | + | 4.96818i | 0.560677 | + | 0.795545i | ||||
\(40\) | 0.850698 | 0.134507 | ||||||||
\(41\) | − | 6.15845i | − | 0.961788i | −0.876779 | − | 0.480894i | \(-0.840312\pi\) | ||
0.876779 | − | 0.480894i | \(-0.159688\pi\) | |||||||
\(42\) | 6.09199 | 0.940015 | ||||||||
\(43\) | −7.12251 | −1.08617 | −0.543087 | − | 0.839677i | \(-0.682744\pi\) | ||||
−0.543087 | + | 0.839677i | \(0.682744\pi\) | |||||||
\(44\) | 2.35104i | 0.354433i | ||||||||
\(45\) | 0.0460124i | 0.00685912i | ||||||||
\(46\) | − | 6.37509i | − | 0.939956i | ||||||
\(47\) | 4.76874i | 0.695592i | 0.937570 | + | 0.347796i | \(0.113070\pi\) | ||||
−0.937570 | + | 0.347796i | \(0.886930\pi\) | |||||||
\(48\) | −0.842031 | −0.121537 | ||||||||
\(49\) | −7.86484 | −1.12355 | ||||||||
\(50\) | 4.60734i | 0.651576i | ||||||||
\(51\) | 8.92003 | 1.24905 | ||||||||
\(52\) | 2.32931 | + | 3.30506i | 0.323017 | + | 0.458329i | ||||
\(53\) | −5.08219 | −0.698093 | −0.349046 | − | 0.937105i | \(-0.613494\pi\) | ||||
−0.349046 | + | 0.937105i | \(0.613494\pi\) | |||||||
\(54\) | − | 4.99029i | − | 0.679092i | ||||||
\(55\) | 0.609564 | 0.0821936 | ||||||||
\(56\) | 11.2803 | 1.50739 | ||||||||
\(57\) | − | 5.43746i | − | 0.720210i | ||||||
\(58\) | − | 4.23967i | − | 0.556696i | ||||||
\(59\) | 9.83912i | 1.28094i | 0.767981 | + | 0.640472i | \(0.221261\pi\) | ||||
−0.767981 | + | 0.640472i | \(0.778739\pi\) | |||||||
\(60\) | − | 0.549671i | − | 0.0709622i | ||||||
\(61\) | −9.60411 | −1.22968 | −0.614840 | − | 0.788652i | \(-0.710780\pi\) | ||||
−0.614840 | + | 0.788652i | \(0.710780\pi\) | |||||||
\(62\) | −0.937316 | −0.119039 | ||||||||
\(63\) | 0.610127i | 0.0768688i | ||||||||
\(64\) | −6.04491 | −0.755614 | ||||||||
\(65\) | 0.856916 | − | 0.603930i | 0.106287 | − | 0.0749083i | ||||
\(66\) | −3.31256 | −0.407748 | ||||||||
\(67\) | − | 6.38630i | − | 0.780210i | −0.920770 | − | 0.390105i | \(-0.872439\pi\) | ||
0.920770 | − | 0.390105i | \(-0.127561\pi\) | |||||||
\(68\) | 5.93402 | 0.719605 | ||||||||
\(69\) | −11.4655 | −1.38029 | ||||||||
\(70\) | − | 1.05075i | − | 0.125589i | ||||||
\(71\) | 3.60967i | 0.428389i | 0.976791 | + | 0.214194i | \(0.0687126\pi\) | ||||
−0.976791 | + | 0.214194i | \(0.931287\pi\) | |||||||
\(72\) | − | 0.463000i | − | 0.0545651i | ||||||
\(73\) | 8.21949i | 0.962018i | 0.876716 | + | 0.481009i | \(0.159730\pi\) | ||||
−0.876716 | + | 0.481009i | \(0.840270\pi\) | |||||||
\(74\) | 4.51499 | 0.524857 | ||||||||
\(75\) | 8.28623 | 0.956812 | ||||||||
\(76\) | − | 3.61725i | − | 0.414927i | ||||||
\(77\) | 8.08285 | 0.921127 | ||||||||
\(78\) | −4.65675 | + | 3.28195i | −0.527273 | + | 0.371607i | ||||
\(79\) | −4.16666 | −0.468786 | −0.234393 | − | 0.972142i | \(-0.575310\pi\) | ||||
−0.234393 | + | 0.972142i | \(0.575310\pi\) | |||||||
\(80\) | 0.145234i | 0.0162377i | ||||||||
\(81\) | −8.50021 | −0.944468 | ||||||||
\(82\) | 5.77241 | 0.637456 | ||||||||
\(83\) | − | 5.60314i | − | 0.615024i | −0.951544 | − | 0.307512i | \(-0.900504\pi\) | ||
0.951544 | − | 0.307512i | \(-0.0994964\pi\) | |||||||
\(84\) | − | 7.28867i | − | 0.795260i | ||||||
\(85\) | − | 1.53854i | − | 0.166878i | ||||||
\(86\) | − | 6.67605i | − | 0.719897i | ||||||
\(87\) | −7.62499 | −0.817484 | ||||||||
\(88\) | −6.13374 | −0.653859 | ||||||||
\(89\) | − | 5.99295i | − | 0.635251i | −0.948216 | − | 0.317626i | \(-0.897115\pi\) | ||
0.948216 | − | 0.317626i | \(-0.102885\pi\) | |||||||
\(90\) | −0.0431282 | −0.00454611 | ||||||||
\(91\) | 11.3628 | − | 8.00815i | 1.19114 | − | 0.839483i | ||||
\(92\) | −7.62739 | −0.795210 | ||||||||
\(93\) | 1.68575i | 0.174804i | ||||||||
\(94\) | −4.46982 | −0.461026 | ||||||||
\(95\) | −0.937859 | −0.0962224 | ||||||||
\(96\) | 9.07500i | 0.926213i | ||||||||
\(97\) | − | 1.49758i | − | 0.152056i | −0.997106 | − | 0.0760282i | \(-0.975776\pi\) | ||
0.997106 | − | 0.0760282i | \(-0.0242239\pi\) | |||||||
\(98\) | − | 7.37184i | − | 0.744668i | ||||||
\(99\) | − | 0.331761i | − | 0.0333432i | ||||||
\(100\) | 5.51238 | 0.551238 | ||||||||
\(101\) | 6.72002 | 0.668667 | 0.334333 | − | 0.942455i | \(-0.391489\pi\) | ||||
0.334333 | + | 0.942455i | \(0.391489\pi\) | |||||||
\(102\) | 8.36089i | 0.827851i | ||||||||
\(103\) | −10.1453 | −0.999647 | −0.499824 | − | 0.866127i | \(-0.666602\pi\) | ||||
−0.499824 | + | 0.866127i | \(0.666602\pi\) | |||||||
\(104\) | −8.62273 | + | 6.07705i | −0.845528 | + | 0.595904i | ||||
\(105\) | −1.88976 | −0.184422 | ||||||||
\(106\) | − | 4.76362i | − | 0.462684i | ||||||
\(107\) | −13.0831 | −1.26479 | −0.632397 | − | 0.774644i | \(-0.717929\pi\) | ||||
−0.632397 | + | 0.774644i | \(0.717929\pi\) | |||||||
\(108\) | −5.97056 | −0.574517 | ||||||||
\(109\) | − | 8.14852i | − | 0.780486i | −0.920712 | − | 0.390243i | \(-0.872391\pi\) | ||
0.920712 | − | 0.390243i | \(-0.127609\pi\) | |||||||
\(110\) | 0.571354i | 0.0544765i | ||||||||
\(111\) | − | 8.12014i | − | 0.770730i | ||||||
\(112\) | 1.92582i | 0.181973i | ||||||||
\(113\) | 20.6286 | 1.94057 | 0.970287 | − | 0.241958i | \(-0.0777895\pi\) | ||||
0.970287 | + | 0.241958i | \(0.0777895\pi\) | |||||||
\(114\) | 5.09662 | 0.477342 | ||||||||
\(115\) | 1.97758i | 0.184411i | ||||||||
\(116\) | −5.07249 | −0.470969 | ||||||||
\(117\) | −0.328695 | − | 0.466385i | −0.0303878 | − | 0.0431173i | ||||
\(118\) | −9.22237 | −0.848988 | ||||||||
\(119\) | − | 20.4011i | − | 1.87016i | ||||||
\(120\) | 1.43406 | 0.130911 | ||||||||
\(121\) | 6.60489 | 0.600445 | ||||||||
\(122\) | − | 9.00209i | − | 0.815011i | ||||||
\(123\) | − | 10.3816i | − | 0.936077i | ||||||
\(124\) | 1.12144i | 0.100708i | ||||||||
\(125\) | − | 2.88302i | − | 0.257865i | ||||||
\(126\) | −0.571882 | −0.0509473 | ||||||||
\(127\) | 1.36933 | 0.121509 | 0.0607544 | − | 0.998153i | \(-0.480649\pi\) | ||||
0.0607544 | + | 0.998153i | \(0.480649\pi\) | |||||||
\(128\) | 5.10073i | 0.450845i | ||||||||
\(129\) | −12.0068 | −1.05714 | ||||||||
\(130\) | 0.566074 | + | 0.803201i | 0.0496479 | + | 0.0704454i | ||||
\(131\) | 9.73999 | 0.850987 | 0.425494 | − | 0.904961i | \(-0.360100\pi\) | ||||
0.425494 | + | 0.904961i | \(0.360100\pi\) | |||||||
\(132\) | 3.96327i | 0.344958i | ||||||||
\(133\) | −12.4361 | −1.07834 | ||||||||
\(134\) | 5.98598 | 0.517110 | ||||||||
\(135\) | 1.54801i | 0.133232i | ||||||||
\(136\) | 15.4815i | 1.32753i | ||||||||
\(137\) | − | 11.0632i | − | 0.945191i | −0.881280 | − | 0.472595i | \(-0.843317\pi\) | ||
0.881280 | − | 0.472595i | \(-0.156683\pi\) | |||||||
\(138\) | − | 10.7468i | − | 0.914829i | ||||||
\(139\) | 15.7894 | 1.33924 | 0.669620 | − | 0.742704i | \(-0.266457\pi\) | ||||
0.669620 | + | 0.742704i | \(0.266457\pi\) | |||||||
\(140\) | −1.25716 | −0.106249 | ||||||||
\(141\) | 8.03890i | 0.676998i | ||||||||
\(142\) | −3.38340 | −0.283929 | ||||||||
\(143\) | −6.17858 | + | 4.35449i | −0.516679 | + | 0.364140i | ||||
\(144\) | 0.0790451 | 0.00658709 | ||||||||
\(145\) | 1.31517i | 0.109219i | ||||||||
\(146\) | −7.70426 | −0.637609 | ||||||||
\(147\) | −13.2581 | −1.09351 | ||||||||
\(148\) | − | 5.40189i | − | 0.444033i | ||||||
\(149\) | − | 2.97069i | − | 0.243368i | −0.992569 | − | 0.121684i | \(-0.961171\pi\) | ||
0.992569 | − | 0.121684i | \(-0.0388295\pi\) | |||||||
\(150\) | 7.76682i | 0.634158i | ||||||||
\(151\) | 20.1243i | 1.63770i | 0.574011 | + | 0.818848i | \(0.305387\pi\) | ||||
−0.574011 | + | 0.818848i | \(0.694613\pi\) | |||||||
\(152\) | 9.43722 | 0.765460 | ||||||||
\(153\) | −0.837363 | −0.0676967 | ||||||||
\(154\) | 7.57619i | 0.610507i | ||||||||
\(155\) | 0.290760 | 0.0233544 | ||||||||
\(156\) | 3.92664 | + | 5.57150i | 0.314383 | + | 0.446077i | ||||
\(157\) | 18.9740 | 1.51429 | 0.757147 | − | 0.653245i | \(-0.226593\pi\) | ||||
0.757147 | + | 0.653245i | \(0.226593\pi\) | |||||||
\(158\) | − | 3.90548i | − | 0.310703i | ||||||
\(159\) | −8.56730 | −0.679431 | ||||||||
\(160\) | 1.56527 | 0.123745 | ||||||||
\(161\) | 26.2229i | 2.06665i | ||||||||
\(162\) | − | 7.96739i | − | 0.625977i | ||||||
\(163\) | − | 19.5049i | − | 1.52774i | −0.645369 | − | 0.763871i | \(-0.723296\pi\) | ||
0.645369 | − | 0.763871i | \(-0.276704\pi\) | |||||||
\(164\) | − | 6.90632i | − | 0.539293i | ||||||
\(165\) | 1.02757 | 0.0799964 | ||||||||
\(166\) | 5.25191 | 0.407627 | ||||||||
\(167\) | 23.5293i | 1.82075i | 0.413785 | + | 0.910375i | \(0.364207\pi\) | ||||
−0.413785 | + | 0.910375i | \(0.635793\pi\) | |||||||
\(168\) | 19.0158 | 1.46710 | ||||||||
\(169\) | −4.37152 | + | 12.2430i | −0.336270 | + | 0.941765i | ||||
\(170\) | 1.44209 | 0.110604 | ||||||||
\(171\) | 0.510439i | 0.0390342i | ||||||||
\(172\) | −7.98746 | −0.609038 | ||||||||
\(173\) | 11.3779 | 0.865043 | 0.432522 | − | 0.901624i | \(-0.357624\pi\) | ||||
0.432522 | + | 0.901624i | \(0.357624\pi\) | |||||||
\(174\) | − | 7.14702i | − | 0.541814i | ||||||
\(175\) | − | 18.9515i | − | 1.43260i | ||||||
\(176\) | − | 1.04718i | − | 0.0789338i | ||||||
\(177\) | 16.5863i | 1.24670i | ||||||||
\(178\) | 5.61729 | 0.421033 | ||||||||
\(179\) | 20.7125 | 1.54813 | 0.774063 | − | 0.633108i | \(-0.218221\pi\) | ||||
0.774063 | + | 0.633108i | \(0.218221\pi\) | |||||||
\(180\) | 0.0516001i | 0.00384604i | ||||||||
\(181\) | 2.21171 | 0.164395 | 0.0821975 | − | 0.996616i | \(-0.473806\pi\) | ||||
0.0821975 | + | 0.996616i | \(0.473806\pi\) | |||||||
\(182\) | 7.50617 | + | 10.6505i | 0.556394 | + | 0.789468i | ||||
\(183\) | −16.1901 | −1.19681 | ||||||||
\(184\) | − | 19.8995i | − | 1.46701i | ||||||
\(185\) | −1.40057 | −0.102972 | ||||||||
\(186\) | −1.58008 | −0.115857 | ||||||||
\(187\) | 11.0932i | 0.811217i | ||||||||
\(188\) | 5.34785i | 0.390032i | ||||||||
\(189\) | 20.5267i | 1.49310i | ||||||||
\(190\) | − | 0.879071i | − | 0.0637745i | ||||||
\(191\) | −5.93737 | −0.429613 | −0.214806 | − | 0.976657i | \(-0.568912\pi\) | ||||
−0.214806 | + | 0.976657i | \(0.568912\pi\) | |||||||
\(192\) | −10.1902 | −0.735415 | ||||||||
\(193\) | 7.67380i | 0.552372i | 0.961104 | + | 0.276186i | \(0.0890706\pi\) | ||||
−0.961104 | + | 0.276186i | \(0.910929\pi\) | |||||||
\(194\) | 1.40371 | 0.100780 | ||||||||
\(195\) | 1.44455 | − | 1.01807i | 0.103446 | − | 0.0729059i | ||||
\(196\) | −8.81993 | −0.629995 | ||||||||
\(197\) | 10.6398i | 0.758057i | 0.925385 | + | 0.379029i | \(0.123742\pi\) | ||||
−0.925385 | + | 0.379029i | \(0.876258\pi\) | |||||||
\(198\) | 0.310965 | 0.0220993 | ||||||||
\(199\) | −21.8838 | −1.55130 | −0.775650 | − | 0.631163i | \(-0.782578\pi\) | ||||
−0.775650 | + | 0.631163i | \(0.782578\pi\) | |||||||
\(200\) | 14.3815i | 1.01693i | ||||||||
\(201\) | − | 10.7657i | − | 0.759354i | ||||||
\(202\) | 6.29878i | 0.443181i | ||||||||
\(203\) | 17.4392i | 1.22399i | ||||||||
\(204\) | 10.0033 | 0.700368 | ||||||||
\(205\) | −1.79063 | −0.125063 | ||||||||
\(206\) | − | 9.50936i | − | 0.662549i | ||||||
\(207\) | 1.07632 | 0.0748093 | ||||||||
\(208\) | −1.03750 | − | 1.47210i | −0.0719375 | − | 0.102072i | ||||
\(209\) | 6.76220 | 0.467751 | ||||||||
\(210\) | − | 1.77131i | − | 0.122232i | ||||||
\(211\) | 27.2902 | 1.87873 | 0.939366 | − | 0.342917i | \(-0.111415\pi\) | ||||
0.939366 | + | 0.342917i | \(0.111415\pi\) | |||||||
\(212\) | −5.69937 | −0.391434 | ||||||||
\(213\) | 6.08500i | 0.416937i | ||||||||
\(214\) | − | 12.2630i | − | 0.838284i | ||||||
\(215\) | 2.07094i | 0.141237i | ||||||||
\(216\) | − | 15.5769i | − | 1.05987i | ||||||
\(217\) | 3.85549 | 0.261728 | ||||||||
\(218\) | 7.63774 | 0.517293 | ||||||||
\(219\) | 13.8560i | 0.936302i | ||||||||
\(220\) | 0.683588 | 0.0460875 | ||||||||
\(221\) | 10.9907 | + | 15.5947i | 0.739315 | + | 1.04901i | ||||
\(222\) | 7.61114 | 0.510826 | ||||||||
\(223\) | − | 23.9038i | − | 1.60071i | −0.599524 | − | 0.800357i | \(-0.704643\pi\) | ||
0.599524 | − | 0.800357i | \(-0.295357\pi\) | |||||||
\(224\) | 20.7555 | 1.38679 | ||||||||
\(225\) | −0.777865 | −0.0518577 | ||||||||
\(226\) | 19.3355i | 1.28618i | ||||||||
\(227\) | − | 14.9621i | − | 0.993072i | −0.868016 | − | 0.496536i | \(-0.834605\pi\) | ||
0.868016 | − | 0.496536i | \(-0.165395\pi\) | |||||||
\(228\) | − | 6.09778i | − | 0.403835i | ||||||
\(229\) | − | 13.2617i | − | 0.876355i | −0.898888 | − | 0.438178i | \(-0.855624\pi\) | ||
0.898888 | − | 0.438178i | \(-0.144376\pi\) | |||||||
\(230\) | −1.85362 | −0.122224 | ||||||||
\(231\) | 13.6257 | 0.896503 | ||||||||
\(232\) | − | 13.2339i | − | 0.868846i | ||||||
\(233\) | −0.641941 | −0.0420549 | −0.0210275 | − | 0.999779i | \(-0.506694\pi\) | ||||
−0.0210275 | + | 0.999779i | \(0.506694\pi\) | |||||||
\(234\) | 0.437150 | − | 0.308091i | 0.0285774 | − | 0.0201405i | ||||
\(235\) | 1.38656 | 0.0904491 | ||||||||
\(236\) | 11.0340i | 0.718250i | ||||||||
\(237\) | −7.02395 | −0.456254 | ||||||||
\(238\) | 19.1223 | 1.23951 | ||||||||
\(239\) | 4.79323i | 0.310048i | 0.987911 | + | 0.155024i | \(0.0495455\pi\) | ||||
−0.987911 | + | 0.155024i | \(0.950454\pi\) | |||||||
\(240\) | 0.244829i | 0.0158036i | ||||||||
\(241\) | 20.2887i | 1.30691i | 0.756966 | + | 0.653454i | \(0.226681\pi\) | ||||
−0.756966 | + | 0.653454i | \(0.773319\pi\) | |||||||
\(242\) | 6.19087i | 0.397964i | ||||||||
\(243\) | 1.64282 | 0.105387 | ||||||||
\(244\) | −10.7704 | −0.689506 | ||||||||
\(245\) | 2.28678i | 0.146097i | ||||||||
\(246\) | 9.73084 | 0.620416 | ||||||||
\(247\) | 9.50620 | − | 6.69970i | 0.604865 | − | 0.426292i | ||||
\(248\) | −2.92577 | −0.185787 | ||||||||
\(249\) | − | 9.44548i | − | 0.598583i | ||||||
\(250\) | 2.70230 | 0.170908 | ||||||||
\(251\) | −21.8713 | −1.38050 | −0.690251 | − | 0.723570i | \(-0.742500\pi\) | ||||
−0.690251 | + | 0.723570i | \(0.742500\pi\) | |||||||
\(252\) | 0.684220i | 0.0431018i | ||||||||
\(253\) | − | 14.2589i | − | 0.896447i | ||||||
\(254\) | 1.28350i | 0.0805339i | ||||||||
\(255\) | − | 2.59359i | − | 0.162417i | ||||||
\(256\) | −16.8708 | −1.05443 | ||||||||
\(257\) | −15.8299 | −0.987444 | −0.493722 | − | 0.869620i | \(-0.664364\pi\) | ||||
−0.493722 | + | 0.869620i | \(0.664364\pi\) | |||||||
\(258\) | − | 11.2541i | − | 0.700652i | ||||||
\(259\) | −18.5717 | −1.15399 | ||||||||
\(260\) | 0.960979 | − | 0.677270i | 0.0595974 | − | 0.0420025i | ||||
\(261\) | 0.715791 | 0.0443064 | ||||||||
\(262\) | 9.12945i | 0.564020i | ||||||||
\(263\) | 3.06797 | 0.189179 | 0.0945897 | − | 0.995516i | \(-0.469846\pi\) | ||||
0.0945897 | + | 0.995516i | \(0.469846\pi\) | |||||||
\(264\) | −10.3400 | −0.636380 | ||||||||
\(265\) | 1.47770i | 0.0907742i | ||||||||
\(266\) | − | 11.6565i | − | 0.714708i | ||||||
\(267\) | − | 10.1026i | − | 0.618269i | ||||||
\(268\) | − | 7.16184i | − | 0.437479i | ||||||
\(269\) | 6.90791 | 0.421183 | 0.210591 | − | 0.977574i | \(-0.432461\pi\) | ||||
0.210591 | + | 0.977574i | \(0.432461\pi\) | |||||||
\(270\) | −1.45098 | −0.0883035 | ||||||||
\(271\) | 32.2346i | 1.95811i | 0.203597 | + | 0.979055i | \(0.434737\pi\) | ||||
−0.203597 | + | 0.979055i | \(0.565263\pi\) | |||||||
\(272\) | −2.64307 | −0.160259 | ||||||||
\(273\) | 19.1548 | − | 13.4997i | 1.15930 | − | 0.817041i | ||||
\(274\) | 10.3697 | 0.626456 | ||||||||
\(275\) | 10.3050i | 0.621416i | ||||||||
\(276\) | −12.8579 | −0.773952 | ||||||||
\(277\) | 16.2761 | 0.977938 | 0.488969 | − | 0.872301i | \(-0.337373\pi\) | ||||
0.488969 | + | 0.872301i | \(0.337373\pi\) | |||||||
\(278\) | 14.7997i | 0.887625i | ||||||||
\(279\) | − | 0.158249i | − | 0.00947410i | ||||||
\(280\) | − | 3.27986i | − | 0.196009i | ||||||
\(281\) | 22.5291i | 1.34397i | 0.740563 | + | 0.671987i | \(0.234559\pi\) | ||||
−0.740563 | + | 0.671987i | \(0.765441\pi\) | |||||||
\(282\) | −7.53499 | −0.448702 | ||||||||
\(283\) | −11.1486 | −0.662718 | −0.331359 | − | 0.943505i | \(-0.607507\pi\) | ||||
−0.331359 | + | 0.943505i | \(0.607507\pi\) | |||||||
\(284\) | 4.04802i | 0.240206i | ||||||||
\(285\) | −1.58100 | −0.0936501 | ||||||||
\(286\) | −4.08153 | − | 5.79128i | −0.241346 | − | 0.342446i | ||||
\(287\) | −23.7439 | −1.40156 | ||||||||
\(288\) | − | 0.851910i | − | 0.0501993i | ||||||
\(289\) | 10.9993 | 0.647015 | ||||||||
\(290\) | −1.23273 | −0.0723882 | ||||||||
\(291\) | − | 2.52455i | − | 0.147992i | ||||||
\(292\) | 9.21765i | 0.539422i | ||||||||
\(293\) | − | 29.1854i | − | 1.70503i | −0.522705 | − | 0.852514i | \(-0.675077\pi\) | ||
0.522705 | − | 0.852514i | \(-0.324923\pi\) | |||||||
\(294\) | − | 12.4271i | − | 0.724762i | ||||||
\(295\) | 2.86082 | 0.166564 | ||||||||
\(296\) | 14.0933 | 0.819154 | ||||||||
\(297\) | − | 11.1615i | − | 0.647658i | ||||||
\(298\) | 2.78447 | 0.161300 | ||||||||
\(299\) | −14.1271 | − | 20.0449i | −0.816991 | − | 1.15923i | ||||
\(300\) | 9.29250 | 0.536503 | ||||||||
\(301\) | 27.4608i | 1.58281i | ||||||||
\(302\) | −18.8629 | −1.08544 | ||||||||
\(303\) | 11.3283 | 0.650792 | ||||||||
\(304\) | 1.61116i | 0.0924062i | ||||||||
\(305\) | 2.79249i | 0.159898i | ||||||||
\(306\) | − | 0.784873i | − | 0.0448682i | ||||||
\(307\) | − | 10.2881i | − | 0.587175i | −0.955932 | − | 0.293588i | \(-0.905151\pi\) | ||
0.955932 | − | 0.293588i | \(-0.0948493\pi\) | |||||||
\(308\) | 9.06442 | 0.516493 | ||||||||
\(309\) | −17.1025 | −0.972925 | ||||||||
\(310\) | 0.272534i | 0.0154789i | ||||||||
\(311\) | 6.14155 | 0.348256 | 0.174128 | − | 0.984723i | \(-0.444289\pi\) | ||||
0.174128 | + | 0.984723i | \(0.444289\pi\) | |||||||
\(312\) | −14.5358 | + | 10.2444i | −0.822925 | + | 0.579974i | ||||
\(313\) | 8.55769 | 0.483709 | 0.241855 | − | 0.970313i | \(-0.422244\pi\) | ||||
0.241855 | + | 0.970313i | \(0.422244\pi\) | |||||||
\(314\) | 17.7847i | 1.00365i | ||||||||
\(315\) | 0.177401 | 0.00999539 | ||||||||
\(316\) | −4.67265 | −0.262857 | ||||||||
\(317\) | − | 14.4222i | − | 0.810032i | −0.914310 | − | 0.405016i | \(-0.867266\pi\) | ||
0.914310 | − | 0.405016i | \(-0.132734\pi\) | |||||||
\(318\) | − | 8.03027i | − | 0.450315i | ||||||
\(319\) | − | 9.48267i | − | 0.530928i | ||||||
\(320\) | 1.75762i | 0.0982538i | ||||||||
\(321\) | −22.0549 | −1.23098 | ||||||||
\(322\) | −24.5791 | −1.36974 | ||||||||
\(323\) | − | 17.0678i | − | 0.949676i | ||||||
\(324\) | −9.53246 | −0.529581 | ||||||||
\(325\) | 10.2098 | + | 14.4866i | 0.566337 | + | 0.803575i | ||||
\(326\) | 18.2823 | 1.01256 | ||||||||
\(327\) | − | 13.7364i | − | 0.759622i | ||||||
\(328\) | 18.0182 | 0.994890 | ||||||||
\(329\) | 18.3859 | 1.01364 | ||||||||
\(330\) | 0.963160i | 0.0530202i | ||||||||
\(331\) | − | 21.6554i | − | 1.19029i | −0.803620 | − | 0.595143i | \(-0.797095\pi\) | ||
0.803620 | − | 0.595143i | \(-0.202905\pi\) | |||||||
\(332\) | − | 6.28357i | − | 0.344856i | ||||||
\(333\) | 0.762274i | 0.0417723i | ||||||||
\(334\) | −22.0544 | −1.20676 | ||||||||
\(335\) | −1.85688 | −0.101452 | ||||||||
\(336\) | 3.24644i | 0.177108i | ||||||||
\(337\) | 14.4456 | 0.786904 | 0.393452 | − | 0.919345i | \(-0.371281\pi\) | ||||
0.393452 | + | 0.919345i | \(0.371281\pi\) | |||||||
\(338\) | −11.4755 | − | 4.09749i | −0.624186 | − | 0.222874i | ||||
\(339\) | 34.7746 | 1.88870 | ||||||||
\(340\) | − | 1.72537i | − | 0.0935715i | ||||||
\(341\) | −2.09645 | −0.113529 | ||||||||
\(342\) | −0.478442 | −0.0258712 | ||||||||
\(343\) | 3.33438i | 0.180039i | ||||||||
\(344\) | − | 20.8389i | − | 1.12356i | ||||||
\(345\) | 3.33371i | 0.179481i | ||||||||
\(346\) | 10.6647i | 0.573335i | ||||||||
\(347\) | −9.70087 | −0.520770 | −0.260385 | − | 0.965505i | \(-0.583849\pi\) | ||||
−0.260385 | + | 0.965505i | \(0.583849\pi\) | |||||||
\(348\) | −8.55095 | −0.458379 | ||||||||
\(349\) | − | 2.05208i | − | 0.109845i | −0.998491 | − | 0.0549227i | \(-0.982509\pi\) | ||
0.998491 | − | 0.0549227i | \(-0.0174912\pi\) | |||||||
\(350\) | 17.7636 | 0.949503 | ||||||||
\(351\) | −11.0584 | − | 15.6907i | −0.590253 | − | 0.837509i | ||||
\(352\) | −11.2860 | −0.601543 | ||||||||
\(353\) | − | 11.7324i | − | 0.624452i | −0.950008 | − | 0.312226i | \(-0.898925\pi\) | ||
0.950008 | − | 0.312226i | \(-0.101075\pi\) | |||||||
\(354\) | −15.5466 | −0.826293 | ||||||||
\(355\) | 1.04955 | 0.0557042 | ||||||||
\(356\) | − | 6.72072i | − | 0.356197i | ||||||
\(357\) | − | 34.3911i | − | 1.82017i | ||||||
\(358\) | 19.4142i | 1.02607i | ||||||||
\(359\) | 24.9325i | 1.31588i | 0.753068 | + | 0.657942i | \(0.228573\pi\) | ||||
−0.753068 | + | 0.657942i | \(0.771427\pi\) | |||||||
\(360\) | −0.134622 | −0.00709520 | ||||||||
\(361\) | 8.59585 | 0.452413 | ||||||||
\(362\) | 2.07307i | 0.108958i | ||||||||
\(363\) | 11.1342 | 0.584394 | ||||||||
\(364\) | 12.7426 | − | 8.98065i | 0.667896 | − | 0.470714i | ||||
\(365\) | 2.38990 | 0.125093 | ||||||||
\(366\) | − | 15.1753i | − | 0.793224i | ||||||
\(367\) | 13.7018 | 0.715230 | 0.357615 | − | 0.933869i | \(-0.383590\pi\) | ||||
0.357615 | + | 0.933869i | \(0.383590\pi\) | |||||||
\(368\) | 3.39731 | 0.177097 | ||||||||
\(369\) | 0.974566i | 0.0507339i | ||||||||
\(370\) | − | 1.31278i | − | 0.0682481i | ||||||
\(371\) | 19.5944i | 1.01729i | ||||||||
\(372\) | 1.89046i | 0.0980160i | ||||||||
\(373\) | −9.22059 | −0.477424 | −0.238712 | − | 0.971090i | \(-0.576725\pi\) | ||||
−0.238712 | + | 0.971090i | \(0.576725\pi\) | |||||||
\(374\) | −10.3979 | −0.537661 | ||||||||
\(375\) | − | 4.86005i | − | 0.250972i | ||||||
\(376\) | −13.9523 | −0.719533 | ||||||||
\(377\) | −9.39503 | − | 13.3306i | −0.483869 | − | 0.686561i | ||||
\(378\) | −19.2400 | −0.989600 | ||||||||
\(379\) | 7.66126i | 0.393532i | 0.980450 | + | 0.196766i | \(0.0630440\pi\) | ||||
−0.980450 | + | 0.196766i | \(0.936956\pi\) | |||||||
\(380\) | −1.05175 | −0.0539537 | ||||||||
\(381\) | 2.30835 | 0.118261 | ||||||||
\(382\) | − | 5.56519i | − | 0.284740i | ||||||
\(383\) | − | 3.77098i | − | 0.192688i | −0.995348 | − | 0.0963440i | \(-0.969285\pi\) | ||
0.995348 | − | 0.0963440i | \(-0.0307149\pi\) | |||||||
\(384\) | 8.59855i | 0.438793i | ||||||||
\(385\) | − | 2.35017i | − | 0.119776i | ||||||
\(386\) | −7.19278 | −0.366103 | ||||||||
\(387\) | 1.12713 | 0.0572952 | ||||||||
\(388\) | − | 1.67944i | − | 0.0852609i | ||||||
\(389\) | −1.98742 | −0.100766 | −0.0503831 | − | 0.998730i | \(-0.516044\pi\) | ||||
−0.0503831 | + | 0.998730i | \(0.516044\pi\) | |||||||
\(390\) | 0.954258 | + | 1.35400i | 0.0483207 | + | 0.0685623i | ||||
\(391\) | −35.9893 | −1.82006 | ||||||||
\(392\) | − | 23.0107i | − | 1.16222i | ||||||
\(393\) | 16.4192 | 0.828239 | ||||||||
\(394\) | −9.97289 | −0.502427 | ||||||||
\(395\) | 1.21150i | 0.0609571i | ||||||||
\(396\) | − | 0.372049i | − | 0.0186962i | ||||||
\(397\) | − | 7.83722i | − | 0.393339i | −0.980470 | − | 0.196669i | \(-0.936987\pi\) | ||
0.980470 | − | 0.196669i | \(-0.0630126\pi\) | |||||||
\(398\) | − | 20.5120i | − | 1.02817i | ||||||
\(399\) | −20.9641 | −1.04952 | ||||||||
\(400\) | −2.45527 | −0.122763 | ||||||||
\(401\) | 23.9276i | 1.19489i | 0.801911 | + | 0.597444i | \(0.203817\pi\) | ||||
−0.801911 | + | 0.597444i | \(0.796183\pi\) | |||||||
\(402\) | 10.0909 | 0.503286 | ||||||||
\(403\) | −2.94716 | + | 2.07708i | −0.146809 | + | 0.103466i | ||||
\(404\) | 7.53609 | 0.374934 | ||||||||
\(405\) | 2.47152i | 0.122811i | ||||||||
\(406\) | −16.3460 | −0.811240 | ||||||||
\(407\) | 10.0985 | 0.500562 | ||||||||
\(408\) | 26.0980i | 1.29204i | ||||||||
\(409\) | 26.7159i | 1.32101i | 0.750820 | + | 0.660507i | \(0.229659\pi\) | ||||
−0.750820 | + | 0.660507i | \(0.770341\pi\) | |||||||
\(410\) | − | 1.67839i | − | 0.0828896i | ||||||
\(411\) | − | 18.6497i | − | 0.919924i | ||||||
\(412\) | −11.3773 | −0.560521 | ||||||||
\(413\) | 37.9347 | 1.86664 | ||||||||
\(414\) | 1.00885i | 0.0495823i | ||||||||
\(415\) | −1.62917 | −0.0799727 | ||||||||
\(416\) | −15.8656 | + | 11.1816i | −0.777877 | + | 0.548225i | ||||
\(417\) | 26.6170 | 1.30344 | ||||||||
\(418\) | 6.33832i | 0.310017i | ||||||||
\(419\) | −17.5555 | −0.857641 | −0.428821 | − | 0.903390i | \(-0.641071\pi\) | ||||
−0.428821 | + | 0.903390i | \(0.641071\pi\) | |||||||
\(420\) | −2.11925 | −0.103409 | ||||||||
\(421\) | 27.6416i | 1.34717i | 0.739110 | + | 0.673585i | \(0.235246\pi\) | ||||
−0.739110 | + | 0.673585i | \(0.764754\pi\) | |||||||
\(422\) | 25.5795i | 1.24519i | ||||||||
\(423\) | − | 0.754647i | − | 0.0366922i | ||||||
\(424\) | − | 14.8693i | − | 0.722119i | ||||||
\(425\) | 26.0098 | 1.26166 | ||||||||
\(426\) | −5.70357 | −0.276339 | ||||||||
\(427\) | 37.0286i | 1.79194i | ||||||||
\(428\) | −14.6719 | −0.709195 | ||||||||
\(429\) | −10.4155 | + | 7.34057i | −0.502867 | + | 0.354406i | ||||
\(430\) | −1.94113 | −0.0936094 | ||||||||
\(431\) | − | 23.6042i | − | 1.13697i | −0.822692 | − | 0.568487i | \(-0.807529\pi\) | ||
0.822692 | − | 0.568487i | \(-0.192471\pi\) | |||||||
\(432\) | 2.65934 | 0.127948 | ||||||||
\(433\) | −17.3815 | −0.835303 | −0.417651 | − | 0.908607i | \(-0.637147\pi\) | ||||
−0.417651 | + | 0.908607i | \(0.637147\pi\) | |||||||
\(434\) | 3.61382i | 0.173469i | ||||||||
\(435\) | 2.21704i | 0.106299i | ||||||||
\(436\) | − | 9.13806i | − | 0.437634i | ||||||
\(437\) | 21.9383i | 1.04945i | ||||||||
\(438\) | −12.9875 | −0.620565 | ||||||||
\(439\) | −20.9810 | −1.00137 | −0.500684 | − | 0.865630i | \(-0.666918\pi\) | ||||
−0.500684 | + | 0.865630i | \(0.666918\pi\) | |||||||
\(440\) | 1.78345i | 0.0850225i | ||||||||
\(441\) | 1.24460 | 0.0592667 | ||||||||
\(442\) | −14.6172 | + | 10.3018i | −0.695268 | + | 0.490005i | ||||
\(443\) | −32.4721 | −1.54280 | −0.771399 | − | 0.636352i | \(-0.780443\pi\) | ||||
−0.771399 | + | 0.636352i | \(0.780443\pi\) | |||||||
\(444\) | − | 9.10624i | − | 0.432163i | ||||||
\(445\) | −1.74251 | −0.0826028 | ||||||||
\(446\) | 22.4054 | 1.06093 | ||||||||
\(447\) | − | 5.00783i | − | 0.236862i | ||||||
\(448\) | 23.3061i | 1.10111i | ||||||||
\(449\) | − | 22.2111i | − | 1.04821i | −0.851655 | − | 0.524103i | \(-0.824401\pi\) | ||
0.851655 | − | 0.524103i | \(-0.175599\pi\) | |||||||
\(450\) | − | 0.729106i | − | 0.0343704i | ||||||
\(451\) | 12.9109 | 0.607950 | ||||||||
\(452\) | 23.1337 | 1.08812 | ||||||||
\(453\) | 33.9246i | 1.59392i | ||||||||
\(454\) | 14.0243 | 0.658191 | ||||||||
\(455\) | −2.32845 | − | 3.30384i | −0.109159 | − | 0.154886i | ||||
\(456\) | 15.9088 | 0.744997 | ||||||||
\(457\) | 24.7016i | 1.15549i | 0.816216 | + | 0.577747i | \(0.196068\pi\) | ||||
−0.816216 | + | 0.577747i | \(0.803932\pi\) | |||||||
\(458\) | 12.4304 | 0.580833 | ||||||||
\(459\) | −28.1717 | −1.31494 | ||||||||
\(460\) | 2.21774i | 0.103403i | ||||||||
\(461\) | − | 1.87166i | − | 0.0871720i | −0.999050 | − | 0.0435860i | \(-0.986122\pi\) | ||
0.999050 | − | 0.0435860i | \(-0.0138783\pi\) | |||||||
\(462\) | 12.7716i | 0.594187i | ||||||||
\(463\) | − | 33.6330i | − | 1.56306i | −0.623869 | − | 0.781529i | \(-0.714440\pi\) | ||
0.623869 | − | 0.781529i | \(-0.285560\pi\) | |||||||
\(464\) | 2.25934 | 0.104887 | ||||||||
\(465\) | 0.490148 | 0.0227301 | ||||||||
\(466\) | − | 0.601701i | − | 0.0278733i | ||||||
\(467\) | −11.9042 | −0.550861 | −0.275430 | − | 0.961321i | \(-0.588820\pi\) | ||||
−0.275430 | + | 0.961321i | \(0.588820\pi\) | |||||||
\(468\) | −0.368611 | − | 0.523022i | −0.0170390 | − | 0.0241767i | ||||
\(469\) | −24.6223 | −1.13695 | ||||||||
\(470\) | 1.29964i | 0.0599481i | ||||||||
\(471\) | 31.9855 | 1.47381 | ||||||||
\(472\) | −28.7871 | −1.32503 | ||||||||
\(473\) | − | 14.9320i | − | 0.686574i | ||||||
\(474\) | − | 6.58366i | − | 0.302397i | ||||||
\(475\) | − | 15.8550i | − | 0.727479i | ||||||
\(476\) | − | 22.8786i | − | 1.04864i | ||||||
\(477\) | 0.804251 | 0.0368241 | ||||||||
\(478\) | −4.49277 | −0.205495 | ||||||||
\(479\) | − | 9.00430i | − | 0.411417i | −0.978613 | − | 0.205708i | \(-0.934050\pi\) | ||
0.978613 | − | 0.205708i | \(-0.0659499\pi\) | |||||||
\(480\) | 2.63865 | 0.120437 | ||||||||
\(481\) | 14.1963 | − | 10.0051i | 0.647295 | − | 0.456195i | ||||
\(482\) | −19.0169 | −0.866196 | ||||||||
\(483\) | 44.2052i | 2.01141i | ||||||||
\(484\) | 7.40698 | 0.336681 | ||||||||
\(485\) | −0.435436 | −0.0197722 | ||||||||
\(486\) | 1.53984i | 0.0698487i | ||||||||
\(487\) | − | 36.5025i | − | 1.65409i | −0.562139 | − | 0.827043i | \(-0.690021\pi\) | ||
0.562139 | − | 0.827043i | \(-0.309979\pi\) | |||||||
\(488\) | − | 28.0995i | − | 1.27200i | ||||||
\(489\) | − | 32.8804i | − | 1.48690i | ||||||
\(490\) | −2.14344 | −0.0968305 | ||||||||
\(491\) | 9.04853 | 0.408355 | 0.204177 | − | 0.978934i | \(-0.434548\pi\) | ||||
0.204177 | + | 0.978934i | \(0.434548\pi\) | |||||||
\(492\) | − | 11.6423i | − | 0.524876i | ||||||
\(493\) | −23.9342 | −1.07794 | ||||||||
\(494\) | 6.27974 | + | 8.91032i | 0.282539 | + | 0.400894i | ||||
\(495\) | −0.0964627 | −0.00433568 | ||||||||
\(496\) | − | 0.499499i | − | 0.0224282i | ||||||
\(497\) | 13.9171 | 0.624265 | ||||||||
\(498\) | 8.85340 | 0.396731 | ||||||||
\(499\) | 26.1949i | 1.17264i | 0.810078 | + | 0.586322i | \(0.199425\pi\) | ||||
−0.810078 | + | 0.586322i | \(0.800575\pi\) | |||||||
\(500\) | − | 3.23313i | − | 0.144590i | ||||||
\(501\) | 39.6645i | 1.77208i | ||||||||
\(502\) | − | 20.5003i | − | 0.914972i | ||||||
\(503\) | −19.4070 | −0.865315 | −0.432657 | − | 0.901558i | \(-0.642424\pi\) | ||||
−0.432657 | + | 0.901558i | \(0.642424\pi\) | |||||||
\(504\) | −1.78509 | −0.0795144 | ||||||||
\(505\) | − | 1.95391i | − | 0.0869479i | ||||||
\(506\) | 13.3651 | 0.594150 | ||||||||
\(507\) | −7.36928 | + | 20.6385i | −0.327281 | + | 0.916590i | ||||
\(508\) | 1.53562 | 0.0681323 | ||||||||
\(509\) | − | 2.27885i | − | 0.101008i | −0.998724 | − | 0.0505041i | \(-0.983917\pi\) | ||
0.998724 | − | 0.0505041i | \(-0.0160828\pi\) | |||||||
\(510\) | 2.43101 | 0.107647 | ||||||||
\(511\) | 31.6902 | 1.40189 | ||||||||
\(512\) | − | 5.61183i | − | 0.248010i | ||||||
\(513\) | 17.1729i | 0.758200i | ||||||||
\(514\) | − | 14.8376i | − | 0.654460i | ||||||
\(515\) | 2.94985i | 0.129986i | ||||||||
\(516\) | −13.4649 | −0.592757 | ||||||||
\(517\) | −9.99743 | −0.439686 | ||||||||
\(518\) | − | 17.4075i | − | 0.764842i | ||||||
\(519\) | 19.1802 | 0.841919 | ||||||||
\(520\) | 1.76696 | + | 2.50714i | 0.0774865 | + | 0.109946i | ||||
\(521\) | 29.5904 | 1.29638 | 0.648189 | − | 0.761479i | \(-0.275527\pi\) | ||||
0.648189 | + | 0.761479i | \(0.275527\pi\) | |||||||
\(522\) | 0.670923i | 0.0293655i | ||||||||
\(523\) | 31.9338 | 1.39637 | 0.698183 | − | 0.715919i | \(-0.253992\pi\) | ||||
0.698183 | + | 0.715919i | \(0.253992\pi\) | |||||||
\(524\) | 10.9228 | 0.477165 | ||||||||
\(525\) | − | 31.9475i | − | 1.39430i | ||||||
\(526\) | 2.87566i | 0.125385i | ||||||||
\(527\) | 5.29143i | 0.230498i | ||||||||
\(528\) | − | 1.76528i | − | 0.0768238i | ||||||
\(529\) | 23.2595 | 1.01128 | ||||||||
\(530\) | −1.38507 | −0.0601636 | ||||||||
\(531\) | − | 1.55703i | − | 0.0675693i | ||||||
\(532\) | −13.9463 | −0.604649 | ||||||||
\(533\) | 18.1499 | − | 12.7916i | 0.786161 | − | 0.554064i | ||||
\(534\) | 9.46934 | 0.409778 | ||||||||
\(535\) | 3.80405i | 0.164464i | ||||||||
\(536\) | 18.6849 | 0.807063 | ||||||||
\(537\) | 34.9161 | 1.50674 | ||||||||
\(538\) | 6.47490i | 0.279153i | ||||||||
\(539\) | − | 16.4882i | − | 0.710199i | ||||||
\(540\) | 1.73600i | 0.0747055i | ||||||||
\(541\) | − | 14.7693i | − | 0.634983i | −0.948261 | − | 0.317491i | \(-0.897160\pi\) | ||
0.948261 | − | 0.317491i | \(-0.102840\pi\) | |||||||
\(542\) | −30.2140 | −1.29780 | ||||||||
\(543\) | 3.72839 | 0.160000 | ||||||||
\(544\) | 28.4857i | 1.22131i | ||||||||
\(545\) | −2.36926 | −0.101488 | ||||||||
\(546\) | 12.6535 | + | 17.9541i | 0.541521 | + | 0.768364i | ||||
\(547\) | 11.1112 | 0.475082 | 0.237541 | − | 0.971377i | \(-0.423659\pi\) | ||||
0.237541 | + | 0.971377i | \(0.423659\pi\) | |||||||
\(548\) | − | 12.4067i | − | 0.529987i | ||||||
\(549\) | 1.51984 | 0.0648651 | ||||||||
\(550\) | −9.65906 | −0.411864 | ||||||||
\(551\) | 14.5898i | 0.621546i | ||||||||
\(552\) | − | 33.5455i | − | 1.42779i | ||||||
\(553\) | 16.0645i | 0.683134i | ||||||||
\(554\) | 15.2559i | 0.648160i | ||||||||
\(555\) | −2.36101 | −0.100219 | ||||||||
\(556\) | 17.7069 | 0.750938 | ||||||||
\(557\) | − | 22.7023i | − | 0.961925i | −0.876741 | − | 0.480963i | \(-0.840287\pi\) | ||
0.876741 | − | 0.480963i | \(-0.159713\pi\) | |||||||
\(558\) | 0.148329 | 0.00627927 | ||||||||
\(559\) | −14.7940 | − | 20.9912i | −0.625719 | − | 0.887833i | ||||
\(560\) | 0.559950 | 0.0236622 | ||||||||
\(561\) | 18.7004i | 0.789532i | ||||||||
\(562\) | −21.1169 | −0.890762 | ||||||||
\(563\) | −1.26121 | −0.0531536 | −0.0265768 | − | 0.999647i | \(-0.508461\pi\) | ||||
−0.0265768 | + | 0.999647i | \(0.508461\pi\) | |||||||
\(564\) | 9.01513i | 0.379606i | ||||||||
\(565\) | − | 5.99796i | − | 0.252336i | ||||||
\(566\) | − | 10.4498i | − | 0.439238i | ||||||
\(567\) | 32.7725i | 1.37632i | ||||||||
\(568\) | −10.5611 | −0.443133 | ||||||||
\(569\) | −5.71226 | −0.239470 | −0.119735 | − | 0.992806i | \(-0.538205\pi\) | ||||
−0.119735 | + | 0.992806i | \(0.538205\pi\) | |||||||
\(570\) | − | 1.48189i | − | 0.0620697i | ||||||
\(571\) | 10.4480 | 0.437234 | 0.218617 | − | 0.975811i | \(-0.429846\pi\) | ||||
0.218617 | + | 0.975811i | \(0.429846\pi\) | |||||||
\(572\) | −6.92889 | + | 4.88329i | −0.289712 | + | 0.204181i | ||||
\(573\) | −10.0089 | −0.418128 | ||||||||
\(574\) | − | 22.2555i | − | 0.928927i | ||||||
\(575\) | −33.4322 | −1.39422 | ||||||||
\(576\) | 0.956599 | 0.0398583 | ||||||||
\(577\) | − | 15.5655i | − | 0.647999i | −0.946057 | − | 0.324000i | \(-0.894972\pi\) | ||
0.946057 | − | 0.324000i | \(-0.105028\pi\) | |||||||
\(578\) | 10.3098i | 0.428830i | ||||||||
\(579\) | 12.9361i | 0.537606i | ||||||||
\(580\) | 1.47488i | 0.0612410i | ||||||||
\(581\) | −21.6029 | −0.896238 | ||||||||
\(582\) | 2.36630 | 0.0980862 | ||||||||
\(583\) | − | 10.6546i | − | 0.441267i | ||||||
\(584\) | −24.0484 | −0.995129 | ||||||||
\(585\) | −0.135606 | + | 0.0955712i | −0.00560661 | + | 0.00395138i | ||||
\(586\) | 27.3559 | 1.13006 | ||||||||
\(587\) | − | 10.6110i | − | 0.437962i | −0.975729 | − | 0.218981i | \(-0.929727\pi\) | ||
0.975729 | − | 0.218981i | \(-0.0702733\pi\) | |||||||
\(588\) | −14.8682 | −0.613154 | ||||||||
\(589\) | 3.22555 | 0.132906 | ||||||||
\(590\) | 2.68149i | 0.110395i | ||||||||
\(591\) | 17.9361i | 0.737793i | ||||||||
\(592\) | 2.40605i | 0.0988882i | ||||||||
\(593\) | 46.0558i | 1.89129i | 0.325206 | + | 0.945643i | \(0.394566\pi\) | ||||
−0.325206 | + | 0.945643i | \(0.605434\pi\) | |||||||
\(594\) | 10.4619 | 0.429257 | ||||||||
\(595\) | −5.93182 | −0.243181 | ||||||||
\(596\) | − | 3.33144i | − | 0.136461i | ||||||
\(597\) | −36.8906 | −1.50983 | ||||||||
\(598\) | 18.7884 | − | 13.2415i | 0.768316 | − | 0.541487i | ||||
\(599\) | −8.40314 | −0.343343 | −0.171672 | − | 0.985154i | \(-0.554917\pi\) | ||||
−0.171672 | + | 0.985154i | \(0.554917\pi\) | |||||||
\(600\) | 24.2436i | 0.989743i | ||||||||
\(601\) | 44.1276 | 1.80000 | 0.900001 | − | 0.435888i | \(-0.143566\pi\) | ||||
0.900001 | + | 0.435888i | \(0.143566\pi\) | |||||||
\(602\) | −25.7395 | −1.04906 | ||||||||
\(603\) | 1.01062i | 0.0411558i | ||||||||
\(604\) | 22.5682i | 0.918287i | ||||||||
\(605\) | − | 1.92044i | − | 0.0780769i | ||||||
\(606\) | 10.6182i | 0.431334i | ||||||||
\(607\) | 10.1399 | 0.411564 | 0.205782 | − | 0.978598i | \(-0.434026\pi\) | ||||
0.205782 | + | 0.978598i | \(0.434026\pi\) | |||||||
\(608\) | 17.3643 | 0.704215 | ||||||||
\(609\) | 29.3981i | 1.19127i | ||||||||
\(610\) | −2.61745 | −0.105977 | ||||||||
\(611\) | −14.0542 | + | 9.90503i | −0.568574 | + | 0.400715i | ||||
\(612\) | −0.939050 | −0.0379589 | ||||||||
\(613\) | − | 0.969289i | − | 0.0391492i | −0.999808 | − | 0.0195746i | \(-0.993769\pi\) | ||
0.999808 | − | 0.0195746i | \(-0.00623119\pi\) | |||||||
\(614\) | 9.64325 | 0.389170 | ||||||||
\(615\) | −3.01855 | −0.121720 | ||||||||
\(616\) | 23.6486i | 0.952830i | ||||||||
\(617\) | 8.86561i | 0.356916i | 0.983948 | + | 0.178458i | \(0.0571108\pi\) | ||||
−0.983948 | + | 0.178458i | \(0.942889\pi\) | |||||||
\(618\) | − | 16.0304i | − | 0.644838i | ||||||
\(619\) | 23.1571i | 0.930763i | 0.885110 | + | 0.465381i | \(0.154083\pi\) | ||||
−0.885110 | + | 0.465381i | \(0.845917\pi\) | |||||||
\(620\) | 0.326069 | 0.0130953 | ||||||||
\(621\) | 36.2109 | 1.45309 | ||||||||
\(622\) | 5.75658i | 0.230818i | ||||||||
\(623\) | −23.1058 | −0.925713 | ||||||||
\(624\) | −1.74896 | − | 2.48160i | −0.0700145 | − | 0.0993435i | ||||
\(625\) | 23.7390 | 0.949561 | ||||||||
\(626\) | 8.02126i | 0.320594i | ||||||||
\(627\) | 11.3994 | 0.455247 | ||||||||
\(628\) | 21.2782 | 0.849094 | ||||||||
\(629\) | − | 25.4885i | − | 1.01629i | ||||||
\(630\) | 0.166280i | 0.00662477i | ||||||||
\(631\) | 0.538705i | 0.0214455i | 0.999943 | + | 0.0107228i | \(0.00341323\pi\) | ||||
−0.999943 | + | 0.0107228i | \(0.996587\pi\) | |||||||
\(632\) | − | 12.1907i | − | 0.484921i | ||||||
\(633\) | 46.0044 | 1.82851 | ||||||||
\(634\) | 13.5182 | 0.536875 | ||||||||
\(635\) | − | 0.398147i | − | 0.0158000i | ||||||
\(636\) | −9.60770 | −0.380970 | ||||||||
\(637\) | −16.3359 | − | 23.1789i | −0.647250 | − | 0.918383i | ||||
\(638\) | 8.88826 | 0.351890 | ||||||||
\(639\) | − | 0.571226i | − | 0.0225973i | ||||||
\(640\) | 1.48309 | 0.0586242 | ||||||||
\(641\) | −10.1422 | −0.400593 | −0.200296 | − | 0.979735i | \(-0.564191\pi\) | ||||
−0.200296 | + | 0.979735i | \(0.564191\pi\) | |||||||
\(642\) | − | 20.6724i | − | 0.815875i | ||||||
\(643\) | 40.0663i | 1.58006i | 0.613068 | + | 0.790030i | \(0.289935\pi\) | ||||
−0.613068 | + | 0.790030i | \(0.710065\pi\) | |||||||
\(644\) | 29.4074i | 1.15881i | ||||||||
\(645\) | 3.49109i | 0.137461i | ||||||||
\(646\) | 15.9979 | 0.629428 | ||||||||
\(647\) | −9.30740 | −0.365912 | −0.182956 | − | 0.983121i | \(-0.558567\pi\) | ||||
−0.182956 | + | 0.983121i | \(0.558567\pi\) | |||||||
\(648\) | − | 24.8697i | − | 0.976974i | ||||||
\(649\) | −20.6272 | −0.809690 | ||||||||
\(650\) | −13.5786 | + | 9.56979i | −0.532595 | + | 0.375358i | ||||
\(651\) | 6.49940 | 0.254731 | ||||||||
\(652\) | − | 21.8735i | − | 0.856634i | ||||||
\(653\) | −18.5912 | −0.727530 | −0.363765 | − | 0.931491i | \(-0.618509\pi\) | ||||
−0.363765 | + | 0.931491i | \(0.618509\pi\) | |||||||
\(654\) | 12.8753 | 0.503464 | ||||||||
\(655\) | − | 2.83200i | − | 0.110655i | ||||||
\(656\) | 3.07614i | 0.120103i | ||||||||
\(657\) | − | 1.30072i | − | 0.0507461i | ||||||
\(658\) | 17.2334i | 0.671826i | ||||||||
\(659\) | 46.6156 | 1.81589 | 0.907944 | − | 0.419092i | \(-0.137651\pi\) | ||||
0.907944 | + | 0.419092i | \(0.137651\pi\) | |||||||
\(660\) | 1.15236 | 0.0448555 | ||||||||
\(661\) | − | 11.4634i | − | 0.445874i | −0.974833 | − | 0.222937i | \(-0.928436\pi\) | ||
0.974833 | − | 0.222937i | \(-0.0715645\pi\) | |||||||
\(662\) | 20.2979 | 0.788901 | ||||||||
\(663\) | 18.5276 | + | 26.2888i | 0.719551 | + | 1.02097i | ||||
\(664\) | 16.3935 | 0.636192 | ||||||||
\(665\) | 3.61591i | 0.140219i | ||||||||
\(666\) | −0.714491 | −0.0276860 | ||||||||
\(667\) | 30.7643 | 1.19120 | ||||||||
\(668\) | 26.3866i | 1.02093i | ||||||||
\(669\) | − | 40.2957i | − | 1.55792i | ||||||
\(670\) | − | 1.74048i | − | 0.0672407i | ||||||
\(671\) | − | 20.1346i | − | 0.777286i | ||||||
\(672\) | 34.9886 | 1.34971 | ||||||||
\(673\) | 21.9979 | 0.847957 | 0.423978 | − | 0.905672i | \(-0.360633\pi\) | ||||
0.423978 | + | 0.905672i | \(0.360633\pi\) | |||||||
\(674\) | 13.5401i | 0.521546i | ||||||||
\(675\) | −26.1700 | −1.00728 | ||||||||
\(676\) | −4.90239 | + | 13.7297i | −0.188553 | + | 0.528066i | ||||
\(677\) | −21.3442 | −0.820325 | −0.410162 | − | 0.912013i | \(-0.634528\pi\) | ||||
−0.410162 | + | 0.912013i | \(0.634528\pi\) | |||||||
\(678\) | 32.5948i | 1.25180i | ||||||||
\(679\) | −5.77392 | −0.221583 | ||||||||
\(680\) | 4.50141 | 0.172621 | ||||||||
\(681\) | − | 25.2224i | − | 0.966525i | ||||||
\(682\) | − | 1.96504i | − | 0.0752452i | ||||||
\(683\) | − | 51.2441i | − | 1.96080i | −0.197019 | − | 0.980400i | \(-0.563126\pi\) | ||
0.197019 | − | 0.980400i | \(-0.436874\pi\) | |||||||
\(684\) | 0.572426i | 0.0218872i | ||||||||
\(685\) | −3.21673 | −0.122905 | ||||||||
\(686\) | −3.12537 | −0.119327 | ||||||||
\(687\) | − | 22.3558i | − | 0.852928i | ||||||
\(688\) | 3.55769 | 0.135636 | ||||||||
\(689\) | −10.5561 | − | 14.9780i | −0.402155 | − | 0.570618i | ||||
\(690\) | −3.12474 | −0.118957 | ||||||||
\(691\) | − | 1.09848i | − | 0.0417883i | −0.999782 | − | 0.0208942i | \(-0.993349\pi\) | ||
0.999782 | − | 0.0208942i | \(-0.00665130\pi\) | |||||||
\(692\) | 12.7596 | 0.485046 | ||||||||
\(693\) | −1.27910 | −0.0485891 | ||||||||
\(694\) | − | 9.09278i | − | 0.345157i | ||||||
\(695\) | − | 4.59093i | − | 0.174144i | ||||||
\(696\) | − | 22.3090i | − | 0.845620i | ||||||
\(697\) | − | 32.5870i | − | 1.23432i | ||||||
\(698\) | 1.92345 | 0.0728036 | ||||||||
\(699\) | −1.08215 | −0.0409307 | ||||||||
\(700\) | − | 21.2530i | − | 0.803287i | ||||||
\(701\) | −15.7633 | −0.595372 | −0.297686 | − | 0.954664i | \(-0.596215\pi\) | ||||
−0.297686 | + | 0.954664i | \(0.596215\pi\) | |||||||
\(702\) | 14.7072 | − | 10.3652i | 0.555087 | − | 0.391209i | ||||
\(703\) | −15.5372 | −0.585998 | ||||||||
\(704\) | − | 12.6729i | − | 0.477626i | ||||||
\(705\) | 2.33739 | 0.0880312 | ||||||||
\(706\) | 10.9970 | 0.413876 | ||||||||
\(707\) | − | 25.9090i | − | 0.974408i | ||||||
\(708\) | 18.6005i | 0.699050i | ||||||||
\(709\) | − | 16.6481i | − | 0.625233i | −0.949879 | − | 0.312617i | \(-0.898794\pi\) | ||
0.949879 | − | 0.312617i | \(-0.101206\pi\) | |||||||
\(710\) | 0.983757i | 0.0369198i | ||||||||
\(711\) | 0.659369 | 0.0247283 | ||||||||
\(712\) | 17.5340 | 0.657115 | ||||||||
\(713\) | − | 6.80143i | − | 0.254716i | ||||||
\(714\) | 32.2354 | 1.20638 | ||||||||
\(715\) | 1.26611 | + | 1.79648i | 0.0473498 | + | 0.0671846i | ||||
\(716\) | 23.2278 | 0.868064 | ||||||||
\(717\) | 8.08018i | 0.301760i | ||||||||
\(718\) | −23.3696 | −0.872145 | ||||||||
\(719\) | −20.8992 | −0.779408 | −0.389704 | − | 0.920940i | \(-0.627423\pi\) | ||||
−0.389704 | + | 0.920940i | \(0.627423\pi\) | |||||||
\(720\) | − | 0.0229831i | − | 0.000856531i | ||||||
\(721\) | 39.1152i | 1.45673i | ||||||||
\(722\) | 8.05703i | 0.299852i | ||||||||
\(723\) | 34.2016i | 1.27197i | ||||||||
\(724\) | 2.48029 | 0.0921794 | ||||||||
\(725\) | −22.2336 | −0.825736 | ||||||||
\(726\) | 10.4363i | 0.387326i | ||||||||
\(727\) | −12.5078 | −0.463889 | −0.231945 | − | 0.972729i | \(-0.574509\pi\) | ||||
−0.231945 | + | 0.972729i | \(0.574509\pi\) | |||||||
\(728\) | 23.4301 | + | 33.2449i | 0.868375 | + | 1.23214i | ||||
\(729\) | 28.2700 | 1.04704 | ||||||||
\(730\) | 2.24009i | 0.0829094i | ||||||||
\(731\) | −37.6883 | −1.39395 | ||||||||
\(732\) | −18.1562 | −0.671074 | ||||||||
\(733\) | 21.1736i | 0.782064i | 0.920377 | + | 0.391032i | \(0.127882\pi\) | ||||
−0.920377 | + | 0.391032i | \(0.872118\pi\) | |||||||
\(734\) | 12.8429i | 0.474042i | ||||||||
\(735\) | 3.85494i | 0.142191i | ||||||||
\(736\) | − | 36.6146i | − | 1.34963i | ||||||
\(737\) | 13.3886 | 0.493174 | ||||||||
\(738\) | −0.913477 | −0.0336255 | ||||||||
\(739\) | 23.8513i | 0.877385i | 0.898637 | + | 0.438693i | \(0.144558\pi\) | ||||
−0.898637 | + | 0.438693i | \(0.855442\pi\) | |||||||
\(740\) | −1.57065 | −0.0577384 | ||||||||
\(741\) | 16.0251 | − | 11.2940i | 0.588696 | − | 0.414896i | ||||
\(742\) | −18.3661 | −0.674241 | ||||||||
\(743\) | − | 10.3245i | − | 0.378771i | −0.981903 | − | 0.189385i | \(-0.939350\pi\) | ||
0.981903 | − | 0.189385i | \(-0.0606496\pi\) | |||||||
\(744\) | −4.93212 | −0.180820 | ||||||||
\(745\) | −0.863756 | −0.0316456 | ||||||||
\(746\) | − | 8.64260i | − | 0.316428i | ||||||
\(747\) | 0.886689i | 0.0324423i | ||||||||
\(748\) | 12.4404i | 0.454865i | ||||||||
\(749\) | 50.4420i | 1.84311i | ||||||||
\(750\) | 4.55540 | 0.166340 | ||||||||
\(751\) | 43.3903 | 1.58333 | 0.791667 | − | 0.610953i | \(-0.209213\pi\) | ||||
0.791667 | + | 0.610953i | \(0.209213\pi\) | |||||||
\(752\) | − | 2.38198i | − | 0.0868619i | ||||||
\(753\) | −36.8695 | −1.34360 | ||||||||
\(754\) | 12.4950 | − | 8.80612i | 0.455041 | − | 0.320700i | ||||
\(755\) | 5.85135 | 0.212952 | ||||||||
\(756\) | 23.0194i | 0.837209i | ||||||||
\(757\) | 14.4887 | 0.526600 | 0.263300 | − | 0.964714i | \(-0.415189\pi\) | ||||
0.263300 | + | 0.964714i | \(0.415189\pi\) | |||||||
\(758\) | −7.18102 | −0.260826 | ||||||||
\(759\) | − | 24.0369i | − | 0.872483i | ||||||
\(760\) | − | 2.74397i | − | 0.0995341i | ||||||
\(761\) | 45.1186i | 1.63555i | 0.575541 | + | 0.817773i | \(0.304792\pi\) | ||||
−0.575541 | + | 0.817773i | \(0.695208\pi\) | |||||||
\(762\) | 2.16366i | 0.0783811i | ||||||||
\(763\) | −31.4166 | −1.13736 | ||||||||
\(764\) | −6.65839 | −0.240892 | ||||||||
\(765\) | 0.243471i | 0.00880273i | ||||||||
\(766\) | 3.53460 | 0.127710 | ||||||||
\(767\) | −28.9975 | + | 20.4366i | −1.04704 | + | 0.737923i | ||||
\(768\) | −28.4400 | −1.02624 | ||||||||
\(769\) | 13.9625i | 0.503502i | 0.967792 | + | 0.251751i | \(0.0810064\pi\) | ||||
−0.967792 | + | 0.251751i | \(0.918994\pi\) | |||||||
\(770\) | 2.20285 | 0.0793853 | ||||||||
\(771\) | −26.6853 | −0.961047 | ||||||||
\(772\) | 8.60569i | 0.309726i | ||||||||
\(773\) | 20.2617i | 0.728762i | 0.931250 | + | 0.364381i | \(0.118719\pi\) | ||||
−0.931250 | + | 0.364381i | \(0.881281\pi\) | |||||||
\(774\) | 1.05648i | 0.0379743i | ||||||||
\(775\) | 4.91546i | 0.176568i | ||||||||
\(776\) | 4.38158 | 0.157290 | ||||||||
\(777\) | −31.3072 | −1.12314 | ||||||||
\(778\) | − | 1.86284i | − | 0.0667860i | ||||||
\(779\) | −19.8644 | −0.711714 | ||||||||
\(780\) | 1.61997 | − | 1.14171i | 0.0580042 | − | 0.0408797i | ||||
\(781\) | −7.56749 | −0.270786 | ||||||||
\(782\) | − | 33.7334i | − | 1.20630i | ||||||
\(783\) | 24.0816 | 0.860606 | ||||||||
\(784\) | 3.92848 | 0.140303 | ||||||||
\(785\) | − | 5.51689i | − | 0.196906i | ||||||
\(786\) | 15.3900i | 0.548942i | ||||||||
\(787\) | − | 39.5845i | − | 1.41103i | −0.708693 | − | 0.705517i | \(-0.750715\pi\) | ||
0.708693 | − | 0.705517i | \(-0.249285\pi\) | |||||||
\(788\) | 11.9319i | 0.425057i | ||||||||
\(789\) | 5.17184 | 0.184122 | ||||||||
\(790\) | −1.13556 | −0.0404013 | ||||||||
\(791\) | − | 79.5334i | − | 2.82788i | ||||||
\(792\) | 0.970657 | 0.0344908 | ||||||||
\(793\) | −19.9485 | − | 28.3049i | −0.708391 | − | 1.00514i | ||||
\(794\) | 7.34596 | 0.260698 | ||||||||
\(795\) | 2.49103i | 0.0883477i | ||||||||
\(796\) | −24.5413 | −0.869844 | ||||||||
\(797\) | −47.8024 | −1.69325 | −0.846625 | − | 0.532190i | \(-0.821369\pi\) | ||||
−0.846625 | + | 0.532190i | \(0.821369\pi\) | |||||||
\(798\) | − | 19.6500i | − | 0.695602i | ||||||
\(799\) | 25.2335i | 0.892696i | ||||||||
\(800\) | 26.4617i | 0.935562i | ||||||||
\(801\) | 0.948376i | 0.0335092i | ||||||||
\(802\) | −22.4277 | −0.791951 | ||||||||
\(803\) | −17.2318 | −0.608095 | ||||||||
\(804\) | − | 12.0731i | − | 0.425784i | ||||||
\(805\) | 7.62456 | 0.268731 | ||||||||
\(806\) | −1.94688 | − | 2.76242i | −0.0685758 | − | 0.0973022i | ||||
\(807\) | 11.6450 | 0.409924 | ||||||||
\(808\) | 19.6613i | 0.691681i | ||||||||
\(809\) | −26.7287 | −0.939730 | −0.469865 | − | 0.882738i | \(-0.655697\pi\) | ||||
−0.469865 | + | 0.882738i | \(0.655697\pi\) | |||||||
\(810\) | −2.31660 | −0.0813969 | ||||||||
\(811\) | − | 27.4420i | − | 0.963621i | −0.876276 | − | 0.481810i | \(-0.839979\pi\) | ||
0.876276 | − | 0.481810i | \(-0.160021\pi\) | |||||||
\(812\) | 19.5570i | 0.686315i | ||||||||
\(813\) | 54.3394i | 1.90577i | ||||||||
\(814\) | 9.46545i | 0.331764i | ||||||||
\(815\) | −5.67124 | −0.198655 | ||||||||
\(816\) | −4.45555 | −0.155975 | ||||||||
\(817\) | 22.9740i | 0.803759i | ||||||||
\(818\) | −25.0412 | −0.875545 | ||||||||
\(819\) | −1.79814 | + | 1.26728i | −0.0628322 | + | 0.0442824i | ||||
\(820\) | −2.00808 | −0.0701252 | ||||||||
\(821\) | − | 30.2439i | − | 1.05552i | −0.849394 | − | 0.527759i | \(-0.823032\pi\) | ||
0.849394 | − | 0.527759i | \(-0.176968\pi\) | |||||||
\(822\) | 17.4807 | 0.609710 | ||||||||
\(823\) | −17.3317 | −0.604144 | −0.302072 | − | 0.953285i | \(-0.597678\pi\) | ||||
−0.302072 | + | 0.953285i | \(0.597678\pi\) | |||||||
\(824\) | − | 29.6829i | − | 1.03405i | ||||||
\(825\) | 17.3717i | 0.604804i | ||||||||
\(826\) | 35.5568i | 1.23718i | ||||||||
\(827\) | 5.96729i | 0.207503i | 0.994603 | + | 0.103751i | \(0.0330847\pi\) | ||||
−0.994603 | + | 0.103751i | \(0.966915\pi\) | |||||||
\(828\) | 1.20702 | 0.0419470 | ||||||||
\(829\) | −9.28049 | −0.322325 | −0.161162 | − | 0.986928i | \(-0.551524\pi\) | ||||
−0.161162 | + | 0.986928i | \(0.551524\pi\) | |||||||
\(830\) | − | 1.52704i | − | 0.0530045i | ||||||
\(831\) | 27.4375 | 0.951795 | ||||||||
\(832\) | −12.5557 | − | 17.8153i | −0.435292 | − | 0.617635i | ||||
\(833\) | −41.6163 | −1.44192 | ||||||||
\(834\) | 24.9485i | 0.863897i | ||||||||
\(835\) | 6.84137 | 0.236755 | ||||||||
\(836\) | 7.58339 | 0.262277 | ||||||||
\(837\) | − | 5.32402i | − | 0.184025i | ||||||
\(838\) | − | 16.4550i | − | 0.568430i | ||||||
\(839\) | − | 47.4252i | − | 1.63730i | −0.574294 | − | 0.818649i | \(-0.694723\pi\) | ||
0.574294 | − | 0.818649i | \(-0.305277\pi\) | |||||||
\(840\) | − | 5.52902i | − | 0.190769i | ||||||
\(841\) | −8.54064 | −0.294505 | ||||||||
\(842\) | −25.9089 | −0.892880 | ||||||||
\(843\) | 37.9784i | 1.30805i | ||||||||
\(844\) | 30.6042 | 1.05344 | ||||||||
\(845\) | 3.55976 | + | 1.27106i | 0.122459 | + | 0.0437258i | ||||
\(846\) | 0.707343 | 0.0243190 | ||||||||
\(847\) | − | 25.4651i | − | 0.874992i | ||||||
\(848\) | 2.53855 | 0.0871742 | ||||||||
\(849\) | −18.7938 | −0.645002 | ||||||||
\(850\) | 24.3794i | 0.836207i | ||||||||
\(851\) | 32.7620i | 1.12307i | ||||||||
\(852\) | 6.82395i | 0.233785i | ||||||||
\(853\) | − | 28.2350i | − | 0.966747i | −0.875414 | − | 0.483374i | \(-0.839411\pi\) | ||
0.875414 | − | 0.483374i | \(-0.160589\pi\) | |||||||
\(854\) | −34.7075 | −1.18767 | ||||||||
\(855\) | 0.148415 | 0.00507569 | ||||||||
\(856\) | − | 38.2783i | − | 1.30833i | ||||||
\(857\) | −36.1912 | −1.23627 | −0.618133 | − | 0.786073i | \(-0.712111\pi\) | ||||
−0.618133 | + | 0.786073i | \(0.712111\pi\) | |||||||
\(858\) | −6.88044 | − | 9.76265i | −0.234894 | − | 0.333291i | ||||
\(859\) | −29.9776 | −1.02282 | −0.511411 | − | 0.859336i | \(-0.670877\pi\) | ||||
−0.511411 | + | 0.859336i | \(0.670877\pi\) | |||||||
\(860\) | 2.32243i | 0.0791943i | ||||||||
\(861\) | −40.0262 | −1.36409 | ||||||||
\(862\) | 22.1246 | 0.753567 | ||||||||
\(863\) | − | 28.1898i | − | 0.959591i | −0.877380 | − | 0.479795i | \(-0.840711\pi\) | ||
0.877380 | − | 0.479795i | \(-0.159289\pi\) | |||||||
\(864\) | − | 28.6611i | − | 0.975070i | ||||||
\(865\) | − | 3.30823i | − | 0.112483i | ||||||
\(866\) | − | 16.2920i | − | 0.553624i | ||||||
\(867\) | 18.5420 | 0.629719 | ||||||||
\(868\) | 4.32370 | 0.146756 | ||||||||
\(869\) | − | 8.73520i | − | 0.296321i | ||||||
\(870\) | −2.07807 | −0.0704531 | ||||||||
\(871\) | 18.8214 | − | 13.2648i | 0.637740 | − | 0.449461i | ||||
\(872\) | 23.8407 | 0.807349 | ||||||||
\(873\) | 0.236990i | 0.00802091i | ||||||||
\(874\) | −20.5632 | −0.695559 | ||||||||
\(875\) | −11.1155 | −0.375771 | ||||||||
\(876\) | 15.5387i | 0.525002i | ||||||||
\(877\) | 5.32985i | 0.179976i | 0.995943 | + | 0.0899882i | \(0.0286829\pi\) | ||||
−0.995943 | + | 0.0899882i | \(0.971317\pi\) | |||||||
\(878\) | − | 19.6658i | − | 0.663689i | ||||||
\(879\) | − | 49.1992i | − | 1.65945i | ||||||
\(880\) | −0.304477 | −0.0102639 | ||||||||
\(881\) | −10.7814 | −0.363235 | −0.181618 | − | 0.983369i | \(-0.558133\pi\) | ||||
−0.181618 | + | 0.983369i | \(0.558133\pi\) | |||||||
\(882\) | 1.16658i | 0.0392809i | ||||||||
\(883\) | 17.5068 | 0.589149 | 0.294575 | − | 0.955628i | \(-0.404822\pi\) | ||||
0.294575 | + | 0.955628i | \(0.404822\pi\) | |||||||
\(884\) | 12.3254 | + | 17.4885i | 0.414548 | + | 0.588202i | ||||
\(885\) | 4.82263 | 0.162111 | ||||||||
\(886\) | − | 30.4367i | − | 1.02254i | ||||||
\(887\) | −15.1926 | −0.510119 | −0.255060 | − | 0.966925i | \(-0.582095\pi\) | ||||
−0.255060 | + | 0.966925i | \(0.582095\pi\) | |||||||
\(888\) | 23.7577 | 0.797257 | ||||||||
\(889\) | − | 5.27946i | − | 0.177067i | ||||||
\(890\) | − | 1.63328i | − | 0.0547477i | ||||||
\(891\) | − | 17.8203i | − | 0.597002i | ||||||
\(892\) | − | 26.8066i | − | 0.897551i | ||||||
\(893\) | 15.3818 | 0.514732 | ||||||||
\(894\) | 4.69392 | 0.156988 | ||||||||
\(895\) | − | 6.02237i | − | 0.201306i | ||||||
\(896\) | 19.6658 | 0.656989 | ||||||||
\(897\) | −23.8147 | − | 33.7907i | −0.795151 | − | 1.12824i | ||||
\(898\) | 20.8188 | 0.694733 | ||||||||
\(899\) | − | 4.52320i | − | 0.150857i | ||||||
\(900\) | −0.872328 | −0.0290776 | ||||||||
\(901\) | −26.8921 | −0.895905 | ||||||||
\(902\) | 12.1016i | 0.402938i | ||||||||
\(903\) | 46.2921i | 1.54050i | ||||||||
\(904\) | 60.3546i | 2.00736i | ||||||||
\(905\) | − | 0.643076i | − | 0.0213766i | ||||||
\(906\) | −31.7981 | −1.05642 | ||||||||
\(907\) | 23.0972 | 0.766928 | 0.383464 | − | 0.923556i | \(-0.374731\pi\) | ||||
0.383464 | + | 0.923556i | \(0.374731\pi\) | |||||||
\(908\) | − | 16.7791i | − | 0.556834i | ||||||
\(909\) | −1.06343 | −0.0352719 | ||||||||
\(910\) | 3.09674 | − | 2.18249i | 0.102656 | − | 0.0723490i | ||||
\(911\) | 45.8733 | 1.51985 | 0.759926 | − | 0.650010i | \(-0.225235\pi\) | ||||
0.759926 | + | 0.650010i | \(0.225235\pi\) | |||||||
\(912\) | 2.71601i | 0.0899360i | ||||||||
\(913\) | 11.7467 | 0.388759 | ||||||||
\(914\) | −23.1532 | −0.765841 | ||||||||
\(915\) | 4.70744i | 0.155623i | ||||||||
\(916\) | − | 14.8721i | − | 0.491389i | ||||||
\(917\) | − | 37.5525i | − | 1.24009i | ||||||
\(918\) | − | 26.4058i | − | 0.871520i | ||||||
\(919\) | 11.6629 | 0.384723 | 0.192362 | − | 0.981324i | \(-0.438385\pi\) | ||||
0.192362 | + | 0.981324i | \(0.438385\pi\) | |||||||
\(920\) | −5.78596 | −0.190758 | ||||||||
\(921\) | − | 17.3432i | − | 0.571479i | ||||||
\(922\) | 1.75434 | 0.0577761 | ||||||||
\(923\) | −10.6383 | + | 7.49755i | −0.350163 | + | 0.246785i | ||||
\(924\) | 15.2803 | 0.502686 | ||||||||
\(925\) | − | 23.6774i | − | 0.778509i | ||||||
\(926\) | 31.5247 | 1.03597 | ||||||||
\(927\) | 1.60548 | 0.0527310 | ||||||||
\(928\) | − | 24.3500i | − | 0.799329i | ||||||
\(929\) | 32.8627i | 1.07819i | 0.842244 | + | 0.539096i | \(0.181234\pi\) | ||||
−0.842244 | + | 0.539096i | \(0.818766\pi\) | |||||||
\(930\) | 0.459424i | 0.0150651i | ||||||||
\(931\) | 25.3684i | 0.831416i | ||||||||
\(932\) | −0.719897 | −0.0235810 | ||||||||
\(933\) | 10.3531 | 0.338946 | ||||||||
\(934\) | − | 11.1580i | − | 0.365101i | ||||||
\(935\) | 3.22547 | 0.105484 | ||||||||
\(936\) | 1.36454 | − | 0.961686i | 0.0446013 | − | 0.0314337i | ||||
\(937\) | −51.2949 | −1.67573 | −0.837865 | − | 0.545877i | \(-0.816197\pi\) | ||||
−0.837865 | + | 0.545877i | \(0.816197\pi\) | |||||||
\(938\) | − | 23.0789i | − | 0.753553i | ||||||
\(939\) | 14.4261 | 0.470779 | ||||||||
\(940\) | 1.55494 | 0.0507165 | ||||||||
\(941\) | − | 41.9245i | − | 1.36670i | −0.730091 | − | 0.683350i | \(-0.760522\pi\) | ||
0.730091 | − | 0.683350i | \(-0.239478\pi\) | |||||||
\(942\) | 29.9805i | 0.976818i | ||||||||
\(943\) | 41.8863i | 1.36400i | ||||||||
\(944\) | − | 4.91463i | − | 0.159958i | ||||||
\(945\) | 5.96835 | 0.194150 | ||||||||
\(946\) | 13.9960 | 0.455049 | ||||||||
\(947\) | − | 26.4877i | − | 0.860736i | −0.902654 | − | 0.430368i | \(-0.858384\pi\) | ||
0.902654 | − | 0.430368i | \(-0.141616\pi\) | |||||||
\(948\) | −7.87692 | −0.255831 | ||||||||
\(949\) | −24.2242 | + | 17.0725i | −0.786349 | + | 0.554197i | ||||
\(950\) | 14.8612 | 0.482161 | ||||||||
\(951\) | − | 24.3122i | − | 0.788378i | ||||||
\(952\) | 59.6890 | 1.93453 | ||||||||
\(953\) | −45.6327 | −1.47819 | −0.739094 | − | 0.673603i | \(-0.764746\pi\) | ||||
−0.739094 | + | 0.673603i | \(0.764746\pi\) | |||||||
\(954\) | 0.753837i | 0.0244064i | ||||||||
\(955\) | 1.72635i | 0.0558633i | ||||||||
\(956\) | 5.37531i | 0.173850i | ||||||||
\(957\) | − | 15.9854i | − | 0.516735i | ||||||
\(958\) | 8.43987 | 0.272680 | ||||||||
\(959\) | −42.6540 | −1.37737 | ||||||||
\(960\) | 2.96290i | 0.0956273i | ||||||||
\(961\) | −1.00000 | −0.0322581 | ||||||||
\(962\) | 9.37797 | + | 13.3064i | 0.302358 | + | 0.429016i | ||||
\(963\) | 2.07039 | 0.0667174 | ||||||||
\(964\) | 22.7525i | 0.732809i | ||||||||
\(965\) | 2.23123 | 0.0718259 | ||||||||
\(966\) | −41.4343 | −1.33313 | ||||||||
\(967\) | 11.1815i | 0.359571i | 0.983706 | + | 0.179786i | \(0.0575404\pi\) | ||||
−0.983706 | + | 0.179786i | \(0.942460\pi\) | |||||||
\(968\) | 19.3244i | 0.621111i | ||||||||
\(969\) | − | 28.7720i | − | 0.924289i | ||||||
\(970\) | − | 0.408142i | − | 0.0131046i | ||||||
\(971\) | −1.14584 | −0.0367716 | −0.0183858 | − | 0.999831i | \(-0.505853\pi\) | ||||
−0.0183858 | + | 0.999831i | \(0.505853\pi\) | |||||||
\(972\) | 1.84232 | 0.0590926 | ||||||||
\(973\) | − | 60.8760i | − | 1.95159i | ||||||
\(974\) | 34.2144 | 1.09630 | ||||||||
\(975\) | 17.2111 | + | 24.4209i | 0.551197 | + | 0.782093i | ||||
\(976\) | 4.79725 | 0.153556 | ||||||||
\(977\) | 60.2613i | 1.92793i | 0.266031 | + | 0.963964i | \(0.414288\pi\) | ||||
−0.266031 | + | 0.963964i | \(0.585712\pi\) | |||||||
\(978\) | 30.8193 | 0.985493 | ||||||||
\(979\) | 12.5639 | 0.401545 | ||||||||
\(980\) | 2.56448i | 0.0819194i | ||||||||
\(981\) | 1.28949i | 0.0411703i | ||||||||
\(982\) | 8.48134i | 0.270650i | ||||||||
\(983\) | − | 0.0739659i | − | 0.00235915i | −0.999999 | − | 0.00117957i | \(-0.999625\pi\) | ||
0.999999 | − | 0.00117957i | \(-0.000375470\pi\) | |||||||
\(984\) | 30.3742 | 0.968295 | ||||||||
\(985\) | 3.09364 | 0.0985715 | ||||||||
\(986\) | − | 22.4339i | − | 0.714442i | ||||||
\(987\) | 30.9939 | 0.986548 | ||||||||
\(988\) | 10.6606 | − | 7.51330i | 0.339160 | − | 0.239030i | ||||
\(989\) | 48.4433 | 1.54041 | ||||||||
\(990\) | − | 0.0904161i | − | 0.00287361i | ||||||
\(991\) | 8.14285 | 0.258666 | 0.129333 | − | 0.991601i | \(-0.458716\pi\) | ||||
0.129333 | + | 0.991601i | \(0.458716\pi\) | |||||||
\(992\) | −5.38336 | −0.170922 | ||||||||
\(993\) | − | 36.5055i | − | 1.15847i | ||||||
\(994\) | 13.0447i | 0.413752i | ||||||||
\(995\) | 6.36293i | 0.201718i | ||||||||
\(996\) | − | 10.5925i | − | 0.335637i | ||||||
\(997\) | −58.8159 | −1.86272 | −0.931359 | − | 0.364102i | \(-0.881376\pi\) | ||||
−0.931359 | + | 0.364102i | \(0.881376\pi\) | |||||||
\(998\) | −24.5529 | −0.777208 | ||||||||
\(999\) | 25.6454i | 0.811386i |
(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 | 403.2.c.b.311.20 | yes | 32 | |
13.5 | odd | 4 | 5239.2.a.k.1.11 | 16 | |||
13.8 | odd | 4 | 5239.2.a.l.1.6 | 16 | |||
13.12 | even | 2 | inner | 403.2.c.b.311.13 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
403.2.c.b.311.13 | ✓ | 32 | 13.12 | even | 2 | inner | |
403.2.c.b.311.20 | yes | 32 | 1.1 | even | 1 | trivial | |
5239.2.a.k.1.11 | 16 | 13.5 | odd | 4 | |||
5239.2.a.l.1.6 | 16 | 13.8 | odd | 4 |