Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,7,Mod(13,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.13");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.j (of order \(18\), degree \(6\), 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: | \(17.4841103551\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 13.9 | ||
Character | \(\chi\) | \(=\) | 76.13 |
Dual form | 76.7.j.a.41.9 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{5}{18}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 10.8061 | − | 29.6895i | 0.400226 | − | 1.09961i | −0.561947 | − | 0.827173i | \(-0.689948\pi\) |
0.962173 | − | 0.272438i | \(-0.0878301\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −26.2824 | − | 149.055i | −0.210259 | − | 1.19244i | −0.888946 | − | 0.458012i | \(-0.848562\pi\) |
0.678687 | − | 0.734428i | \(-0.262549\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 184.362 | − | 319.324i | 0.537498 | − | 0.930974i | −0.461540 | − | 0.887119i | \(-0.652703\pi\) |
0.999038 | − | 0.0438545i | \(-0.0139638\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −206.249 | − | 173.063i | −0.282920 | − | 0.237398i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −225.114 | − | 389.909i | −0.169131 | − | 0.292944i | 0.768983 | − | 0.639269i | \(-0.220763\pi\) |
−0.938115 | + | 0.346325i | \(0.887430\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 37.2019 | + | 102.211i | 0.0169330 | + | 0.0465231i | 0.947871 | − | 0.318654i | \(-0.103231\pi\) |
−0.930938 | + | 0.365177i | \(0.881008\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4709.38 | − | 830.391i | −1.39537 | − | 0.246042i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2568.33 | − | 2155.09i | 0.522762 | − | 0.438650i | −0.342831 | − | 0.939397i | \(-0.611386\pi\) |
0.865593 | + | 0.500747i | \(0.166941\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3464.43 | + | 5919.76i | −0.505093 | + | 0.863065i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7488.34 | − | 8924.26i | −0.808589 | − | 0.963639i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1553.39 | + | 8809.72i | −0.127673 | + | 0.724067i | 0.852012 | + | 0.523522i | \(0.175382\pi\) |
−0.979685 | + | 0.200545i | \(0.935729\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6843.92 | + | 2490.98i | −0.438011 | + | 0.159423i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 12580.0 | − | 7263.06i | 0.639130 | − | 0.369002i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −14794.5 | + | 17631.4i | −0.606607 | + | 0.722926i | −0.978706 | − | 0.205267i | \(-0.934194\pi\) |
0.372099 | + | 0.928193i | \(0.378638\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −44102.3 | − | 25462.5i | −1.48039 | − | 0.854704i | −0.480638 | − | 0.876919i | \(-0.659595\pi\) |
−0.999753 | + | 0.0222148i | \(0.992928\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −14008.8 | + | 2470.13i | −0.389815 | + | 0.0687350i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −52442.3 | − | 19087.4i | −1.22314 | − | 0.445188i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 45616.7i | − | 0.900573i | −0.892884 | − | 0.450287i | \(-0.851322\pi\) | ||
0.892884 | − | 0.450287i | \(-0.148678\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3436.61 | 0.0579344 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10605.5 | − | 29138.3i | 0.153878 | − | 0.422778i | −0.838668 | − | 0.544643i | \(-0.816665\pi\) |
0.992547 | + | 0.121865i | \(0.0388875\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3702.47 | − | 20997.8i | −0.0465679 | − | 0.264100i | 0.952631 | − | 0.304130i | \(-0.0983657\pi\) |
−0.999198 | + | 0.0400303i | \(0.987255\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −20375.2 | + | 35290.9i | −0.223596 | + | 0.387280i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2924.09 | + | 2453.60i | 0.0281642 | + | 0.0236326i | 0.656761 | − | 0.754099i | \(-0.271926\pi\) |
−0.628597 | + | 0.777731i | \(0.716370\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9154.08 | − | 15855.3i | −0.0778084 | − | 0.134768i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −36229.8 | − | 99540.6i | −0.273121 | − | 0.750394i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 185484. | + | 32705.9i | 1.24589 | + | 0.219684i | 0.757438 | − | 0.652907i | \(-0.226451\pi\) |
0.488452 | + | 0.872591i | \(0.337562\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −52201.3 | + | 43802.1i | −0.313757 | + | 0.263273i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 138318. | + | 166827.i | 0.746885 | + | 0.900827i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 46671.8 | + | 55621.3i | 0.227247 | + | 0.270822i | 0.867605 | − | 0.497254i | \(-0.165658\pi\) |
−0.640358 | + | 0.768077i | \(0.721214\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −55776.1 | + | 316322.i | −0.245730 | + | 1.39361i | 0.573060 | + | 0.819514i | \(0.305756\pi\) |
−0.818790 | + | 0.574093i | \(0.805355\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −93287.6 | + | 33953.9i | −0.373080 | + | 0.135790i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 14257.4 | − | 8231.49i | 0.0519157 | − | 0.0299736i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 40189.5 | − | 47895.9i | 0.133625 | − | 0.159248i | −0.695083 | − | 0.718930i | \(-0.744632\pi\) |
0.828708 | + | 0.559682i | \(0.189077\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 244770. | + | 141318.i | 0.745095 | + | 0.430181i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 494343. | − | 87166.0i | 1.38119 | − | 0.243541i | 0.566798 | − | 0.823857i | \(-0.308182\pi\) |
0.814392 | + | 0.580316i | \(0.197071\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 307710. | + | 111997.i | 0.790994 | + | 0.287898i | 0.705749 | − | 0.708462i | \(-0.250611\pi\) |
0.0852448 | + | 0.996360i | \(0.472833\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 230111.i | 0.545447i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −166010. | −0.363631 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 187028. | − | 513856.i | 0.379338 | − | 1.04222i | −0.592293 | − | 0.805722i | \(-0.701777\pi\) |
0.971631 | − | 0.236500i | \(-0.0760004\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −113779. | − | 645272.i | −0.214095 | − | 1.21419i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 487024. | − | 843551.i | 0.851758 | − | 1.47529i | −0.0278621 | − | 0.999612i | \(-0.508870\pi\) |
0.879620 | − | 0.475677i | \(-0.157797\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −388728. | − | 326182.i | −0.632979 | − | 0.531132i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 363597. | + | 629769.i | 0.552158 | + | 0.956365i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6095.00 | − | 16745.9i | −0.00864577 | − | 0.0237541i | 0.935295 | − | 0.353870i | \(-0.115134\pi\) |
−0.943940 | + | 0.330116i | \(0.892912\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 39497.2 | + | 6964.41i | 0.0524133 | + | 0.00924188i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.23254e6 | + | 1.03423e6i | −1.53233 | + | 1.28578i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 973424. | + | 360805.i | 1.13535 | + | 0.420825i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 118115. | + | 140764.i | 0.129416 | + | 0.154232i | 0.826861 | − | 0.562406i | \(-0.190124\pi\) |
−0.697445 | + | 0.716638i | \(0.745680\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −21049.4 | + | 119377.i | −0.0216937 | + | 0.123031i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.17347e6 | + | 427107.i | −1.13896 | + | 0.414546i | −0.841536 | − | 0.540201i | \(-0.818348\pi\) |
−0.297419 | + | 0.954747i | \(0.596126\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 503201. | − | 290523.i | 0.460500 | − | 0.265870i | −0.251754 | − | 0.967791i | \(-0.581007\pi\) |
0.712255 | + | 0.701921i | \(0.247674\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.13339e6 | + | 1.35073e6i | −0.979068 | + | 1.16681i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 164984. | + | 95253.7i | 0.134676 | + | 0.0777554i | 0.565824 | − | 0.824526i | \(-0.308558\pi\) |
−0.431148 | + | 0.902281i | \(0.641891\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.50267e6 | + | 264961.i | −1.16034 | + | 0.204599i | −0.720484 | − | 0.693472i | \(-0.756080\pi\) |
−0.439852 | + | 0.898070i | \(0.644969\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.35434e6 | − | 492939.i | −0.990280 | − | 0.360433i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 892967.i | − | 0.618871i | −0.950920 | − | 0.309435i | \(-0.899860\pi\) | ||
0.950920 | − | 0.309435i | \(-0.100140\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.35396e6 | 0.890251 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10016.2 | − | 27519.2i | 0.00625381 | − | 0.0171822i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −214669. | − | 1.21745e6i | −0.127388 | − | 0.722451i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 784428. | − | 1.35867e6i | 0.442789 | − | 0.766933i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −750497. | − | 629742.i | −0.403305 | − | 0.338413i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −631288. | − | 1.09342e6i | −0.323219 | − | 0.559832i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.35804e6 | − | 3.73119e6i | −0.662983 | − | 1.82153i | −0.562853 | − | 0.826557i | \(-0.690296\pi\) |
−0.100131 | − | 0.994974i | \(-0.531926\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −663423. | − | 116979.i | −0.309045 | − | 0.0544929i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.02333e6 | + | 858677.i | −0.455200 | + | 0.381958i | −0.841361 | − | 0.540473i | \(-0.818245\pi\) |
0.386161 | + | 0.922431i | \(0.373801\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.25161e6 | + | 2.19765e6i | 0.532005 | + | 0.934124i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.41323e6 | − | 1.68422e6i | −0.574395 | − | 0.684538i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −664096. | + | 3.76627e6i | −0.258267 | + | 1.46471i | 0.529278 | + | 0.848448i | \(0.322463\pi\) |
−0.787545 | + | 0.616257i | \(0.788648\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −489194. | + | 178052.i | −0.182153 | + | 0.0662983i | −0.431487 | − | 0.902119i | \(-0.642011\pi\) |
0.249333 | + | 0.968418i | \(0.419789\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 104444. | − | 60301.0i | 0.0372587 | − | 0.0215113i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 31478.4 | − | 37514.5i | 0.0107648 | − | 0.0128290i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.01689e6 | + | 1.74180e6i | 0.989590 | + | 0.571340i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −569657. | + | 100446.i | −0.179334 | + | 0.0316213i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.55770e6 | + | 566955.i | 0.470895 | + | 0.171392i | 0.566558 | − | 0.824022i | \(-0.308275\pi\) |
−0.0956628 | + | 0.995414i | \(0.530497\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 6.59787e6i | − | 1.91634i | −0.286195 | − | 0.958171i | \(-0.592391\pi\) | ||
0.286195 | − | 0.958171i | \(-0.407609\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −902681. | −0.252035 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.63620e6 | + | 7.24289e6i | −0.707917 | + | 1.94499i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 269740. | + | 1.52977e6i | 0.0697021 | + | 0.395300i | 0.999621 | + | 0.0275353i | \(0.00876585\pi\) |
−0.929919 | + | 0.367765i | \(0.880123\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.97538e6 | − | 5.15351e6i | 0.740204 | − | 1.28207i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.52677e6 | + | 2.12021e6i | 0.605464 | + | 0.508045i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 802239. | + | 1.38952e6i | 0.185243 | + | 0.320850i | 0.943658 | − | 0.330922i | \(-0.107360\pi\) |
−0.758416 | + | 0.651771i | \(0.774026\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 736370. | + | 2.02316e6i | 0.163925 | + | 0.450379i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.29458e6 | + | 1.10990e6i | 1.35150 | + | 0.238307i | 0.802070 | − | 0.597230i | \(-0.203732\pi\) |
0.549435 | + | 0.835537i | \(0.314843\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.68849e6 | − | 3.09501e6i | 0.764167 | − | 0.641212i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.73903e6 | − | 621378.i | 0.347791 | − | 0.124270i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.30069e6 | + | 1.55010e6i | 0.251209 | + | 0.299379i | 0.876881 | − | 0.480707i | \(-0.159620\pi\) |
−0.625673 | + | 0.780086i | \(0.715175\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −466327. | + | 2.64467e6i | −0.0870115 | + | 0.493466i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.15571e6 | − | 784613.i | 0.388750 | − | 0.141493i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.13240e6 | + | 1.80849e6i | −0.546158 | + | 0.315324i | −0.747571 | − | 0.664182i | \(-0.768780\pi\) |
0.201413 | + | 0.979506i | \(0.435447\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.70737e6 | + | 5.61002e6i | −0.793858 | + | 0.946083i | −0.999470 | − | 0.0325509i | \(-0.989637\pi\) |
0.205613 | + | 0.978633i | \(0.434081\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.78873e6 | + | 5.07417e6i | 1.43408 | + | 0.827965i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.79940e6 | + | 1.19892e6i | −1.07388 | + | 0.189354i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.41845e6 | − | 516275.i | −0.216915 | − | 0.0789507i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 5.35613e6i | − | 0.793351i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.15455e7 | 1.65696 | 0.828478 | − | 0.560022i | \(-0.189207\pi\) | ||||
0.828478 | + | 0.560022i | \(0.189207\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −486893. | + | 1.33773e6i | −0.0677270 | + | 0.186078i | −0.968939 | − | 0.247300i | \(-0.920457\pi\) |
0.901212 | + | 0.433379i | \(0.142679\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −90322.5 | − | 512244.i | −0.0121813 | − | 0.0690833i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.10625e6 | − | 8.84428e6i | 0.667887 | − | 1.15681i | −0.310607 | − | 0.950539i | \(-0.600532\pi\) |
0.978494 | − | 0.206276i | \(-0.0661345\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.11842e7 | − | 9.38462e6i | −1.41920 | − | 1.19085i | −0.951766 | − | 0.306824i | \(-0.900734\pi\) |
−0.467435 | − | 0.884027i | \(-0.654822\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −987716. | − | 1.71077e6i | −0.121631 | − | 0.210671i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.90259e6 | + | 7.97481e6i | 0.346975 | + | 0.953306i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.62194e6 | − | 814972.i | −0.536491 | − | 0.0945979i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.84502e6 | − | 1.54816e6i | 0.208013 | − | 0.174544i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.08806e6 | + | 18191.1i | 0.338257 | + | 0.00199260i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −400307. | − | 477067.i | −0.0426134 | − | 0.0507846i | 0.744317 | − | 0.667827i | \(-0.232775\pi\) |
−0.786930 | + | 0.617042i | \(0.788331\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.75400e6 | − | 1.56187e7i | 0.284987 | − | 1.61624i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.03251e6 | + | 1.10374e6i | −0.305132 | + | 0.111059i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.62616e7 | + | 9.38863e6i | −1.59141 | + | 0.918804i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.65029e6 | − | 7.92551e6i | 0.633152 | − | 0.754562i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 315821. | + | 182339.i | 0.0292593 | + | 0.0168929i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.46561e7 | + | 2.58426e6i | −1.32161 | + | 0.233035i | −0.789557 | − | 0.613678i | \(-0.789689\pi\) |
−0.532051 | + | 0.846713i | \(0.678578\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.84265e6 | + | 670669.i | 0.161769 | + | 0.0588790i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.31518e6i | 0.283420i | 0.989908 | + | 0.141710i | \(0.0452600\pi\) | ||||
−0.989908 | + | 0.141710i | \(0.954740\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.74965e6 | 0.645321 | 0.322660 | − | 0.946515i | \(-0.395423\pi\) | ||||
0.322660 | + | 0.946515i | \(0.395423\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.79392e6 | + | 4.92874e6i | −0.145535 | + | 0.399853i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.99338e6 | + | 1.69763e7i | 0.236643 | + | 1.34207i | 0.839126 | + | 0.543938i | \(0.183067\pi\) |
−0.602483 | + | 0.798132i | \(0.705822\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 288870. | − | 500337.i | 0.0222586 | − | 0.0385531i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.32351e7 | − | 1.11056e7i | −0.994219 | − | 0.834249i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.61961e6 | − | 4.53729e6i | −0.191886 | − | 0.332356i | 0.753989 | − | 0.656887i | \(-0.228127\pi\) |
−0.945875 | + | 0.324531i | \(0.894794\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.33966e6 | + | 1.19231e7i | 0.310030 | + | 0.851801i | 0.992649 | + | 0.121027i | \(0.0386187\pi\) |
−0.682619 | + | 0.730775i | \(0.739159\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −9.95865e6 | − | 1.75598e6i | −0.694036 | − | 0.122377i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.12273e6 | + | 1.78118e6i | −0.144343 | + | 0.121118i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −733950. | − | 133878.i | −0.0487053 | − | 0.00888419i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.97818e7 | − | 2.35750e7i | −1.28135 | − | 1.52705i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.59717e6 | + | 2.60718e7i | −0.290716 | + | 1.64873i | 0.393406 | + | 0.919365i | \(0.371297\pi\) |
−0.684122 | + | 0.729368i | \(0.739814\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.78468e6 | − | 1.37751e6i | 0.233705 | − | 0.0850615i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.38848e7 | + | 8.01640e6i | −0.837374 | + | 0.483458i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 28759.1 | − | 34273.7i | 0.00169424 | − | 0.00201912i | −0.765197 | − | 0.643797i | \(-0.777358\pi\) |
0.766891 | + | 0.641777i | \(0.221803\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.45665e7 | − | 8.40998e6i | −0.838410 | − | 0.484056i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.10270e6 | − | 1.07607e6i | 0.343242 | − | 0.0605229i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.70928e6 | + | 3.53389e6i | 0.533728 | + | 0.194261i | 0.594802 | − | 0.803872i | \(-0.297230\pi\) |
−0.0610742 | + | 0.998133i | \(0.519453\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 2.85069e7i | − | 1.53184i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −563040. | −0.0295805 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −72655.6 | + | 199620.i | −0.00373261 | + | 0.0102553i | −0.941545 | − | 0.336887i | \(-0.890626\pi\) |
0.937812 | + | 0.347143i | \(0.112848\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −967244. | − | 5.48551e6i | −0.0485991 | − | 0.275619i | 0.950818 | − | 0.309749i | \(-0.100245\pi\) |
−0.999417 | + | 0.0341301i | \(0.989134\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 633580. | − | 1.09739e6i | 0.0311396 | − | 0.0539354i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.51192e6 | + | 2.10775e6i | 0.120783 | + | 0.101349i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.42323e6 | − | 1.28574e7i | −0.349264 | − | 0.604943i | 0.636855 | − | 0.770984i | \(-0.280235\pi\) |
−0.986119 | + | 0.166041i | \(0.946902\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.68943e6 | + | 1.28841e7i | 0.215927 | + | 0.593255i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.62505e7 | + | 6.39194e6i | 1.63379 | + | 0.288081i | 0.913878 | − | 0.405989i | \(-0.133073\pi\) |
0.719908 | + | 0.694069i | \(0.244184\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.82719e7 | − | 1.53319e7i | 0.806166 | − | 0.676454i | −0.143523 | − | 0.989647i | \(-0.545843\pi\) |
0.949689 | + | 0.313193i | \(0.101399\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.12310e7 | − | 2.50016e7i | 0.917142 | − | 1.08002i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.34930e6 | − | 8.75856e6i | −0.310886 | − | 0.370499i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.23951e6 | + | 1.27009e7i | −0.0927813 | + | 0.526189i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.45556e6 | − | 1.98566e6i | 0.221391 | − | 0.0805798i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.37069e7 | + | 1.36872e7i | −0.942479 | + | 0.544140i | −0.890736 | − | 0.454520i | \(-0.849811\pi\) |
−0.0517423 | + | 0.998660i | \(0.516477\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.06398e6 | − | 8.41852e6i | 0.275159 | − | 0.327921i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.66386e6 | − | 3.27003e6i | −0.216194 | − | 0.124820i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −958243. | + | 168964.i | −0.0358478 | + | 0.00632093i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.38769e6 | − | 2.68890e6i | −0.270900 | − | 0.0985995i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.94550e7i | 1.41832i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.86153e7 | 1.71346 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.22093e6 | − | 2.53343e7i | 0.318683 | − | 0.875576i | −0.672141 | − | 0.740423i | \(-0.734625\pi\) |
0.990825 | − | 0.135153i | \(-0.0431525\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.18785e6 | − | 1.80792e7i | −0.108050 | − | 0.612779i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.69261e7 | + | 4.66374e7i | −0.895144 | + | 1.55043i | −0.0615172 | + | 0.998106i | \(0.519594\pi\) |
−0.833627 | + | 0.552328i | \(0.813739\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.63013e7 | + | 3.04604e7i | 1.18383 | + | 0.993350i | 0.999946 | + | 0.0104022i | \(0.00331118\pi\) |
0.183883 | + | 0.982948i | \(0.441133\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.51283e6 | + | 1.30126e7i | 0.240365 | + | 0.416325i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.85632e6 | + | 1.33426e7i | 0.152451 | + | 0.418855i | 0.992283 | − | 0.123990i | \(-0.0395692\pi\) |
−0.839833 | + | 0.542845i | \(0.817347\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.02051e7 | + | 1.79943e6i | 0.314373 | + | 0.0554324i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.61087e6 | − | 3.86898e6i | 0.139402 | − | 0.116972i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.85979e6 | + | 2.26701e7i | 0.114540 | + | 0.672737i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −509214. | − | 606857.i | −0.0148337 | − | 0.0176781i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.37142e6 | + | 4.74767e7i | −0.239418 | + | 1.35780i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.32259e6 | − | 481382.i | 0.0371395 | − | 0.0135177i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.27360e6 | + | 5.35411e6i | −0.255720 | + | 0.147640i | −0.622380 | − | 0.782715i | \(-0.713834\pi\) |
0.366661 | + | 0.930355i | \(0.380501\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.89458e6 | + | 9.40839e6i | −0.213794 | + | 0.254790i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.19541e6 | − | 4.73162e6i | −0.217990 | − | 0.125856i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.37363e7 | − | 7.71189e6i | 1.14275 | − | 0.201498i | 0.429943 | − | 0.902856i | \(-0.358534\pi\) |
0.712809 | + | 0.701358i | \(0.247422\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.65117e7 | − | 9.64948e6i | −0.680517 | − | 0.247688i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.29278e7i | 0.578229i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.66293e7 | 0.907709 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.46310e7 | − | 4.01984e7i | 0.356301 | − | 0.978930i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.13257e6 | + | 4.04508e7i | 0.170710 | + | 0.968142i | 0.942980 | + | 0.332849i | \(0.108010\pi\) |
−0.772271 | + | 0.635294i | \(0.780879\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.25666e7 | − | 5.64069e7i | 0.766118 | − | 1.32695i | −0.173536 | − | 0.984828i | \(-0.555519\pi\) |
0.939654 | − | 0.342127i | \(-0.111147\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.21037e6 | + | 1.01562e6i | 0.0279895 | + | 0.0234860i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.34770e7 | + | 5.79839e7i | 0.761067 | + | 1.31821i | 0.942301 | + | 0.334766i | \(0.108657\pi\) |
−0.181234 | + | 0.983440i | \(0.558009\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.59851e7 | − | 7.13934e7i | −0.580816 | − | 1.59578i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.84651e7 | − | 6.78243e6i | −0.845400 | − | 0.149067i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.21296e7 | − | 1.85690e7i | 0.478290 | − | 0.401333i | −0.371518 | − | 0.928426i | \(-0.621163\pi\) |
0.849808 | + | 0.527093i | \(0.176718\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.30413e7 | − | 4.10172e7i | −0.489762 | − | 0.871856i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.18616e7 | − | 3.79712e7i | −0.666113 | − | 0.793843i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.60639e6 | − | 4.88093e7i | 0.176988 | − | 1.00375i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.50834e7 | + | 2.00487e7i | −1.11435 | + | 0.405591i | −0.832588 | − | 0.553893i | \(-0.813142\pi\) |
−0.281764 | + | 0.959484i | \(0.590920\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.23012e6 | + | 4.17431e6i | −0.143902 | + | 0.0830818i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.46400e7 | − | 5.31999e7i | 0.874183 | − | 1.04181i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.57281e7 | − | 9.08065e6i | −0.303076 | − | 0.174981i | 0.340748 | − | 0.940155i | \(-0.389320\pi\) |
−0.643824 | + | 0.765174i | \(0.722653\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.92849e7 | + | 6.92699e6i | −0.744959 | + | 0.131356i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.35252e6 | − | 856246.i | −0.0439045 | − | 0.0159799i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.26118e7i | 0.415353i | 0.978198 | + | 0.207676i | \(0.0665901\pi\) | ||||
−0.978198 | + | 0.207676i | \(0.933410\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.25452e8 | −2.26832 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.74512e7 | − | 7.54217e7i | 0.488614 | − | 1.34246i | −0.413322 | − | 0.910585i | \(-0.635632\pi\) |
0.901936 | − | 0.431871i | \(-0.142146\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.36313e6 | + | 2.47446e7i | 0.0764568 | + | 0.433608i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.87031e6 | + | 4.97152e6i | −0.0495218 | + | 0.0857742i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.45855e7 | + | 3.74117e7i | 0.757434 | + | 0.635563i | 0.937458 | − | 0.348099i | \(-0.113173\pi\) |
−0.180023 | + | 0.983662i | \(0.557617\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.49961e7 | + | 2.59740e7i | 0.250869 | + | 0.434519i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.44355e7 | + | 3.96612e7i | 0.237823 | + | 0.653413i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.15084e7 | − | 1.43721e7i | −1.32255 | − | 0.233201i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.05042e7 | + | 7.59421e7i | −1.44643 | + | 1.21370i | −0.511295 | + | 0.859405i | \(0.670834\pi\) |
−0.935134 | + | 0.354293i | \(0.884721\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.87724e7 | − | 1.34117e7i | 1.24010 | − | 0.211138i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.23650e7 | − | 1.47361e7i | −0.191762 | − | 0.228533i | 0.661594 | − | 0.749863i | \(-0.269880\pi\) |
−0.853355 | + | 0.521330i | \(0.825436\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 961866. | − | 5.45501e6i | 0.0146960 | − | 0.0833452i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.31906e7 | + | 3.39186e7i | −1.40284 | + | 0.510591i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.77864e7 | + | 1.02690e7i | −0.263818 | + | 0.152315i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.57247e6 | + | 1.02163e7i | −0.125296 | + | 0.149322i | −0.825045 | − | 0.565067i | \(-0.808850\pi\) |
0.699750 | + | 0.714388i | \(0.253295\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.04643e8 | + | 6.04154e7i | 1.50724 | + | 0.870206i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.63657e7 | − | 4.64898e6i | 0.374274 | − | 0.0659945i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.38536e8 | − | 5.04228e7i | −1.93828 | − | 0.705477i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.64480e7i | 0.226832i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.46049e7 | −0.878260 | −0.439130 | − | 0.898424i | \(-0.644713\pi\) | ||||
−0.439130 | + | 0.898424i | \(0.644713\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.84890e7 | − | 7.82730e7i | 0.381796 | − | 1.04898i | −0.588804 | − | 0.808276i | \(-0.700401\pi\) |
0.970600 | − | 0.240700i | \(-0.0773769\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −178461. | − | 1.01211e6i | −0.00235789 | − | 0.0133723i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.22092e7 | + | 2.11469e7i | −0.159045 | + | 0.275474i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.07263e7 | + | 7.61284e7i | 1.16533 | + | 0.977829i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −773629. | − | 1.33996e6i | −0.00979853 | − | 0.0169715i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.67393e7 | − | 7.34656e7i | −0.333978 | − | 0.917598i | −0.987066 | − | 0.160315i | \(-0.948749\pi\) |
0.653088 | − | 0.757282i | \(-0.273473\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.38034e7 | − | 1.30135e7i | −0.909102 | − | 0.160299i | −0.300507 | − | 0.953780i | \(-0.597156\pi\) |
−0.608596 | + | 0.793480i | \(0.708267\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.43140e7 | − | 7.07479e7i | 1.02431 | − | 0.859499i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.67699e7 | − | 3.97164e7i | −0.560431 | − | 0.475911i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.56726e7 | + | 4.25130e7i | 0.421640 | + | 0.502491i | 0.934491 | − | 0.355987i | \(-0.115855\pi\) |
−0.512851 | + | 0.858478i | \(0.671411\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −855958. | + | 4.85438e6i | −0.00998014 | + | 0.0566002i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.25030e7 | − | 3.36684e7i | 1.06401 | − | 0.387267i | 0.250075 | − | 0.968226i | \(-0.419545\pi\) |
0.813933 | + | 0.580959i | \(0.197322\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.33586e6 | + | 1.34861e6i | −0.0265074 | + | 0.0153041i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.36652e7 | − | 4.01207e7i | 0.376929 | − | 0.449206i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.27534e8 | + | 7.36319e7i | 1.40892 | + | 0.813443i | 0.995285 | − | 0.0969978i | \(-0.0309240\pi\) |
0.413640 | + | 0.910441i | \(0.364257\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.37487e7 | + | 2.42426e6i | −0.149876 | + | 0.0264272i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.95888e8 | − | 7.12973e7i | −2.10723 | − | 0.766970i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 6.07029e6i | − | 0.0644429i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.56567e7 | −0.792682 | −0.396341 | − | 0.918103i | \(-0.629720\pi\) | ||||
−0.396341 | + | 0.918103i | \(0.629720\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.66571e7 | − | 4.57649e7i | 0.172250 | − | 0.473254i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.21117e7 | + | 1.25401e8i | 0.225693 | + | 1.27997i | 0.861356 | + | 0.508003i | \(0.169616\pi\) |
−0.635662 | + | 0.771967i | \(0.719273\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.46610e6 | − | 1.11996e7i | 0.0651478 | − | 0.112839i | −0.831612 | − | 0.555357i | \(-0.812581\pi\) |
0.896760 | + | 0.442518i | \(0.145915\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.86551e8 | + | 1.56535e8i | 1.85540 | + | 1.55687i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.44457e6 | − | 9.43027e6i | −0.0534580 | − | 0.0925920i | 0.838058 | − | 0.545581i | \(-0.183691\pi\) |
−0.891516 | + | 0.452989i | \(0.850358\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.88492e6 | − | 2.16637e7i | −0.0764327 | − | 0.209997i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.83330e7 | + | 8.52240e6i | 0.462573 | + | 0.0815642i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.35373e6 | + | 6.17051e6i | −0.0694903 | + | 0.0583093i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.96427e6 | − | 4.91442e7i | 0.0836438 | − | 0.458555i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.25957e7 | − | 3.88461e7i | −0.300335 | − | 0.357925i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.79938e7 | + | 1.02048e8i | −0.163726 | + | 0.928535i | 0.786643 | + | 0.617408i | \(0.211817\pi\) |
−0.950369 | + | 0.311126i | \(0.899294\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.66255e6 | − | 1.69703e6i | 0.0418975 | − | 0.0152494i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.02526e7 | − | 5.21074e7i | 0.800974 | − | 0.462442i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.78772e7 | − | 2.13052e7i | 0.156702 | − | 0.186750i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.82914e7 | + | 1.63341e7i | 0.244945 | + | 0.141419i | 0.617447 | − | 0.786612i | \(-0.288167\pi\) |
−0.372503 | + | 0.928031i | \(0.621500\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.99232e7 | − | 8.80281e6i | 0.426949 | − | 0.0752826i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.23032e8 | − | 4.47798e7i | −1.03937 | − | 0.378301i | −0.234732 | − | 0.972060i | \(-0.575421\pi\) |
−0.804643 | + | 0.593759i | \(0.797643\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.71668e7i | 0.644006i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.83470e7 | 0.151269 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.33038e7 | − | 1.73926e8i | 0.515657 | − | 1.41675i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.22712e7 | + | 1.83019e8i | 0.259725 | + | 1.47297i | 0.783646 | + | 0.621207i | \(0.213357\pi\) |
−0.523921 | + | 0.851767i | \(0.675531\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.00972e8 | − | 1.74889e8i | 0.802952 | − | 1.39075i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.35672e8 | + | 1.13842e8i | 1.06607 | + | 0.894537i | 0.994690 | − | 0.102912i | \(-0.0328161\pi\) |
0.0713774 | + | 0.997449i | \(0.477261\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.45039e7 | + | 1.63686e8i | 0.733797 | + | 1.27097i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.20311e7 | − | 1.42954e8i | −0.399245 | − | 1.09692i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.69354e7 | − | 2.98617e6i | −0.128423 | − | 0.0226444i | 0.109067 | − | 0.994034i | \(-0.465214\pi\) |
−0.237490 | + | 0.971390i | \(0.576325\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.24934e7 | − | 7.76112e7i | 0.693184 | − | 0.581650i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −586918. | + | 9.96329e7i | −0.00434735 | + | 0.737991i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.65293e7 | − | 6.73690e7i | −0.413858 | − | 0.493217i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 298428. | − | 1.69247e6i | 0.00215957 | − | 0.0122475i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.00770e7 | − | 2.18662e7i | 0.429741 | − | 0.156413i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.68696e8 | + | 9.73969e7i | −1.19287 | + | 0.688703i | −0.958956 | − | 0.283555i | \(-0.908486\pi\) |
−0.233912 | + | 0.972258i | \(0.575153\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.28541e7 | − | 7.49066e7i | 0.439368 | − | 0.523618i | −0.500233 | − | 0.865891i | \(-0.666752\pi\) |
0.939601 | + | 0.342273i | \(0.111197\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7.34798e7 | + | 4.24236e7i | 0.507797 | + | 0.293177i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.68143e8 | + | 2.96482e7i | −1.14881 | + | 0.202566i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.39100e7 | + | 2.32613e7i | 0.431720 | + | 0.157133i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 1.95490e7i | − | 0.130569i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.37280e6 | 0.0222746 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.86185e6 | − | 2.70952e7i | 0.0644017 | − | 0.176942i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.98442e7 | + | 1.12542e8i | 0.128148 | + | 0.726762i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.12142e6 | + | 7.13851e6i | −0.0263197 | + | 0.0455870i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.26152e8 | + | 1.05854e8i | 0.796715 | + | 0.668523i | 0.947398 | − | 0.320059i | \(-0.103703\pi\) |
−0.150683 | + | 0.988582i | \(0.548147\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.15691e8 | + | 2.00382e8i | 0.722601 | + | 1.25158i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.89875e7 | + | 2.17017e8i | 0.487943 | + | 1.34061i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.15937e7 | − | 9.09736e6i | −0.315235 | − | 0.0555845i | 0.0137921 | − | 0.999905i | \(-0.495610\pi\) |
−0.329027 | + | 0.944320i | \(0.606721\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.62475e7 | − | 5.55882e7i | 0.400362 | − | 0.335943i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.31193e7 | − | 1.48663e8i | −0.317539 | − | 0.888685i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.29606e8 | − | 1.54458e8i | −0.766389 | − | 0.913347i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.78797e7 | + | 2.14826e8i | −0.221578 | + | 1.25663i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.78323e8 | + | 6.49042e7i | −1.03191 | + | 0.375584i | −0.801807 | − | 0.597583i | \(-0.796128\pi\) |
−0.230101 | + | 0.973167i | \(0.573906\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.00847e6 | − | 1.15959e6i | 0.0114982 | − | 0.00663849i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.06559e7 | + | 3.65343e7i | −0.173630 | + | 0.206924i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.18365e8 | − | 1.26073e8i | −1.22365 | − | 0.706477i | −0.257959 | − | 0.966156i | \(-0.583050\pi\) |
−0.965695 | + | 0.259679i | \(0.916383\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.33101e8 | + | 2.34693e7i | −0.737966 | + | 0.130123i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.27027e8 | − | 8.26312e7i | −1.24546 | − | 0.453310i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.03896e8i | 1.10680i | 0.832914 | + | 0.553402i | \(0.186671\pi\) | ||||
−0.832914 | + | 0.553402i | \(0.813329\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.71370e7 | −0.145765 | −0.0728825 | − | 0.997341i | \(-0.523220\pi\) | ||||
−0.0728825 | + | 0.997341i | \(0.523220\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.24761e8 | − | 3.42779e8i | 0.663156 | − | 1.82201i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.13136e7 | − | 6.41626e7i | −0.0595109 | − | 0.337503i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.73598e7 | + | 8.20296e7i | −0.246537 | + | 0.427015i | −0.962563 | − | 0.271059i | \(-0.912626\pi\) |
0.716026 | + | 0.698074i | \(0.245959\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.44551e7 | + | 2.89112e7i | 0.177508 | + | 0.148947i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.79577e8 | − | 3.11037e8i | −0.915637 | − | 1.58593i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.90028e7 | − | 7.96845e7i | −0.146364 | − | 0.402131i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.36513e6 | − | 769690.i | −0.0218037 | − | 0.00384457i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.00753e8 | − | 8.45419e7i | 0.498132 | − | 0.417982i | −0.358798 | − | 0.933415i | \(-0.616813\pi\) |
0.856930 | + | 0.515433i | \(0.172369\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.03521e8 | − | 1.72862e8i | 1.48540 | − | 0.845969i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.07404e8 | − | 2.47174e8i | −1.00474 | − | 1.19740i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.14002e7 | − | 2.34792e8i | 0.198536 | − | 1.12595i | −0.708758 | − | 0.705452i | \(-0.750744\pi\) |
0.907293 | − | 0.420499i | \(-0.138145\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.75824e8 | + | 6.39948e7i | −0.834695 | + | 0.303804i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.99482e8 | + | 2.30641e8i | −1.87747 | + | 1.08396i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.94899e8 | − | 2.32271e8i | 0.906835 | − | 1.08072i | −0.0895677 | − | 0.995981i | \(-0.528549\pi\) |
0.996403 | − | 0.0847433i | \(-0.0270070\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.36020e8 | + | 1.94001e8i | 1.54790 | + | 0.893679i | 0.998302 | + | 0.0582485i | \(0.0185516\pi\) |
0.549596 | + | 0.835431i | \(0.314782\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.65781e7 | + | 2.92316e6i | −0.0756104 | + | 0.0133322i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.23133e8 | − | 8.12138e7i | −1.00762 | − | 0.366745i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 6.17165e7i | − | 0.275953i | −0.990435 | − | 0.137977i | \(-0.955940\pi\) | ||
0.990435 | − | 0.137977i | \(-0.0440599\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.68134e8 | 1.18713 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −142004. | + | 390154.i | −0.000622556 | + | 0.00171046i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.11788e7 | − | 2.33536e8i | −0.178769 | − | 1.01385i | −0.933703 | − | 0.358048i | \(-0.883442\pi\) |
0.754934 | − | 0.655800i | \(-0.227669\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.41412e7 | + | 1.28416e8i | −0.318738 | + | 0.552071i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.43987e8 | − | 2.88639e8i | −1.46449 | − | 1.22885i | −0.921072 | − | 0.389391i | \(-0.872685\pi\) |
−0.543418 | − | 0.839462i | \(-0.682870\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.28267e8 | + | 2.22166e8i | 0.540809 | + | 0.936709i | 0.998858 | + | 0.0477820i | \(0.0152153\pi\) |
−0.458048 | + | 0.888927i | \(0.651451\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.44439e7 | + | 1.22109e8i | 0.185583 | + | 0.509884i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.47105e6 | − | 1.14102e6i | −0.0267615 | − | 0.00471877i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.33564e8 | + | 1.95983e8i | −0.956676 | + | 0.802747i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.39099e7 | − | 9.14863e7i | 0.137570 | − | 0.371154i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.83080e7 | − | 1.17159e8i | −0.395036 | − | 0.470786i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.48960e7 | + | 2.54618e8i | −0.178698 | + | 1.01345i | 0.755090 | + | 0.655621i | \(0.227593\pi\) |
−0.933788 | + | 0.357826i | \(0.883518\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.84896e7 | + | 6.72968e6i | −0.0728983 | + | 0.0265328i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.20460e8 | + | 3.00488e8i | −2.03267 | + | 1.17356i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.28005e6 | − | 1.52550e6i | 0.00495230 | − | 0.00590193i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.17043e8 | − | 6.75747e7i | −0.448582 | − | 0.258989i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.90880e8 | − | 6.89226e7i | 1.48412 | − | 0.261690i | 0.627897 | − | 0.778297i | \(-0.283916\pi\) |
0.856223 | + | 0.516606i | \(0.172805\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.19268e8 | + | 7.98069e7i | 0.824787 | + | 0.300198i | 0.719717 | − | 0.694267i | \(-0.244271\pi\) |
0.105069 | + | 0.994465i | \(0.466494\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.01961e8i | 0.379975i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.87538e8 | 0.692430 | 0.346215 | − | 0.938155i | \(-0.387467\pi\) | ||||
0.346215 | + | 0.938155i | \(0.387467\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.11807e7 | − | 3.07188e7i | 0.0409012 | − | 0.112375i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.03019e8 | + | 5.84253e8i | 0.373402 | + | 2.11767i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.63875e8 | − | 2.83839e8i | 0.588535 | − | 1.01937i | −0.405889 | − | 0.913922i | \(-0.633038\pi\) |
0.994425 | − | 0.105451i | \(-0.0336286\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.54886e8 | + | 1.29965e8i | 0.551172 | + | 0.462489i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.40822e7 | − | 7.63526e7i | −0.155442 | − | 0.269233i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.52189e8 | + | 4.18137e8i | 0.531775 | + | 1.46104i | 0.856957 | + | 0.515389i | \(0.172352\pi\) |
−0.325181 | + | 0.945652i | \(0.605425\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.44042e8 | − | 6.06639e7i | −1.19126 | − | 0.210052i | −0.457344 | − | 0.889290i | \(-0.651199\pi\) |
−0.733918 | + | 0.679238i | \(0.762310\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.82636e6 | − | 7.40619e6i | 0.0302859 | − | 0.0254129i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.94676e8 | − | 2.44319e8i | 1.00203 | − | 0.830792i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.32346e8 | − | 1.57724e8i | −0.446000 | − | 0.531522i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.16494e7 | + | 4.63057e8i | −0.272693 | + | 1.54652i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.35893e8 | − | 4.94609e7i | 0.449809 | − | 0.163717i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.27015e8 | + | 2.46537e8i | −1.40087 | + | 0.808793i | −0.994482 | − | 0.104908i | \(-0.966545\pi\) |
−0.406388 | + | 0.913701i | \(0.633212\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.80043e7 | + | 8.10444e7i | −0.221119 | + | 0.263519i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.15559e8 | − | 1.82188e8i | −1.01698 | − | 0.587157i | −0.103756 | − | 0.994603i | \(-0.533086\pi\) |
−0.913229 | + | 0.407446i | \(0.866419\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.67251e7 | − | 1.17654e7i | 0.213147 | − | 0.0375836i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.84262e7 | + | 3.58242e7i | 0.311652 | + | 0.113432i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 3.58919e8i | − | 1.12651i | −0.826283 | − | 0.563255i | \(-0.809549\pi\) | ||
0.826283 | − | 0.563255i | \(-0.190451\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.78836e8 | 1.80088 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.37435e7 | − | 2.30083e8i | 0.258274 | − | 0.709602i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.55745e6 | + | 2.01753e7i | 0.0108763 | + | 0.0616826i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.33802e7 | − | 7.51368e7i | 0.131479 | − | 0.227729i | −0.792768 | − | 0.609524i | \(-0.791361\pi\) |
0.924247 | + | 0.381795i | \(0.124694\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.42393e7 | + | 2.87302e7i | 0.102879 | + | 0.0863253i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.93968e7 | + | 6.82372e7i | 0.117356 | + | 0.203267i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.55571e7 | − | 9.76923e7i | −0.105009 | − | 0.288511i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.36364e8 | + | 9.45755e7i | 1.57047 | + | 0.276915i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.22172e8 | − | 3.54244e8i | 1.22556 | − | 1.02837i | 0.227048 | − | 0.973884i | \(-0.427093\pi\) |
0.998515 | − | 0.0544851i | \(-0.0173517\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.70040e8 | + | 1.58036e8i | 0.777253 | + | 0.454873i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.17332e7 | − | 1.39831e7i | −0.0334849 | − | 0.0399058i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.99569e7 | + | 4.53458e8i | −0.226255 | + | 1.28316i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.96618e8 | + | 7.15633e7i | −0.551678 | + | 0.200794i | −0.602792 | − | 0.797898i | \(-0.705945\pi\) |
0.0511139 | + | 0.998693i | \(0.483723\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.27504e8 | + | 7.36145e7i | −0.354744 | + | 0.204812i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.92826e8 | − | 3.48976e8i | 0.807869 | − | 0.962780i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.41906e6 | − | 3.70604e6i | −0.0175612 | − | 0.0101389i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.63018e8 | + | 2.87444e7i | −0.442260 | + | 0.0779823i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.14127e8 | + | 4.15387e7i | 0.307044 | + | 0.111755i | 0.490947 | − | 0.871190i | \(-0.336651\pi\) |
−0.183903 | + | 0.982944i | \(0.558873\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 2.14246e8i | − | 0.571618i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.00886e8 | 1.06073 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.73330e7 | − | 1.57521e8i | 0.150449 | − | 0.413356i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.09178e6 | − | 1.18631e7i | −0.00544392 | − | 0.0308740i | 0.981965 | − | 0.189064i | \(-0.0605453\pi\) |
−0.987409 | + | 0.158190i | \(0.949434\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.90817e7 | − | 1.36974e8i | 0.204124 | − | 0.353553i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.47612e7 | − | 4.59501e7i | −0.140191 | − | 0.117634i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.32635e8 | + | 2.29731e8i | 0.336780 | + | 0.583320i | 0.983825 | − | 0.179132i | \(-0.0573288\pi\) |
−0.647045 | + | 0.762452i | \(0.723995\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.99439e7 | + | 8.22703e7i | 0.0754131 | + | 0.207196i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.77222e7 | − | 4.88818e6i | −0.0692510 | − | 0.0122108i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.76193e8 | − | 4.83483e8i | 1.42769 | − | 1.19798i | 0.480631 | − | 0.876923i | \(-0.340408\pi\) |
0.947061 | − | 0.321053i | \(-0.104037\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.19059e7 | + | 2.03439e7i | −0.0292623 | + | 0.0500012i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.52971e8 | − | 5.39830e8i | −1.10434 | − | 1.31611i | −0.944334 | − | 0.328990i | \(-0.893292\pi\) |
−0.160010 | − | 0.987115i | \(-0.551153\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.35675e7 | − | 2.47083e8i | 0.105364 | − | 0.597550i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.46436e8 | + | 8.96953e7i | −0.591210 | + | 0.215183i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.08336e7 | − | 3.51223e7i | 0.144776 | − | 0.0835867i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.09013e8 | + | 3.68268e8i | −0.729554 | + | 0.869449i | −0.995522 | − | 0.0945331i | \(-0.969864\pi\) |
0.265968 | + | 0.963982i | \(0.414309\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.24382e8 | + | 4.18222e8i | 1.69661 | + | 0.979540i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.83446e8 | + | 1.73408e8i | −2.28512 | + | 0.402929i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.42937e8 | − | 8.84218e7i | −0.560023 | − | 0.203832i | 0.0464713 | − | 0.998920i | \(-0.485202\pi\) |
−0.606494 | + | 0.795088i | \(0.707425\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 1.27251e8i | − | 0.291028i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.41143e8 | 0.774074 | 0.387037 | − | 0.922064i | \(-0.373499\pi\) | ||||
0.387037 | + | 0.922064i | \(0.373499\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.92426e8 | + | 5.28687e8i | −0.433203 | + | 1.19021i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.37246e7 | + | 1.34549e8i | 0.0529926 | + | 0.300536i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.94885e6 | + | 6.83960e6i | −0.00875153 | + | 0.0151581i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.91980e7 | + | 8.32370e7i | 0.218134 | + | 0.183036i | 0.745306 | − | 0.666722i | \(-0.232303\pi\) |
−0.527172 | + | 0.849759i | \(0.676748\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −706796. | − | 1.22421e6i | −0.00154217 | − | 0.00267111i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.97391e8 | + | 5.42328e8i | 0.427355 | + | 1.17415i | 0.947412 | + | 0.320017i | \(0.103689\pi\) |
−0.520056 | + | 0.854132i | \(0.674089\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.65260e8 | + | 6.44051e7i | 0.784687 | + | 0.138362i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.07096e8 | + | 3.41594e8i | −0.867827 | + | 0.728193i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.35750e8 | + | 1.63729e8i | 0.287162 | + | 0.346349i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.45270e8 | − | 1.73126e8i | −0.304946 | − | 0.363421i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.80569e7 | + | 3.29257e8i | −0.120940 | + | 0.685882i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.20930e8 | − | 8.04121e7i | 0.456716 | − | 0.166231i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.01161e8 | + | 3.47080e8i | −1.23329 | + | 0.712042i | −0.967715 | − | 0.252047i | \(-0.918896\pi\) |
−0.265578 | + | 0.964089i | \(0.585563\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.09839e8 | − | 2.50076e8i | 0.427223 | − | 0.509145i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.85146e8 | − | 1.64629e8i | −0.576153 | − | 0.332642i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.44067e7 | + | 6.06683e6i | −0.0689959 | + | 0.0121658i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.46357e8 | − | 3.08049e8i | −1.68443 | − | 0.613081i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.25917e8i | 0.446246i | 0.974790 | + | 0.223123i | \(0.0716252\pi\) | ||||
−0.974790 | + | 0.223123i | \(0.928375\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.27978e7 | 0.0250896 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.64101e6 | + | 4.50864e6i | −0.00319311 | + | 0.00877299i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.56011e7 | − | 1.45191e8i | −0.0494438 | − | 0.280410i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.49619e8 | − | 4.32352e8i | 0.478508 | − | 0.828800i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.14149e6 | + | 4.31422e6i | 0.00978291 | + | 0.00820884i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.70982e7 | + | 1.33538e8i | 0.145612 | + | 0.252208i | 0.929601 | − | 0.368567i | \(-0.120151\pi\) |
−0.783989 | + | 0.620775i | \(0.786818\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.85758e8 | − | 5.10365e8i | −0.348245 | − | 0.956795i | −0.982923 | − | 0.184018i | \(-0.941090\pi\) |
0.634678 | − | 0.772777i | \(-0.281133\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.73314e8 | − | 3.05600e7i | −0.322524 | − | 0.0568698i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.86030e8 | − | 1.56098e8i | 0.343645 | − | 0.288352i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.37129e8 | + | 5.08276e7i | 0.251456 | + | 0.0932037i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.94095e6 | − | 8.27191e6i | −0.0126348 | − | 0.0150575i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.15650e7 | + | 6.55882e7i | −0.0208985 | + | 0.118521i | −0.993472 | − | 0.114073i | \(-0.963610\pi\) |
0.972574 | + | 0.232594i | \(0.0747214\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.54820e7 | + | 5.63498e6i | −0.0277733 | + | 0.0101086i | −0.355869 | − | 0.934536i | \(-0.615815\pi\) |
0.328096 | + | 0.944644i | \(0.393593\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.97221e7 | − | 5.18011e7i | 0.159786 | − | 0.0922522i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.31288e8 | + | 5.13989e8i | −0.762520 | + | 0.908735i | −0.998005 | − | 0.0631426i | \(-0.979888\pi\) |
0.235485 | + | 0.971878i | \(0.424332\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.40853e8 | + | 3.69997e8i | 1.12485 | + | 0.649433i | 0.942635 | − | 0.333826i | \(-0.108340\pi\) |
0.182215 | + | 0.983259i | \(0.441673\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.61946e8 | + | 8.14536e7i | −0.804986 | + | 0.141941i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.76803e7 | − | 2.09939e7i | −0.0997913 | − | 0.0363211i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 9.67410e8i | − | 1.66169i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.39743e8 | −1.26155 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.98732e7 | − | 1.09551e8i | 0.0675141 | − | 0.185494i | −0.901347 | − | 0.433097i | \(-0.857421\pi\) |
0.968861 | + | 0.247603i | \(0.0796430\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.13007e7 | + | 6.40892e7i | 0.0189984 | + | 0.107745i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.81500e8 | − | 1.00719e9i | 0.970660 | − | 1.68123i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.58269e8 | − | 4.68443e8i | −0.925280 | − | 0.776402i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.89237e8 | − | 5.00974e8i | −0.475997 | − | 0.824450i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.57750e8 | − | 7.08162e8i | −0.421188 | − | 1.15720i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.01871e8 | + | 7.08607e7i | 0.652075 | + | 0.114978i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.85755e8 | + | 4.07597e8i | −0.782654 | + | 0.656725i | −0.943916 | − | 0.330187i | \(-0.892888\pi\) |
0.161261 | + | 0.986912i | \(0.448444\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.38325e8 | − | 2.42879e8i | −0.221311 | − | 0.388591i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.43320e8 | − | 4.09153e8i | −0.545452 | − | 0.650045i | 0.420949 | − | 0.907084i | \(-0.361697\pi\) |
−0.966401 | + | 0.257040i | \(0.917253\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.02335e7 | − | 2.28175e8i | 0.0634758 | − | 0.359989i | −0.936481 | − | 0.350718i | \(-0.885938\pi\) |
0.999957 | − | 0.00927140i | \(-0.00295122\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.39455e8 | + | 1.23551e8i | −0.531829 | + | 0.193570i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.16932e8 | + | 3.56186e8i | −0.959854 | + | 0.554172i | −0.896128 | − | 0.443796i | \(-0.853632\pi\) |
−0.0637256 | + | 0.997967i | \(0.520298\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.96865e8 | − | 2.34614e8i | 0.304172 | − | 0.362498i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.52884e8 | + | 2.03737e8i | 0.541470 | + | 0.312618i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.42460e8 | + | 4.27522e7i | −0.369471 | + | 0.0651477i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.39063e6 | + | 2.32600e6i | 0.00967140 | + | 0.00352010i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 4.94736e7i | − | 0.0743586i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.65541e8 | −0.694919 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.45336e8 | + | 6.74054e8i | −0.363715 | + | 0.999300i | 0.613989 | + | 0.789315i | \(0.289564\pi\) |
−0.977705 | + | 0.209985i | \(0.932658\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.50187e8 | + | 8.51751e8i | 0.221139 | + | 1.25414i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.36418e8 | − | 2.36282e8i | 0.199500 | − | 0.345544i | −0.748866 | − | 0.662721i | \(-0.769402\pi\) |
0.948366 | + | 0.317177i | \(0.102735\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.84280e8 | + | 7.41999e8i | 1.28442 | + | 1.07776i | 0.992618 | + | 0.121280i | \(0.0386999\pi\) |
0.291804 | + | 0.956478i | \(0.405745\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.73608e8 | − | 3.00697e8i | −0.250460 | − | 0.433810i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.37195e7 | + | 9.26435e7i | 0.0483181 | + | 0.132753i | 0.961504 | − | 0.274789i | \(-0.0886081\pi\) |
−0.913186 | + | 0.407542i | \(0.866386\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.44183e9 | − | 2.54234e8i | −2.05215 | − | 0.361850i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.25984e8 | + | 1.89623e8i | −0.319481 | + | 0.268076i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.46551e7 | + | 8.80959e6i | −0.0346220 | + | 0.0123709i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.51892e8 | + | 4.19368e8i | 0.490840 | + | 0.584960i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.33841e6 | + | 3.02756e7i | −0.00739664 | + | 0.0419484i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.10141e9 | − | 4.00882e8i | 1.51590 | − | 0.551743i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.46869e8 | − | 3.15735e8i | 0.747668 | − | 0.431667i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.59664e8 | + | 1.90280e8i | −0.216842 | + | 0.258423i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.59923e8 | + | 5.54212e8i | 1.29506 | + | 0.747705i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.76127e8 | − | 1.36852e8i | 1.04019 | − | 0.183413i | 0.372636 | − | 0.927978i | \(-0.378454\pi\) |
0.667550 | + | 0.744565i | \(0.267343\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.15942e8 | + | 1.14994e8i | 0.420646 | + | 0.153102i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.31995e8i | 0.835909i | 0.908468 | + | 0.417954i | \(0.137253\pi\) | ||||
−0.908468 | + | 0.417954i | \(0.862747\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.38544e8 | −0.576236 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.25342e8 | − | 1.44337e9i | 0.685770 | − | 1.88414i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.55330e7 | + | 4.85082e8i | 0.110924 | + | 0.629081i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.15541e8 | − | 2.00123e8i | 0.148864 | − | 0.257840i | −0.781944 | − | 0.623349i | \(-0.785772\pi\) |
0.930808 | + | 0.365509i | \(0.119105\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.52520e8 | − | 5.47530e8i | −0.835248 | − | 0.700856i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.72999e7 | + | 4.72847e7i | 0.0347180 | + | 0.0601334i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.13631e8 | + | 3.12197e8i | 0.143572 | + | 0.394461i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.54063e8 | − | 2.71655e7i | −0.193402 | − | 0.0341020i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.41783e8 | + | 5.38520e8i | −0.800462 | + | 0.671668i | −0.948311 | − | 0.317342i | \(-0.897210\pi\) |
0.147849 | + | 0.989010i | \(0.452765\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.25574e8 | + | 739728.i | 0.155614 | + | 0.000916691i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.09368e9 | + | 1.30339e9i | 1.34662 | + | 1.60483i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.96729e7 | + | 2.24996e8i | −0.0485355 | + | 0.275259i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.28866e9 | + | 4.69032e8i | −1.56646 | + | 0.570143i | −0.972204 | − | 0.234136i | \(-0.924774\pi\) |
−0.594252 | + | 0.804279i | \(0.702552\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.29663e9 | − | 7.48609e8i | 1.56610 | − | 0.904187i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.90860e8 | − | 2.27458e8i | 0.229058 | − | 0.272981i | −0.639258 | − | 0.768993i | \(-0.720758\pi\) |
0.868316 | + | 0.496012i | \(0.165203\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.40226e8 | + | 1.38694e8i | 0.286473 | + | 0.165395i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.98357e8 | + | 1.40772e8i | −0.946023 | + | 0.166809i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.26227e7 | + | 8.23401e6i | 0.0266376 | + | 0.00969530i | 0.355305 | − | 0.934751i | \(-0.384377\pi\) |
−0.328667 | + | 0.944446i | \(0.606599\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.56180e7i | 0.0416745i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.48614e8 | 0.521592 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.49991e7 | + | 1.23634e8i | −0.0519906 | + | 0.142843i | −0.962970 | − | 0.269609i | \(-0.913105\pi\) |
0.910979 | + | 0.412452i | \(0.135328\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.03442e8 | − | 1.72091e9i | −0.348390 | − | 1.97582i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.63702e8 | − | 2.83539e8i | 0.186774 | − | 0.323503i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.08023e9 | + | 9.06419e8i | 1.22478 | + | 1.02772i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.52925e8 | + | 1.47731e9i | 0.961039 | + | 1.66457i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.75429e7 | − | 4.81986e7i | −0.0196436 | − | 0.0539704i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.12192e8 | + | 3.74151e7i | 0.236127 | + | 0.0416356i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.84539e8 | − | 4.90487e8i | 0.646449 | − | 0.542435i | −0.259542 | − | 0.965732i | \(-0.583572\pi\) |
0.905991 | + | 0.423297i | \(0.139127\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.14772e8 | + | 1.30380e8i | 0.785591 | + | 0.143297i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.57997e7 | + | 9.03345e7i | 0.0827960 | + | 0.0986725i | 0.805852 | − | 0.592117i | \(-0.201708\pi\) |
−0.723056 | + | 0.690789i | \(0.757263\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.33324e7 | + | 1.89037e8i | −0.0361850 | + | 0.205215i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.35199e7 | + | 8.56055e6i | −0.0253759 | + | 0.00923608i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.90689e8 | − | 2.83299e8i | 0.526165 | − | 0.303782i | −0.213288 | − | 0.976989i | \(-0.568417\pi\) |
0.739453 | + | 0.673208i | \(0.235084\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.15729e6 | + | 6.14622e6i | −0.00549634 | + | 0.00655028i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.55779e8 | + | 2.05409e8i | 0.376854 | + | 0.217577i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.45217e8 | − | 1.49035e8i | 0.889832 | − | 0.156901i | 0.289999 | − | 0.957027i | \(-0.406345\pi\) |
0.599833 | + | 0.800126i | \(0.295234\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.45249e9 | − | 5.28662e8i | −1.51986 | − | 0.553184i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 4.44688e7i | − | 0.0462492i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.90736e8 | 0.197171 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.40887e8 | + | 9.36578e8i | −0.350259 | + | 0.962328i | 0.632028 | + | 0.774945i | \(0.282223\pi\) |
−0.982287 | + | 0.187383i | \(0.940000\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.87496e7 | + | 3.33186e8i | 0.0600008 | + | 0.340282i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.10488e9 | + | 1.91370e9i | −1.12162 | + | 1.94270i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.50315e8 | + | 1.26129e8i | 0.151676 | + | 0.127271i | 0.715468 | − | 0.698646i | \(-0.246214\pi\) |
−0.563792 | + | 0.825917i | \(0.690658\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.31317e8 | − | 5.73858e8i | −0.332313 | − | 0.575583i |
(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 | 76.7.j.a.13.9 | ✓ | 60 | |
19.3 | odd | 18 | inner | 76.7.j.a.41.9 | yes | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.7.j.a.13.9 | ✓ | 60 | 1.1 | even | 1 | trivial | |
76.7.j.a.41.9 | yes | 60 | 19.3 | odd | 18 | inner |