Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,7,Mod(65,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.65");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.h (of order \(6\), degree \(2\), 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: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 9460 x^{18} + 36670708 x^{16} + 75655761912 x^{14} + 90488614064544 x^{12} + \cdots + 10\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{22}\cdot 3^{8}\cdot 19^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 65.3 | ||
Root | \(-25.0503i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.65 |
Dual form | 76.7.h.a.69.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −23.1942 | − | 13.3912i | −0.859045 | − | 0.495970i | 0.00464710 | − | 0.999989i | \(-0.498521\pi\) |
−0.863693 | + | 0.504019i | \(0.831854\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 16.0954 | − | 27.8780i | 0.128763 | − | 0.223024i | −0.794435 | − | 0.607350i | \(-0.792233\pi\) |
0.923198 | + | 0.384326i | \(0.125566\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −416.808 | −1.21518 | −0.607591 | − | 0.794250i | \(-0.707864\pi\) | ||||
−0.607591 | + | 0.794250i | \(0.707864\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −5.85193 | − | 10.1358i | −0.00802734 | − | 0.0139038i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1031.33 | 0.774852 | 0.387426 | − | 0.921901i | \(-0.373364\pi\) | ||||
0.387426 | + | 0.921901i | \(0.373364\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2202.37 | + | 1271.54i | −1.00245 | + | 0.578762i | −0.908971 | − | 0.416860i | \(-0.863131\pi\) |
−0.0934743 | + | 0.995622i | \(0.529797\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −746.639 | + | 431.072i | −0.221226 | + | 0.127725i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3772.21 | − | 6533.66i | 0.767802 | − | 1.32987i | −0.170950 | − | 0.985280i | \(-0.554684\pi\) |
0.938752 | − | 0.344593i | \(-0.111983\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1245.17 | + | 6745.03i | −0.181537 | + | 0.983384i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9667.53 | + | 5581.55i | 1.04390 | + | 0.602694i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 9773.64 | + | 16928.4i | 0.803291 | + | 1.39134i | 0.917439 | + | 0.397877i | \(0.130253\pi\) |
−0.114148 | + | 0.993464i | \(0.536414\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7294.38 | + | 12634.2i | 0.466840 | + | 0.808591i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 19837.8i | 1.00787i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 29583.8 | − | 17080.2i | 1.21300 | − | 0.700326i | 0.249588 | − | 0.968352i | \(-0.419705\pi\) |
0.963412 | + | 0.268027i | \(0.0863715\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3711.23i | 0.124576i | 0.998058 | + | 0.0622878i | \(0.0198397\pi\) | ||||
−0.998058 | + | 0.0622878i | \(0.980160\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −23920.8 | − | 13810.7i | −0.665633 | − | 0.384303i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6708.68 | + | 11619.8i | −0.156471 | + | 0.271015i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 82758.7i | 1.63384i | 0.576754 | + | 0.816918i | \(0.304319\pi\) | ||||
−0.576754 | + | 0.816918i | \(0.695681\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 68109.7 | 1.14819 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −78507.2 | − | 45326.2i | −1.13909 | − | 0.657654i | −0.192885 | − | 0.981221i | \(-0.561784\pi\) |
−0.946205 | + | 0.323568i | \(0.895118\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10653.4 | − | 18452.3i | 0.133994 | − | 0.232084i | −0.791219 | − | 0.611533i | \(-0.790553\pi\) |
0.925213 | + | 0.379449i | \(0.123886\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −376.756 | −0.00413450 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 46695.0 | + | 80878.1i | 0.449756 | + | 0.779000i | 0.998370 | − | 0.0570760i | \(-0.0181777\pi\) |
−0.548614 | + | 0.836076i | \(0.684844\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 56079.7 | 0.476669 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −174987. | + | 101029.i | −1.31915 | + | 0.761614i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 101047. | − | 58339.5i | 0.678728 | − | 0.391864i | −0.120648 | − | 0.992695i | \(-0.538497\pi\) |
0.799375 | + | 0.600832i | \(0.205164\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 16599.6 | − | 28751.4i | 0.0997722 | − | 0.172811i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 119205. | − | 139772.i | 0.643678 | − | 0.754734i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −20618.2 | − | 11903.9i | −0.100391 | − | 0.0579609i | 0.448964 | − | 0.893550i | \(-0.351793\pi\) |
−0.549355 | + | 0.835589i | \(0.685127\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −158838. | − | 275115.i | −0.699785 | − | 1.21206i | −0.968541 | − | 0.248855i | \(-0.919946\pi\) |
0.268755 | − | 0.963208i | \(-0.413388\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2439.13 | + | 4224.70i | 0.00975468 | + | 0.0168956i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 81863.6i | 0.298092i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −204338. | + | 117975.i | −0.679399 | + | 0.392251i | −0.799629 | − | 0.600495i | \(-0.794970\pi\) |
0.120230 | + | 0.992746i | \(0.461637\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 523523.i | − | 1.59363i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 153902. | + | 88855.3i | 0.430001 | + | 0.248261i | 0.699347 | − | 0.714782i | \(-0.253474\pi\) |
−0.269346 | + | 0.963043i | \(0.586808\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −173594. | + | 300673.i | −0.446237 | + | 0.772905i | −0.998137 | − | 0.0610047i | \(-0.980570\pi\) |
0.551900 | + | 0.833910i | \(0.313903\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 390722.i | − | 0.926155i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −429865. | −0.941587 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −225299. | − | 130077.i | −0.456961 | − | 0.263826i | 0.253805 | − | 0.967255i | \(-0.418318\pi\) |
−0.710765 | + | 0.703429i | \(0.751651\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 261386. | − | 452734.i | 0.491844 | − | 0.851898i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −615686. | −1.07678 | −0.538388 | − | 0.842697i | \(-0.680966\pi\) | ||||
−0.538388 | + | 0.842697i | \(0.680966\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −121430. | − | 210323.i | −0.197729 | − | 0.342477i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −914899. | −1.38936 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 19492.6 | − | 11254.1i | 0.0276503 | − | 0.0159639i | −0.486111 | − | 0.873897i | \(-0.661585\pi\) |
0.513761 | + | 0.857933i | \(0.328252\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 917966. | − | 529988.i | 1.21815 | − | 0.703302i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 49697.9 | − | 86079.2i | 0.0617858 | − | 0.107016i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 167997. | + | 143277.i | 0.195943 | + | 0.167111i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 874109. | + | 504667.i | 0.957746 | + | 0.552955i | 0.895479 | − | 0.445105i | \(-0.146834\pi\) |
0.0622674 | + | 0.998060i | \(0.480167\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6035.26 | − | 10453.4i | −0.00622000 | − | 0.0107734i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 932836. | + | 1.61572e6i | 0.905401 | + | 1.56820i | 0.820378 | + | 0.571822i | \(0.193763\pi\) |
0.0850234 | + | 0.996379i | \(0.472903\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.45965e6i | 1.33579i | 0.744256 | + | 0.667894i | \(0.232804\pi\) | ||||
−0.744256 | + | 0.667894i | \(0.767196\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 311205. | − | 179674.i | 0.268831 | − | 0.155209i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.53090e6i | 1.24967i | 0.780758 | + | 0.624833i | \(0.214833\pi\) | ||||
−0.780758 | + | 0.624833i | \(0.785167\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 445234. | + | 257056.i | 0.343802 | + | 0.198494i | 0.661952 | − | 0.749546i | \(-0.269728\pi\) |
−0.318150 | + | 0.948040i | \(0.603062\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.10824e6 | − | 1.91952e6i | 0.810334 | − | 1.40354i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.67372e6i | − | 1.15997i | −0.814626 | − | 0.579987i | \(-0.803058\pi\) | ||
0.814626 | − | 0.579987i | \(-0.196942\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 629242. | 0.413737 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 25776.2 | + | 14881.9i | 0.0160939 | + | 0.00929183i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.57229e6 | + | 2.72328e6i | −0.933020 | + | 1.61604i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −707924. | −0.399605 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.21394e6 | + | 2.10261e6i | 0.652353 | + | 1.12991i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 972603. | 0.497973 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.71650e6 | + | 991020.i | −0.837976 | + | 0.483806i | −0.856576 | − | 0.516021i | \(-0.827413\pi\) |
0.0185994 | + | 0.999827i | \(0.494079\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −494196. | + | 285324.i | −0.230213 | + | 0.132914i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 215508. | − | 373270.i | 0.0958625 | − | 0.166039i | −0.814106 | − | 0.580717i | \(-0.802772\pi\) |
0.909968 | + | 0.414678i | \(0.136106\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 518994. | − | 2.81138e6i | 0.220601 | − | 1.19499i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 553039. | + | 319297.i | 0.224778 | + | 0.129776i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.09664e6 | + | 1.89943e6i | 0.426483 | + | 0.738691i | 0.996558 | − | 0.0829025i | \(-0.0264190\pi\) |
−0.570074 | + | 0.821593i | \(0.693086\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −107067. | − | 185445.i | −0.0398667 | − | 0.0690511i | 0.845404 | − | 0.534128i | \(-0.179360\pi\) |
−0.885270 | + | 0.465077i | \(0.846027\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 2.50121e6i | − | 0.892261i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.27137e6 | + | 1.31137e6i | −0.776746 | + | 0.448455i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 1.09965e6i | − | 0.360704i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.30072e6 | − | 750974.i | −0.409481 | − | 0.236414i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 875055. | − | 1.51564e6i | 0.264531 | − | 0.458181i | −0.702910 | − | 0.711279i | \(-0.748116\pi\) |
0.967441 | + | 0.253098i | \(0.0814495\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.24436e6i | 1.52322i | 0.648038 | + | 0.761608i | \(0.275590\pi\) | ||||
−0.648038 | + | 0.761608i | \(0.724410\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −88298.9 | −0.0246536 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 103462. | + | 59733.7i | 0.0277834 | + | 0.0160407i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.97123e6 | − | 3.41428e6i | 0.509377 | − | 0.882267i | −0.490564 | − | 0.871405i | \(-0.663209\pi\) |
0.999941 | − | 0.0108617i | \(-0.00345745\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.12494e6 | −0.777411 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.07373e6 | − | 7.05591e6i | −0.976146 | − | 1.69073i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.78269e6 | 1.56617 | 0.783085 | − | 0.621914i | \(-0.213645\pi\) | ||||
0.783085 | + | 0.621914i | \(0.213645\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −770030. | + | 444577.i | −0.171418 | + | 0.0989681i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.19102e6 | + | 1.26499e6i | −0.470432 | + | 0.271604i | −0.716421 | − | 0.697668i | \(-0.754221\pi\) |
0.245988 | + | 0.969273i | \(0.420888\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 820223. | − | 1.42067e6i | 0.169931 | − | 0.294329i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 75653.2 | − | 26850.7i | 0.0151300 | − | 0.00536990i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.00695e6 | + | 1.73607e6i | 0.580749 | + | 0.335296i | 0.761431 | − | 0.648246i | \(-0.224497\pi\) |
−0.180682 | + | 0.983542i | \(0.557830\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.04035e6 | − | 5.26605e6i | −0.567296 | − | 0.982586i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 318816. | + | 552206.i | 0.0574937 | + | 0.0995821i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 4.13863e6i | − | 0.721602i | −0.932643 | − | 0.360801i | \(-0.882503\pi\) | ||
0.932643 | − | 0.360801i | \(-0.117497\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.23288e6 | + | 5.33060e6i | −1.55705 | + | 0.898961i | −0.559508 | + | 0.828825i | \(0.689010\pi\) |
−0.997537 | + | 0.0701361i | \(0.977657\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.50812e6i | 1.38829i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.30715e6 | + | 1.33203e6i | 0.364385 | + | 0.210378i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.89039e6 | − | 6.73835e6i | 0.594933 | − | 1.03045i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 8.26855e6i | − | 1.22474i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.71451e6 | −0.389575 | −0.194788 | − | 0.980845i | \(-0.562402\pi\) | ||||
−0.194788 | + | 0.980845i | \(0.562402\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.71427e6 | − | 3.87648e6i | −0.933957 | − | 0.539220i | −0.0458960 | − | 0.998946i | \(-0.514614\pi\) |
−0.888061 | + | 0.459726i | \(0.847948\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.09625e6 | − | 1.89876e6i | 0.147845 | − | 0.256075i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.02322e6 | 0.526229 | 0.263114 | − | 0.964765i | \(-0.415250\pi\) | ||||
0.263114 | + | 0.964765i | \(0.415250\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.72880e6 | − | 1.33867e7i | −0.980738 | − | 1.69869i | −0.659530 | − | 0.751679i | \(-0.729245\pi\) |
−0.321208 | − | 0.947009i | \(-0.604089\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.31928e6 | 0.778179 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.23308e7 | + | 7.11918e6i | −1.47402 | + | 0.851024i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.52721e6 | + | 1.45908e6i | −0.293345 | + | 0.169363i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 114389. | − | 198128.i | 0.0128966 | − | 0.0223375i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.28417e6 | + | 6.95634e6i | −0.140665 | + | 0.761977i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.85380e6 | + | 2.80234e6i | 0.516695 | + | 0.298314i | 0.735582 | − | 0.677436i | \(-0.236909\pi\) |
−0.218886 | + | 0.975750i | \(0.570242\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.37976e6 | − | 4.12186e6i | −0.246260 | − | 0.426535i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −342942. | − | 593993.i | −0.0345069 | − | 0.0597676i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 1.54687e6i | − | 0.151382i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.05275e6 | − | 4.64926e6i | 0.766676 | − | 0.442641i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.91861e7i | 1.77750i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.25394e7 | + | 7.23963e6i | 1.13074 | + | 0.652833i | 0.944121 | − | 0.329600i | \(-0.106914\pi\) |
0.186619 | + | 0.982432i | \(0.440247\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 85372.4 | − | 147869.i | 0.00749497 | − | 0.0129817i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.89929e6i | 0.504338i | 0.967683 | + | 0.252169i | \(0.0811440\pi\) | ||||
−0.967683 | + | 0.252169i | \(0.918856\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.77108e7 | 1.47480 | 0.737399 | − | 0.675457i | \(-0.236054\pi\) | ||||
0.737399 | + | 0.675457i | \(0.236054\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.97039e6 | + | 5.75641e6i | 0.808866 | + | 0.466999i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.80522e6 | + | 1.52511e7i | −0.696101 | + | 1.20568i | 0.273707 | + | 0.961813i | \(0.411750\pi\) |
−0.969808 | + | 0.243870i | \(0.921583\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.00629e6 | 0.231648 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.48376e6 | + | 6.03406e6i | 0.261700 | + | 0.453278i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −520648. | −0.0381373 | −0.0190687 | − | 0.999818i | \(-0.506070\pi\) | ||||
−0.0190687 | + | 0.999818i | \(0.506070\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.93153e6 | − | 2.84722e6i | 0.352314 | − | 0.203409i | −0.313390 | − | 0.949625i | \(-0.601465\pi\) |
0.665704 | + | 0.746216i | \(0.268131\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 398969. | − | 230345.i | 0.0278048 | − | 0.0160531i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 902623. | − | 1.56339e6i | 0.0613774 | − | 0.106309i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.83426e6 | − | 1.64383e7i | −0.387164 | − | 1.09086i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.42804e7 | + | 8.24478e6i | 0.924999 | + | 0.534049i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.86481e6 | + | 8.42610e6i | 0.307642 | + | 0.532851i | 0.977846 | − | 0.209326i | \(-0.0671269\pi\) |
−0.670204 | + | 0.742177i | \(0.733794\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.00798e7 | + | 1.74588e7i | 0.622432 | + | 1.07808i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.50439e6i | 0.392271i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.82821e7 | + | 1.63287e7i | −1.66615 | + | 0.961950i | −0.696459 | + | 0.717596i | \(0.745242\pi\) |
−0.969686 | + | 0.244353i | \(0.921424\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 3.44945e7i | − | 1.98541i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −346245. | − | 199905.i | −0.0194743 | − | 0.0112435i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.33851e7 | − | 2.31837e7i | 0.735792 | − | 1.27443i | −0.218583 | − | 0.975818i | \(-0.570144\pi\) |
0.954375 | − | 0.298610i | \(-0.0965231\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 3.75598e6i | − | 0.201830i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −602822. | −0.0316705 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −539234. | − | 311327.i | −0.0277026 | − | 0.0159941i | 0.486085 | − | 0.873912i | \(-0.338425\pi\) |
−0.513787 | + | 0.857918i | \(0.671758\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.21678e7 | + | 2.10752e7i | −0.611368 | + | 1.05892i | 0.379642 | + | 0.925133i | \(0.376047\pi\) |
−0.991010 | + | 0.133787i | \(0.957286\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.83887e7 | −1.39527 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.52289e6 | + | 1.30300e7i | 0.361732 | + | 0.626538i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.69111e6 | 0.173667 | 0.0868336 | − | 0.996223i | \(-0.472325\pi\) | ||||
0.0868336 | + | 0.996223i | \(0.472325\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 37616.5 | − | 21717.9i | 0.00173207 | − | 0.00100001i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.07778e6 | + | 5.24106e6i | −0.409129 | + | 0.236211i | −0.690416 | − | 0.723413i | \(-0.742572\pi\) |
0.281286 | + | 0.959624i | \(0.409239\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.09672e6 | − | 1.05598e7i | 0.268991 | − | 0.465906i | −0.699611 | − | 0.714524i | \(-0.746643\pi\) |
0.968601 | + | 0.248619i | \(0.0799766\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.97791e6 | − | 5.57286e6i | −0.0854420 | − | 0.240737i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.27224e7 | + | 1.88923e7i | 1.38420 | + | 0.799170i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.63904e7 | − | 2.83890e7i | −0.679040 | − | 1.17613i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.35162e7 | − | 2.34107e7i | −0.548498 | − | 0.950027i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.16699e7i | 0.463941i | 0.972723 | + | 0.231971i | \(0.0745173\pi\) | ||||
−0.972723 | + | 0.231971i | \(0.925483\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −663717. | + | 383197.i | −0.0258533 | + | 0.0149264i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.04593e7i | 0.780946i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.30504e7 | − | 2.48552e7i | −1.61051 | − | 0.929829i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.44043e6 | + | 7.69106e6i | −0.162827 | + | 0.282024i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 4.99671e7i | − | 1.79621i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.02262e7 | −0.360426 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.44066e7 | − | 1.40911e7i | −0.843513 | − | 0.487002i | 0.0149438 | − | 0.999888i | \(-0.495243\pi\) |
−0.858457 | + | 0.512886i | \(0.828576\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.95465e7 | − | 3.38555e7i | 0.662511 | − | 1.14750i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.20873e6 | −0.173161 | −0.0865807 | − | 0.996245i | \(-0.527594\pi\) | ||||
−0.0865807 | + | 0.996245i | \(0.527594\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.98844e7 | + | 3.44408e7i | 0.648455 | + | 1.12316i | 0.983492 | + | 0.180953i | \(0.0579180\pi\) |
−0.335036 | + | 0.942205i | \(0.608749\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 157035. | 0.00502417 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.08077e7 | + | 6.23984e6i | −0.339278 | + | 0.195882i | −0.659953 | − | 0.751307i | \(-0.729424\pi\) |
0.320675 | + | 0.947189i | \(0.396090\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.05106e7 | − | 1.76153e7i | 0.939895 | − | 0.542649i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.05005e7 | − | 3.55079e7i | 0.619797 | − | 1.07352i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.93727e7 | + | 3.35792e7i | 1.16839 | + | 0.996466i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.21299e7 | − | 1.85502e7i | −0.935963 | − | 0.540379i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.88457e6 | − | 1.19244e7i | −0.196895 | − | 0.341031i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.94628e7 | − | 3.37106e7i | −0.546535 | − | 0.946627i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.61322e7i | 1.27210i | 0.771649 | + | 0.636048i | \(0.219432\pi\) | ||||
−0.771649 | + | 0.636048i | \(0.780568\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 838829. | − | 484298.i | 0.0227165 | − | 0.0131154i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.59538e6i | 0.202030i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.62058e7 | + | 9.35640e6i | 0.423428 | + | 0.244466i | 0.696543 | − | 0.717515i | \(-0.254721\pi\) |
−0.273115 | + | 0.961981i | \(0.588054\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.24131e7 | + | 3.88207e7i | −0.575312 | + | 0.996470i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.82750e6i | 0.0965277i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.56626e7 | 0.635942 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.45948e7 | − | 8.42630e6i | −0.355419 | − | 0.205201i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.59302e6 | + | 1.14195e7i | −0.157796 | + | 0.273311i | −0.934074 | − | 0.357080i | \(-0.883772\pi\) |
0.776278 | + | 0.630391i | \(0.217106\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.78936e7 | 0.420942 | 0.210471 | − | 0.977600i | \(-0.432500\pi\) | ||||
0.210471 | + | 0.977600i | \(0.432500\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.52246e7 | − | 4.36902e7i | −0.583314 | − | 1.01033i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.32161e7 | −1.20982 | −0.604908 | − | 0.796295i | \(-0.706790\pi\) | ||||
−0.604908 | + | 0.796295i | \(0.706790\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.95422e6 | − | 2.86032e6i | 0.110736 | − | 0.0639336i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.29360e7 | − | 4.21096e7i | 1.60301 | − | 0.925500i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.09170e7 | + | 1.89088e7i | −0.235950 | + | 0.408678i | −0.959548 | − | 0.281543i | \(-0.909154\pi\) |
0.723598 | + | 0.690222i | \(0.242487\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.39450e7 | − | 1.67974e7i | −0.934088 | − | 0.357042i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.64198e7 | + | 9.47995e6i | 0.343279 | + | 0.198192i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.58811e6 | + | 9.67890e6i | 0.114918 | + | 0.199043i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.13394e7 | − | 3.69610e7i | −0.431702 | − | 0.747730i | 0.565318 | − | 0.824873i | \(-0.308754\pi\) |
−0.997020 | + | 0.0771428i | \(0.975420\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.06098e6i | 0.0211168i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.21171e7 | + | 2.43163e7i | −0.824778 | + | 0.476186i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.98749e7i | 0.382982i | 0.981494 | + | 0.191491i | \(0.0613323\pi\) | ||||
−0.981494 | + | 0.191491i | \(0.938668\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.25588e7 | − | 1.30243e7i | −0.427781 | − | 0.246980i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.34364e7 | + | 7.52341e7i | −0.810644 | + | 1.40408i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 3.89370e7i | − | 0.715229i | −0.933869 | − | 0.357614i | \(-0.883590\pi\) | ||
0.933869 | − | 0.357614i | \(-0.116410\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.30837e7 | 0.959813 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.64933e7 | + | 1.52959e7i | 0.471563 | + | 0.272257i | 0.716894 | − | 0.697182i | \(-0.245563\pi\) |
−0.245331 | + | 0.969439i | \(0.578897\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.91884e6 | + | 1.19838e7i | −0.121241 | + | 0.209996i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −249373. | −0.00430245 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.19252e7 | + | 7.26165e7i | 0.712240 | + | 1.23364i | 0.964015 | + | 0.265849i | \(0.0856524\pi\) |
−0.251775 | + | 0.967786i | \(0.581014\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.47473e8 | 2.46707 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.99707e6 | + | 5.77181e6i | −0.164700 | + | 0.0950899i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.25256e6 | + | 4.18727e6i | −0.117679 | + | 0.0679421i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.65611e7 | − | 2.86846e7i | 0.264678 | − | 0.458435i | −0.702802 | − | 0.711386i | \(-0.748068\pi\) |
0.967479 | + | 0.252951i | \(0.0814012\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.96854e7 | + | 5.82579e7i | −0.782186 | + | 0.917140i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.29281e7 | + | 2.47846e7i | 0.665746 | + | 0.384369i | 0.794463 | − | 0.607313i | \(-0.207752\pi\) |
−0.128717 | + | 0.991681i | \(0.541086\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.71898e6 | − | 8.17352e6i | −0.0720997 | − | 0.124880i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.41421e6 | − | 1.45738e7i | −0.126663 | − | 0.219386i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.53513e7i | 1.26598i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.55251e7 | + | 1.47369e7i | −0.373076 | + | 0.215395i | −0.674801 | − | 0.738000i | \(-0.735771\pi\) |
0.301726 | + | 0.953395i | \(0.402437\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 5.87412e7i | − | 0.846092i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.59384e6 | + | 4.96166e6i | 0.121994 | + | 0.0704331i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.90970e6 | + | 1.71641e7i | −0.138649 | + | 0.240147i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.73501e6i | 0.0790908i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.15129e8 | 1.56510 | 0.782551 | − | 0.622587i | \(-0.213918\pi\) | ||||
0.782551 | + | 0.622587i | \(0.213918\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.61568e7 | + | 2.08751e7i | 0.484555 | + | 0.279758i | 0.722313 | − | 0.691566i | \(-0.243079\pi\) |
−0.237758 | + | 0.971325i | \(0.576412\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 546511. | − | 946586.i | 0.00722068 | − | 0.0125066i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.10064e8 | 1.43376 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.62049e7 | + | 1.14670e8i | 0.850367 | + | 1.47288i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.02435e7 | 0.889681 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.50216e7 | − | 8.67271e6i | 0.187622 | − | 0.108324i | −0.403247 | − | 0.915091i | \(-0.632118\pi\) |
0.590869 | + | 0.806768i | \(0.298785\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.51933e7 | + | 4.91864e7i | −1.04940 | + | 0.605872i | −0.922482 | − | 0.386041i | \(-0.873842\pi\) |
−0.126920 | + | 0.991913i | \(0.540509\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.47256e7 | + | 2.55056e7i | −0.178898 | + | 0.309861i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.26353e8 | + | 4.48448e7i | −1.51405 | + | 0.537363i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.74476e7 | − | 5.62614e7i | −1.15180 | − | 0.664993i | −0.202476 | − | 0.979287i | \(-0.564899\pi\) |
−0.949325 | + | 0.314295i | \(0.898232\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −328174. | − | 568414.i | −0.00382639 | − | 0.00662749i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.45590e7 | − | 1.29140e8i | −0.857608 | − | 1.48542i | −0.874204 | − | 0.485559i | \(-0.838616\pi\) |
0.0165958 | − | 0.999862i | \(-0.494717\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 724554.i | − | 0.00822225i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.05925e7 | + | 2.34361e7i | −0.454488 | + | 0.262399i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 7.59293e7i | − | 0.838824i | −0.907796 | − | 0.419412i | \(-0.862236\pi\) | ||
0.907796 | − | 0.419412i | \(-0.137764\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.09667e7 | − | 4.67461e7i | −0.882626 | − | 0.509584i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.02282e7 | − | 1.21639e8i | 0.755470 | − | 1.30851i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 3.41214e7i | − | 0.362237i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.72025e6 | 0.0180237 | 0.00901183 | − | 0.999959i | \(-0.497131\pi\) | ||||
0.00901183 | + | 0.999959i | \(0.497131\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.29614e8 | + | 7.48324e7i | 1.34033 | + | 0.773841i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.62328e6 | − | 1.32039e7i | 0.0778107 | − | 0.134772i | −0.824494 | − | 0.565870i | \(-0.808540\pi\) |
0.902305 | + | 0.431098i | \(0.141874\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.27757e7 | 0.531730 | 0.265865 | − | 0.964010i | \(-0.414342\pi\) | ||||
0.265865 | + | 0.964010i | \(0.414342\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.59981e6 | − | 2.77095e6i | −0.0159115 | − | 0.0275594i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.38878e8 | −1.36358 | −0.681792 | − | 0.731546i | \(-0.738799\pi\) | ||||
−0.681792 | + | 0.731546i | \(0.738799\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.51697e7 | − | 4.91727e7i | 0.825594 | − | 0.476657i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.14425e7 | + | 5.27944e7i | −0.875156 | + | 0.505272i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.09872e7 | − | 1.90304e7i | 0.103825 | − | 0.179831i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.43010e7 | + | 3.34691e7i | −0.879904 | + | 0.312294i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.18264e6 | − | 682797.i | −0.0108968 | − | 0.00629124i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.54257e7 | − | 7.86797e7i | −0.413328 | − | 0.715906i | 0.581923 | − | 0.813244i | \(-0.302301\pi\) |
−0.995251 | + | 0.0973381i | \(0.968967\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.05231e8 | − | 1.82265e8i | −0.945602 | − | 1.63783i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.18208e8i | 1.93656i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.81382e7 | − | 1.62456e7i | 0.246644 | − | 0.142400i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.87686e8i | 1.62497i | 0.582982 | + | 0.812485i | \(0.301886\pi\) | ||||
−0.582982 | + | 0.812485i | \(0.698114\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.57319e8 | − | 9.08283e7i | −1.34541 | − | 0.776774i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.02654e7 | − | 3.51008e7i | 0.171203 | − | 0.296532i | −0.767638 | − | 0.640884i | \(-0.778568\pi\) |
0.938841 | + | 0.344352i | \(0.111901\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 2.57721e8i | − | 2.15085i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −388559. | −0.00320362 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.41475e7 | − | 3.70356e7i | −0.522529 | − | 0.301682i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.24558e7 | − | 2.15741e7i | 0.100247 | − | 0.173633i | −0.811539 | − | 0.584298i | \(-0.801370\pi\) |
0.911786 | + | 0.410665i | \(0.134703\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.77587e7 | 0.538830 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.03746e7 | − | 1.39213e8i | −0.631561 | − | 1.09389i | −0.987233 | − | 0.159284i | \(-0.949081\pi\) |
0.355672 | − | 0.934611i | \(-0.384252\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00574e7 | 0.466329 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.80489e7 | + | 2.19675e7i | −0.291956 | + | 0.168561i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.47616e8 | − | 8.52261e7i | 1.11939 | − | 0.646278i | 0.178142 | − | 0.984005i | \(-0.442991\pi\) |
0.941244 | + | 0.337727i | \(0.109658\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.23552e7 | − | 1.25323e8i | 0.542260 | − | 0.939221i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.33807e8 | − | 2.47014e7i | −0.991119 | − | 0.182965i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.06922e7 | + | 2.34936e7i | 0.297913 | + | 0.172000i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.81578e7 | + | 8.34118e7i | 0.348494 | + | 0.603609i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.64960e7 | − | 8.05334e7i | −0.332593 | − | 0.576068i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 1.49534e8i | − | 1.05737i | −0.848818 | − | 0.528686i | \(-0.822685\pi\) | ||
0.848818 | − | 0.528686i | \(-0.177315\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.38622e8 | + | 1.37768e8i | −1.66803 | + | 0.963039i | −0.699337 | + | 0.714793i | \(0.746521\pi\) |
−0.968697 | + | 0.248247i | \(0.920146\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.62856e8i | 1.12545i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.42480e7 | + | 1.39996e7i | 0.165670 | + | 0.0956495i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.17030e8 | + | 2.02702e8i | −0.790553 | + | 1.36928i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 278644.i | 0.00186109i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.30536e8 | 1.52250 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.26783e7 | + | 2.46403e7i | 0.278706 | + | 0.160911i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.54212e7 | + | 9.59924e7i | −0.357893 | + | 0.619889i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.78365e7 | 0.369348 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.62958e7 | + | 9.75071e7i | 0.355536 | + | 0.615807i | 0.987210 | − | 0.159428i | \(-0.0509649\pi\) |
−0.631673 | + | 0.775235i | \(0.717632\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.85533e8 | 1.78343 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.43324e7 | − | 8.27482e6i | 0.0885380 | − | 0.0511175i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.98558e8 | − | 1.14637e8i | 1.21318 | − | 0.700429i | 0.249729 | − | 0.968316i | \(-0.419659\pi\) |
0.963450 | + | 0.267887i | \(0.0863253\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.85902e6 | + | 3.21991e6i | −0.0112348 | + | 0.0194593i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.83700e7 | + | 2.20812e8i | 0.468484 | + | 1.31998i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.39065e7 | + | 5.42170e7i | 0.555291 | + | 0.320597i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.56750e7 | − | 6.17909e7i | −0.208682 | − | 0.361448i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.42830e8 | − | 2.47388e8i | −0.826520 | − | 1.43157i | −0.900752 | − | 0.434333i | \(-0.856984\pi\) |
0.0742326 | − | 0.997241i | \(-0.476349\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.41851e7i | 0.310202i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.80469e8 | + | 1.04194e8i | −1.02215 | + | 0.590138i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 1.94396e8i | − | 1.08934i | −0.838651 | − | 0.544670i | \(-0.816655\pi\) | ||
0.838651 | − | 0.544670i | \(-0.183345\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.66600e7 | − | 2.69392e7i | −0.258702 | − | 0.149362i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.08948e8 | + | 1.88703e8i | −0.597680 | + | 1.03521i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 2.84193e8i | − | 1.54269i | −0.636420 | − | 0.771343i | \(-0.719586\pi\) | ||
0.636420 | − | 0.771343i | \(-0.280414\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.01264e7 | −0.322966 | −0.161483 | − | 0.986875i | \(-0.551628\pi\) | ||||
−0.161483 | + | 0.986875i | \(0.551628\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.29609e7 | + | 3.63505e7i | 0.334663 | + | 0.193218i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.42585e8 | + | 2.46965e8i | −0.750017 | + | 1.29907i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.50087e8 | −1.30186 | −0.650929 | − | 0.759138i | \(-0.725621\pi\) | ||||
−0.650929 | + | 0.759138i | \(0.725621\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.03822e8 | + | 1.79824e8i | 0.534874 | + | 0.926429i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.56623e8 | 1.30848 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.04213e8 | − | 6.01671e7i | 0.525913 | − | 0.303636i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 829757. | − | 479060.i | 0.00414460 | − | 0.00239289i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.84333e7 | − | 1.70492e8i | 0.486663 | − | 0.842924i | −0.513220 | − | 0.858257i | \(-0.671547\pi\) |
0.999882 | + | 0.0153329i | \(0.00488080\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.50324e7 | − | 4.62110e6i | −0.122506 | − | 0.0226151i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.33154e7 | − | 5.38757e7i | −0.452055 | − | 0.260994i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.73896e7 | − | 1.51363e8i | −0.419079 | − | 0.725866i | 0.576768 | − | 0.816908i | \(-0.304314\pi\) |
−0.995847 | + | 0.0910422i | \(0.970980\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.06131e7 | + | 8.76644e7i | 0.240277 | + | 0.416172i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.13991e8i | 1.94567i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.46476e7 | + | 5.46448e7i | −0.440381 | + | 0.254254i | −0.703759 | − | 0.710438i | \(-0.748497\pi\) |
0.263378 | + | 0.964693i | \(0.415163\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.11871e8i | 0.975994i | 0.872845 | + | 0.487997i | \(0.162272\pi\) | ||||
−0.872845 | + | 0.487997i | \(0.837728\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.39154e6 | + | 1.38076e6i | 0.0109075 | + | 0.00629746i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.13943e7 | + | 1.97355e7i | −0.0514543 | + | 0.0891214i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.43070e7i | 0.242823i | 0.992602 | + | 0.121411i | \(0.0387421\pi\) | ||||
−0.992602 | + | 0.121411i | \(0.961258\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.81337e8 | 1.68833 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.05679e8 | − | 1.18749e8i | −0.901711 | − | 0.520603i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.71413e8 | − | 2.96897e8i | 0.744155 | − | 1.28891i | −0.206433 | − | 0.978461i | \(-0.566186\pi\) |
0.950588 | − | 0.310454i | \(-0.100481\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.81554e7 | 0.335996 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.67520e8 | + | 2.90153e8i | 0.713200 | + | 1.23530i | 0.963650 | + | 0.267169i | \(0.0860880\pi\) |
−0.250450 | + | 0.968129i | \(0.580579\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.09542e8 | −0.461856 | −0.230928 | − | 0.972971i | \(-0.574176\pi\) | ||||
−0.230928 | + | 0.972971i | \(0.574176\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.35823e8 | + | 1.93888e8i | −1.40228 | + | 0.809609i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.12468e6 | + | 4.69079e6i | −0.0336002 | + | 0.0193991i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.83202e7 | + | 1.70296e8i | −0.402720 | + | 0.697531i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.22939e8 | − | 1.44150e8i | 0.498755 | − | 0.584807i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.40717e8 | + | 3.12183e8i | 2.17279 | + | 1.25446i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.71363e7 | + | 4.70015e7i | 0.108010 | + | 0.187078i | 0.914964 | − | 0.403536i | \(-0.132219\pi\) |
−0.806954 | + | 0.590614i | \(0.798886\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.50534e7 | − | 1.29996e8i | −0.295910 | − | 0.512531i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.38033e7i | 0.249185i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.23508e8 | + | 7.13075e7i | −0.477835 | + | 0.275878i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 2.07990e6i | − | 0.00797150i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.38613e7 | + | 3.68703e7i | 0.242473 | + | 0.139992i | 0.616313 | − | 0.787501i | \(-0.288626\pi\) |
−0.373840 | + | 0.927493i | \(0.621959\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.87704e8 | − | 3.25113e8i | 0.706058 | − | 1.22293i | −0.260250 | − | 0.965541i | \(-0.583805\pi\) |
0.966308 | − | 0.257387i | \(-0.0828616\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.83696e7i | 0.0684575i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.40689e8 | 0.888677 | 0.444338 | − | 0.895859i | \(-0.353439\pi\) | ||||
0.444338 | + | 0.895859i | \(0.353439\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.12642e7 | − | 1.22769e7i | −0.0777883 | − | 0.0449111i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.07144e7 | + | 3.58785e7i | −0.0750811 | + | 0.130044i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.56641e8 | −1.28083 | −0.640415 | − | 0.768029i | \(-0.721238\pi\) | ||||
−0.640415 | + | 0.768029i | \(0.721238\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.93735e6 | − | 1.20158e7i | −0.0246871 | − | 0.0427593i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.06343e6 | 0.0143284 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.01901e7 | + | 5.88327e6i | −0.0356060 | + | 0.0205571i | −0.517697 | − | 0.855564i | \(-0.673211\pi\) |
0.482091 | + | 0.876121i | \(0.339877\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.28807e7 | + | 2.47572e7i | −0.148476 | + | 0.0857229i | −0.572398 | − | 0.819976i | \(-0.693987\pi\) |
0.423921 | + | 0.905699i | \(0.360653\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.56924e8 | − | 4.45006e8i | 0.881586 | − | 1.52695i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.00223e7 | − | 5.97188e7i | −0.238107 | − | 0.203070i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.78284e8 | + | 3.33872e8i | 1.94878 | + | 1.12513i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.93895e8 | − | 3.35835e8i | −0.647571 | − | 1.12163i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.63814e8 | − | 2.83734e8i | −0.542230 | − | 0.939170i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.83173e8i | 1.58510i | 0.609806 | + | 0.792551i | \(0.291248\pi\) | ||||
−0.609806 | + | 0.792551i | \(0.708752\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.50636e8 | + | 1.44705e8i | −0.814951 | + | 0.470512i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 8.39581e7i | − | 0.270581i | −0.990806 | − | 0.135290i | \(-0.956803\pi\) | ||
0.990806 | − | 0.135290i | \(-0.0431967\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.64335e8 | − | 2.10349e8i | −1.16384 | − | 0.671941i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.89985e7 | − | 1.36829e8i | 0.250137 | − | 0.433250i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 2.28817e8i | − | 0.718170i | −0.933305 | − | 0.359085i | \(-0.883089\pi\) | ||
0.933305 | − | 0.359085i | \(-0.116911\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.06032e7 | 0.219661 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.10789e8 | − | 2.37169e8i | −1.26692 | − | 0.731456i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.48362e8 | + | 2.56970e8i | −0.453591 | + | 0.785643i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.98311e8 | 1.20723 | 0.603613 | − | 0.797277i | \(-0.293727\pi\) | ||||
0.603613 | + | 0.797277i | \(0.293727\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.51554e6 | + | 4.35705e6i | 0.00755843 | + | 0.0130916i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.89312e6 | −0.0205334 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.92292e8 | + | 3.41960e8i | −1.74919 | + | 1.00990i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.08461e8 | − | 2.35825e8i | 1.19597 | − | 0.690491i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.02008e8 | − | 3.49889e8i | 0.586429 | − | 1.01572i | −0.408267 | − | 0.912863i | \(-0.633867\pi\) |
0.994696 | − | 0.102862i | \(-0.0328000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.58210e8 | − | 1.03048e8i | −1.60669 | − | 0.296602i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.97286e7 | − | 4.02578e7i | −0.198996 | − | 0.114890i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.88813e8 | − | 6.73444e8i | −1.10023 | − | 1.90565i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.06420e8 | + | 3.57529e8i | 0.579178 | + | 1.00317i | 0.995574 | + | 0.0939828i | \(0.0299599\pi\) |
−0.416395 | + | 0.909184i | \(0.636707\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.04480e6i | 0.00847129i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.28254e7 | + | 3.62723e7i | −0.173327 | + | 0.100071i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.44282e7i | 0.230977i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.20760e7 | + | 6.97209e6i | 0.0327617 | + | 0.0189150i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.86032e7 | − | 1.70786e8i | 0.265280 | − | 0.459478i | −0.702357 | − | 0.711825i | \(-0.747869\pi\) |
0.967637 | + | 0.252347i | \(0.0812023\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 6.08394e8i | − | 1.62323i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.52511e8 | −0.403539 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.31592e8 | + | 2.49179e8i | 1.13255 | + | 0.653880i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.35592e8 | + | 4.08057e8i | −0.613136 | + | 1.06198i | 0.377573 | + | 0.925980i | \(0.376759\pi\) |
−0.990709 | + | 0.136002i | \(0.956574\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.93439e8 | −1.01554 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.03740e7 | − | 1.39212e8i | −0.205761 | − | 0.356389i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.72655e8 | −0.946226 | −0.473113 | − | 0.881002i | \(-0.656870\pi\) | ||||
−0.473113 | + | 0.881002i | \(0.656870\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.18713e7 | + | 2.41744e7i | −0.105452 | + | 0.0608827i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.10739e8 | + | 1.21670e8i | −0.526433 | + | 0.303936i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.10429e8 | − | 3.64474e8i | 0.521401 | − | 0.903094i | −0.478289 | − | 0.878203i | \(-0.658743\pi\) |
0.999690 | − | 0.0248910i | \(-0.00792386\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.48079e7 | + | 4.59402e8i | −0.208440 | + | 1.12912i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.60325e8 | + | 9.25638e7i | 0.390873 | + | 0.225671i | 0.682538 | − | 0.730850i | \(-0.260876\pi\) |
−0.291665 | + | 0.956520i | \(0.594209\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.81687e7 | − | 4.87896e7i | −0.0681236 | − | 0.117994i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.60295e6 | + | 6.24050e6i | 0.00864364 | + | 0.0149712i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 6.38089e8i | − | 1.51857i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.79041e8 | + | 1.61104e8i | −0.658791 | + | 0.380353i | −0.791816 | − | 0.610759i | \(-0.790864\pi\) |
0.133025 | + | 0.991113i | \(0.457531\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 2.60583e8i | − | 0.610324i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.46202e8 | + | 8.44099e7i | 0.339714 | + | 0.196134i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.61102e7 | − | 2.79037e7i | 0.0371376 | − | 0.0643241i | −0.846859 | − | 0.531817i | \(-0.821509\pi\) |
0.883997 | + | 0.467493i | \(0.154843\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 5.39924e8i | − | 1.23483i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.44863e8 | 0.555609 | 0.277804 | − | 0.960638i | \(-0.410393\pi\) | ||||
0.277804 | + | 0.960638i | \(0.410393\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.85577e8 | − | 1.07143e8i | −0.417783 | − | 0.241207i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.42120e6 | + | 2.46160e6i | −0.00317447 | + | 0.00549835i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.05454e7 | 0.134182 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.36566e8 | − | 5.82949e8i | −0.740101 | − | 1.28189i | −0.952449 | − | 0.304698i | \(-0.901444\pi\) |
0.212348 | − | 0.977194i | \(-0.431889\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.74643e8 | 1.90839 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.72024e8 | − | 2.14788e8i | 0.805439 | − | 0.465021i | −0.0399303 | − | 0.999202i | \(-0.512714\pi\) |
0.845370 | + | 0.534182i | \(0.179380\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.68886e7 | + | 2.70711e7i | −0.100731 | + | 0.0581569i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.61922e8 | + | 8.00072e8i | −0.984704 | + | 1.70556i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.03481e8 | − | 4.73095e8i | 0.853514 | − | 1.00077i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.58723e8 | + | 9.16390e7i | 0.333187 | + | 0.192365i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.38835e8 | + | 5.86879e8i | 0.705834 | + | 1.22254i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.34555e7 | − | 1.09908e8i | −0.131178 | − | 0.227207i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.19240e8i | 1.68069i | 0.542054 | + | 0.840344i | \(0.317647\pi\) | ||||
−0.542054 | + | 0.840344i | \(0.682353\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.20915e8 | + | 3.58485e8i | −1.26416 | + | 0.729861i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.97620e8i | 1.40958i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.99641e8 | + | 4.03938e8i | 1.40299 | + | 0.810018i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.02971e7 | + | 8.71171e7i | −0.100102 | + | 0.173381i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.18496e8i | 0.826639i | 0.910586 | + | 0.413320i | \(0.135631\pi\) | ||||
−0.910586 | + | 0.413320i | \(0.864369\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.04573e8 | 1.38129 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −228139. | − | 131716.i | −0.000443917 | − | 0.000256296i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.79032e8 | + | 3.10093e8i | −0.345768 | + | 0.598887i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.62273e8 | −0.502766 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.33808e6 | + | 1.44420e7i | 0.0158652 | + | 0.0274793i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.48582e8 | 1.79155 | 0.895776 | − | 0.444506i | \(-0.146621\pi\) | ||||
0.895776 | + | 0.444506i | \(0.146621\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.45076e8 | + | 8.37595e7i | −0.271977 | + | 0.157026i | −0.629786 | − | 0.776769i | \(-0.716857\pi\) |
0.357809 | + | 0.933795i | \(0.383524\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.64443e8 | − | 3.25881e8i | 1.05039 | − | 0.606440i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.09170e8 | − | 1.89088e8i | 0.201665 | − | 0.349294i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.11196e8 | + | 9.48339e7i | 0.203903 | + | 0.173899i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.07437e7 | − | 6.20290e6i | −0.0195571 | − | 0.0112913i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.42132e8 | − | 2.46179e8i | −0.256839 | − | 0.444859i | 0.708554 | − | 0.705657i | \(-0.249348\pi\) |
−0.965394 | + | 0.260798i | \(0.916014\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.26163e7 | + | 3.91726e7i | 0.0405716 | + | 0.0702721i | 0.885598 | − | 0.464452i | \(-0.153749\pi\) |
−0.845027 | + | 0.534724i | \(0.820415\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 4.02962e8i | − | 0.717633i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.86623e8 | + | 4.54157e8i | −1.39075 | + | 0.802952i | −0.993399 | − | 0.114713i | \(-0.963405\pi\) |
−0.397355 | + | 0.917665i | \(0.630072\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.63682e8i | 1.16492i | 0.812859 | + | 0.582460i | \(0.197910\pi\) | ||||
−0.812859 | + | 0.582460i | \(0.802090\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.56124e7 | − | 4.94284e7i | −0.149188 | − | 0.0861337i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.11544e8 | − | 3.66406e8i | 0.365988 | − | 0.633909i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.14418e7i | 0.139890i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.36228e7 | −0.125556 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.92376e7 | + | 2.84273e7i | 0.0833702 | + | 0.0481338i | 0.541106 | − | 0.840955i | \(-0.318006\pi\) |
−0.457735 | + | 0.889088i | \(0.651339\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.86058e8 | − | 4.95466e8i | 0.480912 | − | 0.832964i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.80736e8 | 0.468614 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.64036e7 | − | 4.57324e7i | −0.0437616 | − | 0.0757973i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.95068e8 | 0.485593 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.82818e8 | + | 1.63285e8i | −0.462150 | + | 0.266823i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.40098e9 | + | 8.08854e8i | −2.27322 | + | 1.31245i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.80813e7 | + | 8.32793e7i | −0.0774692 | + | 0.134181i | −0.902157 | − | 0.431407i | \(-0.858017\pi\) |
0.824688 | + | 0.565588i | \(0.191351\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 469123. | − | 2.54123e6i | 0.000750566 | − | 0.00406580i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.37812e8 | + | 1.95036e8i | 0.536701 | + | 0.309864i | 0.743741 | − | 0.668468i | \(-0.233050\pi\) |
−0.207040 | + | 0.978332i | \(0.566383\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.21544e8 | − | 2.10520e8i | −0.191758 | − | 0.332135i | 0.754075 | − | 0.656789i | \(-0.228086\pi\) |
−0.945833 | + | 0.324654i | \(0.894752\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.05981e8 | − | 8.76384e8i | −0.792728 | − | 1.37305i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.58699e8i | 0.713667i | 0.934168 | + | 0.356833i | \(0.116144\pi\) | ||||
−0.934168 | + | 0.356833i | \(0.883856\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.67961e7 | − | 5.58852e7i | 0.149558 | − | 0.0863473i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.77947e8i | 1.34713i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.32358e8 | − | 1.34152e8i | −0.354077 | − | 0.204426i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.00019e8 | − | 5.19648e8i | 0.454040 | − | 0.786420i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 1.18131e7i | − | 0.0177550i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.05389e8 | −0.605128 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.02974e8 | + | 2.32657e8i | 0.597418 | + | 0.344919i | 0.768025 | − | 0.640420i | \(-0.221240\pi\) |
−0.170607 | + | 0.985339i | \(0.554573\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.56273e8 | − | 2.70674e8i | 0.230101 | − | 0.398547i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.32256e8 | −0.193414 | −0.0967070 | − | 0.995313i | \(-0.530831\pi\) | ||||
−0.0967070 | + | 0.995313i | \(0.530831\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.39786e8 | + | 2.42117e8i | 0.203041 | + | 0.351677i | 0.949507 | − | 0.313747i | \(-0.101584\pi\) |
−0.746466 | + | 0.665423i | \(0.768251\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.05259e7 | 0.0296123 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.75020e8 | − | 3.31988e8i | 0.823972 | − | 0.475720i | −0.0278124 | − | 0.999613i | \(-0.508854\pi\) |
0.851784 | + | 0.523893i | \(0.175521\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.15449e8 | − | 4.13065e8i | 1.01829 | − | 0.587913i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.69575e8 | − | 4.66917e8i | 0.381106 | − | 0.660095i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.03668e8 | + | 2.14253e8i | −0.847703 | + | 0.300865i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.15377e8 | − | 6.66129e7i | −0.160935 | − | 0.0929157i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.65680e8 | + | 1.15299e9i | 0.922334 | + | 1.59753i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.33888e7 | + | 1.09793e8i | 0.0872435 | + | 0.151110i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 8.80275e8i | − | 1.20349i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.05985e8 | − | 1.18925e8i | 0.279751 | − | 0.161514i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.43192e8i | 0.463011i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.19797e9 | − | 6.91650e8i | −1.60555 | − | 0.926967i | −0.990348 | − | 0.138601i | \(-0.955740\pi\) |
−0.615206 | − | 0.788366i | \(-0.710927\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.09178e7 | − | 1.89101e7i | 0.0145359 | − | 0.0251770i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.82463e8i | 0.902660i | 0.892357 | + | 0.451330i | \(0.149050\pi\) | ||||
−0.892357 | + | 0.451330i | \(0.850950\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.34974e8 | −0.834342 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.37189e8 | + | 1.36941e8i | 0.309622 | + | 0.178760i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.98252e7 | + | 1.55582e8i | −0.116490 | + | 0.201767i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.54832e8 | 1.23021 | 0.615107 | − | 0.788444i | \(-0.289113\pi\) | ||||
0.615107 | + | 0.788444i | \(0.289113\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.77394e8 | + | 6.53666e8i | 0.483077 | + | 0.836714i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.51932e8 | −0.574736 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.04559e9 | + | 6.03673e8i | −1.32110 | + | 0.762740i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.47948e7 | − | 8.54178e6i | 0.0185725 | − | 0.0107228i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.23210e8 | − | 2.13406e8i | 0.153674 | − | 0.266170i | −0.778902 | − | 0.627146i | \(-0.784223\pi\) |
0.932575 | + | 0.360976i | \(0.117556\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.98284e7 | + | 3.78259e8i | −0.0865333 | + | 0.468749i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.20813e8 | + | 6.97512e7i | 0.148753 | + | 0.0858829i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.25234e8 | − | 2.16912e8i | −0.153211 | − | 0.265369i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.71223e8 | − | 2.96566e8i | −0.208134 | − | 0.360498i | 0.742993 | − | 0.669299i | \(-0.233406\pi\) |
−0.951127 | + | 0.308801i | \(0.900072\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 1.06510e9i | − | 1.28646i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.28870e9 | − | 7.44033e8i | 1.54662 | − | 0.892943i | 0.548226 | − | 0.836330i | \(-0.315303\pi\) |
0.998396 | − | 0.0566124i | \(-0.0180299\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.77201e9i | − | 2.11315i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.30511e8 | − | 1.33085e8i | −0.273147 | − | 0.157701i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.37325e8 | + | 7.57470e8i | −0.514938 | + | 0.891898i | 0.484912 | + | 0.874563i | \(0.338852\pi\) |
−0.999850 | + | 0.0173352i | \(0.994482\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 8.82926e8i | − | 1.03306i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.34235e8 | 0.388607 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.75798e8 | − | 1.01497e8i | −0.203112 | − | 0.117267i | 0.394994 | − | 0.918684i | \(-0.370747\pi\) |
−0.598106 | + | 0.801417i | \(0.704080\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.36910e7 | + | 7.56751e7i | −0.0501628 | + | 0.0868846i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.43561e8 | −1.07655 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.57088e8 | − | 7.91699e8i | −0.518255 | − | 0.897644i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.73730e8 | 0.984481 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.55169e7 | − | 8.95869e6i | 0.0173751 | − | 0.0100315i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.16137e8 | + | 1.24787e8i | −0.240518 | + | 0.138863i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.80016e8 | + | 4.85002e8i | −0.309673 | + | 0.536370i | −0.978291 | − | 0.207237i | \(-0.933553\pi\) |
0.668618 | + | 0.743606i | \(0.266886\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.63555e8 | − | 1.30609e9i | −0.509483 | − | 1.43550i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.67300e8 | − | 3.85266e8i | −0.728892 | − | 0.420826i | 0.0891247 | − | 0.996020i | \(-0.471593\pi\) |
−0.818017 | + | 0.575195i | \(0.804926\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.46263e7 | + | 7.72949e7i | 0.0484453 | + | 0.0839098i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.96818e8 | + | 8.60514e8i | 0.536023 | + | 0.928420i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.03135e9i | 1.10592i | 0.833207 | + | 0.552961i | \(0.186502\pi\) | ||||
−0.833207 | + | 0.552961i | \(0.813498\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.01033e7 | − | 1.16066e7i | 0.0214249 | − | 0.0123697i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 6.01709e6i | − | 0.00637353i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.53560e7 | − | 2.04128e7i | −0.0372223 | − | 0.0214903i | 0.481273 | − | 0.876571i | \(-0.340174\pi\) |
−0.518496 | + | 0.855080i | \(0.673508\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.47552e7 | − | 1.12159e8i | 0.0677588 | − | 0.117362i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.04252e9i | 1.08426i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.16492e8 | 0.430544 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.76946e8 | − | 2.75365e8i | −0.490059 | − | 0.282936i | 0.234540 | − | 0.972106i | \(-0.424642\pi\) |
−0.724599 | + | 0.689171i | \(0.757975\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.17765e8 | − | 1.07000e9i | 0.630922 | − | 1.09279i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.97592e8 | −0.505131 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.65102e8 | − | 6.32375e8i | −0.368408 | − | 0.638101i | 0.620909 | − | 0.783883i | \(-0.286764\pi\) |
−0.989317 | + | 0.145782i | \(0.953430\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.64175e9 | −1.64669 |
(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.h.a.65.3 | ✓ | 20 | |
3.2 | odd | 2 | 684.7.y.c.217.5 | 20 | |||
19.12 | odd | 6 | inner | 76.7.h.a.69.3 | yes | 20 | |
57.50 | even | 6 | 684.7.y.c.145.5 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.7.h.a.65.3 | ✓ | 20 | 1.1 | even | 1 | trivial | |
76.7.h.a.69.3 | yes | 20 | 19.12 | odd | 6 | inner | |
684.7.y.c.145.5 | 20 | 57.50 | even | 6 | |||
684.7.y.c.217.5 | 20 | 3.2 | odd | 2 |