Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [27,4,Mod(10,27)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(27, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("27.10");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 27 = 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 27.c (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.59305157015\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 9) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 10.1 | ||
Root | \(-1.18614 - 1.26217i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 27.10 |
Dual form | 27.4.c.a.19.1 |
$q$-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 \(\left(\mathbb{Z}/27\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.686141 | − | 1.18843i | −0.242587 | − | 0.420174i | 0.718863 | − | 0.695152i | \(-0.244663\pi\) |
−0.961451 | + | 0.274978i | \(0.911329\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.05842 | − | 5.29734i | 0.382303 | − | 0.662168i | ||||
\(5\) | 5.18614 | − | 8.98266i | 0.463863 | − | 0.803433i | −0.535287 | − | 0.844670i | \(-0.679796\pi\) |
0.999149 | + | 0.0412369i | \(0.0131298\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.55842 | + | 4.43132i | 0.138142 | + | 0.239269i | 0.926793 | − | 0.375572i | \(-0.122554\pi\) |
−0.788651 | + | 0.614841i | \(0.789220\pi\) | |||||||
\(8\) | −19.3723 | −0.856142 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −14.2337 | −0.450109 | ||||||||
\(11\) | 27.9891 | + | 48.4786i | 0.767185 | + | 1.32880i | 0.939083 | + | 0.343689i | \(0.111677\pi\) |
−0.171898 | + | 0.985115i | \(0.554990\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −18.7921 | + | 32.5489i | −0.400923 | + | 0.694418i | −0.993838 | − | 0.110847i | \(-0.964644\pi\) |
0.592915 | + | 0.805265i | \(0.297977\pi\) | |||||||
\(14\) | 3.51087 | − | 6.08101i | 0.0670229 | − | 0.116087i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −11.1753 | − | 19.3561i | −0.174614 | − | 0.302440i | ||||
\(17\) | −23.6495 | −0.337402 | −0.168701 | − | 0.985667i | \(-0.553957\pi\) | ||||
−0.168701 | + | 0.985667i | \(0.553957\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 39.0516 | 0.471529 | 0.235764 | − | 0.971810i | \(-0.424241\pi\) | ||||
0.235764 | + | 0.971810i | \(0.424241\pi\) | |||||||
\(20\) | −31.7228 | − | 54.9455i | −0.354672 | − | 0.614310i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 38.4090 | − | 66.5263i | 0.372219 | − | 0.644702i | ||||
\(23\) | 35.5367 | − | 61.5513i | 0.322170 | − | 0.558015i | −0.658766 | − | 0.752348i | \(-0.728921\pi\) |
0.980936 | + | 0.194334i | \(0.0622544\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.70789 | + | 15.0825i | 0.0696631 | + | 0.120660i | ||||
\(26\) | 51.5761 | 0.389035 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 31.2989 | 0.211248 | ||||||||
\(29\) | −14.1861 | − | 24.5711i | −0.0908379 | − | 0.157336i | 0.817026 | − | 0.576601i | \(-0.195621\pi\) |
−0.907864 | + | 0.419265i | \(0.862288\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.44158 | + | 11.1571i | −0.0373207 | + | 0.0646413i | −0.884082 | − | 0.467331i | \(-0.845216\pi\) |
0.846762 | + | 0.531972i | \(0.178549\pi\) | |||||||
\(32\) | −92.8247 | + | 160.777i | −0.512789 | + | 0.888177i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 16.2269 | + | 28.1057i | 0.0818495 | + | 0.141768i | ||||
\(35\) | 53.0733 | 0.256315 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −180.103 | −0.800237 | −0.400119 | − | 0.916463i | \(-0.631031\pi\) | ||||
−0.400119 | + | 0.916463i | \(0.631031\pi\) | |||||||
\(38\) | −26.7949 | − | 46.4101i | −0.114387 | − | 0.198124i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −100.467 | + | 174.015i | −0.397132 | + | 0.687853i | ||||
\(41\) | −107.742 | + | 186.614i | −0.410401 | + | 0.710835i | −0.994934 | − | 0.100535i | \(-0.967945\pi\) |
0.584533 | + | 0.811370i | \(0.301278\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −30.6168 | − | 53.0299i | −0.108582 | − | 0.188069i | 0.806614 | − | 0.591078i | \(-0.201298\pi\) |
−0.915196 | + | 0.403009i | \(0.867964\pi\) | |||||||
\(44\) | 342.410 | 1.17319 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −97.5326 | −0.312617 | ||||||||
\(47\) | −30.9388 | − | 53.5876i | −0.0960189 | − | 0.166310i | 0.814014 | − | 0.580845i | \(-0.197278\pi\) |
−0.910033 | + | 0.414535i | \(0.863944\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 158.409 | − | 274.372i | 0.461834 | − | 0.799919i | ||||
\(50\) | 11.9497 | − | 20.6974i | 0.0337988 | − | 0.0585412i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 114.948 | + | 199.096i | 0.306548 | + | 0.530956i | ||||
\(53\) | −492.310 | −1.27592 | −0.637962 | − | 0.770068i | \(-0.720222\pi\) | ||||
−0.637962 | + | 0.770068i | \(0.720222\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 580.622 | 1.42347 | ||||||||
\(56\) | −49.5625 | − | 85.8447i | −0.118269 | − | 0.204848i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −19.4674 | + | 33.7185i | −0.0440723 | + | 0.0763354i | ||||
\(59\) | 394.815 | − | 683.840i | 0.871196 | − | 1.50896i | 0.0104351 | − | 0.999946i | \(-0.496678\pi\) |
0.860761 | − | 0.509010i | \(-0.169988\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −260.545 | − | 451.277i | −0.546874 | − | 0.947214i | −0.998486 | − | 0.0549998i | \(-0.982484\pi\) |
0.451612 | − | 0.892214i | \(-0.350849\pi\) | |||||||
\(62\) | 17.6793 | 0.0362141 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 75.9590 | 0.148358 | ||||||||
\(65\) | 194.917 | + | 337.606i | 0.371946 | + | 0.644229i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −152.215 | + | 263.644i | −0.277552 | + | 0.480734i | −0.970776 | − | 0.239988i | \(-0.922856\pi\) |
0.693224 | + | 0.720722i | \(0.256190\pi\) | |||||||
\(68\) | −72.3301 | + | 125.279i | −0.128990 | + | 0.223417i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −36.4158 | − | 63.0740i | −0.0621788 | − | 0.107697i | ||||
\(71\) | −270.391 | −0.451966 | −0.225983 | − | 0.974131i | \(-0.572559\pi\) | ||||
−0.225983 | + | 0.974131i | \(0.572559\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −925.464 | −1.48380 | −0.741900 | − | 0.670510i | \(-0.766075\pi\) | ||||
−0.741900 | + | 0.670510i | \(0.766075\pi\) | |||||||
\(74\) | 123.576 | + | 214.040i | 0.194127 | + | 0.336239i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 119.436 | − | 206.870i | 0.180267 | − | 0.312231i | ||||
\(77\) | −143.216 | + | 248.057i | −0.211961 | + | 0.367127i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 644.517 | + | 1116.34i | 0.917897 | + | 1.58984i | 0.802603 | + | 0.596513i | \(0.203448\pi\) |
0.115294 | + | 0.993331i | \(0.463219\pi\) | |||||||
\(80\) | −231.826 | −0.323987 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 295.704 | 0.398232 | ||||||||
\(83\) | 356.917 | + | 618.198i | 0.472009 | + | 0.817543i | 0.999487 | − | 0.0320252i | \(-0.0101957\pi\) |
−0.527478 | + | 0.849569i | \(0.676862\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −122.649 | + | 212.435i | −0.156508 | + | 0.271080i | ||||
\(86\) | −42.0149 | + | 72.7720i | −0.0526812 | + | 0.0912466i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −542.213 | − | 939.141i | −0.656820 | − | 1.13764i | ||||
\(89\) | 404.804 | 0.482125 | 0.241063 | − | 0.970510i | \(-0.422504\pi\) | ||||
0.241063 | + | 0.970510i | \(0.422504\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −192.313 | −0.221537 | ||||||||
\(92\) | −217.372 | − | 376.500i | −0.246333 | − | 0.426661i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −42.4567 | + | 73.5372i | −0.0465859 | + | 0.0806892i | ||||
\(95\) | 202.527 | − | 350.787i | 0.218725 | − | 0.378842i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −37.5137 | − | 64.9756i | −0.0392674 | − | 0.0680131i | 0.845724 | − | 0.533621i | \(-0.179169\pi\) |
−0.884991 | + | 0.465608i | \(0.845836\pi\) | |||||||
\(98\) | −434.763 | −0.448140 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 106.530 | 0.106530 | ||||||||
\(101\) | −543.939 | − | 942.130i | −0.535881 | − | 0.928172i | −0.999120 | − | 0.0419392i | \(-0.986646\pi\) |
0.463240 | − | 0.886233i | \(-0.346687\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 545.909 | − | 945.542i | 0.522233 | − | 0.904534i | −0.477432 | − | 0.878669i | \(-0.658432\pi\) |
0.999665 | − | 0.0258657i | \(-0.00823423\pi\) | |||||||
\(104\) | 364.046 | − | 630.546i | 0.343247 | − | 0.594521i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 337.794 | + | 585.076i | 0.309523 | + | 0.536109i | ||||
\(107\) | 1029.15 | 0.929833 | 0.464917 | − | 0.885354i | \(-0.346084\pi\) | ||||
0.464917 | + | 0.885354i | \(0.346084\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1776.52 | 1.56110 | 0.780548 | − | 0.625096i | \(-0.214940\pi\) | ||||
0.780548 | + | 0.625096i | \(0.214940\pi\) | |||||||
\(110\) | −398.388 | − | 690.029i | −0.345317 | − | 0.598106i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 57.1821 | − | 99.0423i | 0.0482429 | − | 0.0835591i | ||||
\(113\) | −807.969 | + | 1399.44i | −0.672631 | + | 1.16503i | 0.304524 | + | 0.952505i | \(0.401502\pi\) |
−0.977155 | + | 0.212526i | \(0.931831\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −368.596 | − | 638.428i | −0.298885 | − | 0.517684i | ||||
\(116\) | −173.549 | −0.138910 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1083.59 | −0.845364 | ||||||||
\(119\) | −60.5053 | − | 104.798i | −0.0466094 | − | 0.0807298i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −901.282 | + | 1561.07i | −0.677147 | + | 1.17285i | ||||
\(122\) | −357.541 | + | 619.279i | −0.265330 | + | 0.459564i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 39.4021 | + | 68.2465i | 0.0285356 | + | 0.0494251i | ||||
\(125\) | 1477.18 | 1.05698 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1206.10 | −0.842711 | −0.421356 | − | 0.906895i | \(-0.638446\pi\) | ||||
−0.421356 | + | 0.906895i | \(0.638446\pi\) | |||||||
\(128\) | 690.479 | + | 1195.95i | 0.476799 | + | 0.825841i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 267.481 | − | 463.291i | 0.180459 | − | 0.312564i | ||||
\(131\) | −513.928 | + | 890.149i | −0.342764 | + | 0.593684i | −0.984945 | − | 0.172869i | \(-0.944696\pi\) |
0.642181 | + | 0.766553i | \(0.278030\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 99.9105 | + | 173.050i | 0.0651379 | + | 0.112822i | ||||
\(134\) | 417.763 | 0.269322 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 458.144 | 0.288864 | ||||||||
\(137\) | −630.454 | − | 1091.98i | −0.393163 | − | 0.680978i | 0.599702 | − | 0.800223i | \(-0.295286\pi\) |
−0.992865 | + | 0.119245i | \(0.961952\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −230.916 | + | 399.958i | −0.140907 | + | 0.244057i | −0.927838 | − | 0.372983i | \(-0.878335\pi\) |
0.786932 | + | 0.617040i | \(0.211668\pi\) | |||||||
\(140\) | 162.321 | − | 281.148i | 0.0979900 | − | 0.169724i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 185.527 | + | 321.341i | 0.109641 | + | 0.189904i | ||||
\(143\) | −2103.90 | −1.23033 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −294.285 | −0.168545 | ||||||||
\(146\) | 634.999 | + | 1099.85i | 0.359951 | + | 0.623454i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −550.832 | + | 954.068i | −0.305933 | + | 0.529891i | ||||
\(149\) | 729.661 | − | 1263.81i | 0.401182 | − | 0.694868i | −0.592687 | − | 0.805433i | \(-0.701933\pi\) |
0.993869 | + | 0.110565i | \(0.0352660\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −770.659 | − | 1334.82i | −0.415333 | − | 0.719378i | 0.580130 | − | 0.814524i | \(-0.303002\pi\) |
−0.995463 | + | 0.0951456i | \(0.969668\pi\) | |||||||
\(152\) | −756.518 | −0.403696 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 393.065 | 0.205676 | ||||||||
\(155\) | 66.8139 | + | 115.725i | 0.0346233 | + | 0.0599694i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1607.79 | − | 2784.77i | 0.817295 | − | 1.41560i | −0.0903734 | − | 0.995908i | \(-0.528806\pi\) |
0.907668 | − | 0.419688i | \(-0.137861\pi\) | |||||||
\(158\) | 884.459 | − | 1531.93i | 0.445341 | − | 0.771352i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 962.804 | + | 1667.63i | 0.475727 | + | 0.823984i | ||||
\(161\) | 363.671 | 0.178021 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 947.587 | 0.455342 | 0.227671 | − | 0.973738i | \(-0.426889\pi\) | ||||
0.227671 | + | 0.973738i | \(0.426889\pi\) | |||||||
\(164\) | 659.040 | + | 1141.49i | 0.313795 | + | 0.543509i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 489.791 | − | 848.342i | 0.229007 | − | 0.396651i | ||||
\(167\) | 342.980 | − | 594.058i | 0.158926 | − | 0.275267i | −0.775556 | − | 0.631279i | \(-0.782530\pi\) |
0.934481 | + | 0.356012i | \(0.115864\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 392.213 | + | 679.333i | 0.178522 | + | 0.309209i | ||||
\(170\) | 336.619 | 0.151868 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −374.557 | −0.166045 | ||||||||
\(173\) | −1106.41 | − | 1916.36i | −0.486237 | − | 0.842188i | 0.513637 | − | 0.858007i | \(-0.328298\pi\) |
−0.999875 | + | 0.0158193i | \(0.994964\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −44.5569 | + | 77.1748i | −0.0192468 | + | 0.0333364i | ||||
\(176\) | 625.572 | − | 1083.52i | 0.267922 | − | 0.464054i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −277.753 | − | 481.082i | −0.116958 | − | 0.202576i | ||||
\(179\) | −3023.22 | −1.26238 | −0.631190 | − | 0.775629i | \(-0.717433\pi\) | ||||
−0.631190 | + | 0.775629i | \(0.717433\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 391.445 | 0.160751 | 0.0803753 | − | 0.996765i | \(-0.474388\pi\) | ||||
0.0803753 | + | 0.996765i | \(0.474388\pi\) | |||||||
\(182\) | 131.953 | + | 228.550i | 0.0537420 | + | 0.0930839i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −688.426 | + | 1192.39i | −0.275823 | + | 0.477740i | ||||
\(185\) | −934.040 | + | 1617.81i | −0.371200 | + | 0.642937i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −661.928 | − | 1146.49i | −0.258850 | − | 0.448341i | ||||
\(188\) | −378.496 | −0.146833 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −555.848 | −0.212239 | ||||||||
\(191\) | 1742.79 | + | 3018.61i | 0.660231 | + | 1.14355i | 0.980555 | + | 0.196246i | \(0.0628750\pi\) |
−0.320324 | + | 0.947308i | \(0.603792\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1107.53 | + | 1918.31i | −0.413068 | + | 0.715455i | −0.995223 | − | 0.0976228i | \(-0.968876\pi\) |
0.582156 | + | 0.813077i | \(0.302209\pi\) | |||||||
\(194\) | −51.4793 | + | 89.1647i | −0.0190515 | + | 0.0329982i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −968.963 | − | 1678.29i | −0.353121 | − | 0.611623i | ||||
\(197\) | 3975.11 | 1.43764 | 0.718820 | − | 0.695196i | \(-0.244682\pi\) | ||||
0.718820 | + | 0.695196i | \(0.244682\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1555.34 | −0.554046 | −0.277023 | − | 0.960863i | \(-0.589348\pi\) | ||||
−0.277023 | + | 0.960863i | \(0.589348\pi\) | |||||||
\(200\) | −168.692 | − | 292.183i | −0.0596415 | − | 0.103302i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −746.437 | + | 1292.87i | −0.259996 | + | 0.450326i | ||||
\(203\) | 72.5883 | − | 125.727i | 0.0250970 | − | 0.0434693i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1117.53 | + | 1935.62i | 0.380739 | + | 0.659460i | ||||
\(206\) | −1498.28 | −0.506749 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 840.027 | 0.280026 | ||||||||
\(209\) | 1093.02 | + | 1893.17i | 0.361750 | + | 0.626570i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −873.865 | + | 1513.58i | −0.285115 | + | 0.493834i | −0.972637 | − | 0.232329i | \(-0.925365\pi\) |
0.687522 | + | 0.726164i | \(0.258699\pi\) | |||||||
\(212\) | −1505.69 | + | 2607.93i | −0.487789 | + | 0.844875i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −706.145 | − | 1223.08i | −0.225566 | − | 0.390691i | ||||
\(215\) | −635.133 | −0.201468 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −65.9211 | −0.0206222 | ||||||||
\(218\) | −1218.94 | − | 2111.27i | −0.378702 | − | 0.655931i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1775.79 | − | 3075.75i | 0.544198 | − | 0.942579i | ||||
\(221\) | 444.423 | − | 769.764i | 0.135272 | − | 0.234298i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1270.97 | + | 2201.39i | 0.381662 | + | 0.661057i | 0.991300 | − | 0.131622i | \(-0.0420187\pi\) |
−0.609638 | + | 0.792680i | \(0.708685\pi\) | |||||||
\(224\) | −949.939 | −0.283350 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2217.52 | 0.652687 | ||||||||
\(227\) | −1496.63 | − | 2592.24i | −0.437598 | − | 0.757943i | 0.559905 | − | 0.828557i | \(-0.310837\pi\) |
−0.997504 | + | 0.0706140i | \(0.977504\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2152.65 | − | 3728.50i | 0.621185 | − | 1.07592i | −0.368081 | − | 0.929794i | \(-0.619985\pi\) |
0.989265 | − | 0.146130i | \(-0.0466816\pi\) | |||||||
\(230\) | −505.818 | + | 876.102i | −0.145012 | + | 0.251167i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 274.818 | + | 475.999i | 0.0777702 | + | 0.134702i | ||||
\(233\) | 5581.34 | 1.56930 | 0.784648 | − | 0.619942i | \(-0.212844\pi\) | ||||
0.784648 | + | 0.619942i | \(0.212844\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −641.812 | −0.178158 | ||||||||
\(236\) | −2415.02 | − | 4182.94i | −0.666121 | − | 1.15376i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −83.0303 | + | 143.813i | −0.0226137 | + | 0.0391680i | ||||
\(239\) | 704.814 | − | 1220.77i | 0.190756 | − | 0.330399i | −0.754745 | − | 0.656018i | \(-0.772239\pi\) |
0.945501 | + | 0.325619i | \(0.105573\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −313.286 | − | 542.627i | −0.0837366 | − | 0.145036i | 0.821116 | − | 0.570762i | \(-0.193352\pi\) |
−0.904852 | + | 0.425726i | \(0.860019\pi\) | |||||||
\(242\) | 2473.63 | 0.657069 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3187.42 | −0.836286 | ||||||||
\(245\) | −1643.06 | − | 2845.87i | −0.428455 | − | 0.742105i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −733.862 | + | 1271.09i | −0.189047 | + | 0.327438i | ||||
\(248\) | 124.788 | − | 216.139i | 0.0319518 | − | 0.0553422i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1013.55 | − | 1755.52i | −0.256410 | − | 0.444116i | ||||
\(251\) | −1705.53 | −0.428892 | −0.214446 | − | 0.976736i | \(-0.568795\pi\) | ||||
−0.214446 | + | 0.976736i | \(0.568795\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3978.56 | 0.988656 | ||||||||
\(254\) | 827.556 | + | 1433.37i | 0.204431 | + | 0.354085i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1251.37 | − | 2167.43i | 0.305510 | − | 0.529158i | ||||
\(257\) | −1798.69 | + | 3115.42i | −0.436573 | + | 0.756166i | −0.997423 | − | 0.0717513i | \(-0.977141\pi\) |
0.560850 | + | 0.827918i | \(0.310475\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −460.780 | − | 798.094i | −0.110546 | − | 0.191472i | ||||
\(260\) | 2384.55 | 0.568784 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1410.51 | 0.332601 | ||||||||
\(263\) | 2068.75 | + | 3583.18i | 0.485037 | + | 0.840108i | 0.999852 | − | 0.0171926i | \(-0.00547285\pi\) |
−0.514815 | + | 0.857301i | \(0.672140\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2553.19 | + | 4422.25i | −0.591853 | + | 1.02512i | ||||
\(266\) | 137.105 | − | 237.473i | 0.0316032 | − | 0.0547384i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 931.074 | + | 1612.67i | 0.212218 | + | 0.367572i | ||||
\(269\) | −6090.99 | −1.38057 | −0.690287 | − | 0.723536i | \(-0.742516\pi\) | ||||
−0.690287 | + | 0.723536i | \(0.742516\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3196.62 | −0.716534 | −0.358267 | − | 0.933619i | \(-0.616632\pi\) | ||||
−0.358267 | + | 0.933619i | \(0.616632\pi\) | |||||||
\(272\) | 264.289 | + | 457.762i | 0.0589150 | + | 0.102044i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −865.160 | + | 1498.50i | −0.190753 | + | 0.330393i | ||||
\(275\) | −487.452 | + | 844.292i | −0.106889 | + | 0.185137i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1559.68 | + | 2701.45i | 0.338311 | + | 0.585972i | 0.984115 | − | 0.177531i | \(-0.0568111\pi\) |
−0.645804 | + | 0.763503i | \(0.723478\pi\) | |||||||
\(278\) | 633.763 | 0.136729 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1028.15 | −0.219442 | ||||||||
\(281\) | 2474.17 | + | 4285.38i | 0.525254 | + | 0.909767i | 0.999567 | + | 0.0294105i | \(0.00936301\pi\) |
−0.474313 | + | 0.880356i | \(0.657304\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2272.47 | − | 3936.03i | 0.477329 | − | 0.826758i | −0.522333 | − | 0.852741i | \(-0.674938\pi\) |
0.999662 | + | 0.0259834i | \(0.00827171\pi\) | |||||||
\(284\) | −826.971 | + | 1432.36i | −0.172788 | + | 0.299277i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1443.57 | + | 2500.34i | 0.298462 | + | 0.516951i | ||||
\(287\) | −1102.60 | −0.226774 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4353.70 | −0.886160 | ||||||||
\(290\) | 201.921 | + | 349.738i | 0.0408869 | + | 0.0708183i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2830.46 | + | 4902.50i | −0.567261 | + | 0.982525i | ||||
\(293\) | 3430.05 | − | 5941.03i | 0.683911 | − | 1.18457i | −0.289867 | − | 0.957067i | \(-0.593611\pi\) |
0.973778 | − | 0.227501i | \(-0.0730555\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4095.13 | − | 7092.98i | −0.808230 | − | 1.39990i | ||||
\(296\) | 3489.01 | 0.685117 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2002.60 | −0.389287 | ||||||||
\(299\) | 1335.62 | + | 2313.36i | 0.258330 | + | 0.447441i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 156.662 | − | 271.346i | 0.0299994 | − | 0.0519605i | ||||
\(302\) | −1057.56 | + | 1831.75i | −0.201509 | + | 0.349024i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −436.412 | − | 755.888i | −0.0823353 | − | 0.142609i | ||||
\(305\) | −5404.89 | −1.01470 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6332.25 | 1.17720 | 0.588600 | − | 0.808424i | \(-0.299679\pi\) | ||||
0.588600 | + | 0.808424i | \(0.299679\pi\) | |||||||
\(308\) | 876.030 | + | 1517.33i | 0.162066 | + | 0.280707i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 91.6874 | − | 158.807i | 0.0167984 | − | 0.0290956i | ||||
\(311\) | 3538.84 | − | 6129.44i | 0.645238 | − | 1.11758i | −0.339009 | − | 0.940783i | \(-0.610092\pi\) |
0.984247 | − | 0.176801i | \(-0.0565750\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −690.649 | − | 1196.24i | −0.124721 | − | 0.216024i | 0.796903 | − | 0.604108i | \(-0.206470\pi\) |
−0.921624 | + | 0.388084i | \(0.873137\pi\) | |||||||
\(314\) | −4412.67 | −0.793062 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7884.83 | 1.40366 | ||||||||
\(317\) | −4087.47 | − | 7079.70i | −0.724211 | − | 1.25437i | −0.959298 | − | 0.282396i | \(-0.908871\pi\) |
0.235086 | − | 0.971974i | \(-0.424463\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 794.115 | − | 1375.45i | 0.139379 | − | 0.241412i | ||||
\(320\) | 393.934 | − | 682.314i | 0.0688175 | − | 0.119195i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −249.530 | − | 432.198i | −0.0431855 | − | 0.0747995i | ||||
\(323\) | −923.549 | −0.159095 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −654.559 | −0.111718 | ||||||||
\(326\) | −650.178 | − | 1126.14i | −0.110460 | − | 0.191323i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2087.20 | − | 3615.14i | 0.351361 | − | 0.608576i | ||||
\(329\) | 158.309 | − | 274.199i | 0.0265284 | − | 0.0459486i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4830.64 | + | 8366.92i | 0.802163 | + | 1.38939i | 0.918189 | + | 0.396142i | \(0.129651\pi\) |
−0.116026 | + | 0.993246i | \(0.537016\pi\) | |||||||
\(332\) | 4366.41 | 0.721801 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −941.329 | −0.154213 | ||||||||
\(335\) | 1578.81 | + | 2734.59i | 0.257492 | + | 0.445989i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2478.01 | − | 4292.04i | 0.400552 | − | 0.693776i | −0.593241 | − | 0.805025i | \(-0.702152\pi\) |
0.993793 | + | 0.111249i | \(0.0354852\pi\) | |||||||
\(338\) | 538.227 | − | 932.236i | 0.0866144 | − | 0.150021i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 750.228 | + | 1299.43i | 0.119667 | + | 0.207269i | ||||
\(341\) | −721.177 | −0.114528 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3376.19 | 0.531478 | ||||||||
\(344\) | 593.118 | + | 1027.31i | 0.0929616 | + | 0.161014i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1518.31 | + | 2629.79i | −0.235910 | + | 0.408608i | ||||
\(347\) | −507.802 | + | 879.540i | −0.0785598 | + | 0.136070i | −0.902629 | − | 0.430420i | \(-0.858365\pi\) |
0.824069 | + | 0.566490i | \(0.191699\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6079.29 | − | 10529.6i | −0.932426 | − | 1.61501i | −0.779160 | − | 0.626825i | \(-0.784354\pi\) |
−0.153267 | − | 0.988185i | \(-0.548979\pi\) | |||||||
\(350\) | 122.289 | 0.0186761 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −10392.3 | −1.57362 | ||||||||
\(353\) | 2118.04 | + | 3668.56i | 0.319354 | + | 0.553138i | 0.980353 | − | 0.197249i | \(-0.0632007\pi\) |
−0.660999 | + | 0.750387i | \(0.729867\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1402.29 | + | 2428.83i | −0.209650 | + | 0.363124i | ||||
\(356\) | 1238.06 | − | 2144.39i | 0.184318 | − | 0.319248i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2074.35 | + | 3592.88i | 0.306237 | + | 0.530418i | ||||
\(359\) | 517.939 | 0.0761443 | 0.0380721 | − | 0.999275i | \(-0.487878\pi\) | ||||
0.0380721 | + | 0.999275i | \(0.487878\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5333.97 | −0.777660 | ||||||||
\(362\) | −268.586 | − | 465.205i | −0.0389961 | − | 0.0675432i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −588.173 | + | 1018.75i | −0.0846941 | + | 0.146694i | ||||
\(365\) | −4799.59 | + | 8313.13i | −0.688279 | + | 1.19213i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2308.15 | + | 3997.83i | 0.328295 | + | 0.568624i | 0.982174 | − | 0.187976i | \(-0.0601926\pi\) |
−0.653879 | + | 0.756600i | \(0.726859\pi\) | |||||||
\(368\) | −1588.53 | −0.225021 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2563.53 | 0.360194 | ||||||||
\(371\) | −1259.54 | − | 2181.58i | −0.176258 | − | 0.305288i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2382.71 | + | 4126.98i | −0.330756 | + | 0.572887i | −0.982660 | − | 0.185415i | \(-0.940637\pi\) |
0.651904 | + | 0.758301i | \(0.273970\pi\) | |||||||
\(374\) | −908.351 | + | 1573.31i | −0.125588 | + | 0.217524i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 599.355 | + | 1038.11i | 0.0822058 | + | 0.142385i | ||||
\(377\) | 1066.35 | 0.145676 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2000.33 | −0.271108 | −0.135554 | − | 0.990770i | \(-0.543281\pi\) | ||||
−0.135554 | + | 0.990770i | \(0.543281\pi\) | |||||||
\(380\) | −1238.83 | − | 2145.71i | −0.167238 | − | 0.289665i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2391.60 | − | 4142.38i | 0.320327 | − | 0.554823i | ||||
\(383\) | 495.147 | − | 857.619i | 0.0660596 | − | 0.114419i | −0.831104 | − | 0.556117i | \(-0.812291\pi\) |
0.897164 | + | 0.441699i | \(0.145624\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1485.48 | + | 2572.92i | 0.196641 | + | 0.340593i | ||||
\(386\) | 3039.70 | 0.400820 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −458.930 | −0.0600481 | ||||||||
\(389\) | 202.205 | + | 350.230i | 0.0263553 | + | 0.0456487i | 0.878902 | − | 0.477002i | \(-0.158277\pi\) |
−0.852547 | + | 0.522651i | \(0.824943\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −840.423 | + | 1455.66i | −0.108701 | + | 0.188275i | ||||
\(392\) | −3068.74 | + | 5315.22i | −0.395395 | + | 0.684845i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2727.49 | − | 4724.15i | −0.348753 | − | 0.604059i | ||||
\(395\) | 13370.2 | 1.70311 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2919.61 | 0.369096 | 0.184548 | − | 0.982824i | \(-0.440918\pi\) | ||||
0.184548 | + | 0.982824i | \(0.440918\pi\) | |||||||
\(398\) | 1067.18 | + | 1848.42i | 0.134405 | + | 0.232796i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 194.626 | − | 337.102i | 0.0243282 | − | 0.0421378i | ||||
\(401\) | −5093.10 | + | 8821.52i | −0.634258 | + | 1.09857i | 0.352414 | + | 0.935844i | \(0.385361\pi\) |
−0.986672 | + | 0.162723i | \(0.947972\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −242.102 | − | 419.332i | −0.0299254 | − | 0.0518323i | ||||
\(404\) | −6654.38 | −0.819474 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −199.223 | −0.0243529 | ||||||||
\(407\) | −5040.93 | − | 8731.15i | −0.613930 | − | 1.06336i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3457.12 | + | 5987.91i | −0.417955 | + | 0.723920i | −0.995734 | − | 0.0922740i | \(-0.970586\pi\) |
0.577778 | + | 0.816194i | \(0.303920\pi\) | |||||||
\(410\) | 1533.56 | − | 2656.21i | 0.184725 | − | 0.319953i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3339.24 | − | 5783.73i | −0.399302 | − | 0.691612i | ||||
\(413\) | 4040.41 | 0.481394 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7404.09 | 0.875789 | ||||||||
\(416\) | −3488.75 | − | 6042.68i | −0.411177 | − | 0.712180i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1499.93 | − | 2597.96i | 0.175512 | − | 0.303996i | ||||
\(419\) | 2560.16 | − | 4434.32i | 0.298501 | − | 0.517019i | −0.677292 | − | 0.735714i | \(-0.736847\pi\) |
0.975793 | + | 0.218695i | \(0.0701801\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −933.246 | − | 1616.43i | −0.108037 | − | 0.187126i | 0.806938 | − | 0.590636i | \(-0.201123\pi\) |
−0.914975 | + | 0.403511i | \(0.867790\pi\) | |||||||
\(422\) | 2398.38 | 0.276662 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9537.16 | 1.09237 | ||||||||
\(425\) | −205.937 | − | 356.693i | −0.0235045 | − | 0.0407110i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1333.17 | − | 2309.11i | 0.151092 | − | 0.261700i | ||||
\(428\) | 3147.59 | − | 5451.79i | 0.355478 | − | 0.615706i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 435.791 | + | 754.811i | 0.0488737 | + | 0.0846517i | ||||
\(431\) | 4090.64 | 0.457168 | 0.228584 | − | 0.973524i | \(-0.426590\pi\) | ||||
0.228584 | + | 0.973524i | \(0.426590\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 633.052 | 0.0702599 | 0.0351299 | − | 0.999383i | \(-0.488815\pi\) | ||||
0.0351299 | + | 0.999383i | \(0.488815\pi\) | |||||||
\(434\) | 45.2311 | + | 78.3426i | 0.00500268 | + | 0.00866490i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5433.34 | − | 9410.81i | 0.596811 | − | 1.03371i | ||||
\(437\) | 1387.76 | − | 2403.68i | 0.151912 | − | 0.263120i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5653.26 | + | 9791.74i | 0.614614 | + | 1.06454i | 0.990452 | + | 0.137857i | \(0.0440214\pi\) |
−0.375838 | + | 0.926685i | \(0.622645\pi\) | |||||||
\(440\) | −11248.0 | −1.21870 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1219.75 | −0.131261 | ||||||||
\(443\) | −4140.65 | − | 7171.82i | −0.444082 | − | 0.769172i | 0.553906 | − | 0.832579i | \(-0.313137\pi\) |
−0.997988 | + | 0.0634071i | \(0.979803\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2099.37 | − | 3636.22i | 0.223640 | − | 0.387356i | ||||
\(446\) | 1744.13 | − | 3020.92i | 0.185173 | − | 0.320728i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 194.335 | + | 336.599i | 0.0204944 | + | 0.0354973i | ||||
\(449\) | −6888.40 | −0.724017 | −0.362008 | − | 0.932175i | \(-0.617909\pi\) | ||||
−0.362008 | + | 0.932175i | \(0.617909\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12062.4 | −1.25941 | ||||||||
\(452\) | 4942.22 | + | 8560.17i | 0.514297 | + | 0.890789i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2053.80 | + | 3557.28i | −0.212312 | + | 0.367735i | ||||
\(455\) | −997.360 | + | 1727.48i | −0.102763 | + | 0.177990i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2141.80 | − | 3709.71i | −0.219233 | − | 0.379722i | 0.735341 | − | 0.677697i | \(-0.237022\pi\) |
−0.954574 | + | 0.297975i | \(0.903689\pi\) | |||||||
\(458\) | −5908.09 | −0.602766 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4509.29 | −0.457058 | ||||||||
\(461\) | 6889.16 | + | 11932.4i | 0.696009 | + | 1.20552i | 0.969840 | + | 0.243744i | \(0.0783758\pi\) |
−0.273831 | + | 0.961778i | \(0.588291\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2867.27 | + | 4966.25i | −0.287804 | + | 0.498491i | −0.973285 | − | 0.229599i | \(-0.926258\pi\) |
0.685481 | + | 0.728090i | \(0.259592\pi\) | |||||||
\(464\) | −317.068 | + | 549.178i | −0.0317231 | + | 0.0549460i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3829.59 | − | 6633.04i | −0.380691 | − | 0.659377i | ||||
\(467\) | 8950.97 | 0.886941 | 0.443470 | − | 0.896289i | \(-0.353747\pi\) | ||||
0.443470 | + | 0.896289i | \(0.353747\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1557.72 | −0.153366 | ||||||||
\(470\) | 440.373 | + | 762.749i | 0.0432189 | + | 0.0748574i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7648.47 | + | 13247.5i | −0.745867 | + | 1.29188i | ||||
\(473\) | 1713.88 | − | 2968.52i | 0.166605 | − | 0.288568i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 340.057 | + | 588.996i | 0.0328482 | + | 0.0568947i | ||||
\(476\) | −740.203 | −0.0712755 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1934.41 | −0.185100 | ||||||||
\(479\) | 4840.51 | + | 8384.00i | 0.461729 | + | 0.799739i | 0.999047 | − | 0.0436411i | \(-0.0138958\pi\) |
−0.537318 | + | 0.843380i | \(0.680562\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3384.52 | − | 5862.16i | 0.320833 | − | 0.555699i | ||||
\(482\) | −429.917 | + | 744.637i | −0.0406269 | + | 0.0703678i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5513.00 | + | 9548.80i | 0.517750 | + | 0.896769i | ||||
\(485\) | −778.204 | −0.0728586 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8704.66 | 0.809950 | 0.404975 | − | 0.914328i | \(-0.367280\pi\) | ||||
0.404975 | + | 0.914328i | \(0.367280\pi\) | |||||||
\(488\) | 5047.35 | + | 8742.26i | 0.468202 | + | 0.810950i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2254.74 | + | 3905.33i | −0.207875 | + | 0.360051i | ||||
\(491\) | −7797.85 | + | 13506.3i | −0.716725 | + | 1.24140i | 0.245565 | + | 0.969380i | \(0.421026\pi\) |
−0.962290 | + | 0.272024i | \(0.912307\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 335.495 | + | 581.094i | 0.0306489 | + | 0.0530855i | ||||
\(494\) | 2014.13 | 0.183441 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 287.945 | 0.0260668 | ||||||||
\(497\) | −691.776 | − | 1198.19i | −0.0624354 | − | 0.108141i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4848.14 | − | 8397.22i | 0.434935 | − | 0.753329i | −0.562355 | − | 0.826896i | \(-0.690105\pi\) |
0.997290 | + | 0.0735663i | \(0.0234381\pi\) | |||||||
\(500\) | 4517.83 | − | 7825.11i | 0.404087 | − | 0.699899i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1170.23 | + | 2026.90i | 0.104044 | + | 0.180209i | ||||
\(503\) | −20949.7 | −1.85706 | −0.928532 | − | 0.371253i | \(-0.878928\pi\) | ||||
−0.928532 | + | 0.371253i | \(0.878928\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11283.8 | −0.994300 | ||||||||
\(506\) | −2729.85 | − | 4728.24i | −0.239835 | − | 0.415407i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3688.77 | + | 6389.14i | −0.322171 | + | 0.558016i | ||||
\(509\) | 5637.37 | − | 9764.22i | 0.490908 | − | 0.850278i | −0.509037 | − | 0.860745i | \(-0.669998\pi\) |
0.999945 | + | 0.0104668i | \(0.00333174\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2367.73 | − | 4101.03i | −0.204975 | − | 0.355027i | ||||
\(512\) | 7613.21 | 0.657148 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4936.62 | 0.423628 | ||||||||
\(515\) | −5662.32 | − | 9807.43i | −0.484489 | − | 0.839159i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1731.90 | − | 2999.74i | 0.147329 | − | 0.255181i | ||||
\(518\) | −632.320 | + | 1095.21i | −0.0536342 | + | 0.0928972i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3775.99 | − | 6540.20i | −0.318439 | − | 0.551552i | ||||
\(521\) | −8675.49 | −0.729520 | −0.364760 | − | 0.931102i | \(-0.618849\pi\) | ||||
−0.364760 | + | 0.931102i | \(0.618849\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4226.14 | −0.353339 | −0.176670 | − | 0.984270i | \(-0.556532\pi\) | ||||
−0.176670 | + | 0.984270i | \(0.556532\pi\) | |||||||
\(524\) | 3143.62 | + | 5444.90i | 0.262079 | + | 0.453934i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2838.91 | − | 4917.14i | 0.235328 | − | 0.407599i | ||||
\(527\) | 152.340 | − | 263.860i | 0.0125921 | − | 0.0218101i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3557.79 | + | 6162.27i | 0.292413 | + | 0.506474i | ||||
\(530\) | 7007.38 | 0.574304 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1222.27 | 0.0996095 | ||||||||
\(533\) | −4049.39 | − | 7013.75i | −0.329078 | − | 0.569980i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5337.34 | − | 9244.55i | 0.431315 | − | 0.747059i | ||||
\(536\) | 2948.75 | − | 5107.38i | 0.237624 | − | 0.411577i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4179.28 | + | 7238.72i | 0.334910 | + | 0.580081i | ||||
\(539\) | 17734.9 | 1.41725 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13357.8 | 1.06154 | 0.530771 | − | 0.847515i | \(-0.321902\pi\) | ||||
0.530771 | + | 0.847515i | \(0.321902\pi\) | |||||||
\(542\) | 2193.33 | + | 3798.96i | 0.173822 | + | 0.301069i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2195.26 | − | 3802.29i | 0.173016 | − | 0.299673i | ||||
\(545\) | 9213.26 | − | 15957.8i | 0.724134 | − | 1.25424i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10835.6 | − | 18767.7i | −0.846974 | − | 1.46700i | −0.883896 | − | 0.467684i | \(-0.845089\pi\) |
0.0369219 | − | 0.999318i | \(-0.488245\pi\) | |||||||
\(548\) | −7712.78 | −0.601229 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1337.84 | 0.103720 | ||||||||
\(551\) | −553.991 | − | 959.541i | −0.0428327 | − | 0.0741884i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3297.90 | + | 5712.12i | −0.253600 | + | 0.439248i | ||||
\(554\) | 2140.32 | − | 3707.15i | 0.164140 | − | 0.284299i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1412.48 | + | 2446.48i | 0.107738 | + | 0.186608i | ||||
\(557\) | −7477.63 | −0.568828 | −0.284414 | − | 0.958702i | \(-0.591799\pi\) | ||||
−0.284414 | + | 0.958702i | \(0.591799\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2301.42 | 0.174132 | ||||||||
\(560\) | −593.109 | − | 1027.29i | −0.0447561 | − | 0.0775198i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3395.25 | − | 5880.75i | 0.254840 | − | 0.441396i | ||||
\(563\) | −11652.3 | + | 20182.4i | −0.872269 | + | 1.51082i | −0.0126262 | + | 0.999920i | \(0.504019\pi\) |
−0.859643 | + | 0.510895i | \(0.829314\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8380.48 | + | 14515.4i | 0.624017 | + | 1.08083i | ||||
\(566\) | −6236.92 | −0.463176 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5238.10 | 0.386947 | ||||||||
\(569\) | −7324.54 | − | 12686.5i | −0.539650 | − | 0.934701i | −0.998923 | − | 0.0464057i | \(-0.985223\pi\) |
0.459273 | − | 0.888295i | \(-0.348110\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11582.0 | + | 20060.6i | −0.848846 | + | 1.47025i | 0.0333922 | + | 0.999442i | \(0.489369\pi\) |
−0.882239 | + | 0.470803i | \(0.843964\pi\) | |||||||
\(572\) | −6434.61 | + | 11145.1i | −0.470358 | + | 0.814683i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 756.536 | + | 1310.36i | 0.0550125 | + | 0.0952845i | ||||
\(575\) | 1237.80 | 0.0897735 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7865.97 | 0.567529 | 0.283765 | − | 0.958894i | \(-0.408417\pi\) | ||||
0.283765 | + | 0.958894i | \(0.408417\pi\) | |||||||
\(578\) | 2987.25 | + | 5174.07i | 0.214971 | + | 0.372341i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −900.049 | + | 1558.93i | −0.0644353 | + | 0.111605i | ||||
\(581\) | −1826.29 | + | 3163.23i | −0.130408 | + | 0.225874i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13779.3 | − | 23866.5i | −0.978869 | − | 1.69545i | ||||
\(584\) | 17928.4 | 1.27034 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9413.99 | −0.663632 | ||||||||
\(587\) | −478.091 | − | 828.078i | −0.0336166 | − | 0.0582256i | 0.848728 | − | 0.528830i | \(-0.177369\pi\) |
−0.882344 | + | 0.470605i | \(0.844036\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −251.554 | + | 435.704i | −0.0175978 | + | 0.0304803i | ||||
\(590\) | −5619.68 | + | 9733.56i | −0.392133 | + | 0.679194i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2012.70 | + | 3486.10i | 0.139732 | + | 0.242023i | ||||
\(593\) | 16966.0 | 1.17489 | 0.587444 | − | 0.809265i | \(-0.300134\pi\) | ||||
0.587444 | + | 0.809265i | \(0.300134\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1255.16 | −0.0864813 | ||||||||
\(596\) | −4463.22 | − | 7730.53i | −0.306746 | − | 0.531300i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1832.84 | − | 3174.58i | 0.125335 | − | 0.217087i | ||||
\(599\) | −3095.70 | + | 5361.92i | −0.211164 | + | 0.365746i | −0.952079 | − | 0.305852i | \(-0.901059\pi\) |
0.740915 | + | 0.671598i | \(0.234392\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1359.27 | + | 2354.33i | 0.0922559 | + | 0.159792i | 0.908460 | − | 0.417972i | \(-0.137259\pi\) |
−0.816204 | + | 0.577764i | \(0.803926\pi\) | |||||||
\(602\) | −429.968 | −0.0291099 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −9428.00 | −0.635132 | ||||||||
\(605\) | 9348.35 | + | 16191.8i | 0.628206 | + | 1.08808i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8412.49 | + | 14570.9i | −0.562524 | + | 0.974321i | 0.434751 | + | 0.900551i | \(0.356836\pi\) |
−0.997275 | + | 0.0737701i | \(0.976497\pi\) | |||||||
\(608\) | −3624.95 | + | 6278.60i | −0.241795 | + | 0.418801i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3708.51 | + | 6423.33i | 0.246153 | + | 0.426349i | ||||
\(611\) | 2325.62 | 0.153985 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20175.1 | −1.32930 | −0.664652 | − | 0.747153i | \(-0.731420\pi\) | ||||
−0.664652 | + | 0.747153i | \(0.731420\pi\) | |||||||
\(614\) | −4344.81 | − | 7525.44i | −0.285574 | − | 0.494629i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2774.42 | − | 4805.44i | 0.181468 | − | 0.314313i | ||||
\(617\) | 5655.31 | − | 9795.29i | 0.369002 | − | 0.639130i | −0.620408 | − | 0.784280i | \(-0.713033\pi\) |
0.989410 | + | 0.145149i | \(0.0463662\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8529.94 | + | 14774.3i | 0.553873 | + | 0.959336i | 0.997990 | + | 0.0633676i | \(0.0201841\pi\) |
−0.444117 | + | 0.895969i | \(0.646483\pi\) | |||||||
\(620\) | 817.380 | 0.0529464 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −9712.56 | −0.626106 | ||||||||
\(623\) | 1035.66 | + | 1793.82i | 0.0666017 | + | 0.115357i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6572.36 | − | 11383.7i | 0.420631 | − | 0.728554i | ||||
\(626\) | −947.764 | + | 1641.58i | −0.0605116 | + | 0.104809i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9834.58 | − | 17034.0i | −0.624908 | − | 1.08237i | ||||
\(629\) | 4259.34 | 0.270002 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13186.3 | −0.831916 | −0.415958 | − | 0.909384i | \(-0.636554\pi\) | ||||
−0.415958 | + | 0.909384i | \(0.636554\pi\) | |||||||
\(632\) | −12485.8 | − | 21626.0i | −0.785850 | − | 1.36113i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5609.15 | + | 9715.34i | −0.351369 | + | 0.608589i | ||||
\(635\) | −6255.02 | + | 10834.0i | −0.390902 | + | 0.677063i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5953.68 | + | 10312.1i | 0.370319 | + | 0.641412i | ||||
\(638\) | −2179.50 | −0.135246 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 14323.7 | 0.884677 | ||||||||
\(641\) | 8180.99 | + | 14169.9i | 0.504102 | + | 0.873131i | 0.999989 | + | 0.00474343i | \(0.00150989\pi\) |
−0.495886 | + | 0.868387i | \(0.665157\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14022.5 | − | 24287.6i | 0.860019 | − | 1.48960i | −0.0118907 | − | 0.999929i | \(-0.503785\pi\) |
0.871910 | − | 0.489667i | \(-0.162882\pi\) | |||||||
\(644\) | 1112.26 | − | 1926.49i | 0.0680577 | − | 0.117879i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 633.685 | + | 1097.57i | 0.0385944 | + | 0.0668475i | ||||
\(647\) | −21247.7 | −1.29109 | −0.645543 | − | 0.763724i | \(-0.723369\pi\) | ||||
−0.645543 | + | 0.763724i | \(0.723369\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 44202.1 | 2.67347 | ||||||||
\(650\) | 449.119 | + | 777.897i | 0.0271014 | + | 0.0469410i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2898.12 | − | 5019.69i | 0.174079 | − | 0.301513i | ||||
\(653\) | 629.928 | − | 1091.07i | 0.0377504 | − | 0.0653856i | −0.846533 | − | 0.532336i | \(-0.821314\pi\) |
0.884283 | + | 0.466951i | \(0.154647\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5330.60 | + | 9232.87i | 0.317991 | + | 0.550776i | ||||
\(656\) | 4816.17 | 0.286646 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −434.489 | −0.0257419 | ||||||||
\(659\) | −6023.35 | − | 10432.7i | −0.356049 | − | 0.616695i | 0.631248 | − | 0.775581i | \(-0.282543\pi\) |
−0.987297 | + | 0.158886i | \(0.949210\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6554.04 | + | 11351.9i | −0.385662 | + | 0.667986i | −0.991861 | − | 0.127327i | \(-0.959360\pi\) |
0.606199 | + | 0.795313i | \(0.292693\pi\) | |||||||
\(662\) | 6629.00 | − | 11481.8i | 0.389189 | − | 0.674096i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6914.30 | − | 11975.9i | −0.404107 | − | 0.699933i | ||||
\(665\) | 2072.60 | 0.120860 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2016.51 | −0.117061 | ||||||||
\(668\) | −2097.95 | − | 3633.76i | −0.121515 | − | 0.210471i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2166.58 | − | 3752.62i | 0.124929 | − | 0.216383i | ||||
\(671\) | 14584.8 | − | 25261.7i | 0.839108 | − | 1.45338i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1371.82 | − | 2376.07i | −0.0785734 | − | 0.136093i | 0.824061 | − | 0.566501i | \(-0.191703\pi\) |
−0.902635 | + | 0.430408i | \(0.858370\pi\) | |||||||
\(674\) | −6801.06 | −0.388675 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4798.21 | 0.272998 | ||||||||
\(677\) | 12502.0 | + | 21654.1i | 0.709735 | + | 1.22930i | 0.964955 | + | 0.262415i | \(0.0845189\pi\) |
−0.255220 | + | 0.966883i | \(0.582148\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 191.952 | − | 332.470i | 0.0108489 | − | 0.0187909i | ||||
\(680\) | 2376.00 | − | 4115.35i | 0.133993 | − | 0.232083i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 494.829 | + | 857.068i | 0.0277829 | + | 0.0481215i | ||||
\(683\) | 4846.23 | 0.271502 | 0.135751 | − | 0.990743i | \(-0.456655\pi\) | ||||
0.135751 | + | 0.990743i | \(0.456655\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13078.5 | −0.729494 | ||||||||
\(686\) | −2316.54 | − | 4012.36i | −0.128930 | − | 0.223313i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −684.303 | + | 1185.25i | −0.0379198 | + | 0.0656790i | ||||
\(689\) | 9251.54 | − | 16024.1i | 0.511546 | − | 0.886024i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1742.29 | − | 3017.73i | −0.0959187 | − | 0.166136i | 0.814073 | − | 0.580763i | \(-0.197246\pi\) |
−0.909992 | + | 0.414627i | \(0.863912\pi\) | |||||||
\(692\) | −13535.5 | −0.743560 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1393.70 | 0.0762305 | ||||||||
\(695\) | 2395.12 | + | 4148.48i | 0.130723 | + | 0.226418i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2548.04 | − | 4413.33i | 0.138470 | − | 0.239837i | ||||
\(698\) | −8342.49 | + | 14449.6i | −0.452390 | + | 0.783562i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 272.548 | + | 472.066i | 0.0147162 | + | 0.0254892i | ||||
\(701\) | −15701.4 | −0.845981 | −0.422991 | − | 0.906134i | \(-0.639020\pi\) | ||||
−0.422991 | + | 0.906134i | \(0.639020\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7033.32 | −0.377335 | ||||||||
\(704\) | 2126.03 | + | 3682.39i | 0.113818 | + | 0.197138i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2906.55 | − | 5034.29i | 0.154943 | − | 0.268368i | ||||
\(707\) | 2783.25 | − | 4820.73i | 0.148055 | − | 0.256439i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7821.72 | − | 13547.6i | −0.414317 | − | 0.717618i | 0.581039 | − | 0.813875i | \(-0.302646\pi\) |
−0.995356 | + | 0.0962572i | \(0.969313\pi\) | |||||||
\(710\) | 3848.67 | 0.203434 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7841.98 | −0.412768 | ||||||||
\(713\) | 457.824 | + | 792.975i | 0.0240472 | + | 0.0416510i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10911.1 | + | 18898.6i | −0.570703 | + | 0.988486i | ||||
\(716\) | −9246.27 | + | 16015.0i | −0.482611 | + | 0.835907i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −355.379 | − | 615.535i | −0.0184716 | − | 0.0319938i | ||||
\(719\) | 6964.13 | 0.361222 | 0.180611 | − | 0.983555i | \(-0.442193\pi\) | ||||
0.180611 | + | 0.983555i | \(0.442193\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5586.66 | 0.288569 | ||||||||
\(722\) | 3659.86 | + | 6339.06i | 0.188651 | + | 0.326752i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1197.20 | − | 2073.62i | 0.0614554 | − | 0.106444i | ||||
\(725\) | 247.063 | − | 427.925i | 0.0126561 | − | 0.0219210i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7103.61 | + | 12303.8i | 0.362391 | + | 0.627680i | 0.988354 | − | 0.152173i | \(-0.0486272\pi\) |
−0.625963 | + | 0.779853i | \(0.715294\pi\) | |||||||
\(728\) | 3725.53 | 0.189667 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 13172.8 | 0.667871 | ||||||||
\(731\) | 724.072 | + | 1254.13i | 0.0366358 | + | 0.0634551i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13265.3 | + | 22976.1i | −0.668437 | + | 1.15777i | 0.309905 | + | 0.950768i | \(0.399703\pi\) |
−0.978341 | + | 0.206998i | \(0.933630\pi\) | |||||||
\(734\) | 3167.43 | − | 5486.15i | 0.159280 | − | 0.275882i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6597.36 | + | 11427.0i | 0.330410 | + | 0.572288i | ||||
\(737\) | −17041.4 | −0.851735 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5683.47 | −0.282909 | −0.141455 | − | 0.989945i | \(-0.545178\pi\) | ||||
−0.141455 | + | 0.989945i | \(0.545178\pi\) | |||||||
\(740\) | 5713.38 | + | 9895.86i | 0.283822 | + | 0.491594i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1728.44 | + | 2993.74i | −0.0855161 | + | 0.148118i | ||||
\(743\) | −7784.28 | + | 13482.8i | −0.384358 | + | 0.665727i | −0.991680 | − | 0.128729i | \(-0.958910\pi\) |
0.607322 | + | 0.794456i | \(0.292244\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7568.25 | − | 13108.6i | −0.372187 | − | 0.644647i | ||||
\(746\) | 6539.50 | 0.320949 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −8097.82 | −0.395836 | ||||||||
\(749\) | 2633.01 | + | 4560.51i | 0.128449 | + | 0.222480i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4130.82 | − | 7154.79i | 0.200713 | − | 0.347646i | −0.748045 | − | 0.663648i | \(-0.769007\pi\) |
0.948758 | + | 0.316002i | \(0.102341\pi\) | |||||||
\(752\) | −691.499 | + | 1197.71i | −0.0335324 | + | 0.0580798i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −731.666 | − | 1267.28i | −0.0353391 | − | 0.0612092i | ||||
\(755\) | −15987.0 | −0.770630 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13381.5 | −0.642481 | −0.321240 | − | 0.946998i | \(-0.604100\pi\) | ||||
−0.321240 | + | 0.946998i | \(0.604100\pi\) | |||||||
\(758\) | 1372.51 | + | 2377.25i | 0.0657674 | + | 0.113913i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3923.41 | + | 6795.55i | −0.187259 | + | 0.324343i | ||||
\(761\) | 2724.92 | − | 4719.70i | 0.129801 | − | 0.224821i | −0.793799 | − | 0.608181i | \(-0.791900\pi\) |
0.923599 | + | 0.383359i | \(0.125233\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4545.08 | + | 7872.31i | 0.215652 | + | 0.373521i | ||||
\(764\) | 21320.8 | 1.00963 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1358.96 | −0.0641009 | ||||||||
\(767\) | 14838.8 | + | 25701.6i | 0.698564 | + | 1.20995i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9681.98 | − | 16769.7i | 0.454020 | − | 0.786385i | −0.544612 | − | 0.838688i | \(-0.683323\pi\) |
0.998631 | + | 0.0523033i | \(0.0166563\pi\) | |||||||
\(770\) | 2038.49 | − | 3530.77i | 0.0954054 | − | 0.165247i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6774.62 | + | 11734.0i | 0.315834 | + | 0.547041i | ||||
\(773\) | 1865.54 | 0.0868033 | 0.0434017 | − | 0.999058i | \(-0.486180\pi\) | ||||
0.0434017 | + | 0.999058i | \(0.486180\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −224.370 | −0.0103995 | ||||||||
\(776\) | 726.725 | + | 1258.72i | 0.0336184 | + | 0.0582288i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 277.483 | − | 480.614i | 0.0127869 | − | 0.0221476i | ||||
\(779\) | −4207.49 | + | 7287.58i | −0.193516 | + | 0.335179i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7568.02 | − | 13108.2i | −0.346741 | − | 0.600574i | ||||
\(782\) | 2306.59 | 0.105478 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −7081.05 | −0.322570 | ||||||||
\(785\) | −16676.4 | − | 28884.4i | −0.758225 | − | 1.31328i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9603.65 | − | 16634.0i | 0.434985 | − | 0.753416i | −0.562310 | − | 0.826927i | \(-0.690087\pi\) |
0.997294 | + | 0.0735110i | \(0.0234204\pi\) | |||||||
\(788\) | 12157.6 | − | 21057.5i | 0.549614 | − | 0.951959i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −9173.86 | − | 15889.6i | −0.413154 | − | 0.715603i | ||||
\(791\) | −8268.50 | −0.371674 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19584.7 | 0.877017 | ||||||||
\(794\) | −2003.26 | − | 3469.76i | −0.0895380 | − | 0.155084i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4756.89 | + | 8239.18i | −0.211813 | + | 0.366872i | ||||
\(797\) | 93.0372 | − | 161.145i | 0.00413494 | − | 0.00716193i | −0.863951 | − | 0.503577i | \(-0.832017\pi\) |
0.868085 | + | 0.496415i | \(0.165350\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 731.686 | + | 1267.32i | 0.0323970 | + | 0.0561132i | ||||
\(800\) | −3233.23 | −0.142890 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 13978.3 | 0.615452 | ||||||||
\(803\) | −25902.9 | − | 44865.2i | −1.13835 | − | 1.97168i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1886.05 | − | 3266.73i | 0.0825771 | − | 0.143028i | ||||
\(806\) | −332.232 | + | 575.442i | −0.0145191 | + | 0.0251477i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10537.3 | + | 18251.2i | 0.458790 | + | 0.794647i | ||||
\(809\) | −5903.09 | −0.256541 | −0.128270 | − | 0.991739i | \(-0.540943\pi\) | ||||
−0.128270 | + | 0.991739i | \(0.540943\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23111.0 | 1.00066 | 0.500331 | − | 0.865834i | \(-0.333212\pi\) | ||||
0.500331 | + | 0.865834i | \(0.333212\pi\) | |||||||
\(812\) | −444.011 | − | 769.050i | −0.0191893 | − | 0.0332369i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6917.58 | + | 11981.6i | −0.297863 | + | 0.515915i | ||||
\(815\) | 4914.32 | − | 8511.85i | 0.211216 | − | 0.365837i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1195.64 | − | 2070.90i | −0.0511995 | − | 0.0886802i | ||||
\(818\) | 9488.29 | 0.405563 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13671.5 | 0.582231 | ||||||||
\(821\) | −4822.14 | − | 8352.20i | −0.204987 | − | 0.355047i | 0.745142 | − | 0.666906i | \(-0.232382\pi\) |
−0.950128 | + | 0.311859i | \(0.899048\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16786.7 | − | 29075.5i | 0.710994 | − | 1.23148i | −0.253490 | − | 0.967338i | \(-0.581578\pi\) |
0.964484 | − | 0.264140i | \(-0.0850882\pi\) | |||||||
\(824\) | −10575.5 | + | 18317.3i | −0.447106 | + | 0.774410i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2772.29 | − | 4801.75i | −0.116780 | − | 0.202269i | ||||
\(827\) | 25916.1 | 1.08971 | 0.544855 | − | 0.838530i | \(-0.316585\pi\) | ||||
0.544855 | + | 0.838530i | \(0.316585\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28650.6 | −1.20033 | −0.600166 | − | 0.799876i | \(-0.704899\pi\) | ||||
−0.600166 | + | 0.799876i | \(0.704899\pi\) | |||||||
\(830\) | −5080.25 | − | 8799.24i | −0.212455 | − | 0.367983i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1427.43 | + | 2472.38i | −0.0594799 | + | 0.103022i | ||||
\(833\) | −3746.29 | + | 6488.76i | −0.155824 | + | 0.269895i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3557.48 | − | 6161.74i | −0.147439 | − | 0.255372i | ||||
\(836\) | 13371.7 | 0.553192 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7026.51 | −0.289650 | ||||||||
\(839\) | 356.480 | + | 617.441i | 0.0146687 | + | 0.0254070i | 0.873267 | − | 0.487243i | \(-0.161997\pi\) |
−0.858598 | + | 0.512650i | \(0.828664\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11792.0 | − | 20424.4i | 0.483497 | − | 0.837441i | ||||
\(842\) | −1280.68 | + | 2218.20i | −0.0524169 | + | 0.0907887i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5345.30 | + | 9258.32i | 0.218001 | + | 0.377588i | ||||
\(845\) | 8136.29 | 0.331239 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9223.44 | −0.374169 | ||||||||
\(848\) | 5501.69 | + | 9529.21i | 0.222793 | + | 0.385890i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −282.603 | + | 489.484i | −0.0114038 | + | 0.0197519i | ||||
\(851\) | −6400.27 | + | 11085.6i | −0.257812 | + | 0.446544i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15183.6 | + | 26298.8i | 0.609469 | + | 1.05563i | 0.991328 | + | 0.131411i | \(0.0419508\pi\) |
−0.381859 | + | 0.924221i | \(0.624716\pi\) | |||||||
\(854\) | −3658.96 | −0.146612 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −19937.1 | −0.796069 | ||||||||
\(857\) | 4540.35 | + | 7864.12i | 0.180975 | + | 0.313458i | 0.942213 | − | 0.335015i | \(-0.108741\pi\) |
−0.761238 | + | 0.648473i | \(0.775408\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13080.1 | + | 22655.4i | −0.519543 | + | 0.899874i | 0.480199 | + | 0.877159i | \(0.340564\pi\) |
−0.999742 | + | 0.0227150i | \(0.992769\pi\) | |||||||
\(860\) | −1942.50 | + | 3364.52i | −0.0770219 | + | 0.133406i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2806.76 | − | 4861.45i | −0.110903 | − | 0.192090i | ||||
\(863\) | 40102.0 | 1.58180 | 0.790898 | − | 0.611949i | \(-0.209614\pi\) | ||||
0.790898 | + | 0.611949i | \(0.209614\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22952.1 | −0.902189 | ||||||||
\(866\) | −434.362 | − | 752.338i | −0.0170442 | − | 0.0295213i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −201.615 | + | 349.207i | −0.00788392 | + | 0.0136554i | ||||
\(869\) | −36079.0 | + | 62490.6i | −1.40839 | + | 2.43941i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5720.87 | − | 9908.84i | −0.222554 | − | 0.385474i | ||||
\(872\) | −34415.2 | −1.33652 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3808.80 | −0.147408 | ||||||||
\(875\) | 3779.24 | + | 6545.84i | 0.146013 | + | 0.252903i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12626.1 | + | 21869.0i | −0.486149 | + | 0.842036i | −0.999873 | − | 0.0159201i | \(-0.994932\pi\) |
0.513724 | + | 0.857956i | \(0.328266\pi\) | |||||||
\(878\) | 7757.86 | − | 13437.0i | 0.298195 | − | 0.516489i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6488.61 | − | 11238.6i | −0.248558 | − | 0.430515i | ||||
\(881\) | 2049.26 | 0.0783670 | 0.0391835 | − | 0.999232i | \(-0.487524\pi\) | ||||
0.0391835 | + | 0.999232i | \(0.487524\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39413.4 | 1.50211 | 0.751057 | − | 0.660237i | \(-0.229544\pi\) | ||||
0.751057 | + | 0.660237i | \(0.229544\pi\) | |||||||
\(884\) | −2718.47 | − | 4708.53i | −0.103430 | − | 0.179146i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5682.14 | + | 9841.75i | −0.215457 | + | 0.373183i | ||||
\(887\) | 18484.2 | − | 32015.6i | 0.699707 | − | 1.21193i | −0.268861 | − | 0.963179i | \(-0.586647\pi\) |
0.968568 | − | 0.248749i | \(-0.0800194\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3085.72 | − | 5344.63i | −0.116414 | − | 0.201634i | ||||
\(890\) | −5761.86 | −0.217009 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 15548.7 | 0.583641 | ||||||||
\(893\) | −1208.21 | − | 2092.68i | −0.0452757 | − | 0.0784198i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15678.8 | + | 27156.5i | −0.585570 | + | 1.01424i | ||||
\(896\) | −3533.07 | + | 6119.46i | −0.131732 | + | 0.228166i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4726.41 | + | 8186.38i | 0.175637 | + | 0.304213i | ||||
\(899\) | 365.525 | 0.0135605 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11642.9 | 0.430499 | ||||||||
\(902\) | 8276.50 | + | 14335.3i | 0.305518 | + | 0.529173i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 15652.2 | − | 27110.4i | 0.575868 | − | 0.997432i | ||||
\(905\) | 2030.09 | − | 3516.21i | 0.0745662 | − | 0.129152i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1355.31 | − | 2347.47i | −0.0496167 | − | 0.0859386i | 0.840150 | − | 0.542353i | \(-0.182467\pi\) |
−0.889767 | + | 0.456415i | \(0.849133\pi\) | |||||||
\(908\) | −18309.3 | −0.669180 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2737.32 | 0.0997156 | ||||||||
\(911\) | 11498.3 | + | 19915.6i | 0.418172 | + | 0.724296i | 0.995756 | − | 0.0920360i | \(-0.0293375\pi\) |
−0.577583 | + | 0.816332i | \(0.696004\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19979.6 | + | 34605.7i | −0.724237 | + | 1.25441i | ||||
\(914\) | −2939.15 | + | 5090.77i | −0.106366 | + | 0.184231i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −13167.4 | − | 22806.7i | −0.474961 | − | 0.822657i | ||||
\(917\) | −5259.38 | −0.189400 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −39103.8 | −1.40361 | −0.701804 | − | 0.712370i | \(-0.747622\pi\) | ||||
−0.701804 | + | 0.712370i | \(0.747622\pi\) | |||||||
\(920\) | 7140.55 | + | 12367.8i | 0.255888 | + | 0.443211i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9453.86 | − | 16374.6i | 0.337686 | − | 0.584889i | ||||
\(923\) | 5081.23 | − | 8800.94i | 0.181203 | − | 0.313853i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1568.32 | − | 2716.41i | −0.0557470 | − | 0.0965567i | ||||
\(926\) | 7869.39 | 0.279270 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5267.30 | 0.186323 | ||||||||
\(929\) | −17977.3 | − | 31137.6i | −0.634894 | − | 1.09967i | −0.986538 | − | 0.163534i | \(-0.947711\pi\) |
0.351644 | − | 0.936134i | \(-0.385623\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6186.12 | − | 10714.7i | 0.217768 | − | 0.377185i | ||||
\(932\) | 17070.1 | − | 29566.3i | 0.599946 | − | 1.03914i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6141.62 | − | 10637.6i | −0.215161 | − | 0.372669i | ||||
\(935\) | −13731.4 | −0.480283 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7263.94 | −0.253258 | −0.126629 | − | 0.991950i | \(-0.540416\pi\) | ||||
−0.126629 | + | 0.991950i | \(0.540416\pi\) | |||||||
\(938\) | 1068.81 | + | 1851.24i | 0.0372047 | + | 0.0644404i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1962.93 | + | 3399.90i | −0.0681104 | + | 0.117971i | ||||
\(941\) | 3739.45 | − | 6476.92i | 0.129546 | − | 0.224380i | −0.793955 | − | 0.607977i | \(-0.791981\pi\) |
0.923501 | + | 0.383597i | \(0.125315\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7657.57 | + | 13263.3i | 0.264438 | + | 0.458020i | ||||
\(944\) | −17648.7 | −0.608490 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4703.84 | −0.161665 | ||||||||
\(947\) | 6745.68 | + | 11683.9i | 0.231473 | + | 0.400923i | 0.958242 | − | 0.285959i | \(-0.0923121\pi\) |
−0.726769 | + | 0.686882i | \(0.758979\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17391.4 | − | 30122.8i | 0.594889 | − | 1.03038i | ||||
\(950\) | 466.654 | − | 808.268i | 0.0159371 | − | 0.0276039i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1172.13 | + | 2030.18i | 0.0399042 | + | 0.0691161i | ||||
\(953\) | 13981.6 | 0.475246 | 0.237623 | − | 0.971357i | \(-0.423632\pi\) | ||||
0.237623 | + | 0.971357i | \(0.423632\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 36153.5 | 1.22503 | ||||||||
\(956\) | −4311.24 | − | 7467.29i | −0.145853 | − | 0.252625i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6642.54 | − | 11505.2i | 0.224019 | − | 0.388013i | ||||
\(959\) | 3225.93 | − | 5587.48i | 0.108624 | − | 0.188143i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14812.5 | + | 25656.0i | 0.497214 | + | 0.861200i | ||||
\(962\) | −9289.02 | −0.311320 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3832.64 | −0.128051 | ||||||||
\(965\) | 11487.7 | + | 19897.2i | 0.383213 | + | 0.663745i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4540.73 | − | 7864.78i | 0.151003 | − | 0.261545i | −0.780593 | − | 0.625039i | \(-0.785083\pi\) |
0.931597 | + | 0.363494i | \(0.118416\pi\) | |||||||
\(968\) | 17459.9 | − | 30241.4i | 0.579734 | − | 1.00413i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 533.958 | + | 924.842i | 0.0176746 | + | 0.0306133i | ||||
\(971\) | 9709.13 | 0.320887 | 0.160443 | − | 0.987045i | \(-0.448708\pi\) | ||||
0.160443 | + | 0.987045i | \(0.448708\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2363.12 | −0.0778604 | ||||||||
\(974\) | −5972.62 | − | 10344.9i | −0.196484 | − | 0.340320i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5823.31 | + | 10086.3i | −0.190983 | + | 0.330793i | ||||
\(977\) | 5427.45 | − | 9400.63i | 0.177727 | − | 0.307833i | −0.763374 | − | 0.645956i | \(-0.776459\pi\) |
0.941102 | + | 0.338123i | \(0.109792\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11330.1 | + | 19624.3i | 0.369880 | + | 0.640650i | ||||
\(980\) | −20100.7 | −0.655198 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 21401.7 | 0.695474 | ||||||||
\(983\) | −3755.05 | − | 6503.94i | −0.121839 | − | 0.211031i | 0.798654 | − | 0.601790i | \(-0.205546\pi\) |
−0.920493 | + | 0.390759i | \(0.872212\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20615.5 | − | 35707.1i | 0.666867 | − | 1.15505i | ||||
\(986\) | 460.393 | − | 797.424i | 0.0148701 | − | 0.0257557i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4488.92 | + | 7775.04i | 0.144546 | + | 0.250361i | ||||
\(989\) | −4352.08 | −0.139927 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46125.6 | 1.47854 | 0.739268 | − | 0.673412i | \(-0.235172\pi\) | ||||
0.739268 | + | 0.673412i | \(0.235172\pi\) | |||||||
\(992\) | −1195.88 | − | 2071.32i | −0.0382753 | − | 0.0662947i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −949.311 | + | 1644.25i | −0.0302921 | + | 0.0524674i | ||||
\(995\) | −8066.22 | + | 13971.1i | −0.257001 | + | 0.445139i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22675.0 | − | 39274.3i | −0.720287 | − | 1.24757i | −0.960885 | − | 0.276948i | \(-0.910677\pi\) |
0.240598 | − | 0.970625i | \(-0.422656\pi\) | |||||||
\(998\) | −13306.0 | −0.422039 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 27.4.c.a.10.1 | 4 | ||
3.2 | odd | 2 | 9.4.c.a.4.2 | ✓ | 4 | ||
4.3 | odd | 2 | 432.4.i.c.145.2 | 4 | |||
9.2 | odd | 6 | 9.4.c.a.7.2 | yes | 4 | ||
9.4 | even | 3 | 81.4.a.a.1.2 | 2 | |||
9.5 | odd | 6 | 81.4.a.d.1.1 | 2 | |||
9.7 | even | 3 | inner | 27.4.c.a.19.1 | 4 | ||
12.11 | even | 2 | 144.4.i.c.49.2 | 4 | |||
15.2 | even | 4 | 225.4.k.b.49.2 | 8 | |||
15.8 | even | 4 | 225.4.k.b.49.3 | 8 | |||
15.14 | odd | 2 | 225.4.e.b.76.1 | 4 | |||
36.7 | odd | 6 | 432.4.i.c.289.2 | 4 | |||
36.11 | even | 6 | 144.4.i.c.97.2 | 4 | |||
36.23 | even | 6 | 1296.4.a.u.1.2 | 2 | |||
36.31 | odd | 6 | 1296.4.a.i.1.1 | 2 | |||
45.2 | even | 12 | 225.4.k.b.124.3 | 8 | |||
45.4 | even | 6 | 2025.4.a.n.1.1 | 2 | |||
45.14 | odd | 6 | 2025.4.a.g.1.2 | 2 | |||
45.29 | odd | 6 | 225.4.e.b.151.1 | 4 | |||
45.38 | even | 12 | 225.4.k.b.124.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9.4.c.a.4.2 | ✓ | 4 | 3.2 | odd | 2 | ||
9.4.c.a.7.2 | yes | 4 | 9.2 | odd | 6 | ||
27.4.c.a.10.1 | 4 | 1.1 | even | 1 | trivial | ||
27.4.c.a.19.1 | 4 | 9.7 | even | 3 | inner | ||
81.4.a.a.1.2 | 2 | 9.4 | even | 3 | |||
81.4.a.d.1.1 | 2 | 9.5 | odd | 6 | |||
144.4.i.c.49.2 | 4 | 12.11 | even | 2 | |||
144.4.i.c.97.2 | 4 | 36.11 | even | 6 | |||
225.4.e.b.76.1 | 4 | 15.14 | odd | 2 | |||
225.4.e.b.151.1 | 4 | 45.29 | odd | 6 | |||
225.4.k.b.49.2 | 8 | 15.2 | even | 4 | |||
225.4.k.b.49.3 | 8 | 15.8 | even | 4 | |||
225.4.k.b.124.2 | 8 | 45.38 | even | 12 | |||
225.4.k.b.124.3 | 8 | 45.2 | even | 12 | |||
432.4.i.c.145.2 | 4 | 4.3 | odd | 2 | |||
432.4.i.c.289.2 | 4 | 36.7 | odd | 6 | |||
1296.4.a.i.1.1 | 2 | 36.31 | odd | 6 | |||
1296.4.a.u.1.2 | 2 | 36.23 | even | 6 | |||
2025.4.a.g.1.2 | 2 | 45.14 | odd | 6 | |||
2025.4.a.n.1.1 | 2 | 45.4 | even | 6 |