Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1680,2,Mod(209,1680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1680.209");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1680.k (of order \(2\), degree \(1\), 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: | \(13.4148675396\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 840) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 209.7 | ||
Character | \(\chi\) | \(=\) | 1680.209 |
Dual form | 1680.2.k.h.209.8 |
$q$-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 \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(421\) | \(1121\) | \(1471\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.773053 | − | 1.54996i | −0.446323 | − | 0.894872i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.194052 | + | 2.22763i | 0.0867826 | + | 0.996227i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.942148 | + | 2.47232i | −0.356099 | + | 0.934448i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.80478 | + | 2.39641i | −0.601592 | + | 0.798803i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.45449i | − | 0.438546i | −0.975664 | − | 0.219273i | \(-0.929631\pi\) | ||
0.975664 | − | 0.219273i | \(-0.0703686\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.42393 | 1.22698 | 0.613489 | − | 0.789703i | \(-0.289766\pi\) | ||||
0.613489 | + | 0.789703i | \(0.289766\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.30274 | − | 2.02285i | 0.852763 | − | 0.522298i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 0.440293i | − | 0.106787i | −0.998574 | − | 0.0533934i | \(-0.982996\pi\) | ||
0.998574 | − | 0.0533934i | \(-0.0170037\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 6.54815i | − | 1.50225i | −0.660160 | − | 0.751125i | \(-0.729512\pi\) | ||
0.660160 | − | 0.751125i | \(-0.270488\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.56033 | − | 0.450938i | 0.995147 | − | 0.0984027i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.43747 | −0.508248 | −0.254124 | − | 0.967172i | \(-0.581787\pi\) | ||||
−0.254124 | + | 0.967172i | \(0.581787\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.92469 | + | 0.864552i | −0.984938 | + | 0.172910i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.10954 | + | 0.944786i | 0.983331 | + | 0.181824i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.30871i | 0.800107i | 0.916492 | + | 0.400054i | \(0.131009\pi\) | ||||
−0.916492 | + | 0.400054i | \(0.868991\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.86295i | 0.514201i | 0.966385 | + | 0.257101i | \(0.0827672\pi\) | ||||
−0.966385 | + | 0.257101i | \(0.917233\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.25441 | + | 1.12440i | −0.392443 | + | 0.195733i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.69024 | − | 1.61900i | −0.961826 | − | 0.273661i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.10153i | 1.49628i | 0.663540 | + | 0.748141i | \(0.269053\pi\) | ||||
−0.663540 | + | 0.748141i | \(0.730947\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.41994 | − | 6.85694i | −0.547628 | − | 1.09799i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.55874 | −0.711955 | −0.355978 | − | 0.934494i | \(-0.615852\pi\) | ||||
−0.355978 | + | 0.934494i | \(0.615852\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.57261i | 1.30731i | 0.756793 | + | 0.653655i | \(0.226765\pi\) | ||||
−0.756793 | + | 0.653655i | \(0.773235\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.68854 | − | 3.55535i | −0.847997 | − | 0.530000i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.31118i | 0.920580i | 0.887769 | + | 0.460290i | \(0.152255\pi\) | ||||
−0.887769 | + | 0.460290i | \(0.847745\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.22471 | − | 4.65858i | −0.746388 | − | 0.665512i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.682438 | + | 0.340370i | −0.0955605 | + | 0.0476613i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.37352 | −1.28755 | −0.643776 | − | 0.765214i | \(-0.722633\pi\) | ||||
−0.643776 | + | 0.765214i | \(0.722633\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.24008 | − | 0.282247i | 0.436892 | − | 0.0380582i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10.1494 | + | 5.06207i | −1.34432 | + | 0.670488i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.33478 | −1.08510 | −0.542548 | − | 0.840025i | \(-0.682540\pi\) | ||||
−0.542548 | + | 0.840025i | \(0.682540\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.14436i | 0.914741i | 0.889276 | + | 0.457371i | \(0.151209\pi\) | ||||
−0.889276 | + | 0.457371i | \(0.848791\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.22432 | − | 6.71976i | −0.532214 | − | 0.846610i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.858472 | + | 9.85489i | 0.106480 | + | 1.22235i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.3488i | 1.38648i | 0.720706 | + | 0.693241i | \(0.243818\pi\) | ||||
−0.720706 | + | 0.693241i | \(0.756182\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.88430 | + | 3.77800i | 0.226843 | + | 0.454817i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.12511i | 0.133526i | 0.997769 | + | 0.0667631i | \(0.0212672\pi\) | ||||
−0.997769 | + | 0.0667631i | \(0.978733\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.2423 | 1.31581 | 0.657904 | − | 0.753102i | \(-0.271443\pi\) | ||||
0.657904 | + | 0.753102i | \(0.271443\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.14707 | + | 6.96474i | 0.594333 | + | 0.804219i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.59597 | + | 1.37035i | 0.409799 | + | 0.156166i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.83987 | 0.769546 | 0.384773 | − | 0.923011i | \(-0.374280\pi\) | ||||
0.384773 | + | 0.923011i | \(0.374280\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.48556 | − | 8.64997i | −0.276174 | − | 0.961108i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 5.75536i | − | 0.631733i | −0.948804 | − | 0.315867i | \(-0.897705\pi\) | ||
0.948804 | − | 0.315867i | \(-0.102295\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.980811 | − | 0.0854397i | 0.106384 | − | 0.00926723i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.67834 | − | 3.33086i | 0.715994 | − | 0.357106i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.7153 | −1.24182 | −0.620908 | − | 0.783883i | \(-0.713236\pi\) | ||||
−0.620908 | + | 0.783883i | \(0.713236\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.16800 | + | 10.9374i | −0.436925 | + | 1.14655i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.43747 | − | 2.21322i | 0.460145 | − | 0.229500i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 14.5869 | − | 1.27068i | 1.49658 | − | 0.130369i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.27856 | 0.637491 | 0.318746 | − | 0.947840i | \(-0.396738\pi\) | ||||
0.318746 | + | 0.947840i | \(0.396738\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.48556 | + | 2.62504i | 0.350312 | + | 0.263826i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.5520 | 1.14946 | 0.574732 | − | 0.818342i | \(-0.305106\pi\) | ||||
0.574732 | + | 0.818342i | \(0.305106\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.9525 | −1.76892 | −0.884458 | − | 0.466619i | \(-0.845472\pi\) | ||||
−0.884458 | + | 0.466619i | \(0.845472\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.88947 | + | 10.0712i | 0.184393 | + | 0.982853i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −18.5926 | −1.79742 | −0.898709 | − | 0.438546i | \(-0.855494\pi\) | ||||
−0.898709 | + | 0.438546i | \(0.855494\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.20960 | 0.403207 | 0.201603 | − | 0.979467i | \(-0.435385\pi\) | ||||
0.201603 | + | 0.979467i | \(0.435385\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.1070 | − | 7.03597i | 1.33898 | − | 0.667825i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.3252 | 0.971316 | 0.485658 | − | 0.874149i | \(-0.338580\pi\) | ||||
0.485658 | + | 0.874149i | \(0.338580\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.472996 | − | 5.42979i | −0.0441071 | − | 0.506331i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.98421 | + | 10.6016i | −0.738140 | + | 0.980114i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.08854 | + | 0.414821i | 0.0997867 | + | 0.0380266i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.88445 | 0.807677 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.52415 | + | 7.06588i | 0.317762 | + | 0.637109i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.88155 | − | 10.8026i | −0.257734 | − | 0.966216i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.00291325i | 0.000258509i | 1.00000 | 0.000129255i | \(4.11430e-5\pi\) | |||||
−1.00000 | 0.000129255i | \(0.999959\pi\) | ||||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 13.2872 | − | 6.62708i | 1.16988 | − | 0.583482i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.00085 | 0.349556 | 0.174778 | − | 0.984608i | \(-0.444079\pi\) | ||||
0.174778 | + | 0.984608i | \(0.444079\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 16.1891 | + | 6.16933i | 1.40377 | + | 0.534949i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.11312 | + | 11.5655i | −0.0958021 | + | 0.995400i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −17.6484 | −1.50781 | −0.753903 | − | 0.656986i | \(-0.771831\pi\) | ||||
−0.753903 | + | 0.656986i | \(0.771831\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.22249i | 0.358147i | 0.983836 | + | 0.179073i | \(0.0573099\pi\) | ||||
−0.983836 | + | 0.179073i | \(0.942690\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.78210 | − | 4.87888i | 0.823801 | − | 0.410876i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 6.43458i | − | 0.538087i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.59822 | + | 0.836113i | −0.797089 | + | 0.0694354i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.18165 | + | 11.6994i | −0.262418 | + | 0.964954i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 17.7877i | − | 1.45723i | −0.684926 | − | 0.728613i | \(-0.740165\pi\) | ||
0.684926 | − | 0.728613i | \(-0.259835\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.17122 | −0.664965 | −0.332482 | − | 0.943109i | \(-0.607886\pi\) | ||||
−0.332482 | + | 0.943109i | \(0.607886\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.05512 | + | 0.794630i | 0.0853016 | + | 0.0642421i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.37760 | + | 0.555561i | −0.512261 | + | 0.0446237i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.0848924 | 0.00677515 | 0.00338758 | − | 0.999994i | \(-0.498922\pi\) | ||||
0.00338758 | + | 0.999994i | \(0.498922\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.24624 | + | 14.5286i | 0.574664 | + | 1.15219i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.29646 | − | 6.02621i | 0.180986 | − | 0.474932i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.9990i | 1.01816i | 0.860718 | + | 0.509082i | \(0.170015\pi\) | ||||
−0.860718 | + | 0.509082i | \(0.829985\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.94222 | − | 4.80381i | −0.229052 | − | 0.373976i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 0.585272i | − | 0.0452897i | −0.999744 | − | 0.0226449i | \(-0.992791\pi\) | ||
0.999744 | − | 0.0226449i | \(-0.00720870\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.57117 | 0.505475 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 15.6921 | + | 11.8180i | 1.20000 | + | 0.903741i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.4963i | 1.33022i | 0.746745 | + | 0.665111i | \(0.231616\pi\) | ||||
−0.746745 | + | 0.665111i | \(0.768384\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.50234 | − | 12.9899i | 0.189159 | − | 0.981946i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.44323 | + | 12.9186i | 0.484303 | + | 0.971022i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.2719i | 1.51519i | 0.652724 | + | 0.757596i | \(0.273626\pi\) | ||||
−0.652724 | + | 0.757596i | \(0.726374\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.9003i | 0.958871i | 0.877577 | + | 0.479435i | \(0.159159\pi\) | ||||
−0.877577 | + | 0.479435i | \(0.840841\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.0735 | − | 5.52297i | 0.818577 | − | 0.408270i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −20.2749 | + | 1.76617i | −1.49064 | + | 0.129851i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.640403 | −0.0468309 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.14975 | + | 11.7423i | −0.520068 | + | 0.854125i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 1.96182i | − | 0.141952i | −0.997478 | − | 0.0709760i | \(-0.977389\pi\) | ||
0.997478 | − | 0.0709760i | \(-0.0226114\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 17.9119i | − | 1.28933i | −0.764466 | − | 0.644664i | \(-0.776997\pi\) | ||
0.764466 | − | 0.644664i | \(-0.223003\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 14.6111 | − | 8.94896i | 1.04632 | − | 0.640848i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.2566 | −0.873249 | −0.436624 | − | 0.899644i | \(-0.643826\pi\) | ||||
−0.436624 | + | 0.899644i | \(0.643826\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.32283i | 0.0937726i | 0.998900 | + | 0.0468863i | \(0.0149298\pi\) | ||||
−0.998900 | + | 0.0468863i | \(0.985070\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 17.5903 | − | 8.77326i | 1.24072 | − | 0.618818i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.6525 | − | 4.05944i | −0.747659 | − | 0.284917i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.884632 | − | 10.1552i | −0.0617854 | − | 0.709269i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.39909 | − | 5.84118i | 0.305758 | − | 0.405990i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.52424 | −0.658806 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.1148 | 1.04054 | 0.520272 | − | 0.854001i | \(-0.325831\pi\) | ||||
0.520272 | + | 0.854001i | \(0.325831\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.74388 | − | 0.869771i | 0.119489 | − | 0.0595958i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −19.0966 | + | 1.66353i | −1.30238 | + | 0.113452i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.07813 | − | 2.69733i | −0.480495 | − | 0.183106i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.69088 | − | 17.4251i | −0.587275 | − | 1.17748i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 1.94783i | − | 0.131025i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.8929 | −1.53302 | −0.766511 | − | 0.642231i | \(-0.778009\pi\) | ||||
−0.766511 | + | 0.642231i | \(0.778009\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.81614 | − | 13.3619i | 0.454409 | − | 0.890793i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.5749i | 0.834629i | 0.908762 | + | 0.417314i | \(0.137029\pi\) | ||||
−0.908762 | + | 0.417314i | \(0.862971\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 0.500577i | − | 0.0330791i | −0.999863 | − | 0.0165395i | \(-0.994735\pi\) | ||
0.999863 | − | 0.0165395i | \(-0.00526494\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.655886 | − | 6.63298i | −0.0431541 | − | 0.436418i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.9171 | 0.846228 | 0.423114 | − | 0.906076i | \(-0.360937\pi\) | ||||
0.423114 | + | 0.906076i | \(0.360937\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.0590 | + | 1.22470i | −0.917107 | + | 0.0798903i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.28759 | − | 10.6016i | −0.343466 | − | 0.688645i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 27.1112i | 1.75368i | 0.480783 | + | 0.876840i | \(0.340353\pi\) | ||||
−0.480783 | + | 0.876840i | \(0.659647\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 4.75478i | − | 0.306282i | −0.988204 | − | 0.153141i | \(-0.951061\pi\) | ||
0.988204 | − | 0.153141i | \(-0.0489389\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.4857 | + | 10.5394i | −0.736806 | + | 0.676104i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.36374 | − | 12.5427i | 0.598227 | − | 0.801326i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 28.9686i | − | 1.84323i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.92061 | + | 4.44920i | −0.565321 | + | 0.281957i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.8100 | 0.682318 | 0.341159 | − | 0.940006i | \(-0.389181\pi\) | ||||
0.341159 | + | 0.940006i | \(0.389181\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.54529i | 0.222890i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.890647 | − | 1.45417i | −0.0557745 | − | 0.0910638i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 22.4592i | − | 1.40097i | −0.713669 | − | 0.700483i | \(-0.752968\pi\) | ||
0.713669 | − | 0.700483i | \(-0.247032\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −22.5019 | − | 8.57499i | −1.39820 | − | 0.532824i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.3254 | − | 7.77626i | −0.639128 | − | 0.481338i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.7846 | 1.09664 | 0.548322 | − | 0.836267i | \(-0.315267\pi\) | ||||
0.548322 | + | 0.836267i | \(0.315267\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.81895 | − | 20.8808i | −0.111737 | − | 1.28269i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.05653 | + | 18.1582i | 0.554251 | + | 1.11127i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.0968 | −0.981438 | −0.490719 | − | 0.871318i | \(-0.663266\pi\) | ||||
−0.490719 | + | 0.871318i | \(0.663266\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 9.44781i | − | 0.573914i | −0.957943 | − | 0.286957i | \(-0.907356\pi\) | ||
0.957943 | − | 0.286957i | \(-0.0926437\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 20.1746 | − | 1.99492i | 1.22102 | − | 0.120738i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.25749 | + | 7.16293i | 0.0758292 | + | 0.431941i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 4.67510i | − | 0.280899i | −0.990088 | − | 0.140450i | \(-0.955145\pi\) | ||
0.990088 | − | 0.140450i | \(-0.0448548\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.86081 | − | 5.16699i | −0.410746 | − | 0.309340i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.8520i | 0.707032i | 0.935429 | + | 0.353516i | \(0.115014\pi\) | ||||
−0.935429 | + | 0.353516i | \(0.884986\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.84917 | −0.347697 | −0.173849 | − | 0.984772i | \(-0.555620\pi\) | ||||
−0.173849 | + | 0.984772i | \(0.555620\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −13.2459 | − | 21.6268i | −0.784622 | − | 1.28106i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.29501 | − | 11.2707i | 0.253526 | − | 0.665285i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.8061 | 0.988597 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.85366 | − | 9.73154i | −0.284527 | − | 0.570473i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 0.346350i | − | 0.0202340i | −0.999949 | − | 0.0101170i | \(-0.996780\pi\) | ||
0.999949 | − | 0.0101170i | \(-0.00322040\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.61738 | − | 18.5668i | −0.0941675 | − | 1.08100i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.37418 | − | 7.43179i | 0.0797383 | − | 0.431236i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.7832 | −0.623609 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.1942 | − | 8.07667i | −1.22161 | − | 0.465531i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.93029 | − | 17.9051i | −0.513032 | − | 1.02862i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −15.9150 | + | 1.38638i | −0.911290 | + | 0.0793837i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.7866 | 1.41465 | 0.707323 | − | 0.706890i | \(-0.249902\pi\) | ||||
0.707323 | + | 0.706890i | \(0.249902\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.8783 | + | 27.8258i | 0.789508 | + | 1.58295i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.0969 | −0.742659 | −0.371330 | − | 0.928501i | \(-0.621098\pi\) | ||||
−0.371330 | + | 0.928501i | \(0.621098\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.69327 | 0.0957092 | 0.0478546 | − | 0.998854i | \(-0.484762\pi\) | ||||
0.0478546 | + | 0.998854i | \(0.484762\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 14.1494 | − | 10.7142i | 0.797229 | − | 0.603677i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 32.6867 | 1.83587 | 0.917934 | − | 0.396734i | \(-0.129857\pi\) | ||||
0.917934 | + | 0.396734i | \(0.129857\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.26699 | 0.350884 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.3731 | + | 28.8179i | 0.802228 | + | 1.60846i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.88311 | −0.160420 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −21.7865 | + | 3.82472i | −1.20850 | + | 0.212157i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.25425 | − | 6.52473i | −0.179960 | − | 0.360819i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −15.6032 | − | 5.94607i | −0.860234 | − | 0.327817i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.5819 | 1.24121 | 0.620606 | − | 0.784123i | \(-0.286887\pi\) | ||||
0.620606 | + | 0.784123i | \(0.286887\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −21.8110 | − | 16.4262i | −1.19524 | − | 0.900152i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −25.2810 | + | 2.20226i | −1.38125 | + | 0.120322i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 26.8892i | − | 1.46475i | −0.680901 | − | 0.732375i | \(-0.738412\pi\) | ||
0.680901 | − | 0.732375i | \(-0.261588\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.98195 | − | 16.0037i | −0.433520 | − | 0.869203i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.16414 | 0.225501 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.4399 | − | 8.52808i | 0.887674 | − | 0.460473i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.05033 | + | 4.93065i | −0.433415 | + | 0.265457i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 29.0533 | 1.55966 | 0.779831 | − | 0.625991i | \(-0.215305\pi\) | ||||
0.779831 | + | 0.625991i | \(0.215305\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 27.1001i | − | 1.45063i | −0.688416 | − | 0.725317i | \(-0.741693\pi\) | ||
0.688416 | − | 0.725317i | \(-0.258307\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 22.6042 | + | 4.17967i | 1.20653 | + | 0.223094i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.7715i | 0.626536i | 0.949665 | + | 0.313268i | \(0.101424\pi\) | ||||
−0.949665 | + | 0.313268i | \(0.898576\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.50633 | + | 0.218330i | −0.133022 | + | 0.0115878i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.198545 | − | 2.00788i | −0.0105081 | − | 0.106268i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 8.39177i | − | 0.442901i | −0.975172 | − | 0.221450i | \(-0.928921\pi\) | ||
0.975172 | − | 0.221450i | \(-0.0710791\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −23.8783 | −1.25675 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.86815 | − | 13.7706i | −0.360485 | − | 0.722768i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.18158 | + | 25.0436i | 0.114189 | + | 1.31084i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.13112 | −0.163443 | −0.0817216 | − | 0.996655i | \(-0.526042\pi\) | ||||
−0.0817216 | + | 0.996655i | \(0.526042\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.22750 | − | 10.9246i | 0.428307 | − | 0.568712i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.83125 | − | 23.1743i | 0.458496 | − | 1.20315i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.27241i | 0.480107i | 0.970760 | + | 0.240054i | \(0.0771650\pi\) | ||||
−0.970760 | + | 0.240054i | \(0.922835\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −14.5161 | + | 12.8173i | −0.749607 | + | 0.661883i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 19.0614i | 0.981714i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.4784 | 1.00054 | 0.500268 | − | 0.865871i | \(-0.333235\pi\) | ||||
0.500268 | + | 0.865871i | \(0.333235\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.00451543 | − | 0.00225210i | 0.000231333 | − | 0.000115378i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 1.95349i | − | 0.0998186i | −0.998754 | − | 0.0499093i | \(-0.984107\pi\) | ||
0.998754 | − | 0.0499093i | \(-0.0158932\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.35483 | + | 8.27642i | −0.120013 | + | 0.421805i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −20.5435 | − | 15.4716i | −1.04428 | − | 0.786468i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 1.48098i | − | 0.0750884i | −0.999295 | − | 0.0375442i | \(-0.988046\pi\) | ||
0.999295 | − | 0.0375442i | \(-0.0119535\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.07320i | 0.0542742i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.09287 | − | 6.20117i | −0.156015 | − | 0.312808i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.32729 | + | 15.2367i | 0.0667832 | + | 0.766642i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.9737 | −0.651132 | −0.325566 | − | 0.945519i | \(-0.605555\pi\) | ||||
−0.325566 | + | 0.945519i | \(0.605555\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.95281 | − | 29.8618i | −0.147825 | − | 1.49496i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.1453i | 1.55532i | 0.628683 | + | 0.777662i | \(0.283594\pi\) | ||||
−0.628683 | + | 0.777662i | \(0.716406\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.6655i | 0.630914i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18.7866 | − | 7.21546i | 0.933515 | − | 0.358539i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.2381 | 0.656189 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.3261i | 1.35119i | 0.737273 | + | 0.675594i | \(0.236113\pi\) | ||||
−0.737273 | + | 0.675594i | \(0.763887\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.6432 | + | 27.3544i | 0.672968 | + | 1.34929i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.85260 | − | 20.6062i | 0.386401 | − | 1.01397i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.8208 | − | 1.11684i | 0.629350 | − | 0.0548235i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.54470 | − | 3.26421i | 0.320495 | − | 0.159849i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.6777 | −1.20559 | −0.602793 | − | 0.797897i | \(-0.705946\pi\) | ||||
−0.602793 | + | 0.797897i | \(0.705946\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.5258 | 1.53647 | 0.768237 | − | 0.640165i | \(-0.221134\pi\) | ||||
0.768237 | + | 0.640165i | \(0.221134\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −15.1242 | − | 11.3903i | −0.735362 | − | 0.553814i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.380656 | + | 2.16831i | 0.0184645 | + | 0.105178i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17.6631 | − | 6.73105i | −0.854779 | − | 0.325738i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.97337 | + | 4.97427i | −0.481519 | + | 0.240160i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 24.6470i | − | 1.18720i | −0.804759 | − | 0.593602i | \(-0.797705\pi\) | ||
0.804759 | − | 0.593602i | \(-0.202295\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.3862 | −0.739412 | −0.369706 | − | 0.929149i | \(-0.620542\pi\) | ||||
−0.369706 | + | 0.929149i | \(0.620542\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.71588 | + | 14.2305i | 0.417895 | + | 0.682302i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.9609i | 0.763515i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 23.8686i | − | 1.13919i | −0.821926 | − | 0.569594i | \(-0.807101\pi\) | ||
0.821926 | − | 0.569594i | \(-0.192899\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.5933 | − | 4.11286i | 0.980634 | − | 0.195850i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.84558 | 0.182709 | 0.0913546 | − | 0.995818i | \(-0.470880\pi\) | ||||
0.0913546 | + | 0.995818i | \(0.470880\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.27337 | − | 26.0973i | −0.107768 | − | 1.23713i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −27.5703 | + | 13.7508i | −1.30403 | + | 0.650393i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 2.50182i | − | 0.118068i | −0.998256 | − | 0.0590340i | \(-0.981198\pi\) | ||
0.998256 | − | 0.0590340i | \(-0.0188020\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.63065i | 0.312225i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.31679 | + | 12.6651i | 0.296789 | + | 0.595058i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −25.1732 | − | 7.16235i | −1.18014 | − | 0.335776i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.4851i | 0.490472i | 0.969463 | + | 0.245236i | \(0.0788655\pi\) | ||||
−0.969463 | + | 0.245236i | \(0.921134\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.415982 | − | 2.24969i | 0.0194164 | − | 0.105007i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.6007 | 1.14577 | 0.572885 | − | 0.819636i | \(-0.305824\pi\) | ||||
0.572885 | + | 0.819636i | \(0.305824\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 1.28981i | − | 0.0599424i | −0.999551 | − | 0.0299712i | \(-0.990458\pi\) | ||
0.999551 | − | 0.0299712i | \(-0.00954156\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.79133 | + | 9.45558i | 0.268566 | + | 0.438492i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 40.9656i | − | 1.89566i | −0.318771 | − | 0.947832i | \(-0.603270\pi\) | ||
0.318771 | − | 0.947832i | \(-0.396730\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −28.0579 | − | 10.6923i | −1.29560 | − | 0.493724i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.0656264 | − | 0.131580i | −0.00302390 | − | 0.00606290i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.4688 | 0.573316 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.66122 | + | 32.2476i | 0.259755 | + | 1.47962i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.9171 | − | 22.4628i | 0.774582 | − | 1.02850i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 28.8388 | 1.31768 | 0.658838 | − | 0.752285i | \(-0.271048\pi\) | ||||
0.658838 | + | 0.752285i | \(0.271048\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 40.2645i | 1.83591i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −11.1157 | + | 1.09915i | −0.505782 | + | 0.0500130i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.21837 | + | 13.9863i | 0.0553232 | + | 0.635086i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 30.1405i | − | 1.36580i | −0.730514 | − | 0.682898i | \(-0.760720\pi\) | ||
0.730514 | − | 0.682898i | \(-0.239280\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 20.1480 | − | 10.0489i | 0.911126 | − | 0.454429i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 15.9029i | − | 0.717690i | −0.933397 | − | 0.358845i | \(-0.883171\pi\) | ||
0.933397 | − | 0.358845i | \(-0.116829\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.89709 | 0.0854408 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.17123 | + | 8.27394i | −0.232430 | + | 0.371886i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.78163 | − | 1.06002i | −0.124773 | − | 0.0475485i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.93099 | −0.0864429 | −0.0432214 | − | 0.999066i | \(-0.513762\pi\) | ||||
−0.0432214 | + | 0.999066i | \(0.513762\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.907151 | + | 0.452447i | −0.0405285 | + | 0.0202138i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.3348i | 0.460807i | 0.973095 | + | 0.230404i | \(0.0740046\pi\) | ||||
−0.973095 | + | 0.230404i | \(0.925995\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.24168 | + | 25.7335i | 0.0997535 | + | 1.14513i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.07987 | − | 10.1851i | −0.225605 | − | 0.452335i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.90113 | 0.438860 | 0.219430 | − | 0.975628i | \(-0.429580\pi\) | ||||
0.219430 | + | 0.975628i | \(0.429580\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.5919 | + | 27.7945i | −0.468558 | + | 1.22956i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.18660 | − | 33.4580i | 0.273145 | − | 1.47721i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.48372 | − | 39.9917i | −0.153511 | − | 1.76224i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.17956 | 0.403717 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 27.1187 | − | 13.5256i | 1.19038 | − | 0.593708i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.3619 | 0.979694 | 0.489847 | − | 0.871808i | \(-0.337053\pi\) | ||||
0.489847 | + | 0.871808i | \(0.337053\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 39.1612 | 1.71240 | 0.856201 | − | 0.516643i | \(-0.172819\pi\) | ||||
0.856201 | + | 0.516643i | \(0.172819\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −22.0684 | + | 6.16338i | −0.963142 | + | 0.268992i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.26054 | 0.0549099 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.0587 | −0.741684 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15.0424 | − | 19.9735i | 0.652785 | − | 0.866778i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −20.1675 | −0.873553 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.60793 | − | 41.4175i | −0.155985 | − | 1.79064i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 31.4207 | − | 15.6712i | 1.35590 | − | 0.676264i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.77587 | + | 7.59931i | −0.291858 | + | 0.327325i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.7660 | 0.548853 | 0.274427 | − | 0.961608i | \(-0.411512\pi\) | ||||
0.274427 | + | 0.961608i | \(0.411512\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 19.9950 | − | 9.97261i | 0.858067 | − | 0.427966i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.816881 | + | 9.37745i | 0.0349913 | + | 0.401686i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.1815i | 0.777383i | 0.921368 | + | 0.388691i | \(0.127073\pi\) | ||||
−0.921368 | + | 0.388691i | \(0.872927\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −17.1208 | − | 12.8940i | −0.730699 | − | 0.550301i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 28.2141 | 1.20196 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.44417 | + | 16.9103i | −0.274034 | + | 0.719101i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 18.4110 | + | 30.0600i | 0.781505 | + | 1.27597i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.18158 | 0.0924367 | 0.0462183 | − | 0.998931i | \(-0.485283\pi\) | ||||
0.0462183 | + | 0.998931i | \(0.485283\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 37.9246i | 1.60404i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.495066 | + | 0.992602i | 0.0209017 | + | 0.0419077i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 36.6727i | 1.54557i | 0.634667 | + | 0.772786i | \(0.281137\pi\) | ||||
−0.634667 | + | 0.772786i | \(0.718863\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.00363 | + | 23.0008i | 0.0842933 | + | 0.967651i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.7272 | + | 2.00445i | 0.996451 | + | 0.0841792i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 6.87817i | − | 0.288348i | −0.989552 | − | 0.144174i | \(-0.953948\pi\) | ||
0.989552 | − | 0.144174i | \(-0.0460525\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.8721 | −0.915319 | −0.457659 | − | 0.889128i | \(-0.651312\pi\) | ||||
−0.457659 | + | 0.889128i | \(0.651312\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.04074 | + | 1.51659i | −0.127029 | + | 0.0633564i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.0038 | − | 2.10732i | 0.500593 | − | 0.0878814i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −40.0096 | −1.66562 | −0.832810 | − | 0.553559i | \(-0.813269\pi\) | ||||
−0.832810 | + | 0.553559i | \(0.813269\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −27.7628 | + | 13.8469i | −1.15378 | + | 0.575456i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.2291 | + | 5.42241i | 0.590322 | + | 0.224959i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.6337i | 0.564651i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −25.1657 | − | 15.7286i | −1.04047 | − | 0.650299i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.0493i | 0.621151i | 0.950549 | + | 0.310576i | \(0.100522\pi\) | ||||
−0.950549 | + | 0.310576i | \(0.899478\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.7470 | 0.772459 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.47503 | + | 18.9973i | 0.389751 | + | 0.781446i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 39.0931i | − | 1.60536i | −0.596408 | − | 0.802681i | \(-0.703406\pi\) | ||
0.596408 | − | 0.802681i | \(-0.296594\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.712835 | + | 2.50537i | −0.0292234 | + | 0.102710i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.05033 | − | 1.02261i | 0.0839145 | − | 0.0418528i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.1576i | 0.578463i | 0.957259 | + | 0.289231i | \(0.0933997\pi\) | ||||
−0.957259 | + | 0.289231i | \(0.906600\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.57952i | 0.186803i | 0.995629 | + | 0.0934013i | \(0.0297740\pi\) | ||||
−0.995629 | + | 0.0934013i | \(0.970226\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −27.1965 | − | 20.4821i | −1.10753 | − | 0.834096i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.72404 | + | 19.7913i | 0.0700923 | + | 0.804630i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.3014 | 0.905188 | 0.452594 | − | 0.891717i | \(-0.350499\pi\) | ||||
0.452594 | + | 0.891717i | \(0.350499\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.94296 | + | 19.6492i | 0.0787327 | + | 0.796224i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 27.9202i | 1.12953i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 44.5311i | 1.79859i | 0.437340 | + | 0.899296i | \(0.355921\pi\) | ||||
−0.437340 | + | 0.899296i | \(0.644079\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −15.0563 | + | 9.22165i | −0.607129 | + | 0.371853i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.11299 | −0.165583 | −0.0827913 | − | 0.996567i | \(-0.526383\pi\) | ||||
−0.0827913 | + | 0.996567i | \(0.526383\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 8.36511i | − | 0.336222i | −0.985768 | − | 0.168111i | \(-0.946233\pi\) | ||
0.985768 | − | 0.168111i | \(-0.0537667\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −12.4544 | − | 2.30289i | −0.499776 | − | 0.0924118i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.0375 | − | 28.9639i | 0.442209 | − | 1.16041i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.5051 | − | 8.51530i | 0.940204 | − | 0.340612i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.36275 | + | 14.7622i | 0.294040 | + | 0.589547i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.00734 | 0.159783 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.3025 | 0.648991 | 0.324496 | − | 0.945887i | \(-0.394805\pi\) | ||||
0.324496 | + | 0.945887i | \(0.394805\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11.6845 | − | 23.4273i | −0.464418 | − | 0.931153i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.00648965 | 0.000565321i | −0.000257534 | 2.24341e-5i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −23.1138 | − | 20.6092i | −0.915801 | − | 0.816568i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.69623 | − | 2.03058i | −0.106661 | − | 0.0803283i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 45.8483i | − | 1.81090i | −0.424455 | − | 0.905449i | \(-0.639534\pi\) | ||
0.424455 | − | 0.905449i | \(-0.360466\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.3467 | 1.03901 | 0.519505 | − | 0.854467i | \(-0.326116\pi\) | ||||
0.519505 | + | 0.854467i | \(0.326116\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 17.3411 | + | 28.3131i | 0.682806 | + | 1.11483i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.41576i | 0.173601i | 0.996226 | + | 0.0868007i | \(0.0276643\pi\) | ||||
−0.996226 | + | 0.0868007i | \(0.972336\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.1229i | 0.475865i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.29101 | + | 13.0560i | 0.0505988 | + | 0.511706i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −46.8989 | −1.83530 | −0.917648 | − | 0.397393i | \(-0.869915\pi\) | ||||
−0.917648 | + | 0.397393i | \(0.869915\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.776372 | + | 8.91242i | 0.0303354 | + | 0.348237i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −20.2898 | + | 26.9411i | −0.791580 | + | 1.05107i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26.9930i | 1.05150i | 0.850640 | + | 0.525748i | \(0.176215\pi\) | ||||
−0.850640 | + | 0.525748i | \(0.823785\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 22.4053i | − | 0.871467i | −0.900076 | − | 0.435733i | \(-0.856489\pi\) | ||
0.900076 | − | 0.435733i | \(-0.143511\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.01906 | + | 1.50577i | −0.117251 | + | 0.0584794i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10.6015 | + | 37.2606i | −0.411107 | + | 1.44490i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 10.5024i | − | 0.406653i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 17.6974 | + | 35.4832i | 0.684222 | + | 1.37186i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.3914 | 0.401156 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.7897i | 0.531554i | 0.964035 | + | 0.265777i | \(0.0856284\pi\) | ||||
−0.964035 | + | 0.265777i | \(0.914372\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −25.9797 | − | 0.235312i | −0.999959 | − | 0.00905717i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 36.5086i | − | 1.40314i | −0.712600 | − | 0.701570i | \(-0.752483\pi\) | ||
0.712600 | − | 0.701570i | \(-0.247517\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.91534 | + | 15.5226i | −0.227010 | + | 0.595703i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.4907 | − | 9.72111i | 0.746886 | − | 0.372514i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −31.7095 | −1.21333 | −0.606666 | − | 0.794957i | \(-0.707493\pi\) | ||||
−0.606666 | + | 0.794957i | \(0.707493\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.42471 | − | 39.3142i | −0.130851 | − | 1.50212i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.775877 | + | 0.386973i | −0.0296015 | + | 0.0147639i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −41.4678 | −1.57980 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 30.2906i | − | 1.15231i | −0.817340 | − | 0.576155i | \(-0.804552\pi\) | ||
0.817340 | − | 0.576155i | \(-0.195448\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.77384 | + | 6.14425i | −0.371277 | + | 0.233401i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.40615 | + | 0.819381i | −0.356795 | + | 0.0310809i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.00718i | 0.0760274i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.98562 | − | 20.0211i | −0.377691 | − | 0.757266i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 23.8010i | − | 0.898952i | −0.893293 | − | 0.449476i | \(-0.851611\pi\) | ||
0.893293 | − | 0.449476i | \(-0.148389\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 59.5982 | 2.24779 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12.7666 | + | 20.8442i | 0.480817 | + | 0.785036i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.8837 | + | 28.5602i | −0.409323 | + | 1.07412i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −39.8188 | −1.49543 | −0.747714 | − | 0.664021i | \(-0.768849\pi\) | ||||
−0.747714 | + | 0.664021i | \(0.768849\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.3444 | + | 16.3911i | −0.462953 | + | 0.614716i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 6.97837i | − | 0.261342i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.3339 | − | 1.24864i | 0.536057 | − | 0.0466966i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 42.0214 | − | 20.9584i | 1.56932 | − | 0.782707i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.97913 | 0.372159 | 0.186079 | − | 0.982535i | \(-0.440422\pi\) | ||||
0.186079 | + | 0.982535i | \(0.440422\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.9140 | − | 44.3844i | 0.629909 | − | 1.65296i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.36973 | + | 3.67570i | −0.274083 | + | 0.136701i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.72510 | − | 21.2190i | −0.138347 | − | 0.788056i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31.2440 | −1.15878 | −0.579388 | − | 0.815052i | \(-0.696709\pi\) | ||||
−0.579388 | + | 0.815052i | \(0.696709\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.2148 | + | 9.65484i | 0.933880 | + | 0.357587i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.77446 | 0.139603 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.4386 | −0.385558 | −0.192779 | − | 0.981242i | \(-0.561750\pi\) | ||||
−0.192779 | + | 0.981242i | \(0.561750\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −26.6795 | − | 4.81725i | −0.984087 | − | 0.177687i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.5068 | 0.608036 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.7381 | −0.873218 | −0.436609 | − | 0.899651i | \(-0.643821\pi\) | ||||
−0.436609 | + | 0.899651i | \(0.643821\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −44.9003 | + | 22.3943i | −1.64945 | + | 0.822674i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.6347 | −0.610269 | −0.305135 | − | 0.952309i | \(-0.598701\pi\) | ||||
−0.305135 | + | 0.952309i | \(0.598701\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 39.6245 | − | 3.45174i | 1.45173 | − | 0.126462i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.7922 | + | 10.3871i | 0.504631 | + | 0.380046i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.5170 | − | 45.9669i | 0.640058 | − | 1.67959i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.46709 | −0.272478 | −0.136239 | − | 0.990676i | \(-0.543501\pi\) | ||||
−0.136239 | + | 0.990676i | \(0.543501\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.35667 | − | 16.7550i | −0.304534 | − | 0.610587i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.58564 | − | 18.2025i | −0.0577074 | − | 0.662456i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.54945i | 0.238044i | 0.992892 | + | 0.119022i | \(0.0379759\pi\) | ||||
−0.992892 | + | 0.119022i | \(0.962024\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.49507 | − | 2.74070i | 0.199458 | − | 0.0994810i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.5194 | −0.453826 | −0.226913 | − | 0.973915i | \(-0.572863\pi\) | ||||
−0.226913 | + | 0.973915i | \(0.572863\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.96607 | + | 10.4075i | −0.143581 | + | 0.376776i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.56540 | + | 2.50462i | −0.0565970 | + | 0.0905549i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −36.8725 | −1.33139 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 15.0198i | − | 0.541629i | −0.962632 | − | 0.270815i | \(-0.912707\pi\) | ||
0.962632 | − | 0.270815i | \(-0.0872931\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −34.8110 | + | 17.3622i | −1.25369 | + | 0.625283i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.2676i | 1.12462i | 0.826927 | + | 0.562309i | \(0.190087\pi\) | ||||
−0.826927 | + | 0.562309i | \(0.809913\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.47517 | − | 14.0991i | −0.0889108 | − | 0.506456i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.10422 | + | 41.5060i | 0.147238 | + | 1.48902i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 29.8513i | 1.06953i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.63647 | 0.0585574 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.07081 | + | 22.0155i | −0.145479 | + | 0.786770i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.0164735 | + | 0.189109i | 0.000587966 | + | 0.00674959i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.0233 | −0.785048 | −0.392524 | − | 0.919742i | \(-0.628398\pi\) | ||||
−0.392524 | + | 0.919742i | \(0.628398\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13.7484 | − | 27.5654i | −0.489457 | − | 0.981356i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.72790 | + | 25.5272i | −0.345884 | + | 0.907644i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 31.6062i | 1.12237i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −30.9583 | + | 18.9613i | −1.09798 | + | 0.672486i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.33314i | 0.295175i | 0.989049 | + | 0.147587i | \(0.0471508\pi\) | ||||
−0.989049 | + | 0.147587i | \(0.952849\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.77877 | 0.0983057 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 21.1434 | − | 28.0746i | 0.747067 | − | 0.991967i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 16.3518i | − | 0.577043i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.8698 | + | 3.94627i | 0.488846 | + | 0.139088i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.4437 | + | 24.9494i | 0.438038 | + | 0.878261i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 5.19293i | − | 0.182574i | −0.995825 | − | 0.0912868i | \(-0.970902\pi\) | ||
0.995825 | − | 0.0912868i | \(-0.0290980\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 30.8998i | − | 1.08504i | −0.840044 | − | 0.542519i | \(-0.817471\pi\) | ||
0.840044 | − | 0.542519i | \(-0.182529\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −14.6438 | + | 7.30367i | −0.513579 | + | 0.256151i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −28.9571 | + | 2.52249i | −1.01432 | + | 0.0883589i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 56.1347 | 1.96391 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −18.6881 | − | 29.7277i | −0.653015 | − | 1.03877i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 16.6956i | − | 0.582679i | −0.956620 | − | 0.291340i | \(-0.905899\pi\) | ||
0.956620 | − | 0.291340i | \(-0.0941010\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30.9576i | 1.07911i | 0.841949 | + | 0.539557i | \(0.181408\pi\) | ||||
−0.841949 | + | 0.539557i | \(0.818592\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10.1302 | − | 7.48638i | 0.352687 | − | 0.260642i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.6612 | 0.857555 | 0.428777 | − | 0.903410i | \(-0.358944\pi\) | ||||
0.428777 | + | 0.903410i | \(0.358944\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.6977i | 0.927249i | 0.886032 | + | 0.463625i | \(0.153451\pi\) | ||||
−0.886032 | + | 0.463625i | \(0.846549\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.24624 | + | 3.61410i | −0.251369 | + | 0.125372i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.05114 | + | 2.30040i | −0.0710678 | + | 0.0797043i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.30377 | − | 0.113573i | 0.0451189 | − | 0.00393036i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.70488 | + | 14.6284i | −0.0934942 | + | 0.505630i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 51.2367 | 1.76889 | 0.884443 | − | 0.466647i | \(-0.154538\pi\) | ||||
0.884443 | + | 0.466647i | \(0.154538\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.4350 | 0.359828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 18.3702 | − | 9.16224i | 0.632703 | − | 0.315564i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.27515 | + | 14.6382i | 0.0438664 | + | 0.503568i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.37047 | + | 21.9652i | −0.287613 | + | 0.754733i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.52172 | + | 9.06600i | 0.155185 | + | 0.311144i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 22.1847i | − | 0.760483i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.3303 | −0.524901 | −0.262450 | − | 0.964946i | \(-0.584531\pi\) | ||||
−0.262450 | + | 0.964946i | \(0.584531\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −23.2810 | + | 37.2494i | −0.796193 | + | 1.27390i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.2905i | 0.351518i | 0.984433 | + | 0.175759i | \(0.0562379\pi\) | ||||
−0.984433 | + | 0.175759i | \(0.943762\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 19.8890i | − | 0.678603i | −0.940678 | − | 0.339301i | \(-0.889809\pi\) | ||
0.940678 | − | 0.339301i | \(-0.110191\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −20.7894 | + | 2.05571i | −0.708500 | + | 0.0700583i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.8374 | 0.607193 | 0.303596 | − | 0.952801i | \(-0.401813\pi\) | ||||
0.303596 | + | 0.952801i | \(0.401813\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −38.9754 | + | 3.39520i | −1.32520 | + | 0.115440i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12.9920 | − | 26.0489i | −0.441233 | − | 0.884668i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 9.94855i | − | 0.337481i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 50.2065i | 1.70118i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11.3314 | + | 15.0460i | −0.383510 | + | 0.509230i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 29.4224 | + | 3.05357i | 0.994658 | + | 0.103230i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.09995i | 0.273516i | 0.990604 | + | 0.136758i | \(0.0436682\pi\) | ||||
−0.990604 | + | 0.136758i | \(0.956332\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.536831 | + | 0.267747i | −0.0181068 | + | 0.00903089i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −46.3728 | −1.56234 | −0.781169 | − | 0.624319i | \(-0.785376\pi\) | ||||
−0.781169 | + | 0.624319i | \(0.785376\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.51933i | 0.286698i | 0.989672 | + | 0.143349i | \(0.0457872\pi\) | ||||
−0.989672 | + | 0.143349i | \(0.954213\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −27.5276 | + | 16.8600i | −0.925330 | + | 0.566744i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 54.7644i | − | 1.83881i | −0.393312 | − | 0.919405i | \(-0.628671\pi\) | ||
0.393312 | − | 0.919405i | \(-0.371329\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.00720248 | − | 0.00274471i | −0.000241563 | − | 9.20547e-5i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −12.5813 | + | 3.61523i | −0.421490 | + | 0.121115i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 41.3265 | 1.38294 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −45.1583 | + | 3.93380i | −1.50947 | + | 0.131492i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.33600 | + | 16.7136i | 0.278331 | + | 0.558051i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.3356 | −0.411416 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.12710i | 0.137494i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.86571 | + | 39.0940i | 0.128643 | + | 1.30097i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −28.7371 | + | 2.50332i | −0.955253 | + | 0.0832133i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 20.6308i | − | 0.685036i | −0.939511 | − | 0.342518i | \(-0.888720\pi\) | ||
0.939511 | − | 0.342518i | \(-0.111280\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −20.8487 | + | 27.6833i | −0.691509 | + | 0.918196i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.4837i | 0.844313i | 0.906523 | + | 0.422156i | \(0.138727\pi\) | ||||
−0.906523 | + | 0.422156i | \(0.861273\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.37114 | −0.277044 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 14.4520 | + | 23.5959i | 0.477768 | + | 0.780058i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.76939 | + | 9.89137i | −0.124476 | + | 0.326642i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.9121 | −0.590865 | −0.295432 | − | 0.955364i | \(-0.595464\pi\) | ||||
−0.295432 | + | 0.955364i | \(0.595464\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −19.1614 | − | 38.4184i | −0.631389 | − | 1.26593i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.97742i | 0.163834i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.86875 | − | 44.8222i | −0.258723 | − | 1.47374i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 32.4003 | − | 43.0217i | 1.06417 | − | 1.41302i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.9000 | 0.357616 | 0.178808 | − | 0.983884i | \(-0.442776\pi\) | ||||
0.178808 | + | 0.983884i | \(0.442776\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −30.5051 | + | 34.2122i | −0.999764 | + | 1.12126i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.1246 | + | 20.2998i | 0.331466 | + | 0.664585i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.124271 | − | 1.42658i | −0.00406411 | − | 0.0466542i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.9791 | −0.881368 | −0.440684 | − | 0.897662i | \(-0.645264\pi\) | ||||
−0.440684 | + | 0.897662i | \(0.645264\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.30899 | − | 2.62451i | −0.0427172 | − | 0.0856475i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.6275 | 1.22662 | 0.613310 | − | 0.789842i | \(-0.289838\pi\) | ||||
0.613310 | + | 0.789842i | \(0.289838\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.1118 | 0.361850 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −27.5449 | − | 13.6484i | −0.896035 | − | 0.443983i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.38298 | −0.0774364 | −0.0387182 | − | 0.999250i | \(-0.512327\pi\) | ||||
−0.0387182 | + | 0.999250i | \(0.512327\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 49.7351 | 1.61447 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −25.2686 | − | 50.6632i | −0.819389 | − | 1.64287i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10.3582 | −0.335534 | −0.167767 | − | 0.985827i | \(-0.553656\pi\) | ||||
−0.167767 | + | 0.985827i | \(0.553656\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.37020 | − | 0.380694i | 0.141416 | − | 0.0123190i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.84472 | − | 9.71361i | −0.156607 | − | 0.313996i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.6274 | − | 43.6325i | 0.536928 | − | 1.40897i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.8035 | 0.735597 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 33.5555 | − | 44.5556i | 1.08131 | − | 1.43578i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 39.9012 | − | 3.47584i | 1.28446 | − | 0.111891i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.3006i | 0.331245i | 0.986189 | + | 0.165622i | \(0.0529633\pi\) | ||||
−0.986189 | + | 0.165622i | \(0.947037\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.22879 | + | 4.46871i | 0.0715992 | + | 0.143556i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.2487 | 0.585629 | 0.292814 | − | 0.956169i | \(-0.405408\pi\) | ||||
0.292814 | + | 0.956169i | \(0.405408\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.4393 | − | 3.97821i | −0.334670 | − | 0.127536i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 22.7703 | + | 30.8116i | 0.729233 | + | 0.986759i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 34.9393 | 1.11781 | 0.558904 | − | 0.829233i | \(-0.311222\pi\) | ||||
0.558904 | + | 0.829233i | \(0.311222\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.0398i | 0.544594i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.59739 | + | 10.0879i | −0.242566 | + | 0.322083i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 37.9493i | 1.21039i | 0.796076 | + | 0.605197i | \(0.206906\pi\) | ||||
−0.796076 | + | 0.605197i | \(0.793094\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.37842 | − | 27.3033i | −0.0757828 | − | 0.869954i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.84595 | + | 28.7811i | 0.0905875 | + | 0.916112i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 20.8955i | − | 0.664438i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.9068 | −0.632359 | −0.316180 | − | 0.948699i | \(-0.602400\pi\) | ||||
−0.316180 | + | 0.948699i | \(0.602400\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −17.4570 | − | 35.0011i | −0.553981 | − | 1.11073i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.94677 | + | 0.256697i | −0.0934188 | + | 0.00813783i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 43.8198 | 1.38779 | 0.693893 | − | 0.720078i | \(-0.255894\pi\) | ||||
0.693893 | + | 0.720078i | \(0.255894\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.59899 | + | 46.5046i | −0.272060 | + | 1.47134i |
(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 | 1680.2.k.h.209.7 | 24 | ||
3.2 | odd | 2 | 1680.2.k.i.209.8 | 24 | |||
4.3 | odd | 2 | 840.2.k.b.209.18 | yes | 24 | ||
5.4 | even | 2 | 1680.2.k.i.209.18 | 24 | |||
7.6 | odd | 2 | inner | 1680.2.k.h.209.18 | 24 | ||
12.11 | even | 2 | 840.2.k.a.209.17 | yes | 24 | ||
15.14 | odd | 2 | inner | 1680.2.k.h.209.17 | 24 | ||
20.19 | odd | 2 | 840.2.k.a.209.7 | ✓ | 24 | ||
21.20 | even | 2 | 1680.2.k.i.209.17 | 24 | |||
28.27 | even | 2 | 840.2.k.b.209.7 | yes | 24 | ||
35.34 | odd | 2 | 1680.2.k.i.209.7 | 24 | |||
60.59 | even | 2 | 840.2.k.b.209.8 | yes | 24 | ||
84.83 | odd | 2 | 840.2.k.a.209.8 | yes | 24 | ||
105.104 | even | 2 | inner | 1680.2.k.h.209.8 | 24 | ||
140.139 | even | 2 | 840.2.k.a.209.18 | yes | 24 | ||
420.419 | odd | 2 | 840.2.k.b.209.17 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
840.2.k.a.209.7 | ✓ | 24 | 20.19 | odd | 2 | ||
840.2.k.a.209.8 | yes | 24 | 84.83 | odd | 2 | ||
840.2.k.a.209.17 | yes | 24 | 12.11 | even | 2 | ||
840.2.k.a.209.18 | yes | 24 | 140.139 | even | 2 | ||
840.2.k.b.209.7 | yes | 24 | 28.27 | even | 2 | ||
840.2.k.b.209.8 | yes | 24 | 60.59 | even | 2 | ||
840.2.k.b.209.17 | yes | 24 | 420.419 | odd | 2 | ||
840.2.k.b.209.18 | yes | 24 | 4.3 | odd | 2 | ||
1680.2.k.h.209.7 | 24 | 1.1 | even | 1 | trivial | ||
1680.2.k.h.209.8 | 24 | 105.104 | even | 2 | inner | ||
1680.2.k.h.209.17 | 24 | 15.14 | odd | 2 | inner | ||
1680.2.k.h.209.18 | 24 | 7.6 | odd | 2 | inner | ||
1680.2.k.i.209.7 | 24 | 35.34 | odd | 2 | |||
1680.2.k.i.209.8 | 24 | 3.2 | odd | 2 | |||
1680.2.k.i.209.17 | 24 | 21.20 | even | 2 | |||
1680.2.k.i.209.18 | 24 | 5.4 | even | 2 |