Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1380,2,Mod(91,1380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1380.91");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1380.p (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.0193554789\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.7 | ||
Character | \(\chi\) | \(=\) | 1380.91 |
Dual form | 1380.2.p.b.91.8 |
$q$-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 \(\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(691\) | \(1201\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.25058 | − | 0.660333i | −0.884296 | − | 0.466926i | ||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 1.12792 | + | 1.65160i | 0.563960 | + | 0.825802i | ||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | −0.660333 | + | 1.25058i | −0.269580 | + | 0.510549i | ||||
\(7\) | 3.91467 | 1.47961 | 0.739803 | − | 0.672824i | \(-0.234919\pi\) | ||||
0.739803 | + | 0.672824i | \(0.234919\pi\) | |||||||
\(8\) | −0.319949 | − | 2.81027i | −0.113119 | − | 0.993581i | ||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0.660333 | − | 1.25058i | 0.208816 | − | 0.395469i | ||||
\(11\) | 3.56454 | 1.07475 | 0.537375 | − | 0.843344i | \(-0.319416\pi\) | ||||
0.537375 | + | 0.843344i | \(0.319416\pi\) | |||||||
\(12\) | 1.65160 | − | 1.12792i | 0.476777 | − | 0.325602i | ||||
\(13\) | −6.21448 | −1.72359 | −0.861793 | − | 0.507259i | \(-0.830659\pi\) | ||||
−0.861793 | + | 0.507259i | \(0.830659\pi\) | |||||||
\(14\) | −4.89562 | − | 2.58498i | −1.30841 | − | 0.690866i | ||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | −1.45559 | + | 3.72575i | −0.363898 | + | 0.931439i | ||||
\(17\) | − | 6.87185i | − | 1.66667i | −0.552769 | − | 0.833335i | \(-0.686429\pi\) | ||
0.552769 | − | 0.833335i | \(-0.313571\pi\) | |||||||
\(18\) | 1.25058 | + | 0.660333i | 0.294765 | + | 0.155642i | ||||
\(19\) | −5.29017 | −1.21365 | −0.606824 | − | 0.794836i | \(-0.707557\pi\) | ||||
−0.606824 | + | 0.794836i | \(0.707557\pi\) | |||||||
\(20\) | −1.65160 | + | 1.12792i | −0.369310 | + | 0.252211i | ||||
\(21\) | − | 3.91467i | − | 0.854250i | ||||||
\(22\) | −4.45776 | − | 2.35379i | −0.950397 | − | 0.501829i | ||||
\(23\) | −3.05366 | − | 3.69800i | −0.636732 | − | 0.771085i | ||||
\(24\) | −2.81027 | + | 0.319949i | −0.573645 | + | 0.0653094i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 7.77173 | + | 4.10363i | 1.52416 | + | 0.804788i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 4.41543 | + | 6.46548i | 0.834438 | + | 1.22186i | ||||
\(29\) | 7.14975 | 1.32768 | 0.663838 | − | 0.747876i | \(-0.268926\pi\) | ||||
0.663838 | + | 0.747876i | \(0.268926\pi\) | |||||||
\(30\) | −1.25058 | − | 0.660333i | −0.228324 | − | 0.120560i | ||||
\(31\) | − | 5.49174i | − | 0.986346i | −0.869931 | − | 0.493173i | \(-0.835837\pi\) | ||
0.869931 | − | 0.493173i | \(-0.164163\pi\) | |||||||
\(32\) | 4.28058 | − | 3.69819i | 0.756707 | − | 0.653754i | ||||
\(33\) | − | 3.56454i | − | 0.620507i | ||||||
\(34\) | −4.53771 | + | 8.59383i | −0.778212 | + | 1.47383i | ||||
\(35\) | 3.91467i | 0.661699i | ||||||||
\(36\) | −1.12792 | − | 1.65160i | −0.187987 | − | 0.275267i | ||||
\(37\) | 1.30997i | 0.215358i | 0.994186 | + | 0.107679i | \(0.0343419\pi\) | ||||
−0.994186 | + | 0.107679i | \(0.965658\pi\) | |||||||
\(38\) | 6.61580 | + | 3.49327i | 1.07322 | + | 0.566684i | ||||
\(39\) | 6.21448i | 0.995113i | ||||||||
\(40\) | 2.81027 | − | 0.319949i | 0.444343 | − | 0.0505884i | ||||
\(41\) | 10.4481 | 1.63172 | 0.815860 | − | 0.578250i | \(-0.196264\pi\) | ||||
0.815860 | + | 0.578250i | \(0.196264\pi\) | |||||||
\(42\) | −2.58498 | + | 4.89562i | −0.398872 | + | 0.755410i | ||||
\(43\) | −3.43010 | −0.523086 | −0.261543 | − | 0.965192i | \(-0.584231\pi\) | ||||
−0.261543 | + | 0.965192i | \(0.584231\pi\) | |||||||
\(44\) | 4.02052 | + | 5.88721i | 0.606116 | + | 0.887530i | ||||
\(45\) | − | 1.00000i | − | 0.149071i | ||||||
\(46\) | 1.37695 | + | 6.64109i | 0.203020 | + | 0.979175i | ||||
\(47\) | − | 2.84469i | − | 0.414940i | −0.978241 | − | 0.207470i | \(-0.933477\pi\) | ||
0.978241 | − | 0.207470i | \(-0.0665230\pi\) | |||||||
\(48\) | 3.72575 | + | 1.45559i | 0.537766 | + | 0.210097i | ||||
\(49\) | 8.32462 | 1.18923 | ||||||||
\(50\) | 1.25058 | + | 0.660333i | 0.176859 | + | 0.0933852i | ||||
\(51\) | −6.87185 | −0.962252 | ||||||||
\(52\) | −7.00944 | − | 10.2639i | −0.972034 | − | 1.42334i | ||||
\(53\) | − | 11.0291i | − | 1.51497i | −0.652855 | − | 0.757483i | \(-0.726429\pi\) | ||
0.652855 | − | 0.757483i | \(-0.273571\pi\) | |||||||
\(54\) | 0.660333 | − | 1.25058i | 0.0898600 | − | 0.170183i | ||||
\(55\) | 3.56454i | 0.480643i | ||||||||
\(56\) | −1.25250 | − | 11.0013i | −0.167372 | − | 1.47011i | ||||
\(57\) | 5.29017i | 0.700700i | ||||||||
\(58\) | −8.94137 | − | 4.72122i | −1.17406 | − | 0.619927i | ||||
\(59\) | − | 5.12833i | − | 0.667652i | −0.942635 | − | 0.333826i | \(-0.891660\pi\) | ||
0.942635 | − | 0.333826i | \(-0.108340\pi\) | |||||||
\(60\) | 1.12792 | + | 1.65160i | 0.145614 | + | 0.213221i | ||||
\(61\) | − | 5.14642i | − | 0.658932i | −0.944168 | − | 0.329466i | \(-0.893131\pi\) | ||
0.944168 | − | 0.329466i | \(-0.106869\pi\) | |||||||
\(62\) | −3.62638 | + | 6.86788i | −0.460551 | + | 0.872222i | ||||
\(63\) | −3.91467 | −0.493202 | ||||||||
\(64\) | −7.79526 | + | 1.79829i | −0.974408 | + | 0.224786i | ||||
\(65\) | − | 6.21448i | − | 0.770811i | ||||||
\(66\) | −2.35379 | + | 4.45776i | −0.289731 | + | 0.548712i | ||||
\(67\) | 14.0791 | 1.72004 | 0.860019 | − | 0.510262i | \(-0.170451\pi\) | ||||
0.860019 | + | 0.510262i | \(0.170451\pi\) | |||||||
\(68\) | 11.3496 | − | 7.75090i | 1.37634 | − | 0.939935i | ||||
\(69\) | −3.69800 | + | 3.05366i | −0.445186 | + | 0.367617i | ||||
\(70\) | 2.58498 | − | 4.89562i | 0.308965 | − | 0.585138i | ||||
\(71\) | 11.6817i | 1.38636i | 0.720764 | + | 0.693181i | \(0.243791\pi\) | ||||
−0.720764 | + | 0.693181i | \(0.756209\pi\) | |||||||
\(72\) | 0.319949 | + | 2.81027i | 0.0377064 | + | 0.331194i | ||||
\(73\) | 11.4110 | 1.33556 | 0.667780 | − | 0.744359i | \(-0.267245\pi\) | ||||
0.667780 | + | 0.744359i | \(0.267245\pi\) | |||||||
\(74\) | 0.865019 | − | 1.63823i | 0.100556 | − | 0.190441i | ||||
\(75\) | 1.00000i | 0.115470i | ||||||||
\(76\) | −5.96689 | − | 8.73726i | −0.684449 | − | 1.00223i | ||||
\(77\) | 13.9540 | 1.59020 | ||||||||
\(78\) | 4.10363 | − | 7.77173i | 0.464644 | − | 0.879975i | ||||
\(79\) | 0.545018 | 0.0613194 | 0.0306597 | − | 0.999530i | \(-0.490239\pi\) | ||||
0.0306597 | + | 0.999530i | \(0.490239\pi\) | |||||||
\(80\) | −3.72575 | − | 1.45559i | −0.416552 | − | 0.162740i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −13.0662 | − | 6.89923i | −1.44292 | − | 0.761892i | ||||
\(83\) | −3.08427 | −0.338543 | −0.169272 | − | 0.985569i | \(-0.554141\pi\) | ||||
−0.169272 | + | 0.985569i | \(0.554141\pi\) | |||||||
\(84\) | 6.46548 | − | 4.41543i | 0.705442 | − | 0.481763i | ||||
\(85\) | 6.87185 | 0.745357 | ||||||||
\(86\) | 4.28963 | + | 2.26501i | 0.462563 | + | 0.244243i | ||||
\(87\) | − | 7.14975i | − | 0.766534i | ||||||
\(88\) | −1.14047 | − | 10.0173i | −0.121575 | − | 1.06785i | ||||
\(89\) | − | 7.41651i | − | 0.786149i | −0.919507 | − | 0.393074i | \(-0.871411\pi\) | ||
0.919507 | − | 0.393074i | \(-0.128589\pi\) | |||||||
\(90\) | −0.660333 | + | 1.25058i | −0.0696052 | + | 0.131823i | ||||
\(91\) | −24.3276 | −2.55023 | ||||||||
\(92\) | 2.66334 | − | 9.21448i | 0.277673 | − | 0.960676i | ||||
\(93\) | −5.49174 | −0.569467 | ||||||||
\(94\) | −1.87844 | + | 3.55752i | −0.193746 | + | 0.366930i | ||||
\(95\) | − | 5.29017i | − | 0.542760i | ||||||
\(96\) | −3.69819 | − | 4.28058i | −0.377445 | − | 0.436885i | ||||
\(97\) | 7.95043i | 0.807244i | 0.914926 | + | 0.403622i | \(0.132249\pi\) | ||||
−0.914926 | + | 0.403622i | \(0.867751\pi\) | |||||||
\(98\) | −10.4106 | − | 5.49702i | −1.05163 | − | 0.555283i | ||||
\(99\) | −3.56454 | −0.358250 | ||||||||
\(100\) | −1.12792 | − | 1.65160i | −0.112792 | − | 0.165160i | ||||
\(101\) | −14.5657 | −1.44934 | −0.724670 | − | 0.689096i | \(-0.758008\pi\) | ||||
−0.724670 | + | 0.689096i | \(0.758008\pi\) | |||||||
\(102\) | 8.59383 | + | 4.53771i | 0.850916 | + | 0.449301i | ||||
\(103\) | 5.43923 | 0.535943 | 0.267971 | − | 0.963427i | \(-0.413647\pi\) | ||||
0.267971 | + | 0.963427i | \(0.413647\pi\) | |||||||
\(104\) | 1.98832 | + | 17.4644i | 0.194971 | + | 1.71252i | ||||
\(105\) | 3.91467 | 0.382032 | ||||||||
\(106\) | −7.28289 | + | 13.7928i | −0.707377 | + | 1.33968i | ||||
\(107\) | −3.07805 | −0.297567 | −0.148783 | − | 0.988870i | \(-0.547536\pi\) | ||||
−0.148783 | + | 0.988870i | \(0.547536\pi\) | |||||||
\(108\) | −1.65160 | + | 1.12792i | −0.158926 | + | 0.108534i | ||||
\(109\) | 5.62701i | 0.538970i | 0.963005 | + | 0.269485i | \(0.0868534\pi\) | ||||
−0.963005 | + | 0.269485i | \(0.913147\pi\) | |||||||
\(110\) | 2.35379 | − | 4.45776i | 0.224425 | − | 0.425031i | ||||
\(111\) | 1.30997 | 0.124337 | ||||||||
\(112\) | −5.69816 | + | 14.5851i | −0.538426 | + | 1.37816i | ||||
\(113\) | − | 9.92254i | − | 0.933434i | −0.884407 | − | 0.466717i | \(-0.845437\pi\) | ||
0.884407 | − | 0.466717i | \(-0.154563\pi\) | |||||||
\(114\) | 3.49327 | − | 6.61580i | 0.327175 | − | 0.619626i | ||||
\(115\) | 3.69800 | − | 3.05366i | 0.344840 | − | 0.284755i | ||||
\(116\) | 8.06435 | + | 11.8086i | 0.748756 | + | 1.09640i | ||||
\(117\) | 6.21448 | 0.574529 | ||||||||
\(118\) | −3.38641 | + | 6.41341i | −0.311744 | + | 0.590402i | ||||
\(119\) | − | 26.9010i | − | 2.46601i | ||||||
\(120\) | −0.319949 | − | 2.81027i | −0.0292072 | − | 0.256542i | ||||
\(121\) | 1.70595 | 0.155087 | ||||||||
\(122\) | −3.39835 | + | 6.43603i | −0.307672 | + | 0.582691i | ||||
\(123\) | − | 10.4481i | − | 0.942073i | ||||||
\(124\) | 9.07018 | − | 6.19425i | 0.814527 | − | 0.556260i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 4.89562 | + | 2.58498i | 0.436136 | + | 0.230289i | ||||
\(127\) | − | 4.13193i | − | 0.366650i | −0.983052 | − | 0.183325i | \(-0.941314\pi\) | ||
0.983052 | − | 0.183325i | \(-0.0586860\pi\) | |||||||
\(128\) | 10.9361 | + | 2.89856i | 0.966624 | + | 0.256199i | ||||
\(129\) | 3.43010i | 0.302004i | ||||||||
\(130\) | −4.10363 | + | 7.77173i | −0.359912 | + | 0.681626i | ||||
\(131\) | 13.3832i | 1.16930i | 0.811287 | + | 0.584649i | \(0.198768\pi\) | ||||
−0.811287 | + | 0.584649i | \(0.801232\pi\) | |||||||
\(132\) | 5.88721 | − | 4.02052i | 0.512416 | − | 0.349941i | ||||
\(133\) | −20.7092 | −1.79572 | ||||||||
\(134\) | −17.6071 | − | 9.29691i | −1.52102 | − | 0.803131i | ||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −19.3118 | + | 2.19865i | −1.65597 | + | 0.188532i | ||||
\(137\) | − | 3.37576i | − | 0.288411i | −0.989548 | − | 0.144205i | \(-0.953937\pi\) | ||
0.989548 | − | 0.144205i | \(-0.0460626\pi\) | |||||||
\(138\) | 6.64109 | − | 1.37695i | 0.565327 | − | 0.117213i | ||||
\(139\) | 6.81463i | 0.578010i | 0.957328 | + | 0.289005i | \(0.0933243\pi\) | ||||
−0.957328 | + | 0.289005i | \(0.906676\pi\) | |||||||
\(140\) | −6.46548 | + | 4.41543i | −0.546433 | + | 0.373172i | ||||
\(141\) | −2.84469 | −0.239566 | ||||||||
\(142\) | 7.71381 | − | 14.6089i | 0.647328 | − | 1.22595i | ||||
\(143\) | −22.1518 | −1.85242 | ||||||||
\(144\) | 1.45559 | − | 3.72575i | 0.121299 | − | 0.310480i | ||||
\(145\) | 7.14975i | 0.593755i | ||||||||
\(146\) | −14.2704 | − | 7.53508i | −1.18103 | − | 0.623608i | ||||
\(147\) | − | 8.32462i | − | 0.686603i | ||||||
\(148\) | −2.16356 | + | 1.47755i | −0.177843 | + | 0.121454i | ||||
\(149\) | − | 0.569849i | − | 0.0466839i | −0.999728 | − | 0.0233419i | \(-0.992569\pi\) | ||
0.999728 | − | 0.0233419i | \(-0.00743065\pi\) | |||||||
\(150\) | 0.660333 | − | 1.25058i | 0.0539160 | − | 0.102110i | ||||
\(151\) | − | 12.8309i | − | 1.04416i | −0.852896 | − | 0.522080i | \(-0.825156\pi\) | ||
0.852896 | − | 0.522080i | \(-0.174844\pi\) | |||||||
\(152\) | 1.69259 | + | 14.8668i | 0.137287 | + | 1.20586i | ||||
\(153\) | 6.87185i | 0.555557i | ||||||||
\(154\) | −17.4506 | − | 9.21428i | −1.40621 | − | 0.742508i | ||||
\(155\) | 5.49174 | 0.441107 | ||||||||
\(156\) | −10.2639 | + | 7.00944i | −0.821767 | + | 0.561204i | ||||
\(157\) | − | 13.7090i | − | 1.09409i | −0.837102 | − | 0.547047i | \(-0.815752\pi\) | ||
0.837102 | − | 0.547047i | \(-0.184248\pi\) | |||||||
\(158\) | −0.681591 | − | 0.359894i | −0.0542245 | − | 0.0286316i | ||||
\(159\) | −11.0291 | −0.874666 | ||||||||
\(160\) | 3.69819 | + | 4.28058i | 0.292368 | + | 0.338410i | ||||
\(161\) | −11.9541 | − | 14.4764i | −0.942111 | − | 1.14090i | ||||
\(162\) | −1.25058 | − | 0.660333i | −0.0982551 | − | 0.0518807i | ||||
\(163\) | 19.9288i | 1.56095i | 0.625189 | + | 0.780474i | \(0.285022\pi\) | ||||
−0.625189 | + | 0.780474i | \(0.714978\pi\) | |||||||
\(164\) | 11.7846 | + | 17.2561i | 0.920224 | + | 1.34748i | ||||
\(165\) | 3.56454 | 0.277499 | ||||||||
\(166\) | 3.85714 | + | 2.03665i | 0.299372 | + | 0.158075i | ||||
\(167\) | − | 5.97291i | − | 0.462198i | −0.972930 | − | 0.231099i | \(-0.925768\pi\) | ||
0.972930 | − | 0.231099i | \(-0.0742321\pi\) | |||||||
\(168\) | −11.0013 | + | 1.25250i | −0.848767 | + | 0.0966321i | ||||
\(169\) | 25.6198 | 1.97075 | ||||||||
\(170\) | −8.59383 | − | 4.53771i | −0.659117 | − | 0.348027i | ||||
\(171\) | 5.29017 | 0.404549 | ||||||||
\(172\) | −3.86888 | − | 5.66518i | −0.295000 | − | 0.431966i | ||||
\(173\) | −0.447042 | −0.0339879 | −0.0169940 | − | 0.999856i | \(-0.505410\pi\) | ||||
−0.0169940 | + | 0.999856i | \(0.505410\pi\) | |||||||
\(174\) | −4.72122 | + | 8.94137i | −0.357915 | + | 0.677843i | ||||
\(175\) | −3.91467 | −0.295921 | ||||||||
\(176\) | −5.18852 | + | 13.2806i | −0.391100 | + | 1.00106i | ||||
\(177\) | −5.12833 | −0.385469 | ||||||||
\(178\) | −4.89737 | + | 9.27497i | −0.367073 | + | 0.695188i | ||||
\(179\) | − | 2.54930i | − | 0.190544i | −0.995451 | − | 0.0952719i | \(-0.969628\pi\) | ||
0.995451 | − | 0.0952719i | \(-0.0303720\pi\) | |||||||
\(180\) | 1.65160 | − | 1.12792i | 0.123103 | − | 0.0840702i | ||||
\(181\) | − | 4.27974i | − | 0.318111i | −0.987270 | − | 0.159055i | \(-0.949155\pi\) | ||
0.987270 | − | 0.159055i | \(-0.0508448\pi\) | |||||||
\(182\) | 30.4237 | + | 16.0643i | 2.25516 | + | 1.19077i | ||||
\(183\) | −5.14642 | −0.380434 | ||||||||
\(184\) | −9.41536 | + | 9.76478i | −0.694110 | + | 0.719869i | ||||
\(185\) | −1.30997 | −0.0963112 | ||||||||
\(186\) | 6.86788 | + | 3.62638i | 0.503578 | + | 0.265899i | ||||
\(187\) | − | 24.4950i | − | 1.79125i | ||||||
\(188\) | 4.69830 | − | 3.20858i | 0.342658 | − | 0.234010i | ||||
\(189\) | 3.91467i | 0.284750i | ||||||||
\(190\) | −3.49327 | + | 6.61580i | −0.253429 | + | 0.479960i | ||||
\(191\) | −18.0629 | −1.30698 | −0.653491 | − | 0.756934i | \(-0.726696\pi\) | ||||
−0.653491 | + | 0.756934i | \(0.726696\pi\) | |||||||
\(192\) | 1.79829 | + | 7.79526i | 0.129780 | + | 0.562575i | ||||
\(193\) | 6.37298 | 0.458737 | 0.229369 | − | 0.973340i | \(-0.426334\pi\) | ||||
0.229369 | + | 0.973340i | \(0.426334\pi\) | |||||||
\(194\) | 5.24993 | − | 9.94268i | 0.376923 | − | 0.713843i | ||||
\(195\) | −6.21448 | −0.445028 | ||||||||
\(196\) | 9.38950 | + | 13.7490i | 0.670679 | + | 0.982070i | ||||
\(197\) | 20.0921 | 1.43150 | 0.715750 | − | 0.698357i | \(-0.246085\pi\) | ||||
0.715750 | + | 0.698357i | \(0.246085\pi\) | |||||||
\(198\) | 4.45776 | + | 2.35379i | 0.316799 | + | 0.167276i | ||||
\(199\) | −5.03970 | −0.357255 | −0.178628 | − | 0.983917i | \(-0.557166\pi\) | ||||
−0.178628 | + | 0.983917i | \(0.557166\pi\) | |||||||
\(200\) | 0.319949 | + | 2.81027i | 0.0226238 | + | 0.198716i | ||||
\(201\) | − | 14.0791i | − | 0.993065i | ||||||
\(202\) | 18.2156 | + | 9.61821i | 1.28165 | + | 0.676735i | ||||
\(203\) | 27.9889 | 1.96444 | ||||||||
\(204\) | −7.75090 | − | 11.3496i | −0.542672 | − | 0.794630i | ||||
\(205\) | 10.4481i | 0.729727i | ||||||||
\(206\) | −6.80221 | − | 3.59170i | −0.473932 | − | 0.250246i | ||||
\(207\) | 3.05366 | + | 3.69800i | 0.212244 | + | 0.257028i | ||||
\(208\) | 9.04575 | − | 23.1536i | 0.627210 | − | 1.60542i | ||||
\(209\) | −18.8570 | −1.30437 | ||||||||
\(210\) | −4.89562 | − | 2.58498i | −0.337830 | − | 0.178381i | ||||
\(211\) | 17.2717i | 1.18903i | 0.804084 | + | 0.594515i | \(0.202656\pi\) | ||||
−0.804084 | + | 0.594515i | \(0.797344\pi\) | |||||||
\(212\) | 18.2157 | − | 12.4400i | 1.25106 | − | 0.854380i | ||||
\(213\) | 11.6817 | 0.800416 | ||||||||
\(214\) | 3.84936 | + | 2.03254i | 0.263137 | + | 0.138942i | ||||
\(215\) | − | 3.43010i | − | 0.233931i | ||||||
\(216\) | 2.81027 | − | 0.319949i | 0.191215 | − | 0.0217698i | ||||
\(217\) | − | 21.4983i | − | 1.45940i | ||||||
\(218\) | 3.71570 | − | 7.03705i | 0.251659 | − | 0.476609i | ||||
\(219\) | − | 11.4110i | − | 0.771086i | ||||||
\(220\) | −5.88721 | + | 4.02052i | −0.396916 | + | 0.271063i | ||||
\(221\) | 42.7050i | 2.87265i | ||||||||
\(222\) | −1.63823 | − | 0.865019i | −0.109951 | − | 0.0580563i | ||||
\(223\) | 1.00859i | 0.0675402i | 0.999430 | + | 0.0337701i | \(0.0107514\pi\) | ||||
−0.999430 | + | 0.0337701i | \(0.989249\pi\) | |||||||
\(224\) | 16.7570 | − | 14.4772i | 1.11963 | − | 0.967298i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −6.55219 | + | 12.4090i | −0.435845 | + | 0.825433i | ||||
\(227\) | −27.6273 | −1.83369 | −0.916844 | − | 0.399246i | \(-0.869272\pi\) | ||||
−0.916844 | + | 0.399246i | \(0.869272\pi\) | |||||||
\(228\) | −8.73726 | + | 5.96689i | −0.578639 | + | 0.395167i | ||||
\(229\) | − | 4.72289i | − | 0.312097i | −0.987749 | − | 0.156049i | \(-0.950124\pi\) | ||
0.987749 | − | 0.156049i | \(-0.0498756\pi\) | |||||||
\(230\) | −6.64109 | + | 1.37695i | −0.437900 | + | 0.0907931i | ||||
\(231\) | − | 13.9540i | − | 0.918105i | ||||||
\(232\) | −2.28756 | − | 20.0928i | −0.150186 | − | 1.31915i | ||||
\(233\) | 8.77953 | 0.575166 | 0.287583 | − | 0.957756i | \(-0.407148\pi\) | ||||
0.287583 | + | 0.957756i | \(0.407148\pi\) | |||||||
\(234\) | −7.77173 | − | 4.10363i | −0.508054 | − | 0.268263i | ||||
\(235\) | 2.84469 | 0.185567 | ||||||||
\(236\) | 8.46997 | − | 5.78435i | 0.551348 | − | 0.376529i | ||||
\(237\) | − | 0.545018i | − | 0.0354028i | ||||||
\(238\) | −17.7636 | + | 33.6420i | −1.15145 | + | 2.18069i | ||||
\(239\) | 10.3755i | 0.671138i | 0.942016 | + | 0.335569i | \(0.108929\pi\) | ||||
−0.942016 | + | 0.335569i | \(0.891071\pi\) | |||||||
\(240\) | −1.45559 | + | 3.72575i | −0.0939581 | + | 0.240496i | ||||
\(241\) | − | 26.7704i | − | 1.72443i | −0.506541 | − | 0.862216i | \(-0.669076\pi\) | ||
0.506541 | − | 0.862216i | \(-0.330924\pi\) | |||||||
\(242\) | −2.13344 | − | 1.12650i | −0.137143 | − | 0.0724140i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 8.49985 | − | 5.80475i | 0.544147 | − | 0.371611i | ||||
\(245\) | 8.32462i | 0.531840i | ||||||||
\(246\) | −6.89923 | + | 13.0662i | −0.439879 | + | 0.833072i | ||||
\(247\) | 32.8756 | 2.09183 | ||||||||
\(248\) | −15.4333 | + | 1.75708i | −0.980015 | + | 0.111575i | ||||
\(249\) | 3.08427i | 0.195458i | ||||||||
\(250\) | −0.660333 | + | 1.25058i | −0.0417631 | + | 0.0790939i | ||||
\(251\) | 28.6509 | 1.80843 | 0.904215 | − | 0.427077i | \(-0.140457\pi\) | ||||
0.904215 | + | 0.427077i | \(0.140457\pi\) | |||||||
\(252\) | −4.41543 | − | 6.46548i | −0.278146 | − | 0.407287i | ||||
\(253\) | −10.8849 | − | 13.1817i | −0.684327 | − | 0.828724i | ||||
\(254\) | −2.72845 | + | 5.16733i | −0.171198 | + | 0.324227i | ||||
\(255\) | − | 6.87185i | − | 0.430332i | ||||||
\(256\) | −11.7625 | − | 10.8464i | −0.735156 | − | 0.677898i | ||||
\(257\) | 17.7379 | 1.10646 | 0.553230 | − | 0.833029i | \(-0.313395\pi\) | ||||
0.553230 | + | 0.833029i | \(0.313395\pi\) | |||||||
\(258\) | 2.26501 | − | 4.28963i | 0.141013 | − | 0.267061i | ||||
\(259\) | 5.12811i | 0.318645i | ||||||||
\(260\) | 10.2639 | − | 7.00944i | 0.636538 | − | 0.434707i | ||||
\(261\) | −7.14975 | −0.442559 | ||||||||
\(262\) | 8.83739 | − | 16.7368i | 0.545975 | − | 1.03401i | ||||
\(263\) | −22.3989 | −1.38118 | −0.690588 | − | 0.723248i | \(-0.742648\pi\) | ||||
−0.690588 | + | 0.723248i | \(0.742648\pi\) | |||||||
\(264\) | −10.0173 | + | 1.14047i | −0.616524 | + | 0.0701912i | ||||
\(265\) | 11.0291 | 0.677513 | ||||||||
\(266\) | 25.8986 | + | 13.6750i | 1.58795 | + | 0.838468i | ||||
\(267\) | −7.41651 | −0.453883 | ||||||||
\(268\) | 15.8801 | + | 23.2531i | 0.970033 | + | 1.42041i | ||||
\(269\) | 9.69449 | 0.591084 | 0.295542 | − | 0.955330i | \(-0.404500\pi\) | ||||
0.295542 | + | 0.955330i | \(0.404500\pi\) | |||||||
\(270\) | 1.25058 | + | 0.660333i | 0.0761081 | + | 0.0401866i | ||||
\(271\) | 2.94386i | 0.178827i | 0.995995 | + | 0.0894134i | \(0.0284992\pi\) | ||||
−0.995995 | + | 0.0894134i | \(0.971501\pi\) | |||||||
\(272\) | 25.6028 | + | 10.0026i | 1.55240 | + | 0.606498i | ||||
\(273\) | 24.3276i | 1.47237i | ||||||||
\(274\) | −2.22913 | + | 4.22167i | −0.134666 | + | 0.255040i | ||||
\(275\) | −3.56454 | −0.214950 | ||||||||
\(276\) | −9.21448 | − | 2.66334i | −0.554646 | − | 0.160314i | ||||
\(277\) | −29.7292 | −1.78625 | −0.893126 | − | 0.449806i | \(-0.851493\pi\) | ||||
−0.893126 | + | 0.449806i | \(0.851493\pi\) | |||||||
\(278\) | 4.49993 | − | 8.52227i | 0.269888 | − | 0.511132i | ||||
\(279\) | 5.49174i | 0.328782i | ||||||||
\(280\) | 11.0013 | − | 1.25250i | 0.657452 | − | 0.0748509i | ||||
\(281\) | − | 1.33749i | − | 0.0797881i | −0.999204 | − | 0.0398941i | \(-0.987298\pi\) | ||
0.999204 | − | 0.0398941i | \(-0.0127020\pi\) | |||||||
\(282\) | 3.55752 | + | 1.87844i | 0.211847 | + | 0.111860i | ||||
\(283\) | −2.40320 | −0.142856 | −0.0714278 | − | 0.997446i | \(-0.522756\pi\) | ||||
−0.0714278 | + | 0.997446i | \(0.522756\pi\) | |||||||
\(284\) | −19.2935 | + | 13.1760i | −1.14486 | + | 0.781852i | ||||
\(285\) | −5.29017 | −0.313362 | ||||||||
\(286\) | 27.7026 | + | 14.6276i | 1.63809 | + | 0.864945i | ||||
\(287\) | 40.9008 | 2.41430 | ||||||||
\(288\) | −4.28058 | + | 3.69819i | −0.252236 | + | 0.217918i | ||||
\(289\) | −30.2224 | −1.77779 | ||||||||
\(290\) | 4.72122 | − | 8.94137i | 0.277240 | − | 0.525055i | ||||
\(291\) | 7.95043 | 0.466062 | ||||||||
\(292\) | 12.8707 | + | 18.8465i | 0.753202 | + | 1.10291i | ||||
\(293\) | 1.76785i | 0.103279i | 0.998666 | + | 0.0516395i | \(0.0164447\pi\) | ||||
−0.998666 | + | 0.0516395i | \(0.983555\pi\) | |||||||
\(294\) | −5.49702 | + | 10.4106i | −0.320593 | + | 0.607160i | ||||
\(295\) | 5.12833 | 0.298583 | ||||||||
\(296\) | 3.68138 | − | 0.419125i | 0.213976 | − | 0.0243612i | ||||
\(297\) | 3.56454i | 0.206836i | ||||||||
\(298\) | −0.376291 | + | 0.712644i | −0.0217979 | + | 0.0412824i | ||||
\(299\) | 18.9769 | + | 22.9811i | 1.09746 | + | 1.32903i | ||||
\(300\) | −1.65160 | + | 1.12792i | −0.0953554 | + | 0.0651205i | ||||
\(301\) | −13.4277 | −0.773961 | ||||||||
\(302\) | −8.47264 | + | 16.0461i | −0.487546 | + | 0.923347i | ||||
\(303\) | 14.5657i | 0.836777i | ||||||||
\(304\) | 7.70033 | − | 19.7099i | 0.441644 | − | 1.13044i | ||||
\(305\) | 5.14642 | 0.294683 | ||||||||
\(306\) | 4.53771 | − | 8.59383i | 0.259404 | − | 0.491277i | ||||
\(307\) | 15.2035i | 0.867709i | 0.900983 | + | 0.433854i | \(0.142847\pi\) | ||||
−0.900983 | + | 0.433854i | \(0.857153\pi\) | |||||||
\(308\) | 15.7390 | + | 23.0465i | 0.896812 | + | 1.31319i | ||||
\(309\) | − | 5.43923i | − | 0.309427i | ||||||
\(310\) | −6.86788 | − | 3.62638i | −0.390070 | − | 0.205965i | ||||
\(311\) | − | 1.53631i | − | 0.0871160i | −0.999051 | − | 0.0435580i | \(-0.986131\pi\) | ||
0.999051 | − | 0.0435580i | \(-0.0138693\pi\) | |||||||
\(312\) | 17.4644 | − | 1.98832i | 0.988726 | − | 0.112566i | ||||
\(313\) | 3.50866i | 0.198321i | 0.995071 | + | 0.0991605i | \(0.0316157\pi\) | ||||
−0.995071 | + | 0.0991605i | \(0.968384\pi\) | |||||||
\(314\) | −9.05248 | + | 17.1442i | −0.510861 | + | 0.967503i | ||||
\(315\) | − | 3.91467i | − | 0.220566i | ||||||
\(316\) | 0.614737 | + | 0.900155i | 0.0345817 | + | 0.0506377i | ||||
\(317\) | 18.8734 | 1.06004 | 0.530018 | − | 0.847986i | \(-0.322185\pi\) | ||||
0.530018 | + | 0.847986i | \(0.322185\pi\) | |||||||
\(318\) | 13.7928 | + | 7.28289i | 0.773464 | + | 0.408404i | ||||
\(319\) | 25.4856 | 1.42692 | ||||||||
\(320\) | −1.79829 | − | 7.79526i | −0.100527 | − | 0.435769i | ||||
\(321\) | 3.07805i | 0.171800i | ||||||||
\(322\) | 5.39028 | + | 25.9976i | 0.300389 | + | 1.44879i | ||||
\(323\) | 36.3533i | 2.02275i | ||||||||
\(324\) | 1.12792 | + | 1.65160i | 0.0626622 | + | 0.0917558i | ||||
\(325\) | 6.21448 | 0.344717 | ||||||||
\(326\) | 13.1597 | − | 24.9227i | 0.728847 | − | 1.38034i | ||||
\(327\) | 5.62701 | 0.311174 | ||||||||
\(328\) | −3.34286 | − | 29.3620i | −0.184579 | − | 1.62125i | ||||
\(329\) | − | 11.1360i | − | 0.613948i | ||||||
\(330\) | −4.45776 | − | 2.35379i | −0.245391 | − | 0.129572i | ||||
\(331\) | 30.4098i | 1.67147i | 0.549130 | + | 0.835737i | \(0.314959\pi\) | ||||
−0.549130 | + | 0.835737i | \(0.685041\pi\) | |||||||
\(332\) | −3.47881 | − | 5.09400i | −0.190925 | − | 0.279570i | ||||
\(333\) | − | 1.30997i | − | 0.0717861i | ||||||
\(334\) | −3.94411 | + | 7.46963i | −0.215812 | + | 0.408720i | ||||
\(335\) | 14.0791i | 0.769225i | ||||||||
\(336\) | 14.5851 | + | 5.69816i | 0.795682 | + | 0.310860i | ||||
\(337\) | 33.9686i | 1.85039i | 0.379494 | + | 0.925194i | \(0.376098\pi\) | ||||
−0.379494 | + | 0.925194i | \(0.623902\pi\) | |||||||
\(338\) | −32.0397 | − | 16.9176i | −1.74273 | − | 0.920195i | ||||
\(339\) | −9.92254 | −0.538919 | ||||||||
\(340\) | 7.75090 | + | 11.3496i | 0.420352 | + | 0.615518i | ||||
\(341\) | − | 19.5755i | − | 1.06008i | ||||||
\(342\) | −6.61580 | − | 3.49327i | −0.357741 | − | 0.188895i | ||||
\(343\) | 5.18544 | 0.279987 | ||||||||
\(344\) | 1.09746 | + | 9.63953i | 0.0591711 | + | 0.519729i | ||||
\(345\) | −3.05366 | − | 3.69800i | −0.164403 | − | 0.199093i | ||||
\(346\) | 0.559063 | + | 0.295196i | 0.0300554 | + | 0.0158699i | ||||
\(347\) | − | 12.0233i | − | 0.645444i | −0.946494 | − | 0.322722i | \(-0.895402\pi\) | ||
0.946494 | − | 0.322722i | \(-0.104598\pi\) | |||||||
\(348\) | 11.8086 | − | 8.06435i | 0.633005 | − | 0.432295i | ||||
\(349\) | −14.6968 | −0.786700 | −0.393350 | − | 0.919389i | \(-0.628684\pi\) | ||||
−0.393350 | + | 0.919389i | \(0.628684\pi\) | |||||||
\(350\) | 4.89562 | + | 2.58498i | 0.261682 | + | 0.138173i | ||||
\(351\) | − | 6.21448i | − | 0.331704i | ||||||
\(352\) | 15.2583 | − | 13.1824i | 0.813270 | − | 0.702622i | ||||
\(353\) | −18.3628 | −0.977353 | −0.488676 | − | 0.872465i | \(-0.662520\pi\) | ||||
−0.488676 | + | 0.872465i | \(0.662520\pi\) | |||||||
\(354\) | 6.41341 | + | 3.38641i | 0.340869 | + | 0.179986i | ||||
\(355\) | −11.6817 | −0.620000 | ||||||||
\(356\) | 12.2491 | − | 8.36523i | 0.649203 | − | 0.443356i | ||||
\(357\) | −26.9010 | −1.42375 | ||||||||
\(358\) | −1.68339 | + | 3.18811i | −0.0889698 | + | 0.168497i | ||||
\(359\) | −7.33490 | −0.387121 | −0.193561 | − | 0.981088i | \(-0.562004\pi\) | ||||
−0.193561 | + | 0.981088i | \(0.562004\pi\) | |||||||
\(360\) | −2.81027 | + | 0.319949i | −0.148114 | + | 0.0168628i | ||||
\(361\) | 8.98588 | 0.472941 | ||||||||
\(362\) | −2.82606 | + | 5.35218i | −0.148534 | + | 0.281304i | ||||
\(363\) | − | 1.70595i | − | 0.0895393i | ||||||
\(364\) | −27.4396 | − | 40.1796i | −1.43823 | − | 2.10598i | ||||
\(365\) | 11.4110i | 0.597280i | ||||||||
\(366\) | 6.43603 | + | 3.39835i | 0.336417 | + | 0.177635i | ||||
\(367\) | 8.66677 | 0.452402 | 0.226201 | − | 0.974081i | \(-0.427369\pi\) | ||||
0.226201 | + | 0.974081i | \(0.427369\pi\) | |||||||
\(368\) | 18.2227 | − | 5.99440i | 0.949924 | − | 0.312480i | ||||
\(369\) | −10.4481 | −0.543906 | ||||||||
\(370\) | 1.63823 | + | 0.865019i | 0.0851676 | + | 0.0449702i | ||||
\(371\) | − | 43.1753i | − | 2.24155i | ||||||
\(372\) | −6.19425 | − | 9.07018i | −0.321157 | − | 0.470267i | ||||
\(373\) | − | 5.74203i | − | 0.297311i | −0.988889 | − | 0.148656i | \(-0.952505\pi\) | ||
0.988889 | − | 0.148656i | \(-0.0474946\pi\) | |||||||
\(374\) | −16.1749 | + | 30.6331i | −0.836383 | + | 1.58400i | ||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | −7.99434 | + | 0.910156i | −0.412277 | + | 0.0469377i | ||||
\(377\) | −44.4320 | −2.28836 | ||||||||
\(378\) | 2.58498 | − | 4.89562i | 0.132957 | − | 0.251803i | ||||
\(379\) | 4.59883 | 0.236226 | 0.118113 | − | 0.993000i | \(-0.462316\pi\) | ||||
0.118113 | + | 0.993000i | \(0.462316\pi\) | |||||||
\(380\) | 8.73726 | − | 5.96689i | 0.448212 | − | 0.306095i | ||||
\(381\) | −4.13193 | −0.211685 | ||||||||
\(382\) | 22.5891 | + | 11.9275i | 1.15576 | + | 0.610264i | ||||
\(383\) | 9.34111 | 0.477308 | 0.238654 | − | 0.971105i | \(-0.423294\pi\) | ||||
0.238654 | + | 0.971105i | \(0.423294\pi\) | |||||||
\(384\) | 2.89856 | − | 10.9361i | 0.147917 | − | 0.558081i | ||||
\(385\) | 13.9540i | 0.711161i | ||||||||
\(386\) | −7.96995 | − | 4.20829i | −0.405660 | − | 0.214196i | ||||
\(387\) | 3.43010 | 0.174362 | ||||||||
\(388\) | −13.1310 | + | 8.96745i | −0.666624 | + | 0.455253i | ||||
\(389\) | 24.9069i | 1.26283i | 0.775445 | + | 0.631416i | \(0.217526\pi\) | ||||
−0.775445 | + | 0.631416i | \(0.782474\pi\) | |||||||
\(390\) | 7.77173 | + | 4.10363i | 0.393537 | + | 0.207795i | ||||
\(391\) | −25.4121 | + | 20.9843i | −1.28514 | + | 1.06122i | ||||
\(392\) | −2.66346 | − | 23.3944i | −0.134525 | − | 1.18160i | ||||
\(393\) | 13.3832 | 0.675094 | ||||||||
\(394\) | −25.1268 | − | 13.2675i | −1.26587 | − | 0.668405i | ||||
\(395\) | 0.545018i | 0.0274229i | ||||||||
\(396\) | −4.02052 | − | 5.88721i | −0.202039 | − | 0.295843i | ||||
\(397\) | 15.9626 | 0.801139 | 0.400570 | − | 0.916266i | \(-0.368812\pi\) | ||||
0.400570 | + | 0.916266i | \(0.368812\pi\) | |||||||
\(398\) | 6.30257 | + | 3.32788i | 0.315919 | + | 0.166812i | ||||
\(399\) | 20.7092i | 1.03676i | ||||||||
\(400\) | 1.45559 | − | 3.72575i | 0.0727797 | − | 0.186288i | ||||
\(401\) | 26.0520i | 1.30098i | 0.759517 | + | 0.650488i | \(0.225435\pi\) | ||||
−0.759517 | + | 0.650488i | \(0.774565\pi\) | |||||||
\(402\) | −9.29691 | + | 17.6071i | −0.463688 | + | 0.878163i | ||||
\(403\) | 34.1283i | 1.70005i | ||||||||
\(404\) | −16.4289 | − | 24.0567i | −0.817370 | − | 1.19687i | ||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | −35.0025 | − | 18.4820i | −1.73714 | − | 0.917246i | ||||
\(407\) | 4.66946i | 0.231456i | ||||||||
\(408\) | 2.19865 | + | 19.3118i | 0.108849 | + | 0.956076i | ||||
\(409\) | 9.84257 | 0.486684 | 0.243342 | − | 0.969941i | \(-0.421756\pi\) | ||||
0.243342 | + | 0.969941i | \(0.421756\pi\) | |||||||
\(410\) | 6.89923 | − | 13.0662i | 0.340729 | − | 0.645295i | ||||
\(411\) | −3.37576 | −0.166514 | ||||||||
\(412\) | 6.13501 | + | 8.98345i | 0.302250 | + | 0.442583i | ||||
\(413\) | − | 20.0757i | − | 0.987861i | ||||||
\(414\) | −1.37695 | − | 6.64109i | −0.0676732 | − | 0.326392i | ||||
\(415\) | − | 3.08427i | − | 0.151401i | ||||||
\(416\) | −26.6016 | + | 22.9823i | −1.30425 | + | 1.12680i | ||||
\(417\) | 6.81463 | 0.333714 | ||||||||
\(418\) | 23.5823 | + | 12.4519i | 1.15345 | + | 0.609043i | ||||
\(419\) | 7.38704 | 0.360881 | 0.180440 | − | 0.983586i | \(-0.442248\pi\) | ||||
0.180440 | + | 0.983586i | \(0.442248\pi\) | |||||||
\(420\) | 4.41543 | + | 6.46548i | 0.215451 | + | 0.315483i | ||||
\(421\) | 6.93017i | 0.337756i | 0.985637 | + | 0.168878i | \(0.0540143\pi\) | ||||
−0.985637 | + | 0.168878i | \(0.945986\pi\) | |||||||
\(422\) | 11.4051 | − | 21.5997i | 0.555189 | − | 1.05145i | ||||
\(423\) | 2.84469i | 0.138313i | ||||||||
\(424\) | −30.9948 | + | 3.52876i | −1.50524 | + | 0.171372i | ||||
\(425\) | 6.87185i | 0.333334i | ||||||||
\(426\) | −14.6089 | − | 7.71381i | −0.707805 | − | 0.373735i | ||||
\(427\) | − | 20.1465i | − | 0.974959i | ||||||
\(428\) | −3.47180 | − | 5.08373i | −0.167816 | − | 0.245731i | ||||
\(429\) | 22.1518i | 1.06950i | ||||||||
\(430\) | −2.26501 | + | 4.28963i | −0.109229 | + | 0.206864i | ||||
\(431\) | 9.62172 | 0.463462 | 0.231731 | − | 0.972780i | \(-0.425561\pi\) | ||||
0.231731 | + | 0.972780i | \(0.425561\pi\) | |||||||
\(432\) | −3.72575 | − | 1.45559i | −0.179255 | − | 0.0700323i | ||||
\(433\) | − | 19.3827i | − | 0.931472i | −0.884924 | − | 0.465736i | \(-0.845790\pi\) | ||
0.884924 | − | 0.465736i | \(-0.154210\pi\) | |||||||
\(434\) | −14.1961 | + | 26.8855i | −0.681433 | + | 1.29054i | ||||
\(435\) | 7.14975 | 0.342804 | ||||||||
\(436\) | −9.29359 | + | 6.34682i | −0.445082 | + | 0.303957i | ||||
\(437\) | 16.1544 | + | 19.5630i | 0.772768 | + | 0.935826i | ||||
\(438\) | −7.53508 | + | 14.2704i | −0.360040 | + | 0.681868i | ||||
\(439\) | − | 4.99409i | − | 0.238355i | −0.992873 | − | 0.119177i | \(-0.961974\pi\) | ||
0.992873 | − | 0.119177i | \(-0.0380257\pi\) | |||||||
\(440\) | 10.0173 | − | 1.14047i | 0.477558 | − | 0.0543699i | ||||
\(441\) | −8.32462 | −0.396410 | ||||||||
\(442\) | 28.1995 | − | 53.4062i | 1.34132 | − | 2.54027i | ||||
\(443\) | 15.0814i | 0.716541i | 0.933618 | + | 0.358271i | \(0.116633\pi\) | ||||
−0.933618 | + | 0.358271i | \(0.883367\pi\) | |||||||
\(444\) | 1.47755 | + | 2.16356i | 0.0701212 | + | 0.102678i | ||||
\(445\) | 7.41651 | 0.351576 | ||||||||
\(446\) | 0.666006 | − | 1.26133i | 0.0315363 | − | 0.0597256i | ||||
\(447\) | −0.569849 | −0.0269530 | ||||||||
\(448\) | −30.5159 | + | 7.03971i | −1.44174 | + | 0.332595i | ||||
\(449\) | 34.9465 | 1.64923 | 0.824614 | − | 0.565696i | \(-0.191392\pi\) | ||||
0.824614 | + | 0.565696i | \(0.191392\pi\) | |||||||
\(450\) | −1.25058 | − | 0.660333i | −0.0589531 | − | 0.0311284i | ||||
\(451\) | 37.2427 | 1.75369 | ||||||||
\(452\) | 16.3881 | − | 11.1918i | 0.770832 | − | 0.526420i | ||||
\(453\) | −12.8309 | −0.602846 | ||||||||
\(454\) | 34.5502 | + | 18.2432i | 1.62152 | + | 0.856197i | ||||
\(455\) | − | 24.3276i | − | 1.14050i | ||||||
\(456\) | 14.8668 | − | 1.69259i | 0.696202 | − | 0.0792626i | ||||
\(457\) | 16.3188i | 0.763361i | 0.924294 | + | 0.381681i | \(0.124655\pi\) | ||||
−0.924294 | + | 0.381681i | \(0.875345\pi\) | |||||||
\(458\) | −3.11868 | + | 5.90637i | −0.145726 | + | 0.275986i | ||||
\(459\) | 6.87185 | 0.320751 | ||||||||
\(460\) | 9.21448 | + | 2.66334i | 0.429627 | + | 0.124179i | ||||
\(461\) | −0.112877 | −0.00525721 | −0.00262861 | − | 0.999997i | \(-0.500837\pi\) | ||||
−0.00262861 | + | 0.999997i | \(0.500837\pi\) | |||||||
\(462\) | −9.21428 | + | 17.4506i | −0.428687 | + | 0.811877i | ||||
\(463\) | 27.4755i | 1.27690i | 0.769665 | + | 0.638448i | \(0.220423\pi\) | ||||
−0.769665 | + | 0.638448i | \(0.779577\pi\) | |||||||
\(464\) | −10.4071 | + | 26.6382i | −0.483139 | + | 1.23665i | ||||
\(465\) | − | 5.49174i | − | 0.254673i | ||||||
\(466\) | −10.9795 | − | 5.79741i | −0.508617 | − | 0.268560i | ||||
\(467\) | −10.1856 | −0.471335 | −0.235667 | − | 0.971834i | \(-0.575728\pi\) | ||||
−0.235667 | + | 0.971834i | \(0.575728\pi\) | |||||||
\(468\) | 7.00944 | + | 10.2639i | 0.324011 | + | 0.474447i | ||||
\(469\) | 55.1151 | 2.54498 | ||||||||
\(470\) | −3.55752 | − | 1.87844i | −0.164096 | − | 0.0866460i | ||||
\(471\) | −13.7090 | −0.631675 | ||||||||
\(472\) | −14.4120 | + | 1.64081i | −0.663367 | + | 0.0755242i | ||||
\(473\) | −12.2267 | −0.562187 | ||||||||
\(474\) | −0.359894 | + | 0.681591i | −0.0165305 | + | 0.0313065i | ||||
\(475\) | 5.29017 | 0.242730 | ||||||||
\(476\) | 44.4298 | − | 30.3422i | 2.03644 | − | 1.39073i | ||||
\(477\) | 11.0291i | 0.504989i | ||||||||
\(478\) | 6.85131 | − | 12.9755i | 0.313372 | − | 0.593485i | ||||
\(479\) | −9.55762 | −0.436699 | −0.218349 | − | 0.975871i | \(-0.570067\pi\) | ||||
−0.218349 | + | 0.975871i | \(0.570067\pi\) | |||||||
\(480\) | 4.28058 | − | 3.69819i | 0.195381 | − | 0.168799i | ||||
\(481\) | − | 8.14081i | − | 0.371189i | ||||||
\(482\) | −17.6774 | + | 33.4786i | −0.805182 | + | 1.52491i | ||||
\(483\) | −14.4764 | + | 11.9541i | −0.658700 | + | 0.543928i | ||||
\(484\) | 1.92418 | + | 2.81756i | 0.0874627 | + | 0.128071i | ||||
\(485\) | −7.95043 | −0.361010 | ||||||||
\(486\) | −0.660333 | + | 1.25058i | −0.0299533 | + | 0.0567276i | ||||
\(487\) | 32.5478i | 1.47488i | 0.675412 | + | 0.737441i | \(0.263966\pi\) | ||||
−0.675412 | + | 0.737441i | \(0.736034\pi\) | |||||||
\(488\) | −14.4628 | + | 1.64659i | −0.654702 | + | 0.0745378i | ||||
\(489\) | 19.9288 | 0.901213 | ||||||||
\(490\) | 5.49702 | − | 10.4106i | 0.248330 | − | 0.470304i | ||||
\(491\) | − | 5.56517i | − | 0.251153i | −0.992084 | − | 0.125576i | \(-0.959922\pi\) | ||
0.992084 | − | 0.125576i | \(-0.0400780\pi\) | |||||||
\(492\) | 17.2561 | − | 11.7846i | 0.777966 | − | 0.531292i | ||||
\(493\) | − | 49.1321i | − | 2.21280i | ||||||
\(494\) | −41.1138 | − | 21.7089i | −1.84980 | − | 0.976729i | ||||
\(495\) | − | 3.56454i | − | 0.160214i | ||||||
\(496\) | 20.4609 | + | 7.99374i | 0.918721 | + | 0.358930i | ||||
\(497\) | 45.7299i | 2.05127i | ||||||||
\(498\) | 2.03665 | − | 3.85714i | 0.0912644 | − | 0.172843i | ||||
\(499\) | − | 32.9843i | − | 1.47658i | −0.674484 | − | 0.738289i | \(-0.735634\pi\) | ||
0.674484 | − | 0.738289i | \(-0.264366\pi\) | |||||||
\(500\) | 1.65160 | − | 1.12792i | 0.0738620 | − | 0.0504421i | ||||
\(501\) | −5.97291 | −0.266850 | ||||||||
\(502\) | −35.8304 | − | 18.9192i | −1.59919 | − | 0.844404i | ||||
\(503\) | −16.7209 | −0.745549 | −0.372775 | − | 0.927922i | \(-0.621594\pi\) | ||||
−0.372775 | + | 0.927922i | \(0.621594\pi\) | |||||||
\(504\) | 1.25250 | + | 11.0013i | 0.0557906 | + | 0.490036i | ||||
\(505\) | − | 14.5657i | − | 0.648164i | ||||||
\(506\) | 4.90818 | + | 23.6724i | 0.218195 | + | 1.05237i | ||||
\(507\) | − | 25.6198i | − | 1.13781i | ||||||
\(508\) | 6.82432 | − | 4.66049i | 0.302780 | − | 0.206776i | ||||
\(509\) | −8.57338 | −0.380008 | −0.190004 | − | 0.981783i | \(-0.560850\pi\) | ||||
−0.190004 | + | 0.981783i | \(0.560850\pi\) | |||||||
\(510\) | −4.53771 | + | 8.59383i | −0.200933 | + | 0.380541i | ||||
\(511\) | 44.6704 | 1.97610 | ||||||||
\(512\) | 7.54777 | + | 21.3315i | 0.333568 | + | 0.942726i | ||||
\(513\) | − | 5.29017i | − | 0.233567i | ||||||
\(514\) | −22.1827 | − | 11.7129i | −0.978438 | − | 0.516635i | ||||
\(515\) | 5.43923i | 0.239681i | ||||||||
\(516\) | −5.66518 | + | 3.86888i | −0.249395 | + | 0.170318i | ||||
\(517\) | − | 10.1400i | − | 0.445957i | ||||||
\(518\) | 3.38626 | − | 6.41313i | 0.148784 | − | 0.281777i | ||||
\(519\) | 0.447042i | 0.0196229i | ||||||||
\(520\) | −17.4644 | + | 1.98832i | −0.765864 | + | 0.0871936i | ||||
\(521\) | − | 9.81425i | − | 0.429970i | −0.976617 | − | 0.214985i | \(-0.931030\pi\) | ||
0.976617 | − | 0.214985i | \(-0.0689703\pi\) | |||||||
\(522\) | 8.94137 | + | 4.72122i | 0.391353 | + | 0.206642i | ||||
\(523\) | −39.4912 | −1.72683 | −0.863416 | − | 0.504493i | \(-0.831679\pi\) | ||||
−0.863416 | + | 0.504493i | \(0.831679\pi\) | |||||||
\(524\) | −22.1038 | + | 15.0952i | −0.965608 | + | 0.659437i | ||||
\(525\) | 3.91467i | 0.170850i | ||||||||
\(526\) | 28.0117 | + | 14.7908i | 1.22137 | + | 0.644908i | ||||
\(527\) | −37.7385 | −1.64391 | ||||||||
\(528\) | 13.2806 | + | 5.18852i | 0.577964 | + | 0.225801i | ||||
\(529\) | −4.35035 | + | 22.5848i | −0.189146 | + | 0.981949i | ||||
\(530\) | −13.7928 | − | 7.28289i | −0.599123 | − | 0.316349i | ||||
\(531\) | 5.12833i | 0.222551i | ||||||||
\(532\) | −23.3584 | − | 34.2035i | −1.01271 | − | 1.48291i | ||||
\(533\) | −64.9295 | −2.81241 | ||||||||
\(534\) | 9.27497 | + | 4.89737i | 0.401367 | + | 0.211930i | ||||
\(535\) | − | 3.07805i | − | 0.133076i | ||||||
\(536\) | −4.50461 | − | 39.5662i | −0.194569 | − | 1.70900i | ||||
\(537\) | −2.54930 | −0.110010 | ||||||||
\(538\) | −12.1238 | − | 6.40160i | −0.522693 | − | 0.275992i | ||||
\(539\) | 29.6734 | 1.27813 | ||||||||
\(540\) | −1.12792 | − | 1.65160i | −0.0485379 | − | 0.0710737i | ||||
\(541\) | 11.5680 | 0.497347 | 0.248673 | − | 0.968587i | \(-0.420005\pi\) | ||||
0.248673 | + | 0.968587i | \(0.420005\pi\) | |||||||
\(542\) | 1.94393 | − | 3.68154i | 0.0834989 | − | 0.158136i | ||||
\(543\) | −4.27974 | −0.183661 | ||||||||
\(544\) | −25.4134 | − | 29.4155i | −1.08959 | − | 1.26118i | ||||
\(545\) | −5.62701 | −0.241035 | ||||||||
\(546\) | 16.0643 | − | 30.4237i | 0.687490 | − | 1.30202i | ||||
\(547\) | − | 21.6493i | − | 0.925658i | −0.886448 | − | 0.462829i | \(-0.846834\pi\) | ||
0.886448 | − | 0.462829i | \(-0.153166\pi\) | |||||||
\(548\) | 5.57542 | − | 3.80759i | 0.238170 | − | 0.162652i | ||||
\(549\) | 5.14642i | 0.219644i | ||||||||
\(550\) | 4.45776 | + | 2.35379i | 0.190079 | + | 0.100366i | ||||
\(551\) | −37.8234 | −1.61133 | ||||||||
\(552\) | 9.76478 | + | 9.41536i | 0.415617 | + | 0.400744i | ||||
\(553\) | 2.13357 | 0.0907284 | ||||||||
\(554\) | 37.1788 | + | 19.6312i | 1.57958 | + | 0.834048i | ||||
\(555\) | 1.30997i | 0.0556053i | ||||||||
\(556\) | −11.2551 | + | 7.68636i | −0.477322 | + | 0.325974i | ||||
\(557\) | 25.5493i | 1.08256i | 0.840843 | + | 0.541279i | \(0.182060\pi\) | ||||
−0.840843 | + | 0.541279i | \(0.817940\pi\) | |||||||
\(558\) | 3.62638 | − | 6.86788i | 0.153517 | − | 0.290741i | ||||
\(559\) | 21.3163 | 0.901584 | ||||||||
\(560\) | −14.5851 | − | 5.69816i | −0.616333 | − | 0.240791i | ||||
\(561\) | −24.4950 | −1.03418 | ||||||||
\(562\) | −0.883191 | + | 1.67265i | −0.0372552 | + | 0.0705564i | ||||
\(563\) | 9.74851 | 0.410851 | 0.205425 | − | 0.978673i | \(-0.434142\pi\) | ||||
0.205425 | + | 0.978673i | \(0.434142\pi\) | |||||||
\(564\) | −3.20858 | − | 4.69830i | −0.135106 | − | 0.197834i | ||||
\(565\) | 9.92254 | 0.417445 | ||||||||
\(566\) | 3.00541 | + | 1.58691i | 0.126327 | + | 0.0667030i | ||||
\(567\) | 3.91467 | 0.164401 | ||||||||
\(568\) | 32.8287 | − | 3.73755i | 1.37746 | − | 0.156824i | ||||
\(569\) | − | 33.0556i | − | 1.38576i | −0.721051 | − | 0.692882i | \(-0.756340\pi\) | ||
0.721051 | − | 0.692882i | \(-0.243660\pi\) | |||||||
\(570\) | 6.61580 | + | 3.49327i | 0.277105 | + | 0.146317i | ||||
\(571\) | 33.0864 | 1.38462 | 0.692311 | − | 0.721599i | \(-0.256593\pi\) | ||||
0.692311 | + | 0.721599i | \(0.256593\pi\) | |||||||
\(572\) | −24.9854 | − | 36.5860i | −1.04469 | − | 1.52974i | ||||
\(573\) | 18.0629i | 0.754587i | ||||||||
\(574\) | −51.1499 | − | 27.0082i | −2.13496 | − | 1.12730i | ||||
\(575\) | 3.05366 | + | 3.69800i | 0.127346 | + | 0.154217i | ||||
\(576\) | 7.79526 | − | 1.79829i | 0.324803 | − | 0.0749287i | ||||
\(577\) | −13.4401 | −0.559517 | −0.279759 | − | 0.960070i | \(-0.590254\pi\) | ||||
−0.279759 | + | 0.960070i | \(0.590254\pi\) | |||||||
\(578\) | 37.7956 | + | 19.9568i | 1.57209 | + | 0.830095i | ||||
\(579\) | − | 6.37298i | − | 0.264852i | ||||||
\(580\) | −11.8086 | + | 8.06435i | −0.490324 | + | 0.334854i | ||||
\(581\) | −12.0739 | −0.500910 | ||||||||
\(582\) | −9.94268 | − | 5.24993i | −0.412137 | − | 0.217617i | ||||
\(583\) | − | 39.3137i | − | 1.62821i | ||||||
\(584\) | −3.65095 | − | 32.0681i | −0.151077 | − | 1.32699i | ||||
\(585\) | 6.21448i | 0.256937i | ||||||||
\(586\) | 1.16737 | − | 2.21084i | 0.0482236 | − | 0.0913292i | ||||
\(587\) | − | 3.66303i | − | 0.151189i | −0.997139 | − | 0.0755947i | \(-0.975914\pi\) | ||
0.997139 | − | 0.0755947i | \(-0.0240855\pi\) | |||||||
\(588\) | 13.7490 | − | 9.38950i | 0.566998 | − | 0.387217i | ||||
\(589\) | 29.0522i | 1.19708i | ||||||||
\(590\) | −6.41341 | − | 3.38641i | −0.264036 | − | 0.139416i | ||||
\(591\) | − | 20.0921i | − | 0.826477i | ||||||
\(592\) | −4.88064 | − | 1.90679i | −0.200593 | − | 0.0783685i | ||||
\(593\) | −17.5134 | −0.719190 | −0.359595 | − | 0.933109i | \(-0.617085\pi\) | ||||
−0.359595 | + | 0.933109i | \(0.617085\pi\) | |||||||
\(594\) | 2.35379 | − | 4.45776i | 0.0965770 | − | 0.182904i | ||||
\(595\) | 26.9010 | 1.10283 | ||||||||
\(596\) | 0.941166 | − | 0.642745i | 0.0385516 | − | 0.0263278i | ||||
\(597\) | 5.03970i | 0.206261i | ||||||||
\(598\) | −8.55700 | − | 41.2709i | −0.349922 | − | 1.68769i | ||||
\(599\) | 8.21639i | 0.335713i | 0.985811 | + | 0.167856i | \(0.0536845\pi\) | ||||
−0.985811 | + | 0.167856i | \(0.946316\pi\) | |||||||
\(600\) | 2.81027 | − | 0.319949i | 0.114729 | − | 0.0130619i | ||||
\(601\) | 21.7813 | 0.888477 | 0.444238 | − | 0.895909i | \(-0.353474\pi\) | ||||
0.444238 | + | 0.895909i | \(0.353474\pi\) | |||||||
\(602\) | 16.7925 | + | 8.86677i | 0.684411 | + | 0.361382i | ||||
\(603\) | −14.0791 | −0.573346 | ||||||||
\(604\) | 21.1915 | − | 14.4722i | 0.862270 | − | 0.588865i | ||||
\(605\) | 1.70595i | 0.0693569i | ||||||||
\(606\) | 9.61821 | − | 18.2156i | 0.390713 | − | 0.739959i | ||||
\(607\) | − | 16.8882i | − | 0.685472i | −0.939432 | − | 0.342736i | \(-0.888646\pi\) | ||
0.939432 | − | 0.342736i | \(-0.111354\pi\) | |||||||
\(608\) | −22.6450 | + | 19.5641i | −0.918376 | + | 0.793427i | ||||
\(609\) | − | 27.9889i | − | 1.13417i | ||||||
\(610\) | −6.43603 | − | 3.39835i | −0.260587 | − | 0.137595i | ||||
\(611\) | 17.6782i | 0.715185i | ||||||||
\(612\) | −11.3496 | + | 7.75090i | −0.458780 | + | 0.313312i | ||||
\(613\) | 17.5741i | 0.709813i | 0.934902 | + | 0.354906i | \(0.115487\pi\) | ||||
−0.934902 | + | 0.354906i | \(0.884513\pi\) | |||||||
\(614\) | 10.0394 | − | 19.0132i | 0.405156 | − | 0.767312i | ||||
\(615\) | 10.4481 | 0.421308 | ||||||||
\(616\) | −4.46457 | − | 39.2145i | −0.179883 | − | 1.58000i | ||||
\(617\) | − | 47.2184i | − | 1.90094i | −0.310814 | − | 0.950471i | \(-0.600602\pi\) | ||
0.310814 | − | 0.950471i | \(-0.399398\pi\) | |||||||
\(618\) | −3.59170 | + | 6.80221i | −0.144479 | + | 0.273625i | ||||
\(619\) | 31.9904 | 1.28580 | 0.642902 | − | 0.765949i | \(-0.277730\pi\) | ||||
0.642902 | + | 0.765949i | \(0.277730\pi\) | |||||||
\(620\) | 6.19425 | + | 9.07018i | 0.248767 | + | 0.364267i | ||||
\(621\) | 3.69800 | − | 3.05366i | 0.148395 | − | 0.122539i | ||||
\(622\) | −1.01447 | + | 1.92128i | −0.0406767 | + | 0.0770363i | ||||
\(623\) | − | 29.0332i | − | 1.16319i | ||||||
\(624\) | −23.1536 | − | 9.04575i | −0.926887 | − | 0.362120i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 2.31688 | − | 4.38787i | 0.0926012 | − | 0.175374i | ||||
\(627\) | 18.8570i | 0.753077i | ||||||||
\(628\) | 22.6418 | − | 15.4626i | 0.903505 | − | 0.617025i | ||||
\(629\) | 9.00195 | 0.358931 | ||||||||
\(630\) | −2.58498 | + | 4.89562i | −0.102988 | + | 0.195046i | ||||
\(631\) | 0.295167 | 0.0117504 | 0.00587521 | − | 0.999983i | \(-0.498130\pi\) | ||||
0.00587521 | + | 0.999983i | \(0.498130\pi\) | |||||||
\(632\) | −0.174378 | − | 1.53165i | −0.00693640 | − | 0.0609258i | ||||
\(633\) | 17.2717 | 0.686487 | ||||||||
\(634\) | −23.6028 | − | 12.4627i | −0.937386 | − | 0.494959i | ||||
\(635\) | 4.13193 | 0.163971 | ||||||||
\(636\) | −12.4400 | − | 18.2157i | −0.493277 | − | 0.722301i | ||||
\(637\) | −51.7332 | −2.04974 | ||||||||
\(638\) | −31.8719 | − | 16.8290i | −1.26182 | − | 0.666266i | ||||
\(639\) | − | 11.6817i | − | 0.462120i | ||||||
\(640\) | −2.89856 | + | 10.9361i | −0.114576 | + | 0.432287i | ||||
\(641\) | − | 42.3493i | − | 1.67270i | −0.548197 | − | 0.836349i | \(-0.684686\pi\) | ||
0.548197 | − | 0.836349i | \(-0.315314\pi\) | |||||||
\(642\) | 2.03254 | − | 3.84936i | 0.0802180 | − | 0.151922i | ||||
\(643\) | 10.9530 | 0.431945 | 0.215972 | − | 0.976399i | \(-0.430708\pi\) | ||||
0.215972 | + | 0.976399i | \(0.430708\pi\) | |||||||
\(644\) | 10.4261 | − | 36.0716i | 0.410846 | − | 1.42142i | ||||
\(645\) | −3.43010 | −0.135060 | ||||||||
\(646\) | 24.0053 | − | 45.4628i | 0.944475 | − | 1.78871i | ||||
\(647\) | 9.57379i | 0.376384i | 0.982132 | + | 0.188192i | \(0.0602628\pi\) | ||||
−0.982132 | + | 0.188192i | \(0.939737\pi\) | |||||||
\(648\) | −0.319949 | − | 2.81027i | −0.0125688 | − | 0.110398i | ||||
\(649\) | − | 18.2802i | − | 0.717559i | ||||||
\(650\) | −7.77173 | − | 4.10363i | −0.304832 | − | 0.160958i | ||||
\(651\) | −21.4983 | −0.842586 | ||||||||
\(652\) | −32.9146 | + | 22.4781i | −1.28903 | + | 0.880312i | ||||
\(653\) | −32.7339 | −1.28098 | −0.640488 | − | 0.767968i | \(-0.721268\pi\) | ||||
−0.640488 | + | 0.767968i | \(0.721268\pi\) | |||||||
\(654\) | −7.03705 | − | 3.71570i | −0.275170 | − | 0.145295i | ||||
\(655\) | −13.3832 | −0.522926 | ||||||||
\(656\) | −15.2082 | + | 38.9271i | −0.593780 | + | 1.51985i | ||||
\(657\) | −11.4110 | −0.445186 | ||||||||
\(658\) | −7.35347 | + | 13.9265i | −0.286668 | + | 0.542912i | ||||
\(659\) | −30.6434 | −1.19370 | −0.596848 | − | 0.802354i | \(-0.703580\pi\) | ||||
−0.596848 | + | 0.802354i | \(0.703580\pi\) | |||||||
\(660\) | 4.02052 | + | 5.88721i | 0.156498 | + | 0.229159i | ||||
\(661\) | 33.9119i | 1.31902i | 0.751695 | + | 0.659511i | \(0.229236\pi\) | ||||
−0.751695 | + | 0.659511i | \(0.770764\pi\) | |||||||
\(662\) | 20.0806 | − | 38.0300i | 0.780455 | − | 1.47808i | ||||
\(663\) | 42.7050 | 1.65853 | ||||||||
\(664\) | 0.986811 | + | 8.66765i | 0.0382957 | + | 0.336370i | ||||
\(665\) | − | 20.7092i | − | 0.803070i | ||||||
\(666\) | −0.865019 | + | 1.63823i | −0.0335188 | + | 0.0634802i | ||||
\(667\) | −21.8329 | − | 26.4398i | −0.845373 | − | 1.02375i | ||||
\(668\) | 9.86489 | − | 6.73697i | 0.381684 | − | 0.260661i | ||||
\(669\) | 1.00859 | 0.0389944 | ||||||||
\(670\) | 9.29691 | − | 17.6071i | 0.359171 | − | 0.680223i | ||||
\(671\) | − | 18.3446i | − | 0.708186i | ||||||
\(672\) | −14.4772 | − | 16.7570i | −0.558470 | − | 0.646417i | ||||
\(673\) | 28.1079 | 1.08348 | 0.541740 | − | 0.840546i | \(-0.317766\pi\) | ||||
0.541740 | + | 0.840546i | \(0.317766\pi\) | |||||||
\(674\) | 22.4306 | − | 42.4806i | 0.863995 | − | 1.63629i | ||||
\(675\) | − | 1.00000i | − | 0.0384900i | ||||||
\(676\) | 28.8971 | + | 42.3137i | 1.11143 | + | 1.62745i | ||||
\(677\) | 27.8099i | 1.06882i | 0.845225 | + | 0.534410i | \(0.179466\pi\) | ||||
−0.845225 | + | 0.534410i | \(0.820534\pi\) | |||||||
\(678\) | 12.4090 | + | 6.55219i | 0.476564 | + | 0.251635i | ||||
\(679\) | 31.1233i | 1.19440i | ||||||||
\(680\) | −2.19865 | − | 19.3118i | −0.0843142 | − | 0.740573i | ||||
\(681\) | 27.6273i | 1.05868i | ||||||||
\(682\) | −12.9264 | + | 24.4809i | −0.494977 | + | 0.937420i | ||||
\(683\) | − | 19.3710i | − | 0.741212i | −0.928790 | − | 0.370606i | \(-0.879150\pi\) | ||
0.928790 | − | 0.370606i | \(-0.120850\pi\) | |||||||
\(684\) | 5.96689 | + | 8.73726i | 0.228150 | + | 0.334078i | ||||
\(685\) | 3.37576 | 0.128981 | ||||||||
\(686\) | −6.48482 | − | 3.42412i | −0.247592 | − | 0.130733i | ||||
\(687\) | −4.72289 | −0.180189 | ||||||||
\(688\) | 4.99284 | − | 12.7797i | 0.190350 | − | 0.487223i | ||||
\(689\) | 68.5402i | 2.61118i | ||||||||
\(690\) | 1.37695 | + | 6.64109i | 0.0524194 | + | 0.252822i | ||||
\(691\) | 26.2417i | 0.998283i | 0.866521 | + | 0.499141i | \(0.166351\pi\) | ||||
−0.866521 | + | 0.499141i | \(0.833649\pi\) | |||||||
\(692\) | −0.504227 | − | 0.738336i | −0.0191678 | − | 0.0280673i | ||||
\(693\) | −13.9540 | −0.530068 | ||||||||
\(694\) | −7.93938 | + | 15.0361i | −0.301375 | + | 0.570764i | ||||
\(695\) | −6.81463 | −0.258494 | ||||||||
\(696\) | −20.0928 | + | 2.28756i | −0.761614 | + | 0.0867097i | ||||
\(697\) | − | 71.7978i | − | 2.71954i | ||||||
\(698\) | 18.3796 | + | 9.70477i | 0.695676 | + | 0.367331i | ||||
\(699\) | − | 8.77953i | − | 0.332072i | ||||||
\(700\) | −4.41543 | − | 6.46548i | −0.166888 | − | 0.244372i | ||||
\(701\) | 11.6964i | 0.441767i | 0.975300 | + | 0.220884i | \(0.0708941\pi\) | ||||
−0.975300 | + | 0.220884i | \(0.929106\pi\) | |||||||
\(702\) | −4.10363 | + | 7.77173i | −0.154881 | + | 0.293325i | ||||
\(703\) | − | 6.92998i | − | 0.261369i | ||||||
\(704\) | −27.7865 | + | 6.41008i | −1.04724 | + | 0.241589i | ||||
\(705\) | − | 2.84469i | − | 0.107137i | ||||||
\(706\) | 22.9642 | + | 12.1256i | 0.864269 | + | 0.456352i | ||||
\(707\) | −57.0198 | −2.14445 | ||||||||
\(708\) | −5.78435 | − | 8.46997i | −0.217389 | − | 0.318321i | ||||
\(709\) | − | 4.90911i | − | 0.184365i | −0.995742 | − | 0.0921827i | \(-0.970616\pi\) | ||
0.995742 | − | 0.0921827i | \(-0.0293844\pi\) | |||||||
\(710\) | 14.6089 | + | 7.71381i | 0.548263 | + | 0.289494i | ||||
\(711\) | −0.545018 | −0.0204398 | ||||||||
\(712\) | −20.8424 | + | 2.37291i | −0.781103 | + | 0.0889285i | ||||
\(713\) | −20.3084 | + | 16.7699i | −0.760557 | + | 0.628038i | ||||
\(714\) | 33.6420 | + | 17.7636i | 1.25902 | + | 0.664788i | ||||
\(715\) | − | 22.1518i | − | 0.828429i | ||||||
\(716\) | 4.21044 | − | 2.87541i | 0.157351 | − | 0.107459i | ||||
\(717\) | 10.3755 | 0.387482 | ||||||||
\(718\) | 9.17291 | + | 4.84348i | 0.342330 | + | 0.180757i | ||||
\(719\) | − | 36.1521i | − | 1.34824i | −0.738620 | − | 0.674122i | \(-0.764522\pi\) | ||
0.738620 | − | 0.674122i | \(-0.235478\pi\) | |||||||
\(720\) | 3.72575 | + | 1.45559i | 0.138851 | + | 0.0542467i | ||||
\(721\) | 21.2928 | 0.792984 | ||||||||
\(722\) | −11.2376 | − | 5.93367i | −0.418220 | − | 0.220828i | ||||
\(723\) | −26.7704 | −0.995601 | ||||||||
\(724\) | 7.06844 | − | 4.82721i | 0.262696 | − | 0.179402i | ||||
\(725\) | −7.14975 | −0.265535 | ||||||||
\(726\) | −1.12650 | + | 2.13344i | −0.0418083 | + | 0.0791793i | ||||
\(727\) | −31.1631 | −1.15578 | −0.577888 | − | 0.816116i | \(-0.696123\pi\) | ||||
−0.577888 | + | 0.816116i | \(0.696123\pi\) | |||||||
\(728\) | 7.78361 | + | 68.3673i | 0.288480 | + | 2.53386i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 7.53508 | − | 14.2704i | 0.278886 | − | 0.528173i | ||||
\(731\) | 23.5712i | 0.871812i | ||||||||
\(732\) | −5.80475 | − | 8.49985i | −0.214550 | − | 0.314163i | ||||
\(733\) | 39.2366i | 1.44924i | 0.689151 | + | 0.724618i | \(0.257984\pi\) | ||||
−0.689151 | + | 0.724618i | \(0.742016\pi\) | |||||||
\(734\) | −10.8385 | − | 5.72296i | −0.400057 | − | 0.211238i | ||||
\(735\) | 8.32462 | 0.307058 | ||||||||
\(736\) | −26.7473 | − | 4.53656i | −0.985920 | − | 0.167220i | ||||
\(737\) | 50.1856 | 1.84861 | ||||||||
\(738\) | 13.0662 | + | 6.89923i | 0.480974 | + | 0.253964i | ||||
\(739\) | 42.3677i | 1.55852i | 0.626699 | + | 0.779261i | \(0.284405\pi\) | ||||
−0.626699 | + | 0.779261i | \(0.715595\pi\) | |||||||
\(740\) | −1.47755 | − | 2.16356i | −0.0543157 | − | 0.0795340i | ||||
\(741\) | − | 32.8756i | − | 1.20772i | ||||||
\(742\) | −28.5101 | + | 53.9944i | −1.04664 | + | 1.98220i | ||||
\(743\) | 0.526357 | 0.0193102 | 0.00965508 | − | 0.999953i | \(-0.496927\pi\) | ||||
0.00965508 | + | 0.999953i | \(0.496927\pi\) | |||||||
\(744\) | 1.75708 | + | 15.4333i | 0.0644177 | + | 0.565812i | ||||
\(745\) | 0.569849 | 0.0208777 | ||||||||
\(746\) | −3.79165 | + | 7.18089i | −0.138822 | + | 0.262911i | ||||
\(747\) | 3.08427 | 0.112848 | ||||||||
\(748\) | 40.4561 | − | 27.6284i | 1.47922 | − | 1.01019i | ||||
\(749\) | −12.0496 | −0.440281 | ||||||||
\(750\) | 1.25058 | + | 0.660333i | 0.0456649 | + | 0.0241120i | ||||
\(751\) | 11.1318 | 0.406205 | 0.203102 | − | 0.979158i | \(-0.434898\pi\) | ||||
0.203102 | + | 0.979158i | \(0.434898\pi\) | |||||||
\(752\) | 10.5986 | + | 4.14071i | 0.386491 | + | 0.150996i | ||||
\(753\) | − | 28.6509i | − | 1.04410i | ||||||
\(754\) | 55.5659 | + | 29.3399i | 2.02359 | + | 1.06850i | ||||
\(755\) | 12.8309 | 0.466963 | ||||||||
\(756\) | −6.46548 | + | 4.41543i | −0.235147 | + | 0.160588i | ||||
\(757\) | 4.84281i | 0.176015i | 0.996120 | + | 0.0880074i | \(0.0280499\pi\) | ||||
−0.996120 | + | 0.0880074i | \(0.971950\pi\) | |||||||
\(758\) | −5.75122 | − | 3.03676i | −0.208894 | − | 0.110300i | ||||
\(759\) | −13.1817 | + | 10.8849i | −0.478464 | + | 0.395096i | ||||
\(760\) | −14.8668 | + | 1.69259i | −0.539276 | + | 0.0613965i | ||||
\(761\) | 47.1174 | 1.70801 | 0.854003 | − | 0.520268i | \(-0.174168\pi\) | ||||
0.854003 | + | 0.520268i | \(0.174168\pi\) | |||||||
\(762\) | 5.16733 | + | 2.72845i | 0.187192 | + | 0.0988414i | ||||
\(763\) | 22.0279i | 0.797462i | ||||||||
\(764\) | −20.3735 | − | 29.8327i | −0.737086 | − | 1.07931i | ||||
\(765\) | −6.87185 | −0.248452 | ||||||||
\(766\) | −11.6818 | − | 6.16825i | −0.422082 | − | 0.222868i | ||||
\(767\) | 31.8699i | 1.15076i | ||||||||
\(768\) | −10.8464 | + | 11.7625i | −0.391385 | + | 0.424443i | ||||
\(769\) | − | 14.7753i | − | 0.532810i | −0.963861 | − | 0.266405i | \(-0.914164\pi\) | ||
0.963861 | − | 0.266405i | \(-0.0858358\pi\) | |||||||
\(770\) | 9.21428 | − | 17.4506i | 0.332060 | − | 0.628877i | ||||
\(771\) | − | 17.7379i | − | 0.638814i | ||||||
\(772\) | 7.18821 | + | 10.5256i | 0.258709 | + | 0.378826i | ||||
\(773\) | 8.69778i | 0.312837i | 0.987691 | + | 0.156419i | \(0.0499949\pi\) | ||||
−0.987691 | + | 0.156419i | \(0.950005\pi\) | |||||||
\(774\) | −4.28963 | − | 2.26501i | −0.154188 | − | 0.0814142i | ||||
\(775\) | 5.49174i | 0.197269i | ||||||||
\(776\) | 22.3429 | − | 2.54373i | 0.802063 | − | 0.0913148i | ||||
\(777\) | 5.12811 | 0.183970 | ||||||||
\(778\) | 16.4469 | − | 31.1482i | 0.589649 | − | 1.11672i | ||||
\(779\) | −55.2722 | −1.98033 | ||||||||
\(780\) | −7.00944 | − | 10.2639i | −0.250978 | − | 0.367505i | ||||
\(781\) | 41.6399i | 1.48999i | ||||||||
\(782\) | 45.6366 | − | 9.46217i | 1.63196 | − | 0.338367i | ||||
\(783\) | 7.14975i | 0.255511i | ||||||||
\(784\) | −12.1173 | + | 31.0155i | −0.432759 | + | 1.10770i | ||||
\(785\) | 13.7090 | 0.489294 | ||||||||
\(786\) | −16.7368 | − | 8.83739i | −0.596983 | − | 0.315219i | ||||
\(787\) | 15.4238 | 0.549798 | 0.274899 | − | 0.961473i | \(-0.411356\pi\) | ||||
0.274899 | + | 0.961473i | \(0.411356\pi\) | |||||||
\(788\) | 22.6622 | + | 33.1841i | 0.807309 | + | 1.18214i | ||||
\(789\) | 22.3989i | 0.797423i | ||||||||
\(790\) | 0.359894 | − | 0.681591i | 0.0128044 | − | 0.0242499i | ||||
\(791\) | − | 38.8435i | − | 1.38111i | ||||||
\(792\) | 1.14047 | + | 10.0173i | 0.0405249 | + | 0.355950i | ||||
\(793\) | 31.9823i | 1.13573i | ||||||||
\(794\) | −19.9626 | − | 10.5406i | −0.708445 | − | 0.374073i | ||||
\(795\) | − | 11.0291i | − | 0.391163i | ||||||
\(796\) | −5.68438 | − | 8.32359i | −0.201478 | − | 0.295022i | ||||
\(797\) | − | 36.7662i | − | 1.30233i | −0.758938 | − | 0.651163i | \(-0.774282\pi\) | ||
0.758938 | − | 0.651163i | \(-0.225718\pi\) | |||||||
\(798\) | 13.6750 | − | 25.8986i | 0.484090 | − | 0.916802i | ||||
\(799\) | −19.5483 | −0.691568 | ||||||||
\(800\) | −4.28058 | + | 3.69819i | −0.151341 | + | 0.130751i | ||||
\(801\) | 7.41651i | 0.262050i | ||||||||
\(802\) | 17.2030 | − | 32.5802i | 0.607459 | − | 1.15045i | ||||
\(803\) | 40.6751 | 1.43539 | ||||||||
\(804\) | 23.2531 | − | 15.8801i | 0.820075 | − | 0.560049i | ||||
\(805\) | 14.4764 | − | 11.9541i | 0.510227 | − | 0.421325i | ||||
\(806\) | 22.5361 | − | 42.6803i | 0.793799 | − | 1.50335i | ||||
\(807\) | − | 9.69449i | − | 0.341262i | ||||||
\(808\) | 4.66028 | + | 40.9335i | 0.163948 | + | 1.44004i | ||||
\(809\) | −10.4329 | −0.366800 | −0.183400 | − | 0.983038i | \(-0.558710\pi\) | ||||
−0.183400 | + | 0.983038i | \(0.558710\pi\) | |||||||
\(810\) | 0.660333 | − | 1.25058i | 0.0232017 | − | 0.0439410i | ||||
\(811\) | − | 10.9645i | − | 0.385017i | −0.981295 | − | 0.192509i | \(-0.938338\pi\) | ||
0.981295 | − | 0.192509i | \(-0.0616623\pi\) | |||||||
\(812\) | 31.5692 | + | 46.2266i | 1.10786 | + | 1.62224i | ||||
\(813\) | 2.94386 | 0.103246 | ||||||||
\(814\) | 3.08340 | − | 5.83955i | 0.108073 | − | 0.204676i | ||||
\(815\) | −19.9288 | −0.698077 | ||||||||
\(816\) | 10.0026 | − | 25.6028i | 0.350162 | − | 0.896279i | ||||
\(817\) | 18.1458 | 0.634842 | ||||||||
\(818\) | −12.3090 | − | 6.49938i | −0.430373 | − | 0.227245i | ||||
\(819\) | 24.3276 | 0.850076 | ||||||||
\(820\) | −17.2561 | + | 11.7846i | −0.602610 | + | 0.411537i | ||||
\(821\) | −35.1027 | −1.22509 | −0.612545 | − | 0.790435i | \(-0.709854\pi\) | ||||
−0.612545 | + | 0.790435i | \(0.709854\pi\) | |||||||
\(822\) | 4.22167 | + | 2.22913i | 0.147248 | + | 0.0777497i | ||||
\(823\) | 46.1419i | 1.60841i | 0.594355 | + | 0.804203i | \(0.297407\pi\) | ||||
−0.594355 | + | 0.804203i | \(0.702593\pi\) | |||||||
\(824\) | −1.74028 | − | 15.2857i | −0.0606254 | − | 0.532503i | ||||
\(825\) | 3.56454i | 0.124101i | ||||||||
\(826\) | −13.2567 | + | 25.1064i | −0.461258 | + | 0.873562i | ||||
\(827\) | 23.8671 | 0.829942 | 0.414971 | − | 0.909835i | \(-0.363792\pi\) | ||||
0.414971 | + | 0.909835i | \(0.363792\pi\) | |||||||
\(828\) | −2.66334 | + | 9.21448i | −0.0925576 | + | 0.320225i | ||||
\(829\) | −5.61865 | −0.195144 | −0.0975719 | − | 0.995228i | \(-0.531108\pi\) | ||||
−0.0975719 | + | 0.995228i | \(0.531108\pi\) | |||||||
\(830\) | −2.03665 | + | 3.85714i | −0.0706931 | + | 0.133883i | ||||
\(831\) | 29.7292i | 1.03129i | ||||||||
\(832\) | 48.4435 | − | 11.1754i | 1.67948 | − | 0.387439i | ||||
\(833\) | − | 57.2056i | − | 1.98206i | ||||||
\(834\) | −8.52227 | − | 4.49993i | −0.295102 | − | 0.155820i | ||||
\(835\) | 5.97291 | 0.206701 | ||||||||
\(836\) | −21.2692 | − | 31.1443i | −0.735611 | − | 1.07715i | ||||
\(837\) | 5.49174 | 0.189822 | ||||||||
\(838\) | −9.23811 | − | 4.87791i | −0.319125 | − | 0.168505i | ||||
\(839\) | 7.47060 | 0.257914 | 0.128957 | − | 0.991650i | \(-0.458837\pi\) | ||||
0.128957 | + | 0.991650i | \(0.458837\pi\) | |||||||
\(840\) | −1.25250 | − | 11.0013i | −0.0432152 | − | 0.379580i | ||||
\(841\) | 22.1190 | 0.762723 | ||||||||
\(842\) | 4.57622 | − | 8.66675i | 0.157707 | − | 0.298676i | ||||
\(843\) | −1.33749 | −0.0460657 | ||||||||
\(844\) | −28.5259 | + | 19.4811i | −0.981904 | + | 0.670565i | ||||
\(845\) | 25.6198i | 0.881347i | ||||||||
\(846\) | 1.87844 | − | 3.55752i | 0.0645821 | − | 0.122310i | ||||
\(847\) | 6.67824 | 0.229467 | ||||||||
\(848\) | 41.0918 | + | 16.0539i | 1.41110 | + | 0.551293i | ||||
\(849\) | 2.40320i | 0.0824777i | ||||||||
\(850\) | 4.53771 | − | 8.59383i | 0.155642 | − | 0.294766i | ||||
\(851\) | 4.84428 | − | 4.00021i | 0.166060 | − | 0.137126i | ||||
\(852\) | 13.1760 | + | 19.2935i | 0.451403 | + | 0.660985i | ||||
\(853\) | −3.94418 | −0.135046 | −0.0675231 | − | 0.997718i | \(-0.521510\pi\) | ||||
−0.0675231 | + | 0.997718i | \(0.521510\pi\) | |||||||
\(854\) | −13.3034 | + | 25.1949i | −0.455234 | + | 0.862152i | ||||
\(855\) | 5.29017i | 0.180920i | ||||||||
\(856\) | 0.984821 | + | 8.65017i | 0.0336605 | + | 0.295657i | ||||
\(857\) | −7.36707 | −0.251654 | −0.125827 | − | 0.992052i | \(-0.540158\pi\) | ||||
−0.125827 | + | 0.992052i | \(0.540158\pi\) | |||||||
\(858\) | 14.6276 | − | 27.7026i | 0.499376 | − | 0.945753i | ||||
\(859\) | 22.4648i | 0.766488i | 0.923647 | + | 0.383244i | \(0.125193\pi\) | ||||
−0.923647 | + | 0.383244i | \(0.874807\pi\) | |||||||
\(860\) | 5.66518 | − | 3.86888i | 0.193181 | − | 0.131928i | ||||
\(861\) | − | 40.9008i | − | 1.39390i | ||||||
\(862\) | −12.0328 | − | 6.35354i | −0.409838 | − | 0.216402i | ||||
\(863\) | − | 14.9997i | − | 0.510597i | −0.966862 | − | 0.255298i | \(-0.917826\pi\) | ||
0.966862 | − | 0.255298i | \(-0.0821737\pi\) | |||||||
\(864\) | 3.69819 | + | 4.28058i | 0.125815 | + | 0.145628i | ||||
\(865\) | − | 0.447042i | − | 0.0151999i | ||||||
\(866\) | −12.7990 | + | 24.2397i | −0.434929 | + | 0.823697i | ||||
\(867\) | 30.2224i | 1.02641i | ||||||||
\(868\) | 35.5068 | − | 24.2484i | 1.20518 | − | 0.823045i | ||||
\(869\) | 1.94274 | 0.0659030 | ||||||||
\(870\) | −8.94137 | − | 4.72122i | −0.303141 | − | 0.160064i | ||||
\(871\) | −87.4944 | −2.96464 | ||||||||
\(872\) | 15.8134 | − | 1.80036i | 0.535510 | − | 0.0609678i | ||||
\(873\) | − | 7.95043i | − | 0.269081i | ||||||
\(874\) | −7.28427 | − | 35.1325i | −0.246394 | − | 1.18837i | ||||
\(875\) | − | 3.91467i | − | 0.132340i | ||||||
\(876\) | 18.8465 | − | 12.8707i | 0.636764 | − | 0.434861i | ||||
\(877\) | −5.85851 | −0.197828 | −0.0989138 | − | 0.995096i | \(-0.531537\pi\) | ||||
−0.0989138 | + | 0.995096i | \(0.531537\pi\) | |||||||
\(878\) | −3.29776 | + | 6.24552i | −0.111294 | + | 0.210776i | ||||
\(879\) | 1.76785 | 0.0596281 | ||||||||
\(880\) | −13.2806 | − | 5.18852i | −0.447689 | − | 0.174905i | ||||
\(881\) | 37.0664i | 1.24880i | 0.781105 | + | 0.624399i | \(0.214656\pi\) | ||||
−0.781105 | + | 0.624399i | \(0.785344\pi\) | |||||||
\(882\) | 10.4106 | + | 5.49702i | 0.350544 | + | 0.185094i | ||||
\(883\) | − | 26.2767i | − | 0.884282i | −0.896946 | − | 0.442141i | \(-0.854219\pi\) | ||
0.896946 | − | 0.442141i | \(-0.145781\pi\) | |||||||
\(884\) | −70.5318 | + | 48.1678i | −2.37224 | + | 1.62006i | ||||
\(885\) | − | 5.12833i | − | 0.172387i | ||||||
\(886\) | 9.95878 | − | 18.8606i | 0.334572 | − | 0.633635i | ||||
\(887\) | 43.4303i | 1.45825i | 0.684382 | + | 0.729124i | \(0.260072\pi\) | ||||
−0.684382 | + | 0.729124i | \(0.739928\pi\) | |||||||
\(888\) | −0.419125 | − | 3.68138i | −0.0140649 | − | 0.123539i | ||||
\(889\) | − | 16.1751i | − | 0.542497i | ||||||
\(890\) | −9.27497 | − | 4.89737i | −0.310898 | − | 0.164160i | ||||
\(891\) | 3.56454 | 0.119417 | ||||||||
\(892\) | −1.66579 | + | 1.13761i | −0.0557748 | + | 0.0380900i | ||||
\(893\) | 15.0489i | 0.503591i | ||||||||
\(894\) | 0.712644 | + | 0.376291i | 0.0238344 | + | 0.0125850i | ||||
\(895\) | 2.54930 | 0.0852137 | ||||||||
\(896\) | 42.8112 | + | 11.3469i | 1.43022 | + | 0.379073i | ||||
\(897\) | 22.9811 | − | 18.9769i | 0.767317 | − | 0.633620i | ||||
\(898\) | −43.7036 | − | 23.0764i | −1.45841 | − | 0.770068i | ||||
\(899\) | − | 39.2646i | − | 1.30955i | ||||||
\(900\) | 1.12792 | + | 1.65160i | 0.0375973 | + | 0.0550535i | ||||
\(901\) | −75.7905 | −2.52495 | ||||||||
\(902\) | −46.5751 | − | 24.5926i | −1.55078 | − | 0.818843i | ||||
\(903\) | 13.4277i | 0.446846i | ||||||||
\(904\) | −27.8851 | + | 3.17471i | −0.927443 | + | 0.105589i | ||||
\(905\) | 4.27974 | 0.142263 | ||||||||
\(906\) | 16.0461 | + | 8.47264i | 0.533095 | + | 0.281485i | ||||
\(907\) | 53.8160 | 1.78693 | 0.893465 | − | 0.449132i | \(-0.148267\pi\) | ||||
0.893465 | + | 0.449132i | \(0.148267\pi\) | |||||||
\(908\) | −31.1614 | − | 45.6294i | −1.03413 | − | 1.51426i | ||||
\(909\) | 14.5657 | 0.483113 | ||||||||
\(910\) | −16.0643 | + | 30.4237i | −0.532528 | + | 1.00854i | ||||
\(911\) | 21.1665 | 0.701277 | 0.350639 | − | 0.936511i | \(-0.385965\pi\) | ||||
0.350639 | + | 0.936511i | \(0.385965\pi\) | |||||||
\(912\) | −19.7099 | − | 7.70033i | −0.652659 | − | 0.254983i | ||||
\(913\) | −10.9940 | −0.363849 | ||||||||
\(914\) | 10.7758 | − | 20.4080i | 0.356433 | − | 0.675038i | ||||
\(915\) | − | 5.14642i | − | 0.170135i | ||||||
\(916\) | 7.80034 | − | 5.32704i | 0.257731 | − | 0.176010i | ||||
\(917\) | 52.3908i | 1.73010i | ||||||||
\(918\) | −8.59383 | − | 4.53771i | −0.283639 | − | 0.149767i | ||||
\(919\) | −18.8274 | −0.621060 | −0.310530 | − | 0.950564i | \(-0.600506\pi\) | ||||
−0.310530 | + | 0.950564i | \(0.600506\pi\) | |||||||
\(920\) | −9.76478 | − | 9.41536i | −0.321935 | − | 0.310415i | ||||
\(921\) | 15.2035 | 0.500972 | ||||||||
\(922\) | 0.141162 | + | 0.0745365i | 0.00464893 | + | 0.00245473i | ||||
\(923\) | − | 72.5956i | − | 2.38951i | ||||||
\(924\) | 23.0465 | − | 15.7390i | 0.758173 | − | 0.517775i | ||||
\(925\) | − | 1.30997i | − | 0.0430717i | ||||||
\(926\) | 18.1430 | − | 34.3605i | 0.596216 | − | 1.12916i | ||||
\(927\) | −5.43923 | −0.178648 | ||||||||
\(928\) | 30.6051 | − | 26.4412i | 1.00466 | − | 0.867974i | ||||
\(929\) | 21.0228 | 0.689734 | 0.344867 | − | 0.938651i | \(-0.387924\pi\) | ||||
0.344867 | + | 0.938651i | \(0.387924\pi\) | |||||||
\(930\) | −3.62638 | + | 6.86788i | −0.118914 | + | 0.225207i | ||||
\(931\) | −44.0386 | −1.44331 | ||||||||
\(932\) | 9.90260 | + | 14.5003i | 0.324371 | + | 0.474973i | ||||
\(933\) | −1.53631 | −0.0502964 | ||||||||
\(934\) | 12.7380 | + | 6.72591i | 0.416800 | + | 0.220079i | ||||
\(935\) | 24.4950 | 0.801072 | ||||||||
\(936\) | −1.98832 | − | 17.4644i | −0.0649902 | − | 0.570841i | ||||
\(937\) | − | 57.7881i | − | 1.88786i | −0.330151 | − | 0.943928i | \(-0.607100\pi\) | ||
0.330151 | − | 0.943928i | \(-0.392900\pi\) | |||||||
\(938\) | −68.9260 | − | 36.3943i | −2.25051 | − | 1.18832i | ||||
\(939\) | 3.50866 | 0.114501 | ||||||||
\(940\) | 3.20858 | + | 4.69830i | 0.104652 | + | 0.153242i | ||||
\(941\) | − | 29.4007i | − | 0.958435i | −0.877696 | − | 0.479217i | \(-0.840921\pi\) | ||
0.877696 | − | 0.479217i | \(-0.159079\pi\) | |||||||
\(942\) | 17.1442 | + | 9.05248i | 0.558588 | + | 0.294946i | ||||
\(943\) | −31.9049 | − | 38.6370i | −1.03897 | − | 1.25819i | ||||
\(944\) | 19.1069 | + | 7.46476i | 0.621877 | + | 0.242957i | ||||
\(945\) | −3.91467 | −0.127344 | ||||||||
\(946\) | 15.2906 | + | 8.07373i | 0.497139 | + | 0.262500i | ||||
\(947\) | 50.6199i | 1.64493i | 0.568819 | + | 0.822463i | \(0.307401\pi\) | ||||
−0.568819 | + | 0.822463i | \(0.692599\pi\) | |||||||
\(948\) | 0.900155 | − | 0.614737i | 0.0292357 | − | 0.0199657i | ||||
\(949\) | −70.9136 | −2.30195 | ||||||||
\(950\) | −6.61580 | − | 3.49327i | −0.214645 | − | 0.113337i | ||||
\(951\) | − | 18.8734i | − | 0.612012i | ||||||
\(952\) | −75.5992 | + | 8.60696i | −2.45018 | + | 0.278953i | ||||
\(953\) | − | 53.7967i | − | 1.74265i | −0.490711 | − | 0.871323i | \(-0.663263\pi\) | ||
0.490711 | − | 0.871323i | \(-0.336737\pi\) | |||||||
\(954\) | 7.28289 | − | 13.7928i | 0.235792 | − | 0.446560i | ||||
\(955\) | − | 18.0629i | − | 0.584500i | ||||||
\(956\) | −17.1363 | + | 11.7028i | −0.554227 | + | 0.378495i | ||||
\(957\) | − | 25.4856i | − | 0.823832i | ||||||
\(958\) | 11.9526 | + | 6.31121i | 0.386171 | + | 0.203906i | ||||
\(959\) | − | 13.2150i | − | 0.426734i | ||||||
\(960\) | −7.79526 | + | 1.79829i | −0.251591 | + | 0.0580396i | ||||
\(961\) | 0.840766 | 0.0271215 | ||||||||
\(962\) | −5.37565 | + | 10.1808i | −0.173318 | + | 0.328241i | ||||
\(963\) | 3.07805 | 0.0991889 | ||||||||
\(964\) | 44.2141 | − | 30.1948i | 1.42404 | − | 0.972510i | ||||
\(965\) | 6.37298i | 0.205154i | ||||||||
\(966\) | 25.9976 | − | 5.39028i | 0.836460 | − | 0.173430i | ||||
\(967\) | 37.8789i | 1.21810i | 0.793131 | + | 0.609051i | \(0.208450\pi\) | ||||
−0.793131 | + | 0.609051i | \(0.791550\pi\) | |||||||
\(968\) | −0.545819 | − | 4.79419i | −0.0175433 | − | 0.154091i | ||||
\(969\) | 36.3533 | 1.16784 | ||||||||
\(970\) | 9.94268 | + | 5.24993i | 0.319240 | + | 0.168565i | ||||
\(971\) | −34.0734 | −1.09347 | −0.546734 | − | 0.837306i | \(-0.684129\pi\) | ||||
−0.546734 | + | 0.837306i | \(0.684129\pi\) | |||||||
\(972\) | 1.65160 | − | 1.12792i | 0.0529752 | − | 0.0361781i | ||||
\(973\) | 26.6770i | 0.855226i | ||||||||
\(974\) | 21.4924 | − | 40.7038i | 0.688661 | − | 1.30423i | ||||
\(975\) | − | 6.21448i | − | 0.199023i | ||||||
\(976\) | 19.1743 | + | 7.49109i | 0.613754 | + | 0.239784i | ||||
\(977\) | 45.1720i | 1.44518i | 0.691277 | + | 0.722590i | \(0.257049\pi\) | ||||
−0.691277 | + | 0.722590i | \(0.742951\pi\) | |||||||
\(978\) | −24.9227 | − | 13.1597i | −0.796940 | − | 0.420800i | ||||
\(979\) | − | 26.4365i | − | 0.844913i | ||||||
\(980\) | −13.7490 | + | 9.38950i | −0.439195 | + | 0.299937i | ||||
\(981\) | − | 5.62701i | − | 0.179657i | ||||||
\(982\) | −3.67487 | + | 6.95972i | −0.117270 | + | 0.222093i | ||||
\(983\) | −18.5440 | −0.591462 | −0.295731 | − | 0.955271i | \(-0.595563\pi\) | ||||
−0.295731 | + | 0.955271i | \(0.595563\pi\) | |||||||
\(984\) | −29.3620 | + | 3.34286i | −0.936027 | + | 0.106567i | ||||
\(985\) | 20.0921i | 0.640186i | ||||||||
\(986\) | −32.4435 | + | 61.4438i | −1.03321 | + | 1.95677i | ||||
\(987\) | −11.1360 | −0.354463 | ||||||||
\(988\) | 37.0811 | + | 54.2976i | 1.17971 | + | 1.72744i | ||||
\(989\) | 10.4744 | + | 12.6845i | 0.333065 | + | 0.403344i | ||||
\(990\) | −2.35379 | + | 4.45776i | −0.0748082 | + | 0.141677i | ||||
\(991\) | 24.2053i | 0.768906i | 0.923145 | + | 0.384453i | \(0.125610\pi\) | ||||
−0.923145 | + | 0.384453i | \(0.874390\pi\) | |||||||
\(992\) | −20.3095 | − | 23.5078i | −0.644828 | − | 0.746375i | ||||
\(993\) | 30.4098 | 0.965026 | ||||||||
\(994\) | 30.1970 | − | 57.1891i | 0.957790 | − | 1.81393i | ||||
\(995\) | − | 5.03970i | − | 0.159769i | ||||||
\(996\) | −5.09400 | + | 3.47881i | −0.161410 | + | 0.110230i | ||||
\(997\) | 20.5579 | 0.651074 | 0.325537 | − | 0.945529i | \(-0.394455\pi\) | ||||
0.325537 | + | 0.945529i | \(0.394455\pi\) | |||||||
\(998\) | −21.7806 | + | 41.2496i | −0.689453 | + | 1.30573i | ||||
\(999\) | −1.30997 | −0.0414457 |
(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 | 1380.2.p.b.91.7 | yes | 48 | |
4.3 | odd | 2 | 1380.2.p.a.91.8 | yes | 48 | ||
23.22 | odd | 2 | 1380.2.p.a.91.7 | ✓ | 48 | ||
92.91 | even | 2 | inner | 1380.2.p.b.91.8 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1380.2.p.a.91.7 | ✓ | 48 | 23.22 | odd | 2 | ||
1380.2.p.a.91.8 | yes | 48 | 4.3 | odd | 2 | ||
1380.2.p.b.91.7 | yes | 48 | 1.1 | even | 1 | trivial | |
1380.2.p.b.91.8 | yes | 48 | 92.91 | even | 2 | inner |