Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(461,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.461");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.g (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: | \(18.8011382409\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 461.14 | ||
Character | \(\chi\) | \(=\) | 690.461 |
Dual form | 690.3.g.a.461.13 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421i | 0.707107i | ||||||||
\(3\) | −1.34299 | + | 2.68261i | −0.447664 | + | 0.894202i | ||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 2.23607i | 0.447214i | ||||||||
\(6\) | −3.79378 | − | 1.89928i | −0.632296 | − | 0.316546i | ||||
\(7\) | −8.50482 | −1.21497 | −0.607487 | − | 0.794329i | \(-0.707822\pi\) | ||||
−0.607487 | + | 0.794329i | \(0.707822\pi\) | |||||||
\(8\) | − | 2.82843i | − | 0.353553i | ||||||
\(9\) | −5.39274 | − | 7.20544i | −0.599194 | − | 0.800604i | ||||
\(10\) | −3.16228 | −0.316228 | ||||||||
\(11\) | 13.2166i | 1.20151i | 0.799434 | + | 0.600754i | \(0.205133\pi\) | ||||
−0.799434 | + | 0.600754i | \(0.794867\pi\) | |||||||
\(12\) | 2.68599 | − | 5.36521i | 0.223832 | − | 0.447101i | ||||
\(13\) | 3.60104 | 0.277003 | 0.138501 | − | 0.990362i | \(-0.455771\pi\) | ||||
0.138501 | + | 0.990362i | \(0.455771\pi\) | |||||||
\(14\) | − | 12.0276i | − | 0.859117i | ||||||
\(15\) | −5.99849 | − | 3.00302i | −0.399899 | − | 0.200202i | ||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − | 0.776501i | − | 0.0456765i | −0.999739 | − | 0.0228383i | \(-0.992730\pi\) | ||
0.999739 | − | 0.0228383i | \(-0.00727028\pi\) | |||||||
\(18\) | 10.1900 | − | 7.62649i | 0.566113 | − | 0.423694i | ||||
\(19\) | −36.7798 | −1.93578 | −0.967888 | − | 0.251380i | \(-0.919116\pi\) | ||||
−0.967888 | + | 0.251380i | \(0.919116\pi\) | |||||||
\(20\) | − | 4.47214i | − | 0.223607i | ||||||
\(21\) | 11.4219 | − | 22.8151i | 0.543901 | − | 1.08643i | ||||
\(22\) | −18.6911 | −0.849594 | ||||||||
\(23\) | − | 4.79583i | − | 0.208514i | ||||||
\(24\) | 7.58755 | + | 3.79856i | 0.316148 | + | 0.158273i | ||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 5.09264i | 0.195871i | ||||||||
\(27\) | 26.5718 | − | 4.78975i | 0.984139 | − | 0.177398i | ||||
\(28\) | 17.0096 | 0.607487 | ||||||||
\(29\) | − | 25.4478i | − | 0.877511i | −0.898607 | − | 0.438755i | \(-0.855419\pi\) | ||
0.898607 | − | 0.438755i | \(-0.144581\pi\) | |||||||
\(30\) | 4.24692 | − | 8.48314i | 0.141564 | − | 0.282771i | ||||
\(31\) | 34.1895 | 1.10289 | 0.551444 | − | 0.834212i | \(-0.314077\pi\) | ||||
0.551444 | + | 0.834212i | \(0.314077\pi\) | |||||||
\(32\) | 5.65685i | 0.176777i | ||||||||
\(33\) | −35.4549 | − | 17.7498i | −1.07439 | − | 0.537872i | ||||
\(34\) | 1.09814 | 0.0322982 | ||||||||
\(35\) | − | 19.0174i | − | 0.543353i | ||||||
\(36\) | 10.7855 | + | 14.4109i | 0.299597 | + | 0.400302i | ||||
\(37\) | 33.7342 | 0.911736 | 0.455868 | − | 0.890047i | \(-0.349329\pi\) | ||||
0.455868 | + | 0.890047i | \(0.349329\pi\) | |||||||
\(38\) | − | 52.0144i | − | 1.36880i | ||||||
\(39\) | −4.83617 | + | 9.66016i | −0.124004 | + | 0.247697i | ||||
\(40\) | 6.32456 | 0.158114 | ||||||||
\(41\) | − | 41.1741i | − | 1.00425i | −0.864796 | − | 0.502124i | \(-0.832552\pi\) | ||
0.864796 | − | 0.502124i | \(-0.167448\pi\) | |||||||
\(42\) | 32.2654 | + | 16.1530i | 0.768224 | + | 0.384596i | ||||
\(43\) | 30.1714 | 0.701659 | 0.350830 | − | 0.936439i | \(-0.385900\pi\) | ||||
0.350830 | + | 0.936439i | \(0.385900\pi\) | |||||||
\(44\) | − | 26.4332i | − | 0.600754i | ||||||
\(45\) | 16.1118 | − | 12.0585i | 0.358041 | − | 0.267967i | ||||
\(46\) | 6.78233 | 0.147442 | ||||||||
\(47\) | − | 6.22979i | − | 0.132549i | −0.997801 | − | 0.0662743i | \(-0.978889\pi\) | ||
0.997801 | − | 0.0662743i | \(-0.0211112\pi\) | |||||||
\(48\) | −5.37197 | + | 10.7304i | −0.111916 | + | 0.223550i | ||||
\(49\) | 23.3320 | 0.476164 | ||||||||
\(50\) | − | 7.07107i | − | 0.141421i | ||||||
\(51\) | 2.08305 | + | 1.04284i | 0.0408440 | + | 0.0204478i | ||||
\(52\) | −7.20208 | −0.138501 | ||||||||
\(53\) | 15.6386i | 0.295068i | 0.989057 | + | 0.147534i | \(0.0471336\pi\) | ||||
−0.989057 | + | 0.147534i | \(0.952866\pi\) | |||||||
\(54\) | 6.77372 | + | 37.5781i | 0.125439 | + | 0.695891i | ||||
\(55\) | −29.5532 | −0.537331 | ||||||||
\(56\) | 24.0553i | 0.429558i | ||||||||
\(57\) | 49.3949 | − | 98.6656i | 0.866578 | − | 1.73097i | ||||
\(58\) | 35.9886 | 0.620494 | ||||||||
\(59\) | 70.7460i | 1.19908i | 0.800343 | + | 0.599542i | \(0.204651\pi\) | ||||
−0.800343 | + | 0.599542i | \(0.795349\pi\) | |||||||
\(60\) | 11.9970 | + | 6.00605i | 0.199950 | + | 0.100101i | ||||
\(61\) | −71.2693 | −1.16835 | −0.584174 | − | 0.811628i | \(-0.698582\pi\) | ||||
−0.584174 | + | 0.811628i | \(0.698582\pi\) | |||||||
\(62\) | 48.3513i | 0.779860i | ||||||||
\(63\) | 45.8643 | + | 61.2810i | 0.728005 | + | 0.972714i | ||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 8.05217i | 0.123879i | ||||||||
\(66\) | 25.1020 | − | 50.1408i | 0.380333 | − | 0.759709i | ||||
\(67\) | −107.782 | −1.60869 | −0.804346 | − | 0.594162i | \(-0.797484\pi\) | ||||
−0.804346 | + | 0.594162i | \(0.797484\pi\) | |||||||
\(68\) | 1.55300i | 0.0228383i | ||||||||
\(69\) | 12.8653 | + | 6.44077i | 0.186454 | + | 0.0933444i | ||||
\(70\) | 26.8946 | 0.384209 | ||||||||
\(71\) | 110.094i | 1.55062i | 0.631581 | + | 0.775310i | \(0.282406\pi\) | ||||
−0.631581 | + | 0.775310i | \(0.717594\pi\) | |||||||
\(72\) | −20.3801 | + | 15.2530i | −0.283056 | + | 0.211847i | ||||
\(73\) | 86.0156 | 1.17830 | 0.589148 | − | 0.808025i | \(-0.299464\pi\) | ||||
0.589148 | + | 0.808025i | \(0.299464\pi\) | |||||||
\(74\) | 47.7074i | 0.644695i | ||||||||
\(75\) | 6.71496 | − | 13.4130i | 0.0895328 | − | 0.178840i | ||||
\(76\) | 73.5595 | 0.967888 | ||||||||
\(77\) | − | 112.405i | − | 1.45980i | ||||||
\(78\) | −13.6615 | − | 6.83937i | −0.175148 | − | 0.0876843i | ||||
\(79\) | 72.6189 | 0.919227 | 0.459614 | − | 0.888119i | \(-0.347988\pi\) | ||||
0.459614 | + | 0.888119i | \(0.347988\pi\) | |||||||
\(80\) | 8.94427i | 0.111803i | ||||||||
\(81\) | −22.8367 | + | 77.7141i | −0.281934 | + | 0.959434i | ||||
\(82\) | 58.2290 | 0.710110 | ||||||||
\(83\) | − | 150.313i | − | 1.81100i | −0.424350 | − | 0.905498i | \(-0.639497\pi\) | ||
0.424350 | − | 0.905498i | \(-0.360503\pi\) | |||||||
\(84\) | −22.8438 | + | 45.6302i | −0.271950 | + | 0.543216i | ||||
\(85\) | 1.73631 | 0.0204272 | ||||||||
\(86\) | 42.6687i | 0.496148i | ||||||||
\(87\) | 68.2664 | + | 34.1762i | 0.784672 | + | 0.392830i | ||||
\(88\) | 37.3822 | 0.424797 | ||||||||
\(89\) | − | 135.965i | − | 1.52770i | −0.645396 | − | 0.763849i | \(-0.723307\pi\) | ||
0.645396 | − | 0.763849i | \(-0.276693\pi\) | |||||||
\(90\) | 17.0533 | + | 22.7856i | 0.189482 | + | 0.253173i | ||||
\(91\) | −30.6262 | −0.336552 | ||||||||
\(92\) | 9.59166i | 0.104257i | ||||||||
\(93\) | −45.9163 | + | 91.7170i | −0.493723 | + | 0.986204i | ||||
\(94\) | 8.81025 | 0.0937260 | ||||||||
\(95\) | − | 82.2420i | − | 0.865706i | ||||||
\(96\) | −15.1751 | − | 7.59711i | −0.158074 | − | 0.0791366i | ||||
\(97\) | 187.823 | 1.93632 | 0.968160 | − | 0.250331i | \(-0.0805396\pi\) | ||||
0.968160 | + | 0.250331i | \(0.0805396\pi\) | |||||||
\(98\) | 32.9965i | 0.336699i | ||||||||
\(99\) | 95.2313 | − | 71.2736i | 0.961932 | − | 0.719936i | ||||
\(100\) | 10.0000 | 0.100000 | ||||||||
\(101\) | 44.1749i | 0.437375i | 0.975795 | + | 0.218687i | \(0.0701775\pi\) | ||||
−0.975795 | + | 0.218687i | \(0.929822\pi\) | |||||||
\(102\) | −1.47479 | + | 2.94587i | −0.0144587 | + | 0.0288811i | ||||
\(103\) | −50.1604 | −0.486994 | −0.243497 | − | 0.969902i | \(-0.578295\pi\) | ||||
−0.243497 | + | 0.969902i | \(0.578295\pi\) | |||||||
\(104\) | − | 10.1853i | − | 0.0979353i | ||||||
\(105\) | 51.0161 | + | 25.5402i | 0.485867 | + | 0.243240i | ||||
\(106\) | −22.1163 | −0.208645 | ||||||||
\(107\) | − | 156.326i | − | 1.46099i | −0.682917 | − | 0.730496i | \(-0.739289\pi\) | ||
0.682917 | − | 0.730496i | \(-0.260711\pi\) | |||||||
\(108\) | −53.1435 | + | 9.57949i | −0.492070 | + | 0.0886990i | ||||
\(109\) | −199.822 | −1.83322 | −0.916612 | − | 0.399777i | \(-0.869088\pi\) | ||||
−0.916612 | + | 0.399777i | \(0.869088\pi\) | |||||||
\(110\) | − | 41.7945i | − | 0.379950i | ||||||
\(111\) | −45.3048 | + | 90.4957i | −0.408152 | + | 0.815276i | ||||
\(112\) | −34.0193 | −0.303744 | ||||||||
\(113\) | − | 9.47173i | − | 0.0838207i | −0.999121 | − | 0.0419103i | \(-0.986656\pi\) | ||
0.999121 | − | 0.0419103i | \(-0.0133444\pi\) | |||||||
\(114\) | 139.534 | + | 69.8550i | 1.22398 | + | 0.612763i | ||||
\(115\) | 10.7238 | 0.0932505 | ||||||||
\(116\) | 50.8956i | 0.438755i | ||||||||
\(117\) | −19.4195 | − | 25.9471i | −0.165978 | − | 0.221770i | ||||
\(118\) | −100.050 | −0.847880 | ||||||||
\(119\) | 6.60401i | 0.0554959i | ||||||||
\(120\) | −8.49383 | + | 16.9663i | −0.0707819 | + | 0.141386i | ||||
\(121\) | −53.6782 | −0.443621 | ||||||||
\(122\) | − | 100.790i | − | 0.826147i | ||||||
\(123\) | 110.454 | + | 55.2966i | 0.897999 | + | 0.449565i | ||||
\(124\) | −68.3791 | −0.551444 | ||||||||
\(125\) | − | 11.1803i | − | 0.0894427i | ||||||
\(126\) | −86.6644 | + | 64.8619i | −0.687813 | + | 0.514777i | ||||
\(127\) | 87.0946 | 0.685784 | 0.342892 | − | 0.939375i | \(-0.388594\pi\) | ||||
0.342892 | + | 0.939375i | \(0.388594\pi\) | |||||||
\(128\) | − | 11.3137i | − | 0.0883883i | ||||||
\(129\) | −40.5199 | + | 80.9378i | −0.314108 | + | 0.627425i | ||||
\(130\) | −11.3875 | −0.0875960 | ||||||||
\(131\) | − | 55.2935i | − | 0.422088i | −0.977477 | − | 0.211044i | \(-0.932314\pi\) | ||
0.977477 | − | 0.211044i | \(-0.0676863\pi\) | |||||||
\(132\) | 70.9098 | + | 35.4996i | 0.537195 | + | 0.268936i | ||||
\(133\) | 312.805 | 2.35192 | ||||||||
\(134\) | − | 152.427i | − | 1.13752i | ||||||
\(135\) | 10.7102 | + | 59.4163i | 0.0793348 | + | 0.440120i | ||||
\(136\) | −2.19628 | −0.0161491 | ||||||||
\(137\) | − | 128.257i | − | 0.936181i | −0.883681 | − | 0.468090i | \(-0.844942\pi\) | ||
0.883681 | − | 0.468090i | \(-0.155058\pi\) | |||||||
\(138\) | −9.10862 | + | 18.1943i | −0.0660045 | + | 0.131843i | ||||
\(139\) | −142.423 | −1.02463 | −0.512313 | − | 0.858799i | \(-0.671211\pi\) | ||||
−0.512313 | + | 0.858799i | \(0.671211\pi\) | |||||||
\(140\) | 38.0347i | 0.271677i | ||||||||
\(141\) | 16.7121 | + | 8.36656i | 0.118525 | + | 0.0593373i | ||||
\(142\) | −155.696 | −1.09645 | ||||||||
\(143\) | 47.5934i | 0.332821i | ||||||||
\(144\) | −21.5710 | − | 28.8218i | −0.149798 | − | 0.200151i | ||||
\(145\) | 56.9030 | 0.392435 | ||||||||
\(146\) | 121.644i | 0.833181i | ||||||||
\(147\) | −31.3347 | + | 62.5906i | −0.213161 | + | 0.425786i | ||||
\(148\) | −67.4685 | −0.455868 | ||||||||
\(149\) | − | 143.307i | − | 0.961793i | −0.876777 | − | 0.480897i | \(-0.840311\pi\) | ||
0.876777 | − | 0.480897i | \(-0.159689\pi\) | |||||||
\(150\) | 18.9689 | + | 9.49639i | 0.126459 | + | 0.0633093i | ||||
\(151\) | −146.838 | −0.972439 | −0.486219 | − | 0.873837i | \(-0.661624\pi\) | ||||
−0.486219 | + | 0.873837i | \(0.661624\pi\) | |||||||
\(152\) | 104.029i | 0.684400i | ||||||||
\(153\) | −5.59503 | + | 4.18747i | −0.0365688 | + | 0.0273691i | ||||
\(154\) | 158.964 | 1.03224 | ||||||||
\(155\) | 76.4501i | 0.493226i | ||||||||
\(156\) | 9.67234 | − | 19.3203i | 0.0620022 | − | 0.123848i | ||||
\(157\) | −200.244 | −1.27544 | −0.637720 | − | 0.770269i | \(-0.720122\pi\) | ||||
−0.637720 | + | 0.770269i | \(0.720122\pi\) | |||||||
\(158\) | 102.699i | 0.649992i | ||||||||
\(159\) | −41.9522 | − | 21.0025i | −0.263850 | − | 0.132091i | ||||
\(160\) | −12.6491 | −0.0790569 | ||||||||
\(161\) | 40.7877i | 0.253340i | ||||||||
\(162\) | −109.904 | − | 32.2959i | −0.678422 | − | 0.199358i | ||||
\(163\) | −185.503 | −1.13805 | −0.569027 | − | 0.822319i | \(-0.692680\pi\) | ||||
−0.569027 | + | 0.822319i | \(0.692680\pi\) | |||||||
\(164\) | 82.3483i | 0.502124i | ||||||||
\(165\) | 39.6897 | − | 79.2795i | 0.240544 | − | 0.480482i | ||||
\(166\) | 212.574 | 1.28057 | ||||||||
\(167\) | − | 158.560i | − | 0.949462i | −0.880131 | − | 0.474731i | \(-0.842545\pi\) | ||
0.880131 | − | 0.474731i | \(-0.157455\pi\) | |||||||
\(168\) | −64.5308 | − | 32.3061i | −0.384112 | − | 0.192298i | ||||
\(169\) | −156.033 | −0.923269 | ||||||||
\(170\) | 2.45551i | 0.0144442i | ||||||||
\(171\) | 198.344 | + | 265.014i | 1.15990 | + | 1.54979i | ||||
\(172\) | −60.3427 | −0.350830 | ||||||||
\(173\) | 55.2641i | 0.319446i | 0.987162 | + | 0.159723i | \(0.0510601\pi\) | ||||
−0.987162 | + | 0.159723i | \(0.948940\pi\) | |||||||
\(174\) | −48.3325 | + | 96.5433i | −0.277773 | + | 0.554847i | ||||
\(175\) | 42.5241 | 0.242995 | ||||||||
\(176\) | 52.8663i | 0.300377i | ||||||||
\(177\) | −189.783 | − | 95.0113i | −1.07222 | − | 0.536787i | ||||
\(178\) | 192.284 | 1.08024 | ||||||||
\(179\) | 103.383i | 0.577558i | 0.957396 | + | 0.288779i | \(0.0932493\pi\) | ||||
−0.957396 | + | 0.288779i | \(0.906751\pi\) | |||||||
\(180\) | −32.2237 | + | 24.1171i | −0.179021 | + | 0.133984i | ||||
\(181\) | −161.443 | −0.891949 | −0.445974 | − | 0.895046i | \(-0.647143\pi\) | ||||
−0.445974 | + | 0.895046i | \(0.647143\pi\) | |||||||
\(182\) | − | 43.3120i | − | 0.237978i | ||||||
\(183\) | 95.7141 | − | 191.187i | 0.523028 | − | 1.04474i | ||||
\(184\) | −13.5647 | −0.0737210 | ||||||||
\(185\) | 75.4321i | 0.407741i | ||||||||
\(186\) | −129.707 | − | 64.9354i | −0.697352 | − | 0.349115i | ||||
\(187\) | 10.2627 | 0.0548807 | ||||||||
\(188\) | 12.4596i | 0.0662743i | ||||||||
\(189\) | −225.988 | + | 40.7359i | −1.19570 | + | 0.215534i | ||||
\(190\) | 116.308 | 0.612146 | ||||||||
\(191\) | − | 57.0826i | − | 0.298862i | −0.988772 | − | 0.149431i | \(-0.952256\pi\) | ||
0.988772 | − | 0.149431i | \(-0.0477442\pi\) | |||||||
\(192\) | 10.7439 | − | 21.4608i | 0.0559580 | − | 0.111775i | ||||
\(193\) | −106.150 | −0.549998 | −0.274999 | − | 0.961445i | \(-0.588678\pi\) | ||||
−0.274999 | + | 0.961445i | \(0.588678\pi\) | |||||||
\(194\) | 265.622i | 1.36919i | ||||||||
\(195\) | −21.6008 | − | 10.8140i | −0.110773 | − | 0.0554564i | ||||
\(196\) | −46.6640 | −0.238082 | ||||||||
\(197\) | − | 188.120i | − | 0.954925i | −0.878652 | − | 0.477463i | \(-0.841557\pi\) | ||
0.878652 | − | 0.477463i | \(-0.158443\pi\) | |||||||
\(198\) | 100.796 | + | 134.677i | 0.509071 | + | 0.680189i | ||||
\(199\) | −258.348 | −1.29823 | −0.649115 | − | 0.760691i | \(-0.724860\pi\) | ||||
−0.649115 | + | 0.760691i | \(0.724860\pi\) | |||||||
\(200\) | 14.1421i | 0.0707107i | ||||||||
\(201\) | 144.751 | − | 289.137i | 0.720154 | − | 1.43849i | ||||
\(202\) | −62.4727 | −0.309271 | ||||||||
\(203\) | 216.429i | 1.06615i | ||||||||
\(204\) | −4.16609 | − | 2.08567i | −0.0204220 | − | 0.0102239i | ||||
\(205\) | 92.0682 | 0.449113 | ||||||||
\(206\) | − | 70.9376i | − | 0.344357i | ||||||
\(207\) | −34.5561 | + | 25.8627i | −0.166938 | + | 0.124940i | ||||
\(208\) | 14.4042 | 0.0692507 | ||||||||
\(209\) | − | 486.103i | − | 2.32585i | ||||||
\(210\) | −36.1193 | + | 72.1476i | −0.171997 | + | 0.343560i | ||||
\(211\) | −8.22042 | −0.0389593 | −0.0194797 | − | 0.999810i | \(-0.506201\pi\) | ||||
−0.0194797 | + | 0.999810i | \(0.506201\pi\) | |||||||
\(212\) | − | 31.2772i | − | 0.147534i | ||||||
\(213\) | −295.339 | − | 147.855i | −1.38657 | − | 0.694157i | ||||
\(214\) | 221.078 | 1.03308 | ||||||||
\(215\) | 67.4652i | 0.313792i | ||||||||
\(216\) | −13.5474 | − | 75.1563i | −0.0627197 | − | 0.347946i | ||||
\(217\) | −290.776 | −1.33998 | ||||||||
\(218\) | − | 282.590i | − | 1.29629i | ||||||
\(219\) | −115.518 | + | 230.746i | −0.527481 | + | 1.05363i | ||||
\(220\) | 59.1064 | 0.268665 | ||||||||
\(221\) | − | 2.79621i | − | 0.0126525i | ||||||
\(222\) | −127.980 | − | 64.0707i | −0.576487 | − | 0.288607i | ||||
\(223\) | 134.067 | 0.601198 | 0.300599 | − | 0.953751i | \(-0.402813\pi\) | ||||
0.300599 | + | 0.953751i | \(0.402813\pi\) | |||||||
\(224\) | − | 48.1105i | − | 0.214779i | ||||||
\(225\) | 26.9637 | + | 36.0272i | 0.119839 | + | 0.160121i | ||||
\(226\) | 13.3951 | 0.0592702 | ||||||||
\(227\) | − | 252.146i | − | 1.11078i | −0.831591 | − | 0.555388i | \(-0.812570\pi\) | ||
0.831591 | − | 0.555388i | \(-0.187430\pi\) | |||||||
\(228\) | −98.7899 | + | 197.331i | −0.433289 | + | 0.865487i | ||||
\(229\) | −405.638 | −1.77134 | −0.885672 | − | 0.464312i | \(-0.846302\pi\) | ||||
−0.885672 | + | 0.464312i | \(0.846302\pi\) | |||||||
\(230\) | 15.1658i | 0.0659380i | ||||||||
\(231\) | 301.538 | + | 150.959i | 1.30536 | + | 0.653501i | ||||
\(232\) | −71.9773 | −0.310247 | ||||||||
\(233\) | − | 176.120i | − | 0.755879i | −0.925830 | − | 0.377940i | \(-0.876633\pi\) | ||
0.925830 | − | 0.377940i | \(-0.123367\pi\) | |||||||
\(234\) | 36.6947 | − | 27.4633i | 0.156815 | − | 0.117364i | ||||
\(235\) | 13.9302 | 0.0592776 | ||||||||
\(236\) | − | 141.492i | − | 0.599542i | ||||||
\(237\) | −97.5267 | + | 194.808i | −0.411505 | + | 0.821974i | ||||
\(238\) | −9.33948 | −0.0392415 | ||||||||
\(239\) | 52.4894i | 0.219621i | 0.993953 | + | 0.109810i | \(0.0350244\pi\) | ||||
−0.993953 | + | 0.109810i | \(0.964976\pi\) | |||||||
\(240\) | −23.9940 | − | 12.0121i | −0.0999748 | − | 0.0500504i | ||||
\(241\) | 240.203 | 0.996692 | 0.498346 | − | 0.866978i | \(-0.333941\pi\) | ||||
0.498346 | + | 0.866978i | \(0.333941\pi\) | |||||||
\(242\) | − | 75.9124i | − | 0.313688i | ||||||
\(243\) | −177.807 | − | 165.631i | −0.731715 | − | 0.681610i | ||||
\(244\) | 142.539 | 0.584174 | ||||||||
\(245\) | 52.1720i | 0.212947i | ||||||||
\(246\) | −78.2011 | + | 156.205i | −0.317891 | + | 0.634982i | ||||
\(247\) | −132.445 | −0.536216 | ||||||||
\(248\) | − | 96.7026i | − | 0.389930i | ||||||
\(249\) | 403.230 | + | 201.869i | 1.61940 | + | 0.810718i | ||||
\(250\) | 15.8114 | 0.0632456 | ||||||||
\(251\) | 207.455i | 0.826514i | 0.910614 | + | 0.413257i | \(0.135609\pi\) | ||||
−0.910614 | + | 0.413257i | \(0.864391\pi\) | |||||||
\(252\) | −91.7286 | − | 122.562i | −0.364002 | − | 0.486357i | ||||
\(253\) | 63.3845 | 0.250532 | ||||||||
\(254\) | 123.170i | 0.484922i | ||||||||
\(255\) | −2.33185 | + | 4.65783i | −0.00914451 | + | 0.0182660i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 97.7262i | 0.380257i | 0.981759 | + | 0.190129i | \(0.0608905\pi\) | ||||
−0.981759 | + | 0.190129i | \(0.939109\pi\) | |||||||
\(258\) | −114.463 | − | 57.3038i | −0.443657 | − | 0.222108i | ||||
\(259\) | −286.904 | −1.10774 | ||||||||
\(260\) | − | 16.1043i | − | 0.0619397i | ||||||
\(261\) | −183.363 | + | 137.233i | −0.702539 | + | 0.525799i | ||||
\(262\) | 78.1968 | 0.298461 | ||||||||
\(263\) | 93.5480i | 0.355696i | 0.984058 | + | 0.177848i | \(0.0569135\pi\) | ||||
−0.984058 | + | 0.177848i | \(0.943086\pi\) | |||||||
\(264\) | −50.2040 | + | 100.282i | −0.190167 | + | 0.379854i | ||||
\(265\) | −34.9690 | −0.131958 | ||||||||
\(266\) | 442.374i | 1.66306i | ||||||||
\(267\) | 364.741 | + | 182.600i | 1.36607 | + | 0.683895i | ||||
\(268\) | 215.565 | 0.804346 | ||||||||
\(269\) | − | 213.987i | − | 0.795492i | −0.917496 | − | 0.397746i | \(-0.869793\pi\) | ||
0.917496 | − | 0.397746i | \(-0.130207\pi\) | |||||||
\(270\) | −84.0273 | + | 15.1465i | −0.311212 | + | 0.0560982i | ||||
\(271\) | 287.786 | 1.06194 | 0.530970 | − | 0.847391i | \(-0.321828\pi\) | ||||
0.530970 | + | 0.847391i | \(0.321828\pi\) | |||||||
\(272\) | − | 3.10601i | − | 0.0114191i | ||||||
\(273\) | 41.1308 | − | 82.1580i | 0.150662 | − | 0.300945i | ||||
\(274\) | 181.382 | 0.661980 | ||||||||
\(275\) | − | 66.0829i | − | 0.240302i | ||||||
\(276\) | −25.7306 | − | 12.8815i | −0.0932270 | − | 0.0466722i | ||||
\(277\) | 122.451 | 0.442060 | 0.221030 | − | 0.975267i | \(-0.429058\pi\) | ||||
0.221030 | + | 0.975267i | \(0.429058\pi\) | |||||||
\(278\) | − | 201.417i | − | 0.724520i | ||||||
\(279\) | −184.375 | − | 246.351i | −0.660843 | − | 0.882977i | ||||
\(280\) | −53.7892 | −0.192104 | ||||||||
\(281\) | 180.885i | 0.643718i | 0.946788 | + | 0.321859i | \(0.104308\pi\) | ||||
−0.946788 | + | 0.321859i | \(0.895692\pi\) | |||||||
\(282\) | −11.8321 | + | 23.6344i | −0.0419578 | + | 0.0838100i | ||||
\(283\) | 156.462 | 0.552869 | 0.276435 | − | 0.961033i | \(-0.410847\pi\) | ||||
0.276435 | + | 0.961033i | \(0.410847\pi\) | |||||||
\(284\) | − | 220.188i | − | 0.775310i | ||||||
\(285\) | 220.623 | + | 110.450i | 0.774116 | + | 0.387545i | ||||
\(286\) | −67.3073 | −0.235340 | ||||||||
\(287\) | 350.179i | 1.22013i | ||||||||
\(288\) | 40.7601 | − | 30.5060i | 0.141528 | − | 0.105923i | ||||
\(289\) | 288.397 | 0.997914 | ||||||||
\(290\) | 80.4730i | 0.277493i | ||||||||
\(291\) | −252.245 | + | 503.855i | −0.866821 | + | 1.73146i | ||||
\(292\) | −172.031 | −0.589148 | ||||||||
\(293\) | 2.88676i | 0.00985241i | 0.999988 | + | 0.00492620i | \(0.00156807\pi\) | ||||
−0.999988 | + | 0.00492620i | \(0.998432\pi\) | |||||||
\(294\) | −88.5165 | − | 44.3140i | −0.301076 | − | 0.150728i | ||||
\(295\) | −158.193 | −0.536247 | ||||||||
\(296\) | − | 95.4149i | − | 0.322347i | ||||||
\(297\) | 63.3041 | + | 351.188i | 0.213145 | + | 1.18245i | ||||
\(298\) | 202.667 | 0.680090 | ||||||||
\(299\) | − | 17.2700i | − | 0.0577591i | ||||||
\(300\) | −13.4299 | + | 26.8261i | −0.0447664 | + | 0.0894202i | ||||
\(301\) | −256.602 | −0.852498 | ||||||||
\(302\) | − | 207.661i | − | 0.687618i | ||||||
\(303\) | −118.504 | − | 59.3265i | −0.391101 | − | 0.195797i | ||||
\(304\) | −147.119 | −0.483944 | ||||||||
\(305\) | − | 159.363i | − | 0.522501i | ||||||
\(306\) | −5.92198 | − | 7.91257i | −0.0193529 | − | 0.0258581i | ||||
\(307\) | −271.452 | −0.884207 | −0.442104 | − | 0.896964i | \(-0.645768\pi\) | ||||
−0.442104 | + | 0.896964i | \(0.645768\pi\) | |||||||
\(308\) | 224.809i | 0.729901i | ||||||||
\(309\) | 67.3651 | − | 134.561i | 0.218010 | − | 0.435471i | ||||
\(310\) | −108.117 | −0.348764 | ||||||||
\(311\) | 198.082i | 0.636918i | 0.947937 | + | 0.318459i | \(0.103165\pi\) | ||||
−0.947937 | + | 0.318459i | \(0.896835\pi\) | |||||||
\(312\) | 27.3231 | + | 13.6787i | 0.0875740 | + | 0.0438421i | ||||
\(313\) | −67.5994 | −0.215973 | −0.107986 | − | 0.994152i | \(-0.534440\pi\) | ||||
−0.107986 | + | 0.994152i | \(0.534440\pi\) | |||||||
\(314\) | − | 283.188i | − | 0.901872i | ||||||
\(315\) | −137.028 | + | 102.556i | −0.435011 | + | 0.325574i | ||||
\(316\) | −145.238 | −0.459614 | ||||||||
\(317\) | − | 397.841i | − | 1.25502i | −0.778609 | − | 0.627509i | \(-0.784074\pi\) | ||
0.778609 | − | 0.627509i | \(-0.215926\pi\) | |||||||
\(318\) | 29.7021 | − | 59.3294i | 0.0934028 | − | 0.186570i | ||||
\(319\) | 336.333 | 1.05434 | ||||||||
\(320\) | − | 17.8885i | − | 0.0559017i | ||||||
\(321\) | 419.361 | + | 209.945i | 1.30642 | + | 0.654034i | ||||
\(322\) | −57.6825 | −0.179138 | ||||||||
\(323\) | 28.5595i | 0.0884196i | ||||||||
\(324\) | 45.6734 | − | 155.428i | 0.140967 | − | 0.479717i | ||||
\(325\) | −18.0052 | −0.0554006 | ||||||||
\(326\) | − | 262.341i | − | 0.804726i | ||||||
\(327\) | 268.359 | − | 536.042i | 0.820669 | − | 1.63927i | ||||
\(328\) | −116.458 | −0.355055 | ||||||||
\(329\) | 52.9832i | 0.161043i | ||||||||
\(330\) | 112.118 | + | 56.1297i | 0.339752 | + | 0.170090i | ||||
\(331\) | −426.686 | −1.28908 | −0.644540 | − | 0.764570i | \(-0.722951\pi\) | ||||
−0.644540 | + | 0.764570i | \(0.722951\pi\) | |||||||
\(332\) | 300.625i | 0.905498i | ||||||||
\(333\) | −181.920 | − | 243.070i | −0.546307 | − | 0.729940i | ||||
\(334\) | 224.238 | 0.671371 | ||||||||
\(335\) | − | 241.009i | − | 0.719429i | ||||||
\(336\) | 45.6877 | − | 91.2603i | 0.135975 | − | 0.271608i | ||||
\(337\) | −480.323 | −1.42529 | −0.712646 | − | 0.701524i | \(-0.752503\pi\) | ||||
−0.712646 | + | 0.701524i | \(0.752503\pi\) | |||||||
\(338\) | − | 220.663i | − | 0.652850i | ||||||
\(339\) | 25.4089 | + | 12.7205i | 0.0749526 | + | 0.0375235i | ||||
\(340\) | −3.47262 | −0.0102136 | ||||||||
\(341\) | 451.869i | 1.32513i | ||||||||
\(342\) | −374.787 | + | 280.500i | −1.09587 | + | 0.820177i | ||||
\(343\) | 218.302 | 0.636448 | ||||||||
\(344\) | − | 85.3375i | − | 0.248074i | ||||||
\(345\) | −14.4020 | + | 28.7677i | −0.0417449 | + | 0.0833847i | ||||
\(346\) | −78.1553 | −0.225882 | ||||||||
\(347\) | 397.363i | 1.14514i | 0.819857 | + | 0.572569i | \(0.194053\pi\) | ||||
−0.819857 | + | 0.572569i | \(0.805947\pi\) | |||||||
\(348\) | −136.533 | − | 68.3524i | −0.392336 | − | 0.196415i | ||||
\(349\) | 504.033 | 1.44422 | 0.722110 | − | 0.691778i | \(-0.243172\pi\) | ||||
0.722110 | + | 0.691778i | \(0.243172\pi\) | |||||||
\(350\) | 60.1382i | 0.171823i | ||||||||
\(351\) | 95.6859 | − | 17.2481i | 0.272609 | − | 0.0491398i | ||||
\(352\) | −74.7643 | −0.212399 | ||||||||
\(353\) | 567.131i | 1.60660i | 0.595572 | + | 0.803302i | \(0.296925\pi\) | ||||
−0.595572 | + | 0.803302i | \(0.703075\pi\) | |||||||
\(354\) | 134.366 | − | 268.394i | 0.379566 | − | 0.758176i | ||||
\(355\) | −246.178 | −0.693458 | ||||||||
\(356\) | 271.930i | 0.763849i | ||||||||
\(357\) | −17.7159 | − | 8.86913i | −0.0496245 | − | 0.0248435i | ||||
\(358\) | −146.206 | −0.408395 | ||||||||
\(359\) | − | 296.132i | − | 0.824881i | −0.910984 | − | 0.412441i | \(-0.864676\pi\) | ||
0.910984 | − | 0.412441i | \(-0.135324\pi\) | |||||||
\(360\) | −34.1067 | − | 45.5712i | −0.0947408 | − | 0.126587i | ||||
\(361\) | 991.751 | 2.74723 | ||||||||
\(362\) | − | 228.315i | − | 0.630703i | ||||||
\(363\) | 72.0894 | − | 143.997i | 0.198593 | − | 0.396687i | ||||
\(364\) | 61.2524 | 0.168276 | ||||||||
\(365\) | 192.337i | 0.526950i | ||||||||
\(366\) | 270.380 | + | 135.360i | 0.738742 | + | 0.369837i | ||||
\(367\) | −28.7924 | −0.0784535 | −0.0392268 | − | 0.999230i | \(-0.512489\pi\) | ||||
−0.0392268 | + | 0.999230i | \(0.512489\pi\) | |||||||
\(368\) | − | 19.1833i | − | 0.0521286i | ||||||
\(369\) | −296.678 | + | 222.041i | −0.804004 | + | 0.601738i | ||||
\(370\) | −106.677 | −0.288316 | ||||||||
\(371\) | − | 133.004i | − | 0.358500i | ||||||
\(372\) | 91.8326 | − | 183.434i | 0.246862 | − | 0.493102i | ||||
\(373\) | −215.231 | −0.577026 | −0.288513 | − | 0.957476i | \(-0.593161\pi\) | ||||
−0.288513 | + | 0.957476i | \(0.593161\pi\) | |||||||
\(374\) | 14.5136i | 0.0388065i | ||||||||
\(375\) | 29.9924 | + | 15.0151i | 0.0799798 | + | 0.0400403i | ||||
\(376\) | −17.6205 | −0.0468630 | ||||||||
\(377\) | − | 91.6385i | − | 0.243073i | ||||||
\(378\) | −57.6093 | − | 319.595i | −0.152406 | − | 0.845491i | ||||
\(379\) | −557.330 | −1.47053 | −0.735264 | − | 0.677781i | \(-0.762942\pi\) | ||||
−0.735264 | + | 0.677781i | \(0.762942\pi\) | |||||||
\(380\) | 164.484i | 0.432853i | ||||||||
\(381\) | −116.967 | + | 233.640i | −0.307001 | + | 0.613229i | ||||
\(382\) | 80.7270 | 0.211327 | ||||||||
\(383\) | 27.7534i | 0.0724631i | 0.999343 | + | 0.0362316i | \(0.0115354\pi\) | ||||
−0.999343 | + | 0.0362316i | \(0.988465\pi\) | |||||||
\(384\) | 30.3502 | + | 15.1942i | 0.0790370 | + | 0.0395683i | ||||
\(385\) | 251.345 | 0.652843 | ||||||||
\(386\) | − | 150.118i | − | 0.388907i | ||||||
\(387\) | −162.706 | − | 217.398i | −0.420430 | − | 0.561751i | ||||
\(388\) | −375.646 | −0.968160 | ||||||||
\(389\) | − | 352.556i | − | 0.906312i | −0.891431 | − | 0.453156i | \(-0.850298\pi\) | ||
0.891431 | − | 0.453156i | \(-0.149702\pi\) | |||||||
\(390\) | 15.2933 | − | 30.5481i | 0.0392136 | − | 0.0783285i | ||||
\(391\) | −3.72397 | −0.00952422 | ||||||||
\(392\) | − | 65.9929i | − | 0.168349i | ||||||
\(393\) | 148.331 | + | 74.2587i | 0.377431 | + | 0.188953i | ||||
\(394\) | 266.042 | 0.675234 | ||||||||
\(395\) | 162.381i | 0.411091i | ||||||||
\(396\) | −190.463 | + | 142.547i | −0.480966 | + | 0.359968i | ||||
\(397\) | 0.224835 | 0.000566334 | 0.000283167 | − | 1.00000i | \(-0.499910\pi\) | ||||
0.000283167 | 1.00000i | \(0.499910\pi\) | ||||||||
\(398\) | − | 365.359i | − | 0.917987i | ||||||
\(399\) | −420.095 | + | 839.133i | −1.05287 | + | 2.10309i | ||||
\(400\) | −20.0000 | −0.0500000 | ||||||||
\(401\) | 442.929i | 1.10456i | 0.833658 | + | 0.552280i | \(0.186242\pi\) | ||||
−0.833658 | + | 0.552280i | \(0.813758\pi\) | |||||||
\(402\) | 408.902 | + | 204.709i | 1.01717 | + | 0.509225i | ||||
\(403\) | 123.118 | 0.305503 | ||||||||
\(404\) | − | 88.3497i | − | 0.218687i | ||||||
\(405\) | −173.774 | − | 51.0644i | −0.429072 | − | 0.126085i | ||||
\(406\) | −306.077 | −0.753884 | ||||||||
\(407\) | 445.852i | 1.09546i | ||||||||
\(408\) | 2.94958 | − | 5.89175i | 0.00722937 | − | 0.0144406i | ||||
\(409\) | 69.2653 | 0.169353 | 0.0846764 | − | 0.996409i | \(-0.473014\pi\) | ||||
0.0846764 | + | 0.996409i | \(0.473014\pi\) | |||||||
\(410\) | 130.204i | 0.317571i | ||||||||
\(411\) | 344.062 | + | 172.248i | 0.837134 | + | 0.419095i | ||||
\(412\) | 100.321 | 0.243497 | ||||||||
\(413\) | − | 601.682i | − | 1.45686i | ||||||
\(414\) | −36.5754 | − | 48.8697i | −0.0883463 | − | 0.118043i | ||||
\(415\) | 336.109 | 0.809902 | ||||||||
\(416\) | 20.3706i | 0.0489677i | ||||||||
\(417\) | 191.273 | − | 382.065i | 0.458688 | − | 0.916222i | ||||
\(418\) | 687.453 | 1.64463 | ||||||||
\(419\) | 776.330i | 1.85282i | 0.376522 | + | 0.926408i | \(0.377120\pi\) | ||||
−0.376522 | + | 0.926408i | \(0.622880\pi\) | |||||||
\(420\) | −102.032 | − | 51.0804i | −0.242934 | − | 0.121620i | ||||
\(421\) | −700.311 | −1.66345 | −0.831723 | − | 0.555190i | \(-0.812645\pi\) | ||||
−0.831723 | + | 0.555190i | \(0.812645\pi\) | |||||||
\(422\) | − | 11.6254i | − | 0.0275484i | ||||||
\(423\) | −44.8883 | + | 33.5956i | −0.106119 | + | 0.0794223i | ||||
\(424\) | 44.2327 | 0.104322 | ||||||||
\(425\) | 3.88251i | 0.00913531i | ||||||||
\(426\) | 209.099 | − | 417.672i | 0.490843 | − | 0.980451i | ||||
\(427\) | 606.133 | 1.41951 | ||||||||
\(428\) | 312.652i | 0.730496i | ||||||||
\(429\) | −127.674 | − | 63.9176i | −0.297609 | − | 0.148992i | ||||
\(430\) | −95.4102 | −0.221884 | ||||||||
\(431\) | − | 554.331i | − | 1.28615i | −0.765803 | − | 0.643075i | \(-0.777658\pi\) | ||
0.765803 | − | 0.643075i | \(-0.222342\pi\) | |||||||
\(432\) | 106.287 | − | 19.1590i | 0.246035 | − | 0.0443495i | ||||
\(433\) | 423.019 | 0.976950 | 0.488475 | − | 0.872578i | \(-0.337553\pi\) | ||||
0.488475 | + | 0.872578i | \(0.337553\pi\) | |||||||
\(434\) | − | 411.219i | − | 0.947510i | ||||||
\(435\) | −76.4203 | + | 152.648i | −0.175679 | + | 0.350916i | ||||
\(436\) | 399.643 | 0.916612 | ||||||||
\(437\) | 176.390i | 0.403637i | ||||||||
\(438\) | −326.324 | − | 163.368i | −0.745032 | − | 0.372985i | ||||
\(439\) | 436.088 | 0.993366 | 0.496683 | − | 0.867932i | \(-0.334551\pi\) | ||||
0.496683 | + | 0.867932i | \(0.334551\pi\) | |||||||
\(440\) | 83.5890i | 0.189975i | ||||||||
\(441\) | −125.824 | − | 168.117i | −0.285314 | − | 0.381219i | ||||
\(442\) | 3.95444 | 0.00894670 | ||||||||
\(443\) | 425.568i | 0.960649i | 0.877091 | + | 0.480325i | \(0.159481\pi\) | ||||
−0.877091 | + | 0.480325i | \(0.840519\pi\) | |||||||
\(444\) | 90.6097 | − | 180.991i | 0.204076 | − | 0.407638i | ||||
\(445\) | 304.027 | 0.683207 | ||||||||
\(446\) | 189.600i | 0.425111i | ||||||||
\(447\) | 384.437 | + | 192.460i | 0.860037 | + | 0.430560i | ||||
\(448\) | 68.0386 | 0.151872 | ||||||||
\(449\) | − | 355.131i | − | 0.790938i | −0.918479 | − | 0.395469i | \(-0.870582\pi\) | ||
0.918479 | − | 0.395469i | \(-0.129418\pi\) | |||||||
\(450\) | −50.9501 | + | 38.1324i | −0.113223 | + | 0.0847388i | ||||
\(451\) | 544.181 | 1.20661 | ||||||||
\(452\) | 18.9435i | 0.0419103i | ||||||||
\(453\) | 197.203 | − | 393.909i | 0.435326 | − | 0.869556i | ||||
\(454\) | 356.589 | 0.785438 | ||||||||
\(455\) | − | 68.4823i | − | 0.150510i | ||||||
\(456\) | −279.068 | − | 139.710i | −0.611992 | − | 0.306382i | ||||
\(457\) | −398.620 | −0.872255 | −0.436127 | − | 0.899885i | \(-0.643650\pi\) | ||||
−0.436127 | + | 0.899885i | \(0.643650\pi\) | |||||||
\(458\) | − | 573.658i | − | 1.25253i | ||||||
\(459\) | −3.71924 | − | 20.6330i | −0.00810293 | − | 0.0449521i | ||||
\(460\) | −21.4476 | −0.0466252 | ||||||||
\(461\) | − | 573.580i | − | 1.24421i | −0.782935 | − | 0.622104i | \(-0.786278\pi\) | ||
0.782935 | − | 0.622104i | \(-0.213722\pi\) | |||||||
\(462\) | −213.488 | + | 426.438i | −0.462095 | + | 0.923027i | ||||
\(463\) | −268.662 | −0.580263 | −0.290131 | − | 0.956987i | \(-0.593699\pi\) | ||||
−0.290131 | + | 0.956987i | \(0.593699\pi\) | |||||||
\(464\) | − | 101.791i | − | 0.219378i | ||||||
\(465\) | −205.085 | − | 102.672i | −0.441044 | − | 0.220800i | ||||
\(466\) | 249.071 | 0.534487 | ||||||||
\(467\) | − | 562.394i | − | 1.20427i | −0.798394 | − | 0.602135i | \(-0.794317\pi\) | ||
0.798394 | − | 0.602135i | \(-0.205683\pi\) | |||||||
\(468\) | 38.8389 | + | 51.8941i | 0.0829892 | + | 0.110885i | ||||
\(469\) | 916.670 | 1.95452 | ||||||||
\(470\) | 19.7003i | 0.0419156i | ||||||||
\(471\) | 268.926 | − | 537.175i | 0.570968 | − | 1.14050i | ||||
\(472\) | 200.100 | 0.423940 | ||||||||
\(473\) | 398.762i | 0.843049i | ||||||||
\(474\) | −275.500 | − | 137.924i | −0.581224 | − | 0.290978i | ||||
\(475\) | 183.899 | 0.387155 | ||||||||
\(476\) | − | 13.2080i | − | 0.0277479i | ||||||
\(477\) | 112.683 | − | 84.3350i | 0.236233 | − | 0.176803i | ||||
\(478\) | −74.2312 | −0.155295 | ||||||||
\(479\) | 502.529i | 1.04912i | 0.851373 | + | 0.524561i | \(0.175770\pi\) | ||||
−0.851373 | + | 0.524561i | \(0.824230\pi\) | |||||||
\(480\) | 16.9877 | − | 33.9326i | 0.0353910 | − | 0.0706929i | ||||
\(481\) | 121.478 | 0.252554 | ||||||||
\(482\) | 339.698i | 0.704768i | ||||||||
\(483\) | −109.417 | − | 54.7776i | −0.226537 | − | 0.113411i | ||||
\(484\) | 107.356 | 0.221811 | ||||||||
\(485\) | 419.985i | 0.865949i | ||||||||
\(486\) | 234.238 | − | 251.457i | 0.481971 | − | 0.517401i | ||||
\(487\) | 266.197 | 0.546606 | 0.273303 | − | 0.961928i | \(-0.411884\pi\) | ||||
0.273303 | + | 0.961928i | \(0.411884\pi\) | |||||||
\(488\) | 201.580i | 0.413074i | ||||||||
\(489\) | 249.129 | − | 497.631i | 0.509466 | − | 1.01765i | ||||
\(490\) | −73.7823 | −0.150576 | ||||||||
\(491\) | − | 13.7295i | − | 0.0279624i | −0.999902 | − | 0.0139812i | \(-0.995550\pi\) | ||
0.999902 | − | 0.0139812i | \(-0.00445049\pi\) | |||||||
\(492\) | −220.908 | − | 110.593i | −0.449000 | − | 0.224783i | ||||
\(493\) | −19.7603 | −0.0400817 | ||||||||
\(494\) | − | 187.306i | − | 0.379162i | ||||||
\(495\) | 159.373 | + | 212.944i | 0.321965 | + | 0.430189i | ||||
\(496\) | 136.758 | 0.275722 | ||||||||
\(497\) | − | 936.330i | − | 1.88396i | ||||||
\(498\) | −285.486 | + | 570.253i | −0.573265 | + | 1.14509i | ||||
\(499\) | 305.888 | 0.613002 | 0.306501 | − | 0.951870i | \(-0.400842\pi\) | ||||
0.306501 | + | 0.951870i | \(0.400842\pi\) | |||||||
\(500\) | 22.3607i | 0.0447214i | ||||||||
\(501\) | 425.354 | + | 212.945i | 0.849010 | + | 0.425040i | ||||
\(502\) | −293.386 | −0.584434 | ||||||||
\(503\) | 787.569i | 1.56574i | 0.622183 | + | 0.782872i | \(0.286246\pi\) | ||||
−0.622183 | + | 0.782872i | \(0.713754\pi\) | |||||||
\(504\) | 173.329 | − | 129.724i | 0.343906 | − | 0.257389i | ||||
\(505\) | −98.7780 | −0.195600 | ||||||||
\(506\) | 89.6393i | 0.177153i | ||||||||
\(507\) | 209.551 | − | 418.574i | 0.413315 | − | 0.825589i | ||||
\(508\) | −174.189 | −0.342892 | ||||||||
\(509\) | − | 785.384i | − | 1.54299i | −0.636233 | − | 0.771497i | \(-0.719508\pi\) | ||
0.636233 | − | 0.771497i | \(-0.280492\pi\) | |||||||
\(510\) | −6.58717 | − | 3.29774i | −0.0129160 | − | 0.00646615i | ||||
\(511\) | −731.547 | −1.43160 | ||||||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | −977.303 | + | 176.166i | −1.90507 | + | 0.343403i | ||||
\(514\) | −138.206 | −0.268883 | ||||||||
\(515\) | − | 112.162i | − | 0.217791i | ||||||
\(516\) | 81.0398 | − | 161.876i | 0.157054 | − | 0.313713i | ||||
\(517\) | 82.3365 | 0.159258 | ||||||||
\(518\) | − | 405.743i | − | 0.783288i | ||||||
\(519\) | −148.252 | − | 74.2193i | −0.285649 | − | 0.143004i | ||||
\(520\) | 22.7750 | 0.0437980 | ||||||||
\(521\) | − | 858.879i | − | 1.64852i | −0.566211 | − | 0.824260i | \(-0.691591\pi\) | ||
0.566211 | − | 0.824260i | \(-0.308409\pi\) | |||||||
\(522\) | −194.077 | − | 259.314i | −0.371796 | − | 0.496770i | ||||
\(523\) | −7.44546 | −0.0142361 | −0.00711803 | − | 0.999975i | \(-0.502266\pi\) | ||||
−0.00711803 | + | 0.999975i | \(0.502266\pi\) | |||||||
\(524\) | 110.587i | 0.211044i | ||||||||
\(525\) | −57.1096 | + | 114.075i | −0.108780 | + | 0.217287i | ||||
\(526\) | −132.297 | −0.251515 | ||||||||
\(527\) | − | 26.5482i | − | 0.0503761i | ||||||
\(528\) | −141.820 | − | 70.9991i | −0.268598 | − | 0.134468i | ||||
\(529\) | −23.0000 | −0.0434783 | ||||||||
\(530\) | − | 49.4536i | − | 0.0933087i | ||||||
\(531\) | 509.756 | − | 381.515i | 0.959992 | − | 0.718483i | ||||
\(532\) | −625.611 | −1.17596 | ||||||||
\(533\) | − | 148.270i | − | 0.278179i | ||||||
\(534\) | −258.235 | + | 515.821i | −0.483587 | + | 0.965957i | ||||
\(535\) | 349.556 | 0.653375 | ||||||||
\(536\) | 304.854i | 0.568758i | ||||||||
\(537\) | −277.336 | − | 138.842i | −0.516454 | − | 0.258552i | ||||
\(538\) | 302.624 | 0.562497 | ||||||||
\(539\) | 308.370i | 0.572114i | ||||||||
\(540\) | −21.4204 | − | 118.833i | −0.0396674 | − | 0.220060i | ||||
\(541\) | −90.9543 | −0.168123 | −0.0840613 | − | 0.996461i | \(-0.526789\pi\) | ||||
−0.0840613 | + | 0.996461i | \(0.526789\pi\) | |||||||
\(542\) | 406.990i | 0.750905i | ||||||||
\(543\) | 216.816 | − | 433.087i | 0.399294 | − | 0.797582i | ||||
\(544\) | 4.39255 | 0.00807455 | ||||||||
\(545\) | − | 446.814i | − | 0.819843i | ||||||
\(546\) | 116.189 | + | 58.1677i | 0.212800 | + | 0.106534i | ||||
\(547\) | 487.663 | 0.891522 | 0.445761 | − | 0.895152i | \(-0.352933\pi\) | ||||
0.445761 | + | 0.895152i | \(0.352933\pi\) | |||||||
\(548\) | 256.514i | 0.468090i | ||||||||
\(549\) | 384.337 | + | 513.526i | 0.700067 | + | 0.935385i | ||||
\(550\) | 93.4554 | 0.169919 | ||||||||
\(551\) | 935.964i | 1.69866i | ||||||||
\(552\) | 18.2172 | − | 36.3886i | 0.0330022 | − | 0.0659214i | ||||
\(553\) | −617.611 | −1.11684 | ||||||||
\(554\) | 173.171i | 0.312584i | ||||||||
\(555\) | −202.354 | − | 101.305i | −0.364603 | − | 0.182531i | ||||
\(556\) | 284.846 | 0.512313 | ||||||||
\(557\) | 571.368i | 1.02579i | 0.858450 | + | 0.512897i | \(0.171428\pi\) | ||||
−0.858450 | + | 0.512897i | \(0.828572\pi\) | |||||||
\(558\) | 348.392 | − | 260.746i | 0.624359 | − | 0.467287i | ||||
\(559\) | 108.648 | 0.194362 | ||||||||
\(560\) | − | 76.0695i | − | 0.135838i | ||||||
\(561\) | −13.7827 | + | 27.5308i | −0.0245681 | + | 0.0490744i | ||||
\(562\) | −255.810 | −0.455177 | ||||||||
\(563\) | 239.855i | 0.426031i | 0.977049 | + | 0.213015i | \(0.0683285\pi\) | ||||
−0.977049 | + | 0.213015i | \(0.931672\pi\) | |||||||
\(564\) | −33.4241 | − | 16.7331i | −0.0592626 | − | 0.0296686i | ||||
\(565\) | 21.1794 | 0.0374857 | ||||||||
\(566\) | 221.271i | 0.390938i | ||||||||
\(567\) | 194.222 | − | 660.945i | 0.342543 | − | 1.16569i | ||||
\(568\) | 311.393 | 0.548227 | ||||||||
\(569\) | − | 71.0260i | − | 0.124826i | −0.998050 | − | 0.0624130i | \(-0.980120\pi\) | ||
0.998050 | − | 0.0624130i | \(-0.0198796\pi\) | |||||||
\(570\) | −156.201 | + | 312.008i | −0.274036 | + | 0.547382i | ||||
\(571\) | 751.566 | 1.31623 | 0.658114 | − | 0.752919i | \(-0.271355\pi\) | ||||
0.658114 | + | 0.752919i | \(0.271355\pi\) | |||||||
\(572\) | − | 95.1869i | − | 0.166411i | ||||||
\(573\) | 153.130 | + | 76.6616i | 0.267243 | + | 0.133790i | ||||
\(574\) | −495.227 | −0.862766 | ||||||||
\(575\) | 23.9792i | 0.0417029i | ||||||||
\(576\) | 43.1419 | + | 57.6435i | 0.0748992 | + | 0.100076i | ||||
\(577\) | 99.6649 | 0.172729 | 0.0863647 | − | 0.996264i | \(-0.472475\pi\) | ||||
0.0863647 | + | 0.996264i | \(0.472475\pi\) | |||||||
\(578\) | 407.855i | 0.705632i | ||||||||
\(579\) | 142.558 | − | 284.757i | 0.246214 | − | 0.491809i | ||||
\(580\) | −113.806 | −0.196217 | ||||||||
\(581\) | 1278.38i | 2.20032i | ||||||||
\(582\) | −712.559 | − | 356.728i | −1.22433 | − | 0.612935i | ||||
\(583\) | −206.689 | −0.354527 | ||||||||
\(584\) | − | 243.289i | − | 0.416590i | ||||||
\(585\) | 58.0194 | − | 43.4233i | 0.0991784 | − | 0.0742278i | ||||
\(586\) | −4.08249 | −0.00696671 | ||||||||
\(587\) | 150.122i | 0.255744i | 0.991791 | + | 0.127872i | \(0.0408147\pi\) | ||||
−0.991791 | + | 0.127872i | \(0.959185\pi\) | |||||||
\(588\) | 62.6695 | − | 125.181i | 0.106581 | − | 0.212893i | ||||
\(589\) | −1257.48 | −2.13494 | ||||||||
\(590\) | − | 223.718i | − | 0.379184i | ||||||
\(591\) | 504.652 | + | 252.644i | 0.853896 | + | 0.427486i | ||||
\(592\) | 134.937 | 0.227934 | ||||||||
\(593\) | 482.976i | 0.814461i | 0.913325 | + | 0.407231i | \(0.133505\pi\) | ||||
−0.913325 | + | 0.407231i | \(0.866495\pi\) | |||||||
\(594\) | −496.655 | + | 89.5255i | −0.836119 | + | 0.150716i | ||||
\(595\) | −14.7670 | −0.0248185 | ||||||||
\(596\) | 286.614i | 0.480897i | ||||||||
\(597\) | 346.959 | − | 693.045i | 0.581171 | − | 1.16088i | ||||
\(598\) | 24.4234 | 0.0408419 | ||||||||
\(599\) | − | 531.979i | − | 0.888112i | −0.895999 | − | 0.444056i | \(-0.853539\pi\) | ||
0.895999 | − | 0.444056i | \(-0.146461\pi\) | |||||||
\(600\) | −37.9378 | − | 18.9928i | −0.0632296 | − | 0.0316546i | ||||
\(601\) | 312.027 | 0.519180 | 0.259590 | − | 0.965719i | \(-0.416413\pi\) | ||||
0.259590 | + | 0.965719i | \(0.416413\pi\) | |||||||
\(602\) | − | 362.890i | − | 0.602807i | ||||||
\(603\) | 581.242 | + | 776.619i | 0.963917 | + | 1.28793i | ||||
\(604\) | 293.676 | 0.486219 | ||||||||
\(605\) | − | 120.028i | − | 0.198393i | ||||||
\(606\) | 83.9004 | − | 167.590i | 0.138449 | − | 0.276550i | ||||
\(607\) | 137.992 | 0.227335 | 0.113667 | − | 0.993519i | \(-0.463740\pi\) | ||||
0.113667 | + | 0.993519i | \(0.463740\pi\) | |||||||
\(608\) | − | 208.058i | − | 0.342200i | ||||||
\(609\) | −580.594 | − | 290.663i | −0.953356 | − | 0.477279i | ||||
\(610\) | 225.373 | 0.369464 | ||||||||
\(611\) | − | 22.4337i | − | 0.0367164i | ||||||
\(612\) | 11.1901 | − | 8.37494i | 0.0182844 | − | 0.0136845i | ||||
\(613\) | −92.8359 | −0.151445 | −0.0757226 | − | 0.997129i | \(-0.524126\pi\) | ||||
−0.0757226 | + | 0.997129i | \(0.524126\pi\) | |||||||
\(614\) | − | 383.891i | − | 0.625229i | ||||||
\(615\) | −123.647 | + | 246.983i | −0.201052 | + | 0.401598i | ||||
\(616\) | −317.929 | −0.516118 | ||||||||
\(617\) | 954.229i | 1.54656i | 0.634063 | + | 0.773281i | \(0.281386\pi\) | ||||
−0.634063 | + | 0.773281i | \(0.718614\pi\) | |||||||
\(618\) | 190.297 | + | 95.2686i | 0.307925 | + | 0.154156i | ||||
\(619\) | 36.1660 | 0.0584265 | 0.0292132 | − | 0.999573i | \(-0.490700\pi\) | ||||
0.0292132 | + | 0.999573i | \(0.490700\pi\) | |||||||
\(620\) | − | 152.900i | − | 0.246613i | ||||||
\(621\) | −22.9708 | − | 127.434i | −0.0369900 | − | 0.205207i | ||||
\(622\) | −280.130 | −0.450369 | ||||||||
\(623\) | 1156.36i | 1.85611i | ||||||||
\(624\) | −19.3447 | + | 38.6407i | −0.0310011 | + | 0.0619241i | ||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | − | 95.6000i | − | 0.152716i | ||||||
\(627\) | 1304.02 | + | 652.833i | 2.07978 | + | 1.04120i | ||||
\(628\) | 400.488 | 0.637720 | ||||||||
\(629\) | − | 26.1947i | − | 0.0416450i | ||||||
\(630\) | −145.036 | − | 193.787i | −0.230215 | − | 0.307599i | ||||
\(631\) | −503.591 | −0.798084 | −0.399042 | − | 0.916933i | \(-0.630657\pi\) | ||||
−0.399042 | + | 0.916933i | \(0.630657\pi\) | |||||||
\(632\) | − | 205.397i | − | 0.324996i | ||||||
\(633\) | 11.0400 | − | 22.0521i | 0.0174407 | − | 0.0348375i | ||||
\(634\) | 562.632 | 0.887432 | ||||||||
\(635\) | 194.749i | 0.306692i | ||||||||
\(636\) | 83.9044 | + | 42.0051i | 0.131925 | + | 0.0660457i | ||||
\(637\) | 84.0195 | 0.131899 | ||||||||
\(638\) | 475.647i | 0.745528i | ||||||||
\(639\) | 793.275 | − | 593.708i | 1.24143 | − | 0.929121i | ||||
\(640\) | 25.2982 | 0.0395285 | ||||||||
\(641\) | − | 589.686i | − | 0.919947i | −0.887933 | − | 0.459974i | \(-0.847859\pi\) | ||
0.887933 | − | 0.459974i | \(-0.152141\pi\) | |||||||
\(642\) | −296.907 | + | 593.066i | −0.462472 | + | 0.923779i | ||||
\(643\) | −53.2769 | −0.0828567 | −0.0414283 | − | 0.999141i | \(-0.513191\pi\) | ||||
−0.0414283 | + | 0.999141i | \(0.513191\pi\) | |||||||
\(644\) | − | 81.5754i | − | 0.126670i | ||||||
\(645\) | −180.982 | − | 90.6053i | −0.280593 | − | 0.140473i | ||||
\(646\) | −40.3893 | −0.0625221 | ||||||||
\(647\) | 110.016i | 0.170040i | 0.996379 | + | 0.0850202i | \(0.0270955\pi\) | ||||
−0.996379 | + | 0.0850202i | \(0.972905\pi\) | |||||||
\(648\) | 219.809 | + | 64.5919i | 0.339211 | + | 0.0996788i | ||||
\(649\) | −935.020 | −1.44071 | ||||||||
\(650\) | − | 25.4632i | − | 0.0391741i | ||||||
\(651\) | 390.510 | − | 780.037i | 0.599862 | − | 1.19821i | ||||
\(652\) | 371.006 | 0.569027 | ||||||||
\(653\) | − | 442.472i | − | 0.677599i | −0.940859 | − | 0.338800i | \(-0.889979\pi\) | ||
0.940859 | − | 0.338800i | \(-0.110021\pi\) | |||||||
\(654\) | 758.078 | + | 379.517i | 1.15914 | + | 0.580301i | ||||
\(655\) | 123.640 | 0.188763 | ||||||||
\(656\) | − | 164.697i | − | 0.251062i | ||||||
\(657\) | −463.860 | − | 619.780i | −0.706027 | − | 0.943348i | ||||
\(658\) | −74.9296 | −0.113875 | ||||||||
\(659\) | 561.159i | 0.851531i | 0.904833 | + | 0.425766i | \(0.139995\pi\) | ||||
−0.904833 | + | 0.425766i | \(0.860005\pi\) | |||||||
\(660\) | −79.3794 | + | 158.559i | −0.120272 | + | 0.240241i | ||||
\(661\) | −801.121 | −1.21198 | −0.605992 | − | 0.795471i | \(-0.707224\pi\) | ||||
−0.605992 | + | 0.795471i | \(0.707224\pi\) | |||||||
\(662\) | − | 603.425i | − | 0.911518i | ||||||
\(663\) | 7.50113 | + | 3.75529i | 0.0113139 | + | 0.00566409i | ||||
\(664\) | −425.149 | −0.640284 | ||||||||
\(665\) | 699.454i | 1.05181i | ||||||||
\(666\) | 343.753 | − | 257.274i | 0.516146 | − | 0.386297i | ||||
\(667\) | −122.043 | −0.182974 | ||||||||
\(668\) | 317.120i | 0.474731i | ||||||||
\(669\) | −180.051 | + | 359.649i | −0.269135 | + | 0.537592i | ||||
\(670\) | 340.838 | 0.508713 | ||||||||
\(671\) | − | 941.937i | − | 1.40378i | ||||||
\(672\) | 129.062 | + | 64.6121i | 0.192056 | + | 0.0961490i | ||||
\(673\) | −96.4810 | −0.143360 | −0.0716798 | − | 0.997428i | \(-0.522836\pi\) | ||||
−0.0716798 | + | 0.997428i | \(0.522836\pi\) | |||||||
\(674\) | − | 679.279i | − | 1.00783i | ||||||
\(675\) | −132.859 | + | 23.9487i | −0.196828 | + | 0.0354796i | ||||
\(676\) | 312.065 | 0.461635 | ||||||||
\(677\) | 314.499i | 0.464549i | 0.972650 | + | 0.232274i | \(0.0746167\pi\) | ||||
−0.972650 | + | 0.232274i | \(0.925383\pi\) | |||||||
\(678\) | −17.9895 | + | 35.9336i | −0.0265331 | + | 0.0529995i | ||||
\(679\) | −1597.40 | −2.35258 | ||||||||
\(680\) | − | 4.91103i | − | 0.00722210i | ||||||
\(681\) | 676.409 | + | 338.631i | 0.993258 | + | 0.497255i | ||||
\(682\) | −639.039 | −0.937007 | ||||||||
\(683\) | − | 189.054i | − | 0.276800i | −0.990376 | − | 0.138400i | \(-0.955804\pi\) | ||
0.990376 | − | 0.138400i | \(-0.0441959\pi\) | |||||||
\(684\) | −396.687 | − | 530.029i | −0.579952 | − | 0.774896i | ||||
\(685\) | 286.791 | 0.418673 | ||||||||
\(686\) | 308.725i | 0.450037i | ||||||||
\(687\) | 544.768 | − | 1088.17i | 0.792967 | − | 1.58394i | ||||
\(688\) | 120.685 | 0.175415 | ||||||||
\(689\) | 56.3152i | 0.0817347i | ||||||||
\(690\) | −40.6837 | − | 20.3675i | −0.0589619 | − | 0.0295181i | ||||
\(691\) | −491.731 | −0.711622 | −0.355811 | − | 0.934558i | \(-0.615795\pi\) | ||||
−0.355811 | + | 0.934558i | \(0.615795\pi\) | |||||||
\(692\) | − | 110.528i | − | 0.159723i | ||||||
\(693\) | −809.925 | + | 606.170i | −1.16872 | + | 0.874704i | ||||
\(694\) | −561.955 | −0.809734 | ||||||||
\(695\) | − | 318.468i | − | 0.458227i | ||||||
\(696\) | 96.6649 | − | 193.087i | 0.138886 | − | 0.277423i | ||||
\(697\) | −31.9718 | −0.0458705 | ||||||||
\(698\) | 712.810i | 1.02122i | ||||||||
\(699\) | 472.460 | + | 236.528i | 0.675909 | + | 0.338380i | ||||
\(700\) | −85.0482 | −0.121497 | ||||||||
\(701\) | 873.449i | 1.24600i | 0.782220 | + | 0.623002i | \(0.214087\pi\) | ||||
−0.782220 | + | 0.623002i | \(0.785913\pi\) | |||||||
\(702\) | 24.3924 | + | 135.320i | 0.0347471 | + | 0.192764i | ||||
\(703\) | −1240.74 | −1.76492 | ||||||||
\(704\) | − | 105.733i | − | 0.150188i | ||||||
\(705\) | −18.7082 | + | 37.3693i | −0.0265364 | + | 0.0530061i | ||||
\(706\) | −802.045 | −1.13604 | ||||||||
\(707\) | − | 375.699i | − | 0.531400i | ||||||
\(708\) | 379.567 | + | 190.023i | 0.536111 | + | 0.268393i | ||||
\(709\) | −1127.06 | −1.58965 | −0.794825 | − | 0.606839i | \(-0.792437\pi\) | ||||
−0.794825 | + | 0.606839i | \(0.792437\pi\) | |||||||
\(710\) | − | 348.148i | − | 0.490349i | ||||||
\(711\) | −391.615 | − | 523.251i | −0.550795 | − | 0.735937i | ||||
\(712\) | −384.567 | −0.540122 | ||||||||
\(713\) | − | 163.967i | − | 0.229968i | ||||||
\(714\) | 12.5428 | − | 25.0541i | 0.0175670 | − | 0.0350898i | ||||
\(715\) | −106.422 | −0.148842 | ||||||||
\(716\) | − | 206.766i | − | 0.288779i | ||||||
\(717\) | −140.808 | − | 70.4929i | −0.196385 | − | 0.0983164i | ||||
\(718\) | 418.795 | 0.583279 | ||||||||
\(719\) | − | 826.971i | − | 1.15017i | −0.818094 | − | 0.575084i | \(-0.804969\pi\) | ||
0.818094 | − | 0.575084i | \(-0.195031\pi\) | |||||||
\(720\) | 64.4474 | − | 48.2341i | 0.0895103 | − | 0.0669919i | ||||
\(721\) | 426.606 | 0.591686 | ||||||||
\(722\) | 1402.55i | 1.94259i | ||||||||
\(723\) | −322.591 | + | 644.369i | −0.446184 | + | 0.891244i | ||||
\(724\) | 322.885 | 0.445974 | ||||||||
\(725\) | 127.239i | 0.175502i | ||||||||
\(726\) | 203.643 | + | 101.950i | 0.280500 | + | 0.140427i | ||||
\(727\) | 587.838 | 0.808580 | 0.404290 | − | 0.914631i | \(-0.367519\pi\) | ||||
0.404290 | + | 0.914631i | \(0.367519\pi\) | |||||||
\(728\) | 86.6240i | 0.118989i | ||||||||
\(729\) | 683.117 | − | 254.544i | 0.937060 | − | 0.349169i | ||||
\(730\) | −272.005 | −0.372610 | ||||||||
\(731\) | − | 23.4281i | − | 0.0320494i | ||||||
\(732\) | −191.428 | + | 382.375i | −0.261514 | + | 0.522370i | ||||
\(733\) | 240.718 | 0.328401 | 0.164200 | − | 0.986427i | \(-0.447496\pi\) | ||||
0.164200 | + | 0.986427i | \(0.447496\pi\) | |||||||
\(734\) | − | 40.7187i | − | 0.0554750i | ||||||
\(735\) | −139.957 | − | 70.0666i | −0.190417 | − | 0.0953287i | ||||
\(736\) | 27.1293 | 0.0368605 | ||||||||
\(737\) | − | 1424.51i | − | 1.93286i | ||||||
\(738\) | −314.014 | − | 419.566i | −0.425493 | − | 0.568517i | ||||
\(739\) | 430.770 | 0.582909 | 0.291455 | − | 0.956585i | \(-0.405861\pi\) | ||||
0.291455 | + | 0.956585i | \(0.405861\pi\) | |||||||
\(740\) | − | 150.864i | − | 0.203870i | ||||||
\(741\) | 177.873 | − | 355.299i | 0.240045 | − | 0.479485i | ||||
\(742\) | 188.096 | 0.253498 | ||||||||
\(743\) | − | 1255.07i | − | 1.68919i | −0.535408 | − | 0.844594i | \(-0.679842\pi\) | ||
0.535408 | − | 0.844594i | \(-0.320158\pi\) | |||||||
\(744\) | 259.415 | + | 129.871i | 0.348676 | + | 0.174558i | ||||
\(745\) | 320.445 | 0.430127 | ||||||||
\(746\) | − | 304.382i | − | 0.408019i | ||||||
\(747\) | −1083.07 | + | 810.598i | −1.44989 | + | 1.08514i | ||||
\(748\) | −20.5254 | −0.0274404 | ||||||||
\(749\) | 1329.53i | 1.77507i | ||||||||
\(750\) | −21.2346 | + | 42.4157i | −0.0283128 | + | 0.0565543i | ||||
\(751\) | −447.953 | −0.596476 | −0.298238 | − | 0.954492i | \(-0.596399\pi\) | ||||
−0.298238 | + | 0.954492i | \(0.596399\pi\) | |||||||
\(752\) | − | 24.9191i | − | 0.0331372i | ||||||
\(753\) | −556.520 | − | 278.611i | −0.739070 | − | 0.370001i | ||||
\(754\) | 129.596 | 0.171879 | ||||||||
\(755\) | − | 328.340i | − | 0.434888i | ||||||
\(756\) | 451.976 | − | 81.4719i | 0.597852 | − | 0.107767i | ||||
\(757\) | 439.559 | 0.580660 | 0.290330 | − | 0.956927i | \(-0.406235\pi\) | ||||
0.290330 | + | 0.956927i | \(0.406235\pi\) | |||||||
\(758\) | − | 788.184i | − | 1.03982i | ||||||
\(759\) | −85.1250 | + | 170.036i | −0.112154 | + | 0.224026i | ||||
\(760\) | −232.616 | −0.306073 | ||||||||
\(761\) | − | 74.4722i | − | 0.0978609i | −0.998802 | − | 0.0489305i | \(-0.984419\pi\) | ||
0.998802 | − | 0.0489305i | \(-0.0155813\pi\) | |||||||
\(762\) | −330.417 | − | 165.417i | −0.433618 | − | 0.217082i | ||||
\(763\) | 1699.45 | 2.22732 | ||||||||
\(764\) | 114.165i | 0.149431i | ||||||||
\(765\) | −9.36347 | − | 12.5109i | −0.0122398 | − | 0.0163541i | ||||
\(766\) | −39.2492 | −0.0512392 | ||||||||
\(767\) | 254.759i | 0.332150i | ||||||||
\(768\) | −21.4879 | + | 42.9217i | −0.0279790 | + | 0.0558876i | ||||
\(769\) | −496.554 | −0.645714 | −0.322857 | − | 0.946448i | \(-0.604643\pi\) | ||||
−0.322857 | + | 0.946448i | \(0.604643\pi\) | |||||||
\(770\) | 355.455i | 0.461630i | ||||||||
\(771\) | −262.161 | − | 131.246i | −0.340027 | − | 0.170228i | ||||
\(772\) | 212.299 | 0.274999 | ||||||||
\(773\) | − | 1431.40i | − | 1.85175i | −0.377829 | − | 0.925876i | \(-0.623329\pi\) | ||
0.377829 | − | 0.925876i | \(-0.376671\pi\) | |||||||
\(774\) | 307.447 | − | 230.101i | 0.397218 | − | 0.297289i | ||||
\(775\) | −170.948 | −0.220578 | ||||||||
\(776\) | − | 531.244i | − | 0.684593i | ||||||
\(777\) | 385.310 | − | 769.650i | 0.495894 | − | 0.990540i | ||||
\(778\) | 498.589 | 0.640860 | ||||||||
\(779\) | 1514.37i | 1.94400i | ||||||||
\(780\) | 43.2016 | + | 21.6280i | 0.0553866 | + | 0.0277282i | ||||
\(781\) | −1455.07 | −1.86308 | ||||||||
\(782\) | − | 5.26649i | − | 0.00673464i | ||||||
\(783\) | −121.889 | − | 676.193i | −0.155669 | − | 0.863593i | ||||
\(784\) | 93.3281 | 0.119041 | ||||||||
\(785\) | − | 447.759i | − | 0.570394i | ||||||
\(786\) | −105.018 | + | 209.771i | −0.133610 | + | 0.266884i | ||||
\(787\) | 212.110 | 0.269517 | 0.134758 | − | 0.990878i | \(-0.456974\pi\) | ||||
0.134758 | + | 0.990878i | \(0.456974\pi\) | |||||||
\(788\) | 376.241i | 0.477463i | ||||||||
\(789\) | −250.952 | − | 125.634i | −0.318064 | − | 0.159232i | ||||
\(790\) | −229.641 | −0.290685 | ||||||||
\(791\) | 80.5554i | 0.101840i | ||||||||
\(792\) | −201.592 | − | 269.355i | −0.254536 | − | 0.340094i | ||||
\(793\) | −256.643 | −0.323636 | ||||||||
\(794\) | 0.317964i | 0.000400459i | ||||||||
\(795\) | 46.9631 | − | 93.8080i | 0.0590731 | − | 0.117997i | ||||
\(796\) | 516.695 | 0.649115 | ||||||||
\(797\) | 638.216i | 0.800773i | 0.916346 | + | 0.400387i | \(0.131124\pi\) | ||||
−0.916346 | + | 0.400387i | \(0.868876\pi\) | |||||||
\(798\) | −1186.71 | − | 594.104i | −1.48711 | − | 0.744492i | ||||
\(799\) | −4.83744 | −0.00605436 | ||||||||
\(800\) | − | 28.2843i | − | 0.0353553i | ||||||
\(801\) | −979.688 | + | 733.224i | −1.22308 | + | 0.915386i | ||||
\(802\) | −626.396 | −0.781043 | ||||||||
\(803\) | 1136.83i | 1.41573i | ||||||||
\(804\) | −289.502 | + | 578.275i | −0.360077 | + | 0.719247i | ||||
\(805\) | −91.2041 | −0.113297 | ||||||||
\(806\) | 174.115i | 0.216023i | ||||||||
\(807\) | 574.043 | + | 287.383i | 0.711330 | + | 0.356113i | ||||
\(808\) | 124.945 | 0.154635 | ||||||||
\(809\) | 1260.54i | 1.55814i | 0.626936 | + | 0.779071i | \(0.284309\pi\) | ||||
−0.626936 | + | 0.779071i | \(0.715691\pi\) | |||||||
\(810\) | 72.2159 | − | 245.754i | 0.0891554 | − | 0.303400i | ||||
\(811\) | −679.934 | −0.838389 | −0.419195 | − | 0.907896i | \(-0.637688\pi\) | ||||
−0.419195 | + | 0.907896i | \(0.637688\pi\) | |||||||
\(812\) | − | 432.858i | − | 0.533077i | ||||||
\(813\) | −386.494 | + | 772.015i | −0.475392 | + | 0.949588i | ||||
\(814\) | −630.529 | −0.774606 | ||||||||
\(815\) | − | 414.797i | − | 0.508953i | ||||||
\(816\) | 8.33219 | + | 4.17134i | 0.0102110 | + | 0.00511194i | ||||
\(817\) | −1109.70 | −1.35826 | ||||||||
\(818\) | 97.9559i | 0.119751i | ||||||||
\(819\) | 165.159 | + | 220.675i | 0.201660 | + | 0.269445i | ||||
\(820\) | −184.136 | −0.224556 | ||||||||
\(821\) | 395.989i | 0.482325i | 0.970485 | + | 0.241163i | \(0.0775287\pi\) | ||||
−0.970485 | + | 0.241163i | \(0.922471\pi\) | |||||||
\(822\) | −243.595 | + | 486.578i | −0.296345 | + | 0.591943i | ||||
\(823\) | −992.123 | −1.20550 | −0.602748 | − | 0.797931i | \(-0.705928\pi\) | ||||
−0.602748 | + | 0.797931i | \(0.705928\pi\) | |||||||
\(824\) | 141.875i | 0.172179i | ||||||||
\(825\) | 177.274 | + | 88.7489i | 0.214878 | + | 0.107574i | ||||
\(826\) | 850.907 | 1.03015 | ||||||||
\(827\) | − | 258.849i | − | 0.312998i | −0.987678 | − | 0.156499i | \(-0.949979\pi\) | ||
0.987678 | − | 0.156499i | \(-0.0500207\pi\) | |||||||
\(828\) | 69.1121 | − | 51.7254i | 0.0834688 | − | 0.0624702i | ||||
\(829\) | 195.288 | 0.235571 | 0.117786 | − | 0.993039i | \(-0.462420\pi\) | ||||
0.117786 | + | 0.993039i | \(0.462420\pi\) | |||||||
\(830\) | 475.331i | 0.572687i | ||||||||
\(831\) | −164.450 | + | 328.487i | −0.197895 | + | 0.395291i | ||||
\(832\) | −28.8083 | −0.0346254 | ||||||||
\(833\) | − | 18.1173i | − | 0.0217495i | ||||||
\(834\) | 540.321 | + | 270.501i | 0.647867 | + | 0.324342i | ||||
\(835\) | 354.551 | 0.424612 | ||||||||
\(836\) | 972.206i | 1.16293i | ||||||||
\(837\) | 908.476 | − | 163.759i | 1.08540 | − | 0.195650i | ||||
\(838\) | −1097.90 | −1.31014 | ||||||||
\(839\) | 737.892i | 0.879490i | 0.898123 | + | 0.439745i | \(0.144931\pi\) | ||||
−0.898123 | + | 0.439745i | \(0.855069\pi\) | |||||||
\(840\) | 72.2385 | − | 144.295i | 0.0859983 | − | 0.171780i | ||||
\(841\) | 193.409 | 0.229975 | ||||||||
\(842\) | − | 990.389i | − | 1.17623i | ||||||
\(843\) | −485.243 | − | 242.927i | −0.575614 | − | 0.288170i | ||||
\(844\) | 16.4408 | 0.0194797 | ||||||||
\(845\) | − | 348.899i | − | 0.412899i | ||||||
\(846\) | −47.5114 | − | 63.4817i | −0.0561600 | − | 0.0750375i | ||||
\(847\) | 456.523 | 0.538989 | ||||||||
\(848\) | 62.5544i | 0.0737670i | ||||||||
\(849\) | −210.127 | + | 419.726i | −0.247500 | + | 0.494377i | ||||
\(850\) | −5.49069 | −0.00645964 | ||||||||
\(851\) | − | 161.784i | − | 0.190110i | ||||||
\(852\) | 590.677 | + | 295.711i | 0.693283 | + | 0.347078i | ||||
\(853\) | 273.990 | 0.321207 | 0.160604 | − | 0.987019i | \(-0.448656\pi\) | ||||
0.160604 | + | 0.987019i | \(0.448656\pi\) | |||||||
\(854\) | 857.201i | 1.00375i | ||||||||
\(855\) | −592.590 | + | 443.510i | −0.693088 | + | 0.518725i | ||||
\(856\) | −442.157 | −0.516538 | ||||||||
\(857\) | − | 953.725i | − | 1.11287i | −0.830893 | − | 0.556433i | \(-0.812170\pi\) | ||
0.830893 | − | 0.556433i | \(-0.187830\pi\) | |||||||
\(858\) | 90.3932 | − | 180.559i | 0.105353 | − | 0.210442i | ||||
\(859\) | 702.096 | 0.817341 | 0.408671 | − | 0.912682i | \(-0.365993\pi\) | ||||
0.408671 | + | 0.912682i | \(0.365993\pi\) | |||||||
\(860\) | − | 134.930i | − | 0.156896i | ||||||
\(861\) | −939.391 | − | 470.287i | −1.09105 | − | 0.546211i | ||||
\(862\) | 783.942 | 0.909446 | ||||||||
\(863\) | − | 635.320i | − | 0.736176i | −0.929791 | − | 0.368088i | \(-0.880012\pi\) | ||
0.929791 | − | 0.368088i | \(-0.119988\pi\) | |||||||
\(864\) | 27.0949 | + | 150.313i | 0.0313598 | + | 0.173973i | ||||
\(865\) | −123.574 | −0.142861 | ||||||||
\(866\) | 598.239i | 0.690808i | ||||||||
\(867\) | −387.315 | + | 773.655i | −0.446730 | + | 0.892336i | ||||
\(868\) | 581.552 | 0.669990 | ||||||||
\(869\) | 959.775i | 1.10446i | ||||||||
\(870\) | −215.877 | − | 108.075i | −0.248135 | − | 0.124224i | ||||
\(871\) | −388.128 | −0.445612 | ||||||||
\(872\) | 565.181i | 0.648143i | ||||||||
\(873\) | −1012.88 | − | 1353.35i | −1.16023 | − | 1.55023i | ||||
\(874\) | −249.452 | −0.285415 | ||||||||
\(875\) | 95.0868i | 0.108671i | ||||||||
\(876\) | 231.037 | − | 461.492i | 0.263740 | − | 0.526817i | ||||
\(877\) | 45.3899 | 0.0517559 | 0.0258780 | − | 0.999665i | \(-0.491762\pi\) | ||||
0.0258780 | + | 0.999665i | \(0.491762\pi\) | |||||||
\(878\) | 616.721i | 0.702416i | ||||||||
\(879\) | −7.74403 | − | 3.87689i | −0.00881004 | − | 0.00441057i | ||||
\(880\) | −118.213 | −0.134333 | ||||||||
\(881\) | 644.412i | 0.731455i | 0.930722 | + | 0.365727i | \(0.119180\pi\) | ||||
−0.930722 | + | 0.365727i | \(0.880820\pi\) | |||||||
\(882\) | 237.754 | − | 177.941i | 0.269562 | − | 0.201748i | ||||
\(883\) | −1586.87 | −1.79713 | −0.898565 | − | 0.438840i | \(-0.855390\pi\) | ||||
−0.898565 | + | 0.438840i | \(0.855390\pi\) | |||||||
\(884\) | 5.59242i | 0.00632627i | ||||||||
\(885\) | 212.452 | − | 424.369i | 0.240058 | − | 0.479513i | ||||
\(886\) | −601.843 | −0.679281 | ||||||||
\(887\) | 1561.91i | 1.76089i | 0.474148 | + | 0.880445i | \(0.342756\pi\) | ||||
−0.474148 | + | 0.880445i | \(0.657244\pi\) | |||||||
\(888\) | 255.960 | + | 128.141i | 0.288244 | + | 0.144303i | ||||
\(889\) | −740.724 | −0.833210 | ||||||||
\(890\) | 429.959i | 0.483100i | ||||||||
\(891\) | −1027.12 | − | 301.823i | −1.15277 | − | 0.338746i | ||||
\(892\) | −268.134 | −0.300599 | ||||||||
\(893\) | 229.130i | 0.256585i | ||||||||
\(894\) | −272.180 | + | 543.675i | −0.304452 | + | 0.608138i | ||||
\(895\) | −231.171 | −0.258292 | ||||||||
\(896\) | 96.2211i | 0.107390i | ||||||||
\(897\) | 46.3285 | + | 23.1934i | 0.0516483 | + | 0.0258567i | ||||
\(898\) | 502.231 | 0.559277 | ||||||||
\(899\) | − | 870.048i | − | 0.967796i | ||||||
\(900\) | −53.9274 | − | 72.0544i | −0.0599194 | − | 0.0800604i | ||||
\(901\) | 12.1434 | 0.0134777 | ||||||||
\(902\) | 769.589i | 0.853203i | ||||||||
\(903\) | 344.615 | − | 688.362i | 0.381633 | − | 0.762306i | ||||
\(904\) | −26.7901 | −0.0296351 | ||||||||
\(905\) | − | 360.997i | − | 0.398892i | ||||||
\(906\) | 557.071 | + | 278.887i | 0.614869 | + | 0.307822i | ||||
\(907\) | 1128.40 | 1.24410 | 0.622049 | − | 0.782979i | \(-0.286301\pi\) | ||||
0.622049 | + | 0.782979i | \(0.286301\pi\) | |||||||
\(908\) | 504.293i | 0.555388i | ||||||||
\(909\) | 318.299 | − | 238.224i | 0.350164 | − | 0.262072i | ||||
\(910\) | 96.8485 | 0.106427 | ||||||||
\(911\) | 953.339i | 1.04648i | 0.852187 | + | 0.523238i | \(0.175276\pi\) | ||||
−0.852187 | + | 0.523238i | \(0.824724\pi\) | |||||||
\(912\) | 197.580 | − | 394.662i | 0.216644 | − | 0.432744i | ||||
\(913\) | 1986.62 | 2.17593 | ||||||||
\(914\) | − | 563.734i | − | 0.616777i | ||||||
\(915\) | 427.508 | + | 214.023i | 0.467222 | + | 0.233905i | ||||
\(916\) | 811.275 | 0.885672 | ||||||||
\(917\) | 470.261i | 0.512826i | ||||||||
\(918\) | 29.1795 | − | 5.25981i | 0.0317859 | − | 0.00572964i | ||||
\(919\) | −449.412 | −0.489023 | −0.244512 | − | 0.969646i | \(-0.578628\pi\) | ||||
−0.244512 | + | 0.969646i | \(0.578628\pi\) | |||||||
\(920\) | − | 30.3315i | − | 0.0329690i | ||||||
\(921\) | 364.558 | − | 728.198i | 0.395828 | − | 0.790660i | ||||
\(922\) | 811.164 | 0.879788 | ||||||||
\(923\) | 396.453i | 0.429526i | ||||||||
\(924\) | −603.075 | − | 301.917i | −0.652679 | − | 0.326751i | ||||
\(925\) | −168.671 | −0.182347 | ||||||||
\(926\) | − | 379.945i | − | 0.410308i | ||||||
\(927\) | 270.502 | + | 361.428i | 0.291804 | + | 0.389890i | ||||
\(928\) | 143.955 | 0.155123 | ||||||||
\(929\) | − | 434.163i | − | 0.467345i | −0.972315 | − | 0.233672i | \(-0.924926\pi\) | ||
0.972315 | − | 0.233672i | \(-0.0750743\pi\) | |||||||
\(930\) | 145.200 | − | 290.035i | 0.156129 | − | 0.311865i | ||||
\(931\) | −858.146 | −0.921747 | ||||||||
\(932\) | 352.240i | 0.377940i | ||||||||
\(933\) | −531.375 | − | 266.022i | −0.569534 | − | 0.285126i | ||||
\(934\) | 795.345 | 0.851548 | ||||||||
\(935\) | 22.9481i | 0.0245434i | ||||||||
\(936\) | −73.3894 | + | 54.9266i | −0.0784074 | + | 0.0586822i | ||||
\(937\) | 411.423 | 0.439085 | 0.219543 | − | 0.975603i | \(-0.429544\pi\) | ||||
0.219543 | + | 0.975603i | \(0.429544\pi\) | |||||||
\(938\) | 1296.37i | 1.38205i | ||||||||
\(939\) | 90.7855 | − | 181.343i | 0.0966832 | − | 0.193123i | ||||
\(940\) | −27.8604 | −0.0296388 | ||||||||
\(941\) | 593.790i | 0.631020i | 0.948922 | + | 0.315510i | \(0.102176\pi\) | ||||
−0.948922 | + | 0.315510i | \(0.897824\pi\) | |||||||
\(942\) | 759.681 | + | 380.319i | 0.806455 | + | 0.403736i | ||||
\(943\) | −197.464 | −0.209400 | ||||||||
\(944\) | 282.984i | 0.299771i | ||||||||
\(945\) | −91.0883 | − | 505.325i | −0.0963898 | − | 0.534735i | ||||
\(946\) | −563.935 | −0.596126 | ||||||||
\(947\) | − | 1059.68i | − | 1.11899i | −0.828834 | − | 0.559495i | \(-0.810995\pi\) | ||
0.828834 | − | 0.559495i | \(-0.189005\pi\) | |||||||
\(948\) | 195.053 | − | 389.616i | 0.205753 | − | 0.410987i | ||||
\(949\) | 309.745 | 0.326391 | ||||||||
\(950\) | 260.072i | 0.273760i | ||||||||
\(951\) | 1067.25 | + | 534.297i | 1.12224 | + | 0.561827i | ||||
\(952\) | 18.6790 | 0.0196207 | ||||||||
\(953\) | 166.354i | 0.174558i | 0.996184 | + | 0.0872790i | \(0.0278172\pi\) | ||||
−0.996184 | + | 0.0872790i | \(0.972183\pi\) | |||||||
\(954\) | 119.268 | + | 159.358i | 0.125019 | + | 0.167042i | ||||
\(955\) | 127.641 | 0.133655 | ||||||||
\(956\) | − | 104.979i | − | 0.109810i | ||||||
\(957\) | −451.693 | + | 902.249i | −0.471988 | + | 0.942789i | ||||
\(958\) | −710.684 | −0.741841 | ||||||||
\(959\) | 1090.80i | 1.13744i | ||||||||
\(960\) | 47.9879 | + | 24.0242i | 0.0499874 | + | 0.0250252i | ||||
\(961\) | 207.924 | 0.216362 | ||||||||
\(962\) | 171.796i | 0.178582i | ||||||||
\(963\) | −1126.40 | + | 843.026i | −1.16968 | + | 0.875416i | ||||
\(964\) | −480.406 | −0.498346 | ||||||||
\(965\) | − | 237.358i | − | 0.245967i | ||||||
\(966\) | 77.4672 | − | 154.739i | 0.0801938 | − | 0.160186i | ||||
\(967\) | −1600.34 | −1.65495 | −0.827474 | − | 0.561503i | \(-0.810223\pi\) | ||||
−0.827474 | + | 0.561503i | \(0.810223\pi\) | |||||||
\(968\) | 151.825i | 0.156844i | ||||||||
\(969\) | −76.6139 | − | 38.3552i | −0.0790650 | − | 0.0395823i | ||||
\(970\) | −593.949 | −0.612318 | ||||||||
\(971\) | − | 1574.23i | − | 1.62125i | −0.585568 | − | 0.810623i | \(-0.699128\pi\) | ||
0.585568 | − | 0.810623i | \(-0.300872\pi\) | |||||||
\(972\) | 355.614 | + | 331.263i | 0.365858 | + | 0.340805i | ||||
\(973\) | 1211.28 | 1.24489 | ||||||||
\(974\) | 376.460i | 0.386509i | ||||||||
\(975\) | 24.1808 | − | 48.3008i | 0.0248009 | − | 0.0495393i | ||||
\(976\) | −285.077 | −0.292087 | ||||||||
\(977\) | 1060.94i | 1.08592i | 0.839759 | + | 0.542960i | \(0.182696\pi\) | ||||
−0.839759 | + | 0.542960i | \(0.817304\pi\) | |||||||
\(978\) | 703.756 | + | 352.321i | 0.719587 | + | 0.360247i | ||||
\(979\) | 1796.99 | 1.83554 | ||||||||
\(980\) | − | 104.344i | − | 0.106473i | ||||||
\(981\) | 1077.59 | + | 1439.80i | 1.09846 | + | 1.46769i | ||||
\(982\) | 19.4165 | 0.0197724 | ||||||||
\(983\) | − | 1315.50i | − | 1.33825i | −0.743148 | − | 0.669127i | \(-0.766668\pi\) | ||
0.743148 | − | 0.669127i | \(-0.233332\pi\) | |||||||
\(984\) | 156.402 | − | 312.411i | 0.158945 | − | 0.317491i | ||||
\(985\) | 420.650 | 0.427056 | ||||||||
\(986\) | − | 27.9452i | − | 0.0283420i | ||||||
\(987\) | −142.133 | − | 71.1561i | −0.144005 | − | 0.0720933i | ||||
\(988\) | 264.891 | 0.268108 | ||||||||
\(989\) | − | 144.697i | − | 0.146306i | ||||||
\(990\) | −301.148 | + | 225.387i | −0.304190 | + | 0.227664i | ||||
\(991\) | −994.920 | −1.00396 | −0.501978 | − | 0.864881i | \(-0.667394\pi\) | ||||
−0.501978 | + | 0.864881i | \(0.667394\pi\) | |||||||
\(992\) | 193.405i | 0.194965i | ||||||||
\(993\) | 573.036 | − | 1144.63i | 0.577075 | − | 1.15270i | ||||
\(994\) | 1324.17 | 1.33216 | ||||||||
\(995\) | − | 577.683i | − | 0.580586i | ||||||
\(996\) | −806.459 | − | 403.738i | −0.809698 | − | 0.405359i | ||||
\(997\) | 602.837 | 0.604651 | 0.302325 | − | 0.953205i | \(-0.402237\pi\) | ||||
0.302325 | + | 0.953205i | \(0.402237\pi\) | |||||||
\(998\) | 432.591i | 0.433458i | ||||||||
\(999\) | 896.378 | − | 161.578i | 0.897275 | − | 0.161740i |
(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 | 690.3.g.a.461.14 | yes | 56 | |
3.2 | odd | 2 | inner | 690.3.g.a.461.13 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.g.a.461.13 | ✓ | 56 | 3.2 | odd | 2 | inner | |
690.3.g.a.461.14 | yes | 56 | 1.1 | even | 1 | trivial |