Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.a (trivial) |
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: | yes |
Analytic conductor: | \(64.0240523407\) |
Analytic rank: | \(1\) |
Dimension: | \(34\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −3.17050 | −1.83049 | −0.915246 | − | 0.402896i | \(-0.868004\pi\) | ||||
−0.915246 | + | 0.402896i | \(0.868004\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 4.15425 | 1.85784 | 0.928919 | − | 0.370284i | \(-0.120740\pi\) | ||||
0.928919 | + | 0.370284i | \(0.120740\pi\) | |||||||
\(6\) | 3.17050 | 1.29435 | ||||||||
\(7\) | 1.45443 | 0.549723 | 0.274862 | − | 0.961484i | \(-0.411368\pi\) | ||||
0.274862 | + | 0.961484i | \(0.411368\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 7.05209 | 2.35070 | ||||||||
\(10\) | −4.15425 | −1.31369 | ||||||||
\(11\) | −3.03789 | −0.915957 | −0.457979 | − | 0.888963i | \(-0.651426\pi\) | ||||
−0.457979 | + | 0.888963i | \(0.651426\pi\) | |||||||
\(12\) | −3.17050 | −0.915246 | ||||||||
\(13\) | 3.91980 | 1.08716 | 0.543579 | − | 0.839358i | \(-0.317069\pi\) | ||||
0.543579 | + | 0.839358i | \(0.317069\pi\) | |||||||
\(14\) | −1.45443 | −0.388713 | ||||||||
\(15\) | −13.1711 | −3.40075 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.0576653 | −0.0139859 | −0.00699294 | − | 0.999976i | \(-0.502226\pi\) | ||||
−0.00699294 | + | 0.999976i | \(0.502226\pi\) | |||||||
\(18\) | −7.05209 | −1.66219 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 4.15425 | 0.928919 | ||||||||
\(21\) | −4.61128 | −1.00626 | ||||||||
\(22\) | 3.03789 | 0.647679 | ||||||||
\(23\) | 0.939084 | 0.195813 | 0.0979063 | − | 0.995196i | \(-0.468785\pi\) | ||||
0.0979063 | + | 0.995196i | \(0.468785\pi\) | |||||||
\(24\) | 3.17050 | 0.647176 | ||||||||
\(25\) | 12.2578 | 2.45156 | ||||||||
\(26\) | −3.91980 | −0.768736 | ||||||||
\(27\) | −12.8472 | −2.47244 | ||||||||
\(28\) | 1.45443 | 0.274862 | ||||||||
\(29\) | −9.74846 | −1.81024 | −0.905122 | − | 0.425152i | \(-0.860221\pi\) | ||||
−0.905122 | + | 0.425152i | \(0.860221\pi\) | |||||||
\(30\) | 13.1711 | 2.40470 | ||||||||
\(31\) | 3.98084 | 0.714981 | 0.357490 | − | 0.933917i | \(-0.383633\pi\) | ||||
0.357490 | + | 0.933917i | \(0.383633\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 9.63163 | 1.67665 | ||||||||
\(34\) | 0.0576653 | 0.00988951 | ||||||||
\(35\) | 6.04207 | 1.02130 | ||||||||
\(36\) | 7.05209 | 1.17535 | ||||||||
\(37\) | −10.1478 | −1.66829 | −0.834145 | − | 0.551545i | \(-0.814038\pi\) | ||||
−0.834145 | + | 0.551545i | \(0.814038\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | −12.4277 | −1.99003 | ||||||||
\(40\) | −4.15425 | −0.656845 | ||||||||
\(41\) | 6.40788 | 1.00074 | 0.500372 | − | 0.865811i | \(-0.333197\pi\) | ||||
0.500372 | + | 0.865811i | \(0.333197\pi\) | |||||||
\(42\) | 4.61128 | 0.711536 | ||||||||
\(43\) | −0.156989 | −0.0239406 | −0.0119703 | − | 0.999928i | \(-0.503810\pi\) | ||||
−0.0119703 | + | 0.999928i | \(0.503810\pi\) | |||||||
\(44\) | −3.03789 | −0.457979 | ||||||||
\(45\) | 29.2962 | 4.36721 | ||||||||
\(46\) | −0.939084 | −0.138460 | ||||||||
\(47\) | −3.44285 | −0.502191 | −0.251095 | − | 0.967962i | \(-0.580791\pi\) | ||||
−0.251095 | + | 0.967962i | \(0.580791\pi\) | |||||||
\(48\) | −3.17050 | −0.457623 | ||||||||
\(49\) | −4.88463 | −0.697805 | ||||||||
\(50\) | −12.2578 | −1.73351 | ||||||||
\(51\) | 0.182828 | 0.0256010 | ||||||||
\(52\) | 3.91980 | 0.543579 | ||||||||
\(53\) | 8.72651 | 1.19868 | 0.599339 | − | 0.800495i | \(-0.295430\pi\) | ||||
0.599339 | + | 0.800495i | \(0.295430\pi\) | |||||||
\(54\) | 12.8472 | 1.74828 | ||||||||
\(55\) | −12.6201 | −1.70170 | ||||||||
\(56\) | −1.45443 | −0.194356 | ||||||||
\(57\) | 3.17050 | 0.419943 | ||||||||
\(58\) | 9.74846 | 1.28004 | ||||||||
\(59\) | −6.77204 | −0.881644 | −0.440822 | − | 0.897595i | \(-0.645313\pi\) | ||||
−0.440822 | + | 0.897595i | \(0.645313\pi\) | |||||||
\(60\) | −13.1711 | −1.70038 | ||||||||
\(61\) | 0.287029 | 0.0367503 | 0.0183751 | − | 0.999831i | \(-0.494151\pi\) | ||||
0.0183751 | + | 0.999831i | \(0.494151\pi\) | |||||||
\(62\) | −3.98084 | −0.505568 | ||||||||
\(63\) | 10.2568 | 1.29223 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 16.2838 | 2.01976 | ||||||||
\(66\) | −9.63163 | −1.18557 | ||||||||
\(67\) | −0.311296 | −0.0380309 | −0.0190155 | − | 0.999819i | \(-0.506053\pi\) | ||||
−0.0190155 | + | 0.999819i | \(0.506053\pi\) | |||||||
\(68\) | −0.0576653 | −0.00699294 | ||||||||
\(69\) | −2.97737 | −0.358433 | ||||||||
\(70\) | −6.04207 | −0.722165 | ||||||||
\(71\) | −4.31993 | −0.512681 | −0.256341 | − | 0.966587i | \(-0.582517\pi\) | ||||
−0.256341 | + | 0.966587i | \(0.582517\pi\) | |||||||
\(72\) | −7.05209 | −0.831097 | ||||||||
\(73\) | −12.8177 | −1.50020 | −0.750099 | − | 0.661325i | \(-0.769994\pi\) | ||||
−0.750099 | + | 0.661325i | \(0.769994\pi\) | |||||||
\(74\) | 10.1478 | 1.17966 | ||||||||
\(75\) | −38.8634 | −4.48756 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −4.41839 | −0.503523 | ||||||||
\(78\) | 12.4277 | 1.40717 | ||||||||
\(79\) | −12.9034 | −1.45174 | −0.725872 | − | 0.687830i | \(-0.758564\pi\) | ||||
−0.725872 | + | 0.687830i | \(0.758564\pi\) | |||||||
\(80\) | 4.15425 | 0.464459 | ||||||||
\(81\) | 19.5758 | 2.17508 | ||||||||
\(82\) | −6.40788 | −0.707632 | ||||||||
\(83\) | −3.11104 | −0.341481 | −0.170741 | − | 0.985316i | \(-0.554616\pi\) | ||||
−0.170741 | + | 0.985316i | \(0.554616\pi\) | |||||||
\(84\) | −4.61128 | −0.503132 | ||||||||
\(85\) | −0.239556 | −0.0259835 | ||||||||
\(86\) | 0.156989 | 0.0169285 | ||||||||
\(87\) | 30.9075 | 3.31364 | ||||||||
\(88\) | 3.03789 | 0.323840 | ||||||||
\(89\) | −9.56741 | −1.01414 | −0.507072 | − | 0.861904i | \(-0.669272\pi\) | ||||
−0.507072 | + | 0.861904i | \(0.669272\pi\) | |||||||
\(90\) | −29.2962 | −3.08809 | ||||||||
\(91\) | 5.70108 | 0.597635 | ||||||||
\(92\) | 0.939084 | 0.0979063 | ||||||||
\(93\) | −12.6213 | −1.30877 | ||||||||
\(94\) | 3.44285 | 0.355102 | ||||||||
\(95\) | −4.15425 | −0.426217 | ||||||||
\(96\) | 3.17050 | 0.323588 | ||||||||
\(97\) | −18.1356 | −1.84140 | −0.920698 | − | 0.390276i | \(-0.872380\pi\) | ||||
−0.920698 | + | 0.390276i | \(0.872380\pi\) | |||||||
\(98\) | 4.88463 | 0.493422 | ||||||||
\(99\) | −21.4235 | −2.15314 | ||||||||
\(100\) | 12.2578 | 1.22578 | ||||||||
\(101\) | −7.67850 | −0.764039 | −0.382019 | − | 0.924154i | \(-0.624771\pi\) | ||||
−0.382019 | + | 0.924154i | \(0.624771\pi\) | |||||||
\(102\) | −0.182828 | −0.0181027 | ||||||||
\(103\) | −13.1794 | −1.29861 | −0.649304 | − | 0.760529i | \(-0.724940\pi\) | ||||
−0.649304 | + | 0.760529i | \(0.724940\pi\) | |||||||
\(104\) | −3.91980 | −0.384368 | ||||||||
\(105\) | −19.1564 | −1.86947 | ||||||||
\(106\) | −8.72651 | −0.847594 | ||||||||
\(107\) | −14.2013 | −1.37289 | −0.686445 | − | 0.727182i | \(-0.740830\pi\) | ||||
−0.686445 | + | 0.727182i | \(0.740830\pi\) | |||||||
\(108\) | −12.8472 | −1.23622 | ||||||||
\(109\) | −0.357816 | −0.0342726 | −0.0171363 | − | 0.999853i | \(-0.505455\pi\) | ||||
−0.0171363 | + | 0.999853i | \(0.505455\pi\) | |||||||
\(110\) | 12.6201 | 1.20328 | ||||||||
\(111\) | 32.1737 | 3.05379 | ||||||||
\(112\) | 1.45443 | 0.137431 | ||||||||
\(113\) | −6.97326 | −0.655989 | −0.327995 | − | 0.944680i | \(-0.606373\pi\) | ||||
−0.327995 | + | 0.944680i | \(0.606373\pi\) | |||||||
\(114\) | −3.17050 | −0.296945 | ||||||||
\(115\) | 3.90119 | 0.363788 | ||||||||
\(116\) | −9.74846 | −0.905122 | ||||||||
\(117\) | 27.6428 | 2.55558 | ||||||||
\(118\) | 6.77204 | 0.623416 | ||||||||
\(119\) | −0.0838701 | −0.00768836 | ||||||||
\(120\) | 13.1711 | 1.20235 | ||||||||
\(121\) | −1.77125 | −0.161023 | ||||||||
\(122\) | −0.287029 | −0.0259864 | ||||||||
\(123\) | −20.3162 | −1.83185 | ||||||||
\(124\) | 3.98084 | 0.357490 | ||||||||
\(125\) | 30.1507 | 2.69676 | ||||||||
\(126\) | −10.2568 | −0.913747 | ||||||||
\(127\) | −8.53078 | −0.756985 | −0.378492 | − | 0.925604i | \(-0.623557\pi\) | ||||
−0.378492 | + | 0.925604i | \(0.623557\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0.497733 | 0.0438230 | ||||||||
\(130\) | −16.2838 | −1.42819 | ||||||||
\(131\) | 10.4714 | 0.914889 | 0.457445 | − | 0.889238i | \(-0.348765\pi\) | ||||
0.457445 | + | 0.889238i | \(0.348765\pi\) | |||||||
\(132\) | 9.63163 | 0.838326 | ||||||||
\(133\) | −1.45443 | −0.126115 | ||||||||
\(134\) | 0.311296 | 0.0268919 | ||||||||
\(135\) | −53.3704 | −4.59339 | ||||||||
\(136\) | 0.0576653 | 0.00494476 | ||||||||
\(137\) | 2.96722 | 0.253507 | 0.126753 | − | 0.991934i | \(-0.459544\pi\) | ||||
0.126753 | + | 0.991934i | \(0.459544\pi\) | |||||||
\(138\) | 2.97737 | 0.253451 | ||||||||
\(139\) | −13.6710 | −1.15956 | −0.579781 | − | 0.814772i | \(-0.696862\pi\) | ||||
−0.579781 | + | 0.814772i | \(0.696862\pi\) | |||||||
\(140\) | 6.04207 | 0.510648 | ||||||||
\(141\) | 10.9156 | 0.919256 | ||||||||
\(142\) | 4.31993 | 0.362520 | ||||||||
\(143\) | −11.9079 | −0.995789 | ||||||||
\(144\) | 7.05209 | 0.587675 | ||||||||
\(145\) | −40.4975 | −3.36314 | ||||||||
\(146\) | 12.8177 | 1.06080 | ||||||||
\(147\) | 15.4867 | 1.27733 | ||||||||
\(148\) | −10.1478 | −0.834145 | ||||||||
\(149\) | 23.5793 | 1.93169 | 0.965847 | − | 0.259114i | \(-0.0834305\pi\) | ||||
0.965847 | + | 0.259114i | \(0.0834305\pi\) | |||||||
\(150\) | 38.8634 | 3.17318 | ||||||||
\(151\) | −10.2850 | −0.836983 | −0.418492 | − | 0.908221i | \(-0.637441\pi\) | ||||
−0.418492 | + | 0.908221i | \(0.637441\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | −0.406661 | −0.0328766 | ||||||||
\(154\) | 4.41839 | 0.356044 | ||||||||
\(155\) | 16.5374 | 1.32832 | ||||||||
\(156\) | −12.4277 | −0.995016 | ||||||||
\(157\) | 12.3626 | 0.986643 | 0.493321 | − | 0.869847i | \(-0.335783\pi\) | ||||
0.493321 | + | 0.869847i | \(0.335783\pi\) | |||||||
\(158\) | 12.9034 | 1.02654 | ||||||||
\(159\) | −27.6674 | −2.19417 | ||||||||
\(160\) | −4.15425 | −0.328422 | ||||||||
\(161\) | 1.36583 | 0.107643 | ||||||||
\(162\) | −19.5758 | −1.53802 | ||||||||
\(163\) | −6.34732 | −0.497160 | −0.248580 | − | 0.968611i | \(-0.579964\pi\) | ||||
−0.248580 | + | 0.968611i | \(0.579964\pi\) | |||||||
\(164\) | 6.40788 | 0.500372 | ||||||||
\(165\) | 40.0122 | 3.11495 | ||||||||
\(166\) | 3.11104 | 0.241464 | ||||||||
\(167\) | −10.5337 | −0.815122 | −0.407561 | − | 0.913178i | \(-0.633621\pi\) | ||||
−0.407561 | + | 0.913178i | \(0.633621\pi\) | |||||||
\(168\) | 4.61128 | 0.355768 | ||||||||
\(169\) | 2.36484 | 0.181911 | ||||||||
\(170\) | 0.239556 | 0.0183731 | ||||||||
\(171\) | −7.05209 | −0.539287 | ||||||||
\(172\) | −0.156989 | −0.0119703 | ||||||||
\(173\) | 8.42256 | 0.640355 | 0.320178 | − | 0.947358i | \(-0.396257\pi\) | ||||
0.320178 | + | 0.947358i | \(0.396257\pi\) | |||||||
\(174\) | −30.9075 | −2.34309 | ||||||||
\(175\) | 17.8281 | 1.34768 | ||||||||
\(176\) | −3.03789 | −0.228989 | ||||||||
\(177\) | 21.4708 | 1.61384 | ||||||||
\(178\) | 9.56741 | 0.717107 | ||||||||
\(179\) | 7.95295 | 0.594431 | 0.297216 | − | 0.954810i | \(-0.403942\pi\) | ||||
0.297216 | + | 0.954810i | \(0.403942\pi\) | |||||||
\(180\) | 29.2962 | 2.18361 | ||||||||
\(181\) | 14.8269 | 1.10208 | 0.551038 | − | 0.834480i | \(-0.314232\pi\) | ||||
0.551038 | + | 0.834480i | \(0.314232\pi\) | |||||||
\(182\) | −5.70108 | −0.422592 | ||||||||
\(183\) | −0.910026 | −0.0672710 | ||||||||
\(184\) | −0.939084 | −0.0692302 | ||||||||
\(185\) | −42.1566 | −3.09941 | ||||||||
\(186\) | 12.6213 | 0.925437 | ||||||||
\(187\) | 0.175180 | 0.0128105 | ||||||||
\(188\) | −3.44285 | −0.251095 | ||||||||
\(189\) | −18.6853 | −1.35916 | ||||||||
\(190\) | 4.15425 | 0.301381 | ||||||||
\(191\) | −9.97021 | −0.721419 | −0.360710 | − | 0.932678i | \(-0.617465\pi\) | ||||
−0.360710 | + | 0.932678i | \(0.617465\pi\) | |||||||
\(192\) | −3.17050 | −0.228811 | ||||||||
\(193\) | 1.78617 | 0.128572 | 0.0642858 | − | 0.997932i | \(-0.479523\pi\) | ||||
0.0642858 | + | 0.997932i | \(0.479523\pi\) | |||||||
\(194\) | 18.1356 | 1.30206 | ||||||||
\(195\) | −51.6280 | −3.69716 | ||||||||
\(196\) | −4.88463 | −0.348902 | ||||||||
\(197\) | −13.7517 | −0.979765 | −0.489883 | − | 0.871788i | \(-0.662960\pi\) | ||||
−0.489883 | + | 0.871788i | \(0.662960\pi\) | |||||||
\(198\) | 21.4235 | 1.52250 | ||||||||
\(199\) | −19.8784 | −1.40914 | −0.704571 | − | 0.709634i | \(-0.748860\pi\) | ||||
−0.704571 | + | 0.709634i | \(0.748860\pi\) | |||||||
\(200\) | −12.2578 | −0.866757 | ||||||||
\(201\) | 0.986967 | 0.0696153 | ||||||||
\(202\) | 7.67850 | 0.540257 | ||||||||
\(203\) | −14.1785 | −0.995133 | ||||||||
\(204\) | 0.182828 | 0.0128005 | ||||||||
\(205\) | 26.6200 | 1.85922 | ||||||||
\(206\) | 13.1794 | 0.918255 | ||||||||
\(207\) | 6.62251 | 0.460296 | ||||||||
\(208\) | 3.91980 | 0.271789 | ||||||||
\(209\) | 3.03789 | 0.210135 | ||||||||
\(210\) | 19.1564 | 1.32192 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | 8.72651 | 0.599339 | ||||||||
\(213\) | 13.6964 | 0.938458 | ||||||||
\(214\) | 14.2013 | 0.970780 | ||||||||
\(215\) | −0.652171 | −0.0444777 | ||||||||
\(216\) | 12.8472 | 0.874140 | ||||||||
\(217\) | 5.78986 | 0.393041 | ||||||||
\(218\) | 0.357816 | 0.0242344 | ||||||||
\(219\) | 40.6386 | 2.74610 | ||||||||
\(220\) | −12.6201 | −0.850850 | ||||||||
\(221\) | −0.226036 | −0.0152049 | ||||||||
\(222\) | −32.1737 | −2.15936 | ||||||||
\(223\) | 4.38025 | 0.293323 | 0.146662 | − | 0.989187i | \(-0.453147\pi\) | ||||
0.146662 | + | 0.989187i | \(0.453147\pi\) | |||||||
\(224\) | −1.45443 | −0.0971782 | ||||||||
\(225\) | 86.4431 | 5.76288 | ||||||||
\(226\) | 6.97326 | 0.463854 | ||||||||
\(227\) | 19.0575 | 1.26489 | 0.632445 | − | 0.774605i | \(-0.282051\pi\) | ||||
0.632445 | + | 0.774605i | \(0.282051\pi\) | |||||||
\(228\) | 3.17050 | 0.209972 | ||||||||
\(229\) | −11.0057 | −0.727275 | −0.363638 | − | 0.931540i | \(-0.618465\pi\) | ||||
−0.363638 | + | 0.931540i | \(0.618465\pi\) | |||||||
\(230\) | −3.90119 | −0.257237 | ||||||||
\(231\) | 14.0085 | 0.921694 | ||||||||
\(232\) | 9.74846 | 0.640018 | ||||||||
\(233\) | 20.5312 | 1.34504 | 0.672522 | − | 0.740077i | \(-0.265211\pi\) | ||||
0.672522 | + | 0.740077i | \(0.265211\pi\) | |||||||
\(234\) | −27.6428 | −1.80707 | ||||||||
\(235\) | −14.3024 | −0.932989 | ||||||||
\(236\) | −6.77204 | −0.440822 | ||||||||
\(237\) | 40.9102 | 2.65741 | ||||||||
\(238\) | 0.0838701 | 0.00543649 | ||||||||
\(239\) | 7.63091 | 0.493603 | 0.246801 | − | 0.969066i | \(-0.420621\pi\) | ||||
0.246801 | + | 0.969066i | \(0.420621\pi\) | |||||||
\(240\) | −13.1711 | −0.850189 | ||||||||
\(241\) | 7.91820 | 0.510056 | 0.255028 | − | 0.966934i | \(-0.417915\pi\) | ||||
0.255028 | + | 0.966934i | \(0.417915\pi\) | |||||||
\(242\) | 1.77125 | 0.113860 | ||||||||
\(243\) | −23.5235 | −1.50903 | ||||||||
\(244\) | 0.287029 | 0.0183751 | ||||||||
\(245\) | −20.2920 | −1.29641 | ||||||||
\(246\) | 20.3162 | 1.29531 | ||||||||
\(247\) | −3.91980 | −0.249411 | ||||||||
\(248\) | −3.98084 | −0.252784 | ||||||||
\(249\) | 9.86357 | 0.625078 | ||||||||
\(250\) | −30.1507 | −1.90690 | ||||||||
\(251\) | 16.9552 | 1.07020 | 0.535102 | − | 0.844787i | \(-0.320273\pi\) | ||||
0.535102 | + | 0.844787i | \(0.320273\pi\) | |||||||
\(252\) | 10.2568 | 0.646116 | ||||||||
\(253\) | −2.85283 | −0.179356 | ||||||||
\(254\) | 8.53078 | 0.535269 | ||||||||
\(255\) | 0.759513 | 0.0475625 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −6.24300 | −0.389428 | −0.194714 | − | 0.980860i | \(-0.562378\pi\) | ||||
−0.194714 | + | 0.980860i | \(0.562378\pi\) | |||||||
\(258\) | −0.497733 | −0.0309875 | ||||||||
\(259\) | −14.7593 | −0.917097 | ||||||||
\(260\) | 16.2838 | 1.00988 | ||||||||
\(261\) | −68.7471 | −4.25534 | ||||||||
\(262\) | −10.4714 | −0.646924 | ||||||||
\(263\) | −12.6080 | −0.777442 | −0.388721 | − | 0.921356i | \(-0.627083\pi\) | ||||
−0.388721 | + | 0.921356i | \(0.627083\pi\) | |||||||
\(264\) | −9.63163 | −0.592786 | ||||||||
\(265\) | 36.2521 | 2.22695 | ||||||||
\(266\) | 1.45443 | 0.0891769 | ||||||||
\(267\) | 30.3335 | 1.85638 | ||||||||
\(268\) | −0.311296 | −0.0190155 | ||||||||
\(269\) | 29.0252 | 1.76970 | 0.884850 | − | 0.465876i | \(-0.154261\pi\) | ||||
0.884850 | + | 0.465876i | \(0.154261\pi\) | |||||||
\(270\) | 53.3704 | 3.24802 | ||||||||
\(271\) | −7.49327 | −0.455184 | −0.227592 | − | 0.973757i | \(-0.573085\pi\) | ||||
−0.227592 | + | 0.973757i | \(0.573085\pi\) | |||||||
\(272\) | −0.0576653 | −0.00349647 | ||||||||
\(273\) | −18.0753 | −1.09397 | ||||||||
\(274\) | −2.96722 | −0.179256 | ||||||||
\(275\) | −37.2378 | −2.24552 | ||||||||
\(276\) | −2.97737 | −0.179217 | ||||||||
\(277\) | −6.01689 | −0.361520 | −0.180760 | − | 0.983527i | \(-0.557856\pi\) | ||||
−0.180760 | + | 0.983527i | \(0.557856\pi\) | |||||||
\(278\) | 13.6710 | 0.819934 | ||||||||
\(279\) | 28.0733 | 1.68070 | ||||||||
\(280\) | −6.04207 | −0.361083 | ||||||||
\(281\) | 14.4898 | 0.864389 | 0.432194 | − | 0.901781i | \(-0.357739\pi\) | ||||
0.432194 | + | 0.901781i | \(0.357739\pi\) | |||||||
\(282\) | −10.9156 | −0.650012 | ||||||||
\(283\) | −2.63201 | −0.156457 | −0.0782284 | − | 0.996935i | \(-0.524926\pi\) | ||||
−0.0782284 | + | 0.996935i | \(0.524926\pi\) | |||||||
\(284\) | −4.31993 | −0.256341 | ||||||||
\(285\) | 13.1711 | 0.780187 | ||||||||
\(286\) | 11.9079 | 0.704129 | ||||||||
\(287\) | 9.31982 | 0.550132 | ||||||||
\(288\) | −7.05209 | −0.415549 | ||||||||
\(289\) | −16.9967 | −0.999804 | ||||||||
\(290\) | 40.4975 | 2.37810 | ||||||||
\(291\) | 57.4991 | 3.37066 | ||||||||
\(292\) | −12.8177 | −0.750099 | ||||||||
\(293\) | −24.2872 | −1.41888 | −0.709438 | − | 0.704768i | \(-0.751051\pi\) | ||||
−0.709438 | + | 0.704768i | \(0.751051\pi\) | |||||||
\(294\) | −15.4867 | −0.903205 | ||||||||
\(295\) | −28.1327 | −1.63795 | ||||||||
\(296\) | 10.1478 | 0.589830 | ||||||||
\(297\) | 39.0283 | 2.26465 | ||||||||
\(298\) | −23.5793 | −1.36591 | ||||||||
\(299\) | 3.68102 | 0.212879 | ||||||||
\(300\) | −38.8634 | −2.24378 | ||||||||
\(301\) | −0.228329 | −0.0131607 | ||||||||
\(302\) | 10.2850 | 0.591837 | ||||||||
\(303\) | 24.3447 | 1.39857 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 1.19239 | 0.0682760 | ||||||||
\(306\) | 0.406661 | 0.0232473 | ||||||||
\(307\) | 8.75471 | 0.499658 | 0.249829 | − | 0.968290i | \(-0.419626\pi\) | ||||
0.249829 | + | 0.968290i | \(0.419626\pi\) | |||||||
\(308\) | −4.41839 | −0.251761 | ||||||||
\(309\) | 41.7855 | 2.37709 | ||||||||
\(310\) | −16.5374 | −0.939262 | ||||||||
\(311\) | 15.4390 | 0.875466 | 0.437733 | − | 0.899105i | \(-0.355782\pi\) | ||||
0.437733 | + | 0.899105i | \(0.355782\pi\) | |||||||
\(312\) | 12.4277 | 0.703583 | ||||||||
\(313\) | −0.386613 | −0.0218526 | −0.0109263 | − | 0.999940i | \(-0.503478\pi\) | ||||
−0.0109263 | + | 0.999940i | \(0.503478\pi\) | |||||||
\(314\) | −12.3626 | −0.697662 | ||||||||
\(315\) | 42.6092 | 2.40076 | ||||||||
\(316\) | −12.9034 | −0.725872 | ||||||||
\(317\) | −13.7997 | −0.775068 | −0.387534 | − | 0.921855i | \(-0.626673\pi\) | ||||
−0.387534 | + | 0.921855i | \(0.626673\pi\) | |||||||
\(318\) | 27.6674 | 1.55151 | ||||||||
\(319\) | 29.6147 | 1.65811 | ||||||||
\(320\) | 4.15425 | 0.232230 | ||||||||
\(321\) | 45.0252 | 2.51306 | ||||||||
\(322\) | −1.36583 | −0.0761149 | ||||||||
\(323\) | 0.0576653 | 0.00320858 | ||||||||
\(324\) | 19.5758 | 1.08754 | ||||||||
\(325\) | 48.0481 | 2.66523 | ||||||||
\(326\) | 6.34732 | 0.351545 | ||||||||
\(327\) | 1.13446 | 0.0627356 | ||||||||
\(328\) | −6.40788 | −0.353816 | ||||||||
\(329\) | −5.00738 | −0.276066 | ||||||||
\(330\) | −40.0122 | −2.20260 | ||||||||
\(331\) | 19.8794 | 1.09267 | 0.546334 | − | 0.837567i | \(-0.316023\pi\) | ||||
0.546334 | + | 0.837567i | \(0.316023\pi\) | |||||||
\(332\) | −3.11104 | −0.170741 | ||||||||
\(333\) | −71.5633 | −3.92165 | ||||||||
\(334\) | 10.5337 | 0.576379 | ||||||||
\(335\) | −1.29320 | −0.0706552 | ||||||||
\(336\) | −4.61128 | −0.251566 | ||||||||
\(337\) | −12.9732 | −0.706693 | −0.353346 | − | 0.935493i | \(-0.614956\pi\) | ||||
−0.353346 | + | 0.935493i | \(0.614956\pi\) | |||||||
\(338\) | −2.36484 | −0.128631 | ||||||||
\(339\) | 22.1087 | 1.20078 | ||||||||
\(340\) | −0.239556 | −0.0129917 | ||||||||
\(341\) | −12.0933 | −0.654892 | ||||||||
\(342\) | 7.05209 | 0.381334 | ||||||||
\(343\) | −17.2854 | −0.933322 | ||||||||
\(344\) | 0.156989 | 0.00846427 | ||||||||
\(345\) | −12.3687 | −0.665911 | ||||||||
\(346\) | −8.42256 | −0.452799 | ||||||||
\(347\) | 27.7440 | 1.48937 | 0.744687 | − | 0.667414i | \(-0.232599\pi\) | ||||
0.744687 | + | 0.667414i | \(0.232599\pi\) | |||||||
\(348\) | 30.9075 | 1.65682 | ||||||||
\(349\) | 6.35553 | 0.340204 | 0.170102 | − | 0.985426i | \(-0.445590\pi\) | ||||
0.170102 | + | 0.985426i | \(0.445590\pi\) | |||||||
\(350\) | −17.8281 | −0.952953 | ||||||||
\(351\) | −50.3584 | −2.68793 | ||||||||
\(352\) | 3.03789 | 0.161920 | ||||||||
\(353\) | 7.68243 | 0.408894 | 0.204447 | − | 0.978878i | \(-0.434460\pi\) | ||||
0.204447 | + | 0.978878i | \(0.434460\pi\) | |||||||
\(354\) | −21.4708 | −1.14116 | ||||||||
\(355\) | −17.9461 | −0.952478 | ||||||||
\(356\) | −9.56741 | −0.507072 | ||||||||
\(357\) | 0.265911 | 0.0140735 | ||||||||
\(358\) | −7.95295 | −0.420326 | ||||||||
\(359\) | 9.93902 | 0.524561 | 0.262281 | − | 0.964992i | \(-0.415525\pi\) | ||||
0.262281 | + | 0.964992i | \(0.415525\pi\) | |||||||
\(360\) | −29.2962 | −1.54404 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −14.8269 | −0.779285 | ||||||||
\(363\) | 5.61575 | 0.294750 | ||||||||
\(364\) | 5.70108 | 0.298818 | ||||||||
\(365\) | −53.2479 | −2.78712 | ||||||||
\(366\) | 0.910026 | 0.0475678 | ||||||||
\(367\) | 4.61257 | 0.240774 | 0.120387 | − | 0.992727i | \(-0.461586\pi\) | ||||
0.120387 | + | 0.992727i | \(0.461586\pi\) | |||||||
\(368\) | 0.939084 | 0.0489532 | ||||||||
\(369\) | 45.1890 | 2.35245 | ||||||||
\(370\) | 42.1566 | 2.19161 | ||||||||
\(371\) | 12.6921 | 0.658941 | ||||||||
\(372\) | −12.6213 | −0.654383 | ||||||||
\(373\) | 16.1022 | 0.833743 | 0.416871 | − | 0.908965i | \(-0.363127\pi\) | ||||
0.416871 | + | 0.908965i | \(0.363127\pi\) | |||||||
\(374\) | −0.175180 | −0.00905837 | ||||||||
\(375\) | −95.5929 | −4.93640 | ||||||||
\(376\) | 3.44285 | 0.177551 | ||||||||
\(377\) | −38.2120 | −1.96802 | ||||||||
\(378\) | 18.6853 | 0.961070 | ||||||||
\(379\) | 29.8705 | 1.53434 | 0.767171 | − | 0.641442i | \(-0.221664\pi\) | ||||
0.767171 | + | 0.641442i | \(0.221664\pi\) | |||||||
\(380\) | −4.15425 | −0.213109 | ||||||||
\(381\) | 27.0469 | 1.38565 | ||||||||
\(382\) | 9.97021 | 0.510120 | ||||||||
\(383\) | −23.5745 | −1.20460 | −0.602301 | − | 0.798269i | \(-0.705749\pi\) | ||||
−0.602301 | + | 0.798269i | \(0.705749\pi\) | |||||||
\(384\) | 3.17050 | 0.161794 | ||||||||
\(385\) | −18.3551 | −0.935463 | ||||||||
\(386\) | −1.78617 | −0.0909138 | ||||||||
\(387\) | −1.10710 | −0.0562770 | ||||||||
\(388\) | −18.1356 | −0.920698 | ||||||||
\(389\) | −19.8553 | −1.00671 | −0.503353 | − | 0.864081i | \(-0.667900\pi\) | ||||
−0.503353 | + | 0.864081i | \(0.667900\pi\) | |||||||
\(390\) | 51.6280 | 2.61428 | ||||||||
\(391\) | −0.0541525 | −0.00273861 | ||||||||
\(392\) | 4.88463 | 0.246711 | ||||||||
\(393\) | −33.1996 | −1.67470 | ||||||||
\(394\) | 13.7517 | 0.692799 | ||||||||
\(395\) | −53.6039 | −2.69710 | ||||||||
\(396\) | −21.4235 | −1.07657 | ||||||||
\(397\) | −13.7957 | −0.692388 | −0.346194 | − | 0.938163i | \(-0.612526\pi\) | ||||
−0.346194 | + | 0.938163i | \(0.612526\pi\) | |||||||
\(398\) | 19.8784 | 0.996413 | ||||||||
\(399\) | 4.61128 | 0.230853 | ||||||||
\(400\) | 12.2578 | 0.612890 | ||||||||
\(401\) | 14.5213 | 0.725159 | 0.362579 | − | 0.931953i | \(-0.381896\pi\) | ||||
0.362579 | + | 0.931953i | \(0.381896\pi\) | |||||||
\(402\) | −0.986967 | −0.0492254 | ||||||||
\(403\) | 15.6041 | 0.777296 | ||||||||
\(404\) | −7.67850 | −0.382019 | ||||||||
\(405\) | 81.3226 | 4.04095 | ||||||||
\(406\) | 14.1785 | 0.703665 | ||||||||
\(407\) | 30.8279 | 1.52808 | ||||||||
\(408\) | −0.182828 | −0.00905133 | ||||||||
\(409\) | 11.8236 | 0.584637 | 0.292319 | − | 0.956321i | \(-0.405573\pi\) | ||||
0.292319 | + | 0.956321i | \(0.405573\pi\) | |||||||
\(410\) | −26.6200 | −1.31467 | ||||||||
\(411\) | −9.40759 | −0.464042 | ||||||||
\(412\) | −13.1794 | −0.649304 | ||||||||
\(413\) | −9.84946 | −0.484660 | ||||||||
\(414\) | −6.62251 | −0.325479 | ||||||||
\(415\) | −12.9240 | −0.634416 | ||||||||
\(416\) | −3.91980 | −0.192184 | ||||||||
\(417\) | 43.3441 | 2.12257 | ||||||||
\(418\) | −3.03789 | −0.148588 | ||||||||
\(419\) | −33.1411 | −1.61905 | −0.809525 | − | 0.587085i | \(-0.800276\pi\) | ||||
−0.809525 | + | 0.587085i | \(0.800276\pi\) | |||||||
\(420\) | −19.1564 | −0.934737 | ||||||||
\(421\) | 19.8284 | 0.966377 | 0.483188 | − | 0.875516i | \(-0.339479\pi\) | ||||
0.483188 | + | 0.875516i | \(0.339479\pi\) | |||||||
\(422\) | 1.00000 | 0.0486792 | ||||||||
\(423\) | −24.2793 | −1.18050 | ||||||||
\(424\) | −8.72651 | −0.423797 | ||||||||
\(425\) | −0.706849 | −0.0342872 | ||||||||
\(426\) | −13.6964 | −0.663590 | ||||||||
\(427\) | 0.417463 | 0.0202025 | ||||||||
\(428\) | −14.2013 | −0.686445 | ||||||||
\(429\) | 37.7541 | 1.82278 | ||||||||
\(430\) | 0.652171 | 0.0314505 | ||||||||
\(431\) | 8.59521 | 0.414017 | 0.207008 | − | 0.978339i | \(-0.433627\pi\) | ||||
0.207008 | + | 0.978339i | \(0.433627\pi\) | |||||||
\(432\) | −12.8472 | −0.618110 | ||||||||
\(433\) | 32.5387 | 1.56371 | 0.781854 | − | 0.623461i | \(-0.214274\pi\) | ||||
0.781854 | + | 0.623461i | \(0.214274\pi\) | |||||||
\(434\) | −5.78986 | −0.277922 | ||||||||
\(435\) | 128.398 | 6.15620 | ||||||||
\(436\) | −0.357816 | −0.0171363 | ||||||||
\(437\) | −0.939084 | −0.0449225 | ||||||||
\(438\) | −40.6386 | −1.94179 | ||||||||
\(439\) | −29.6704 | −1.41609 | −0.708045 | − | 0.706167i | \(-0.750423\pi\) | ||||
−0.708045 | + | 0.706167i | \(0.750423\pi\) | |||||||
\(440\) | 12.6201 | 0.601642 | ||||||||
\(441\) | −34.4469 | −1.64033 | ||||||||
\(442\) | 0.226036 | 0.0107515 | ||||||||
\(443\) | 24.8856 | 1.18235 | 0.591176 | − | 0.806543i | \(-0.298664\pi\) | ||||
0.591176 | + | 0.806543i | \(0.298664\pi\) | |||||||
\(444\) | 32.1737 | 1.52690 | ||||||||
\(445\) | −39.7454 | −1.88411 | ||||||||
\(446\) | −4.38025 | −0.207411 | ||||||||
\(447\) | −74.7583 | −3.53595 | ||||||||
\(448\) | 1.45443 | 0.0687154 | ||||||||
\(449\) | 9.84769 | 0.464741 | 0.232371 | − | 0.972627i | \(-0.425352\pi\) | ||||
0.232371 | + | 0.972627i | \(0.425352\pi\) | |||||||
\(450\) | −86.4431 | −4.07497 | ||||||||
\(451\) | −19.4664 | −0.916638 | ||||||||
\(452\) | −6.97326 | −0.327995 | ||||||||
\(453\) | 32.6087 | 1.53209 | ||||||||
\(454\) | −19.0575 | −0.894412 | ||||||||
\(455\) | 23.6837 | 1.11031 | ||||||||
\(456\) | −3.17050 | −0.148472 | ||||||||
\(457\) | 0.777880 | 0.0363877 | 0.0181939 | − | 0.999834i | \(-0.494208\pi\) | ||||
0.0181939 | + | 0.999834i | \(0.494208\pi\) | |||||||
\(458\) | 11.0057 | 0.514261 | ||||||||
\(459\) | 0.740836 | 0.0345793 | ||||||||
\(460\) | 3.90119 | 0.181894 | ||||||||
\(461\) | 19.4510 | 0.905922 | 0.452961 | − | 0.891530i | \(-0.350368\pi\) | ||||
0.452961 | + | 0.891530i | \(0.350368\pi\) | |||||||
\(462\) | −14.0085 | −0.651736 | ||||||||
\(463\) | −27.1820 | −1.26325 | −0.631626 | − | 0.775273i | \(-0.717612\pi\) | ||||
−0.631626 | + | 0.775273i | \(0.717612\pi\) | |||||||
\(464\) | −9.74846 | −0.452561 | ||||||||
\(465\) | −52.4320 | −2.43147 | ||||||||
\(466\) | −20.5312 | −0.951090 | ||||||||
\(467\) | −24.0989 | −1.11517 | −0.557583 | − | 0.830121i | \(-0.688271\pi\) | ||||
−0.557583 | + | 0.830121i | \(0.688271\pi\) | |||||||
\(468\) | 27.6428 | 1.27779 | ||||||||
\(469\) | −0.452759 | −0.0209065 | ||||||||
\(470\) | 14.3024 | 0.659723 | ||||||||
\(471\) | −39.1957 | −1.80604 | ||||||||
\(472\) | 6.77204 | 0.311708 | ||||||||
\(473\) | 0.476914 | 0.0219285 | ||||||||
\(474\) | −40.9102 | −1.87907 | ||||||||
\(475\) | −12.2578 | −0.562426 | ||||||||
\(476\) | −0.0838701 | −0.00384418 | ||||||||
\(477\) | 61.5402 | 2.81773 | ||||||||
\(478\) | −7.63091 | −0.349030 | ||||||||
\(479\) | −21.9273 | −1.00188 | −0.500942 | − | 0.865481i | \(-0.667013\pi\) | ||||
−0.500942 | + | 0.865481i | \(0.667013\pi\) | |||||||
\(480\) | 13.1711 | 0.601174 | ||||||||
\(481\) | −39.7774 | −1.81369 | ||||||||
\(482\) | −7.91820 | −0.360664 | ||||||||
\(483\) | −4.33038 | −0.197039 | ||||||||
\(484\) | −1.77125 | −0.0805113 | ||||||||
\(485\) | −75.3400 | −3.42101 | ||||||||
\(486\) | 23.5235 | 1.06705 | ||||||||
\(487\) | −21.2962 | −0.965021 | −0.482511 | − | 0.875890i | \(-0.660275\pi\) | ||||
−0.482511 | + | 0.875890i | \(0.660275\pi\) | |||||||
\(488\) | −0.287029 | −0.0129932 | ||||||||
\(489\) | 20.1242 | 0.910048 | ||||||||
\(490\) | 20.2920 | 0.916698 | ||||||||
\(491\) | 25.6131 | 1.15590 | 0.577952 | − | 0.816071i | \(-0.303852\pi\) | ||||
0.577952 | + | 0.816071i | \(0.303852\pi\) | |||||||
\(492\) | −20.3162 | −0.915926 | ||||||||
\(493\) | 0.562148 | 0.0253179 | ||||||||
\(494\) | 3.91980 | 0.176360 | ||||||||
\(495\) | −88.9984 | −4.00018 | ||||||||
\(496\) | 3.98084 | 0.178745 | ||||||||
\(497\) | −6.28304 | −0.281833 | ||||||||
\(498\) | −9.86357 | −0.441997 | ||||||||
\(499\) | 18.2866 | 0.818619 | 0.409309 | − | 0.912396i | \(-0.365770\pi\) | ||||
0.409309 | + | 0.912396i | \(0.365770\pi\) | |||||||
\(500\) | 30.1507 | 1.34838 | ||||||||
\(501\) | 33.3971 | 1.49207 | ||||||||
\(502\) | −16.9552 | −0.756749 | ||||||||
\(503\) | −6.95013 | −0.309891 | −0.154945 | − | 0.987923i | \(-0.549520\pi\) | ||||
−0.154945 | + | 0.987923i | \(0.549520\pi\) | |||||||
\(504\) | −10.2568 | −0.456873 | ||||||||
\(505\) | −31.8984 | −1.41946 | ||||||||
\(506\) | 2.85283 | 0.126824 | ||||||||
\(507\) | −7.49775 | −0.332987 | ||||||||
\(508\) | −8.53078 | −0.378492 | ||||||||
\(509\) | −20.8092 | −0.922353 | −0.461176 | − | 0.887308i | \(-0.652572\pi\) | ||||
−0.461176 | + | 0.887308i | \(0.652572\pi\) | |||||||
\(510\) | −0.759513 | −0.0336318 | ||||||||
\(511\) | −18.6425 | −0.824694 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 12.8472 | 0.567217 | ||||||||
\(514\) | 6.24300 | 0.275367 | ||||||||
\(515\) | −54.7507 | −2.41260 | ||||||||
\(516\) | 0.497733 | 0.0219115 | ||||||||
\(517\) | 10.4590 | 0.459985 | ||||||||
\(518\) | 14.7593 | 0.648486 | ||||||||
\(519\) | −26.7037 | −1.17216 | ||||||||
\(520\) | −16.2838 | −0.714093 | ||||||||
\(521\) | 3.50225 | 0.153437 | 0.0767183 | − | 0.997053i | \(-0.475556\pi\) | ||||
0.0767183 | + | 0.997053i | \(0.475556\pi\) | |||||||
\(522\) | 68.7471 | 3.00898 | ||||||||
\(523\) | −21.4134 | −0.936342 | −0.468171 | − | 0.883638i | \(-0.655087\pi\) | ||||
−0.468171 | + | 0.883638i | \(0.655087\pi\) | |||||||
\(524\) | 10.4714 | 0.457445 | ||||||||
\(525\) | −56.5241 | −2.46691 | ||||||||
\(526\) | 12.6080 | 0.549734 | ||||||||
\(527\) | −0.229556 | −0.00999963 | ||||||||
\(528\) | 9.63163 | 0.419163 | ||||||||
\(529\) | −22.1181 | −0.961657 | ||||||||
\(530\) | −36.2521 | −1.57469 | ||||||||
\(531\) | −47.7570 | −2.07248 | ||||||||
\(532\) | −1.45443 | −0.0630576 | ||||||||
\(533\) | 25.1176 | 1.08797 | ||||||||
\(534\) | −30.3335 | −1.31266 | ||||||||
\(535\) | −58.9957 | −2.55061 | ||||||||
\(536\) | 0.311296 | 0.0134460 | ||||||||
\(537\) | −25.2148 | −1.08810 | ||||||||
\(538\) | −29.0252 | −1.25137 | ||||||||
\(539\) | 14.8390 | 0.639159 | ||||||||
\(540\) | −53.3704 | −2.29670 | ||||||||
\(541\) | −9.83922 | −0.423021 | −0.211511 | − | 0.977376i | \(-0.567838\pi\) | ||||
−0.211511 | + | 0.977376i | \(0.567838\pi\) | |||||||
\(542\) | 7.49327 | 0.321864 | ||||||||
\(543\) | −47.0088 | −2.01734 | ||||||||
\(544\) | 0.0576653 | 0.00247238 | ||||||||
\(545\) | −1.48646 | −0.0636728 | ||||||||
\(546\) | 18.0753 | 0.773551 | ||||||||
\(547\) | 37.8317 | 1.61757 | 0.808784 | − | 0.588106i | \(-0.200126\pi\) | ||||
0.808784 | + | 0.588106i | \(0.200126\pi\) | |||||||
\(548\) | 2.96722 | 0.126753 | ||||||||
\(549\) | 2.02415 | 0.0863888 | ||||||||
\(550\) | 37.2378 | 1.58782 | ||||||||
\(551\) | 9.74846 | 0.415298 | ||||||||
\(552\) | 2.97737 | 0.126725 | ||||||||
\(553\) | −18.7671 | −0.798057 | ||||||||
\(554\) | 6.01689 | 0.255633 | ||||||||
\(555\) | 133.658 | 5.67345 | ||||||||
\(556\) | −13.6710 | −0.579781 | ||||||||
\(557\) | 34.4159 | 1.45825 | 0.729123 | − | 0.684382i | \(-0.239928\pi\) | ||||
0.729123 | + | 0.684382i | \(0.239928\pi\) | |||||||
\(558\) | −28.0733 | −1.18844 | ||||||||
\(559\) | −0.615365 | −0.0260272 | ||||||||
\(560\) | 6.04207 | 0.255324 | ||||||||
\(561\) | −0.555410 | −0.0234494 | ||||||||
\(562\) | −14.4898 | −0.611215 | ||||||||
\(563\) | −22.0278 | −0.928360 | −0.464180 | − | 0.885741i | \(-0.653651\pi\) | ||||
−0.464180 | + | 0.885741i | \(0.653651\pi\) | |||||||
\(564\) | 10.9156 | 0.459628 | ||||||||
\(565\) | −28.9687 | −1.21872 | ||||||||
\(566\) | 2.63201 | 0.110632 | ||||||||
\(567\) | 28.4716 | 1.19569 | ||||||||
\(568\) | 4.31993 | 0.181260 | ||||||||
\(569\) | 4.21399 | 0.176660 | 0.0883299 | − | 0.996091i | \(-0.471847\pi\) | ||||
0.0883299 | + | 0.996091i | \(0.471847\pi\) | |||||||
\(570\) | −13.1711 | −0.551675 | ||||||||
\(571\) | 17.3831 | 0.727460 | 0.363730 | − | 0.931505i | \(-0.381503\pi\) | ||||
0.363730 | + | 0.931505i | \(0.381503\pi\) | |||||||
\(572\) | −11.9079 | −0.497895 | ||||||||
\(573\) | 31.6106 | 1.32055 | ||||||||
\(574\) | −9.31982 | −0.389002 | ||||||||
\(575\) | 11.5111 | 0.480046 | ||||||||
\(576\) | 7.05209 | 0.293837 | ||||||||
\(577\) | −4.62484 | −0.192534 | −0.0962672 | − | 0.995356i | \(-0.530690\pi\) | ||||
−0.0962672 | + | 0.995356i | \(0.530690\pi\) | |||||||
\(578\) | 16.9967 | 0.706968 | ||||||||
\(579\) | −5.66307 | −0.235349 | ||||||||
\(580\) | −40.4975 | −1.68157 | ||||||||
\(581\) | −4.52479 | −0.187720 | ||||||||
\(582\) | −57.4991 | −2.38342 | ||||||||
\(583\) | −26.5102 | −1.09794 | ||||||||
\(584\) | 12.8177 | 0.530400 | ||||||||
\(585\) | 114.835 | 4.74785 | ||||||||
\(586\) | 24.2872 | 1.00330 | ||||||||
\(587\) | −42.3463 | −1.74782 | −0.873909 | − | 0.486090i | \(-0.838423\pi\) | ||||
−0.873909 | + | 0.486090i | \(0.838423\pi\) | |||||||
\(588\) | 15.4867 | 0.638663 | ||||||||
\(589\) | −3.98084 | −0.164028 | ||||||||
\(590\) | 28.1327 | 1.15821 | ||||||||
\(591\) | 43.5997 | 1.79345 | ||||||||
\(592\) | −10.1478 | −0.417073 | ||||||||
\(593\) | 2.60427 | 0.106944 | 0.0534722 | − | 0.998569i | \(-0.482971\pi\) | ||||
0.0534722 | + | 0.998569i | \(0.482971\pi\) | |||||||
\(594\) | −39.0283 | −1.60135 | ||||||||
\(595\) | −0.348417 | −0.0142837 | ||||||||
\(596\) | 23.5793 | 0.965847 | ||||||||
\(597\) | 63.0245 | 2.57942 | ||||||||
\(598\) | −3.68102 | −0.150528 | ||||||||
\(599\) | −30.3389 | −1.23961 | −0.619806 | − | 0.784755i | \(-0.712789\pi\) | ||||
−0.619806 | + | 0.784755i | \(0.712789\pi\) | |||||||
\(600\) | 38.8634 | 1.58659 | ||||||||
\(601\) | 1.18657 | 0.0484014 | 0.0242007 | − | 0.999707i | \(-0.492296\pi\) | ||||
0.0242007 | + | 0.999707i | \(0.492296\pi\) | |||||||
\(602\) | 0.228329 | 0.00930600 | ||||||||
\(603\) | −2.19529 | −0.0893992 | ||||||||
\(604\) | −10.2850 | −0.418492 | ||||||||
\(605\) | −7.35821 | −0.299154 | ||||||||
\(606\) | −24.3447 | −0.988936 | ||||||||
\(607\) | 14.9293 | 0.605961 | 0.302980 | − | 0.952997i | \(-0.402018\pi\) | ||||
0.302980 | + | 0.952997i | \(0.402018\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 44.9529 | 1.82158 | ||||||||
\(610\) | −1.19239 | −0.0482784 | ||||||||
\(611\) | −13.4953 | −0.545960 | ||||||||
\(612\) | −0.406661 | −0.0164383 | ||||||||
\(613\) | −2.75792 | −0.111391 | −0.0556957 | − | 0.998448i | \(-0.517738\pi\) | ||||
−0.0556957 | + | 0.998448i | \(0.517738\pi\) | |||||||
\(614\) | −8.75471 | −0.353311 | ||||||||
\(615\) | −84.3987 | −3.40328 | ||||||||
\(616\) | 4.41839 | 0.178022 | ||||||||
\(617\) | −44.1691 | −1.77818 | −0.889090 | − | 0.457733i | \(-0.848662\pi\) | ||||
−0.889090 | + | 0.457733i | \(0.848662\pi\) | |||||||
\(618\) | −41.7855 | −1.68086 | ||||||||
\(619\) | 44.7128 | 1.79716 | 0.898580 | − | 0.438810i | \(-0.144600\pi\) | ||||
0.898580 | + | 0.438810i | \(0.144600\pi\) | |||||||
\(620\) | 16.5374 | 0.664159 | ||||||||
\(621\) | −12.0646 | −0.484135 | ||||||||
\(622\) | −15.4390 | −0.619048 | ||||||||
\(623\) | −13.9151 | −0.557498 | ||||||||
\(624\) | −12.4277 | −0.497508 | ||||||||
\(625\) | 63.9646 | 2.55858 | ||||||||
\(626\) | 0.386613 | 0.0154521 | ||||||||
\(627\) | −9.63163 | −0.384650 | ||||||||
\(628\) | 12.3626 | 0.493321 | ||||||||
\(629\) | 0.585176 | 0.0233325 | ||||||||
\(630\) | −42.6092 | −1.69759 | ||||||||
\(631\) | −37.2117 | −1.48137 | −0.740687 | − | 0.671851i | \(-0.765500\pi\) | ||||
−0.740687 | + | 0.671851i | \(0.765500\pi\) | |||||||
\(632\) | 12.9034 | 0.513269 | ||||||||
\(633\) | 3.17050 | 0.126016 | ||||||||
\(634\) | 13.7997 | 0.548056 | ||||||||
\(635\) | −35.4390 | −1.40635 | ||||||||
\(636\) | −27.6674 | −1.09709 | ||||||||
\(637\) | −19.1468 | −0.758623 | ||||||||
\(638\) | −29.6147 | −1.17246 | ||||||||
\(639\) | −30.4645 | −1.20516 | ||||||||
\(640\) | −4.15425 | −0.164211 | ||||||||
\(641\) | −28.2909 | −1.11742 | −0.558711 | − | 0.829362i | \(-0.688704\pi\) | ||||
−0.558711 | + | 0.829362i | \(0.688704\pi\) | |||||||
\(642\) | −45.0252 | −1.77700 | ||||||||
\(643\) | 19.9394 | 0.786334 | 0.393167 | − | 0.919467i | \(-0.371380\pi\) | ||||
0.393167 | + | 0.919467i | \(0.371380\pi\) | |||||||
\(644\) | 1.36583 | 0.0538214 | ||||||||
\(645\) | 2.06771 | 0.0814160 | ||||||||
\(646\) | −0.0576653 | −0.00226881 | ||||||||
\(647\) | 10.1935 | 0.400747 | 0.200374 | − | 0.979720i | \(-0.435784\pi\) | ||||
0.200374 | + | 0.979720i | \(0.435784\pi\) | |||||||
\(648\) | −19.5758 | −0.769008 | ||||||||
\(649\) | 20.5727 | 0.807548 | ||||||||
\(650\) | −48.0481 | −1.88460 | ||||||||
\(651\) | −18.3568 | −0.719459 | ||||||||
\(652\) | −6.34732 | −0.248580 | ||||||||
\(653\) | 30.1532 | 1.17998 | 0.589992 | − | 0.807409i | \(-0.299131\pi\) | ||||
0.589992 | + | 0.807409i | \(0.299131\pi\) | |||||||
\(654\) | −1.13446 | −0.0443608 | ||||||||
\(655\) | 43.5008 | 1.69972 | ||||||||
\(656\) | 6.40788 | 0.250186 | ||||||||
\(657\) | −90.3916 | −3.52651 | ||||||||
\(658\) | 5.00738 | 0.195208 | ||||||||
\(659\) | 48.1829 | 1.87694 | 0.938470 | − | 0.345361i | \(-0.112244\pi\) | ||||
0.938470 | + | 0.345361i | \(0.112244\pi\) | |||||||
\(660\) | 40.0122 | 1.55747 | ||||||||
\(661\) | −27.8493 | −1.08321 | −0.541606 | − | 0.840633i | \(-0.682183\pi\) | ||||
−0.541606 | + | 0.840633i | \(0.682183\pi\) | |||||||
\(662\) | −19.8794 | −0.772634 | ||||||||
\(663\) | 0.716649 | 0.0278323 | ||||||||
\(664\) | 3.11104 | 0.120732 | ||||||||
\(665\) | −6.04207 | −0.234301 | ||||||||
\(666\) | 71.5633 | 2.77302 | ||||||||
\(667\) | −9.15463 | −0.354469 | ||||||||
\(668\) | −10.5337 | −0.407561 | ||||||||
\(669\) | −13.8876 | −0.536926 | ||||||||
\(670\) | 1.29320 | 0.0499608 | ||||||||
\(671\) | −0.871961 | −0.0336617 | ||||||||
\(672\) | 4.61128 | 0.177884 | ||||||||
\(673\) | −9.17870 | −0.353813 | −0.176906 | − | 0.984228i | \(-0.556609\pi\) | ||||
−0.176906 | + | 0.984228i | \(0.556609\pi\) | |||||||
\(674\) | 12.9732 | 0.499707 | ||||||||
\(675\) | −157.478 | −6.06134 | ||||||||
\(676\) | 2.36484 | 0.0909555 | ||||||||
\(677\) | −24.6506 | −0.947398 | −0.473699 | − | 0.880687i | \(-0.657082\pi\) | ||||
−0.473699 | + | 0.880687i | \(0.657082\pi\) | |||||||
\(678\) | −22.1087 | −0.849081 | ||||||||
\(679\) | −26.3770 | −1.01226 | ||||||||
\(680\) | 0.239556 | 0.00918655 | ||||||||
\(681\) | −60.4218 | −2.31537 | ||||||||
\(682\) | 12.0933 | 0.463078 | ||||||||
\(683\) | 25.3240 | 0.968996 | 0.484498 | − | 0.874792i | \(-0.339002\pi\) | ||||
0.484498 | + | 0.874792i | \(0.339002\pi\) | |||||||
\(684\) | −7.05209 | −0.269644 | ||||||||
\(685\) | 12.3266 | 0.470975 | ||||||||
\(686\) | 17.2854 | 0.659959 | ||||||||
\(687\) | 34.8935 | 1.33127 | ||||||||
\(688\) | −0.156989 | −0.00598514 | ||||||||
\(689\) | 34.2062 | 1.30315 | ||||||||
\(690\) | 12.3687 | 0.470870 | ||||||||
\(691\) | −17.2389 | −0.655799 | −0.327900 | − | 0.944713i | \(-0.606341\pi\) | ||||
−0.327900 | + | 0.944713i | \(0.606341\pi\) | |||||||
\(692\) | 8.42256 | 0.320178 | ||||||||
\(693\) | −31.1589 | −1.18363 | ||||||||
\(694\) | −27.7440 | −1.05315 | ||||||||
\(695\) | −56.7929 | −2.15428 | ||||||||
\(696\) | −30.9075 | −1.17155 | ||||||||
\(697\) | −0.369512 | −0.0139963 | ||||||||
\(698\) | −6.35553 | −0.240560 | ||||||||
\(699\) | −65.0943 | −2.46209 | ||||||||
\(700\) | 17.8281 | 0.673839 | ||||||||
\(701\) | −4.73529 | −0.178850 | −0.0894248 | − | 0.995994i | \(-0.528503\pi\) | ||||
−0.0894248 | + | 0.995994i | \(0.528503\pi\) | |||||||
\(702\) | 50.3584 | 1.90066 | ||||||||
\(703\) | 10.1478 | 0.382732 | ||||||||
\(704\) | −3.03789 | −0.114495 | ||||||||
\(705\) | 45.3460 | 1.70783 | ||||||||
\(706\) | −7.68243 | −0.289132 | ||||||||
\(707\) | −11.1678 | −0.420010 | ||||||||
\(708\) | 21.4708 | 0.806921 | ||||||||
\(709\) | 20.3422 | 0.763969 | 0.381984 | − | 0.924169i | \(-0.375241\pi\) | ||||
0.381984 | + | 0.924169i | \(0.375241\pi\) | |||||||
\(710\) | 17.9461 | 0.673504 | ||||||||
\(711\) | −90.9959 | −3.41261 | ||||||||
\(712\) | 9.56741 | 0.358554 | ||||||||
\(713\) | 3.73835 | 0.140002 | ||||||||
\(714\) | −0.265911 | −0.00995145 | ||||||||
\(715\) | −49.4684 | −1.85001 | ||||||||
\(716\) | 7.95295 | 0.297216 | ||||||||
\(717\) | −24.1938 | −0.903535 | ||||||||
\(718\) | −9.93902 | −0.370921 | ||||||||
\(719\) | 34.9210 | 1.30233 | 0.651167 | − | 0.758935i | \(-0.274280\pi\) | ||||
0.651167 | + | 0.758935i | \(0.274280\pi\) | |||||||
\(720\) | 29.2962 | 1.09180 | ||||||||
\(721\) | −19.1686 | −0.713875 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −25.1047 | −0.933653 | ||||||||
\(724\) | 14.8269 | 0.551038 | ||||||||
\(725\) | −119.495 | −4.43792 | ||||||||
\(726\) | −5.61575 | −0.208420 | ||||||||
\(727\) | 37.0004 | 1.37227 | 0.686134 | − | 0.727475i | \(-0.259306\pi\) | ||||
0.686134 | + | 0.727475i | \(0.259306\pi\) | |||||||
\(728\) | −5.70108 | −0.211296 | ||||||||
\(729\) | 15.8539 | 0.587183 | ||||||||
\(730\) | 53.2479 | 1.97079 | ||||||||
\(731\) | 0.00905280 | 0.000334830 0 | ||||||||
\(732\) | −0.910026 | −0.0336355 | ||||||||
\(733\) | 5.92531 | 0.218856 | 0.109428 | − | 0.993995i | \(-0.465098\pi\) | ||||
0.109428 | + | 0.993995i | \(0.465098\pi\) | |||||||
\(734\) | −4.61257 | −0.170253 | ||||||||
\(735\) | 64.3358 | 2.37306 | ||||||||
\(736\) | −0.939084 | −0.0346151 | ||||||||
\(737\) | 0.945683 | 0.0348347 | ||||||||
\(738\) | −45.1890 | −1.66343 | ||||||||
\(739\) | −5.80209 | −0.213433 | −0.106717 | − | 0.994289i | \(-0.534034\pi\) | ||||
−0.106717 | + | 0.994289i | \(0.534034\pi\) | |||||||
\(740\) | −42.1566 | −1.54971 | ||||||||
\(741\) | 12.4277 | 0.456545 | ||||||||
\(742\) | −12.6921 | −0.465942 | ||||||||
\(743\) | −30.1097 | −1.10462 | −0.552309 | − | 0.833640i | \(-0.686253\pi\) | ||||
−0.552309 | + | 0.833640i | \(0.686253\pi\) | |||||||
\(744\) | 12.6213 | 0.462719 | ||||||||
\(745\) | 97.9544 | 3.58877 | ||||||||
\(746\) | −16.1022 | −0.589545 | ||||||||
\(747\) | −21.9394 | −0.802719 | ||||||||
\(748\) | 0.175180 | 0.00640523 | ||||||||
\(749\) | −20.6548 | −0.754709 | ||||||||
\(750\) | 95.5929 | 3.49056 | ||||||||
\(751\) | 35.8092 | 1.30670 | 0.653348 | − | 0.757058i | \(-0.273364\pi\) | ||||
0.653348 | + | 0.757058i | \(0.273364\pi\) | |||||||
\(752\) | −3.44285 | −0.125548 | ||||||||
\(753\) | −53.7566 | −1.95900 | ||||||||
\(754\) | 38.2120 | 1.39160 | ||||||||
\(755\) | −42.7266 | −1.55498 | ||||||||
\(756\) | −18.6853 | −0.679579 | ||||||||
\(757\) | −51.7008 | −1.87910 | −0.939549 | − | 0.342413i | \(-0.888756\pi\) | ||||
−0.939549 | + | 0.342413i | \(0.888756\pi\) | |||||||
\(758\) | −29.8705 | −1.08494 | ||||||||
\(759\) | 9.04491 | 0.328310 | ||||||||
\(760\) | 4.15425 | 0.150691 | ||||||||
\(761\) | 6.50864 | 0.235938 | 0.117969 | − | 0.993017i | \(-0.462362\pi\) | ||||
0.117969 | + | 0.993017i | \(0.462362\pi\) | |||||||
\(762\) | −27.0469 | −0.979805 | ||||||||
\(763\) | −0.520419 | −0.0188404 | ||||||||
\(764\) | −9.97021 | −0.360710 | ||||||||
\(765\) | −1.68937 | −0.0610793 | ||||||||
\(766\) | 23.5745 | 0.851782 | ||||||||
\(767\) | −26.5450 | −0.958486 | ||||||||
\(768\) | −3.17050 | −0.114406 | ||||||||
\(769\) | 43.9051 | 1.58326 | 0.791630 | − | 0.611001i | \(-0.209233\pi\) | ||||
0.791630 | + | 0.611001i | \(0.209233\pi\) | |||||||
\(770\) | 18.3551 | 0.661472 | ||||||||
\(771\) | 19.7935 | 0.712844 | ||||||||
\(772\) | 1.78617 | 0.0642858 | ||||||||
\(773\) | 2.09840 | 0.0754742 | 0.0377371 | − | 0.999288i | \(-0.487985\pi\) | ||||
0.0377371 | + | 0.999288i | \(0.487985\pi\) | |||||||
\(774\) | 1.10710 | 0.0397939 | ||||||||
\(775\) | 48.7964 | 1.75282 | ||||||||
\(776\) | 18.1356 | 0.651032 | ||||||||
\(777\) | 46.7944 | 1.67874 | ||||||||
\(778\) | 19.8553 | 0.711848 | ||||||||
\(779\) | −6.40788 | −0.229586 | ||||||||
\(780\) | −51.6280 | −1.84858 | ||||||||
\(781\) | 13.1235 | 0.469594 | ||||||||
\(782\) | 0.0541525 | 0.00193649 | ||||||||
\(783\) | 125.240 | 4.47572 | ||||||||
\(784\) | −4.88463 | −0.174451 | ||||||||
\(785\) | 51.3573 | 1.83302 | ||||||||
\(786\) | 33.1996 | 1.18419 | ||||||||
\(787\) | −33.1316 | −1.18101 | −0.590507 | − | 0.807033i | \(-0.701072\pi\) | ||||
−0.590507 | + | 0.807033i | \(0.701072\pi\) | |||||||
\(788\) | −13.7517 | −0.489883 | ||||||||
\(789\) | 39.9737 | 1.42310 | ||||||||
\(790\) | 53.6039 | 1.90714 | ||||||||
\(791\) | −10.1421 | −0.360612 | ||||||||
\(792\) | 21.4235 | 0.761249 | ||||||||
\(793\) | 1.12510 | 0.0399533 | ||||||||
\(794\) | 13.7957 | 0.489592 | ||||||||
\(795\) | −114.937 | −4.07641 | ||||||||
\(796\) | −19.8784 | −0.704571 | ||||||||
\(797\) | −33.8646 | −1.19955 | −0.599773 | − | 0.800170i | \(-0.704742\pi\) | ||||
−0.599773 | + | 0.800170i | \(0.704742\pi\) | |||||||
\(798\) | −4.61128 | −0.163237 | ||||||||
\(799\) | 0.198533 | 0.00702358 | ||||||||
\(800\) | −12.2578 | −0.433379 | ||||||||
\(801\) | −67.4703 | −2.38394 | ||||||||
\(802\) | −14.5213 | −0.512765 | ||||||||
\(803\) | 38.9387 | 1.37412 | ||||||||
\(804\) | 0.986967 | 0.0348076 | ||||||||
\(805\) | 5.67401 | 0.199983 | ||||||||
\(806\) | −15.6041 | −0.549632 | ||||||||
\(807\) | −92.0246 | −3.23942 | ||||||||
\(808\) | 7.67850 | 0.270129 | ||||||||
\(809\) | −20.2397 | −0.711589 | −0.355794 | − | 0.934564i | \(-0.615790\pi\) | ||||
−0.355794 | + | 0.934564i | \(0.615790\pi\) | |||||||
\(810\) | −81.3226 | −2.85738 | ||||||||
\(811\) | 10.4968 | 0.368593 | 0.184297 | − | 0.982871i | \(-0.440999\pi\) | ||||
0.184297 | + | 0.982871i | \(0.440999\pi\) | |||||||
\(812\) | −14.1785 | −0.497566 | ||||||||
\(813\) | 23.7575 | 0.833210 | ||||||||
\(814\) | −30.8279 | −1.08052 | ||||||||
\(815\) | −26.3684 | −0.923643 | ||||||||
\(816\) | 0.182828 | 0.00640026 | ||||||||
\(817\) | 0.156989 | 0.00549234 | ||||||||
\(818\) | −11.8236 | −0.413401 | ||||||||
\(819\) | 40.2045 | 1.40486 | ||||||||
\(820\) | 26.6200 | 0.929609 | ||||||||
\(821\) | 52.5147 | 1.83277 | 0.916387 | − | 0.400293i | \(-0.131092\pi\) | ||||
0.916387 | + | 0.400293i | \(0.131092\pi\) | |||||||
\(822\) | 9.40759 | 0.328127 | ||||||||
\(823\) | −33.5956 | −1.17107 | −0.585534 | − | 0.810648i | \(-0.699115\pi\) | ||||
−0.585534 | + | 0.810648i | \(0.699115\pi\) | |||||||
\(824\) | 13.1794 | 0.459127 | ||||||||
\(825\) | 118.063 | 4.11041 | ||||||||
\(826\) | 9.84946 | 0.342706 | ||||||||
\(827\) | 3.54004 | 0.123099 | 0.0615497 | − | 0.998104i | \(-0.480396\pi\) | ||||
0.0615497 | + | 0.998104i | \(0.480396\pi\) | |||||||
\(828\) | 6.62251 | 0.230148 | ||||||||
\(829\) | 33.7704 | 1.17289 | 0.586447 | − | 0.809988i | \(-0.300526\pi\) | ||||
0.586447 | + | 0.809988i | \(0.300526\pi\) | |||||||
\(830\) | 12.9240 | 0.448600 | ||||||||
\(831\) | 19.0766 | 0.661759 | ||||||||
\(832\) | 3.91980 | 0.135895 | ||||||||
\(833\) | 0.281674 | 0.00975941 | ||||||||
\(834\) | −43.3441 | −1.50088 | ||||||||
\(835\) | −43.7596 | −1.51436 | ||||||||
\(836\) | 3.03789 | 0.105067 | ||||||||
\(837\) | −51.1426 | −1.76775 | ||||||||
\(838\) | 33.1411 | 1.14484 | ||||||||
\(839\) | 45.3293 | 1.56494 | 0.782471 | − | 0.622687i | \(-0.213959\pi\) | ||||
0.782471 | + | 0.622687i | \(0.213959\pi\) | |||||||
\(840\) | 19.1564 | 0.660959 | ||||||||
\(841\) | 66.0325 | 2.27698 | ||||||||
\(842\) | −19.8284 | −0.683332 | ||||||||
\(843\) | −45.9399 | −1.58226 | ||||||||
\(844\) | −1.00000 | −0.0344214 | ||||||||
\(845\) | 9.82415 | 0.337961 | ||||||||
\(846\) | 24.2793 | 0.834739 | ||||||||
\(847\) | −2.57616 | −0.0885178 | ||||||||
\(848\) | 8.72651 | 0.299670 | ||||||||
\(849\) | 8.34480 | 0.286393 | ||||||||
\(850\) | 0.706849 | 0.0242447 | ||||||||
\(851\) | −9.52965 | −0.326672 | ||||||||
\(852\) | 13.6964 | 0.469229 | ||||||||
\(853\) | −6.92761 | −0.237197 | −0.118598 | − | 0.992942i | \(-0.537840\pi\) | ||||
−0.118598 | + | 0.992942i | \(0.537840\pi\) | |||||||
\(854\) | −0.417463 | −0.0142853 | ||||||||
\(855\) | −29.2962 | −1.00191 | ||||||||
\(856\) | 14.2013 | 0.485390 | ||||||||
\(857\) | −41.2487 | −1.40903 | −0.704515 | − | 0.709689i | \(-0.748836\pi\) | ||||
−0.704515 | + | 0.709689i | \(0.748836\pi\) | |||||||
\(858\) | −37.7541 | −1.28890 | ||||||||
\(859\) | 45.2548 | 1.54407 | 0.772037 | − | 0.635578i | \(-0.219238\pi\) | ||||
0.772037 | + | 0.635578i | \(0.219238\pi\) | |||||||
\(860\) | −0.652171 | −0.0222388 | ||||||||
\(861\) | −29.5485 | −1.00701 | ||||||||
\(862\) | −8.59521 | −0.292754 | ||||||||
\(863\) | 49.3379 | 1.67948 | 0.839741 | − | 0.542987i | \(-0.182707\pi\) | ||||
0.839741 | + | 0.542987i | \(0.182707\pi\) | |||||||
\(864\) | 12.8472 | 0.437070 | ||||||||
\(865\) | 34.9894 | 1.18968 | ||||||||
\(866\) | −32.5387 | −1.10571 | ||||||||
\(867\) | 53.8880 | 1.83013 | ||||||||
\(868\) | 5.78986 | 0.196521 | ||||||||
\(869\) | 39.1990 | 1.32974 | ||||||||
\(870\) | −128.398 | −4.35309 | ||||||||
\(871\) | −1.22022 | −0.0413456 | ||||||||
\(872\) | 0.357816 | 0.0121172 | ||||||||
\(873\) | −127.894 | −4.32857 | ||||||||
\(874\) | 0.939084 | 0.0317650 | ||||||||
\(875\) | 43.8521 | 1.48247 | ||||||||
\(876\) | 40.6386 | 1.37305 | ||||||||
\(877\) | −32.3710 | −1.09309 | −0.546545 | − | 0.837430i | \(-0.684057\pi\) | ||||
−0.546545 | + | 0.837430i | \(0.684057\pi\) | |||||||
\(878\) | 29.6704 | 1.00133 | ||||||||
\(879\) | 77.0028 | 2.59724 | ||||||||
\(880\) | −12.6201 | −0.425425 | ||||||||
\(881\) | −39.5537 | −1.33260 | −0.666299 | − | 0.745685i | \(-0.732123\pi\) | ||||
−0.666299 | + | 0.745685i | \(0.732123\pi\) | |||||||
\(882\) | 34.4469 | 1.15989 | ||||||||
\(883\) | 39.4514 | 1.32765 | 0.663823 | − | 0.747890i | \(-0.268933\pi\) | ||||
0.663823 | + | 0.747890i | \(0.268933\pi\) | |||||||
\(884\) | −0.226036 | −0.00760243 | ||||||||
\(885\) | 89.1949 | 2.99826 | ||||||||
\(886\) | −24.8856 | −0.836049 | ||||||||
\(887\) | 8.24868 | 0.276964 | 0.138482 | − | 0.990365i | \(-0.455778\pi\) | ||||
0.138482 | + | 0.990365i | \(0.455778\pi\) | |||||||
\(888\) | −32.1737 | −1.07968 | ||||||||
\(889\) | −12.4074 | −0.416132 | ||||||||
\(890\) | 39.7454 | 1.33227 | ||||||||
\(891\) | −59.4689 | −1.99228 | ||||||||
\(892\) | 4.38025 | 0.146662 | ||||||||
\(893\) | 3.44285 | 0.115210 | ||||||||
\(894\) | 74.7583 | 2.50029 | ||||||||
\(895\) | 33.0385 | 1.10436 | ||||||||
\(896\) | −1.45443 | −0.0485891 | ||||||||
\(897\) | −11.6707 | −0.389673 | ||||||||
\(898\) | −9.84769 | −0.328622 | ||||||||
\(899\) | −38.8071 | −1.29429 | ||||||||
\(900\) | 86.4431 | 2.88144 | ||||||||
\(901\) | −0.503217 | −0.0167646 | ||||||||
\(902\) | 19.4664 | 0.648161 | ||||||||
\(903\) | 0.723919 | 0.0240905 | ||||||||
\(904\) | 6.97326 | 0.231927 | ||||||||
\(905\) | 61.5947 | 2.04748 | ||||||||
\(906\) | −32.6087 | −1.08335 | ||||||||
\(907\) | 0.955559 | 0.0317288 | 0.0158644 | − | 0.999874i | \(-0.494950\pi\) | ||||
0.0158644 | + | 0.999874i | \(0.494950\pi\) | |||||||
\(908\) | 19.0575 | 0.632445 | ||||||||
\(909\) | −54.1495 | −1.79602 | ||||||||
\(910\) | −23.6837 | −0.785107 | ||||||||
\(911\) | 48.9747 | 1.62260 | 0.811302 | − | 0.584628i | \(-0.198759\pi\) | ||||
0.811302 | + | 0.584628i | \(0.198759\pi\) | |||||||
\(912\) | 3.17050 | 0.104986 | ||||||||
\(913\) | 9.45099 | 0.312782 | ||||||||
\(914\) | −0.777880 | −0.0257300 | ||||||||
\(915\) | −3.78047 | −0.124979 | ||||||||
\(916\) | −11.0057 | −0.363638 | ||||||||
\(917\) | 15.2299 | 0.502936 | ||||||||
\(918\) | −0.740836 | −0.0244512 | ||||||||
\(919\) | 30.8314 | 1.01704 | 0.508518 | − | 0.861051i | \(-0.330194\pi\) | ||||
0.508518 | + | 0.861051i | \(0.330194\pi\) | |||||||
\(920\) | −3.90119 | −0.128618 | ||||||||
\(921\) | −27.7568 | −0.914619 | ||||||||
\(922\) | −19.4510 | −0.640584 | ||||||||
\(923\) | −16.9333 | −0.557365 | ||||||||
\(924\) | 14.0085 | 0.460847 | ||||||||
\(925\) | −124.390 | −4.08991 | ||||||||
\(926\) | 27.1820 | 0.893255 | ||||||||
\(927\) | −92.9426 | −3.05264 | ||||||||
\(928\) | 9.74846 | 0.320009 | ||||||||
\(929\) | 9.70941 | 0.318555 | 0.159278 | − | 0.987234i | \(-0.449083\pi\) | ||||
0.159278 | + | 0.987234i | \(0.449083\pi\) | |||||||
\(930\) | 52.4320 | 1.71931 | ||||||||
\(931\) | 4.88463 | 0.160087 | ||||||||
\(932\) | 20.5312 | 0.672522 | ||||||||
\(933\) | −48.9494 | −1.60253 | ||||||||
\(934\) | 24.0989 | 0.788541 | ||||||||
\(935\) | 0.727744 | 0.0237998 | ||||||||
\(936\) | −27.6428 | −0.903533 | ||||||||
\(937\) | −8.70932 | −0.284521 | −0.142260 | − | 0.989829i | \(-0.545437\pi\) | ||||
−0.142260 | + | 0.989829i | \(0.545437\pi\) | |||||||
\(938\) | 0.452759 | 0.0147831 | ||||||||
\(939\) | 1.22576 | 0.0400010 | ||||||||
\(940\) | −14.3024 | −0.466494 | ||||||||
\(941\) | −33.6765 | −1.09782 | −0.548911 | − | 0.835881i | \(-0.684957\pi\) | ||||
−0.548911 | + | 0.835881i | \(0.684957\pi\) | |||||||
\(942\) | 39.1957 | 1.27706 | ||||||||
\(943\) | 6.01754 | 0.195958 | ||||||||
\(944\) | −6.77204 | −0.220411 | ||||||||
\(945\) | −77.6235 | −2.52509 | ||||||||
\(946\) | −0.476914 | −0.0155058 | ||||||||
\(947\) | −33.7792 | −1.09768 | −0.548838 | − | 0.835929i | \(-0.684930\pi\) | ||||
−0.548838 | + | 0.835929i | \(0.684930\pi\) | |||||||
\(948\) | 40.9102 | 1.32870 | ||||||||
\(949\) | −50.2428 | −1.63095 | ||||||||
\(950\) | 12.2578 | 0.397695 | ||||||||
\(951\) | 43.7520 | 1.41875 | ||||||||
\(952\) | 0.0838701 | 0.00271825 | ||||||||
\(953\) | 3.70589 | 0.120045 | 0.0600227 | − | 0.998197i | \(-0.480883\pi\) | ||||
0.0600227 | + | 0.998197i | \(0.480883\pi\) | |||||||
\(954\) | −61.5402 | −1.99244 | ||||||||
\(955\) | −41.4188 | −1.34028 | ||||||||
\(956\) | 7.63091 | 0.246801 | ||||||||
\(957\) | −93.8936 | −3.03515 | ||||||||
\(958\) | 21.9273 | 0.708439 | ||||||||
\(959\) | 4.31562 | 0.139359 | ||||||||
\(960\) | −13.1711 | −0.425094 | ||||||||
\(961\) | −15.1529 | −0.488803 | ||||||||
\(962\) | 39.7774 | 1.28248 | ||||||||
\(963\) | −100.149 | −3.22725 | ||||||||
\(964\) | 7.91820 | 0.255028 | ||||||||
\(965\) | 7.42021 | 0.238865 | ||||||||
\(966\) | 4.33038 | 0.139328 | ||||||||
\(967\) | 21.3235 | 0.685716 | 0.342858 | − | 0.939387i | \(-0.388605\pi\) | ||||
0.342858 | + | 0.939387i | \(0.388605\pi\) | |||||||
\(968\) | 1.77125 | 0.0569301 | ||||||||
\(969\) | −0.182828 | −0.00587328 | ||||||||
\(970\) | 75.3400 | 2.41902 | ||||||||
\(971\) | 25.9844 | 0.833877 | 0.416939 | − | 0.908935i | \(-0.363103\pi\) | ||||
0.416939 | + | 0.908935i | \(0.363103\pi\) | |||||||
\(972\) | −23.5235 | −0.754515 | ||||||||
\(973\) | −19.8836 | −0.637438 | ||||||||
\(974\) | 21.2962 | 0.682373 | ||||||||
\(975\) | −152.337 | −4.87868 | ||||||||
\(976\) | 0.287029 | 0.00918757 | ||||||||
\(977\) | −3.60541 | −0.115347 | −0.0576737 | − | 0.998335i | \(-0.518368\pi\) | ||||
−0.0576737 | + | 0.998335i | \(0.518368\pi\) | |||||||
\(978\) | −20.1242 | −0.643501 | ||||||||
\(979\) | 29.0647 | 0.928912 | ||||||||
\(980\) | −20.2920 | −0.648204 | ||||||||
\(981\) | −2.52335 | −0.0805645 | ||||||||
\(982\) | −25.6131 | −0.817348 | ||||||||
\(983\) | −23.2306 | −0.740941 | −0.370470 | − | 0.928844i | \(-0.620803\pi\) | ||||
−0.370470 | + | 0.928844i | \(0.620803\pi\) | |||||||
\(984\) | 20.3162 | 0.647657 | ||||||||
\(985\) | −57.1279 | −1.82024 | ||||||||
\(986\) | −0.562148 | −0.0179024 | ||||||||
\(987\) | 15.8759 | 0.505336 | ||||||||
\(988\) | −3.91980 | −0.124705 | ||||||||
\(989\) | −0.147426 | −0.00468786 | ||||||||
\(990\) | 88.9984 | 2.82856 | ||||||||
\(991\) | −0.555456 | −0.0176446 | −0.00882232 | − | 0.999961i | \(-0.502808\pi\) | ||||
−0.00882232 | + | 0.999961i | \(0.502808\pi\) | |||||||
\(992\) | −3.98084 | −0.126392 | ||||||||
\(993\) | −63.0276 | −2.00012 | ||||||||
\(994\) | 6.28304 | 0.199286 | ||||||||
\(995\) | −82.5798 | −2.61795 | ||||||||
\(996\) | 9.86357 | 0.312539 | ||||||||
\(997\) | −42.7170 | −1.35286 | −0.676431 | − | 0.736506i | \(-0.736474\pi\) | ||||
−0.676431 | + | 0.736506i | \(0.736474\pi\) | |||||||
\(998\) | −18.2866 | −0.578851 | ||||||||
\(999\) | 130.371 | 4.12475 |
(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 | 8018.2.a.f.1.2 | ✓ | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.f.1.2 | ✓ | 34 | 1.1 | even | 1 | trivial |