Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8003,2,Mod(1,8003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8003, 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("8003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8003 = 53 \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8003.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: | \(63.9042767376\) |
Analytic rank: | \(1\) |
Dimension: | \(153\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 8003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.62408 | −1.85550 | −0.927751 | − | 0.373200i | \(-0.878261\pi\) | ||||
−0.927751 | + | 0.373200i | \(0.878261\pi\) | |||||||
\(3\) | −2.48215 | −1.43307 | −0.716536 | − | 0.697550i | \(-0.754273\pi\) | ||||
−0.716536 | + | 0.697550i | \(0.754273\pi\) | |||||||
\(4\) | 4.88578 | 2.44289 | ||||||||
\(5\) | −3.25865 | −1.45731 | −0.728656 | − | 0.684880i | \(-0.759855\pi\) | ||||
−0.728656 | + | 0.684880i | \(0.759855\pi\) | |||||||
\(6\) | 6.51336 | 2.65907 | ||||||||
\(7\) | 0.610888 | 0.230894 | 0.115447 | − | 0.993314i | \(-0.463170\pi\) | ||||
0.115447 | + | 0.993314i | \(0.463170\pi\) | |||||||
\(8\) | −7.57250 | −2.67728 | ||||||||
\(9\) | 3.16108 | 1.05369 | ||||||||
\(10\) | 8.55094 | 2.70404 | ||||||||
\(11\) | 6.56696 | 1.98001 | 0.990006 | − | 0.141027i | \(-0.0450403\pi\) | ||||
0.990006 | + | 0.141027i | \(0.0450403\pi\) | |||||||
\(12\) | −12.1272 | −3.50083 | ||||||||
\(13\) | −0.553887 | −0.153621 | −0.0768104 | − | 0.997046i | \(-0.524474\pi\) | ||||
−0.0768104 | + | 0.997046i | \(0.524474\pi\) | |||||||
\(14\) | −1.60302 | −0.428424 | ||||||||
\(15\) | 8.08846 | 2.08843 | ||||||||
\(16\) | 10.0993 | 2.52481 | ||||||||
\(17\) | 6.81718 | 1.65341 | 0.826705 | − | 0.562636i | \(-0.190213\pi\) | ||||
0.826705 | + | 0.562636i | \(0.190213\pi\) | |||||||
\(18\) | −8.29493 | −1.95513 | ||||||||
\(19\) | 7.03627 | 1.61423 | 0.807116 | − | 0.590393i | \(-0.201027\pi\) | ||||
0.807116 | + | 0.590393i | \(0.201027\pi\) | |||||||
\(20\) | −15.9210 | −3.56005 | ||||||||
\(21\) | −1.51632 | −0.330888 | ||||||||
\(22\) | −17.2322 | −3.67392 | ||||||||
\(23\) | −1.85353 | −0.386488 | −0.193244 | − | 0.981151i | \(-0.561901\pi\) | ||||
−0.193244 | + | 0.981151i | \(0.561901\pi\) | |||||||
\(24\) | 18.7961 | 3.83674 | ||||||||
\(25\) | 5.61878 | 1.12376 | ||||||||
\(26\) | 1.45344 | 0.285044 | ||||||||
\(27\) | −0.399838 | −0.0769488 | ||||||||
\(28\) | 2.98466 | 0.564048 | ||||||||
\(29\) | 6.42256 | 1.19264 | 0.596320 | − | 0.802747i | \(-0.296629\pi\) | ||||
0.596320 | + | 0.802747i | \(0.296629\pi\) | |||||||
\(30\) | −21.2247 | −3.87509 | ||||||||
\(31\) | −1.64144 | −0.294811 | −0.147405 | − | 0.989076i | \(-0.547092\pi\) | ||||
−0.147405 | + | 0.989076i | \(0.547092\pi\) | |||||||
\(32\) | −11.3562 | −2.00752 | ||||||||
\(33\) | −16.3002 | −2.83750 | ||||||||
\(34\) | −17.8888 | −3.06791 | ||||||||
\(35\) | −1.99067 | −0.336484 | ||||||||
\(36\) | 15.4444 | 2.57406 | ||||||||
\(37\) | −2.92399 | −0.480701 | −0.240350 | − | 0.970686i | \(-0.577262\pi\) | ||||
−0.240350 | + | 0.970686i | \(0.577262\pi\) | |||||||
\(38\) | −18.4637 | −2.99521 | ||||||||
\(39\) | 1.37483 | 0.220150 | ||||||||
\(40\) | 24.6761 | 3.90163 | ||||||||
\(41\) | 4.41849 | 0.690053 | 0.345026 | − | 0.938593i | \(-0.387870\pi\) | ||||
0.345026 | + | 0.938593i | \(0.387870\pi\) | |||||||
\(42\) | 3.97893 | 0.613963 | ||||||||
\(43\) | −2.75943 | −0.420810 | −0.210405 | − | 0.977614i | \(-0.567478\pi\) | ||||
−0.210405 | + | 0.977614i | \(0.567478\pi\) | |||||||
\(44\) | 32.0847 | 4.83695 | ||||||||
\(45\) | −10.3009 | −1.53556 | ||||||||
\(46\) | 4.86381 | 0.717129 | ||||||||
\(47\) | 0.122965 | 0.0179362 | 0.00896812 | − | 0.999960i | \(-0.497145\pi\) | ||||
0.00896812 | + | 0.999960i | \(0.497145\pi\) | |||||||
\(48\) | −25.0679 | −3.61824 | ||||||||
\(49\) | −6.62682 | −0.946688 | ||||||||
\(50\) | −14.7441 | −2.08513 | ||||||||
\(51\) | −16.9213 | −2.36946 | ||||||||
\(52\) | −2.70617 | −0.375278 | ||||||||
\(53\) | −1.00000 | −0.137361 | ||||||||
\(54\) | 1.04920 | 0.142779 | ||||||||
\(55\) | −21.3994 | −2.88549 | ||||||||
\(56\) | −4.62595 | −0.618168 | ||||||||
\(57\) | −17.4651 | −2.31331 | ||||||||
\(58\) | −16.8533 | −2.21295 | ||||||||
\(59\) | 2.05909 | 0.268071 | 0.134035 | − | 0.990977i | \(-0.457206\pi\) | ||||
0.134035 | + | 0.990977i | \(0.457206\pi\) | |||||||
\(60\) | 39.5184 | 5.10181 | ||||||||
\(61\) | −8.14786 | −1.04323 | −0.521613 | − | 0.853182i | \(-0.674670\pi\) | ||||
−0.521613 | + | 0.853182i | \(0.674670\pi\) | |||||||
\(62\) | 4.30725 | 0.547022 | ||||||||
\(63\) | 1.93107 | 0.243292 | ||||||||
\(64\) | 9.60108 | 1.20014 | ||||||||
\(65\) | 1.80492 | 0.223873 | ||||||||
\(66\) | 42.7729 | 5.26499 | ||||||||
\(67\) | −5.00407 | −0.611344 | −0.305672 | − | 0.952137i | \(-0.598881\pi\) | ||||
−0.305672 | + | 0.952137i | \(0.598881\pi\) | |||||||
\(68\) | 33.3072 | 4.03910 | ||||||||
\(69\) | 4.60075 | 0.553865 | ||||||||
\(70\) | 5.22366 | 0.624347 | ||||||||
\(71\) | 0.658063 | 0.0780977 | 0.0390488 | − | 0.999237i | \(-0.487567\pi\) | ||||
0.0390488 | + | 0.999237i | \(0.487567\pi\) | |||||||
\(72\) | −23.9373 | −2.82104 | ||||||||
\(73\) | 5.08046 | 0.594622 | 0.297311 | − | 0.954781i | \(-0.403910\pi\) | ||||
0.297311 | + | 0.954781i | \(0.403910\pi\) | |||||||
\(74\) | 7.67277 | 0.891942 | ||||||||
\(75\) | −13.9467 | −1.61042 | ||||||||
\(76\) | 34.3777 | 3.94339 | ||||||||
\(77\) | 4.01167 | 0.457173 | ||||||||
\(78\) | −3.60767 | −0.408488 | ||||||||
\(79\) | −9.53151 | −1.07238 | −0.536189 | − | 0.844098i | \(-0.680137\pi\) | ||||
−0.536189 | + | 0.844098i | \(0.680137\pi\) | |||||||
\(80\) | −32.9099 | −3.67944 | ||||||||
\(81\) | −8.49080 | −0.943422 | ||||||||
\(82\) | −11.5945 | −1.28039 | ||||||||
\(83\) | −0.567433 | −0.0622839 | −0.0311419 | − | 0.999515i | \(-0.509914\pi\) | ||||
−0.0311419 | + | 0.999515i | \(0.509914\pi\) | |||||||
\(84\) | −7.40839 | −0.808321 | ||||||||
\(85\) | −22.2148 | −2.40953 | ||||||||
\(86\) | 7.24097 | 0.780814 | ||||||||
\(87\) | −15.9418 | −1.70914 | ||||||||
\(88\) | −49.7282 | −5.30105 | ||||||||
\(89\) | −2.38038 | −0.252320 | −0.126160 | − | 0.992010i | \(-0.540265\pi\) | ||||
−0.126160 | + | 0.992010i | \(0.540265\pi\) | |||||||
\(90\) | 27.0302 | 2.84924 | ||||||||
\(91\) | −0.338363 | −0.0354701 | ||||||||
\(92\) | −9.05594 | −0.944147 | ||||||||
\(93\) | 4.07430 | 0.422485 | ||||||||
\(94\) | −0.322669 | −0.0332807 | ||||||||
\(95\) | −22.9287 | −2.35244 | ||||||||
\(96\) | 28.1879 | 2.87691 | ||||||||
\(97\) | −12.0139 | −1.21982 | −0.609911 | − | 0.792470i | \(-0.708795\pi\) | ||||
−0.609911 | + | 0.792470i | \(0.708795\pi\) | |||||||
\(98\) | 17.3893 | 1.75658 | ||||||||
\(99\) | 20.7587 | 2.08633 | ||||||||
\(100\) | 27.4521 | 2.74521 | ||||||||
\(101\) | 7.81888 | 0.778007 | 0.389004 | − | 0.921236i | \(-0.372819\pi\) | ||||
0.389004 | + | 0.921236i | \(0.372819\pi\) | |||||||
\(102\) | 44.4028 | 4.39653 | ||||||||
\(103\) | −4.44738 | −0.438213 | −0.219107 | − | 0.975701i | \(-0.570314\pi\) | ||||
−0.219107 | + | 0.975701i | \(0.570314\pi\) | |||||||
\(104\) | 4.19431 | 0.411286 | ||||||||
\(105\) | 4.94114 | 0.482206 | ||||||||
\(106\) | 2.62408 | 0.254873 | ||||||||
\(107\) | 1.68699 | 0.163088 | 0.0815439 | − | 0.996670i | \(-0.474015\pi\) | ||||
0.0815439 | + | 0.996670i | \(0.474015\pi\) | |||||||
\(108\) | −1.95352 | −0.187977 | ||||||||
\(109\) | −7.52303 | −0.720575 | −0.360288 | − | 0.932841i | \(-0.617321\pi\) | ||||
−0.360288 | + | 0.932841i | \(0.617321\pi\) | |||||||
\(110\) | 56.1536 | 5.35404 | ||||||||
\(111\) | 7.25779 | 0.688879 | ||||||||
\(112\) | 6.16951 | 0.582964 | ||||||||
\(113\) | −9.84428 | −0.926072 | −0.463036 | − | 0.886340i | \(-0.653240\pi\) | ||||
−0.463036 | + | 0.886340i | \(0.653240\pi\) | |||||||
\(114\) | 45.8298 | 4.29235 | ||||||||
\(115\) | 6.04000 | 0.563233 | ||||||||
\(116\) | 31.3792 | 2.91349 | ||||||||
\(117\) | −1.75088 | −0.161869 | ||||||||
\(118\) | −5.40321 | −0.497406 | ||||||||
\(119\) | 4.16454 | 0.381762 | ||||||||
\(120\) | −61.2498 | −5.59132 | ||||||||
\(121\) | 32.1249 | 2.92045 | ||||||||
\(122\) | 21.3806 | 1.93571 | ||||||||
\(123\) | −10.9674 | −0.988896 | ||||||||
\(124\) | −8.01969 | −0.720189 | ||||||||
\(125\) | −2.01640 | −0.180352 | ||||||||
\(126\) | −5.06727 | −0.451428 | ||||||||
\(127\) | −18.4441 | −1.63665 | −0.818323 | − | 0.574758i | \(-0.805096\pi\) | ||||
−0.818323 | + | 0.574758i | \(0.805096\pi\) | |||||||
\(128\) | −2.48153 | −0.219338 | ||||||||
\(129\) | 6.84934 | 0.603051 | ||||||||
\(130\) | −4.73626 | −0.415397 | ||||||||
\(131\) | 7.41549 | 0.647894 | 0.323947 | − | 0.946075i | \(-0.394990\pi\) | ||||
0.323947 | + | 0.946075i | \(0.394990\pi\) | |||||||
\(132\) | −79.6391 | −6.93169 | ||||||||
\(133\) | 4.29837 | 0.372716 | ||||||||
\(134\) | 13.1310 | 1.13435 | ||||||||
\(135\) | 1.30293 | 0.112138 | ||||||||
\(136\) | −51.6231 | −4.42664 | ||||||||
\(137\) | 6.68839 | 0.571428 | 0.285714 | − | 0.958315i | \(-0.407769\pi\) | ||||
0.285714 | + | 0.958315i | \(0.407769\pi\) | |||||||
\(138\) | −12.0727 | −1.02770 | ||||||||
\(139\) | −5.83713 | −0.495099 | −0.247549 | − | 0.968875i | \(-0.579625\pi\) | ||||
−0.247549 | + | 0.968875i | \(0.579625\pi\) | |||||||
\(140\) | −9.72596 | −0.821993 | ||||||||
\(141\) | −0.305217 | −0.0257039 | ||||||||
\(142\) | −1.72681 | −0.144910 | ||||||||
\(143\) | −3.63735 | −0.304171 | ||||||||
\(144\) | 31.9246 | 2.66038 | ||||||||
\(145\) | −20.9289 | −1.73805 | ||||||||
\(146\) | −13.3315 | −1.10332 | ||||||||
\(147\) | 16.4488 | 1.35667 | ||||||||
\(148\) | −14.2860 | −1.17430 | ||||||||
\(149\) | −19.5185 | −1.59902 | −0.799508 | − | 0.600656i | \(-0.794906\pi\) | ||||
−0.799508 | + | 0.600656i | \(0.794906\pi\) | |||||||
\(150\) | 36.5972 | 2.98815 | ||||||||
\(151\) | −1.00000 | −0.0813788 | ||||||||
\(152\) | −53.2821 | −4.32175 | ||||||||
\(153\) | 21.5497 | 1.74219 | ||||||||
\(154\) | −10.5269 | −0.848285 | ||||||||
\(155\) | 5.34886 | 0.429631 | ||||||||
\(156\) | 6.71713 | 0.537801 | ||||||||
\(157\) | −3.54755 | −0.283125 | −0.141563 | − | 0.989929i | \(-0.545213\pi\) | ||||
−0.141563 | + | 0.989929i | \(0.545213\pi\) | |||||||
\(158\) | 25.0114 | 1.98980 | ||||||||
\(159\) | 2.48215 | 0.196848 | ||||||||
\(160\) | 37.0059 | 2.92558 | ||||||||
\(161\) | −1.13230 | −0.0892377 | ||||||||
\(162\) | 22.2805 | 1.75052 | ||||||||
\(163\) | −0.226666 | −0.0177539 | −0.00887693 | − | 0.999961i | \(-0.502826\pi\) | ||||
−0.00887693 | + | 0.999961i | \(0.502826\pi\) | |||||||
\(164\) | 21.5878 | 1.68572 | ||||||||
\(165\) | 53.1166 | 4.13512 | ||||||||
\(166\) | 1.48899 | 0.115568 | ||||||||
\(167\) | −7.25741 | −0.561595 | −0.280797 | − | 0.959767i | \(-0.590599\pi\) | ||||
−0.280797 | + | 0.959767i | \(0.590599\pi\) | |||||||
\(168\) | 11.4823 | 0.885879 | ||||||||
\(169\) | −12.6932 | −0.976401 | ||||||||
\(170\) | 58.2933 | 4.47089 | ||||||||
\(171\) | 22.2423 | 1.70091 | ||||||||
\(172\) | −13.4820 | −1.02799 | ||||||||
\(173\) | −22.8210 | −1.73505 | −0.867525 | − | 0.497393i | \(-0.834291\pi\) | ||||
−0.867525 | + | 0.497393i | \(0.834291\pi\) | |||||||
\(174\) | 41.8324 | 3.17131 | ||||||||
\(175\) | 3.43245 | 0.259469 | ||||||||
\(176\) | 66.3214 | 4.99916 | ||||||||
\(177\) | −5.11098 | −0.384164 | ||||||||
\(178\) | 6.24630 | 0.468180 | ||||||||
\(179\) | 11.8175 | 0.883284 | 0.441642 | − | 0.897191i | \(-0.354396\pi\) | ||||
0.441642 | + | 0.897191i | \(0.354396\pi\) | |||||||
\(180\) | −50.3277 | −3.75121 | ||||||||
\(181\) | 0.285597 | 0.0212282 | 0.0106141 | − | 0.999944i | \(-0.496621\pi\) | ||||
0.0106141 | + | 0.999944i | \(0.496621\pi\) | |||||||
\(182\) | 0.887890 | 0.0658148 | ||||||||
\(183\) | 20.2242 | 1.49502 | ||||||||
\(184\) | 14.0359 | 1.03474 | ||||||||
\(185\) | 9.52825 | 0.700531 | ||||||||
\(186\) | −10.6913 | −0.783921 | ||||||||
\(187\) | 44.7681 | 3.27377 | ||||||||
\(188\) | 0.600778 | 0.0438162 | ||||||||
\(189\) | −0.244256 | −0.0177670 | ||||||||
\(190\) | 60.1667 | 4.36495 | ||||||||
\(191\) | −25.2649 | −1.82810 | −0.914052 | − | 0.405596i | \(-0.867064\pi\) | ||||
−0.914052 | + | 0.405596i | \(0.867064\pi\) | |||||||
\(192\) | −23.8314 | −1.71988 | ||||||||
\(193\) | 3.29886 | 0.237457 | 0.118729 | − | 0.992927i | \(-0.462118\pi\) | ||||
0.118729 | + | 0.992927i | \(0.462118\pi\) | |||||||
\(194\) | 31.5253 | 2.26338 | ||||||||
\(195\) | −4.48010 | −0.320826 | ||||||||
\(196\) | −32.3771 | −2.31265 | ||||||||
\(197\) | −2.84106 | −0.202417 | −0.101209 | − | 0.994865i | \(-0.532271\pi\) | ||||
−0.101209 | + | 0.994865i | \(0.532271\pi\) | |||||||
\(198\) | −54.4724 | −3.87119 | ||||||||
\(199\) | −13.3172 | −0.944034 | −0.472017 | − | 0.881589i | \(-0.656474\pi\) | ||||
−0.472017 | + | 0.881589i | \(0.656474\pi\) | |||||||
\(200\) | −42.5482 | −3.00861 | ||||||||
\(201\) | 12.4209 | 0.876100 | ||||||||
\(202\) | −20.5173 | −1.44359 | ||||||||
\(203\) | 3.92346 | 0.275373 | ||||||||
\(204\) | −82.6737 | −5.78831 | ||||||||
\(205\) | −14.3983 | −1.00562 | ||||||||
\(206\) | 11.6703 | 0.813105 | ||||||||
\(207\) | −5.85917 | −0.407240 | ||||||||
\(208\) | −5.59385 | −0.387864 | ||||||||
\(209\) | 46.2069 | 3.19620 | ||||||||
\(210\) | −12.9659 | −0.894735 | ||||||||
\(211\) | 8.10242 | 0.557794 | 0.278897 | − | 0.960321i | \(-0.410031\pi\) | ||||
0.278897 | + | 0.960321i | \(0.410031\pi\) | |||||||
\(212\) | −4.88578 | −0.335556 | ||||||||
\(213\) | −1.63341 | −0.111920 | ||||||||
\(214\) | −4.42680 | −0.302610 | ||||||||
\(215\) | 8.99203 | 0.613251 | ||||||||
\(216\) | 3.02777 | 0.206014 | ||||||||
\(217\) | −1.00273 | −0.0680700 | ||||||||
\(218\) | 19.7410 | 1.33703 | ||||||||
\(219\) | −12.6105 | −0.852137 | ||||||||
\(220\) | −104.553 | −7.04894 | ||||||||
\(221\) | −3.77595 | −0.253998 | ||||||||
\(222\) | −19.0450 | −1.27822 | ||||||||
\(223\) | −12.9999 | −0.870536 | −0.435268 | − | 0.900301i | \(-0.643346\pi\) | ||||
−0.435268 | + | 0.900301i | \(0.643346\pi\) | |||||||
\(224\) | −6.93738 | −0.463523 | ||||||||
\(225\) | 17.7615 | 1.18410 | ||||||||
\(226\) | 25.8321 | 1.71833 | ||||||||
\(227\) | −19.2694 | −1.27895 | −0.639476 | − | 0.768811i | \(-0.720849\pi\) | ||||
−0.639476 | + | 0.768811i | \(0.720849\pi\) | |||||||
\(228\) | −85.3306 | −5.65116 | ||||||||
\(229\) | −10.3824 | −0.686090 | −0.343045 | − | 0.939319i | \(-0.611458\pi\) | ||||
−0.343045 | + | 0.939319i | \(0.611458\pi\) | |||||||
\(230\) | −15.8494 | −1.04508 | ||||||||
\(231\) | −9.95759 | −0.655161 | ||||||||
\(232\) | −48.6348 | −3.19303 | ||||||||
\(233\) | 12.6518 | 0.828846 | 0.414423 | − | 0.910084i | \(-0.363983\pi\) | ||||
0.414423 | + | 0.910084i | \(0.363983\pi\) | |||||||
\(234\) | 4.59446 | 0.300349 | ||||||||
\(235\) | −0.400699 | −0.0261387 | ||||||||
\(236\) | 10.0602 | 0.654866 | ||||||||
\(237\) | 23.6587 | 1.53680 | ||||||||
\(238\) | −10.9281 | −0.708361 | ||||||||
\(239\) | 0.236038 | 0.0152680 | 0.00763402 | − | 0.999971i | \(-0.497570\pi\) | ||||
0.00763402 | + | 0.999971i | \(0.497570\pi\) | |||||||
\(240\) | 81.6874 | 5.27290 | ||||||||
\(241\) | 11.9739 | 0.771304 | 0.385652 | − | 0.922644i | \(-0.373976\pi\) | ||||
0.385652 | + | 0.922644i | \(0.373976\pi\) | |||||||
\(242\) | −84.2982 | −5.41889 | ||||||||
\(243\) | 22.2750 | 1.42894 | ||||||||
\(244\) | −39.8086 | −2.54849 | ||||||||
\(245\) | 21.5945 | 1.37962 | ||||||||
\(246\) | 28.7792 | 1.83490 | ||||||||
\(247\) | −3.89730 | −0.247979 | ||||||||
\(248\) | 12.4298 | 0.789291 | ||||||||
\(249\) | 1.40846 | 0.0892573 | ||||||||
\(250\) | 5.29118 | 0.334643 | ||||||||
\(251\) | −23.0954 | −1.45777 | −0.728885 | − | 0.684636i | \(-0.759961\pi\) | ||||
−0.728885 | + | 0.684636i | \(0.759961\pi\) | |||||||
\(252\) | 9.43477 | 0.594334 | ||||||||
\(253\) | −12.1721 | −0.765251 | ||||||||
\(254\) | 48.3987 | 3.03680 | ||||||||
\(255\) | 55.1405 | 3.45303 | ||||||||
\(256\) | −12.6904 | −0.793153 | ||||||||
\(257\) | −13.6842 | −0.853599 | −0.426800 | − | 0.904346i | \(-0.640359\pi\) | ||||
−0.426800 | + | 0.904346i | \(0.640359\pi\) | |||||||
\(258\) | −17.9732 | −1.11896 | ||||||||
\(259\) | −1.78623 | −0.110991 | ||||||||
\(260\) | 8.81845 | 0.546897 | ||||||||
\(261\) | 20.3023 | 1.25668 | ||||||||
\(262\) | −19.4588 | −1.20217 | ||||||||
\(263\) | 25.8285 | 1.59266 | 0.796328 | − | 0.604865i | \(-0.206773\pi\) | ||||
0.796328 | + | 0.604865i | \(0.206773\pi\) | |||||||
\(264\) | 123.433 | 7.59678 | ||||||||
\(265\) | 3.25865 | 0.200177 | ||||||||
\(266\) | −11.2793 | −0.691576 | ||||||||
\(267\) | 5.90847 | 0.361592 | ||||||||
\(268\) | −24.4487 | −1.49344 | ||||||||
\(269\) | −11.7068 | −0.713779 | −0.356889 | − | 0.934147i | \(-0.616163\pi\) | ||||
−0.356889 | + | 0.934147i | \(0.616163\pi\) | |||||||
\(270\) | −3.41899 | −0.208073 | ||||||||
\(271\) | 26.6988 | 1.62184 | 0.810918 | − | 0.585159i | \(-0.198968\pi\) | ||||
0.810918 | + | 0.585159i | \(0.198968\pi\) | |||||||
\(272\) | 68.8485 | 4.17455 | ||||||||
\(273\) | 0.839869 | 0.0508312 | ||||||||
\(274\) | −17.5509 | −1.06029 | ||||||||
\(275\) | 36.8983 | 2.22505 | ||||||||
\(276\) | 22.4782 | 1.35303 | ||||||||
\(277\) | 2.31899 | 0.139335 | 0.0696674 | − | 0.997570i | \(-0.477806\pi\) | ||||
0.0696674 | + | 0.997570i | \(0.477806\pi\) | |||||||
\(278\) | 15.3171 | 0.918656 | ||||||||
\(279\) | −5.18872 | −0.310640 | ||||||||
\(280\) | 15.0743 | 0.900863 | ||||||||
\(281\) | 13.0713 | 0.779770 | 0.389885 | − | 0.920864i | \(-0.372515\pi\) | ||||
0.389885 | + | 0.920864i | \(0.372515\pi\) | |||||||
\(282\) | 0.800913 | 0.0476937 | ||||||||
\(283\) | −31.7668 | −1.88834 | −0.944170 | − | 0.329460i | \(-0.893133\pi\) | ||||
−0.944170 | + | 0.329460i | \(0.893133\pi\) | |||||||
\(284\) | 3.21515 | 0.190784 | ||||||||
\(285\) | 56.9126 | 3.37121 | ||||||||
\(286\) | 9.54469 | 0.564390 | ||||||||
\(287\) | 2.69920 | 0.159329 | ||||||||
\(288\) | −35.8980 | −2.11531 | ||||||||
\(289\) | 29.4740 | 1.73377 | ||||||||
\(290\) | 54.9189 | 3.22495 | ||||||||
\(291\) | 29.8202 | 1.74809 | ||||||||
\(292\) | 24.8220 | 1.45260 | ||||||||
\(293\) | −26.8730 | −1.56994 | −0.784969 | − | 0.619535i | \(-0.787321\pi\) | ||||
−0.784969 | + | 0.619535i | \(0.787321\pi\) | |||||||
\(294\) | −43.1628 | −2.51731 | ||||||||
\(295\) | −6.70985 | −0.390662 | ||||||||
\(296\) | 22.1419 | 1.28697 | ||||||||
\(297\) | −2.62572 | −0.152359 | ||||||||
\(298\) | 51.2180 | 2.96698 | ||||||||
\(299\) | 1.02665 | 0.0593725 | ||||||||
\(300\) | −68.1404 | −3.93409 | ||||||||
\(301\) | −1.68571 | −0.0971624 | ||||||||
\(302\) | 2.62408 | 0.150999 | ||||||||
\(303\) | −19.4077 | −1.11494 | ||||||||
\(304\) | 71.0611 | 4.07563 | ||||||||
\(305\) | 26.5510 | 1.52031 | ||||||||
\(306\) | −56.5481 | −3.23264 | ||||||||
\(307\) | −30.9630 | −1.76715 | −0.883576 | − | 0.468288i | \(-0.844871\pi\) | ||||
−0.883576 | + | 0.468288i | \(0.844871\pi\) | |||||||
\(308\) | 19.6001 | 1.11682 | ||||||||
\(309\) | 11.0391 | 0.627991 | ||||||||
\(310\) | −14.0358 | −0.797181 | ||||||||
\(311\) | −14.7720 | −0.837643 | −0.418821 | − | 0.908069i | \(-0.637557\pi\) | ||||
−0.418821 | + | 0.908069i | \(0.637557\pi\) | |||||||
\(312\) | −10.4109 | −0.589402 | ||||||||
\(313\) | 25.1441 | 1.42123 | 0.710615 | − | 0.703581i | \(-0.248417\pi\) | ||||
0.710615 | + | 0.703581i | \(0.248417\pi\) | |||||||
\(314\) | 9.30903 | 0.525339 | ||||||||
\(315\) | −6.29267 | −0.354552 | ||||||||
\(316\) | −46.5688 | −2.61970 | ||||||||
\(317\) | −18.9254 | −1.06296 | −0.531479 | − | 0.847071i | \(-0.678364\pi\) | ||||
−0.531479 | + | 0.847071i | \(0.678364\pi\) | |||||||
\(318\) | −6.51336 | −0.365251 | ||||||||
\(319\) | 42.1767 | 2.36144 | ||||||||
\(320\) | −31.2865 | −1.74897 | ||||||||
\(321\) | −4.18738 | −0.233716 | ||||||||
\(322\) | 2.97124 | 0.165581 | ||||||||
\(323\) | 47.9676 | 2.66899 | ||||||||
\(324\) | −41.4841 | −2.30467 | ||||||||
\(325\) | −3.11217 | −0.172632 | ||||||||
\(326\) | 0.594789 | 0.0329423 | ||||||||
\(327\) | 18.6733 | 1.03264 | ||||||||
\(328\) | −33.4590 | −1.84747 | ||||||||
\(329\) | 0.0751177 | 0.00414137 | ||||||||
\(330\) | −139.382 | −7.67272 | ||||||||
\(331\) | −3.59576 | −0.197641 | −0.0988205 | − | 0.995105i | \(-0.531507\pi\) | ||||
−0.0988205 | + | 0.995105i | \(0.531507\pi\) | |||||||
\(332\) | −2.77235 | −0.152153 | ||||||||
\(333\) | −9.24298 | −0.506512 | ||||||||
\(334\) | 19.0440 | 1.04204 | ||||||||
\(335\) | 16.3065 | 0.890918 | ||||||||
\(336\) | −15.3137 | −0.835429 | ||||||||
\(337\) | −19.9423 | −1.08633 | −0.543163 | − | 0.839627i | \(-0.682774\pi\) | ||||
−0.543163 | + | 0.839627i | \(0.682774\pi\) | |||||||
\(338\) | 33.3079 | 1.81171 | ||||||||
\(339\) | 24.4350 | 1.32713 | ||||||||
\(340\) | −108.537 | −5.88622 | ||||||||
\(341\) | −10.7792 | −0.583728 | ||||||||
\(342\) | −58.3654 | −3.15604 | ||||||||
\(343\) | −8.32446 | −0.449478 | ||||||||
\(344\) | 20.8958 | 1.12663 | ||||||||
\(345\) | −14.9922 | −0.807154 | ||||||||
\(346\) | 59.8841 | 3.21939 | ||||||||
\(347\) | −12.8463 | −0.689624 | −0.344812 | − | 0.938672i | \(-0.612057\pi\) | ||||
−0.344812 | + | 0.938672i | \(0.612057\pi\) | |||||||
\(348\) | −77.8880 | −4.17523 | ||||||||
\(349\) | −14.6891 | −0.786288 | −0.393144 | − | 0.919477i | \(-0.628613\pi\) | ||||
−0.393144 | + | 0.919477i | \(0.628613\pi\) | |||||||
\(350\) | −9.00700 | −0.481444 | ||||||||
\(351\) | 0.221465 | 0.0118209 | ||||||||
\(352\) | −74.5758 | −3.97490 | ||||||||
\(353\) | 31.0255 | 1.65132 | 0.825660 | − | 0.564168i | \(-0.190803\pi\) | ||||
0.825660 | + | 0.564168i | \(0.190803\pi\) | |||||||
\(354\) | 13.4116 | 0.712818 | ||||||||
\(355\) | −2.14439 | −0.113813 | ||||||||
\(356\) | −11.6300 | −0.616389 | ||||||||
\(357\) | −10.3370 | −0.547093 | ||||||||
\(358\) | −31.0101 | −1.63894 | ||||||||
\(359\) | −0.915912 | −0.0483400 | −0.0241700 | − | 0.999708i | \(-0.507694\pi\) | ||||
−0.0241700 | + | 0.999708i | \(0.507694\pi\) | |||||||
\(360\) | 78.0032 | 4.11113 | ||||||||
\(361\) | 30.5091 | 1.60574 | ||||||||
\(362\) | −0.749427 | −0.0393890 | ||||||||
\(363\) | −79.7389 | −4.18521 | ||||||||
\(364\) | −1.65317 | −0.0866494 | ||||||||
\(365\) | −16.5554 | −0.866550 | ||||||||
\(366\) | −53.0700 | −2.77401 | ||||||||
\(367\) | −20.3916 | −1.06443 | −0.532217 | − | 0.846608i | \(-0.678641\pi\) | ||||
−0.532217 | + | 0.846608i | \(0.678641\pi\) | |||||||
\(368\) | −18.7193 | −0.975810 | ||||||||
\(369\) | 13.9672 | 0.727105 | ||||||||
\(370\) | −25.0029 | −1.29984 | ||||||||
\(371\) | −0.610888 | −0.0317157 | ||||||||
\(372\) | 19.9061 | 1.03208 | ||||||||
\(373\) | 27.9887 | 1.44920 | 0.724601 | − | 0.689169i | \(-0.242024\pi\) | ||||
0.724601 | + | 0.689169i | \(0.242024\pi\) | |||||||
\(374\) | −117.475 | −6.07449 | ||||||||
\(375\) | 5.00500 | 0.258457 | ||||||||
\(376\) | −0.931150 | −0.0480204 | ||||||||
\(377\) | −3.55738 | −0.183214 | ||||||||
\(378\) | 0.640946 | 0.0329667 | ||||||||
\(379\) | 2.93247 | 0.150631 | 0.0753155 | − | 0.997160i | \(-0.476004\pi\) | ||||
0.0753155 | + | 0.997160i | \(0.476004\pi\) | |||||||
\(380\) | −112.025 | −5.74674 | ||||||||
\(381\) | 45.7810 | 2.34543 | ||||||||
\(382\) | 66.2970 | 3.39205 | ||||||||
\(383\) | −28.5613 | −1.45942 | −0.729708 | − | 0.683759i | \(-0.760344\pi\) | ||||
−0.729708 | + | 0.683759i | \(0.760344\pi\) | |||||||
\(384\) | 6.15953 | 0.314327 | ||||||||
\(385\) | −13.0726 | −0.666243 | ||||||||
\(386\) | −8.65647 | −0.440603 | ||||||||
\(387\) | −8.72281 | −0.443405 | ||||||||
\(388\) | −58.6970 | −2.97989 | ||||||||
\(389\) | 24.0747 | 1.22064 | 0.610318 | − | 0.792156i | \(-0.291041\pi\) | ||||
0.610318 | + | 0.792156i | \(0.291041\pi\) | |||||||
\(390\) | 11.7561 | 0.595294 | ||||||||
\(391\) | −12.6359 | −0.639023 | ||||||||
\(392\) | 50.1815 | 2.53455 | ||||||||
\(393\) | −18.4064 | −0.928479 | ||||||||
\(394\) | 7.45516 | 0.375586 | ||||||||
\(395\) | 31.0598 | 1.56279 | ||||||||
\(396\) | 101.422 | 5.09667 | ||||||||
\(397\) | 10.1374 | 0.508782 | 0.254391 | − | 0.967101i | \(-0.418125\pi\) | ||||
0.254391 | + | 0.967101i | \(0.418125\pi\) | |||||||
\(398\) | 34.9455 | 1.75166 | ||||||||
\(399\) | −10.6692 | −0.534129 | ||||||||
\(400\) | 56.7455 | 2.83728 | ||||||||
\(401\) | 4.33304 | 0.216382 | 0.108191 | − | 0.994130i | \(-0.465494\pi\) | ||||
0.108191 | + | 0.994130i | \(0.465494\pi\) | |||||||
\(402\) | −32.5933 | −1.62560 | ||||||||
\(403\) | 0.909171 | 0.0452890 | ||||||||
\(404\) | 38.2013 | 1.90058 | ||||||||
\(405\) | 27.6685 | 1.37486 | ||||||||
\(406\) | −10.2955 | −0.510956 | ||||||||
\(407\) | −19.2017 | −0.951794 | ||||||||
\(408\) | 128.136 | 6.34370 | ||||||||
\(409\) | 8.95975 | 0.443031 | 0.221516 | − | 0.975157i | \(-0.428900\pi\) | ||||
0.221516 | + | 0.975157i | \(0.428900\pi\) | |||||||
\(410\) | 37.7823 | 1.86593 | ||||||||
\(411\) | −16.6016 | −0.818898 | ||||||||
\(412\) | −21.7289 | −1.07051 | ||||||||
\(413\) | 1.25787 | 0.0618959 | ||||||||
\(414\) | 15.3749 | 0.755635 | ||||||||
\(415\) | 1.84906 | 0.0907670 | ||||||||
\(416\) | 6.29007 | 0.308396 | ||||||||
\(417\) | 14.4886 | 0.709512 | ||||||||
\(418\) | −121.250 | −5.93055 | ||||||||
\(419\) | −33.1607 | −1.62001 | −0.810003 | − | 0.586425i | \(-0.800535\pi\) | ||||
−0.810003 | + | 0.586425i | \(0.800535\pi\) | |||||||
\(420\) | 24.1413 | 1.17798 | ||||||||
\(421\) | 25.2215 | 1.22922 | 0.614611 | − | 0.788830i | \(-0.289313\pi\) | ||||
0.614611 | + | 0.788830i | \(0.289313\pi\) | |||||||
\(422\) | −21.2614 | −1.03499 | ||||||||
\(423\) | 0.388702 | 0.0188993 | ||||||||
\(424\) | 7.57250 | 0.367753 | ||||||||
\(425\) | 38.3043 | 1.85803 | ||||||||
\(426\) | 4.28620 | 0.207667 | ||||||||
\(427\) | −4.97743 | −0.240875 | ||||||||
\(428\) | 8.24227 | 0.398405 | ||||||||
\(429\) | 9.02847 | 0.435899 | ||||||||
\(430\) | −23.5958 | −1.13789 | ||||||||
\(431\) | −18.3840 | −0.885527 | −0.442763 | − | 0.896638i | \(-0.646002\pi\) | ||||
−0.442763 | + | 0.896638i | \(0.646002\pi\) | |||||||
\(432\) | −4.03806 | −0.194281 | ||||||||
\(433\) | 21.5689 | 1.03653 | 0.518267 | − | 0.855219i | \(-0.326577\pi\) | ||||
0.518267 | + | 0.855219i | \(0.326577\pi\) | |||||||
\(434\) | 2.63125 | 0.126304 | ||||||||
\(435\) | 51.9486 | 2.49075 | ||||||||
\(436\) | −36.7558 | −1.76028 | ||||||||
\(437\) | −13.0419 | −0.623881 | ||||||||
\(438\) | 33.0908 | 1.58114 | ||||||||
\(439\) | 29.1914 | 1.39323 | 0.696616 | − | 0.717444i | \(-0.254688\pi\) | ||||
0.696616 | + | 0.717444i | \(0.254688\pi\) | |||||||
\(440\) | 162.047 | 7.72528 | ||||||||
\(441\) | −20.9479 | −0.997520 | ||||||||
\(442\) | 9.90839 | 0.471294 | ||||||||
\(443\) | 29.4471 | 1.39908 | 0.699538 | − | 0.714596i | \(-0.253389\pi\) | ||||
0.699538 | + | 0.714596i | \(0.253389\pi\) | |||||||
\(444\) | 35.4599 | 1.68285 | ||||||||
\(445\) | 7.75682 | 0.367709 | ||||||||
\(446\) | 34.1127 | 1.61528 | ||||||||
\(447\) | 48.4478 | 2.29150 | ||||||||
\(448\) | 5.86518 | 0.277104 | ||||||||
\(449\) | −31.0829 | −1.46689 | −0.733446 | − | 0.679748i | \(-0.762089\pi\) | ||||
−0.733446 | + | 0.679748i | \(0.762089\pi\) | |||||||
\(450\) | −46.6074 | −2.19709 | ||||||||
\(451\) | 29.0161 | 1.36631 | ||||||||
\(452\) | −48.0969 | −2.26229 | ||||||||
\(453\) | 2.48215 | 0.116622 | ||||||||
\(454\) | 50.5643 | 2.37310 | ||||||||
\(455\) | 1.10261 | 0.0516910 | ||||||||
\(456\) | 132.254 | 6.19338 | ||||||||
\(457\) | 8.29414 | 0.387984 | 0.193992 | − | 0.981003i | \(-0.437856\pi\) | ||||
0.193992 | + | 0.981003i | \(0.437856\pi\) | |||||||
\(458\) | 27.2443 | 1.27304 | ||||||||
\(459\) | −2.72577 | −0.127228 | ||||||||
\(460\) | 29.5101 | 1.37592 | ||||||||
\(461\) | −15.1643 | −0.706271 | −0.353135 | − | 0.935572i | \(-0.614885\pi\) | ||||
−0.353135 | + | 0.935572i | \(0.614885\pi\) | |||||||
\(462\) | 26.1295 | 1.21565 | ||||||||
\(463\) | −13.0326 | −0.605677 | −0.302838 | − | 0.953042i | \(-0.597934\pi\) | ||||
−0.302838 | + | 0.953042i | \(0.597934\pi\) | |||||||
\(464\) | 64.8631 | 3.01119 | ||||||||
\(465\) | −13.2767 | −0.615692 | ||||||||
\(466\) | −33.1992 | −1.53792 | ||||||||
\(467\) | −1.15375 | −0.0533891 | −0.0266946 | − | 0.999644i | \(-0.508498\pi\) | ||||
−0.0266946 | + | 0.999644i | \(0.508498\pi\) | |||||||
\(468\) | −8.55443 | −0.395429 | ||||||||
\(469\) | −3.05692 | −0.141156 | ||||||||
\(470\) | 1.05146 | 0.0485004 | ||||||||
\(471\) | 8.80556 | 0.405739 | ||||||||
\(472\) | −15.5924 | −0.717700 | ||||||||
\(473\) | −18.1211 | −0.833208 | ||||||||
\(474\) | −62.0821 | −2.85153 | ||||||||
\(475\) | 39.5353 | 1.81400 | ||||||||
\(476\) | 20.3470 | 0.932603 | ||||||||
\(477\) | −3.16108 | −0.144736 | ||||||||
\(478\) | −0.619382 | −0.0283299 | ||||||||
\(479\) | −29.9037 | −1.36634 | −0.683168 | − | 0.730262i | \(-0.739398\pi\) | ||||
−0.683168 | + | 0.730262i | \(0.739398\pi\) | |||||||
\(480\) | −91.8544 | −4.19256 | ||||||||
\(481\) | 1.61956 | 0.0738456 | ||||||||
\(482\) | −31.4203 | −1.43116 | ||||||||
\(483\) | 2.81054 | 0.127884 | ||||||||
\(484\) | 156.955 | 7.13432 | ||||||||
\(485\) | 39.1489 | 1.77766 | ||||||||
\(486\) | −58.4512 | −2.65140 | ||||||||
\(487\) | −7.16599 | −0.324722 | −0.162361 | − | 0.986731i | \(-0.551911\pi\) | ||||
−0.162361 | + | 0.986731i | \(0.551911\pi\) | |||||||
\(488\) | 61.6996 | 2.79301 | ||||||||
\(489\) | 0.562620 | 0.0254425 | ||||||||
\(490\) | −56.6655 | −2.55989 | ||||||||
\(491\) | −18.0096 | −0.812762 | −0.406381 | − | 0.913704i | \(-0.633209\pi\) | ||||
−0.406381 | + | 0.913704i | \(0.633209\pi\) | |||||||
\(492\) | −53.5842 | −2.41576 | ||||||||
\(493\) | 43.7838 | 1.97192 | ||||||||
\(494\) | 10.2268 | 0.460126 | ||||||||
\(495\) | −67.6453 | −3.04043 | ||||||||
\(496\) | −16.5773 | −0.744342 | ||||||||
\(497\) | 0.402002 | 0.0180323 | ||||||||
\(498\) | −3.69590 | −0.165617 | ||||||||
\(499\) | 33.9682 | 1.52062 | 0.760312 | − | 0.649558i | \(-0.225046\pi\) | ||||
0.760312 | + | 0.649558i | \(0.225046\pi\) | |||||||
\(500\) | −9.85166 | −0.440579 | ||||||||
\(501\) | 18.0140 | 0.804806 | ||||||||
\(502\) | 60.6042 | 2.70490 | ||||||||
\(503\) | 34.9480 | 1.55825 | 0.779126 | − | 0.626867i | \(-0.215663\pi\) | ||||
0.779126 | + | 0.626867i | \(0.215663\pi\) | |||||||
\(504\) | −14.6230 | −0.651361 | ||||||||
\(505\) | −25.4790 | −1.13380 | ||||||||
\(506\) | 31.9404 | 1.41992 | ||||||||
\(507\) | 31.5065 | 1.39925 | ||||||||
\(508\) | −90.1136 | −3.99814 | ||||||||
\(509\) | −18.3056 | −0.811382 | −0.405691 | − | 0.914010i | \(-0.632969\pi\) | ||||
−0.405691 | + | 0.914010i | \(0.632969\pi\) | |||||||
\(510\) | −144.693 | −6.40711 | ||||||||
\(511\) | 3.10359 | 0.137295 | ||||||||
\(512\) | 38.2638 | 1.69104 | ||||||||
\(513\) | −2.81337 | −0.124213 | ||||||||
\(514\) | 35.9085 | 1.58386 | ||||||||
\(515\) | 14.4924 | 0.638613 | ||||||||
\(516\) | 33.4643 | 1.47319 | ||||||||
\(517\) | 0.807504 | 0.0355140 | ||||||||
\(518\) | 4.68720 | 0.205944 | ||||||||
\(519\) | 56.6453 | 2.48645 | ||||||||
\(520\) | −13.6678 | −0.599372 | ||||||||
\(521\) | −36.0676 | −1.58015 | −0.790076 | − | 0.613009i | \(-0.789959\pi\) | ||||
−0.790076 | + | 0.613009i | \(0.789959\pi\) | |||||||
\(522\) | −53.2747 | −2.33177 | ||||||||
\(523\) | −35.3948 | −1.54771 | −0.773853 | − | 0.633365i | \(-0.781673\pi\) | ||||
−0.773853 | + | 0.633365i | \(0.781673\pi\) | |||||||
\(524\) | 36.2304 | 1.58273 | ||||||||
\(525\) | −8.51986 | −0.371837 | ||||||||
\(526\) | −67.7761 | −2.95518 | ||||||||
\(527\) | −11.1900 | −0.487443 | ||||||||
\(528\) | −164.620 | −7.16416 | ||||||||
\(529\) | −19.5644 | −0.850627 | ||||||||
\(530\) | −8.55094 | −0.371429 | ||||||||
\(531\) | 6.50896 | 0.282465 | ||||||||
\(532\) | 21.0009 | 0.910504 | ||||||||
\(533\) | −2.44735 | −0.106006 | ||||||||
\(534\) | −15.5043 | −0.670936 | ||||||||
\(535\) | −5.49732 | −0.237670 | ||||||||
\(536\) | 37.8933 | 1.63674 | ||||||||
\(537\) | −29.3329 | −1.26581 | ||||||||
\(538\) | 30.7196 | 1.32442 | ||||||||
\(539\) | −43.5180 | −1.87445 | ||||||||
\(540\) | 6.36582 | 0.273941 | ||||||||
\(541\) | 31.9562 | 1.37390 | 0.686952 | − | 0.726703i | \(-0.258948\pi\) | ||||
0.686952 | + | 0.726703i | \(0.258948\pi\) | |||||||
\(542\) | −70.0597 | −3.00932 | ||||||||
\(543\) | −0.708895 | −0.0304216 | ||||||||
\(544\) | −77.4175 | −3.31925 | ||||||||
\(545\) | 24.5149 | 1.05010 | ||||||||
\(546\) | −2.20388 | −0.0943174 | ||||||||
\(547\) | −15.7117 | −0.671784 | −0.335892 | − | 0.941900i | \(-0.609038\pi\) | ||||
−0.335892 | + | 0.941900i | \(0.609038\pi\) | |||||||
\(548\) | 32.6780 | 1.39593 | ||||||||
\(549\) | −25.7561 | −1.09924 | ||||||||
\(550\) | −96.8239 | −4.12859 | ||||||||
\(551\) | 45.1909 | 1.92520 | ||||||||
\(552\) | −34.8391 | −1.48285 | ||||||||
\(553\) | −5.82268 | −0.247606 | ||||||||
\(554\) | −6.08522 | −0.258536 | ||||||||
\(555\) | −23.6506 | −1.00391 | ||||||||
\(556\) | −28.5189 | −1.20947 | ||||||||
\(557\) | 26.5186 | 1.12363 | 0.561814 | − | 0.827264i | \(-0.310104\pi\) | ||||
0.561814 | + | 0.827264i | \(0.310104\pi\) | |||||||
\(558\) | 13.6156 | 0.576394 | ||||||||
\(559\) | 1.52842 | 0.0646451 | ||||||||
\(560\) | −20.1043 | −0.849560 | ||||||||
\(561\) | −111.121 | −4.69155 | ||||||||
\(562\) | −34.3002 | −1.44687 | ||||||||
\(563\) | 8.16045 | 0.343922 | 0.171961 | − | 0.985104i | \(-0.444990\pi\) | ||||
0.171961 | + | 0.985104i | \(0.444990\pi\) | |||||||
\(564\) | −1.49122 | −0.0627918 | ||||||||
\(565\) | 32.0790 | 1.34957 | ||||||||
\(566\) | 83.3585 | 3.50382 | ||||||||
\(567\) | −5.18692 | −0.217830 | ||||||||
\(568\) | −4.98318 | −0.209089 | ||||||||
\(569\) | −43.7433 | −1.83381 | −0.916907 | − | 0.399101i | \(-0.869322\pi\) | ||||
−0.916907 | + | 0.399101i | \(0.869322\pi\) | |||||||
\(570\) | −149.343 | −6.25529 | ||||||||
\(571\) | −8.93501 | −0.373919 | −0.186959 | − | 0.982368i | \(-0.559863\pi\) | ||||
−0.186959 | + | 0.982368i | \(0.559863\pi\) | |||||||
\(572\) | −17.7713 | −0.743055 | ||||||||
\(573\) | 62.7114 | 2.61981 | ||||||||
\(574\) | −7.08292 | −0.295635 | ||||||||
\(575\) | −10.4146 | −0.434318 | ||||||||
\(576\) | 30.3498 | 1.26458 | ||||||||
\(577\) | −32.6009 | −1.35720 | −0.678598 | − | 0.734510i | \(-0.737412\pi\) | ||||
−0.678598 | + | 0.734510i | \(0.737412\pi\) | |||||||
\(578\) | −77.3420 | −3.21700 | ||||||||
\(579\) | −8.18829 | −0.340294 | ||||||||
\(580\) | −102.254 | −4.24586 | ||||||||
\(581\) | −0.346638 | −0.0143810 | ||||||||
\(582\) | −78.2506 | −3.24359 | ||||||||
\(583\) | −6.56696 | −0.271976 | ||||||||
\(584\) | −38.4717 | −1.59197 | ||||||||
\(585\) | 5.70552 | 0.235894 | ||||||||
\(586\) | 70.5168 | 2.91302 | ||||||||
\(587\) | 23.2205 | 0.958414 | 0.479207 | − | 0.877702i | \(-0.340924\pi\) | ||||
0.479207 | + | 0.877702i | \(0.340924\pi\) | |||||||
\(588\) | 80.3650 | 3.31420 | ||||||||
\(589\) | −11.5496 | −0.475893 | ||||||||
\(590\) | 17.6071 | 0.724875 | ||||||||
\(591\) | 7.05195 | 0.290078 | ||||||||
\(592\) | −29.5301 | −1.21368 | ||||||||
\(593\) | −7.00612 | −0.287707 | −0.143853 | − | 0.989599i | \(-0.545949\pi\) | ||||
−0.143853 | + | 0.989599i | \(0.545949\pi\) | |||||||
\(594\) | 6.89008 | 0.282703 | ||||||||
\(595\) | −13.5708 | −0.556347 | ||||||||
\(596\) | −95.3629 | −3.90622 | ||||||||
\(597\) | 33.0554 | 1.35287 | ||||||||
\(598\) | −2.69400 | −0.110166 | ||||||||
\(599\) | −33.3961 | −1.36453 | −0.682264 | − | 0.731106i | \(-0.739004\pi\) | ||||
−0.682264 | + | 0.731106i | \(0.739004\pi\) | |||||||
\(600\) | 105.611 | 4.31156 | ||||||||
\(601\) | 37.4337 | 1.52695 | 0.763476 | − | 0.645836i | \(-0.223491\pi\) | ||||
0.763476 | + | 0.645836i | \(0.223491\pi\) | |||||||
\(602\) | 4.42342 | 0.180285 | ||||||||
\(603\) | −15.8183 | −0.644170 | ||||||||
\(604\) | −4.88578 | −0.198799 | ||||||||
\(605\) | −104.684 | −4.25600 | ||||||||
\(606\) | 50.9272 | 2.06877 | ||||||||
\(607\) | 4.71995 | 0.191577 | 0.0957885 | − | 0.995402i | \(-0.469463\pi\) | ||||
0.0957885 | + | 0.995402i | \(0.469463\pi\) | |||||||
\(608\) | −79.9055 | −3.24059 | ||||||||
\(609\) | −9.73864 | −0.394630 | ||||||||
\(610\) | −69.6719 | −2.82093 | ||||||||
\(611\) | −0.0681086 | −0.00275538 | ||||||||
\(612\) | 105.287 | 4.25597 | ||||||||
\(613\) | −21.0932 | −0.851946 | −0.425973 | − | 0.904736i | \(-0.640068\pi\) | ||||
−0.425973 | + | 0.904736i | \(0.640068\pi\) | |||||||
\(614\) | 81.2493 | 3.27895 | ||||||||
\(615\) | 35.7388 | 1.44113 | ||||||||
\(616\) | −30.3784 | −1.22398 | ||||||||
\(617\) | 36.2892 | 1.46095 | 0.730473 | − | 0.682941i | \(-0.239299\pi\) | ||||
0.730473 | + | 0.682941i | \(0.239299\pi\) | |||||||
\(618\) | −28.9674 | −1.16524 | ||||||||
\(619\) | −43.3640 | −1.74295 | −0.871473 | − | 0.490444i | \(-0.836835\pi\) | ||||
−0.871473 | + | 0.490444i | \(0.836835\pi\) | |||||||
\(620\) | 26.1333 | 1.04954 | ||||||||
\(621\) | 0.741111 | 0.0297398 | ||||||||
\(622\) | 38.7628 | 1.55425 | ||||||||
\(623\) | −1.45415 | −0.0582591 | ||||||||
\(624\) | 13.8848 | 0.555837 | ||||||||
\(625\) | −21.5232 | −0.860928 | ||||||||
\(626\) | −65.9801 | −2.63710 | ||||||||
\(627\) | −114.693 | −4.58038 | ||||||||
\(628\) | −17.3325 | −0.691643 | ||||||||
\(629\) | −19.9334 | −0.794796 | ||||||||
\(630\) | 16.5124 | 0.657872 | ||||||||
\(631\) | −22.2315 | −0.885022 | −0.442511 | − | 0.896763i | \(-0.645912\pi\) | ||||
−0.442511 | + | 0.896763i | \(0.645912\pi\) | |||||||
\(632\) | 72.1773 | 2.87106 | ||||||||
\(633\) | −20.1115 | −0.799358 | ||||||||
\(634\) | 49.6618 | 1.97232 | ||||||||
\(635\) | 60.1027 | 2.38510 | ||||||||
\(636\) | 12.1272 | 0.480877 | ||||||||
\(637\) | 3.67051 | 0.145431 | ||||||||
\(638\) | −110.675 | −4.38166 | ||||||||
\(639\) | 2.08019 | 0.0822911 | ||||||||
\(640\) | 8.08642 | 0.319644 | ||||||||
\(641\) | 26.9528 | 1.06457 | 0.532285 | − | 0.846565i | \(-0.321333\pi\) | ||||
0.532285 | + | 0.846565i | \(0.321333\pi\) | |||||||
\(642\) | 10.9880 | 0.433661 | ||||||||
\(643\) | 6.94492 | 0.273881 | 0.136941 | − | 0.990579i | \(-0.456273\pi\) | ||||
0.136941 | + | 0.990579i | \(0.456273\pi\) | |||||||
\(644\) | −5.53216 | −0.217998 | ||||||||
\(645\) | −22.3196 | −0.878833 | ||||||||
\(646\) | −125.871 | −4.95231 | ||||||||
\(647\) | −2.19558 | −0.0863171 | −0.0431586 | − | 0.999068i | \(-0.513742\pi\) | ||||
−0.0431586 | + | 0.999068i | \(0.513742\pi\) | |||||||
\(648\) | 64.2965 | 2.52581 | ||||||||
\(649\) | 13.5219 | 0.530783 | ||||||||
\(650\) | 8.16658 | 0.320320 | ||||||||
\(651\) | 2.48894 | 0.0975492 | ||||||||
\(652\) | −1.10744 | −0.0433707 | ||||||||
\(653\) | −15.9755 | −0.625168 | −0.312584 | − | 0.949890i | \(-0.601195\pi\) | ||||
−0.312584 | + | 0.949890i | \(0.601195\pi\) | |||||||
\(654\) | −49.0002 | −1.91606 | ||||||||
\(655\) | −24.1645 | −0.944183 | ||||||||
\(656\) | 44.6235 | 1.74226 | ||||||||
\(657\) | 16.0598 | 0.626551 | ||||||||
\(658\) | −0.197114 | −0.00768432 | ||||||||
\(659\) | −31.7292 | −1.23599 | −0.617996 | − | 0.786181i | \(-0.712055\pi\) | ||||
−0.617996 | + | 0.786181i | \(0.712055\pi\) | |||||||
\(660\) | 259.516 | 10.1016 | ||||||||
\(661\) | 8.11186 | 0.315515 | 0.157757 | − | 0.987478i | \(-0.449574\pi\) | ||||
0.157757 | + | 0.987478i | \(0.449574\pi\) | |||||||
\(662\) | 9.43556 | 0.366723 | ||||||||
\(663\) | 9.37249 | 0.363997 | ||||||||
\(664\) | 4.29688 | 0.166751 | ||||||||
\(665\) | −14.0069 | −0.543164 | ||||||||
\(666\) | 24.2543 | 0.939834 | ||||||||
\(667\) | −11.9044 | −0.460941 | ||||||||
\(668\) | −35.4581 | −1.37191 | ||||||||
\(669\) | 32.2677 | 1.24754 | ||||||||
\(670\) | −42.7895 | −1.65310 | ||||||||
\(671\) | −53.5066 | −2.06560 | ||||||||
\(672\) | 17.2196 | 0.664262 | ||||||||
\(673\) | −33.1516 | −1.27790 | −0.638949 | − | 0.769249i | \(-0.720631\pi\) | ||||
−0.638949 | + | 0.769249i | \(0.720631\pi\) | |||||||
\(674\) | 52.3301 | 2.01568 | ||||||||
\(675\) | −2.24660 | −0.0864717 | ||||||||
\(676\) | −62.0162 | −2.38524 | ||||||||
\(677\) | −23.4270 | −0.900372 | −0.450186 | − | 0.892935i | \(-0.648642\pi\) | ||||
−0.450186 | + | 0.892935i | \(0.648642\pi\) | |||||||
\(678\) | −64.1193 | −2.46249 | ||||||||
\(679\) | −7.33912 | −0.281650 | ||||||||
\(680\) | 168.221 | 6.45100 | ||||||||
\(681\) | 47.8295 | 1.83283 | ||||||||
\(682\) | 28.2855 | 1.08311 | ||||||||
\(683\) | 9.70710 | 0.371432 | 0.185716 | − | 0.982603i | \(-0.440540\pi\) | ||||
0.185716 | + | 0.982603i | \(0.440540\pi\) | |||||||
\(684\) | 108.671 | 4.15513 | ||||||||
\(685\) | −21.7951 | −0.832749 | ||||||||
\(686\) | 21.8440 | 0.834008 | ||||||||
\(687\) | 25.7708 | 0.983217 | ||||||||
\(688\) | −27.8682 | −1.06247 | ||||||||
\(689\) | 0.553887 | 0.0211014 | ||||||||
\(690\) | 39.3407 | 1.49768 | ||||||||
\(691\) | −16.7230 | −0.636172 | −0.318086 | − | 0.948062i | \(-0.603040\pi\) | ||||
−0.318086 | + | 0.948062i | \(0.603040\pi\) | |||||||
\(692\) | −111.498 | −4.23853 | ||||||||
\(693\) | 12.6812 | 0.481720 | ||||||||
\(694\) | 33.7096 | 1.27960 | ||||||||
\(695\) | 19.0211 | 0.721513 | ||||||||
\(696\) | 120.719 | 4.57584 | ||||||||
\(697\) | 30.1217 | 1.14094 | ||||||||
\(698\) | 38.5453 | 1.45896 | ||||||||
\(699\) | −31.4037 | −1.18780 | ||||||||
\(700\) | 16.7702 | 0.633853 | ||||||||
\(701\) | −14.6816 | −0.554517 | −0.277259 | − | 0.960795i | \(-0.589426\pi\) | ||||
−0.277259 | + | 0.960795i | \(0.589426\pi\) | |||||||
\(702\) | −0.581141 | −0.0219338 | ||||||||
\(703\) | −20.5740 | −0.775963 | ||||||||
\(704\) | 63.0499 | 2.37628 | ||||||||
\(705\) | 0.994596 | 0.0374586 | ||||||||
\(706\) | −81.4132 | −3.06403 | ||||||||
\(707\) | 4.77646 | 0.179637 | ||||||||
\(708\) | −24.9711 | −0.938471 | ||||||||
\(709\) | −23.2063 | −0.871531 | −0.435766 | − | 0.900060i | \(-0.643522\pi\) | ||||
−0.435766 | + | 0.900060i | \(0.643522\pi\) | |||||||
\(710\) | 5.62705 | 0.211180 | ||||||||
\(711\) | −30.1299 | −1.12996 | ||||||||
\(712\) | 18.0254 | 0.675531 | ||||||||
\(713\) | 3.04245 | 0.113941 | ||||||||
\(714\) | 27.1251 | 1.01513 | ||||||||
\(715\) | 11.8529 | 0.443272 | ||||||||
\(716\) | 57.7379 | 2.15776 | ||||||||
\(717\) | −0.585883 | −0.0218802 | ||||||||
\(718\) | 2.40342 | 0.0896950 | ||||||||
\(719\) | 50.5760 | 1.88617 | 0.943083 | − | 0.332556i | \(-0.107911\pi\) | ||||
0.943083 | + | 0.332556i | \(0.107911\pi\) | |||||||
\(720\) | −104.031 | −3.87701 | ||||||||
\(721\) | −2.71685 | −0.101181 | ||||||||
\(722\) | −80.0583 | −2.97946 | ||||||||
\(723\) | −29.7210 | −1.10533 | ||||||||
\(724\) | 1.39536 | 0.0518582 | ||||||||
\(725\) | 36.0870 | 1.34024 | ||||||||
\(726\) | 209.241 | 7.76566 | ||||||||
\(727\) | 25.1604 | 0.933148 | 0.466574 | − | 0.884482i | \(-0.345488\pi\) | ||||
0.466574 | + | 0.884482i | \(0.345488\pi\) | |||||||
\(728\) | 2.56225 | 0.0949634 | ||||||||
\(729\) | −29.8175 | −1.10435 | ||||||||
\(730\) | 43.4427 | 1.60789 | ||||||||
\(731\) | −18.8116 | −0.695771 | ||||||||
\(732\) | 98.8111 | 3.65216 | ||||||||
\(733\) | −43.2926 | −1.59905 | −0.799524 | − | 0.600635i | \(-0.794915\pi\) | ||||
−0.799524 | + | 0.600635i | \(0.794915\pi\) | |||||||
\(734\) | 53.5092 | 1.97506 | ||||||||
\(735\) | −53.6008 | −1.97709 | ||||||||
\(736\) | 21.0491 | 0.775880 | ||||||||
\(737\) | −32.8615 | −1.21047 | ||||||||
\(738\) | −36.6511 | −1.34915 | ||||||||
\(739\) | −47.3007 | −1.73998 | −0.869992 | − | 0.493065i | \(-0.835876\pi\) | ||||
−0.869992 | + | 0.493065i | \(0.835876\pi\) | |||||||
\(740\) | 46.5529 | 1.71132 | ||||||||
\(741\) | 9.67370 | 0.355372 | ||||||||
\(742\) | 1.60302 | 0.0588486 | ||||||||
\(743\) | 4.94915 | 0.181567 | 0.0907834 | − | 0.995871i | \(-0.471063\pi\) | ||||
0.0907834 | + | 0.995871i | \(0.471063\pi\) | |||||||
\(744\) | −30.8526 | −1.13111 | ||||||||
\(745\) | 63.6038 | 2.33026 | ||||||||
\(746\) | −73.4446 | −2.68900 | ||||||||
\(747\) | −1.79370 | −0.0656282 | ||||||||
\(748\) | 218.727 | 7.99746 | ||||||||
\(749\) | 1.03056 | 0.0376560 | ||||||||
\(750\) | −13.1335 | −0.479568 | ||||||||
\(751\) | 1.07182 | 0.0391112 | 0.0195556 | − | 0.999809i | \(-0.493775\pi\) | ||||
0.0195556 | + | 0.999809i | \(0.493775\pi\) | |||||||
\(752\) | 1.24185 | 0.0452857 | ||||||||
\(753\) | 57.3264 | 2.08909 | ||||||||
\(754\) | 9.33482 | 0.339954 | ||||||||
\(755\) | 3.25865 | 0.118594 | ||||||||
\(756\) | −1.19338 | −0.0434028 | ||||||||
\(757\) | 24.3791 | 0.886075 | 0.443037 | − | 0.896503i | \(-0.353901\pi\) | ||||
0.443037 | + | 0.896503i | \(0.353901\pi\) | |||||||
\(758\) | −7.69504 | −0.279496 | ||||||||
\(759\) | 30.2129 | 1.09666 | ||||||||
\(760\) | 173.628 | 6.29814 | ||||||||
\(761\) | −5.04882 | −0.183020 | −0.0915098 | − | 0.995804i | \(-0.529169\pi\) | ||||
−0.0915098 | + | 0.995804i | \(0.529169\pi\) | |||||||
\(762\) | −120.133 | −4.35195 | ||||||||
\(763\) | −4.59572 | −0.166376 | ||||||||
\(764\) | −123.439 | −4.46585 | ||||||||
\(765\) | −70.2229 | −2.53891 | ||||||||
\(766\) | 74.9471 | 2.70795 | ||||||||
\(767\) | −1.14050 | −0.0411812 | ||||||||
\(768\) | 31.4996 | 1.13665 | ||||||||
\(769\) | −22.2005 | −0.800572 | −0.400286 | − | 0.916390i | \(-0.631089\pi\) | ||||
−0.400286 | + | 0.916390i | \(0.631089\pi\) | |||||||
\(770\) | 34.3036 | 1.23622 | ||||||||
\(771\) | 33.9664 | 1.22327 | ||||||||
\(772\) | 16.1175 | 0.580082 | ||||||||
\(773\) | 15.3380 | 0.551668 | 0.275834 | − | 0.961205i | \(-0.411046\pi\) | ||||
0.275834 | + | 0.961205i | \(0.411046\pi\) | |||||||
\(774\) | 22.8893 | 0.822739 | ||||||||
\(775\) | −9.22287 | −0.331295 | ||||||||
\(776\) | 90.9749 | 3.26581 | ||||||||
\(777\) | 4.43370 | 0.159058 | ||||||||
\(778\) | −63.1739 | −2.26489 | ||||||||
\(779\) | 31.0897 | 1.11391 | ||||||||
\(780\) | −21.8888 | −0.783743 | ||||||||
\(781\) | 4.32147 | 0.154634 | ||||||||
\(782\) | 33.1575 | 1.18571 | ||||||||
\(783\) | −2.56798 | −0.0917722 | ||||||||
\(784\) | −66.9259 | −2.39021 | ||||||||
\(785\) | 11.5602 | 0.412601 | ||||||||
\(786\) | 48.2997 | 1.72279 | ||||||||
\(787\) | −16.4908 | −0.587832 | −0.293916 | − | 0.955831i | \(-0.594959\pi\) | ||||
−0.293916 | + | 0.955831i | \(0.594959\pi\) | |||||||
\(788\) | −13.8808 | −0.494483 | ||||||||
\(789\) | −64.1104 | −2.28239 | ||||||||
\(790\) | −81.5033 | −2.89976 | ||||||||
\(791\) | −6.01375 | −0.213824 | ||||||||
\(792\) | −157.195 | −5.58569 | ||||||||
\(793\) | 4.51300 | 0.160261 | ||||||||
\(794\) | −26.6014 | −0.944047 | ||||||||
\(795\) | −8.08846 | −0.286868 | ||||||||
\(796\) | −65.0651 | −2.30617 | ||||||||
\(797\) | −16.1067 | −0.570528 | −0.285264 | − | 0.958449i | \(-0.592081\pi\) | ||||
−0.285264 | + | 0.958449i | \(0.592081\pi\) | |||||||
\(798\) | 27.9968 | 0.991078 | ||||||||
\(799\) | 0.838273 | 0.0296560 | ||||||||
\(800\) | −63.8081 | −2.25596 | ||||||||
\(801\) | −7.52458 | −0.265868 | ||||||||
\(802\) | −11.3702 | −0.401497 | ||||||||
\(803\) | 33.3631 | 1.17736 | ||||||||
\(804\) | 60.6855 | 2.14021 | ||||||||
\(805\) | 3.68976 | 0.130047 | ||||||||
\(806\) | −2.38573 | −0.0840339 | ||||||||
\(807\) | 29.0582 | 1.02290 | ||||||||
\(808\) | −59.2084 | −2.08295 | ||||||||
\(809\) | −35.3972 | −1.24450 | −0.622250 | − | 0.782819i | \(-0.713781\pi\) | ||||
−0.622250 | + | 0.782819i | \(0.713781\pi\) | |||||||
\(810\) | −72.6043 | −2.55105 | ||||||||
\(811\) | 16.7415 | 0.587874 | 0.293937 | − | 0.955825i | \(-0.405034\pi\) | ||||
0.293937 | + | 0.955825i | \(0.405034\pi\) | |||||||
\(812\) | 19.1692 | 0.672706 | ||||||||
\(813\) | −66.2705 | −2.32421 | ||||||||
\(814\) | 50.3868 | 1.76605 | ||||||||
\(815\) | 0.738625 | 0.0258729 | ||||||||
\(816\) | −170.892 | −5.98243 | ||||||||
\(817\) | −19.4161 | −0.679285 | ||||||||
\(818\) | −23.5111 | −0.822046 | ||||||||
\(819\) | −1.06959 | −0.0373747 | ||||||||
\(820\) | −70.3470 | −2.45662 | ||||||||
\(821\) | −17.7154 | −0.618272 | −0.309136 | − | 0.951018i | \(-0.600040\pi\) | ||||
−0.309136 | + | 0.951018i | \(0.600040\pi\) | |||||||
\(822\) | 43.5639 | 1.51947 | ||||||||
\(823\) | 21.3083 | 0.742759 | 0.371379 | − | 0.928481i | \(-0.378885\pi\) | ||||
0.371379 | + | 0.928481i | \(0.378885\pi\) | |||||||
\(824\) | 33.6777 | 1.17322 | ||||||||
\(825\) | −91.5872 | −3.18866 | ||||||||
\(826\) | −3.30075 | −0.114848 | ||||||||
\(827\) | −19.6490 | −0.683262 | −0.341631 | − | 0.939834i | \(-0.610979\pi\) | ||||
−0.341631 | + | 0.939834i | \(0.610979\pi\) | |||||||
\(828\) | −28.6266 | −0.994843 | ||||||||
\(829\) | −39.7903 | −1.38197 | −0.690987 | − | 0.722867i | \(-0.742824\pi\) | ||||
−0.690987 | + | 0.722867i | \(0.742824\pi\) | |||||||
\(830\) | −4.85209 | −0.168418 | ||||||||
\(831\) | −5.75610 | −0.199677 | ||||||||
\(832\) | −5.31792 | −0.184366 | ||||||||
\(833\) | −45.1762 | −1.56526 | ||||||||
\(834\) | −38.0193 | −1.31650 | ||||||||
\(835\) | 23.6493 | 0.818419 | ||||||||
\(836\) | 225.757 | 7.80795 | ||||||||
\(837\) | 0.656308 | 0.0226853 | ||||||||
\(838\) | 87.0162 | 3.00593 | ||||||||
\(839\) | 10.5594 | 0.364552 | 0.182276 | − | 0.983247i | \(-0.441654\pi\) | ||||
0.182276 | + | 0.983247i | \(0.441654\pi\) | |||||||
\(840\) | −37.4168 | −1.29100 | ||||||||
\(841\) | 12.2493 | 0.422389 | ||||||||
\(842\) | −66.1832 | −2.28082 | ||||||||
\(843\) | −32.4450 | −1.11747 | ||||||||
\(844\) | 39.5866 | 1.36263 | ||||||||
\(845\) | 41.3627 | 1.42292 | ||||||||
\(846\) | −1.01998 | −0.0350678 | ||||||||
\(847\) | 19.6247 | 0.674313 | ||||||||
\(848\) | −10.0993 | −0.346810 | ||||||||
\(849\) | 78.8500 | 2.70613 | ||||||||
\(850\) | −100.513 | −3.44758 | ||||||||
\(851\) | 5.41971 | 0.185785 | ||||||||
\(852\) | −7.98049 | −0.273407 | ||||||||
\(853\) | −40.7463 | −1.39513 | −0.697563 | − | 0.716523i | \(-0.745732\pi\) | ||||
−0.697563 | + | 0.716523i | \(0.745732\pi\) | |||||||
\(854\) | 13.0612 | 0.446943 | ||||||||
\(855\) | −72.4797 | −2.47875 | ||||||||
\(856\) | −12.7747 | −0.436632 | ||||||||
\(857\) | 30.8214 | 1.05284 | 0.526420 | − | 0.850225i | \(-0.323534\pi\) | ||||
0.526420 | + | 0.850225i | \(0.323534\pi\) | |||||||
\(858\) | −23.6914 | −0.808811 | ||||||||
\(859\) | −14.8826 | −0.507789 | −0.253895 | − | 0.967232i | \(-0.581712\pi\) | ||||
−0.253895 | + | 0.967232i | \(0.581712\pi\) | |||||||
\(860\) | 43.9330 | 1.49810 | ||||||||
\(861\) | −6.69984 | −0.228330 | ||||||||
\(862\) | 48.2411 | 1.64310 | ||||||||
\(863\) | 43.9674 | 1.49667 | 0.748333 | − | 0.663323i | \(-0.230854\pi\) | ||||
0.748333 | + | 0.663323i | \(0.230854\pi\) | |||||||
\(864\) | 4.54064 | 0.154476 | ||||||||
\(865\) | 74.3657 | 2.52851 | ||||||||
\(866\) | −56.5984 | −1.92329 | ||||||||
\(867\) | −73.1590 | −2.48461 | ||||||||
\(868\) | −4.89913 | −0.166287 | ||||||||
\(869\) | −62.5930 | −2.12332 | ||||||||
\(870\) | −136.317 | −4.62159 | ||||||||
\(871\) | 2.77169 | 0.0939151 | ||||||||
\(872\) | 56.9681 | 1.92918 | ||||||||
\(873\) | −37.9768 | −1.28532 | ||||||||
\(874\) | 34.2231 | 1.15761 | ||||||||
\(875\) | −1.23179 | −0.0416422 | ||||||||
\(876\) | −61.6119 | −2.08167 | ||||||||
\(877\) | −28.9962 | −0.979133 | −0.489567 | − | 0.871966i | \(-0.662845\pi\) | ||||
−0.489567 | + | 0.871966i | \(0.662845\pi\) | |||||||
\(878\) | −76.6006 | −2.58514 | ||||||||
\(879\) | 66.7029 | 2.24983 | ||||||||
\(880\) | −216.118 | −7.28533 | ||||||||
\(881\) | −6.97946 | −0.235144 | −0.117572 | − | 0.993064i | \(-0.537511\pi\) | ||||
−0.117572 | + | 0.993064i | \(0.537511\pi\) | |||||||
\(882\) | 54.9690 | 1.85090 | ||||||||
\(883\) | 52.4084 | 1.76368 | 0.881841 | − | 0.471547i | \(-0.156304\pi\) | ||||
0.881841 | + | 0.471547i | \(0.156304\pi\) | |||||||
\(884\) | −18.4485 | −0.620489 | ||||||||
\(885\) | 16.6549 | 0.559847 | ||||||||
\(886\) | −77.2715 | −2.59599 | ||||||||
\(887\) | −20.4074 | −0.685215 | −0.342607 | − | 0.939479i | \(-0.611310\pi\) | ||||
−0.342607 | + | 0.939479i | \(0.611310\pi\) | |||||||
\(888\) | −54.9596 | −1.84432 | ||||||||
\(889\) | −11.2673 | −0.377892 | ||||||||
\(890\) | −20.3545 | −0.682284 | ||||||||
\(891\) | −55.7587 | −1.86799 | ||||||||
\(892\) | −63.5145 | −2.12662 | ||||||||
\(893\) | 0.865213 | 0.0289533 | ||||||||
\(894\) | −127.131 | −4.25189 | ||||||||
\(895\) | −38.5092 | −1.28722 | ||||||||
\(896\) | −1.51593 | −0.0506438 | ||||||||
\(897\) | −2.54830 | −0.0850851 | ||||||||
\(898\) | 81.5638 | 2.72182 | ||||||||
\(899\) | −10.5422 | −0.351603 | ||||||||
\(900\) | 86.7785 | 2.89262 | ||||||||
\(901\) | −6.81718 | −0.227113 | ||||||||
\(902\) | −76.1404 | −2.53520 | ||||||||
\(903\) | 4.18418 | 0.139241 | ||||||||
\(904\) | 74.5457 | 2.47935 | ||||||||
\(905\) | −0.930659 | −0.0309361 | ||||||||
\(906\) | −6.51336 | −0.216392 | ||||||||
\(907\) | −10.9648 | −0.364081 | −0.182040 | − | 0.983291i | \(-0.558270\pi\) | ||||
−0.182040 | + | 0.983291i | \(0.558270\pi\) | |||||||
\(908\) | −94.1458 | −3.12434 | ||||||||
\(909\) | 24.7161 | 0.819783 | ||||||||
\(910\) | −2.89332 | −0.0959127 | ||||||||
\(911\) | 0.704225 | 0.0233320 | 0.0116660 | − | 0.999932i | \(-0.496287\pi\) | ||||
0.0116660 | + | 0.999932i | \(0.496287\pi\) | |||||||
\(912\) | −176.385 | −5.84068 | ||||||||
\(913\) | −3.72631 | −0.123323 | ||||||||
\(914\) | −21.7645 | −0.719904 | ||||||||
\(915\) | −65.9037 | −2.17871 | ||||||||
\(916\) | −50.7262 | −1.67604 | ||||||||
\(917\) | 4.53003 | 0.149595 | ||||||||
\(918\) | 7.15262 | 0.236072 | ||||||||
\(919\) | 24.9517 | 0.823081 | 0.411540 | − | 0.911392i | \(-0.364991\pi\) | ||||
0.411540 | + | 0.911392i | \(0.364991\pi\) | |||||||
\(920\) | −45.7379 | −1.50793 | ||||||||
\(921\) | 76.8549 | 2.53245 | ||||||||
\(922\) | 39.7922 | 1.31049 | ||||||||
\(923\) | −0.364493 | −0.0119974 | ||||||||
\(924\) | −48.6505 | −1.60049 | ||||||||
\(925\) | −16.4293 | −0.540191 | ||||||||
\(926\) | 34.1986 | 1.12383 | ||||||||
\(927\) | −14.0585 | −0.461743 | ||||||||
\(928\) | −72.9360 | −2.39424 | ||||||||
\(929\) | 49.3087 | 1.61777 | 0.808883 | − | 0.587970i | \(-0.200073\pi\) | ||||
0.808883 | + | 0.587970i | \(0.200073\pi\) | |||||||
\(930\) | 34.8391 | 1.14242 | ||||||||
\(931\) | −46.6281 | −1.52817 | ||||||||
\(932\) | 61.8138 | 2.02478 | ||||||||
\(933\) | 36.6664 | 1.20040 | ||||||||
\(934\) | 3.02752 | 0.0990636 | ||||||||
\(935\) | −145.884 | −4.77090 | ||||||||
\(936\) | 13.2586 | 0.433370 | ||||||||
\(937\) | −40.0037 | −1.30686 | −0.653432 | − | 0.756985i | \(-0.726671\pi\) | ||||
−0.653432 | + | 0.756985i | \(0.726671\pi\) | |||||||
\(938\) | 8.02160 | 0.261914 | ||||||||
\(939\) | −62.4116 | −2.03673 | ||||||||
\(940\) | −1.95772 | −0.0638539 | ||||||||
\(941\) | 13.6800 | 0.445955 | 0.222977 | − | 0.974824i | \(-0.428422\pi\) | ||||
0.222977 | + | 0.974824i | \(0.428422\pi\) | |||||||
\(942\) | −23.1065 | −0.752849 | ||||||||
\(943\) | −8.18982 | −0.266697 | ||||||||
\(944\) | 20.7953 | 0.676828 | ||||||||
\(945\) | 0.795944 | 0.0258921 | ||||||||
\(946\) | 47.5511 | 1.54602 | ||||||||
\(947\) | 45.8467 | 1.48982 | 0.744908 | − | 0.667167i | \(-0.232493\pi\) | ||||
0.744908 | + | 0.667167i | \(0.232493\pi\) | |||||||
\(948\) | 115.591 | 3.75422 | ||||||||
\(949\) | −2.81400 | −0.0913463 | ||||||||
\(950\) | −103.744 | −3.36589 | ||||||||
\(951\) | 46.9758 | 1.52330 | ||||||||
\(952\) | −31.5359 | −1.02209 | ||||||||
\(953\) | 56.5045 | 1.83036 | 0.915179 | − | 0.403047i | \(-0.132049\pi\) | ||||
0.915179 | + | 0.403047i | \(0.132049\pi\) | |||||||
\(954\) | 8.29493 | 0.268558 | ||||||||
\(955\) | 82.3294 | 2.66412 | ||||||||
\(956\) | 1.15323 | 0.0372981 | ||||||||
\(957\) | −104.689 | −3.38411 | ||||||||
\(958\) | 78.4696 | 2.53524 | ||||||||
\(959\) | 4.08586 | 0.131939 | ||||||||
\(960\) | 77.6580 | 2.50640 | ||||||||
\(961\) | −28.3057 | −0.913087 | ||||||||
\(962\) | −4.24985 | −0.137021 | ||||||||
\(963\) | 5.33273 | 0.171845 | ||||||||
\(964\) | 58.5016 | 1.88421 | ||||||||
\(965\) | −10.7498 | −0.346049 | ||||||||
\(966\) | −7.37507 | −0.237289 | ||||||||
\(967\) | −7.79697 | −0.250734 | −0.125367 | − | 0.992110i | \(-0.540011\pi\) | ||||
−0.125367 | + | 0.992110i | \(0.540011\pi\) | |||||||
\(968\) | −243.266 | −7.81886 | ||||||||
\(969\) | −119.063 | −3.82485 | ||||||||
\(970\) | −102.730 | −3.29845 | ||||||||
\(971\) | −36.8392 | −1.18223 | −0.591113 | − | 0.806589i | \(-0.701311\pi\) | ||||
−0.591113 | + | 0.806589i | \(0.701311\pi\) | |||||||
\(972\) | 108.831 | 3.49074 | ||||||||
\(973\) | −3.56583 | −0.114315 | ||||||||
\(974\) | 18.8041 | 0.602522 | ||||||||
\(975\) | 7.72489 | 0.247394 | ||||||||
\(976\) | −82.2873 | −2.63395 | ||||||||
\(977\) | 11.3592 | 0.363412 | 0.181706 | − | 0.983353i | \(-0.441838\pi\) | ||||
0.181706 | + | 0.983353i | \(0.441838\pi\) | |||||||
\(978\) | −1.47636 | −0.0472087 | ||||||||
\(979\) | −15.6319 | −0.499596 | ||||||||
\(980\) | 105.506 | 3.37026 | ||||||||
\(981\) | −23.7809 | −0.759266 | ||||||||
\(982\) | 47.2585 | 1.50808 | ||||||||
\(983\) | 3.31628 | 0.105773 | 0.0528864 | − | 0.998601i | \(-0.483158\pi\) | ||||
0.0528864 | + | 0.998601i | \(0.483158\pi\) | |||||||
\(984\) | 83.0505 | 2.64755 | ||||||||
\(985\) | 9.25802 | 0.294985 | ||||||||
\(986\) | −114.892 | −3.65891 | ||||||||
\(987\) | −0.186454 | −0.00593488 | ||||||||
\(988\) | −19.0413 | −0.605786 | ||||||||
\(989\) | 5.11470 | 0.162638 | ||||||||
\(990\) | 177.506 | 5.64152 | ||||||||
\(991\) | 44.0319 | 1.39872 | 0.699360 | − | 0.714770i | \(-0.253468\pi\) | ||||
0.699360 | + | 0.714770i | \(0.253468\pi\) | |||||||
\(992\) | 18.6405 | 0.591837 | ||||||||
\(993\) | 8.92524 | 0.283234 | ||||||||
\(994\) | −1.05488 | −0.0334589 | ||||||||
\(995\) | 43.3962 | 1.37575 | ||||||||
\(996\) | 6.88140 | 0.218045 | ||||||||
\(997\) | −30.5965 | −0.969002 | −0.484501 | − | 0.874791i | \(-0.660999\pi\) | ||||
−0.484501 | + | 0.874791i | \(0.660999\pi\) | |||||||
\(998\) | −89.1351 | −2.82152 | ||||||||
\(999\) | 1.16912 | 0.0369894 |
(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 | 8003.2.a.b.1.6 | ✓ | 153 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8003.2.a.b.1.6 | ✓ | 153 | 1.1 | even | 1 | trivial |