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: | \(0\) |
Dimension: | \(47\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
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 | ||||||||
\(3\) | −2.28341 | −1.31833 | −0.659165 | − | 0.751999i | \(-0.729090\pi\) | ||||
−0.659165 | + | 0.751999i | \(0.729090\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 4.33431 | 1.93836 | 0.969180 | − | 0.246352i | \(-0.0792321\pi\) | ||||
0.969180 | + | 0.246352i | \(0.0792321\pi\) | |||||||
\(6\) | −2.28341 | −0.932200 | ||||||||
\(7\) | −0.955796 | −0.361257 | −0.180628 | − | 0.983551i | \(-0.557813\pi\) | ||||
−0.180628 | + | 0.983551i | \(0.557813\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.21398 | 0.737993 | ||||||||
\(10\) | 4.33431 | 1.37063 | ||||||||
\(11\) | −5.13031 | −1.54685 | −0.773423 | − | 0.633890i | \(-0.781457\pi\) | ||||
−0.773423 | + | 0.633890i | \(0.781457\pi\) | |||||||
\(12\) | −2.28341 | −0.659165 | ||||||||
\(13\) | −0.223732 | −0.0620522 | −0.0310261 | − | 0.999519i | \(-0.509877\pi\) | ||||
−0.0310261 | + | 0.999519i | \(0.509877\pi\) | |||||||
\(14\) | −0.955796 | −0.255447 | ||||||||
\(15\) | −9.89701 | −2.55540 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.89292 | 0.701637 | 0.350819 | − | 0.936443i | \(-0.385903\pi\) | ||||
0.350819 | + | 0.936443i | \(0.385903\pi\) | |||||||
\(18\) | 2.21398 | 0.521840 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 4.33431 | 0.969180 | ||||||||
\(21\) | 2.18248 | 0.476256 | ||||||||
\(22\) | −5.13031 | −1.09379 | ||||||||
\(23\) | −3.30652 | −0.689458 | −0.344729 | − | 0.938702i | \(-0.612029\pi\) | ||||
−0.344729 | + | 0.938702i | \(0.612029\pi\) | |||||||
\(24\) | −2.28341 | −0.466100 | ||||||||
\(25\) | 13.7862 | 2.75724 | ||||||||
\(26\) | −0.223732 | −0.0438775 | ||||||||
\(27\) | 1.79481 | 0.345412 | ||||||||
\(28\) | −0.955796 | −0.180628 | ||||||||
\(29\) | −0.0537792 | −0.00998654 | −0.00499327 | − | 0.999988i | \(-0.501589\pi\) | ||||
−0.00499327 | + | 0.999988i | \(0.501589\pi\) | |||||||
\(30\) | −9.89701 | −1.80694 | ||||||||
\(31\) | −1.90761 | −0.342617 | −0.171308 | − | 0.985217i | \(-0.554799\pi\) | ||||
−0.171308 | + | 0.985217i | \(0.554799\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 11.7146 | 2.03925 | ||||||||
\(34\) | 2.89292 | 0.496132 | ||||||||
\(35\) | −4.14271 | −0.700246 | ||||||||
\(36\) | 2.21398 | 0.368996 | ||||||||
\(37\) | −2.29313 | −0.376989 | −0.188494 | − | 0.982074i | \(-0.560361\pi\) | ||||
−0.188494 | + | 0.982074i | \(0.560361\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 0.510873 | 0.0818052 | ||||||||
\(40\) | 4.33431 | 0.685314 | ||||||||
\(41\) | 0.965538 | 0.150792 | 0.0753958 | − | 0.997154i | \(-0.475978\pi\) | ||||
0.0753958 | + | 0.997154i | \(0.475978\pi\) | |||||||
\(42\) | 2.18248 | 0.336764 | ||||||||
\(43\) | −5.82516 | −0.888328 | −0.444164 | − | 0.895945i | \(-0.646499\pi\) | ||||
−0.444164 | + | 0.895945i | \(0.646499\pi\) | |||||||
\(44\) | −5.13031 | −0.773423 | ||||||||
\(45\) | 9.59606 | 1.43050 | ||||||||
\(46\) | −3.30652 | −0.487520 | ||||||||
\(47\) | 9.69579 | 1.41428 | 0.707138 | − | 0.707076i | \(-0.249986\pi\) | ||||
0.707138 | + | 0.707076i | \(0.249986\pi\) | |||||||
\(48\) | −2.28341 | −0.329582 | ||||||||
\(49\) | −6.08645 | −0.869493 | ||||||||
\(50\) | 13.7862 | 1.94966 | ||||||||
\(51\) | −6.60574 | −0.924989 | ||||||||
\(52\) | −0.223732 | −0.0310261 | ||||||||
\(53\) | 10.8683 | 1.49287 | 0.746437 | − | 0.665456i | \(-0.231763\pi\) | ||||
0.746437 | + | 0.665456i | \(0.231763\pi\) | |||||||
\(54\) | 1.79481 | 0.244243 | ||||||||
\(55\) | −22.2363 | −2.99835 | ||||||||
\(56\) | −0.955796 | −0.127724 | ||||||||
\(57\) | 2.28341 | 0.302446 | ||||||||
\(58\) | −0.0537792 | −0.00706155 | ||||||||
\(59\) | 4.27122 | 0.556066 | 0.278033 | − | 0.960572i | \(-0.410318\pi\) | ||||
0.278033 | + | 0.960572i | \(0.410318\pi\) | |||||||
\(60\) | −9.89701 | −1.27770 | ||||||||
\(61\) | 1.64689 | 0.210862 | 0.105431 | − | 0.994427i | \(-0.466378\pi\) | ||||
0.105431 | + | 0.994427i | \(0.466378\pi\) | |||||||
\(62\) | −1.90761 | −0.242267 | ||||||||
\(63\) | −2.11611 | −0.266605 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.969724 | −0.120280 | ||||||||
\(66\) | 11.7146 | 1.44197 | ||||||||
\(67\) | −11.7055 | −1.43006 | −0.715028 | − | 0.699096i | \(-0.753586\pi\) | ||||
−0.715028 | + | 0.699096i | \(0.753586\pi\) | |||||||
\(68\) | 2.89292 | 0.350819 | ||||||||
\(69\) | 7.55016 | 0.908933 | ||||||||
\(70\) | −4.14271 | −0.495149 | ||||||||
\(71\) | 6.06103 | 0.719312 | 0.359656 | − | 0.933085i | \(-0.382894\pi\) | ||||
0.359656 | + | 0.933085i | \(0.382894\pi\) | |||||||
\(72\) | 2.21398 | 0.260920 | ||||||||
\(73\) | 3.78080 | 0.442509 | 0.221255 | − | 0.975216i | \(-0.428985\pi\) | ||||
0.221255 | + | 0.975216i | \(0.428985\pi\) | |||||||
\(74\) | −2.29313 | −0.266571 | ||||||||
\(75\) | −31.4796 | −3.63495 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 4.90353 | 0.558809 | ||||||||
\(78\) | 0.510873 | 0.0578450 | ||||||||
\(79\) | 9.19955 | 1.03503 | 0.517515 | − | 0.855674i | \(-0.326857\pi\) | ||||
0.517515 | + | 0.855674i | \(0.326857\pi\) | |||||||
\(80\) | 4.33431 | 0.484590 | ||||||||
\(81\) | −10.7402 | −1.19336 | ||||||||
\(82\) | 0.965538 | 0.106626 | ||||||||
\(83\) | 16.2278 | 1.78123 | 0.890616 | − | 0.454756i | \(-0.150273\pi\) | ||||
0.890616 | + | 0.454756i | \(0.150273\pi\) | |||||||
\(84\) | 2.18248 | 0.238128 | ||||||||
\(85\) | 12.5388 | 1.36003 | ||||||||
\(86\) | −5.82516 | −0.628143 | ||||||||
\(87\) | 0.122800 | 0.0131656 | ||||||||
\(88\) | −5.13031 | −0.546893 | ||||||||
\(89\) | 15.5406 | 1.64730 | 0.823652 | − | 0.567095i | \(-0.191933\pi\) | ||||
0.823652 | + | 0.567095i | \(0.191933\pi\) | |||||||
\(90\) | 9.59606 | 1.01151 | ||||||||
\(91\) | 0.213842 | 0.0224168 | ||||||||
\(92\) | −3.30652 | −0.344729 | ||||||||
\(93\) | 4.35586 | 0.451682 | ||||||||
\(94\) | 9.69579 | 1.00004 | ||||||||
\(95\) | −4.33431 | −0.444690 | ||||||||
\(96\) | −2.28341 | −0.233050 | ||||||||
\(97\) | 12.7256 | 1.29209 | 0.646045 | − | 0.763299i | \(-0.276422\pi\) | ||||
0.646045 | + | 0.763299i | \(0.276422\pi\) | |||||||
\(98\) | −6.08645 | −0.614825 | ||||||||
\(99\) | −11.3584 | −1.14156 | ||||||||
\(100\) | 13.7862 | 1.37862 | ||||||||
\(101\) | 17.0356 | 1.69510 | 0.847551 | − | 0.530714i | \(-0.178076\pi\) | ||||
0.847551 | + | 0.530714i | \(0.178076\pi\) | |||||||
\(102\) | −6.60574 | −0.654066 | ||||||||
\(103\) | −10.5631 | −1.04081 | −0.520407 | − | 0.853918i | \(-0.674220\pi\) | ||||
−0.520407 | + | 0.853918i | \(0.674220\pi\) | |||||||
\(104\) | −0.223732 | −0.0219388 | ||||||||
\(105\) | 9.45952 | 0.923155 | ||||||||
\(106\) | 10.8683 | 1.05562 | ||||||||
\(107\) | −3.59047 | −0.347104 | −0.173552 | − | 0.984825i | \(-0.555524\pi\) | ||||
−0.173552 | + | 0.984825i | \(0.555524\pi\) | |||||||
\(108\) | 1.79481 | 0.172706 | ||||||||
\(109\) | 4.87950 | 0.467372 | 0.233686 | − | 0.972312i | \(-0.424921\pi\) | ||||
0.233686 | + | 0.972312i | \(0.424921\pi\) | |||||||
\(110\) | −22.2363 | −2.12015 | ||||||||
\(111\) | 5.23617 | 0.496996 | ||||||||
\(112\) | −0.955796 | −0.0903142 | ||||||||
\(113\) | −8.29563 | −0.780388 | −0.390194 | − | 0.920733i | \(-0.627592\pi\) | ||||
−0.390194 | + | 0.920733i | \(0.627592\pi\) | |||||||
\(114\) | 2.28341 | 0.213861 | ||||||||
\(115\) | −14.3315 | −1.33642 | ||||||||
\(116\) | −0.0537792 | −0.00499327 | ||||||||
\(117\) | −0.495339 | −0.0457941 | ||||||||
\(118\) | 4.27122 | 0.393198 | ||||||||
\(119\) | −2.76504 | −0.253471 | ||||||||
\(120\) | −9.89701 | −0.903470 | ||||||||
\(121\) | 15.3201 | 1.39273 | ||||||||
\(122\) | 1.64689 | 0.149102 | ||||||||
\(123\) | −2.20472 | −0.198793 | ||||||||
\(124\) | −1.90761 | −0.171308 | ||||||||
\(125\) | 38.0821 | 3.40617 | ||||||||
\(126\) | −2.11611 | −0.188518 | ||||||||
\(127\) | 19.3439 | 1.71649 | 0.858247 | − | 0.513237i | \(-0.171554\pi\) | ||||
0.858247 | + | 0.513237i | \(0.171554\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 13.3012 | 1.17111 | ||||||||
\(130\) | −0.969724 | −0.0850505 | ||||||||
\(131\) | 9.20602 | 0.804334 | 0.402167 | − | 0.915566i | \(-0.368257\pi\) | ||||
0.402167 | + | 0.915566i | \(0.368257\pi\) | |||||||
\(132\) | 11.7146 | 1.01963 | ||||||||
\(133\) | 0.955796 | 0.0828780 | ||||||||
\(134\) | −11.7055 | −1.01120 | ||||||||
\(135\) | 7.77926 | 0.669532 | ||||||||
\(136\) | 2.89292 | 0.248066 | ||||||||
\(137\) | −16.3335 | −1.39547 | −0.697734 | − | 0.716357i | \(-0.745808\pi\) | ||||
−0.697734 | + | 0.716357i | \(0.745808\pi\) | |||||||
\(138\) | 7.55016 | 0.642713 | ||||||||
\(139\) | 9.81016 | 0.832087 | 0.416043 | − | 0.909345i | \(-0.363416\pi\) | ||||
0.416043 | + | 0.909345i | \(0.363416\pi\) | |||||||
\(140\) | −4.14271 | −0.350123 | ||||||||
\(141\) | −22.1395 | −1.86448 | ||||||||
\(142\) | 6.06103 | 0.508631 | ||||||||
\(143\) | 1.14782 | 0.0959852 | ||||||||
\(144\) | 2.21398 | 0.184498 | ||||||||
\(145\) | −0.233095 | −0.0193575 | ||||||||
\(146\) | 3.78080 | 0.312901 | ||||||||
\(147\) | 13.8979 | 1.14628 | ||||||||
\(148\) | −2.29313 | −0.188494 | ||||||||
\(149\) | 0.990937 | 0.0811808 | 0.0405904 | − | 0.999176i | \(-0.487076\pi\) | ||||
0.0405904 | + | 0.999176i | \(0.487076\pi\) | |||||||
\(150\) | −31.4796 | −2.57030 | ||||||||
\(151\) | 10.4306 | 0.848827 | 0.424414 | − | 0.905468i | \(-0.360480\pi\) | ||||
0.424414 | + | 0.905468i | \(0.360480\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 6.40487 | 0.517803 | ||||||||
\(154\) | 4.90353 | 0.395137 | ||||||||
\(155\) | −8.26816 | −0.664115 | ||||||||
\(156\) | 0.510873 | 0.0409026 | ||||||||
\(157\) | −8.84405 | −0.705832 | −0.352916 | − | 0.935655i | \(-0.614810\pi\) | ||||
−0.352916 | + | 0.935655i | \(0.614810\pi\) | |||||||
\(158\) | 9.19955 | 0.731877 | ||||||||
\(159\) | −24.8168 | −1.96810 | ||||||||
\(160\) | 4.33431 | 0.342657 | ||||||||
\(161\) | 3.16036 | 0.249071 | ||||||||
\(162\) | −10.7402 | −0.843832 | ||||||||
\(163\) | 0.889463 | 0.0696681 | 0.0348340 | − | 0.999393i | \(-0.488910\pi\) | ||||
0.0348340 | + | 0.999393i | \(0.488910\pi\) | |||||||
\(164\) | 0.965538 | 0.0753958 | ||||||||
\(165\) | 50.7747 | 3.95281 | ||||||||
\(166\) | 16.2278 | 1.25952 | ||||||||
\(167\) | 7.07473 | 0.547459 | 0.273729 | − | 0.961807i | \(-0.411743\pi\) | ||||
0.273729 | + | 0.961807i | \(0.411743\pi\) | |||||||
\(168\) | 2.18248 | 0.168382 | ||||||||
\(169\) | −12.9499 | −0.996150 | ||||||||
\(170\) | 12.5388 | 0.961683 | ||||||||
\(171\) | −2.21398 | −0.169307 | ||||||||
\(172\) | −5.82516 | −0.444164 | ||||||||
\(173\) | −2.39066 | −0.181758 | −0.0908792 | − | 0.995862i | \(-0.528968\pi\) | ||||
−0.0908792 | + | 0.995862i | \(0.528968\pi\) | |||||||
\(174\) | 0.122800 | 0.00930945 | ||||||||
\(175\) | −13.1768 | −0.996073 | ||||||||
\(176\) | −5.13031 | −0.386712 | ||||||||
\(177\) | −9.75297 | −0.733078 | ||||||||
\(178\) | 15.5406 | 1.16482 | ||||||||
\(179\) | 8.08589 | 0.604368 | 0.302184 | − | 0.953250i | \(-0.402284\pi\) | ||||
0.302184 | + | 0.953250i | \(0.402284\pi\) | |||||||
\(180\) | 9.59606 | 0.715248 | ||||||||
\(181\) | 0.291984 | 0.0217030 | 0.0108515 | − | 0.999941i | \(-0.496546\pi\) | ||||
0.0108515 | + | 0.999941i | \(0.496546\pi\) | |||||||
\(182\) | 0.213842 | 0.0158511 | ||||||||
\(183\) | −3.76053 | −0.277986 | ||||||||
\(184\) | −3.30652 | −0.243760 | ||||||||
\(185\) | −9.93915 | −0.730741 | ||||||||
\(186\) | 4.35586 | 0.319387 | ||||||||
\(187\) | −14.8416 | −1.08532 | ||||||||
\(188\) | 9.69579 | 0.707138 | ||||||||
\(189\) | −1.71547 | −0.124782 | ||||||||
\(190\) | −4.33431 | −0.314444 | ||||||||
\(191\) | −16.3318 | −1.18172 | −0.590862 | − | 0.806772i | \(-0.701212\pi\) | ||||
−0.590862 | + | 0.806772i | \(0.701212\pi\) | |||||||
\(192\) | −2.28341 | −0.164791 | ||||||||
\(193\) | −22.2848 | −1.60410 | −0.802048 | − | 0.597260i | \(-0.796256\pi\) | ||||
−0.802048 | + | 0.597260i | \(0.796256\pi\) | |||||||
\(194\) | 12.7256 | 0.913646 | ||||||||
\(195\) | 2.21428 | 0.158568 | ||||||||
\(196\) | −6.08645 | −0.434747 | ||||||||
\(197\) | −7.01787 | −0.500003 | −0.250001 | − | 0.968245i | \(-0.580431\pi\) | ||||
−0.250001 | + | 0.968245i | \(0.580431\pi\) | |||||||
\(198\) | −11.3584 | −0.807206 | ||||||||
\(199\) | −8.26753 | −0.586069 | −0.293035 | − | 0.956102i | \(-0.594665\pi\) | ||||
−0.293035 | + | 0.956102i | \(0.594665\pi\) | |||||||
\(200\) | 13.7862 | 0.974832 | ||||||||
\(201\) | 26.7285 | 1.88529 | ||||||||
\(202\) | 17.0356 | 1.19862 | ||||||||
\(203\) | 0.0514019 | 0.00360771 | ||||||||
\(204\) | −6.60574 | −0.462494 | ||||||||
\(205\) | 4.18494 | 0.292289 | ||||||||
\(206\) | −10.5631 | −0.735967 | ||||||||
\(207\) | −7.32058 | −0.508815 | ||||||||
\(208\) | −0.223732 | −0.0155130 | ||||||||
\(209\) | 5.13031 | 0.354871 | ||||||||
\(210\) | 9.45952 | 0.652769 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | 10.8683 | 0.746437 | ||||||||
\(213\) | −13.8398 | −0.948291 | ||||||||
\(214\) | −3.59047 | −0.245439 | ||||||||
\(215\) | −25.2480 | −1.72190 | ||||||||
\(216\) | 1.79481 | 0.122121 | ||||||||
\(217\) | 1.82329 | 0.123773 | ||||||||
\(218\) | 4.87950 | 0.330482 | ||||||||
\(219\) | −8.63313 | −0.583373 | ||||||||
\(220\) | −22.2363 | −1.49917 | ||||||||
\(221\) | −0.647241 | −0.0435381 | ||||||||
\(222\) | 5.23617 | 0.351429 | ||||||||
\(223\) | 20.6508 | 1.38288 | 0.691441 | − | 0.722433i | \(-0.256976\pi\) | ||||
0.691441 | + | 0.722433i | \(0.256976\pi\) | |||||||
\(224\) | −0.955796 | −0.0638618 | ||||||||
\(225\) | 30.5224 | 2.03483 | ||||||||
\(226\) | −8.29563 | −0.551817 | ||||||||
\(227\) | 7.68360 | 0.509979 | 0.254989 | − | 0.966944i | \(-0.417928\pi\) | ||||
0.254989 | + | 0.966944i | \(0.417928\pi\) | |||||||
\(228\) | 2.28341 | 0.151223 | ||||||||
\(229\) | −29.6585 | −1.95989 | −0.979945 | − | 0.199269i | \(-0.936143\pi\) | ||||
−0.979945 | + | 0.199269i | \(0.936143\pi\) | |||||||
\(230\) | −14.3315 | −0.944990 | ||||||||
\(231\) | −11.1968 | −0.736694 | ||||||||
\(232\) | −0.0537792 | −0.00353078 | ||||||||
\(233\) | 2.77318 | 0.181677 | 0.0908385 | − | 0.995866i | \(-0.471045\pi\) | ||||
0.0908385 | + | 0.995866i | \(0.471045\pi\) | |||||||
\(234\) | −0.495339 | −0.0323813 | ||||||||
\(235\) | 42.0245 | 2.74138 | ||||||||
\(236\) | 4.27122 | 0.278033 | ||||||||
\(237\) | −21.0064 | −1.36451 | ||||||||
\(238\) | −2.76504 | −0.179231 | ||||||||
\(239\) | −5.22141 | −0.337745 | −0.168872 | − | 0.985638i | \(-0.554013\pi\) | ||||
−0.168872 | + | 0.985638i | \(0.554013\pi\) | |||||||
\(240\) | −9.89701 | −0.638850 | ||||||||
\(241\) | −2.31966 | −0.149422 | −0.0747111 | − | 0.997205i | \(-0.523803\pi\) | ||||
−0.0747111 | + | 0.997205i | \(0.523803\pi\) | |||||||
\(242\) | 15.3201 | 0.984811 | ||||||||
\(243\) | 19.1400 | 1.22783 | ||||||||
\(244\) | 1.64689 | 0.105431 | ||||||||
\(245\) | −26.3806 | −1.68539 | ||||||||
\(246\) | −2.20472 | −0.140568 | ||||||||
\(247\) | 0.223732 | 0.0142357 | ||||||||
\(248\) | −1.90761 | −0.121133 | ||||||||
\(249\) | −37.0548 | −2.34825 | ||||||||
\(250\) | 38.0821 | 2.40852 | ||||||||
\(251\) | 17.6215 | 1.11226 | 0.556130 | − | 0.831095i | \(-0.312286\pi\) | ||||
0.556130 | + | 0.831095i | \(0.312286\pi\) | |||||||
\(252\) | −2.11611 | −0.133303 | ||||||||
\(253\) | 16.9635 | 1.06649 | ||||||||
\(254\) | 19.3439 | 1.21374 | ||||||||
\(255\) | −28.6313 | −1.79296 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −18.0907 | −1.12847 | −0.564233 | − | 0.825616i | \(-0.690828\pi\) | ||||
−0.564233 | + | 0.825616i | \(0.690828\pi\) | |||||||
\(258\) | 13.3012 | 0.828099 | ||||||||
\(259\) | 2.19177 | 0.136190 | ||||||||
\(260\) | −0.969724 | −0.0601398 | ||||||||
\(261\) | −0.119066 | −0.00737000 | ||||||||
\(262\) | 9.20602 | 0.568750 | ||||||||
\(263\) | −5.52366 | −0.340603 | −0.170302 | − | 0.985392i | \(-0.554474\pi\) | ||||
−0.170302 | + | 0.985392i | \(0.554474\pi\) | |||||||
\(264\) | 11.7146 | 0.720985 | ||||||||
\(265\) | 47.1065 | 2.89373 | ||||||||
\(266\) | 0.955796 | 0.0586036 | ||||||||
\(267\) | −35.4857 | −2.17169 | ||||||||
\(268\) | −11.7055 | −0.715028 | ||||||||
\(269\) | 22.3892 | 1.36509 | 0.682546 | − | 0.730843i | \(-0.260873\pi\) | ||||
0.682546 | + | 0.730843i | \(0.260873\pi\) | |||||||
\(270\) | 7.77926 | 0.473431 | ||||||||
\(271\) | 21.1723 | 1.28613 | 0.643063 | − | 0.765813i | \(-0.277663\pi\) | ||||
0.643063 | + | 0.765813i | \(0.277663\pi\) | |||||||
\(272\) | 2.89292 | 0.175409 | ||||||||
\(273\) | −0.488291 | −0.0295527 | ||||||||
\(274\) | −16.3335 | −0.986745 | ||||||||
\(275\) | −70.7275 | −4.26503 | ||||||||
\(276\) | 7.55016 | 0.454466 | ||||||||
\(277\) | 30.5060 | 1.83293 | 0.916464 | − | 0.400117i | \(-0.131031\pi\) | ||||
0.916464 | + | 0.400117i | \(0.131031\pi\) | |||||||
\(278\) | 9.81016 | 0.588374 | ||||||||
\(279\) | −4.22341 | −0.252849 | ||||||||
\(280\) | −4.14271 | −0.247574 | ||||||||
\(281\) | 0.299543 | 0.0178692 | 0.00893461 | − | 0.999960i | \(-0.497156\pi\) | ||||
0.00893461 | + | 0.999960i | \(0.497156\pi\) | |||||||
\(282\) | −22.1395 | −1.31839 | ||||||||
\(283\) | 6.89607 | 0.409929 | 0.204964 | − | 0.978769i | \(-0.434292\pi\) | ||||
0.204964 | + | 0.978769i | \(0.434292\pi\) | |||||||
\(284\) | 6.06103 | 0.359656 | ||||||||
\(285\) | 9.89701 | 0.586249 | ||||||||
\(286\) | 1.14782 | 0.0678718 | ||||||||
\(287\) | −0.922857 | −0.0544745 | ||||||||
\(288\) | 2.21398 | 0.130460 | ||||||||
\(289\) | −8.63099 | −0.507705 | ||||||||
\(290\) | −0.233095 | −0.0136878 | ||||||||
\(291\) | −29.0579 | −1.70340 | ||||||||
\(292\) | 3.78080 | 0.221255 | ||||||||
\(293\) | 10.4173 | 0.608586 | 0.304293 | − | 0.952578i | \(-0.401580\pi\) | ||||
0.304293 | + | 0.952578i | \(0.401580\pi\) | |||||||
\(294\) | 13.8979 | 0.810542 | ||||||||
\(295\) | 18.5128 | 1.07786 | ||||||||
\(296\) | −2.29313 | −0.133286 | ||||||||
\(297\) | −9.20794 | −0.534299 | ||||||||
\(298\) | 0.990937 | 0.0574035 | ||||||||
\(299\) | 0.739776 | 0.0427824 | ||||||||
\(300\) | −31.4796 | −1.81748 | ||||||||
\(301\) | 5.56766 | 0.320915 | ||||||||
\(302\) | 10.4306 | 0.600212 | ||||||||
\(303\) | −38.8992 | −2.23470 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 7.13812 | 0.408727 | ||||||||
\(306\) | 6.40487 | 0.366142 | ||||||||
\(307\) | −24.1824 | −1.38016 | −0.690080 | − | 0.723733i | \(-0.742425\pi\) | ||||
−0.690080 | + | 0.723733i | \(0.742425\pi\) | |||||||
\(308\) | 4.90353 | 0.279404 | ||||||||
\(309\) | 24.1199 | 1.37214 | ||||||||
\(310\) | −8.26816 | −0.469600 | ||||||||
\(311\) | 4.73300 | 0.268384 | 0.134192 | − | 0.990955i | \(-0.457156\pi\) | ||||
0.134192 | + | 0.990955i | \(0.457156\pi\) | |||||||
\(312\) | 0.510873 | 0.0289225 | ||||||||
\(313\) | 9.38214 | 0.530310 | 0.265155 | − | 0.964206i | \(-0.414577\pi\) | ||||
0.265155 | + | 0.964206i | \(0.414577\pi\) | |||||||
\(314\) | −8.84405 | −0.499099 | ||||||||
\(315\) | −9.17188 | −0.516777 | ||||||||
\(316\) | 9.19955 | 0.517515 | ||||||||
\(317\) | 16.9015 | 0.949282 | 0.474641 | − | 0.880179i | \(-0.342578\pi\) | ||||
0.474641 | + | 0.880179i | \(0.342578\pi\) | |||||||
\(318\) | −24.8168 | −1.39166 | ||||||||
\(319\) | 0.275904 | 0.0154476 | ||||||||
\(320\) | 4.33431 | 0.242295 | ||||||||
\(321\) | 8.19853 | 0.457597 | ||||||||
\(322\) | 3.16036 | 0.176120 | ||||||||
\(323\) | −2.89292 | −0.160967 | ||||||||
\(324\) | −10.7402 | −0.596680 | ||||||||
\(325\) | −3.08442 | −0.171093 | ||||||||
\(326\) | 0.889463 | 0.0492628 | ||||||||
\(327\) | −11.1419 | −0.616150 | ||||||||
\(328\) | 0.965538 | 0.0533129 | ||||||||
\(329\) | −9.26719 | −0.510917 | ||||||||
\(330\) | 50.7747 | 2.79506 | ||||||||
\(331\) | 3.06898 | 0.168686 | 0.0843432 | − | 0.996437i | \(-0.473121\pi\) | ||||
0.0843432 | + | 0.996437i | \(0.473121\pi\) | |||||||
\(332\) | 16.2278 | 0.890616 | ||||||||
\(333\) | −5.07695 | −0.278215 | ||||||||
\(334\) | 7.07473 | 0.387112 | ||||||||
\(335\) | −50.7353 | −2.77197 | ||||||||
\(336\) | 2.18248 | 0.119064 | ||||||||
\(337\) | 12.0774 | 0.657898 | 0.328949 | − | 0.944348i | \(-0.393306\pi\) | ||||
0.328949 | + | 0.944348i | \(0.393306\pi\) | |||||||
\(338\) | −12.9499 | −0.704384 | ||||||||
\(339\) | 18.9424 | 1.02881 | ||||||||
\(340\) | 12.5388 | 0.680013 | ||||||||
\(341\) | 9.78662 | 0.529975 | ||||||||
\(342\) | −2.21398 | −0.119718 | ||||||||
\(343\) | 12.5080 | 0.675367 | ||||||||
\(344\) | −5.82516 | −0.314071 | ||||||||
\(345\) | 32.7247 | 1.76184 | ||||||||
\(346\) | −2.39066 | −0.128523 | ||||||||
\(347\) | −30.2646 | −1.62469 | −0.812345 | − | 0.583177i | \(-0.801809\pi\) | ||||
−0.812345 | + | 0.583177i | \(0.801809\pi\) | |||||||
\(348\) | 0.122800 | 0.00658278 | ||||||||
\(349\) | −0.577196 | −0.0308966 | −0.0154483 | − | 0.999881i | \(-0.504918\pi\) | ||||
−0.0154483 | + | 0.999881i | \(0.504918\pi\) | |||||||
\(350\) | −13.1768 | −0.704330 | ||||||||
\(351\) | −0.401557 | −0.0214335 | ||||||||
\(352\) | −5.13031 | −0.273446 | ||||||||
\(353\) | −32.8742 | −1.74972 | −0.874860 | − | 0.484376i | \(-0.839047\pi\) | ||||
−0.874860 | + | 0.484376i | \(0.839047\pi\) | |||||||
\(354\) | −9.75297 | −0.518365 | ||||||||
\(355\) | 26.2704 | 1.39429 | ||||||||
\(356\) | 15.5406 | 0.823652 | ||||||||
\(357\) | 6.31374 | 0.334159 | ||||||||
\(358\) | 8.08589 | 0.427353 | ||||||||
\(359\) | −22.0424 | −1.16336 | −0.581678 | − | 0.813419i | \(-0.697604\pi\) | ||||
−0.581678 | + | 0.813419i | \(0.697604\pi\) | |||||||
\(360\) | 9.59606 | 0.505757 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0.291984 | 0.0153463 | ||||||||
\(363\) | −34.9820 | −1.83608 | ||||||||
\(364\) | 0.213842 | 0.0112084 | ||||||||
\(365\) | 16.3872 | 0.857743 | ||||||||
\(366\) | −3.76053 | −0.196566 | ||||||||
\(367\) | 28.0980 | 1.46670 | 0.733352 | − | 0.679849i | \(-0.237955\pi\) | ||||
0.733352 | + | 0.679849i | \(0.237955\pi\) | |||||||
\(368\) | −3.30652 | −0.172365 | ||||||||
\(369\) | 2.13768 | 0.111283 | ||||||||
\(370\) | −9.93915 | −0.516712 | ||||||||
\(371\) | −10.3879 | −0.539311 | ||||||||
\(372\) | 4.35586 | 0.225841 | ||||||||
\(373\) | 32.0311 | 1.65851 | 0.829255 | − | 0.558871i | \(-0.188765\pi\) | ||||
0.829255 | + | 0.558871i | \(0.188765\pi\) | |||||||
\(374\) | −14.8416 | −0.767440 | ||||||||
\(375\) | −86.9572 | −4.49045 | ||||||||
\(376\) | 9.69579 | 0.500022 | ||||||||
\(377\) | 0.0120321 | 0.000619687 0 | ||||||||
\(378\) | −1.71547 | −0.0882344 | ||||||||
\(379\) | −37.9753 | −1.95066 | −0.975331 | − | 0.220749i | \(-0.929150\pi\) | ||||
−0.975331 | + | 0.220749i | \(0.929150\pi\) | |||||||
\(380\) | −4.33431 | −0.222345 | ||||||||
\(381\) | −44.1701 | −2.26291 | ||||||||
\(382\) | −16.3318 | −0.835606 | ||||||||
\(383\) | 7.68475 | 0.392672 | 0.196336 | − | 0.980537i | \(-0.437096\pi\) | ||||
0.196336 | + | 0.980537i | \(0.437096\pi\) | |||||||
\(384\) | −2.28341 | −0.116525 | ||||||||
\(385\) | 21.2534 | 1.08317 | ||||||||
\(386\) | −22.2848 | −1.13427 | ||||||||
\(387\) | −12.8968 | −0.655580 | ||||||||
\(388\) | 12.7256 | 0.646045 | ||||||||
\(389\) | 30.6879 | 1.55594 | 0.777968 | − | 0.628304i | \(-0.216251\pi\) | ||||
0.777968 | + | 0.628304i | \(0.216251\pi\) | |||||||
\(390\) | 2.21428 | 0.112125 | ||||||||
\(391\) | −9.56552 | −0.483749 | ||||||||
\(392\) | −6.08645 | −0.307412 | ||||||||
\(393\) | −21.0212 | −1.06038 | ||||||||
\(394\) | −7.01787 | −0.353555 | ||||||||
\(395\) | 39.8737 | 2.00626 | ||||||||
\(396\) | −11.3584 | −0.570781 | ||||||||
\(397\) | −11.9920 | −0.601860 | −0.300930 | − | 0.953646i | \(-0.597297\pi\) | ||||
−0.300930 | + | 0.953646i | \(0.597297\pi\) | |||||||
\(398\) | −8.26753 | −0.414414 | ||||||||
\(399\) | −2.18248 | −0.109261 | ||||||||
\(400\) | 13.7862 | 0.689310 | ||||||||
\(401\) | −3.28872 | −0.164231 | −0.0821154 | − | 0.996623i | \(-0.526168\pi\) | ||||
−0.0821154 | + | 0.996623i | \(0.526168\pi\) | |||||||
\(402\) | 26.7285 | 1.33310 | ||||||||
\(403\) | 0.426794 | 0.0212601 | ||||||||
\(404\) | 17.0356 | 0.847551 | ||||||||
\(405\) | −46.5515 | −2.31316 | ||||||||
\(406\) | 0.0514019 | 0.00255103 | ||||||||
\(407\) | 11.7645 | 0.583144 | ||||||||
\(408\) | −6.60574 | −0.327033 | ||||||||
\(409\) | 29.2267 | 1.44517 | 0.722584 | − | 0.691283i | \(-0.242954\pi\) | ||||
0.722584 | + | 0.691283i | \(0.242954\pi\) | |||||||
\(410\) | 4.18494 | 0.206679 | ||||||||
\(411\) | 37.2962 | 1.83969 | ||||||||
\(412\) | −10.5631 | −0.520407 | ||||||||
\(413\) | −4.08242 | −0.200883 | ||||||||
\(414\) | −7.32058 | −0.359787 | ||||||||
\(415\) | 70.3363 | 3.45267 | ||||||||
\(416\) | −0.223732 | −0.0109694 | ||||||||
\(417\) | −22.4007 | −1.09696 | ||||||||
\(418\) | 5.13031 | 0.250932 | ||||||||
\(419\) | 35.5644 | 1.73744 | 0.868718 | − | 0.495307i | \(-0.164945\pi\) | ||||
0.868718 | + | 0.495307i | \(0.164945\pi\) | |||||||
\(420\) | 9.45952 | 0.461578 | ||||||||
\(421\) | −18.5289 | −0.903045 | −0.451523 | − | 0.892260i | \(-0.649119\pi\) | ||||
−0.451523 | + | 0.892260i | \(0.649119\pi\) | |||||||
\(422\) | −1.00000 | −0.0486792 | ||||||||
\(423\) | 21.4663 | 1.04373 | ||||||||
\(424\) | 10.8683 | 0.527811 | ||||||||
\(425\) | 39.8825 | 1.93458 | ||||||||
\(426\) | −13.8398 | −0.670543 | ||||||||
\(427\) | −1.57409 | −0.0761755 | ||||||||
\(428\) | −3.59047 | −0.173552 | ||||||||
\(429\) | −2.62094 | −0.126540 | ||||||||
\(430\) | −25.2480 | −1.21757 | ||||||||
\(431\) | 24.6150 | 1.18566 | 0.592830 | − | 0.805327i | \(-0.298010\pi\) | ||||
0.592830 | + | 0.805327i | \(0.298010\pi\) | |||||||
\(432\) | 1.79481 | 0.0863529 | ||||||||
\(433\) | −38.2251 | −1.83698 | −0.918491 | − | 0.395441i | \(-0.870592\pi\) | ||||
−0.918491 | + | 0.395441i | \(0.870592\pi\) | |||||||
\(434\) | 1.82329 | 0.0875205 | ||||||||
\(435\) | 0.532253 | 0.0255196 | ||||||||
\(436\) | 4.87950 | 0.233686 | ||||||||
\(437\) | 3.30652 | 0.158173 | ||||||||
\(438\) | −8.63313 | −0.412507 | ||||||||
\(439\) | 4.87452 | 0.232648 | 0.116324 | − | 0.993211i | \(-0.462889\pi\) | ||||
0.116324 | + | 0.993211i | \(0.462889\pi\) | |||||||
\(440\) | −22.2363 | −1.06008 | ||||||||
\(441\) | −13.4753 | −0.641680 | ||||||||
\(442\) | −0.647241 | −0.0307861 | ||||||||
\(443\) | 36.7284 | 1.74502 | 0.872509 | − | 0.488598i | \(-0.162492\pi\) | ||||
0.872509 | + | 0.488598i | \(0.162492\pi\) | |||||||
\(444\) | 5.23617 | 0.248498 | ||||||||
\(445\) | 67.3579 | 3.19307 | ||||||||
\(446\) | 20.6508 | 0.977845 | ||||||||
\(447\) | −2.26272 | −0.107023 | ||||||||
\(448\) | −0.955796 | −0.0451571 | ||||||||
\(449\) | 14.8606 | 0.701316 | 0.350658 | − | 0.936504i | \(-0.385958\pi\) | ||||
0.350658 | + | 0.936504i | \(0.385958\pi\) | |||||||
\(450\) | 30.5224 | 1.43884 | ||||||||
\(451\) | −4.95351 | −0.233252 | ||||||||
\(452\) | −8.29563 | −0.390194 | ||||||||
\(453\) | −23.8173 | −1.11903 | ||||||||
\(454\) | 7.68360 | 0.360609 | ||||||||
\(455\) | 0.926858 | 0.0434518 | ||||||||
\(456\) | 2.28341 | 0.106931 | ||||||||
\(457\) | −34.4174 | −1.60998 | −0.804990 | − | 0.593288i | \(-0.797829\pi\) | ||||
−0.804990 | + | 0.593288i | \(0.797829\pi\) | |||||||
\(458\) | −29.6585 | −1.38585 | ||||||||
\(459\) | 5.19225 | 0.242354 | ||||||||
\(460\) | −14.3315 | −0.668209 | ||||||||
\(461\) | −12.0352 | −0.560533 | −0.280267 | − | 0.959922i | \(-0.590423\pi\) | ||||
−0.280267 | + | 0.959922i | \(0.590423\pi\) | |||||||
\(462\) | −11.1968 | −0.520921 | ||||||||
\(463\) | 13.7270 | 0.637949 | 0.318974 | − | 0.947763i | \(-0.396662\pi\) | ||||
0.318974 | + | 0.947763i | \(0.396662\pi\) | |||||||
\(464\) | −0.0537792 | −0.00249664 | ||||||||
\(465\) | 18.8796 | 0.875522 | ||||||||
\(466\) | 2.77318 | 0.128465 | ||||||||
\(467\) | 16.6043 | 0.768355 | 0.384178 | − | 0.923259i | \(-0.374485\pi\) | ||||
0.384178 | + | 0.923259i | \(0.374485\pi\) | |||||||
\(468\) | −0.495339 | −0.0228970 | ||||||||
\(469\) | 11.1881 | 0.516618 | ||||||||
\(470\) | 42.0245 | 1.93845 | ||||||||
\(471\) | 20.1946 | 0.930519 | ||||||||
\(472\) | 4.27122 | 0.196599 | ||||||||
\(473\) | 29.8848 | 1.37411 | ||||||||
\(474\) | −21.0064 | −0.964855 | ||||||||
\(475\) | −13.7862 | −0.632555 | ||||||||
\(476\) | −2.76504 | −0.126736 | ||||||||
\(477\) | 24.0622 | 1.10173 | ||||||||
\(478\) | −5.22141 | −0.238822 | ||||||||
\(479\) | −35.6304 | −1.62800 | −0.813998 | − | 0.580867i | \(-0.802714\pi\) | ||||
−0.813998 | + | 0.580867i | \(0.802714\pi\) | |||||||
\(480\) | −9.89701 | −0.451735 | ||||||||
\(481\) | 0.513048 | 0.0233930 | ||||||||
\(482\) | −2.31966 | −0.105657 | ||||||||
\(483\) | −7.21641 | −0.328358 | ||||||||
\(484\) | 15.3201 | 0.696366 | ||||||||
\(485\) | 55.1567 | 2.50454 | ||||||||
\(486\) | 19.1400 | 0.868206 | ||||||||
\(487\) | −27.0689 | −1.22661 | −0.613304 | − | 0.789847i | \(-0.710160\pi\) | ||||
−0.613304 | + | 0.789847i | \(0.710160\pi\) | |||||||
\(488\) | 1.64689 | 0.0745511 | ||||||||
\(489\) | −2.03101 | −0.0918455 | ||||||||
\(490\) | −26.3806 | −1.19175 | ||||||||
\(491\) | 20.6028 | 0.929791 | 0.464896 | − | 0.885365i | \(-0.346092\pi\) | ||||
0.464896 | + | 0.885365i | \(0.346092\pi\) | |||||||
\(492\) | −2.20472 | −0.0993966 | ||||||||
\(493\) | −0.155579 | −0.00700693 | ||||||||
\(494\) | 0.223732 | 0.0100662 | ||||||||
\(495\) | −49.2308 | −2.21276 | ||||||||
\(496\) | −1.90761 | −0.0856542 | ||||||||
\(497\) | −5.79311 | −0.259857 | ||||||||
\(498\) | −37.0548 | −1.66046 | ||||||||
\(499\) | 19.1318 | 0.856459 | 0.428229 | − | 0.903670i | \(-0.359138\pi\) | ||||
0.428229 | + | 0.903670i | \(0.359138\pi\) | |||||||
\(500\) | 38.0821 | 1.70308 | ||||||||
\(501\) | −16.1545 | −0.721731 | ||||||||
\(502\) | 17.6215 | 0.786487 | ||||||||
\(503\) | 19.4783 | 0.868493 | 0.434246 | − | 0.900794i | \(-0.357015\pi\) | ||||
0.434246 | + | 0.900794i | \(0.357015\pi\) | |||||||
\(504\) | −2.11611 | −0.0942591 | ||||||||
\(505\) | 73.8373 | 3.28572 | ||||||||
\(506\) | 16.9635 | 0.754119 | ||||||||
\(507\) | 29.5701 | 1.31325 | ||||||||
\(508\) | 19.3439 | 0.858247 | ||||||||
\(509\) | 15.6613 | 0.694174 | 0.347087 | − | 0.937833i | \(-0.387171\pi\) | ||||
0.347087 | + | 0.937833i | \(0.387171\pi\) | |||||||
\(510\) | −28.6313 | −1.26782 | ||||||||
\(511\) | −3.61367 | −0.159860 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.79481 | −0.0792429 | ||||||||
\(514\) | −18.0907 | −0.797945 | ||||||||
\(515\) | −45.7837 | −2.01747 | ||||||||
\(516\) | 13.3012 | 0.585555 | ||||||||
\(517\) | −49.7424 | −2.18767 | ||||||||
\(518\) | 2.19177 | 0.0963008 | ||||||||
\(519\) | 5.45887 | 0.239618 | ||||||||
\(520\) | −0.969724 | −0.0425252 | ||||||||
\(521\) | 24.7153 | 1.08280 | 0.541398 | − | 0.840766i | \(-0.317895\pi\) | ||||
0.541398 | + | 0.840766i | \(0.317895\pi\) | |||||||
\(522\) | −0.119066 | −0.00521137 | ||||||||
\(523\) | 31.4808 | 1.37656 | 0.688280 | − | 0.725445i | \(-0.258366\pi\) | ||||
0.688280 | + | 0.725445i | \(0.258366\pi\) | |||||||
\(524\) | 9.20602 | 0.402167 | ||||||||
\(525\) | 30.0881 | 1.31315 | ||||||||
\(526\) | −5.52366 | −0.240843 | ||||||||
\(527\) | −5.51857 | −0.240393 | ||||||||
\(528\) | 11.7146 | 0.509813 | ||||||||
\(529\) | −12.0669 | −0.524648 | ||||||||
\(530\) | 47.1065 | 2.04618 | ||||||||
\(531\) | 9.45640 | 0.410373 | ||||||||
\(532\) | 0.955796 | 0.0414390 | ||||||||
\(533\) | −0.216022 | −0.00935695 | ||||||||
\(534\) | −35.4857 | −1.53562 | ||||||||
\(535\) | −15.5622 | −0.672812 | ||||||||
\(536\) | −11.7055 | −0.505601 | ||||||||
\(537\) | −18.4634 | −0.796756 | ||||||||
\(538\) | 22.3892 | 0.965266 | ||||||||
\(539\) | 31.2254 | 1.34497 | ||||||||
\(540\) | 7.77926 | 0.334766 | ||||||||
\(541\) | −16.1161 | −0.692887 | −0.346444 | − | 0.938071i | \(-0.612611\pi\) | ||||
−0.346444 | + | 0.938071i | \(0.612611\pi\) | |||||||
\(542\) | 21.1723 | 0.909429 | ||||||||
\(543\) | −0.666719 | −0.0286117 | ||||||||
\(544\) | 2.89292 | 0.124033 | ||||||||
\(545\) | 21.1493 | 0.905935 | ||||||||
\(546\) | −0.488291 | −0.0208969 | ||||||||
\(547\) | −16.4297 | −0.702485 | −0.351242 | − | 0.936285i | \(-0.614241\pi\) | ||||
−0.351242 | + | 0.936285i | \(0.614241\pi\) | |||||||
\(548\) | −16.3335 | −0.697734 | ||||||||
\(549\) | 3.64618 | 0.155615 | ||||||||
\(550\) | −70.7275 | −3.01583 | ||||||||
\(551\) | 0.0537792 | 0.00229107 | ||||||||
\(552\) | 7.55016 | 0.321356 | ||||||||
\(553\) | −8.79289 | −0.373912 | ||||||||
\(554\) | 30.5060 | 1.29608 | ||||||||
\(555\) | 22.6952 | 0.963357 | ||||||||
\(556\) | 9.81016 | 0.416043 | ||||||||
\(557\) | −40.4682 | −1.71469 | −0.857347 | − | 0.514739i | \(-0.827889\pi\) | ||||
−0.857347 | + | 0.514739i | \(0.827889\pi\) | |||||||
\(558\) | −4.22341 | −0.178791 | ||||||||
\(559\) | 1.30328 | 0.0551227 | ||||||||
\(560\) | −4.14271 | −0.175062 | ||||||||
\(561\) | 33.8895 | 1.43082 | ||||||||
\(562\) | 0.299543 | 0.0126354 | ||||||||
\(563\) | 8.20347 | 0.345735 | 0.172868 | − | 0.984945i | \(-0.444697\pi\) | ||||
0.172868 | + | 0.984945i | \(0.444697\pi\) | |||||||
\(564\) | −22.1395 | −0.932241 | ||||||||
\(565\) | −35.9558 | −1.51267 | ||||||||
\(566\) | 6.89607 | 0.289864 | ||||||||
\(567\) | 10.2655 | 0.431109 | ||||||||
\(568\) | 6.06103 | 0.254315 | ||||||||
\(569\) | 22.1725 | 0.929520 | 0.464760 | − | 0.885437i | \(-0.346141\pi\) | ||||
0.464760 | + | 0.885437i | \(0.346141\pi\) | |||||||
\(570\) | 9.89701 | 0.414540 | ||||||||
\(571\) | −36.4729 | −1.52634 | −0.763172 | − | 0.646195i | \(-0.776359\pi\) | ||||
−0.763172 | + | 0.646195i | \(0.776359\pi\) | |||||||
\(572\) | 1.14782 | 0.0479926 | ||||||||
\(573\) | 37.2922 | 1.55790 | ||||||||
\(574\) | −0.922857 | −0.0385193 | ||||||||
\(575\) | −45.5844 | −1.90100 | ||||||||
\(576\) | 2.21398 | 0.0922491 | ||||||||
\(577\) | 4.67388 | 0.194576 | 0.0972881 | − | 0.995256i | \(-0.468983\pi\) | ||||
0.0972881 | + | 0.995256i | \(0.468983\pi\) | |||||||
\(578\) | −8.63099 | −0.359002 | ||||||||
\(579\) | 50.8855 | 2.11473 | ||||||||
\(580\) | −0.233095 | −0.00967876 | ||||||||
\(581\) | −15.5105 | −0.643482 | ||||||||
\(582\) | −29.0579 | −1.20449 | ||||||||
\(583\) | −55.7577 | −2.30925 | ||||||||
\(584\) | 3.78080 | 0.156451 | ||||||||
\(585\) | −2.14695 | −0.0887654 | ||||||||
\(586\) | 10.4173 | 0.430335 | ||||||||
\(587\) | −0.250896 | −0.0103556 | −0.00517780 | − | 0.999987i | \(-0.501648\pi\) | ||||
−0.00517780 | + | 0.999987i | \(0.501648\pi\) | |||||||
\(588\) | 13.8979 | 0.573140 | ||||||||
\(589\) | 1.90761 | 0.0786017 | ||||||||
\(590\) | 18.5128 | 0.762160 | ||||||||
\(591\) | 16.0247 | 0.659169 | ||||||||
\(592\) | −2.29313 | −0.0942472 | ||||||||
\(593\) | 32.7873 | 1.34641 | 0.673207 | − | 0.739454i | \(-0.264916\pi\) | ||||
0.673207 | + | 0.739454i | \(0.264916\pi\) | |||||||
\(594\) | −9.20794 | −0.377806 | ||||||||
\(595\) | −11.9845 | −0.491319 | ||||||||
\(596\) | 0.990937 | 0.0405904 | ||||||||
\(597\) | 18.8782 | 0.772633 | ||||||||
\(598\) | 0.739776 | 0.0302517 | ||||||||
\(599\) | −15.4877 | −0.632812 | −0.316406 | − | 0.948624i | \(-0.602476\pi\) | ||||
−0.316406 | + | 0.948624i | \(0.602476\pi\) | |||||||
\(600\) | −31.4796 | −1.28515 | ||||||||
\(601\) | 21.1575 | 0.863031 | 0.431516 | − | 0.902106i | \(-0.357979\pi\) | ||||
0.431516 | + | 0.902106i | \(0.357979\pi\) | |||||||
\(602\) | 5.56766 | 0.226921 | ||||||||
\(603\) | −25.9158 | −1.05537 | ||||||||
\(604\) | 10.4306 | 0.424414 | ||||||||
\(605\) | 66.4018 | 2.69962 | ||||||||
\(606\) | −38.8992 | −1.58017 | ||||||||
\(607\) | 3.06005 | 0.124204 | 0.0621018 | − | 0.998070i | \(-0.480220\pi\) | ||||
0.0621018 | + | 0.998070i | \(0.480220\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | −0.117372 | −0.00475615 | ||||||||
\(610\) | 7.13812 | 0.289014 | ||||||||
\(611\) | −2.16926 | −0.0877589 | ||||||||
\(612\) | 6.40487 | 0.258902 | ||||||||
\(613\) | −18.4730 | −0.746117 | −0.373059 | − | 0.927808i | \(-0.621691\pi\) | ||||
−0.373059 | + | 0.927808i | \(0.621691\pi\) | |||||||
\(614\) | −24.1824 | −0.975921 | ||||||||
\(615\) | −9.55594 | −0.385333 | ||||||||
\(616\) | 4.90353 | 0.197569 | ||||||||
\(617\) | 18.4812 | 0.744026 | 0.372013 | − | 0.928227i | \(-0.378668\pi\) | ||||
0.372013 | + | 0.928227i | \(0.378668\pi\) | |||||||
\(618\) | 24.1199 | 0.970247 | ||||||||
\(619\) | −19.8455 | −0.797659 | −0.398829 | − | 0.917025i | \(-0.630583\pi\) | ||||
−0.398829 | + | 0.917025i | \(0.630583\pi\) | |||||||
\(620\) | −8.26816 | −0.332057 | ||||||||
\(621\) | −5.93459 | −0.238147 | ||||||||
\(622\) | 4.73300 | 0.189776 | ||||||||
\(623\) | −14.8537 | −0.595100 | ||||||||
\(624\) | 0.510873 | 0.0204513 | ||||||||
\(625\) | 96.1285 | 3.84514 | ||||||||
\(626\) | 9.38214 | 0.374986 | ||||||||
\(627\) | −11.7146 | −0.467837 | ||||||||
\(628\) | −8.84405 | −0.352916 | ||||||||
\(629\) | −6.63386 | −0.264509 | ||||||||
\(630\) | −9.17188 | −0.365416 | ||||||||
\(631\) | 0.596367 | 0.0237410 | 0.0118705 | − | 0.999930i | \(-0.496221\pi\) | ||||
0.0118705 | + | 0.999930i | \(0.496221\pi\) | |||||||
\(632\) | 9.19955 | 0.365939 | ||||||||
\(633\) | 2.28341 | 0.0907576 | ||||||||
\(634\) | 16.9015 | 0.671244 | ||||||||
\(635\) | 83.8424 | 3.32718 | ||||||||
\(636\) | −24.8168 | −0.984050 | ||||||||
\(637\) | 1.36174 | 0.0539540 | ||||||||
\(638\) | 0.275904 | 0.0109231 | ||||||||
\(639\) | 13.4190 | 0.530847 | ||||||||
\(640\) | 4.33431 | 0.171328 | ||||||||
\(641\) | −16.1306 | −0.637121 | −0.318560 | − | 0.947903i | \(-0.603199\pi\) | ||||
−0.318560 | + | 0.947903i | \(0.603199\pi\) | |||||||
\(642\) | 8.19853 | 0.323570 | ||||||||
\(643\) | 39.1153 | 1.54256 | 0.771278 | − | 0.636498i | \(-0.219618\pi\) | ||||
0.771278 | + | 0.636498i | \(0.219618\pi\) | |||||||
\(644\) | 3.16036 | 0.124536 | ||||||||
\(645\) | 57.6517 | 2.27003 | ||||||||
\(646\) | −2.89292 | −0.113821 | ||||||||
\(647\) | −19.0893 | −0.750478 | −0.375239 | − | 0.926928i | \(-0.622439\pi\) | ||||
−0.375239 | + | 0.926928i | \(0.622439\pi\) | |||||||
\(648\) | −10.7402 | −0.421916 | ||||||||
\(649\) | −21.9127 | −0.860149 | ||||||||
\(650\) | −3.08442 | −0.120981 | ||||||||
\(651\) | −4.16331 | −0.163173 | ||||||||
\(652\) | 0.889463 | 0.0348340 | ||||||||
\(653\) | 21.4411 | 0.839056 | 0.419528 | − | 0.907742i | \(-0.362196\pi\) | ||||
0.419528 | + | 0.907742i | \(0.362196\pi\) | |||||||
\(654\) | −11.1419 | −0.435684 | ||||||||
\(655\) | 39.9017 | 1.55909 | ||||||||
\(656\) | 0.965538 | 0.0376979 | ||||||||
\(657\) | 8.37061 | 0.326569 | ||||||||
\(658\) | −9.26719 | −0.361273 | ||||||||
\(659\) | 4.82406 | 0.187919 | 0.0939593 | − | 0.995576i | \(-0.470048\pi\) | ||||
0.0939593 | + | 0.995576i | \(0.470048\pi\) | |||||||
\(660\) | 50.7747 | 1.97640 | ||||||||
\(661\) | 20.1301 | 0.782969 | 0.391484 | − | 0.920185i | \(-0.371962\pi\) | ||||
0.391484 | + | 0.920185i | \(0.371962\pi\) | |||||||
\(662\) | 3.06898 | 0.119279 | ||||||||
\(663\) | 1.47792 | 0.0573976 | ||||||||
\(664\) | 16.2278 | 0.629761 | ||||||||
\(665\) | 4.14271 | 0.160647 | ||||||||
\(666\) | −5.07695 | −0.196728 | ||||||||
\(667\) | 0.177822 | 0.00688530 | ||||||||
\(668\) | 7.07473 | 0.273729 | ||||||||
\(669\) | −47.1544 | −1.82309 | ||||||||
\(670\) | −50.7353 | −1.96008 | ||||||||
\(671\) | −8.44904 | −0.326172 | ||||||||
\(672\) | 2.18248 | 0.0841909 | ||||||||
\(673\) | 18.7453 | 0.722577 | 0.361288 | − | 0.932454i | \(-0.382337\pi\) | ||||
0.361288 | + | 0.932454i | \(0.382337\pi\) | |||||||
\(674\) | 12.0774 | 0.465204 | ||||||||
\(675\) | 24.7436 | 0.952383 | ||||||||
\(676\) | −12.9499 | −0.498075 | ||||||||
\(677\) | 29.3705 | 1.12880 | 0.564399 | − | 0.825502i | \(-0.309108\pi\) | ||||
0.564399 | + | 0.825502i | \(0.309108\pi\) | |||||||
\(678\) | 18.9424 | 0.727477 | ||||||||
\(679\) | −12.1631 | −0.466777 | ||||||||
\(680\) | 12.5388 | 0.480842 | ||||||||
\(681\) | −17.5448 | −0.672320 | ||||||||
\(682\) | 9.78662 | 0.374749 | ||||||||
\(683\) | −10.0911 | −0.386125 | −0.193062 | − | 0.981186i | \(-0.561842\pi\) | ||||
−0.193062 | + | 0.981186i | \(0.561842\pi\) | |||||||
\(684\) | −2.21398 | −0.0846536 | ||||||||
\(685\) | −70.7945 | −2.70492 | ||||||||
\(686\) | 12.5080 | 0.477557 | ||||||||
\(687\) | 67.7227 | 2.58378 | ||||||||
\(688\) | −5.82516 | −0.222082 | ||||||||
\(689\) | −2.43159 | −0.0926361 | ||||||||
\(690\) | 32.7247 | 1.24581 | ||||||||
\(691\) | 0.478655 | 0.0182089 | 0.00910445 | − | 0.999959i | \(-0.497102\pi\) | ||||
0.00910445 | + | 0.999959i | \(0.497102\pi\) | |||||||
\(692\) | −2.39066 | −0.0908792 | ||||||||
\(693\) | 10.8563 | 0.412397 | ||||||||
\(694\) | −30.2646 | −1.14883 | ||||||||
\(695\) | 42.5202 | 1.61288 | ||||||||
\(696\) | 0.122800 | 0.00465473 | ||||||||
\(697\) | 2.79323 | 0.105801 | ||||||||
\(698\) | −0.577196 | −0.0218472 | ||||||||
\(699\) | −6.33231 | −0.239510 | ||||||||
\(700\) | −13.1768 | −0.498036 | ||||||||
\(701\) | −51.6805 | −1.95194 | −0.975972 | − | 0.217895i | \(-0.930081\pi\) | ||||
−0.975972 | + | 0.217895i | \(0.930081\pi\) | |||||||
\(702\) | −0.401557 | −0.0151558 | ||||||||
\(703\) | 2.29313 | 0.0864872 | ||||||||
\(704\) | −5.13031 | −0.193356 | ||||||||
\(705\) | −95.9593 | −3.61404 | ||||||||
\(706\) | −32.8742 | −1.23724 | ||||||||
\(707\) | −16.2825 | −0.612367 | ||||||||
\(708\) | −9.75297 | −0.366539 | ||||||||
\(709\) | −34.8782 | −1.30988 | −0.654940 | − | 0.755681i | \(-0.727306\pi\) | ||||
−0.654940 | + | 0.755681i | \(0.727306\pi\) | |||||||
\(710\) | 26.2704 | 0.985910 | ||||||||
\(711\) | 20.3676 | 0.763845 | ||||||||
\(712\) | 15.5406 | 0.582410 | ||||||||
\(713\) | 6.30756 | 0.236220 | ||||||||
\(714\) | 6.31374 | 0.236286 | ||||||||
\(715\) | 4.97498 | 0.186054 | ||||||||
\(716\) | 8.08589 | 0.302184 | ||||||||
\(717\) | 11.9226 | 0.445259 | ||||||||
\(718\) | −22.0424 | −0.822617 | ||||||||
\(719\) | −44.3798 | −1.65509 | −0.827544 | − | 0.561400i | \(-0.810263\pi\) | ||||
−0.827544 | + | 0.561400i | \(0.810263\pi\) | |||||||
\(720\) | 9.59606 | 0.357624 | ||||||||
\(721\) | 10.0962 | 0.376001 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 5.29673 | 0.196988 | ||||||||
\(724\) | 0.291984 | 0.0108515 | ||||||||
\(725\) | −0.741411 | −0.0275353 | ||||||||
\(726\) | −34.9820 | −1.29831 | ||||||||
\(727\) | −28.5440 | −1.05864 | −0.529319 | − | 0.848423i | \(-0.677552\pi\) | ||||
−0.529319 | + | 0.848423i | \(0.677552\pi\) | |||||||
\(728\) | 0.213842 | 0.00792553 | ||||||||
\(729\) | −11.4838 | −0.425324 | ||||||||
\(730\) | 16.3872 | 0.606516 | ||||||||
\(731\) | −16.8517 | −0.623284 | ||||||||
\(732\) | −3.76053 | −0.138993 | ||||||||
\(733\) | −38.2904 | −1.41429 | −0.707143 | − | 0.707070i | \(-0.750016\pi\) | ||||
−0.707143 | + | 0.707070i | \(0.750016\pi\) | |||||||
\(734\) | 28.0980 | 1.03712 | ||||||||
\(735\) | 60.2377 | 2.22190 | ||||||||
\(736\) | −3.30652 | −0.121880 | ||||||||
\(737\) | 60.0529 | 2.21208 | ||||||||
\(738\) | 2.13768 | 0.0786891 | ||||||||
\(739\) | −4.86293 | −0.178886 | −0.0894429 | − | 0.995992i | \(-0.528509\pi\) | ||||
−0.0894429 | + | 0.995992i | \(0.528509\pi\) | |||||||
\(740\) | −9.93915 | −0.365370 | ||||||||
\(741\) | −0.510873 | −0.0187674 | ||||||||
\(742\) | −10.3879 | −0.381350 | ||||||||
\(743\) | −0.793285 | −0.0291028 | −0.0145514 | − | 0.999894i | \(-0.504632\pi\) | ||||
−0.0145514 | + | 0.999894i | \(0.504632\pi\) | |||||||
\(744\) | 4.35586 | 0.159694 | ||||||||
\(745\) | 4.29503 | 0.157358 | ||||||||
\(746\) | 32.0311 | 1.17274 | ||||||||
\(747\) | 35.9280 | 1.31454 | ||||||||
\(748\) | −14.8416 | −0.542662 | ||||||||
\(749\) | 3.43176 | 0.125394 | ||||||||
\(750\) | −86.9572 | −3.17523 | ||||||||
\(751\) | 4.93314 | 0.180013 | 0.0900065 | − | 0.995941i | \(-0.471311\pi\) | ||||
0.0900065 | + | 0.995941i | \(0.471311\pi\) | |||||||
\(752\) | 9.69579 | 0.353569 | ||||||||
\(753\) | −40.2372 | −1.46633 | ||||||||
\(754\) | 0.0120321 | 0.000438185 0 | ||||||||
\(755\) | 45.2093 | 1.64533 | ||||||||
\(756\) | −1.71547 | −0.0623912 | ||||||||
\(757\) | −39.2225 | −1.42557 | −0.712783 | − | 0.701385i | \(-0.752566\pi\) | ||||
−0.712783 | + | 0.701385i | \(0.752566\pi\) | |||||||
\(758\) | −37.9753 | −1.37933 | ||||||||
\(759\) | −38.7347 | −1.40598 | ||||||||
\(760\) | −4.33431 | −0.157222 | ||||||||
\(761\) | 35.6627 | 1.29277 | 0.646387 | − | 0.763010i | \(-0.276279\pi\) | ||||
0.646387 | + | 0.763010i | \(0.276279\pi\) | |||||||
\(762\) | −44.1701 | −1.60012 | ||||||||
\(763\) | −4.66381 | −0.168841 | ||||||||
\(764\) | −16.3318 | −0.590862 | ||||||||
\(765\) | 27.7607 | 1.00369 | ||||||||
\(766\) | 7.68475 | 0.277661 | ||||||||
\(767\) | −0.955611 | −0.0345051 | ||||||||
\(768\) | −2.28341 | −0.0823956 | ||||||||
\(769\) | −32.0463 | −1.15562 | −0.577810 | − | 0.816172i | \(-0.696092\pi\) | ||||
−0.577810 | + | 0.816172i | \(0.696092\pi\) | |||||||
\(770\) | 21.2534 | 0.765919 | ||||||||
\(771\) | 41.3085 | 1.48769 | ||||||||
\(772\) | −22.2848 | −0.802048 | ||||||||
\(773\) | −36.0321 | −1.29598 | −0.647992 | − | 0.761647i | \(-0.724391\pi\) | ||||
−0.647992 | + | 0.761647i | \(0.724391\pi\) | |||||||
\(774\) | −12.8968 | −0.463565 | ||||||||
\(775\) | −26.2987 | −0.944677 | ||||||||
\(776\) | 12.7256 | 0.456823 | ||||||||
\(777\) | −5.00471 | −0.179543 | ||||||||
\(778\) | 30.6879 | 1.10021 | ||||||||
\(779\) | −0.965538 | −0.0345940 | ||||||||
\(780\) | 2.21428 | 0.0792840 | ||||||||
\(781\) | −31.0950 | −1.11267 | ||||||||
\(782\) | −9.56552 | −0.342062 | ||||||||
\(783\) | −0.0965235 | −0.00344947 | ||||||||
\(784\) | −6.08645 | −0.217373 | ||||||||
\(785\) | −38.3328 | −1.36816 | ||||||||
\(786\) | −21.0212 | −0.749800 | ||||||||
\(787\) | −15.8706 | −0.565726 | −0.282863 | − | 0.959160i | \(-0.591284\pi\) | ||||
−0.282863 | + | 0.959160i | \(0.591284\pi\) | |||||||
\(788\) | −7.01787 | −0.250001 | ||||||||
\(789\) | 12.6128 | 0.449027 | ||||||||
\(790\) | 39.8737 | 1.41864 | ||||||||
\(791\) | 7.92893 | 0.281920 | ||||||||
\(792\) | −11.3584 | −0.403603 | ||||||||
\(793\) | −0.368462 | −0.0130845 | ||||||||
\(794\) | −11.9920 | −0.425579 | ||||||||
\(795\) | −107.564 | −3.81489 | ||||||||
\(796\) | −8.26753 | −0.293035 | ||||||||
\(797\) | −20.3226 | −0.719862 | −0.359931 | − | 0.932979i | \(-0.617200\pi\) | ||||
−0.359931 | + | 0.932979i | \(0.617200\pi\) | |||||||
\(798\) | −2.18248 | −0.0772589 | ||||||||
\(799\) | 28.0492 | 0.992308 | ||||||||
\(800\) | 13.7862 | 0.487416 | ||||||||
\(801\) | 34.4067 | 1.21570 | ||||||||
\(802\) | −3.28872 | −0.116129 | ||||||||
\(803\) | −19.3967 | −0.684494 | ||||||||
\(804\) | 26.7285 | 0.942643 | ||||||||
\(805\) | 13.6980 | 0.482790 | ||||||||
\(806\) | 0.426794 | 0.0150332 | ||||||||
\(807\) | −51.1238 | −1.79964 | ||||||||
\(808\) | 17.0356 | 0.599309 | ||||||||
\(809\) | −19.0189 | −0.668669 | −0.334334 | − | 0.942454i | \(-0.608512\pi\) | ||||
−0.334334 | + | 0.942454i | \(0.608512\pi\) | |||||||
\(810\) | −46.5515 | −1.63565 | ||||||||
\(811\) | −14.8294 | −0.520730 | −0.260365 | − | 0.965510i | \(-0.583843\pi\) | ||||
−0.260365 | + | 0.965510i | \(0.583843\pi\) | |||||||
\(812\) | 0.0514019 | 0.00180385 | ||||||||
\(813\) | −48.3452 | −1.69554 | ||||||||
\(814\) | 11.7645 | 0.412345 | ||||||||
\(815\) | 3.85520 | 0.135042 | ||||||||
\(816\) | −6.60574 | −0.231247 | ||||||||
\(817\) | 5.82516 | 0.203796 | ||||||||
\(818\) | 29.2267 | 1.02189 | ||||||||
\(819\) | 0.473443 | 0.0165434 | ||||||||
\(820\) | 4.18494 | 0.146144 | ||||||||
\(821\) | 14.0275 | 0.489562 | 0.244781 | − | 0.969578i | \(-0.421284\pi\) | ||||
0.244781 | + | 0.969578i | \(0.421284\pi\) | |||||||
\(822\) | 37.2962 | 1.30086 | ||||||||
\(823\) | 28.2974 | 0.986386 | 0.493193 | − | 0.869920i | \(-0.335830\pi\) | ||||
0.493193 | + | 0.869920i | \(0.335830\pi\) | |||||||
\(824\) | −10.5631 | −0.367983 | ||||||||
\(825\) | 161.500 | 5.62271 | ||||||||
\(826\) | −4.08242 | −0.142046 | ||||||||
\(827\) | 14.4380 | 0.502057 | 0.251029 | − | 0.967980i | \(-0.419231\pi\) | ||||
0.251029 | + | 0.967980i | \(0.419231\pi\) | |||||||
\(828\) | −7.32058 | −0.254408 | ||||||||
\(829\) | 44.2391 | 1.53649 | 0.768244 | − | 0.640157i | \(-0.221131\pi\) | ||||
0.768244 | + | 0.640157i | \(0.221131\pi\) | |||||||
\(830\) | 70.3363 | 2.44141 | ||||||||
\(831\) | −69.6578 | −2.41640 | ||||||||
\(832\) | −0.223732 | −0.00775652 | ||||||||
\(833\) | −17.6076 | −0.610069 | ||||||||
\(834\) | −22.4007 | −0.775671 | ||||||||
\(835\) | 30.6640 | 1.06117 | ||||||||
\(836\) | 5.13031 | 0.177435 | ||||||||
\(837\) | −3.42380 | −0.118344 | ||||||||
\(838\) | 35.5644 | 1.22855 | ||||||||
\(839\) | −8.61764 | −0.297514 | −0.148757 | − | 0.988874i | \(-0.547527\pi\) | ||||
−0.148757 | + | 0.988874i | \(0.547527\pi\) | |||||||
\(840\) | 9.45952 | 0.326385 | ||||||||
\(841\) | −28.9971 | −0.999900 | ||||||||
\(842\) | −18.5289 | −0.638549 | ||||||||
\(843\) | −0.683980 | −0.0235575 | ||||||||
\(844\) | −1.00000 | −0.0344214 | ||||||||
\(845\) | −56.1290 | −1.93090 | ||||||||
\(846\) | 21.4663 | 0.738025 | ||||||||
\(847\) | −14.6428 | −0.503134 | ||||||||
\(848\) | 10.8683 | 0.373219 | ||||||||
\(849\) | −15.7466 | −0.540421 | ||||||||
\(850\) | 39.8825 | 1.36796 | ||||||||
\(851\) | 7.58230 | 0.259918 | ||||||||
\(852\) | −13.8398 | −0.474145 | ||||||||
\(853\) | 43.5815 | 1.49220 | 0.746101 | − | 0.665833i | \(-0.231924\pi\) | ||||
0.746101 | + | 0.665833i | \(0.231924\pi\) | |||||||
\(854\) | −1.57409 | −0.0538642 | ||||||||
\(855\) | −9.59606 | −0.328178 | ||||||||
\(856\) | −3.59047 | −0.122720 | ||||||||
\(857\) | 7.04546 | 0.240668 | 0.120334 | − | 0.992733i | \(-0.461603\pi\) | ||||
0.120334 | + | 0.992733i | \(0.461603\pi\) | |||||||
\(858\) | −2.62094 | −0.0894774 | ||||||||
\(859\) | −14.2081 | −0.484774 | −0.242387 | − | 0.970180i | \(-0.577930\pi\) | ||||
−0.242387 | + | 0.970180i | \(0.577930\pi\) | |||||||
\(860\) | −25.2480 | −0.860950 | ||||||||
\(861\) | 2.10726 | 0.0718154 | ||||||||
\(862\) | 24.6150 | 0.838389 | ||||||||
\(863\) | −22.7307 | −0.773763 | −0.386882 | − | 0.922129i | \(-0.626448\pi\) | ||||
−0.386882 | + | 0.922129i | \(0.626448\pi\) | |||||||
\(864\) | 1.79481 | 0.0610607 | ||||||||
\(865\) | −10.3619 | −0.352313 | ||||||||
\(866\) | −38.2251 | −1.29894 | ||||||||
\(867\) | 19.7081 | 0.669323 | ||||||||
\(868\) | 1.82329 | 0.0618863 | ||||||||
\(869\) | −47.1965 | −1.60103 | ||||||||
\(870\) | 0.532253 | 0.0180451 | ||||||||
\(871\) | 2.61890 | 0.0887381 | ||||||||
\(872\) | 4.87950 | 0.165241 | ||||||||
\(873\) | 28.1743 | 0.953554 | ||||||||
\(874\) | 3.30652 | 0.111845 | ||||||||
\(875\) | −36.3987 | −1.23050 | ||||||||
\(876\) | −8.63313 | −0.291687 | ||||||||
\(877\) | 35.8319 | 1.20996 | 0.604979 | − | 0.796241i | \(-0.293182\pi\) | ||||
0.604979 | + | 0.796241i | \(0.293182\pi\) | |||||||
\(878\) | 4.87452 | 0.164507 | ||||||||
\(879\) | −23.7871 | −0.802317 | ||||||||
\(880\) | −22.2363 | −0.749586 | ||||||||
\(881\) | 8.59293 | 0.289503 | 0.144752 | − | 0.989468i | \(-0.453762\pi\) | ||||
0.144752 | + | 0.989468i | \(0.453762\pi\) | |||||||
\(882\) | −13.4753 | −0.453736 | ||||||||
\(883\) | 20.6165 | 0.693799 | 0.346899 | − | 0.937902i | \(-0.387235\pi\) | ||||
0.346899 | + | 0.937902i | \(0.387235\pi\) | |||||||
\(884\) | −0.647241 | −0.0217691 | ||||||||
\(885\) | −42.2724 | −1.42097 | ||||||||
\(886\) | 36.7284 | 1.23391 | ||||||||
\(887\) | 47.8875 | 1.60790 | 0.803952 | − | 0.594694i | \(-0.202727\pi\) | ||||
0.803952 | + | 0.594694i | \(0.202727\pi\) | |||||||
\(888\) | 5.23617 | 0.175715 | ||||||||
\(889\) | −18.4888 | −0.620095 | ||||||||
\(890\) | 67.3579 | 2.25784 | ||||||||
\(891\) | 55.1007 | 1.84594 | ||||||||
\(892\) | 20.6508 | 0.691441 | ||||||||
\(893\) | −9.69579 | −0.324457 | ||||||||
\(894\) | −2.26272 | −0.0756767 | ||||||||
\(895\) | 35.0467 | 1.17148 | ||||||||
\(896\) | −0.955796 | −0.0319309 | ||||||||
\(897\) | −1.68922 | −0.0564013 | ||||||||
\(898\) | 14.8606 | 0.495906 | ||||||||
\(899\) | 0.102590 | 0.00342156 | ||||||||
\(900\) | 30.5224 | 1.01741 | ||||||||
\(901\) | 31.4411 | 1.04746 | ||||||||
\(902\) | −4.95351 | −0.164934 | ||||||||
\(903\) | −12.7133 | −0.423071 | ||||||||
\(904\) | −8.29563 | −0.275909 | ||||||||
\(905\) | 1.26555 | 0.0420682 | ||||||||
\(906\) | −23.8173 | −0.791277 | ||||||||
\(907\) | −7.85610 | −0.260857 | −0.130429 | − | 0.991458i | \(-0.541635\pi\) | ||||
−0.130429 | + | 0.991458i | \(0.541635\pi\) | |||||||
\(908\) | 7.68360 | 0.254989 | ||||||||
\(909\) | 37.7164 | 1.25097 | ||||||||
\(910\) | 0.926858 | 0.0307251 | ||||||||
\(911\) | 31.2631 | 1.03579 | 0.517897 | − | 0.855443i | \(-0.326715\pi\) | ||||
0.517897 | + | 0.855443i | \(0.326715\pi\) | |||||||
\(912\) | 2.28341 | 0.0756114 | ||||||||
\(913\) | −83.2536 | −2.75529 | ||||||||
\(914\) | −34.4174 | −1.13843 | ||||||||
\(915\) | −16.2993 | −0.538837 | ||||||||
\(916\) | −29.6585 | −0.979945 | ||||||||
\(917\) | −8.79908 | −0.290571 | ||||||||
\(918\) | 5.19225 | 0.171370 | ||||||||
\(919\) | −34.9245 | −1.15205 | −0.576027 | − | 0.817431i | \(-0.695398\pi\) | ||||
−0.576027 | + | 0.817431i | \(0.695398\pi\) | |||||||
\(920\) | −14.3315 | −0.472495 | ||||||||
\(921\) | 55.2184 | 1.81951 | ||||||||
\(922\) | −12.0352 | −0.396357 | ||||||||
\(923\) | −1.35605 | −0.0446349 | ||||||||
\(924\) | −11.1968 | −0.368347 | ||||||||
\(925\) | −31.6136 | −1.03945 | ||||||||
\(926\) | 13.7270 | 0.451098 | ||||||||
\(927\) | −23.3865 | −0.768113 | ||||||||
\(928\) | −0.0537792 | −0.00176539 | ||||||||
\(929\) | 40.7402 | 1.33664 | 0.668321 | − | 0.743873i | \(-0.267013\pi\) | ||||
0.668321 | + | 0.743873i | \(0.267013\pi\) | |||||||
\(930\) | 18.8796 | 0.619088 | ||||||||
\(931\) | 6.08645 | 0.199475 | ||||||||
\(932\) | 2.77318 | 0.0908385 | ||||||||
\(933\) | −10.8074 | −0.353818 | ||||||||
\(934\) | 16.6043 | 0.543309 | ||||||||
\(935\) | −64.3280 | −2.10375 | ||||||||
\(936\) | −0.495339 | −0.0161907 | ||||||||
\(937\) | 26.8862 | 0.878333 | 0.439167 | − | 0.898406i | \(-0.355274\pi\) | ||||
0.439167 | + | 0.898406i | \(0.355274\pi\) | |||||||
\(938\) | 11.1881 | 0.365304 | ||||||||
\(939\) | −21.4233 | −0.699123 | ||||||||
\(940\) | 42.0245 | 1.37069 | ||||||||
\(941\) | −22.0354 | −0.718334 | −0.359167 | − | 0.933273i | \(-0.616939\pi\) | ||||
−0.359167 | + | 0.933273i | \(0.616939\pi\) | |||||||
\(942\) | 20.1946 | 0.657976 | ||||||||
\(943\) | −3.19257 | −0.103965 | ||||||||
\(944\) | 4.27122 | 0.139017 | ||||||||
\(945\) | −7.43539 | −0.241873 | ||||||||
\(946\) | 29.8848 | 0.971640 | ||||||||
\(947\) | −18.9954 | −0.617266 | −0.308633 | − | 0.951181i | \(-0.599871\pi\) | ||||
−0.308633 | + | 0.951181i | \(0.599871\pi\) | |||||||
\(948\) | −21.0064 | −0.682256 | ||||||||
\(949\) | −0.845887 | −0.0274587 | ||||||||
\(950\) | −13.7862 | −0.447284 | ||||||||
\(951\) | −38.5931 | −1.25147 | ||||||||
\(952\) | −2.76504 | −0.0896156 | ||||||||
\(953\) | −16.2966 | −0.527899 | −0.263949 | − | 0.964537i | \(-0.585025\pi\) | ||||
−0.263949 | + | 0.964537i | \(0.585025\pi\) | |||||||
\(954\) | 24.0622 | 0.779041 | ||||||||
\(955\) | −70.7869 | −2.29061 | ||||||||
\(956\) | −5.22141 | −0.168872 | ||||||||
\(957\) | −0.630002 | −0.0203651 | ||||||||
\(958\) | −35.6304 | −1.15117 | ||||||||
\(959\) | 15.6115 | 0.504122 | ||||||||
\(960\) | −9.89701 | −0.319425 | ||||||||
\(961\) | −27.3610 | −0.882614 | ||||||||
\(962\) | 0.513048 | 0.0165413 | ||||||||
\(963\) | −7.94922 | −0.256160 | ||||||||
\(964\) | −2.31966 | −0.0747111 | ||||||||
\(965\) | −96.5892 | −3.10932 | ||||||||
\(966\) | −7.21641 | −0.232184 | ||||||||
\(967\) | 2.68153 | 0.0862323 | 0.0431161 | − | 0.999070i | \(-0.486271\pi\) | ||||
0.0431161 | + | 0.999070i | \(0.486271\pi\) | |||||||
\(968\) | 15.3201 | 0.492405 | ||||||||
\(969\) | 6.60574 | 0.212207 | ||||||||
\(970\) | 55.1567 | 1.77098 | ||||||||
\(971\) | 47.4001 | 1.52114 | 0.760571 | − | 0.649255i | \(-0.224919\pi\) | ||||
0.760571 | + | 0.649255i | \(0.224919\pi\) | |||||||
\(972\) | 19.1400 | 0.613915 | ||||||||
\(973\) | −9.37651 | −0.300597 | ||||||||
\(974\) | −27.0689 | −0.867343 | ||||||||
\(975\) | 7.04301 | 0.225557 | ||||||||
\(976\) | 1.64689 | 0.0527156 | ||||||||
\(977\) | −42.5792 | −1.36223 | −0.681114 | − | 0.732177i | \(-0.738504\pi\) | ||||
−0.681114 | + | 0.732177i | \(0.738504\pi\) | |||||||
\(978\) | −2.03101 | −0.0649446 | ||||||||
\(979\) | −79.7283 | −2.54813 | ||||||||
\(980\) | −26.3806 | −0.842696 | ||||||||
\(981\) | 10.8031 | 0.344917 | ||||||||
\(982\) | 20.6028 | 0.657462 | ||||||||
\(983\) | −27.2983 | −0.870681 | −0.435340 | − | 0.900266i | \(-0.643372\pi\) | ||||
−0.435340 | + | 0.900266i | \(0.643372\pi\) | |||||||
\(984\) | −2.20472 | −0.0702840 | ||||||||
\(985\) | −30.4176 | −0.969186 | ||||||||
\(986\) | −0.155579 | −0.00495465 | ||||||||
\(987\) | 21.1608 | 0.673557 | ||||||||
\(988\) | 0.223732 | 0.00711787 | ||||||||
\(989\) | 19.2610 | 0.612465 | ||||||||
\(990\) | −49.2308 | −1.56466 | ||||||||
\(991\) | −60.9292 | −1.93548 | −0.967740 | − | 0.251951i | \(-0.918928\pi\) | ||||
−0.967740 | + | 0.251951i | \(0.918928\pi\) | |||||||
\(992\) | −1.90761 | −0.0605667 | ||||||||
\(993\) | −7.00776 | −0.222384 | ||||||||
\(994\) | −5.79311 | −0.183746 | ||||||||
\(995\) | −35.8340 | −1.13601 | ||||||||
\(996\) | −37.0548 | −1.17413 | ||||||||
\(997\) | −3.25619 | −0.103125 | −0.0515623 | − | 0.998670i | \(-0.516420\pi\) | ||||
−0.0515623 | + | 0.998670i | \(0.516420\pi\) | |||||||
\(998\) | 19.1318 | 0.605608 | ||||||||
\(999\) | −4.11574 | −0.130216 |
(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.j.1.8 | ✓ | 47 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.j.1.8 | ✓ | 47 | 1.1 | even | 1 | trivial |