Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6001,2,Mod(1,6001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6001, 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("6001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6001 = 17 \cdot 353 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6001.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: | \(47.9182262530\) |
Analytic rank: | \(1\) |
Dimension: | \(114\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 6001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.31496 | −1.63693 | −0.818464 | − | 0.574558i | \(-0.805174\pi\) | ||||
−0.818464 | + | 0.574558i | \(0.805174\pi\) | |||||||
\(3\) | −0.975130 | −0.562991 | −0.281496 | − | 0.959563i | \(-0.590831\pi\) | ||||
−0.281496 | + | 0.959563i | \(0.590831\pi\) | |||||||
\(4\) | 3.35906 | 1.67953 | ||||||||
\(5\) | −3.23089 | −1.44490 | −0.722449 | − | 0.691424i | \(-0.756984\pi\) | ||||
−0.722449 | + | 0.691424i | \(0.756984\pi\) | |||||||
\(6\) | 2.25739 | 0.921576 | ||||||||
\(7\) | 5.09566 | 1.92598 | 0.962989 | − | 0.269539i | \(-0.0868713\pi\) | ||||
0.962989 | + | 0.269539i | \(0.0868713\pi\) | |||||||
\(8\) | −3.14618 | −1.11234 | ||||||||
\(9\) | −2.04912 | −0.683041 | ||||||||
\(10\) | 7.47940 | 2.36519 | ||||||||
\(11\) | 3.94926 | 1.19075 | 0.595374 | − | 0.803449i | \(-0.297004\pi\) | ||||
0.595374 | + | 0.803449i | \(0.297004\pi\) | |||||||
\(12\) | −3.27552 | −0.945561 | ||||||||
\(13\) | 1.47706 | 0.409662 | 0.204831 | − | 0.978797i | \(-0.434336\pi\) | ||||
0.204831 | + | 0.978797i | \(0.434336\pi\) | |||||||
\(14\) | −11.7963 | −3.15269 | ||||||||
\(15\) | 3.15054 | 0.813465 | ||||||||
\(16\) | 0.565168 | 0.141292 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 4.74365 | 1.11809 | ||||||||
\(19\) | 0.961810 | 0.220654 | 0.110327 | − | 0.993895i | \(-0.464810\pi\) | ||||
0.110327 | + | 0.993895i | \(0.464810\pi\) | |||||||
\(20\) | −10.8528 | −2.42675 | ||||||||
\(21\) | −4.96893 | −1.08431 | ||||||||
\(22\) | −9.14240 | −1.94917 | ||||||||
\(23\) | 0.0822184 | 0.0171437 | 0.00857186 | − | 0.999963i | \(-0.497271\pi\) | ||||
0.00857186 | + | 0.999963i | \(0.497271\pi\) | |||||||
\(24\) | 3.06793 | 0.626239 | ||||||||
\(25\) | 5.43865 | 1.08773 | ||||||||
\(26\) | −3.41933 | −0.670586 | ||||||||
\(27\) | 4.92355 | 0.947537 | ||||||||
\(28\) | 17.1166 | 3.23474 | ||||||||
\(29\) | 1.83070 | 0.339953 | 0.169976 | − | 0.985448i | \(-0.445631\pi\) | ||||
0.169976 | + | 0.985448i | \(0.445631\pi\) | |||||||
\(30\) | −7.29338 | −1.33158 | ||||||||
\(31\) | −1.55664 | −0.279580 | −0.139790 | − | 0.990181i | \(-0.544643\pi\) | ||||
−0.139790 | + | 0.990181i | \(0.544643\pi\) | |||||||
\(32\) | 4.98401 | 0.881057 | ||||||||
\(33\) | −3.85104 | −0.670380 | ||||||||
\(34\) | −2.31496 | −0.397013 | ||||||||
\(35\) | −16.4635 | −2.78284 | ||||||||
\(36\) | −6.88313 | −1.14719 | ||||||||
\(37\) | −2.94351 | −0.483910 | −0.241955 | − | 0.970287i | \(-0.577789\pi\) | ||||
−0.241955 | + | 0.970287i | \(0.577789\pi\) | |||||||
\(38\) | −2.22656 | −0.361195 | ||||||||
\(39\) | −1.44032 | −0.230636 | ||||||||
\(40\) | 10.1650 | 1.60722 | ||||||||
\(41\) | −5.60727 | −0.875709 | −0.437855 | − | 0.899046i | \(-0.644262\pi\) | ||||
−0.437855 | + | 0.899046i | \(0.644262\pi\) | |||||||
\(42\) | 11.5029 | 1.77494 | ||||||||
\(43\) | −4.26746 | −0.650781 | −0.325390 | − | 0.945580i | \(-0.605496\pi\) | ||||
−0.325390 | + | 0.945580i | \(0.605496\pi\) | |||||||
\(44\) | 13.2658 | 1.99990 | ||||||||
\(45\) | 6.62049 | 0.986924 | ||||||||
\(46\) | −0.190333 | −0.0280630 | ||||||||
\(47\) | −2.32412 | −0.339008 | −0.169504 | − | 0.985529i | \(-0.554217\pi\) | ||||
−0.169504 | + | 0.985529i | \(0.554217\pi\) | |||||||
\(48\) | −0.551112 | −0.0795462 | ||||||||
\(49\) | 18.9658 | 2.70939 | ||||||||
\(50\) | −12.5903 | −1.78053 | ||||||||
\(51\) | −0.975130 | −0.136545 | ||||||||
\(52\) | 4.96152 | 0.688039 | ||||||||
\(53\) | −12.8541 | −1.76565 | −0.882825 | − | 0.469702i | \(-0.844361\pi\) | ||||
−0.882825 | + | 0.469702i | \(0.844361\pi\) | |||||||
\(54\) | −11.3978 | −1.55105 | ||||||||
\(55\) | −12.7596 | −1.72051 | ||||||||
\(56\) | −16.0319 | −2.14235 | ||||||||
\(57\) | −0.937889 | −0.124226 | ||||||||
\(58\) | −4.23801 | −0.556478 | ||||||||
\(59\) | −3.51340 | −0.457406 | −0.228703 | − | 0.973496i | \(-0.573448\pi\) | ||||
−0.228703 | + | 0.973496i | \(0.573448\pi\) | |||||||
\(60\) | 10.5828 | 1.36624 | ||||||||
\(61\) | 11.7464 | 1.50397 | 0.751987 | − | 0.659178i | \(-0.229096\pi\) | ||||
0.751987 | + | 0.659178i | \(0.229096\pi\) | |||||||
\(62\) | 3.60356 | 0.457653 | ||||||||
\(63\) | −10.4416 | −1.31552 | ||||||||
\(64\) | −12.6681 | −1.58352 | ||||||||
\(65\) | −4.77221 | −0.591919 | ||||||||
\(66\) | 8.91502 | 1.09736 | ||||||||
\(67\) | −7.16350 | −0.875161 | −0.437580 | − | 0.899179i | \(-0.644164\pi\) | ||||
−0.437580 | + | 0.899179i | \(0.644164\pi\) | |||||||
\(68\) | 3.35906 | 0.407346 | ||||||||
\(69\) | −0.0801736 | −0.00965176 | ||||||||
\(70\) | 38.1125 | 4.55531 | ||||||||
\(71\) | −3.49907 | −0.415263 | −0.207631 | − | 0.978207i | \(-0.566575\pi\) | ||||
−0.207631 | + | 0.978207i | \(0.566575\pi\) | |||||||
\(72\) | 6.44690 | 0.759775 | ||||||||
\(73\) | 3.92593 | 0.459496 | 0.229748 | − | 0.973250i | \(-0.426210\pi\) | ||||
0.229748 | + | 0.973250i | \(0.426210\pi\) | |||||||
\(74\) | 6.81412 | 0.792125 | ||||||||
\(75\) | −5.30339 | −0.612383 | ||||||||
\(76\) | 3.23078 | 0.370596 | ||||||||
\(77\) | 20.1241 | 2.29335 | ||||||||
\(78\) | 3.33429 | 0.377534 | ||||||||
\(79\) | −15.0133 | −1.68912 | −0.844562 | − | 0.535458i | \(-0.820139\pi\) | ||||
−0.844562 | + | 0.535458i | \(0.820139\pi\) | |||||||
\(80\) | −1.82600 | −0.204153 | ||||||||
\(81\) | 1.34627 | 0.149585 | ||||||||
\(82\) | 12.9806 | 1.43347 | ||||||||
\(83\) | −12.0942 | −1.32751 | −0.663753 | − | 0.747952i | \(-0.731037\pi\) | ||||
−0.663753 | + | 0.747952i | \(0.731037\pi\) | |||||||
\(84\) | −16.6909 | −1.82113 | ||||||||
\(85\) | −3.23089 | −0.350439 | ||||||||
\(86\) | 9.87901 | 1.06528 | ||||||||
\(87\) | −1.78517 | −0.191390 | ||||||||
\(88\) | −12.4251 | −1.32452 | ||||||||
\(89\) | −9.02816 | −0.956983 | −0.478491 | − | 0.878092i | \(-0.658816\pi\) | ||||
−0.478491 | + | 0.878092i | \(0.658816\pi\) | |||||||
\(90\) | −15.3262 | −1.61552 | ||||||||
\(91\) | 7.52658 | 0.789000 | ||||||||
\(92\) | 0.276176 | 0.0287934 | ||||||||
\(93\) | 1.51792 | 0.157401 | ||||||||
\(94\) | 5.38026 | 0.554932 | ||||||||
\(95\) | −3.10750 | −0.318823 | ||||||||
\(96\) | −4.86006 | −0.496027 | ||||||||
\(97\) | −15.5578 | −1.57966 | −0.789830 | − | 0.613326i | \(-0.789831\pi\) | ||||
−0.789830 | + | 0.613326i | \(0.789831\pi\) | |||||||
\(98\) | −43.9051 | −4.43508 | ||||||||
\(99\) | −8.09252 | −0.813329 | ||||||||
\(100\) | 18.2688 | 1.82688 | ||||||||
\(101\) | −17.1315 | −1.70465 | −0.852325 | − | 0.523013i | \(-0.824808\pi\) | ||||
−0.852325 | + | 0.523013i | \(0.824808\pi\) | |||||||
\(102\) | 2.25739 | 0.223515 | ||||||||
\(103\) | 11.3524 | 1.11858 | 0.559291 | − | 0.828972i | \(-0.311074\pi\) | ||||
0.559291 | + | 0.828972i | \(0.311074\pi\) | |||||||
\(104\) | −4.64708 | −0.455684 | ||||||||
\(105\) | 16.0541 | 1.56672 | ||||||||
\(106\) | 29.7569 | 2.89024 | ||||||||
\(107\) | 6.89544 | 0.666608 | 0.333304 | − | 0.942819i | \(-0.391837\pi\) | ||||
0.333304 | + | 0.942819i | \(0.391837\pi\) | |||||||
\(108\) | 16.5385 | 1.59142 | ||||||||
\(109\) | 4.21954 | 0.404159 | 0.202079 | − | 0.979369i | \(-0.435230\pi\) | ||||
0.202079 | + | 0.979369i | \(0.435230\pi\) | |||||||
\(110\) | 29.5381 | 2.81635 | ||||||||
\(111\) | 2.87030 | 0.272437 | ||||||||
\(112\) | 2.87991 | 0.272126 | ||||||||
\(113\) | −15.1434 | −1.42457 | −0.712285 | − | 0.701890i | \(-0.752340\pi\) | ||||
−0.712285 | + | 0.701890i | \(0.752340\pi\) | |||||||
\(114\) | 2.17118 | 0.203350 | ||||||||
\(115\) | −0.265638 | −0.0247709 | ||||||||
\(116\) | 6.14944 | 0.570961 | ||||||||
\(117\) | −3.02667 | −0.279816 | ||||||||
\(118\) | 8.13340 | 0.748740 | ||||||||
\(119\) | 5.09566 | 0.467119 | ||||||||
\(120\) | −9.91215 | −0.904851 | ||||||||
\(121\) | 4.59666 | 0.417879 | ||||||||
\(122\) | −27.1925 | −2.46190 | ||||||||
\(123\) | 5.46782 | 0.493017 | ||||||||
\(124\) | −5.22884 | −0.469564 | ||||||||
\(125\) | −1.41723 | −0.126761 | ||||||||
\(126\) | 24.1720 | 2.15341 | ||||||||
\(127\) | 11.7883 | 1.04604 | 0.523022 | − | 0.852319i | \(-0.324804\pi\) | ||||
0.523022 | + | 0.852319i | \(0.324804\pi\) | |||||||
\(128\) | 19.3583 | 1.71105 | ||||||||
\(129\) | 4.16132 | 0.366384 | ||||||||
\(130\) | 11.0475 | 0.968929 | ||||||||
\(131\) | 14.2259 | 1.24292 | 0.621461 | − | 0.783445i | \(-0.286540\pi\) | ||||
0.621461 | + | 0.783445i | \(0.286540\pi\) | |||||||
\(132\) | −12.9359 | −1.12592 | ||||||||
\(133\) | 4.90106 | 0.424976 | ||||||||
\(134\) | 16.5833 | 1.43257 | ||||||||
\(135\) | −15.9074 | −1.36909 | ||||||||
\(136\) | −3.14618 | −0.269783 | ||||||||
\(137\) | −15.3869 | −1.31459 | −0.657296 | − | 0.753633i | \(-0.728300\pi\) | ||||
−0.657296 | + | 0.753633i | \(0.728300\pi\) | |||||||
\(138\) | 0.185599 | 0.0157992 | ||||||||
\(139\) | 8.67144 | 0.735502 | 0.367751 | − | 0.929924i | \(-0.380128\pi\) | ||||
0.367751 | + | 0.929924i | \(0.380128\pi\) | |||||||
\(140\) | −55.3020 | −4.67387 | ||||||||
\(141\) | 2.26632 | 0.190859 | ||||||||
\(142\) | 8.10022 | 0.679755 | ||||||||
\(143\) | 5.83328 | 0.487803 | ||||||||
\(144\) | −1.15810 | −0.0965083 | ||||||||
\(145\) | −5.91479 | −0.491197 | ||||||||
\(146\) | −9.08840 | −0.752161 | ||||||||
\(147\) | −18.4941 | −1.52537 | ||||||||
\(148\) | −9.88743 | −0.812741 | ||||||||
\(149\) | 9.16059 | 0.750465 | 0.375233 | − | 0.926931i | \(-0.377563\pi\) | ||||
0.375233 | + | 0.926931i | \(0.377563\pi\) | |||||||
\(150\) | 12.2772 | 1.00243 | ||||||||
\(151\) | 19.7017 | 1.60330 | 0.801652 | − | 0.597791i | \(-0.203955\pi\) | ||||
0.801652 | + | 0.597791i | \(0.203955\pi\) | |||||||
\(152\) | −3.02602 | −0.245443 | ||||||||
\(153\) | −2.04912 | −0.165662 | ||||||||
\(154\) | −46.5866 | −3.75405 | ||||||||
\(155\) | 5.02933 | 0.403965 | ||||||||
\(156\) | −4.83813 | −0.387360 | ||||||||
\(157\) | 9.17987 | 0.732633 | 0.366317 | − | 0.930490i | \(-0.380619\pi\) | ||||
0.366317 | + | 0.930490i | \(0.380619\pi\) | |||||||
\(158\) | 34.7552 | 2.76497 | ||||||||
\(159\) | 12.5344 | 0.994046 | ||||||||
\(160\) | −16.1028 | −1.27304 | ||||||||
\(161\) | 0.418957 | 0.0330184 | ||||||||
\(162\) | −3.11657 | −0.244861 | ||||||||
\(163\) | 12.5729 | 0.984784 | 0.492392 | − | 0.870374i | \(-0.336123\pi\) | ||||
0.492392 | + | 0.870374i | \(0.336123\pi\) | |||||||
\(164\) | −18.8352 | −1.47078 | ||||||||
\(165\) | 12.4423 | 0.968631 | ||||||||
\(166\) | 27.9975 | 2.17303 | ||||||||
\(167\) | −12.1075 | −0.936905 | −0.468452 | − | 0.883489i | \(-0.655188\pi\) | ||||
−0.468452 | + | 0.883489i | \(0.655188\pi\) | |||||||
\(168\) | 15.6331 | 1.20612 | ||||||||
\(169\) | −10.8183 | −0.832177 | ||||||||
\(170\) | 7.47940 | 0.573643 | ||||||||
\(171\) | −1.97087 | −0.150716 | ||||||||
\(172\) | −14.3346 | −1.09301 | ||||||||
\(173\) | −2.70441 | −0.205613 | −0.102806 | − | 0.994701i | \(-0.532782\pi\) | ||||
−0.102806 | + | 0.994701i | \(0.532782\pi\) | |||||||
\(174\) | 4.13261 | 0.313292 | ||||||||
\(175\) | 27.7135 | 2.09495 | ||||||||
\(176\) | 2.23200 | 0.168243 | ||||||||
\(177\) | 3.42602 | 0.257516 | ||||||||
\(178\) | 20.8999 | 1.56651 | ||||||||
\(179\) | −8.36383 | −0.625142 | −0.312571 | − | 0.949894i | \(-0.601190\pi\) | ||||
−0.312571 | + | 0.949894i | \(0.601190\pi\) | |||||||
\(180\) | 22.2386 | 1.65757 | ||||||||
\(181\) | −26.4137 | −1.96332 | −0.981659 | − | 0.190645i | \(-0.938942\pi\) | ||||
−0.981659 | + | 0.190645i | \(0.938942\pi\) | |||||||
\(182\) | −17.4238 | −1.29154 | ||||||||
\(183\) | −11.4543 | −0.846724 | ||||||||
\(184\) | −0.258674 | −0.0190697 | ||||||||
\(185\) | 9.51015 | 0.699200 | ||||||||
\(186\) | −3.51394 | −0.257654 | ||||||||
\(187\) | 3.94926 | 0.288799 | ||||||||
\(188\) | −7.80687 | −0.569375 | ||||||||
\(189\) | 25.0887 | 1.82494 | ||||||||
\(190\) | 7.19376 | 0.521890 | ||||||||
\(191\) | 16.7188 | 1.20973 | 0.604863 | − | 0.796329i | \(-0.293228\pi\) | ||||
0.604863 | + | 0.796329i | \(0.293228\pi\) | |||||||
\(192\) | 12.3531 | 0.891507 | ||||||||
\(193\) | −8.30325 | −0.597681 | −0.298840 | − | 0.954303i | \(-0.596600\pi\) | ||||
−0.298840 | + | 0.954303i | \(0.596600\pi\) | |||||||
\(194\) | 36.0158 | 2.58579 | ||||||||
\(195\) | 4.65352 | 0.333245 | ||||||||
\(196\) | 63.7072 | 4.55051 | ||||||||
\(197\) | 16.4215 | 1.16999 | 0.584993 | − | 0.811038i | \(-0.301097\pi\) | ||||
0.584993 | + | 0.811038i | \(0.301097\pi\) | |||||||
\(198\) | 18.7339 | 1.33136 | ||||||||
\(199\) | 3.74110 | 0.265200 | 0.132600 | − | 0.991170i | \(-0.457668\pi\) | ||||
0.132600 | + | 0.991170i | \(0.457668\pi\) | |||||||
\(200\) | −17.1110 | −1.20993 | ||||||||
\(201\) | 6.98534 | 0.492708 | ||||||||
\(202\) | 39.6588 | 2.79039 | ||||||||
\(203\) | 9.32863 | 0.654742 | ||||||||
\(204\) | −3.27552 | −0.229332 | ||||||||
\(205\) | 18.1165 | 1.26531 | ||||||||
\(206\) | −26.2803 | −1.83104 | ||||||||
\(207\) | −0.168475 | −0.0117099 | ||||||||
\(208\) | 0.834786 | 0.0578820 | ||||||||
\(209\) | 3.79844 | 0.262743 | ||||||||
\(210\) | −37.1646 | −2.56460 | ||||||||
\(211\) | 6.58421 | 0.453276 | 0.226638 | − | 0.973979i | \(-0.427227\pi\) | ||||
0.226638 | + | 0.973979i | \(0.427227\pi\) | |||||||
\(212\) | −43.1778 | −2.96546 | ||||||||
\(213\) | 3.41204 | 0.233789 | ||||||||
\(214\) | −15.9627 | −1.09119 | ||||||||
\(215\) | 13.7877 | 0.940312 | ||||||||
\(216\) | −15.4904 | −1.05399 | ||||||||
\(217\) | −7.93210 | −0.538466 | ||||||||
\(218\) | −9.76809 | −0.661579 | ||||||||
\(219\) | −3.82829 | −0.258692 | ||||||||
\(220\) | −42.8604 | −2.88965 | ||||||||
\(221\) | 1.47706 | 0.0993576 | ||||||||
\(222\) | −6.64465 | −0.445960 | ||||||||
\(223\) | −1.28082 | −0.0857699 | −0.0428849 | − | 0.999080i | \(-0.513655\pi\) | ||||
−0.0428849 | + | 0.999080i | \(0.513655\pi\) | |||||||
\(224\) | 25.3968 | 1.69690 | ||||||||
\(225\) | −11.1445 | −0.742964 | ||||||||
\(226\) | 35.0564 | 2.33192 | ||||||||
\(227\) | 4.99025 | 0.331215 | 0.165607 | − | 0.986192i | \(-0.447042\pi\) | ||||
0.165607 | + | 0.986192i | \(0.447042\pi\) | |||||||
\(228\) | −3.15043 | −0.208642 | ||||||||
\(229\) | −21.5807 | −1.42609 | −0.713046 | − | 0.701118i | \(-0.752685\pi\) | ||||
−0.713046 | + | 0.701118i | \(0.752685\pi\) | |||||||
\(230\) | 0.614944 | 0.0405482 | ||||||||
\(231\) | −19.6236 | −1.29114 | ||||||||
\(232\) | −5.75971 | −0.378144 | ||||||||
\(233\) | 10.1690 | 0.666196 | 0.333098 | − | 0.942892i | \(-0.391906\pi\) | ||||
0.333098 | + | 0.942892i | \(0.391906\pi\) | |||||||
\(234\) | 7.00663 | 0.458038 | ||||||||
\(235\) | 7.50899 | 0.489832 | ||||||||
\(236\) | −11.8017 | −0.768227 | ||||||||
\(237\) | 14.6399 | 0.950962 | ||||||||
\(238\) | −11.7963 | −0.764639 | ||||||||
\(239\) | 5.95173 | 0.384986 | 0.192493 | − | 0.981298i | \(-0.438343\pi\) | ||||
0.192493 | + | 0.981298i | \(0.438343\pi\) | |||||||
\(240\) | 1.78058 | 0.114936 | ||||||||
\(241\) | −9.56344 | −0.616036 | −0.308018 | − | 0.951381i | \(-0.599666\pi\) | ||||
−0.308018 | + | 0.951381i | \(0.599666\pi\) | |||||||
\(242\) | −10.6411 | −0.684037 | ||||||||
\(243\) | −16.0834 | −1.03175 | ||||||||
\(244\) | 39.4569 | 2.52597 | ||||||||
\(245\) | −61.2763 | −3.91480 | ||||||||
\(246\) | −12.6578 | −0.807032 | ||||||||
\(247\) | 1.42065 | 0.0903936 | ||||||||
\(248\) | 4.89746 | 0.310989 | ||||||||
\(249\) | 11.7934 | 0.747375 | ||||||||
\(250\) | 3.28084 | 0.207499 | ||||||||
\(251\) | −19.5596 | −1.23459 | −0.617296 | − | 0.786731i | \(-0.711772\pi\) | ||||
−0.617296 | + | 0.786731i | \(0.711772\pi\) | |||||||
\(252\) | −35.0741 | −2.20946 | ||||||||
\(253\) | 0.324702 | 0.0204138 | ||||||||
\(254\) | −27.2896 | −1.71230 | ||||||||
\(255\) | 3.15054 | 0.197294 | ||||||||
\(256\) | −19.4775 | −1.21734 | ||||||||
\(257\) | −23.5030 | −1.46607 | −0.733037 | − | 0.680189i | \(-0.761898\pi\) | ||||
−0.733037 | + | 0.680189i | \(0.761898\pi\) | |||||||
\(258\) | −9.63331 | −0.599744 | ||||||||
\(259\) | −14.9991 | −0.932000 | ||||||||
\(260\) | −16.0301 | −0.994147 | ||||||||
\(261\) | −3.75133 | −0.232201 | ||||||||
\(262\) | −32.9324 | −2.03457 | ||||||||
\(263\) | 8.47884 | 0.522827 | 0.261414 | − | 0.965227i | \(-0.415811\pi\) | ||||
0.261414 | + | 0.965227i | \(0.415811\pi\) | |||||||
\(264\) | 12.1161 | 0.745692 | ||||||||
\(265\) | 41.5303 | 2.55118 | ||||||||
\(266\) | −11.3458 | −0.695654 | ||||||||
\(267\) | 8.80362 | 0.538773 | ||||||||
\(268\) | −24.0626 | −1.46986 | ||||||||
\(269\) | 5.93906 | 0.362111 | 0.181056 | − | 0.983473i | \(-0.442049\pi\) | ||||
0.181056 | + | 0.983473i | \(0.442049\pi\) | |||||||
\(270\) | 36.8252 | 2.24111 | ||||||||
\(271\) | 5.79440 | 0.351985 | 0.175992 | − | 0.984392i | \(-0.443687\pi\) | ||||
0.175992 | + | 0.984392i | \(0.443687\pi\) | |||||||
\(272\) | 0.565168 | 0.0342684 | ||||||||
\(273\) | −7.33939 | −0.444200 | ||||||||
\(274\) | 35.6201 | 2.15189 | ||||||||
\(275\) | 21.4787 | 1.29521 | ||||||||
\(276\) | −0.269308 | −0.0162104 | ||||||||
\(277\) | 14.7705 | 0.887471 | 0.443736 | − | 0.896158i | \(-0.353653\pi\) | ||||
0.443736 | + | 0.896158i | \(0.353653\pi\) | |||||||
\(278\) | −20.0741 | −1.20396 | ||||||||
\(279\) | 3.18974 | 0.190965 | ||||||||
\(280\) | 51.7972 | 3.09547 | ||||||||
\(281\) | 1.52330 | 0.0908726 | 0.0454363 | − | 0.998967i | \(-0.485532\pi\) | ||||
0.0454363 | + | 0.998967i | \(0.485532\pi\) | |||||||
\(282\) | −5.24645 | −0.312422 | ||||||||
\(283\) | 4.88616 | 0.290452 | 0.145226 | − | 0.989399i | \(-0.453609\pi\) | ||||
0.145226 | + | 0.989399i | \(0.453609\pi\) | |||||||
\(284\) | −11.7536 | −0.697447 | ||||||||
\(285\) | 3.03022 | 0.179495 | ||||||||
\(286\) | −13.5038 | −0.798499 | ||||||||
\(287\) | −28.5728 | −1.68660 | ||||||||
\(288\) | −10.2128 | −0.601798 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 13.6925 | 0.804053 | ||||||||
\(291\) | 15.1709 | 0.889334 | ||||||||
\(292\) | 13.1875 | 0.771737 | ||||||||
\(293\) | −30.0061 | −1.75297 | −0.876487 | − | 0.481426i | \(-0.840119\pi\) | ||||
−0.876487 | + | 0.481426i | \(0.840119\pi\) | |||||||
\(294\) | 42.8131 | 2.49691 | ||||||||
\(295\) | 11.3514 | 0.660905 | ||||||||
\(296\) | 9.26080 | 0.538273 | ||||||||
\(297\) | 19.4444 | 1.12828 | ||||||||
\(298\) | −21.2064 | −1.22846 | ||||||||
\(299\) | 0.121441 | 0.00702312 | ||||||||
\(300\) | −17.8144 | −1.02852 | ||||||||
\(301\) | −21.7455 | −1.25339 | ||||||||
\(302\) | −45.6088 | −2.62449 | ||||||||
\(303\) | 16.7054 | 0.959703 | ||||||||
\(304\) | 0.543585 | 0.0311767 | ||||||||
\(305\) | −37.9514 | −2.17309 | ||||||||
\(306\) | 4.74365 | 0.271176 | ||||||||
\(307\) | 22.0721 | 1.25972 | 0.629862 | − | 0.776707i | \(-0.283112\pi\) | ||||
0.629862 | + | 0.776707i | \(0.283112\pi\) | |||||||
\(308\) | 67.5981 | 3.85176 | ||||||||
\(309\) | −11.0700 | −0.629752 | ||||||||
\(310\) | −11.6427 | −0.661261 | ||||||||
\(311\) | 8.92023 | 0.505820 | 0.252910 | − | 0.967490i | \(-0.418612\pi\) | ||||
0.252910 | + | 0.967490i | \(0.418612\pi\) | |||||||
\(312\) | 4.53151 | 0.256546 | ||||||||
\(313\) | −3.71894 | −0.210207 | −0.105103 | − | 0.994461i | \(-0.533517\pi\) | ||||
−0.105103 | + | 0.994461i | \(0.533517\pi\) | |||||||
\(314\) | −21.2511 | −1.19927 | ||||||||
\(315\) | 33.7358 | 1.90080 | ||||||||
\(316\) | −50.4305 | −2.83694 | ||||||||
\(317\) | 16.4600 | 0.924488 | 0.462244 | − | 0.886753i | \(-0.347044\pi\) | ||||
0.462244 | + | 0.886753i | \(0.347044\pi\) | |||||||
\(318\) | −29.0168 | −1.62718 | ||||||||
\(319\) | 7.22992 | 0.404798 | ||||||||
\(320\) | 40.9294 | 2.28802 | ||||||||
\(321\) | −6.72395 | −0.375294 | ||||||||
\(322\) | −0.969870 | −0.0540488 | ||||||||
\(323\) | 0.961810 | 0.0535165 | ||||||||
\(324\) | 4.52220 | 0.251233 | ||||||||
\(325\) | 8.03319 | 0.445601 | ||||||||
\(326\) | −29.1058 | −1.61202 | ||||||||
\(327\) | −4.11460 | −0.227538 | ||||||||
\(328\) | 17.6415 | 0.974088 | ||||||||
\(329\) | −11.8429 | −0.652923 | ||||||||
\(330\) | −28.8035 | −1.58558 | ||||||||
\(331\) | 13.7072 | 0.753415 | 0.376708 | − | 0.926332i | \(-0.377056\pi\) | ||||
0.376708 | + | 0.926332i | \(0.377056\pi\) | |||||||
\(332\) | −40.6250 | −2.22959 | ||||||||
\(333\) | 6.03161 | 0.330530 | ||||||||
\(334\) | 28.0284 | 1.53364 | ||||||||
\(335\) | 23.1445 | 1.26452 | ||||||||
\(336\) | −2.80828 | −0.153204 | ||||||||
\(337\) | −3.18886 | −0.173709 | −0.0868543 | − | 0.996221i | \(-0.527681\pi\) | ||||
−0.0868543 | + | 0.996221i | \(0.527681\pi\) | |||||||
\(338\) | 25.0440 | 1.36221 | ||||||||
\(339\) | 14.7668 | 0.802021 | ||||||||
\(340\) | −10.8528 | −0.588573 | ||||||||
\(341\) | −6.14757 | −0.332910 | ||||||||
\(342\) | 4.56249 | 0.246711 | ||||||||
\(343\) | 60.9735 | 3.29226 | ||||||||
\(344\) | 13.4262 | 0.723891 | ||||||||
\(345\) | 0.259032 | 0.0139458 | ||||||||
\(346\) | 6.26062 | 0.336573 | ||||||||
\(347\) | −11.3690 | −0.610322 | −0.305161 | − | 0.952301i | \(-0.598710\pi\) | ||||
−0.305161 | + | 0.952301i | \(0.598710\pi\) | |||||||
\(348\) | −5.99650 | −0.321446 | ||||||||
\(349\) | −32.1142 | −1.71903 | −0.859517 | − | 0.511107i | \(-0.829235\pi\) | ||||
−0.859517 | + | 0.511107i | \(0.829235\pi\) | |||||||
\(350\) | −64.1558 | −3.42927 | ||||||||
\(351\) | 7.27236 | 0.388170 | ||||||||
\(352\) | 19.6832 | 1.04912 | ||||||||
\(353\) | 1.00000 | 0.0532246 | ||||||||
\(354\) | −7.93112 | −0.421534 | ||||||||
\(355\) | 11.3051 | 0.600013 | ||||||||
\(356\) | −30.3261 | −1.60728 | ||||||||
\(357\) | −4.96893 | −0.262984 | ||||||||
\(358\) | 19.3620 | 1.02331 | ||||||||
\(359\) | −8.22777 | −0.434245 | −0.217123 | − | 0.976144i | \(-0.569667\pi\) | ||||
−0.217123 | + | 0.976144i | \(0.569667\pi\) | |||||||
\(360\) | −20.8292 | −1.09780 | ||||||||
\(361\) | −18.0749 | −0.951312 | ||||||||
\(362\) | 61.1469 | 3.21381 | ||||||||
\(363\) | −4.48234 | −0.235262 | ||||||||
\(364\) | 25.2822 | 1.32515 | ||||||||
\(365\) | −12.6843 | −0.663925 | ||||||||
\(366\) | 26.5162 | 1.38603 | ||||||||
\(367\) | 2.86471 | 0.149537 | 0.0747683 | − | 0.997201i | \(-0.476178\pi\) | ||||
0.0747683 | + | 0.997201i | \(0.476178\pi\) | |||||||
\(368\) | 0.0464672 | 0.00242227 | ||||||||
\(369\) | 11.4900 | 0.598145 | ||||||||
\(370\) | −22.0157 | −1.14454 | ||||||||
\(371\) | −65.5003 | −3.40061 | ||||||||
\(372\) | 5.09880 | 0.264360 | ||||||||
\(373\) | −11.1652 | −0.578113 | −0.289056 | − | 0.957312i | \(-0.593342\pi\) | ||||
−0.289056 | + | 0.957312i | \(0.593342\pi\) | |||||||
\(374\) | −9.14240 | −0.472742 | ||||||||
\(375\) | 1.38198 | 0.0713654 | ||||||||
\(376\) | 7.31211 | 0.377093 | ||||||||
\(377\) | 2.70405 | 0.139266 | ||||||||
\(378\) | −58.0795 | −2.98729 | ||||||||
\(379\) | 13.1683 | 0.676410 | 0.338205 | − | 0.941072i | \(-0.390180\pi\) | ||||
0.338205 | + | 0.941072i | \(0.390180\pi\) | |||||||
\(380\) | −10.4383 | −0.535473 | ||||||||
\(381\) | −11.4951 | −0.588914 | ||||||||
\(382\) | −38.7033 | −1.98023 | ||||||||
\(383\) | −3.94285 | −0.201470 | −0.100735 | − | 0.994913i | \(-0.532119\pi\) | ||||
−0.100735 | + | 0.994913i | \(0.532119\pi\) | |||||||
\(384\) | −18.8768 | −0.963305 | ||||||||
\(385\) | −65.0187 | −3.31366 | ||||||||
\(386\) | 19.2217 | 0.978360 | ||||||||
\(387\) | 8.74454 | 0.444510 | ||||||||
\(388\) | −52.2597 | −2.65309 | ||||||||
\(389\) | −38.1938 | −1.93650 | −0.968251 | − | 0.249978i | \(-0.919577\pi\) | ||||
−0.968251 | + | 0.249978i | \(0.919577\pi\) | |||||||
\(390\) | −10.7727 | −0.545499 | ||||||||
\(391\) | 0.0822184 | 0.00415796 | ||||||||
\(392\) | −59.6697 | −3.01377 | ||||||||
\(393\) | −13.8721 | −0.699754 | ||||||||
\(394\) | −38.0153 | −1.91518 | ||||||||
\(395\) | 48.5062 | 2.44061 | ||||||||
\(396\) | −27.1833 | −1.36601 | ||||||||
\(397\) | 1.40125 | 0.0703266 | 0.0351633 | − | 0.999382i | \(-0.488805\pi\) | ||||
0.0351633 | + | 0.999382i | \(0.488805\pi\) | |||||||
\(398\) | −8.66051 | −0.434112 | ||||||||
\(399\) | −4.77917 | −0.239258 | ||||||||
\(400\) | 3.07375 | 0.153688 | ||||||||
\(401\) | 13.4242 | 0.670372 | 0.335186 | − | 0.942152i | \(-0.391201\pi\) | ||||
0.335186 | + | 0.942152i | \(0.391201\pi\) | |||||||
\(402\) | −16.1708 | −0.806527 | ||||||||
\(403\) | −2.29924 | −0.114533 | ||||||||
\(404\) | −57.5458 | −2.86301 | ||||||||
\(405\) | −4.34965 | −0.216136 | ||||||||
\(406\) | −21.5955 | −1.07176 | ||||||||
\(407\) | −11.6247 | −0.576214 | ||||||||
\(408\) | 3.06793 | 0.151885 | ||||||||
\(409\) | −12.4585 | −0.616031 | −0.308016 | − | 0.951381i | \(-0.599665\pi\) | ||||
−0.308016 | + | 0.951381i | \(0.599665\pi\) | |||||||
\(410\) | −41.9390 | −2.07122 | ||||||||
\(411\) | 15.0042 | 0.740103 | ||||||||
\(412\) | 38.1333 | 1.87869 | ||||||||
\(413\) | −17.9031 | −0.880954 | ||||||||
\(414\) | 0.390015 | 0.0191682 | ||||||||
\(415\) | 39.0749 | 1.91811 | ||||||||
\(416\) | 7.36166 | 0.360935 | ||||||||
\(417\) | −8.45578 | −0.414081 | ||||||||
\(418\) | −8.79325 | −0.430092 | ||||||||
\(419\) | 34.5718 | 1.68894 | 0.844471 | − | 0.535601i | \(-0.179915\pi\) | ||||
0.844471 | + | 0.535601i | \(0.179915\pi\) | |||||||
\(420\) | 53.9266 | 2.63135 | ||||||||
\(421\) | −34.9102 | −1.70142 | −0.850709 | − | 0.525638i | \(-0.823827\pi\) | ||||
−0.850709 | + | 0.525638i | \(0.823827\pi\) | |||||||
\(422\) | −15.2422 | −0.741980 | ||||||||
\(423\) | 4.76241 | 0.231556 | ||||||||
\(424\) | 40.4414 | 1.96401 | ||||||||
\(425\) | 5.43865 | 0.263813 | ||||||||
\(426\) | −7.89876 | −0.382696 | ||||||||
\(427\) | 59.8557 | 2.89662 | ||||||||
\(428\) | 23.1622 | 1.11959 | ||||||||
\(429\) | −5.68820 | −0.274629 | ||||||||
\(430\) | −31.9180 | −1.53922 | ||||||||
\(431\) | −21.9997 | −1.05969 | −0.529844 | − | 0.848095i | \(-0.677750\pi\) | ||||
−0.529844 | + | 0.848095i | \(0.677750\pi\) | |||||||
\(432\) | 2.78263 | 0.133880 | ||||||||
\(433\) | −7.96814 | −0.382924 | −0.191462 | − | 0.981500i | \(-0.561323\pi\) | ||||
−0.191462 | + | 0.981500i | \(0.561323\pi\) | |||||||
\(434\) | 18.3625 | 0.881429 | ||||||||
\(435\) | 5.76769 | 0.276540 | ||||||||
\(436\) | 14.1737 | 0.678797 | ||||||||
\(437\) | 0.0790784 | 0.00378283 | ||||||||
\(438\) | 8.86237 | 0.423460 | ||||||||
\(439\) | −28.1535 | −1.34369 | −0.671846 | − | 0.740691i | \(-0.734498\pi\) | ||||
−0.671846 | + | 0.740691i | \(0.734498\pi\) | |||||||
\(440\) | 40.1441 | 1.91379 | ||||||||
\(441\) | −38.8632 | −1.85063 | ||||||||
\(442\) | −3.41933 | −0.162641 | ||||||||
\(443\) | −8.12688 | −0.386120 | −0.193060 | − | 0.981187i | \(-0.561841\pi\) | ||||
−0.193060 | + | 0.981187i | \(0.561841\pi\) | |||||||
\(444\) | 9.64152 | 0.457566 | ||||||||
\(445\) | 29.1690 | 1.38274 | ||||||||
\(446\) | 2.96505 | 0.140399 | ||||||||
\(447\) | −8.93277 | −0.422505 | ||||||||
\(448\) | −64.5526 | −3.04982 | ||||||||
\(449\) | 21.6675 | 1.02255 | 0.511276 | − | 0.859417i | \(-0.329173\pi\) | ||||
0.511276 | + | 0.859417i | \(0.329173\pi\) | |||||||
\(450\) | 25.7990 | 1.21618 | ||||||||
\(451\) | −22.1446 | −1.04275 | ||||||||
\(452\) | −50.8676 | −2.39261 | ||||||||
\(453\) | −19.2117 | −0.902646 | ||||||||
\(454\) | −11.5523 | −0.542174 | ||||||||
\(455\) | −24.3175 | −1.14002 | ||||||||
\(456\) | 2.95077 | 0.138182 | ||||||||
\(457\) | 15.7052 | 0.734660 | 0.367330 | − | 0.930091i | \(-0.380272\pi\) | ||||
0.367330 | + | 0.930091i | \(0.380272\pi\) | |||||||
\(458\) | 49.9585 | 2.33441 | ||||||||
\(459\) | 4.92355 | 0.229812 | ||||||||
\(460\) | −0.892296 | −0.0416035 | ||||||||
\(461\) | 23.6910 | 1.10340 | 0.551701 | − | 0.834042i | \(-0.313979\pi\) | ||||
0.551701 | + | 0.834042i | \(0.313979\pi\) | |||||||
\(462\) | 45.4279 | 2.11350 | ||||||||
\(463\) | −13.9742 | −0.649436 | −0.324718 | − | 0.945811i | \(-0.605269\pi\) | ||||
−0.324718 | + | 0.945811i | \(0.605269\pi\) | |||||||
\(464\) | 1.03465 | 0.0480326 | ||||||||
\(465\) | −4.90424 | −0.227429 | ||||||||
\(466\) | −23.5410 | −1.09051 | ||||||||
\(467\) | 30.2264 | 1.39871 | 0.699355 | − | 0.714774i | \(-0.253471\pi\) | ||||
0.699355 | + | 0.714774i | \(0.253471\pi\) | |||||||
\(468\) | −10.1668 | −0.469959 | ||||||||
\(469\) | −36.5028 | −1.68554 | ||||||||
\(470\) | −17.3830 | −0.801820 | ||||||||
\(471\) | −8.95156 | −0.412466 | ||||||||
\(472\) | 11.0538 | 0.508792 | ||||||||
\(473\) | −16.8533 | −0.774916 | ||||||||
\(474\) | −33.8908 | −1.55666 | ||||||||
\(475\) | 5.23095 | 0.240012 | ||||||||
\(476\) | 17.1166 | 0.784540 | ||||||||
\(477\) | 26.3397 | 1.20601 | ||||||||
\(478\) | −13.7781 | −0.630194 | ||||||||
\(479\) | −18.9822 | −0.867321 | −0.433660 | − | 0.901076i | \(-0.642778\pi\) | ||||
−0.433660 | + | 0.901076i | \(0.642778\pi\) | |||||||
\(480\) | 15.7023 | 0.716709 | ||||||||
\(481\) | −4.34773 | −0.198239 | ||||||||
\(482\) | 22.1390 | 1.00841 | ||||||||
\(483\) | −0.408537 | −0.0185891 | ||||||||
\(484\) | 15.4405 | 0.701840 | ||||||||
\(485\) | 50.2657 | 2.28245 | ||||||||
\(486\) | 37.2326 | 1.68890 | ||||||||
\(487\) | 21.7268 | 0.984536 | 0.492268 | − | 0.870444i | \(-0.336168\pi\) | ||||
0.492268 | + | 0.870444i | \(0.336168\pi\) | |||||||
\(488\) | −36.9563 | −1.67293 | ||||||||
\(489\) | −12.2602 | −0.554425 | ||||||||
\(490\) | 141.852 | 6.40824 | ||||||||
\(491\) | −28.8138 | −1.30035 | −0.650175 | − | 0.759785i | \(-0.725304\pi\) | ||||
−0.650175 | + | 0.759785i | \(0.725304\pi\) | |||||||
\(492\) | 18.3667 | 0.828036 | ||||||||
\(493\) | 1.83070 | 0.0824506 | ||||||||
\(494\) | −3.28875 | −0.147968 | ||||||||
\(495\) | 26.1460 | 1.17518 | ||||||||
\(496\) | −0.879763 | −0.0395025 | ||||||||
\(497\) | −17.8301 | −0.799788 | ||||||||
\(498\) | −27.3012 | −1.22340 | ||||||||
\(499\) | 17.2099 | 0.770421 | 0.385211 | − | 0.922829i | \(-0.374129\pi\) | ||||
0.385211 | + | 0.922829i | \(0.374129\pi\) | |||||||
\(500\) | −4.76057 | −0.212899 | ||||||||
\(501\) | 11.8064 | 0.527469 | ||||||||
\(502\) | 45.2798 | 2.02094 | ||||||||
\(503\) | 12.1872 | 0.543401 | 0.271700 | − | 0.962382i | \(-0.412414\pi\) | ||||
0.271700 | + | 0.962382i | \(0.412414\pi\) | |||||||
\(504\) | 32.8512 | 1.46331 | ||||||||
\(505\) | 55.3500 | 2.46304 | ||||||||
\(506\) | −0.751673 | −0.0334159 | ||||||||
\(507\) | 10.5492 | 0.468509 | ||||||||
\(508\) | 39.5977 | 1.75686 | ||||||||
\(509\) | 4.30600 | 0.190860 | 0.0954300 | − | 0.995436i | \(-0.469577\pi\) | ||||
0.0954300 | + | 0.995436i | \(0.469577\pi\) | |||||||
\(510\) | −7.29338 | −0.322956 | ||||||||
\(511\) | 20.0052 | 0.884979 | ||||||||
\(512\) | 6.37305 | 0.281652 | ||||||||
\(513\) | 4.73552 | 0.209078 | ||||||||
\(514\) | 54.4085 | 2.39986 | ||||||||
\(515\) | −36.6782 | −1.61624 | ||||||||
\(516\) | 13.9781 | 0.615353 | ||||||||
\(517\) | −9.17857 | −0.403673 | ||||||||
\(518\) | 34.7224 | 1.52562 | ||||||||
\(519\) | 2.63715 | 0.115758 | ||||||||
\(520\) | 15.0142 | 0.658417 | ||||||||
\(521\) | 18.0573 | 0.791105 | 0.395552 | − | 0.918443i | \(-0.370553\pi\) | ||||
0.395552 | + | 0.918443i | \(0.370553\pi\) | |||||||
\(522\) | 8.68420 | 0.380097 | ||||||||
\(523\) | 9.01805 | 0.394332 | 0.197166 | − | 0.980370i | \(-0.436826\pi\) | ||||
0.197166 | + | 0.980370i | \(0.436826\pi\) | |||||||
\(524\) | 47.7856 | 2.08752 | ||||||||
\(525\) | −27.0243 | −1.17944 | ||||||||
\(526\) | −19.6282 | −0.855830 | ||||||||
\(527\) | −1.55664 | −0.0678082 | ||||||||
\(528\) | −2.17649 | −0.0947194 | ||||||||
\(529\) | −22.9932 | −0.999706 | ||||||||
\(530\) | −96.1411 | −4.17610 | ||||||||
\(531\) | 7.19939 | 0.312427 | ||||||||
\(532\) | 16.4629 | 0.713759 | ||||||||
\(533\) | −8.28226 | −0.358744 | ||||||||
\(534\) | −20.3801 | −0.881932 | ||||||||
\(535\) | −22.2784 | −0.963180 | ||||||||
\(536\) | 22.5376 | 0.973478 | ||||||||
\(537\) | 8.15582 | 0.351950 | ||||||||
\(538\) | −13.7487 | −0.592750 | ||||||||
\(539\) | 74.9008 | 3.22620 | ||||||||
\(540\) | −53.4341 | −2.29944 | ||||||||
\(541\) | −18.2680 | −0.785403 | −0.392701 | − | 0.919666i | \(-0.628459\pi\) | ||||
−0.392701 | + | 0.919666i | \(0.628459\pi\) | |||||||
\(542\) | −13.4138 | −0.576173 | ||||||||
\(543\) | 25.7568 | 1.10533 | ||||||||
\(544\) | 4.98401 | 0.213688 | ||||||||
\(545\) | −13.6329 | −0.583968 | ||||||||
\(546\) | 16.9904 | 0.727123 | ||||||||
\(547\) | 17.9544 | 0.767675 | 0.383837 | − | 0.923401i | \(-0.374602\pi\) | ||||
0.383837 | + | 0.923401i | \(0.374602\pi\) | |||||||
\(548\) | −51.6855 | −2.20790 | ||||||||
\(549\) | −24.0698 | −1.02728 | ||||||||
\(550\) | −49.7223 | −2.12017 | ||||||||
\(551\) | 1.76079 | 0.0750120 | ||||||||
\(552\) | 0.252240 | 0.0107361 | ||||||||
\(553\) | −76.5025 | −3.25322 | ||||||||
\(554\) | −34.1931 | −1.45273 | ||||||||
\(555\) | −9.27363 | −0.393644 | ||||||||
\(556\) | 29.1279 | 1.23530 | ||||||||
\(557\) | −7.03492 | −0.298079 | −0.149040 | − | 0.988831i | \(-0.547618\pi\) | ||||
−0.149040 | + | 0.988831i | \(0.547618\pi\) | |||||||
\(558\) | −7.38414 | −0.312595 | ||||||||
\(559\) | −6.30327 | −0.266600 | ||||||||
\(560\) | −9.30466 | −0.393194 | ||||||||
\(561\) | −3.85104 | −0.162591 | ||||||||
\(562\) | −3.52639 | −0.148752 | ||||||||
\(563\) | −6.54504 | −0.275841 | −0.137920 | − | 0.990443i | \(-0.544042\pi\) | ||||
−0.137920 | + | 0.990443i | \(0.544042\pi\) | |||||||
\(564\) | 7.61271 | 0.320553 | ||||||||
\(565\) | 48.9266 | 2.05836 | ||||||||
\(566\) | −11.3113 | −0.475449 | ||||||||
\(567\) | 6.86013 | 0.288099 | ||||||||
\(568\) | 11.0087 | 0.461914 | ||||||||
\(569\) | 12.9868 | 0.544435 | 0.272217 | − | 0.962236i | \(-0.412243\pi\) | ||||
0.272217 | + | 0.962236i | \(0.412243\pi\) | |||||||
\(570\) | −7.01484 | −0.293820 | ||||||||
\(571\) | −45.1872 | −1.89103 | −0.945513 | − | 0.325583i | \(-0.894439\pi\) | ||||
−0.945513 | + | 0.325583i | \(0.894439\pi\) | |||||||
\(572\) | 19.5943 | 0.819281 | ||||||||
\(573\) | −16.3030 | −0.681066 | ||||||||
\(574\) | 66.1450 | 2.76084 | ||||||||
\(575\) | 0.447157 | 0.0186477 | ||||||||
\(576\) | 25.9586 | 1.08161 | ||||||||
\(577\) | 19.8916 | 0.828099 | 0.414050 | − | 0.910254i | \(-0.364114\pi\) | ||||
0.414050 | + | 0.910254i | \(0.364114\pi\) | |||||||
\(578\) | −2.31496 | −0.0962898 | ||||||||
\(579\) | 8.09674 | 0.336489 | ||||||||
\(580\) | −19.8682 | −0.824980 | ||||||||
\(581\) | −61.6277 | −2.55675 | ||||||||
\(582\) | −35.1201 | −1.45578 | ||||||||
\(583\) | −50.7643 | −2.10244 | ||||||||
\(584\) | −12.3517 | −0.511116 | ||||||||
\(585\) | 9.77883 | 0.404305 | ||||||||
\(586\) | 69.4630 | 2.86949 | ||||||||
\(587\) | −0.895011 | −0.0369411 | −0.0184705 | − | 0.999829i | \(-0.505880\pi\) | ||||
−0.0184705 | + | 0.999829i | \(0.505880\pi\) | |||||||
\(588\) | −62.1227 | −2.56190 | ||||||||
\(589\) | −1.49719 | −0.0616906 | ||||||||
\(590\) | −26.2781 | −1.08185 | ||||||||
\(591\) | −16.0131 | −0.658692 | ||||||||
\(592\) | −1.66358 | −0.0683726 | ||||||||
\(593\) | 28.0200 | 1.15064 | 0.575322 | − | 0.817927i | \(-0.304877\pi\) | ||||
0.575322 | + | 0.817927i | \(0.304877\pi\) | |||||||
\(594\) | −45.0130 | −1.84691 | ||||||||
\(595\) | −16.4635 | −0.674939 | ||||||||
\(596\) | 30.7710 | 1.26043 | ||||||||
\(597\) | −3.64806 | −0.149305 | ||||||||
\(598\) | −0.281132 | −0.0114963 | ||||||||
\(599\) | −31.3412 | −1.28057 | −0.640284 | − | 0.768138i | \(-0.721183\pi\) | ||||
−0.640284 | + | 0.768138i | \(0.721183\pi\) | |||||||
\(600\) | 16.6854 | 0.681179 | ||||||||
\(601\) | −7.60498 | −0.310214 | −0.155107 | − | 0.987898i | \(-0.549572\pi\) | ||||
−0.155107 | + | 0.987898i | \(0.549572\pi\) | |||||||
\(602\) | 50.3401 | 2.05171 | ||||||||
\(603\) | 14.6789 | 0.597771 | ||||||||
\(604\) | 66.1793 | 2.69280 | ||||||||
\(605\) | −14.8513 | −0.603792 | ||||||||
\(606\) | −38.6725 | −1.57096 | ||||||||
\(607\) | −38.9874 | −1.58245 | −0.791225 | − | 0.611525i | \(-0.790556\pi\) | ||||
−0.791225 | + | 0.611525i | \(0.790556\pi\) | |||||||
\(608\) | 4.79367 | 0.194409 | ||||||||
\(609\) | −9.09662 | −0.368614 | ||||||||
\(610\) | 87.8561 | 3.55719 | ||||||||
\(611\) | −3.43286 | −0.138879 | ||||||||
\(612\) | −6.88313 | −0.278234 | ||||||||
\(613\) | −24.1124 | −0.973892 | −0.486946 | − | 0.873432i | \(-0.661889\pi\) | ||||
−0.486946 | + | 0.873432i | \(0.661889\pi\) | |||||||
\(614\) | −51.0962 | −2.06207 | ||||||||
\(615\) | −17.6659 | −0.712359 | ||||||||
\(616\) | −63.3140 | −2.55099 | ||||||||
\(617\) | 5.91291 | 0.238045 | 0.119022 | − | 0.992892i | \(-0.462024\pi\) | ||||
0.119022 | + | 0.992892i | \(0.462024\pi\) | |||||||
\(618\) | 25.6267 | 1.03086 | ||||||||
\(619\) | −29.2263 | −1.17471 | −0.587353 | − | 0.809331i | \(-0.699830\pi\) | ||||
−0.587353 | + | 0.809331i | \(0.699830\pi\) | |||||||
\(620\) | 16.8938 | 0.678472 | ||||||||
\(621\) | 0.404806 | 0.0162443 | ||||||||
\(622\) | −20.6500 | −0.827990 | ||||||||
\(623\) | −46.0044 | −1.84313 | ||||||||
\(624\) | −0.814024 | −0.0325870 | ||||||||
\(625\) | −22.6143 | −0.904573 | ||||||||
\(626\) | 8.60921 | 0.344093 | ||||||||
\(627\) | −3.70397 | −0.147922 | ||||||||
\(628\) | 30.8357 | 1.23048 | ||||||||
\(629\) | −2.94351 | −0.117365 | ||||||||
\(630\) | −78.0971 | −3.11146 | ||||||||
\(631\) | −31.1366 | −1.23953 | −0.619764 | − | 0.784788i | \(-0.712772\pi\) | ||||
−0.619764 | + | 0.784788i | \(0.712772\pi\) | |||||||
\(632\) | 47.2344 | 1.87888 | ||||||||
\(633\) | −6.42046 | −0.255190 | ||||||||
\(634\) | −38.1044 | −1.51332 | ||||||||
\(635\) | −38.0868 | −1.51143 | ||||||||
\(636\) | 42.1040 | 1.66953 | ||||||||
\(637\) | 28.0135 | 1.10994 | ||||||||
\(638\) | −16.7370 | −0.662624 | ||||||||
\(639\) | 7.17002 | 0.283642 | ||||||||
\(640\) | −62.5445 | −2.47229 | ||||||||
\(641\) | −20.8234 | −0.822473 | −0.411237 | − | 0.911529i | \(-0.634903\pi\) | ||||
−0.411237 | + | 0.911529i | \(0.634903\pi\) | |||||||
\(642\) | 15.5657 | 0.614329 | ||||||||
\(643\) | −44.6488 | −1.76078 | −0.880388 | − | 0.474254i | \(-0.842718\pi\) | ||||
−0.880388 | + | 0.474254i | \(0.842718\pi\) | |||||||
\(644\) | 1.40730 | 0.0554555 | ||||||||
\(645\) | −13.4448 | −0.529388 | ||||||||
\(646\) | −2.22656 | −0.0876027 | ||||||||
\(647\) | 5.83462 | 0.229382 | 0.114691 | − | 0.993401i | \(-0.463412\pi\) | ||||
0.114691 | + | 0.993401i | \(0.463412\pi\) | |||||||
\(648\) | −4.23560 | −0.166390 | ||||||||
\(649\) | −13.8753 | −0.544655 | ||||||||
\(650\) | −18.5966 | −0.729417 | ||||||||
\(651\) | 7.73482 | 0.303152 | ||||||||
\(652\) | 42.2331 | 1.65397 | ||||||||
\(653\) | 7.78089 | 0.304490 | 0.152245 | − | 0.988343i | \(-0.451350\pi\) | ||||
0.152245 | + | 0.988343i | \(0.451350\pi\) | |||||||
\(654\) | 9.52515 | 0.372463 | ||||||||
\(655\) | −45.9623 | −1.79589 | ||||||||
\(656\) | −3.16905 | −0.123731 | ||||||||
\(657\) | −8.04472 | −0.313854 | ||||||||
\(658\) | 27.4160 | 1.06879 | ||||||||
\(659\) | 12.2616 | 0.477644 | 0.238822 | − | 0.971063i | \(-0.423239\pi\) | ||||
0.238822 | + | 0.971063i | \(0.423239\pi\) | |||||||
\(660\) | 41.7944 | 1.62685 | ||||||||
\(661\) | 12.7416 | 0.495592 | 0.247796 | − | 0.968812i | \(-0.420294\pi\) | ||||
0.247796 | + | 0.968812i | \(0.420294\pi\) | |||||||
\(662\) | −31.7316 | −1.23329 | ||||||||
\(663\) | −1.44032 | −0.0559374 | ||||||||
\(664\) | 38.0504 | 1.47664 | ||||||||
\(665\) | −15.8348 | −0.614046 | ||||||||
\(666\) | −13.9630 | −0.541054 | ||||||||
\(667\) | 0.150517 | 0.00582805 | ||||||||
\(668\) | −40.6698 | −1.57356 | ||||||||
\(669\) | 1.24896 | 0.0482877 | ||||||||
\(670\) | −53.5787 | −2.06992 | ||||||||
\(671\) | 46.3897 | 1.79085 | ||||||||
\(672\) | −24.7652 | −0.955338 | ||||||||
\(673\) | −31.2782 | −1.20569 | −0.602843 | − | 0.797860i | \(-0.705966\pi\) | ||||
−0.602843 | + | 0.797860i | \(0.705966\pi\) | |||||||
\(674\) | 7.38211 | 0.284348 | ||||||||
\(675\) | 26.7775 | 1.03066 | ||||||||
\(676\) | −36.3393 | −1.39767 | ||||||||
\(677\) | 47.4505 | 1.82367 | 0.911835 | − | 0.410557i | \(-0.134666\pi\) | ||||
0.911835 | + | 0.410557i | \(0.134666\pi\) | |||||||
\(678\) | −34.1846 | −1.31285 | ||||||||
\(679\) | −79.2775 | −3.04239 | ||||||||
\(680\) | 10.1650 | 0.389808 | ||||||||
\(681\) | −4.86614 | −0.186471 | ||||||||
\(682\) | 14.2314 | 0.544949 | ||||||||
\(683\) | 7.81016 | 0.298848 | 0.149424 | − | 0.988773i | \(-0.452258\pi\) | ||||
0.149424 | + | 0.988773i | \(0.452258\pi\) | |||||||
\(684\) | −6.62026 | −0.253132 | ||||||||
\(685\) | 49.7134 | 1.89945 | ||||||||
\(686\) | −141.151 | −5.38919 | ||||||||
\(687\) | 21.0440 | 0.802877 | ||||||||
\(688\) | −2.41183 | −0.0919502 | ||||||||
\(689\) | −18.9863 | −0.723319 | ||||||||
\(690\) | −0.599650 | −0.0228283 | ||||||||
\(691\) | −2.52960 | −0.0962306 | −0.0481153 | − | 0.998842i | \(-0.515321\pi\) | ||||
−0.0481153 | + | 0.998842i | \(0.515321\pi\) | |||||||
\(692\) | −9.08428 | −0.345333 | ||||||||
\(693\) | −41.2367 | −1.56645 | ||||||||
\(694\) | 26.3189 | 0.999053 | ||||||||
\(695\) | −28.0165 | −1.06273 | ||||||||
\(696\) | 5.61646 | 0.212892 | ||||||||
\(697\) | −5.60727 | −0.212391 | ||||||||
\(698\) | 74.3432 | 2.81393 | ||||||||
\(699\) | −9.91614 | −0.375063 | ||||||||
\(700\) | 93.0914 | 3.51852 | ||||||||
\(701\) | −32.2114 | −1.21661 | −0.608304 | − | 0.793704i | \(-0.708150\pi\) | ||||
−0.608304 | + | 0.793704i | \(0.708150\pi\) | |||||||
\(702\) | −16.8353 | −0.635406 | ||||||||
\(703\) | −2.83110 | −0.106777 | ||||||||
\(704\) | −50.0298 | −1.88557 | ||||||||
\(705\) | −7.32223 | −0.275771 | ||||||||
\(706\) | −2.31496 | −0.0871248 | ||||||||
\(707\) | −87.2964 | −3.28312 | ||||||||
\(708\) | 11.5082 | 0.432505 | ||||||||
\(709\) | 19.3867 | 0.728082 | 0.364041 | − | 0.931383i | \(-0.381397\pi\) | ||||
0.364041 | + | 0.931383i | \(0.381397\pi\) | |||||||
\(710\) | −26.1709 | −0.982177 | ||||||||
\(711\) | 30.7640 | 1.15374 | ||||||||
\(712\) | 28.4042 | 1.06449 | ||||||||
\(713\) | −0.127984 | −0.00479305 | ||||||||
\(714\) | 11.5029 | 0.430485 | ||||||||
\(715\) | −18.8467 | −0.704826 | ||||||||
\(716\) | −28.0946 | −1.04995 | ||||||||
\(717\) | −5.80371 | −0.216744 | ||||||||
\(718\) | 19.0470 | 0.710828 | ||||||||
\(719\) | −38.5136 | −1.43632 | −0.718158 | − | 0.695880i | \(-0.755015\pi\) | ||||
−0.718158 | + | 0.695880i | \(0.755015\pi\) | |||||||
\(720\) | 3.74169 | 0.139445 | ||||||||
\(721\) | 57.8478 | 2.15436 | ||||||||
\(722\) | 41.8428 | 1.55723 | ||||||||
\(723\) | 9.32560 | 0.346823 | ||||||||
\(724\) | −88.7254 | −3.29745 | ||||||||
\(725\) | 9.95654 | 0.369777 | ||||||||
\(726\) | 10.3765 | 0.385107 | ||||||||
\(727\) | 20.2795 | 0.752125 | 0.376062 | − | 0.926594i | \(-0.377278\pi\) | ||||
0.376062 | + | 0.926594i | \(0.377278\pi\) | |||||||
\(728\) | −23.6800 | −0.877637 | ||||||||
\(729\) | 11.6446 | 0.431282 | ||||||||
\(730\) | 29.3636 | 1.08680 | ||||||||
\(731\) | −4.26746 | −0.157838 | ||||||||
\(732\) | −38.4756 | −1.42210 | ||||||||
\(733\) | −25.2118 | −0.931220 | −0.465610 | − | 0.884990i | \(-0.654165\pi\) | ||||
−0.465610 | + | 0.884990i | \(0.654165\pi\) | |||||||
\(734\) | −6.63170 | −0.244780 | ||||||||
\(735\) | 59.7523 | 2.20400 | ||||||||
\(736\) | 0.409777 | 0.0151046 | ||||||||
\(737\) | −28.2905 | −1.04210 | ||||||||
\(738\) | −26.5989 | −0.979120 | ||||||||
\(739\) | 44.6719 | 1.64328 | 0.821641 | − | 0.570006i | \(-0.193059\pi\) | ||||
0.821641 | + | 0.570006i | \(0.193059\pi\) | |||||||
\(740\) | 31.9452 | 1.17433 | ||||||||
\(741\) | −1.38532 | −0.0508908 | ||||||||
\(742\) | 151.631 | 5.56654 | ||||||||
\(743\) | −44.7104 | −1.64026 | −0.820132 | − | 0.572174i | \(-0.806100\pi\) | ||||
−0.820132 | + | 0.572174i | \(0.806100\pi\) | |||||||
\(744\) | −4.77566 | −0.175084 | ||||||||
\(745\) | −29.5969 | −1.08435 | ||||||||
\(746\) | 25.8471 | 0.946329 | ||||||||
\(747\) | 24.7824 | 0.906741 | ||||||||
\(748\) | 13.2658 | 0.485046 | ||||||||
\(749\) | 35.1368 | 1.28387 | ||||||||
\(750\) | −3.19925 | −0.116820 | ||||||||
\(751\) | −32.5783 | −1.18880 | −0.594399 | − | 0.804170i | \(-0.702610\pi\) | ||||
−0.594399 | + | 0.804170i | \(0.702610\pi\) | |||||||
\(752\) | −1.31352 | −0.0478992 | ||||||||
\(753\) | 19.0732 | 0.695065 | ||||||||
\(754\) | −6.25978 | −0.227968 | ||||||||
\(755\) | −63.6541 | −2.31661 | ||||||||
\(756\) | 84.2746 | 3.06504 | ||||||||
\(757\) | −26.4883 | −0.962735 | −0.481368 | − | 0.876519i | \(-0.659860\pi\) | ||||
−0.481368 | + | 0.876519i | \(0.659860\pi\) | |||||||
\(758\) | −30.4841 | −1.10723 | ||||||||
\(759\) | −0.316626 | −0.0114928 | ||||||||
\(760\) | 9.77675 | 0.354640 | ||||||||
\(761\) | −4.50312 | −0.163238 | −0.0816189 | − | 0.996664i | \(-0.526009\pi\) | ||||
−0.0816189 | + | 0.996664i | \(0.526009\pi\) | |||||||
\(762\) | 26.6109 | 0.964010 | ||||||||
\(763\) | 21.5014 | 0.778401 | ||||||||
\(764\) | 56.1593 | 2.03177 | ||||||||
\(765\) | 6.62049 | 0.239364 | ||||||||
\(766\) | 9.12757 | 0.329792 | ||||||||
\(767\) | −5.18949 | −0.187382 | ||||||||
\(768\) | 18.9930 | 0.685352 | ||||||||
\(769\) | −38.6285 | −1.39298 | −0.696489 | − | 0.717567i | \(-0.745256\pi\) | ||||
−0.696489 | + | 0.717567i | \(0.745256\pi\) | |||||||
\(770\) | 150.516 | 5.42422 | ||||||||
\(771\) | 22.9184 | 0.825387 | ||||||||
\(772\) | −27.8911 | −1.00382 | ||||||||
\(773\) | 2.65589 | 0.0955257 | 0.0477629 | − | 0.998859i | \(-0.484791\pi\) | ||||
0.0477629 | + | 0.998859i | \(0.484791\pi\) | |||||||
\(774\) | −20.2433 | −0.727630 | ||||||||
\(775\) | −8.46601 | −0.304108 | ||||||||
\(776\) | 48.9477 | 1.75712 | ||||||||
\(777\) | 14.6261 | 0.524708 | ||||||||
\(778\) | 88.4173 | 3.16991 | ||||||||
\(779\) | −5.39313 | −0.193229 | ||||||||
\(780\) | 15.6315 | 0.559696 | ||||||||
\(781\) | −13.8187 | −0.494473 | ||||||||
\(782\) | −0.190333 | −0.00680628 | ||||||||
\(783\) | 9.01354 | 0.322118 | ||||||||
\(784\) | 10.7189 | 0.382816 | ||||||||
\(785\) | −29.6592 | −1.05858 | ||||||||
\(786\) | 32.1134 | 1.14545 | ||||||||
\(787\) | 20.3729 | 0.726214 | 0.363107 | − | 0.931747i | \(-0.381716\pi\) | ||||
0.363107 | + | 0.931747i | \(0.381716\pi\) | |||||||
\(788\) | 55.1610 | 1.96503 | ||||||||
\(789\) | −8.26796 | −0.294347 | ||||||||
\(790\) | −112.290 | −3.99510 | ||||||||
\(791\) | −77.1656 | −2.74369 | ||||||||
\(792\) | 25.4605 | 0.904700 | ||||||||
\(793\) | 17.3501 | 0.616121 | ||||||||
\(794\) | −3.24384 | −0.115120 | ||||||||
\(795\) | −40.4974 | −1.43629 | ||||||||
\(796\) | 12.5666 | 0.445411 | ||||||||
\(797\) | 13.5277 | 0.479177 | 0.239588 | − | 0.970875i | \(-0.422988\pi\) | ||||
0.239588 | + | 0.970875i | \(0.422988\pi\) | |||||||
\(798\) | 11.0636 | 0.391647 | ||||||||
\(799\) | −2.32412 | −0.0822216 | ||||||||
\(800\) | 27.1063 | 0.958352 | ||||||||
\(801\) | 18.4998 | 0.653658 | ||||||||
\(802\) | −31.0765 | −1.09735 | ||||||||
\(803\) | 15.5045 | 0.547143 | ||||||||
\(804\) | 23.4642 | 0.827518 | ||||||||
\(805\) | −1.35360 | −0.0477083 | ||||||||
\(806\) | 5.32266 | 0.187483 | ||||||||
\(807\) | −5.79136 | −0.203865 | ||||||||
\(808\) | 53.8988 | 1.89615 | ||||||||
\(809\) | −55.1260 | −1.93813 | −0.969063 | − | 0.246815i | \(-0.920616\pi\) | ||||
−0.969063 | + | 0.246815i | \(0.920616\pi\) | |||||||
\(810\) | 10.0693 | 0.353799 | ||||||||
\(811\) | 3.64856 | 0.128118 | 0.0640592 | − | 0.997946i | \(-0.479595\pi\) | ||||
0.0640592 | + | 0.997946i | \(0.479595\pi\) | |||||||
\(812\) | 31.3354 | 1.09966 | ||||||||
\(813\) | −5.65029 | −0.198164 | ||||||||
\(814\) | 26.9107 | 0.943221 | ||||||||
\(815\) | −40.6216 | −1.42291 | ||||||||
\(816\) | −0.551112 | −0.0192928 | ||||||||
\(817\) | −4.10448 | −0.143598 | ||||||||
\(818\) | 28.8409 | 1.00840 | ||||||||
\(819\) | −15.4229 | −0.538919 | ||||||||
\(820\) | 60.8544 | 2.12513 | ||||||||
\(821\) | 8.15487 | 0.284607 | 0.142303 | − | 0.989823i | \(-0.454549\pi\) | ||||
0.142303 | + | 0.989823i | \(0.454549\pi\) | |||||||
\(822\) | −34.7342 | −1.21150 | ||||||||
\(823\) | 43.5122 | 1.51674 | 0.758369 | − | 0.651825i | \(-0.225996\pi\) | ||||
0.758369 | + | 0.651825i | \(0.225996\pi\) | |||||||
\(824\) | −35.7165 | −1.24424 | ||||||||
\(825\) | −20.9445 | −0.729193 | ||||||||
\(826\) | 41.4450 | 1.44206 | ||||||||
\(827\) | −34.9566 | −1.21556 | −0.607780 | − | 0.794105i | \(-0.707940\pi\) | ||||
−0.607780 | + | 0.794105i | \(0.707940\pi\) | |||||||
\(828\) | −0.565919 | −0.0196671 | ||||||||
\(829\) | −11.9545 | −0.415197 | −0.207599 | − | 0.978214i | \(-0.566565\pi\) | ||||
−0.207599 | + | 0.978214i | \(0.566565\pi\) | |||||||
\(830\) | −90.4570 | −3.13981 | ||||||||
\(831\) | −14.4031 | −0.499639 | ||||||||
\(832\) | −18.7116 | −0.648707 | ||||||||
\(833\) | 18.9658 | 0.657125 | ||||||||
\(834\) | 19.5748 | 0.677821 | ||||||||
\(835\) | 39.1179 | 1.35373 | ||||||||
\(836\) | 12.7592 | 0.441286 | ||||||||
\(837\) | −7.66418 | −0.264913 | ||||||||
\(838\) | −80.0325 | −2.76468 | ||||||||
\(839\) | −31.5780 | −1.09019 | −0.545096 | − | 0.838374i | \(-0.683507\pi\) | ||||
−0.545096 | + | 0.838374i | \(0.683507\pi\) | |||||||
\(840\) | −50.5089 | −1.74272 | ||||||||
\(841\) | −25.6485 | −0.884432 | ||||||||
\(842\) | 80.8158 | 2.78510 | ||||||||
\(843\) | −1.48542 | −0.0511605 | ||||||||
\(844\) | 22.1168 | 0.761291 | ||||||||
\(845\) | 34.9528 | 1.20241 | ||||||||
\(846\) | −11.0248 | −0.379041 | ||||||||
\(847\) | 23.4230 | 0.804825 | ||||||||
\(848\) | −7.26475 | −0.249472 | ||||||||
\(849\) | −4.76464 | −0.163522 | ||||||||
\(850\) | −12.5903 | −0.431843 | ||||||||
\(851\) | −0.242010 | −0.00829601 | ||||||||
\(852\) | 11.4613 | 0.392657 | ||||||||
\(853\) | −9.22541 | −0.315872 | −0.157936 | − | 0.987449i | \(-0.550484\pi\) | ||||
−0.157936 | + | 0.987449i | \(0.550484\pi\) | |||||||
\(854\) | −138.564 | −4.74156 | ||||||||
\(855\) | 6.36765 | 0.217769 | ||||||||
\(856\) | −21.6943 | −0.741496 | ||||||||
\(857\) | −2.24654 | −0.0767402 | −0.0383701 | − | 0.999264i | \(-0.512217\pi\) | ||||
−0.0383701 | + | 0.999264i | \(0.512217\pi\) | |||||||
\(858\) | 13.1680 | 0.449548 | ||||||||
\(859\) | 7.79945 | 0.266114 | 0.133057 | − | 0.991108i | \(-0.457521\pi\) | ||||
0.133057 | + | 0.991108i | \(0.457521\pi\) | |||||||
\(860\) | 46.3137 | 1.57928 | ||||||||
\(861\) | 27.8622 | 0.949540 | ||||||||
\(862\) | 50.9285 | 1.73463 | ||||||||
\(863\) | −2.54935 | −0.0867810 | −0.0433905 | − | 0.999058i | \(-0.513816\pi\) | ||||
−0.0433905 | + | 0.999058i | \(0.513816\pi\) | |||||||
\(864\) | 24.5390 | 0.834834 | ||||||||
\(865\) | 8.73766 | 0.297089 | ||||||||
\(866\) | 18.4460 | 0.626819 | ||||||||
\(867\) | −0.975130 | −0.0331171 | ||||||||
\(868\) | −26.6444 | −0.904370 | ||||||||
\(869\) | −59.2913 | −2.01132 | ||||||||
\(870\) | −13.3520 | −0.452675 | ||||||||
\(871\) | −10.5809 | −0.358520 | ||||||||
\(872\) | −13.2754 | −0.449563 | ||||||||
\(873\) | 31.8799 | 1.07897 | ||||||||
\(874\) | −0.183064 | −0.00619222 | ||||||||
\(875\) | −7.22173 | −0.244139 | ||||||||
\(876\) | −12.8595 | −0.434481 | ||||||||
\(877\) | 17.4325 | 0.588653 | 0.294326 | − | 0.955705i | \(-0.404905\pi\) | ||||
0.294326 | + | 0.955705i | \(0.404905\pi\) | |||||||
\(878\) | 65.1743 | 2.19953 | ||||||||
\(879\) | 29.2598 | 0.986909 | ||||||||
\(880\) | −7.21134 | −0.243094 | ||||||||
\(881\) | −11.9016 | −0.400977 | −0.200488 | − | 0.979696i | \(-0.564253\pi\) | ||||
−0.200488 | + | 0.979696i | \(0.564253\pi\) | |||||||
\(882\) | 89.9669 | 3.02934 | ||||||||
\(883\) | 0.299105 | 0.0100657 | 0.00503285 | − | 0.999987i | \(-0.498398\pi\) | ||||
0.00503285 | + | 0.999987i | \(0.498398\pi\) | |||||||
\(884\) | 4.96152 | 0.166874 | ||||||||
\(885\) | −11.0691 | −0.372084 | ||||||||
\(886\) | 18.8134 | 0.632050 | ||||||||
\(887\) | 15.6498 | 0.525468 | 0.262734 | − | 0.964868i | \(-0.415376\pi\) | ||||
0.262734 | + | 0.964868i | \(0.415376\pi\) | |||||||
\(888\) | −9.03048 | −0.303043 | ||||||||
\(889\) | 60.0693 | 2.01466 | ||||||||
\(890\) | −67.5251 | −2.26345 | ||||||||
\(891\) | 5.31677 | 0.178118 | ||||||||
\(892\) | −4.30234 | −0.144053 | ||||||||
\(893\) | −2.23536 | −0.0748036 | ||||||||
\(894\) | 20.6790 | 0.691610 | ||||||||
\(895\) | 27.0226 | 0.903267 | ||||||||
\(896\) | 98.6433 | 3.29544 | ||||||||
\(897\) | −0.118421 | −0.00395396 | ||||||||
\(898\) | −50.1594 | −1.67384 | ||||||||
\(899\) | −2.84974 | −0.0950441 | ||||||||
\(900\) | −37.4349 | −1.24783 | ||||||||
\(901\) | −12.8541 | −0.428233 | ||||||||
\(902\) | 51.2639 | 1.70690 | ||||||||
\(903\) | 21.2047 | 0.705648 | ||||||||
\(904\) | 47.6438 | 1.58461 | ||||||||
\(905\) | 85.3399 | 2.83679 | ||||||||
\(906\) | 44.4745 | 1.47757 | ||||||||
\(907\) | 29.7957 | 0.989349 | 0.494675 | − | 0.869078i | \(-0.335287\pi\) | ||||
0.494675 | + | 0.869078i | \(0.335287\pi\) | |||||||
\(908\) | 16.7626 | 0.556285 | ||||||||
\(909\) | 35.1046 | 1.16435 | ||||||||
\(910\) | 56.2943 | 1.86614 | ||||||||
\(911\) | 48.9586 | 1.62207 | 0.811035 | − | 0.584998i | \(-0.198905\pi\) | ||||
0.811035 | + | 0.584998i | \(0.198905\pi\) | |||||||
\(912\) | −0.530065 | −0.0175522 | ||||||||
\(913\) | −47.7630 | −1.58072 | ||||||||
\(914\) | −36.3571 | −1.20258 | ||||||||
\(915\) | 37.0075 | 1.22343 | ||||||||
\(916\) | −72.4908 | −2.39516 | ||||||||
\(917\) | 72.4903 | 2.39384 | ||||||||
\(918\) | −11.3978 | −0.376185 | ||||||||
\(919\) | 15.9791 | 0.527102 | 0.263551 | − | 0.964645i | \(-0.415106\pi\) | ||||
0.263551 | + | 0.964645i | \(0.415106\pi\) | |||||||
\(920\) | 0.835746 | 0.0275537 | ||||||||
\(921\) | −21.5232 | −0.709213 | ||||||||
\(922\) | −54.8439 | −1.80619 | ||||||||
\(923\) | −5.16832 | −0.170117 | ||||||||
\(924\) | −65.9169 | −2.16851 | ||||||||
\(925\) | −16.0087 | −0.526363 | ||||||||
\(926\) | 32.3498 | 1.06308 | ||||||||
\(927\) | −23.2624 | −0.764037 | ||||||||
\(928\) | 9.12423 | 0.299518 | ||||||||
\(929\) | 50.0587 | 1.64237 | 0.821186 | − | 0.570660i | \(-0.193313\pi\) | ||||
0.821186 | + | 0.570660i | \(0.193313\pi\) | |||||||
\(930\) | 11.3532 | 0.372284 | ||||||||
\(931\) | 18.2415 | 0.597840 | ||||||||
\(932\) | 34.1584 | 1.11890 | ||||||||
\(933\) | −8.69838 | −0.284772 | ||||||||
\(934\) | −69.9730 | −2.28959 | ||||||||
\(935\) | −12.7596 | −0.417284 | ||||||||
\(936\) | 9.52244 | 0.311251 | ||||||||
\(937\) | 25.4041 | 0.829917 | 0.414958 | − | 0.909840i | \(-0.363796\pi\) | ||||
0.414958 | + | 0.909840i | \(0.363796\pi\) | |||||||
\(938\) | 84.5026 | 2.75911 | ||||||||
\(939\) | 3.62645 | 0.118345 | ||||||||
\(940\) | 25.2231 | 0.822688 | ||||||||
\(941\) | 43.9137 | 1.43155 | 0.715773 | − | 0.698333i | \(-0.246074\pi\) | ||||
0.715773 | + | 0.698333i | \(0.246074\pi\) | |||||||
\(942\) | 20.7226 | 0.675177 | ||||||||
\(943\) | −0.461021 | −0.0150129 | ||||||||
\(944\) | −1.98566 | −0.0646278 | ||||||||
\(945\) | −81.0589 | −2.63685 | ||||||||
\(946\) | 39.0148 | 1.26848 | ||||||||
\(947\) | −7.18780 | −0.233572 | −0.116786 | − | 0.993157i | \(-0.537259\pi\) | ||||
−0.116786 | + | 0.993157i | \(0.537259\pi\) | |||||||
\(948\) | 49.1762 | 1.59717 | ||||||||
\(949\) | 5.79883 | 0.188238 | ||||||||
\(950\) | −12.1095 | −0.392883 | ||||||||
\(951\) | −16.0507 | −0.520478 | ||||||||
\(952\) | −16.0319 | −0.519595 | ||||||||
\(953\) | 7.07513 | 0.229186 | 0.114593 | − | 0.993413i | \(-0.463444\pi\) | ||||
0.114593 | + | 0.993413i | \(0.463444\pi\) | |||||||
\(954\) | −60.9754 | −1.97415 | ||||||||
\(955\) | −54.0165 | −1.74793 | ||||||||
\(956\) | 19.9922 | 0.646595 | ||||||||
\(957\) | −7.05010 | −0.227898 | ||||||||
\(958\) | 43.9432 | 1.41974 | ||||||||
\(959\) | −78.4064 | −2.53188 | ||||||||
\(960\) | −39.9115 | −1.28814 | ||||||||
\(961\) | −28.5769 | −0.921835 | ||||||||
\(962\) | 10.0648 | 0.324503 | ||||||||
\(963\) | −14.1296 | −0.455320 | ||||||||
\(964\) | −32.1242 | −1.03465 | ||||||||
\(965\) | 26.8269 | 0.863588 | ||||||||
\(966\) | 0.945749 | 0.0304290 | ||||||||
\(967\) | −51.2004 | −1.64649 | −0.823247 | − | 0.567684i | \(-0.807840\pi\) | ||||
−0.823247 | + | 0.567684i | \(0.807840\pi\) | |||||||
\(968\) | −14.4619 | −0.464824 | ||||||||
\(969\) | −0.937889 | −0.0301293 | ||||||||
\(970\) | −116.363 | −3.73620 | ||||||||
\(971\) | 55.5540 | 1.78281 | 0.891407 | − | 0.453204i | \(-0.149719\pi\) | ||||
0.891407 | + | 0.453204i | \(0.149719\pi\) | |||||||
\(972\) | −54.0252 | −1.73286 | ||||||||
\(973\) | 44.1867 | 1.41656 | ||||||||
\(974\) | −50.2968 | −1.61161 | ||||||||
\(975\) | −7.83340 | −0.250870 | ||||||||
\(976\) | 6.63870 | 0.212500 | ||||||||
\(977\) | −58.5148 | −1.87205 | −0.936026 | − | 0.351930i | \(-0.885526\pi\) | ||||
−0.936026 | + | 0.351930i | \(0.885526\pi\) | |||||||
\(978\) | 28.3819 | 0.907553 | ||||||||
\(979\) | −35.6545 | −1.13952 | ||||||||
\(980\) | −205.831 | −6.57502 | ||||||||
\(981\) | −8.64636 | −0.276057 | ||||||||
\(982\) | 66.7030 | 2.12858 | ||||||||
\(983\) | 24.1245 | 0.769453 | 0.384727 | − | 0.923031i | \(-0.374296\pi\) | ||||
0.384727 | + | 0.923031i | \(0.374296\pi\) | |||||||
\(984\) | −17.2027 | −0.548403 | ||||||||
\(985\) | −53.0562 | −1.69051 | ||||||||
\(986\) | −4.23801 | −0.134966 | ||||||||
\(987\) | 11.5484 | 0.367590 | ||||||||
\(988\) | 4.77204 | 0.151819 | ||||||||
\(989\) | −0.350863 | −0.0111568 | ||||||||
\(990\) | −60.5272 | −1.92368 | ||||||||
\(991\) | −42.6626 | −1.35522 | −0.677611 | − | 0.735421i | \(-0.736985\pi\) | ||||
−0.677611 | + | 0.735421i | \(0.736985\pi\) | |||||||
\(992\) | −7.75830 | −0.246326 | ||||||||
\(993\) | −13.3663 | −0.424166 | ||||||||
\(994\) | 41.2760 | 1.30919 | ||||||||
\(995\) | −12.0871 | −0.383186 | ||||||||
\(996\) | 39.6147 | 1.25524 | ||||||||
\(997\) | 7.28060 | 0.230579 | 0.115290 | − | 0.993332i | \(-0.463220\pi\) | ||||
0.115290 | + | 0.993332i | \(0.463220\pi\) | |||||||
\(998\) | −39.8403 | −1.26112 | ||||||||
\(999\) | −14.4925 | −0.458523 |
(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 | 6001.2.a.b.1.13 | ✓ | 114 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6001.2.a.b.1.13 | ✓ | 114 | 1.1 | even | 1 | trivial |