Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1859,2,Mod(1,1859)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1859, 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("1859.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1859 = 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1859.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: | \(14.8441897358\) |
Analytic rank: | \(0\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 1859.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.26490 | 1.60153 | 0.800764 | − | 0.598980i | \(-0.204427\pi\) | ||||
0.800764 | + | 0.598980i | \(0.204427\pi\) | |||||||
\(3\) | 3.17598 | 1.83365 | 0.916827 | − | 0.399284i | \(-0.130741\pi\) | ||||
0.916827 | + | 0.399284i | \(0.130741\pi\) | |||||||
\(4\) | 3.12978 | 1.56489 | ||||||||
\(5\) | 2.32745 | 1.04087 | 0.520433 | − | 0.853902i | \(-0.325770\pi\) | ||||
0.520433 | + | 0.853902i | \(0.325770\pi\) | |||||||
\(6\) | 7.19329 | 2.93665 | ||||||||
\(7\) | −4.39568 | −1.66141 | −0.830706 | − | 0.556711i | \(-0.812063\pi\) | ||||
−0.830706 | + | 0.556711i | \(0.812063\pi\) | |||||||
\(8\) | 2.55884 | 0.904686 | ||||||||
\(9\) | 7.08687 | 2.36229 | ||||||||
\(10\) | 5.27144 | 1.66698 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 9.94013 | 2.86947 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −9.95579 | −2.66080 | ||||||||
\(15\) | 7.39194 | 1.90859 | ||||||||
\(16\) | −0.464040 | −0.116010 | ||||||||
\(17\) | −3.60615 | −0.874619 | −0.437309 | − | 0.899311i | \(-0.644069\pi\) | ||||
−0.437309 | + | 0.899311i | \(0.644069\pi\) | |||||||
\(18\) | 16.0511 | 3.78327 | ||||||||
\(19\) | −2.34411 | −0.537775 | −0.268887 | − | 0.963172i | \(-0.586656\pi\) | ||||
−0.268887 | + | 0.963172i | \(0.586656\pi\) | |||||||
\(20\) | 7.28440 | 1.62884 | ||||||||
\(21\) | −13.9606 | −3.04646 | ||||||||
\(22\) | 2.26490 | 0.482879 | ||||||||
\(23\) | 2.46089 | 0.513131 | 0.256566 | − | 0.966527i | \(-0.417409\pi\) | ||||
0.256566 | + | 0.966527i | \(0.417409\pi\) | |||||||
\(24\) | 8.12683 | 1.65888 | ||||||||
\(25\) | 0.417018 | 0.0834036 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 12.9798 | 2.49797 | ||||||||
\(28\) | −13.7575 | −2.59993 | ||||||||
\(29\) | 6.42191 | 1.19252 | 0.596259 | − | 0.802792i | \(-0.296653\pi\) | ||||
0.596259 | + | 0.802792i | \(0.296653\pi\) | |||||||
\(30\) | 16.7420 | 3.05666 | ||||||||
\(31\) | −4.49503 | −0.807332 | −0.403666 | − | 0.914906i | \(-0.632264\pi\) | ||||
−0.403666 | + | 0.914906i | \(0.632264\pi\) | |||||||
\(32\) | −6.16868 | −1.09048 | ||||||||
\(33\) | 3.17598 | 0.552868 | ||||||||
\(34\) | −8.16757 | −1.40073 | ||||||||
\(35\) | −10.2307 | −1.72931 | ||||||||
\(36\) | 22.1803 | 3.69672 | ||||||||
\(37\) | 3.91017 | 0.642828 | 0.321414 | − | 0.946939i | \(-0.395842\pi\) | ||||
0.321414 | + | 0.946939i | \(0.395842\pi\) | |||||||
\(38\) | −5.30917 | −0.861261 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.95557 | 0.941658 | ||||||||
\(41\) | −9.00689 | −1.40664 | −0.703320 | − | 0.710873i | \(-0.748300\pi\) | ||||
−0.703320 | + | 0.710873i | \(0.748300\pi\) | |||||||
\(42\) | −31.6194 | −4.87898 | ||||||||
\(43\) | −0.179144 | −0.0273192 | −0.0136596 | − | 0.999907i | \(-0.504348\pi\) | ||||
−0.0136596 | + | 0.999907i | \(0.504348\pi\) | |||||||
\(44\) | 3.12978 | 0.471832 | ||||||||
\(45\) | 16.4943 | 2.45883 | ||||||||
\(46\) | 5.57368 | 0.821794 | ||||||||
\(47\) | 0.0336641 | 0.00491042 | 0.00245521 | − | 0.999997i | \(-0.499218\pi\) | ||||
0.00245521 | + | 0.999997i | \(0.499218\pi\) | |||||||
\(48\) | −1.47378 | −0.212722 | ||||||||
\(49\) | 12.3220 | 1.76029 | ||||||||
\(50\) | 0.944504 | 0.133573 | ||||||||
\(51\) | −11.4531 | −1.60375 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.80795 | −1.07250 | −0.536252 | − | 0.844058i | \(-0.680160\pi\) | ||||
−0.536252 | + | 0.844058i | \(0.680160\pi\) | |||||||
\(54\) | 29.3980 | 4.00056 | ||||||||
\(55\) | 2.32745 | 0.313833 | ||||||||
\(56\) | −11.2478 | −1.50306 | ||||||||
\(57\) | −7.44484 | −0.986094 | ||||||||
\(58\) | 14.5450 | 1.90985 | ||||||||
\(59\) | 7.69487 | 1.00179 | 0.500893 | − | 0.865509i | \(-0.333005\pi\) | ||||
0.500893 | + | 0.865509i | \(0.333005\pi\) | |||||||
\(60\) | 23.1351 | 2.98673 | ||||||||
\(61\) | 3.02228 | 0.386963 | 0.193482 | − | 0.981104i | \(-0.438022\pi\) | ||||
0.193482 | + | 0.981104i | \(0.438022\pi\) | |||||||
\(62\) | −10.1808 | −1.29296 | ||||||||
\(63\) | −31.1516 | −3.92474 | ||||||||
\(64\) | −13.0434 | −1.63042 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 7.19329 | 0.885433 | ||||||||
\(67\) | −12.9678 | −1.58427 | −0.792135 | − | 0.610346i | \(-0.791031\pi\) | ||||
−0.792135 | + | 0.610346i | \(0.791031\pi\) | |||||||
\(68\) | −11.2864 | −1.36868 | ||||||||
\(69\) | 7.81575 | 0.940906 | ||||||||
\(70\) | −23.1716 | −2.76954 | ||||||||
\(71\) | 7.10607 | 0.843335 | 0.421668 | − | 0.906750i | \(-0.361445\pi\) | ||||
0.421668 | + | 0.906750i | \(0.361445\pi\) | |||||||
\(72\) | 18.1342 | 2.13713 | ||||||||
\(73\) | −11.7832 | −1.37912 | −0.689561 | − | 0.724228i | \(-0.742196\pi\) | ||||
−0.689561 | + | 0.724228i | \(0.742196\pi\) | |||||||
\(74\) | 8.85615 | 1.02951 | ||||||||
\(75\) | 1.32444 | 0.152933 | ||||||||
\(76\) | −7.33654 | −0.841559 | ||||||||
\(77\) | −4.39568 | −0.500935 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.77099 | 0.311761 | 0.155881 | − | 0.987776i | \(-0.450179\pi\) | ||||
0.155881 | + | 0.987776i | \(0.450179\pi\) | |||||||
\(80\) | −1.08003 | −0.120751 | ||||||||
\(81\) | 19.9631 | 2.21812 | ||||||||
\(82\) | −20.3997 | −2.25277 | ||||||||
\(83\) | 9.48182 | 1.04077 | 0.520383 | − | 0.853933i | \(-0.325789\pi\) | ||||
0.520383 | + | 0.853933i | \(0.325789\pi\) | |||||||
\(84\) | −43.6936 | −4.76737 | ||||||||
\(85\) | −8.39312 | −0.910362 | ||||||||
\(86\) | −0.405744 | −0.0437525 | ||||||||
\(87\) | 20.3959 | 2.18667 | ||||||||
\(88\) | 2.55884 | 0.272773 | ||||||||
\(89\) | 11.5018 | 1.21919 | 0.609595 | − | 0.792713i | \(-0.291332\pi\) | ||||
0.609595 | + | 0.792713i | \(0.291332\pi\) | |||||||
\(90\) | 37.3580 | 3.93788 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 7.70205 | 0.802994 | ||||||||
\(93\) | −14.2761 | −1.48037 | ||||||||
\(94\) | 0.0762459 | 0.00786417 | ||||||||
\(95\) | −5.45579 | −0.559752 | ||||||||
\(96\) | −19.5916 | −1.99956 | ||||||||
\(97\) | 5.83595 | 0.592551 | 0.296275 | − | 0.955103i | \(-0.404255\pi\) | ||||
0.296275 | + | 0.955103i | \(0.404255\pi\) | |||||||
\(98\) | 27.9082 | 2.81915 | ||||||||
\(99\) | 7.08687 | 0.712257 | ||||||||
\(100\) | 1.30517 | 0.130517 | ||||||||
\(101\) | 9.65478 | 0.960686 | 0.480343 | − | 0.877081i | \(-0.340512\pi\) | ||||
0.480343 | + | 0.877081i | \(0.340512\pi\) | |||||||
\(102\) | −25.9400 | −2.56845 | ||||||||
\(103\) | 8.58581 | 0.845985 | 0.422993 | − | 0.906133i | \(-0.360980\pi\) | ||||
0.422993 | + | 0.906133i | \(0.360980\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −32.4926 | −3.17095 | ||||||||
\(106\) | −17.6842 | −1.71765 | ||||||||
\(107\) | 10.4959 | 1.01468 | 0.507340 | − | 0.861746i | \(-0.330629\pi\) | ||||
0.507340 | + | 0.861746i | \(0.330629\pi\) | |||||||
\(108\) | 40.6240 | 3.90904 | ||||||||
\(109\) | 4.20186 | 0.402465 | 0.201232 | − | 0.979544i | \(-0.435505\pi\) | ||||
0.201232 | + | 0.979544i | \(0.435505\pi\) | |||||||
\(110\) | 5.27144 | 0.502612 | ||||||||
\(111\) | 12.4186 | 1.17872 | ||||||||
\(112\) | 2.03977 | 0.192740 | ||||||||
\(113\) | −16.4640 | −1.54880 | −0.774401 | − | 0.632695i | \(-0.781949\pi\) | ||||
−0.774401 | + | 0.632695i | \(0.781949\pi\) | |||||||
\(114\) | −16.8618 | −1.57926 | ||||||||
\(115\) | 5.72760 | 0.534101 | ||||||||
\(116\) | 20.0992 | 1.86616 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 17.4281 | 1.60439 | ||||||||
\(119\) | 15.8515 | 1.45310 | ||||||||
\(120\) | 18.9148 | 1.72668 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 6.84516 | 0.619732 | ||||||||
\(123\) | −28.6057 | −2.57929 | ||||||||
\(124\) | −14.0685 | −1.26339 | ||||||||
\(125\) | −10.6667 | −0.954055 | ||||||||
\(126\) | −70.5554 | −6.28557 | ||||||||
\(127\) | −16.6381 | −1.47639 | −0.738197 | − | 0.674585i | \(-0.764323\pi\) | ||||
−0.738197 | + | 0.674585i | \(0.764323\pi\) | |||||||
\(128\) | −17.2046 | −1.52069 | ||||||||
\(129\) | −0.568958 | −0.0500940 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.56292 | 0.573405 | 0.286702 | − | 0.958020i | \(-0.407441\pi\) | ||||
0.286702 | + | 0.958020i | \(0.407441\pi\) | |||||||
\(132\) | 9.94013 | 0.865177 | ||||||||
\(133\) | 10.3040 | 0.893466 | ||||||||
\(134\) | −29.3708 | −2.53725 | ||||||||
\(135\) | 30.2099 | 2.60005 | ||||||||
\(136\) | −9.22755 | −0.791256 | ||||||||
\(137\) | 1.55770 | 0.133084 | 0.0665418 | − | 0.997784i | \(-0.478803\pi\) | ||||
0.0665418 | + | 0.997784i | \(0.478803\pi\) | |||||||
\(138\) | 17.7019 | 1.50689 | ||||||||
\(139\) | −8.10863 | −0.687765 | −0.343882 | − | 0.939013i | \(-0.611742\pi\) | ||||
−0.343882 | + | 0.939013i | \(0.611742\pi\) | |||||||
\(140\) | −32.0199 | −2.70618 | ||||||||
\(141\) | 0.106917 | 0.00900401 | ||||||||
\(142\) | 16.0945 | 1.35062 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −3.28859 | −0.274049 | ||||||||
\(145\) | 14.9467 | 1.24125 | ||||||||
\(146\) | −26.6878 | −2.20870 | ||||||||
\(147\) | 39.1346 | 3.22776 | ||||||||
\(148\) | 12.2380 | 1.00595 | ||||||||
\(149\) | −5.48659 | −0.449479 | −0.224739 | − | 0.974419i | \(-0.572153\pi\) | ||||
−0.224739 | + | 0.974419i | \(0.572153\pi\) | |||||||
\(150\) | 2.99973 | 0.244927 | ||||||||
\(151\) | −6.97757 | −0.567826 | −0.283913 | − | 0.958850i | \(-0.591633\pi\) | ||||
−0.283913 | + | 0.958850i | \(0.591633\pi\) | |||||||
\(152\) | −5.99819 | −0.486518 | ||||||||
\(153\) | −25.5563 | −2.06610 | ||||||||
\(154\) | −9.95579 | −0.802260 | ||||||||
\(155\) | −10.4620 | −0.840325 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.03843 | −0.402111 | −0.201055 | − | 0.979580i | \(-0.564437\pi\) | ||||
−0.201055 | + | 0.979580i | \(0.564437\pi\) | |||||||
\(158\) | 6.27603 | 0.499294 | ||||||||
\(159\) | −24.7979 | −1.96660 | ||||||||
\(160\) | −14.3573 | −1.13504 | ||||||||
\(161\) | −10.8173 | −0.852523 | ||||||||
\(162\) | 45.2144 | 3.55238 | ||||||||
\(163\) | −17.8890 | −1.40118 | −0.700589 | − | 0.713565i | \(-0.747079\pi\) | ||||
−0.700589 | + | 0.713565i | \(0.747079\pi\) | |||||||
\(164\) | −28.1896 | −2.20124 | ||||||||
\(165\) | 7.39194 | 0.575462 | ||||||||
\(166\) | 21.4754 | 1.66681 | ||||||||
\(167\) | 1.60051 | 0.123851 | 0.0619256 | − | 0.998081i | \(-0.480276\pi\) | ||||
0.0619256 | + | 0.998081i | \(0.480276\pi\) | |||||||
\(168\) | −35.7230 | −2.75609 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −19.0096 | −1.45797 | ||||||||
\(171\) | −16.6124 | −1.27038 | ||||||||
\(172\) | −0.560681 | −0.0427515 | ||||||||
\(173\) | 16.3925 | 1.24630 | 0.623148 | − | 0.782104i | \(-0.285854\pi\) | ||||
0.623148 | + | 0.782104i | \(0.285854\pi\) | |||||||
\(174\) | 46.1947 | 3.50201 | ||||||||
\(175\) | −1.83308 | −0.138568 | ||||||||
\(176\) | −0.464040 | −0.0349783 | ||||||||
\(177\) | 24.4388 | 1.83693 | ||||||||
\(178\) | 26.0505 | 1.95257 | ||||||||
\(179\) | 13.0693 | 0.976848 | 0.488424 | − | 0.872606i | \(-0.337572\pi\) | ||||
0.488424 | + | 0.872606i | \(0.337572\pi\) | |||||||
\(180\) | 51.6236 | 3.84779 | ||||||||
\(181\) | 7.53850 | 0.560332 | 0.280166 | − | 0.959952i | \(-0.409610\pi\) | ||||
0.280166 | + | 0.959952i | \(0.409610\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.59870 | 0.709557 | ||||||||
\(184\) | 6.29703 | 0.464223 | ||||||||
\(185\) | 9.10072 | 0.669098 | ||||||||
\(186\) | −32.3341 | −2.37085 | ||||||||
\(187\) | −3.60615 | −0.263708 | ||||||||
\(188\) | 0.105361 | 0.00768426 | ||||||||
\(189\) | −57.0552 | −4.15015 | ||||||||
\(190\) | −12.3568 | −0.896458 | ||||||||
\(191\) | −8.09206 | −0.585521 | −0.292760 | − | 0.956186i | \(-0.594574\pi\) | ||||
−0.292760 | + | 0.956186i | \(0.594574\pi\) | |||||||
\(192\) | −41.4256 | −2.98963 | ||||||||
\(193\) | 6.87618 | 0.494958 | 0.247479 | − | 0.968893i | \(-0.420398\pi\) | ||||
0.247479 | + | 0.968893i | \(0.420398\pi\) | |||||||
\(194\) | 13.2178 | 0.948986 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 38.5652 | 2.75466 | ||||||||
\(197\) | 7.03820 | 0.501451 | 0.250725 | − | 0.968058i | \(-0.419331\pi\) | ||||
0.250725 | + | 0.968058i | \(0.419331\pi\) | |||||||
\(198\) | 16.0511 | 1.14070 | ||||||||
\(199\) | −21.2915 | −1.50932 | −0.754658 | − | 0.656119i | \(-0.772197\pi\) | ||||
−0.754658 | + | 0.656119i | \(0.772197\pi\) | |||||||
\(200\) | 1.06708 | 0.0754541 | ||||||||
\(201\) | −41.1856 | −2.90500 | ||||||||
\(202\) | 21.8671 | 1.53857 | ||||||||
\(203\) | −28.2287 | −1.98127 | ||||||||
\(204\) | −35.8455 | −2.50969 | ||||||||
\(205\) | −20.9631 | −1.46412 | ||||||||
\(206\) | 19.4460 | 1.35487 | ||||||||
\(207\) | 17.4400 | 1.21216 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.34411 | −0.162145 | ||||||||
\(210\) | −73.5926 | −5.07837 | ||||||||
\(211\) | 2.17049 | 0.149423 | 0.0747113 | − | 0.997205i | \(-0.476196\pi\) | ||||
0.0747113 | + | 0.997205i | \(0.476196\pi\) | |||||||
\(212\) | −24.4372 | −1.67835 | ||||||||
\(213\) | 22.5688 | 1.54639 | ||||||||
\(214\) | 23.7722 | 1.62504 | ||||||||
\(215\) | −0.416949 | −0.0284357 | ||||||||
\(216\) | 33.2133 | 2.25988 | ||||||||
\(217\) | 19.7587 | 1.34131 | ||||||||
\(218\) | 9.51679 | 0.644559 | ||||||||
\(219\) | −37.4233 | −2.52883 | ||||||||
\(220\) | 7.28440 | 0.491114 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 28.1270 | 1.88776 | ||||||||
\(223\) | −20.0941 | −1.34560 | −0.672802 | − | 0.739823i | \(-0.734909\pi\) | ||||
−0.672802 | + | 0.739823i | \(0.734909\pi\) | |||||||
\(224\) | 27.1156 | 1.81174 | ||||||||
\(225\) | 2.95535 | 0.197023 | ||||||||
\(226\) | −37.2893 | −2.48045 | ||||||||
\(227\) | −2.03771 | −0.135248 | −0.0676239 | − | 0.997711i | \(-0.521542\pi\) | ||||
−0.0676239 | + | 0.997711i | \(0.521542\pi\) | |||||||
\(228\) | −23.3007 | −1.54313 | ||||||||
\(229\) | 26.4780 | 1.74972 | 0.874858 | − | 0.484379i | \(-0.160954\pi\) | ||||
0.874858 | + | 0.484379i | \(0.160954\pi\) | |||||||
\(230\) | 12.9724 | 0.855378 | ||||||||
\(231\) | −13.9606 | −0.918541 | ||||||||
\(232\) | 16.4326 | 1.07886 | ||||||||
\(233\) | 13.2446 | 0.867684 | 0.433842 | − | 0.900989i | \(-0.357158\pi\) | ||||
0.433842 | + | 0.900989i | \(0.357158\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.0783515 | 0.00511109 | ||||||||
\(236\) | 24.0832 | 1.56769 | ||||||||
\(237\) | 8.80063 | 0.571662 | ||||||||
\(238\) | 35.9020 | 2.32718 | ||||||||
\(239\) | 14.9348 | 0.966049 | 0.483024 | − | 0.875607i | \(-0.339538\pi\) | ||||
0.483024 | + | 0.875607i | \(0.339538\pi\) | |||||||
\(240\) | −3.43015 | −0.221415 | ||||||||
\(241\) | 21.9593 | 1.41452 | 0.707262 | − | 0.706952i | \(-0.249930\pi\) | ||||
0.707262 | + | 0.706952i | \(0.249930\pi\) | |||||||
\(242\) | 2.26490 | 0.145593 | ||||||||
\(243\) | 24.4629 | 1.56930 | ||||||||
\(244\) | 9.45906 | 0.605555 | ||||||||
\(245\) | 28.6789 | 1.83223 | ||||||||
\(246\) | −64.7892 | −4.13081 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −11.5021 | −0.730382 | ||||||||
\(249\) | 30.1141 | 1.90840 | ||||||||
\(250\) | −24.1589 | −1.52794 | ||||||||
\(251\) | −6.67219 | −0.421145 | −0.210572 | − | 0.977578i | \(-0.567533\pi\) | ||||
−0.210572 | + | 0.977578i | \(0.567533\pi\) | |||||||
\(252\) | −97.4977 | −6.14178 | ||||||||
\(253\) | 2.46089 | 0.154715 | ||||||||
\(254\) | −37.6837 | −2.36449 | ||||||||
\(255\) | −26.6564 | −1.66929 | ||||||||
\(256\) | −12.8800 | −0.804999 | ||||||||
\(257\) | 14.5884 | 0.909997 | 0.454998 | − | 0.890492i | \(-0.349640\pi\) | ||||
0.454998 | + | 0.890492i | \(0.349640\pi\) | |||||||
\(258\) | −1.28863 | −0.0802269 | ||||||||
\(259\) | −17.1879 | −1.06800 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 45.5112 | 2.81707 | ||||||||
\(262\) | 14.8644 | 0.918323 | ||||||||
\(263\) | 22.5923 | 1.39310 | 0.696550 | − | 0.717508i | \(-0.254717\pi\) | ||||
0.696550 | + | 0.717508i | \(0.254717\pi\) | |||||||
\(264\) | 8.12683 | 0.500172 | ||||||||
\(265\) | −18.1726 | −1.11633 | ||||||||
\(266\) | 23.3374 | 1.43091 | ||||||||
\(267\) | 36.5296 | 2.23557 | ||||||||
\(268\) | −40.5864 | −2.47921 | ||||||||
\(269\) | 27.6973 | 1.68873 | 0.844367 | − | 0.535765i | \(-0.179977\pi\) | ||||
0.844367 | + | 0.535765i | \(0.179977\pi\) | |||||||
\(270\) | 68.4224 | 4.16405 | ||||||||
\(271\) | −8.51223 | −0.517081 | −0.258541 | − | 0.966000i | \(-0.583242\pi\) | ||||
−0.258541 | + | 0.966000i | \(0.583242\pi\) | |||||||
\(272\) | 1.67340 | 0.101464 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.52804 | 0.213137 | ||||||||
\(275\) | 0.417018 | 0.0251471 | ||||||||
\(276\) | 24.4616 | 1.47241 | ||||||||
\(277\) | 22.0263 | 1.32343 | 0.661716 | − | 0.749754i | \(-0.269828\pi\) | ||||
0.661716 | + | 0.749754i | \(0.269828\pi\) | |||||||
\(278\) | −18.3652 | −1.10147 | ||||||||
\(279\) | −31.8557 | −1.90715 | ||||||||
\(280\) | −26.1788 | −1.56448 | ||||||||
\(281\) | 18.6880 | 1.11483 | 0.557415 | − | 0.830234i | \(-0.311793\pi\) | ||||
0.557415 | + | 0.830234i | \(0.311793\pi\) | |||||||
\(282\) | 0.242156 | 0.0144202 | ||||||||
\(283\) | −12.2498 | −0.728173 | −0.364087 | − | 0.931365i | \(-0.618619\pi\) | ||||
−0.364087 | + | 0.931365i | \(0.618619\pi\) | |||||||
\(284\) | 22.2404 | 1.31973 | ||||||||
\(285\) | −17.3275 | −1.02639 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 39.5914 | 2.33701 | ||||||||
\(288\) | −43.7166 | −2.57603 | ||||||||
\(289\) | −3.99571 | −0.235042 | ||||||||
\(290\) | 33.8527 | 1.98790 | ||||||||
\(291\) | 18.5349 | 1.08653 | ||||||||
\(292\) | −36.8789 | −2.15817 | ||||||||
\(293\) | −17.7766 | −1.03852 | −0.519259 | − | 0.854617i | \(-0.673792\pi\) | ||||
−0.519259 | + | 0.854617i | \(0.673792\pi\) | |||||||
\(294\) | 88.6359 | 5.16935 | ||||||||
\(295\) | 17.9094 | 1.04273 | ||||||||
\(296\) | 10.0055 | 0.581558 | ||||||||
\(297\) | 12.9798 | 0.753165 | ||||||||
\(298\) | −12.4266 | −0.719853 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 4.14521 | 0.239324 | ||||||||
\(301\) | 0.787460 | 0.0453885 | ||||||||
\(302\) | −15.8035 | −0.909389 | ||||||||
\(303\) | 30.6634 | 1.76157 | ||||||||
\(304\) | 1.08776 | 0.0623873 | ||||||||
\(305\) | 7.03420 | 0.402777 | ||||||||
\(306\) | −57.8825 | −3.30892 | ||||||||
\(307\) | 2.57203 | 0.146793 | 0.0733967 | − | 0.997303i | \(-0.476616\pi\) | ||||
0.0733967 | + | 0.997303i | \(0.476616\pi\) | |||||||
\(308\) | −13.7575 | −0.783907 | ||||||||
\(309\) | 27.2684 | 1.55124 | ||||||||
\(310\) | −23.6953 | −1.34580 | ||||||||
\(311\) | 9.54000 | 0.540964 | 0.270482 | − | 0.962725i | \(-0.412817\pi\) | ||||
0.270482 | + | 0.962725i | \(0.412817\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −31.8648 | −1.80110 | −0.900552 | − | 0.434748i | \(-0.856837\pi\) | ||||
−0.900552 | + | 0.434748i | \(0.856837\pi\) | |||||||
\(314\) | −11.4116 | −0.643991 | ||||||||
\(315\) | −72.5038 | −4.08513 | ||||||||
\(316\) | 8.67260 | 0.487872 | ||||||||
\(317\) | 32.1914 | 1.80805 | 0.904024 | − | 0.427482i | \(-0.140599\pi\) | ||||
0.904024 | + | 0.427482i | \(0.140599\pi\) | |||||||
\(318\) | −56.1649 | −3.14957 | ||||||||
\(319\) | 6.42191 | 0.359558 | ||||||||
\(320\) | −30.3578 | −1.69705 | ||||||||
\(321\) | 33.3349 | 1.86057 | ||||||||
\(322\) | −24.5001 | −1.36534 | ||||||||
\(323\) | 8.45319 | 0.470348 | ||||||||
\(324\) | 62.4800 | 3.47111 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −40.5169 | −2.24402 | ||||||||
\(327\) | 13.3450 | 0.737982 | ||||||||
\(328\) | −23.0472 | −1.27257 | ||||||||
\(329\) | −0.147977 | −0.00815823 | ||||||||
\(330\) | 16.7420 | 0.921617 | ||||||||
\(331\) | −2.42102 | −0.133072 | −0.0665358 | − | 0.997784i | \(-0.521195\pi\) | ||||
−0.0665358 | + | 0.997784i | \(0.521195\pi\) | |||||||
\(332\) | 29.6760 | 1.62868 | ||||||||
\(333\) | 27.7109 | 1.51855 | ||||||||
\(334\) | 3.62500 | 0.198351 | ||||||||
\(335\) | −30.1819 | −1.64901 | ||||||||
\(336\) | 6.47828 | 0.353419 | ||||||||
\(337\) | −31.1343 | −1.69599 | −0.847996 | − | 0.530003i | \(-0.822191\pi\) | ||||
−0.847996 | + | 0.530003i | \(0.822191\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −52.2894 | −2.83997 | ||||||||
\(340\) | −26.2686 | −1.42462 | ||||||||
\(341\) | −4.49503 | −0.243420 | ||||||||
\(342\) | −37.6254 | −2.03455 | ||||||||
\(343\) | −23.3940 | −1.26316 | ||||||||
\(344\) | −0.458401 | −0.0247153 | ||||||||
\(345\) | 18.1908 | 0.979357 | ||||||||
\(346\) | 37.1273 | 1.99598 | ||||||||
\(347\) | −21.5915 | −1.15909 | −0.579546 | − | 0.814939i | \(-0.696770\pi\) | ||||
−0.579546 | + | 0.814939i | \(0.696770\pi\) | |||||||
\(348\) | 63.8346 | 3.42189 | ||||||||
\(349\) | 7.51782 | 0.402420 | 0.201210 | − | 0.979548i | \(-0.435513\pi\) | ||||
0.201210 | + | 0.979548i | \(0.435513\pi\) | |||||||
\(350\) | −4.15174 | −0.221920 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.16868 | −0.328792 | ||||||||
\(353\) | 32.6049 | 1.73538 | 0.867692 | − | 0.497102i | \(-0.165603\pi\) | ||||
0.867692 | + | 0.497102i | \(0.165603\pi\) | |||||||
\(354\) | 55.3514 | 2.94190 | ||||||||
\(355\) | 16.5390 | 0.877800 | ||||||||
\(356\) | 35.9982 | 1.90790 | ||||||||
\(357\) | 50.3440 | 2.66449 | ||||||||
\(358\) | 29.6008 | 1.56445 | ||||||||
\(359\) | −36.7060 | −1.93727 | −0.968633 | − | 0.248495i | \(-0.920064\pi\) | ||||
−0.968633 | + | 0.248495i | \(0.920064\pi\) | |||||||
\(360\) | 42.2063 | 2.22447 | ||||||||
\(361\) | −13.5052 | −0.710798 | ||||||||
\(362\) | 17.0740 | 0.897388 | ||||||||
\(363\) | 3.17598 | 0.166696 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −27.4248 | −1.43548 | ||||||||
\(366\) | 21.7401 | 1.13637 | ||||||||
\(367\) | 10.5024 | 0.548219 | 0.274109 | − | 0.961699i | \(-0.411617\pi\) | ||||
0.274109 | + | 0.961699i | \(0.411617\pi\) | |||||||
\(368\) | −1.14195 | −0.0595283 | ||||||||
\(369\) | −63.8306 | −3.32289 | ||||||||
\(370\) | 20.6122 | 1.07158 | ||||||||
\(371\) | 34.3213 | 1.78187 | ||||||||
\(372\) | −44.6812 | −2.31661 | ||||||||
\(373\) | 11.2568 | 0.582853 | 0.291427 | − | 0.956593i | \(-0.405870\pi\) | ||||
0.291427 | + | 0.956593i | \(0.405870\pi\) | |||||||
\(374\) | −8.16757 | −0.422335 | ||||||||
\(375\) | −33.8771 | −1.74941 | ||||||||
\(376\) | 0.0861411 | 0.00444239 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −129.224 | −6.64658 | ||||||||
\(379\) | −30.9736 | −1.59101 | −0.795505 | − | 0.605948i | \(-0.792794\pi\) | ||||
−0.795505 | + | 0.605948i | \(0.792794\pi\) | |||||||
\(380\) | −17.0754 | −0.875950 | ||||||||
\(381\) | −52.8424 | −2.70720 | ||||||||
\(382\) | −18.3277 | −0.937727 | ||||||||
\(383\) | −1.64383 | −0.0839956 | −0.0419978 | − | 0.999118i | \(-0.513372\pi\) | ||||
−0.0419978 | + | 0.999118i | \(0.513372\pi\) | |||||||
\(384\) | −54.6415 | −2.78841 | ||||||||
\(385\) | −10.2307 | −0.521406 | ||||||||
\(386\) | 15.5739 | 0.792689 | ||||||||
\(387\) | −1.26957 | −0.0645359 | ||||||||
\(388\) | 18.2652 | 0.927277 | ||||||||
\(389\) | −10.5028 | −0.532513 | −0.266257 | − | 0.963902i | \(-0.585787\pi\) | ||||
−0.266257 | + | 0.963902i | \(0.585787\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.87434 | −0.448794 | ||||||||
\(392\) | 31.5301 | 1.59251 | ||||||||
\(393\) | 20.8437 | 1.05143 | ||||||||
\(394\) | 15.9408 | 0.803087 | ||||||||
\(395\) | 6.44934 | 0.324502 | ||||||||
\(396\) | 22.1803 | 1.11460 | ||||||||
\(397\) | 2.37693 | 0.119295 | 0.0596474 | − | 0.998220i | \(-0.481002\pi\) | ||||
0.0596474 | + | 0.998220i | \(0.481002\pi\) | |||||||
\(398\) | −48.2232 | −2.41721 | ||||||||
\(399\) | 32.7252 | 1.63831 | ||||||||
\(400\) | −0.193513 | −0.00967564 | ||||||||
\(401\) | −10.5726 | −0.527971 | −0.263985 | − | 0.964527i | \(-0.585037\pi\) | ||||
−0.263985 | + | 0.964527i | \(0.585037\pi\) | |||||||
\(402\) | −93.2812 | −4.65244 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 30.2173 | 1.50337 | ||||||||
\(405\) | 46.4630 | 2.30877 | ||||||||
\(406\) | −63.9352 | −3.17305 | ||||||||
\(407\) | 3.91017 | 0.193820 | ||||||||
\(408\) | −29.3065 | −1.45089 | ||||||||
\(409\) | 32.7342 | 1.61860 | 0.809301 | − | 0.587395i | \(-0.199846\pi\) | ||||
0.809301 | + | 0.587395i | \(0.199846\pi\) | |||||||
\(410\) | −47.4793 | −2.34484 | ||||||||
\(411\) | 4.94724 | 0.244029 | ||||||||
\(412\) | 26.8717 | 1.32387 | ||||||||
\(413\) | −33.8242 | −1.66438 | ||||||||
\(414\) | 39.4999 | 1.94131 | ||||||||
\(415\) | 22.0685 | 1.08330 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −25.7529 | −1.26112 | ||||||||
\(418\) | −5.30917 | −0.259680 | ||||||||
\(419\) | 10.3533 | 0.505793 | 0.252896 | − | 0.967493i | \(-0.418617\pi\) | ||||
0.252896 | + | 0.967493i | \(0.418617\pi\) | |||||||
\(420\) | −101.695 | −4.96219 | ||||||||
\(421\) | −9.96868 | −0.485844 | −0.242922 | − | 0.970046i | \(-0.578106\pi\) | ||||
−0.242922 | + | 0.970046i | \(0.578106\pi\) | |||||||
\(422\) | 4.91594 | 0.239304 | ||||||||
\(423\) | 0.238573 | 0.0115998 | ||||||||
\(424\) | −19.9793 | −0.970280 | ||||||||
\(425\) | −1.50383 | −0.0729463 | ||||||||
\(426\) | 51.1160 | 2.47658 | ||||||||
\(427\) | −13.2850 | −0.642905 | ||||||||
\(428\) | 32.8499 | 1.58786 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.944347 | −0.0455405 | ||||||||
\(431\) | −7.20363 | −0.346987 | −0.173493 | − | 0.984835i | \(-0.555506\pi\) | ||||
−0.173493 | + | 0.984835i | \(0.555506\pi\) | |||||||
\(432\) | −6.02315 | −0.289789 | ||||||||
\(433\) | −38.2837 | −1.83980 | −0.919899 | − | 0.392156i | \(-0.871729\pi\) | ||||
−0.919899 | + | 0.392156i | \(0.871729\pi\) | |||||||
\(434\) | 44.7516 | 2.14815 | ||||||||
\(435\) | 47.4704 | 2.27603 | ||||||||
\(436\) | 13.1509 | 0.629813 | ||||||||
\(437\) | −5.76859 | −0.275949 | ||||||||
\(438\) | −84.7601 | −4.04999 | ||||||||
\(439\) | 5.38316 | 0.256924 | 0.128462 | − | 0.991714i | \(-0.458996\pi\) | ||||
0.128462 | + | 0.991714i | \(0.458996\pi\) | |||||||
\(440\) | 5.95557 | 0.283921 | ||||||||
\(441\) | 87.3246 | 4.15831 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.3401 | 0.966389 | 0.483194 | − | 0.875513i | \(-0.339476\pi\) | ||||
0.483194 | + | 0.875513i | \(0.339476\pi\) | |||||||
\(444\) | 38.8676 | 1.84457 | ||||||||
\(445\) | 26.7699 | 1.26902 | ||||||||
\(446\) | −45.5113 | −2.15502 | ||||||||
\(447\) | −17.4253 | −0.824189 | ||||||||
\(448\) | 57.3346 | 2.70880 | ||||||||
\(449\) | −4.25666 | −0.200884 | −0.100442 | − | 0.994943i | \(-0.532026\pi\) | ||||
−0.100442 | + | 0.994943i | \(0.532026\pi\) | |||||||
\(450\) | 6.69358 | 0.315538 | ||||||||
\(451\) | −9.00689 | −0.424118 | ||||||||
\(452\) | −51.5287 | −2.42371 | ||||||||
\(453\) | −22.1606 | −1.04120 | ||||||||
\(454\) | −4.61522 | −0.216603 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −19.0502 | −0.892105 | ||||||||
\(457\) | −6.00959 | −0.281117 | −0.140558 | − | 0.990072i | \(-0.544890\pi\) | ||||
−0.140558 | + | 0.990072i | \(0.544890\pi\) | |||||||
\(458\) | 59.9701 | 2.80222 | ||||||||
\(459\) | −46.8071 | −2.18477 | ||||||||
\(460\) | 17.9261 | 0.835810 | ||||||||
\(461\) | 9.81702 | 0.457224 | 0.228612 | − | 0.973518i | \(-0.426581\pi\) | ||||
0.228612 | + | 0.973518i | \(0.426581\pi\) | |||||||
\(462\) | −31.6194 | −1.47107 | ||||||||
\(463\) | 24.9919 | 1.16147 | 0.580736 | − | 0.814092i | \(-0.302765\pi\) | ||||
0.580736 | + | 0.814092i | \(0.302765\pi\) | |||||||
\(464\) | −2.98002 | −0.138344 | ||||||||
\(465\) | −33.2270 | −1.54087 | ||||||||
\(466\) | 29.9978 | 1.38962 | ||||||||
\(467\) | −13.4570 | −0.622716 | −0.311358 | − | 0.950293i | \(-0.600784\pi\) | ||||
−0.311358 | + | 0.950293i | \(0.600784\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 57.0024 | 2.63213 | ||||||||
\(470\) | 0.177459 | 0.00818555 | ||||||||
\(471\) | −16.0020 | −0.737332 | ||||||||
\(472\) | 19.6899 | 0.906303 | ||||||||
\(473\) | −0.179144 | −0.00823705 | ||||||||
\(474\) | 19.9326 | 0.915532 | ||||||||
\(475\) | −0.977534 | −0.0448524 | ||||||||
\(476\) | 49.6116 | 2.27395 | ||||||||
\(477\) | −55.3339 | −2.53357 | ||||||||
\(478\) | 33.8257 | 1.54715 | ||||||||
\(479\) | −9.57851 | −0.437653 | −0.218827 | − | 0.975764i | \(-0.570223\pi\) | ||||
−0.218827 | + | 0.975764i | \(0.570223\pi\) | |||||||
\(480\) | −45.5985 | −2.08128 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 49.7357 | 2.26540 | ||||||||
\(483\) | −34.3556 | −1.56323 | ||||||||
\(484\) | 3.12978 | 0.142263 | ||||||||
\(485\) | 13.5829 | 0.616766 | ||||||||
\(486\) | 55.4061 | 2.51327 | ||||||||
\(487\) | 2.21089 | 0.100185 | 0.0500925 | − | 0.998745i | \(-0.484048\pi\) | ||||
0.0500925 | + | 0.998745i | \(0.484048\pi\) | |||||||
\(488\) | 7.73352 | 0.350080 | ||||||||
\(489\) | −56.8153 | −2.56928 | ||||||||
\(490\) | 64.9549 | 2.93436 | ||||||||
\(491\) | 20.7032 | 0.934323 | 0.467162 | − | 0.884172i | \(-0.345277\pi\) | ||||
0.467162 | + | 0.884172i | \(0.345277\pi\) | |||||||
\(492\) | −89.5296 | −4.03631 | ||||||||
\(493\) | −23.1584 | −1.04300 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 16.4943 | 0.741365 | ||||||||
\(496\) | 2.08587 | 0.0936585 | ||||||||
\(497\) | −31.2360 | −1.40113 | ||||||||
\(498\) | 68.2055 | 3.05636 | ||||||||
\(499\) | −15.0934 | −0.675672 | −0.337836 | − | 0.941205i | \(-0.609695\pi\) | ||||
−0.337836 | + | 0.941205i | \(0.609695\pi\) | |||||||
\(500\) | −33.3843 | −1.49299 | ||||||||
\(501\) | 5.08319 | 0.227100 | ||||||||
\(502\) | −15.1119 | −0.674475 | ||||||||
\(503\) | −21.4709 | −0.957338 | −0.478669 | − | 0.877995i | \(-0.658881\pi\) | ||||
−0.478669 | + | 0.877995i | \(0.658881\pi\) | |||||||
\(504\) | −79.7120 | −3.55065 | ||||||||
\(505\) | 22.4710 | 0.999946 | ||||||||
\(506\) | 5.57368 | 0.247780 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −52.0737 | −2.31039 | ||||||||
\(509\) | 20.2395 | 0.897100 | 0.448550 | − | 0.893758i | \(-0.351941\pi\) | ||||
0.448550 | + | 0.893758i | \(0.351941\pi\) | |||||||
\(510\) | −60.3741 | −2.67341 | ||||||||
\(511\) | 51.7953 | 2.29129 | ||||||||
\(512\) | 5.23732 | 0.231459 | ||||||||
\(513\) | −30.4261 | −1.34334 | ||||||||
\(514\) | 33.0412 | 1.45738 | ||||||||
\(515\) | 19.9830 | 0.880558 | ||||||||
\(516\) | −1.78071 | −0.0783916 | ||||||||
\(517\) | 0.0336641 | 0.00148055 | ||||||||
\(518\) | −38.9288 | −1.71043 | ||||||||
\(519\) | 52.0621 | 2.28527 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.9430 | −0.961341 | −0.480670 | − | 0.876901i | \(-0.659607\pi\) | ||||
−0.480670 | + | 0.876901i | \(0.659607\pi\) | |||||||
\(522\) | 103.078 | 4.51162 | ||||||||
\(523\) | 3.87346 | 0.169374 | 0.0846872 | − | 0.996408i | \(-0.473011\pi\) | ||||
0.0846872 | + | 0.996408i | \(0.473011\pi\) | |||||||
\(524\) | 20.5405 | 0.897315 | ||||||||
\(525\) | −5.82183 | −0.254085 | ||||||||
\(526\) | 51.1693 | 2.23109 | ||||||||
\(527\) | 16.2097 | 0.706108 | ||||||||
\(528\) | −1.47378 | −0.0641381 | ||||||||
\(529\) | −16.9440 | −0.736696 | ||||||||
\(530\) | −41.1592 | −1.78784 | ||||||||
\(531\) | 54.5325 | 2.36651 | ||||||||
\(532\) | 32.2491 | 1.39818 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 82.7359 | 3.58033 | ||||||||
\(535\) | 24.4287 | 1.05615 | ||||||||
\(536\) | −33.1825 | −1.43327 | ||||||||
\(537\) | 41.5080 | 1.79120 | ||||||||
\(538\) | 62.7317 | 2.70455 | ||||||||
\(539\) | 12.3220 | 0.530748 | ||||||||
\(540\) | 94.5502 | 4.06879 | ||||||||
\(541\) | 39.4975 | 1.69813 | 0.849066 | − | 0.528288i | \(-0.177166\pi\) | ||||
0.849066 | + | 0.528288i | \(0.177166\pi\) | |||||||
\(542\) | −19.2794 | −0.828120 | ||||||||
\(543\) | 23.9422 | 1.02746 | ||||||||
\(544\) | 22.2452 | 0.953754 | ||||||||
\(545\) | 9.77961 | 0.418912 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.9320 | −0.510176 | −0.255088 | − | 0.966918i | \(-0.582104\pi\) | ||||
−0.255088 | + | 0.966918i | \(0.582104\pi\) | |||||||
\(548\) | 4.87527 | 0.208261 | ||||||||
\(549\) | 21.4185 | 0.914119 | ||||||||
\(550\) | 0.944504 | 0.0402738 | ||||||||
\(551\) | −15.0536 | −0.641307 | ||||||||
\(552\) | 19.9992 | 0.851224 | ||||||||
\(553\) | −12.1804 | −0.517964 | ||||||||
\(554\) | 49.8874 | 2.11951 | ||||||||
\(555\) | 28.9037 | 1.22690 | ||||||||
\(556\) | −25.3782 | −1.07628 | ||||||||
\(557\) | −16.2002 | −0.686423 | −0.343212 | − | 0.939258i | \(-0.611515\pi\) | ||||
−0.343212 | + | 0.939258i | \(0.611515\pi\) | |||||||
\(558\) | −72.1500 | −3.05435 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 4.74747 | 0.200617 | ||||||||
\(561\) | −11.4531 | −0.483548 | ||||||||
\(562\) | 42.3264 | 1.78543 | ||||||||
\(563\) | −34.2081 | −1.44170 | −0.720850 | − | 0.693091i | \(-0.756248\pi\) | ||||
−0.720850 | + | 0.693091i | \(0.756248\pi\) | |||||||
\(564\) | 0.334626 | 0.0140903 | ||||||||
\(565\) | −38.3191 | −1.61210 | ||||||||
\(566\) | −27.7445 | −1.16619 | ||||||||
\(567\) | −87.7514 | −3.68521 | ||||||||
\(568\) | 18.1833 | 0.762954 | ||||||||
\(569\) | 4.35080 | 0.182395 | 0.0911975 | − | 0.995833i | \(-0.470931\pi\) | ||||
0.0911975 | + | 0.995833i | \(0.470931\pi\) | |||||||
\(570\) | −39.2451 | −1.64379 | ||||||||
\(571\) | −8.32394 | −0.348346 | −0.174173 | − | 0.984715i | \(-0.555725\pi\) | ||||
−0.174173 | + | 0.984715i | \(0.555725\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −25.7002 | −1.07364 | ||||||||
\(574\) | 89.6707 | 3.74278 | ||||||||
\(575\) | 1.02624 | 0.0427970 | ||||||||
\(576\) | −92.4367 | −3.85153 | ||||||||
\(577\) | 18.6210 | 0.775202 | 0.387601 | − | 0.921827i | \(-0.373304\pi\) | ||||
0.387601 | + | 0.921827i | \(0.373304\pi\) | |||||||
\(578\) | −9.04989 | −0.376426 | ||||||||
\(579\) | 21.8386 | 0.907583 | ||||||||
\(580\) | 46.7798 | 1.94242 | ||||||||
\(581\) | −41.6791 | −1.72914 | ||||||||
\(582\) | 41.9797 | 1.74011 | ||||||||
\(583\) | −7.80795 | −0.323372 | ||||||||
\(584\) | −30.1514 | −1.24767 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −40.2622 | −1.66321 | ||||||||
\(587\) | 7.39069 | 0.305046 | 0.152523 | − | 0.988300i | \(-0.451260\pi\) | ||||
0.152523 | + | 0.988300i | \(0.451260\pi\) | |||||||
\(588\) | 122.483 | 5.05110 | ||||||||
\(589\) | 10.5368 | 0.434163 | ||||||||
\(590\) | 40.5631 | 1.66996 | ||||||||
\(591\) | 22.3532 | 0.919488 | ||||||||
\(592\) | −1.81447 | −0.0745744 | ||||||||
\(593\) | 38.9506 | 1.59951 | 0.799754 | − | 0.600328i | \(-0.204963\pi\) | ||||
0.799754 | + | 0.600328i | \(0.204963\pi\) | |||||||
\(594\) | 29.3980 | 1.20621 | ||||||||
\(595\) | 36.8935 | 1.51249 | ||||||||
\(596\) | −17.1718 | −0.703385 | ||||||||
\(597\) | −67.6215 | −2.76756 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.6775 | 0.558847 | 0.279423 | − | 0.960168i | \(-0.409857\pi\) | ||||
0.279423 | + | 0.960168i | \(0.409857\pi\) | |||||||
\(600\) | 3.38903 | 0.138357 | ||||||||
\(601\) | −39.2674 | −1.60175 | −0.800876 | − | 0.598831i | \(-0.795632\pi\) | ||||
−0.800876 | + | 0.598831i | \(0.795632\pi\) | |||||||
\(602\) | 1.78352 | 0.0726909 | ||||||||
\(603\) | −91.9012 | −3.74250 | ||||||||
\(604\) | −21.8382 | −0.888585 | ||||||||
\(605\) | 2.32745 | 0.0946242 | ||||||||
\(606\) | 69.4496 | 2.82120 | ||||||||
\(607\) | −22.8474 | −0.927345 | −0.463673 | − | 0.886007i | \(-0.653469\pi\) | ||||
−0.463673 | + | 0.886007i | \(0.653469\pi\) | |||||||
\(608\) | 14.4601 | 0.586433 | ||||||||
\(609\) | −89.6538 | −3.63296 | ||||||||
\(610\) | 15.9318 | 0.645058 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −79.9855 | −3.23322 | ||||||||
\(613\) | −15.2795 | −0.617132 | −0.308566 | − | 0.951203i | \(-0.599849\pi\) | ||||
−0.308566 | + | 0.951203i | \(0.599849\pi\) | |||||||
\(614\) | 5.82539 | 0.235094 | ||||||||
\(615\) | −66.5784 | −2.68470 | ||||||||
\(616\) | −11.2478 | −0.453189 | ||||||||
\(617\) | 27.1029 | 1.09112 | 0.545561 | − | 0.838071i | \(-0.316316\pi\) | ||||
0.545561 | + | 0.838071i | \(0.316316\pi\) | |||||||
\(618\) | 61.7602 | 2.48436 | ||||||||
\(619\) | −21.4251 | −0.861146 | −0.430573 | − | 0.902556i | \(-0.641688\pi\) | ||||
−0.430573 | + | 0.902556i | \(0.641688\pi\) | |||||||
\(620\) | −32.7436 | −1.31502 | ||||||||
\(621\) | 31.9419 | 1.28179 | ||||||||
\(622\) | 21.6072 | 0.866369 | ||||||||
\(623\) | −50.5584 | −2.02558 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.9112 | −1.07645 | ||||||||
\(626\) | −72.1706 | −2.88452 | ||||||||
\(627\) | −7.44484 | −0.297318 | ||||||||
\(628\) | −15.7692 | −0.629259 | ||||||||
\(629\) | −14.1006 | −0.562229 | ||||||||
\(630\) | −164.214 | −6.54244 | ||||||||
\(631\) | −26.5023 | −1.05504 | −0.527521 | − | 0.849542i | \(-0.676878\pi\) | ||||
−0.527521 | + | 0.849542i | \(0.676878\pi\) | |||||||
\(632\) | 7.09052 | 0.282046 | ||||||||
\(633\) | 6.89344 | 0.273989 | ||||||||
\(634\) | 72.9103 | 2.89564 | ||||||||
\(635\) | −38.7244 | −1.53673 | ||||||||
\(636\) | −77.6120 | −3.07752 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 14.5450 | 0.575842 | ||||||||
\(639\) | 50.3598 | 1.99220 | ||||||||
\(640\) | −40.0428 | −1.58283 | ||||||||
\(641\) | −1.18681 | −0.0468761 | −0.0234380 | − | 0.999725i | \(-0.507461\pi\) | ||||
−0.0234380 | + | 0.999725i | \(0.507461\pi\) | |||||||
\(642\) | 75.5002 | 2.97976 | ||||||||
\(643\) | −35.0462 | −1.38209 | −0.691043 | − | 0.722813i | \(-0.742849\pi\) | ||||
−0.691043 | + | 0.722813i | \(0.742849\pi\) | |||||||
\(644\) | −33.8558 | −1.33410 | ||||||||
\(645\) | −1.32422 | −0.0521412 | ||||||||
\(646\) | 19.1456 | 0.753275 | ||||||||
\(647\) | 24.5856 | 0.966559 | 0.483280 | − | 0.875466i | \(-0.339445\pi\) | ||||
0.483280 | + | 0.875466i | \(0.339445\pi\) | |||||||
\(648\) | 51.0823 | 2.00670 | ||||||||
\(649\) | 7.69487 | 0.302050 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 62.7534 | 2.45950 | ||||||||
\(652\) | −55.9888 | −2.19269 | ||||||||
\(653\) | 5.01763 | 0.196355 | 0.0981774 | − | 0.995169i | \(-0.468699\pi\) | ||||
0.0981774 | + | 0.995169i | \(0.468699\pi\) | |||||||
\(654\) | 30.2252 | 1.18190 | ||||||||
\(655\) | 15.2749 | 0.596838 | ||||||||
\(656\) | 4.17956 | 0.163184 | ||||||||
\(657\) | −83.5061 | −3.25788 | ||||||||
\(658\) | −0.335153 | −0.0130656 | ||||||||
\(659\) | −44.2947 | −1.72547 | −0.862737 | − | 0.505652i | \(-0.831252\pi\) | ||||
−0.862737 | + | 0.505652i | \(0.831252\pi\) | |||||||
\(660\) | 23.1351 | 0.900534 | ||||||||
\(661\) | 39.2602 | 1.52704 | 0.763522 | − | 0.645782i | \(-0.223468\pi\) | ||||
0.763522 | + | 0.645782i | \(0.223468\pi\) | |||||||
\(662\) | −5.48338 | −0.213118 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 24.2625 | 0.941566 | ||||||||
\(665\) | 23.9819 | 0.929979 | ||||||||
\(666\) | 62.7624 | 2.43199 | ||||||||
\(667\) | 15.8036 | 0.611919 | ||||||||
\(668\) | 5.00924 | 0.193813 | ||||||||
\(669\) | −63.8187 | −2.46737 | ||||||||
\(670\) | −68.3591 | −2.64094 | ||||||||
\(671\) | 3.02228 | 0.116674 | ||||||||
\(672\) | 86.1186 | 3.32210 | ||||||||
\(673\) | −30.5790 | −1.17873 | −0.589367 | − | 0.807865i | \(-0.700623\pi\) | ||||
−0.589367 | + | 0.807865i | \(0.700623\pi\) | |||||||
\(674\) | −70.5160 | −2.71618 | ||||||||
\(675\) | 5.41282 | 0.208339 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.59361 | 0.253413 | 0.126706 | − | 0.991940i | \(-0.459559\pi\) | ||||
0.126706 | + | 0.991940i | \(0.459559\pi\) | |||||||
\(678\) | −118.430 | −4.54829 | ||||||||
\(679\) | −25.6530 | −0.984471 | ||||||||
\(680\) | −21.4766 | −0.823592 | ||||||||
\(681\) | −6.47174 | −0.247998 | ||||||||
\(682\) | −10.1808 | −0.389843 | ||||||||
\(683\) | −15.4414 | −0.590850 | −0.295425 | − | 0.955366i | \(-0.595461\pi\) | ||||
−0.295425 | + | 0.955366i | \(0.595461\pi\) | |||||||
\(684\) | −51.9931 | −1.98800 | ||||||||
\(685\) | 3.62547 | 0.138522 | ||||||||
\(686\) | −52.9850 | −2.02298 | ||||||||
\(687\) | 84.0937 | 3.20838 | ||||||||
\(688\) | 0.0831300 | 0.00316930 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 41.2003 | 1.56847 | ||||||||
\(691\) | −10.8955 | −0.414484 | −0.207242 | − | 0.978290i | \(-0.566449\pi\) | ||||
−0.207242 | + | 0.978290i | \(0.566449\pi\) | |||||||
\(692\) | 51.3048 | 1.95031 | ||||||||
\(693\) | −31.1516 | −1.18335 | ||||||||
\(694\) | −48.9026 | −1.85632 | ||||||||
\(695\) | −18.8724 | −0.715872 | ||||||||
\(696\) | 52.1898 | 1.97825 | ||||||||
\(697\) | 32.4802 | 1.23027 | ||||||||
\(698\) | 17.0271 | 0.644486 | ||||||||
\(699\) | 42.0647 | 1.59103 | ||||||||
\(700\) | −5.73713 | −0.216843 | ||||||||
\(701\) | 6.30826 | 0.238260 | 0.119130 | − | 0.992879i | \(-0.461990\pi\) | ||||
0.119130 | + | 0.992879i | \(0.461990\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.16586 | −0.345697 | ||||||||
\(704\) | −13.0434 | −0.491591 | ||||||||
\(705\) | 0.248843 | 0.00937197 | ||||||||
\(706\) | 73.8469 | 2.77926 | ||||||||
\(707\) | −42.4393 | −1.59610 | ||||||||
\(708\) | 76.4880 | 2.87459 | ||||||||
\(709\) | 26.2553 | 0.986038 | 0.493019 | − | 0.870019i | \(-0.335893\pi\) | ||||
0.493019 | + | 0.870019i | \(0.335893\pi\) | |||||||
\(710\) | 37.4592 | 1.40582 | ||||||||
\(711\) | 19.6377 | 0.736470 | ||||||||
\(712\) | 29.4313 | 1.10299 | ||||||||
\(713\) | −11.0618 | −0.414267 | ||||||||
\(714\) | 114.024 | 4.26725 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 40.9041 | 1.52866 | ||||||||
\(717\) | 47.4325 | 1.77140 | ||||||||
\(718\) | −83.1354 | −3.10259 | ||||||||
\(719\) | 37.9637 | 1.41581 | 0.707903 | − | 0.706309i | \(-0.249641\pi\) | ||||
0.707903 | + | 0.706309i | \(0.249641\pi\) | |||||||
\(720\) | −7.65402 | −0.285249 | ||||||||
\(721\) | −37.7405 | −1.40553 | ||||||||
\(722\) | −30.5879 | −1.13836 | ||||||||
\(723\) | 69.7424 | 2.59375 | ||||||||
\(724\) | 23.5938 | 0.876858 | ||||||||
\(725\) | 2.67805 | 0.0994603 | ||||||||
\(726\) | 7.19329 | 0.266968 | ||||||||
\(727\) | −42.4503 | −1.57439 | −0.787197 | − | 0.616701i | \(-0.788469\pi\) | ||||
−0.787197 | + | 0.616701i | \(0.788469\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17.8046 | 0.659431 | ||||||||
\(730\) | −62.1146 | −2.29896 | ||||||||
\(731\) | 0.646019 | 0.0238939 | ||||||||
\(732\) | 30.0418 | 1.11038 | ||||||||
\(733\) | 28.7508 | 1.06193 | 0.530967 | − | 0.847393i | \(-0.321829\pi\) | ||||
0.530967 | + | 0.847393i | \(0.321829\pi\) | |||||||
\(734\) | 23.7868 | 0.877987 | ||||||||
\(735\) | 91.0837 | 3.35967 | ||||||||
\(736\) | −15.1805 | −0.559559 | ||||||||
\(737\) | −12.9678 | −0.477676 | ||||||||
\(738\) | −144.570 | −5.32170 | ||||||||
\(739\) | 15.4432 | 0.568086 | 0.284043 | − | 0.958812i | \(-0.408324\pi\) | ||||
0.284043 | + | 0.958812i | \(0.408324\pi\) | |||||||
\(740\) | 28.4832 | 1.04706 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 77.7343 | 2.85372 | ||||||||
\(743\) | 36.2998 | 1.33171 | 0.665855 | − | 0.746081i | \(-0.268067\pi\) | ||||
0.665855 | + | 0.746081i | \(0.268067\pi\) | |||||||
\(744\) | −36.5304 | −1.33927 | ||||||||
\(745\) | −12.7698 | −0.467848 | ||||||||
\(746\) | 25.4955 | 0.933455 | ||||||||
\(747\) | 67.1964 | 2.45859 | ||||||||
\(748\) | −11.2864 | −0.412673 | ||||||||
\(749\) | −46.1368 | −1.68580 | ||||||||
\(750\) | −76.7283 | −2.80172 | ||||||||
\(751\) | −2.15250 | −0.0785458 | −0.0392729 | − | 0.999229i | \(-0.512504\pi\) | ||||
−0.0392729 | + | 0.999229i | \(0.512504\pi\) | |||||||
\(752\) | −0.0156215 | −0.000569657 0 | ||||||||
\(753\) | −21.1908 | −0.772234 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.2399 | −0.591031 | ||||||||
\(756\) | −178.570 | −6.49453 | ||||||||
\(757\) | 14.7876 | 0.537465 | 0.268733 | − | 0.963215i | \(-0.413395\pi\) | ||||
0.268733 | + | 0.963215i | \(0.413395\pi\) | |||||||
\(758\) | −70.1522 | −2.54804 | ||||||||
\(759\) | 7.81575 | 0.283694 | ||||||||
\(760\) | −13.9605 | −0.506400 | ||||||||
\(761\) | −11.4983 | −0.416813 | −0.208406 | − | 0.978042i | \(-0.566828\pi\) | ||||
−0.208406 | + | 0.978042i | \(0.566828\pi\) | |||||||
\(762\) | −119.683 | −4.33565 | ||||||||
\(763\) | −18.4700 | −0.668660 | ||||||||
\(764\) | −25.3264 | −0.916275 | ||||||||
\(765\) | −59.4809 | −2.15054 | ||||||||
\(766\) | −3.72310 | −0.134521 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −40.9066 | −1.47609 | ||||||||
\(769\) | 0.165953 | 0.00598443 | 0.00299221 | − | 0.999996i | \(-0.499048\pi\) | ||||
0.00299221 | + | 0.999996i | \(0.499048\pi\) | |||||||
\(770\) | −23.1716 | −0.835046 | ||||||||
\(771\) | 46.3324 | 1.66862 | ||||||||
\(772\) | 21.5209 | 0.774555 | ||||||||
\(773\) | 29.7127 | 1.06869 | 0.534346 | − | 0.845266i | \(-0.320558\pi\) | ||||
0.534346 | + | 0.845266i | \(0.320558\pi\) | |||||||
\(774\) | −2.87545 | −0.103356 | ||||||||
\(775\) | −1.87451 | −0.0673343 | ||||||||
\(776\) | 14.9333 | 0.536073 | ||||||||
\(777\) | −54.5884 | −1.95835 | ||||||||
\(778\) | −23.7878 | −0.852834 | ||||||||
\(779\) | 21.1131 | 0.756456 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.10607 | 0.254275 | ||||||||
\(782\) | −20.0995 | −0.718757 | ||||||||
\(783\) | 83.3552 | 2.97887 | ||||||||
\(784\) | −5.71791 | −0.204211 | ||||||||
\(785\) | −11.7267 | −0.418544 | ||||||||
\(786\) | 47.2090 | 1.68389 | ||||||||
\(787\) | 21.6909 | 0.773198 | 0.386599 | − | 0.922248i | \(-0.373650\pi\) | ||||
0.386599 | + | 0.922248i | \(0.373650\pi\) | |||||||
\(788\) | 22.0280 | 0.784715 | ||||||||
\(789\) | 71.7527 | 2.55446 | ||||||||
\(790\) | 14.6071 | 0.519698 | ||||||||
\(791\) | 72.3705 | 2.57320 | ||||||||
\(792\) | 18.1342 | 0.644369 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 5.38352 | 0.191054 | ||||||||
\(795\) | −57.7159 | −2.04697 | ||||||||
\(796\) | −66.6377 | −2.36191 | ||||||||
\(797\) | −34.8232 | −1.23350 | −0.616750 | − | 0.787159i | \(-0.711551\pi\) | ||||
−0.616750 | + | 0.787159i | \(0.711551\pi\) | |||||||
\(798\) | 74.1193 | 2.62379 | ||||||||
\(799\) | −0.121398 | −0.00429474 | ||||||||
\(800\) | −2.57245 | −0.0909499 | ||||||||
\(801\) | 81.5119 | 2.88008 | ||||||||
\(802\) | −23.9459 | −0.845560 | ||||||||
\(803\) | −11.7832 | −0.415821 | ||||||||
\(804\) | −128.902 | −4.54601 | ||||||||
\(805\) | −25.1767 | −0.887363 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 87.9662 | 3.09656 | ||||||||
\(808\) | 24.7050 | 0.869120 | ||||||||
\(809\) | −30.2774 | −1.06450 | −0.532248 | − | 0.846588i | \(-0.678653\pi\) | ||||
−0.532248 | + | 0.846588i | \(0.678653\pi\) | |||||||
\(810\) | 105.234 | 3.69755 | ||||||||
\(811\) | 29.7788 | 1.04567 | 0.522837 | − | 0.852433i | \(-0.324874\pi\) | ||||
0.522837 | + | 0.852433i | \(0.324874\pi\) | |||||||
\(812\) | −88.3496 | −3.10046 | ||||||||
\(813\) | −27.0347 | −0.948148 | ||||||||
\(814\) | 8.85615 | 0.310408 | ||||||||
\(815\) | −41.6358 | −1.45844 | ||||||||
\(816\) | 5.31467 | 0.186051 | ||||||||
\(817\) | 0.419933 | 0.0146916 | ||||||||
\(818\) | 74.1397 | 2.59223 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −65.6098 | −2.29119 | ||||||||
\(821\) | −7.67232 | −0.267766 | −0.133883 | − | 0.990997i | \(-0.542745\pi\) | ||||
−0.133883 | + | 0.990997i | \(0.542745\pi\) | |||||||
\(822\) | 11.2050 | 0.390819 | ||||||||
\(823\) | 41.5169 | 1.44719 | 0.723595 | − | 0.690225i | \(-0.242489\pi\) | ||||
0.723595 | + | 0.690225i | \(0.242489\pi\) | |||||||
\(824\) | 21.9697 | 0.765351 | ||||||||
\(825\) | 1.32444 | 0.0461111 | ||||||||
\(826\) | −76.6085 | −2.66555 | ||||||||
\(827\) | 7.05778 | 0.245423 | 0.122711 | − | 0.992442i | \(-0.460841\pi\) | ||||
0.122711 | + | 0.992442i | \(0.460841\pi\) | |||||||
\(828\) | 54.5834 | 1.89690 | ||||||||
\(829\) | 43.2766 | 1.50306 | 0.751529 | − | 0.659701i | \(-0.229317\pi\) | ||||
0.751529 | + | 0.659701i | \(0.229317\pi\) | |||||||
\(830\) | 49.9829 | 1.73493 | ||||||||
\(831\) | 69.9552 | 2.42672 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −44.4351 | −1.53958 | ||||||||
\(834\) | −58.3277 | −2.01972 | ||||||||
\(835\) | 3.72510 | 0.128913 | ||||||||
\(836\) | −7.33654 | −0.253739 | ||||||||
\(837\) | −58.3447 | −2.01669 | ||||||||
\(838\) | 23.4492 | 0.810041 | ||||||||
\(839\) | 34.4289 | 1.18862 | 0.594308 | − | 0.804238i | \(-0.297426\pi\) | ||||
0.594308 | + | 0.804238i | \(0.297426\pi\) | |||||||
\(840\) | −83.1434 | −2.86872 | ||||||||
\(841\) | 12.2409 | 0.422102 | ||||||||
\(842\) | −22.5781 | −0.778092 | ||||||||
\(843\) | 59.3526 | 2.04421 | ||||||||
\(844\) | 6.79315 | 0.233830 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.540345 | 0.0185774 | ||||||||
\(847\) | −4.39568 | −0.151037 | ||||||||
\(848\) | 3.62320 | 0.124421 | ||||||||
\(849\) | −38.9051 | −1.33522 | ||||||||
\(850\) | −3.40602 | −0.116826 | ||||||||
\(851\) | 9.62250 | 0.329855 | ||||||||
\(852\) | 70.6352 | 2.41992 | ||||||||
\(853\) | −41.3342 | −1.41526 | −0.707628 | − | 0.706585i | \(-0.750235\pi\) | ||||
−0.707628 | + | 0.706585i | \(0.750235\pi\) | |||||||
\(854\) | −30.0892 | −1.02963 | ||||||||
\(855\) | −38.6644 | −1.32230 | ||||||||
\(856\) | 26.8574 | 0.917966 | ||||||||
\(857\) | −40.7028 | −1.39038 | −0.695191 | − | 0.718825i | \(-0.744680\pi\) | ||||
−0.695191 | + | 0.718825i | \(0.744680\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.36084 | 0.217029 | 0.108515 | − | 0.994095i | \(-0.465391\pi\) | ||||
0.108515 | + | 0.994095i | \(0.465391\pi\) | |||||||
\(860\) | −1.30496 | −0.0444987 | ||||||||
\(861\) | 125.742 | 4.28527 | ||||||||
\(862\) | −16.3155 | −0.555709 | ||||||||
\(863\) | −40.9662 | −1.39451 | −0.697253 | − | 0.716825i | \(-0.745595\pi\) | ||||
−0.697253 | + | 0.716825i | \(0.745595\pi\) | |||||||
\(864\) | −80.0684 | −2.72398 | ||||||||
\(865\) | 38.1526 | 1.29723 | ||||||||
\(866\) | −86.7088 | −2.94649 | ||||||||
\(867\) | −12.6903 | −0.430985 | ||||||||
\(868\) | 61.8405 | 2.09900 | ||||||||
\(869\) | 2.77099 | 0.0939995 | ||||||||
\(870\) | 107.516 | 3.64512 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 10.7519 | 0.364104 | ||||||||
\(873\) | 41.3586 | 1.39978 | ||||||||
\(874\) | −13.0653 | −0.441940 | ||||||||
\(875\) | 46.8872 | 1.58508 | ||||||||
\(876\) | −117.127 | −3.95734 | ||||||||
\(877\) | −48.1858 | −1.62712 | −0.813560 | − | 0.581481i | \(-0.802473\pi\) | ||||
−0.813560 | + | 0.581481i | \(0.802473\pi\) | |||||||
\(878\) | 12.1923 | 0.411471 | ||||||||
\(879\) | −56.4581 | −1.90428 | ||||||||
\(880\) | −1.08003 | −0.0364078 | ||||||||
\(881\) | 41.1749 | 1.38722 | 0.693609 | − | 0.720351i | \(-0.256019\pi\) | ||||
0.693609 | + | 0.720351i | \(0.256019\pi\) | |||||||
\(882\) | 197.782 | 6.65965 | ||||||||
\(883\) | −34.8551 | −1.17297 | −0.586484 | − | 0.809961i | \(-0.699488\pi\) | ||||
−0.586484 | + | 0.809961i | \(0.699488\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 56.8800 | 1.91200 | ||||||||
\(886\) | 46.0684 | 1.54770 | ||||||||
\(887\) | −23.7296 | −0.796763 | −0.398382 | − | 0.917220i | \(-0.630428\pi\) | ||||
−0.398382 | + | 0.917220i | \(0.630428\pi\) | |||||||
\(888\) | 31.7773 | 1.06638 | ||||||||
\(889\) | 73.1359 | 2.45290 | ||||||||
\(890\) | 60.6312 | 2.03236 | ||||||||
\(891\) | 19.9631 | 0.668788 | ||||||||
\(892\) | −62.8903 | −2.10572 | ||||||||
\(893\) | −0.0789123 | −0.00264070 | ||||||||
\(894\) | −39.4666 | −1.31996 | ||||||||
\(895\) | 30.4182 | 1.01677 | ||||||||
\(896\) | 75.6260 | 2.52649 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −9.64090 | −0.321721 | ||||||||
\(899\) | −28.8667 | −0.962758 | ||||||||
\(900\) | 9.24959 | 0.308320 | ||||||||
\(901\) | 28.1566 | 0.938033 | ||||||||
\(902\) | −20.3997 | −0.679236 | ||||||||
\(903\) | 2.50096 | 0.0832268 | ||||||||
\(904\) | −42.1287 | −1.40118 | ||||||||
\(905\) | 17.5455 | 0.583231 | ||||||||
\(906\) | −50.1916 | −1.66751 | ||||||||
\(907\) | −41.3010 | −1.37138 | −0.685689 | − | 0.727895i | \(-0.740499\pi\) | ||||
−0.685689 | + | 0.727895i | \(0.740499\pi\) | |||||||
\(908\) | −6.37759 | −0.211648 | ||||||||
\(909\) | 68.4221 | 2.26942 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −30.7960 | −1.02032 | −0.510159 | − | 0.860080i | \(-0.670413\pi\) | ||||
−0.510159 | + | 0.860080i | \(0.670413\pi\) | |||||||
\(912\) | 3.45470 | 0.114397 | ||||||||
\(913\) | 9.48182 | 0.313803 | ||||||||
\(914\) | −13.6111 | −0.450216 | ||||||||
\(915\) | 22.3405 | 0.738554 | ||||||||
\(916\) | 82.8704 | 2.73811 | ||||||||
\(917\) | −28.8485 | −0.952662 | ||||||||
\(918\) | −106.014 | −3.49897 | ||||||||
\(919\) | 19.7956 | 0.652998 | 0.326499 | − | 0.945198i | \(-0.394131\pi\) | ||||
0.326499 | + | 0.945198i | \(0.394131\pi\) | |||||||
\(920\) | 14.6560 | 0.483194 | ||||||||
\(921\) | 8.16871 | 0.269168 | ||||||||
\(922\) | 22.2346 | 0.732257 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −43.6936 | −1.43742 | ||||||||
\(925\) | 1.63061 | 0.0536141 | ||||||||
\(926\) | 56.6042 | 1.86013 | ||||||||
\(927\) | 60.8465 | 1.99846 | ||||||||
\(928\) | −39.6147 | −1.30042 | ||||||||
\(929\) | −39.9249 | −1.30989 | −0.654947 | − | 0.755675i | \(-0.727309\pi\) | ||||
−0.654947 | + | 0.755675i | \(0.727309\pi\) | |||||||
\(930\) | −75.2559 | −2.46774 | ||||||||
\(931\) | −28.8842 | −0.946640 | ||||||||
\(932\) | 41.4527 | 1.35783 | ||||||||
\(933\) | 30.2989 | 0.991941 | ||||||||
\(934\) | −30.4788 | −0.997297 | ||||||||
\(935\) | −8.39312 | −0.274484 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.42120 | −0.209771 | −0.104886 | − | 0.994484i | \(-0.533448\pi\) | ||||
−0.104886 | + | 0.994484i | \(0.533448\pi\) | |||||||
\(938\) | 129.105 | 4.21542 | ||||||||
\(939\) | −101.202 | −3.30260 | ||||||||
\(940\) | 0.245223 | 0.00799829 | ||||||||
\(941\) | −33.8003 | −1.10186 | −0.550928 | − | 0.834553i | \(-0.685726\pi\) | ||||
−0.550928 | + | 0.834553i | \(0.685726\pi\) | |||||||
\(942\) | −36.2429 | −1.18086 | ||||||||
\(943\) | −22.1650 | −0.721791 | ||||||||
\(944\) | −3.57073 | −0.116217 | ||||||||
\(945\) | −132.793 | −4.31976 | ||||||||
\(946\) | −0.405744 | −0.0131919 | ||||||||
\(947\) | 21.7598 | 0.707100 | 0.353550 | − | 0.935416i | \(-0.384974\pi\) | ||||
0.353550 | + | 0.935416i | \(0.384974\pi\) | |||||||
\(948\) | 27.5440 | 0.894588 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −2.21402 | −0.0718323 | ||||||||
\(951\) | 102.239 | 3.31533 | ||||||||
\(952\) | 40.5614 | 1.31460 | ||||||||
\(953\) | 46.8789 | 1.51856 | 0.759278 | − | 0.650766i | \(-0.225552\pi\) | ||||
0.759278 | + | 0.650766i | \(0.225552\pi\) | |||||||
\(954\) | −125.326 | −4.05757 | ||||||||
\(955\) | −18.8338 | −0.609449 | ||||||||
\(956\) | 46.7425 | 1.51176 | ||||||||
\(957\) | 20.3959 | 0.659305 | ||||||||
\(958\) | −21.6944 | −0.700914 | ||||||||
\(959\) | −6.84717 | −0.221107 | ||||||||
\(960\) | −96.4158 | −3.11181 | ||||||||
\(961\) | −10.7947 | −0.348215 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 74.3832 | 2.39697 | ||||||||
\(964\) | 68.7278 | 2.21357 | ||||||||
\(965\) | 16.0040 | 0.515186 | ||||||||
\(966\) | −77.8120 | −2.50356 | ||||||||
\(967\) | 60.6688 | 1.95098 | 0.975489 | − | 0.220048i | \(-0.0706213\pi\) | ||||
0.975489 | + | 0.220048i | \(0.0706213\pi\) | |||||||
\(968\) | 2.55884 | 0.0822442 | ||||||||
\(969\) | 26.8472 | 0.862456 | ||||||||
\(970\) | 30.7639 | 0.987768 | ||||||||
\(971\) | −21.4566 | −0.688575 | −0.344287 | − | 0.938864i | \(-0.611879\pi\) | ||||
−0.344287 | + | 0.938864i | \(0.611879\pi\) | |||||||
\(972\) | 76.5636 | 2.45578 | ||||||||
\(973\) | 35.6430 | 1.14266 | ||||||||
\(974\) | 5.00745 | 0.160449 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.40246 | −0.0448916 | ||||||||
\(977\) | −44.1140 | −1.41133 | −0.705667 | − | 0.708544i | \(-0.749352\pi\) | ||||
−0.705667 | + | 0.708544i | \(0.749352\pi\) | |||||||
\(978\) | −128.681 | −4.11477 | ||||||||
\(979\) | 11.5018 | 0.367600 | ||||||||
\(980\) | 89.7586 | 2.86723 | ||||||||
\(981\) | 29.7780 | 0.950738 | ||||||||
\(982\) | 46.8907 | 1.49634 | ||||||||
\(983\) | −3.52430 | −0.112408 | −0.0562038 | − | 0.998419i | \(-0.517900\pi\) | ||||
−0.0562038 | + | 0.998419i | \(0.517900\pi\) | |||||||
\(984\) | −73.1975 | −2.33345 | ||||||||
\(985\) | 16.3810 | 0.521944 | ||||||||
\(986\) | −52.4514 | −1.67039 | ||||||||
\(987\) | −0.469972 | −0.0149594 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.440854 | −0.0140183 | ||||||||
\(990\) | 37.3580 | 1.18732 | ||||||||
\(991\) | 25.9551 | 0.824491 | 0.412246 | − | 0.911073i | \(-0.364745\pi\) | ||||
0.412246 | + | 0.911073i | \(0.364745\pi\) | |||||||
\(992\) | 27.7284 | 0.880379 | ||||||||
\(993\) | −7.68913 | −0.244007 | ||||||||
\(994\) | −70.7465 | −2.24394 | ||||||||
\(995\) | −49.5549 | −1.57100 | ||||||||
\(996\) | 94.2505 | 2.98644 | ||||||||
\(997\) | −9.76069 | −0.309124 | −0.154562 | − | 0.987983i | \(-0.549397\pi\) | ||||
−0.154562 | + | 0.987983i | \(0.549397\pi\) | |||||||
\(998\) | −34.1850 | −1.08211 | ||||||||
\(999\) | 50.7533 | 1.60576 |
(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 | 1859.2.a.t.1.19 | yes | 21 | |
13.12 | even | 2 | 1859.2.a.s.1.3 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1859.2.a.s.1.3 | ✓ | 21 | 13.12 | even | 2 | ||
1859.2.a.t.1.19 | yes | 21 | 1.1 | even | 1 | trivial |