Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(47,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.i (of order \(4\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(5.50967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 47.6 | ||
Character | \(\chi\) | \(=\) | 690.47 |
Dual form | 690.2.i.f.323.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 0.707107i | −0.500000 | + | 0.500000i | ||||
\(3\) | 0.906765 | + | 1.47573i | 0.523521 | + | 0.852013i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −1.96911 | − | 1.05954i | −0.880611 | − | 0.473840i | ||||
\(6\) | −1.68468 | − | 0.402318i | −0.687767 | − | 0.164246i | ||||
\(7\) | −0.621187 | − | 0.621187i | −0.234787 | − | 0.234787i | 0.579901 | − | 0.814687i | \(-0.303091\pi\) |
−0.814687 | + | 0.579901i | \(0.803091\pi\) | |||||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | −1.35555 | + | 2.67628i | −0.451851 | + | 0.892093i | ||||
\(10\) | 2.14157 | − | 0.643162i | 0.677225 | − | 0.203386i | ||||
\(11\) | 4.12939i | 1.24506i | 0.782597 | + | 0.622529i | \(0.213895\pi\) | ||||
−0.782597 | + | 0.622529i | \(0.786105\pi\) | |||||||
\(12\) | 1.47573 | − | 0.906765i | 0.426006 | − | 0.261761i | ||||
\(13\) | −0.734549 | + | 0.734549i | −0.203727 | + | 0.203727i | −0.801595 | − | 0.597868i | \(-0.796015\pi\) |
0.597868 | + | 0.801595i | \(0.296015\pi\) | |||||||
\(14\) | 0.878491 | 0.234787 | ||||||||
\(15\) | −0.221927 | − | 3.86662i | −0.0573013 | − | 0.998357i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −2.50190 | + | 2.50190i | −0.606801 | + | 0.606801i | −0.942109 | − | 0.335308i | \(-0.891160\pi\) |
0.335308 | + | 0.942109i | \(0.391160\pi\) | |||||||
\(18\) | −0.933895 | − | 2.85094i | −0.220121 | − | 0.671972i | ||||
\(19\) | − | 7.88126i | − | 1.80808i | −0.427443 | − | 0.904042i | \(-0.640586\pi\) | ||
0.427443 | − | 0.904042i | \(-0.359414\pi\) | |||||||
\(20\) | −1.05954 | + | 1.96911i | −0.236920 | + | 0.440306i | ||||
\(21\) | 0.353433 | − | 1.47997i | 0.0771253 | − | 0.322957i | ||||
\(22\) | −2.91992 | − | 2.91992i | −0.622529 | − | 0.622529i | ||||
\(23\) | −0.707107 | − | 0.707107i | −0.147442 | − | 0.147442i | ||||
\(24\) | −0.402318 | + | 1.68468i | −0.0821228 | + | 0.343883i | ||||
\(25\) | 2.75476 | + | 4.17269i | 0.550952 | + | 0.834537i | ||||
\(26\) | − | 1.03881i | − | 0.203727i | ||||||
\(27\) | −5.17863 | + | 0.426330i | −0.996628 | + | 0.0820472i | ||||
\(28\) | −0.621187 | + | 0.621187i | −0.117393 | + | 0.117393i | ||||
\(29\) | −7.83802 | −1.45548 | −0.727742 | − | 0.685851i | \(-0.759430\pi\) | ||||
−0.727742 | + | 0.685851i | \(0.759430\pi\) | |||||||
\(30\) | 2.89104 | + | 2.57719i | 0.527829 | + | 0.470528i | ||||
\(31\) | −7.07325 | −1.27039 | −0.635197 | − | 0.772350i | \(-0.719081\pi\) | ||||
−0.635197 | + | 0.772350i | \(0.719081\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | −6.09386 | + | 3.74439i | −1.06080 | + | 0.651814i | ||||
\(34\) | − | 3.53823i | − | 0.606801i | ||||||
\(35\) | 0.565012 | + | 1.88135i | 0.0955044 | + | 0.318007i | ||||
\(36\) | 2.67628 | + | 1.35555i | 0.446047 | + | 0.225925i | ||||
\(37\) | −6.46585 | − | 6.46585i | −1.06298 | − | 1.06298i | −0.997879 | − | 0.0651000i | \(-0.979263\pi\) |
−0.0651000 | − | 0.997879i | \(-0.520737\pi\) | |||||||
\(38\) | 5.57289 | + | 5.57289i | 0.904042 | + | 0.904042i | ||||
\(39\) | −1.75006 | − | 0.417931i | −0.280234 | − | 0.0669226i | ||||
\(40\) | −0.643162 | − | 2.14157i | −0.101693 | − | 0.338613i | ||||
\(41\) | − | 1.77236i | − | 0.276796i | −0.990377 | − | 0.138398i | \(-0.955805\pi\) | ||
0.990377 | − | 0.138398i | \(-0.0441954\pi\) | |||||||
\(42\) | 0.796585 | + | 1.29641i | 0.122916 | + | 0.200041i | ||||
\(43\) | −6.31426 | + | 6.31426i | −0.962915 | + | 0.962915i | −0.999337 | − | 0.0364216i | \(-0.988404\pi\) |
0.0364216 | + | 0.999337i | \(0.488404\pi\) | |||||||
\(44\) | 4.12939 | 0.622529 | ||||||||
\(45\) | 5.50485 | − | 3.83362i | 0.820614 | − | 0.571482i | ||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −0.0280085 | + | 0.0280085i | −0.00408546 | + | 0.00408546i | −0.709147 | − | 0.705061i | \(-0.750920\pi\) |
0.705061 | + | 0.709147i | \(0.250920\pi\) | |||||||
\(48\) | −0.906765 | − | 1.47573i | −0.130880 | − | 0.213003i | ||||
\(49\) | − | 6.22825i | − | 0.889751i | ||||||
\(50\) | −4.89844 | − | 1.00262i | −0.692744 | − | 0.141793i | ||||
\(51\) | −5.96077 | − | 1.42349i | −0.834675 | − | 0.199329i | ||||
\(52\) | 0.734549 | + | 0.734549i | 0.101864 | + | 0.101864i | ||||
\(53\) | 9.77127 | + | 9.77127i | 1.34219 | + | 1.34219i | 0.893880 | + | 0.448307i | \(0.147973\pi\) |
0.448307 | + | 0.893880i | \(0.352027\pi\) | |||||||
\(54\) | 3.36039 | − | 3.96331i | 0.457291 | − | 0.539338i | ||||
\(55\) | 4.37524 | − | 8.13121i | 0.589958 | − | 1.09641i | ||||
\(56\) | − | 0.878491i | − | 0.117393i | ||||||
\(57\) | 11.6306 | − | 7.14645i | 1.54051 | − | 0.946571i | ||||
\(58\) | 5.54232 | − | 5.54232i | 0.727742 | − | 0.727742i | ||||
\(59\) | −10.9630 | −1.42726 | −0.713629 | − | 0.700524i | \(-0.752950\pi\) | ||||
−0.713629 | + | 0.700524i | \(0.752950\pi\) | |||||||
\(60\) | −3.86662 | + | 0.221927i | −0.499178 | + | 0.0286506i | ||||
\(61\) | 11.0841 | 1.41917 | 0.709587 | − | 0.704618i | \(-0.248882\pi\) | ||||
0.709587 | + | 0.704618i | \(0.248882\pi\) | |||||||
\(62\) | 5.00154 | − | 5.00154i | 0.635197 | − | 0.635197i | ||||
\(63\) | 2.50452 | − | 0.820418i | 0.315540 | − | 0.103363i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 2.22469 | − | 0.668122i | 0.275938 | − | 0.0828704i | ||||
\(66\) | 1.66133 | − | 6.95669i | 0.204495 | − | 0.856309i | ||||
\(67\) | 10.8288 | + | 10.8288i | 1.32295 | + | 1.32295i | 0.911373 | + | 0.411581i | \(0.135023\pi\) |
0.411581 | + | 0.911373i | \(0.364977\pi\) | |||||||
\(68\) | 2.50190 | + | 2.50190i | 0.303401 | + | 0.303401i | ||||
\(69\) | 0.402318 | − | 1.68468i | 0.0484334 | − | 0.202811i | ||||
\(70\) | −1.72984 | − | 0.930794i | −0.206756 | − | 0.111251i | ||||
\(71\) | − | 2.25608i | − | 0.267747i | −0.990998 | − | 0.133874i | \(-0.957258\pi\) | ||
0.990998 | − | 0.133874i | \(-0.0427417\pi\) | |||||||
\(72\) | −2.85094 | + | 0.933895i | −0.335986 | + | 0.110061i | ||||
\(73\) | −8.48742 | + | 8.48742i | −0.993378 | + | 0.993378i | −0.999978 | − | 0.00660049i | \(-0.997899\pi\) |
0.00660049 | + | 0.999978i | \(0.497899\pi\) | |||||||
\(74\) | 9.14409 | 1.06298 | ||||||||
\(75\) | −3.65983 | + | 7.84893i | −0.422601 | + | 0.906316i | ||||
\(76\) | −7.88126 | −0.904042 | ||||||||
\(77\) | 2.56512 | − | 2.56512i | 0.292323 | − | 0.292323i | ||||
\(78\) | 1.53300 | − | 0.941956i | 0.173578 | − | 0.106655i | ||||
\(79\) | − | 1.98214i | − | 0.223008i | −0.993764 | − | 0.111504i | \(-0.964433\pi\) | ||
0.993764 | − | 0.111504i | \(-0.0355668\pi\) | |||||||
\(80\) | 1.96911 | + | 1.05954i | 0.220153 | + | 0.118460i | ||||
\(81\) | −5.32495 | − | 7.25568i | −0.591661 | − | 0.806187i | ||||
\(82\) | 1.25325 | + | 1.25325i | 0.138398 | + | 0.138398i | ||||
\(83\) | −2.21281 | − | 2.21281i | −0.242887 | − | 0.242887i | 0.575156 | − | 0.818043i | \(-0.304941\pi\) |
−0.818043 | + | 0.575156i | \(0.804941\pi\) | |||||||
\(84\) | −1.47997 | − | 0.353433i | −0.161478 | − | 0.0385627i | ||||
\(85\) | 7.57738 | − | 2.27565i | 0.821882 | − | 0.246829i | ||||
\(86\) | − | 8.92971i | − | 0.962915i | ||||||
\(87\) | −7.10725 | − | 11.5668i | −0.761977 | − | 1.24009i | ||||
\(88\) | −2.91992 | + | 2.91992i | −0.311264 | + | 0.311264i | ||||
\(89\) | −6.08809 | −0.645336 | −0.322668 | − | 0.946512i | \(-0.604580\pi\) | ||||
−0.322668 | + | 0.946512i | \(0.604580\pi\) | |||||||
\(90\) | −1.18174 | + | 6.60329i | −0.124566 | + | 0.696048i | ||||
\(91\) | 0.912584 | 0.0956648 | ||||||||
\(92\) | −0.707107 | + | 0.707107i | −0.0737210 | + | 0.0737210i | ||||
\(93\) | −6.41378 | − | 10.4382i | −0.665078 | − | 1.08239i | ||||
\(94\) | − | 0.0396100i | − | 0.00408546i | ||||||
\(95\) | −8.35049 | + | 15.5190i | −0.856742 | + | 1.59222i | ||||
\(96\) | 1.68468 | + | 0.402318i | 0.171942 | + | 0.0410614i | ||||
\(97\) | 11.8246 | + | 11.8246i | 1.20061 | + | 1.20061i | 0.973982 | + | 0.226625i | \(0.0727691\pi\) |
0.226625 | + | 0.973982i | \(0.427231\pi\) | |||||||
\(98\) | 4.40404 | + | 4.40404i | 0.444875 | + | 0.444875i | ||||
\(99\) | −11.0514 | − | 5.59760i | −1.11071 | − | 0.562580i | ||||
\(100\) | 4.17269 | − | 2.75476i | 0.417269 | − | 0.275476i | ||||
\(101\) | − | 1.36233i | − | 0.135557i | −0.997700 | − | 0.0677786i | \(-0.978409\pi\) | ||
0.997700 | − | 0.0677786i | \(-0.0215911\pi\) | |||||||
\(102\) | 5.22147 | − | 3.20834i | 0.517002 | − | 0.317673i | ||||
\(103\) | 3.37589 | − | 3.37589i | 0.332636 | − | 0.332636i | −0.520950 | − | 0.853587i | \(-0.674422\pi\) |
0.853587 | + | 0.520950i | \(0.174422\pi\) | |||||||
\(104\) | −1.03881 | −0.101864 | ||||||||
\(105\) | −2.26403 | + | 2.53975i | −0.220947 | + | 0.247854i | ||||
\(106\) | −13.8187 | −1.34219 | ||||||||
\(107\) | −2.39803 | + | 2.39803i | −0.231826 | + | 0.231826i | −0.813455 | − | 0.581628i | \(-0.802416\pi\) |
0.581628 | + | 0.813455i | \(0.302416\pi\) | |||||||
\(108\) | 0.426330 | + | 5.17863i | 0.0410236 | + | 0.498314i | ||||
\(109\) | − | 0.531902i | − | 0.0509470i | −0.999675 | − | 0.0254735i | \(-0.991891\pi\) | ||
0.999675 | − | 0.0254735i | \(-0.00810934\pi\) | |||||||
\(110\) | 2.65587 | + | 8.84339i | 0.253227 | + | 0.843185i | ||||
\(111\) | 3.67883 | − | 15.4048i | 0.349179 | − | 1.46216i | ||||
\(112\) | 0.621187 | + | 0.621187i | 0.0586966 | + | 0.0586966i | ||||
\(113\) | 4.14725 | + | 4.14725i | 0.390140 | + | 0.390140i | 0.874737 | − | 0.484597i | \(-0.161034\pi\) |
−0.484597 | + | 0.874737i | \(0.661034\pi\) | |||||||
\(114\) | −3.17077 | + | 13.2774i | −0.296970 | + | 1.24354i | ||||
\(115\) | 0.643162 | + | 2.14157i | 0.0599752 | + | 0.199703i | ||||
\(116\) | 7.83802i | 0.727742i | ||||||||
\(117\) | −0.970139 | − | 2.96158i | −0.0896893 | − | 0.273798i | ||||
\(118\) | 7.75200 | − | 7.75200i | 0.713629 | − | 0.713629i | ||||
\(119\) | 3.10830 | 0.284937 | ||||||||
\(120\) | 2.57719 | − | 2.89104i | 0.235264 | − | 0.263915i | ||||
\(121\) | −6.05185 | −0.550168 | ||||||||
\(122\) | −7.83764 | + | 7.83764i | −0.709587 | + | 0.709587i | ||||
\(123\) | 2.61553 | − | 1.60712i | 0.235834 | − | 0.144909i | ||||
\(124\) | 7.07325i | 0.635197i | ||||||||
\(125\) | −1.00330 | − | 11.1352i | −0.0897376 | − | 0.995965i | ||||
\(126\) | −1.19084 | + | 2.35109i | −0.106089 | + | 0.209452i | ||||
\(127\) | 8.34126 | + | 8.34126i | 0.740167 | + | 0.740167i | 0.972610 | − | 0.232443i | \(-0.0746718\pi\) |
−0.232443 | + | 0.972610i | \(0.574672\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | −15.0437 | − | 3.59258i | −1.32452 | − | 0.316309i | ||||
\(130\) | −1.10066 | + | 2.04552i | −0.0965340 | + | 0.179404i | ||||
\(131\) | 2.68737i | 0.234797i | 0.993085 | + | 0.117398i | \(0.0374554\pi\) | ||||
−0.993085 | + | 0.117398i | \(0.962545\pi\) | |||||||
\(132\) | 3.74439 | + | 6.09386i | 0.325907 | + | 0.530402i | ||||
\(133\) | −4.89573 | + | 4.89573i | −0.424514 | + | 0.424514i | ||||
\(134\) | −15.3143 | −1.32295 | ||||||||
\(135\) | 10.6490 | + | 4.64747i | 0.916519 | + | 0.399990i | ||||
\(136\) | −3.53823 | −0.303401 | ||||||||
\(137\) | 3.75896 | − | 3.75896i | 0.321150 | − | 0.321150i | −0.528058 | − | 0.849208i | \(-0.677080\pi\) |
0.849208 | + | 0.528058i | \(0.177080\pi\) | |||||||
\(138\) | 0.906765 | + | 1.47573i | 0.0771890 | + | 0.125622i | ||||
\(139\) | 20.7808i | 1.76261i | 0.472551 | + | 0.881303i | \(0.343333\pi\) | ||||
−0.472551 | + | 0.881303i | \(0.656667\pi\) | |||||||
\(140\) | 1.88135 | − | 0.565012i | 0.159003 | − | 0.0477522i | ||||
\(141\) | −0.0667301 | − | 0.0159358i | −0.00561969 | − | 0.00134204i | ||||
\(142\) | 1.59529 | + | 1.59529i | 0.133874 | + | 0.133874i | ||||
\(143\) | −3.03324 | − | 3.03324i | −0.253652 | − | 0.253652i | ||||
\(144\) | 1.35555 | − | 2.67628i | 0.112963 | − | 0.223023i | ||||
\(145\) | 15.4339 | + | 8.30468i | 1.28172 | + | 0.689666i | ||||
\(146\) | − | 12.0030i | − | 0.993378i | ||||||
\(147\) | 9.19122 | − | 5.64757i | 0.758079 | − | 0.465803i | ||||
\(148\) | −6.46585 | + | 6.46585i | −0.531489 | + | 0.531489i | ||||
\(149\) | −6.11984 | −0.501357 | −0.250678 | − | 0.968070i | \(-0.580654\pi\) | ||||
−0.250678 | + | 0.968070i | \(0.580654\pi\) | |||||||
\(150\) | −2.96214 | − | 8.13792i | −0.241857 | − | 0.664458i | ||||
\(151\) | 8.00975 | 0.651825 | 0.325912 | − | 0.945400i | \(-0.394329\pi\) | ||||
0.325912 | + | 0.945400i | \(0.394329\pi\) | |||||||
\(152\) | 5.57289 | − | 5.57289i | 0.452021 | − | 0.452021i | ||||
\(153\) | −3.30433 | − | 10.0873i | −0.267140 | − | 0.815507i | ||||
\(154\) | 3.62763i | 0.292323i | ||||||||
\(155\) | 13.9280 | + | 7.49438i | 1.11872 | + | 0.601963i | ||||
\(156\) | −0.417931 | + | 1.75006i | −0.0334613 | + | 0.140117i | ||||
\(157\) | −9.56563 | − | 9.56563i | −0.763420 | − | 0.763420i | 0.213519 | − | 0.976939i | \(-0.431508\pi\) |
−0.976939 | + | 0.213519i | \(0.931508\pi\) | |||||||
\(158\) | 1.40159 | + | 1.40159i | 0.111504 | + | 0.111504i | ||||
\(159\) | −5.55950 | + | 23.2800i | −0.440897 | + | 1.84622i | ||||
\(160\) | −2.14157 | + | 0.643162i | −0.169306 | + | 0.0508464i | ||||
\(161\) | 0.878491i | 0.0692348i | ||||||||
\(162\) | 8.89585 | + | 1.36523i | 0.698924 | + | 0.107263i | ||||
\(163\) | 1.30077 | − | 1.30077i | 0.101884 | − | 0.101884i | −0.654327 | − | 0.756211i | \(-0.727048\pi\) |
0.756211 | + | 0.654327i | \(0.227048\pi\) | |||||||
\(164\) | −1.77236 | −0.138398 | ||||||||
\(165\) | 15.9668 | − | 0.916422i | 1.24301 | − | 0.0713434i | ||||
\(166\) | 3.12938 | 0.242887 | ||||||||
\(167\) | −7.75358 | + | 7.75358i | −0.599990 | + | 0.599990i | −0.940310 | − | 0.340320i | \(-0.889465\pi\) |
0.340320 | + | 0.940310i | \(0.389465\pi\) | |||||||
\(168\) | 1.29641 | − | 0.796585i | 0.100021 | − | 0.0614579i | ||||
\(169\) | 11.9209i | 0.916991i | ||||||||
\(170\) | −3.74889 | + | 6.96715i | −0.287526 | + | 0.534356i | ||||
\(171\) | 21.0925 | + | 10.6835i | 1.61298 | + | 0.816985i | ||||
\(172\) | 6.31426 | + | 6.31426i | 0.481457 | + | 0.481457i | ||||
\(173\) | −10.4290 | − | 10.4290i | −0.792899 | − | 0.792899i | 0.189066 | − | 0.981964i | \(-0.439454\pi\) |
−0.981964 | + | 0.189066i | \(0.939454\pi\) | |||||||
\(174\) | 13.2045 | + | 3.15338i | 1.00103 | + | 0.239057i | ||||
\(175\) | 0.880797 | − | 4.30324i | 0.0665820 | − | 0.325294i | ||||
\(176\) | − | 4.12939i | − | 0.311264i | ||||||
\(177\) | −9.94085 | − | 16.1784i | −0.747200 | − | 1.21604i | ||||
\(178\) | 4.30493 | − | 4.30493i | 0.322668 | − | 0.322668i | ||||
\(179\) | 0.719378 | 0.0537688 | 0.0268844 | − | 0.999639i | \(-0.491441\pi\) | ||||
0.0268844 | + | 0.999639i | \(0.491441\pi\) | |||||||
\(180\) | −3.83362 | − | 5.50485i | −0.285741 | − | 0.410307i | ||||
\(181\) | 16.7156 | 1.24246 | 0.621229 | − | 0.783629i | \(-0.286634\pi\) | ||||
0.621229 | + | 0.783629i | \(0.286634\pi\) | |||||||
\(182\) | −0.645294 | + | 0.645294i | −0.0478324 | + | 0.0478324i | ||||
\(183\) | 10.0507 | + | 16.3571i | 0.742967 | + | 1.20915i | ||||
\(184\) | − | 1.00000i | − | 0.0737210i | ||||||
\(185\) | 5.88113 | + | 19.5828i | 0.432389 | + | 1.43975i | ||||
\(186\) | 11.9162 | + | 2.84570i | 0.873735 | + | 0.208657i | ||||
\(187\) | −10.3313 | − | 10.3313i | −0.755502 | − | 0.755502i | ||||
\(188\) | 0.0280085 | + | 0.0280085i | 0.00204273 | + | 0.00204273i | ||||
\(189\) | 3.48173 | + | 2.95207i | 0.253258 | + | 0.214731i | ||||
\(190\) | −5.06893 | − | 16.8783i | −0.367739 | − | 1.22448i | ||||
\(191\) | 10.6239i | 0.768718i | 0.923184 | + | 0.384359i | \(0.125577\pi\) | ||||
−0.923184 | + | 0.384359i | \(0.874423\pi\) | |||||||
\(192\) | −1.47573 | + | 0.906765i | −0.106502 | + | 0.0654402i | ||||
\(193\) | −0.732855 | + | 0.732855i | −0.0527520 | + | 0.0527520i | −0.732991 | − | 0.680239i | \(-0.761876\pi\) |
0.680239 | + | 0.732991i | \(0.261876\pi\) | |||||||
\(194\) | −16.7225 | −1.20061 | ||||||||
\(195\) | 3.00324 | + | 2.67720i | 0.215066 | + | 0.191719i | ||||
\(196\) | −6.22825 | −0.444875 | ||||||||
\(197\) | 10.4745 | − | 10.4745i | 0.746279 | − | 0.746279i | −0.227499 | − | 0.973778i | \(-0.573055\pi\) |
0.973778 | + | 0.227499i | \(0.0730548\pi\) | |||||||
\(198\) | 11.7726 | − | 3.85642i | 0.836644 | − | 0.274064i | ||||
\(199\) | − | 3.02413i | − | 0.214375i | −0.994239 | − | 0.107188i | \(-0.965815\pi\) | ||
0.994239 | − | 0.107188i | \(-0.0341845\pi\) | |||||||
\(200\) | −1.00262 | + | 4.89844i | −0.0708963 | + | 0.346372i | ||||
\(201\) | −6.16122 | + | 25.7997i | −0.434579 | + | 1.81977i | ||||
\(202\) | 0.963314 | + | 0.963314i | 0.0677786 | + | 0.0677786i | ||||
\(203\) | 4.86887 | + | 4.86887i | 0.341728 | + | 0.341728i | ||||
\(204\) | −1.42349 | + | 5.96077i | −0.0996644 | + | 0.417338i | ||||
\(205\) | −1.87788 | + | 3.48997i | −0.131157 | + | 0.243750i | ||||
\(206\) | 4.77423i | 0.332636i | ||||||||
\(207\) | 2.85094 | − | 0.933895i | 0.198154 | − | 0.0649102i | ||||
\(208\) | 0.734549 | − | 0.734549i | 0.0509318 | − | 0.0509318i | ||||
\(209\) | 32.5448 | 2.25117 | ||||||||
\(210\) | −0.194961 | − | 3.39679i | −0.0134536 | − | 0.234401i | ||||
\(211\) | −19.3102 | −1.32937 | −0.664684 | − | 0.747125i | \(-0.731434\pi\) | ||||
−0.664684 | + | 0.747125i | \(0.731434\pi\) | |||||||
\(212\) | 9.77127 | − | 9.77127i | 0.671093 | − | 0.671093i | ||||
\(213\) | 3.32936 | − | 2.04574i | 0.228124 | − | 0.140171i | ||||
\(214\) | − | 3.39132i | − | 0.231826i | ||||||
\(215\) | 19.1236 | − | 5.74325i | 1.30422 | − | 0.391686i | ||||
\(216\) | −3.96331 | − | 3.36039i | −0.269669 | − | 0.228645i | ||||
\(217\) | 4.39381 | + | 4.39381i | 0.298271 | + | 0.298271i | ||||
\(218\) | 0.376112 | + | 0.376112i | 0.0254735 | + | 0.0254735i | ||||
\(219\) | −20.2212 | − | 4.82904i | −1.36642 | − | 0.326316i | ||||
\(220\) | −8.13121 | − | 4.37524i | −0.548206 | − | 0.294979i | ||||
\(221\) | − | 3.67554i | − | 0.247244i | ||||||
\(222\) | 8.29154 | + | 13.4942i | 0.556492 | + | 0.905671i | ||||
\(223\) | −7.87712 | + | 7.87712i | −0.527491 | + | 0.527491i | −0.919824 | − | 0.392332i | \(-0.871668\pi\) |
0.392332 | + | 0.919824i | \(0.371668\pi\) | |||||||
\(224\) | −0.878491 | −0.0586966 | ||||||||
\(225\) | −14.9015 | + | 1.71621i | −0.993433 | + | 0.114414i | ||||
\(226\) | −5.86509 | −0.390140 | ||||||||
\(227\) | 8.11980 | − | 8.11980i | 0.538930 | − | 0.538930i | −0.384284 | − | 0.923215i | \(-0.625552\pi\) |
0.923215 | + | 0.384284i | \(0.125552\pi\) | |||||||
\(228\) | −7.14645 | − | 11.6306i | −0.473285 | − | 0.770255i | ||||
\(229\) | − | 8.83078i | − | 0.583554i | −0.956486 | − | 0.291777i | \(-0.905753\pi\) | ||
0.956486 | − | 0.291777i | \(-0.0942465\pi\) | |||||||
\(230\) | −1.96911 | − | 1.05954i | −0.129839 | − | 0.0698639i | ||||
\(231\) | 6.11139 | + | 1.45946i | 0.402100 | + | 0.0960255i | ||||
\(232\) | −5.54232 | − | 5.54232i | −0.363871 | − | 0.363871i | ||||
\(233\) | 13.3537 | + | 13.3537i | 0.874831 | + | 0.874831i | 0.992994 | − | 0.118163i | \(-0.0377005\pi\) |
−0.118163 | + | 0.992994i | \(0.537701\pi\) | |||||||
\(234\) | 2.78014 | + | 1.40816i | 0.181744 | + | 0.0920543i | ||||
\(235\) | 0.0848278 | − | 0.0254757i | 0.00553356 | − | 0.00166185i | ||||
\(236\) | 10.9630i | 0.713629i | ||||||||
\(237\) | 2.92510 | − | 1.79734i | 0.190006 | − | 0.116750i | ||||
\(238\) | −2.19790 | + | 2.19790i | −0.142469 | + | 0.142469i | ||||
\(239\) | 5.29769 | 0.342679 | 0.171340 | − | 0.985212i | \(-0.445190\pi\) | ||||
0.171340 | + | 0.985212i | \(0.445190\pi\) | |||||||
\(240\) | 0.221927 | + | 3.86662i | 0.0143253 | + | 0.249589i | ||||
\(241\) | 3.24318 | 0.208912 | 0.104456 | − | 0.994530i | \(-0.466690\pi\) | ||||
0.104456 | + | 0.994530i | \(0.466690\pi\) | |||||||
\(242\) | 4.27930 | − | 4.27930i | 0.275084 | − | 0.275084i | ||||
\(243\) | 5.87893 | − | 14.4374i | 0.377134 | − | 0.926159i | ||||
\(244\) | − | 11.0841i | − | 0.709587i | ||||||
\(245\) | −6.59907 | + | 12.2641i | −0.421599 | + | 0.783524i | ||||
\(246\) | −0.713053 | + | 2.98586i | −0.0454626 | + | 0.190371i | ||||
\(247\) | 5.78917 | + | 5.78917i | 0.368356 | + | 0.368356i | ||||
\(248\) | −5.00154 | − | 5.00154i | −0.317598 | − | 0.317598i | ||||
\(249\) | 1.25901 | − | 5.27200i | 0.0797863 | − | 0.334099i | ||||
\(250\) | 8.58324 | + | 7.16436i | 0.542852 | + | 0.453114i | ||||
\(251\) | − | 17.6589i | − | 1.11462i | −0.830304 | − | 0.557310i | \(-0.811833\pi\) | ||
0.830304 | − | 0.557310i | \(-0.188167\pi\) | |||||||
\(252\) | −0.820418 | − | 2.50452i | −0.0516815 | − | 0.157770i | ||||
\(253\) | 2.91992 | − | 2.91992i | 0.183574 | − | 0.183574i | ||||
\(254\) | −11.7963 | −0.740167 | ||||||||
\(255\) | 10.2292 | + | 9.11868i | 0.640575 | + | 0.571034i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −3.83128 | + | 3.83128i | −0.238989 | + | 0.238989i | −0.816431 | − | 0.577442i | \(-0.804051\pi\) |
0.577442 | + | 0.816431i | \(0.304051\pi\) | |||||||
\(258\) | 13.1778 | − | 8.09715i | 0.820416 | − | 0.504106i | ||||
\(259\) | 8.03300i | 0.499146i | ||||||||
\(260\) | −0.668122 | − | 2.22469i | −0.0414352 | − | 0.137969i | ||||
\(261\) | 10.6249 | − | 20.9767i | 0.657662 | − | 1.29843i | ||||
\(262\) | −1.90026 | − | 1.90026i | −0.117398 | − | 0.117398i | ||||
\(263\) | 9.95007 | + | 9.95007i | 0.613548 | + | 0.613548i | 0.943869 | − | 0.330321i | \(-0.107157\pi\) |
−0.330321 | + | 0.943869i | \(0.607157\pi\) | |||||||
\(264\) | −6.95669 | − | 1.66133i | −0.428155 | − | 0.102248i | ||||
\(265\) | −8.88764 | − | 29.5937i | −0.545963 | − | 1.81793i | ||||
\(266\) | − | 6.92361i | − | 0.424514i | ||||||
\(267\) | −5.52047 | − | 8.98437i | −0.337847 | − | 0.549835i | ||||
\(268\) | 10.8288 | − | 10.8288i | 0.661477 | − | 0.661477i | ||||
\(269\) | −10.4792 | −0.638928 | −0.319464 | − | 0.947598i | \(-0.603503\pi\) | ||||
−0.319464 | + | 0.947598i | \(0.603503\pi\) | |||||||
\(270\) | −10.8162 | + | 4.24372i | −0.658255 | + | 0.258264i | ||||
\(271\) | −15.4253 | −0.937021 | −0.468511 | − | 0.883458i | \(-0.655209\pi\) | ||||
−0.468511 | + | 0.883458i | \(0.655209\pi\) | |||||||
\(272\) | 2.50190 | − | 2.50190i | 0.151700 | − | 0.151700i | ||||
\(273\) | 0.827499 | + | 1.34673i | 0.0500825 | + | 0.0815076i | ||||
\(274\) | 5.31597i | 0.321150i | ||||||||
\(275\) | −17.2306 | + | 11.3755i | −1.03905 | + | 0.685967i | ||||
\(276\) | −1.68468 | − | 0.402318i | −0.101406 | − | 0.0242167i | ||||
\(277\) | −8.17257 | − | 8.17257i | −0.491042 | − | 0.491042i | 0.417592 | − | 0.908634i | \(-0.362874\pi\) |
−0.908634 | + | 0.417592i | \(0.862874\pi\) | |||||||
\(278\) | −14.6943 | − | 14.6943i | −0.881303 | − | 0.881303i | ||||
\(279\) | 9.58817 | − | 18.9300i | 0.574028 | − | 1.13331i | ||||
\(280\) | −0.930794 | + | 1.72984i | −0.0556256 | + | 0.103378i | ||||
\(281\) | − | 24.0787i | − | 1.43641i | −0.695830 | − | 0.718206i | \(-0.744963\pi\) | ||
0.695830 | − | 0.718206i | \(-0.255037\pi\) | |||||||
\(282\) | 0.0584537 | − | 0.0359170i | 0.00348087 | − | 0.00213883i | ||||
\(283\) | −19.2731 | + | 19.2731i | −1.14567 | + | 1.14567i | −0.158271 | + | 0.987396i | \(0.550592\pi\) |
−0.987396 | + | 0.158271i | \(0.949408\pi\) | |||||||
\(284\) | −2.25608 | −0.133874 | ||||||||
\(285\) | −30.4738 | + | 1.74906i | −1.80511 | + | 0.103606i | ||||
\(286\) | 4.28964 | 0.253652 | ||||||||
\(287\) | −1.10097 | + | 1.10097i | −0.0649880 | + | 0.0649880i | ||||
\(288\) | 0.933895 | + | 2.85094i | 0.0550303 | + | 0.167993i | ||||
\(289\) | 4.48094i | 0.263585i | ||||||||
\(290\) | −16.7857 | + | 5.04112i | −0.985691 | + | 0.296025i | ||||
\(291\) | −6.72777 | + | 28.1721i | −0.394389 | + | 1.65148i | ||||
\(292\) | 8.48742 | + | 8.48742i | 0.496689 | + | 0.496689i | ||||
\(293\) | −17.5754 | − | 17.5754i | −1.02677 | − | 1.02677i | −0.999632 | − | 0.0271332i | \(-0.991362\pi\) |
−0.0271332 | − | 0.999632i | \(-0.508638\pi\) | |||||||
\(294\) | −2.50574 | + | 10.4926i | −0.146138 | + | 0.611941i | ||||
\(295\) | 21.5873 | + | 11.6157i | 1.25686 | + | 0.676292i | ||||
\(296\) | − | 9.14409i | − | 0.531489i | ||||||
\(297\) | −1.76048 | − | 21.3846i | −0.102153 | − | 1.24086i | ||||
\(298\) | 4.32738 | − | 4.32738i | 0.250678 | − | 0.250678i | ||||
\(299\) | 1.03881 | 0.0600759 | ||||||||
\(300\) | 7.84893 | + | 3.65983i | 0.453158 | + | 0.211301i | ||||
\(301\) | 7.84466 | 0.452159 | ||||||||
\(302\) | −5.66375 | + | 5.66375i | −0.325912 | + | 0.325912i | ||||
\(303\) | 2.01043 | − | 1.23532i | 0.115496 | − | 0.0709670i | ||||
\(304\) | 7.88126i | 0.452021i | ||||||||
\(305\) | −21.8258 | − | 11.7440i | −1.24974 | − | 0.672461i | ||||
\(306\) | 9.46929 | + | 4.79625i | 0.541323 | + | 0.274184i | ||||
\(307\) | 6.34290 | + | 6.34290i | 0.362008 | + | 0.362008i | 0.864552 | − | 0.502544i | \(-0.167602\pi\) |
−0.502544 | + | 0.864552i | \(0.667602\pi\) | |||||||
\(308\) | −2.56512 | − | 2.56512i | −0.146161 | − | 0.146161i | ||||
\(309\) | 8.04304 | + | 1.92076i | 0.457553 | + | 0.109268i | ||||
\(310\) | −15.1479 | + | 4.54925i | −0.860343 | + | 0.258380i | ||||
\(311\) | 1.54924i | 0.0878496i | 0.999035 | + | 0.0439248i | \(0.0139862\pi\) | ||||
−0.999035 | + | 0.0439248i | \(0.986014\pi\) | |||||||
\(312\) | −0.941956 | − | 1.53300i | −0.0533277 | − | 0.0867890i | ||||
\(313\) | 0.449127 | − | 0.449127i | 0.0253861 | − | 0.0253861i | −0.694300 | − | 0.719686i | \(-0.744286\pi\) |
0.719686 | + | 0.694300i | \(0.244286\pi\) | |||||||
\(314\) | 13.5278 | 0.763420 | ||||||||
\(315\) | −5.80093 | − | 1.03814i | −0.326846 | − | 0.0584928i | ||||
\(316\) | −1.98214 | −0.111504 | ||||||||
\(317\) | −17.7857 | + | 17.7857i | −0.998943 | + | 0.998943i | −0.999999 | − | 0.00105667i | \(-0.999664\pi\) |
0.00105667 | + | 0.999999i | \(0.499664\pi\) | |||||||
\(318\) | −12.5303 | − | 20.3926i | −0.702663 | − | 1.14356i | ||||
\(319\) | − | 32.3662i | − | 1.81216i | ||||||
\(320\) | 1.05954 | − | 1.96911i | 0.0592300 | − | 0.110076i | ||||
\(321\) | −5.71329 | − | 1.36439i | −0.318885 | − | 0.0761529i | ||||
\(322\) | −0.621187 | − | 0.621187i | −0.0346174 | − | 0.0346174i | ||||
\(323\) | 19.7182 | + | 19.7182i | 1.09715 | + | 1.09715i | ||||
\(324\) | −7.25568 | + | 5.32495i | −0.403093 | + | 0.295831i | ||||
\(325\) | −5.08854 | − | 1.04154i | −0.282262 | − | 0.0577740i | ||||
\(326\) | 1.83956i | 0.101884i | ||||||||
\(327\) | 0.784943 | − | 0.482310i | 0.0434075 | − | 0.0266718i | ||||
\(328\) | 1.25325 | − | 1.25325i | 0.0691991 | − | 0.0691991i | ||||
\(329\) | 0.0347970 | 0.00191842 | ||||||||
\(330\) | −10.6422 | + | 11.9382i | −0.585834 | + | 0.657178i | ||||
\(331\) | −9.69040 | −0.532633 | −0.266316 | − | 0.963886i | \(-0.585807\pi\) | ||||
−0.266316 | + | 0.963886i | \(0.585807\pi\) | |||||||
\(332\) | −2.21281 | + | 2.21281i | −0.121443 | + | 0.121443i | ||||
\(333\) | 26.0692 | − | 8.53962i | 1.42858 | − | 0.467968i | ||||
\(334\) | − | 10.9652i | − | 0.599990i | ||||||
\(335\) | −9.84958 | − | 32.7967i | −0.538140 | − | 1.79188i | ||||
\(336\) | −0.353433 | + | 1.47997i | −0.0192813 | + | 0.0807392i | ||||
\(337\) | 4.98944 | + | 4.98944i | 0.271792 | + | 0.271792i | 0.829821 | − | 0.558029i | \(-0.188442\pi\) |
−0.558029 | + | 0.829821i | \(0.688442\pi\) | |||||||
\(338\) | −8.42933 | − | 8.42933i | −0.458495 | − | 0.458495i | ||||
\(339\) | −2.35963 | + | 9.88080i | −0.128158 | + | 0.536651i | ||||
\(340\) | −2.27565 | − | 7.57738i | −0.123415 | − | 0.410941i | ||||
\(341\) | − | 29.2082i | − | 1.58171i | ||||||
\(342\) | −22.4690 | + | 7.36027i | −1.21498 | + | 0.397998i | ||||
\(343\) | −8.21722 | + | 8.21722i | −0.443688 | + | 0.443688i | ||||
\(344\) | −8.92971 | −0.481457 | ||||||||
\(345\) | −2.57719 | + | 2.89104i | −0.138751 | + | 0.155648i | ||||
\(346\) | 14.7488 | 0.792899 | ||||||||
\(347\) | −11.2296 | + | 11.2296i | −0.602837 | + | 0.602837i | −0.941064 | − | 0.338228i | \(-0.890173\pi\) |
0.338228 | + | 0.941064i | \(0.390173\pi\) | |||||||
\(348\) | −11.5668 | + | 7.10725i | −0.620045 | + | 0.380988i | ||||
\(349\) | − | 23.8817i | − | 1.27836i | −0.769059 | − | 0.639178i | \(-0.779275\pi\) | ||
0.769059 | − | 0.639178i | \(-0.220725\pi\) | |||||||
\(350\) | 2.42003 | + | 3.66566i | 0.129356 | + | 0.195938i | ||||
\(351\) | 3.49080 | − | 4.11712i | 0.186325 | − | 0.219756i | ||||
\(352\) | 2.91992 | + | 2.91992i | 0.155632 | + | 0.155632i | ||||
\(353\) | −12.1901 | − | 12.1901i | −0.648813 | − | 0.648813i | 0.303893 | − | 0.952706i | \(-0.401713\pi\) |
−0.952706 | + | 0.303893i | \(0.901713\pi\) | |||||||
\(354\) | 18.4691 | + | 4.41060i | 0.981621 | + | 0.234421i | ||||
\(355\) | −2.39040 | + | 4.44246i | −0.126869 | + | 0.235781i | ||||
\(356\) | 6.08809i | 0.322668i | ||||||||
\(357\) | 2.81850 | + | 4.58701i | 0.149171 | + | 0.242770i | ||||
\(358\) | −0.508677 | + | 0.508677i | −0.0268844 | + | 0.0268844i | ||||
\(359\) | 7.16299 | 0.378048 | 0.189024 | − | 0.981972i | \(-0.439468\pi\) | ||||
0.189024 | + | 0.981972i | \(0.439468\pi\) | |||||||
\(360\) | 6.60329 | + | 1.18174i | 0.348024 | + | 0.0622829i | ||||
\(361\) | −43.1142 | −2.26917 | ||||||||
\(362\) | −11.8197 | + | 11.8197i | −0.621229 | + | 0.621229i | ||||
\(363\) | −5.48761 | − | 8.93089i | −0.288025 | − | 0.468750i | ||||
\(364\) | − | 0.912584i | − | 0.0478324i | ||||||
\(365\) | 25.7054 | − | 7.71989i | 1.34548 | − | 0.404078i | ||||
\(366\) | −18.6731 | − | 4.45933i | −0.976060 | − | 0.233093i | ||||
\(367\) | 13.3521 | + | 13.3521i | 0.696971 | + | 0.696971i | 0.963756 | − | 0.266785i | \(-0.0859613\pi\) |
−0.266785 | + | 0.963756i | \(0.585961\pi\) | |||||||
\(368\) | 0.707107 | + | 0.707107i | 0.0368605 | + | 0.0368605i | ||||
\(369\) | 4.74334 | + | 2.40253i | 0.246928 | + | 0.125071i | ||||
\(370\) | −18.0057 | − | 9.68851i | −0.936071 | − | 0.503682i | ||||
\(371\) | − | 12.1396i | − | 0.630255i | ||||||
\(372\) | −10.4382 | + | 6.41378i | −0.541196 | + | 0.332539i | ||||
\(373\) | −2.87275 | + | 2.87275i | −0.148745 | + | 0.148745i | −0.777557 | − | 0.628812i | \(-0.783541\pi\) |
0.628812 | + | 0.777557i | \(0.283541\pi\) | |||||||
\(374\) | 14.6107 | 0.755502 | ||||||||
\(375\) | 15.5228 | − | 11.5776i | 0.801596 | − | 0.597867i | ||||
\(376\) | −0.0396100 | −0.00204273 | ||||||||
\(377\) | 5.75741 | − | 5.75741i | 0.296522 | − | 0.296522i | ||||
\(378\) | −4.54938 | + | 0.374527i | −0.233995 | + | 0.0192636i | ||||
\(379\) | 24.7455i | 1.27109i | 0.772063 | + | 0.635546i | \(0.219225\pi\) | ||||
−0.772063 | + | 0.635546i | \(0.780775\pi\) | |||||||
\(380\) | 15.5190 | + | 8.35049i | 0.796110 | + | 0.428371i | ||||
\(381\) | −4.74587 | + | 19.8730i | −0.243139 | + | 1.01813i | ||||
\(382\) | −7.51222 | − | 7.51222i | −0.384359 | − | 0.384359i | ||||
\(383\) | 15.8012 | + | 15.8012i | 0.807405 | + | 0.807405i | 0.984240 | − | 0.176836i | \(-0.0565861\pi\) |
−0.176836 | + | 0.984240i | \(0.556586\pi\) | |||||||
\(384\) | 0.402318 | − | 1.68468i | 0.0205307 | − | 0.0859709i | ||||
\(385\) | −7.76884 | + | 2.33315i | −0.395937 | + | 0.118909i | ||||
\(386\) | − | 1.03641i | − | 0.0527520i | ||||||
\(387\) | −8.33941 | − | 25.4580i | −0.423916 | − | 1.29410i | ||||
\(388\) | 11.8246 | − | 11.8246i | 0.600303 | − | 0.600303i | ||||
\(389\) | 1.35053 | 0.0684745 | 0.0342372 | − | 0.999414i | \(-0.489100\pi\) | ||||
0.0342372 | + | 0.999414i | \(0.489100\pi\) | |||||||
\(390\) | −4.01668 | + | 0.230540i | −0.203392 | + | 0.0116738i | ||||
\(391\) | 3.53823 | 0.178936 | ||||||||
\(392\) | 4.40404 | − | 4.40404i | 0.222438 | − | 0.222438i | ||||
\(393\) | −3.96583 | + | 2.43682i | −0.200050 | + | 0.122921i | ||||
\(394\) | 14.8132i | 0.746279i | ||||||||
\(395\) | −2.10015 | + | 3.90305i | −0.105670 | + | 0.196384i | ||||
\(396\) | −5.59760 | + | 11.0514i | −0.281290 | + | 0.555354i | ||||
\(397\) | −5.00981 | − | 5.00981i | −0.251435 | − | 0.251435i | 0.570124 | − | 0.821559i | \(-0.306895\pi\) |
−0.821559 | + | 0.570124i | \(0.806895\pi\) | |||||||
\(398\) | 2.13839 | + | 2.13839i | 0.107188 | + | 0.107188i | ||||
\(399\) | −11.6641 | − | 2.78549i | −0.583933 | − | 0.139449i | ||||
\(400\) | −2.75476 | − | 4.17269i | −0.137738 | − | 0.208634i | ||||
\(401\) | − | 13.0718i | − | 0.652775i | −0.945236 | − | 0.326387i | \(-0.894169\pi\) | ||
0.945236 | − | 0.326387i | \(-0.105831\pi\) | |||||||
\(402\) | −13.8865 | − | 22.5998i | −0.692595 | − | 1.12717i | ||||
\(403\) | 5.19565 | − | 5.19565i | 0.258814 | − | 0.258814i | ||||
\(404\) | −1.36233 | −0.0677786 | ||||||||
\(405\) | 2.79773 | + | 19.9292i | 0.139020 | + | 0.990290i | ||||
\(406\) | −6.88563 | −0.341728 | ||||||||
\(407\) | 26.7000 | − | 26.7000i | 1.32347 | − | 1.32347i | ||||
\(408\) | −3.20834 | − | 5.22147i | −0.158837 | − | 0.258501i | ||||
\(409\) | − | 15.7658i | − | 0.779567i | −0.920907 | − | 0.389784i | \(-0.872550\pi\) | ||
0.920907 | − | 0.389784i | \(-0.127450\pi\) | |||||||
\(410\) | −1.13992 | − | 3.79564i | −0.0562964 | − | 0.187454i | ||||
\(411\) | 8.95570 | + | 2.13871i | 0.441752 | + | 0.105495i | ||||
\(412\) | −3.37589 | − | 3.37589i | −0.166318 | − | 0.166318i | ||||
\(413\) | 6.81006 | + | 6.81006i | 0.335101 | + | 0.335101i | ||||
\(414\) | −1.35555 | + | 2.67628i | −0.0666218 | + | 0.131532i | ||||
\(415\) | 2.01270 | + | 6.70180i | 0.0987995 | + | 0.328978i | ||||
\(416\) | 1.03881i | 0.0509318i | ||||||||
\(417\) | −30.6669 | + | 18.8433i | −1.50176 | + | 0.922762i | ||||
\(418\) | −23.0126 | + | 23.0126i | −1.12558 | + | 1.12558i | ||||
\(419\) | −28.4327 | −1.38903 | −0.694514 | − | 0.719480i | \(-0.744380\pi\) | ||||
−0.694514 | + | 0.719480i | \(0.744380\pi\) | |||||||
\(420\) | 2.53975 | + | 2.26403i | 0.123927 | + | 0.110474i | ||||
\(421\) | 24.0167 | 1.17050 | 0.585252 | − | 0.810851i | \(-0.300995\pi\) | ||||
0.585252 | + | 0.810851i | \(0.300995\pi\) | |||||||
\(422\) | 13.6544 | − | 13.6544i | 0.664684 | − | 0.664684i | ||||
\(423\) | −0.0369916 | − | 0.112926i | −0.00179859 | − | 0.00549063i | ||||
\(424\) | 13.8187i | 0.671093i | ||||||||
\(425\) | −17.3318 | − | 3.54752i | −0.840716 | − | 0.172080i | ||||
\(426\) | −0.907662 | + | 3.80077i | −0.0439764 | + | 0.184148i | ||||
\(427\) | −6.88529 | − | 6.88529i | −0.333203 | − | 0.333203i | ||||
\(428\) | 2.39803 | + | 2.39803i | 0.115913 | + | 0.115913i | ||||
\(429\) | 1.72580 | − | 7.22667i | 0.0833225 | − | 0.348907i | ||||
\(430\) | −9.46136 | + | 17.5835i | −0.456267 | + | 0.847954i | ||||
\(431\) | 26.9458i | 1.29793i | 0.760817 | + | 0.648967i | \(0.224798\pi\) | ||||
−0.760817 | + | 0.648967i | \(0.775202\pi\) | |||||||
\(432\) | 5.17863 | − | 0.426330i | 0.249157 | − | 0.0205118i | ||||
\(433\) | 10.1590 | − | 10.1590i | 0.488212 | − | 0.488212i | −0.419530 | − | 0.907742i | \(-0.637805\pi\) |
0.907742 | + | 0.419530i | \(0.137805\pi\) | |||||||
\(434\) | −6.21379 | −0.298271 | ||||||||
\(435\) | 1.73947 | + | 30.3067i | 0.0834011 | + | 1.45309i | ||||
\(436\) | −0.531902 | −0.0254735 | ||||||||
\(437\) | −5.57289 | + | 5.57289i | −0.266588 | + | 0.266588i | ||||
\(438\) | 17.7132 | − | 10.8839i | 0.846370 | − | 0.520054i | ||||
\(439\) | − | 2.41233i | − | 0.115134i | −0.998342 | − | 0.0575670i | \(-0.981666\pi\) | ||
0.998342 | − | 0.0575670i | \(-0.0183343\pi\) | |||||||
\(440\) | 8.84339 | − | 2.65587i | 0.421592 | − | 0.126613i | ||||
\(441\) | 16.6686 | + | 8.44273i | 0.793741 | + | 0.402035i | ||||
\(442\) | 2.59900 | + | 2.59900i | 0.123622 | + | 0.123622i | ||||
\(443\) | 7.57559 | + | 7.57559i | 0.359927 | + | 0.359927i | 0.863786 | − | 0.503859i | \(-0.168087\pi\) |
−0.503859 | + | 0.863786i | \(0.668087\pi\) | |||||||
\(444\) | −15.4048 | − | 3.67883i | −0.731082 | − | 0.174590i | ||||
\(445\) | 11.9881 | + | 6.45056i | 0.568290 | + | 0.305786i | ||||
\(446\) | − | 11.1399i | − | 0.527491i | ||||||
\(447\) | −5.54926 | − | 9.03122i | −0.262471 | − | 0.427162i | ||||
\(448\) | 0.621187 | − | 0.621187i | 0.0293483 | − | 0.0293483i | ||||
\(449\) | 31.6647 | 1.49435 | 0.747174 | − | 0.664628i | \(-0.231410\pi\) | ||||
0.747174 | + | 0.664628i | \(0.231410\pi\) | |||||||
\(450\) | 9.32340 | − | 11.7505i | 0.439509 | − | 0.553924i | ||||
\(451\) | 7.31877 | 0.344627 | ||||||||
\(452\) | 4.14725 | − | 4.14725i | 0.195070 | − | 0.195070i | ||||
\(453\) | 7.26297 | + | 11.8202i | 0.341244 | + | 0.555363i | ||||
\(454\) | 11.4831i | 0.538930i | ||||||||
\(455\) | −1.79697 | − | 0.966917i | −0.0842435 | − | 0.0453298i | ||||
\(456\) | 13.2774 | + | 3.17077i | 0.621770 | + | 0.148485i | ||||
\(457\) | −27.2159 | − | 27.2159i | −1.27310 | − | 1.27310i | −0.944451 | − | 0.328653i | \(-0.893405\pi\) |
−0.328653 | − | 0.944451i | \(-0.606595\pi\) | |||||||
\(458\) | 6.24430 | + | 6.24430i | 0.291777 | + | 0.291777i | ||||
\(459\) | 11.8898 | − | 14.0231i | 0.554969 | − | 0.654542i | ||||
\(460\) | 2.14157 | − | 0.643162i | 0.0998514 | − | 0.0299876i | ||||
\(461\) | 19.1053i | 0.889824i | 0.895574 | + | 0.444912i | \(0.146765\pi\) | ||||
−0.895574 | + | 0.444912i | \(0.853235\pi\) | |||||||
\(462\) | −5.35340 | + | 3.28941i | −0.249063 | + | 0.153037i | ||||
\(463\) | 17.9935 | − | 17.9935i | 0.836230 | − | 0.836230i | −0.152131 | − | 0.988360i | \(-0.548613\pi\) |
0.988360 | + | 0.152131i | \(0.0486135\pi\) | |||||||
\(464\) | 7.83802 | 0.363871 | ||||||||
\(465\) | 1.56974 | + | 27.3496i | 0.0727952 | + | 1.26831i | ||||
\(466\) | −18.8850 | −0.874831 | ||||||||
\(467\) | −13.5425 | + | 13.5425i | −0.626673 | + | 0.626673i | −0.947229 | − | 0.320557i | \(-0.896130\pi\) |
0.320557 | + | 0.947229i | \(0.396130\pi\) | |||||||
\(468\) | −2.96158 | + | 0.970139i | −0.136899 | + | 0.0448447i | ||||
\(469\) | − | 13.4535i | − | 0.621224i | ||||||
\(470\) | −0.0419683 | + | 0.0779963i | −0.00193585 | + | 0.00359770i | ||||
\(471\) | 5.44250 | − | 22.7901i | 0.250777 | − | 1.05011i | ||||
\(472\) | −7.75200 | − | 7.75200i | −0.356815 | − | 0.356815i | ||||
\(473\) | −26.0740 | − | 26.0740i | −1.19888 | − | 1.19888i | ||||
\(474\) | −0.797451 | + | 3.33927i | −0.0366281 | + | 0.153378i | ||||
\(475\) | 32.8860 | − | 21.7110i | 1.50891 | − | 0.996168i | ||||
\(476\) | − | 3.10830i | − | 0.142469i | ||||||
\(477\) | −39.3961 | + | 12.9052i | −1.80382 | + | 0.590888i | ||||
\(478\) | −3.74603 | + | 3.74603i | −0.171340 | + | 0.171340i | ||||
\(479\) | 10.1525 | 0.463880 | 0.231940 | − | 0.972730i | \(-0.425493\pi\) | ||||
0.231940 | + | 0.972730i | \(0.425493\pi\) | |||||||
\(480\) | −2.89104 | − | 2.57719i | −0.131957 | − | 0.117632i | ||||
\(481\) | 9.49896 | 0.433115 | ||||||||
\(482\) | −2.29328 | + | 2.29328i | −0.104456 | + | 0.104456i | ||||
\(483\) | −1.29641 | + | 0.796585i | −0.0589889 | + | 0.0362459i | ||||
\(484\) | 6.05185i | 0.275084i | ||||||||
\(485\) | −10.7553 | − | 35.8125i | −0.488373 | − | 1.62616i | ||||
\(486\) | 6.05174 | + | 14.3658i | 0.274513 | + | 0.651646i | ||||
\(487\) | 6.51439 | + | 6.51439i | 0.295195 | + | 0.295195i | 0.839128 | − | 0.543933i | \(-0.183066\pi\) |
−0.543933 | + | 0.839128i | \(0.683066\pi\) | |||||||
\(488\) | 7.83764 | + | 7.83764i | 0.354793 | + | 0.354793i | ||||
\(489\) | 3.09907 | + | 0.740089i | 0.140145 | + | 0.0334680i | ||||
\(490\) | −4.00578 | − | 13.3383i | −0.180963 | − | 0.602562i | ||||
\(491\) | − | 40.0908i | − | 1.80927i | −0.426186 | − | 0.904636i | \(-0.640143\pi\) | ||
0.426186 | − | 0.904636i | \(-0.359857\pi\) | |||||||
\(492\) | −1.60712 | − | 2.61553i | −0.0724544 | − | 0.117917i | ||||
\(493\) | 19.6100 | − | 19.6100i | 0.883189 | − | 0.883189i | ||||
\(494\) | −8.18712 | −0.368356 | ||||||||
\(495\) | 15.8305 | + | 22.7317i | 0.711529 | + | 1.02171i | ||||
\(496\) | 7.07325 | 0.317598 | ||||||||
\(497\) | −1.40145 | + | 1.40145i | −0.0628635 | + | 0.0628635i | ||||
\(498\) | 2.83761 | + | 4.61812i | 0.127157 | + | 0.206943i | ||||
\(499\) | − | 3.33567i | − | 0.149325i | −0.997209 | − | 0.0746625i | \(-0.976212\pi\) | ||
0.997209 | − | 0.0746625i | \(-0.0237880\pi\) | |||||||
\(500\) | −11.1352 | + | 1.00330i | −0.497983 | + | 0.0448688i | ||||
\(501\) | −18.4729 | − | 4.41151i | −0.825307 | − | 0.197092i | ||||
\(502\) | 12.4867 | + | 12.4867i | 0.557310 | + | 0.557310i | ||||
\(503\) | −5.33310 | − | 5.33310i | −0.237791 | − | 0.237791i | 0.578144 | − | 0.815935i | \(-0.303777\pi\) |
−0.815935 | + | 0.578144i | \(0.803777\pi\) | |||||||
\(504\) | 2.35109 | + | 1.19084i | 0.104726 | + | 0.0530443i | ||||
\(505\) | −1.44344 | + | 2.68258i | −0.0642323 | + | 0.119373i | ||||
\(506\) | 4.12939i | 0.183574i | ||||||||
\(507\) | −17.5920 | + | 10.8094i | −0.781287 | + | 0.480064i | ||||
\(508\) | 8.34126 | − | 8.34126i | 0.370084 | − | 0.370084i | ||||
\(509\) | 0.551066 | 0.0244256 | 0.0122128 | − | 0.999925i | \(-0.496112\pi\) | ||||
0.0122128 | + | 0.999925i | \(0.496112\pi\) | |||||||
\(510\) | −13.6810 | + | 0.785228i | −0.605804 | + | 0.0347705i | ||||
\(511\) | 10.5445 | 0.466463 | ||||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 3.36002 | + | 40.8141i | 0.148348 | + | 1.80199i | ||||
\(514\) | − | 5.41825i | − | 0.238989i | ||||||
\(515\) | −10.2244 | + | 3.07060i | −0.450540 | + | 0.135307i | ||||
\(516\) | −3.59258 | + | 15.0437i | −0.158155 | + | 0.662261i | ||||
\(517\) | −0.115658 | − | 0.115658i | −0.00508664 | − | 0.00508664i | ||||
\(518\) | −5.68019 | − | 5.68019i | −0.249573 | − | 0.249573i | ||||
\(519\) | 5.93370 | − | 24.8469i | 0.260460 | − | 1.09066i | ||||
\(520\) | 2.04552 | + | 1.10066i | 0.0897022 | + | 0.0482670i | ||||
\(521\) | − | 7.81178i | − | 0.342240i | −0.985250 | − | 0.171120i | \(-0.945261\pi\) | ||
0.985250 | − | 0.171120i | \(-0.0547387\pi\) | |||||||
\(522\) | 7.31989 | + | 22.3457i | 0.320383 | + | 0.978045i | ||||
\(523\) | 3.95100 | − | 3.95100i | 0.172765 | − | 0.172765i | −0.615428 | − | 0.788193i | \(-0.711017\pi\) |
0.788193 | + | 0.615428i | \(0.211017\pi\) | |||||||
\(524\) | 2.68737 | 0.117398 | ||||||||
\(525\) | 7.14909 | − | 2.60221i | 0.312012 | − | 0.113570i | ||||
\(526\) | −14.0715 | −0.613548 | ||||||||
\(527\) | 17.6966 | − | 17.6966i | 0.770876 | − | 0.770876i | ||||
\(528\) | 6.09386 | − | 3.74439i | 0.265201 | − | 0.162954i | ||||
\(529\) | 1.00000i | 0.0434783i | ||||||||
\(530\) | 27.2104 | + | 14.6414i | 1.18194 | + | 0.635981i | ||||
\(531\) | 14.8609 | − | 29.3400i | 0.644908 | − | 1.27325i | ||||
\(532\) | 4.89573 | + | 4.89573i | 0.212257 | + | 0.212257i | ||||
\(533\) | 1.30189 | + | 1.30189i | 0.0563909 | + | 0.0563909i | ||||
\(534\) | 10.2565 | + | 2.44935i | 0.443841 | + | 0.105994i | ||||
\(535\) | 7.26278 | − | 2.18117i | 0.313997 | − | 0.0943003i | ||||
\(536\) | 15.3143i | 0.661477i | ||||||||
\(537\) | 0.652307 | + | 1.06161i | 0.0281491 | + | 0.0458117i | ||||
\(538\) | 7.40991 | − | 7.40991i | 0.319464 | − | 0.319464i | ||||
\(539\) | 25.7189 | 1.10779 | ||||||||
\(540\) | 4.64747 | − | 10.6490i | 0.199995 | − | 0.458260i | ||||
\(541\) | −12.6873 | −0.545469 | −0.272735 | − | 0.962089i | \(-0.587928\pi\) | ||||
−0.272735 | + | 0.962089i | \(0.587928\pi\) | |||||||
\(542\) | 10.9073 | − | 10.9073i | 0.468511 | − | 0.468511i | ||||
\(543\) | 15.1571 | + | 24.6676i | 0.650453 | + | 1.05859i | ||||
\(544\) | 3.53823i | 0.151700i | ||||||||
\(545\) | −0.563570 | + | 1.04737i | −0.0241407 | + | 0.0448645i | ||||
\(546\) | −1.53741 | − | 0.367149i | −0.0657951 | − | 0.0157125i | ||||
\(547\) | 4.43286 | + | 4.43286i | 0.189535 | + | 0.189535i | 0.795495 | − | 0.605960i | \(-0.207211\pi\) |
−0.605960 | + | 0.795495i | \(0.707211\pi\) | |||||||
\(548\) | −3.75896 | − | 3.75896i | −0.160575 | − | 0.160575i | ||||
\(549\) | −15.0251 | + | 29.6641i | −0.641255 | + | 1.26603i | ||||
\(550\) | 4.14023 | − | 20.2276i | 0.176540 | − | 0.862507i | ||||
\(551\) | 61.7735i | 2.63164i | ||||||||
\(552\) | 1.47573 | − | 0.906765i | 0.0628112 | − | 0.0385945i | ||||
\(553\) | −1.23128 | + | 1.23128i | −0.0523593 | + | 0.0523593i | ||||
\(554\) | 11.5578 | 0.491042 | ||||||||
\(555\) | −23.5660 | + | 26.4359i | −1.00032 | + | 1.12214i | ||||
\(556\) | 20.7808 | 0.881303 | ||||||||
\(557\) | −19.7470 | + | 19.7470i | −0.836707 | + | 0.836707i | −0.988424 | − | 0.151717i | \(-0.951520\pi\) |
0.151717 | + | 0.988424i | \(0.451520\pi\) | |||||||
\(558\) | 6.60568 | + | 20.1654i | 0.279641 | + | 0.853669i | ||||
\(559\) | − | 9.27626i | − | 0.392344i | ||||||
\(560\) | −0.565012 | − | 1.88135i | −0.0238761 | − | 0.0795017i | ||||
\(561\) | 5.87816 | − | 24.6144i | 0.248176 | − | 1.03922i | ||||
\(562\) | 17.0262 | + | 17.0262i | 0.718206 | + | 0.718206i | ||||
\(563\) | −14.6245 | − | 14.6245i | −0.616349 | − | 0.616349i | 0.328244 | − | 0.944593i | \(-0.393543\pi\) |
−0.944593 | + | 0.328244i | \(0.893543\pi\) | |||||||
\(564\) | −0.0159358 | + | 0.0667301i | −0.000671019 | + | 0.00280985i | ||||
\(565\) | −3.77221 | − | 12.5605i | −0.158698 | − | 0.528426i | ||||
\(566\) | − | 27.2563i | − | 1.14567i | ||||||
\(567\) | −1.19934 | + | 7.81492i | −0.0503676 | + | 0.328196i | ||||
\(568\) | 1.59529 | − | 1.59529i | 0.0669369 | − | 0.0669369i | ||||
\(569\) | 45.5814 | 1.91087 | 0.955436 | − | 0.295197i | \(-0.0953854\pi\) | ||||
0.955436 | + | 0.295197i | \(0.0953854\pi\) | |||||||
\(570\) | 20.3115 | − | 22.7850i | 0.850754 | − | 0.954360i | ||||
\(571\) | −13.8634 | −0.580166 | −0.290083 | − | 0.957001i | \(-0.593683\pi\) | ||||
−0.290083 | + | 0.957001i | \(0.593683\pi\) | |||||||
\(572\) | −3.03324 | + | 3.03324i | −0.126826 | + | 0.126826i | ||||
\(573\) | −15.6780 | + | 9.63337i | −0.654957 | + | 0.402440i | ||||
\(574\) | − | 1.55700i | − | 0.0649880i | ||||||
\(575\) | 1.00262 | − | 4.89844i | 0.0418123 | − | 0.204279i | ||||
\(576\) | −2.67628 | − | 1.35555i | −0.111512 | − | 0.0564814i | ||||
\(577\) | 26.2357 | + | 26.2357i | 1.09221 | + | 1.09221i | 0.995293 | + | 0.0969147i | \(0.0308974\pi\) |
0.0969147 | + | 0.995293i | \(0.469103\pi\) | |||||||
\(578\) | −3.16851 | − | 3.16851i | −0.131792 | − | 0.131792i | ||||
\(579\) | −1.74602 | − | 0.416968i | −0.0725622 | − | 0.0173286i | ||||
\(580\) | 8.30468 | − | 15.4339i | 0.344833 | − | 0.640858i | ||||
\(581\) | 2.74913i | 0.114053i | ||||||||
\(582\) | −15.1634 | − | 24.6779i | −0.628543 | − | 1.02293i | ||||
\(583\) | −40.3494 | + | 40.3494i | −1.67110 | + | 1.67110i | ||||
\(584\) | −12.0030 | −0.496689 | ||||||||
\(585\) | −1.22760 | + | 6.85956i | −0.0507549 | + | 0.283608i | ||||
\(586\) | 24.8553 | 1.02677 | ||||||||
\(587\) | 1.72536 | − | 1.72536i | 0.0712134 | − | 0.0712134i | −0.670603 | − | 0.741816i | \(-0.733965\pi\) |
0.741816 | + | 0.670603i | \(0.233965\pi\) | |||||||
\(588\) | −5.64757 | − | 9.19122i | −0.232902 | − | 0.379039i | ||||
\(589\) | 55.7461i | 2.29698i | ||||||||
\(590\) | −23.4780 | + | 7.05097i | −0.966576 | + | 0.290284i | ||||
\(591\) | 24.9555 | + | 5.95963i | 1.02653 | + | 0.245146i | ||||
\(592\) | 6.46585 | + | 6.46585i | 0.265745 | + | 0.265745i | ||||
\(593\) | 2.77888 | + | 2.77888i | 0.114115 | + | 0.114115i | 0.761858 | − | 0.647744i | \(-0.224287\pi\) |
−0.647744 | + | 0.761858i | \(0.724287\pi\) | |||||||
\(594\) | 16.3660 | + | 13.8763i | 0.671507 | + | 0.569353i | ||||
\(595\) | −6.12057 | − | 3.29336i | −0.250919 | − | 0.135015i | ||||
\(596\) | 6.11984i | 0.250678i | ||||||||
\(597\) | 4.46280 | − | 2.74218i | 0.182650 | − | 0.112230i | ||||
\(598\) | −0.734549 | + | 0.734549i | −0.0300379 | + | 0.0300379i | ||||
\(599\) | −37.0107 | −1.51222 | −0.756108 | − | 0.654447i | \(-0.772902\pi\) | ||||
−0.756108 | + | 0.654447i | \(0.772902\pi\) | |||||||
\(600\) | −8.13792 | + | 2.96214i | −0.332229 | + | 0.120929i | ||||
\(601\) | 34.9685 | 1.42639 | 0.713196 | − | 0.700964i | \(-0.247247\pi\) | ||||
0.713196 | + | 0.700964i | \(0.247247\pi\) | |||||||
\(602\) | −5.54701 | + | 5.54701i | −0.226079 | + | 0.226079i | ||||
\(603\) | −43.6601 | + | 14.3020i | −1.77798 | + | 0.582421i | ||||
\(604\) | − | 8.00975i | − | 0.325912i | ||||||
\(605\) | 11.9167 | + | 6.41216i | 0.484484 | + | 0.260692i | ||||
\(606\) | −0.548091 | + | 2.29509i | −0.0222647 | + | 0.0932317i | ||||
\(607\) | −3.77458 | − | 3.77458i | −0.153205 | − | 0.153205i | 0.626343 | − | 0.779548i | \(-0.284551\pi\) |
−0.779548 | + | 0.626343i | \(0.784551\pi\) | |||||||
\(608\) | −5.57289 | − | 5.57289i | −0.226011 | − | 0.226011i | ||||
\(609\) | −2.77021 | + | 11.6001i | −0.112255 | + | 0.470058i | ||||
\(610\) | 23.7374 | − | 7.12887i | 0.961100 | − | 0.288640i | ||||
\(611\) | − | 0.0411472i | − | 0.00166464i | ||||||
\(612\) | −10.0873 | + | 3.30433i | −0.407753 | + | 0.133570i | ||||
\(613\) | −12.5789 | + | 12.5789i | −0.508056 | + | 0.508056i | −0.913929 | − | 0.405873i | \(-0.866967\pi\) |
0.405873 | + | 0.913929i | \(0.366967\pi\) | |||||||
\(614\) | −8.97021 | −0.362008 | ||||||||
\(615\) | −6.85305 | + | 0.393335i | −0.276342 | + | 0.0158608i | ||||
\(616\) | 3.62763 | 0.146161 | ||||||||
\(617\) | 3.87788 | − | 3.87788i | 0.156118 | − | 0.156118i | −0.624726 | − | 0.780844i | \(-0.714789\pi\) |
0.780844 | + | 0.624726i | \(0.214789\pi\) | |||||||
\(618\) | −7.04547 | + | 4.32911i | −0.283410 | + | 0.174142i | ||||
\(619\) | − | 8.64542i | − | 0.347489i | −0.984791 | − | 0.173744i | \(-0.944413\pi\) | ||
0.984791 | − | 0.173744i | \(-0.0555867\pi\) | |||||||
\(620\) | 7.49438 | − | 13.9280i | 0.300981 | − | 0.559361i | ||||
\(621\) | 3.96331 | + | 3.36039i | 0.159042 | + | 0.134848i | ||||
\(622\) | −1.09548 | − | 1.09548i | −0.0439248 | − | 0.0439248i | ||||
\(623\) | 3.78184 | + | 3.78184i | 0.151516 | + | 0.151516i | ||||
\(624\) | 1.75006 | + | 0.417931i | 0.0700584 | + | 0.0167306i | ||||
\(625\) | −9.82260 | + | 22.9895i | −0.392904 | + | 0.919579i | ||||
\(626\) | 0.635161i | 0.0253861i | ||||||||
\(627\) | 29.5105 | + | 48.0273i | 1.17854 | + | 1.91802i | ||||
\(628\) | −9.56563 | + | 9.56563i | −0.381710 | + | 0.381710i | ||||
\(629\) | 32.3539 | 1.29003 | ||||||||
\(630\) | 4.83596 | − | 3.36780i | 0.192669 | − | 0.134176i | ||||
\(631\) | −41.6995 | −1.66003 | −0.830015 | − | 0.557742i | \(-0.811668\pi\) | ||||
−0.830015 | + | 0.557742i | \(0.811668\pi\) | |||||||
\(632\) | 1.40159 | − | 1.40159i | 0.0557521 | − | 0.0557521i | ||||
\(633\) | −17.5098 | − | 28.4966i | −0.695952 | − | 1.13264i | ||||
\(634\) | − | 25.1527i | − | 0.998943i | ||||||
\(635\) | −7.58695 | − | 25.2627i | −0.301079 | − | 1.00252i | ||||
\(636\) | 23.2800 | + | 5.55950i | 0.923112 | + | 0.220448i | ||||
\(637\) | 4.57496 | + | 4.57496i | 0.181266 | + | 0.181266i | ||||
\(638\) | 22.8864 | + | 22.8864i | 0.906081 | + | 0.906081i | ||||
\(639\) | 6.03790 | + | 3.05824i | 0.238856 | + | 0.120982i | ||||
\(640\) | 0.643162 | + | 2.14157i | 0.0254232 | + | 0.0846532i | ||||
\(641\) | − | 2.72989i | − | 0.107824i | −0.998546 | − | 0.0539121i | \(-0.982831\pi\) | ||
0.998546 | − | 0.0539121i | \(-0.0171691\pi\) | |||||||
\(642\) | 5.00468 | − | 3.07514i | 0.197519 | − | 0.121366i | ||||
\(643\) | 17.4028 | − | 17.4028i | 0.686298 | − | 0.686298i | −0.275114 | − | 0.961412i | \(-0.588715\pi\) |
0.961412 | + | 0.275114i | \(0.0887155\pi\) | |||||||
\(644\) | 0.878491 | 0.0346174 | ||||||||
\(645\) | 25.8161 | + | 23.0135i | 1.01651 | + | 0.906157i | ||||
\(646\) | −27.8857 | −1.09715 | ||||||||
\(647\) | −9.72994 | + | 9.72994i | −0.382523 | + | 0.382523i | −0.872011 | − | 0.489487i | \(-0.837184\pi\) |
0.489487 | + | 0.872011i | \(0.337184\pi\) | |||||||
\(648\) | 1.36523 | − | 8.89585i | 0.0536313 | − | 0.349462i | ||||
\(649\) | − | 45.2704i | − | 1.77702i | ||||||
\(650\) | 4.33462 | − | 2.86167i | 0.170018 | − | 0.112244i | ||||
\(651\) | −2.49992 | + | 10.4682i | −0.0979795 | + | 0.410282i | ||||
\(652\) | −1.30077 | − | 1.30077i | −0.0509420 | − | 0.0509420i | ||||
\(653\) | −21.5513 | − | 21.5513i | −0.843367 | − | 0.843367i | 0.145928 | − | 0.989295i | \(-0.453383\pi\) |
−0.989295 | + | 0.145928i | \(0.953383\pi\) | |||||||
\(654\) | −0.213994 | + | 0.896084i | −0.00836782 | + | 0.0350396i | ||||
\(655\) | 2.84737 | − | 5.29172i | 0.111256 | − | 0.206765i | ||||
\(656\) | 1.77236i | 0.0691991i | ||||||||
\(657\) | −11.2096 | − | 34.2199i | −0.437327 | − | 1.33504i | ||||
\(658\) | −0.0246052 | + | 0.0246052i | −0.000959211 | + | 0.000959211i | ||||
\(659\) | −44.3615 | −1.72808 | −0.864039 | − | 0.503425i | \(-0.832073\pi\) | ||||
−0.864039 | + | 0.503425i | \(0.832073\pi\) | |||||||
\(660\) | −0.916422 | − | 15.9668i | −0.0356717 | − | 0.621506i | ||||
\(661\) | 43.3242 | 1.68512 | 0.842559 | − | 0.538605i | \(-0.181048\pi\) | ||||
0.842559 | + | 0.538605i | \(0.181048\pi\) | |||||||
\(662\) | 6.85215 | − | 6.85215i | 0.266316 | − | 0.266316i | ||||
\(663\) | 5.42410 | − | 3.33285i | 0.210655 | − | 0.129437i | ||||
\(664\) | − | 3.12938i | − | 0.121443i | ||||||
\(665\) | 14.8274 | − | 4.45300i | 0.574983 | − | 0.172680i | ||||
\(666\) | −12.3953 | + | 24.4721i | −0.480308 | + | 0.948276i | ||||
\(667\) | 5.54232 | + | 5.54232i | 0.214599 | + | 0.214599i | ||||
\(668\) | 7.75358 | + | 7.75358i | 0.299995 | + | 0.299995i | ||||
\(669\) | −18.7672 | − | 4.48180i | −0.725582 | − | 0.173276i | ||||
\(670\) | 30.1555 | + | 16.2261i | 1.16501 | + | 0.626868i | ||||
\(671\) | 45.7705i | 1.76695i | ||||||||
\(672\) | −0.796585 | − | 1.29641i | −0.0307289 | − | 0.0500103i | ||||
\(673\) | −30.3342 | + | 30.3342i | −1.16930 | + | 1.16930i | −0.186921 | + | 0.982375i | \(0.559851\pi\) |
−0.982375 | + | 0.186921i | \(0.940149\pi\) | |||||||
\(674\) | −7.05614 | −0.271792 | ||||||||
\(675\) | −16.0448 | − | 20.4344i | −0.617566 | − | 0.786519i | ||||
\(676\) | 11.9209 | 0.458495 | ||||||||
\(677\) | 8.39686 | − | 8.39686i | 0.322718 | − | 0.322718i | −0.527091 | − | 0.849809i | \(-0.676717\pi\) |
0.849809 | + | 0.527091i | \(0.176717\pi\) | |||||||
\(678\) | −5.31826 | − | 8.65529i | −0.204247 | − | 0.332404i | ||||
\(679\) | − | 14.6906i | − | 0.563773i | ||||||
\(680\) | 6.96715 | + | 3.74889i | 0.267178 | + | 0.143763i | ||||
\(681\) | 19.3454 | + | 4.61987i | 0.741317 | + | 0.177034i | ||||
\(682\) | 20.6533 | + | 20.6533i | 0.790856 | + | 0.790856i | ||||
\(683\) | −16.0879 | − | 16.0879i | −0.615584 | − | 0.615584i | 0.328811 | − | 0.944396i | \(-0.393352\pi\) |
−0.944396 | + | 0.328811i | \(0.893352\pi\) | |||||||
\(684\) | 10.6835 | − | 21.0925i | 0.408492 | − | 0.806490i | ||||
\(685\) | −11.3845 | + | 3.41903i | −0.434981 | + | 0.130634i | ||||
\(686\) | − | 11.6209i | − | 0.443688i | ||||||
\(687\) | 13.0318 | − | 8.00744i | 0.497196 | − | 0.305503i | ||||
\(688\) | 6.31426 | − | 6.31426i | 0.240729 | − | 0.240729i | ||||
\(689\) | −14.3549 | −0.546880 | ||||||||
\(690\) | −0.221927 | − | 3.86662i | −0.00844861 | − | 0.147200i | ||||
\(691\) | −13.0690 | −0.497169 | −0.248585 | − | 0.968610i | \(-0.579965\pi\) | ||||
−0.248585 | + | 0.968610i | \(0.579965\pi\) | |||||||
\(692\) | −10.4290 | + | 10.4290i | −0.396449 | + | 0.396449i | ||||
\(693\) | 3.38783 | + | 10.3421i | 0.128693 | + | 0.392865i | ||||
\(694\) | − | 15.8811i | − | 0.602837i | ||||||
\(695\) | 22.0181 | − | 40.9197i | 0.835193 | − | 1.55217i | ||||
\(696\) | 3.15338 | − | 13.2045i | 0.119528 | − | 0.500517i | ||||
\(697\) | 4.43428 | + | 4.43428i | 0.167960 | + | 0.167960i | ||||
\(698\) | 16.8869 | + | 16.8869i | 0.639178 | + | 0.639178i | ||||
\(699\) | −7.59778 | + | 31.8152i | −0.287374 | + | 1.20336i | ||||
\(700\) | −4.30324 | − | 0.880797i | −0.162647 | − | 0.0332910i | ||||
\(701\) | 26.8220i | 1.01305i | 0.862225 | + | 0.506526i | \(0.169070\pi\) | ||||
−0.862225 | + | 0.506526i | \(0.830930\pi\) | |||||||
\(702\) | 0.442875 | + | 5.37961i | 0.0167152 | + | 0.203040i | ||||
\(703\) | −50.9590 | + | 50.9590i | −1.92196 | + | 1.92196i | ||||
\(704\) | −4.12939 | −0.155632 | ||||||||
\(705\) | 0.114514 | + | 0.102082i | 0.00431285 | + | 0.00384465i | ||||
\(706\) | 17.2394 | 0.648813 | ||||||||
\(707\) | −0.846263 | + | 0.846263i | −0.0318270 | + | 0.0318270i | ||||
\(708\) | −16.1784 | + | 9.94085i | −0.608021 | + | 0.373600i | ||||
\(709\) | − | 4.26519i | − | 0.160183i | −0.996788 | − | 0.0800914i | \(-0.974479\pi\) | ||
0.996788 | − | 0.0800914i | \(-0.0255212\pi\) | |||||||
\(710\) | −1.45103 | − | 4.83156i | −0.0544560 | − | 0.181325i | ||||
\(711\) | 5.30476 | + | 2.68690i | 0.198944 | + | 0.100766i | ||||
\(712\) | −4.30493 | − | 4.30493i | −0.161334 | − | 0.161334i | ||||
\(713\) | 5.00154 | + | 5.00154i | 0.187309 | + | 0.187309i | ||||
\(714\) | −5.23649 | − | 1.25053i | −0.195971 | − | 0.0467997i | ||||
\(715\) | 2.75894 | + | 9.18659i | 0.103178 | + | 0.343559i | ||||
\(716\) | − | 0.719378i | − | 0.0268844i | ||||||
\(717\) | 4.80376 | + | 7.81796i | 0.179400 | + | 0.291967i | ||||
\(718\) | −5.06500 | + | 5.06500i | −0.189024 | + | 0.189024i | ||||
\(719\) | 34.9727 | 1.30426 | 0.652130 | − | 0.758107i | \(-0.273875\pi\) | ||||
0.652130 | + | 0.758107i | \(0.273875\pi\) | |||||||
\(720\) | −5.50485 | + | 3.83362i | −0.205154 | + | 0.142871i | ||||
\(721\) | −4.19412 | −0.156197 | ||||||||
\(722\) | 30.4864 | − | 30.4864i | 1.13459 | − | 1.13459i | ||||
\(723\) | 2.94081 | + | 4.78606i | 0.109370 | + | 0.177996i | ||||
\(724\) | − | 16.7156i | − | 0.621229i | ||||||
\(725\) | −21.5919 | − | 32.7056i | −0.801902 | − | 1.21466i | ||||
\(726\) | 10.1954 | + | 2.43477i | 0.378388 | + | 0.0903627i | ||||
\(727\) | 13.4827 | + | 13.4827i | 0.500044 | + | 0.500044i | 0.911452 | − | 0.411407i | \(-0.134963\pi\) |
−0.411407 | + | 0.911452i | \(0.634963\pi\) | |||||||
\(728\) | 0.645294 | + | 0.645294i | 0.0239162 | + | 0.0239162i | ||||
\(729\) | 26.6365 | − | 4.41561i | 0.986537 | − | 0.163541i | ||||
\(730\) | −12.7177 | + | 23.6352i | −0.470702 | + | 0.874779i | ||||
\(731\) | − | 31.5953i | − | 1.16860i | ||||||
\(732\) | 16.3571 | − | 10.0507i | 0.604577 | − | 0.371484i | ||||
\(733\) | 32.6105 | − | 32.6105i | 1.20450 | − | 1.20450i | 0.231710 | − | 0.972785i | \(-0.425568\pi\) |
0.972785 | − | 0.231710i | \(-0.0744321\pi\) | |||||||
\(734\) | −18.8827 | −0.696971 | ||||||||
\(735\) | −24.0823 | + | 1.38222i | −0.888289 | + | 0.0509838i | ||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −44.7165 | + | 44.7165i | −1.64715 | + | 1.64715i | ||||
\(738\) | −5.05289 | + | 1.65520i | −0.185999 | + | 0.0609288i | ||||
\(739\) | 7.71809i | 0.283915i | 0.989873 | + | 0.141957i | \(0.0453396\pi\) | ||||
−0.989873 | + | 0.141957i | \(0.954660\pi\) | |||||||
\(740\) | 19.5828 | − | 5.88113i | 0.719876 | − | 0.216195i | ||||
\(741\) | −3.29383 | + | 13.7927i | −0.121002 | + | 0.506686i | ||||
\(742\) | 8.58397 | + | 8.58397i | 0.315127 | + | 0.315127i | ||||
\(743\) | −4.77261 | − | 4.77261i | −0.175090 | − | 0.175090i | 0.614121 | − | 0.789212i | \(-0.289511\pi\) |
−0.789212 | + | 0.614121i | \(0.789511\pi\) | |||||||
\(744\) | 2.84570 | − | 11.9162i | 0.104328 | − | 0.436867i | ||||
\(745\) | 12.0506 | + | 6.48420i | 0.441500 | + | 0.237563i | ||||
\(746\) | − | 4.06268i | − | 0.148745i | ||||||
\(747\) | 8.92166 | − | 2.92251i | 0.326427 | − | 0.106929i | ||||
\(748\) | −10.3313 | + | 10.3313i | −0.377751 | + | 0.377751i | ||||
\(749\) | 2.97925 | 0.108859 | ||||||||
\(750\) | −2.78967 | + | 19.1629i | −0.101864 | + | 0.699731i | ||||
\(751\) | −52.9204 | −1.93109 | −0.965547 | − | 0.260229i | \(-0.916202\pi\) | ||||
−0.965547 | + | 0.260229i | \(0.916202\pi\) | |||||||
\(752\) | 0.0280085 | − | 0.0280085i | 0.00102137 | − | 0.00102137i | ||||
\(753\) | 26.0598 | − | 16.0125i | 0.949671 | − | 0.583528i | ||||
\(754\) | 8.14220i | 0.296522i | ||||||||
\(755\) | −15.7721 | − | 8.48664i | −0.574004 | − | 0.308860i | ||||
\(756\) | 2.95207 | − | 3.48173i | 0.107366 | − | 0.126629i | ||||
\(757\) | −4.25493 | − | 4.25493i | −0.154648 | − | 0.154648i | 0.625542 | − | 0.780190i | \(-0.284878\pi\) |
−0.780190 | + | 0.625542i | \(0.784878\pi\) | |||||||
\(758\) | −17.4977 | − | 17.4977i | −0.635546 | − | 0.635546i | ||||
\(759\) | 6.95669 | + | 1.66133i | 0.252512 | + | 0.0603024i | ||||
\(760\) | −16.8783 | + | 5.06893i | −0.612240 | + | 0.183869i | ||||
\(761\) | 10.5196i | 0.381334i | 0.981655 | + | 0.190667i | \(0.0610650\pi\) | ||||
−0.981655 | + | 0.190667i | \(0.938935\pi\) | |||||||
\(762\) | −10.6965 | − | 17.4082i | −0.387493 | − | 0.630632i | ||||
\(763\) | −0.330410 | + | 0.330410i | −0.0119617 | + | 0.0119617i | ||||
\(764\) | 10.6239 | 0.384359 | ||||||||
\(765\) | −4.18125 | + | 23.3640i | −0.151173 | + | 0.844726i | ||||
\(766\) | −22.3463 | −0.807405 | ||||||||
\(767\) | 8.05284 | − | 8.05284i | 0.290771 | − | 0.290771i | ||||
\(768\) | 0.906765 | + | 1.47573i | 0.0327201 | + | 0.0532508i | ||||
\(769\) | − | 20.7974i | − | 0.749972i | −0.927030 | − | 0.374986i | \(-0.877647\pi\) | ||
0.927030 | − | 0.374986i | \(-0.122353\pi\) | |||||||
\(770\) | 3.84361 | − | 7.14319i | 0.138514 | − | 0.257423i | ||||
\(771\) | −9.12801 | − | 2.17986i | −0.328737 | − | 0.0785058i | ||||
\(772\) | 0.732855 | + | 0.732855i | 0.0263760 | + | 0.0263760i | ||||
\(773\) | −7.11987 | − | 7.11987i | −0.256084 | − | 0.256084i | 0.567375 | − | 0.823459i | \(-0.307959\pi\) |
−0.823459 | + | 0.567375i | \(0.807959\pi\) | |||||||
\(774\) | 23.8984 | + | 12.1047i | 0.859010 | + | 0.435094i | ||||
\(775\) | −19.4851 | − | 29.5145i | −0.699926 | − | 1.06019i | ||||
\(776\) | 16.7225i | 0.600303i | ||||||||
\(777\) | −11.8545 | + | 7.28404i | −0.425279 | + | 0.261314i | ||||
\(778\) | −0.954967 | + | 0.954967i | −0.0342372 | + | 0.0342372i | ||||
\(779\) | −13.9684 | −0.500471 | ||||||||
\(780\) | 2.67720 | − | 3.00324i | 0.0958593 | − | 0.107533i | ||||
\(781\) | 9.31623 | 0.333361 | ||||||||
\(782\) | −2.50190 | + | 2.50190i | −0.0894679 | + | 0.0894679i | ||||
\(783\) | 40.5902 | − | 3.34158i | 1.45058 | − | 0.119418i | ||||
\(784\) | 6.22825i | 0.222438i | ||||||||
\(785\) | 8.70060 | + | 28.9709i | 0.310538 | + | 1.03402i | ||||
\(786\) | 1.08118 | − | 4.52736i | 0.0385644 | − | 0.161485i | ||||
\(787\) | −13.3738 | − | 13.3738i | −0.476724 | − | 0.476724i | 0.427358 | − | 0.904082i | \(-0.359444\pi\) |
−0.904082 | + | 0.427358i | \(0.859444\pi\) | |||||||
\(788\) | −10.4745 | − | 10.4745i | −0.373140 | − | 0.373140i | ||||
\(789\) | −5.66123 | + | 23.7060i | −0.201545 | + | 0.843956i | ||||
\(790\) | −1.27484 | − | 4.24490i | −0.0453567 | − | 0.151027i | ||||
\(791\) | − | 5.15243i | − | 0.183199i | ||||||
\(792\) | −3.85642 | − | 11.7726i | −0.137032 | − | 0.418322i | ||||
\(793\) | −8.14181 | + | 8.14181i | −0.289124 | + | 0.289124i | ||||
\(794\) | 7.08495 | 0.251435 | ||||||||
\(795\) | 35.6133 | − | 39.9503i | 1.26307 | − | 1.41689i | ||||
\(796\) | −3.02413 | −0.107188 | ||||||||
\(797\) | −13.4137 | + | 13.4137i | −0.475136 | + | 0.475136i | −0.903572 | − | 0.428436i | \(-0.859065\pi\) |
0.428436 | + | 0.903572i | \(0.359065\pi\) | |||||||
\(798\) | 10.2174 | − | 6.27809i | 0.361691 | − | 0.222242i | ||||
\(799\) | − | 0.140149i | − | 0.00495813i | ||||||
\(800\) | 4.89844 | + | 1.00262i | 0.173186 | + | 0.0354481i | ||||
\(801\) | 8.25273 | − | 16.2934i | 0.291596 | − | 0.575700i | ||||
\(802\) | 9.24316 | + | 9.24316i | 0.326387 | + | 0.326387i | ||||
\(803\) | −35.0479 | − | 35.0479i | −1.23681 | − | 1.23681i | ||||
\(804\) | 25.7997 | + | 6.16122i | 0.909884 | + | 0.217290i | ||||
\(805\) | 0.930794 | − | 1.72984i | 0.0328062 | − | 0.0609689i | ||||
\(806\) | 7.34775i | 0.258814i | ||||||||
\(807\) | −9.50218 | − | 15.4645i | −0.334492 | − | 0.544375i | ||||
\(808\) | 0.963314 | − | 0.963314i | 0.0338893 | − | 0.0338893i | ||||
\(809\) | 38.5121 | 1.35401 | 0.677007 | − | 0.735977i | \(-0.263277\pi\) | ||||
0.677007 | + | 0.735977i | \(0.263277\pi\) | |||||||
\(810\) | −16.0704 | − | 12.1138i | −0.564655 | − | 0.425635i | ||||
\(811\) | 19.8732 | 0.697842 | 0.348921 | − | 0.937152i | \(-0.386548\pi\) | ||||
0.348921 | + | 0.937152i | \(0.386548\pi\) | |||||||
\(812\) | 4.86887 | − | 4.86887i | 0.170864 | − | 0.170864i | ||||
\(813\) | −13.9871 | − | 22.7636i | −0.490551 | − | 0.798354i | ||||
\(814\) | 37.7595i | 1.32347i | ||||||||
\(815\) | −3.93956 | + | 1.18314i | −0.137997 | + | 0.0414435i | ||||
\(816\) | 5.96077 | + | 1.42349i | 0.208669 | + | 0.0498322i | ||||
\(817\) | 49.7643 | + | 49.7643i | 1.74103 | + | 1.74103i | ||||
\(818\) | 11.1481 | + | 11.1481i | 0.389784 | + | 0.389784i | ||||
\(819\) | −1.23706 | + | 2.44233i | −0.0432262 | + | 0.0853419i | ||||
\(820\) | 3.48997 | + | 1.87788i | 0.121875 | + | 0.0655785i | ||||
\(821\) | 1.22214i | 0.0426530i | 0.999773 | + | 0.0213265i | \(0.00678895\pi\) | ||||
−0.999773 | + | 0.0213265i | \(0.993211\pi\) | |||||||
\(822\) | −7.84493 | + | 4.82034i | −0.273623 | + | 0.168129i | ||||
\(823\) | 8.41266 | − | 8.41266i | 0.293247 | − | 0.293247i | −0.545115 | − | 0.838362i | \(-0.683514\pi\) |
0.838362 | + | 0.545115i | \(0.183514\pi\) | |||||||
\(824\) | 4.77423 | 0.166318 | ||||||||
\(825\) | −32.4113 | − | 15.1129i | −1.12842 | − | 0.526163i | ||||
\(826\) | −9.63087 | −0.335101 | ||||||||
\(827\) | −25.7734 | + | 25.7734i | −0.896227 | + | 0.896227i | −0.995100 | − | 0.0988727i | \(-0.968476\pi\) |
0.0988727 | + | 0.995100i | \(0.468476\pi\) | |||||||
\(828\) | −0.933895 | − | 2.85094i | −0.0324551 | − | 0.0990769i | ||||
\(829\) | − | 9.26672i | − | 0.321846i | −0.986967 | − | 0.160923i | \(-0.948553\pi\) | ||
0.986967 | − | 0.160923i | \(-0.0514471\pi\) | |||||||
\(830\) | −6.16208 | − | 3.31570i | −0.213889 | − | 0.115089i | ||||
\(831\) | 4.64989 | − | 19.4711i | 0.161303 | − | 0.675445i | ||||
\(832\) | −0.734549 | − | 0.734549i | −0.0254659 | − | 0.0254659i | ||||
\(833\) | 15.5825 | + | 15.5825i | 0.539902 | + | 0.539902i | ||||
\(834\) | 8.36050 | − | 35.0090i | 0.289501 | − | 1.21226i | ||||
\(835\) | 23.4828 | − | 7.05241i | 0.812657 | − | 0.244059i | ||||
\(836\) | − | 32.5448i | − | 1.12558i | ||||||
\(837\) | 36.6298 | − | 3.01554i | 1.26611 | − | 0.104232i | ||||
\(838\) | 20.1049 | − | 20.1049i | 0.694514 | − | 0.694514i | ||||
\(839\) | −0.301061 | −0.0103938 | −0.00519690 | − | 0.999986i | \(-0.501654\pi\) | ||||
−0.00519690 | + | 0.999986i | \(0.501654\pi\) | |||||||
\(840\) | −3.39679 | + | 0.194961i | −0.117200 | + | 0.00672678i | ||||
\(841\) | 32.4346 | 1.11843 | ||||||||
\(842\) | −16.9824 | + | 16.9824i | −0.585252 | + | 0.585252i | ||||
\(843\) | 35.5336 | − | 21.8337i | 1.22384 | − | 0.751993i | ||||
\(844\) | 19.3102i | 0.664684i | ||||||||
\(845\) | 12.6306 | − | 23.4735i | 0.434507 | − | 0.807512i | ||||
\(846\) | 0.106008 | + | 0.0536935i | 0.00364461 | + | 0.00184602i | ||||
\(847\) | 3.75933 | + | 3.75933i | 0.129172 | + | 0.129172i | ||||
\(848\) | −9.77127 | − | 9.77127i | −0.335547 | − | 0.335547i | ||||
\(849\) | −45.9180 | − | 10.9657i | −1.57590 | − | 0.376341i | ||||
\(850\) | 14.7639 | − | 9.74697i | 0.506398 | − | 0.334318i | ||||
\(851\) | 9.14409i | 0.313455i | ||||||||
\(852\) | −2.04574 | − | 3.32936i | −0.0700857 | − | 0.114062i | ||||
\(853\) | 7.46140 | − | 7.46140i | 0.255474 | − | 0.255474i | −0.567737 | − | 0.823210i | \(-0.692181\pi\) |
0.823210 | + | 0.567737i | \(0.192181\pi\) | |||||||
\(854\) | 9.73727 | 0.333203 | ||||||||
\(855\) | −30.2138 | − | 43.3851i | −1.03329 | − | 1.48374i | ||||
\(856\) | −3.39132 | −0.115913 | ||||||||
\(857\) | 4.73782 | − | 4.73782i | 0.161841 | − | 0.161841i | −0.621541 | − | 0.783382i | \(-0.713493\pi\) |
0.783382 | + | 0.621541i | \(0.213493\pi\) | |||||||
\(858\) | 3.88970 | + | 6.33035i | 0.132792 | + | 0.216115i | ||||
\(859\) | 8.54021i | 0.291388i | 0.989330 | + | 0.145694i | \(0.0465416\pi\) | ||||
−0.989330 | + | 0.145694i | \(0.953458\pi\) | |||||||
\(860\) | −5.74325 | − | 19.1236i | −0.195843 | − | 0.652110i | ||||
\(861\) | −2.62305 | − | 0.626410i | −0.0893933 | − | 0.0213480i | ||||
\(862\) | −19.0536 | − | 19.0536i | −0.648967 | − | 0.648967i | ||||
\(863\) | 11.2556 | + | 11.2556i | 0.383144 | + | 0.383144i | 0.872234 | − | 0.489090i | \(-0.162671\pi\) |
−0.489090 | + | 0.872234i | \(0.662671\pi\) | |||||||
\(864\) | −3.36039 | + | 3.96331i | −0.114323 | + | 0.134834i | ||||
\(865\) | 9.48585 | + | 31.5856i | 0.322529 | + | 1.07394i | ||||
\(866\) | 14.3670i | 0.488212i | ||||||||
\(867\) | −6.61266 | + | 4.06316i | −0.224578 | + | 0.137992i | ||||
\(868\) | 4.39381 | − | 4.39381i | 0.149136 | − | 0.149136i | ||||
\(869\) | 8.18503 | 0.277658 | ||||||||
\(870\) | −22.6600 | − | 20.2000i | −0.768247 | − | 0.684846i | ||||
\(871\) | −15.9086 | −0.539043 | ||||||||
\(872\) | 0.376112 | − | 0.376112i | 0.0127367 | − | 0.0127367i | ||||
\(873\) | −47.6748 | + | 15.6171i | −1.61355 | + | 0.528558i | ||||
\(874\) | − | 7.88126i | − | 0.266588i | ||||||
\(875\) | −6.29382 | + | 7.54029i | −0.212770 | + | 0.254908i | ||||
\(876\) | −4.82904 | + | 20.2212i | −0.163158 | + | 0.683212i | ||||
\(877\) | −12.3346 | − | 12.3346i | −0.416510 | − | 0.416510i | 0.467489 | − | 0.883999i | \(-0.345159\pi\) |
−0.883999 | + | 0.467489i | \(0.845159\pi\) | |||||||
\(878\) | 1.70577 | + | 1.70577i | 0.0575670 | + | 0.0575670i | ||||
\(879\) | 9.99976 | − | 41.8733i | 0.337283 | − | 1.41235i | ||||
\(880\) | −4.37524 | + | 8.13121i | −0.147489 | + | 0.274103i | ||||
\(881\) | 48.9725i | 1.64992i | 0.565188 | + | 0.824962i | \(0.308804\pi\) | ||||
−0.565188 | + | 0.824962i | \(0.691196\pi\) | |||||||
\(882\) | −17.7564 | + | 5.81654i | −0.597888 | + | 0.195853i | ||||
\(883\) | −20.3767 | + | 20.3767i | −0.685732 | + | 0.685732i | −0.961286 | − | 0.275554i | \(-0.911139\pi\) |
0.275554 | + | 0.961286i | \(0.411139\pi\) | |||||||
\(884\) | −3.67554 | −0.123622 | ||||||||
\(885\) | 2.43298 | + | 42.3897i | 0.0817837 | + | 1.42491i | ||||
\(886\) | −10.7135 | −0.359927 | ||||||||
\(887\) | −35.8940 | + | 35.8940i | −1.20520 | + | 1.20520i | −0.232638 | + | 0.972563i | \(0.574736\pi\) |
−0.972563 | + | 0.232638i | \(0.925264\pi\) | |||||||
\(888\) | 13.4942 | − | 8.29154i | 0.452836 | − | 0.278246i | ||||
\(889\) | − | 10.3630i | − | 0.347563i | ||||||
\(890\) | −13.0381 | + | 3.91563i | −0.437038 | + | 0.131252i | ||||
\(891\) | 29.9615 | − | 21.9888i | 1.00375 | − | 0.736653i | ||||
\(892\) | 7.87712 | + | 7.87712i | 0.263746 | + | 0.263746i | ||||
\(893\) | 0.220742 | + | 0.220742i | 0.00738686 | + | 0.00738686i | ||||
\(894\) | 10.3100 | + | 2.46212i | 0.344817 | + | 0.0823457i | ||||
\(895\) | −1.41653 | − | 0.762208i | −0.0473494 | − | 0.0254778i | ||||
\(896\) | 0.878491i | 0.0293483i | ||||||||
\(897\) | 0.941956 | + | 1.53300i | 0.0314510 | + | 0.0511854i | ||||
\(898\) | −22.3903 | + | 22.3903i | −0.747174 | + | 0.747174i | ||||
\(899\) | 55.4403 | 1.84904 | ||||||||
\(900\) | 1.71621 | + | 14.9015i | 0.0572071 | + | 0.496717i | ||||
\(901\) | −48.8936 | −1.62888 | ||||||||
\(902\) | −5.17515 | + | 5.17515i | −0.172314 | + | 0.172314i | ||||
\(903\) | 7.11327 | + | 11.5766i | 0.236715 | + | 0.385245i | ||||
\(904\) | 5.86509i | 0.195070i | ||||||||
\(905\) | −32.9147 | − | 17.7108i | −1.09412 | − | 0.588726i | ||||
\(906\) | −13.4939 | − | 3.22247i | −0.448303 | − | 0.107059i | ||||
\(907\) | 9.80890 | + | 9.80890i | 0.325699 | + | 0.325699i | 0.850948 | − | 0.525249i | \(-0.176028\pi\) |
−0.525249 | + | 0.850948i | \(0.676028\pi\) | |||||||
\(908\) | −8.11980 | − | 8.11980i | −0.269465 | − | 0.269465i | ||||
\(909\) | 3.64598 | + | 1.84671i | 0.120930 | + | 0.0612516i | ||||
\(910\) | 1.95437 | − | 0.586939i | 0.0647866 | − | 0.0194568i | ||||
\(911\) | − | 39.2776i | − | 1.30132i | −0.759368 | − | 0.650662i | \(-0.774492\pi\) | ||
0.759368 | − | 0.650662i | \(-0.225508\pi\) | |||||||
\(912\) | −11.6306 | + | 7.14645i | −0.385128 | + | 0.236643i | ||||
\(913\) | 9.13753 | − | 9.13753i | 0.302408 | − | 0.302408i | ||||
\(914\) | 38.4890 | 1.27310 | ||||||||
\(915\) | −2.45986 | − | 42.8580i | −0.0813204 | − | 1.41684i | ||||
\(916\) | −8.83078 | −0.291777 | ||||||||
\(917\) | 1.66936 | − | 1.66936i | 0.0551271 | − | 0.0551271i | ||||
\(918\) | 1.50845 | + | 18.3232i | 0.0497863 | + | 0.604755i | ||||
\(919\) | − | 7.64006i | − | 0.252022i | −0.992029 | − | 0.126011i | \(-0.959782\pi\) | ||
0.992029 | − | 0.126011i | \(-0.0402175\pi\) | |||||||
\(920\) | −1.05954 | + | 1.96911i | −0.0349319 | + | 0.0649195i | ||||
\(921\) | −3.60888 | + | 15.1119i | −0.118917 | + | 0.497954i | ||||
\(922\) | −13.5095 | − | 13.5095i | −0.444912 | − | 0.444912i | ||||
\(923\) | 1.65720 | + | 1.65720i | 0.0545474 | + | 0.0545474i | ||||
\(924\) | 1.45946 | − | 6.11139i | 0.0480127 | − | 0.201050i | ||||
\(925\) | 9.16809 | − | 44.7918i | 0.301445 | − | 1.47275i | ||||
\(926\) | 25.4467i | 0.836230i | ||||||||
\(927\) | 4.45863 | + | 13.6110i | 0.146441 | + | 0.447045i | ||||
\(928\) | −5.54232 | + | 5.54232i | −0.181936 | + | 0.181936i | ||||
\(929\) | 7.70924 | 0.252932 | 0.126466 | − | 0.991971i | \(-0.459637\pi\) | ||||
0.126466 | + | 0.991971i | \(0.459637\pi\) | |||||||
\(930\) | −20.4490 | − | 18.2291i | −0.670551 | − | 0.597755i | ||||
\(931\) | −49.0865 | −1.60874 | ||||||||
\(932\) | 13.3537 | − | 13.3537i | 0.437416 | − | 0.437416i | ||||
\(933\) | −2.28626 | + | 1.40480i | −0.0748489 | + | 0.0459911i | ||||
\(934\) | − | 19.1520i | − | 0.626673i | ||||||
\(935\) | 9.39706 | + | 31.2899i | 0.307317 | + | 1.02329i | ||||
\(936\) | 1.40816 | − | 2.78014i | 0.0460271 | − | 0.0908718i | ||||
\(937\) | −10.1233 | − | 10.1233i | −0.330713 | − | 0.330713i | 0.522144 | − | 0.852857i | \(-0.325132\pi\) |
−0.852857 | + | 0.522144i | \(0.825132\pi\) | |||||||
\(938\) | 9.51304 | + | 9.51304i | 0.310612 | + | 0.310612i | ||||
\(939\) | 1.07004 | + | 0.255537i | 0.0349195 | + | 0.00833912i | ||||
\(940\) | −0.0254757 | − | 0.0848278i | −0.000830925 | − | 0.00276678i | ||||
\(941\) | 19.0647i | 0.621492i | 0.950493 | + | 0.310746i | \(0.100579\pi\) | ||||
−0.950493 | + | 0.310746i | \(0.899421\pi\) | |||||||
\(942\) | 12.2666 | + | 19.9634i | 0.399667 | + | 0.650444i | ||||
\(943\) | −1.25325 | + | 1.25325i | −0.0408114 | + | 0.0408114i | ||||
\(944\) | 10.9630 | 0.356815 | ||||||||
\(945\) | −3.72807 | − | 9.50196i | −0.121274 | − | 0.309099i | ||||
\(946\) | 36.8742 | 1.19888 | ||||||||
\(947\) | −16.0189 | + | 16.0189i | −0.520543 | + | 0.520543i | −0.917735 | − | 0.397192i | \(-0.869985\pi\) |
0.397192 | + | 0.917735i | \(0.369985\pi\) | |||||||
\(948\) | −1.79734 | − | 2.92510i | −0.0583748 | − | 0.0950029i | ||||
\(949\) | − | 12.4689i | − | 0.404756i | ||||||
\(950\) | −7.90195 | + | 38.6059i | −0.256373 | + | 1.25254i | ||||
\(951\) | −42.3743 | − | 10.1194i | −1.37408 | − | 0.328144i | ||||
\(952\) | 2.19790 | + | 2.19790i | 0.0712344 | + | 0.0712344i | ||||
\(953\) | −23.5761 | − | 23.5761i | −0.763704 | − | 0.763704i | 0.213286 | − | 0.976990i | \(-0.431583\pi\) |
−0.976990 | + | 0.213286i | \(0.931583\pi\) | |||||||
\(954\) | 18.7319 | − | 36.9826i | 0.606468 | − | 1.19736i | ||||
\(955\) | 11.2564 | − | 20.9196i | 0.364249 | − | 0.676941i | ||||
\(956\) | − | 5.29769i | − | 0.171340i | ||||||
\(957\) | 47.7638 | − | 29.3486i | 1.54398 | − | 0.948705i | ||||
\(958\) | −7.17891 | + | 7.17891i | −0.231940 | + | 0.231940i | ||||
\(959\) | −4.67003 | −0.150803 | ||||||||
\(960\) | 3.86662 | − | 0.221927i | 0.124795 | − | 0.00716266i | ||||
\(961\) | 19.0309 | 0.613899 | ||||||||
\(962\) | −6.71678 | + | 6.71678i | −0.216558 | + | 0.216558i | ||||
\(963\) | −3.16714 | − | 9.66845i | −0.102060 | − | 0.311561i | ||||
\(964\) | − | 3.24318i | − | 0.104456i | ||||||
\(965\) | 2.21956 | − | 0.666581i | 0.0714500 | − | 0.0214580i | ||||
\(966\) | 0.353433 | − | 1.47997i | 0.0113715 | − | 0.0476174i | ||||
\(967\) | −27.9358 | − | 27.9358i | −0.898354 | − | 0.898354i | 0.0969368 | − | 0.995291i | \(-0.469096\pi\) |
−0.995291 | + | 0.0969368i | \(0.969096\pi\) | |||||||
\(968\) | −4.27930 | − | 4.27930i | −0.137542 | − | 0.137542i | ||||
\(969\) | −11.2189 | + | 46.9784i | −0.360404 | + | 1.50916i | ||||
\(970\) | 32.9284 | + | 17.7181i | 1.05727 | + | 0.568895i | ||||
\(971\) | 59.7771i | 1.91834i | 0.282833 | + | 0.959169i | \(0.408726\pi\) | ||||
−0.282833 | + | 0.959169i | \(0.591274\pi\) | |||||||
\(972\) | −14.4374 | − | 5.87893i | −0.463079 | − | 0.188567i | ||||
\(973\) | 12.9088 | − | 12.9088i | 0.413836 | − | 0.413836i | ||||
\(974\) | −9.21274 | −0.295195 | ||||||||
\(975\) | −3.07709 | − | 8.45374i | −0.0985458 | − | 0.270736i | ||||
\(976\) | −11.0841 | −0.354793 | ||||||||
\(977\) | 1.55002 | − | 1.55002i | 0.0495896 | − | 0.0495896i | −0.681877 | − | 0.731467i | \(-0.738836\pi\) |
0.731467 | + | 0.681877i | \(0.238836\pi\) | |||||||
\(978\) | −2.71470 | + | 1.66805i | −0.0868064 | + | 0.0533384i | ||||
\(979\) | − | 25.1401i | − | 0.803481i | ||||||
\(980\) | 12.2641 | + | 6.59907i | 0.391762 | + | 0.210800i | ||||
\(981\) | 1.42352 | + | 0.721021i | 0.0454495 | + | 0.0230204i | ||||
\(982\) | 28.3485 | + | 28.3485i | 0.904636 | + | 0.904636i | ||||
\(983\) | 5.24119 | + | 5.24119i | 0.167168 | + | 0.167168i | 0.785733 | − | 0.618565i | \(-0.212286\pi\) |
−0.618565 | + | 0.785733i | \(0.712286\pi\) | |||||||
\(984\) | 2.98586 | + | 0.713053i | 0.0951857 | + | 0.0227313i | ||||
\(985\) | −31.7236 | + | 9.52730i | −1.01080 | + | 0.303565i | ||||
\(986\) | 27.7327i | 0.883189i | ||||||||
\(987\) | 0.0315527 | + | 0.0513510i | 0.00100434 | + | 0.00163452i | ||||
\(988\) | 5.78917 | − | 5.78917i | 0.184178 | − | 0.184178i | ||||
\(989\) | 8.92971 | 0.283948 | ||||||||
\(990\) | −27.2676 | − | 4.87985i | −0.866620 | − | 0.155092i | ||||
\(991\) | −9.17923 | −0.291588 | −0.145794 | − | 0.989315i | \(-0.546574\pi\) | ||||
−0.145794 | + | 0.989315i | \(0.546574\pi\) | |||||||
\(992\) | −5.00154 | + | 5.00154i | −0.158799 | + | 0.158799i | ||||
\(993\) | −8.78692 | − | 14.3004i | −0.278845 | − | 0.453810i | ||||
\(994\) | − | 1.98195i | − | 0.0628635i | ||||||
\(995\) | −3.20418 | + | 5.95484i | −0.101579 | + | 0.188781i | ||||
\(996\) | −5.27200 | − | 1.25901i | −0.167050 | − | 0.0398931i | ||||
\(997\) | −23.7592 | − | 23.7592i | −0.752462 | − | 0.752462i | 0.222476 | − | 0.974938i | \(-0.428586\pi\) |
−0.974938 | + | 0.222476i | \(0.928586\pi\) | |||||||
\(998\) | 2.35867 | + | 2.35867i | 0.0746625 | + | 0.0746625i | ||||
\(999\) | 36.2408 | + | 30.7277i | 1.14661 | + | 0.972180i |
(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 | 690.2.i.f.47.6 | ✓ | 32 | |
3.2 | odd | 2 | inner | 690.2.i.f.47.9 | yes | 32 | |
5.3 | odd | 4 | inner | 690.2.i.f.323.9 | yes | 32 | |
15.8 | even | 4 | inner | 690.2.i.f.323.6 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.i.f.47.6 | ✓ | 32 | 1.1 | even | 1 | trivial | |
690.2.i.f.47.9 | yes | 32 | 3.2 | odd | 2 | inner | |
690.2.i.f.323.6 | yes | 32 | 15.8 | even | 4 | inner | |
690.2.i.f.323.9 | yes | 32 | 5.3 | odd | 4 | inner |