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 | 323.9 | ||
Character | \(\chi\) | \(=\) | 690.323 |
Dual form | 690.2.i.f.47.9 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) |
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 | ||||
\(3\) | −1.47573 | + | 0.906765i | −0.852013 | + | 0.523521i | ||||
\(4\) | 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 | −0.814687 | − | 0.579901i | \(-0.803091\pi\) |
0.579901 | + | 0.814687i | \(0.303091\pi\) | |||||||
\(8\) | −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 | \(0.786105\pi\) | |||||||
\(12\) | −0.906765 | − | 1.47573i | −0.261761 | − | 0.426006i | ||||
\(13\) | −0.734549 | − | 0.734549i | −0.203727 | − | 0.203727i | 0.597868 | − | 0.801595i | \(-0.296015\pi\) |
−0.801595 | + | 0.597868i | \(0.796015\pi\) | |||||||
\(14\) | −0.878491 | −0.234787 | ||||||||
\(15\) | −1.94512 | + | 3.34911i | −0.502227 | + | 0.864736i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 2.50190 | + | 2.50190i | 0.606801 | + | 0.606801i | 0.942109 | − | 0.335308i | \(-0.108840\pi\) |
−0.335308 | + | 0.942109i | \(0.608840\pi\) | |||||||
\(18\) | 2.85094 | − | 0.933895i | 0.671972 | − | 0.220121i | ||||
\(19\) | 7.88126i | 1.80808i | 0.427443 | + | 0.904042i | \(0.359414\pi\) | ||||
−0.427443 | + | 0.904042i | \(0.640586\pi\) | |||||||
\(20\) | 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 | ||||||
\(27\) | 0.426330 | + | 5.17863i | 0.0820472 | + | 0.996628i | ||||
\(28\) | −0.621187 | − | 0.621187i | −0.117393 | − | 0.117393i | ||||
\(29\) | 7.83802 | 1.45548 | 0.727742 | − | 0.685851i | \(-0.240570\pi\) | ||||
0.727742 | + | 0.685851i | \(0.240570\pi\) | |||||||
\(30\) | −3.74358 | + | 0.992773i | −0.683481 | + | 0.181255i | ||||
\(31\) | −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 | ||||
\(33\) | −3.74439 | − | 6.09386i | −0.651814 | − | 1.06080i | ||||
\(34\) | 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 | −0.0651000 | + | 0.997879i | \(0.520737\pi\) |
−0.997879 | + | 0.0651000i | \(0.979263\pi\) | |||||||
\(38\) | −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 | \(-0.0441954\pi\) | |||||||
\(42\) | 1.29641 | − | 0.796585i | 0.200041 | − | 0.122916i | ||||
\(43\) | −6.31426 | − | 6.31426i | −0.962915 | − | 0.962915i | 0.0364216 | − | 0.999337i | \(-0.488404\pi\) |
−0.999337 | + | 0.0364216i | \(0.988404\pi\) | |||||||
\(44\) | −4.12939 | −0.622529 | ||||||||
\(45\) | −0.166392 | − | 6.70614i | −0.0248043 | − | 0.999692i | ||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 0.0280085 | + | 0.0280085i | 0.00408546 | + | 0.00408546i | 0.709147 | − | 0.705061i | \(-0.249080\pi\) |
−0.705061 | + | 0.709147i | \(0.749080\pi\) | |||||||
\(48\) | 1.47573 | − | 0.906765i | 0.213003 | − | 0.130880i | ||||
\(49\) | 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 | −0.448307 | + | 0.893880i | \(0.647973\pi\) |
−0.893880 | + | 0.448307i | \(0.852027\pi\) | |||||||
\(54\) | −3.36039 | + | 3.96331i | −0.457291 | + | 0.539338i | ||||
\(55\) | 4.37524 | + | 8.13121i | 0.589958 | + | 1.09641i | ||||
\(56\) | − | 0.878491i | − | 0.117393i | ||||||
\(57\) | −7.14645 | − | 11.6306i | −0.946571 | − | 1.54051i | ||||
\(58\) | 5.54232 | + | 5.54232i | 0.727742 | + | 0.727742i | ||||
\(59\) | 10.9630 | 1.42726 | 0.713629 | − | 0.700524i | \(-0.247050\pi\) | ||||
0.713629 | + | 0.700524i | \(0.247050\pi\) | |||||||
\(60\) | −3.34911 | − | 1.94512i | −0.432368 | − | 0.251113i | ||||
\(61\) | 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 | ||||
\(63\) | 0.820418 | + | 2.50452i | 0.103363 | + | 0.315540i | ||||
\(64\) | − | 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 | 0.411581 | − | 0.911373i | \(-0.364977\pi\) |
0.911373 | − | 0.411581i | \(-0.135023\pi\) | |||||||
\(68\) | −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 | \(-0.0427417\pi\) | |||||||
\(72\) | 0.933895 | + | 2.85094i | 0.110061 | + | 0.335986i | ||||
\(73\) | −8.48742 | − | 8.48742i | −0.993378 | − | 0.993378i | 0.00660049 | − | 0.999978i | \(-0.497899\pi\) |
−0.999978 | + | 0.00660049i | \(0.997899\pi\) | |||||||
\(74\) | −9.14409 | −1.06298 | ||||||||
\(75\) | −0.281632 | + | 8.65567i | −0.0325201 | + | 0.999471i | ||||
\(76\) | −7.88126 | −0.904042 | ||||||||
\(77\) | −2.56512 | − | 2.56512i | −0.292323 | − | 0.292323i | ||||
\(78\) | 0.941956 | + | 1.53300i | 0.106655 | + | 0.173578i | ||||
\(79\) | 1.98214i | 0.223008i | 0.993764 | + | 0.111504i | \(0.0355668\pi\) | ||||
−0.993764 | + | 0.111504i | \(0.964433\pi\) | |||||||
\(80\) | −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 | \(-0.695059\pi\) |
0.818043 | + | 0.575156i | \(0.195059\pi\) | |||||||
\(84\) | 1.47997 | + | 0.353433i | 0.161478 | + | 0.0385627i | ||||
\(85\) | 7.57738 | + | 2.27565i | 0.821882 | + | 0.246829i | ||||
\(86\) | − | 8.92971i | − | 0.962915i | ||||||
\(87\) | −11.5668 | + | 7.10725i | −1.24009 | + | 0.761977i | ||||
\(88\) | −2.91992 | − | 2.91992i | −0.311264 | − | 0.311264i | ||||
\(89\) | 6.08809 | 0.645336 | 0.322668 | − | 0.946512i | \(-0.395420\pi\) | ||||
0.322668 | + | 0.946512i | \(0.395420\pi\) | |||||||
\(90\) | 4.62430 | − | 4.85961i | 0.487444 | − | 0.512248i | ||||
\(91\) | 0.912584 | 0.0956648 | ||||||||
\(92\) | 0.707107 | + | 0.707107i | 0.0737210 | + | 0.0737210i | ||||
\(93\) | 10.4382 | − | 6.41378i | 1.08239 | − | 0.665078i | ||||
\(94\) | 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 | 0.226625 | − | 0.973982i | \(-0.427231\pi\) |
0.973982 | − | 0.226625i | \(-0.0727691\pi\) | |||||||
\(98\) | −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 | \(-0.0215911\pi\) | |||||||
\(102\) | −3.20834 | − | 5.22147i | −0.317673 | − | 0.517002i | ||||
\(103\) | 3.37589 | + | 3.37589i | 0.332636 | + | 0.332636i | 0.853587 | − | 0.520950i | \(-0.174422\pi\) |
−0.520950 | + | 0.853587i | \(0.674422\pi\) | |||||||
\(104\) | 1.03881 | 0.101864 | ||||||||
\(105\) | −0.872142 | − | 3.28870i | −0.0851123 | − | 0.320944i | ||||
\(106\) | −13.8187 | −1.34219 | ||||||||
\(107\) | 2.39803 | + | 2.39803i | 0.231826 | + | 0.231826i | 0.813455 | − | 0.581628i | \(-0.197584\pi\) |
−0.581628 | + | 0.813455i | \(0.697584\pi\) | |||||||
\(108\) | −5.17863 | + | 0.426330i | −0.498314 | + | 0.0410236i | ||||
\(109\) | 0.531902i | 0.0509470i | 0.999675 | + | 0.0254735i | \(0.00810934\pi\) | ||||
−0.999675 | + | 0.0254735i | \(0.991891\pi\) | |||||||
\(110\) | −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 | \(-0.838966\pi\) |
0.484597 | + | 0.874737i | \(0.338966\pi\) | |||||||
\(114\) | 3.17077 | − | 13.2774i | 0.296970 | − | 1.24354i | ||||
\(115\) | 0.643162 | − | 2.14157i | 0.0599752 | − | 0.199703i | ||||
\(116\) | 7.83802i | 0.727742i | ||||||||
\(117\) | −2.96158 | + | 0.970139i | −0.273798 | + | 0.0896893i | ||||
\(118\) | 7.75200 | + | 7.75200i | 0.713629 | + | 0.713629i | ||||
\(119\) | −3.10830 | −0.284937 | ||||||||
\(120\) | −0.992773 | − | 3.74358i | −0.0906274 | − | 0.341741i | ||||
\(121\) | −6.05185 | −0.550168 | ||||||||
\(122\) | 7.83764 | + | 7.83764i | 0.709587 | + | 0.709587i | ||||
\(123\) | 1.60712 | + | 2.61553i | 0.144909 | + | 0.235834i | ||||
\(124\) | − | 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 | −0.232443 | − | 0.972610i | \(-0.574672\pi\) |
0.972610 | + | 0.232443i | \(0.0746718\pi\) | |||||||
\(128\) | 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 | \(0.962545\pi\) | |||||||
\(132\) | 6.09386 | − | 3.74439i | 0.530402 | − | 0.325907i | ||||
\(133\) | −4.89573 | − | 4.89573i | −0.424514 | − | 0.424514i | ||||
\(134\) | 15.3143 | 1.32295 | ||||||||
\(135\) | 6.32645 | + | 9.74557i | 0.544494 | + | 0.838765i | ||||
\(136\) | −3.53823 | −0.303401 | ||||||||
\(137\) | −3.75896 | − | 3.75896i | −0.321150 | − | 0.321150i | 0.528058 | − | 0.849208i | \(-0.322920\pi\) |
−0.849208 | + | 0.528058i | \(0.822920\pi\) | |||||||
\(138\) | −1.47573 | + | 0.906765i | −0.125622 | + | 0.0771890i | ||||
\(139\) | − | 20.7808i | − | 1.76261i | −0.472551 | − | 0.881303i | \(-0.656667\pi\) | ||
0.472551 | − | 0.881303i | \(-0.343333\pi\) | |||||||
\(140\) | −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 | ||||||
\(147\) | −5.64757 | − | 9.19122i | −0.465803 | − | 0.758079i | ||||
\(148\) | −6.46585 | − | 6.46585i | −0.531489 | − | 0.531489i | ||||
\(149\) | 6.11984 | 0.501357 | 0.250678 | − | 0.968070i | \(-0.419346\pi\) | ||||
0.250678 | + | 0.968070i | \(0.419346\pi\) | |||||||
\(150\) | −6.31963 | + | 5.92134i | −0.515996 | + | 0.483476i | ||||
\(151\) | 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 | ||||
\(153\) | 10.0873 | − | 3.30433i | 0.815507 | − | 0.267140i | ||||
\(154\) | − | 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 | −0.976939 | − | 0.213519i | \(-0.931508\pi\) |
0.213519 | + | 0.976939i | \(0.431508\pi\) | |||||||
\(158\) | −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 | ||||||||
\(162\) | 1.36523 | − | 8.89585i | 0.107263 | − | 0.698924i | ||||
\(163\) | 1.30077 | + | 1.30077i | 0.101884 | + | 0.101884i | 0.756211 | − | 0.654327i | \(-0.227048\pi\) |
−0.654327 | + | 0.756211i | \(0.727048\pi\) | |||||||
\(164\) | 1.77236 | 0.138398 | ||||||||
\(165\) | −13.8298 | − | 8.03214i | −1.07665 | − | 0.625301i | ||||
\(166\) | 3.12938 | 0.242887 | ||||||||
\(167\) | 7.75358 | + | 7.75358i | 0.599990 | + | 0.599990i | 0.940310 | − | 0.340320i | \(-0.110535\pi\) |
−0.340320 | + | 0.940310i | \(0.610535\pi\) | |||||||
\(168\) | 0.796585 | + | 1.29641i | 0.0614579 | + | 0.100021i | ||||
\(169\) | − | 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 | \(-0.560546\pi\) |
0.981964 | + | 0.189066i | \(0.0605459\pi\) | |||||||
\(174\) | −13.2045 | − | 3.15338i | −1.00103 | − | 0.239057i | ||||
\(175\) | 0.880797 | + | 4.30324i | 0.0665820 | + | 0.325294i | ||||
\(176\) | − | 4.12939i | − | 0.311264i | ||||||
\(177\) | −16.1784 | + | 9.94085i | −1.21604 | + | 0.747200i | ||||
\(178\) | 4.30493 | + | 4.30493i | 0.322668 | + | 0.322668i | ||||
\(179\) | −0.719378 | −0.0537688 | −0.0268844 | − | 0.999639i | \(-0.508559\pi\) | ||||
−0.0268844 | + | 0.999639i | \(0.508559\pi\) | |||||||
\(180\) | 6.70614 | − | 0.166392i | 0.499846 | − | 0.0124022i | ||||
\(181\) | 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 | ||||
\(183\) | −16.3571 | + | 10.0507i | −1.20915 | + | 0.742967i | ||||
\(184\) | 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 | \(0.874423\pi\) | |||||||
\(192\) | 0.906765 | + | 1.47573i | 0.0654402 | + | 0.106502i | ||||
\(193\) | −0.732855 | − | 0.732855i | −0.0527520 | − | 0.0527520i | 0.680239 | − | 0.732991i | \(-0.261876\pi\) |
−0.732991 | + | 0.680239i | \(0.761876\pi\) | |||||||
\(194\) | 16.7225 | 1.20061 | ||||||||
\(195\) | 3.88886 | − | 1.03130i | 0.278487 | − | 0.0738530i | ||||
\(196\) | −6.22825 | −0.444875 | ||||||||
\(197\) | −10.4745 | − | 10.4745i | −0.746279 | − | 0.746279i | 0.227499 | − | 0.973778i | \(-0.426945\pi\) |
−0.973778 | + | 0.227499i | \(0.926945\pi\) | |||||||
\(198\) | 3.85642 | + | 11.7726i | 0.274064 | + | 0.836644i | ||||
\(199\) | 3.02413i | 0.214375i | 0.994239 | + | 0.107188i | \(0.0341845\pi\) | ||||
−0.994239 | + | 0.107188i | \(0.965815\pi\) | |||||||
\(200\) | 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 | ||||||||
\(207\) | −0.933895 | − | 2.85094i | −0.0649102 | − | 0.198154i | ||||
\(208\) | 0.734549 | + | 0.734549i | 0.0509318 | + | 0.0509318i | ||||
\(209\) | −32.5448 | −2.25117 | ||||||||
\(210\) | 1.70877 | − | 2.94216i | 0.117916 | − | 0.203028i | ||||
\(211\) | −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 | ||||
\(213\) | 2.04574 | + | 3.32936i | 0.140171 | + | 0.228124i | ||||
\(214\) | 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 | ||||||
\(222\) | 13.4942 | − | 8.29154i | 0.905671 | − | 0.556492i | ||||
\(223\) | −7.87712 | − | 7.87712i | −0.527491 | − | 0.527491i | 0.392332 | − | 0.919824i | \(-0.371668\pi\) |
−0.919824 | + | 0.392332i | \(0.871668\pi\) | |||||||
\(224\) | 0.878491 | 0.0586966 | ||||||||
\(225\) | −7.43305 | − | 13.0288i | −0.495537 | − | 0.868587i | ||||
\(226\) | −5.86509 | −0.390140 | ||||||||
\(227\) | −8.11980 | − | 8.11980i | −0.538930 | − | 0.538930i | 0.384284 | − | 0.923215i | \(-0.374448\pi\) |
−0.923215 | + | 0.384284i | \(0.874448\pi\) | |||||||
\(228\) | 11.6306 | − | 7.14645i | 0.770255 | − | 0.473285i | ||||
\(229\) | 8.83078i | 0.583554i | 0.956486 | + | 0.291777i | \(0.0942465\pi\) | ||||
−0.956486 | + | 0.291777i | \(0.905753\pi\) | |||||||
\(230\) | 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 | \(-0.962299\pi\) |
0.118163 | + | 0.992994i | \(0.462299\pi\) | |||||||
\(234\) | −2.78014 | − | 1.40816i | −0.181744 | − | 0.0920543i | ||||
\(235\) | 0.0848278 | + | 0.0254757i | 0.00553356 | + | 0.00166185i | ||||
\(236\) | 10.9630i | 0.713629i | ||||||||
\(237\) | −1.79734 | − | 2.92510i | −0.116750 | − | 0.190006i | ||||
\(238\) | −2.19790 | − | 2.19790i | −0.142469 | − | 0.142469i | ||||
\(239\) | −5.29769 | −0.342679 | −0.171340 | − | 0.985212i | \(-0.554810\pi\) | ||||
−0.171340 | + | 0.985212i | \(0.554810\pi\) | |||||||
\(240\) | 1.94512 | − | 3.34911i | 0.125557 | − | 0.216184i | ||||
\(241\) | 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 | ||||
\(243\) | 14.4374 | + | 5.87893i | 0.926159 | + | 0.377134i | ||||
\(244\) | 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 | \(-0.188167\pi\) | |||||||
\(252\) | −2.50452 | + | 0.820418i | −0.157770 | + | 0.0516815i | ||||
\(253\) | 2.91992 | + | 2.91992i | 0.183574 | + | 0.183574i | ||||
\(254\) | 11.7963 | 0.740167 | ||||||||
\(255\) | −13.2456 | + | 3.51266i | −0.829474 | + | 0.219971i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.83128 | + | 3.83128i | 0.238989 | + | 0.238989i | 0.816431 | − | 0.577442i | \(-0.195949\pi\) |
−0.577442 | + | 0.816431i | \(0.695949\pi\) | |||||||
\(258\) | 8.09715 | + | 13.1778i | 0.504106 | + | 0.820416i | ||||
\(259\) | − | 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 | \(-0.892843\pi\) |
0.330321 | + | 0.943869i | \(0.392843\pi\) | |||||||
\(264\) | 6.95669 | + | 1.66133i | 0.428155 | + | 0.102248i | ||||
\(265\) | −8.88764 | + | 29.5937i | −0.545963 | + | 1.81793i | ||||
\(266\) | − | 6.92361i | − | 0.424514i | ||||||
\(267\) | −8.98437 | + | 5.52047i | −0.549835 | + | 0.337847i | ||||
\(268\) | 10.8288 | + | 10.8288i | 0.661477 | + | 0.661477i | ||||
\(269\) | 10.4792 | 0.638928 | 0.319464 | − | 0.947598i | \(-0.396497\pi\) | ||||
0.319464 | + | 0.947598i | \(0.396497\pi\) | |||||||
\(270\) | −2.41768 | + | 11.3646i | −0.147136 | + | 0.691629i | ||||
\(271\) | −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 | ||||
\(273\) | −1.34673 | + | 0.827499i | −0.0815076 | + | 0.0500825i | ||||
\(274\) | − | 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 | −0.908634 | − | 0.417592i | \(-0.862874\pi\) |
0.417592 | + | 0.908634i | \(0.362874\pi\) | |||||||
\(278\) | 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 | \(-0.255037\pi\) | |||||||
\(282\) | −0.0359170 | − | 0.0584537i | −0.00213883 | − | 0.00348087i | ||||
\(283\) | −19.2731 | − | 19.2731i | −1.14567 | − | 1.14567i | −0.987396 | − | 0.158271i | \(-0.949408\pi\) |
−0.158271 | − | 0.987396i | \(-0.550592\pi\) | |||||||
\(284\) | 2.25608 | 0.133874 | ||||||||
\(285\) | −26.3952 | − | 15.3300i | −1.56352 | − | 0.908068i | ||||
\(286\) | 4.28964 | 0.253652 | ||||||||
\(287\) | 1.10097 | + | 1.10097i | 0.0649880 | + | 0.0649880i | ||||
\(288\) | −2.85094 | + | 0.933895i | −0.167993 | + | 0.0550303i | ||||
\(289\) | − | 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 | 0.0271332 | − | 0.999632i | \(-0.491362\pi\) |
0.999632 | − | 0.0271332i | \(-0.00863783\pi\) | |||||||
\(294\) | 2.50574 | − | 10.4926i | 0.146138 | − | 0.611941i | ||||
\(295\) | 21.5873 | − | 11.6157i | 1.25686 | − | 0.676292i | ||||
\(296\) | − | 9.14409i | − | 0.531489i | ||||||
\(297\) | −21.3846 | + | 1.76048i | −1.24086 | + | 0.102153i | ||||
\(298\) | 4.32738 | + | 4.32738i | 0.250678 | + | 0.250678i | ||||
\(299\) | −1.03881 | −0.0600759 | ||||||||
\(300\) | −8.65567 | − | 0.281632i | −0.499736 | − | 0.0162600i | ||||
\(301\) | 7.84466 | 0.452159 | ||||||||
\(302\) | 5.66375 | + | 5.66375i | 0.325912 | + | 0.325912i | ||||
\(303\) | 1.23532 | + | 2.01043i | 0.0709670 | + | 0.115496i | ||||
\(304\) | − | 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 | −0.502544 | − | 0.864552i | \(-0.667602\pi\) |
0.864552 | + | 0.502544i | \(0.167602\pi\) | |||||||
\(308\) | 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 | \(0.986014\pi\) | |||||||
\(312\) | −1.53300 | + | 0.941956i | −0.0867890 | + | 0.0533277i | ||||
\(313\) | 0.449127 | + | 0.449127i | 0.0253861 | + | 0.0253861i | 0.719686 | − | 0.694300i | \(-0.244286\pi\) |
−0.694300 | + | 0.719686i | \(0.744286\pi\) | |||||||
\(314\) | −13.5278 | −0.763420 | ||||||||
\(315\) | 4.26913 | + | 4.06240i | 0.240538 | + | 0.228891i | ||||
\(316\) | −1.98214 | −0.111504 | ||||||||
\(317\) | 17.7857 | + | 17.7857i | 0.998943 | + | 0.998943i | 0.999999 | − | 0.00105667i | \(-0.000336349\pi\) |
−0.00105667 | + | 0.999999i | \(0.500336\pi\) | |||||||
\(318\) | 20.3926 | − | 12.5303i | 1.14356 | − | 0.702663i | ||||
\(319\) | 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 | ||||||||
\(327\) | −0.482310 | − | 0.784943i | −0.0266718 | − | 0.0434075i | ||||
\(328\) | 1.25325 | + | 1.25325i | 0.0691991 | + | 0.0691991i | ||||
\(329\) | −0.0347970 | −0.00191842 | ||||||||
\(330\) | −4.09955 | − | 15.4587i | −0.225673 | − | 0.850974i | ||||
\(331\) | −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 | ||||
\(333\) | 8.53962 | + | 26.0692i | 0.467968 | + | 1.42858i | ||||
\(334\) | 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 | −0.558029 | − | 0.829821i | \(-0.688442\pi\) |
0.829821 | + | 0.558029i | \(0.188442\pi\) | |||||||
\(338\) | 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 | ||||||
\(342\) | 7.36027 | + | 22.4690i | 0.397998 | + | 1.21498i | ||||
\(343\) | −8.21722 | − | 8.21722i | −0.443688 | − | 0.443688i | ||||
\(344\) | 8.92971 | 0.481457 | ||||||||
\(345\) | 0.992773 | + | 3.74358i | 0.0534491 | + | 0.201548i | ||||
\(346\) | 14.7488 | 0.792899 | ||||||||
\(347\) | 11.2296 | + | 11.2296i | 0.602837 | + | 0.602837i | 0.941064 | − | 0.338228i | \(-0.109827\pi\) |
−0.338228 | + | 0.941064i | \(0.609827\pi\) | |||||||
\(348\) | −7.10725 | − | 11.5668i | −0.380988 | − | 0.620045i | ||||
\(349\) | 23.8817i | 1.27836i | 0.769059 | + | 0.639178i | \(0.220725\pi\) | ||||
−0.769059 | + | 0.639178i | \(0.779275\pi\) | |||||||
\(350\) | −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 | \(-0.598287\pi\) |
0.952706 | + | 0.303893i | \(0.0982865\pi\) | |||||||
\(354\) | −18.4691 | − | 4.41060i | −0.981621 | − | 0.234421i | ||||
\(355\) | −2.39040 | − | 4.44246i | −0.126869 | − | 0.235781i | ||||
\(356\) | 6.08809i | 0.322668i | ||||||||
\(357\) | 4.58701 | − | 2.81850i | 0.242770 | − | 0.149171i | ||||
\(358\) | −0.508677 | − | 0.508677i | −0.0268844 | − | 0.0268844i | ||||
\(359\) | −7.16299 | −0.378048 | −0.189024 | − | 0.981972i | \(-0.560532\pi\) | ||||
−0.189024 | + | 0.981972i | \(0.560532\pi\) | |||||||
\(360\) | 4.85961 | + | 4.62430i | 0.256124 | + | 0.243722i | ||||
\(361\) | −43.1142 | −2.26917 | ||||||||
\(362\) | 11.8197 | + | 11.8197i | 0.621229 | + | 0.621229i | ||||
\(363\) | 8.93089 | − | 5.48761i | 0.468750 | − | 0.288025i | ||||
\(364\) | 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 | −0.266785 | − | 0.963756i | \(-0.585961\pi\) |
0.963756 | + | 0.266785i | \(0.0859613\pi\) | |||||||
\(368\) | −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 | ||||||
\(372\) | 6.41378 | + | 10.4382i | 0.332539 | + | 0.541196i | ||||
\(373\) | −2.87275 | − | 2.87275i | −0.148745 | − | 0.148745i | 0.628812 | − | 0.777557i | \(-0.283541\pi\) |
−0.777557 | + | 0.628812i | \(0.783541\pi\) | |||||||
\(374\) | −14.6107 | −0.755502 | ||||||||
\(375\) | 8.61645 | + | 17.3423i | 0.444952 | + | 0.895555i | ||||
\(376\) | −0.0396100 | −0.00204273 | ||||||||
\(377\) | −5.75741 | − | 5.75741i | −0.296522 | − | 0.296522i | ||||
\(378\) | −0.374527 | − | 4.54938i | −0.0192636 | − | 0.233995i | ||||
\(379\) | − | 24.7455i | − | 1.27109i | −0.772063 | − | 0.635546i | \(-0.780775\pi\) | ||
0.772063 | − | 0.635546i | \(-0.219225\pi\) | |||||||
\(380\) | −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 | \(-0.943414\pi\) |
0.176836 | + | 0.984240i | \(0.443414\pi\) | |||||||
\(384\) | −0.402318 | + | 1.68468i | −0.0205307 | + | 0.0859709i | ||||
\(385\) | −7.76884 | − | 2.33315i | −0.395937 | − | 0.118909i | ||||
\(386\) | − | 1.03641i | − | 0.0527520i | ||||||
\(387\) | −25.4580 | + | 8.33941i | −1.29410 | + | 0.423916i | ||||
\(388\) | 11.8246 | + | 11.8246i | 0.600303 | + | 0.600303i | ||||
\(389\) | −1.35053 | −0.0684745 | −0.0342372 | − | 0.999414i | \(-0.510900\pi\) | ||||
−0.0342372 | + | 0.999414i | \(0.510900\pi\) | |||||||
\(390\) | 3.47908 | + | 2.02060i | 0.176170 | + | 0.102317i | ||||
\(391\) | 3.53823 | 0.178936 | ||||||||
\(392\) | −4.40404 | − | 4.40404i | −0.222438 | − | 0.222438i | ||||
\(393\) | −2.43682 | − | 3.96583i | −0.122921 | − | 0.200050i | ||||
\(394\) | − | 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 | −0.821559 | − | 0.570124i | \(-0.806895\pi\) |
0.570124 | + | 0.821559i | \(0.306895\pi\) | |||||||
\(398\) | −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 | \(-0.105831\pi\) | |||||||
\(402\) | −22.5998 | + | 13.8865i | −1.12717 | + | 0.692595i | ||||
\(403\) | 5.19565 | + | 5.19565i | 0.258814 | + | 0.258814i | ||||
\(404\) | 1.36233 | 0.0677786 | ||||||||
\(405\) | −18.1731 | − | 8.64521i | −0.903027 | − | 0.429584i | ||||
\(406\) | −6.88563 | −0.341728 | ||||||||
\(407\) | −26.7000 | − | 26.7000i | −1.32347 | − | 1.32347i | ||||
\(408\) | 5.22147 | − | 3.20834i | 0.258501 | − | 0.158837i | ||||
\(409\) | 15.7658i | 0.779567i | 0.920907 | + | 0.389784i | \(0.127450\pi\) | ||||
−0.920907 | + | 0.389784i | \(0.872550\pi\) | |||||||
\(410\) | 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 | ||||||||
\(417\) | 18.8433 | + | 30.6669i | 0.922762 | + | 1.50176i | ||||
\(418\) | −23.0126 | − | 23.0126i | −1.12558 | − | 1.12558i | ||||
\(419\) | 28.4327 | 1.38903 | 0.694514 | − | 0.719480i | \(-0.255620\pi\) | ||||
0.694514 | + | 0.719480i | \(0.255620\pi\) | |||||||
\(420\) | 3.28870 | − | 0.872142i | 0.160472 | − | 0.0425562i | ||||
\(421\) | 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 | ||||
\(423\) | 0.112926 | − | 0.0369916i | 0.00549063 | − | 0.00179859i | ||||
\(424\) | − | 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 | \(0.775202\pi\) | |||||||
\(432\) | −0.426330 | − | 5.17863i | −0.0205118 | − | 0.249157i | ||||
\(433\) | 10.1590 | + | 10.1590i | 0.488212 | + | 0.488212i | 0.907742 | − | 0.419530i | \(-0.137805\pi\) |
−0.419530 | + | 0.907742i | \(0.637805\pi\) | |||||||
\(434\) | 6.21379 | 0.298271 | ||||||||
\(435\) | −15.2459 | + | 26.2504i | −0.730983 | + | 1.25861i | ||||
\(436\) | −0.531902 | −0.0254735 | ||||||||
\(437\) | 5.57289 | + | 5.57289i | 0.266588 | + | 0.266588i | ||||
\(438\) | 10.8839 | + | 17.7132i | 0.520054 | + | 0.846370i | ||||
\(439\) | 2.41233i | 0.115134i | 0.998342 | + | 0.0575670i | \(0.0183343\pi\) | ||||
−0.998342 | + | 0.0575670i | \(0.981666\pi\) | |||||||
\(440\) | −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 | \(-0.831913\pi\) |
0.503859 | + | 0.863786i | \(0.331913\pi\) | |||||||
\(444\) | 15.4048 | + | 3.67883i | 0.731082 | + | 0.174590i | ||||
\(445\) | 11.9881 | − | 6.45056i | 0.568290 | − | 0.305786i | ||||
\(446\) | − | 11.1399i | − | 0.527491i | ||||||
\(447\) | −9.03122 | + | 5.54926i | −0.427162 | + | 0.262471i | ||||
\(448\) | 0.621187 | + | 0.621187i | 0.0293483 | + | 0.0293483i | ||||
\(449\) | −31.6647 | −1.49435 | −0.747174 | − | 0.664628i | \(-0.768590\pi\) | ||||
−0.747174 | + | 0.664628i | \(0.768590\pi\) | |||||||
\(450\) | 3.95679 | − | 14.4687i | 0.186525 | − | 0.682062i | ||||
\(451\) | 7.31877 | 0.344627 | ||||||||
\(452\) | −4.14725 | − | 4.14725i | −0.195070 | − | 0.195070i | ||||
\(453\) | −11.8202 | + | 7.26297i | −0.555363 | + | 0.341244i | ||||
\(454\) | − | 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 | −0.328653 | + | 0.944451i | \(0.606595\pi\) |
−0.944451 | + | 0.328653i | \(0.893405\pi\) | |||||||
\(458\) | −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 | \(0.853235\pi\) | |||||||
\(462\) | 3.28941 | + | 5.35340i | 0.153037 | + | 0.249063i | ||||
\(463\) | 17.9935 | + | 17.9935i | 0.836230 | + | 0.836230i | 0.988360 | − | 0.152131i | \(-0.0486135\pi\) |
−0.152131 | + | 0.988360i | \(0.548613\pi\) | |||||||
\(464\) | −7.83802 | −0.363871 | ||||||||
\(465\) | 13.7583 | − | 23.6891i | 0.638025 | − | 1.09856i | ||||
\(466\) | −18.8850 | −0.874831 | ||||||||
\(467\) | 13.5425 | + | 13.5425i | 0.626673 | + | 0.626673i | 0.947229 | − | 0.320557i | \(-0.103870\pi\) |
−0.320557 | + | 0.947229i | \(0.603870\pi\) | |||||||
\(468\) | −0.970139 | − | 2.96158i | −0.0448447 | − | 0.136899i | ||||
\(469\) | 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 | ||||||
\(477\) | 12.9052 | + | 39.3961i | 0.590888 | + | 1.80382i | ||||
\(478\) | −3.74603 | − | 3.74603i | −0.171340 | − | 0.171340i | ||||
\(479\) | −10.1525 | −0.463880 | −0.231940 | − | 0.972730i | \(-0.574507\pi\) | ||||
−0.231940 | + | 0.972730i | \(0.574507\pi\) | |||||||
\(480\) | 3.74358 | − | 0.992773i | 0.170870 | − | 0.0453137i | ||||
\(481\) | 9.49896 | 0.433115 | ||||||||
\(482\) | 2.29328 | + | 2.29328i | 0.104456 | + | 0.104456i | ||||
\(483\) | −0.796585 | − | 1.29641i | −0.0362459 | − | 0.0589889i | ||||
\(484\) | − | 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 | −0.543933 | − | 0.839128i | \(-0.683066\pi\) |
0.839128 | + | 0.543933i | \(0.183066\pi\) | |||||||
\(488\) | −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 | \(-0.359857\pi\) | |||||||
\(492\) | −2.61553 | + | 1.60712i | −0.117917 | + | 0.0724544i | ||||
\(493\) | 19.6100 | + | 19.6100i | 0.883189 | + | 0.883189i | ||||
\(494\) | 8.18712 | 0.368356 | ||||||||
\(495\) | 27.6923 | − | 0.687099i | 1.24467 | − | 0.0308828i | ||||
\(496\) | 7.07325 | 0.317598 | ||||||||
\(497\) | 1.40145 | + | 1.40145i | 0.0628635 | + | 0.0628635i | ||||
\(498\) | −4.61812 | + | 2.83761i | −0.206943 | + | 0.127157i | ||||
\(499\) | 3.33567i | 0.149325i | 0.997209 | + | 0.0746625i | \(0.0237880\pi\) | ||||
−0.997209 | + | 0.0746625i | \(0.976212\pi\) | |||||||
\(500\) | 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 | \(-0.696223\pi\) |
0.815935 | + | 0.578144i | \(0.196223\pi\) | |||||||
\(504\) | −2.35109 | − | 1.19084i | −0.104726 | − | 0.0530443i | ||||
\(505\) | −1.44344 | − | 2.68258i | −0.0642323 | − | 0.119373i | ||||
\(506\) | 4.12939i | 0.183574i | ||||||||
\(507\) | 10.8094 | + | 17.5920i | 0.480064 | + | 0.781287i | ||||
\(508\) | 8.34126 | + | 8.34126i | 0.370084 | + | 0.370084i | ||||
\(509\) | −0.551066 | −0.0244256 | −0.0122128 | − | 0.999925i | \(-0.503888\pi\) | ||||
−0.0122128 | + | 0.999925i | \(0.503888\pi\) | |||||||
\(510\) | −11.8499 | − | 6.88226i | −0.524723 | − | 0.304752i | ||||
\(511\) | 10.5445 | 0.466463 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −40.8141 | + | 3.36002i | −1.80199 | + | 0.148348i | ||||
\(514\) | 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 | \(-0.0547387\pi\) | |||||||
\(522\) | 22.3457 | − | 7.31989i | 0.978045 | − | 0.320383i | ||||
\(523\) | 3.95100 | + | 3.95100i | 0.172765 | + | 0.172765i | 0.788193 | − | 0.615428i | \(-0.211017\pi\) |
−0.615428 | + | 0.788193i | \(0.711017\pi\) | |||||||
\(524\) | −2.68737 | −0.117398 | ||||||||
\(525\) | −5.20184 | − | 5.55174i | −0.227027 | − | 0.242298i | ||||
\(526\) | −14.0715 | −0.613548 | ||||||||
\(527\) | −17.6966 | − | 17.6966i | −0.770876 | − | 0.770876i | ||||
\(528\) | 3.74439 | + | 6.09386i | 0.162954 | + | 0.265201i | ||||
\(529\) | − | 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 | ||||||||
\(537\) | 1.06161 | − | 0.652307i | 0.0458117 | − | 0.0281491i | ||||
\(538\) | 7.40991 | + | 7.40991i | 0.319464 | + | 0.319464i | ||||
\(539\) | −25.7189 | −1.10779 | ||||||||
\(540\) | −9.74557 | + | 6.32645i | −0.419382 | + | 0.272247i | ||||
\(541\) | −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 | ||||
\(543\) | −24.6676 | + | 15.1571i | −1.05859 | + | 0.650453i | ||||
\(544\) | − | 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 | −0.605960 | − | 0.795495i | \(-0.707211\pi\) |
0.795495 | + | 0.605960i | \(0.207211\pi\) | |||||||
\(548\) | 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 | ||||||||
\(552\) | −0.906765 | − | 1.47573i | −0.0385945 | − | 0.0628112i | ||||
\(553\) | −1.23128 | − | 1.23128i | −0.0523593 | − | 0.0523593i | ||||
\(554\) | −11.5578 | −0.491042 | ||||||||
\(555\) | −9.07800 | − | 34.2316i | −0.385340 | − | 1.45305i | ||||
\(556\) | 20.7808 | 0.881303 | ||||||||
\(557\) | 19.7470 | + | 19.7470i | 0.836707 | + | 0.836707i | 0.988424 | − | 0.151717i | \(-0.0484803\pi\) |
−0.151717 | + | 0.988424i | \(0.548480\pi\) | |||||||
\(558\) | −20.1654 | + | 6.60568i | −0.853669 | + | 0.279641i | ||||
\(559\) | 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 | \(-0.606457\pi\) |
0.944593 | + | 0.328244i | \(0.106457\pi\) | |||||||
\(564\) | 0.0159358 | − | 0.0667301i | 0.000671019 | − | 0.00280985i | ||||
\(565\) | −3.77221 | + | 12.5605i | −0.158698 | + | 0.528426i | ||||
\(566\) | − | 27.2563i | − | 1.14567i | ||||||
\(567\) | 7.81492 | + | 1.19934i | 0.328196 | + | 0.0503676i | ||||
\(568\) | 1.59529 | + | 1.59529i | 0.0669369 | + | 0.0669369i | ||||
\(569\) | −45.5814 | −1.91087 | −0.955436 | − | 0.295197i | \(-0.904615\pi\) | ||||
−0.955436 | + | 0.295197i | \(0.904615\pi\) | |||||||
\(570\) | −7.82430 | − | 29.5041i | −0.327724 | − | 1.23579i | ||||
\(571\) | −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 | ||||
\(573\) | −9.63337 | − | 15.6780i | −0.402440 | − | 0.654957i | ||||
\(574\) | 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 | 0.0969147 | − | 0.995293i | \(-0.469103\pi\) |
0.995293 | − | 0.0969147i | \(-0.0308974\pi\) | |||||||
\(578\) | 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 | ||||||||
\(582\) | −24.6779 | + | 15.1634i | −1.02293 | + | 0.628543i | ||||
\(583\) | −40.3494 | − | 40.3494i | −1.67110 | − | 1.67110i | ||||
\(584\) | 12.0030 | 0.496689 | ||||||||
\(585\) | −4.80376 | + | 5.04821i | −0.198611 | + | 0.208718i | ||||
\(586\) | 24.8553 | 1.02677 | ||||||||
\(587\) | −1.72536 | − | 1.72536i | −0.0712134 | − | 0.0712134i | 0.670603 | − | 0.741816i | \(-0.266035\pi\) |
−0.741816 | + | 0.670603i | \(0.766035\pi\) | |||||||
\(588\) | 9.19122 | − | 5.64757i | 0.379039 | − | 0.232902i | ||||
\(589\) | − | 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 | \(-0.775713\pi\) |
0.647744 | + | 0.761858i | \(0.275713\pi\) | |||||||
\(594\) | −16.3660 | − | 13.8763i | −0.671507 | − | 0.569353i | ||||
\(595\) | −6.12057 | + | 3.29336i | −0.250919 | + | 0.135015i | ||||
\(596\) | 6.11984i | 0.250678i | ||||||||
\(597\) | −2.74218 | − | 4.46280i | −0.112230 | − | 0.182650i | ||||
\(598\) | −0.734549 | − | 0.734549i | −0.0300379 | − | 0.0300379i | ||||
\(599\) | 37.0107 | 1.51222 | 0.756108 | − | 0.654447i | \(-0.227098\pi\) | ||||
0.756108 | + | 0.654447i | \(0.227098\pi\) | |||||||
\(600\) | −5.92134 | − | 6.31963i | −0.241738 | − | 0.257998i | ||||
\(601\) | 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 | ||||
\(603\) | −14.3020 | − | 43.6601i | −0.582421 | − | 1.77798i | ||||
\(604\) | 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 | −0.779548 | − | 0.626343i | \(-0.784551\pi\) |
0.626343 | + | 0.779548i | \(0.284551\pi\) | |||||||
\(608\) | 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 | ||||||
\(612\) | 3.30433 | + | 10.0873i | 0.133570 | + | 0.407753i | ||||
\(613\) | −12.5789 | − | 12.5789i | −0.508056 | − | 0.508056i | 0.405873 | − | 0.913929i | \(-0.366967\pi\) |
−0.913929 | + | 0.405873i | \(0.866967\pi\) | |||||||
\(614\) | 8.97021 | 0.362008 | ||||||||
\(615\) | 5.93583 | + | 3.44745i | 0.239356 | + | 0.139014i | ||||
\(616\) | 3.62763 | 0.146161 | ||||||||
\(617\) | −3.87788 | − | 3.87788i | −0.156118 | − | 0.156118i | 0.624726 | − | 0.780844i | \(-0.285211\pi\) |
−0.780844 | + | 0.624726i | \(0.785211\pi\) | |||||||
\(618\) | −4.32911 | − | 7.04547i | −0.174142 | − | 0.283410i | ||||
\(619\) | 8.64542i | 0.347489i | 0.984791 | + | 0.173744i | \(0.0555867\pi\) | ||||
−0.984791 | + | 0.173744i | \(0.944413\pi\) | |||||||
\(620\) | −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 | ||||||||
\(627\) | 48.0273 | − | 29.5105i | 1.91802 | − | 1.17854i | ||||
\(628\) | −9.56563 | − | 9.56563i | −0.381710 | − | 0.381710i | ||||
\(629\) | −32.3539 | −1.29003 | ||||||||
\(630\) | 0.146174 | + | 5.89128i | 0.00582372 | + | 0.234714i | ||||
\(631\) | −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 | ||||
\(633\) | 28.4966 | − | 17.5098i | 1.13264 | − | 0.695952i | ||||
\(634\) | 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 | \(-0.0171691\pi\) | |||||||
\(642\) | −3.07514 | − | 5.00468i | −0.121366 | − | 0.197519i | ||||
\(643\) | 17.4028 | + | 17.4028i | 0.686298 | + | 0.686298i | 0.961412 | − | 0.275114i | \(-0.0887155\pi\) |
−0.275114 | + | 0.961412i | \(0.588715\pi\) | |||||||
\(644\) | −0.878491 | −0.0346174 | ||||||||
\(645\) | 33.4291 | − | 8.86517i | 1.31627 | − | 0.349066i | ||||
\(646\) | −27.8857 | −1.09715 | ||||||||
\(647\) | 9.72994 | + | 9.72994i | 0.382523 | + | 0.382523i | 0.872011 | − | 0.489487i | \(-0.162816\pi\) |
−0.489487 | + | 0.872011i | \(0.662816\pi\) | |||||||
\(648\) | 8.89585 | + | 1.36523i | 0.349462 | + | 0.0536313i | ||||
\(649\) | 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 | \(-0.546617\pi\) |
0.989295 | + | 0.145928i | \(0.0466169\pi\) | |||||||
\(654\) | 0.213994 | − | 0.896084i | 0.00836782 | − | 0.0350396i | ||||
\(655\) | 2.84737 | + | 5.29172i | 0.111256 | + | 0.206765i | ||||
\(656\) | 1.77236i | 0.0691991i | ||||||||
\(657\) | −34.2199 | + | 11.2096i | −1.33504 | + | 0.437327i | ||||
\(658\) | −0.0246052 | − | 0.0246052i | −0.000959211 | − | 0.000959211i | ||||
\(659\) | 44.3615 | 1.72808 | 0.864039 | − | 0.503425i | \(-0.167927\pi\) | ||||
0.864039 | + | 0.503425i | \(0.167927\pi\) | |||||||
\(660\) | 8.03214 | − | 13.8298i | 0.312651 | − | 0.538323i | ||||
\(661\) | 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 | ||||
\(663\) | 3.33285 | + | 5.42410i | 0.129437 | + | 0.210655i | ||||
\(664\) | 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 | ||||||||
\(672\) | −1.29641 | + | 0.796585i | −0.0500103 | + | 0.0307289i | ||||
\(673\) | −30.3342 | − | 30.3342i | −1.16930 | − | 1.16930i | −0.982375 | − | 0.186921i | \(-0.940149\pi\) |
−0.186921 | − | 0.982375i | \(-0.559851\pi\) | |||||||
\(674\) | 7.05614 | 0.271792 | ||||||||
\(675\) | 22.7832 | + | 12.4869i | 0.876927 | + | 0.480623i | ||||
\(676\) | 11.9209 | 0.458495 | ||||||||
\(677\) | −8.39686 | − | 8.39686i | −0.322718 | − | 0.322718i | 0.527091 | − | 0.849809i | \(-0.323283\pi\) |
−0.849809 | + | 0.527091i | \(0.823283\pi\) | |||||||
\(678\) | 8.65529 | − | 5.31826i | 0.332404 | − | 0.204247i | ||||
\(679\) | 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 | \(-0.606648\pi\) |
0.944396 | + | 0.328811i | \(0.106648\pi\) | |||||||
\(684\) | −10.6835 | + | 21.0925i | −0.408492 | + | 0.806490i | ||||
\(685\) | −11.3845 | − | 3.41903i | −0.434981 | − | 0.130634i | ||||
\(686\) | − | 11.6209i | − | 0.443688i | ||||||
\(687\) | −8.00744 | − | 13.0318i | −0.305503 | − | 0.497196i | ||||
\(688\) | 6.31426 | + | 6.31426i | 0.240729 | + | 0.240729i | ||||
\(689\) | 14.3549 | 0.546880 | ||||||||
\(690\) | −1.94512 | + | 3.34911i | −0.0740493 | + | 0.127498i | ||||
\(691\) | −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 | ||||
\(693\) | −10.3421 | + | 3.38783i | −0.392865 | + | 0.128693i | ||||
\(694\) | 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 | \(0.830930\pi\) | |||||||
\(702\) | 5.37961 | − | 0.442875i | 0.203040 | − | 0.0167152i | ||||
\(703\) | −50.9590 | − | 50.9590i | −1.92196 | − | 1.92196i | ||||
\(704\) | 4.12939 | 0.155632 | ||||||||
\(705\) | −0.148283 | + | 0.0393238i | −0.00558467 | + | 0.00148102i | ||||
\(706\) | 17.2394 | 0.648813 | ||||||||
\(707\) | 0.846263 | + | 0.846263i | 0.0318270 | + | 0.0318270i | ||||
\(708\) | −9.94085 | − | 16.1784i | −0.373600 | − | 0.608021i | ||||
\(709\) | 4.26519i | 0.160183i | 0.996788 | + | 0.0800914i | \(0.0255212\pi\) | ||||
−0.996788 | + | 0.0800914i | \(0.974479\pi\) | |||||||
\(710\) | 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 | ||||||
\(717\) | 7.81796 | − | 4.80376i | 0.291967 | − | 0.179400i | ||||
\(718\) | −5.06500 | − | 5.06500i | −0.189024 | − | 0.189024i | ||||
\(719\) | −34.9727 | −1.30426 | −0.652130 | − | 0.758107i | \(-0.726125\pi\) | ||||
−0.652130 | + | 0.758107i | \(0.726125\pi\) | |||||||
\(720\) | 0.166392 | + | 6.70614i | 0.00620108 | + | 0.249923i | ||||
\(721\) | −4.19412 | −0.156197 | ||||||||
\(722\) | −30.4864 | − | 30.4864i | −1.13459 | − | 1.13459i | ||||
\(723\) | −4.78606 | + | 2.94081i | −0.177996 | + | 0.109370i | ||||
\(724\) | 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 | −0.411407 | − | 0.911452i | \(-0.634963\pi\) |
0.911452 | + | 0.411407i | \(0.134963\pi\) | |||||||
\(728\) | −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 | ||||||
\(732\) | −10.0507 | − | 16.3571i | −0.371484 | − | 0.604577i | ||||
\(733\) | 32.6105 | + | 32.6105i | 1.20450 | + | 1.20450i | 0.972785 | + | 0.231710i | \(0.0744321\pi\) |
0.231710 | + | 0.972785i | \(0.425568\pi\) | |||||||
\(734\) | 18.8827 | 0.696971 | ||||||||
\(735\) | −20.8591 | − | 12.1147i | −0.769399 | − | 0.446856i | ||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 44.7165 | + | 44.7165i | 1.64715 | + | 1.64715i | ||||
\(738\) | −1.65520 | − | 5.05289i | −0.0609288 | − | 0.185999i | ||||
\(739\) | − | 7.71809i | − | 0.283915i | −0.989873 | − | 0.141957i | \(-0.954660\pi\) | ||
0.989873 | − | 0.141957i | \(-0.0453396\pi\) | |||||||
\(740\) | −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 | \(-0.710489\pi\) |
0.789212 | + | 0.614121i | \(0.210489\pi\) | |||||||
\(744\) | −2.84570 | + | 11.9162i | −0.104328 | + | 0.436867i | ||||
\(745\) | 12.0506 | − | 6.48420i | 0.441500 | − | 0.237563i | ||||
\(746\) | − | 4.06268i | − | 0.148745i | ||||||
\(747\) | −2.92251 | − | 8.92166i | −0.106929 | − | 0.326427i | ||||
\(748\) | −10.3313 | − | 10.3313i | −0.377751 | − | 0.377751i | ||||
\(749\) | −2.97925 | −0.108859 | ||||||||
\(750\) | −6.17014 | + | 18.3556i | −0.225302 | + | 0.670253i | ||||
\(751\) | −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 | ||||
\(753\) | 16.0125 | + | 26.0598i | 0.583528 | + | 0.949671i | ||||
\(754\) | − | 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 | −0.780190 | − | 0.625542i | \(-0.784878\pi\) |
0.625542 | + | 0.780190i | \(0.284878\pi\) | |||||||
\(758\) | 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 | \(0.938935\pi\) | |||||||
\(762\) | −17.4082 | + | 10.6965i | −0.630632 | + | 0.387493i | ||||
\(763\) | −0.330410 | − | 0.330410i | −0.0119617 | − | 0.0119617i | ||||
\(764\) | −10.6239 | −0.384359 | ||||||||
\(765\) | 16.3618 | − | 17.1944i | 0.591563 | − | 0.621666i | ||||
\(766\) | −22.3463 | −0.807405 | ||||||||
\(767\) | −8.05284 | − | 8.05284i | −0.290771 | − | 0.290771i | ||||
\(768\) | −1.47573 | + | 0.906765i | −0.0532508 | + | 0.0327201i | ||||
\(769\) | 20.7974i | 0.749972i | 0.927030 | + | 0.374986i | \(0.122353\pi\) | ||||
−0.927030 | + | 0.374986i | \(0.877647\pi\) | |||||||
\(770\) | −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 | \(-0.692041\pi\) |
0.823459 | + | 0.567375i | \(0.192041\pi\) | |||||||
\(774\) | −23.8984 | − | 12.1047i | −0.859010 | − | 0.435094i | ||||
\(775\) | −19.4851 | + | 29.5145i | −0.699926 | + | 1.06019i | ||||
\(776\) | 16.7225i | 0.600303i | ||||||||
\(777\) | 7.28404 | + | 11.8545i | 0.261314 | + | 0.425279i | ||||
\(778\) | −0.954967 | − | 0.954967i | −0.0342372 | − | 0.0342372i | ||||
\(779\) | 13.9684 | 0.500471 | ||||||||
\(780\) | 1.03130 | + | 3.88886i | 0.0369265 | + | 0.139244i | ||||
\(781\) | 9.31623 | 0.333361 | ||||||||
\(782\) | 2.50190 | + | 2.50190i | 0.0894679 | + | 0.0894679i | ||||
\(783\) | 3.34158 | + | 40.5902i | 0.119418 | + | 1.45058i | ||||
\(784\) | − | 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 | −0.904082 | − | 0.427358i | \(-0.859444\pi\) |
0.427358 | + | 0.904082i | \(0.359444\pi\) | |||||||
\(788\) | 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 | ||||||
\(792\) | −11.7726 | + | 3.85642i | −0.418322 | + | 0.137032i | ||||
\(793\) | −8.14181 | − | 8.14181i | −0.289124 | − | 0.289124i | ||||
\(794\) | −7.08495 | −0.251435 | ||||||||
\(795\) | −13.7188 | − | 51.7313i | −0.486555 | − | 1.83472i | ||||
\(796\) | −3.02413 | −0.107188 | ||||||||
\(797\) | 13.4137 | + | 13.4137i | 0.475136 | + | 0.475136i | 0.903572 | − | 0.428436i | \(-0.140935\pi\) |
−0.428436 | + | 0.903572i | \(0.640935\pi\) | |||||||
\(798\) | 6.27809 | + | 10.2174i | 0.222242 | + | 0.361691i | ||||
\(799\) | 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 | ||||||||
\(807\) | −15.4645 | + | 9.50218i | −0.544375 | + | 0.334492i | ||||
\(808\) | 0.963314 | + | 0.963314i | 0.0338893 | + | 0.0338893i | ||||
\(809\) | −38.5121 | −1.35401 | −0.677007 | − | 0.735977i | \(-0.736723\pi\) | ||||
−0.677007 | + | 0.735977i | \(0.736723\pi\) | |||||||
\(810\) | −6.73721 | − | 18.9634i | −0.236721 | − | 0.666305i | ||||
\(811\) | 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 | ||||
\(813\) | 22.7636 | − | 13.9871i | 0.798354 | − | 0.490551i | ||||
\(814\) | − | 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 | \(0.993211\pi\) | |||||||
\(822\) | 4.82034 | + | 7.84493i | 0.168129 | + | 0.273623i | ||||
\(823\) | 8.41266 | + | 8.41266i | 0.293247 | + | 0.293247i | 0.838362 | − | 0.545115i | \(-0.183514\pi\) |
−0.545115 | + | 0.838362i | \(0.683514\pi\) | |||||||
\(824\) | −4.77423 | −0.166318 | ||||||||
\(825\) | −35.7426 | − | 1.16297i | −1.24440 | − | 0.0404894i | ||||
\(826\) | −9.63087 | −0.335101 | ||||||||
\(827\) | 25.7734 | + | 25.7734i | 0.896227 | + | 0.896227i | 0.995100 | − | 0.0988727i | \(-0.0315237\pi\) |
−0.0988727 | + | 0.995100i | \(0.531524\pi\) | |||||||
\(828\) | 2.85094 | − | 0.933895i | 0.0990769 | − | 0.0324551i | ||||
\(829\) | 9.26672i | 0.321846i | 0.986967 | + | 0.160923i | \(0.0514471\pi\) | ||||
−0.986967 | + | 0.160923i | \(0.948553\pi\) | |||||||
\(830\) | 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 | ||||||
\(837\) | −3.01554 | − | 36.6298i | −0.104232 | − | 1.26611i | ||||
\(838\) | 20.1049 | + | 20.1049i | 0.694514 | + | 0.694514i | ||||
\(839\) | 0.301061 | 0.0103938 | 0.00519690 | − | 0.999986i | \(-0.498346\pi\) | ||||
0.00519690 | + | 0.999986i | \(0.498346\pi\) | |||||||
\(840\) | 2.94216 | + | 1.70877i | 0.101514 | + | 0.0589580i | ||||
\(841\) | 32.4346 | 1.11843 | ||||||||
\(842\) | 16.9824 | + | 16.9824i | 0.585252 | + | 0.585252i | ||||
\(843\) | 21.8337 | + | 35.5336i | 0.751993 | + | 1.22384i | ||||
\(844\) | − | 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 | ||||||||
\(852\) | −3.32936 | + | 2.04574i | −0.114062 | + | 0.0700857i | ||||
\(853\) | 7.46140 | + | 7.46140i | 0.255474 | + | 0.255474i | 0.823210 | − | 0.567737i | \(-0.192181\pi\) |
−0.567737 | + | 0.823210i | \(0.692181\pi\) | |||||||
\(854\) | −9.73727 | −0.333203 | ||||||||
\(855\) | 52.8528 | − | 1.31138i | 1.80753 | − | 0.0448483i | ||||
\(856\) | −3.39132 | −0.115913 | ||||||||
\(857\) | −4.73782 | − | 4.73782i | −0.161841 | − | 0.161841i | 0.621541 | − | 0.783382i | \(-0.286507\pi\) |
−0.783382 | + | 0.621541i | \(0.786507\pi\) | |||||||
\(858\) | −6.33035 | + | 3.88970i | −0.216115 | + | 0.132792i | ||||
\(859\) | − | 8.54021i | − | 0.291388i | −0.989330 | − | 0.145694i | \(-0.953458\pi\) | ||
0.989330 | − | 0.145694i | \(-0.0465416\pi\) | |||||||
\(860\) | 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 | \(-0.837329\pi\) |
0.489090 | + | 0.872234i | \(0.337329\pi\) | |||||||
\(864\) | 3.36039 | − | 3.96331i | 0.114323 | − | 0.134834i | ||||
\(865\) | 9.48585 | − | 31.5856i | 0.322529 | − | 1.07394i | ||||
\(866\) | 14.3670i | 0.488212i | ||||||||
\(867\) | 4.06316 | + | 6.61266i | 0.137992 | + | 0.224578i | ||||
\(868\) | 4.39381 | + | 4.39381i | 0.149136 | + | 0.149136i | ||||
\(869\) | −8.18503 | −0.277658 | ||||||||
\(870\) | −29.3423 | + | 7.78138i | −0.994796 | + | 0.263813i | ||||
\(871\) | −15.9086 | −0.539043 | ||||||||
\(872\) | −0.376112 | − | 0.376112i | −0.0127367 | − | 0.0127367i | ||||
\(873\) | −15.6171 | − | 47.6748i | −0.528558 | − | 1.61355i | ||||
\(874\) | 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 | −0.883999 | − | 0.467489i | \(-0.845159\pi\) |
0.467489 | + | 0.883999i | \(0.345159\pi\) | |||||||
\(878\) | −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 | \(0.691196\pi\) | |||||||
\(882\) | 5.81654 | + | 17.7564i | 0.195853 | + | 0.597888i | ||||
\(883\) | −20.3767 | − | 20.3767i | −0.685732 | − | 0.685732i | 0.275554 | − | 0.961286i | \(-0.411139\pi\) |
−0.961286 | + | 0.275554i | \(0.911139\pi\) | |||||||
\(884\) | 3.67554 | 0.123622 | ||||||||
\(885\) | −21.3243 | + | 36.7162i | −0.716807 | + | 1.23420i | ||||
\(886\) | −10.7135 | −0.359927 | ||||||||
\(887\) | 35.8940 | + | 35.8940i | 1.20520 | + | 1.20520i | 0.972563 | + | 0.232638i | \(0.0747358\pi\) |
0.232638 | + | 0.972563i | \(0.425264\pi\) | |||||||
\(888\) | 8.29154 | + | 13.4942i | 0.278246 | + | 0.452836i | ||||
\(889\) | 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 | ||||||||
\(897\) | 1.53300 | − | 0.941956i | 0.0511854 | − | 0.0314510i | ||||
\(898\) | −22.3903 | − | 22.3903i | −0.747174 | − | 0.747174i | ||||
\(899\) | −55.4403 | −1.84904 | ||||||||
\(900\) | 13.0288 | − | 7.43305i | 0.434293 | − | 0.247768i | ||||
\(901\) | −48.8936 | −1.62888 | ||||||||
\(902\) | 5.17515 | + | 5.17515i | 0.172314 | + | 0.172314i | ||||
\(903\) | −11.5766 | + | 7.11327i | −0.385245 | + | 0.236715i | ||||
\(904\) | − | 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 | −0.525249 | − | 0.850948i | \(-0.676028\pi\) |
0.850948 | + | 0.525249i | \(0.176028\pi\) | |||||||
\(908\) | 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 | \(-0.225508\pi\) | |||||||
\(912\) | 7.14645 | + | 11.6306i | 0.236643 | + | 0.385128i | ||||
\(913\) | 9.13753 | + | 9.13753i | 0.302408 | + | 0.302408i | ||||
\(914\) | −38.4890 | −1.27310 | ||||||||
\(915\) | −21.5598 | + | 37.1218i | −0.712746 | + | 1.22721i | ||||
\(916\) | −8.83078 | −0.291777 | ||||||||
\(917\) | −1.66936 | − | 1.66936i | −0.0551271 | − | 0.0551271i | ||||
\(918\) | −18.3232 | + | 1.50845i | −0.604755 | + | 0.0497863i | ||||
\(919\) | 7.64006i | 0.252022i | 0.992029 | + | 0.126011i | \(0.0402175\pi\) | ||||
−0.992029 | + | 0.126011i | \(0.959782\pi\) | |||||||
\(920\) | 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 | ||||||||
\(927\) | 13.6110 | − | 4.45863i | 0.447045 | − | 0.146441i | ||||
\(928\) | −5.54232 | − | 5.54232i | −0.181936 | − | 0.181936i | ||||
\(929\) | −7.70924 | −0.252932 | −0.126466 | − | 0.991971i | \(-0.540363\pi\) | ||||
−0.126466 | + | 0.991971i | \(0.540363\pi\) | |||||||
\(930\) | 26.4793 | − | 7.02213i | 0.868290 | − | 0.230265i | ||||
\(931\) | −49.0865 | −1.60874 | ||||||||
\(932\) | −13.3537 | − | 13.3537i | −0.437416 | − | 0.437416i | ||||
\(933\) | −1.40480 | − | 2.28626i | −0.0459911 | − | 0.0748489i | ||||
\(934\) | 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 | −0.852857 | − | 0.522144i | \(-0.825132\pi\) |
0.522144 | + | 0.852857i | \(0.325132\pi\) | |||||||
\(938\) | −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 | \(0.899421\pi\) | |||||||
\(942\) | 19.9634 | − | 12.2666i | 0.650444 | − | 0.399667i | ||||
\(943\) | −1.25325 | − | 1.25325i | −0.0408114 | − | 0.0408114i | ||||
\(944\) | −10.9630 | −0.356815 | ||||||||
\(945\) | −9.98372 | − | 2.12391i | −0.324770 | − | 0.0690909i | ||||
\(946\) | 36.8742 | 1.19888 | ||||||||
\(947\) | 16.0189 | + | 16.0189i | 0.520543 | + | 0.520543i | 0.917735 | − | 0.397192i | \(-0.130015\pi\) |
−0.397192 | + | 0.917735i | \(0.630015\pi\) | |||||||
\(948\) | 2.92510 | − | 1.79734i | 0.0950029 | − | 0.0583748i | ||||
\(949\) | 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 | \(-0.568417\pi\) |
0.976990 | + | 0.213286i | \(0.0684166\pi\) | |||||||
\(954\) | −18.7319 | + | 36.9826i | −0.606468 | + | 1.19736i | ||||
\(955\) | 11.2564 | + | 20.9196i | 0.364249 | + | 0.676941i | ||||
\(956\) | − | 5.29769i | − | 0.171340i | ||||||
\(957\) | −29.3486 | − | 47.7638i | −0.948705 | − | 1.54398i | ||||
\(958\) | −7.17891 | − | 7.17891i | −0.231940 | − | 0.231940i | ||||
\(959\) | 4.67003 | 0.150803 | ||||||||
\(960\) | 3.34911 | + | 1.94512i | 0.108092 | + | 0.0627783i | ||||
\(961\) | 19.0309 | 0.613899 | ||||||||
\(962\) | 6.71678 | + | 6.71678i | 0.216558 | + | 0.216558i | ||||
\(963\) | 9.66845 | − | 3.16714i | 0.311561 | − | 0.102060i | ||||
\(964\) | 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 | −0.995291 | − | 0.0969368i | \(-0.969096\pi\) |
0.0969368 | + | 0.995291i | \(0.469096\pi\) | |||||||
\(968\) | 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 | \(0.591274\pi\) | |||||||
\(972\) | −5.87893 | + | 14.4374i | −0.188567 | + | 0.463079i | ||||
\(973\) | 12.9088 | + | 12.9088i | 0.413836 | + | 0.413836i | ||||
\(974\) | 9.21274 | 0.295195 | ||||||||
\(975\) | 6.56489 | − | 6.15114i | 0.210245 | − | 0.196994i | ||||
\(976\) | −11.0841 | −0.354793 | ||||||||
\(977\) | −1.55002 | − | 1.55002i | −0.0495896 | − | 0.0495896i | 0.681877 | − | 0.731467i | \(-0.261164\pi\) |
−0.731467 | + | 0.681877i | \(0.761164\pi\) | |||||||
\(978\) | −1.66805 | − | 2.71470i | −0.0533384 | − | 0.0868064i | ||||
\(979\) | 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 | \(-0.787714\pi\) |
0.618565 | + | 0.785733i | \(0.287714\pi\) | |||||||
\(984\) | −2.98586 | − | 0.713053i | −0.0951857 | − | 0.0227313i | ||||
\(985\) | −31.7236 | − | 9.52730i | −1.01080 | − | 0.303565i | ||||
\(986\) | 27.7327i | 0.883189i | ||||||||
\(987\) | 0.0513510 | − | 0.0315527i | 0.00163452 | − | 0.00100434i | ||||
\(988\) | 5.78917 | + | 5.78917i | 0.184178 | + | 0.184178i | ||||
\(989\) | −8.92971 | −0.283948 | ||||||||
\(990\) | 20.0672 | + | 19.0955i | 0.637779 | + | 0.606896i | ||||
\(991\) | −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 | ||||
\(993\) | 14.3004 | − | 8.78692i | 0.453810 | − | 0.278845i | ||||
\(994\) | 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 | −0.974938 | − | 0.222476i | \(-0.928586\pi\) |
0.222476 | + | 0.974938i | \(0.428586\pi\) | |||||||
\(998\) | −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.323.9 | yes | 32 | |
3.2 | odd | 2 | inner | 690.2.i.f.323.6 | yes | 32 | |
5.2 | odd | 4 | inner | 690.2.i.f.47.6 | ✓ | 32 | |
15.2 | even | 4 | inner | 690.2.i.f.47.9 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.i.f.47.6 | ✓ | 32 | 5.2 | odd | 4 | inner | |
690.2.i.f.47.9 | yes | 32 | 15.2 | even | 4 | inner | |
690.2.i.f.323.6 | yes | 32 | 3.2 | odd | 2 | inner | |
690.2.i.f.323.9 | yes | 32 | 1.1 | even | 1 | trivial |