Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [552,2,Mod(277,552)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(552, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("552.277");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 552 = 2^{3} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 552.f (of order \(2\), degree \(1\), 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: | \(4.40774219157\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 4 x^{16} - 2 x^{15} + 5 x^{14} + 2 x^{13} + 6 x^{12} + 24 x^{11} - 12 x^{10} - 88 x^{9} - 24 x^{8} + 96 x^{7} + 48 x^{6} + 32 x^{5} + 160 x^{4} - 128 x^{3} - 512 x^{2} + 512 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 277.7 | ||
Root | \(1.37219 - 0.342174i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 552.277 |
Dual form | 552.2.f.c.277.8 |
$q$-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 \(\left(\mathbb{Z}/552\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(185\) | \(277\) | \(415\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.342174 | − | 1.37219i | −0.241953 | − | 0.970288i | ||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | −1.76583 | + | 0.939057i | −0.882917 | + | 0.469529i | ||||
\(5\) | 0.957976i | 0.428420i | 0.976788 | + | 0.214210i | \(0.0687177\pi\) | ||||
−0.976788 | + | 0.214210i | \(0.931282\pi\) | |||||||
\(6\) | −1.37219 | + | 0.342174i | −0.560196 | + | 0.139692i | ||||
\(7\) | 2.14538 | 0.810877 | 0.405439 | − | 0.914122i | \(-0.367119\pi\) | ||||
0.405439 | + | 0.914122i | \(0.367119\pi\) | |||||||
\(8\) | 1.89279 | + | 2.10175i | 0.669203 | + | 0.743080i | ||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 1.31453 | − | 0.327794i | 0.415691 | − | 0.103658i | ||||
\(11\) | − | 5.87650i | − | 1.77183i | −0.463845 | − | 0.885916i | \(-0.653531\pi\) | ||
0.463845 | − | 0.885916i | \(-0.346469\pi\) | |||||||
\(12\) | 0.939057 | + | 1.76583i | 0.271082 | + | 0.509753i | ||||
\(13\) | 1.37506i | 0.381372i | 0.981651 | + | 0.190686i | \(0.0610713\pi\) | ||||
−0.981651 | + | 0.190686i | \(0.938929\pi\) | |||||||
\(14\) | −0.734092 | − | 2.94388i | −0.196194 | − | 0.786784i | ||||
\(15\) | 0.957976 | 0.247348 | ||||||||
\(16\) | 2.23634 | − | 3.31644i | 0.559086 | − | 0.829110i | ||||
\(17\) | −0.163763 | −0.0397184 | −0.0198592 | − | 0.999803i | \(-0.506322\pi\) | ||||
−0.0198592 | + | 0.999803i | \(0.506322\pi\) | |||||||
\(18\) | 0.342174 | + | 1.37219i | 0.0806511 | + | 0.323429i | ||||
\(19\) | − | 5.82746i | − | 1.33691i | −0.743752 | − | 0.668455i | \(-0.766956\pi\) | ||
0.743752 | − | 0.668455i | \(-0.233044\pi\) | |||||||
\(20\) | −0.899594 | − | 1.69163i | −0.201155 | − | 0.378259i | ||||
\(21\) | − | 2.14538i | − | 0.468160i | ||||||
\(22\) | −8.06370 | + | 2.01078i | −1.71919 | + | 0.428701i | ||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 2.10175 | − | 1.89279i | 0.429017 | − | 0.386364i | ||||
\(25\) | 4.08228 | 0.816456 | ||||||||
\(26\) | 1.88685 | − | 0.470508i | 0.370041 | − | 0.0922743i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | −3.78839 | + | 2.01463i | −0.715937 | + | 0.380730i | ||||
\(29\) | − | 9.19473i | − | 1.70742i | −0.520750 | − | 0.853709i | \(-0.674348\pi\) | ||
0.520750 | − | 0.853709i | \(-0.325652\pi\) | |||||||
\(30\) | −0.327794 | − | 1.31453i | −0.0598467 | − | 0.239999i | ||||
\(31\) | −1.00647 | −0.180767 | −0.0903835 | − | 0.995907i | \(-0.528809\pi\) | ||||
−0.0903835 | + | 0.995907i | \(0.528809\pi\) | |||||||
\(32\) | −5.31602 | − | 1.93390i | −0.939748 | − | 0.341868i | ||||
\(33\) | −5.87650 | −1.02297 | ||||||||
\(34\) | 0.0560354 | + | 0.224715i | 0.00960999 | + | 0.0385383i | ||||
\(35\) | 2.05522i | 0.347396i | ||||||||
\(36\) | 1.76583 | − | 0.939057i | 0.294306 | − | 0.156510i | ||||
\(37\) | − | 1.82285i | − | 0.299675i | −0.988711 | − | 0.149837i | \(-0.952125\pi\) | ||
0.988711 | − | 0.149837i | \(-0.0478750\pi\) | |||||||
\(38\) | −7.99641 | + | 1.99400i | −1.29719 | + | 0.323470i | ||||
\(39\) | 1.37506 | 0.220185 | ||||||||
\(40\) | −2.01342 | + | 1.81325i | −0.318350 | + | 0.286700i | ||||
\(41\) | −8.24354 | −1.28742 | −0.643712 | − | 0.765267i | \(-0.722607\pi\) | ||||
−0.643712 | + | 0.765267i | \(0.722607\pi\) | |||||||
\(42\) | −2.94388 | + | 0.734092i | −0.454250 | + | 0.113273i | ||||
\(43\) | 8.14477i | 1.24207i | 0.783784 | + | 0.621033i | \(0.213287\pi\) | ||||
−0.783784 | + | 0.621033i | \(0.786713\pi\) | |||||||
\(44\) | 5.51837 | + | 10.3769i | 0.831926 | + | 1.56438i | ||||
\(45\) | − | 0.957976i | − | 0.142807i | ||||||
\(46\) | 0.342174 | + | 1.37219i | 0.0504507 | + | 0.202319i | ||||
\(47\) | 8.24511 | 1.20267 | 0.601336 | − | 0.798996i | \(-0.294635\pi\) | ||||
0.601336 | + | 0.798996i | \(0.294635\pi\) | |||||||
\(48\) | −3.31644 | − | 2.23634i | −0.478687 | − | 0.322788i | ||||
\(49\) | −2.39735 | −0.342478 | ||||||||
\(50\) | −1.39685 | − | 5.60168i | −0.197544 | − | 0.792198i | ||||
\(51\) | 0.163763i | 0.0229314i | ||||||||
\(52\) | −1.29126 | − | 2.42812i | −0.179065 | − | 0.336720i | ||||
\(53\) | − | 2.08900i | − | 0.286946i | −0.989654 | − | 0.143473i | \(-0.954173\pi\) | ||
0.989654 | − | 0.143473i | \(-0.0458270\pi\) | |||||||
\(54\) | 1.37219 | − | 0.342174i | 0.186732 | − | 0.0465639i | ||||
\(55\) | 5.62955 | 0.759088 | ||||||||
\(56\) | 4.06075 | + | 4.50905i | 0.542641 | + | 0.602547i | ||||
\(57\) | −5.82746 | −0.771866 | ||||||||
\(58\) | −12.6170 | + | 3.14619i | −1.65669 | + | 0.413115i | ||||
\(59\) | − | 9.20740i | − | 1.19870i | −0.800486 | − | 0.599351i | \(-0.795425\pi\) | ||
0.800486 | − | 0.599351i | \(-0.204575\pi\) | |||||||
\(60\) | −1.69163 | + | 0.899594i | −0.218388 | + | 0.116137i | ||||
\(61\) | 10.7403i | 1.37516i | 0.726109 | + | 0.687579i | \(0.241327\pi\) | ||||
−0.726109 | + | 0.687579i | \(0.758673\pi\) | |||||||
\(62\) | 0.344387 | + | 1.38107i | 0.0437371 | + | 0.175396i | ||||
\(63\) | −2.14538 | −0.270292 | ||||||||
\(64\) | −0.834685 | + | 7.95634i | −0.104336 | + | 0.994542i | ||||
\(65\) | −1.31727 | −0.163388 | ||||||||
\(66\) | 2.01078 | + | 8.06370i | 0.247510 | + | 0.992573i | ||||
\(67\) | 6.22959i | 0.761066i | 0.924767 | + | 0.380533i | \(0.124259\pi\) | ||||
−0.924767 | + | 0.380533i | \(0.875741\pi\) | |||||||
\(68\) | 0.289178 | − | 0.153783i | 0.0350680 | − | 0.0186489i | ||||
\(69\) | 1.00000i | 0.120386i | ||||||||
\(70\) | 2.82016 | − | 0.703242i | 0.337074 | − | 0.0840536i | ||||
\(71\) | 13.1930 | 1.56572 | 0.782860 | − | 0.622198i | \(-0.213760\pi\) | ||||
0.782860 | + | 0.622198i | \(0.213760\pi\) | |||||||
\(72\) | −1.89279 | − | 2.10175i | −0.223068 | − | 0.247693i | ||||
\(73\) | 6.18391 | 0.723771 | 0.361886 | − | 0.932222i | \(-0.382133\pi\) | ||||
0.361886 | + | 0.932222i | \(0.382133\pi\) | |||||||
\(74\) | −2.50130 | + | 0.623731i | −0.290771 | + | 0.0725073i | ||||
\(75\) | − | 4.08228i | − | 0.471381i | ||||||
\(76\) | 5.47232 | + | 10.2903i | 0.627718 | + | 1.18038i | ||||
\(77\) | − | 12.6073i | − | 1.43674i | ||||||
\(78\) | −0.470508 | − | 1.88685i | −0.0532746 | − | 0.213643i | ||||
\(79\) | 2.86636 | 0.322491 | 0.161245 | − | 0.986914i | \(-0.448449\pi\) | ||||
0.161245 | + | 0.986914i | \(0.448449\pi\) | |||||||
\(80\) | 3.17707 | + | 2.14236i | 0.355207 | + | 0.239523i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.82072 | + | 11.3117i | 0.311497 | + | 1.24917i | ||||
\(83\) | − | 3.36850i | − | 0.369741i | −0.982763 | − | 0.184871i | \(-0.940813\pi\) | ||
0.982763 | − | 0.184871i | \(-0.0591866\pi\) | |||||||
\(84\) | 2.01463 | + | 3.78839i | 0.219815 | + | 0.413347i | ||||
\(85\) | − | 0.156881i | − | 0.0170161i | ||||||
\(86\) | 11.1762 | − | 2.78693i | 1.20516 | − | 0.300522i | ||||
\(87\) | −9.19473 | −0.985778 | ||||||||
\(88\) | 12.3509 | − | 11.1230i | 1.31661 | − | 1.18571i | ||||
\(89\) | −8.21077 | −0.870340 | −0.435170 | − | 0.900348i | \(-0.643312\pi\) | ||||
−0.435170 | + | 0.900348i | \(0.643312\pi\) | |||||||
\(90\) | −1.31453 | + | 0.327794i | −0.138564 | + | 0.0345525i | ||||
\(91\) | 2.95002i | 0.309246i | ||||||||
\(92\) | 1.76583 | − | 0.939057i | 0.184101 | − | 0.0979035i | ||||
\(93\) | 1.00647i | 0.104366i | ||||||||
\(94\) | −2.82126 | − | 11.3139i | −0.290991 | − | 1.16694i | ||||
\(95\) | 5.58256 | 0.572759 | ||||||||
\(96\) | −1.93390 | + | 5.31602i | −0.197378 | + | 0.542564i | ||||
\(97\) | −5.18778 | −0.526739 | −0.263370 | − | 0.964695i | \(-0.584834\pi\) | ||||
−0.263370 | + | 0.964695i | \(0.584834\pi\) | |||||||
\(98\) | 0.820309 | + | 3.28963i | 0.0828637 | + | 0.332302i | ||||
\(99\) | 5.87650i | 0.590611i | ||||||||
\(100\) | −7.20864 | + | 3.83350i | −0.720864 | + | 0.383350i | ||||
\(101\) | 5.89378i | 0.586453i | 0.956043 | + | 0.293226i | \(0.0947290\pi\) | ||||
−0.956043 | + | 0.293226i | \(0.905271\pi\) | |||||||
\(102\) | 0.224715 | − | 0.0560354i | 0.0222501 | − | 0.00554833i | ||||
\(103\) | 8.05266 | 0.793452 | 0.396726 | − | 0.917937i | \(-0.370146\pi\) | ||||
0.396726 | + | 0.917937i | \(0.370146\pi\) | |||||||
\(104\) | −2.89002 | + | 2.60270i | −0.283390 | + | 0.255215i | ||||
\(105\) | 2.05522 | 0.200569 | ||||||||
\(106\) | −2.86651 | + | 0.714799i | −0.278420 | + | 0.0694274i | ||||
\(107\) | − | 17.9336i | − | 1.73370i | −0.498567 | − | 0.866851i | \(-0.666140\pi\) | ||
0.498567 | − | 0.866851i | \(-0.333860\pi\) | |||||||
\(108\) | −0.939057 | − | 1.76583i | −0.0903608 | − | 0.169918i | ||||
\(109\) | − | 15.2577i | − | 1.46142i | −0.682685 | − | 0.730712i | \(-0.739188\pi\) | ||
0.682685 | − | 0.730712i | \(-0.260812\pi\) | |||||||
\(110\) | −1.92628 | − | 7.72483i | −0.183664 | − | 0.736534i | ||||
\(111\) | −1.82285 | −0.173017 | ||||||||
\(112\) | 4.79780 | − | 7.11502i | 0.453350 | − | 0.672306i | ||||
\(113\) | 5.74351 | 0.540304 | 0.270152 | − | 0.962818i | \(-0.412926\pi\) | ||||
0.270152 | + | 0.962818i | \(0.412926\pi\) | |||||||
\(114\) | 1.99400 | + | 7.99641i | 0.186755 | + | 0.748932i | ||||
\(115\) | − | 0.957976i | − | 0.0893317i | ||||||
\(116\) | 8.63438 | + | 16.2364i | 0.801682 | + | 1.50751i | ||||
\(117\) | − | 1.37506i | − | 0.127124i | ||||||
\(118\) | −12.6343 | + | 3.15053i | −1.16309 | + | 0.290030i | ||||
\(119\) | −0.351334 | −0.0322067 | ||||||||
\(120\) | 1.81325 | + | 2.01342i | 0.165526 | + | 0.183800i | ||||
\(121\) | −23.5333 | −2.13939 | ||||||||
\(122\) | 14.7378 | − | 3.67506i | 1.33430 | − | 0.332724i | ||||
\(123\) | 8.24354i | 0.743295i | ||||||||
\(124\) | 1.77726 | − | 0.945131i | 0.159602 | − | 0.0848752i | ||||
\(125\) | 8.70061i | 0.778206i | ||||||||
\(126\) | 0.734092 | + | 2.94388i | 0.0653981 | + | 0.262261i | ||||
\(127\) | 5.66040 | 0.502279 | 0.251139 | − | 0.967951i | \(-0.419195\pi\) | ||||
0.251139 | + | 0.967951i | \(0.419195\pi\) | |||||||
\(128\) | 11.2032 | − | 1.57710i | 0.990237 | − | 0.139397i | ||||
\(129\) | 8.14477 | 0.717107 | ||||||||
\(130\) | 0.450736 | + | 1.80755i | 0.0395321 | + | 0.158533i | ||||
\(131\) | 12.7656i | 1.11533i | 0.830065 | + | 0.557666i | \(0.188303\pi\) | ||||
−0.830065 | + | 0.557666i | \(0.811697\pi\) | |||||||
\(132\) | 10.3769 | − | 5.51837i | 0.903196 | − | 0.480313i | ||||
\(133\) | − | 12.5021i | − | 1.08407i | ||||||
\(134\) | 8.54821 | − | 2.13160i | 0.738453 | − | 0.184142i | ||||
\(135\) | −0.957976 | −0.0824494 | ||||||||
\(136\) | −0.309969 | − | 0.344189i | −0.0265796 | − | 0.0295139i | ||||
\(137\) | 10.6909 | 0.913382 | 0.456691 | − | 0.889625i | \(-0.349035\pi\) | ||||
0.456691 | + | 0.889625i | \(0.349035\pi\) | |||||||
\(138\) | 1.37219 | − | 0.342174i | 0.116809 | − | 0.0291277i | ||||
\(139\) | 8.76418i | 0.743368i | 0.928359 | + | 0.371684i | \(0.121220\pi\) | ||||
−0.928359 | + | 0.371684i | \(0.878780\pi\) | |||||||
\(140\) | −1.92997 | − | 3.62918i | −0.163112 | − | 0.306722i | ||||
\(141\) | − | 8.24511i | − | 0.694364i | ||||||
\(142\) | −4.51429 | − | 18.1034i | −0.378831 | − | 1.51920i | ||||
\(143\) | 8.08053 | 0.675728 | ||||||||
\(144\) | −2.23634 | + | 3.31644i | −0.186362 | + | 0.276370i | ||||
\(145\) | 8.80833 | 0.731492 | ||||||||
\(146\) | −2.11597 | − | 8.48552i | −0.175119 | − | 0.702267i | ||||
\(147\) | 2.39735i | 0.197730i | ||||||||
\(148\) | 1.71176 | + | 3.21885i | 0.140706 | + | 0.264588i | ||||
\(149\) | 20.4589i | 1.67606i | 0.545624 | + | 0.838030i | \(0.316293\pi\) | ||||
−0.545624 | + | 0.838030i | \(0.683707\pi\) | |||||||
\(150\) | −5.60168 | + | 1.39685i | −0.457376 | + | 0.114052i | ||||
\(151\) | 14.2531 | 1.15990 | 0.579952 | − | 0.814651i | \(-0.303071\pi\) | ||||
0.579952 | + | 0.814651i | \(0.303071\pi\) | |||||||
\(152\) | 12.2478 | − | 11.0302i | 0.993432 | − | 0.894664i | ||||
\(153\) | 0.163763 | 0.0132395 | ||||||||
\(154\) | −17.2997 | + | 4.31389i | −1.39405 | + | 0.347624i | ||||
\(155\) | − | 0.964172i | − | 0.0774441i | ||||||
\(156\) | −2.42812 | + | 1.29126i | −0.194406 | + | 0.103383i | ||||
\(157\) | − | 3.79042i | − | 0.302508i | −0.988495 | − | 0.151254i | \(-0.951669\pi\) | ||
0.988495 | − | 0.151254i | \(-0.0483312\pi\) | |||||||
\(158\) | −0.980793 | − | 3.93321i | −0.0780277 | − | 0.312909i | ||||
\(159\) | −2.08900 | −0.165668 | ||||||||
\(160\) | 1.85263 | − | 5.09262i | 0.146463 | − | 0.402607i | ||||
\(161\) | −2.14538 | −0.169080 | ||||||||
\(162\) | −0.342174 | − | 1.37219i | −0.0268837 | − | 0.107810i | ||||
\(163\) | 4.87780i | 0.382059i | 0.981584 | + | 0.191030i | \(0.0611826\pi\) | ||||
−0.981584 | + | 0.191030i | \(0.938817\pi\) | |||||||
\(164\) | 14.5567 | − | 7.74116i | 1.13669 | − | 0.604483i | ||||
\(165\) | − | 5.62955i | − | 0.438260i | ||||||
\(166\) | −4.62224 | + | 1.15261i | −0.358755 | + | 0.0894601i | ||||
\(167\) | −18.4925 | −1.43100 | −0.715498 | − | 0.698615i | \(-0.753800\pi\) | ||||
−0.715498 | + | 0.698615i | \(0.753800\pi\) | |||||||
\(168\) | 4.50905 | − | 4.06075i | 0.347880 | − | 0.313294i | ||||
\(169\) | 11.1092 | 0.854555 | ||||||||
\(170\) | −0.215271 | + | 0.0536805i | −0.0165105 | + | 0.00411711i | ||||
\(171\) | 5.82746i | 0.445637i | ||||||||
\(172\) | −7.64841 | − | 14.3823i | −0.583186 | − | 1.09664i | ||||
\(173\) | 14.2971i | 1.08699i | 0.839414 | + | 0.543493i | \(0.182899\pi\) | ||||
−0.839414 | + | 0.543493i | \(0.817101\pi\) | |||||||
\(174\) | 3.14619 | + | 12.6170i | 0.238512 | + | 0.956489i | ||||
\(175\) | 8.75804 | 0.662046 | ||||||||
\(176\) | −19.4891 | − | 13.1419i | −1.46904 | − | 0.990606i | ||||
\(177\) | −9.20740 | −0.692071 | ||||||||
\(178\) | 2.80951 | + | 11.2668i | 0.210582 | + | 0.844481i | ||||
\(179\) | 24.4035i | 1.82400i | 0.410189 | + | 0.912000i | \(0.365463\pi\) | ||||
−0.410189 | + | 0.912000i | \(0.634537\pi\) | |||||||
\(180\) | 0.899594 | + | 1.69163i | 0.0670518 | + | 0.126086i | ||||
\(181\) | 20.6424i | 1.53434i | 0.641445 | + | 0.767169i | \(0.278335\pi\) | ||||
−0.641445 | + | 0.767169i | \(0.721665\pi\) | |||||||
\(182\) | 4.04800 | − | 1.00942i | 0.300058 | − | 0.0748231i | ||||
\(183\) | 10.7403 | 0.793948 | ||||||||
\(184\) | −1.89279 | − | 2.10175i | −0.139538 | − | 0.154943i | ||||
\(185\) | 1.74625 | 0.128387 | ||||||||
\(186\) | 1.38107 | − | 0.344387i | 0.101265 | − | 0.0252517i | ||||
\(187\) | 0.962354i | 0.0703743i | ||||||||
\(188\) | −14.5595 | + | 7.74263i | −1.06186 | + | 0.564689i | ||||
\(189\) | 2.14538i | 0.156053i | ||||||||
\(190\) | −1.91021 | − | 7.66036i | −0.138581 | − | 0.555741i | ||||
\(191\) | −10.0790 | −0.729290 | −0.364645 | − | 0.931147i | \(-0.618810\pi\) | ||||
−0.364645 | + | 0.931147i | \(0.618810\pi\) | |||||||
\(192\) | 7.95634 | + | 0.834685i | 0.574199 | + | 0.0602382i | ||||
\(193\) | 13.8031 | 0.993566 | 0.496783 | − | 0.867875i | \(-0.334514\pi\) | ||||
0.496783 | + | 0.867875i | \(0.334514\pi\) | |||||||
\(194\) | 1.77512 | + | 7.11864i | 0.127446 | + | 0.511089i | ||||
\(195\) | 1.31727i | 0.0943318i | ||||||||
\(196\) | 4.23332 | − | 2.25125i | 0.302380 | − | 0.160803i | ||||
\(197\) | 8.40195i | 0.598614i | 0.954157 | + | 0.299307i | \(0.0967555\pi\) | ||||
−0.954157 | + | 0.299307i | \(0.903244\pi\) | |||||||
\(198\) | 8.06370 | − | 2.01078i | 0.573062 | − | 0.142900i | ||||
\(199\) | −5.07488 | −0.359749 | −0.179874 | − | 0.983690i | \(-0.557569\pi\) | ||||
−0.179874 | + | 0.983690i | \(0.557569\pi\) | |||||||
\(200\) | 7.72691 | + | 8.57993i | 0.546375 | + | 0.606692i | ||||
\(201\) | 6.22959 | 0.439401 | ||||||||
\(202\) | 8.08741 | − | 2.01669i | 0.569028 | − | 0.141894i | ||||
\(203\) | − | 19.7262i | − | 1.38451i | ||||||
\(204\) | −0.153783 | − | 0.289178i | −0.0107670 | − | 0.0202465i | ||||
\(205\) | − | 7.89711i | − | 0.551558i | ||||||
\(206\) | −2.75541 | − | 11.0498i | −0.191978 | − | 0.769877i | ||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 4.56030 | + | 3.07510i | 0.316200 | + | 0.213220i | ||||
\(209\) | −34.2451 | −2.36878 | ||||||||
\(210\) | −0.703242 | − | 2.82016i | −0.0485283 | − | 0.194610i | ||||
\(211\) | 26.2297i | 1.80572i | 0.429930 | + | 0.902862i | \(0.358538\pi\) | ||||
−0.429930 | + | 0.902862i | \(0.641462\pi\) | |||||||
\(212\) | 1.96169 | + | 3.68882i | 0.134729 | + | 0.253349i | ||||
\(213\) | − | 13.1930i | − | 0.903969i | ||||||
\(214\) | −24.6083 | + | 6.13639i | −1.68219 | + | 0.419475i | ||||
\(215\) | −7.80249 | −0.532126 | ||||||||
\(216\) | −2.10175 | + | 1.89279i | −0.143006 | + | 0.128788i | ||||
\(217\) | −2.15925 | −0.146580 | ||||||||
\(218\) | −20.9366 | + | 5.22079i | −1.41800 | + | 0.353596i | ||||
\(219\) | − | 6.18391i | − | 0.417870i | ||||||
\(220\) | −9.94085 | + | 5.28647i | −0.670212 | + | 0.356414i | ||||
\(221\) | − | 0.225184i | − | 0.0151475i | ||||||
\(222\) | 0.623731 | + | 2.50130i | 0.0418621 | + | 0.167877i | ||||
\(223\) | −19.5439 | −1.30876 | −0.654379 | − | 0.756166i | \(-0.727070\pi\) | ||||
−0.654379 | + | 0.756166i | \(0.727070\pi\) | |||||||
\(224\) | −11.4049 | − | 4.14895i | −0.762020 | − | 0.277213i | ||||
\(225\) | −4.08228 | −0.272152 | ||||||||
\(226\) | −1.96528 | − | 7.88122i | −0.130728 | − | 0.524251i | ||||
\(227\) | 1.06802i | 0.0708873i | 0.999372 | + | 0.0354436i | \(0.0112844\pi\) | ||||
−0.999372 | + | 0.0354436i | \(0.988716\pi\) | |||||||
\(228\) | 10.2903 | − | 5.47232i | 0.681494 | − | 0.362413i | ||||
\(229\) | − | 19.1138i | − | 1.26308i | −0.775344 | − | 0.631539i | \(-0.782424\pi\) | ||
0.775344 | − | 0.631539i | \(-0.217576\pi\) | |||||||
\(230\) | −1.31453 | + | 0.327794i | −0.0866775 | + | 0.0216141i | ||||
\(231\) | −12.6073 | −0.829501 | ||||||||
\(232\) | 19.3250 | − | 17.4037i | 1.26875 | − | 1.14261i | ||||
\(233\) | −6.40572 | −0.419652 | −0.209826 | − | 0.977739i | \(-0.567290\pi\) | ||||
−0.209826 | + | 0.977739i | \(0.567290\pi\) | |||||||
\(234\) | −1.88685 | + | 0.470508i | −0.123347 | + | 0.0307581i | ||||
\(235\) | 7.89862i | 0.515249i | ||||||||
\(236\) | 8.64628 | + | 16.2587i | 0.562825 | + | 1.05835i | ||||
\(237\) | − | 2.86636i | − | 0.186190i | ||||||
\(238\) | 0.120217 | + | 0.482098i | 0.00779252 | + | 0.0312498i | ||||
\(239\) | −6.99571 | −0.452515 | −0.226257 | − | 0.974068i | \(-0.572649\pi\) | ||||
−0.226257 | + | 0.974068i | \(0.572649\pi\) | |||||||
\(240\) | 2.14236 | − | 3.17707i | 0.138289 | − | 0.205079i | ||||
\(241\) | −0.0382051 | −0.00246101 | −0.00123050 | − | 0.999999i | \(-0.500392\pi\) | ||||
−0.00123050 | + | 0.999999i | \(0.500392\pi\) | |||||||
\(242\) | 8.05247 | + | 32.2922i | 0.517632 | + | 2.07582i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | −10.0858 | − | 18.9656i | −0.645676 | − | 1.21415i | ||||
\(245\) | − | 2.29660i | − | 0.146724i | ||||||
\(246\) | 11.3117 | − | 2.82072i | 0.721210 | − | 0.179843i | ||||
\(247\) | 8.01309 | 0.509861 | ||||||||
\(248\) | −1.90503 | − | 2.11534i | −0.120970 | − | 0.134324i | ||||
\(249\) | −3.36850 | −0.213470 | ||||||||
\(250\) | 11.9389 | − | 2.97712i | 0.755084 | − | 0.188289i | ||||
\(251\) | − | 16.4795i | − | 1.04017i | −0.854113 | − | 0.520087i | \(-0.825899\pi\) | ||
0.854113 | − | 0.520087i | \(-0.174101\pi\) | |||||||
\(252\) | 3.78839 | − | 2.01463i | 0.238646 | − | 0.126910i | ||||
\(253\) | 5.87650i | 0.369453i | ||||||||
\(254\) | −1.93684 | − | 7.76716i | −0.121528 | − | 0.487355i | ||||
\(255\) | −0.156881 | −0.00982427 | ||||||||
\(256\) | −5.99754 | − | 14.8334i | −0.374846 | − | 0.927087i | ||||
\(257\) | −5.93490 | −0.370209 | −0.185105 | − | 0.982719i | \(-0.559262\pi\) | ||||
−0.185105 | + | 0.982719i | \(0.559262\pi\) | |||||||
\(258\) | −2.78693 | − | 11.1762i | −0.173506 | − | 0.695800i | ||||
\(259\) | − | 3.91071i | − | 0.242999i | ||||||
\(260\) | 2.32608 | − | 1.23699i | 0.144258 | − | 0.0767151i | ||||
\(261\) | 9.19473i | 0.569139i | ||||||||
\(262\) | 17.5168 | − | 4.36804i | 1.08219 | − | 0.269858i | ||||
\(263\) | 24.4364 | 1.50681 | 0.753406 | − | 0.657556i | \(-0.228410\pi\) | ||||
0.753406 | + | 0.657556i | \(0.228410\pi\) | |||||||
\(264\) | −11.1230 | − | 12.3509i | −0.684573 | − | 0.760147i | ||||
\(265\) | 2.00121 | 0.122933 | ||||||||
\(266\) | −17.1553 | + | 4.27789i | −1.05186 | + | 0.262294i | ||||
\(267\) | 8.21077i | 0.502491i | ||||||||
\(268\) | −5.84994 | − | 11.0004i | −0.357342 | − | 0.671958i | ||||
\(269\) | 12.0472i | 0.734533i | 0.930116 | + | 0.367267i | \(0.119706\pi\) | ||||
−0.930116 | + | 0.367267i | \(0.880294\pi\) | |||||||
\(270\) | 0.327794 | + | 1.31453i | 0.0199489 | + | 0.0799997i | ||||
\(271\) | 7.03469 | 0.427327 | 0.213663 | − | 0.976907i | \(-0.431460\pi\) | ||||
0.213663 | + | 0.976907i | \(0.431460\pi\) | |||||||
\(272\) | −0.366230 | + | 0.543110i | −0.0222060 | + | 0.0329309i | ||||
\(273\) | 2.95002 | 0.178543 | ||||||||
\(274\) | −3.65813 | − | 14.6699i | −0.220996 | − | 0.886243i | ||||
\(275\) | − | 23.9895i | − | 1.44662i | ||||||
\(276\) | −0.939057 | − | 1.76583i | −0.0565246 | − | 0.106291i | ||||
\(277\) | 11.0796i | 0.665711i | 0.942978 | + | 0.332856i | \(0.108012\pi\) | ||||
−0.942978 | + | 0.332856i | \(0.891988\pi\) | |||||||
\(278\) | 12.0262 | − | 2.99887i | 0.721281 | − | 0.179860i | ||||
\(279\) | 1.00647 | 0.0602556 | ||||||||
\(280\) | −4.31956 | + | 3.89010i | −0.258143 | + | 0.232478i | ||||
\(281\) | −4.12434 | −0.246037 | −0.123019 | − | 0.992404i | \(-0.539258\pi\) | ||||
−0.123019 | + | 0.992404i | \(0.539258\pi\) | |||||||
\(282\) | −11.3139 | + | 2.82126i | −0.673733 | + | 0.168004i | ||||
\(283\) | 4.43435i | 0.263595i | 0.991277 | + | 0.131797i | \(0.0420748\pi\) | ||||
−0.991277 | + | 0.131797i | \(0.957925\pi\) | |||||||
\(284\) | −23.2966 | + | 12.3890i | −1.38240 | + | 0.735151i | ||||
\(285\) | − | 5.58256i | − | 0.330683i | ||||||
\(286\) | −2.76494 | − | 11.0881i | −0.163495 | − | 0.655651i | ||||
\(287\) | −17.6855 | −1.04394 | ||||||||
\(288\) | 5.31602 | + | 1.93390i | 0.313249 | + | 0.113956i | ||||
\(289\) | −16.9732 | −0.998422 | ||||||||
\(290\) | −3.01398 | − | 12.0867i | −0.176987 | − | 0.709758i | ||||
\(291\) | 5.18778i | 0.304113i | ||||||||
\(292\) | −10.9198 | + | 5.80704i | −0.639030 | + | 0.339831i | ||||
\(293\) | 13.6440i | 0.797093i | 0.917148 | + | 0.398547i | \(0.130485\pi\) | ||||
−0.917148 | + | 0.398547i | \(0.869515\pi\) | |||||||
\(294\) | 3.28963 | − | 0.820309i | 0.191855 | − | 0.0478414i | ||||
\(295\) | 8.82047 | 0.513548 | ||||||||
\(296\) | 3.83117 | − | 3.45027i | 0.222682 | − | 0.200543i | ||||
\(297\) | 5.87650 | 0.340989 | ||||||||
\(298\) | 28.0736 | − | 7.00050i | 1.62626 | − | 0.405528i | ||||
\(299\) | − | 1.37506i | − | 0.0795217i | ||||||
\(300\) | 3.83350 | + | 7.20864i | 0.221327 | + | 0.416191i | ||||
\(301\) | 17.4736i | 1.00716i | ||||||||
\(302\) | −4.87705 | − | 19.5581i | −0.280642 | − | 1.12544i | ||||
\(303\) | 5.89378 | 0.338589 | ||||||||
\(304\) | −19.3264 | − | 13.0322i | −1.10845 | − | 0.747448i | ||||
\(305\) | −10.2890 | −0.589145 | ||||||||
\(306\) | −0.0560354 | − | 0.224715i | −0.00320333 | − | 0.0128461i | ||||
\(307\) | − | 14.5188i | − | 0.828631i | −0.910133 | − | 0.414315i | \(-0.864021\pi\) | ||
0.910133 | − | 0.414315i | \(-0.135979\pi\) | |||||||
\(308\) | 11.8390 | + | 22.2625i | 0.674590 | + | 1.26852i | ||||
\(309\) | − | 8.05266i | − | 0.458100i | ||||||
\(310\) | −1.32303 | + | 0.329914i | −0.0751431 | + | 0.0187379i | ||||
\(311\) | 20.9648 | 1.18880 | 0.594401 | − | 0.804169i | \(-0.297389\pi\) | ||||
0.594401 | + | 0.804169i | \(0.297389\pi\) | |||||||
\(312\) | 2.60270 | + | 2.89002i | 0.147349 | + | 0.163615i | ||||
\(313\) | 18.5992 | 1.05129 | 0.525646 | − | 0.850704i | \(-0.323824\pi\) | ||||
0.525646 | + | 0.850704i | \(0.323824\pi\) | |||||||
\(314\) | −5.20119 | + | 1.29698i | −0.293520 | + | 0.0731929i | ||||
\(315\) | − | 2.05522i | − | 0.115799i | ||||||
\(316\) | −5.06152 | + | 2.69168i | −0.284733 | + | 0.151419i | ||||
\(317\) | 10.6709i | 0.599338i | 0.954043 | + | 0.299669i | \(0.0968763\pi\) | ||||
−0.954043 | + | 0.299669i | \(0.903124\pi\) | |||||||
\(318\) | 0.714799 | + | 2.86651i | 0.0400839 | + | 0.160746i | ||||
\(319\) | −54.0329 | −3.02526 | ||||||||
\(320\) | −7.62198 | − | 0.799608i | −0.426082 | − | 0.0446995i | ||||
\(321\) | −17.9336 | −1.00095 | ||||||||
\(322\) | 0.734092 | + | 2.94388i | 0.0409094 | + | 0.164056i | ||||
\(323\) | 0.954322i | 0.0530999i | ||||||||
\(324\) | −1.76583 | + | 0.939057i | −0.0981019 | + | 0.0521698i | ||||
\(325\) | 5.61337i | 0.311374i | ||||||||
\(326\) | 6.69330 | − | 1.66906i | 0.370707 | − | 0.0924404i | ||||
\(327\) | −15.2577 | −0.843754 | ||||||||
\(328\) | −15.6033 | − | 17.3258i | −0.861548 | − | 0.956660i | ||||
\(329\) | 17.6889 | 0.975220 | ||||||||
\(330\) | −7.72483 | + | 1.92628i | −0.425238 | + | 0.106038i | ||||
\(331\) | − | 16.1398i | − | 0.887121i | −0.896244 | − | 0.443561i | \(-0.853715\pi\) | ||
0.896244 | − | 0.443561i | \(-0.146285\pi\) | |||||||
\(332\) | 3.16322 | + | 5.94822i | 0.173604 | + | 0.326451i | ||||
\(333\) | 1.82285i | 0.0998916i | ||||||||
\(334\) | 6.32766 | + | 25.3754i | 0.346234 | + | 1.38848i | ||||
\(335\) | −5.96780 | −0.326056 | ||||||||
\(336\) | −7.11502 | − | 4.79780i | −0.388156 | − | 0.261742i | ||||
\(337\) | −5.26522 | −0.286815 | −0.143407 | − | 0.989664i | \(-0.545806\pi\) | ||||
−0.143407 | + | 0.989664i | \(0.545806\pi\) | |||||||
\(338\) | −3.80128 | − | 15.2440i | −0.206762 | − | 0.829164i | ||||
\(339\) | − | 5.74351i | − | 0.311945i | ||||||
\(340\) | 0.147320 | + | 0.277026i | 0.00798956 | + | 0.0150238i | ||||
\(341\) | 5.91451i | 0.320289i | ||||||||
\(342\) | 7.99641 | − | 1.99400i | 0.432396 | − | 0.107823i | ||||
\(343\) | −20.1609 | −1.08858 | ||||||||
\(344\) | −17.1183 | + | 15.4164i | −0.922954 | + | 0.831194i | ||||
\(345\) | −0.957976 | −0.0515757 | ||||||||
\(346\) | 19.6184 | − | 4.89208i | 1.05469 | − | 0.263000i | ||||
\(347\) | − | 7.51081i | − | 0.403201i | −0.979468 | − | 0.201601i | \(-0.935386\pi\) | ||
0.979468 | − | 0.201601i | \(-0.0646143\pi\) | |||||||
\(348\) | 16.2364 | − | 8.63438i | 0.870361 | − | 0.462851i | ||||
\(349\) | − | 13.4864i | − | 0.721911i | −0.932583 | − | 0.360955i | \(-0.882451\pi\) | ||
0.932583 | − | 0.360955i | \(-0.117549\pi\) | |||||||
\(350\) | −2.99677 | − | 12.0177i | −0.160184 | − | 0.642375i | ||||
\(351\) | −1.37506 | −0.0733952 | ||||||||
\(352\) | −11.3646 | + | 31.2396i | −0.605733 | + | 1.66508i | ||||
\(353\) | −29.4707 | −1.56857 | −0.784285 | − | 0.620401i | \(-0.786970\pi\) | ||||
−0.784285 | + | 0.620401i | \(0.786970\pi\) | |||||||
\(354\) | 3.15053 | + | 12.6343i | 0.167449 | + | 0.671508i | ||||
\(355\) | 12.6386i | 0.670786i | ||||||||
\(356\) | 14.4989 | − | 7.71039i | 0.768439 | − | 0.408650i | ||||
\(357\) | 0.351334i | 0.0185946i | ||||||||
\(358\) | 33.4863 | − | 8.35022i | 1.76981 | − | 0.441323i | ||||
\(359\) | −27.4578 | −1.44917 | −0.724585 | − | 0.689186i | \(-0.757968\pi\) | ||||
−0.724585 | + | 0.689186i | \(0.757968\pi\) | |||||||
\(360\) | 2.01342 | − | 1.81325i | 0.106117 | − | 0.0955666i | ||||
\(361\) | −14.9593 | −0.787331 | ||||||||
\(362\) | 28.3254 | − | 7.06329i | 1.48875 | − | 0.371238i | ||||
\(363\) | 23.5333i | 1.23518i | ||||||||
\(364\) | −2.77024 | − | 5.20925i | −0.145200 | − | 0.273039i | ||||
\(365\) | 5.92403i | 0.310078i | ||||||||
\(366\) | −3.67506 | − | 14.7378i | −0.192098 | − | 0.770358i | ||||
\(367\) | 30.8406 | 1.60987 | 0.804933 | − | 0.593366i | \(-0.202201\pi\) | ||||
0.804933 | + | 0.593366i | \(0.202201\pi\) | |||||||
\(368\) | −2.23634 | + | 3.31644i | −0.116577 | + | 0.172881i | ||||
\(369\) | 8.24354 | 0.429142 | ||||||||
\(370\) | −0.597519 | − | 2.39619i | −0.0310636 | − | 0.124572i | ||||
\(371\) | − | 4.48169i | − | 0.232678i | ||||||
\(372\) | −0.945131 | − | 1.77726i | −0.0490027 | − | 0.0921464i | ||||
\(373\) | − | 14.5772i | − | 0.754779i | −0.926055 | − | 0.377390i | \(-0.876822\pi\) | ||
0.926055 | − | 0.377390i | \(-0.123178\pi\) | |||||||
\(374\) | 1.32054 | − | 0.329292i | 0.0682833 | − | 0.0170273i | ||||
\(375\) | 8.70061 | 0.449297 | ||||||||
\(376\) | 15.6063 | + | 17.3291i | 0.804832 | + | 0.893682i | ||||
\(377\) | 12.6433 | 0.651162 | ||||||||
\(378\) | 2.94388 | − | 0.734092i | 0.151417 | − | 0.0377576i | ||||
\(379\) | − | 26.4365i | − | 1.35795i | −0.734160 | − | 0.678977i | \(-0.762424\pi\) | ||
0.734160 | − | 0.678977i | \(-0.237576\pi\) | |||||||
\(380\) | −9.85789 | + | 5.24235i | −0.505699 | + | 0.268927i | ||||
\(381\) | − | 5.66040i | − | 0.289991i | ||||||
\(382\) | 3.44877 | + | 13.8303i | 0.176454 | + | 0.707622i | ||||
\(383\) | −27.7211 | −1.41648 | −0.708240 | − | 0.705972i | \(-0.750510\pi\) | ||||
−0.708240 | + | 0.705972i | \(0.750510\pi\) | |||||||
\(384\) | −1.57710 | − | 11.2032i | −0.0804809 | − | 0.571713i | ||||
\(385\) | 12.0775 | 0.615527 | ||||||||
\(386\) | −4.72304 | − | 18.9405i | −0.240397 | − | 0.964045i | ||||
\(387\) | − | 8.14477i | − | 0.414022i | ||||||
\(388\) | 9.16076 | − | 4.87162i | 0.465067 | − | 0.247319i | ||||
\(389\) | − | 1.44716i | − | 0.0733741i | −0.999327 | − | 0.0366871i | \(-0.988320\pi\) | ||
0.999327 | − | 0.0366871i | \(-0.0116805\pi\) | |||||||
\(390\) | 1.80755 | − | 0.450736i | 0.0915290 | − | 0.0228239i | ||||
\(391\) | 0.163763 | 0.00828185 | ||||||||
\(392\) | −4.53768 | − | 5.03862i | −0.229187 | − | 0.254489i | ||||
\(393\) | 12.7656 | 0.643938 | ||||||||
\(394\) | 11.5291 | − | 2.87493i | 0.580828 | − | 0.144837i | ||||
\(395\) | 2.74591i | 0.138162i | ||||||||
\(396\) | −5.51837 | − | 10.3769i | −0.277309 | − | 0.521460i | ||||
\(397\) | 1.57533i | 0.0790636i | 0.999218 | + | 0.0395318i | \(0.0125866\pi\) | ||||
−0.999218 | + | 0.0395318i | \(0.987413\pi\) | |||||||
\(398\) | 1.73649 | + | 6.96372i | 0.0870423 | + | 0.349060i | ||||
\(399\) | −12.5021 | −0.625888 | ||||||||
\(400\) | 9.12938 | − | 13.5386i | 0.456469 | − | 0.676932i | ||||
\(401\) | 20.9284 | 1.04511 | 0.522557 | − | 0.852604i | \(-0.324978\pi\) | ||||
0.522557 | + | 0.852604i | \(0.324978\pi\) | |||||||
\(402\) | −2.13160 | − | 8.54821i | −0.106315 | − | 0.426346i | ||||
\(403\) | − | 1.38395i | − | 0.0689395i | ||||||
\(404\) | −5.53459 | − | 10.4074i | −0.275356 | − | 0.517789i | ||||
\(405\) | 0.957976i | 0.0476022i | ||||||||
\(406\) | −27.0682 | + | 6.74978i | −1.34337 | + | 0.334986i | ||||
\(407\) | −10.7120 | −0.530973 | ||||||||
\(408\) | −0.344189 | + | 0.309969i | −0.0170399 | + | 0.0153458i | ||||
\(409\) | 34.4027 | 1.70110 | 0.850552 | − | 0.525890i | \(-0.176268\pi\) | ||||
0.850552 | + | 0.525890i | \(0.176268\pi\) | |||||||
\(410\) | −10.8364 | + | 2.70218i | −0.535170 | + | 0.133451i | ||||
\(411\) | − | 10.6909i | − | 0.527341i | ||||||
\(412\) | −14.2197 | + | 7.56190i | −0.700552 | + | 0.372548i | ||||
\(413\) | − | 19.7534i | − | 0.972000i | ||||||
\(414\) | −0.342174 | − | 1.37219i | −0.0168169 | − | 0.0674397i | ||||
\(415\) | 3.22694 | 0.158404 | ||||||||
\(416\) | 2.65922 | − | 7.30983i | 0.130379 | − | 0.358394i | ||||
\(417\) | 8.76418 | 0.429184 | ||||||||
\(418\) | 11.7178 | + | 46.9909i | 0.573134 | + | 2.29840i | ||||
\(419\) | 11.8285i | 0.577858i | 0.957350 | + | 0.288929i | \(0.0932992\pi\) | ||||
−0.957350 | + | 0.288929i | \(0.906701\pi\) | |||||||
\(420\) | −3.62918 | + | 1.92997i | −0.177086 | + | 0.0941729i | ||||
\(421\) | − | 4.48030i | − | 0.218357i | −0.994022 | − | 0.109178i | \(-0.965178\pi\) | ||
0.994022 | − | 0.109178i | \(-0.0348219\pi\) | |||||||
\(422\) | 35.9922 | − | 8.97510i | 1.75207 | − | 0.436901i | ||||
\(423\) | −8.24511 | −0.400891 | ||||||||
\(424\) | 4.39054 | − | 3.95403i | 0.213224 | − | 0.192025i | ||||
\(425\) | −0.668527 | −0.0324283 | ||||||||
\(426\) | −18.1034 | + | 4.51429i | −0.877110 | + | 0.218718i | ||||
\(427\) | 23.0421i | 1.11508i | ||||||||
\(428\) | 16.8406 | + | 31.6677i | 0.814023 | + | 1.53072i | ||||
\(429\) | − | 8.08053i | − | 0.390132i | ||||||
\(430\) | 2.66981 | + | 10.7065i | 0.128750 | + | 0.516315i | ||||
\(431\) | 37.1607 | 1.78997 | 0.894985 | − | 0.446097i | \(-0.147186\pi\) | ||||
0.894985 | + | 0.446097i | \(0.147186\pi\) | |||||||
\(432\) | 3.31644 | + | 2.23634i | 0.159562 | + | 0.107596i | ||||
\(433\) | 29.9902 | 1.44124 | 0.720620 | − | 0.693331i | \(-0.243857\pi\) | ||||
0.720620 | + | 0.693331i | \(0.243857\pi\) | |||||||
\(434\) | 0.738840 | + | 2.96292i | 0.0354655 | + | 0.142225i | ||||
\(435\) | − | 8.80833i | − | 0.422327i | ||||||
\(436\) | 14.3279 | + | 26.9426i | 0.686181 | + | 1.29032i | ||||
\(437\) | 5.82746i | 0.278765i | ||||||||
\(438\) | −8.48552 | + | 2.11597i | −0.405454 | + | 0.101105i | ||||
\(439\) | 0.0326011 | 0.00155597 | 0.000777984 | − | 1.00000i | \(-0.499752\pi\) | ||||
0.000777984 | 1.00000i | \(0.499752\pi\) | ||||||||
\(440\) | 10.6556 | + | 11.8319i | 0.507984 | + | 0.564063i | ||||
\(441\) | 2.39735 | 0.114159 | ||||||||
\(442\) | −0.308996 | + | 0.0770519i | −0.0146974 | + | 0.00366498i | ||||
\(443\) | − | 5.57880i | − | 0.265057i | −0.991179 | − | 0.132528i | \(-0.957690\pi\) | ||
0.991179 | − | 0.132528i | \(-0.0423096\pi\) | |||||||
\(444\) | 3.21885 | − | 1.71176i | 0.152760 | − | 0.0812366i | ||||
\(445\) | − | 7.86572i | − | 0.372871i | ||||||
\(446\) | 6.68742 | + | 26.8181i | 0.316658 | + | 1.26987i | ||||
\(447\) | 20.4589 | 0.967674 | ||||||||
\(448\) | −1.79072 | + | 17.0694i | −0.0846034 | + | 0.806452i | ||||
\(449\) | −14.6776 | −0.692680 | −0.346340 | − | 0.938109i | \(-0.612576\pi\) | ||||
−0.346340 | + | 0.938109i | \(0.612576\pi\) | |||||||
\(450\) | 1.39685 | + | 5.60168i | 0.0658481 | + | 0.264066i | ||||
\(451\) | 48.4432i | 2.28110i | ||||||||
\(452\) | −10.1421 | + | 5.39349i | −0.477044 | + | 0.253688i | ||||
\(453\) | − | 14.2531i | − | 0.669671i | ||||||
\(454\) | 1.46554 | − | 0.365450i | 0.0687811 | − | 0.0171514i | ||||
\(455\) | −2.82605 | −0.132487 | ||||||||
\(456\) | −11.0302 | − | 12.2478i | −0.516535 | − | 0.573558i | ||||
\(457\) | 4.17137 | 0.195128 | 0.0975642 | − | 0.995229i | \(-0.468895\pi\) | ||||
0.0975642 | + | 0.995229i | \(0.468895\pi\) | |||||||
\(458\) | −26.2279 | + | 6.54025i | −1.22555 | + | 0.305606i | ||||
\(459\) | − | 0.163763i | − | 0.00764380i | ||||||
\(460\) | 0.899594 | + | 1.69163i | 0.0419438 | + | 0.0788725i | ||||
\(461\) | 28.3795i | 1.32177i | 0.750489 | + | 0.660883i | \(0.229818\pi\) | ||||
−0.750489 | + | 0.660883i | \(0.770182\pi\) | |||||||
\(462\) | 4.31389 | + | 17.2997i | 0.200701 | + | 0.804855i | ||||
\(463\) | −21.7291 | −1.00984 | −0.504919 | − | 0.863167i | \(-0.668478\pi\) | ||||
−0.504919 | + | 0.863167i | \(0.668478\pi\) | |||||||
\(464\) | −30.4938 | − | 20.5626i | −1.41564 | − | 0.954593i | ||||
\(465\) | −0.964172 | −0.0447124 | ||||||||
\(466\) | 2.19187 | + | 8.78989i | 0.101536 | + | 0.407184i | ||||
\(467\) | 2.94330i | 0.136199i | 0.997679 | + | 0.0680997i | \(0.0216936\pi\) | ||||
−0.997679 | + | 0.0680997i | \(0.978306\pi\) | |||||||
\(468\) | 1.29126 | + | 2.42812i | 0.0596884 | + | 0.112240i | ||||
\(469\) | 13.3648i | 0.617131i | ||||||||
\(470\) | 10.8384 | − | 2.70270i | 0.499940 | − | 0.124666i | ||||
\(471\) | −3.79042 | −0.174653 | ||||||||
\(472\) | 19.3516 | − | 17.4277i | 0.890731 | − | 0.802174i | ||||
\(473\) | 47.8628 | 2.20073 | ||||||||
\(474\) | −3.93321 | + | 0.980793i | −0.180658 | + | 0.0450493i | ||||
\(475\) | − | 23.7893i | − | 1.09153i | ||||||
\(476\) | 0.620397 | − | 0.329923i | 0.0284359 | − | 0.0151220i | ||||
\(477\) | 2.08900i | 0.0956485i | ||||||||
\(478\) | 2.39375 | + | 9.59947i | 0.109487 | + | 0.439070i | ||||
\(479\) | 16.7957 | 0.767414 | 0.383707 | − | 0.923455i | \(-0.374647\pi\) | ||||
0.383707 | + | 0.923455i | \(0.374647\pi\) | |||||||
\(480\) | −5.09262 | − | 1.85263i | −0.232445 | − | 0.0845605i | ||||
\(481\) | 2.50652 | 0.114288 | ||||||||
\(482\) | 0.0130728 | + | 0.0524248i | 0.000595448 | + | 0.00238788i | ||||
\(483\) | 2.14538i | 0.0976181i | ||||||||
\(484\) | 41.5559 | − | 22.0991i | 1.88890 | − | 1.00450i | ||||
\(485\) | − | 4.96977i | − | 0.225666i | ||||||
\(486\) | −1.37219 | + | 0.342174i | −0.0622440 | + | 0.0155213i | ||||
\(487\) | −22.4359 | −1.01667 | −0.508334 | − | 0.861160i | \(-0.669739\pi\) | ||||
−0.508334 | + | 0.861160i | \(0.669739\pi\) | |||||||
\(488\) | −22.5735 | + | 20.3292i | −1.02185 | + | 0.920260i | ||||
\(489\) | 4.87780 | 0.220582 | ||||||||
\(490\) | −3.15138 | + | 0.785836i | −0.142365 | + | 0.0355004i | ||||
\(491\) | − | 22.5240i | − | 1.01650i | −0.861211 | − | 0.508248i | \(-0.830293\pi\) | ||
0.861211 | − | 0.508248i | \(-0.169707\pi\) | |||||||
\(492\) | −7.74116 | − | 14.5567i | −0.348998 | − | 0.656268i | ||||
\(493\) | 1.50576i | 0.0678159i | ||||||||
\(494\) | −2.74187 | − | 10.9955i | −0.123363 | − | 0.494712i | ||||
\(495\) | −5.62955 | −0.253029 | ||||||||
\(496\) | −2.25081 | + | 3.33789i | −0.101064 | + | 0.149876i | ||||
\(497\) | 28.3040 | 1.26961 | ||||||||
\(498\) | 1.15261 | + | 4.62224i | 0.0516498 | + | 0.207128i | ||||
\(499\) | − | 15.7359i | − | 0.704436i | −0.935918 | − | 0.352218i | \(-0.885428\pi\) | ||
0.935918 | − | 0.352218i | \(-0.114572\pi\) | |||||||
\(500\) | −8.17037 | − | 15.3638i | −0.365390 | − | 0.687091i | ||||
\(501\) | 18.4925i | 0.826186i | ||||||||
\(502\) | −22.6130 | + | 5.63883i | −1.00927 | + | 0.251674i | ||||
\(503\) | 18.9239 | 0.843777 | 0.421889 | − | 0.906648i | \(-0.361367\pi\) | ||||
0.421889 | + | 0.906648i | \(0.361367\pi\) | |||||||
\(504\) | −4.06075 | − | 4.50905i | −0.180880 | − | 0.200849i | ||||
\(505\) | −5.64610 | −0.251248 | ||||||||
\(506\) | 8.06370 | − | 2.01078i | 0.358475 | − | 0.0893903i | ||||
\(507\) | − | 11.1092i | − | 0.493378i | ||||||
\(508\) | −9.99532 | + | 5.31544i | −0.443471 | + | 0.235834i | ||||
\(509\) | 2.68826i | 0.119155i | 0.998224 | + | 0.0595776i | \(0.0189754\pi\) | ||||
−0.998224 | + | 0.0595776i | \(0.981025\pi\) | |||||||
\(510\) | 0.0536805 | + | 0.215271i | 0.00237701 | + | 0.00953237i | ||||
\(511\) | 13.2668 | 0.586890 | ||||||||
\(512\) | −18.3021 | + | 13.3054i | −0.808846 | + | 0.588021i | ||||
\(513\) | 5.82746 | 0.257289 | ||||||||
\(514\) | 2.03077 | + | 8.14384i | 0.0895733 | + | 0.359209i | ||||
\(515\) | 7.71425i | 0.339930i | ||||||||
\(516\) | −14.3823 | + | 7.64841i | −0.633146 | + | 0.336702i | ||||
\(517\) | − | 48.4524i | − | 2.13093i | ||||||
\(518\) | −5.36625 | + | 1.33814i | −0.235779 | + | 0.0587945i | ||||
\(519\) | 14.2971 | 0.627572 | ||||||||
\(520\) | −2.49332 | − | 2.76857i | −0.109339 | − | 0.121410i | ||||
\(521\) | 25.2684 | 1.10703 | 0.553515 | − | 0.832839i | \(-0.313286\pi\) | ||||
0.553515 | + | 0.832839i | \(0.313286\pi\) | |||||||
\(522\) | 12.6170 | − | 3.14619i | 0.552229 | − | 0.137705i | ||||
\(523\) | − | 29.2960i | − | 1.28103i | −0.767947 | − | 0.640513i | \(-0.778722\pi\) | ||
0.767947 | − | 0.640513i | \(-0.221278\pi\) | |||||||
\(524\) | −11.9876 | − | 22.5419i | −0.523681 | − | 0.984746i | ||||
\(525\) | − | 8.75804i | − | 0.382232i | ||||||
\(526\) | −8.36148 | − | 33.5315i | −0.364578 | − | 1.46204i | ||||
\(527\) | 0.164822 | 0.00717977 | ||||||||
\(528\) | −13.1419 | + | 19.4891i | −0.571927 | + | 0.848153i | ||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −0.684760 | − | 2.74604i | −0.0297441 | − | 0.119281i | ||||
\(531\) | 9.20740i | 0.399567i | ||||||||
\(532\) | 11.7402 | + | 22.0767i | 0.509002 | + | 0.957145i | ||||
\(533\) | − | 11.3353i | − | 0.490988i | ||||||
\(534\) | 11.2668 | − | 2.80951i | 0.487561 | − | 0.121579i | ||||
\(535\) | 17.1799 | 0.742752 | ||||||||
\(536\) | −13.0930 | + | 11.7913i | −0.565533 | + | 0.509307i | ||||
\(537\) | 24.4035 | 1.05309 | ||||||||
\(538\) | 16.5312 | − | 4.12225i | 0.712709 | − | 0.177723i | ||||
\(539\) | 14.0880i | 0.606814i | ||||||||
\(540\) | 1.69163 | − | 0.899594i | 0.0727960 | − | 0.0387124i | ||||
\(541\) | 26.6842i | 1.14724i | 0.819120 | + | 0.573622i | \(0.194462\pi\) | ||||
−0.819120 | + | 0.573622i | \(0.805538\pi\) | |||||||
\(542\) | −2.40708 | − | 9.65296i | −0.103393 | − | 0.414630i | ||||
\(543\) | 20.6424 | 0.885851 | ||||||||
\(544\) | 0.870567 | + | 0.316701i | 0.0373252 | + | 0.0135785i | ||||
\(545\) | 14.6165 | 0.626103 | ||||||||
\(546\) | −1.00942 | − | 4.04800i | −0.0431992 | − | 0.173238i | ||||
\(547\) | − | 11.2854i | − | 0.482528i | −0.970459 | − | 0.241264i | \(-0.922438\pi\) | ||
0.970459 | − | 0.241264i | \(-0.0775620\pi\) | |||||||
\(548\) | −18.8783 | + | 10.0393i | −0.806440 | + | 0.428859i | ||||
\(549\) | − | 10.7403i | − | 0.458386i | ||||||
\(550\) | −32.9183 | + | 8.20859i | −1.40364 | + | 0.350015i | ||||
\(551\) | −53.5819 | −2.28267 | ||||||||
\(552\) | −2.10175 | + | 1.89279i | −0.0894563 | + | 0.0805625i | ||||
\(553\) | 6.14943 | 0.261501 | ||||||||
\(554\) | 15.2034 | − | 3.79116i | 0.645932 | − | 0.161071i | ||||
\(555\) | − | 1.74625i | − | 0.0741240i | ||||||
\(556\) | −8.23007 | − | 15.4761i | −0.349033 | − | 0.656332i | ||||
\(557\) | 35.3016i | 1.49578i | 0.663825 | + | 0.747888i | \(0.268932\pi\) | ||||
−0.663825 | + | 0.747888i | \(0.731068\pi\) | |||||||
\(558\) | −0.344387 | − | 1.38107i | −0.0145790 | − | 0.0584653i | ||||
\(559\) | −11.1995 | −0.473690 | ||||||||
\(560\) | 6.81602 | + | 4.59618i | 0.288029 | + | 0.194224i | ||||
\(561\) | 0.962354 | 0.0406306 | ||||||||
\(562\) | 1.41124 | + | 5.65939i | 0.0595295 | + | 0.238727i | ||||
\(563\) | 13.0685i | 0.550772i | 0.961334 | + | 0.275386i | \(0.0888057\pi\) | ||||
−0.961334 | + | 0.275386i | \(0.911194\pi\) | |||||||
\(564\) | 7.74263 | + | 14.5595i | 0.326024 | + | 0.613066i | ||||
\(565\) | 5.50215i | 0.231477i | ||||||||
\(566\) | 6.08479 | − | 1.51732i | 0.255763 | − | 0.0637776i | ||||
\(567\) | 2.14538 | 0.0900975 | ||||||||
\(568\) | 24.9716 | + | 27.7283i | 1.04778 | + | 1.16346i | ||||
\(569\) | −8.19299 | −0.343468 | −0.171734 | − | 0.985143i | \(-0.554937\pi\) | ||||
−0.171734 | + | 0.985143i | \(0.554937\pi\) | |||||||
\(570\) | −7.66036 | + | 1.91021i | −0.320857 | + | 0.0800097i | ||||
\(571\) | − | 1.89406i | − | 0.0792638i | −0.999214 | − | 0.0396319i | \(-0.987381\pi\) | ||
0.999214 | − | 0.0396319i | \(-0.0126185\pi\) | |||||||
\(572\) | −14.2689 | + | 7.58808i | −0.596612 | + | 0.317274i | ||||
\(573\) | 10.0790i | 0.421056i | ||||||||
\(574\) | 6.05152 | + | 24.2680i | 0.252586 | + | 1.01293i | ||||
\(575\) | −4.08228 | −0.170243 | ||||||||
\(576\) | 0.834685 | − | 7.95634i | 0.0347785 | − | 0.331514i | ||||
\(577\) | −24.4901 | −1.01954 | −0.509769 | − | 0.860311i | \(-0.670269\pi\) | ||||
−0.509769 | + | 0.860311i | \(0.670269\pi\) | |||||||
\(578\) | 5.80777 | + | 23.2905i | 0.241572 | + | 0.968757i | ||||
\(579\) | − | 13.8031i | − | 0.573636i | ||||||
\(580\) | −15.5540 | + | 8.27152i | −0.645847 | + | 0.343456i | ||||
\(581\) | − | 7.22672i | − | 0.299815i | ||||||
\(582\) | 7.11864 | − | 1.77512i | 0.295077 | − | 0.0735812i | ||||
\(583\) | −12.2760 | −0.508419 | ||||||||
\(584\) | 11.7048 | + | 12.9970i | 0.484350 | + | 0.537820i | ||||
\(585\) | 1.31727 | 0.0544625 | ||||||||
\(586\) | 18.7223 | − | 4.66863i | 0.773410 | − | 0.192859i | ||||
\(587\) | − | 21.6080i | − | 0.891859i | −0.895068 | − | 0.445929i | \(-0.852873\pi\) | ||
0.895068 | − | 0.445929i | \(-0.147127\pi\) | |||||||
\(588\) | −2.25125 | − | 4.23332i | −0.0928398 | − | 0.174579i | ||||
\(589\) | 5.86515i | 0.241669i | ||||||||
\(590\) | −3.01813 | − | 12.1034i | −0.124255 | − | 0.498289i | ||||
\(591\) | 8.40195 | 0.345610 | ||||||||
\(592\) | −6.04537 | − | 4.07652i | −0.248463 | − | 0.167544i | ||||
\(593\) | −33.8498 | −1.39004 | −0.695021 | − | 0.718989i | \(-0.744605\pi\) | ||||
−0.695021 | + | 0.718989i | \(0.744605\pi\) | |||||||
\(594\) | −2.01078 | − | 8.06370i | −0.0825035 | − | 0.330858i | ||||
\(595\) | − | 0.336569i | − | 0.0137980i | ||||||
\(596\) | −19.2121 | − | 36.1271i | −0.786958 | − | 1.47982i | ||||
\(597\) | 5.07488i | 0.207701i | ||||||||
\(598\) | −1.88685 | + | 0.470508i | −0.0771589 | + | 0.0192405i | ||||
\(599\) | −19.2826 | −0.787864 | −0.393932 | − | 0.919140i | \(-0.628886\pi\) | ||||
−0.393932 | + | 0.919140i | \(0.628886\pi\) | |||||||
\(600\) | 8.57993 | − | 7.72691i | 0.350274 | − | 0.315450i | ||||
\(601\) | −19.5636 | −0.798015 | −0.399008 | − | 0.916948i | \(-0.630645\pi\) | ||||
−0.399008 | + | 0.916948i | \(0.630645\pi\) | |||||||
\(602\) | 23.9772 | − | 5.97901i | 0.977238 | − | 0.243686i | ||||
\(603\) | − | 6.22959i | − | 0.253689i | ||||||
\(604\) | −25.1687 | + | 13.3845i | −1.02410 | + | 0.544608i | ||||
\(605\) | − | 22.5443i | − | 0.916557i | ||||||
\(606\) | −2.01669 | − | 8.08741i | −0.0819226 | − | 0.328528i | ||||
\(607\) | 14.8914 | 0.604424 | 0.302212 | − | 0.953241i | \(-0.402275\pi\) | ||||
0.302212 | + | 0.953241i | \(0.402275\pi\) | |||||||
\(608\) | −11.2697 | + | 30.9789i | −0.457047 | + | 1.25636i | ||||
\(609\) | −19.7262 | −0.799345 | ||||||||
\(610\) | 3.52062 | + | 14.1185i | 0.142546 | + | 0.571640i | ||||
\(611\) | 11.3375i | 0.458666i | ||||||||
\(612\) | −0.289178 | + | 0.153783i | −0.0116893 | + | 0.00621630i | ||||
\(613\) | − | 0.628938i | − | 0.0254026i | −0.999919 | − | 0.0127013i | \(-0.995957\pi\) | ||
0.999919 | − | 0.0127013i | \(-0.00404306\pi\) | |||||||
\(614\) | −19.9226 | + | 4.96794i | −0.804010 | + | 0.200490i | ||||
\(615\) | −7.89711 | −0.318442 | ||||||||
\(616\) | 26.4974 | − | 23.8630i | 1.06761 | − | 0.961469i | ||||
\(617\) | 3.93037 | 0.158231 | 0.0791153 | − | 0.996865i | \(-0.474790\pi\) | ||||
0.0791153 | + | 0.996865i | \(0.474790\pi\) | |||||||
\(618\) | −11.0498 | + | 2.75541i | −0.444488 | + | 0.110839i | ||||
\(619\) | − | 38.6550i | − | 1.55368i | −0.629700 | − | 0.776838i | \(-0.716822\pi\) | ||
0.629700 | − | 0.776838i | \(-0.283178\pi\) | |||||||
\(620\) | 0.905412 | + | 1.70257i | 0.0363622 | + | 0.0683768i | ||||
\(621\) | − | 1.00000i | − | 0.0401286i | ||||||
\(622\) | −7.17358 | − | 28.7677i | −0.287635 | − | 1.15348i | ||||
\(623\) | −17.6152 | −0.705739 | ||||||||
\(624\) | 3.07510 | − | 4.56030i | 0.123103 | − | 0.182558i | ||||
\(625\) | 12.0764 | 0.483058 | ||||||||
\(626\) | −6.36417 | − | 25.5218i | −0.254363 | − | 1.02006i | ||||
\(627\) | 34.2451i | 1.36762i | ||||||||
\(628\) | 3.55942 | + | 6.69326i | 0.142036 | + | 0.267090i | ||||
\(629\) | 0.298515i | 0.0119026i | ||||||||
\(630\) | −2.82016 | + | 0.703242i | −0.112358 | + | 0.0280179i | ||||
\(631\) | 34.7355 | 1.38280 | 0.691399 | − | 0.722473i | \(-0.256995\pi\) | ||||
0.691399 | + | 0.722473i | \(0.256995\pi\) | |||||||
\(632\) | 5.42542 | + | 6.02437i | 0.215812 | + | 0.239637i | ||||
\(633\) | 26.2297 | 1.04254 | ||||||||
\(634\) | 14.6426 | − | 3.65130i | 0.581531 | − | 0.145012i | ||||
\(635\) | 5.42252i | 0.215186i | ||||||||
\(636\) | 3.68882 | − | 1.96169i | 0.146271 | − | 0.0777859i | ||||
\(637\) | − | 3.29649i | − | 0.130612i | ||||||
\(638\) | 18.4886 | + | 74.1436i | 0.731971 | + | 2.93537i | ||||
\(639\) | −13.1930 | −0.521907 | ||||||||
\(640\) | 1.51082 | + | 10.7324i | 0.0597205 | + | 0.424237i | ||||
\(641\) | 16.3740 | 0.646733 | 0.323367 | − | 0.946274i | \(-0.395185\pi\) | ||||
0.323367 | + | 0.946274i | \(0.395185\pi\) | |||||||
\(642\) | 6.13639 | + | 24.6083i | 0.242184 | + | 0.971213i | ||||
\(643\) | − | 3.58023i | − | 0.141191i | −0.997505 | − | 0.0705953i | \(-0.977510\pi\) | ||
0.997505 | − | 0.0705953i | \(-0.0224899\pi\) | |||||||
\(644\) | 3.78839 | − | 2.01463i | 0.149283 | − | 0.0793877i | ||||
\(645\) | 7.80249i | 0.307223i | ||||||||
\(646\) | 1.30952 | − | 0.326544i | 0.0515222 | − | 0.0128477i | ||||
\(647\) | 15.1628 | 0.596111 | 0.298055 | − | 0.954549i | \(-0.403662\pi\) | ||||
0.298055 | + | 0.954549i | \(0.403662\pi\) | |||||||
\(648\) | 1.89279 | + | 2.10175i | 0.0743558 | + | 0.0825644i | ||||
\(649\) | −54.1073 | −2.12390 | ||||||||
\(650\) | 7.70264 | − | 1.92075i | 0.302122 | − | 0.0753380i | ||||
\(651\) | 2.15925i | 0.0846279i | ||||||||
\(652\) | −4.58054 | − | 8.61340i | −0.179388 | − | 0.337327i | ||||
\(653\) | 29.5588i | 1.15673i | 0.815779 | + | 0.578363i | \(0.196308\pi\) | ||||
−0.815779 | + | 0.578363i | \(0.803692\pi\) | |||||||
\(654\) | 5.22079 | + | 20.9366i | 0.204149 | + | 0.818684i | ||||
\(655\) | −12.2291 | −0.477831 | ||||||||
\(656\) | −18.4354 | + | 27.3392i | −0.719781 | + | 1.06742i | ||||
\(657\) | −6.18391 | −0.241257 | ||||||||
\(658\) | −6.05267 | − | 24.2726i | −0.235958 | − | 0.946244i | ||||
\(659\) | − | 12.7243i | − | 0.495667i | −0.968803 | − | 0.247833i | \(-0.920281\pi\) | ||
0.968803 | − | 0.247833i | \(-0.0797185\pi\) | |||||||
\(660\) | 5.28647 | + | 9.94085i | 0.205775 | + | 0.386947i | ||||
\(661\) | − | 5.82562i | − | 0.226590i | −0.993561 | − | 0.113295i | \(-0.963859\pi\) | ||
0.993561 | − | 0.113295i | \(-0.0361406\pi\) | |||||||
\(662\) | −22.1469 | + | 5.52260i | −0.860763 | + | 0.214642i | ||||
\(663\) | −0.225184 | −0.00874541 | ||||||||
\(664\) | 7.07974 | − | 6.37587i | 0.274747 | − | 0.247432i | ||||
\(665\) | 11.9767 | 0.464437 | ||||||||
\(666\) | 2.50130 | − | 0.623731i | 0.0969236 | − | 0.0241691i | ||||
\(667\) | 9.19473i | 0.356021i | ||||||||
\(668\) | 32.6548 | − | 17.3656i | 1.26345 | − | 0.671894i | ||||
\(669\) | 19.5439i | 0.755612i | ||||||||
\(670\) | 2.04202 | + | 8.18898i | 0.0788902 | + | 0.316368i | ||||
\(671\) | 63.1156 | 2.43655 | ||||||||
\(672\) | −4.14895 | + | 11.4049i | −0.160049 | + | 0.439953i | ||||
\(673\) | 7.46202 | 0.287640 | 0.143820 | − | 0.989604i | \(-0.454061\pi\) | ||||
0.143820 | + | 0.989604i | \(0.454061\pi\) | |||||||
\(674\) | 1.80162 | + | 7.22490i | 0.0693957 | + | 0.278293i | ||||
\(675\) | 4.08228i | 0.157127i | ||||||||
\(676\) | −19.6170 | + | 10.4322i | −0.754501 | + | 0.401238i | ||||
\(677\) | − | 2.58854i | − | 0.0994857i | −0.998762 | − | 0.0497428i | \(-0.984160\pi\) | ||
0.998762 | − | 0.0497428i | \(-0.0158402\pi\) | |||||||
\(678\) | −7.88122 | + | 1.96528i | −0.302676 | + | 0.0754761i | ||||
\(679\) | −11.1298 | −0.427121 | ||||||||
\(680\) | 0.329724 | − | 0.296943i | 0.0126443 | − | 0.0113872i | ||||
\(681\) | 1.06802 | 0.0409268 | ||||||||
\(682\) | 8.11586 | − | 2.02379i | 0.310772 | − | 0.0774949i | ||||
\(683\) | − | 48.7370i | − | 1.86487i | −0.361337 | − | 0.932435i | \(-0.617680\pi\) | ||
0.361337 | − | 0.932435i | \(-0.382320\pi\) | |||||||
\(684\) | −5.47232 | − | 10.2903i | −0.209239 | − | 0.393461i | ||||
\(685\) | 10.2416i | 0.391311i | ||||||||
\(686\) | 6.89852 | + | 27.6646i | 0.263387 | + | 1.05624i | ||||
\(687\) | −19.1138 | −0.729239 | ||||||||
\(688\) | 27.0116 | + | 18.2145i | 1.02981 | + | 0.694421i | ||||
\(689\) | 2.87249 | 0.109433 | ||||||||
\(690\) | 0.327794 | + | 1.31453i | 0.0124789 | + | 0.0500433i | ||||
\(691\) | 40.3418i | 1.53468i | 0.641243 | + | 0.767338i | \(0.278419\pi\) | ||||
−0.641243 | + | 0.767338i | \(0.721581\pi\) | |||||||
\(692\) | −13.4258 | − | 25.2463i | −0.510371 | − | 0.959719i | ||||
\(693\) | 12.6073i | 0.478913i | ||||||||
\(694\) | −10.3063 | + | 2.57000i | −0.391221 | + | 0.0975559i | ||||
\(695\) | −8.39587 | −0.318474 | ||||||||
\(696\) | −17.4037 | − | 19.3250i | −0.659686 | − | 0.732512i | ||||
\(697\) | 1.34999 | 0.0511344 | ||||||||
\(698\) | −18.5060 | + | 4.61469i | −0.700461 | + | 0.174669i | ||||
\(699\) | 6.40572i | 0.242286i | ||||||||
\(700\) | −15.4653 | + | 8.22431i | −0.584532 | + | 0.310850i | ||||
\(701\) | − | 23.8105i | − | 0.899309i | −0.893202 | − | 0.449655i | \(-0.851547\pi\) | ||
0.893202 | − | 0.449655i | \(-0.148453\pi\) | |||||||
\(702\) | 0.470508 | + | 1.88685i | 0.0177582 | + | 0.0712144i | ||||
\(703\) | −10.6226 | −0.400638 | ||||||||
\(704\) | 46.7554 | + | 4.90503i | 1.76216 | + | 0.184865i | ||||
\(705\) | 7.89862 | 0.297479 | ||||||||
\(706\) | 10.0841 | + | 40.4396i | 0.379520 | + | 1.52196i | ||||
\(707\) | 12.6444i | 0.475541i | ||||||||
\(708\) | 16.2587 | − | 8.64628i | 0.611041 | − | 0.324947i | ||||
\(709\) | − | 39.2778i | − | 1.47511i | −0.675288 | − | 0.737554i | \(-0.735981\pi\) | ||
0.675288 | − | 0.737554i | \(-0.264019\pi\) | |||||||
\(710\) | 17.3426 | − | 4.32458i | 0.650855 | − | 0.162299i | ||||
\(711\) | −2.86636 | −0.107497 | ||||||||
\(712\) | −15.5413 | − | 17.2570i | −0.582434 | − | 0.646733i | ||||
\(713\) | 1.00647 | 0.0376925 | ||||||||
\(714\) | 0.482098 | − | 0.120217i | 0.0180421 | − | 0.00449901i | ||||
\(715\) | 7.74095i | 0.289495i | ||||||||
\(716\) | −22.9163 | − | 43.0925i | −0.856421 | − | 1.61044i | ||||
\(717\) | 6.99571i | 0.261260i | ||||||||
\(718\) | 9.39535 | + | 37.6775i | 0.350631 | + | 1.40611i | ||||
\(719\) | −6.94844 | −0.259133 | −0.129567 | − | 0.991571i | \(-0.541359\pi\) | ||||
−0.129567 | + | 0.991571i | \(0.541359\pi\) | |||||||
\(720\) | −3.17707 | − | 2.14236i | −0.118402 | − | 0.0798411i | ||||
\(721\) | 17.2760 | 0.643392 | ||||||||
\(722\) | 5.11867 | + | 20.5270i | 0.190497 | + | 0.763937i | ||||
\(723\) | 0.0382051i | 0.00142086i | ||||||||
\(724\) | −19.3844 | − | 36.4511i | −0.720416 | − | 1.35469i | ||||
\(725\) | − | 37.5355i | − | 1.39403i | ||||||
\(726\) | 32.2922 | − | 8.05247i | 1.19848 | − | 0.298855i | ||||
\(727\) | −43.5001 | −1.61333 | −0.806665 | − | 0.591008i | \(-0.798730\pi\) | ||||
−0.806665 | + | 0.591008i | \(0.798730\pi\) | |||||||
\(728\) | −6.20020 | + | 5.58377i | −0.229795 | + | 0.206948i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 8.12892 | − | 2.02705i | 0.300865 | − | 0.0750244i | ||||
\(731\) | − | 1.33381i | − | 0.0493328i | ||||||
\(732\) | −18.9656 | + | 10.0858i | −0.700990 | + | 0.372781i | ||||
\(733\) | − | 33.4363i | − | 1.23500i | −0.786571 | − | 0.617499i | \(-0.788146\pi\) | ||
0.786571 | − | 0.617499i | \(-0.211854\pi\) | |||||||
\(734\) | −10.5528 | − | 42.3193i | −0.389512 | − | 1.56203i | ||||
\(735\) | −2.29660 | −0.0847114 | ||||||||
\(736\) | 5.31602 | + | 1.93390i | 0.195951 | + | 0.0712845i | ||||
\(737\) | 36.6082 | 1.34848 | ||||||||
\(738\) | −2.82072 | − | 11.3117i | −0.103832 | − | 0.416391i | ||||
\(739\) | 32.3025i | 1.18827i | 0.804367 | + | 0.594133i | \(0.202505\pi\) | ||||
−0.804367 | + | 0.594133i | \(0.797495\pi\) | |||||||
\(740\) | −3.08358 | + | 1.63983i | −0.113355 | + | 0.0602812i | ||||
\(741\) | − | 8.01309i | − | 0.294368i | ||||||
\(742\) | −6.14975 | + | 1.53352i | −0.225764 | + | 0.0562971i | ||||
\(743\) | 26.3041 | 0.965002 | 0.482501 | − | 0.875895i | \(-0.339728\pi\) | ||||
0.482501 | + | 0.875895i | \(0.339728\pi\) | |||||||
\(744\) | −2.11534 | + | 1.90503i | −0.0775522 | + | 0.0698419i | ||||
\(745\) | −19.5992 | −0.718057 | ||||||||
\(746\) | −20.0028 | + | 4.98794i | −0.732353 | + | 0.182621i | ||||
\(747\) | 3.36850i | 0.123247i | ||||||||
\(748\) | −0.903705 | − | 1.69936i | −0.0330427 | − | 0.0621347i | ||||
\(749\) | − | 38.4743i | − | 1.40582i | ||||||
\(750\) | −2.97712 | − | 11.9389i | −0.108709 | − | 0.435948i | ||||
\(751\) | −11.2368 | −0.410037 | −0.205019 | − | 0.978758i | \(-0.565725\pi\) | ||||
−0.205019 | + | 0.978758i | \(0.565725\pi\) | |||||||
\(752\) | 18.4389 | − | 27.3444i | 0.672397 | − | 0.997148i | ||||
\(753\) | −16.4795 | −0.600545 | ||||||||
\(754\) | −4.32620 | − | 17.3490i | −0.157551 | − | 0.631815i | ||||
\(755\) | 13.6542i | 0.496926i | ||||||||
\(756\) | −2.01463 | − | 3.78839i | −0.0732715 | − | 0.137782i | ||||
\(757\) | 35.2690i | 1.28187i | 0.767594 | + | 0.640937i | \(0.221454\pi\) | ||||
−0.767594 | + | 0.640937i | \(0.778546\pi\) | |||||||
\(758\) | −36.2761 | + | 9.04589i | −1.31761 | + | 0.328561i | ||||
\(759\) | 5.87650 | 0.213304 | ||||||||
\(760\) | 10.5666 | + | 11.7331i | 0.383292 | + | 0.425606i | ||||
\(761\) | −47.9490 | −1.73815 | −0.869075 | − | 0.494681i | \(-0.835285\pi\) | ||||
−0.869075 | + | 0.494681i | \(0.835285\pi\) | |||||||
\(762\) | −7.76716 | + | 1.93684i | −0.281375 | + | 0.0701642i | ||||
\(763\) | − | 32.7336i | − | 1.18504i | ||||||
\(764\) | 17.7978 | − | 9.46475i | 0.643903 | − | 0.342423i | ||||
\(765\) | 0.156881i | 0.00567204i | ||||||||
\(766\) | 9.48541 | + | 38.0387i | 0.342722 | + | 1.37439i | ||||
\(767\) | 12.6607 | 0.457152 | ||||||||
\(768\) | −14.8334 | + | 5.99754i | −0.535254 | + | 0.216418i | ||||
\(769\) | 36.9947 | 1.33406 | 0.667032 | − | 0.745029i | \(-0.267565\pi\) | ||||
0.667032 | + | 0.745029i | \(0.267565\pi\) | |||||||
\(770\) | −4.13261 | − | 16.5727i | −0.148929 | − | 0.597239i | ||||
\(771\) | 5.93490i | 0.213740i | ||||||||
\(772\) | −24.3739 | + | 12.9619i | −0.877237 | + | 0.466508i | ||||
\(773\) | 33.2787i | 1.19695i | 0.801141 | + | 0.598475i | \(0.204227\pi\) | ||||
−0.801141 | + | 0.598475i | \(0.795773\pi\) | |||||||
\(774\) | −11.1762 | + | 2.78693i | −0.401721 | + | 0.100174i | ||||
\(775\) | −4.10869 | −0.147588 | ||||||||
\(776\) | −9.81939 | − | 10.9034i | −0.352495 | − | 0.391409i | ||||
\(777\) | −3.91071 | −0.140296 | ||||||||
\(778\) | −1.98579 | + | 0.495181i | −0.0711940 | + | 0.0177531i | ||||
\(779\) | 48.0389i | 1.72117i | ||||||||
\(780\) | −1.23699 | − | 2.32608i | −0.0442915 | − | 0.0832872i | ||||
\(781\) | − | 77.5287i | − | 2.77419i | ||||||
\(782\) | −0.0560354 | − | 0.224715i | −0.00200382 | − | 0.00803578i | ||||
\(783\) | 9.19473 | 0.328593 | ||||||||
\(784\) | −5.36129 | + | 7.95066i | −0.191475 | + | 0.283952i | ||||
\(785\) | 3.63113 | 0.129601 | ||||||||
\(786\) | −4.36804 | − | 17.5168i | −0.155803 | − | 0.624805i | ||||
\(787\) | − | 6.77438i | − | 0.241481i | −0.992684 | − | 0.120740i | \(-0.961473\pi\) | ||
0.992684 | − | 0.120740i | \(-0.0385268\pi\) | |||||||
\(788\) | −7.88991 | − | 14.8365i | −0.281067 | − | 0.528527i | ||||
\(789\) | − | 24.4364i | − | 0.869958i | ||||||
\(790\) | 3.76792 | − | 0.939576i | 0.134056 | − | 0.0334286i | ||||
\(791\) | 12.3220 | 0.438120 | ||||||||
\(792\) | −12.3509 | + | 11.1230i | −0.438871 | + | 0.395238i | ||||
\(793\) | −14.7686 | −0.524448 | ||||||||
\(794\) | 2.16166 | − | 0.539037i | 0.0767145 | − | 0.0191297i | ||||
\(795\) | − | 2.00121i | − | 0.0709755i | ||||||
\(796\) | 8.96139 | − | 4.76560i | 0.317628 | − | 0.168912i | ||||
\(797\) | − | 14.0543i | − | 0.497830i | −0.968525 | − | 0.248915i | \(-0.919926\pi\) | ||
0.968525 | − | 0.248915i | \(-0.0800741\pi\) | |||||||
\(798\) | 4.27789 | + | 17.1553i | 0.151436 | + | 0.607292i | ||||
\(799\) | −1.35024 | −0.0477682 | ||||||||
\(800\) | −21.7015 | − | 7.89472i | −0.767263 | − | 0.279121i | ||||
\(801\) | 8.21077 | 0.290113 | ||||||||
\(802\) | −7.16115 | − | 28.7178i | −0.252869 | − | 1.01406i | ||||
\(803\) | − | 36.3397i | − | 1.28240i | ||||||
\(804\) | −11.0004 | + | 5.84994i | −0.387955 | + | 0.206312i | ||||
\(805\) | − | 2.05522i | − | 0.0724370i | ||||||
\(806\) | −1.89905 | + | 0.473552i | −0.0668912 | + | 0.0166801i | ||||
\(807\) | 12.0472 | 0.424083 | ||||||||
\(808\) | −12.3872 | + | 11.1557i | −0.435781 | + | 0.392456i | ||||
\(809\) | −7.72143 | −0.271471 | −0.135735 | − | 0.990745i | \(-0.543340\pi\) | ||||
−0.135735 | + | 0.990745i | \(0.543340\pi\) | |||||||
\(810\) | 1.31453 | − | 0.327794i | 0.0461878 | − | 0.0115175i | ||||
\(811\) | − | 22.6984i | − | 0.797048i | −0.917158 | − | 0.398524i | \(-0.869523\pi\) | ||
0.917158 | − | 0.398524i | \(-0.130477\pi\) | |||||||
\(812\) | 18.5240 | + | 34.8332i | 0.650065 | + | 1.22240i | ||||
\(813\) | − | 7.03469i | − | 0.246717i | ||||||
\(814\) | 3.66536 | + | 14.6989i | 0.128471 | + | 0.515197i | ||||
\(815\) | −4.67282 | −0.163682 | ||||||||
\(816\) | 0.543110 | + | 0.366230i | 0.0190127 | + | 0.0128206i | ||||
\(817\) | 47.4633 | 1.66053 | ||||||||
\(818\) | −11.7717 | − | 47.2072i | −0.411588 | − | 1.65056i | ||||
\(819\) | − | 2.95002i | − | 0.103082i | ||||||
\(820\) | 7.41584 | + | 13.9450i | 0.258972 | + | 0.486980i | ||||
\(821\) | − | 1.38524i | − | 0.0483453i | −0.999708 | − | 0.0241726i | \(-0.992305\pi\) | ||
0.999708 | − | 0.0241726i | \(-0.00769514\pi\) | |||||||
\(822\) | −14.6699 | + | 3.65813i | −0.511673 | + | 0.127592i | ||||
\(823\) | −15.9740 | −0.556819 | −0.278410 | − | 0.960462i | \(-0.589807\pi\) | ||||
−0.278410 | + | 0.960462i | \(0.589807\pi\) | |||||||
\(824\) | 15.2420 | + | 16.9246i | 0.530980 | + | 0.589598i | ||||
\(825\) | −23.9895 | −0.835209 | ||||||||
\(826\) | −27.1055 | + | 6.75908i | −0.943120 | + | 0.235179i | ||||
\(827\) | − | 29.8593i | − | 1.03831i | −0.854680 | − | 0.519155i | \(-0.826247\pi\) | ||
0.854680 | − | 0.519155i | \(-0.173753\pi\) | |||||||
\(828\) | −1.76583 | + | 0.939057i | −0.0613670 | + | 0.0326345i | ||||
\(829\) | 14.9900i | 0.520624i | 0.965525 | + | 0.260312i | \(0.0838255\pi\) | ||||
−0.965525 | + | 0.260312i | \(0.916175\pi\) | |||||||
\(830\) | −1.10418 | − | 4.42799i | −0.0383265 | − | 0.153698i | ||||
\(831\) | 11.0796 | 0.384349 | ||||||||
\(832\) | −10.9404 | − | 1.14774i | −0.379291 | − | 0.0397907i | ||||
\(833\) | 0.392597 | 0.0136027 | ||||||||
\(834\) | −2.99887 | − | 12.0262i | −0.103842 | − | 0.416432i | ||||
\(835\) | − | 17.7154i | − | 0.613067i | ||||||
\(836\) | 60.4711 | − | 32.1581i | 2.09144 | − | 1.11221i | ||||
\(837\) | − | 1.00647i | − | 0.0347886i | ||||||
\(838\) | 16.2309 | − | 4.04739i | 0.560689 | − | 0.139815i | ||||
\(839\) | −25.4186 | −0.877548 | −0.438774 | − | 0.898597i | \(-0.644587\pi\) | ||||
−0.438774 | + | 0.898597i | \(0.644587\pi\) | |||||||
\(840\) | 3.89010 | + | 4.31956i | 0.134221 | + | 0.149039i | ||||
\(841\) | −55.5430 | −1.91528 | ||||||||
\(842\) | −6.14784 | + | 1.53304i | −0.211869 | + | 0.0528321i | ||||
\(843\) | 4.12434i | 0.142050i | ||||||||
\(844\) | −24.6312 | − | 46.3172i | −0.847839 | − | 1.59431i | ||||
\(845\) | 10.6424i | 0.366108i | ||||||||
\(846\) | 2.82126 | + | 11.3139i | 0.0969969 | + | 0.388980i | ||||
\(847\) | −50.4878 | −1.73478 | ||||||||
\(848\) | −6.92803 | − | 4.67171i | −0.237909 | − | 0.160427i | ||||
\(849\) | 4.43435 | 0.152187 | ||||||||
\(850\) | 0.228752 | + | 0.917349i | 0.00784614 | + | 0.0314648i | ||||
\(851\) | 1.82285i | 0.0624865i | ||||||||
\(852\) | 12.3890 | + | 23.2966i | 0.424439 | + | 0.798130i | ||||
\(853\) | 28.3482i | 0.970623i | 0.874341 | + | 0.485311i | \(0.161294\pi\) | ||||
−0.874341 | + | 0.485311i | \(0.838706\pi\) | |||||||
\(854\) | 31.6182 | − | 7.88439i | 1.08195 | − | 0.269798i | ||||
\(855\) | −5.58256 | −0.190920 | ||||||||
\(856\) | 37.6918 | − | 33.9445i | 1.28828 | − | 1.16020i | ||||
\(857\) | −40.6814 | −1.38965 | −0.694826 | − | 0.719178i | \(-0.744518\pi\) | ||||
−0.694826 | + | 0.719178i | \(0.744518\pi\) | |||||||
\(858\) | −11.0881 | + | 2.76494i | −0.378540 | + | 0.0943936i | ||||
\(859\) | 21.2337i | 0.724483i | 0.932084 | + | 0.362242i | \(0.117988\pi\) | ||||
−0.932084 | + | 0.362242i | \(0.882012\pi\) | |||||||
\(860\) | 13.7779 | − | 7.32699i | 0.469823 | − | 0.249848i | ||||
\(861\) | 17.6855i | 0.602721i | ||||||||
\(862\) | −12.7154 | − | 50.9917i | −0.433089 | − | 1.73679i | ||||
\(863\) | 41.9316 | 1.42737 | 0.713683 | − | 0.700468i | \(-0.247026\pi\) | ||||
0.713683 | + | 0.700468i | \(0.247026\pi\) | |||||||
\(864\) | 1.93390 | − | 5.31602i | 0.0657926 | − | 0.180855i | ||||
\(865\) | −13.6962 | −0.465686 | ||||||||
\(866\) | −10.2619 | − | 41.1524i | −0.348712 | − | 1.39842i | ||||
\(867\) | 16.9732i | 0.576439i | ||||||||
\(868\) | 3.81289 | − | 2.02766i | 0.129418 | − | 0.0688234i | ||||
\(869\) | − | 16.8442i | − | 0.571400i | ||||||
\(870\) | −12.0867 | + | 3.01398i | −0.409779 | + | 0.102183i | ||||
\(871\) | −8.56605 | −0.290249 | ||||||||
\(872\) | 32.0679 | − | 28.8797i | 1.08596 | − | 0.977989i | ||||
\(873\) | 5.18778 | 0.175580 | ||||||||
\(874\) | 7.99641 | − | 1.99400i | 0.270482 | − | 0.0674481i | ||||
\(875\) | 18.6661i | 0.631029i | ||||||||
\(876\) | 5.80704 | + | 10.9198i | 0.196202 | + | 0.368944i | ||||
\(877\) | 19.1900i | 0.647999i | 0.946057 | + | 0.324000i | \(0.105028\pi\) | ||||
−0.946057 | + | 0.324000i | \(0.894972\pi\) | |||||||
\(878\) | −0.0111552 | − | 0.0447351i | −0.000376471 | − | 0.00150974i | ||||
\(879\) | 13.6440 | 0.460202 | ||||||||
\(880\) | 12.5896 | − | 18.6701i | 0.424395 | − | 0.629367i | ||||
\(881\) | 31.0035 | 1.04453 | 0.522267 | − | 0.852782i | \(-0.325086\pi\) | ||||
0.522267 | + | 0.852782i | \(0.325086\pi\) | |||||||
\(882\) | −0.820309 | − | 3.28963i | −0.0276212 | − | 0.110767i | ||||
\(883\) | − | 22.0192i | − | 0.741005i | −0.928832 | − | 0.370502i | \(-0.879186\pi\) | ||
0.928832 | − | 0.370502i | \(-0.120814\pi\) | |||||||
\(884\) | 0.211460 | + | 0.397637i | 0.00711218 | + | 0.0133740i | ||||
\(885\) | − | 8.82047i | − | 0.296497i | ||||||
\(886\) | −7.65520 | + | 1.90892i | −0.257181 | + | 0.0641314i | ||||
\(887\) | 55.3189 | 1.85743 | 0.928714 | − | 0.370797i | \(-0.120915\pi\) | ||||
0.928714 | + | 0.370797i | \(0.120915\pi\) | |||||||
\(888\) | −3.45027 | − | 3.83117i | −0.115784 | − | 0.128566i | ||||
\(889\) | 12.1437 | 0.407287 | ||||||||
\(890\) | −10.7933 | + | 2.69144i | −0.361792 | + | 0.0902174i | ||||
\(891\) | − | 5.87650i | − | 0.196870i | ||||||
\(892\) | 34.5114 | − | 18.3529i | 1.15553 | − | 0.614500i | ||||
\(893\) | − | 48.0480i | − | 1.60787i | ||||||
\(894\) | −7.00050 | − | 28.0736i | −0.234132 | − | 0.938922i | ||||
\(895\) | −23.3779 | −0.781438 | ||||||||
\(896\) | 24.0352 | − | 3.38347i | 0.802960 | − | 0.113034i | ||||
\(897\) | −1.37506 | −0.0459118 | ||||||||
\(898\) | 5.02230 | + | 20.1406i | 0.167596 | + | 0.672099i | ||||
\(899\) | 9.25420i | 0.308645i | ||||||||
\(900\) | 7.20864 | − | 3.83350i | 0.240288 | − | 0.127783i | ||||
\(901\) | 0.342100i | 0.0113970i | ||||||||
\(902\) | 66.4735 | − | 16.5760i | 2.21332 | − | 0.551920i | ||||
\(903\) | 17.4736 | 0.581486 | ||||||||
\(904\) | 10.8713 | + | 12.0714i | 0.361573 | + | 0.401489i | ||||
\(905\) | −19.7749 | −0.657341 | ||||||||
\(906\) | −19.5581 | + | 4.87705i | −0.649773 | + | 0.162029i | ||||
\(907\) | − | 51.8307i | − | 1.72101i | −0.509441 | − | 0.860506i | \(-0.670148\pi\) | ||
0.509441 | − | 0.860506i | \(-0.329852\pi\) | |||||||
\(908\) | −1.00294 | − | 1.88596i | −0.0332836 | − | 0.0625876i | ||||
\(909\) | − | 5.89378i | − | 0.195484i | ||||||
\(910\) | 0.966999 | + | 3.87789i | 0.0320557 | + | 0.128551i | ||||
\(911\) | −48.2153 | −1.59744 | −0.798722 | − | 0.601701i | \(-0.794490\pi\) | ||||
−0.798722 | + | 0.601701i | \(0.794490\pi\) | |||||||
\(912\) | −13.0322 | + | 19.3264i | −0.431539 | + | 0.639962i | ||||
\(913\) | −19.7950 | −0.655120 | ||||||||
\(914\) | −1.42733 | − | 5.72393i | −0.0472120 | − | 0.189331i | ||||
\(915\) | 10.2890i | 0.340143i | ||||||||
\(916\) | 17.9490 | + | 33.7519i | 0.593051 | + | 1.11519i | ||||
\(917\) | 27.3870i | 0.904398i | ||||||||
\(918\) | −0.224715 | + | 0.0560354i | −0.00741669 | + | 0.00184944i | ||||
\(919\) | −6.05837 | −0.199847 | −0.0999236 | − | 0.994995i | \(-0.531860\pi\) | ||||
−0.0999236 | + | 0.994995i | \(0.531860\pi\) | |||||||
\(920\) | 2.01342 | − | 1.81325i | 0.0663806 | − | 0.0597810i | ||||
\(921\) | −14.5188 | −0.478410 | ||||||||
\(922\) | 38.9422 | − | 9.71072i | 1.28249 | − | 0.319806i | ||||
\(923\) | 18.1411i | 0.597123i | ||||||||
\(924\) | 22.2625 | − | 11.8390i | 0.732381 | − | 0.389475i | ||||
\(925\) | − | 7.44139i | − | 0.244671i | ||||||
\(926\) | 7.43513 | + | 29.8166i | 0.244334 | + | 0.979833i | ||||
\(927\) | −8.05266 | −0.264484 | ||||||||
\(928\) | −17.7817 | + | 48.8793i | −0.583712 | + | 1.60454i | ||||
\(929\) | 23.6089 | 0.774583 | 0.387292 | − | 0.921957i | \(-0.373411\pi\) | ||||
0.387292 | + | 0.921957i | \(0.373411\pi\) | |||||||
\(930\) | 0.329914 | + | 1.32303i | 0.0108183 | + | 0.0433839i | ||||
\(931\) | 13.9704i | 0.457863i | ||||||||
\(932\) | 11.3114 | − | 6.01534i | 0.370518 | − | 0.197039i | ||||
\(933\) | − | 20.9648i | − | 0.686355i | ||||||
\(934\) | 4.03877 | − | 1.00712i | 0.132153 | − | 0.0329539i | ||||
\(935\) | −0.921912 | −0.0301497 | ||||||||
\(936\) | 2.89002 | − | 2.60270i | 0.0944634 | − | 0.0850718i | ||||
\(937\) | −54.4608 | −1.77916 | −0.889578 | − | 0.456784i | \(-0.849001\pi\) | ||||
−0.889578 | + | 0.456784i | \(0.849001\pi\) | |||||||
\(938\) | 18.3392 | − | 4.57309i | 0.598795 | − | 0.149317i | ||||
\(939\) | − | 18.5992i | − | 0.606963i | ||||||
\(940\) | −7.41725 | − | 13.9476i | −0.241924 | − | 0.454922i | ||||
\(941\) | 27.6530i | 0.901462i | 0.892660 | + | 0.450731i | \(0.148837\pi\) | ||||
−0.892660 | + | 0.450731i | \(0.851163\pi\) | |||||||
\(942\) | 1.29698 | + | 5.20119i | 0.0422579 | + | 0.169464i | ||||
\(943\) | 8.24354 | 0.268447 | ||||||||
\(944\) | −30.5358 | − | 20.5909i | −0.993855 | − | 0.670177i | ||||
\(945\) | −2.05522 | −0.0668564 | ||||||||
\(946\) | −16.3774 | − | 65.6770i | −0.532474 | − | 2.13534i | ||||
\(947\) | − | 24.4302i | − | 0.793874i | −0.917846 | − | 0.396937i | \(-0.870073\pi\) | ||
0.917846 | − | 0.396937i | \(-0.129927\pi\) | |||||||
\(948\) | 2.69168 | + | 5.06152i | 0.0874216 | + | 0.164391i | ||||
\(949\) | 8.50323i | 0.276027i | ||||||||
\(950\) | −32.6436 | + | 8.14008i | −1.05910 | + | 0.264099i | ||||
\(951\) | 10.6709 | 0.346028 | ||||||||
\(952\) | −0.665001 | − | 0.738415i | −0.0215528 | − | 0.0239322i | ||||
\(953\) | −17.4510 | −0.565292 | −0.282646 | − | 0.959224i | \(-0.591212\pi\) | ||||
−0.282646 | + | 0.959224i | \(0.591212\pi\) | |||||||
\(954\) | 2.86651 | − | 0.714799i | 0.0928066 | − | 0.0231425i | ||||
\(955\) | − | 9.65543i | − | 0.312442i | ||||||
\(956\) | 12.3533 | − | 6.56937i | 0.399533 | − | 0.212469i | ||||
\(957\) | 54.0329i | 1.74663i | ||||||||
\(958\) | −5.74704 | − | 23.0469i | −0.185678 | − | 0.744613i | ||||
\(959\) | 22.9359 | 0.740640 | ||||||||
\(960\) | −0.799608 | + | 7.62198i | −0.0258072 | + | 0.245998i | ||||
\(961\) | −29.9870 | −0.967323 | ||||||||
\(962\) | −0.857666 | − | 3.43944i | −0.0276523 | − | 0.110892i | ||||
\(963\) | 17.9336i | 0.577901i | ||||||||
\(964\) | 0.0674639 | − | 0.0358768i | 0.00217286 | − | 0.00115551i | ||||
\(965\) | 13.2230i | 0.425663i | ||||||||
\(966\) | 2.94388 | − | 0.734092i | 0.0947177 | − | 0.0236190i | ||||
\(967\) | −44.2308 | −1.42237 | −0.711183 | − | 0.703007i | \(-0.751840\pi\) | ||||
−0.711183 | + | 0.703007i | \(0.751840\pi\) | |||||||
\(968\) | −44.5436 | − | 49.4610i | −1.43169 | − | 1.58974i | ||||
\(969\) | 0.954322 | 0.0306573 | ||||||||
\(970\) | −6.81949 | + | 1.70052i | −0.218961 | + | 0.0546005i | ||||
\(971\) | 42.6198i | 1.36774i | 0.729606 | + | 0.683868i | \(0.239703\pi\) | ||||
−0.729606 | + | 0.683868i | \(0.760297\pi\) | |||||||
\(972\) | 0.939057 | + | 1.76583i | 0.0301203 | + | 0.0566392i | ||||
\(973\) | 18.8025i | 0.602780i | ||||||||
\(974\) | 7.67698 | + | 30.7864i | 0.245986 | + | 0.986461i | ||||
\(975\) | 5.61337 | 0.179772 | ||||||||
\(976\) | 35.6197 | + | 24.0191i | 1.14016 | + | 0.768831i | ||||
\(977\) | 37.3495 | 1.19492 | 0.597458 | − | 0.801900i | \(-0.296177\pi\) | ||||
0.597458 | + | 0.801900i | \(0.296177\pi\) | |||||||
\(978\) | −1.66906 | − | 6.69330i | −0.0533705 | − | 0.214028i | ||||
\(979\) | 48.2506i | 1.54210i | ||||||||
\(980\) | 2.15664 | + | 4.05542i | 0.0688913 | + | 0.129546i | ||||
\(981\) | 15.2577i | 0.487142i | ||||||||
\(982\) | −30.9074 | + | 7.70713i | −0.986293 | + | 0.245944i | ||||
\(983\) | 33.7223 | 1.07557 | 0.537787 | − | 0.843081i | \(-0.319260\pi\) | ||||
0.537787 | + | 0.843081i | \(0.319260\pi\) | |||||||
\(984\) | −17.3258 | + | 15.6033i | −0.552328 | + | 0.497415i | ||||
\(985\) | −8.04887 | −0.256458 | ||||||||
\(986\) | 2.06619 | − | 0.515230i | 0.0658009 | − | 0.0164083i | ||||
\(987\) | − | 17.6889i | − | 0.563044i | ||||||
\(988\) | −14.1498 | + | 7.52475i | −0.450165 | + | 0.239394i | ||||
\(989\) | − | 8.14477i | − | 0.258989i | ||||||
\(990\) | 1.92628 | + | 7.72483i | 0.0612213 | + | 0.245511i | ||||
\(991\) | 39.1447 | 1.24347 | 0.621736 | − | 0.783227i | \(-0.286428\pi\) | ||||
0.621736 | + | 0.783227i | \(0.286428\pi\) | |||||||
\(992\) | 5.35040 | + | 1.94641i | 0.169875 | + | 0.0617985i | ||||
\(993\) | −16.1398 | −0.512180 | ||||||||
\(994\) | −9.68487 | − | 38.8386i | −0.307186 | − | 1.23188i | ||||
\(995\) | − | 4.86161i | − | 0.154123i | ||||||
\(996\) | 5.94822 | − | 3.16322i | 0.188477 | − | 0.100230i | ||||
\(997\) | 18.6528i | 0.590742i | 0.955383 | + | 0.295371i | \(0.0954432\pi\) | ||||
−0.955383 | + | 0.295371i | \(0.904557\pi\) | |||||||
\(998\) | −21.5927 | + | 5.38441i | −0.683506 | + | 0.170441i | ||||
\(999\) | 1.82285 | 0.0576724 |
(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 | 552.2.f.c.277.7 | ✓ | 18 | |
4.3 | odd | 2 | 2208.2.f.c.1105.15 | 18 | |||
8.3 | odd | 2 | 2208.2.f.c.1105.4 | 18 | |||
8.5 | even | 2 | inner | 552.2.f.c.277.8 | yes | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
552.2.f.c.277.7 | ✓ | 18 | 1.1 | even | 1 | trivial | |
552.2.f.c.277.8 | yes | 18 | 8.5 | even | 2 | inner | |
2208.2.f.c.1105.4 | 18 | 8.3 | odd | 2 | |||
2208.2.f.c.1105.15 | 18 | 4.3 | odd | 2 |