Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(199,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.199");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.q (of order \(6\), degree \(2\), not 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: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 649.1 | ||
Root | \(-0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.649 |
Dual form | 1050.3.q.a.199.1 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22474 | − | 0.707107i | −0.612372 | − | 0.353553i | ||||
\(3\) | −0.866025 | − | 1.50000i | −0.288675 | − | 0.500000i | ||||
\(4\) | 1.00000 | + | 1.73205i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.44949i | 0.408248i | ||||||||
\(7\) | −1.88064 | − | 6.74264i | −0.268662 | − | 0.963234i | ||||
\(8\) | − | 2.82843i | − | 0.353553i | ||||||
\(9\) | −1.50000 | + | 2.59808i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.00000 | − | 5.19615i | −0.272727 | − | 0.472377i | 0.696832 | − | 0.717234i | \(-0.254592\pi\) |
−0.969559 | + | 0.244857i | \(0.921259\pi\) | |||||||
\(12\) | 1.73205 | − | 3.00000i | 0.144338 | − | 0.250000i | ||||
\(13\) | −17.8639 | −1.37414 | −0.687072 | − | 0.726590i | \(-0.741104\pi\) | ||||
−0.687072 | + | 0.726590i | \(0.741104\pi\) | |||||||
\(14\) | −2.46447 | + | 9.58783i | −0.176033 | + | 0.684845i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.125000 | + | 0.216506i | ||||
\(17\) | −9.37769 | − | 16.2426i | −0.551629 | − | 0.955449i | −0.998157 | − | 0.0606799i | \(-0.980673\pi\) |
0.446528 | − | 0.894770i | \(-0.352660\pi\) | |||||||
\(18\) | 3.67423 | − | 2.12132i | 0.204124 | − | 0.117851i | ||||
\(19\) | 14.7426 | + | 8.51167i | 0.775928 | + | 0.447983i | 0.834985 | − | 0.550272i | \(-0.185476\pi\) |
−0.0590569 | + | 0.998255i | \(0.518809\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.48528 | + | 8.66025i | −0.404061 | + | 0.412393i | ||||
\(22\) | 8.48528i | 0.385695i | ||||||||
\(23\) | 11.6531 | + | 6.72792i | 0.506657 | + | 0.292518i | 0.731458 | − | 0.681886i | \(-0.238840\pi\) |
−0.224802 | + | 0.974405i | \(0.572173\pi\) | |||||||
\(24\) | −4.24264 | + | 2.44949i | −0.176777 | + | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 21.8787 | + | 12.6317i | 0.841488 | + | 0.485833i | ||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | 9.79796 | − | 10.0000i | 0.349927 | − | 0.357143i | ||||
\(29\) | −33.9411 | −1.17038 | −0.585192 | − | 0.810895i | \(-0.698981\pi\) | ||||
−0.585192 | + | 0.810895i | \(0.698981\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 12.7721 | − | 7.37396i | 0.412003 | − | 0.237870i | −0.279647 | − | 0.960103i | \(-0.590218\pi\) |
0.691650 | + | 0.722233i | \(0.256884\pi\) | |||||||
\(32\) | 4.89898 | − | 2.82843i | 0.153093 | − | 0.0883883i | ||||
\(33\) | −5.19615 | + | 9.00000i | −0.157459 | + | 0.272727i | ||||
\(34\) | 26.5241i | 0.780121i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | −5.17066 | − | 2.98528i | −0.139748 | − | 0.0806833i | 0.428496 | − | 0.903544i | \(-0.359044\pi\) |
−0.568244 | + | 0.822860i | \(0.692377\pi\) | |||||||
\(38\) | −12.0373 | − | 20.8492i | −0.316771 | − | 0.548664i | ||||
\(39\) | 15.4706 | + | 26.7958i | 0.396681 | + | 0.687072i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 35.2354i | 0.859399i | 0.902972 | + | 0.429700i | \(0.141381\pi\) | ||||
−0.902972 | + | 0.429700i | \(0.858619\pi\) | |||||||
\(42\) | 16.5160 | − | 4.60660i | 0.393239 | − | 0.109681i | ||||
\(43\) | − | 15.4853i | − | 0.360123i | −0.983655 | − | 0.180061i | \(-0.942370\pi\) | ||
0.983655 | − | 0.180061i | \(-0.0576296\pi\) | |||||||
\(44\) | 6.00000 | − | 10.3923i | 0.136364 | − | 0.236189i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9.51472 | − | 16.4800i | −0.206842 | − | 0.358260i | ||||
\(47\) | 16.6031 | − | 28.7574i | 0.353257 | − | 0.611859i | −0.633561 | − | 0.773693i | \(-0.718408\pi\) |
0.986818 | + | 0.161834i | \(0.0517409\pi\) | |||||||
\(48\) | 6.92820 | 0.144338 | ||||||||
\(49\) | −41.9264 | + | 25.3609i | −0.855641 | + | 0.517570i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −16.2426 | + | 28.1331i | −0.318483 | + | 0.551629i | ||||
\(52\) | −17.8639 | − | 30.9411i | −0.343536 | − | 0.595022i | ||||
\(53\) | 29.9161 | − | 17.2721i | 0.564455 | − | 0.325888i | −0.190477 | − | 0.981692i | \(-0.561003\pi\) |
0.754932 | + | 0.655803i | \(0.227670\pi\) | |||||||
\(54\) | −6.36396 | − | 3.67423i | −0.117851 | − | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −19.0711 | + | 5.31925i | −0.340555 | + | 0.0949865i | ||||
\(57\) | − | 29.4853i | − | 0.517286i | ||||||
\(58\) | 41.5692 | + | 24.0000i | 0.716711 | + | 0.413793i | ||||
\(59\) | −23.6985 | + | 13.6823i | −0.401669 | + | 0.231904i | −0.687204 | − | 0.726465i | \(-0.741162\pi\) |
0.285535 | + | 0.958368i | \(0.407829\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −34.9706 | − | 20.1903i | −0.573288 | − | 0.330988i | 0.185174 | − | 0.982706i | \(-0.440715\pi\) |
−0.758461 | + | 0.651718i | \(0.774049\pi\) | |||||||
\(62\) | −20.8567 | −0.336399 | ||||||||
\(63\) | 20.3389 | + | 5.22792i | 0.322839 | + | 0.0829829i | ||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 12.7279 | − | 7.34847i | 0.192847 | − | 0.111340i | ||||
\(67\) | −99.0707 | + | 57.1985i | −1.47867 | + | 0.853709i | −0.999709 | − | 0.0241291i | \(-0.992319\pi\) |
−0.478958 | + | 0.877838i | \(0.658985\pi\) | |||||||
\(68\) | 18.7554 | − | 32.4853i | 0.275814 | − | 0.477725i | ||||
\(69\) | − | 23.3062i | − | 0.337771i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 18.6030 | 0.262015 | 0.131007 | − | 0.991381i | \(-0.458179\pi\) | ||||
0.131007 | + | 0.991381i | \(0.458179\pi\) | |||||||
\(72\) | 7.34847 | + | 4.24264i | 0.102062 | + | 0.0589256i | ||||
\(73\) | 58.5161 | + | 101.353i | 0.801590 | + | 1.38839i | 0.918569 | + | 0.395260i | \(0.129346\pi\) |
−0.116979 | + | 0.993134i | \(0.537321\pi\) | |||||||
\(74\) | 4.22183 | + | 7.31242i | 0.0570517 | + | 0.0988164i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 34.0467i | 0.447983i | ||||||||
\(77\) | −29.3939 | + | 30.0000i | −0.381739 | + | 0.389610i | ||||
\(78\) | − | 43.7574i | − | 0.560992i | ||||||
\(79\) | −44.1690 | + | 76.5030i | −0.559102 | + | 0.968393i | 0.438470 | + | 0.898746i | \(0.355521\pi\) |
−0.997572 | + | 0.0696469i | \(0.977813\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 24.9152 | − | 43.1543i | 0.303843 | − | 0.526272i | ||||
\(83\) | 75.7601 | 0.912772 | 0.456386 | − | 0.889782i | \(-0.349144\pi\) | ||||
0.456386 | + | 0.889782i | \(0.349144\pi\) | |||||||
\(84\) | −23.4853 | − | 6.03668i | −0.279587 | − | 0.0718653i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −10.9497 | + | 18.9655i | −0.127323 | + | 0.220529i | ||||
\(87\) | 29.3939 | + | 50.9117i | 0.337861 | + | 0.585192i | ||||
\(88\) | −14.6969 | + | 8.48528i | −0.167011 | + | 0.0964237i | ||||
\(89\) | 18.0000 | + | 10.3923i | 0.202247 | + | 0.116767i | 0.597703 | − | 0.801717i | \(-0.296080\pi\) |
−0.395456 | + | 0.918485i | \(0.629413\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 33.5955 | + | 120.450i | 0.369181 | + | 1.32362i | ||||
\(92\) | 26.9117i | 0.292518i | ||||||||
\(93\) | −22.1219 | − | 12.7721i | −0.237870 | − | 0.137334i | ||||
\(94\) | −40.6690 | + | 23.4803i | −0.432649 | + | 0.249790i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −8.48528 | − | 4.89898i | −0.0883883 | − | 0.0510310i | ||||
\(97\) | −30.5826 | −0.315284 | −0.157642 | − | 0.987496i | \(-0.550389\pi\) | ||||
−0.157642 | + | 0.987496i | \(0.550389\pi\) | |||||||
\(98\) | 69.2820 | − | 1.41421i | 0.706960 | − | 0.0144308i | ||||
\(99\) | 18.0000 | 0.181818 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 110.823 | − | 63.9839i | 1.09726 | − | 0.633504i | 0.161761 | − | 0.986830i | \(-0.448283\pi\) |
0.935500 | + | 0.353326i | \(0.114949\pi\) | |||||||
\(102\) | 39.7862 | − | 22.9706i | 0.390061 | − | 0.225202i | ||||
\(103\) | −40.4781 | + | 70.1102i | −0.392992 | + | 0.680681i | −0.992843 | − | 0.119430i | \(-0.961893\pi\) |
0.599851 | + | 0.800112i | \(0.295226\pi\) | |||||||
\(104\) | 50.5266i | 0.485833i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −48.8528 | −0.460876 | ||||||||
\(107\) | −146.753 | − | 84.7279i | −1.37152 | − | 0.791850i | −0.380404 | − | 0.924820i | \(-0.624215\pi\) |
−0.991120 | + | 0.132971i | \(0.957548\pi\) | |||||||
\(108\) | 5.19615 | + | 9.00000i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | 89.4706 | + | 154.968i | 0.820831 | + | 1.42172i | 0.905064 | + | 0.425275i | \(0.139823\pi\) |
−0.0842335 | + | 0.996446i | \(0.526844\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.3413i | 0.0931650i | ||||||||
\(112\) | 27.1185 | + | 6.97056i | 0.242129 | + | 0.0622372i | ||||
\(113\) | 17.3970i | 0.153955i | 0.997033 | + | 0.0769777i | \(0.0245270\pi\) | ||||
−0.997033 | + | 0.0769777i | \(0.975473\pi\) | |||||||
\(114\) | −20.8492 | + | 36.1119i | −0.182888 | + | 0.316771i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −33.9411 | − | 58.7878i | −0.292596 | − | 0.506791i | ||||
\(117\) | 26.7958 | − | 46.4117i | 0.229024 | − | 0.396681i | ||||
\(118\) | 38.6995 | 0.327962 | ||||||||
\(119\) | −91.8823 | + | 93.7769i | −0.772120 | + | 0.788041i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 42.5000 | − | 73.6122i | 0.351240 | − | 0.608365i | ||||
\(122\) | 28.5533 | + | 49.4558i | 0.234044 | + | 0.405376i | ||||
\(123\) | 52.8530 | − | 30.5147i | 0.429700 | − | 0.248087i | ||||
\(124\) | 25.5442 | + | 14.7479i | 0.206001 | + | 0.118935i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −21.2132 | − | 20.7846i | −0.168359 | − | 0.164957i | ||||
\(127\) | 167.426i | 1.31832i | 0.752004 | + | 0.659159i | \(0.229088\pi\) | ||||
−0.752004 | + | 0.659159i | \(0.770912\pi\) | |||||||
\(128\) | 9.79796 | + | 5.65685i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | −23.2279 | + | 13.4106i | −0.180061 | + | 0.103959i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.54416 | − | 0.891519i | −0.0117874 | − | 0.00680549i | 0.494095 | − | 0.869408i | \(-0.335500\pi\) |
−0.505882 | + | 0.862603i | \(0.668833\pi\) | |||||||
\(132\) | −20.7846 | −0.157459 | ||||||||
\(133\) | 29.6656 | − | 115.412i | 0.223049 | − | 0.867757i | ||||
\(134\) | 161.782 | 1.20733 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −45.9411 | + | 26.5241i | −0.337802 | + | 0.195030i | ||||
\(137\) | 87.4431 | − | 50.4853i | 0.638271 | − | 0.368506i | −0.145677 | − | 0.989332i | \(-0.546536\pi\) |
0.783948 | + | 0.620826i | \(0.213203\pi\) | |||||||
\(138\) | −16.4800 | + | 28.5442i | −0.119420 | + | 0.206842i | ||||
\(139\) | 140.542i | 1.01110i | 0.862799 | + | 0.505548i | \(0.168710\pi\) | ||||
−0.862799 | + | 0.505548i | \(0.831290\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −57.5147 | −0.407906 | ||||||||
\(142\) | −22.7840 | − | 13.1543i | −0.160450 | − | 0.0926361i | ||||
\(143\) | 53.5916 | + | 92.8234i | 0.374766 | + | 0.649115i | ||||
\(144\) | −6.00000 | − | 10.3923i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 165.508i | − | 1.13362i | ||||||
\(147\) | 74.3507 | + | 40.9264i | 0.505787 | + | 0.278411i | ||||
\(148\) | − | 11.9411i | − | 0.0806833i | ||||||
\(149\) | 91.4558 | − | 158.406i | 0.613798 | − | 1.06313i | −0.376797 | − | 0.926296i | \(-0.622974\pi\) |
0.990594 | − | 0.136833i | \(-0.0436922\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 144.397 | + | 250.103i | 0.956271 | + | 1.65631i | 0.731432 | + | 0.681915i | \(0.238852\pi\) |
0.224840 | + | 0.974396i | \(0.427814\pi\) | |||||||
\(152\) | 24.0746 | − | 41.6985i | 0.158386 | − | 0.274332i | ||||
\(153\) | 56.2662 | 0.367753 | ||||||||
\(154\) | 57.2132 | − | 15.9577i | 0.371514 | − | 0.103622i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −30.9411 | + | 53.5916i | −0.198341 | + | 0.343536i | ||||
\(157\) | 93.5307 | + | 162.000i | 0.595737 | + | 1.03185i | 0.993442 | + | 0.114334i | \(0.0364734\pi\) |
−0.397705 | + | 0.917513i | \(0.630193\pi\) | |||||||
\(158\) | 108.192 | − | 62.4645i | 0.684757 | − | 0.395345i | ||||
\(159\) | −51.8162 | − | 29.9161i | −0.325888 | − | 0.188152i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 23.4487 | − | 91.2255i | 0.145644 | − | 0.566618i | ||||
\(162\) | 12.7279i | 0.0785674i | ||||||||
\(163\) | 13.9074 | + | 8.02944i | 0.0853214 | + | 0.0492604i | 0.542054 | − | 0.840344i | \(-0.317647\pi\) |
−0.456732 | + | 0.889604i | \(0.650980\pi\) | |||||||
\(164\) | −61.0294 | + | 35.2354i | −0.372131 | + | 0.214850i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −92.7868 | − | 53.5705i | −0.558957 | − | 0.322714i | ||||
\(167\) | 176.117 | 1.05459 | 0.527297 | − | 0.849681i | \(-0.323206\pi\) | ||||
0.527297 | + | 0.849681i | \(0.323206\pi\) | |||||||
\(168\) | 24.4949 | + | 24.0000i | 0.145803 | + | 0.142857i | ||||
\(169\) | 150.118 | 0.888271 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −44.2279 | + | 25.5350i | −0.258643 | + | 0.149328i | ||||
\(172\) | 26.8213 | − | 15.4853i | 0.155938 | − | 0.0900307i | ||||
\(173\) | −115.576 | + | 200.184i | −0.668070 | + | 1.15713i | 0.310373 | + | 0.950615i | \(0.399546\pi\) |
−0.978443 | + | 0.206517i | \(0.933787\pi\) | |||||||
\(174\) | − | 83.1384i | − | 0.477807i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 24.0000 | 0.136364 | ||||||||
\(177\) | 41.0470 | + | 23.6985i | 0.231904 | + | 0.133890i | ||||
\(178\) | −14.6969 | − | 25.4558i | −0.0825671 | − | 0.143010i | ||||
\(179\) | −42.6396 | − | 73.8540i | −0.238210 | − | 0.412592i | 0.721991 | − | 0.691903i | \(-0.243227\pi\) |
−0.960201 | + | 0.279311i | \(0.909894\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 5.58655i | − | 0.0308649i | −0.999881 | − | 0.0154325i | \(-0.995087\pi\) | ||
0.999881 | − | 0.0154325i | \(-0.00491250\pi\) | |||||||
\(182\) | 44.0249 | − | 171.276i | 0.241895 | − | 0.941075i | ||||
\(183\) | 69.9411i | 0.382192i | ||||||||
\(184\) | 19.0294 | − | 32.9600i | 0.103421 | − | 0.179130i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 18.0624 | + | 31.2851i | 0.0971099 | + | 0.168199i | ||||
\(187\) | −56.2662 | + | 97.4558i | −0.300889 | + | 0.521154i | ||||
\(188\) | 66.4123 | 0.353257 | ||||||||
\(189\) | −9.77208 | − | 35.0358i | −0.0517041 | − | 0.185375i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −92.6985 | + | 160.558i | −0.485332 | + | 0.840620i | −0.999858 | − | 0.0168547i | \(-0.994635\pi\) |
0.514526 | + | 0.857475i | \(0.327968\pi\) | |||||||
\(192\) | 6.92820 | + | 12.0000i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | −197.275 | + | 113.897i | −1.02215 | + | 0.590140i | −0.914727 | − | 0.404073i | \(-0.867594\pi\) |
−0.107425 | + | 0.994213i | \(0.534261\pi\) | |||||||
\(194\) | 37.4558 | + | 21.6251i | 0.193071 | + | 0.111470i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −85.8528 | − | 47.2577i | −0.438025 | − | 0.241111i | ||||
\(197\) | 123.161i | 0.625185i | 0.949887 | + | 0.312593i | \(0.101197\pi\) | ||||
−0.949887 | + | 0.312593i | \(0.898803\pi\) | |||||||
\(198\) | −22.0454 | − | 12.7279i | −0.111340 | − | 0.0642824i | ||||
\(199\) | −5.39697 | + | 3.11594i | −0.0271205 | + | 0.0156580i | −0.513499 | − | 0.858090i | \(-0.671651\pi\) |
0.486378 | + | 0.873748i | \(0.338318\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 171.595 | + | 99.0707i | 0.853709 | + | 0.492889i | ||||
\(202\) | −180.974 | −0.895910 | ||||||||
\(203\) | 63.8309 | + | 228.853i | 0.314438 | + | 1.12735i | ||||
\(204\) | −64.9706 | −0.318483 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 99.1508 | − | 57.2447i | 0.481314 | − | 0.277887i | ||||
\(207\) | −34.9593 | + | 20.1838i | −0.168886 | + | 0.0975061i | ||||
\(208\) | 35.7277 | − | 61.8823i | 0.171768 | − | 0.297511i | ||||
\(209\) | − | 102.140i | − | 0.488708i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −124.912 | −0.591999 | −0.295999 | − | 0.955188i | \(-0.595653\pi\) | ||||
−0.295999 | + | 0.955188i | \(0.595653\pi\) | |||||||
\(212\) | 59.8322 | + | 34.5442i | 0.282228 | + | 0.162944i | ||||
\(213\) | −16.1107 | − | 27.9045i | −0.0756371 | − | 0.131007i | ||||
\(214\) | 119.823 | + | 207.540i | 0.559922 | + | 0.969814i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 14.6969i | − | 0.0680414i | ||||||
\(217\) | −73.7396 | − | 72.2498i | −0.339814 | − | 0.332948i | ||||
\(218\) | − | 253.061i | − | 1.16083i | ||||||
\(219\) | 101.353 | − | 175.548i | 0.462798 | − | 0.801590i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 167.522 | + | 290.156i | 0.758017 | + | 1.31292i | ||||
\(222\) | 7.31242 | − | 12.6655i | 0.0329388 | − | 0.0570517i | ||||
\(223\) | −228.631 | −1.02525 | −0.512625 | − | 0.858613i | \(-0.671327\pi\) | ||||
−0.512625 | + | 0.858613i | \(0.671327\pi\) | |||||||
\(224\) | −28.2843 | − | 27.7128i | −0.126269 | − | 0.123718i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12.3015 | − | 21.3068i | 0.0544315 | − | 0.0942781i | ||||
\(227\) | −84.7685 | − | 146.823i | −0.373430 | − | 0.646799i | 0.616661 | − | 0.787229i | \(-0.288485\pi\) |
−0.990091 | + | 0.140430i | \(0.955152\pi\) | |||||||
\(228\) | 51.0700 | − | 29.4853i | 0.223991 | − | 0.129321i | ||||
\(229\) | −30.0442 | − | 17.3460i | −0.131197 | − | 0.0757467i | 0.432965 | − | 0.901411i | \(-0.357467\pi\) |
−0.564162 | + | 0.825664i | \(0.690801\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 70.4558 | + | 18.1101i | 0.305004 | + | 0.0783985i | ||||
\(232\) | 96.0000i | 0.413793i | ||||||||
\(233\) | −220.391 | − | 127.243i | −0.945883 | − | 0.546106i | −0.0540833 | − | 0.998536i | \(-0.517224\pi\) |
−0.891800 | + | 0.452431i | \(0.850557\pi\) | |||||||
\(234\) | −65.6360 | + | 37.8950i | −0.280496 | + | 0.161944i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −47.3970 | − | 27.3647i | −0.200835 | − | 0.115952i | ||||
\(237\) | 153.006 | 0.645595 | ||||||||
\(238\) | 178.843 | − | 49.8823i | 0.751440 | − | 0.209589i | ||||
\(239\) | −197.147 | −0.824884 | −0.412442 | − | 0.910984i | \(-0.635324\pi\) | ||||
−0.412442 | + | 0.910984i | \(0.635324\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 76.6173 | − | 44.2350i | 0.317914 | − | 0.183548i | −0.332548 | − | 0.943086i | \(-0.607908\pi\) |
0.650462 | + | 0.759538i | \(0.274575\pi\) | |||||||
\(242\) | −104.103 | + | 60.1041i | −0.430179 | + | 0.248364i | ||||
\(243\) | −7.79423 | + | 13.5000i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | − | 80.7611i | − | 0.330988i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −86.3087 | −0.350848 | ||||||||
\(247\) | −263.361 | − | 152.051i | −1.06624 | − | 0.615592i | ||||
\(248\) | −20.8567 | − | 36.1249i | −0.0840997 | − | 0.145665i | ||||
\(249\) | −65.6102 | − | 113.640i | −0.263495 | − | 0.456386i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 215.903i | − | 0.860172i | −0.902788 | − | 0.430086i | \(-0.858483\pi\) | ||
0.902788 | − | 0.430086i | \(-0.141517\pi\) | |||||||
\(252\) | 11.2838 | + | 40.4558i | 0.0447771 | + | 0.160539i | ||||
\(253\) | − | 80.7351i | − | 0.319111i | ||||||
\(254\) | 118.388 | − | 205.055i | 0.466096 | − | 0.807302i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 2.15232 | − | 3.72792i | 0.00837477 | − | 0.0145055i | −0.861808 | − | 0.507235i | \(-0.830668\pi\) |
0.870182 | + | 0.492730i | \(0.164001\pi\) | |||||||
\(258\) | 37.9310 | 0.147020 | ||||||||
\(259\) | −10.4045 | + | 40.4781i | −0.0401720 | + | 0.156286i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 50.9117 | − | 88.1816i | 0.195064 | − | 0.337861i | ||||
\(262\) | 1.26080 | + | 2.18377i | 0.00481221 | + | 0.00833499i | ||||
\(263\) | −244.805 | + | 141.338i | −0.930817 | + | 0.537407i | −0.887070 | − | 0.461635i | \(-0.847263\pi\) |
−0.0437468 | + | 0.999043i | \(0.513929\pi\) | |||||||
\(264\) | 25.4558 | + | 14.6969i | 0.0964237 | + | 0.0556702i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −117.941 | + | 120.373i | −0.443388 | + | 0.452531i | ||||
\(267\) | − | 36.0000i | − | 0.134831i | ||||||
\(268\) | −198.141 | − | 114.397i | −0.739333 | − | 0.426854i | ||||
\(269\) | 330.765 | − | 190.967i | 1.22961 | − | 0.709914i | 0.262660 | − | 0.964888i | \(-0.415400\pi\) |
0.966948 | + | 0.254974i | \(0.0820669\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −73.0294 | − | 42.1636i | −0.269481 | − | 0.155585i | 0.359171 | − | 0.933272i | \(-0.383060\pi\) |
−0.628652 | + | 0.777687i | \(0.716393\pi\) | |||||||
\(272\) | 75.0215 | 0.275814 | ||||||||
\(273\) | 151.580 | − | 154.706i | 0.555238 | − | 0.566687i | ||||
\(274\) | −142.794 | −0.521146 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 40.3675 | − | 23.3062i | 0.146259 | − | 0.0844428i | ||||
\(277\) | −118.747 | + | 68.5589i | −0.428691 | + | 0.247505i | −0.698789 | − | 0.715328i | \(-0.746277\pi\) |
0.270098 | + | 0.962833i | \(0.412944\pi\) | |||||||
\(278\) | 99.3784 | − | 172.128i | 0.357476 | − | 0.619167i | ||||
\(279\) | 44.2438i | 0.158580i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −325.103 | −1.15695 | −0.578474 | − | 0.815701i | \(-0.696352\pi\) | ||||
−0.578474 | + | 0.815701i | \(0.696352\pi\) | |||||||
\(282\) | 70.4409 | + | 40.6690i | 0.249790 | + | 0.144216i | ||||
\(283\) | −97.2876 | − | 168.507i | −0.343773 | − | 0.595432i | 0.641357 | − | 0.767242i | \(-0.278372\pi\) |
−0.985130 | + | 0.171811i | \(0.945038\pi\) | |||||||
\(284\) | 18.6030 | + | 32.2214i | 0.0655036 | + | 0.113456i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 151.580i | − | 0.530000i | ||||||
\(287\) | 237.579 | − | 66.2649i | 0.827803 | − | 0.230888i | ||||
\(288\) | 16.9706i | 0.0589256i | ||||||||
\(289\) | −31.3823 | + | 54.3557i | −0.108589 | + | 0.188082i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 26.4853 | + | 45.8739i | 0.0910147 | + | 0.157642i | ||||
\(292\) | −117.032 | + | 202.706i | −0.400795 | + | 0.694197i | ||||
\(293\) | −239.702 | −0.818095 | −0.409048 | − | 0.912513i | \(-0.634139\pi\) | ||||
−0.409048 | + | 0.912513i | \(0.634139\pi\) | |||||||
\(294\) | −62.1213 | − | 102.698i | −0.211297 | − | 0.349314i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8.44365 | + | 14.6248i | −0.0285258 | + | 0.0494082i | ||||
\(297\) | −15.5885 | − | 27.0000i | −0.0524864 | − | 0.0909091i | ||||
\(298\) | −224.020 | + | 129.338i | −0.751745 | + | 0.434020i | ||||
\(299\) | −208.169 | − | 120.187i | −0.696219 | − | 0.401962i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −104.412 | + | 29.1222i | −0.346883 | + | 0.0967515i | ||||
\(302\) | − | 408.416i | − | 1.35237i | ||||||
\(303\) | −191.952 | − | 110.823i | −0.633504 | − | 0.365754i | ||||
\(304\) | −58.9706 | + | 34.0467i | −0.193982 | + | 0.111996i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −68.9117 | − | 39.7862i | −0.225202 | − | 0.130020i | ||||
\(307\) | −540.272 | −1.75984 | −0.879921 | − | 0.475120i | \(-0.842405\pi\) | ||||
−0.879921 | + | 0.475120i | \(0.842405\pi\) | |||||||
\(308\) | −81.3554 | − | 20.9117i | −0.264141 | − | 0.0678951i | ||||
\(309\) | 140.220 | 0.453788 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 350.044 | − | 202.098i | 1.12554 | − | 0.649832i | 0.182732 | − | 0.983163i | \(-0.441506\pi\) |
0.942810 | + | 0.333330i | \(0.108172\pi\) | |||||||
\(312\) | 75.7900 | − | 43.7574i | 0.242917 | − | 0.140248i | ||||
\(313\) | −65.6482 | + | 113.706i | −0.209739 | + | 0.363278i | −0.951632 | − | 0.307240i | \(-0.900595\pi\) |
0.741893 | + | 0.670518i | \(0.233928\pi\) | |||||||
\(314\) | − | 264.545i | − | 0.842500i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −176.676 | −0.559102 | ||||||||
\(317\) | 81.3554 | + | 46.9706i | 0.256642 | + | 0.148172i | 0.622802 | − | 0.782380i | \(-0.285994\pi\) |
−0.366160 | + | 0.930552i | \(0.619328\pi\) | |||||||
\(318\) | 42.3078 | + | 73.2792i | 0.133043 | + | 0.230438i | ||||
\(319\) | 101.823 | + | 176.363i | 0.319196 | + | 0.552863i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 293.506i | 0.914349i | ||||||||
\(322\) | −93.2248 | + | 95.1472i | −0.289518 | + | 0.295488i | ||||
\(323\) | − | 319.279i | − | 0.988481i | ||||||
\(324\) | 9.00000 | − | 15.5885i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −11.3553 | − | 19.6680i | −0.0348323 | − | 0.0603314i | ||||
\(327\) | 154.968 | − | 268.412i | 0.473907 | − | 0.820831i | ||||
\(328\) | 99.6607 | 0.303843 | ||||||||
\(329\) | −225.125 | − | 57.8664i | −0.684270 | − | 0.175886i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 130.684 | − | 226.351i | 0.394815 | − | 0.683840i | −0.598263 | − | 0.801300i | \(-0.704142\pi\) |
0.993078 | + | 0.117460i | \(0.0374754\pi\) | |||||||
\(332\) | 75.7601 | + | 131.220i | 0.228193 | + | 0.395242i | ||||
\(333\) | 15.5120 | − | 8.95584i | 0.0465825 | − | 0.0268944i | ||||
\(334\) | −215.698 | − | 124.534i | −0.645804 | − | 0.372855i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −13.0294 | − | 46.7144i | −0.0387781 | − | 0.139031i | ||||
\(337\) | 136.265i | 0.404347i | 0.979350 | + | 0.202173i | \(0.0648005\pi\) | ||||
−0.979350 | + | 0.202173i | \(0.935200\pi\) | |||||||
\(338\) | −183.856 | − | 106.149i | −0.543952 | − | 0.314051i | ||||
\(339\) | 26.0955 | − | 15.0662i | 0.0769777 | − | 0.0444431i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −76.6325 | − | 44.2438i | −0.224729 | − | 0.129747i | ||||
\(342\) | 72.2239 | 0.211181 | ||||||||
\(343\) | 249.848 | + | 235.000i | 0.728420 | + | 0.685131i | ||||
\(344\) | −43.7990 | −0.127323 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 283.103 | − | 163.449i | 0.818216 | − | 0.472397i | ||||
\(347\) | −279.026 | + | 161.095i | −0.804108 | + | 0.464252i | −0.844906 | − | 0.534915i | \(-0.820343\pi\) |
0.0407975 | + | 0.999167i | \(0.487010\pi\) | |||||||
\(348\) | −58.7878 | + | 101.823i | −0.168930 | + | 0.292596i | ||||
\(349\) | − | 346.495i | − | 0.992821i | −0.868088 | − | 0.496411i | \(-0.834651\pi\) | ||
0.868088 | − | 0.496411i | \(-0.165349\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −92.8234 | −0.264454 | ||||||||
\(352\) | −29.3939 | − | 16.9706i | −0.0835053 | − | 0.0482118i | ||||
\(353\) | 310.296 | + | 537.448i | 0.879025 | + | 1.52252i | 0.852413 | + | 0.522869i | \(0.175138\pi\) |
0.0266116 | + | 0.999646i | \(0.491528\pi\) | |||||||
\(354\) | −33.5147 | − | 58.0492i | −0.0946743 | − | 0.163981i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 41.5692i | 0.116767i | ||||||||
\(357\) | 220.238 | + | 56.6102i | 0.616912 | + | 0.158572i | ||||
\(358\) | 120.603i | 0.336880i | ||||||||
\(359\) | 10.1177 | − | 17.5245i | 0.0281831 | − | 0.0488146i | −0.851590 | − | 0.524209i | \(-0.824361\pi\) |
0.879773 | + | 0.475394i | \(0.157695\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −35.6030 | − | 61.6663i | −0.0986234 | − | 0.170821i | ||||
\(362\) | −3.95029 | + | 6.84210i | −0.0109124 | + | 0.0189008i | ||||
\(363\) | −147.224 | −0.405577 | ||||||||
\(364\) | −175.029 | + | 178.639i | −0.480850 | + | 0.490766i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 49.4558 | − | 85.6600i | 0.135125 | − | 0.234044i | ||||
\(367\) | −155.787 | − | 269.831i | −0.424488 | − | 0.735234i | 0.571885 | − | 0.820334i | \(-0.306212\pi\) |
−0.996372 | + | 0.0850998i | \(0.972879\pi\) | |||||||
\(368\) | −46.6124 | + | 26.9117i | −0.126664 | + | 0.0731296i | ||||
\(369\) | −91.5442 | − | 52.8530i | −0.248087 | − | 0.143233i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −172.721 | − | 169.231i | −0.465555 | − | 0.456149i | ||||
\(372\) | − | 51.0883i | − | 0.137334i | ||||||
\(373\) | −590.094 | − | 340.691i | −1.58202 | − | 0.913380i | −0.994564 | − | 0.104125i | \(-0.966796\pi\) |
−0.587457 | − | 0.809255i | \(-0.699871\pi\) | |||||||
\(374\) | 137.823 | − | 79.5724i | 0.368512 | − | 0.212760i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −81.3381 | − | 46.9606i | −0.216325 | − | 0.124895i | ||||
\(377\) | 606.320 | 1.60828 | ||||||||
\(378\) | −12.8057 | + | 49.8198i | −0.0338776 | + | 0.131798i | ||||
\(379\) | 624.779 | 1.64849 | 0.824246 | − | 0.566231i | \(-0.191599\pi\) | ||||
0.824246 | + | 0.566231i | \(0.191599\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 251.140 | − | 144.996i | 0.659159 | − | 0.380566i | ||||
\(382\) | 227.064 | − | 131.095i | 0.594408 | − | 0.343182i | ||||
\(383\) | 69.1502 | − | 119.772i | 0.180549 | − | 0.312720i | −0.761519 | − | 0.648143i | \(-0.775546\pi\) |
0.942068 | + | 0.335423i | \(0.108879\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 322.149 | 0.834584 | ||||||||
\(387\) | 40.2319 | + | 23.2279i | 0.103959 | + | 0.0600205i | ||||
\(388\) | −30.5826 | − | 52.9706i | −0.0788211 | − | 0.136522i | ||||
\(389\) | −281.787 | − | 488.069i | −0.724388 | − | 1.25468i | −0.959226 | − | 0.282642i | \(-0.908789\pi\) |
0.234838 | − | 0.972035i | \(-0.424544\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 252.370i | − | 0.645446i | ||||||
\(392\) | 71.7315 | + | 118.586i | 0.182989 | + | 0.302515i | ||||
\(393\) | 3.08831i | 0.00785830i | ||||||||
\(394\) | 87.0883 | − | 150.841i | 0.221036 | − | 0.382846i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 18.0000 | + | 31.1769i | 0.0454545 | + | 0.0787296i | ||||
\(397\) | 226.669 | − | 392.603i | 0.570955 | − | 0.988923i | −0.425513 | − | 0.904952i | \(-0.639906\pi\) |
0.996468 | − | 0.0839711i | \(-0.0267603\pi\) | |||||||
\(398\) | 8.81321 | 0.0221438 | ||||||||
\(399\) | −198.809 | + | 55.4511i | −0.498267 | + | 0.138975i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 137.875 | − | 238.807i | 0.343828 | − | 0.595528i | −0.641312 | − | 0.767280i | \(-0.721610\pi\) |
0.985140 | + | 0.171752i | \(0.0549429\pi\) | |||||||
\(402\) | −140.107 | − | 242.673i | −0.348525 | − | 0.603663i | ||||
\(403\) | −228.159 | + | 131.727i | −0.566151 | + | 0.326867i | ||||
\(404\) | 221.647 | + | 127.968i | 0.548631 | + | 0.316752i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 83.6468 | − | 325.422i | 0.206026 | − | 0.801531i | ||||
\(407\) | 35.8234i | 0.0880181i | ||||||||
\(408\) | 79.5724 | + | 45.9411i | 0.195030 | + | 0.112601i | ||||
\(409\) | 377.441 | − | 217.916i | 0.922839 | − | 0.532801i | 0.0382993 | − | 0.999266i | \(-0.487806\pi\) |
0.884540 | + | 0.466465i | \(0.154473\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −151.456 | − | 87.4431i | −0.368506 | − | 0.212757i | ||||
\(412\) | −161.913 | −0.392992 | ||||||||
\(413\) | 136.823 | + | 134.059i | 0.331291 | + | 0.324598i | ||||
\(414\) | 57.0883 | 0.137894 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −87.5147 | + | 50.5266i | −0.210372 | + | 0.121458i | ||||
\(417\) | 210.813 | − | 121.713i | 0.505548 | − | 0.291878i | ||||
\(418\) | −72.2239 | + | 125.095i | −0.172784 | + | 0.299271i | ||||
\(419\) | 301.257i | 0.718991i | 0.933147 | + | 0.359496i | \(0.117051\pi\) | ||||
−0.933147 | + | 0.359496i | \(0.882949\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −203.794 | −0.484071 | −0.242036 | − | 0.970267i | \(-0.577815\pi\) | ||||
−0.242036 | + | 0.970267i | \(0.577815\pi\) | |||||||
\(422\) | 152.985 | + | 88.3259i | 0.362524 | + | 0.209303i | ||||
\(423\) | 49.8092 | + | 86.2721i | 0.117752 | + | 0.203953i | ||||
\(424\) | −48.8528 | − | 84.6156i | −0.115219 | − | 0.199565i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 45.5679i | 0.106967i | ||||||||
\(427\) | −70.3688 | + | 273.765i | −0.164798 | + | 0.641135i | ||||
\(428\) | − | 338.912i | − | 0.791850i | ||||||
\(429\) | 92.8234 | − | 160.775i | 0.216372 | − | 0.374766i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 197.860 | + | 342.703i | 0.459072 | + | 0.795136i | 0.998912 | − | 0.0466317i | \(-0.0148487\pi\) |
−0.539840 | + | 0.841767i | \(0.681515\pi\) | |||||||
\(432\) | −10.3923 | + | 18.0000i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | −44.2685 | −0.102237 | −0.0511184 | − | 0.998693i | \(-0.516279\pi\) | ||||
−0.0511184 | + | 0.998693i | \(0.516279\pi\) | |||||||
\(434\) | 39.2239 | + | 140.629i | 0.0903777 | + | 0.324031i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −178.941 | + | 309.935i | −0.410415 | + | 0.710860i | ||||
\(437\) | 114.532 | + | 198.375i | 0.262086 | + | 0.453947i | ||||
\(438\) | −248.263 | + | 143.335i | −0.566810 | + | 0.327248i | ||||
\(439\) | −344.558 | − | 198.931i | −0.784871 | − | 0.453146i | 0.0532827 | − | 0.998579i | \(-0.483032\pi\) |
−0.838154 | + | 0.545434i | \(0.816365\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | − | 146.969i | −0.00680272 | − | 0.333264i | ||||
\(442\) | − | 473.823i | − | 1.07200i | ||||||
\(443\) | −102.662 | − | 59.2721i | −0.231743 | − | 0.133797i | 0.379633 | − | 0.925137i | \(-0.376050\pi\) |
−0.611376 | + | 0.791340i | \(0.709384\pi\) | |||||||
\(444\) | −17.9117 | + | 10.3413i | −0.0403416 | + | 0.0232913i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 280.014 | + | 161.666i | 0.627835 | + | 0.362481i | ||||
\(447\) | −316.812 | −0.708752 | ||||||||
\(448\) | 15.0451 | + | 53.9411i | 0.0335828 | + | 0.120404i | ||||
\(449\) | −713.897 | −1.58997 | −0.794985 | − | 0.606629i | \(-0.792521\pi\) | ||||
−0.794985 | + | 0.606629i | \(0.792521\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 183.088 | − | 105.706i | 0.405961 | − | 0.234382i | ||||
\(452\) | −30.1324 | + | 17.3970i | −0.0666647 | + | 0.0384889i | ||||
\(453\) | 250.103 | − | 433.191i | 0.552104 | − | 0.956271i | ||||
\(454\) | 239.762i | 0.528109i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −83.3970 | −0.182888 | ||||||||
\(457\) | 108.406 | + | 62.5883i | 0.237213 | + | 0.136955i | 0.613895 | − | 0.789388i | \(-0.289602\pi\) |
−0.376682 | + | 0.926342i | \(0.622935\pi\) | |||||||
\(458\) | 24.5310 | + | 42.4889i | 0.0535610 | + | 0.0927704i | ||||
\(459\) | −48.7279 | − | 84.3992i | −0.106161 | − | 0.183876i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 655.767i | 1.42249i | 0.702945 | + | 0.711244i | \(0.251868\pi\) | ||||
−0.702945 | + | 0.711244i | \(0.748132\pi\) | |||||||
\(462\) | −73.4847 | − | 72.0000i | −0.159058 | − | 0.155844i | ||||
\(463\) | − | 869.396i | − | 1.87775i | −0.344265 | − | 0.938873i | \(-0.611872\pi\) | ||
0.344265 | − | 0.938873i | \(-0.388128\pi\) | |||||||
\(464\) | 67.8823 | − | 117.576i | 0.146298 | − | 0.253395i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 179.948 | + | 311.680i | 0.386155 | + | 0.668840i | ||||
\(467\) | 133.686 | − | 231.551i | 0.286266 | − | 0.495827i | −0.686649 | − | 0.726989i | \(-0.740919\pi\) |
0.972915 | + | 0.231162i | \(0.0742526\pi\) | |||||||
\(468\) | 107.183 | 0.229024 | ||||||||
\(469\) | 571.985 | + | 560.428i | 1.21958 | + | 1.19494i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 162.000 | − | 280.592i | 0.343949 | − | 0.595737i | ||||
\(472\) | 38.6995 | + | 67.0294i | 0.0819904 | + | 0.142012i | ||||
\(473\) | −80.4639 | + | 46.4558i | −0.170114 | + | 0.0982153i | ||||
\(474\) | −187.393 | − | 108.192i | −0.395345 | − | 0.228252i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −254.309 | − | 65.3678i | −0.534262 | − | 0.137327i | ||||
\(477\) | 103.632i | 0.217259i | ||||||||
\(478\) | 241.455 | + | 139.404i | 0.505136 | + | 0.291640i | ||||
\(479\) | −235.331 | + | 135.868i | −0.491296 | + | 0.283650i | −0.725112 | − | 0.688631i | \(-0.758212\pi\) |
0.233816 | + | 0.972281i | \(0.424879\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 92.3680 | + | 53.3287i | 0.192033 | + | 0.110870i | ||||
\(482\) | −125.116 | −0.259576 | ||||||||
\(483\) | −157.145 | + | 43.8305i | −0.325353 | + | 0.0907464i | ||||
\(484\) | 170.000 | 0.351240 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 19.0919 | − | 11.0227i | 0.0392837 | − | 0.0226805i | ||||
\(487\) | −486.285 | + | 280.757i | −0.998532 | + | 0.576503i | −0.907814 | − | 0.419374i | \(-0.862250\pi\) |
−0.0907186 | + | 0.995877i | \(0.528916\pi\) | |||||||
\(488\) | −57.1067 | + | 98.9117i | −0.117022 | + | 0.202688i | ||||
\(489\) | − | 27.8148i | − | 0.0568810i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −406.441 | −0.827781 | −0.413891 | − | 0.910327i | \(-0.635830\pi\) | ||||
−0.413891 | + | 0.910327i | \(0.635830\pi\) | |||||||
\(492\) | 105.706 | + | 61.0294i | 0.214850 | + | 0.124044i | ||||
\(493\) | 318.289 | + | 551.294i | 0.645618 | + | 1.11824i | ||||
\(494\) | 215.033 | + | 372.448i | 0.435289 | + | 0.753944i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 58.9917i | 0.118935i | ||||||||
\(497\) | −34.9856 | − | 125.434i | −0.0703935 | − | 0.252381i | ||||
\(498\) | 185.574i | 0.372638i | ||||||||
\(499\) | −185.713 | + | 321.665i | −0.372171 | + | 0.644619i | −0.989899 | − | 0.141773i | \(-0.954720\pi\) |
0.617728 | + | 0.786391i | \(0.288053\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −152.522 | − | 264.176i | −0.304435 | − | 0.527297i | ||||
\(502\) | −152.667 | + | 264.426i | −0.304117 | + | 0.526746i | ||||
\(503\) | 64.6292 | 0.128488 | 0.0642438 | − | 0.997934i | \(-0.479536\pi\) | ||||
0.0642438 | + | 0.997934i | \(0.479536\pi\) | |||||||
\(504\) | 14.7868 | − | 57.5270i | 0.0293389 | − | 0.114141i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −57.0883 | + | 98.8799i | −0.112823 | + | 0.195415i | ||||
\(507\) | −130.006 | − | 225.177i | −0.256422 | − | 0.444135i | ||||
\(508\) | −289.991 | + | 167.426i | −0.570849 | + | 0.329580i | ||||
\(509\) | −871.889 | − | 503.385i | −1.71294 | − | 0.988969i | −0.930534 | − | 0.366205i | \(-0.880657\pi\) |
−0.782410 | − | 0.622764i | \(-0.786010\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 573.338 | − | 585.161i | 1.12199 | − | 1.14513i | ||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | 76.6050 | + | 44.2279i | 0.149328 | + | 0.0862143i | ||||
\(514\) | −5.27208 | + | 3.04384i | −0.0102570 | + | 0.00592186i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −46.4558 | − | 26.8213i | −0.0900307 | − | 0.0519793i | ||||
\(517\) | −199.237 | −0.385371 | ||||||||
\(518\) | 41.3653 | − | 42.2183i | 0.0798557 | − | 0.0815024i | ||||
\(519\) | 400.368 | 0.771421 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −322.294 | + | 186.077i | −0.618607 | + | 0.357153i | −0.776327 | − | 0.630331i | \(-0.782919\pi\) |
0.157719 | + | 0.987484i | \(0.449586\pi\) | |||||||
\(522\) | −124.708 | + | 72.0000i | −0.238904 | + | 0.137931i | ||||
\(523\) | −318.642 | + | 551.904i | −0.609258 | + | 1.05527i | 0.382105 | + | 0.924119i | \(0.375199\pi\) |
−0.991363 | + | 0.131147i | \(0.958134\pi\) | |||||||
\(524\) | − | 3.56608i | − | 0.00680549i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 399.765 | 0.760009 | ||||||||
\(527\) | −239.545 | − | 138.302i | −0.454545 | − | 0.262432i | ||||
\(528\) | −20.7846 | − | 36.0000i | −0.0393648 | − | 0.0681818i | ||||
\(529\) | −173.970 | − | 301.325i | −0.328866 | − | 0.569613i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 82.0940i | − | 0.154603i | ||||||
\(532\) | 229.564 | − | 64.0294i | 0.431512 | − | 0.120356i | ||||
\(533\) | − | 629.440i | − | 1.18094i | ||||||
\(534\) | −25.4558 | + | 44.0908i | −0.0476701 | + | 0.0825671i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 161.782 | + | 280.214i | 0.301832 | + | 0.522788i | ||||
\(537\) | −73.8540 | + | 127.919i | −0.137531 | + | 0.238210i | ||||
\(538\) | −540.136 | −1.00397 | ||||||||
\(539\) | 257.558 | + | 141.773i | 0.477845 | + | 0.263030i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −110.412 | + | 191.239i | −0.204088 | + | 0.353491i | −0.949842 | − | 0.312731i | \(-0.898756\pi\) |
0.745754 | + | 0.666222i | \(0.232090\pi\) | |||||||
\(542\) | 59.6283 | + | 103.279i | 0.110015 | + | 0.190552i | ||||
\(543\) | −8.37983 | + | 4.83810i | −0.0154325 | + | 0.00890994i | ||||
\(544\) | −91.8823 | − | 53.0482i | −0.168901 | − | 0.0975152i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −295.040 | + | 82.2917i | −0.540367 | + | 0.150717i | ||||
\(547\) | − | 160.676i | − | 0.293741i | −0.989156 | − | 0.146870i | \(-0.953080\pi\) | ||
0.989156 | − | 0.146870i | \(-0.0469200\pi\) | |||||||
\(548\) | 174.886 | + | 100.971i | 0.319135 | + | 0.184253i | ||||
\(549\) | 104.912 | − | 60.5708i | 0.191096 | − | 0.110329i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −500.382 | − | 288.896i | −0.908134 | − | 0.524311i | ||||
\(552\) | −65.9199 | −0.119420 | ||||||||
\(553\) | 598.898 | + | 153.942i | 1.08300 | + | 0.278375i | ||||
\(554\) | 193.914 | 0.350025 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −243.426 | + | 140.542i | −0.437817 | + | 0.252774i | ||||
\(557\) | −410.802 | + | 237.177i | −0.737526 | + | 0.425811i | −0.821169 | − | 0.570685i | \(-0.806678\pi\) |
0.0836431 | + | 0.996496i | \(0.473344\pi\) | |||||||
\(558\) | 31.2851 | − | 54.1873i | 0.0560664 | − | 0.0971099i | ||||
\(559\) | 276.627i | 0.494860i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 194.912 | 0.347436 | ||||||||
\(562\) | 398.168 | + | 229.882i | 0.708484 | + | 0.409043i | ||||
\(563\) | 248.434 | + | 430.301i | 0.441269 | + | 0.764300i | 0.997784 | − | 0.0665378i | \(-0.0211953\pi\) |
−0.556515 | + | 0.830837i | \(0.687862\pi\) | |||||||
\(564\) | −57.5147 | − | 99.6184i | −0.101976 | − | 0.176628i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 275.171i | 0.486168i | ||||||||
\(567\) | −44.0908 | + | 45.0000i | −0.0777616 | + | 0.0793651i | ||||
\(568\) | − | 52.6173i | − | 0.0926361i | ||||||
\(569\) | 392.647 | − | 680.084i | 0.690065 | − | 1.19523i | −0.281752 | − | 0.959487i | \(-0.590915\pi\) |
0.971816 | − | 0.235740i | \(-0.0757512\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 357.521 | + | 619.245i | 0.626132 | + | 1.08449i | 0.988321 | + | 0.152388i | \(0.0486963\pi\) |
−0.362189 | + | 0.932105i | \(0.617970\pi\) | |||||||
\(572\) | −107.183 | + | 185.647i | −0.187383 | + | 0.324557i | ||||
\(573\) | 321.117 | 0.560414 | ||||||||
\(574\) | −337.831 | − | 86.8364i | −0.588555 | − | 0.151283i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 12.0000 | − | 20.7846i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | 386.315 | + | 669.117i | 0.669524 | + | 1.15965i | 0.978038 | + | 0.208429i | \(0.0668350\pi\) |
−0.308514 | + | 0.951220i | \(0.599832\pi\) | |||||||
\(578\) | 76.8705 | − | 44.3812i | 0.132994 | − | 0.0767841i | ||||
\(579\) | 341.691 | + | 197.275i | 0.590140 | + | 0.340717i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −142.477 | − | 510.823i | −0.245228 | − | 0.879214i | ||||
\(582\) | − | 74.9117i | − | 0.128714i | ||||||
\(583\) | −179.497 | − | 103.632i | −0.307885 | − | 0.177757i | ||||
\(584\) | 286.669 | − | 165.508i | 0.490872 | − | 0.283405i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 293.574 | + | 169.495i | 0.500979 | + | 0.289240i | ||||
\(587\) | 436.477 | 0.743572 | 0.371786 | − | 0.928318i | \(-0.378746\pi\) | ||||
0.371786 | + | 0.928318i | \(0.378746\pi\) | |||||||
\(588\) | 3.46410 | + | 169.706i | 0.00589133 | + | 0.288615i | ||||
\(589\) | 251.059 | 0.426246 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 184.742 | − | 106.661i | 0.312593 | − | 0.180475i | ||||
\(592\) | 20.6826 | − | 11.9411i | 0.0349369 | − | 0.0201708i | ||||
\(593\) | 417.076 | − | 722.397i | 0.703332 | − | 1.21821i | −0.263958 | − | 0.964534i | \(-0.585028\pi\) |
0.967290 | − | 0.253673i | \(-0.0816387\pi\) | |||||||
\(594\) | 44.0908i | 0.0742270i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 365.823 | 0.613798 | ||||||||
\(597\) | 9.34783 | + | 5.39697i | 0.0156580 | + | 0.00904015i | ||||
\(598\) | 169.970 | + | 294.396i | 0.284230 | + | 0.492301i | ||||
\(599\) | 436.794 | + | 756.549i | 0.729205 | + | 1.26302i | 0.957220 | + | 0.289363i | \(0.0934434\pi\) |
−0.228014 | + | 0.973658i | \(0.573223\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 198.982i | 0.331085i | 0.986203 | + | 0.165542i | \(0.0529375\pi\) | ||||
−0.986203 | + | 0.165542i | \(0.947063\pi\) | |||||||
\(602\) | 148.470 | + | 38.1630i | 0.246628 | + | 0.0633936i | ||||
\(603\) | − | 343.191i | − | 0.569139i | ||||||
\(604\) | −288.794 | + | 500.206i | −0.478136 | + | 0.828155i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 156.728 | + | 271.461i | 0.258627 | + | 0.447955i | ||||
\(607\) | −79.4748 | + | 137.654i | −0.130930 | + | 0.226778i | −0.924035 | − | 0.382307i | \(-0.875130\pi\) |
0.793105 | + | 0.609085i | \(0.208463\pi\) | |||||||
\(608\) | 96.2985 | 0.158386 | ||||||||
\(609\) | 288.000 | − | 293.939i | 0.472906 | − | 0.482658i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −296.595 | + | 513.718i | −0.485426 | + | 0.840782i | ||||
\(612\) | 56.2662 | + | 97.4558i | 0.0919382 | + | 0.159242i | ||||
\(613\) | 618.979 | − | 357.368i | 1.00975 | − | 0.582981i | 0.0986338 | − | 0.995124i | \(-0.468553\pi\) |
0.911119 | + | 0.412143i | \(0.135219\pi\) | |||||||
\(614\) | 661.695 | + | 382.030i | 1.07768 | + | 0.622198i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 84.8528 | + | 83.1384i | 0.137748 | + | 0.134965i | ||||
\(617\) | − | 639.381i | − | 1.03627i | −0.855298 | − | 0.518137i | \(-0.826626\pi\) | ||
0.855298 | − | 0.518137i | \(-0.173374\pi\) | |||||||
\(618\) | −171.734 | − | 99.1508i | −0.277887 | − | 0.160438i | ||||
\(619\) | −148.978 | + | 86.0126i | −0.240676 | + | 0.138954i | −0.615487 | − | 0.788147i | \(-0.711041\pi\) |
0.374812 | + | 0.927101i | \(0.377707\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 60.5513 | + | 34.9593i | 0.0975061 | + | 0.0562952i | ||||
\(622\) | −571.619 | −0.919002 | ||||||||
\(623\) | 36.2201 | − | 140.912i | 0.0581382 | − | 0.226182i | ||||
\(624\) | −123.765 | −0.198341 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 160.805 | − | 92.8406i | 0.256876 | − | 0.148308i | ||||
\(627\) | −153.210 | + | 88.4558i | −0.244354 | + | 0.141078i | ||||
\(628\) | −187.061 | + | 324.000i | −0.297869 | + | 0.515924i | ||||
\(629\) | 111.980i | 0.178029i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1141.06 | −1.80833 | −0.904166 | − | 0.427180i | \(-0.859507\pi\) | ||||
−0.904166 | + | 0.427180i | \(0.859507\pi\) | |||||||
\(632\) | 216.383 | + | 124.929i | 0.342379 | + | 0.197672i | ||||
\(633\) | 108.177 | + | 187.368i | 0.170895 | + | 0.295999i | ||||
\(634\) | −66.4264 | − | 115.054i | −0.104774 | − | 0.181473i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 119.664i | − | 0.188152i | ||||||
\(637\) | 748.968 | − | 453.044i | 1.17577 | − | 0.711215i | ||||
\(638\) | − | 288.000i | − | 0.451411i | ||||||
\(639\) | −27.9045 | + | 48.3321i | −0.0436691 | + | 0.0756371i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −114.551 | − | 198.409i | −0.178707 | − | 0.309530i | 0.762731 | − | 0.646716i | \(-0.223858\pi\) |
−0.941438 | + | 0.337186i | \(0.890525\pi\) | |||||||
\(642\) | 207.540 | − | 359.470i | 0.323271 | − | 0.559922i | ||||
\(643\) | 707.670 | 1.10058 | 0.550288 | − | 0.834975i | \(-0.314518\pi\) | ||||
0.550288 | + | 0.834975i | \(0.314518\pi\) | |||||||
\(644\) | 181.456 | − | 50.6111i | 0.281764 | − | 0.0785887i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −225.765 | + | 391.036i | −0.349481 | + | 0.605318i | ||||
\(647\) | 589.687 | + | 1021.37i | 0.911417 | + | 1.57862i | 0.812064 | + | 0.583568i | \(0.198344\pi\) |
0.0993530 | + | 0.995052i | \(0.468323\pi\) | |||||||
\(648\) | −22.0454 | + | 12.7279i | −0.0340207 | + | 0.0196419i | ||||
\(649\) | 142.191 | + | 82.0940i | 0.219092 | + | 0.126493i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −44.5143 | + | 173.180i | −0.0683783 | + | 0.266021i | ||||
\(652\) | 32.1177i | 0.0492604i | ||||||||
\(653\) | −134.029 | − | 77.3818i | −0.205252 | − | 0.118502i | 0.393851 | − | 0.919174i | \(-0.371143\pi\) |
−0.599103 | + | 0.800672i | \(0.704476\pi\) | |||||||
\(654\) | −379.591 | + | 219.157i | −0.580415 | + | 0.335103i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −122.059 | − | 70.4707i | −0.186065 | − | 0.107425i | ||||
\(657\) | −351.096 | −0.534393 | ||||||||
\(658\) | 234.803 | + | 230.059i | 0.356843 | + | 0.349634i | ||||
\(659\) | −591.308 | −0.897280 | −0.448640 | − | 0.893712i | \(-0.648092\pi\) | ||||
−0.448640 | + | 0.893712i | \(0.648092\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 140.441 | − | 81.0837i | 0.212468 | − | 0.122668i | −0.389990 | − | 0.920819i | \(-0.627522\pi\) |
0.602458 | + | 0.798151i | \(0.294188\pi\) | |||||||
\(662\) | −320.109 | + | 184.815i | −0.483548 | + | 0.279176i | ||||
\(663\) | 290.156 | − | 502.566i | 0.437642 | − | 0.758017i | ||||
\(664\) | − | 214.282i | − | 0.322714i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −25.3310 | −0.0380345 | ||||||||
\(667\) | −395.519 | − | 228.353i | −0.592983 | − | 0.342359i | ||||
\(668\) | 176.117 | + | 305.044i | 0.263648 | + | 0.456652i | ||||
\(669\) | 198.000 | + | 342.946i | 0.295964 | + | 0.512625i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 242.283i | 0.361078i | ||||||||
\(672\) | −17.0743 | + | 66.4264i | −0.0254082 | + | 0.0988488i | ||||
\(673\) | − | 42.3238i | − | 0.0628883i | −0.999506 | − | 0.0314441i | \(-0.989989\pi\) | ||
0.999506 | − | 0.0314441i | \(-0.0100106\pi\) | |||||||
\(674\) | 96.3539 | − | 166.890i | 0.142958 | − | 0.247611i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 150.118 | + | 260.012i | 0.222068 | + | 0.384632i | ||||
\(677\) | −248.677 | + | 430.721i | −0.367322 | + | 0.636220i | −0.989146 | − | 0.146937i | \(-0.953059\pi\) |
0.621824 | + | 0.783157i | \(0.286392\pi\) | |||||||
\(678\) | −42.6137 | −0.0628521 | ||||||||
\(679\) | 57.5147 | + | 206.207i | 0.0847050 | + | 0.303693i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −146.823 | + | 254.306i | −0.215600 | + | 0.373430i | ||||
\(682\) | 62.5701 | + | 108.375i | 0.0917451 | + | 0.158907i | ||||
\(683\) | −1053.23 | + | 608.080i | −1.54206 | + | 0.890308i | −0.543350 | + | 0.839506i | \(0.682844\pi\) |
−0.998709 | + | 0.0508015i | \(0.983822\pi\) | |||||||
\(684\) | −88.4558 | − | 51.0700i | −0.129321 | − | 0.0746638i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −139.830 | − | 464.484i | −0.203834 | − | 0.677091i | ||||
\(687\) | 60.0883i | 0.0874648i | ||||||||
\(688\) | 53.6426 | + | 30.9706i | 0.0779689 | + | 0.0450154i | ||||
\(689\) | −534.418 | + | 308.546i | −0.775642 | + | 0.447817i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −932.182 | − | 538.196i | −1.34903 | − | 0.778865i | −0.360921 | − | 0.932596i | \(-0.617538\pi\) |
−0.988113 | + | 0.153731i | \(0.950871\pi\) | |||||||
\(692\) | −462.305 | −0.668070 | ||||||||
\(693\) | −33.8515 | − | 121.368i | −0.0488477 | − | 0.175134i | ||||
\(694\) | 455.647 | 0.656552 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 144.000 | − | 83.1384i | 0.206897 | − | 0.119452i | ||||
\(697\) | 572.315 | − | 330.426i | 0.821112 | − | 0.474069i | ||||
\(698\) | −245.009 | + | 424.368i | −0.351015 | + | 0.607976i | ||||
\(699\) | 440.781i | 0.630589i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −695.897 | −0.992720 | −0.496360 | − | 0.868117i | \(-0.665330\pi\) | ||||
−0.496360 | + | 0.868117i | \(0.665330\pi\) | |||||||
\(702\) | 113.685 | + | 65.6360i | 0.161944 | + | 0.0934986i | ||||
\(703\) | −50.8194 | − | 88.0219i | −0.0722894 | − | 0.125209i | ||||
\(704\) | 24.0000 | + | 41.5692i | 0.0340909 | + | 0.0590472i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 877.649i | − | 1.24313i | ||||||
\(707\) | −639.839 | − | 626.912i | −0.905006 | − | 0.886721i | ||||
\(708\) | 94.7939i | 0.133890i | ||||||||
\(709\) | 127.412 | − | 220.684i | 0.179707 | − | 0.311261i | −0.762073 | − | 0.647491i | \(-0.775818\pi\) |
0.941780 | + | 0.336229i | \(0.109152\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −132.507 | − | 229.509i | −0.186367 | − | 0.322798i | ||||
\(712\) | 29.3939 | − | 50.9117i | 0.0412835 | − | 0.0715052i | ||||
\(713\) | 198.446 | 0.278325 | ||||||||
\(714\) | −229.706 | − | 225.065i | −0.321717 | − | 0.315217i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 85.2792 | − | 147.708i | 0.119105 | − | 0.206296i | ||||
\(717\) | 170.734 | + | 295.721i | 0.238123 | + | 0.412442i | ||||
\(718\) | −24.7833 | + | 14.3087i | −0.0345172 | + | 0.0199285i | ||||
\(719\) | 964.925 | + | 557.100i | 1.34204 | + | 0.774826i | 0.987106 | − | 0.160066i | \(-0.0511709\pi\) |
0.354931 | + | 0.934892i | \(0.384504\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 548.852 | + | 141.078i | 0.761238 | + | 0.195669i | ||||
\(722\) | 100.701i | 0.139474i | ||||||||
\(723\) | −132.705 | − | 76.6173i | −0.183548 | − | 0.105971i | ||||
\(724\) | 9.67619 | − | 5.58655i | 0.0133649 | − | 0.00771623i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 180.312 | + | 104.103i | 0.248364 | + | 0.143393i | ||||
\(727\) | 398.345 | 0.547930 | 0.273965 | − | 0.961740i | \(-0.411665\pi\) | ||||
0.273965 | + | 0.961740i | \(0.411665\pi\) | |||||||
\(728\) | 340.683 | − | 95.0223i | 0.467971 | − | 0.130525i | ||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −251.522 | + | 145.216i | −0.344079 | + | 0.198654i | ||||
\(732\) | −121.142 | + | 69.9411i | −0.165494 | + | 0.0955480i | ||||
\(733\) | 472.569 | − | 818.514i | 0.644706 | − | 1.11666i | −0.339663 | − | 0.940547i | \(-0.610313\pi\) |
0.984369 | − | 0.176116i | \(-0.0563535\pi\) | |||||||
\(734\) | 440.632i | 0.600316i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 76.1177 | 0.103421 | ||||||||
\(737\) | 594.424 | + | 343.191i | 0.806546 | + | 0.465659i | ||||
\(738\) | 74.7455 | + | 129.463i | 0.101281 | + | 0.175424i | ||||
\(739\) | 96.3162 | + | 166.825i | 0.130333 | + | 0.225744i | 0.923805 | − | 0.382863i | \(-0.125062\pi\) |
−0.793472 | + | 0.608607i | \(0.791729\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 526.721i | 0.710825i | ||||||||
\(742\) | 91.8744 | + | 329.397i | 0.123820 | + | 0.443931i | ||||
\(743\) | 911.616i | 1.22694i | 0.789718 | + | 0.613470i | \(0.210227\pi\) | ||||
−0.789718 | + | 0.613470i | \(0.789773\pi\) | |||||||
\(744\) | −36.1249 | + | 62.5701i | −0.0485550 | + | 0.0840997i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 481.810 | + | 834.519i | 0.645858 | + | 1.11866i | ||||
\(747\) | −113.640 | + | 196.831i | −0.152129 | + | 0.263495i | ||||
\(748\) | −225.065 | −0.300889 | ||||||||
\(749\) | −295.301 | + | 1148.85i | −0.394260 | + | 1.53384i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 195.831 | − | 339.189i | 0.260760 | − | 0.451650i | −0.705684 | − | 0.708527i | \(-0.749360\pi\) |
0.966444 | + | 0.256877i | \(0.0826935\pi\) | |||||||
\(752\) | 66.4123 | + | 115.029i | 0.0883142 | + | 0.152965i | ||||
\(753\) | −323.855 | + | 186.978i | −0.430086 | + | 0.248310i | ||||
\(754\) | −742.587 | − | 428.733i | −0.984863 | − | 0.568611i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 50.9117 | − | 51.9615i | 0.0673435 | − | 0.0687322i | ||||
\(757\) | − | 152.823i | − | 0.201879i | −0.994893 | − | 0.100940i | \(-0.967815\pi\) | ||
0.994893 | − | 0.100940i | \(-0.0321849\pi\) | |||||||
\(758\) | −765.195 | − | 441.785i | −1.00949 | − | 0.582830i | ||||
\(759\) | −121.103 | + | 69.9186i | −0.159555 | + | 0.0921194i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −109.331 | − | 63.1223i | −0.143667 | − | 0.0829465i | 0.426443 | − | 0.904514i | \(-0.359766\pi\) |
−0.570111 | + | 0.821568i | \(0.693100\pi\) | |||||||
\(762\) | −410.109 | −0.538201 | ||||||||
\(763\) | 876.629 | − | 894.706i | 1.14892 | − | 1.17262i | ||||
\(764\) | −370.794 | −0.485332 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −169.383 | + | 97.7931i | −0.221126 | + | 0.127667i | ||||
\(767\) | 423.347 | − | 244.419i | 0.551951 | − | 0.318669i | ||||
\(768\) | −13.8564 | + | 24.0000i | −0.0180422 | + | 0.0312500i | ||||
\(769\) | 369.148i | 0.480037i | 0.970768 | + | 0.240018i | \(0.0771535\pi\) | ||||
−0.970768 | + | 0.240018i | \(0.922847\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.45584 | −0.00967036 | ||||||||
\(772\) | −394.551 | − | 227.794i | −0.511076 | − | 0.295070i | ||||
\(773\) | 701.853 | + | 1215.65i | 0.907961 | + | 1.57263i | 0.816893 | + | 0.576789i | \(0.195695\pi\) |
0.0910674 | + | 0.995845i | \(0.470972\pi\) | |||||||
\(774\) | −32.8492 | − | 56.8966i | −0.0424409 | − | 0.0735098i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 86.5006i | 0.111470i | ||||||||
\(777\) | 69.7278 | − | 19.4483i | 0.0897398 | − | 0.0250299i | ||||
\(778\) | 797.013i | 1.02444i | ||||||||
\(779\) | −299.912 | + | 519.462i | −0.384996 | + | 0.666832i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −55.8091 | − | 96.6642i | −0.0714585 | − | 0.123770i | ||||
\(782\) | −178.452 | + | 309.088i | −0.228200 | + | 0.395254i | ||||
\(783\) | −176.363 | −0.225240 | ||||||||
\(784\) | −4.00000 | − | 195.959i | −0.00510204 | − | 0.249948i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.18377 | − | 3.78239i | 0.00277833 | − | 0.00481221i | ||||
\(787\) | 113.253 | + | 196.161i | 0.143905 | + | 0.249251i | 0.928964 | − | 0.370170i | \(-0.120701\pi\) |
−0.785059 | + | 0.619421i | \(0.787367\pi\) | |||||||
\(788\) | −213.322 | + | 123.161i | −0.270713 | + | 0.156296i | ||||
\(789\) | 424.014 | + | 244.805i | 0.537407 | + | 0.310272i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 117.302 | − | 32.7174i | 0.148295 | − | 0.0413621i | ||||
\(792\) | − | 50.9117i | − | 0.0642824i | ||||||
\(793\) | 624.709 | + | 360.676i | 0.787780 | + | 0.454825i | ||||
\(794\) | −555.224 | + | 320.559i | −0.699274 | + | 0.403726i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.7939 | − | 6.23188i | −0.0135602 | − | 0.00782900i | ||||
\(797\) | 688.414 | 0.863756 | 0.431878 | − | 0.901932i | \(-0.357851\pi\) | ||||
0.431878 | + | 0.901932i | \(0.357851\pi\) | |||||||
\(798\) | 282.700 | + | 72.6655i | 0.354260 | + | 0.0910595i | ||||
\(799\) | −622.794 | −0.779467 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −54.0000 | + | 31.1769i | −0.0674157 | + | 0.0389225i | ||||
\(802\) | −337.724 | + | 194.985i | −0.421102 | + | 0.243123i | ||||
\(803\) | 351.096 | − | 608.117i | 0.437231 | − | 0.757306i | ||||
\(804\) | 396.283i | 0.492889i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 372.582 | 0.462260 | ||||||||
\(807\) | −572.901 | − | 330.765i | −0.709914 | − | 0.409869i | ||||
\(808\) | −180.974 | − | 313.456i | −0.223977 | − | 0.387940i | ||||
\(809\) | 12.6396 | + | 21.8924i | 0.0156237 | + | 0.0270611i | 0.873732 | − | 0.486408i | \(-0.161693\pi\) |
−0.858108 | + | 0.513470i | \(0.828360\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1527.62i | 1.88362i | 0.336145 | + | 0.941810i | \(0.390877\pi\) | ||||
−0.336145 | + | 0.941810i | \(0.609123\pi\) | |||||||
\(812\) | −332.554 | + | 339.411i | −0.409549 | + | 0.417994i | ||||
\(813\) | 146.059i | 0.179654i | ||||||||
\(814\) | 25.3310 | − | 43.8745i | 0.0311191 | − | 0.0538999i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −64.9706 | − | 112.532i | −0.0796208 | − | 0.137907i | ||||
\(817\) | 131.806 | − | 228.294i | 0.161329 | − | 0.279430i | ||||
\(818\) | −616.359 | −0.753495 | ||||||||
\(819\) | −363.331 | − | 93.3909i | −0.443627 | − | 0.114030i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 58.3310 | − | 101.032i | 0.0710487 | − | 0.123060i | −0.828312 | − | 0.560266i | \(-0.810699\pi\) |
0.899361 | + | 0.437206i | \(0.144032\pi\) | |||||||
\(822\) | 123.663 | + | 214.191i | 0.150442 | + | 0.260573i | ||||
\(823\) | −109.042 | + | 62.9554i | −0.132493 | + | 0.0764950i | −0.564782 | − | 0.825240i | \(-0.691040\pi\) |
0.432288 | + | 0.901735i | \(0.357706\pi\) | |||||||
\(824\) | 198.302 | + | 114.489i | 0.240657 | + | 0.138943i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −72.7797 | − | 260.937i | −0.0881110 | − | 0.315904i | ||||
\(827\) | − | 1434.40i | − | 1.73446i | −0.497910 | − | 0.867229i | \(-0.665899\pi\) | ||
0.497910 | − | 0.867229i | \(-0.334101\pi\) | |||||||
\(828\) | −69.9186 | − | 40.3675i | −0.0844428 | − | 0.0487531i | ||||
\(829\) | 32.3225 | − | 18.6614i | 0.0389898 | − | 0.0225107i | −0.480378 | − | 0.877061i | \(-0.659501\pi\) |
0.519368 | + | 0.854551i | \(0.326167\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 205.677 | + | 118.747i | 0.247505 | + | 0.142897i | ||||
\(832\) | 142.911 | 0.171768 | ||||||||
\(833\) | 805.101 | + | 443.169i | 0.966508 | + | 0.532015i | ||||
\(834\) | −344.257 | −0.412778 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 176.912 | − | 102.140i | 0.211617 | − | 0.122177i | ||||
\(837\) | 66.3657 | − | 38.3162i | 0.0792899 | − | 0.0457781i | ||||
\(838\) | 213.021 | − | 368.963i | 0.254202 | − | 0.440290i | ||||
\(839\) | − | 3.07370i | − | 0.00366353i | −0.999998 | − | 0.00183177i | \(-0.999417\pi\) | ||
0.999998 | − | 0.00183177i | \(-0.000583069\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 311.000 | 0.369798 | ||||||||
\(842\) | 249.596 | + | 144.104i | 0.296432 | + | 0.171145i | ||||
\(843\) | 281.547 | + | 487.654i | 0.333982 | + | 0.578474i | ||||
\(844\) | −124.912 | − | 216.353i | −0.148000 | − | 0.256343i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 140.882i | − | 0.166527i | ||||||
\(847\) | −576.267 | − | 148.124i | −0.680363 | − | 0.174881i | ||||
\(848\) | 138.177i | 0.162944i | ||||||||
\(849\) | −168.507 | + | 291.863i | −0.198477 | + | 0.343773i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −40.1695 | − | 69.5756i | −0.0472027 | − | 0.0817574i | ||||
\(852\) | 32.2214 | − | 55.8091i | 0.0378185 | − | 0.0655036i | ||||
\(853\) | −155.257 | −0.182013 | −0.0910063 | − | 0.995850i | \(-0.529008\pi\) | ||||
−0.0910063 | + | 0.995850i | \(0.529008\pi\) | |||||||
\(854\) | 279.765 | − | 285.533i | 0.327593 | − | 0.334348i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −239.647 | + | 415.080i | −0.279961 | + | 0.484907i | ||||
\(857\) | −801.931 | − | 1388.98i | −0.935742 | − | 1.62075i | −0.773306 | − | 0.634033i | \(-0.781398\pi\) |
−0.162436 | − | 0.986719i | \(-0.551935\pi\) | |||||||
\(858\) | −227.370 | + | 131.272i | −0.265000 | + | 0.152998i | ||||
\(859\) | −545.367 | − | 314.868i | −0.634886 | − | 0.366551i | 0.147756 | − | 0.989024i | \(-0.452795\pi\) |
−0.782642 | + | 0.622472i | \(0.786128\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −305.147 | − | 298.982i | −0.354410 | − | 0.347250i | ||||
\(862\) | − | 559.632i | − | 0.649226i | ||||||
\(863\) | 891.496 | + | 514.706i | 1.03302 | + | 0.596414i | 0.917848 | − | 0.396931i | \(-0.129925\pi\) |
0.115172 | + | 0.993346i | \(0.463258\pi\) | |||||||
\(864\) | 25.4558 | − | 14.6969i | 0.0294628 | − | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 54.2176 | + | 31.3026i | 0.0626070 | + | 0.0361462i | ||||
\(867\) | 108.711 | 0.125388 | ||||||||
\(868\) | 51.4007 | − | 199.971i | 0.0592174 | − | 0.230381i | ||||
\(869\) | 530.029 | 0.609929 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1769.79 | − | 1021.79i | 2.03190 | − | 1.17312i | ||||
\(872\) | 438.314 | − | 253.061i | 0.502654 | − | 0.290208i | ||||
\(873\) | 45.8739 | − | 79.4558i | 0.0525474 | − | 0.0910147i | ||||
\(874\) | − | 323.944i | − | 0.370646i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 405.411 | 0.462798 | ||||||||
\(877\) | −561.566 | − | 324.220i | −0.640326 | − | 0.369693i | 0.144414 | − | 0.989517i | \(-0.453870\pi\) |
−0.784740 | + | 0.619825i | \(0.787204\pi\) | |||||||
\(878\) | 281.331 | + | 487.279i | 0.320422 | + | 0.554988i | ||||
\(879\) | 207.588 | + | 359.553i | 0.236164 | + | 0.409048i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 363.857i | − | 0.413005i | −0.978446 | − | 0.206502i | \(-0.933792\pi\) | ||
0.978446 | − | 0.206502i | \(-0.0662082\pi\) | |||||||
\(882\) | −100.249 | + | 182.121i | −0.113661 | + | 0.206487i | ||||
\(883\) | − | 1536.16i | − | 1.73971i | −0.493312 | − | 0.869853i | \(-0.664214\pi\) | ||
0.493312 | − | 0.869853i | \(-0.335786\pi\) | |||||||
\(884\) | −335.044 | + | 580.313i | −0.379009 | + | 0.656462i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 83.8234 | + | 145.186i | 0.0946088 | + | 0.163867i | ||||
\(887\) | −562.755 | + | 974.720i | −0.634447 | + | 1.09890i | 0.352185 | + | 0.935931i | \(0.385439\pi\) |
−0.986632 | + | 0.162964i | \(0.947894\pi\) | |||||||
\(888\) | 29.2497 | 0.0329388 | ||||||||
\(889\) | 1128.90 | − | 314.868i | 1.26985 | − | 0.354183i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −27.0000 | + | 46.7654i | −0.0303030 | + | 0.0524864i | ||||
\(892\) | −228.631 | − | 396.000i | −0.256312 | − | 0.443946i | ||||
\(893\) | 489.546 | − | 282.640i | 0.548204 | − | 0.316506i | ||||
\(894\) | 388.014 | + | 224.020i | 0.434020 | + | 0.250582i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 19.7157 | − | 76.7026i | 0.0220042 | − | 0.0856056i | ||||
\(897\) | 416.339i | 0.464146i | ||||||||
\(898\) | 874.341 | + | 504.801i | 0.973654 | + | 0.562139i | ||||
\(899\) | −433.499 | + | 250.281i | −0.482201 | + | 0.278399i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −561.088 | − | 323.944i | −0.622740 | − | 0.359539i | ||||
\(902\) | −298.982 | −0.331466 | ||||||||
\(903\) | 134.106 | + | 131.397i | 0.148512 | + | 0.145512i | ||||
\(904\) | 49.2061 | 0.0544315 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −612.624 | + | 353.699i | −0.676186 | + | 0.390396i | ||||
\(907\) | 203.426 | − | 117.448i | 0.224285 | − | 0.129491i | −0.383648 | − | 0.923479i | \(-0.625332\pi\) |
0.607933 | + | 0.793989i | \(0.291999\pi\) | |||||||
\(908\) | 169.537 | − | 293.647i | 0.186715 | − | 0.323400i | ||||
\(909\) | 383.903i | 0.422336i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 224.278 | 0.246189 | 0.123095 | − | 0.992395i | \(-0.460718\pi\) | ||||
0.123095 | + | 0.992395i | \(0.460718\pi\) | |||||||
\(912\) | 102.140 | + | 58.9706i | 0.111996 | + | 0.0646607i | ||||
\(913\) | −227.280 | − | 393.661i | −0.248938 | − | 0.431173i | ||||
\(914\) | −88.5132 | − | 153.309i | −0.0968416 | − | 0.167735i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 69.3840i | − | 0.0757467i | ||||||
\(917\) | −3.10719 | + | 12.0883i | −0.00338843 | + | 0.0131825i | ||||
\(918\) | 137.823i | 0.150134i | ||||||||
\(919\) | −466.081 | + | 807.276i | −0.507161 | + | 0.878428i | 0.492805 | + | 0.870140i | \(0.335972\pi\) |
−0.999966 | + | 0.00828836i | \(0.997362\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 467.889 | + | 810.407i | 0.508023 | + | 0.879921i | ||||
\(922\) | 463.697 | − | 803.147i | 0.502925 | − | 0.871092i | ||||
\(923\) | −332.322 | −0.360046 | ||||||||
\(924\) | 39.0883 | + | 140.143i | 0.0423034 | + | 0.151670i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −614.756 | + | 1064.79i | −0.663883 | + | 1.14988i | ||||
\(927\) | −121.434 | − | 210.331i | −0.130997 | − | 0.226894i | ||||
\(928\) | −166.277 | + | 96.0000i | −0.179178 | + | 0.103448i | ||||
\(929\) | 618.390 | + | 357.028i | 0.665651 | + | 0.384314i | 0.794427 | − | 0.607360i | \(-0.207771\pi\) |
−0.128776 | + | 0.991674i | \(0.541105\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −833.970 | + | 17.0233i | −0.895778 | + | 0.0182850i | ||||
\(932\) | − | 508.971i | − | 0.546106i | ||||||
\(933\) | −606.294 | − | 350.044i | −0.649832 | − | 0.375181i | ||||
\(934\) | −327.463 | + | 189.061i | −0.350603 | + | 0.202421i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −131.272 | − | 75.7900i | −0.140248 | − | 0.0809722i | ||||
\(937\) | 1723.25 | 1.83912 | 0.919559 | − | 0.392952i | \(-0.128546\pi\) | ||||
0.919559 | + | 0.392952i | \(0.128546\pi\) | |||||||
\(938\) | −304.253 | − | 1090.84i | −0.324363 | − | 1.16294i | ||||
\(939\) | 227.412 | 0.242185 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 835.508 | − | 482.381i | 0.887893 | − | 0.512625i | 0.0146405 | − | 0.999893i | \(-0.495340\pi\) |
0.873253 | + | 0.487267i | \(0.162006\pi\) | |||||||
\(942\) | −396.817 | + | 229.103i | −0.421250 | + | 0.243209i | ||||
\(943\) | −237.061 | + | 410.601i | −0.251390 | + | 0.435420i | ||||
\(944\) | − | 109.459i | − | 0.115952i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 131.397 | 0.138897 | ||||||||
\(947\) | −1257.26 | − | 725.881i | −1.32763 | − | 0.766506i | −0.342695 | − | 0.939447i | \(-0.611340\pi\) |
−0.984932 | + | 0.172940i | \(0.944673\pi\) | |||||||
\(948\) | 153.006 | + | 265.014i | 0.161399 | + | 0.279551i | ||||
\(949\) | −1045.32 | − | 1810.55i | −1.10150 | − | 1.90785i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 162.711i | − | 0.171094i | ||||||
\(952\) | 265.241 | + | 259.882i | 0.278615 | + | 0.272986i | ||||
\(953\) | − | 1147.43i | − | 1.20401i | −0.798491 | − | 0.602007i | \(-0.794368\pi\) | ||
0.798491 | − | 0.602007i | \(-0.205632\pi\) | |||||||
\(954\) | 73.2792 | − | 126.923i | 0.0768126 | − | 0.133043i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −197.147 | − | 341.469i | −0.206221 | − | 0.357185i | ||||
\(957\) | 176.363 | − | 305.470i | 0.184288 | − | 0.319196i | ||||
\(958\) | 384.294 | 0.401142 | ||||||||
\(959\) | −504.853 | − | 494.653i | −0.526437 | − | 0.515801i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −371.749 | + | 643.889i | −0.386836 | + | 0.670020i | ||||
\(962\) | −75.4181 | − | 130.628i | −0.0783972 | − | 0.135788i | ||||
\(963\) | 440.259 | − | 254.184i | 0.457175 | − | 0.263950i | ||||
\(964\) | 153.235 | + | 88.4701i | 0.158957 | + | 0.0917739i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 223.456 | + | 57.4374i | 0.231321 | + | 0.0594590i | ||||
\(967\) | 412.190i | 0.426257i | 0.977024 | + | 0.213128i | \(0.0683652\pi\) | ||||
−0.977024 | + | 0.213128i | \(0.931635\pi\) | |||||||
\(968\) | −208.207 | − | 120.208i | −0.215089 | − | 0.124182i | ||||
\(969\) | −478.919 | + | 276.504i | −0.494240 | + | 0.285350i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 869.595 | + | 502.061i | 0.895566 | + | 0.517056i | 0.875759 | − | 0.482748i | \(-0.160361\pi\) |
0.0198073 | + | 0.999804i | \(0.493695\pi\) | |||||||
\(972\) | −31.1769 | −0.0320750 | ||||||||
\(973\) | 947.626 | − | 264.309i | 0.973922 | − | 0.271643i | ||||
\(974\) | 794.101 | 0.815298 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 139.882 | − | 80.7611i | 0.143322 | − | 0.0827470i | ||||
\(977\) | −1375.45 | + | 794.117i | −1.40783 | + | 0.812812i | −0.995179 | − | 0.0980772i | \(-0.968731\pi\) |
−0.412652 | + | 0.910889i | \(0.635397\pi\) | |||||||
\(978\) | −19.6680 | + | 34.0660i | −0.0201105 | + | 0.0348323i | ||||
\(979\) | − | 124.708i | − | 0.127383i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −536.823 | −0.547221 | ||||||||
\(982\) | 497.786 | + | 287.397i | 0.506911 | + | 0.292665i | ||||
\(983\) | −416.767 | − | 721.861i | −0.423974 | − | 0.734345i | 0.572350 | − | 0.820009i | \(-0.306032\pi\) |
−0.996324 | + | 0.0856648i | \(0.972699\pi\) | |||||||
\(984\) | −86.3087 | − | 149.491i | −0.0877121 | − | 0.151922i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 900.259i | − | 0.913041i | ||||||
\(987\) | 108.164 | + | 387.801i | 0.109589 | + | 0.392909i | ||||
\(988\) | − | 608.205i | − | 0.615592i | ||||||
\(989\) | 104.184 | − | 180.452i | 0.105343 | − | 0.182459i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33.4483 | − | 57.9341i | −0.0337520 | − | 0.0584602i | 0.848656 | − | 0.528945i | \(-0.177412\pi\) |
−0.882408 | + | 0.470485i | \(0.844079\pi\) | |||||||
\(992\) | 41.7134 | − | 72.2498i | 0.0420498 | − | 0.0728324i | ||||
\(993\) | −452.702 | −0.455893 | ||||||||
\(994\) | −45.8465 | + | 178.363i | −0.0461233 | + | 0.179439i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 131.220 | − | 227.280i | 0.131747 | − | 0.228193i | ||||
\(997\) | 732.453 | + | 1268.65i | 0.734657 | + | 1.27246i | 0.954874 | + | 0.297012i | \(0.0959901\pi\) |
−0.220217 | + | 0.975451i | \(0.570677\pi\) | |||||||
\(998\) | 454.903 | − | 262.638i | 0.455814 | − | 0.263164i | ||||
\(999\) | −26.8675 | − | 15.5120i | −0.0268944 | − | 0.0155275i |
(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 | 1050.3.q.a.649.1 | 8 | ||
5.2 | odd | 4 | 1050.3.p.a.901.2 | 4 | |||
5.3 | odd | 4 | 42.3.g.a.19.1 | ✓ | 4 | ||
5.4 | even | 2 | inner | 1050.3.q.a.649.4 | 8 | ||
7.3 | odd | 6 | inner | 1050.3.q.a.199.4 | 8 | ||
15.8 | even | 4 | 126.3.n.a.19.2 | 4 | |||
20.3 | even | 4 | 336.3.bh.e.145.2 | 4 | |||
35.3 | even | 12 | 42.3.g.a.31.1 | yes | 4 | ||
35.13 | even | 4 | 294.3.g.a.19.1 | 4 | |||
35.17 | even | 12 | 1050.3.p.a.451.2 | 4 | |||
35.18 | odd | 12 | 294.3.g.a.31.1 | 4 | |||
35.23 | odd | 12 | 294.3.c.a.97.4 | 4 | |||
35.24 | odd | 6 | inner | 1050.3.q.a.199.1 | 8 | ||
35.33 | even | 12 | 294.3.c.a.97.3 | 4 | |||
60.23 | odd | 4 | 1008.3.cg.h.145.1 | 4 | |||
105.23 | even | 12 | 882.3.c.b.685.2 | 4 | |||
105.38 | odd | 12 | 126.3.n.a.73.2 | 4 | |||
105.53 | even | 12 | 882.3.n.e.325.2 | 4 | |||
105.68 | odd | 12 | 882.3.c.b.685.1 | 4 | |||
105.83 | odd | 4 | 882.3.n.e.19.2 | 4 | |||
140.3 | odd | 12 | 336.3.bh.e.241.2 | 4 | |||
140.23 | even | 12 | 2352.3.f.e.97.1 | 4 | |||
140.103 | odd | 12 | 2352.3.f.e.97.4 | 4 | |||
420.143 | even | 12 | 1008.3.cg.h.577.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.3.g.a.19.1 | ✓ | 4 | 5.3 | odd | 4 | ||
42.3.g.a.31.1 | yes | 4 | 35.3 | even | 12 | ||
126.3.n.a.19.2 | 4 | 15.8 | even | 4 | |||
126.3.n.a.73.2 | 4 | 105.38 | odd | 12 | |||
294.3.c.a.97.3 | 4 | 35.33 | even | 12 | |||
294.3.c.a.97.4 | 4 | 35.23 | odd | 12 | |||
294.3.g.a.19.1 | 4 | 35.13 | even | 4 | |||
294.3.g.a.31.1 | 4 | 35.18 | odd | 12 | |||
336.3.bh.e.145.2 | 4 | 20.3 | even | 4 | |||
336.3.bh.e.241.2 | 4 | 140.3 | odd | 12 | |||
882.3.c.b.685.1 | 4 | 105.68 | odd | 12 | |||
882.3.c.b.685.2 | 4 | 105.23 | even | 12 | |||
882.3.n.e.19.2 | 4 | 105.83 | odd | 4 | |||
882.3.n.e.325.2 | 4 | 105.53 | even | 12 | |||
1008.3.cg.h.145.1 | 4 | 60.23 | odd | 4 | |||
1008.3.cg.h.577.1 | 4 | 420.143 | even | 12 | |||
1050.3.p.a.451.2 | 4 | 35.17 | even | 12 | |||
1050.3.p.a.901.2 | 4 | 5.2 | odd | 4 | |||
1050.3.q.a.199.1 | 8 | 35.24 | odd | 6 | inner | ||
1050.3.q.a.199.4 | 8 | 7.3 | odd | 6 | inner | ||
1050.3.q.a.649.1 | 8 | 1.1 | even | 1 | trivial | ||
1050.3.q.a.649.4 | 8 | 5.4 | even | 2 | inner | ||
2352.3.f.e.97.1 | 4 | 140.23 | even | 12 | |||
2352.3.f.e.97.4 | 4 | 140.103 | odd | 12 |