Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,3,Mod(245,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 8]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.245");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.h (of order \(10\), degree \(4\), 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: | \(9.89103359628\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 8.0.228765625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 2x^{6} + 5x^{5} + x^{4} + 15x^{3} - 18x^{2} - 27x + 81 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 33) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 269.2 | ||
Root | \(1.37924 + 1.04771i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.269 |
Dual form | 363.3.h.d.251.2 |
$q$-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 \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.15430 | − | 1.02489i | 1.57715 | − | 0.512447i | 0.615829 | − | 0.787880i | \(-0.288821\pi\) |
0.961320 | + | 0.275433i | \(0.0888214\pi\) | |||||||
\(3\) | −2.42705 | − | 1.76336i | −0.809017 | − | 0.587785i | ||||
\(4\) | 5.66312 | − | 4.11450i | 1.41578 | − | 1.02862i | ||||
\(5\) | −6.30860 | − | 2.04979i | −1.26172 | − | 0.409957i | −0.399612 | − | 0.916684i | \(-0.630855\pi\) |
−0.862107 | + | 0.506727i | \(0.830855\pi\) | |||||||
\(6\) | −9.46289 | − | 3.07468i | −1.57715 | − | 0.512447i | ||||
\(7\) | −6.47214 | + | 4.70228i | −0.924591 | + | 0.671755i | −0.944662 | − | 0.328044i | \(-0.893611\pi\) |
0.0200716 | + | 0.999799i | \(0.493611\pi\) | |||||||
\(8\) | 5.84839 | − | 8.04962i | 0.731049 | − | 1.00620i | ||||
\(9\) | 2.78115 | + | 8.55951i | 0.309017 | + | 0.951057i | ||||
\(10\) | −22.0000 | −2.20000 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −21.0000 | −1.75000 | ||||||||
\(13\) | −1.23607 | − | 3.80423i | −0.0950822 | − | 0.292633i | 0.892193 | − | 0.451654i | \(-0.149166\pi\) |
−0.987275 | + | 0.159022i | \(0.949166\pi\) | |||||||
\(14\) | −15.5957 | + | 21.4656i | −1.11398 | + | 1.53326i | ||||
\(15\) | 11.6968 | + | 16.0992i | 0.779785 | + | 1.07328i | ||||
\(16\) | 1.54508 | − | 4.75528i | 0.0965678 | − | 0.297205i | ||||
\(17\) | −12.6172 | − | 4.09957i | −0.742188 | − | 0.241151i | −0.0865714 | − | 0.996246i | \(-0.527591\pi\) |
−0.655616 | + | 0.755094i | \(0.727591\pi\) | |||||||
\(18\) | 17.5452 | + | 24.1489i | 0.974732 | + | 1.34160i | ||||
\(19\) | −4.85410 | − | 3.52671i | −0.255479 | − | 0.185616i | 0.452673 | − | 0.891677i | \(-0.350471\pi\) |
−0.708152 | + | 0.706060i | \(0.750471\pi\) | |||||||
\(20\) | −44.1602 | + | 14.3485i | −2.20801 | + | 0.717425i | ||||
\(21\) | 24.0000 | 1.14286 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.63325i | 0.288402i | 0.989548 | + | 0.144201i | \(0.0460612\pi\) | ||||
−0.989548 | + | 0.144201i | \(0.953939\pi\) | |||||||
\(24\) | −28.3887 | + | 9.22404i | −1.18286 | + | 0.384335i | ||||
\(25\) | 15.3713 | + | 11.1679i | 0.614853 | + | 0.446717i | ||||
\(26\) | −7.79785 | − | 10.7328i | −0.299917 | − | 0.412801i | ||||
\(27\) | 8.34346 | − | 25.6785i | 0.309017 | − | 0.951057i | ||||
\(28\) | −17.3050 | + | 53.2592i | −0.618034 | + | 1.90211i | ||||
\(29\) | −23.3936 | − | 32.1985i | −0.806674 | − | 1.11029i | −0.991828 | − | 0.127582i | \(-0.959278\pi\) |
0.185154 | − | 0.982710i | \(-0.440722\pi\) | |||||||
\(30\) | 53.3951 | + | 38.7938i | 1.77984 | + | 1.29313i | ||||
\(31\) | −8.03444 | − | 24.7275i | −0.259176 | − | 0.797660i | −0.992978 | − | 0.118298i | \(-0.962256\pi\) |
0.733803 | − | 0.679363i | \(-0.237744\pi\) | |||||||
\(32\) | 23.2164i | 0.725512i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −44.0000 | −1.29412 | ||||||||
\(35\) | 50.4688 | − | 16.3983i | 1.44196 | − | 0.468523i | ||||
\(36\) | 50.9681 | + | 37.0305i | 1.41578 | + | 1.02862i | ||||
\(37\) | −24.2705 | + | 17.6336i | −0.655960 | + | 0.476583i | −0.865296 | − | 0.501261i | \(-0.832870\pi\) |
0.209336 | + | 0.977844i | \(0.432870\pi\) | |||||||
\(38\) | −18.9258 | − | 6.14936i | −0.498047 | − | 0.161825i | ||||
\(39\) | −3.70820 | + | 11.4127i | −0.0950822 | + | 0.292633i | ||||
\(40\) | −53.3951 | + | 38.7938i | −1.33488 | + | 0.969846i | ||||
\(41\) | −7.79785 | + | 10.7328i | −0.190192 | + | 0.261776i | −0.893455 | − | 0.449154i | \(-0.851726\pi\) |
0.703263 | + | 0.710930i | \(0.251726\pi\) | |||||||
\(42\) | 75.7031 | − | 24.5974i | 1.80246 | − | 0.585653i | ||||
\(43\) | −42.0000 | −0.976744 | −0.488372 | − | 0.872635i | \(-0.662409\pi\) | ||||
−0.488372 | + | 0.872635i | \(0.662409\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 59.6992i | − | 1.32665i | ||||||
\(46\) | 6.79837 | + | 20.9232i | 0.147791 | + | 0.454853i | ||||
\(47\) | 50.6860 | − | 69.7634i | 1.07843 | − | 1.48433i | 0.217185 | − | 0.976130i | \(-0.430312\pi\) |
0.861241 | − | 0.508196i | \(-0.169688\pi\) | |||||||
\(48\) | −12.1353 | + | 8.81678i | −0.252818 | + | 0.183683i | ||||
\(49\) | 4.63525 | − | 14.2658i | 0.0945970 | − | 0.291140i | ||||
\(50\) | 59.9317 | + | 19.4730i | 1.19863 | + | 0.389460i | ||||
\(51\) | 23.3936 | + | 32.1985i | 0.458697 | + | 0.631343i | ||||
\(52\) | −22.6525 | − | 16.4580i | −0.435625 | − | 0.316500i | ||||
\(53\) | 56.7774 | − | 18.4481i | 1.07127 | − | 0.348077i | 0.280288 | − | 0.959916i | \(-0.409570\pi\) |
0.790982 | + | 0.611839i | \(0.209570\pi\) | |||||||
\(54\) | − | 89.5489i | − | 1.65831i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 79.5990i | 1.42141i | ||||||||
\(57\) | 5.56231 | + | 17.1190i | 0.0975843 | + | 0.300334i | ||||
\(58\) | −106.790 | − | 77.5877i | −1.84121 | − | 1.33772i | ||||
\(59\) | −38.9893 | − | 53.6641i | −0.660835 | − | 0.909561i | 0.338674 | − | 0.940904i | \(-0.390022\pi\) |
−0.999509 | + | 0.0313426i | \(0.990022\pi\) | |||||||
\(60\) | 132.480 | + | 43.0455i | 2.20801 | + | 0.717425i | ||||
\(61\) | −3.70820 | + | 11.4127i | −0.0607902 | + | 0.187093i | −0.976840 | − | 0.213972i | \(-0.931360\pi\) |
0.916050 | + | 0.401065i | \(0.131360\pi\) | |||||||
\(62\) | −50.6860 | − | 69.7634i | −0.817517 | − | 1.12522i | ||||
\(63\) | −58.2492 | − | 42.3205i | −0.924591 | − | 0.671755i | ||||
\(64\) | 29.9746 | + | 92.2525i | 0.468354 | + | 1.44145i | ||||
\(65\) | 26.5330i | 0.408200i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000 | 0.0298507 | 0.0149254 | − | 0.999889i | \(-0.495249\pi\) | ||||
0.0149254 | + | 0.999889i | \(0.495249\pi\) | |||||||
\(68\) | −88.3203 | + | 28.6970i | −1.29883 | + | 0.422015i | ||||
\(69\) | 11.6968 | − | 16.0992i | 0.169519 | − | 0.233322i | ||||
\(70\) | 142.387 | − | 103.450i | 2.03410 | − | 1.47786i | ||||
\(71\) | −56.7774 | − | 18.4481i | −0.799681 | − | 0.259832i | −0.119460 | − | 0.992839i | \(-0.538116\pi\) |
−0.680221 | + | 0.733007i | \(0.738116\pi\) | |||||||
\(72\) | 85.1660 | + | 27.6721i | 1.18286 | + | 0.384335i | ||||
\(73\) | −59.8673 | + | 43.4961i | −0.820099 | + | 0.595837i | −0.916741 | − | 0.399482i | \(-0.869190\pi\) |
0.0966416 | + | 0.995319i | \(0.469190\pi\) | |||||||
\(74\) | −58.4839 | + | 80.4962i | −0.790323 | + | 1.08779i | ||||
\(75\) | −17.6140 | − | 54.2102i | −0.234853 | − | 0.722803i | ||||
\(76\) | −42.0000 | −0.552632 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 39.7995i | 0.510250i | ||||||||
\(79\) | 12.3607 | + | 38.0423i | 0.156464 | + | 0.481548i | 0.998306 | − | 0.0581764i | \(-0.0185286\pi\) |
−0.841842 | + | 0.539724i | \(0.818529\pi\) | |||||||
\(80\) | −19.4946 | + | 26.8321i | −0.243683 | + | 0.335401i | ||||
\(81\) | −65.5304 | + | 47.6106i | −0.809017 | + | 0.587785i | ||||
\(82\) | −13.5967 | + | 41.8465i | −0.165814 | + | 0.510323i | ||||
\(83\) | 37.8516 | + | 12.2987i | 0.456043 | + | 0.148177i | 0.528025 | − | 0.849229i | \(-0.322933\pi\) |
−0.0719824 | + | 0.997406i | \(0.522933\pi\) | |||||||
\(84\) | 135.915 | − | 98.7479i | 1.61803 | − | 1.17557i | ||||
\(85\) | 71.1935 | + | 51.7251i | 0.837571 | + | 0.608531i | ||||
\(86\) | −132.480 | + | 43.0455i | −1.54047 | + | 0.500529i | ||||
\(87\) | 119.398i | 1.37240i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 119.398i | − | 1.34156i | −0.741658 | − | 0.670778i | \(-0.765960\pi\) | ||
0.741658 | − | 0.670778i | \(-0.234040\pi\) | |||||||
\(90\) | −61.1854 | − | 188.309i | −0.679837 | − | 2.09232i | ||||
\(91\) | 25.8885 | + | 18.8091i | 0.284489 | + | 0.206694i | ||||
\(92\) | 27.2925 | + | 37.5649i | 0.296657 | + | 0.408314i | ||||
\(93\) | −24.1033 | + | 74.1824i | −0.259176 | + | 0.797660i | ||||
\(94\) | 88.3789 | − | 272.002i | 0.940201 | − | 2.89364i | ||||
\(95\) | 23.3936 | + | 32.1985i | 0.246248 | + | 0.338931i | ||||
\(96\) | 40.9387 | − | 56.3473i | 0.426445 | − | 0.586951i | ||||
\(97\) | 19.1591 | + | 58.9655i | 0.197516 | + | 0.607892i | 0.999938 | + | 0.0111348i | \(0.00354438\pi\) |
−0.802422 | + | 0.596757i | \(0.796456\pi\) | |||||||
\(98\) | − | 49.7494i | − | 0.507647i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 133.000 | 1.33000 | ||||||||
\(101\) | 100.938 | − | 32.7966i | 0.999381 | − | 0.324719i | 0.236763 | − | 0.971567i | \(-0.423913\pi\) |
0.762618 | + | 0.646849i | \(0.223913\pi\) | |||||||
\(102\) | 106.790 | + | 77.5877i | 1.04696 | + | 0.760663i | ||||
\(103\) | −59.8673 | + | 43.4961i | −0.581236 | + | 0.422292i | −0.839169 | − | 0.543870i | \(-0.816958\pi\) |
0.257934 | + | 0.966163i | \(0.416958\pi\) | |||||||
\(104\) | −37.8516 | − | 12.2987i | −0.363957 | − | 0.118257i | ||||
\(105\) | −151.406 | − | 49.1949i | −1.44196 | − | 0.468523i | ||||
\(106\) | 160.185 | − | 116.381i | 1.51118 | − | 1.09794i | ||||
\(107\) | 23.3936 | − | 32.1985i | 0.218631 | − | 0.300920i | −0.685587 | − | 0.727991i | \(-0.740454\pi\) |
0.904218 | + | 0.427070i | \(0.140454\pi\) | |||||||
\(108\) | −58.4042 | − | 179.750i | −0.540780 | − | 1.66435i | ||||
\(109\) | 200.000 | 1.83486 | 0.917431 | − | 0.397894i | \(-0.130259\pi\) | ||||
0.917431 | + | 0.397894i | \(0.130259\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 90.0000 | 0.810811 | ||||||||
\(112\) | 12.3607 | + | 38.0423i | 0.110363 | + | 0.339663i | ||||
\(113\) | −23.3936 | + | 32.1985i | −0.207023 | + | 0.284942i | −0.899885 | − | 0.436128i | \(-0.856349\pi\) |
0.692862 | + | 0.721070i | \(0.256349\pi\) | |||||||
\(114\) | 35.0903 | + | 48.2977i | 0.307810 | + | 0.423664i | ||||
\(115\) | 13.5967 | − | 41.8465i | 0.118233 | − | 0.363882i | ||||
\(116\) | −264.961 | − | 86.0910i | −2.28415 | − | 0.742164i | ||||
\(117\) | 29.1246 | − | 21.1603i | 0.248928 | − | 0.180857i | ||||
\(118\) | −177.984 | − | 129.313i | −1.50834 | − | 1.09587i | ||||
\(119\) | 100.938 | − | 32.7966i | 0.848214 | − | 0.275602i | ||||
\(120\) | 198.000 | 1.65000 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 39.7995i | 0.326225i | ||||||||
\(123\) | 37.8516 | − | 12.2987i | 0.307736 | − | 0.0999896i | ||||
\(124\) | −147.241 | − | 106.977i | −1.18743 | − | 0.862717i | ||||
\(125\) | 23.3936 | + | 32.1985i | 0.187148 | + | 0.257588i | ||||
\(126\) | −227.109 | − | 73.7923i | −1.80246 | − | 0.585653i | ||||
\(127\) | −58.0952 | + | 178.799i | −0.457442 | + | 1.40786i | 0.410801 | + | 0.911725i | \(0.365249\pi\) |
−0.868244 | + | 0.496138i | \(0.834751\pi\) | |||||||
\(128\) | 134.513 | + | 185.141i | 1.05088 | + | 1.44642i | ||||
\(129\) | 101.936 | + | 74.0609i | 0.790203 | + | 0.574116i | ||||
\(130\) | 27.1935 | + | 83.6930i | 0.209181 | + | 0.643792i | ||||
\(131\) | − | 39.7995i | − | 0.303813i | −0.988395 | − | 0.151906i | \(-0.951459\pi\) | ||
0.988395 | − | 0.151906i | \(-0.0485413\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 48.0000 | 0.360902 | ||||||||
\(134\) | 6.30860 | − | 2.04979i | 0.0470791 | − | 0.0152969i | ||||
\(135\) | −105.271 | + | 144.893i | −0.779785 | + | 1.07328i | ||||
\(136\) | −106.790 | + | 77.5877i | −0.785222 | + | 0.570497i | ||||
\(137\) | 100.938 | + | 32.7966i | 0.736770 | + | 0.239391i | 0.653279 | − | 0.757117i | \(-0.273393\pi\) |
0.0834913 | + | 0.996509i | \(0.473393\pi\) | |||||||
\(138\) | 20.3951 | − | 62.7697i | 0.147791 | − | 0.454853i | ||||
\(139\) | −59.8673 | + | 43.4961i | −0.430700 | + | 0.312922i | −0.781929 | − | 0.623368i | \(-0.785764\pi\) |
0.351229 | + | 0.936290i | \(0.385764\pi\) | |||||||
\(140\) | 218.340 | − | 300.519i | 1.55957 | − | 2.14656i | ||||
\(141\) | −246.035 | + | 79.9417i | −1.74493 | + | 0.566962i | ||||
\(142\) | −198.000 | −1.39437 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 45.0000 | 0.312500 | ||||||||
\(145\) | 81.5805 | + | 251.079i | 0.562624 | + | 1.73158i | ||||
\(146\) | −144.260 | + | 198.557i | −0.988084 | + | 1.35998i | ||||
\(147\) | −36.4058 | + | 26.4503i | −0.247658 | + | 0.179934i | ||||
\(148\) | −64.8936 | + | 199.722i | −0.438470 | + | 1.34947i | ||||
\(149\) | 88.3203 | + | 28.6970i | 0.592754 | + | 0.192597i | 0.590006 | − | 0.807399i | \(-0.299125\pi\) |
0.00274784 | + | 0.999996i | \(0.499125\pi\) | |||||||
\(150\) | −111.119 | − | 152.943i | −0.740796 | − | 1.01962i | ||||
\(151\) | −129.443 | − | 94.0456i | −0.857237 | − | 0.622819i | 0.0698952 | − | 0.997554i | \(-0.477734\pi\) |
−0.927132 | + | 0.374736i | \(0.877734\pi\) | |||||||
\(152\) | −56.7774 | + | 18.4481i | −0.373535 | + | 0.121369i | ||||
\(153\) | − | 119.398i | − | 0.780382i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 172.464i | 1.11267i | ||||||||
\(156\) | 25.9574 | + | 79.8887i | 0.166394 | + | 0.512107i | ||||
\(157\) | −147.241 | − | 106.977i | −0.937841 | − | 0.681382i | 0.0100587 | − | 0.999949i | \(-0.496798\pi\) |
−0.947900 | + | 0.318568i | \(0.896798\pi\) | |||||||
\(158\) | 77.9785 | + | 107.328i | 0.493535 | + | 0.679293i | ||||
\(159\) | −170.332 | − | 55.3442i | −1.07127 | − | 0.348077i | ||||
\(160\) | 47.5886 | − | 146.463i | 0.297429 | − | 0.915392i | ||||
\(161\) | −31.1914 | − | 42.9313i | −0.193735 | − | 0.266654i | ||||
\(162\) | −157.907 | + | 217.340i | −0.974732 | + | 1.34160i | ||||
\(163\) | −89.6149 | − | 275.806i | −0.549785 | − | 1.69206i | −0.709333 | − | 0.704874i | \(-0.751004\pi\) |
0.159548 | − | 0.987190i | \(-0.448996\pi\) | |||||||
\(164\) | 92.8655i | 0.566253i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 132.000 | 0.795181 | ||||||||
\(167\) | −227.109 | + | 73.7923i | −1.35994 | + | 0.441870i | −0.896022 | − | 0.444010i | \(-0.853556\pi\) |
−0.463915 | + | 0.885880i | \(0.653556\pi\) | |||||||
\(168\) | 140.361 | − | 193.191i | 0.835484 | − | 1.14995i | ||||
\(169\) | 123.780 | − | 89.9311i | 0.732424 | − | 0.532137i | ||||
\(170\) | 277.578 | + | 90.1906i | 1.63281 | + | 0.530533i | ||||
\(171\) | 16.6869 | − | 51.3571i | 0.0975843 | − | 0.300334i | ||||
\(172\) | −237.851 | + | 172.809i | −1.38285 | + | 1.00470i | ||||
\(173\) | −116.968 | + | 160.992i | −0.676114 | + | 0.930592i | −0.999879 | − | 0.0155460i | \(-0.995051\pi\) |
0.323765 | + | 0.946138i | \(0.395051\pi\) | |||||||
\(174\) | 122.371 | + | 376.618i | 0.703280 | + | 2.16447i | ||||
\(175\) | −152.000 | −0.868571 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 198.997i | 1.12428i | ||||||||
\(178\) | −122.371 | − | 376.618i | −0.687476 | − | 2.11583i | ||||
\(179\) | 116.968 | − | 160.992i | 0.653451 | − | 0.899399i | −0.345791 | − | 0.938311i | \(-0.612389\pi\) |
0.999243 | + | 0.0389129i | \(0.0123895\pi\) | |||||||
\(180\) | −245.632 | − | 338.084i | −1.36462 | − | 1.87824i | ||||
\(181\) | 3.09017 | − | 9.51057i | 0.0170728 | − | 0.0525446i | −0.942157 | − | 0.335171i | \(-0.891206\pi\) |
0.959230 | + | 0.282627i | \(0.0912058\pi\) | |||||||
\(182\) | 100.938 | + | 32.7966i | 0.554602 | + | 0.180201i | ||||
\(183\) | 29.1246 | − | 21.1603i | 0.159151 | − | 0.115630i | ||||
\(184\) | 53.3951 | + | 38.7938i | 0.290191 | + | 0.210836i | ||||
\(185\) | 189.258 | − | 61.4936i | 1.02302 | − | 0.332398i | ||||
\(186\) | 258.697i | 1.39084i | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 603.626i | − | 3.21078i | ||||||
\(189\) | 66.7477 | + | 205.428i | 0.353162 | + | 1.08692i | ||||
\(190\) | 106.790 | + | 77.5877i | 0.562054 | + | 0.408356i | ||||
\(191\) | 66.2817 | + | 91.2290i | 0.347025 | + | 0.477639i | 0.946477 | − | 0.322772i | \(-0.104615\pi\) |
−0.599452 | + | 0.800411i | \(0.704615\pi\) | |||||||
\(192\) | 89.9239 | − | 276.757i | 0.468354 | − | 1.44145i | ||||
\(193\) | −92.0871 | + | 283.415i | −0.477135 | + | 1.46847i | 0.365921 | + | 0.930646i | \(0.380754\pi\) |
−0.843057 | + | 0.537825i | \(0.819246\pi\) | |||||||
\(194\) | 120.867 | + | 166.359i | 0.623024 | + | 0.857519i | ||||
\(195\) | 46.7871 | − | 64.3969i | 0.239934 | − | 0.330241i | ||||
\(196\) | −32.4468 | − | 99.8609i | −0.165545 | − | 0.509495i | ||||
\(197\) | − | 132.665i | − | 0.673426i | −0.941607 | − | 0.336713i | \(-0.890685\pi\) | ||
0.941607 | − | 0.336713i | \(-0.109315\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −42.0000 | −0.211055 | −0.105528 | − | 0.994416i | \(-0.533653\pi\) | ||||
−0.105528 | + | 0.994416i | \(0.533653\pi\) | |||||||
\(200\) | 179.795 | − | 58.4189i | 0.898975 | − | 0.292095i | ||||
\(201\) | −4.85410 | − | 3.52671i | −0.0241498 | − | 0.0175458i | ||||
\(202\) | 284.774 | − | 206.900i | 1.40977 | − | 1.02426i | ||||
\(203\) | 302.813 | + | 98.3898i | 1.49169 | + | 0.484679i | ||||
\(204\) | 264.961 | + | 86.0910i | 1.29883 | + | 0.422015i | ||||
\(205\) | 71.1935 | − | 51.7251i | 0.347285 | − | 0.252318i | ||||
\(206\) | −144.260 | + | 198.557i | −0.700293 | + | 0.963870i | ||||
\(207\) | −56.7774 | + | 18.4481i | −0.274287 | + | 0.0891212i | ||||
\(208\) | −20.0000 | −0.0961538 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −528.000 | −2.51429 | ||||||||
\(211\) | −76.0182 | − | 233.960i | −0.360276 | − | 1.10881i | −0.952887 | − | 0.303326i | \(-0.901903\pi\) |
0.592611 | − | 0.805489i | \(-0.298097\pi\) | |||||||
\(212\) | 245.632 | − | 338.084i | 1.15864 | − | 1.59474i | ||||
\(213\) | 105.271 | + | 144.893i | 0.494230 | + | 0.680249i | ||||
\(214\) | 40.7902 | − | 125.539i | 0.190609 | − | 0.586633i | ||||
\(215\) | 264.961 | + | 86.0910i | 1.23238 | + | 0.400423i | ||||
\(216\) | −157.907 | − | 217.340i | −0.731049 | − | 1.00620i | ||||
\(217\) | 168.276 | + | 122.259i | 0.775463 | + | 0.563407i | ||||
\(218\) | 630.860 | − | 204.979i | 2.89385 | − | 0.940269i | ||||
\(219\) | 222.000 | 1.01370 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 53.0660i | 0.240118i | ||||||||
\(222\) | 283.887 | − | 92.2404i | 1.27877 | − | 0.415497i | ||||
\(223\) | 244.323 | + | 177.511i | 1.09562 | + | 0.796014i | 0.980339 | − | 0.197319i | \(-0.0632234\pi\) |
0.115280 | + | 0.993333i | \(0.463223\pi\) | |||||||
\(224\) | −109.170 | − | 150.260i | −0.487366 | − | 0.670801i | ||||
\(225\) | −52.8419 | + | 162.631i | −0.234853 | + | 0.722803i | ||||
\(226\) | −40.7902 | + | 125.539i | −0.180488 | + | 0.555484i | ||||
\(227\) | −116.968 | − | 160.992i | −0.515277 | − | 0.709217i | 0.469521 | − | 0.882921i | \(-0.344426\pi\) |
−0.984798 | + | 0.173704i | \(0.944426\pi\) | |||||||
\(228\) | 101.936 | + | 74.0609i | 0.447088 | + | 0.324829i | ||||
\(229\) | 46.3525 | + | 142.658i | 0.202413 | + | 0.622963i | 0.999810 | + | 0.0195075i | \(0.00620982\pi\) |
−0.797397 | + | 0.603455i | \(0.793790\pi\) | |||||||
\(230\) | − | 145.931i | − | 0.634485i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −396.000 | −1.70690 | ||||||||
\(233\) | −416.367 | + | 135.286i | −1.78698 | + | 0.580626i | −0.999368 | − | 0.0355403i | \(-0.988685\pi\) |
−0.787616 | + | 0.616167i | \(0.788685\pi\) | |||||||
\(234\) | 70.1807 | − | 96.5954i | 0.299917 | − | 0.412801i | ||||
\(235\) | −462.758 | + | 336.213i | −1.96918 | + | 1.43069i | ||||
\(236\) | −441.602 | − | 143.485i | −1.87119 | − | 0.607988i | ||||
\(237\) | 37.0820 | − | 114.127i | 0.156464 | − | 0.481548i | ||||
\(238\) | 284.774 | − | 206.900i | 1.19653 | − | 0.869329i | ||||
\(239\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(240\) | 94.6289 | − | 30.7468i | 0.394287 | − | 0.128112i | ||||
\(241\) | −130.000 | −0.539419 | −0.269710 | − | 0.962942i | \(-0.586928\pi\) | ||||
−0.269710 | + | 0.962942i | \(0.586928\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 1.00000 | ||||||||
\(244\) | 25.9574 | + | 79.8887i | 0.106383 | + | 0.327413i | ||||
\(245\) | −58.4839 | + | 80.4962i | −0.238710 | + | 0.328556i | ||||
\(246\) | 106.790 | − | 77.5877i | 0.434107 | − | 0.315397i | ||||
\(247\) | −7.41641 | + | 22.8254i | −0.0300259 | + | 0.0924103i | ||||
\(248\) | −246.035 | − | 79.9417i | −0.992077 | − | 0.322346i | ||||
\(249\) | −70.1807 | − | 96.5954i | −0.281850 | − | 0.387933i | ||||
\(250\) | 106.790 | + | 77.5877i | 0.427161 | + | 0.310351i | ||||
\(251\) | −277.578 | + | 90.1906i | −1.10589 | + | 0.359325i | −0.804366 | − | 0.594134i | \(-0.797495\pi\) |
−0.301523 | + | 0.953459i | \(0.597495\pi\) | |||||||
\(252\) | −504.000 | −2.00000 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 623.525i | 2.45482i | ||||||||
\(255\) | −81.5805 | − | 251.079i | −0.319923 | − | 0.984623i | ||||
\(256\) | 300.145 | + | 218.068i | 1.17244 | + | 0.851829i | ||||
\(257\) | −288.521 | − | 397.114i | −1.12265 | − | 1.54519i | −0.801331 | − | 0.598221i | \(-0.795875\pi\) |
−0.321317 | − | 0.946972i | \(-0.604125\pi\) | |||||||
\(258\) | 397.441 | + | 129.137i | 1.54047 | + | 0.500529i | ||||
\(259\) | 74.1641 | − | 228.254i | 0.286348 | − | 0.881288i | ||||
\(260\) | 109.170 | + | 150.260i | 0.419884 | + | 0.577921i | ||||
\(261\) | 210.542 | − | 289.786i | 0.806674 | − | 1.11029i | ||||
\(262\) | −40.7902 | − | 125.539i | −0.155688 | − | 0.479158i | ||||
\(263\) | − | 225.530i | − | 0.857530i | −0.903416 | − | 0.428765i | \(-0.858949\pi\) | ||
0.903416 | − | 0.428765i | \(-0.141051\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −396.000 | −1.49434 | ||||||||
\(266\) | 151.406 | − | 49.1949i | 0.569197 | − | 0.184943i | ||||
\(267\) | −210.542 | + | 289.786i | −0.788547 | + | 1.08534i | ||||
\(268\) | 11.3262 | − | 8.22899i | 0.0422621 | − | 0.0307052i | ||||
\(269\) | 69.3945 | + | 22.5477i | 0.257972 | + | 0.0838203i | 0.435148 | − | 0.900359i | \(-0.356696\pi\) |
−0.177176 | + | 0.984179i | \(0.556696\pi\) | |||||||
\(270\) | −183.556 | + | 564.928i | −0.679837 | + | 2.09232i | ||||
\(271\) | −362.440 | + | 263.328i | −1.33742 | + | 0.971689i | −0.337881 | + | 0.941189i | \(0.609710\pi\) |
−0.999535 | + | 0.0305004i | \(0.990290\pi\) | |||||||
\(272\) | −38.9893 | + | 53.6641i | −0.143343 | + | 0.197295i | ||||
\(273\) | −29.6656 | − | 91.3014i | −0.108665 | − | 0.334437i | ||||
\(274\) | 352.000 | 1.28467 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | − | 139.298i | − | 0.504704i | ||||||
\(277\) | 80.3444 | + | 247.275i | 0.290052 | + | 0.892688i | 0.984839 | + | 0.173473i | \(0.0554988\pi\) |
−0.694787 | + | 0.719216i | \(0.744501\pi\) | |||||||
\(278\) | −144.260 | + | 198.557i | −0.518922 | + | 0.714235i | ||||
\(279\) | 189.310 | − | 137.542i | 0.678530 | − | 0.492981i | ||||
\(280\) | 163.161 | − | 502.158i | 0.582718 | − | 1.79342i | ||||
\(281\) | 189.258 | + | 61.4936i | 0.673516 | + | 0.218838i | 0.625754 | − | 0.780020i | \(-0.284791\pi\) |
0.0477613 | + | 0.998859i | \(0.484791\pi\) | |||||||
\(282\) | −694.137 | + | 504.320i | −2.46148 | + | 1.78837i | ||||
\(283\) | −40.4508 | − | 29.3893i | −0.142936 | − | 0.103849i | 0.514019 | − | 0.857779i | \(-0.328156\pi\) |
−0.656955 | + | 0.753930i | \(0.728156\pi\) | |||||||
\(284\) | −397.441 | + | 129.137i | −1.39944 | + | 0.454706i | ||||
\(285\) | − | 119.398i | − | 0.418942i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 106.132i | − | 0.369798i | ||||||
\(288\) | −198.721 | + | 64.5683i | −0.690003 | + | 0.224195i | ||||
\(289\) | −91.4189 | − | 66.4197i | −0.316328 | − | 0.229826i | ||||
\(290\) | 514.658 | + | 708.366i | 1.77468 | + | 2.44264i | ||||
\(291\) | 57.4772 | − | 176.897i | 0.197516 | − | 0.607892i | ||||
\(292\) | −160.071 | + | 492.647i | −0.548188 | + | 1.68715i | ||||
\(293\) | 280.723 | + | 386.382i | 0.958098 | + | 1.31871i | 0.947835 | + | 0.318761i | \(0.103267\pi\) |
0.0102629 | + | 0.999947i | \(0.496733\pi\) | |||||||
\(294\) | −87.7258 | + | 120.744i | −0.298387 | + | 0.410695i | ||||
\(295\) | 135.967 | + | 418.465i | 0.460907 | + | 1.41852i | ||||
\(296\) | 298.496i | 1.00843i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 308.000 | 1.03356 | ||||||||
\(299\) | 25.2344 | − | 8.19915i | 0.0843959 | − | 0.0274219i | ||||
\(300\) | −322.798 | − | 234.526i | −1.07599 | − | 0.781754i | ||||
\(301\) | 271.830 | − | 197.496i | 0.903089 | − | 0.656132i | ||||
\(302\) | −504.688 | − | 163.983i | −1.67115 | − | 0.542990i | ||||
\(303\) | −302.813 | − | 98.3898i | −0.999381 | − | 0.324719i | ||||
\(304\) | −24.2705 | + | 17.6336i | −0.0798372 | + | 0.0580051i | ||||
\(305\) | 46.7871 | − | 64.3969i | 0.153400 | − | 0.211138i | ||||
\(306\) | −122.371 | − | 376.618i | −0.399904 | − | 1.23078i | ||||
\(307\) | −86.0000 | −0.280130 | −0.140065 | − | 0.990142i | \(-0.544731\pi\) | ||||
−0.140065 | + | 0.990142i | \(0.544731\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 222.000 | 0.718447 | ||||||||
\(310\) | 176.758 | + | 544.004i | 0.570186 | + | 1.75485i | ||||
\(311\) | 11.6968 | − | 16.0992i | 0.0376102 | − | 0.0517660i | −0.789798 | − | 0.613367i | \(-0.789815\pi\) |
0.827408 | + | 0.561601i | \(0.189815\pi\) | |||||||
\(312\) | 70.1807 | + | 96.5954i | 0.224938 | + | 0.309601i | ||||
\(313\) | 30.2837 | − | 93.2035i | 0.0967529 | − | 0.297775i | −0.890954 | − | 0.454094i | \(-0.849963\pi\) |
0.987707 | + | 0.156319i | \(0.0499629\pi\) | |||||||
\(314\) | −574.082 | − | 186.531i | −1.82829 | − | 0.594047i | ||||
\(315\) | 280.723 | + | 386.382i | 0.891183 | + | 1.22661i | ||||
\(316\) | 226.525 | + | 164.580i | 0.716851 | + | 0.520822i | ||||
\(317\) | −296.504 | + | 96.3400i | −0.935344 | + | 0.303912i | −0.736746 | − | 0.676169i | \(-0.763639\pi\) |
−0.198598 | + | 0.980081i | \(0.563639\pi\) | |||||||
\(318\) | −594.000 | −1.86792 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | − | 643.425i | − | 2.01070i | ||||||
\(321\) | −113.555 | + | 36.8962i | −0.353753 | + | 0.114941i | ||||
\(322\) | −142.387 | − | 103.450i | −0.442196 | − | 0.321274i | ||||
\(323\) | 46.7871 | + | 64.3969i | 0.144852 | + | 0.199371i | ||||
\(324\) | −175.213 | + | 539.249i | −0.540780 | + | 1.66435i | ||||
\(325\) | 23.4853 | − | 72.2803i | 0.0722624 | − | 0.222401i | ||||
\(326\) | −565.344 | − | 778.130i | −1.73419 | − | 2.38690i | ||||
\(327\) | −485.410 | − | 352.671i | −1.48443 | − | 1.07851i | ||||
\(328\) | 40.7902 | + | 125.539i | 0.124360 | + | 0.382742i | ||||
\(329\) | 689.858i | 2.09683i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −218.000 | −0.658610 | −0.329305 | − | 0.944224i | \(-0.606814\pi\) | ||||
−0.329305 | + | 0.944224i | \(0.606814\pi\) | |||||||
\(332\) | 264.961 | − | 86.0910i | 0.798075 | − | 0.259310i | ||||
\(333\) | −218.435 | − | 158.702i | −0.655960 | − | 0.476583i | ||||
\(334\) | −640.741 | + | 465.526i | −1.91839 | + | 1.39379i | ||||
\(335\) | −12.6172 | − | 4.09957i | −0.0376633 | − | 0.0122375i | ||||
\(336\) | 37.0820 | − | 114.127i | 0.110363 | − | 0.339663i | ||||
\(337\) | 224.907 | − | 163.404i | 0.667379 | − | 0.484879i | −0.201768 | − | 0.979433i | \(-0.564669\pi\) |
0.869147 | + | 0.494554i | \(0.164669\pi\) | |||||||
\(338\) | 298.268 | − | 410.530i | 0.882449 | − | 1.21459i | ||||
\(339\) | 113.555 | − | 36.8962i | 0.334970 | − | 0.108838i | ||||
\(340\) | 616.000 | 1.81176 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | − | 179.098i | − | 0.523678i | ||||||
\(343\) | −84.0526 | − | 258.687i | −0.245051 | − | 0.754191i | ||||
\(344\) | −245.632 | + | 338.084i | −0.714048 | + | 0.982802i | ||||
\(345\) | −106.790 | + | 77.5877i | −0.309537 | + | 0.224892i | ||||
\(346\) | −203.951 | + | 627.697i | −0.589454 | + | 1.81415i | ||||
\(347\) | −315.430 | − | 102.489i | −0.909019 | − | 0.295358i | −0.183065 | − | 0.983101i | \(-0.558602\pi\) |
−0.725955 | + | 0.687743i | \(0.758602\pi\) | |||||||
\(348\) | 491.265 | + | 676.168i | 1.41168 | + | 1.94301i | ||||
\(349\) | 262.122 | + | 190.442i | 0.751064 | + | 0.545680i | 0.896157 | − | 0.443738i | \(-0.146348\pi\) |
−0.145092 | + | 0.989418i | \(0.546348\pi\) | |||||||
\(350\) | −479.453 | + | 155.784i | −1.36987 | + | 0.445097i | ||||
\(351\) | −108.000 | −0.307692 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 397.995i | 1.12746i | 0.825958 | + | 0.563732i | \(0.190635\pi\) | ||||
−0.825958 | + | 0.563732i | \(0.809365\pi\) | |||||||
\(354\) | 203.951 | + | 627.697i | 0.576133 | + | 1.77316i | ||||
\(355\) | 320.371 | + | 232.763i | 0.902453 | + | 0.655670i | ||||
\(356\) | −491.265 | − | 676.168i | −1.37996 | − | 1.89935i | ||||
\(357\) | −302.813 | − | 98.3898i | −0.848214 | − | 0.275602i | ||||
\(358\) | 203.951 | − | 627.697i | 0.569696 | − | 1.75334i | ||||
\(359\) | −179.351 | − | 246.855i | −0.499584 | − | 0.687618i | 0.482536 | − | 0.875876i | \(-0.339716\pi\) |
−0.982120 | + | 0.188258i | \(0.939716\pi\) | |||||||
\(360\) | −480.556 | − | 349.144i | −1.33488 | − | 0.969846i | ||||
\(361\) | −100.431 | − | 309.093i | −0.278201 | − | 0.856214i | ||||
\(362\) | − | 33.1662i | − | 0.0916195i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 224.000 | 0.615385 | ||||||||
\(365\) | 466.836 | − | 151.684i | 1.27900 | − | 0.415573i | ||||
\(366\) | 70.1807 | − | 96.5954i | 0.191750 | − | 0.263922i | ||||
\(367\) | 224.907 | − | 163.404i | 0.612825 | − | 0.445243i | −0.237583 | − | 0.971367i | \(-0.576355\pi\) |
0.850408 | + | 0.526124i | \(0.176355\pi\) | |||||||
\(368\) | 31.5430 | + | 10.2489i | 0.0857146 | + | 0.0278504i | ||||
\(369\) | −113.555 | − | 36.8962i | −0.307736 | − | 0.0999896i | ||||
\(370\) | 533.951 | − | 387.938i | 1.44311 | − | 1.04848i | ||||
\(371\) | −280.723 | + | 386.382i | −0.756665 | + | 1.04146i | ||||
\(372\) | 168.723 | + | 519.277i | 0.453557 | + | 1.39591i | ||||
\(373\) | 68.0000 | 0.182306 | 0.0911528 | − | 0.995837i | \(-0.470945\pi\) | ||||
0.0911528 | + | 0.995837i | \(0.470945\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 119.398i | − | 0.318396i | ||||||
\(376\) | −265.137 | − | 816.006i | −0.705150 | − | 2.17023i | ||||
\(377\) | −93.5742 | + | 128.794i | −0.248208 | + | 0.341628i | ||||
\(378\) | 421.084 | + | 579.572i | 1.11398 | + | 1.53326i | ||||
\(379\) | 207.041 | − | 637.208i | 0.546283 | − | 1.68129i | −0.171636 | − | 0.985161i | \(-0.554905\pi\) |
0.717919 | − | 0.696127i | \(-0.245095\pi\) | |||||||
\(380\) | 264.961 | + | 86.0910i | 0.697266 | + | 0.226555i | ||||
\(381\) | 456.286 | − | 331.511i | 1.19760 | − | 0.870107i | ||||
\(382\) | 302.572 | + | 219.832i | 0.792074 | + | 0.575476i | ||||
\(383\) | 31.5430 | − | 10.2489i | 0.0823576 | − | 0.0267596i | −0.267548 | − | 0.963544i | \(-0.586214\pi\) |
0.349906 | + | 0.936785i | \(0.386214\pi\) | |||||||
\(384\) | − | 686.541i | − | 1.78787i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 988.354i | 2.56050i | ||||||||
\(387\) | −116.808 | − | 359.499i | −0.301831 | − | 0.928939i | ||||
\(388\) | 351.113 | + | 255.099i | 0.904931 | + | 0.657471i | ||||
\(389\) | 245.632 | + | 338.084i | 0.631446 | + | 0.869110i | 0.998123 | − | 0.0612377i | \(-0.0195048\pi\) |
−0.366678 | + | 0.930348i | \(0.619505\pi\) | |||||||
\(390\) | 81.5805 | − | 251.079i | 0.209181 | − | 0.643792i | ||||
\(391\) | 27.1935 | − | 83.6930i | 0.0695486 | − | 0.214049i | ||||
\(392\) | −87.7258 | − | 120.744i | −0.223790 | − | 0.308021i | ||||
\(393\) | −70.1807 | + | 96.5954i | −0.178577 | + | 0.245790i | ||||
\(394\) | −135.967 | − | 418.465i | −0.345095 | − | 1.06209i | ||||
\(395\) | − | 265.330i | − | 0.671721i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −86.0000 | −0.216625 | −0.108312 | − | 0.994117i | \(-0.534545\pi\) | ||||
−0.108312 | + | 0.994117i | \(0.534545\pi\) | |||||||
\(398\) | −132.480 | + | 43.0455i | −0.332866 | + | 0.108155i | ||||
\(399\) | −116.498 | − | 84.6411i | −0.291976 | − | 0.212133i | ||||
\(400\) | 76.8566 | − | 55.8396i | 0.192142 | − | 0.139599i | ||||
\(401\) | −239.727 | − | 77.8919i | −0.597822 | − | 0.194244i | −0.00555318 | − | 0.999985i | \(-0.501768\pi\) |
−0.592269 | + | 0.805740i | \(0.701768\pi\) | |||||||
\(402\) | −18.9258 | − | 6.14936i | −0.0470791 | − | 0.0152969i | ||||
\(403\) | −84.1378 | + | 61.1297i | −0.208779 | + | 0.151687i | ||||
\(404\) | 436.680 | − | 601.038i | 1.08089 | − | 1.48772i | ||||
\(405\) | 510.996 | − | 166.033i | 1.26172 | − | 0.409957i | ||||
\(406\) | 1056.00 | 2.60099 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 396.000 | 0.970588 | ||||||||
\(409\) | −157.599 | − | 485.039i | −0.385327 | − | 1.18591i | −0.936243 | − | 0.351353i | \(-0.885722\pi\) |
0.550916 | − | 0.834561i | \(-0.314278\pi\) | |||||||
\(410\) | 171.553 | − | 236.122i | 0.418421 | − | 0.575908i | ||||
\(411\) | −187.148 | − | 257.588i | −0.455349 | − | 0.626734i | ||||
\(412\) | −160.071 | + | 492.647i | −0.388521 | + | 1.19575i | ||||
\(413\) | 504.688 | + | 163.983i | 1.22200 | + | 0.397053i | ||||
\(414\) | −160.185 | + | 116.381i | −0.386921 | + | 0.281115i | ||||
\(415\) | −213.580 | − | 155.175i | −0.514652 | − | 0.373916i | ||||
\(416\) | 88.3203 | − | 28.6970i | 0.212308 | − | 0.0689832i | ||||
\(417\) | 222.000 | 0.532374 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 530.660i | − | 1.26649i | −0.773951 | − | 0.633246i | \(-0.781722\pi\) | ||
0.773951 | − | 0.633246i | \(-0.218278\pi\) | |||||||
\(420\) | −1059.84 | + | 344.364i | −2.52344 | + | 0.819915i | ||||
\(421\) | 137.533 | + | 99.9235i | 0.326681 | + | 0.237348i | 0.739021 | − | 0.673682i | \(-0.235288\pi\) |
−0.412340 | + | 0.911030i | \(0.635288\pi\) | |||||||
\(422\) | −479.568 | − | 660.069i | −1.13642 | − | 1.56414i | ||||
\(423\) | 738.106 | + | 239.825i | 1.74493 | + | 0.566962i | ||||
\(424\) | 183.556 | − | 564.928i | 0.432915 | − | 1.33238i | ||||
\(425\) | −148.159 | − | 203.924i | −0.348610 | − | 0.479820i | ||||
\(426\) | 480.556 | + | 349.144i | 1.12807 | + | 0.819588i | ||||
\(427\) | −29.6656 | − | 91.3014i | −0.0694745 | − | 0.213821i | ||||
\(428\) | − | 278.596i | − | 0.650926i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 924.000 | 2.14884 | ||||||||
\(431\) | 264.961 | − | 86.0910i | 0.614759 | − | 0.199747i | 0.0149469 | − | 0.999888i | \(-0.495242\pi\) |
0.599812 | + | 0.800141i | \(0.295242\pi\) | |||||||
\(432\) | −109.217 | − | 79.3510i | −0.252818 | − | 0.183683i | ||||
\(433\) | 438.487 | − | 318.580i | 1.01267 | − | 0.735750i | 0.0479046 | − | 0.998852i | \(-0.484746\pi\) |
0.964768 | + | 0.263102i | \(0.0847457\pi\) | |||||||
\(434\) | 656.094 | + | 213.178i | 1.51174 | + | 0.491193i | ||||
\(435\) | 244.741 | − | 753.237i | 0.562624 | − | 1.73158i | ||||
\(436\) | 1132.62 | − | 822.899i | 2.59776 | − | 1.88738i | ||||
\(437\) | 23.3936 | − | 32.1985i | 0.0535322 | − | 0.0736807i | ||||
\(438\) | 700.254 | − | 227.526i | 1.59875 | − | 0.519467i | ||||
\(439\) | −328.000 | −0.747153 | −0.373576 | − | 0.927599i | \(-0.621869\pi\) | ||||
−0.373576 | + | 0.927599i | \(0.621869\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 135.000 | 0.306122 | ||||||||
\(442\) | 54.3870 | + | 167.386i | 0.123047 | + | 0.378701i | ||||
\(443\) | 77.9785 | − | 107.328i | 0.176024 | − | 0.242276i | −0.711884 | − | 0.702297i | \(-0.752158\pi\) |
0.887908 | + | 0.460021i | \(0.152158\pi\) | |||||||
\(444\) | 509.681 | − | 370.305i | 1.14793 | − | 0.834020i | ||||
\(445\) | −244.741 | + | 753.237i | −0.549981 | + | 1.69267i | ||||
\(446\) | 952.598 | + | 309.518i | 2.13587 | + | 0.693986i | ||||
\(447\) | −163.755 | − | 225.389i | −0.366342 | − | 0.504227i | ||||
\(448\) | −627.797 | − | 456.121i | −1.40133 | − | 1.01813i | ||||
\(449\) | 428.984 | − | 139.386i | 0.955422 | − | 0.310435i | 0.210505 | − | 0.977593i | \(-0.432489\pi\) |
0.744917 | + | 0.667157i | \(0.232489\pi\) | |||||||
\(450\) | 567.143i | 1.26032i | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 278.596i | 0.616364i | ||||||||
\(453\) | 148.328 | + | 456.507i | 0.327435 | + | 1.00774i | ||||
\(454\) | −533.951 | − | 387.938i | −1.17610 | − | 0.854490i | ||||
\(455\) | −124.766 | − | 171.725i | −0.274210 | − | 0.377418i | ||||
\(456\) | 170.332 | + | 55.3442i | 0.373535 | + | 0.121369i | ||||
\(457\) | −105.684 | + | 325.261i | −0.231256 | + | 0.711732i | 0.766340 | + | 0.642435i | \(0.222076\pi\) |
−0.997596 | + | 0.0692969i | \(0.977924\pi\) | |||||||
\(458\) | 292.419 | + | 402.481i | 0.638470 | + | 0.878779i | ||||
\(459\) | −210.542 | + | 289.786i | −0.458697 | + | 0.631343i | ||||
\(460\) | −95.1772 | − | 292.925i | −0.206907 | − | 0.636794i | ||||
\(461\) | 79.5990i | 0.172666i | 0.996266 | + | 0.0863330i | \(0.0275149\pi\) | ||||
−0.996266 | + | 0.0863330i | \(0.972485\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −86.0000 | −0.185745 | −0.0928726 | − | 0.995678i | \(-0.529605\pi\) | ||||
−0.0928726 | + | 0.995678i | \(0.529605\pi\) | |||||||
\(464\) | −189.258 | + | 61.4936i | −0.407883 | + | 0.132529i | ||||
\(465\) | 304.116 | − | 418.580i | 0.654013 | − | 0.900172i | ||||
\(466\) | −1174.69 | + | 853.464i | −2.52080 | + | 1.83147i | ||||
\(467\) | −567.774 | − | 184.481i | −1.21579 | − | 0.395034i | −0.370242 | − | 0.928935i | \(-0.620725\pi\) |
−0.845547 | + | 0.533901i | \(0.820725\pi\) | |||||||
\(468\) | 77.8723 | − | 239.666i | 0.166394 | − | 0.512107i | ||||
\(469\) | −12.9443 | + | 9.40456i | −0.0275997 | + | 0.0200524i | ||||
\(470\) | −1115.09 | + | 1534.79i | −2.37254 | + | 3.26552i | ||||
\(471\) | 168.723 | + | 519.277i | 0.358224 | + | 1.10250i | ||||
\(472\) | −660.000 | −1.39831 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | − | 397.995i | − | 0.839652i | ||||||
\(475\) | −35.2279 | − | 108.420i | −0.0741641 | − | 0.228254i | ||||
\(476\) | 436.680 | − | 601.038i | 0.917394 | − | 1.26269i | ||||
\(477\) | 315.813 | + | 434.679i | 0.662082 | + | 0.911277i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −214.492 | − | 69.6928i | −0.447792 | − | 0.145496i | 0.0764360 | − | 0.997074i | \(-0.475646\pi\) |
−0.524228 | + | 0.851578i | \(0.675646\pi\) | |||||||
\(480\) | −373.766 | + | 271.557i | −0.778679 | + | 0.565743i | ||||
\(481\) | 97.0820 | + | 70.5342i | 0.201834 | + | 0.146641i | ||||
\(482\) | −410.059 | + | 133.236i | −0.850744 | + | 0.276424i | ||||
\(483\) | 159.198i | 0.329602i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 411.261i | − | 0.847962i | ||||||
\(486\) | 766.494 | − | 249.049i | 1.57715 | − | 0.512447i | ||||
\(487\) | −360.822 | − | 262.152i | −0.740907 | − | 0.538300i | 0.152088 | − | 0.988367i | \(-0.451400\pi\) |
−0.892995 | + | 0.450067i | \(0.851400\pi\) | |||||||
\(488\) | 70.1807 | + | 96.5954i | 0.143813 | + | 0.197941i | ||||
\(489\) | −268.845 | + | 827.419i | −0.549785 | + | 1.69206i | ||||
\(490\) | −101.976 | + | 313.849i | −0.208113 | + | 0.640507i | ||||
\(491\) | −413.286 | − | 568.840i | −0.841723 | − | 1.15853i | −0.985626 | − | 0.168941i | \(-0.945965\pi\) |
0.143903 | − | 0.989592i | \(-0.454035\pi\) | |||||||
\(492\) | 163.755 | − | 225.389i | 0.332835 | − | 0.458108i | ||||
\(493\) | 163.161 | + | 502.158i | 0.330955 | + | 1.01858i | ||||
\(494\) | 79.5990i | 0.161132i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −130.000 | −0.262097 | ||||||||
\(497\) | 454.219 | − | 147.585i | 0.913921 | − | 0.296951i | ||||
\(498\) | −320.371 | − | 232.763i | −0.643315 | − | 0.467396i | ||||
\(499\) | 46.9230 | − | 34.0915i | 0.0940340 | − | 0.0683197i | −0.539775 | − | 0.841809i | \(-0.681491\pi\) |
0.633809 | + | 0.773490i | \(0.281491\pi\) | |||||||
\(500\) | 264.961 | + | 86.0910i | 0.529922 | + | 0.172182i | ||||
\(501\) | 681.328 | + | 221.377i | 1.35994 | + | 0.441870i | ||||
\(502\) | −783.128 | + | 568.976i | −1.56002 | + | 1.13342i | ||||
\(503\) | 296.318 | − | 407.847i | 0.589102 | − | 0.810830i | −0.405554 | − | 0.914071i | \(-0.632921\pi\) |
0.994656 | + | 0.103241i | \(0.0329214\pi\) | |||||||
\(504\) | −681.328 | + | 221.377i | −1.35184 | + | 0.439240i | ||||
\(505\) | −704.000 | −1.39406 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −459.000 | −0.905325 | ||||||||
\(508\) | 406.666 | + | 1251.59i | 0.800524 | + | 2.46376i | ||||
\(509\) | 432.781 | − | 595.672i | 0.850257 | − | 1.17028i | −0.133549 | − | 0.991042i | \(-0.542637\pi\) |
0.983806 | − | 0.179236i | \(-0.0573626\pi\) | |||||||
\(510\) | −514.658 | − | 708.366i | −1.00913 | − | 1.38895i | ||||
\(511\) | 182.938 | − | 563.025i | 0.358000 | − | 1.10181i | ||||
\(512\) | 299.658 | + | 97.3649i | 0.585270 | + | 0.190166i | ||||
\(513\) | −131.061 | + | 95.2212i | −0.255479 | + | 0.185616i | ||||
\(514\) | −1317.08 | − | 956.914i | −2.56241 | − | 1.86170i | ||||
\(515\) | 466.836 | − | 151.684i | 0.906478 | − | 0.294532i | ||||
\(516\) | 882.000 | 1.70930 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | − | 795.990i | − | 1.53666i | ||||||
\(519\) | 567.774 | − | 184.481i | 1.09398 | − | 0.355454i | ||||
\(520\) | 213.580 | + | 155.175i | 0.410732 | + | 0.298414i | ||||
\(521\) | −163.755 | − | 225.389i | −0.314309 | − | 0.432609i | 0.622410 | − | 0.782691i | \(-0.286154\pi\) |
−0.936719 | + | 0.350082i | \(0.886154\pi\) | |||||||
\(522\) | 367.112 | − | 1129.86i | 0.703280 | − | 2.16447i | ||||
\(523\) | 43.8804 | − | 135.050i | 0.0839014 | − | 0.258222i | −0.900301 | − | 0.435267i | \(-0.856654\pi\) |
0.984203 | + | 0.177045i | \(0.0566539\pi\) | |||||||
\(524\) | −163.755 | − | 225.389i | −0.312509 | − | 0.430132i | ||||
\(525\) | 368.912 | + | 268.030i | 0.702689 | + | 0.510533i | ||||
\(526\) | −231.145 | − | 711.390i | −0.439439 | − | 1.35245i | ||||
\(527\) | 344.929i | 0.654514i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 485.000 | 0.916824 | ||||||||
\(530\) | −1249.10 | + | 405.858i | −2.35680 | + | 0.765769i | ||||
\(531\) | 350.903 | − | 482.977i | 0.660835 | − | 0.909561i | ||||
\(532\) | 271.830 | − | 197.496i | 0.510958 | − | 0.371233i | ||||
\(533\) | 50.4688 | + | 16.3983i | 0.0946881 | + | 0.0307660i | ||||
\(534\) | −367.112 | + | 1129.86i | −0.687476 | + | 2.11583i | ||||
\(535\) | −213.580 | + | 155.175i | −0.399216 | + | 0.290047i | ||||
\(536\) | 11.6968 | − | 16.0992i | 0.0218223 | − | 0.0300359i | ||||
\(537\) | −567.774 | + | 184.481i | −1.05731 | + | 0.343540i | ||||
\(538\) | 242.000 | 0.449814 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1253.68i | 2.32164i | ||||||||
\(541\) | −123.607 | − | 380.423i | −0.228478 | − | 0.703184i | −0.997920 | − | 0.0644668i | \(-0.979465\pi\) |
0.769441 | − | 0.638717i | \(-0.220535\pi\) | |||||||
\(542\) | −873.359 | + | 1202.08i | −1.61136 | + | 2.21785i | ||||
\(543\) | −24.2705 | + | 17.6336i | −0.0446971 | + | 0.0324743i | ||||
\(544\) | 95.1772 | − | 292.925i | 0.174958 | − | 0.538466i | ||||
\(545\) | −1261.72 | − | 409.957i | −2.31508 | − | 0.752215i | ||||
\(546\) | −187.148 | − | 257.588i | −0.342763 | − | 0.471772i | ||||
\(547\) | 137.533 | + | 99.9235i | 0.251431 | + | 0.182675i | 0.706361 | − | 0.707852i | \(-0.250336\pi\) |
−0.454930 | + | 0.890527i | \(0.650336\pi\) | |||||||
\(548\) | 706.563 | − | 229.576i | 1.28935 | − | 0.418935i | ||||
\(549\) | −108.000 | −0.196721 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 238.797i | 0.433388i | ||||||||
\(552\) | −61.1854 | − | 188.309i | −0.110843 | − | 0.341140i | ||||
\(553\) | −258.885 | − | 188.091i | −0.468147 | − | 0.340129i | ||||
\(554\) | 506.860 | + | 697.634i | 0.914910 | + | 1.25927i | ||||
\(555\) | −567.774 | − | 184.481i | −1.02302 | − | 0.332398i | ||||
\(556\) | −160.071 | + | 492.647i | −0.287897 | + | 0.886056i | ||||
\(557\) | 499.063 | + | 686.901i | 0.895983 | + | 1.23321i | 0.971732 | + | 0.236088i | \(0.0758653\pi\) |
−0.0757486 | + | 0.997127i | \(0.524135\pi\) | |||||||
\(558\) | 456.174 | − | 627.870i | 0.817517 | − | 1.12522i | ||||
\(559\) | 51.9149 | + | 159.777i | 0.0928709 | + | 0.285827i | ||||
\(560\) | − | 265.330i | − | 0.473804i | ||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 660.000 | 1.17438 | ||||||||
\(563\) | −668.711 | + | 217.277i | −1.18776 | + | 0.385928i | −0.835246 | − | 0.549877i | \(-0.814675\pi\) |
−0.352518 | + | 0.935805i | \(0.614675\pi\) | |||||||
\(564\) | −1064.41 | + | 1465.03i | −1.88725 | + | 2.59757i | ||||
\(565\) | 213.580 | − | 155.175i | 0.378019 | − | 0.274647i | ||||
\(566\) | −157.715 | − | 51.2447i | −0.278648 | − | 0.0905383i | ||||
\(567\) | 200.243 | − | 616.285i | 0.353162 | − | 1.08692i | ||||
\(568\) | −480.556 | + | 349.144i | −0.846049 | + | 0.614691i | ||||
\(569\) | 70.1807 | − | 96.5954i | 0.123340 | − | 0.169763i | −0.742882 | − | 0.669423i | \(-0.766541\pi\) |
0.866222 | + | 0.499659i | \(0.166541\pi\) | |||||||
\(570\) | −122.371 | − | 376.618i | −0.214685 | − | 0.660734i | ||||
\(571\) | 706.000 | 1.23643 | 0.618214 | − | 0.786010i | \(-0.287857\pi\) | ||||
0.618214 | + | 0.786010i | \(0.287857\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 338.296i | − | 0.590394i | ||||||
\(574\) | −108.774 | − | 334.772i | −0.189502 | − | 0.583226i | ||||
\(575\) | −74.0796 | + | 101.962i | −0.128834 | + | 0.177325i | ||||
\(576\) | −706.272 | + | 513.137i | −1.22617 | + | 0.890862i | ||||
\(577\) | −228.055 | + | 701.880i | −0.395242 | + | 1.21643i | 0.533531 | + | 0.845780i | \(0.320865\pi\) |
−0.928773 | + | 0.370649i | \(0.879135\pi\) | |||||||
\(578\) | −356.436 | − | 115.813i | −0.616671 | − | 0.200368i | ||||
\(579\) | 723.261 | − | 525.480i | 1.24916 | − | 0.907565i | ||||
\(580\) | 1495.06 | + | 1086.23i | 2.57770 | + | 1.87281i | ||||
\(581\) | −302.813 | + | 98.3898i | −0.521192 | + | 0.169346i | ||||
\(582\) | − | 616.892i | − | 1.05995i | ||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 736.291i | 1.26077i | ||||||||
\(585\) | −227.109 | + | 73.7923i | −0.388221 | + | 0.126141i | ||||
\(586\) | 1281.48 | + | 931.052i | 2.18683 | + | 1.58883i | ||||
\(587\) | 553.648 | + | 762.030i | 0.943181 | + | 1.29818i | 0.954490 | + | 0.298242i | \(0.0964002\pi\) |
−0.0113088 | + | 0.999936i | \(0.503600\pi\) | |||||||
\(588\) | −97.3404 | + | 299.583i | −0.165545 | + | 0.509495i | ||||
\(589\) | −48.2067 | + | 148.365i | −0.0818449 | + | 0.251893i | ||||
\(590\) | 857.764 | + | 1180.61i | 1.45384 | + | 2.00103i | ||||
\(591\) | −233.936 | + | 321.985i | −0.395830 | + | 0.544813i | ||||
\(592\) | 46.3525 | + | 142.658i | 0.0782982 | + | 0.240977i | ||||
\(593\) | − | 543.926i | − | 0.917245i | −0.888631 | − | 0.458623i | \(-0.848343\pi\) | ||
0.888631 | − | 0.458623i | \(-0.151657\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −704.000 | −1.18319 | ||||||||
\(596\) | 618.242 | − | 200.879i | 1.03732 | − | 0.337045i | ||||
\(597\) | 101.936 | + | 74.0609i | 0.170747 | + | 0.124055i | ||||
\(598\) | 71.1935 | − | 51.7251i | 0.119053 | − | 0.0864968i | ||||
\(599\) | −44.1602 | − | 14.3485i | −0.0737231 | − | 0.0239541i | 0.271923 | − | 0.962319i | \(-0.412340\pi\) |
−0.345646 | + | 0.938365i | \(0.612340\pi\) | |||||||
\(600\) | −539.385 | − | 175.257i | −0.898975 | − | 0.292095i | ||||
\(601\) | 438.487 | − | 318.580i | 0.729596 | − | 0.530083i | −0.159840 | − | 0.987143i | \(-0.551098\pi\) |
0.889436 | + | 0.457060i | \(0.151098\pi\) | |||||||
\(602\) | 655.020 | − | 901.557i | 1.08807 | − | 1.49760i | ||||
\(603\) | 5.56231 | + | 17.1190i | 0.00922439 | + | 0.0283897i | ||||
\(604\) | −1120.00 | −1.85430 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1056.00 | −1.74257 | ||||||||
\(607\) | 216.312 | + | 665.740i | 0.356362 | + | 1.09677i | 0.955215 | + | 0.295911i | \(0.0956233\pi\) |
−0.598853 | + | 0.800859i | \(0.704377\pi\) | |||||||
\(608\) | 81.8775 | − | 112.695i | 0.134667 | − | 0.185353i | ||||
\(609\) | −561.445 | − | 772.763i | −0.921914 | − | 1.26891i | ||||
\(610\) | 81.5805 | − | 251.079i | 0.133739 | − | 0.411605i | ||||
\(611\) | −328.047 | − | 106.589i | −0.536902 | − | 0.174450i | ||||
\(612\) | −491.265 | − | 676.168i | −0.802720 | − | 1.10485i | ||||
\(613\) | 618.089 | + | 449.068i | 1.00830 | + | 0.732574i | 0.963852 | − | 0.266438i | \(-0.0858466\pi\) |
0.0444496 | + | 0.999012i | \(0.485847\pi\) | |||||||
\(614\) | −271.270 | + | 88.1408i | −0.441807 | + | 0.143552i | ||||
\(615\) | −264.000 | −0.429268 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 39.7995i | 0.0645049i | 0.999480 | + | 0.0322524i | \(0.0102680\pi\) | ||||
−0.999480 | + | 0.0322524i | \(0.989732\pi\) | |||||||
\(618\) | 700.254 | − | 227.526i | 1.13310 | − | 0.368166i | ||||
\(619\) | 600.291 | + | 436.137i | 0.969775 | + | 0.704583i | 0.955400 | − | 0.295314i | \(-0.0954243\pi\) |
0.0143746 | + | 0.999897i | \(0.495424\pi\) | |||||||
\(620\) | 709.605 | + | 976.687i | 1.14452 | + | 1.57530i | ||||
\(621\) | 170.332 | + | 55.3442i | 0.274287 | + | 0.0891212i | ||||
\(622\) | 20.3951 | − | 62.7697i | 0.0327896 | − | 0.100916i | ||||
\(623\) | 561.445 | + | 772.763i | 0.901196 | + | 1.24039i | ||||
\(624\) | 48.5410 | + | 35.2671i | 0.0777901 | + | 0.0565178i | ||||
\(625\) | −228.364 | − | 702.831i | −0.365382 | − | 1.12453i | ||||
\(626\) | − | 325.029i | − | 0.519216i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1274.00 | −2.02866 | ||||||||
\(629\) | 378.516 | − | 122.987i | 0.601774 | − | 0.195528i | ||||
\(630\) | 1281.48 | + | 931.052i | 2.03410 | + | 1.47786i | ||||
\(631\) | 331.697 | − | 240.992i | 0.525669 | − | 0.381921i | −0.293066 | − | 0.956092i | \(-0.594676\pi\) |
0.818735 | + | 0.574171i | \(0.194676\pi\) | |||||||
\(632\) | 378.516 | + | 122.987i | 0.598917 | + | 0.194600i | ||||
\(633\) | −228.055 | + | 701.880i | −0.360276 | + | 1.10881i | ||||
\(634\) | −836.524 | + | 607.770i | −1.31944 | + | 0.958628i | ||||
\(635\) | 732.998 | − | 1008.89i | 1.15433 | − | 1.58880i | ||||
\(636\) | −1192.32 | + | 387.410i | −1.87472 | + | 0.609135i | ||||
\(637\) | −60.0000 | −0.0941915 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 537.293i | − | 0.840834i | ||||||
\(640\) | −469.088 | − | 1443.70i | −0.732950 | − | 2.25579i | ||||
\(641\) | −444.478 | + | 611.771i | −0.693413 | + | 0.954401i | 0.306584 | + | 0.951844i | \(0.400814\pi\) |
−0.999997 | + | 0.00255720i | \(0.999186\pi\) | |||||||
\(642\) | −320.371 | + | 232.763i | −0.499020 | + | 0.362559i | ||||
\(643\) | 275.025 | − | 846.440i | 0.427722 | − | 1.31639i | −0.472642 | − | 0.881255i | \(-0.656700\pi\) |
0.900364 | − | 0.435138i | \(-0.143300\pi\) | |||||||
\(644\) | −353.281 | − | 114.788i | −0.548573 | − | 0.178242i | ||||
\(645\) | −491.265 | − | 676.168i | −0.761651 | − | 1.04832i | ||||
\(646\) | 213.580 | + | 155.175i | 0.330620 | + | 0.240209i | ||||
\(647\) | −460.527 | + | 149.634i | −0.711789 | + | 0.231274i | −0.642460 | − | 0.766320i | \(-0.722086\pi\) |
−0.0693294 | + | 0.997594i | \(0.522086\pi\) | |||||||
\(648\) | 805.940i | 1.24373i | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | − | 252.063i | − | 0.387790i | ||||||
\(651\) | −192.827 | − | 593.459i | −0.296201 | − | 0.911612i | ||||
\(652\) | −1642.30 | − | 1193.20i | −2.51887 | − | 1.83007i | ||||
\(653\) | −230.037 | − | 316.618i | −0.352277 | − | 0.484867i | 0.595700 | − | 0.803207i | \(-0.296875\pi\) |
−0.947977 | + | 0.318340i | \(0.896875\pi\) | |||||||
\(654\) | −1892.58 | − | 614.936i | −2.89385 | − | 0.940269i | ||||
\(655\) | −81.5805 | + | 251.079i | −0.124550 | + | 0.383327i | ||||
\(656\) | 38.9893 | + | 53.6641i | 0.0594349 | + | 0.0818051i | ||||
\(657\) | −538.805 | − | 391.465i | −0.820099 | − | 0.595837i | ||||
\(658\) | 707.031 | + | 2176.02i | 1.07452 | + | 3.30702i | ||||
\(659\) | 384.728i | 0.583806i | 0.956448 | + | 0.291903i | \(0.0942885\pi\) | ||||
−0.956448 | + | 0.291903i | \(0.905711\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −746.000 | −1.12859 | −0.564297 | − | 0.825572i | \(-0.690853\pi\) | ||||
−0.564297 | + | 0.825572i | \(0.690853\pi\) | |||||||
\(662\) | −687.637 | + | 223.427i | −1.03873 | + | 0.337503i | ||||
\(663\) | 93.5742 | − | 128.794i | 0.141138 | − | 0.194259i | ||||
\(664\) | 320.371 | − | 232.763i | 0.482486 | − | 0.350547i | ||||
\(665\) | −302.813 | − | 98.3898i | −0.455357 | − | 0.147955i | ||||
\(666\) | −851.660 | − | 276.721i | −1.27877 | − | 0.415497i | ||||
\(667\) | 213.580 | − | 155.175i | 0.320211 | − | 0.232647i | ||||
\(668\) | −982.529 | + | 1352.34i | −1.47085 | + | 2.02445i | ||||
\(669\) | −279.969 | − | 861.657i | −0.418489 | − | 1.28798i | ||||
\(670\) | −44.0000 | −0.0656716 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 557.193i | 0.829156i | ||||||||
\(673\) | 195.917 | + | 602.970i | 0.291110 | + | 0.895943i | 0.984501 | + | 0.175382i | \(0.0561159\pi\) |
−0.693391 | + | 0.720562i | \(0.743884\pi\) | |||||||
\(674\) | 541.951 | − | 745.931i | 0.804081 | − | 1.10672i | ||||
\(675\) | 415.026 | − | 301.534i | 0.614853 | − | 0.446717i | ||||
\(676\) | 330.957 | − | 1018.58i | 0.489582 | − | 1.50678i | ||||
\(677\) | −757.031 | − | 245.974i | −1.11821 | − | 0.363330i | −0.309129 | − | 0.951020i | \(-0.600037\pi\) |
−0.809086 | + | 0.587690i | \(0.800037\pi\) | |||||||
\(678\) | 320.371 | − | 232.763i | 0.472523 | − | 0.343308i | ||||
\(679\) | −401.272 | − | 291.541i | −0.590976 | − | 0.429369i | ||||
\(680\) | 832.735 | − | 270.572i | 1.22461 | − | 0.397900i | ||||
\(681\) | 596.992i | 0.876641i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 451.061i | − | 0.660411i | −0.943909 | − | 0.330206i | \(-0.892882\pi\) | ||
0.943909 | − | 0.330206i | \(-0.107118\pi\) | |||||||
\(684\) | −116.808 | − | 359.499i | −0.170773 | − | 0.525584i | ||||
\(685\) | −569.548 | − | 413.801i | −0.831457 | − | 0.604089i | ||||
\(686\) | −530.254 | − | 729.832i | −0.772965 | − | 1.06390i | ||||
\(687\) | 139.058 | − | 427.975i | 0.202413 | − | 0.622963i | ||||
\(688\) | −64.8936 | + | 199.722i | −0.0943220 | + | 0.290293i | ||||
\(689\) | −140.361 | − | 193.191i | −0.203717 | − | 0.280393i | ||||
\(690\) | −257.329 | + | 354.183i | −0.372941 | + | 0.513309i | ||||
\(691\) | 141.530 | + | 435.584i | 0.204819 | + | 0.630367i | 0.999721 | + | 0.0236296i | \(0.00752222\pi\) |
−0.794902 | + | 0.606738i | \(0.792478\pi\) | |||||||
\(692\) | 1392.98i | 2.01298i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1100.00 | −1.58501 | ||||||||
\(695\) | 466.836 | − | 151.684i | 0.671707 | − | 0.218251i | ||||
\(696\) | 961.112 | + | 698.289i | 1.38091 | + | 1.00329i | ||||
\(697\) | 142.387 | − | 103.450i | 0.204285 | − | 0.148422i | ||||
\(698\) | 1021.99 | + | 332.065i | 1.46417 | + | 0.475738i | ||||
\(699\) | 1249.10 | + | 405.858i | 1.78698 | + | 0.580626i | ||||
\(700\) | −860.794 | + | 625.404i | −1.22971 | + | 0.893434i | ||||
\(701\) | −296.318 | + | 407.847i | −0.422708 | + | 0.581808i | −0.966260 | − | 0.257568i | \(-0.917079\pi\) |
0.543552 | + | 0.839375i | \(0.317079\pi\) | |||||||
\(702\) | −340.664 | + | 110.688i | −0.485277 | + | 0.157676i | ||||
\(703\) | 180.000 | 0.256046 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1716.00 | 2.43404 | ||||||||
\(706\) | 407.902 | + | 1255.39i | 0.577765 | + | 1.77818i | ||||
\(707\) | −499.063 | + | 686.901i | −0.705888 | + | 0.971571i | ||||
\(708\) | 818.775 | + | 1126.95i | 1.15646 | + | 1.59173i | ||||
\(709\) | −173.668 | + | 534.494i | −0.244947 | + | 0.753870i | 0.750698 | + | 0.660646i | \(0.229717\pi\) |
−0.995645 | + | 0.0932243i | \(0.970283\pi\) | |||||||
\(710\) | 1249.10 | + | 405.858i | 1.75930 | + | 0.571631i | ||||
\(711\) | −291.246 | + | 211.603i | −0.409629 | + | 0.297613i | ||||
\(712\) | −961.112 | − | 698.289i | −1.34988 | − | 0.980743i | ||||
\(713\) | 164.023 | − | 53.2945i | 0.230047 | − | 0.0747468i | ||||
\(714\) | −1056.00 | −1.47899 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 1392.98i | − | 1.94551i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −818.725 | − | 594.839i | −1.14029 | − | 0.828466i | ||||
\(719\) | −198.845 | − | 273.687i | −0.276558 | − | 0.380650i | 0.648032 | − | 0.761613i | \(-0.275592\pi\) |
−0.924590 | + | 0.380964i | \(0.875592\pi\) | |||||||
\(720\) | −283.887 | − | 92.2404i | −0.394287 | − | 0.128112i | ||||
\(721\) | 182.938 | − | 563.025i | 0.253728 | − | 0.780895i | ||||
\(722\) | −633.576 | − | 872.042i | −0.877528 | − | 1.20781i | ||||
\(723\) | 315.517 | + | 229.236i | 0.436399 | + | 0.317063i | ||||
\(724\) | −21.6312 | − | 66.5740i | −0.0298773 | − | 0.0919530i | ||||
\(725\) | − | 756.190i | − | 1.04302i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −42.0000 | −0.0577717 | −0.0288858 | − | 0.999583i | \(-0.509196\pi\) | ||||
−0.0288858 | + | 0.999583i | \(0.509196\pi\) | |||||||
\(728\) | 302.813 | − | 98.3898i | 0.415951 | − | 0.135151i | ||||
\(729\) | −589.773 | − | 428.495i | −0.809017 | − | 0.587785i | ||||
\(730\) | 1317.08 | − | 956.914i | 1.80422 | − | 1.31084i | ||||
\(731\) | 529.922 | + | 172.182i | 0.724927 | + | 0.235543i | ||||
\(732\) | 77.8723 | − | 239.666i | 0.106383 | − | 0.327413i | ||||
\(733\) | −504.827 | + | 366.778i | −0.688713 | + | 0.500379i | −0.876237 | − | 0.481881i | \(-0.839954\pi\) |
0.187524 | + | 0.982260i | \(0.439954\pi\) | |||||||
\(734\) | 541.951 | − | 745.931i | 0.738353 | − | 1.01626i | ||||
\(735\) | 283.887 | − | 92.2404i | 0.386241 | − | 0.125497i | ||||
\(736\) | −154.000 | −0.209239 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −396.000 | −0.536585 | ||||||||
\(739\) | −211.986 | − | 652.425i | −0.286855 | − | 0.882848i | −0.985837 | − | 0.167709i | \(-0.946363\pi\) |
0.698982 | − | 0.715139i | \(-0.253637\pi\) | |||||||
\(740\) | 818.775 | − | 1126.95i | 1.10645 | − | 1.52290i | ||||
\(741\) | 58.2492 | − | 42.3205i | 0.0786089 | − | 0.0571127i | ||||
\(742\) | −489.483 | + | 1506.47i | −0.659680 | + | 2.03029i | ||||
\(743\) | 820.117 | + | 266.472i | 1.10379 | + | 0.358644i | 0.803561 | − | 0.595223i | \(-0.202936\pi\) |
0.300231 | + | 0.953866i | \(0.402936\pi\) | |||||||
\(744\) | 456.174 | + | 627.870i | 0.613138 | + | 0.843912i | ||||
\(745\) | −498.354 | − | 362.076i | −0.668932 | − | 0.486008i | ||||
\(746\) | 214.492 | − | 69.6928i | 0.287523 | − | 0.0934219i | ||||
\(747\) | 358.195i | 0.479512i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 318.396i | 0.425095i | ||||||||
\(750\) | −122.371 | − | 376.618i | −0.163161 | − | 0.502158i | ||||
\(751\) | −76.0476 | − | 55.2518i | −0.101262 | − | 0.0735710i | 0.536002 | − | 0.844217i | \(-0.319934\pi\) |
−0.637264 | + | 0.770646i | \(0.719934\pi\) | |||||||
\(752\) | −253.430 | − | 348.817i | −0.337008 | − | 0.463852i | ||||
\(753\) | 832.735 | + | 270.572i | 1.10589 | + | 0.359325i | ||||
\(754\) | −163.161 | + | 502.158i | −0.216394 | + | 0.665992i | ||||
\(755\) | 623.828 | + | 858.626i | 0.826263 | + | 1.13725i | ||||
\(756\) | 1223.23 | + | 888.731i | 1.61803 | + | 1.17557i | ||||
\(757\) | 345.481 | + | 1063.28i | 0.456382 | + | 1.40460i | 0.869505 | + | 0.493924i | \(0.164438\pi\) |
−0.413124 | + | 0.910675i | \(0.635562\pi\) | |||||||
\(758\) | − | 2222.14i | − | 2.93158i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 396.000 | 0.521053 | ||||||||
\(761\) | −1097.70 | + | 356.663i | −1.44244 | + | 0.468677i | −0.922657 | − | 0.385623i | \(-0.873987\pi\) |
−0.519782 | + | 0.854299i | \(0.673987\pi\) | |||||||
\(762\) | 1099.50 | − | 1513.33i | 1.44291 | − | 1.98599i | ||||
\(763\) | −1294.43 | + | 940.456i | −1.69650 | + | 1.23258i | ||||
\(764\) | 750.723 | + | 243.925i | 0.982622 | + | 0.319273i | ||||
\(765\) | −244.741 | + | 753.237i | −0.319923 | + | 0.984623i | ||||
\(766\) | 88.9919 | − | 64.6564i | 0.116177 | − | 0.0844078i | ||||
\(767\) | −155.957 | + | 214.656i | −0.203334 | + | 0.279865i | ||||
\(768\) | −343.936 | − | 1058.53i | −0.447833 | − | 1.37829i | ||||
\(769\) | −1274.00 | −1.65670 | −0.828349 | − | 0.560213i | \(-0.810719\pi\) | ||||
−0.828349 | + | 0.560213i | \(0.810719\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1472.58i | 1.90996i | ||||||||
\(772\) | 644.609 | + | 1983.90i | 0.834986 | + | 2.56982i | ||||
\(773\) | −549.749 | + | 756.664i | −0.711188 | + | 0.978867i | 0.288582 | + | 0.957455i | \(0.406816\pi\) |
−0.999771 | + | 0.0214117i | \(0.993184\pi\) | |||||||
\(774\) | −736.897 | − | 1014.25i | −0.952063 | − | 1.31040i | ||||
\(775\) | 152.654 | − | 469.822i | 0.196973 | − | 0.606222i | ||||
\(776\) | 586.699 | + | 190.630i | 0.756056 | + | 0.245657i | ||||
\(777\) | −582.492 | + | 423.205i | −0.749668 | + | 0.544666i | ||||
\(778\) | 1121.30 | + | 814.670i | 1.44126 | + | 1.04713i | ||||
\(779\) | 75.7031 | − | 24.5974i | 0.0971799 | − | 0.0315757i | ||||
\(780\) | − | 557.193i | − | 0.714350i | ||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − | 291.863i | − | 0.373226i | ||||||
\(783\) | −1021.99 | + | 332.065i | −1.30523 | + | 0.424094i | ||||
\(784\) | −60.6763 | − | 44.0839i | −0.0773932 | − | 0.0562295i | ||||
\(785\) | 709.605 | + | 976.687i | 0.903955 | + | 1.24419i | ||||
\(786\) | −122.371 | + | 376.618i | −0.155688 | + | 0.479158i | ||||
\(787\) | −92.0871 | + | 283.415i | −0.117010 | + | 0.360121i | −0.992361 | − | 0.123368i | \(-0.960630\pi\) |
0.875351 | + | 0.483488i | \(0.160630\pi\) | |||||||
\(788\) | −545.850 | − | 751.298i | −0.692703 | − | 0.953423i | ||||
\(789\) | −397.690 | + | 547.374i | −0.504044 | + | 0.693757i | ||||
\(790\) | −271.935 | − | 836.930i | −0.344221 | − | 1.05940i | ||||
\(791\) | − | 318.396i | − | 0.402523i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 48.0000 | 0.0605296 | ||||||||
\(794\) | −271.270 | + | 88.1408i | −0.341649 | + | 0.111009i | ||||
\(795\) | 961.112 | + | 698.289i | 1.20895 | + | 0.878351i | ||||
\(796\) | −237.851 | + | 172.809i | −0.298808 | + | 0.217097i | ||||
\(797\) | 498.379 | + | 161.933i | 0.625319 | + | 0.203178i | 0.604500 | − | 0.796605i | \(-0.293373\pi\) |
0.0208184 | + | 0.999783i | \(0.493373\pi\) | |||||||
\(798\) | −454.219 | − | 147.585i | −0.569197 | − | 0.184943i | ||||
\(799\) | −925.515 | + | 672.426i | −1.15834 | + | 0.841585i | ||||
\(800\) | −259.279 | + | 356.866i | −0.324098 | + | 0.446083i | ||||
\(801\) | 1021.99 | − | 332.065i | 1.27590 | − | 0.414564i | ||||
\(802\) | −836.000 | −1.04239 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −42.0000 | −0.0522388 | ||||||||
\(805\) | 108.774 | + | 334.772i | 0.135123 | + | 0.415866i | ||||
\(806\) | −202.744 | + | 279.053i | −0.251544 | + | 0.346220i | ||||
\(807\) | −128.665 | − | 177.092i | −0.159436 | − | 0.219444i | ||||
\(808\) | 326.322 | − | 1004.32i | 0.403864 | − | 1.24296i | ||||
\(809\) | 870.586 | + | 282.871i | 1.07613 | + | 0.349655i | 0.792871 | − | 0.609390i | \(-0.208586\pi\) |
0.283256 | + | 0.959044i | \(0.408586\pi\) | |||||||
\(810\) | 1441.67 | − | 1047.43i | 1.77984 | − | 1.29313i | ||||
\(811\) | −147.241 | − | 106.977i | −0.181555 | − | 0.131907i | 0.493296 | − | 0.869862i | \(-0.335792\pi\) |
−0.674851 | + | 0.737954i | \(0.735792\pi\) | |||||||
\(812\) | 2119.69 | − | 688.728i | 2.61045 | − | 0.848188i | ||||
\(813\) | 1344.00 | 1.65314 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1923.64i | 2.36030i | ||||||||
\(816\) | 189.258 | − | 61.4936i | 0.231934 | − | 0.0753598i | ||||
\(817\) | 203.872 | + | 148.122i | 0.249538 | + | 0.181300i | ||||
\(818\) | −994.226 | − | 1368.43i | −1.21544 | − | 1.67290i | ||||
\(819\) | −88.9969 | + | 273.904i | −0.108665 | + | 0.334437i | ||||
\(820\) | 190.354 | − | 585.851i | 0.232140 | − | 0.714452i | ||||
\(821\) | −483.467 | − | 665.435i | −0.588876 | − | 0.810518i | 0.405758 | − | 0.913981i | \(-0.367008\pi\) |
−0.994633 | + | 0.103463i | \(0.967008\pi\) | |||||||
\(822\) | −854.322 | − | 620.701i | −1.03932 | − | 0.755111i | ||||
\(823\) | −76.0182 | − | 233.960i | −0.0923672 | − | 0.284277i | 0.894191 | − | 0.447685i | \(-0.147751\pi\) |
−0.986559 | + | 0.163408i | \(0.947751\pi\) | |||||||
\(824\) | 736.291i | 0.893557i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1760.00 | 2.13075 | ||||||||
\(827\) | 517.305 | − | 168.083i | 0.625520 | − | 0.203244i | 0.0209303 | − | 0.999781i | \(-0.493337\pi\) |
0.604589 | + | 0.796537i | \(0.293337\pi\) | |||||||
\(828\) | −245.632 | + | 338.084i | −0.296657 | + | 0.408314i | ||||
\(829\) | −202.254 | + | 146.946i | −0.243974 | + | 0.177257i | −0.703052 | − | 0.711139i | \(-0.748180\pi\) |
0.459078 | + | 0.888396i | \(0.348180\pi\) | |||||||
\(830\) | −832.735 | − | 270.572i | −1.00329 | − | 0.325990i | ||||
\(831\) | 241.033 | − | 741.824i | 0.290052 | − | 0.892688i | ||||
\(832\) | 313.899 | − | 228.061i | 0.377282 | − | 0.274111i | ||||
\(833\) | −116.968 | + | 160.992i | −0.140418 | + | 0.193268i | ||||
\(834\) | 700.254 | − | 227.526i | 0.839633 | − | 0.272813i | ||||
\(835\) | 1584.00 | 1.89701 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −702.000 | −0.838710 | ||||||||
\(838\) | −543.870 | − | 1673.86i | −0.649009 | − | 1.99745i | ||||
\(839\) | 276.824 | − | 381.015i | 0.329945 | − | 0.454130i | −0.611526 | − | 0.791224i | \(-0.709444\pi\) |
0.941471 | + | 0.337094i | \(0.109444\pi\) | |||||||
\(840\) | −1281.48 | + | 931.052i | −1.52557 | + | 1.10840i | ||||
\(841\) | −229.600 | + | 706.635i | −0.273008 | + | 0.840232i | ||||
\(842\) | 536.231 | + | 174.232i | 0.636853 | + | 0.206926i | ||||
\(843\) | −350.903 | − | 482.977i | −0.416255 | − | 0.572927i | ||||
\(844\) | −1393.13 | − | 1012.17i | −1.65062 | − | 1.19925i | ||||
\(845\) | −965.215 | + | 313.617i | −1.14227 | + | 0.371145i | ||||
\(846\) | 2574.00 | 3.04255 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 298.496i | − | 0.352000i | ||||||
\(849\) | 46.3525 | + | 142.658i | 0.0545966 | + | 0.168031i | ||||
\(850\) | −676.338 | − | 491.388i | −0.795692 | − | 0.578104i | ||||
\(851\) | −116.968 | − | 160.992i | −0.137447 | − | 0.189180i | ||||
\(852\) | 1192.32 | + | 387.410i | 1.39944 | + | 0.454706i | ||||
\(853\) | −17.3050 | + | 53.2592i | −0.0202872 | + | 0.0624375i | −0.960688 | − | 0.277632i | \(-0.910451\pi\) |
0.940400 | + | 0.340069i | \(0.110451\pi\) | |||||||
\(854\) | −187.148 | − | 257.588i | −0.219143 | − | 0.301625i | ||||
\(855\) | −210.542 | + | 289.786i | −0.246248 | + | 0.338931i | ||||
\(856\) | −122.371 | − | 376.618i | −0.142956 | − | 0.439975i | ||||
\(857\) | 252.063i | 0.294123i | 0.989127 | + | 0.147062i | \(0.0469815\pi\) | ||||
−0.989127 | + | 0.147062i | \(0.953018\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1278.00 | 1.48778 | 0.743888 | − | 0.668304i | \(-0.232979\pi\) | ||||
0.743888 | + | 0.668304i | \(0.232979\pi\) | |||||||
\(860\) | 1854.73 | − | 602.637i | 2.15666 | − | 0.700741i | ||||
\(861\) | −187.148 | + | 257.588i | −0.217362 | + | 0.299173i | ||||
\(862\) | 747.532 | − | 543.114i | 0.867206 | − | 0.630062i | ||||
\(863\) | −1078.77 | − | 350.514i | −1.25002 | − | 0.406157i | −0.392094 | − | 0.919925i | \(-0.628249\pi\) |
−0.857929 | + | 0.513768i | \(0.828249\pi\) | |||||||
\(864\) | 596.162 | + | 193.705i | 0.690003 | + | 0.224195i | ||||
\(865\) | 1067.90 | − | 775.877i | 1.23457 | − | 0.896967i | ||||
\(866\) | 1056.61 | − | 1454.30i | 1.22010 | − | 1.67933i | ||||
\(867\) | 104.757 | + | 322.408i | 0.120827 | + | 0.371866i | ||||
\(868\) | 1456.00 | 1.67742 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | − | 2626.77i | − | 3.01927i | ||||||
\(871\) | −2.47214 | − | 7.60845i | −0.00283827 | − | 0.00873531i | ||||
\(872\) | 1169.68 | − | 1609.92i | 1.34137 | − | 1.84624i | ||||
\(873\) | −451.431 | + | 327.984i | −0.517104 | + | 0.375698i | ||||
\(874\) | 40.7902 | − | 125.539i | 0.0466708 | − | 0.143638i | ||||
\(875\) | −302.813 | − | 98.3898i | −0.346072 | − | 0.112445i | ||||
\(876\) | 1257.21 | − | 913.418i | 1.43517 | − | 1.04271i | ||||
\(877\) | 368.912 | + | 268.030i | 0.420652 | + | 0.305622i | 0.777900 | − | 0.628388i | \(-0.216285\pi\) |
−0.357248 | + | 0.934010i | \(0.616285\pi\) | |||||||
\(878\) | −1034.61 | + | 336.165i | −1.17837 | + | 0.382876i | ||||
\(879\) | − | 1432.78i | − | 1.63001i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 610.259i | − | 0.692689i | −0.938107 | − | 0.346344i | \(-0.887423\pi\) | ||
0.938107 | − | 0.346344i | \(-0.112577\pi\) | |||||||
\(882\) | 425.830 | − | 138.361i | 0.482801 | − | 0.156871i | ||||
\(883\) | 885.065 | + | 643.037i | 1.00234 | + | 0.728241i | 0.962588 | − | 0.270968i | \(-0.0873439\pi\) |
0.0397499 | + | 0.999210i | \(0.487344\pi\) | |||||||
\(884\) | 218.340 | + | 300.519i | 0.246991 | + | 0.339954i | ||||
\(885\) | 407.902 | − | 1255.39i | 0.460907 | − | 1.41852i | ||||
\(886\) | 135.967 | − | 418.465i | 0.153462 | − | 0.472308i | ||||
\(887\) | 85.7764 | + | 118.061i | 0.0967039 | + | 0.133102i | 0.854627 | − | 0.519242i | \(-0.173786\pi\) |
−0.757923 | + | 0.652344i | \(0.773786\pi\) | |||||||
\(888\) | 526.355 | − | 724.466i | 0.592742 | − | 0.815840i | ||||
\(889\) | −464.762 | − | 1430.39i | −0.522791 | − | 1.60899i | ||||
\(890\) | 2626.77i | 2.95142i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2114.00 | 2.36996 | ||||||||
\(893\) | −492.070 | + | 159.883i | −0.551031 | + | 0.179041i | ||||
\(894\) | −747.532 | − | 543.114i | −0.836165 | − | 0.607510i | ||||
\(895\) | −1067.90 | + | 775.877i | −1.19319 | + | 0.866901i | ||||
\(896\) | −1741.17 | − | 565.741i | −1.94327 | − | 0.631408i | ||||
\(897\) | −75.7031 | − | 24.5974i | −0.0843959 | − | 0.0274219i | ||||
\(898\) | 1210.29 | − | 879.327i | 1.34776 | − | 0.979206i | ||||
\(899\) | −608.232 | + | 837.160i | −0.676566 | + | 0.931213i | ||||
\(900\) | 369.893 | + | 1138.41i | 0.410993 | + | 1.26491i | ||||
\(901\) | −792.000 | −0.879023 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1008.00 | −1.11628 | ||||||||
\(904\) | 122.371 | + | 376.618i | 0.135366 | + | 0.416613i | ||||
\(905\) | −38.9893 | + | 53.6641i | −0.0430821 | + | 0.0592974i | ||||
\(906\) | 935.742 | + | 1287.94i | 1.03283 | + | 1.42157i | ||||
\(907\) | 57.4772 | − | 176.897i | 0.0633706 | − | 0.195035i | −0.914358 | − | 0.404906i | \(-0.867304\pi\) |
0.977729 | + | 0.209871i | \(0.0673044\pi\) | |||||||
\(908\) | −1324.80 | − | 430.455i | −1.45904 | − | 0.474070i | ||||
\(909\) | 561.445 | + | 772.763i | 0.617652 | + | 0.850125i | ||||
\(910\) | −569.548 | − | 413.801i | −0.625877 | − | 0.454726i | ||||
\(911\) | −813.809 | + | 264.423i | −0.893314 | + | 0.290255i | −0.719475 | − | 0.694519i | \(-0.755617\pi\) |
−0.173839 | + | 0.984774i | \(0.555617\pi\) | |||||||
\(912\) | 90.0000 | 0.0986842 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 1134.29i | 1.24101i | ||||||||
\(915\) | −227.109 | + | 73.7923i | −0.248207 | + | 0.0806474i | ||||
\(916\) | 849.468 | + | 617.175i | 0.927367 | + | 0.673771i | ||||
\(917\) | 187.148 | + | 257.588i | 0.204088 | + | 0.280903i | ||||
\(918\) | −367.112 | + | 1129.86i | −0.399904 | + | 1.23078i | ||||
\(919\) | 132.259 | − | 407.052i | 0.143917 | − | 0.442929i | −0.852954 | − | 0.521987i | \(-0.825191\pi\) |
0.996870 | + | 0.0790573i | \(0.0251910\pi\) | |||||||
\(920\) | −257.329 | − | 354.183i | −0.279706 | − | 0.384982i | ||||
\(921\) | 208.726 | + | 151.649i | 0.226630 | + | 0.164656i | ||||
\(922\) | 81.5805 | + | 251.079i | 0.0884821 | + | 0.272320i | ||||
\(923\) | 238.797i | 0.258718i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −570.000 | −0.616216 | ||||||||
\(926\) | −271.270 | + | 88.1408i | −0.292948 | + | 0.0951845i | ||||
\(927\) | −538.805 | − | 391.465i | −0.581236 | − | 0.422292i | ||||
\(928\) | 747.532 | − | 543.114i | 0.805530 | − | 0.585252i | ||||
\(929\) | 605.625 | + | 196.780i | 0.651911 | + | 0.211819i | 0.616256 | − | 0.787546i | \(-0.288648\pi\) |
0.0356543 | + | 0.999364i | \(0.488648\pi\) | |||||||
\(930\) | 530.273 | − | 1632.01i | 0.570186 | − | 1.75485i | ||||
\(931\) | −72.8115 | + | 52.9007i | −0.0782079 | + | 0.0568213i | ||||
\(932\) | −1801.30 | + | 2479.28i | −1.93273 | + | 2.66017i | ||||
\(933\) | −56.7774 | + | 18.4481i | −0.0608546 | + | 0.0197729i | ||||
\(934\) | −1980.00 | −2.11991 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | − | 358.195i | − | 0.382687i | ||||||
\(937\) | −89.6149 | − | 275.806i | −0.0956403 | − | 0.294350i | 0.891780 | − | 0.452470i | \(-0.149457\pi\) |
−0.987420 | + | 0.158119i | \(0.949457\pi\) | |||||||
\(938\) | −31.1914 | + | 42.9313i | −0.0332531 | + | 0.0457690i | ||||
\(939\) | −237.851 | + | 172.809i | −0.253302 | + | 0.184035i | ||||
\(940\) | −1237.30 | + | 3808.03i | −1.31628 | + | 4.05110i | ||||
\(941\) | −832.735 | − | 270.572i | −0.884946 | − | 0.287537i | −0.168937 | − | 0.985627i | \(-0.554033\pi\) |
−0.716010 | + | 0.698090i | \(0.754033\pi\) | |||||||
\(942\) | 1064.41 | + | 1465.03i | 1.12994 | + | 1.55523i | ||||
\(943\) | −71.1935 | − | 51.7251i | −0.0754968 | − | 0.0548516i | ||||
\(944\) | −315.430 | + | 102.489i | −0.334142 | + | 0.108569i | ||||
\(945\) | − | 1432.78i | − | 1.51617i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 79.5990i | − | 0.0840538i | −0.999116 | − | 0.0420269i | \(-0.986618\pi\) | ||
0.999116 | − | 0.0420269i | \(-0.0133815\pi\) | |||||||
\(948\) | −259.574 | − | 798.887i | −0.273813 | − | 0.842708i | ||||
\(949\) | 239.469 | + | 173.984i | 0.252338 | + | 0.183334i | ||||
\(950\) | −222.239 | − | 305.885i | −0.233936 | − | 0.321985i | ||||
\(951\) | 889.512 | + | 289.020i | 0.935344 | + | 0.303912i | ||||
\(952\) | 326.322 | − | 1004.32i | 0.342775 | − | 1.05495i | ||||
\(953\) | −460.073 | − | 633.237i | −0.482763 | − | 0.664466i | 0.496270 | − | 0.868168i | \(-0.334703\pi\) |
−0.979033 | + | 0.203702i | \(0.934703\pi\) | |||||||
\(954\) | 1441.67 | + | 1047.43i | 1.51118 | + | 1.09794i | ||||
\(955\) | −231.145 | − | 711.390i | −0.242036 | − | 0.744911i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −748.000 | −0.780793 | ||||||||
\(959\) | −807.500 | + | 262.373i | −0.842023 | + | 0.273590i | ||||
\(960\) | −1134.59 | + | 1561.63i | −1.18186 | + | 1.62669i | ||||
\(961\) | 230.570 | − | 167.519i | 0.239927 | − | 0.174317i | ||||
\(962\) | 378.516 | + | 122.987i | 0.393467 | + | 0.127845i | ||||
\(963\) | 340.664 | + | 110.688i | 0.353753 | + | 0.114941i | ||||
\(964\) | −736.205 | + | 534.885i | −0.763699 | + | 0.554860i | ||||
\(965\) | 1161.88 | − | 1599.19i | 1.20402 | − | 1.65719i | ||||
\(966\) | 163.161 | + | 502.158i | 0.168904 | + | 0.519832i | ||||
\(967\) | −460.000 | −0.475698 | −0.237849 | − | 0.971302i | \(-0.576442\pi\) | ||||
−0.237849 | + | 0.971302i | \(0.576442\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 238.797i | − | 0.246437i | ||||||
\(970\) | −421.499 | − | 1297.24i | −0.434535 | − | 1.33736i | ||||
\(971\) | −686.211 | + | 944.488i | −0.706705 | + | 0.972697i | 0.293156 | + | 0.956065i | \(0.405294\pi\) |
−0.999862 | + | 0.0166321i | \(0.994706\pi\) | |||||||
\(972\) | 1376.14 | − | 999.823i | 1.41578 | − | 1.02862i | ||||
\(973\) | 182.938 | − | 563.025i | 0.188014 | − | 0.578649i | ||||
\(974\) | −1406.82 | − | 457.102i | −1.44437 | − | 0.469304i | ||||
\(975\) | −184.456 | + | 134.015i | −0.189186 | + | 0.137451i | ||||
\(976\) | 48.5410 | + | 35.2671i | 0.0497347 | + | 0.0361343i | ||||
\(977\) | −1249.10 | + | 405.858i | −1.27851 | + | 0.415412i | −0.868054 | − | 0.496469i | \(-0.834630\pi\) |
−0.410453 | + | 0.911882i | \(0.634630\pi\) | |||||||
\(978\) | 2885.46i | 2.95037i | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 696.491i | 0.710705i | ||||||||
\(981\) | 556.231 | + | 1711.90i | 0.567004 | + | 1.74506i | ||||
\(982\) | −1886.63 | − | 1370.72i | −1.92121 | − | 1.39584i | ||||
\(983\) | −245.632 | − | 338.084i | −0.249880 | − | 0.343931i | 0.665589 | − | 0.746318i | \(-0.268180\pi\) |
−0.915469 | + | 0.402388i | \(0.868180\pi\) | |||||||
\(984\) | 122.371 | − | 376.618i | 0.124360 | − | 0.382742i | ||||
\(985\) | −271.935 | + | 836.930i | −0.276076 | + | 0.849675i | ||||
\(986\) | 1029.32 | + | 1416.73i | 1.04393 | + | 1.43685i | ||||
\(987\) | 1216.46 | − | 1674.32i | 1.23249 | − | 1.69637i | ||||
\(988\) | 51.9149 | + | 159.777i | 0.0525454 | + | 0.161718i | ||||
\(989\) | − | 278.596i | − | 0.281695i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 838.000 | 0.845610 | 0.422805 | − | 0.906221i | \(-0.361045\pi\) | ||||
0.422805 | + | 0.906221i | \(0.361045\pi\) | |||||||
\(992\) | 574.082 | − | 186.531i | 0.578712 | − | 0.188035i | ||||
\(993\) | 529.097 | + | 384.412i | 0.532827 | + | 0.387121i | ||||
\(994\) | 1281.48 | − | 931.052i | 1.28922 | − | 0.936672i | ||||
\(995\) | 264.961 | + | 86.0910i | 0.266292 | + | 0.0865237i | ||||
\(996\) | −794.883 | − | 258.273i | −0.798075 | − | 0.259310i | ||||
\(997\) | −42.0689 | + | 30.5648i | −0.0421955 | + | 0.0306568i | −0.608683 | − | 0.793413i | \(-0.708302\pi\) |
0.566488 | + | 0.824070i | \(0.308302\pi\) | |||||||
\(998\) | 113.069 | − | 155.626i | 0.113295 | − | 0.155938i | ||||
\(999\) | 250.304 | + | 770.356i | 0.250554 | + | 0.771127i |
(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 | 363.3.h.d.269.2 | 8 | ||
3.2 | odd | 2 | inner | 363.3.h.d.269.1 | 8 | ||
11.2 | odd | 10 | 363.3.h.e.251.2 | 8 | |||
11.3 | even | 5 | 363.3.b.d.122.1 | 2 | |||
11.4 | even | 5 | inner | 363.3.h.d.245.2 | 8 | ||
11.5 | even | 5 | inner | 363.3.h.d.323.1 | 8 | ||
11.6 | odd | 10 | 363.3.h.e.323.2 | 8 | |||
11.7 | odd | 10 | 363.3.h.e.245.1 | 8 | |||
11.8 | odd | 10 | 33.3.b.a.23.2 | yes | 2 | ||
11.9 | even | 5 | inner | 363.3.h.d.251.1 | 8 | ||
11.10 | odd | 2 | 363.3.h.e.269.1 | 8 | |||
33.2 | even | 10 | 363.3.h.e.251.1 | 8 | |||
33.5 | odd | 10 | inner | 363.3.h.d.323.2 | 8 | ||
33.8 | even | 10 | 33.3.b.a.23.1 | ✓ | 2 | ||
33.14 | odd | 10 | 363.3.b.d.122.2 | 2 | |||
33.17 | even | 10 | 363.3.h.e.323.1 | 8 | |||
33.20 | odd | 10 | inner | 363.3.h.d.251.2 | 8 | ||
33.26 | odd | 10 | inner | 363.3.h.d.245.1 | 8 | ||
33.29 | even | 10 | 363.3.h.e.245.2 | 8 | |||
33.32 | even | 2 | 363.3.h.e.269.2 | 8 | |||
44.19 | even | 10 | 528.3.i.a.353.1 | 2 | |||
132.107 | odd | 10 | 528.3.i.a.353.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.3.b.a.23.1 | ✓ | 2 | 33.8 | even | 10 | ||
33.3.b.a.23.2 | yes | 2 | 11.8 | odd | 10 | ||
363.3.b.d.122.1 | 2 | 11.3 | even | 5 | |||
363.3.b.d.122.2 | 2 | 33.14 | odd | 10 | |||
363.3.h.d.245.1 | 8 | 33.26 | odd | 10 | inner | ||
363.3.h.d.245.2 | 8 | 11.4 | even | 5 | inner | ||
363.3.h.d.251.1 | 8 | 11.9 | even | 5 | inner | ||
363.3.h.d.251.2 | 8 | 33.20 | odd | 10 | inner | ||
363.3.h.d.269.1 | 8 | 3.2 | odd | 2 | inner | ||
363.3.h.d.269.2 | 8 | 1.1 | even | 1 | trivial | ||
363.3.h.d.323.1 | 8 | 11.5 | even | 5 | inner | ||
363.3.h.d.323.2 | 8 | 33.5 | odd | 10 | inner | ||
363.3.h.e.245.1 | 8 | 11.7 | odd | 10 | |||
363.3.h.e.245.2 | 8 | 33.29 | even | 10 | |||
363.3.h.e.251.1 | 8 | 33.2 | even | 10 | |||
363.3.h.e.251.2 | 8 | 11.2 | odd | 10 | |||
363.3.h.e.269.1 | 8 | 11.10 | odd | 2 | |||
363.3.h.e.269.2 | 8 | 33.32 | even | 2 | |||
363.3.h.e.323.1 | 8 | 33.17 | even | 10 | |||
363.3.h.e.323.2 | 8 | 11.6 | odd | 10 | |||
528.3.i.a.353.1 | 2 | 44.19 | even | 10 | |||
528.3.i.a.353.2 | 2 | 132.107 | odd | 10 |