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: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 649.16 | ||
Character | \(\chi\) | \(=\) | 1050.649 |
Dual form | 1050.3.q.e.199.16 |
$q$-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 | ||||||||
\(7\) | −4.61524 | − | 5.26304i | −0.659320 | − | 0.751863i | ||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | −1.50000 | + | 2.59808i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.41099 | + | 9.37211i | 0.491908 | + | 0.852010i | 0.999957 | − | 0.00931868i | \(-0.00296627\pi\) |
−0.508049 | + | 0.861328i | \(0.669633\pi\) | |||||||
\(12\) | −1.73205 | + | 3.00000i | −0.144338 | + | 0.250000i | ||||
\(13\) | 19.2715 | 1.48242 | 0.741211 | − | 0.671273i | \(-0.234252\pi\) | ||||
0.741211 | + | 0.671273i | \(0.234252\pi\) | |||||||
\(14\) | −1.93096 | − | 9.70935i | −0.137926 | − | 0.693525i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.125000 | + | 0.216506i | ||||
\(17\) | −5.13686 | − | 8.89730i | −0.302168 | − | 0.523371i | 0.674459 | − | 0.738313i | \(-0.264377\pi\) |
−0.976627 | + | 0.214942i | \(0.931044\pi\) | |||||||
\(18\) | −3.67423 | + | 2.12132i | −0.204124 | + | 0.117851i | ||||
\(19\) | 18.0756 | + | 10.4359i | 0.951346 | + | 0.549260i | 0.893499 | − | 0.449066i | \(-0.148243\pi\) |
0.0578471 | + | 0.998325i | \(0.481576\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.89764 | − | 11.4808i | 0.185602 | − | 0.546704i | ||||
\(22\) | 15.3046i | 0.695663i | ||||||||
\(23\) | 18.2511 | + | 10.5373i | 0.793527 | + | 0.458143i | 0.841203 | − | 0.540720i | \(-0.181848\pi\) |
−0.0476755 | + | 0.998863i | \(0.515181\pi\) | |||||||
\(24\) | −4.24264 | + | 2.44949i | −0.176777 | + | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 23.6026 | + | 13.6270i | 0.907794 | + | 0.524115i | ||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | 4.50061 | − | 13.2569i | 0.160736 | − | 0.473460i | ||||
\(29\) | −19.0888 | −0.658235 | −0.329118 | − | 0.944289i | \(-0.606751\pi\) | ||||
−0.329118 | + | 0.944289i | \(0.606751\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −34.6556 | + | 20.0084i | −1.11792 | + | 0.645434i | −0.940870 | − | 0.338768i | \(-0.889990\pi\) |
−0.177054 | + | 0.984201i | \(0.556657\pi\) | |||||||
\(32\) | −4.89898 | + | 2.82843i | −0.153093 | + | 0.0883883i | ||||
\(33\) | −9.37211 | + | 16.2330i | −0.284003 | + | 0.491908i | ||||
\(34\) | − | 14.5292i | − | 0.427330i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | 43.6177 | + | 25.1827i | 1.17886 | + | 0.680614i | 0.955750 | − | 0.294180i | \(-0.0950466\pi\) |
0.223107 | + | 0.974794i | \(0.428380\pi\) | |||||||
\(38\) | 14.7586 | + | 25.5627i | 0.388385 | + | 0.672703i | ||||
\(39\) | 16.6896 | + | 28.9072i | 0.427938 | + | 0.741211i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 22.7706i | − | 0.555382i | −0.960671 | − | 0.277691i | \(-0.910431\pi\) | ||
0.960671 | − | 0.277691i | \(-0.0895691\pi\) | |||||||
\(42\) | 12.8918 | − | 11.3050i | 0.306947 | − | 0.269166i | ||||
\(43\) | 48.4307i | 1.12629i | 0.826357 | + | 0.563147i | \(0.190410\pi\) | ||||
−0.826357 | + | 0.563147i | \(0.809590\pi\) | |||||||
\(44\) | −10.8220 | + | 18.7442i | −0.245954 | + | 0.426005i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 14.9020 | + | 25.8110i | 0.323956 | + | 0.561109i | ||||
\(47\) | −33.2690 | + | 57.6236i | −0.707851 | + | 1.22603i | 0.257802 | + | 0.966198i | \(0.417002\pi\) |
−0.965653 | + | 0.259836i | \(0.916332\pi\) | |||||||
\(48\) | −6.92820 | −0.144338 | ||||||||
\(49\) | −6.39913 | + | 48.5804i | −0.130595 | + | 0.991436i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.89730 | − | 15.4106i | 0.174457 | − | 0.302168i | ||||
\(52\) | 19.2715 | + | 33.3792i | 0.370605 | + | 0.641907i | ||||
\(53\) | −4.28736 | + | 2.47531i | −0.0808937 | + | 0.0467040i | −0.539901 | − | 0.841728i | \(-0.681538\pi\) |
0.459008 | + | 0.888432i | \(0.348205\pi\) | |||||||
\(54\) | −6.36396 | − | 3.67423i | −0.117851 | − | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 14.8861 | − | 13.0539i | 0.265824 | − | 0.233105i | ||||
\(57\) | 36.1511i | 0.634231i | ||||||||
\(58\) | −23.3789 | − | 13.4978i | −0.403085 | − | 0.232721i | ||||
\(59\) | 24.4105 | − | 14.0934i | 0.413737 | − | 0.238871i | −0.278657 | − | 0.960391i | \(-0.589889\pi\) |
0.692394 | + | 0.721520i | \(0.256556\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −60.6988 | − | 35.0445i | −0.995062 | − | 0.574499i | −0.0882785 | − | 0.996096i | \(-0.528137\pi\) |
−0.906784 | + | 0.421596i | \(0.861470\pi\) | |||||||
\(62\) | −56.5924 | −0.912781 | ||||||||
\(63\) | 20.5966 | − | 4.09619i | 0.326931 | − | 0.0650188i | ||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −22.9569 | + | 13.2542i | −0.347832 | + | 0.200821i | ||||
\(67\) | 16.7193 | − | 9.65287i | 0.249541 | − | 0.144073i | −0.370013 | − | 0.929027i | \(-0.620647\pi\) |
0.619554 | + | 0.784954i | \(0.287313\pi\) | |||||||
\(68\) | 10.2737 | − | 17.7946i | 0.151084 | − | 0.261685i | ||||
\(69\) | 36.5023i | 0.529018i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 49.4968 | 0.697138 | 0.348569 | − | 0.937283i | \(-0.386668\pi\) | ||||
0.348569 | + | 0.937283i | \(0.386668\pi\) | |||||||
\(72\) | −7.34847 | − | 4.24264i | −0.102062 | − | 0.0589256i | ||||
\(73\) | 66.4872 | + | 115.159i | 0.910783 | + | 1.57752i | 0.812961 | + | 0.582318i | \(0.197854\pi\) |
0.0978221 | + | 0.995204i | \(0.468812\pi\) | |||||||
\(74\) | 35.6137 | + | 61.6848i | 0.481266 | + | 0.833578i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 41.7437i | 0.549260i | ||||||||
\(77\) | 24.3527 | − | 71.7328i | 0.316269 | − | 0.931594i | ||||
\(78\) | 47.2053i | 0.605196i | ||||||||
\(79\) | −45.0404 | + | 78.0122i | −0.570132 | + | 0.987497i | 0.426420 | + | 0.904525i | \(0.359774\pi\) |
−0.996552 | + | 0.0829717i | \(0.973559\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 16.1013 | − | 27.8882i | 0.196357 | − | 0.340100i | ||||
\(83\) | 101.045 | 1.21741 | 0.608706 | − | 0.793396i | \(-0.291689\pi\) | ||||
0.608706 | + | 0.793396i | \(0.291689\pi\) | |||||||
\(84\) | 23.7829 | − | 4.72987i | 0.283130 | − | 0.0563080i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −34.2456 | + | 59.3152i | −0.398205 | + | 0.689712i | ||||
\(87\) | −16.5314 | − | 28.6332i | −0.190016 | − | 0.329118i | ||||
\(88\) | −26.5083 | + | 15.3046i | −0.301231 | + | 0.173916i | ||||
\(89\) | −34.3077 | − | 19.8075i | −0.385479 | − | 0.222557i | 0.294720 | − | 0.955584i | \(-0.404774\pi\) |
−0.680200 | + | 0.733027i | \(0.738107\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −88.9425 | − | 101.427i | −0.977390 | − | 1.11458i | ||||
\(92\) | 42.1492i | 0.458143i | ||||||||
\(93\) | −60.0253 | − | 34.6556i | −0.645434 | − | 0.372641i | ||||
\(94\) | −81.4920 | + | 47.0495i | −0.866937 | + | 0.500526i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −8.48528 | − | 4.89898i | −0.0883883 | − | 0.0510310i | ||||
\(97\) | 68.6944 | 0.708190 | 0.354095 | − | 0.935210i | \(-0.384789\pi\) | ||||
0.354095 | + | 0.935210i | \(0.384789\pi\) | |||||||
\(98\) | −42.1888 | + | 54.9737i | −0.430498 | + | 0.560956i | ||||
\(99\) | −32.4659 | −0.327939 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.96199 | + | 4.01951i | −0.0689306 | + | 0.0397971i | −0.534069 | − | 0.845441i | \(-0.679338\pi\) |
0.465139 | + | 0.885238i | \(0.346004\pi\) | |||||||
\(102\) | 21.7939 | − | 12.5827i | 0.213665 | − | 0.123360i | ||||
\(103\) | 102.282 | − | 177.158i | 0.993033 | − | 1.71998i | 0.394465 | − | 0.918911i | \(-0.370930\pi\) |
0.598568 | − | 0.801072i | \(-0.295737\pi\) | |||||||
\(104\) | 54.5080i | 0.524115i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.00124 | −0.0660494 | ||||||||
\(107\) | −142.508 | − | 82.2769i | −1.33185 | − | 0.768943i | −0.346266 | − | 0.938136i | \(-0.612551\pi\) |
−0.985583 | + | 0.169193i | \(0.945884\pi\) | |||||||
\(108\) | −5.19615 | − | 9.00000i | −0.0481125 | − | 0.0833333i | ||||
\(109\) | −39.5050 | − | 68.4247i | −0.362432 | − | 0.627750i | 0.625929 | − | 0.779880i | \(-0.284720\pi\) |
−0.988360 | + | 0.152130i | \(0.951387\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 87.2354i | 0.785905i | ||||||||
\(112\) | 27.4622 | − | 5.46158i | 0.245198 | − | 0.0487641i | ||||
\(113\) | − | 84.5690i | − | 0.748398i | −0.927348 | − | 0.374199i | \(-0.877918\pi\) | ||
0.927348 | − | 0.374199i | \(-0.122082\pi\) | |||||||
\(114\) | −25.5627 | + | 44.2759i | −0.224234 | + | 0.388385i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −19.0888 | − | 33.0628i | −0.164559 | − | 0.285024i | ||||
\(117\) | −28.9072 | + | 50.0688i | −0.247070 | + | 0.427938i | ||||
\(118\) | 39.8621 | 0.337815 | ||||||||
\(119\) | −23.1190 | + | 68.0987i | −0.194277 | + | 0.572258i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.94240 | − | 3.36434i | 0.0160529 | − | 0.0278044i | ||||
\(122\) | −49.5603 | − | 85.8410i | −0.406232 | − | 0.703615i | ||||
\(123\) | 34.1560 | − | 19.7200i | 0.277691 | − | 0.160325i | ||||
\(124\) | −69.3113 | − | 40.0169i | −0.558962 | − | 0.322717i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 28.1221 | + | 9.54723i | 0.223191 | + | 0.0757717i | ||||
\(127\) | − | 101.777i | − | 0.801393i | −0.916211 | − | 0.400697i | \(-0.868768\pi\) | ||
0.916211 | − | 0.400697i | \(-0.131232\pi\) | |||||||
\(128\) | −9.79796 | − | 5.65685i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | −72.6460 | + | 41.9422i | −0.563147 | + | 0.325133i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 61.2264 | + | 35.3491i | 0.467377 | + | 0.269840i | 0.715141 | − | 0.698980i | \(-0.246362\pi\) |
−0.247764 | + | 0.968820i | \(0.579696\pi\) | |||||||
\(132\) | −37.4884 | −0.284003 | ||||||||
\(133\) | −28.4984 | − | 143.297i | −0.214273 | − | 1.07742i | ||||
\(134\) | 27.3024 | 0.203750 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 25.1654 | − | 14.5292i | 0.185039 | − | 0.106833i | ||||
\(137\) | −102.042 | + | 58.9138i | −0.744829 | + | 0.430027i | −0.823823 | − | 0.566848i | \(-0.808163\pi\) |
0.0789932 | + | 0.996875i | \(0.474829\pi\) | |||||||
\(138\) | −25.8110 | + | 44.7060i | −0.187036 | + | 0.323956i | ||||
\(139\) | − | 158.507i | − | 1.14034i | −0.821528 | − | 0.570168i | \(-0.806878\pi\) | ||
0.821528 | − | 0.570168i | \(-0.193122\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −115.247 | −0.817356 | ||||||||
\(142\) | 60.6209 | + | 34.9995i | 0.426908 | + | 0.246475i | ||||
\(143\) | 104.278 | + | 180.614i | 0.729215 | + | 1.26304i | ||||
\(144\) | −6.00000 | − | 10.3923i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 188.054i | 1.28804i | ||||||||
\(147\) | −78.4123 | + | 32.4731i | −0.533417 | + | 0.220906i | ||||
\(148\) | 100.731i | 0.680614i | ||||||||
\(149\) | −147.948 | + | 256.254i | −0.992940 | + | 1.71982i | −0.393747 | + | 0.919219i | \(0.628821\pi\) |
−0.599193 | + | 0.800604i | \(0.704512\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 62.6478 | + | 108.509i | 0.414886 | + | 0.718604i | 0.995417 | − | 0.0956344i | \(-0.0304880\pi\) |
−0.580530 | + | 0.814239i | \(0.697155\pi\) | |||||||
\(152\) | −29.5173 | + | 51.1254i | −0.194193 | + | 0.336352i | ||||
\(153\) | 30.8212 | 0.201445 | ||||||||
\(154\) | 80.5486 | − | 70.6343i | 0.523043 | − | 0.458665i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −33.3792 | + | 57.8144i | −0.213969 | + | 0.370605i | ||||
\(157\) | 2.66684 | + | 4.61909i | 0.0169862 | + | 0.0294210i | 0.874394 | − | 0.485217i | \(-0.161260\pi\) |
−0.857407 | + | 0.514638i | \(0.827926\pi\) | |||||||
\(158\) | −110.326 | + | 63.6967i | −0.698266 | + | 0.403144i | ||||
\(159\) | −7.42593 | − | 4.28736i | −0.0467040 | − | 0.0269646i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −28.7752 | − | 144.689i | −0.178728 | − | 0.898686i | ||||
\(162\) | − | 12.7279i | − | 0.0785674i | ||||||
\(163\) | 207.193 | + | 119.623i | 1.27112 | + | 0.733883i | 0.975199 | − | 0.221329i | \(-0.0710394\pi\) |
0.295923 | + | 0.955212i | \(0.404373\pi\) | |||||||
\(164\) | 39.4399 | − | 22.7706i | 0.240487 | − | 0.138845i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 123.754 | + | 71.4497i | 0.745509 | + | 0.430420i | ||||
\(167\) | 310.440 | 1.85892 | 0.929462 | − | 0.368918i | \(-0.120272\pi\) | ||||
0.929462 | + | 0.368918i | \(0.120272\pi\) | |||||||
\(168\) | 32.4726 | + | 11.0242i | 0.193289 | + | 0.0656202i | ||||
\(169\) | 202.390 | 1.19757 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −54.2267 | + | 31.3078i | −0.317115 | + | 0.183087i | ||||
\(172\) | −83.8844 | + | 48.4307i | −0.487700 | + | 0.281574i | ||||
\(173\) | 45.4539 | − | 78.7285i | 0.262739 | − | 0.455078i | −0.704230 | − | 0.709972i | \(-0.748707\pi\) |
0.966969 | + | 0.254894i | \(0.0820407\pi\) | |||||||
\(174\) | − | 46.7579i | − | 0.268723i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −43.2879 | −0.245954 | ||||||||
\(177\) | 42.2802 | + | 24.4105i | 0.238871 | + | 0.137912i | ||||
\(178\) | −28.0121 | − | 48.5184i | −0.157371 | − | 0.272575i | ||||
\(179\) | −121.577 | − | 210.577i | −0.679200 | − | 1.17641i | −0.975222 | − | 0.221228i | \(-0.928993\pi\) |
0.296022 | − | 0.955181i | \(-0.404340\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 245.993i | 1.35907i | 0.733641 | + | 0.679537i | \(0.237819\pi\) | ||||
−0.733641 | + | 0.679537i | \(0.762181\pi\) | |||||||
\(182\) | −37.2125 | − | 187.113i | −0.204464 | − | 1.02810i | ||||
\(183\) | − | 121.398i | − | 0.663375i | ||||||
\(184\) | −29.8040 | + | 51.6220i | −0.161978 | + | 0.280554i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −49.0105 | − | 84.8886i | −0.263497 | − | 0.456390i | ||||
\(187\) | 55.5910 | − | 96.2864i | 0.297278 | − | 0.514901i | ||||
\(188\) | −133.076 | −0.707851 | ||||||||
\(189\) | 23.9815 | + | 27.3475i | 0.126886 | + | 0.144696i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.6108 | − | 35.6989i | 0.107910 | − | 0.186905i | −0.807014 | − | 0.590533i | \(-0.798918\pi\) |
0.914923 | + | 0.403628i | \(0.132251\pi\) | |||||||
\(192\) | −6.92820 | − | 12.0000i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | 164.324 | − | 94.8727i | 0.851422 | − | 0.491568i | −0.00970872 | − | 0.999953i | \(-0.503090\pi\) |
0.861130 | + | 0.508384i | \(0.169757\pi\) | |||||||
\(194\) | 84.1331 | + | 48.5743i | 0.433676 | + | 0.250383i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −90.5428 | + | 37.4967i | −0.461953 | + | 0.191310i | ||||
\(197\) | − | 362.318i | − | 1.83918i | −0.392882 | − | 0.919589i | \(-0.628522\pi\) | ||
0.392882 | − | 0.919589i | \(-0.371478\pi\) | |||||||
\(198\) | −39.7625 | − | 22.9569i | −0.200821 | − | 0.115944i | ||||
\(199\) | 33.4433 | − | 19.3085i | 0.168057 | − | 0.0970278i | −0.413612 | − | 0.910453i | \(-0.635733\pi\) |
0.581669 | + | 0.813425i | \(0.302400\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 28.9586 | + | 16.7193i | 0.144073 | + | 0.0831804i | ||||
\(202\) | −11.3689 | −0.0562816 | ||||||||
\(203\) | 88.0995 | + | 100.465i | 0.433987 | + | 0.494902i | ||||
\(204\) | 35.5892 | 0.174457 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 250.540 | − | 144.649i | 1.21621 | − | 0.702180i | ||||
\(207\) | −54.7534 | + | 31.6119i | −0.264509 | + | 0.152714i | ||||
\(208\) | −38.5430 | + | 66.7584i | −0.185303 | + | 0.320954i | ||||
\(209\) | 225.875i | 1.08074i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −136.551 | −0.647163 | −0.323581 | − | 0.946200i | \(-0.604887\pi\) | ||||
−0.323581 | + | 0.946200i | \(0.604887\pi\) | |||||||
\(212\) | −8.57473 | − | 4.95062i | −0.0404468 | − | 0.0233520i | ||||
\(213\) | 42.8655 | + | 74.2452i | 0.201246 | + | 0.348569i | ||||
\(214\) | −116.357 | − | 201.537i | −0.543725 | − | 0.941760i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 14.6969i | − | 0.0680414i | ||||||
\(217\) | 265.249 | + | 90.0502i | 1.22235 | + | 0.414978i | ||||
\(218\) | − | 111.737i | − | 0.512556i | ||||||
\(219\) | −115.159 | + | 199.461i | −0.525841 | + | 0.910783i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −98.9949 | − | 171.464i | −0.447941 | − | 0.775856i | ||||
\(222\) | −61.6848 | + | 106.841i | −0.277859 | + | 0.481266i | ||||
\(223\) | −154.949 | −0.694839 | −0.347419 | − | 0.937710i | \(-0.612942\pi\) | ||||
−0.347419 | + | 0.937710i | \(0.612942\pi\) | |||||||
\(224\) | 37.4961 | + | 12.7296i | 0.167393 | + | 0.0568288i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 59.7993 | − | 103.575i | 0.264599 | − | 0.458299i | ||||
\(227\) | 11.1769 | + | 19.3590i | 0.0492375 | + | 0.0852818i | 0.889594 | − | 0.456753i | \(-0.150988\pi\) |
−0.840356 | + | 0.542034i | \(0.817654\pi\) | |||||||
\(228\) | −62.6156 | + | 36.1511i | −0.274630 | + | 0.158558i | ||||
\(229\) | −25.9105 | − | 14.9594i | −0.113146 | − | 0.0653250i | 0.442359 | − | 0.896838i | \(-0.354142\pi\) |
−0.555505 | + | 0.831513i | \(0.687475\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 128.689 | − | 25.5933i | 0.557096 | − | 0.110793i | ||||
\(232\) | − | 53.9913i | − | 0.232721i | ||||||
\(233\) | −219.176 | − | 126.541i | −0.940669 | − | 0.543095i | −0.0504987 | − | 0.998724i | \(-0.516081\pi\) |
−0.890170 | + | 0.455629i | \(0.849414\pi\) | |||||||
\(234\) | −70.8079 | + | 40.8810i | −0.302598 | + | 0.174705i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 48.8209 | + | 28.1868i | 0.206868 | + | 0.119436i | ||||
\(237\) | −156.024 | −0.658331 | ||||||||
\(238\) | −76.4679 | + | 67.0559i | −0.321294 | + | 0.281747i | ||||
\(239\) | −121.009 | −0.506315 | −0.253158 | − | 0.967425i | \(-0.581469\pi\) | ||||
−0.253158 | + | 0.967425i | \(0.581469\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 249.755 | − | 144.196i | 1.03633 | − | 0.598323i | 0.117536 | − | 0.993069i | \(-0.462501\pi\) |
0.918791 | + | 0.394745i | \(0.129167\pi\) | |||||||
\(242\) | 4.75789 | − | 2.74697i | 0.0196607 | − | 0.0113511i | ||||
\(243\) | 7.79423 | − | 13.5000i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | − | 140.178i | − | 0.574499i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 55.7765 | 0.226734 | ||||||||
\(247\) | 348.343 | + | 201.116i | 1.41030 | + | 0.814234i | ||||
\(248\) | −56.5924 | − | 98.0209i | −0.228195 | − | 0.395246i | ||||
\(249\) | 87.5076 | + | 151.568i | 0.351436 | + | 0.608706i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 422.260i | − | 1.68231i | −0.540795 | − | 0.841155i | \(-0.681876\pi\) | ||
0.540795 | − | 0.841155i | \(-0.318124\pi\) | |||||||
\(252\) | 27.6914 | + | 31.5782i | 0.109887 | + | 0.125310i | ||||
\(253\) | 228.069i | 0.901457i | ||||||||
\(254\) | 71.9672 | − | 124.651i | 0.283335 | − | 0.490751i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −37.2435 | + | 64.5077i | −0.144916 | + | 0.251003i | −0.929342 | − | 0.369221i | \(-0.879625\pi\) |
0.784425 | + | 0.620223i | \(0.212958\pi\) | |||||||
\(258\) | −118.630 | −0.459808 | ||||||||
\(259\) | −68.7687 | − | 345.786i | −0.265516 | − | 1.33508i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 28.6332 | − | 49.5942i | 0.109706 | − | 0.190016i | ||||
\(262\) | 49.9911 | + | 86.5872i | 0.190806 | + | 0.330486i | ||||
\(263\) | −271.304 | + | 156.637i | −1.03157 | + | 0.595579i | −0.917435 | − | 0.397885i | \(-0.869744\pi\) |
−0.114139 | + | 0.993465i | \(0.536411\pi\) | |||||||
\(264\) | −45.9138 | − | 26.5083i | −0.173916 | − | 0.100410i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 66.4229 | − | 195.653i | 0.249710 | − | 0.735539i | ||||
\(267\) | − | 68.6153i | − | 0.256986i | ||||||
\(268\) | 33.4385 | + | 19.3057i | 0.124771 | + | 0.0720363i | ||||
\(269\) | 138.011 | − | 79.6809i | 0.513053 | − | 0.296211i | −0.221035 | − | 0.975266i | \(-0.570943\pi\) |
0.734088 | + | 0.679055i | \(0.237610\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −163.041 | − | 94.1320i | −0.601629 | − | 0.347350i | 0.168053 | − | 0.985778i | \(-0.446252\pi\) |
−0.769682 | + | 0.638427i | \(0.779585\pi\) | |||||||
\(272\) | 41.0949 | 0.151084 | ||||||||
\(273\) | 75.1133 | − | 221.252i | 0.275140 | − | 0.810446i | ||||
\(274\) | −166.633 | −0.608151 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −63.2238 | + | 36.5023i | −0.229072 | + | 0.132255i | ||||
\(277\) | 6.10326 | − | 3.52372i | 0.0220334 | − | 0.0127210i | −0.488943 | − | 0.872316i | \(-0.662617\pi\) |
0.510976 | + | 0.859595i | \(0.329284\pi\) | |||||||
\(278\) | 112.081 | − | 194.130i | 0.403170 | − | 0.698311i | ||||
\(279\) | − | 120.051i | − | 0.430289i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 198.386 | 0.705998 | 0.352999 | − | 0.935624i | \(-0.385162\pi\) | ||||
0.352999 | + | 0.935624i | \(0.385162\pi\) | |||||||
\(282\) | −141.148 | − | 81.4920i | −0.500526 | − | 0.288979i | ||||
\(283\) | 94.5641 | + | 163.790i | 0.334149 | + | 0.578763i | 0.983321 | − | 0.181879i | \(-0.0582179\pi\) |
−0.649172 | + | 0.760641i | \(0.724885\pi\) | |||||||
\(284\) | 49.4968 | + | 85.7309i | 0.174284 | + | 0.301869i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 294.942i | 1.03127i | ||||||||
\(287\) | −119.843 | + | 105.092i | −0.417571 | + | 0.366174i | ||||
\(288\) | − | 16.9706i | − | 0.0589256i | ||||||
\(289\) | 91.7253 | − | 158.873i | 0.317389 | − | 0.549733i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 59.4911 | + | 103.042i | 0.204437 | + | 0.354095i | ||||
\(292\) | −132.974 | + | 230.318i | −0.455391 | + | 0.788761i | ||||
\(293\) | −486.090 | −1.65901 | −0.829505 | − | 0.558499i | \(-0.811378\pi\) | ||||
−0.829505 | + | 0.558499i | \(0.811378\pi\) | |||||||
\(294\) | −118.997 | − | 15.6746i | −0.404752 | − | 0.0533150i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −71.2274 | + | 123.370i | −0.240633 | + | 0.416789i | ||||
\(297\) | −28.1163 | − | 48.6989i | −0.0946678 | − | 0.163969i | ||||
\(298\) | −362.397 | + | 209.230i | −1.21610 | + | 0.702115i | ||||
\(299\) | 351.726 | + | 203.069i | 1.17634 | + | 0.679161i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 254.892 | − | 223.519i | 0.846818 | − | 0.742588i | ||||
\(302\) | 177.195i | 0.586738i | ||||||||
\(303\) | −12.0585 | − | 6.96199i | −0.0397971 | − | 0.0229769i | ||||
\(304\) | −72.3023 | + | 41.7437i | −0.237836 | + | 0.137315i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 37.7481 | + | 21.7939i | 0.123360 | + | 0.0712217i | ||||
\(307\) | 427.589 | 1.39280 | 0.696399 | − | 0.717655i | \(-0.254784\pi\) | ||||
0.696399 | + | 0.717655i | \(0.254784\pi\) | |||||||
\(308\) | 148.598 | − | 29.5526i | 0.482460 | − | 0.0959499i | ||||
\(309\) | 354.317 | 1.14666 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −311.852 | + | 180.048i | −1.00274 | + | 0.578931i | −0.909057 | − | 0.416671i | \(-0.863197\pi\) |
−0.0936811 | + | 0.995602i | \(0.529863\pi\) | |||||||
\(312\) | −81.7620 | + | 47.2053i | −0.262058 | + | 0.151299i | ||||
\(313\) | 291.964 | − | 505.696i | 0.932792 | − | 1.61564i | 0.154267 | − | 0.988029i | \(-0.450698\pi\) |
0.778525 | − | 0.627614i | \(-0.215968\pi\) | |||||||
\(314\) | 7.54295i | 0.0240221i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −180.162 | −0.570132 | ||||||||
\(317\) | −312.982 | − | 180.700i | −0.987324 | − | 0.570032i | −0.0828508 | − | 0.996562i | \(-0.526403\pi\) |
−0.904473 | + | 0.426530i | \(0.859736\pi\) | |||||||
\(318\) | −6.06325 | − | 10.5019i | −0.0190668 | − | 0.0330247i | ||||
\(319\) | −103.289 | − | 178.902i | −0.323791 | − | 0.560823i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 285.016i | − | 0.887899i | ||||||
\(322\) | 67.0680 | − | 197.554i | 0.208286 | − | 0.613521i | ||||
\(323\) | − | 214.432i | − | 0.663875i | ||||||
\(324\) | 9.00000 | − | 15.5885i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 169.172 | + | 293.015i | 0.518934 | + | 0.898819i | ||||
\(327\) | 68.4247 | − | 118.515i | 0.209250 | − | 0.362432i | ||||
\(328\) | 64.4051 | 0.196357 | ||||||||
\(329\) | 456.819 | − | 90.8507i | 1.38851 | − | 0.276142i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −147.993 | + | 256.331i | −0.447108 | + | 0.774415i | −0.998196 | − | 0.0600326i | \(-0.980880\pi\) |
0.551088 | + | 0.834447i | \(0.314213\pi\) | |||||||
\(332\) | 101.045 | + | 175.015i | 0.304353 | + | 0.527154i | ||||
\(333\) | −130.853 | + | 75.5481i | −0.392952 | + | 0.226871i | ||||
\(334\) | 380.210 | + | 219.514i | 1.13835 | + | 0.657229i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 31.9753 | + | 36.4634i | 0.0951646 | + | 0.108522i | ||||
\(337\) | − | 22.0162i | − | 0.0653300i | −0.999466 | − | 0.0326650i | \(-0.989601\pi\) | ||
0.999466 | − | 0.0326650i | \(-0.0103994\pi\) | |||||||
\(338\) | 247.876 | + | 143.111i | 0.733361 | + | 0.423406i | ||||
\(339\) | 126.854 | − | 73.2389i | 0.374199 | − | 0.216044i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −375.043 | − | 216.531i | −1.09983 | − | 0.634988i | ||||
\(342\) | −88.5519 | −0.258924 | ||||||||
\(343\) | 285.214 | − | 190.531i | 0.831527 | − | 0.555484i | ||||
\(344\) | −136.983 | −0.398205 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 111.339 | − | 64.2815i | 0.321789 | − | 0.185785i | ||||
\(347\) | −245.870 | + | 141.953i | −0.708559 | + | 0.409086i | −0.810527 | − | 0.585701i | \(-0.800819\pi\) |
0.101969 | + | 0.994788i | \(0.467486\pi\) | |||||||
\(348\) | 33.0628 | − | 57.2665i | 0.0950080 | − | 0.164559i | ||||
\(349\) | − | 317.175i | − | 0.908811i | −0.890795 | − | 0.454406i | \(-0.849852\pi\) | ||
0.890795 | − | 0.454406i | \(-0.150148\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −100.138 | −0.285292 | ||||||||
\(352\) | −53.0166 | − | 30.6092i | −0.150615 | − | 0.0869579i | ||||
\(353\) | 58.4712 | + | 101.275i | 0.165641 | + | 0.286898i | 0.936883 | − | 0.349644i | \(-0.113697\pi\) |
−0.771242 | + | 0.636542i | \(0.780364\pi\) | |||||||
\(354\) | 34.5216 | + | 59.7932i | 0.0975187 | + | 0.168907i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 79.2302i | − | 0.222557i | ||||||
\(357\) | −122.170 | + | 24.2967i | −0.342212 | + | 0.0680579i | ||||
\(358\) | − | 343.871i | − | 0.960534i | ||||||
\(359\) | 116.793 | − | 202.291i | 0.325329 | − | 0.563486i | −0.656250 | − | 0.754543i | \(-0.727858\pi\) |
0.981579 | + | 0.191058i | \(0.0611918\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 37.3175 | + | 64.6359i | 0.103373 | + | 0.179047i | ||||
\(362\) | −173.943 | + | 301.278i | −0.480505 | + | 0.832260i | ||||
\(363\) | 6.72867 | 0.0185363 | ||||||||
\(364\) | 86.7334 | − | 255.479i | 0.238279 | − | 0.701866i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 85.8410 | − | 148.681i | 0.234538 | − | 0.406232i | ||||
\(367\) | 256.037 | + | 443.469i | 0.697648 | + | 1.20836i | 0.969280 | + | 0.245960i | \(0.0791033\pi\) |
−0.271632 | + | 0.962401i | \(0.587563\pi\) | |||||||
\(368\) | −73.0045 | + | 42.1492i | −0.198382 | + | 0.114536i | ||||
\(369\) | 59.1599 | + | 34.1560i | 0.160325 | + | 0.0925636i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 32.8149 | + | 11.1404i | 0.0884498 | + | 0.0300280i | ||||
\(372\) | − | 138.623i | − | 0.372641i | ||||||
\(373\) | −481.863 | − | 278.204i | −1.29186 | − | 0.745854i | −0.312874 | − | 0.949795i | \(-0.601292\pi\) |
−0.978983 | + | 0.203941i | \(0.934625\pi\) | |||||||
\(374\) | 136.170 | − | 78.6175i | 0.364090 | − | 0.210207i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −162.984 | − | 94.0989i | −0.433468 | − | 0.250263i | ||||
\(377\) | −367.870 | −0.975782 | ||||||||
\(378\) | 10.0336 | + | 50.4512i | 0.0265438 | + | 0.133469i | ||||
\(379\) | 536.301 | 1.41504 | 0.707521 | − | 0.706692i | \(-0.249813\pi\) | ||||
0.707521 | + | 0.706692i | \(0.249813\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 152.665 | − | 88.1414i | 0.400697 | − | 0.231342i | ||||
\(382\) | 50.4859 | − | 29.1480i | 0.132162 | − | 0.0763038i | ||||
\(383\) | 14.6753 | − | 25.4184i | 0.0383168 | − | 0.0663666i | −0.846231 | − | 0.532816i | \(-0.821134\pi\) |
0.884548 | + | 0.466450i | \(0.154467\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 268.341 | 0.695183 | ||||||||
\(387\) | −125.827 | − | 72.6460i | −0.325133 | − | 0.187716i | ||||
\(388\) | 68.6944 | + | 118.982i | 0.177047 | + | 0.306655i | ||||
\(389\) | −349.242 | − | 604.905i | −0.897795 | − | 1.55503i | −0.830307 | − | 0.557306i | \(-0.811835\pi\) |
−0.0674875 | − | 0.997720i | \(-0.521498\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 216.514i | − | 0.553745i | ||||||
\(392\) | −137.406 | − | 18.0995i | −0.350526 | − | 0.0461721i | ||||
\(393\) | 122.453i | 0.311585i | ||||||||
\(394\) | 256.198 | − | 443.747i | 0.650248 | − | 1.12626i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −32.4659 | − | 56.2326i | −0.0819847 | − | 0.142002i | ||||
\(397\) | 102.347 | − | 177.270i | 0.257801 | − | 0.446525i | −0.707851 | − | 0.706361i | \(-0.750335\pi\) |
0.965653 | + | 0.259837i | \(0.0836687\pi\) | |||||||
\(398\) | 54.6127 | 0.137218 | ||||||||
\(399\) | 190.265 | − | 166.846i | 0.476854 | − | 0.418161i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −214.984 | + | 372.363i | −0.536119 | + | 0.928585i | 0.462989 | + | 0.886364i | \(0.346777\pi\) |
−0.999108 | + | 0.0422215i | \(0.986556\pi\) | |||||||
\(402\) | 23.6446 | + | 40.9537i | 0.0588174 | + | 0.101875i | ||||
\(403\) | −667.865 | + | 385.592i | −1.65723 | + | 0.956805i | ||||
\(404\) | −13.9240 | − | 8.03902i | −0.0344653 | − | 0.0198986i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 36.8598 | + | 185.340i | 0.0907876 | + | 0.456502i | ||||
\(407\) | 545.053i | 1.33920i | ||||||||
\(408\) | 43.5877 | + | 25.1654i | 0.106833 | + | 0.0616798i | ||||
\(409\) | −15.3567 | + | 8.86618i | −0.0375469 | + | 0.0216777i | −0.518656 | − | 0.854983i | \(-0.673567\pi\) |
0.481109 | + | 0.876661i | \(0.340234\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −176.741 | − | 102.042i | −0.430027 | − | 0.248276i | ||||
\(412\) | 409.129 | 0.993033 | ||||||||
\(413\) | −186.834 | − | 63.4289i | −0.452383 | − | 0.153581i | ||||
\(414\) | −89.4119 | −0.215971 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −94.4106 | + | 54.5080i | −0.226948 | + | 0.131029i | ||||
\(417\) | 237.760 | − | 137.271i | 0.570168 | − | 0.329187i | ||||
\(418\) | −159.718 | + | 276.639i | −0.382100 | + | 0.661816i | ||||
\(419\) | − | 440.768i | − | 1.05195i | −0.850499 | − | 0.525977i | \(-0.823700\pi\) | ||
0.850499 | − | 0.525977i | \(-0.176300\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −143.012 | −0.339696 | −0.169848 | − | 0.985470i | \(-0.554328\pi\) | ||||
−0.169848 | + | 0.985470i | \(0.554328\pi\) | |||||||
\(422\) | −167.241 | − | 96.5564i | −0.396305 | − | 0.228807i | ||||
\(423\) | −99.8070 | − | 172.871i | −0.235950 | − | 0.408678i | ||||
\(424\) | −7.00124 | − | 12.1265i | −0.0165123 | − | 0.0286002i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 121.242i | 0.284605i | ||||||||
\(427\) | 95.6991 | + | 481.199i | 0.224120 | + | 1.12693i | ||||
\(428\) | − | 329.108i | − | 0.768943i | ||||||
\(429\) | −180.614 | + | 312.833i | −0.421012 | + | 0.729215i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 391.608 | + | 678.285i | 0.908604 | + | 1.57375i | 0.816005 | + | 0.578045i | \(0.196184\pi\) |
0.0925988 | + | 0.995704i | \(0.470483\pi\) | |||||||
\(432\) | 10.3923 | − | 18.0000i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | 286.669 | 0.662053 | 0.331026 | − | 0.943622i | \(-0.392605\pi\) | ||||
0.331026 | + | 0.943622i | \(0.392605\pi\) | |||||||
\(434\) | 261.188 | + | 297.848i | 0.601815 | + | 0.686286i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 79.0101 | − | 136.849i | 0.181216 | − | 0.313875i | ||||
\(437\) | 219.933 | + | 380.935i | 0.503279 | + | 0.871705i | ||||
\(438\) | −282.081 | + | 162.860i | −0.644021 | + | 0.371826i | ||||
\(439\) | 295.016 | + | 170.328i | 0.672018 | + | 0.387990i | 0.796841 | − | 0.604189i | \(-0.206503\pi\) |
−0.124823 | + | 0.992179i | \(0.539836\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −116.617 | − | 89.4960i | −0.264437 | − | 0.202939i | ||||
\(442\) | − | 280.000i | − | 0.633484i | ||||||
\(443\) | 342.304 | + | 197.629i | 0.772696 | + | 0.446116i | 0.833835 | − | 0.552013i | \(-0.186140\pi\) |
−0.0611396 | + | 0.998129i | \(0.519473\pi\) | |||||||
\(444\) | −151.096 | + | 87.2354i | −0.340307 | + | 0.196476i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −189.773 | − | 109.566i | −0.425500 | − | 0.245663i | ||||
\(447\) | −512.507 | −1.14655 | ||||||||
\(448\) | 36.9219 | + | 42.1043i | 0.0824150 | + | 0.0939828i | ||||
\(449\) | −665.078 | −1.48124 | −0.740621 | − | 0.671923i | \(-0.765469\pi\) | ||||
−0.740621 | + | 0.671923i | \(0.765469\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 213.409 | − | 123.212i | 0.473190 | − | 0.273197i | ||||
\(452\) | 146.478 | − | 84.5690i | 0.324066 | − | 0.187100i | ||||
\(453\) | −108.509 | + | 187.944i | −0.239535 | + | 0.414886i | ||||
\(454\) | 31.6131i | 0.0696323i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −102.251 | −0.224234 | ||||||||
\(457\) | −442.484 | − | 255.468i | −0.968236 | − | 0.559012i | −0.0695382 | − | 0.997579i | \(-0.522153\pi\) |
−0.898698 | + | 0.438568i | \(0.855486\pi\) | |||||||
\(458\) | −21.1558 | − | 36.6429i | −0.0461917 | − | 0.0800064i | ||||
\(459\) | 26.6919 | + | 46.2317i | 0.0581523 | + | 0.100723i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 174.303i | − | 0.378097i | −0.981968 | − | 0.189049i | \(-0.939460\pi\) | ||
0.981968 | − | 0.189049i | \(-0.0605404\pi\) | |||||||
\(462\) | 175.709 | + | 59.6518i | 0.380322 | + | 0.129116i | ||||
\(463\) | − | 755.187i | − | 1.63107i | −0.578705 | − | 0.815537i | \(-0.696442\pi\) | ||
0.578705 | − | 0.815537i | \(-0.303558\pi\) | |||||||
\(464\) | 38.1776 | − | 66.1256i | 0.0822794 | − | 0.142512i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −178.956 | − | 309.961i | −0.384026 | − | 0.665153i | ||||
\(467\) | 283.286 | − | 490.666i | 0.606609 | − | 1.05068i | −0.385186 | − | 0.922839i | \(-0.625863\pi\) |
0.991795 | − | 0.127839i | \(-0.0408039\pi\) | |||||||
\(468\) | −115.629 | −0.247070 | ||||||||
\(469\) | −127.967 | − | 43.4438i | −0.272850 | − | 0.0926307i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.61909 | + | 8.00051i | −0.00980699 | + | 0.0169862i | ||||
\(472\) | 39.8621 | + | 69.0432i | 0.0844537 | + | 0.146278i | ||||
\(473\) | −453.897 | + | 262.058i | −0.959614 | + | 0.554033i | ||||
\(474\) | −191.090 | − | 110.326i | −0.403144 | − | 0.232755i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −141.069 | + | 28.0554i | −0.296364 | + | 0.0589399i | ||||
\(477\) | − | 14.8519i | − | 0.0311360i | ||||||
\(478\) | −148.206 | − | 85.5665i | −0.310053 | − | 0.179009i | ||||
\(479\) | −445.286 | + | 257.086i | −0.929615 | + | 0.536714i | −0.886690 | − | 0.462365i | \(-0.847001\pi\) |
−0.0429255 | + | 0.999078i | \(0.513668\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 840.578 | + | 485.308i | 1.74756 | + | 1.00896i | ||||
\(482\) | 407.848 | 0.846157 | ||||||||
\(483\) | 192.113 | − | 168.467i | 0.397749 | − | 0.348792i | ||||
\(484\) | 7.76960 | 0.0160529 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 19.0919 | − | 11.0227i | 0.0392837 | − | 0.0226805i | ||||
\(487\) | 283.473 | − | 163.663i | 0.582081 | − | 0.336064i | −0.179879 | − | 0.983689i | \(-0.557571\pi\) |
0.761960 | + | 0.647624i | \(0.224237\pi\) | |||||||
\(488\) | 99.1207 | − | 171.682i | 0.203116 | − | 0.351808i | ||||
\(489\) | 414.386i | 0.847415i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −41.8889 | −0.0853134 | −0.0426567 | − | 0.999090i | \(-0.513582\pi\) | ||||
−0.0426567 | + | 0.999090i | \(0.513582\pi\) | |||||||
\(492\) | 68.3119 | + | 39.4399i | 0.138845 | + | 0.0801624i | ||||
\(493\) | 98.0566 | + | 169.839i | 0.198898 | + | 0.344501i | ||||
\(494\) | 284.421 | + | 492.631i | 0.575751 | + | 0.997229i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 160.068i | − | 0.322717i | ||||||
\(497\) | −228.439 | − | 260.503i | −0.459637 | − | 0.524152i | ||||
\(498\) | 247.509i | 0.497006i | ||||||||
\(499\) | 207.685 | − | 359.721i | 0.416203 | − | 0.720885i | −0.579351 | − | 0.815078i | \(-0.696694\pi\) |
0.995554 | + | 0.0941936i | \(0.0300273\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 268.849 | + | 465.660i | 0.536625 | + | 0.929462i | ||||
\(502\) | 298.583 | − | 517.160i | 0.594786 | − | 1.03020i | ||||
\(503\) | −51.7604 | −0.102903 | −0.0514517 | − | 0.998675i | \(-0.516385\pi\) | ||||
−0.0514517 | + | 0.998675i | \(0.516385\pi\) | |||||||
\(504\) | 11.5858 | + | 58.2561i | 0.0229876 | + | 0.115587i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −161.269 | + | 279.326i | −0.318713 | + | 0.552028i | ||||
\(507\) | 175.275 | + | 303.585i | 0.345709 | + | 0.598786i | ||||
\(508\) | 176.283 | − | 101.777i | 0.347014 | − | 0.200348i | ||||
\(509\) | −136.916 | − | 79.0486i | −0.268991 | − | 0.155302i | 0.359438 | − | 0.933169i | \(-0.382968\pi\) |
−0.628429 | + | 0.777867i | \(0.716302\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 299.233 | − | 881.411i | 0.585583 | − | 1.72488i | ||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | −93.9234 | − | 54.2267i | −0.183087 | − | 0.105705i | ||||
\(514\) | −91.2276 | + | 52.6703i | −0.177486 | + | 0.102471i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −145.292 | − | 83.8844i | −0.281574 | − | 0.162567i | ||||
\(517\) | −720.073 | −1.39279 | ||||||||
\(518\) | 160.283 | − | 472.126i | 0.309428 | − | 0.911441i | ||||
\(519\) | 157.457 | 0.303385 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 306.214 | − | 176.793i | 0.587744 | − | 0.339334i | −0.176461 | − | 0.984308i | \(-0.556465\pi\) |
0.764205 | + | 0.644974i | \(0.223132\pi\) | |||||||
\(522\) | 70.1368 | − | 40.4935i | 0.134362 | − | 0.0775737i | ||||
\(523\) | −59.7756 | + | 103.534i | −0.114294 | + | 0.197962i | −0.917497 | − | 0.397742i | \(-0.869794\pi\) |
0.803204 | + | 0.595705i | \(0.203127\pi\) | |||||||
\(524\) | 141.396i | 0.269840i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −443.037 | −0.842277 | ||||||||
\(527\) | 356.042 | + | 205.561i | 0.675602 | + | 0.390059i | ||||
\(528\) | −37.4884 | − | 64.9319i | −0.0710008 | − | 0.122977i | ||||
\(529\) | −42.4308 | − | 73.4924i | −0.0802095 | − | 0.138927i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 84.5604i | 0.159247i | ||||||||
\(532\) | 219.699 | − | 192.657i | 0.412968 | − | 0.362138i | ||||
\(533\) | − | 438.824i | − | 0.823309i | ||||||
\(534\) | 48.5184 | − | 84.0363i | 0.0908584 | − | 0.157371i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 27.3024 | + | 47.2892i | 0.0509374 | + | 0.0882261i | ||||
\(537\) | 210.577 | − | 364.731i | 0.392136 | − | 0.679200i | ||||
\(538\) | 225.372 | 0.418906 | ||||||||
\(539\) | −489.926 | + | 202.894i | −0.908954 | + | 0.376427i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −272.691 | + | 472.315i | −0.504051 | + | 0.873041i | 0.495938 | + | 0.868358i | \(0.334824\pi\) |
−0.999989 | + | 0.00468349i | \(0.998509\pi\) | |||||||
\(542\) | −133.123 | − | 230.575i | −0.245614 | − | 0.425416i | ||||
\(543\) | −368.989 | + | 213.036i | −0.679537 | + | 0.392331i | ||||
\(544\) | 50.3307 | + | 29.0585i | 0.0925197 | + | 0.0534163i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 248.443 | − | 217.864i | 0.455024 | − | 0.399018i | ||||
\(547\) | − | 117.783i | − | 0.215325i | −0.994188 | − | 0.107663i | \(-0.965663\pi\) | ||
0.994188 | − | 0.107663i | \(-0.0343366\pi\) | |||||||
\(548\) | −204.083 | − | 117.828i | −0.372415 | − | 0.215014i | ||||
\(549\) | 182.096 | − | 105.133i | 0.331687 | − | 0.191500i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −345.041 | − | 199.210i | −0.626209 | − | 0.361542i | ||||
\(552\) | −103.244 | −0.187036 | ||||||||
\(553\) | 618.454 | − | 122.996i | 1.11836 | − | 0.222416i | ||||
\(554\) | 9.96659 | 0.0179902 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 274.542 | − | 158.507i | 0.493780 | − | 0.285084i | ||||
\(557\) | −533.028 | + | 307.744i | −0.956963 | + | 0.552503i | −0.895237 | − | 0.445590i | \(-0.852994\pi\) |
−0.0617258 | + | 0.998093i | \(0.519660\pi\) | |||||||
\(558\) | 84.8886 | − | 147.031i | 0.152130 | − | 0.263497i | ||||
\(559\) | 933.330i | 1.66964i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 192.573 | 0.343267 | ||||||||
\(562\) | 242.972 | + | 140.280i | 0.432334 | + | 0.249608i | ||||
\(563\) | 239.628 | + | 415.047i | 0.425626 | + | 0.737207i | 0.996479 | − | 0.0838462i | \(-0.0267205\pi\) |
−0.570852 | + | 0.821053i | \(0.693387\pi\) | |||||||
\(564\) | −115.247 | − | 199.614i | −0.204339 | − | 0.353925i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 267.468i | 0.472558i | ||||||||
\(567\) | −20.2527 | + | 59.6559i | −0.0357191 | + | 0.105213i | ||||
\(568\) | 139.998i | 0.246475i | ||||||||
\(569\) | −228.674 | + | 396.074i | −0.401887 | + | 0.696088i | −0.993954 | − | 0.109800i | \(-0.964979\pi\) |
0.592067 | + | 0.805889i | \(0.298312\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −186.601 | − | 323.203i | −0.326797 | − | 0.566029i | 0.655077 | − | 0.755562i | \(-0.272636\pi\) |
−0.981874 | + | 0.189532i | \(0.939303\pi\) | |||||||
\(572\) | −208.555 | + | 361.229i | −0.364607 | + | 0.631519i | ||||
\(573\) | 71.3978 | 0.124604 | ||||||||
\(574\) | −221.088 | + | 43.9692i | −0.385171 | + | 0.0766014i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 12.0000 | − | 20.7846i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | −445.777 | − | 772.108i | −0.772577 | − | 1.33814i | −0.936146 | − | 0.351611i | \(-0.885634\pi\) |
0.163569 | − | 0.986532i | \(-0.447699\pi\) | |||||||
\(578\) | 224.680 | − | 129.719i | 0.388720 | − | 0.224428i | ||||
\(579\) | 284.618 | + | 164.324i | 0.491568 | + | 0.283807i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −466.347 | − | 531.804i | −0.802663 | − | 0.915326i | ||||
\(582\) | 168.266i | 0.289117i | ||||||||
\(583\) | −46.3978 | − | 26.7878i | −0.0795845 | − | 0.0459481i | ||||
\(584\) | −325.719 | + | 188.054i | −0.557738 | + | 0.322010i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −595.336 | − | 343.718i | −1.01593 | − | 0.586549i | ||||
\(587\) | 786.758 | 1.34030 | 0.670151 | − | 0.742224i | \(-0.266229\pi\) | ||||
0.670151 | + | 0.742224i | \(0.266229\pi\) | |||||||
\(588\) | −134.657 | − | 103.341i | −0.229009 | − | 0.175750i | ||||
\(589\) | −835.227 | −1.41804 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 543.477 | − | 313.777i | 0.919589 | − | 0.530925i | ||||
\(592\) | −174.471 | + | 100.731i | −0.294714 | + | 0.170153i | ||||
\(593\) | −312.676 | + | 541.571i | −0.527278 | + | 0.913273i | 0.472216 | + | 0.881483i | \(0.343454\pi\) |
−0.999495 | + | 0.0317903i | \(0.989879\pi\) | |||||||
\(594\) | − | 79.5250i | − | 0.133880i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −591.792 | −0.992940 | ||||||||
\(597\) | 57.9256 | + | 33.4433i | 0.0970278 | + | 0.0560190i | ||||
\(598\) | 287.183 | + | 497.416i | 0.480240 | + | 0.831799i | ||||
\(599\) | 75.2476 | + | 130.333i | 0.125622 | + | 0.217584i | 0.921976 | − | 0.387247i | \(-0.126574\pi\) |
−0.796354 | + | 0.604831i | \(0.793241\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 521.601i | 0.867888i | 0.900940 | + | 0.433944i | \(0.142878\pi\) | ||||
−0.900940 | + | 0.433944i | \(0.857122\pi\) | |||||||
\(602\) | 470.230 | − | 93.5177i | 0.781113 | − | 0.155345i | ||||
\(603\) | 57.9172i | 0.0960485i | ||||||||
\(604\) | −125.296 | + | 217.019i | −0.207443 | + | 0.359302i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −9.84575 | − | 17.0533i | −0.0162471 | − | 0.0281408i | ||||
\(607\) | 348.375 | − | 603.404i | 0.573930 | − | 0.994075i | −0.422228 | − | 0.906490i | \(-0.638752\pi\) |
0.996157 | − | 0.0875852i | \(-0.0279150\pi\) | |||||||
\(608\) | −118.069 | −0.194193 | ||||||||
\(609\) | −74.4014 | + | 219.155i | −0.122170 | + | 0.359860i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −641.143 | + | 1110.49i | −1.04933 | + | 1.81750i | ||||
\(612\) | 30.8212 | + | 53.3838i | 0.0503614 | + | 0.0872285i | ||||
\(613\) | −46.9809 | + | 27.1244i | −0.0766410 | + | 0.0442487i | −0.537831 | − | 0.843053i | \(-0.680756\pi\) |
0.461190 | + | 0.887302i | \(0.347423\pi\) | |||||||
\(614\) | 523.687 | + | 302.351i | 0.852911 | + | 0.492428i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 202.891 | + | 68.8800i | 0.329368 | + | 0.111818i | ||||
\(617\) | − | 969.852i | − | 1.57188i | −0.618301 | − | 0.785941i | \(-0.712179\pi\) | ||
0.618301 | − | 0.785941i | \(-0.287821\pi\) | |||||||
\(618\) | 433.947 | + | 250.540i | 0.702180 | + | 0.405404i | ||||
\(619\) | 111.240 | − | 64.2247i | 0.179710 | − | 0.103756i | −0.407446 | − | 0.913229i | \(-0.633581\pi\) |
0.587156 | + | 0.809474i | \(0.300247\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −94.8357 | − | 54.7534i | −0.152714 | − | 0.0881697i | ||||
\(622\) | −509.252 | −0.818733 | ||||||||
\(623\) | 54.0903 | + | 271.979i | 0.0868223 | + | 0.436564i | ||||
\(624\) | −133.517 | −0.213969 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 715.163 | − | 412.899i | 1.14243 | − | 0.659584i | ||||
\(627\) | −338.812 | + | 195.613i | −0.540371 | + | 0.311983i | ||||
\(628\) | −5.33367 | + | 9.23819i | −0.00849311 | + | 0.0147105i | ||||
\(629\) | − | 517.440i | − | 0.822639i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 115.457 | 0.182975 | 0.0914877 | − | 0.995806i | \(-0.470838\pi\) | ||||
0.0914877 | + | 0.995806i | \(0.470838\pi\) | |||||||
\(632\) | −220.652 | − | 127.393i | −0.349133 | − | 0.201572i | ||||
\(633\) | −118.257 | − | 204.827i | −0.186820 | − | 0.323581i | ||||
\(634\) | −255.549 | − | 442.623i | −0.403073 | − | 0.698144i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 17.1495i | − | 0.0269646i | ||||||
\(637\) | −123.321 | + | 936.215i | −0.193596 | + | 1.46973i | ||||
\(638\) | − | 292.146i | − | 0.457910i | ||||||
\(639\) | −74.2452 | + | 128.596i | −0.116190 | + | 0.201246i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 476.249 | + | 824.887i | 0.742978 | + | 1.28688i | 0.951134 | + | 0.308780i | \(0.0999206\pi\) |
−0.208156 | + | 0.978096i | \(0.566746\pi\) | |||||||
\(642\) | 201.537 | − | 349.072i | 0.313920 | − | 0.543725i | ||||
\(643\) | −253.254 | −0.393863 | −0.196931 | − | 0.980417i | \(-0.563098\pi\) | ||||
−0.196931 | + | 0.980417i | \(0.563098\pi\) | |||||||
\(644\) | 221.833 | − | 194.529i | 0.344461 | − | 0.302063i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 151.626 | − | 262.624i | 0.234715 | − | 0.406539i | ||||
\(647\) | 502.388 | + | 870.161i | 0.776488 | + | 1.34492i | 0.933954 | + | 0.357393i | \(0.116334\pi\) |
−0.157466 | + | 0.987524i | \(0.550332\pi\) | |||||||
\(648\) | 22.0454 | − | 12.7279i | 0.0340207 | − | 0.0196419i | ||||
\(649\) | 264.170 | + | 152.518i | 0.407041 | + | 0.235005i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 94.6373 | + | 475.860i | 0.145372 | + | 0.730967i | ||||
\(652\) | 478.492i | 0.733883i | ||||||||
\(653\) | 922.831 | + | 532.797i | 1.41322 | + | 0.815922i | 0.995690 | − | 0.0927422i | \(-0.0295632\pi\) |
0.417528 | + | 0.908664i | \(0.362897\pi\) | |||||||
\(654\) | 167.606 | − | 96.7672i | 0.256278 | − | 0.147962i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 78.8798 | + | 45.5413i | 0.120244 | + | 0.0694227i | ||||
\(657\) | −398.923 | −0.607189 | ||||||||
\(658\) | 623.728 | + | 211.751i | 0.947915 | + | 0.321810i | ||||
\(659\) | −432.265 | −0.655941 | −0.327970 | − | 0.944688i | \(-0.606365\pi\) | ||||
−0.327970 | + | 0.944688i | \(0.606365\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 327.626 | − | 189.155i | 0.495652 | − | 0.286165i | −0.231264 | − | 0.972891i | \(-0.574286\pi\) |
0.726916 | + | 0.686726i | \(0.240953\pi\) | |||||||
\(662\) | −362.507 | + | 209.294i | −0.547594 | + | 0.316153i | ||||
\(663\) | 171.464 | − | 296.985i | 0.258619 | − | 0.447941i | ||||
\(664\) | 285.799i | 0.430420i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −213.682 | −0.320844 | ||||||||
\(667\) | −348.392 | − | 201.144i | −0.522328 | − | 0.301566i | ||||
\(668\) | 310.440 | + | 537.698i | 0.464731 | + | 0.804937i | ||||
\(669\) | −134.190 | − | 232.424i | −0.200583 | − | 0.347419i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 758.501i | − | 1.13040i | ||||||
\(672\) | 13.3781 | + | 67.2683i | 0.0199079 | + | 0.100102i | ||||
\(673\) | 689.666i | 1.02476i | 0.858758 | + | 0.512382i | \(0.171237\pi\) | ||||
−0.858758 | + | 0.512382i | \(0.828763\pi\) | |||||||
\(674\) | 15.5678 | − | 26.9642i | 0.0230976 | − | 0.0400063i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 202.390 | + | 350.549i | 0.299393 | + | 0.518564i | ||||
\(677\) | −189.754 | + | 328.663i | −0.280286 | + | 0.485470i | −0.971455 | − | 0.237223i | \(-0.923763\pi\) |
0.691169 | + | 0.722693i | \(0.257096\pi\) | |||||||
\(678\) | 207.151 | 0.305532 | ||||||||
\(679\) | −317.041 | − | 361.541i | −0.466924 | − | 0.532461i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −19.3590 | + | 33.5307i | −0.0284273 | + | 0.0492375i | ||||
\(682\) | −306.221 | − | 530.390i | −0.449004 | − | 0.777698i | ||||
\(683\) | −647.360 | + | 373.753i | −0.947818 | + | 0.547223i | −0.892403 | − | 0.451240i | \(-0.850982\pi\) |
−0.0554159 | + | 0.998463i | \(0.517648\pi\) | |||||||
\(684\) | −108.453 | − | 62.6156i | −0.158558 | − | 0.0915433i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 484.040 | − | 31.6754i | 0.705598 | − | 0.0461740i | ||||
\(687\) | − | 51.8209i | − | 0.0754308i | ||||||
\(688\) | −167.769 | − | 96.8613i | −0.243850 | − | 0.140787i | ||||
\(689\) | −82.6238 | + | 47.7029i | −0.119918 | + | 0.0692350i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 771.026 | + | 445.152i | 1.11581 | + | 0.644214i | 0.940328 | − | 0.340268i | \(-0.110518\pi\) |
0.175483 | + | 0.984482i | \(0.443851\pi\) | |||||||
\(692\) | 181.816 | 0.262739 | ||||||||
\(693\) | 149.838 | + | 170.869i | 0.216217 | + | 0.246565i | ||||
\(694\) | −401.504 | −0.578536 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 80.9870 | − | 46.7579i | 0.116361 | − | 0.0671808i | ||||
\(697\) | −202.597 | + | 116.970i | −0.290670 | + | 0.167819i | ||||
\(698\) | 224.277 | − | 388.459i | 0.321313 | − | 0.556531i | ||||
\(699\) | − | 438.352i | − | 0.627112i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −650.703 | −0.928250 | −0.464125 | − | 0.885770i | \(-0.653631\pi\) | ||||
−0.464125 | + | 0.885770i | \(0.653631\pi\) | |||||||
\(702\) | −122.643 | − | 70.8079i | −0.174705 | − | 0.100866i | ||||
\(703\) | 525.610 | + | 910.384i | 0.747667 | + | 1.29500i | ||||
\(704\) | −43.2879 | − | 74.9769i | −0.0614885 | − | 0.106501i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 165.382i | 0.234251i | ||||||||
\(707\) | 53.2861 | + | 18.0902i | 0.0753693 | + | 0.0255873i | ||||
\(708\) | 97.6419i | 0.137912i | ||||||||
\(709\) | −196.427 | + | 340.222i | −0.277048 | + | 0.479862i | −0.970650 | − | 0.240497i | \(-0.922690\pi\) |
0.693602 | + | 0.720359i | \(0.256023\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −135.121 | − | 234.037i | −0.190044 | − | 0.329166i | ||||
\(712\) | 56.0242 | − | 97.0368i | 0.0786857 | − | 0.136288i | ||||
\(713\) | −843.339 | −1.18280 | ||||||||
\(714\) | −166.807 | − | 56.6298i | −0.233623 | − | 0.0793134i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 243.154 | − | 421.155i | 0.339600 | − | 0.588205i | ||||
\(717\) | −104.797 | − | 181.514i | −0.146161 | − | 0.253158i | ||||
\(718\) | 286.083 | − | 165.170i | 0.398444 | − | 0.230042i | ||||
\(719\) | −899.919 | − | 519.569i | −1.25163 | − | 0.722627i | −0.280194 | − | 0.959943i | \(-0.590399\pi\) |
−0.971432 | + | 0.237317i | \(0.923732\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1404.45 | + | 279.312i | −1.94792 | + | 0.387395i | ||||
\(722\) | 105.550i | 0.146191i | ||||||||
\(723\) | 432.588 | + | 249.755i | 0.598323 | + | 0.345442i | ||||
\(724\) | −426.072 | + | 245.993i | −0.588497 | + | 0.339769i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 8.24091 | + | 4.75789i | 0.0113511 | + | 0.00655357i | ||||
\(727\) | −610.568 | −0.839846 | −0.419923 | − | 0.907560i | \(-0.637943\pi\) | ||||
−0.419923 | + | 0.907560i | \(0.637943\pi\) | |||||||
\(728\) | 286.877 | − | 251.567i | 0.394062 | − | 0.345559i | ||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 430.902 | − | 248.781i | 0.589469 | − | 0.340330i | ||||
\(732\) | 210.267 | − | 121.398i | 0.287250 | − | 0.165844i | ||||
\(733\) | 539.576 | − | 934.574i | 0.736121 | − | 1.27500i | −0.218109 | − | 0.975924i | \(-0.569989\pi\) |
0.954230 | − | 0.299074i | \(-0.0966777\pi\) | |||||||
\(734\) | 724.181i | 0.986623i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −119.216 | −0.161978 | ||||||||
\(737\) | 180.935 | + | 104.463i | 0.245503 | + | 0.141741i | ||||
\(738\) | 48.3038 | + | 83.6647i | 0.0654523 | + | 0.113367i | ||||
\(739\) | 378.082 | + | 654.857i | 0.511613 | + | 0.886139i | 0.999909 | + | 0.0134615i | \(0.00428507\pi\) |
−0.488297 | + | 0.872678i | \(0.662382\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 696.686i | 0.940197i | ||||||||
\(742\) | 32.3124 | + | 36.8478i | 0.0435477 | + | 0.0496601i | ||||
\(743\) | − | 963.993i | − | 1.29743i | −0.761030 | − | 0.648717i | \(-0.775306\pi\) | ||
0.761030 | − | 0.648717i | \(-0.224694\pi\) | |||||||
\(744\) | 98.0209 | − | 169.777i | 0.131749 | − | 0.228195i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −393.439 | − | 681.457i | −0.527398 | − | 0.913481i | ||||
\(747\) | −151.568 | + | 262.523i | −0.202902 | + | 0.351436i | ||||
\(748\) | 222.364 | 0.297278 | ||||||||
\(749\) | 224.681 | + | 1129.75i | 0.299975 | + | 1.50835i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −416.806 | + | 721.929i | −0.555001 | + | 0.961290i | 0.442902 | + | 0.896570i | \(0.353949\pi\) |
−0.997903 | + | 0.0647203i | \(0.979384\pi\) | |||||||
\(752\) | −133.076 | − | 230.494i | −0.176963 | − | 0.306508i | ||||
\(753\) | 633.389 | − | 365.688i | 0.841155 | − | 0.485641i | ||||
\(754\) | −450.547 | − | 260.123i | −0.597542 | − | 0.344991i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −23.3859 | + | 68.8847i | −0.0309337 | + | 0.0911173i | ||||
\(757\) | − | 744.966i | − | 0.984103i | −0.870566 | − | 0.492051i | \(-0.836247\pi\) | ||
0.870566 | − | 0.492051i | \(-0.163753\pi\) | |||||||
\(758\) | 656.832 | + | 379.222i | 0.866533 | + | 0.500293i | ||||
\(759\) | −342.103 | + | 197.513i | −0.450729 | + | 0.260228i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −64.1518 | − | 37.0381i | −0.0842993 | − | 0.0486702i | 0.457258 | − | 0.889334i | \(-0.348832\pi\) |
−0.541557 | + | 0.840664i | \(0.682165\pi\) | |||||||
\(762\) | 249.302 | 0.327167 | ||||||||
\(763\) | −177.797 | + | 523.713i | −0.233023 | + | 0.686387i | ||||
\(764\) | 82.4431 | 0.107910 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 35.9471 | − | 20.7540i | 0.0469283 | − | 0.0270941i | ||||
\(767\) | 470.426 | − | 271.601i | 0.613332 | − | 0.354108i | ||||
\(768\) | 13.8564 | − | 24.0000i | 0.0180422 | − | 0.0312500i | ||||
\(769\) | 961.553i | 1.25039i | 0.780467 | + | 0.625197i | \(0.214981\pi\) | ||||
−0.780467 | + | 0.625197i | \(0.785019\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −129.015 | −0.167335 | ||||||||
\(772\) | 328.649 | + | 189.745i | 0.425711 | + | 0.245784i | ||||
\(773\) | 687.723 | + | 1191.17i | 0.889680 | + | 1.54097i | 0.840253 | + | 0.542194i | \(0.182406\pi\) |
0.0494271 | + | 0.998778i | \(0.484260\pi\) | |||||||
\(774\) | −102.737 | − | 177.946i | −0.132735 | − | 0.229904i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 194.297i | 0.250383i | ||||||||
\(777\) | 459.123 | − | 402.612i | 0.590892 | − | 0.518163i | ||||
\(778\) | − | 987.806i | − | 1.26967i | ||||||
\(779\) | 237.633 | − | 411.592i | 0.305049 | − | 0.528360i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 267.826 | + | 463.889i | 0.342928 | + | 0.593968i | ||||
\(782\) | 153.099 | − | 265.175i | 0.195779 | − | 0.339098i | ||||
\(783\) | 99.1884 | 0.126677 | ||||||||
\(784\) | −155.489 | − | 119.328i | −0.198328 | − | 0.152204i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −86.5872 | + | 149.973i | −0.110162 | + | 0.190806i | ||||
\(787\) | 190.340 | + | 329.679i | 0.241856 | + | 0.418906i | 0.961243 | − | 0.275703i | \(-0.0889106\pi\) |
−0.719387 | + | 0.694609i | \(0.755577\pi\) | |||||||
\(788\) | 627.553 | − | 362.318i | 0.796387 | − | 0.459795i | ||||
\(789\) | −469.912 | − | 271.304i | −0.595579 | − | 0.343858i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −445.090 | + | 390.306i | −0.562693 | + | 0.493434i | ||||
\(792\) | − | 91.8275i | − | 0.115944i | ||||||
\(793\) | −1169.76 | − | 675.358i | −1.47510 | − | 0.851650i | ||||
\(794\) | 250.698 | − | 144.741i | 0.315741 | − | 0.182293i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 66.8867 | + | 38.6170i | 0.0840285 | + | 0.0485139i | ||||
\(797\) | −511.440 | −0.641706 | −0.320853 | − | 0.947129i | \(-0.603970\pi\) | ||||
−0.320853 | + | 0.947129i | \(0.603970\pi\) | |||||||
\(798\) | 351.004 | − | 69.8064i | 0.439855 | − | 0.0874768i | ||||
\(799\) | 683.593 | 0.855560 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 102.923 | − | 59.4226i | 0.128493 | − | 0.0741856i | ||||
\(802\) | −526.600 | + | 304.033i | −0.656609 | + | 0.379093i | ||||
\(803\) | −719.522 | + | 1246.25i | −0.896043 | + | 1.55199i | ||||
\(804\) | 66.8770i | 0.0831804i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1090.62 | −1.35313 | ||||||||
\(807\) | 239.043 | + | 138.011i | 0.296211 | + | 0.171018i | ||||
\(808\) | −11.3689 | − | 19.6915i | −0.0140704 | − | 0.0243707i | ||||
\(809\) | 579.187 | + | 1003.18i | 0.715930 | + | 1.24003i | 0.962600 | + | 0.270927i | \(0.0873302\pi\) |
−0.246670 | + | 0.969099i | \(0.579336\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 92.0692i | − | 0.113526i | −0.998388 | − | 0.0567628i | \(-0.981922\pi\) | ||
0.998388 | − | 0.0567628i | \(-0.0180779\pi\) | |||||||
\(812\) | −85.9113 | + | 253.058i | −0.105802 | + | 0.311648i | ||||
\(813\) | − | 326.083i | − | 0.401086i | ||||||
\(814\) | −385.411 | + | 667.551i | −0.473478 | + | 0.820088i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 35.5892 | + | 61.6423i | 0.0436142 | + | 0.0755421i | ||||
\(817\) | −505.419 | + | 875.412i | −0.618628 | + | 1.07150i | ||||
\(818\) | −25.0774 | −0.0306569 | ||||||||
\(819\) | 396.928 | − | 78.9396i | 0.484649 | − | 0.0963853i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 493.467 | − | 854.711i | 0.601057 | − | 1.04106i | −0.391605 | − | 0.920134i | \(-0.628080\pi\) |
0.992661 | − | 0.120927i | \(-0.0385867\pi\) | |||||||
\(822\) | −144.309 | − | 249.950i | −0.175558 | − | 0.304075i | ||||
\(823\) | −481.074 | + | 277.748i | −0.584537 | + | 0.337483i | −0.762935 | − | 0.646476i | \(-0.776242\pi\) |
0.178397 | + | 0.983959i | \(0.442909\pi\) | |||||||
\(824\) | 501.079 | + | 289.298i | 0.608106 | + | 0.351090i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −183.973 | − | 209.796i | −0.222728 | − | 0.253990i | ||||
\(827\) | − | 1323.46i | − | 1.60032i | −0.599787 | − | 0.800160i | \(-0.704748\pi\) | ||
0.599787 | − | 0.800160i | \(-0.295252\pi\) | |||||||
\(828\) | −109.507 | − | 63.2238i | −0.132255 | − | 0.0763572i | ||||
\(829\) | −911.903 | + | 526.488i | −1.10000 | + | 0.635088i | −0.936222 | − | 0.351409i | \(-0.885703\pi\) |
−0.163782 | + | 0.986497i | \(0.552369\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.5712 | + | 6.10326i | 0.0127210 | + | 0.00734448i | ||||
\(832\) | −154.172 | −0.185303 | ||||||||
\(833\) | 465.106 | − | 192.615i | 0.558350 | − | 0.231231i | ||||
\(834\) | 388.261 | 0.465540 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −391.227 | + | 225.875i | −0.467975 | + | 0.270185i | ||||
\(837\) | 180.076 | − | 103.967i | 0.215145 | − | 0.124214i | ||||
\(838\) | 311.670 | − | 539.829i | 0.371922 | − | 0.644187i | ||||
\(839\) | − | 1254.98i | − | 1.49580i | −0.663810 | − | 0.747901i | \(-0.731062\pi\) | ||
0.663810 | − | 0.747901i | \(-0.268938\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −476.617 | −0.566727 | ||||||||
\(842\) | −175.153 | − | 101.125i | −0.208020 | − | 0.120101i | ||||
\(843\) | 171.807 | + | 297.578i | 0.203804 | + | 0.352999i | ||||
\(844\) | −136.551 | − | 236.514i | −0.161791 | − | 0.280230i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 282.297i | − | 0.333684i | ||||||
\(847\) | −26.6713 | + | 5.30429i | −0.0314891 | + | 0.00626244i | ||||
\(848\) | − | 19.8025i | − | 0.0233520i | ||||||
\(849\) | −163.790 | + | 283.692i | −0.192921 | + | 0.334149i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 530.715 | + | 919.226i | 0.623637 | + | 1.08017i | ||||
\(852\) | −85.7309 | + | 148.490i | −0.100623 | + | 0.174284i | ||||
\(853\) | −454.825 | −0.533207 | −0.266603 | − | 0.963806i | \(-0.585901\pi\) | ||||
−0.266603 | + | 0.963806i | \(0.585901\pi\) | |||||||
\(854\) | −223.052 | + | 657.015i | −0.261185 | + | 0.769338i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 232.714 | − | 403.073i | 0.271863 | − | 0.470880i | ||||
\(857\) | −84.3691 | − | 146.132i | −0.0984470 | − | 0.170515i | 0.812595 | − | 0.582829i | \(-0.198054\pi\) |
−0.911042 | + | 0.412314i | \(0.864721\pi\) | |||||||
\(858\) | −442.413 | + | 255.427i | −0.515633 | + | 0.297701i | ||||
\(859\) | 707.715 | + | 408.599i | 0.823882 | + | 0.475669i | 0.851753 | − | 0.523943i | \(-0.175539\pi\) |
−0.0278711 | + | 0.999612i | \(0.508873\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −261.425 | − | 88.7518i | −0.303629 | − | 0.103080i | ||||
\(862\) | 1107.64i | 1.28496i | ||||||||
\(863\) | −1068.59 | − | 616.950i | −1.23823 | − | 0.714890i | −0.269495 | − | 0.963002i | \(-0.586857\pi\) |
−0.968731 | + | 0.248112i | \(0.920190\pi\) | |||||||
\(864\) | 25.4558 | − | 14.6969i | 0.0294628 | − | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 351.096 | + | 202.705i | 0.405423 | + | 0.234071i | ||||
\(867\) | 317.746 | 0.366489 | ||||||||
\(868\) | 109.278 | + | 549.475i | 0.125896 | + | 0.633036i | ||||
\(869\) | −974.852 | −1.12181 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 322.205 | − | 186.025i | 0.369925 | − | 0.213576i | ||||
\(872\) | 193.534 | − | 111.737i | 0.221943 | − | 0.128139i | ||||
\(873\) | −103.042 | + | 178.473i | −0.118032 | + | 0.204437i | ||||
\(874\) | 622.065i | 0.711744i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −460.637 | −0.525841 | ||||||||
\(877\) | −64.9136 | − | 37.4779i | −0.0740177 | − | 0.0427342i | 0.462534 | − | 0.886601i | \(-0.346940\pi\) |
−0.536552 | + | 0.843867i | \(0.680274\pi\) | |||||||
\(878\) | 240.880 | + | 417.216i | 0.274350 | + | 0.475189i | ||||
\(879\) | −420.966 | − | 729.135i | −0.478915 | − | 0.829505i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 461.343i | 0.523658i | 0.965114 | + | 0.261829i | \(0.0843257\pi\) | ||||
−0.965114 | + | 0.261829i | \(0.915674\pi\) | |||||||
\(882\) | −79.5426 | − | 192.070i | −0.0901843 | − | 0.217767i | ||||
\(883\) | − | 237.840i | − | 0.269354i | −0.990890 | − | 0.134677i | \(-0.957000\pi\) | ||
0.990890 | − | 0.134677i | \(-0.0429997\pi\) | |||||||
\(884\) | 197.990 | − | 342.928i | 0.223970 | − | 0.387928i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 279.490 | + | 484.091i | 0.315452 | + | 0.546379i | ||||
\(887\) | −4.55679 | + | 7.89260i | −0.00513731 | + | 0.00889808i | −0.868583 | − | 0.495544i | \(-0.834969\pi\) |
0.863445 | + | 0.504442i | \(0.168302\pi\) | |||||||
\(888\) | −246.739 | −0.277859 | ||||||||
\(889\) | −535.656 | + | 469.725i | −0.602538 | + | 0.528375i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 48.6989 | − | 84.3490i | 0.0546565 | − | 0.0946678i | ||||
\(892\) | −154.949 | − | 268.380i | −0.173710 | − | 0.300874i | ||||
\(893\) | −1202.71 | + | 694.386i | −1.34682 | + | 0.777588i | ||||
\(894\) | −627.691 | − | 362.397i | −0.702115 | − | 0.405366i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 15.4477 | + | 77.6748i | 0.0172407 | + | 0.0866906i | ||||
\(897\) | 703.452i | 0.784228i | ||||||||
\(898\) | −814.551 | − | 470.281i | −0.907072 | − | 0.523698i | ||||
\(899\) | 661.535 | − | 381.938i | 0.735857 | − | 0.424847i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 44.0472 | + | 25.4306i | 0.0488870 | + | 0.0282249i | ||||
\(902\) | 348.495 | 0.386358 | ||||||||
\(903\) | 556.022 | + | 188.765i | 0.615750 | + | 0.209042i | ||||
\(904\) | 239.197 | 0.264599 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −265.792 | + | 153.455i | −0.293369 | + | 0.169377i | ||||
\(907\) | 728.070 | − | 420.352i | 0.802723 | − | 0.463453i | −0.0416991 | − | 0.999130i | \(-0.513277\pi\) |
0.844423 | + | 0.535678i | \(0.179944\pi\) | |||||||
\(908\) | −22.3538 | + | 38.7179i | −0.0246187 | + | 0.0426409i | ||||
\(909\) | − | 24.1171i | − | 0.0265314i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35.4735 | −0.0389390 | −0.0194695 | − | 0.999810i | \(-0.506198\pi\) | ||||
−0.0194695 | + | 0.999810i | \(0.506198\pi\) | |||||||
\(912\) | −125.231 | − | 72.3023i | −0.137315 | − | 0.0792788i | ||||
\(913\) | 546.754 | + | 947.006i | 0.598854 | + | 1.03725i | ||||
\(914\) | −361.287 | − | 625.767i | −0.395281 | − | 0.684646i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 59.8377i | − | 0.0653250i | ||||||
\(917\) | −96.5310 | − | 485.381i | −0.105268 | − | 0.529314i | ||||
\(918\) | 75.4961i | 0.0822398i | ||||||||
\(919\) | 215.680 | − | 373.569i | 0.234690 | − | 0.406495i | −0.724493 | − | 0.689282i | \(-0.757926\pi\) |
0.959182 | + | 0.282788i | \(0.0912592\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 370.303 | + | 641.384i | 0.402066 | + | 0.696399i | ||||
\(922\) | 123.251 | − | 213.477i | 0.133678 | − | 0.231536i | ||||
\(923\) | 953.876 | 1.03345 | ||||||||
\(924\) | 173.018 | + | 197.303i | 0.187249 | + | 0.213531i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 533.998 | − | 924.911i | 0.576671 | − | 0.998824i | ||||
\(927\) | 306.847 | + | 531.475i | 0.331011 | + | 0.573328i | ||||
\(928\) | 93.5157 | − | 53.9913i | 0.100771 | − | 0.0581803i | ||||
\(929\) | −531.053 | − | 306.603i | −0.571639 | − | 0.330036i | 0.186165 | − | 0.982519i | \(-0.440394\pi\) |
−0.757804 | + | 0.652483i | \(0.773728\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −622.649 | + | 811.337i | −0.668796 | + | 0.871468i | ||||
\(932\) | − | 506.165i | − | 0.543095i | ||||||
\(933\) | −540.143 | − | 311.852i | −0.578931 | − | 0.334246i | ||||
\(934\) | 693.907 | − | 400.627i | 0.742941 | − | 0.428937i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −141.616 | − | 81.7620i | −0.151299 | − | 0.0873525i | ||||
\(937\) | −1360.68 | −1.45216 | −0.726081 | − | 0.687609i | \(-0.758660\pi\) | ||||
−0.726081 | + | 0.687609i | \(0.758660\pi\) | |||||||
\(938\) | −126.007 | − | 143.694i | −0.134336 | − | 0.153192i | ||||
\(939\) | 1011.39 | 1.07710 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −146.671 | + | 84.6806i | −0.155867 | + | 0.0899900i | −0.575905 | − | 0.817517i | \(-0.695350\pi\) |
0.420038 | + | 0.907507i | \(0.362017\pi\) | |||||||
\(942\) | −11.3144 | + | 6.53239i | −0.0120111 | + | 0.00693459i | ||||
\(943\) | 239.941 | − | 415.590i | 0.254444 | − | 0.440710i | ||||
\(944\) | 112.747i | 0.119436i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −741.211 | −0.783521 | ||||||||
\(947\) | 1107.79 | + | 639.583i | 1.16979 | + | 0.675378i | 0.953630 | − | 0.300981i | \(-0.0973140\pi\) |
0.216158 | + | 0.976358i | \(0.430647\pi\) | |||||||
\(948\) | −156.024 | − | 270.242i | −0.164583 | − | 0.285066i | ||||
\(949\) | 1281.31 | + | 2219.29i | 1.35016 | + | 2.33855i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 625.964i | − | 0.658216i | ||||||
\(952\) | −192.612 | − | 65.3904i | −0.202324 | − | 0.0686874i | ||||
\(953\) | 1.43779i | 0.00150870i | 1.00000 | 0.000754349i | \(0.000240117\pi\) | |||||
−1.00000 | 0.000754349i | \(0.999760\pi\) | ||||||||
\(954\) | 10.5019 | − | 18.1897i | 0.0110082 | − | 0.0190668i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −121.009 | − | 209.594i | −0.126579 | − | 0.219241i | ||||
\(957\) | 178.902 | − | 309.868i | 0.186941 | − | 0.323791i | ||||
\(958\) | −727.149 | −0.759028 | ||||||||
\(959\) | 781.012 | + | 265.148i | 0.814402 | + | 0.276484i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 320.176 | − | 554.560i | 0.333169 | − | 0.577066i | ||||
\(962\) | 686.329 | + | 1188.76i | 0.713440 | + | 1.23571i | ||||
\(963\) | 427.524 | − | 246.831i | 0.443950 | − | 0.256314i | ||||
\(964\) | 499.509 | + | 288.392i | 0.518163 | + | 0.299162i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 354.413 | − | 70.4844i | 0.366887 | − | 0.0729653i | ||||
\(967\) | 486.815i | 0.503428i | 0.967802 | + | 0.251714i | \(0.0809942\pi\) | ||||
−0.967802 | + | 0.251714i | \(0.919006\pi\) | |||||||
\(968\) | 9.51578 | + | 5.49394i | 0.00983035 | + | 0.00567556i | ||||
\(969\) | 321.648 | − | 185.703i | 0.331938 | − | 0.191644i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 378.215 | + | 218.362i | 0.389511 | + | 0.224884i | 0.681948 | − | 0.731401i | \(-0.261133\pi\) |
−0.292437 | + | 0.956285i | \(0.594466\pi\) | |||||||
\(972\) | 31.1769 | 0.0320750 | ||||||||
\(973\) | −834.227 | + | 731.547i | −0.857376 | + | 0.751847i | ||||
\(974\) | 462.910 | 0.475267 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 242.795 | − | 140.178i | 0.248766 | − | 0.143625i | ||||
\(977\) | 220.866 | − | 127.517i | 0.226066 | − | 0.130519i | −0.382690 | − | 0.923877i | \(-0.625002\pi\) |
0.608756 | + | 0.793358i | \(0.291669\pi\) | |||||||
\(978\) | −293.015 | + | 507.517i | −0.299606 | + | 0.518934i | ||||
\(979\) | − | 428.714i | − | 0.437910i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 237.030 | 0.241621 | ||||||||
\(982\) | −51.3032 | − | 29.6199i | −0.0522436 | − | 0.0301628i | ||||
\(983\) | −690.443 | − | 1195.88i | −0.702383 | − | 1.21656i | −0.967628 | − | 0.252383i | \(-0.918786\pi\) |
0.265244 | − | 0.964181i | \(-0.414547\pi\) | |||||||
\(984\) | 55.7765 | + | 96.6077i | 0.0566834 | + | 0.0981785i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 277.346i | 0.281284i | ||||||||
\(987\) | 531.893 | + | 606.550i | 0.538899 | + | 0.614539i | ||||
\(988\) | 804.464i | 0.814234i | ||||||||
\(989\) | −510.328 | + | 883.914i | −0.516004 | + | 0.893745i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 311.554 | + | 539.628i | 0.314384 | + | 0.544528i | 0.979306 | − | 0.202384i | \(-0.0648688\pi\) |
−0.664923 | + | 0.746912i | \(0.731535\pi\) | |||||||
\(992\) | 113.185 | − | 196.042i | 0.114098 | − | 0.197623i | ||||
\(993\) | −512.662 | −0.516276 | ||||||||
\(994\) | −95.5763 | − | 480.581i | −0.0961533 | − | 0.483482i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −175.015 | + | 303.135i | −0.175718 | + | 0.304353i | ||||
\(997\) | 280.158 | + | 485.248i | 0.281001 | + | 0.486708i | 0.971632 | − | 0.236499i | \(-0.0760001\pi\) |
−0.690630 | + | 0.723208i | \(0.742667\pi\) | |||||||
\(998\) | 508.723 | − | 293.711i | 0.509742 | − | 0.294300i | ||||
\(999\) | −226.644 | − | 130.853i | −0.226871 | − | 0.130984i |
(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.e.649.16 | 32 | ||
5.2 | odd | 4 | 1050.3.p.i.901.3 | 16 | |||
5.3 | odd | 4 | 210.3.o.b.61.5 | yes | 16 | ||
5.4 | even | 2 | inner | 1050.3.q.e.649.7 | 32 | ||
7.3 | odd | 6 | inner | 1050.3.q.e.199.7 | 32 | ||
15.8 | even | 4 | 630.3.v.c.271.3 | 16 | |||
35.3 | even | 12 | 210.3.o.b.31.5 | ✓ | 16 | ||
35.17 | even | 12 | 1050.3.p.i.451.3 | 16 | |||
35.23 | odd | 12 | 1470.3.f.d.391.3 | 16 | |||
35.24 | odd | 6 | inner | 1050.3.q.e.199.16 | 32 | ||
35.33 | even | 12 | 1470.3.f.d.391.5 | 16 | |||
105.38 | odd | 12 | 630.3.v.c.451.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.o.b.31.5 | ✓ | 16 | 35.3 | even | 12 | ||
210.3.o.b.61.5 | yes | 16 | 5.3 | odd | 4 | ||
630.3.v.c.271.3 | 16 | 15.8 | even | 4 | |||
630.3.v.c.451.3 | 16 | 105.38 | odd | 12 | |||
1050.3.p.i.451.3 | 16 | 35.17 | even | 12 | |||
1050.3.p.i.901.3 | 16 | 5.2 | odd | 4 | |||
1050.3.q.e.199.7 | 32 | 7.3 | odd | 6 | inner | ||
1050.3.q.e.199.16 | 32 | 35.24 | odd | 6 | inner | ||
1050.3.q.e.649.7 | 32 | 5.4 | even | 2 | inner | ||
1050.3.q.e.649.16 | 32 | 1.1 | even | 1 | trivial | ||
1470.3.f.d.391.3 | 16 | 35.23 | odd | 12 | |||
1470.3.f.d.391.5 | 16 | 35.33 | even | 12 |