Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,4,Mod(22,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.22");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.f (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.71712033036\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 58 x^{14} - 129 x^{13} + 2107 x^{12} - 4455 x^{11} + 42901 x^{10} - 76404 x^{9} + \cdots + 21307456 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 43.3 | ||
Root | \(1.30789 - 2.26533i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 63.43 |
Dual form | 63.4.f.b.22.3 |
$q$-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 \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.30789 | + | 2.26533i | −0.462408 | + | 0.800913i | −0.999080 | − | 0.0428770i | \(-0.986348\pi\) |
0.536673 | + | 0.843790i | \(0.319681\pi\) | |||||||
\(3\) | −3.13193 | + | 4.14620i | −0.602741 | + | 0.797937i | ||||
\(4\) | 0.578868 | + | 1.00263i | 0.0723584 | + | 0.125328i | ||||
\(5\) | 6.77153 | + | 11.7286i | 0.605664 | + | 1.04904i | 0.991946 | + | 0.126660i | \(0.0404257\pi\) |
−0.386282 | + | 0.922381i | \(0.626241\pi\) | |||||||
\(6\) | −5.29628 | − | 12.5176i | −0.360366 | − | 0.851715i | ||||
\(7\) | 3.50000 | − | 6.06218i | 0.188982 | − | 0.327327i | ||||
\(8\) | −23.9546 | −1.05865 | ||||||||
\(9\) | −7.38198 | − | 25.9713i | −0.273407 | − | 0.961899i | ||||
\(10\) | −35.4255 | −1.12025 | ||||||||
\(11\) | −12.0346 | + | 20.8445i | −0.329870 | + | 0.571351i | −0.982486 | − | 0.186338i | \(-0.940338\pi\) |
0.652616 | + | 0.757689i | \(0.273671\pi\) | |||||||
\(12\) | −5.97007 | − | 0.740063i | −0.143618 | − | 0.0178031i | ||||
\(13\) | −11.9972 | − | 20.7798i | −0.255956 | − | 0.443329i | 0.709199 | − | 0.705009i | \(-0.249057\pi\) |
−0.965155 | + | 0.261680i | \(0.915724\pi\) | |||||||
\(14\) | 9.15520 | + | 15.8573i | 0.174774 | + | 0.302717i | ||||
\(15\) | −69.8372 | − | 8.65717i | −1.20213 | − | 0.149018i | ||||
\(16\) | 26.6989 | − | 46.2438i | 0.417170 | − | 0.722560i | ||||
\(17\) | 79.6971 | 1.13702 | 0.568511 | − | 0.822675i | \(-0.307520\pi\) | ||||
0.568511 | + | 0.822675i | \(0.307520\pi\) | |||||||
\(18\) | 68.4881 | + | 17.2449i | 0.896823 | + | 0.225814i | ||||
\(19\) | −50.0463 | −0.604284 | −0.302142 | − | 0.953263i | \(-0.597702\pi\) | ||||
−0.302142 | + | 0.953263i | \(0.597702\pi\) | |||||||
\(20\) | −7.83963 | + | 13.5786i | −0.0876498 | + | 0.151814i | ||||
\(21\) | 14.1732 | + | 33.4980i | 0.147279 | + | 0.348089i | ||||
\(22\) | −31.4798 | − | 54.5245i | −0.305069 | − | 0.528394i | ||||
\(23\) | 75.8039 | + | 131.296i | 0.687226 | + | 1.19031i | 0.972732 | + | 0.231933i | \(0.0745051\pi\) |
−0.285506 | + | 0.958377i | \(0.592162\pi\) | |||||||
\(24\) | 75.0241 | − | 99.3204i | 0.638093 | − | 0.844737i | ||||
\(25\) | −29.2071 | + | 50.5883i | −0.233657 | + | 0.404706i | ||||
\(26\) | 62.7639 | 0.473424 | ||||||||
\(27\) | 130.802 | + | 50.7331i | 0.932328 | + | 0.361614i | ||||
\(28\) | 8.10415 | 0.0546978 | ||||||||
\(29\) | −128.062 | + | 221.810i | −0.820018 | + | 1.42031i | 0.0856508 | + | 0.996325i | \(0.472703\pi\) |
−0.905668 | + | 0.423987i | \(0.860630\pi\) | |||||||
\(30\) | 110.950 | − | 146.881i | 0.675223 | − | 0.893892i | ||||
\(31\) | 1.36254 | + | 2.35999i | 0.00789417 | + | 0.0136731i | 0.869946 | − | 0.493148i | \(-0.164154\pi\) |
−0.862051 | + | 0.506821i | \(0.830821\pi\) | |||||||
\(32\) | −25.9800 | − | 44.9987i | −0.143521 | − | 0.248585i | ||||
\(33\) | −48.7341 | − | 115.182i | −0.257076 | − | 0.607592i | ||||
\(34\) | −104.235 | + | 180.540i | −0.525768 | + | 0.910657i | ||||
\(35\) | 94.8014 | 0.457839 | ||||||||
\(36\) | 21.7663 | − | 22.4353i | 0.100770 | − | 0.103867i | ||||
\(37\) | 319.617 | 1.42013 | 0.710065 | − | 0.704137i | \(-0.248666\pi\) | ||||
0.710065 | + | 0.704137i | \(0.248666\pi\) | |||||||
\(38\) | 65.4548 | − | 113.371i | 0.279426 | − | 0.483979i | ||||
\(39\) | 123.732 | + | 15.3380i | 0.508023 | + | 0.0629756i | ||||
\(40\) | −162.209 | − | 280.954i | −0.641187 | − | 1.11057i | ||||
\(41\) | −82.3892 | − | 142.702i | −0.313830 | − | 0.543570i | 0.665358 | − | 0.746524i | \(-0.268279\pi\) |
−0.979188 | + | 0.202955i | \(0.934946\pi\) | |||||||
\(42\) | −94.4210 | − | 11.7046i | −0.346892 | − | 0.0430015i | ||||
\(43\) | −211.384 | + | 366.129i | −0.749670 | + | 1.29847i | 0.198310 | + | 0.980139i | \(0.436455\pi\) |
−0.947981 | + | 0.318328i | \(0.896879\pi\) | |||||||
\(44\) | −27.8657 | −0.0954754 | ||||||||
\(45\) | 254.620 | − | 262.446i | 0.843478 | − | 0.869402i | ||||
\(46\) | −396.571 | −1.27111 | ||||||||
\(47\) | −50.0386 | + | 86.6693i | −0.155295 | + | 0.268979i | −0.933166 | − | 0.359444i | \(-0.882966\pi\) |
0.777871 | + | 0.628424i | \(0.216300\pi\) | |||||||
\(48\) | 108.117 | + | 255.532i | 0.325112 | + | 0.768392i | ||||
\(49\) | −24.5000 | − | 42.4352i | −0.0714286 | − | 0.123718i | ||||
\(50\) | −76.3992 | − | 132.327i | −0.216090 | − | 0.374278i | ||||
\(51\) | −249.606 | + | 330.440i | −0.685330 | + | 0.907272i | ||||
\(52\) | 13.8896 | − | 24.0575i | 0.0370411 | − | 0.0641571i | ||||
\(53\) | 194.981 | 0.505333 | 0.252667 | − | 0.967553i | \(-0.418692\pi\) | ||||
0.252667 | + | 0.967553i | \(0.418692\pi\) | |||||||
\(54\) | −286.001 | + | 229.956i | −0.720737 | + | 0.579501i | ||||
\(55\) | −325.970 | −0.799160 | ||||||||
\(56\) | −83.8409 | + | 145.217i | −0.200066 | + | 0.346525i | ||||
\(57\) | 156.742 | − | 207.502i | 0.364227 | − | 0.482181i | ||||
\(58\) | −334.981 | − | 580.204i | −0.758365 | − | 1.31353i | ||||
\(59\) | −288.258 | − | 499.277i | −0.636067 | − | 1.10170i | −0.986288 | − | 0.165033i | \(-0.947227\pi\) |
0.350221 | − | 0.936667i | \(-0.386106\pi\) | |||||||
\(60\) | −31.7466 | − | 75.0321i | −0.0683078 | − | 0.161443i | ||||
\(61\) | 21.5192 | − | 37.2723i | 0.0451680 | − | 0.0782332i | −0.842558 | − | 0.538606i | \(-0.818951\pi\) |
0.887726 | + | 0.460373i | \(0.152284\pi\) | |||||||
\(62\) | −7.12819 | −0.0146013 | ||||||||
\(63\) | −183.279 | − | 46.1485i | −0.366524 | − | 0.0922884i | ||||
\(64\) | 563.098 | 1.09980 | ||||||||
\(65\) | 162.479 | − | 281.422i | 0.310046 | − | 0.537016i | ||||
\(66\) | 324.662 | + | 40.2458i | 0.605502 | + | 0.0750594i | ||||
\(67\) | 508.257 | + | 880.326i | 0.926768 | + | 1.60521i | 0.788693 | + | 0.614787i | \(0.210758\pi\) |
0.138074 | + | 0.990422i | \(0.455909\pi\) | |||||||
\(68\) | 46.1341 | + | 79.9065i | 0.0822732 | + | 0.142501i | ||||
\(69\) | −781.793 | − | 96.9127i | −1.36401 | − | 0.169086i | ||||
\(70\) | −123.989 | + | 214.756i | −0.211708 | + | 0.366689i | ||||
\(71\) | −509.305 | −0.851315 | −0.425657 | − | 0.904884i | \(-0.639957\pi\) | ||||
−0.425657 | + | 0.904884i | \(0.639957\pi\) | |||||||
\(72\) | 176.832 | + | 622.130i | 0.289442 | + | 1.01832i | ||||
\(73\) | 1039.67 | 1.66690 | 0.833452 | − | 0.552592i | \(-0.186361\pi\) | ||||
0.833452 | + | 0.552592i | \(0.186361\pi\) | |||||||
\(74\) | −418.023 | + | 724.037i | −0.656678 | + | 1.13740i | ||||
\(75\) | −118.274 | − | 279.538i | −0.182095 | − | 0.430377i | ||||
\(76\) | −28.9702 | − | 50.1778i | −0.0437251 | − | 0.0757341i | ||||
\(77\) | 84.2422 | + | 145.912i | 0.124679 | + | 0.215950i | ||||
\(78\) | −196.572 | + | 260.232i | −0.285352 | + | 0.377762i | ||||
\(79\) | 447.071 | − | 774.349i | 0.636701 | − | 1.10280i | −0.349451 | − | 0.936955i | \(-0.613632\pi\) |
0.986152 | − | 0.165844i | \(-0.0530347\pi\) | |||||||
\(80\) | 723.169 | 1.01066 | ||||||||
\(81\) | −620.013 | + | 383.439i | −0.850498 | + | 0.525979i | ||||
\(82\) | 431.023 | 0.580470 | ||||||||
\(83\) | −7.23057 | + | 12.5237i | −0.00956214 | + | 0.0165621i | −0.870767 | − | 0.491696i | \(-0.836377\pi\) |
0.861205 | + | 0.508258i | \(0.169710\pi\) | |||||||
\(84\) | −25.3816 | + | 33.6014i | −0.0329686 | + | 0.0436454i | ||||
\(85\) | 539.671 | + | 934.738i | 0.688653 | + | 1.19278i | ||||
\(86\) | −552.934 | − | 957.709i | −0.693307 | − | 1.20084i | ||||
\(87\) | −518.587 | − | 1225.66i | −0.639061 | − | 1.51040i | ||||
\(88\) | 288.283 | − | 499.321i | 0.349217 | − | 0.604862i | ||||
\(89\) | 1532.12 | 1.82477 | 0.912384 | − | 0.409336i | \(-0.134240\pi\) | ||||
0.912384 | + | 0.409336i | \(0.134240\pi\) | |||||||
\(90\) | 261.511 | + | 920.046i | 0.306285 | + | 1.07757i | ||||
\(91\) | −167.961 | −0.193484 | ||||||||
\(92\) | −87.7608 | + | 152.006i | −0.0994532 | + | 0.172258i | ||||
\(93\) | −14.0524 | − | 1.74196i | −0.0156684 | − | 0.00194229i | ||||
\(94\) | −130.889 | − | 226.707i | −0.143619 | − | 0.248756i | ||||
\(95\) | −338.890 | − | 586.974i | −0.365993 | − | 0.633919i | ||||
\(96\) | 267.941 | + | 33.2146i | 0.284861 | + | 0.0353119i | ||||
\(97\) | 887.575 | − | 1537.32i | 0.929067 | − | 1.60919i | 0.144182 | − | 0.989551i | \(-0.453945\pi\) |
0.784886 | − | 0.619641i | \(-0.212722\pi\) | |||||||
\(98\) | 128.173 | 0.132116 | ||||||||
\(99\) | 630.198 | + | 158.680i | 0.639770 | + | 0.161090i | ||||
\(100\) | −67.6283 | −0.0676283 | ||||||||
\(101\) | −169.349 | + | 293.320i | −0.166840 | + | 0.288975i | −0.937307 | − | 0.348504i | \(-0.886690\pi\) |
0.770467 | + | 0.637480i | \(0.220023\pi\) | |||||||
\(102\) | −422.098 | − | 997.617i | −0.409745 | − | 0.968420i | ||||
\(103\) | 225.235 | + | 390.119i | 0.215467 | + | 0.373200i | 0.953417 | − | 0.301656i | \(-0.0975393\pi\) |
−0.737950 | + | 0.674855i | \(0.764206\pi\) | |||||||
\(104\) | 287.388 | + | 497.770i | 0.270968 | + | 0.469331i | ||||
\(105\) | −296.912 | + | 393.066i | −0.275958 | + | 0.365326i | ||||
\(106\) | −255.013 | + | 441.695i | −0.233670 | + | 0.404728i | ||||
\(107\) | −581.208 | −0.525117 | −0.262558 | − | 0.964916i | \(-0.584566\pi\) | ||||
−0.262558 | + | 0.964916i | \(0.584566\pi\) | |||||||
\(108\) | 24.8506 | + | 160.513i | 0.0221412 | + | 0.143013i | ||||
\(109\) | −1381.38 | −1.21388 | −0.606938 | − | 0.794749i | \(-0.707602\pi\) | ||||
−0.606938 | + | 0.794749i | \(0.707602\pi\) | |||||||
\(110\) | 426.332 | − | 738.429i | 0.369538 | − | 0.640058i | ||||
\(111\) | −1001.02 | + | 1325.20i | −0.855970 | + | 1.13317i | ||||
\(112\) | −186.892 | − | 323.707i | −0.157675 | − | 0.273102i | ||||
\(113\) | −749.878 | − | 1298.83i | −0.624271 | − | 1.08127i | −0.988681 | − | 0.150031i | \(-0.952063\pi\) |
0.364410 | − | 0.931239i | \(-0.381271\pi\) | |||||||
\(114\) | 265.059 | + | 626.460i | 0.217764 | + | 0.514678i | ||||
\(115\) | −1026.62 | + | 1778.15i | −0.832456 | + | 1.44186i | ||||
\(116\) | −296.524 | −0.237341 | ||||||||
\(117\) | −451.114 | + | 464.978i | −0.356457 | + | 0.367413i | ||||
\(118\) | 1508.03 | 1.17649 | ||||||||
\(119\) | 278.940 | − | 483.138i | 0.214877 | − | 0.372178i | ||||
\(120\) | 1672.92 | + | 207.379i | 1.27263 | + | 0.157758i | ||||
\(121\) | 375.837 | + | 650.969i | 0.282372 | + | 0.489083i | ||||
\(122\) | 56.2892 | + | 97.4958i | 0.0417720 | + | 0.0723513i | ||||
\(123\) | 849.710 | + | 105.332i | 0.622892 | + | 0.0772150i | ||||
\(124\) | −1.57746 | + | 2.73224i | −0.00114242 | + | 0.00197873i | ||||
\(125\) | 901.774 | 0.645257 | ||||||||
\(126\) | 344.250 | − | 354.830i | 0.243399 | − | 0.250879i | ||||
\(127\) | −908.229 | −0.634585 | −0.317292 | − | 0.948328i | \(-0.602774\pi\) | ||||
−0.317292 | + | 0.948328i | \(0.602774\pi\) | |||||||
\(128\) | −528.628 | + | 915.610i | −0.365035 | + | 0.632260i | ||||
\(129\) | −856.001 | − | 2023.13i | −0.584238 | − | 1.38083i | ||||
\(130\) | 425.008 | + | 736.135i | 0.286736 | + | 0.496641i | ||||
\(131\) | 309.932 | + | 536.818i | 0.206709 | + | 0.358030i | 0.950676 | − | 0.310186i | \(-0.100391\pi\) |
−0.743967 | + | 0.668216i | \(0.767058\pi\) | |||||||
\(132\) | 87.2737 | − | 115.537i | 0.0575469 | − | 0.0761834i | ||||
\(133\) | −175.162 | + | 303.389i | −0.114199 | + | 0.197798i | ||||
\(134\) | −2658.97 | −1.71418 | ||||||||
\(135\) | 290.700 | + | 1877.67i | 0.185329 | + | 1.19707i | ||||
\(136\) | −1909.11 | −1.20371 | ||||||||
\(137\) | 381.288 | − | 660.410i | 0.237778 | − | 0.411844i | −0.722298 | − | 0.691582i | \(-0.756914\pi\) |
0.960076 | + | 0.279738i | \(0.0902475\pi\) | |||||||
\(138\) | 1242.03 | − | 1644.26i | 0.766152 | − | 1.01427i | ||||
\(139\) | −696.068 | − | 1205.63i | −0.424746 | − | 0.735682i | 0.571651 | − | 0.820497i | \(-0.306303\pi\) |
−0.996397 | + | 0.0848153i | \(0.972970\pi\) | |||||||
\(140\) | 54.8774 | + | 95.0505i | 0.0331285 | + | 0.0573802i | ||||
\(141\) | −202.631 | − | 478.913i | −0.121026 | − | 0.286041i | ||||
\(142\) | 666.113 | − | 1153.74i | 0.393654 | − | 0.681830i | ||||
\(143\) | 577.526 | 0.337728 | ||||||||
\(144\) | −1398.10 | − | 352.033i | −0.809086 | − | 0.203723i | ||||
\(145\) | −3468.70 | −1.98662 | ||||||||
\(146\) | −1359.77 | + | 2355.19i | −0.770789 | + | 1.33505i | ||||
\(147\) | 252.677 | + | 31.3224i | 0.141772 | + | 0.0175744i | ||||
\(148\) | 185.016 | + | 320.457i | 0.102758 | + | 0.177983i | ||||
\(149\) | −521.124 | − | 902.613i | −0.286525 | − | 0.496275i | 0.686453 | − | 0.727174i | \(-0.259167\pi\) |
−0.972978 | + | 0.230899i | \(0.925833\pi\) | |||||||
\(150\) | 787.933 | + | 97.6739i | 0.428897 | + | 0.0531669i | ||||
\(151\) | −49.9139 | + | 86.4533i | −0.0269002 | + | 0.0465925i | −0.879162 | − | 0.476523i | \(-0.841897\pi\) |
0.852262 | + | 0.523115i | \(0.175230\pi\) | |||||||
\(152\) | 1198.84 | 0.639727 | ||||||||
\(153\) | −588.322 | − | 2069.83i | −0.310870 | − | 1.09370i | ||||
\(154\) | −440.717 | −0.230610 | ||||||||
\(155\) | −18.4529 | + | 31.9614i | −0.00956243 | + | 0.0165626i | ||||
\(156\) | 56.2459 | + | 132.935i | 0.0288671 | + | 0.0682266i | ||||
\(157\) | −246.721 | − | 427.334i | −0.125417 | − | 0.217229i | 0.796479 | − | 0.604666i | \(-0.206694\pi\) |
−0.921896 | + | 0.387438i | \(0.873360\pi\) | |||||||
\(158\) | 1169.43 | + | 2025.52i | 0.588831 | + | 1.01988i | ||||
\(159\) | −610.667 | + | 808.430i | −0.304585 | + | 0.403224i | ||||
\(160\) | 351.848 | − | 609.419i | 0.173850 | − | 0.301118i | ||||
\(161\) | 1061.25 | 0.519494 | ||||||||
\(162\) | −57.7075 | − | 1906.02i | −0.0279872 | − | 0.924392i | ||||
\(163\) | 2174.81 | 1.04506 | 0.522529 | − | 0.852622i | \(-0.324989\pi\) | ||||
0.522529 | + | 0.852622i | \(0.324989\pi\) | |||||||
\(164\) | 95.3849 | − | 165.211i | 0.0454165 | − | 0.0786637i | ||||
\(165\) | 1020.92 | − | 1351.54i | 0.481687 | − | 0.637680i | ||||
\(166\) | −18.9135 | − | 32.7592i | −0.00884321 | − | 0.0153169i | ||||
\(167\) | −1150.10 | − | 1992.04i | −0.532921 | − | 0.923045i | −0.999261 | − | 0.0384401i | \(-0.987761\pi\) |
0.466340 | − | 0.884605i | \(-0.345572\pi\) | |||||||
\(168\) | −339.514 | − | 802.431i | −0.155917 | − | 0.368505i | ||||
\(169\) | 810.634 | − | 1404.06i | 0.368973 | − | 0.639080i | ||||
\(170\) | −2823.31 | −1.27375 | ||||||||
\(171\) | 369.441 | + | 1299.76i | 0.165215 | + | 0.581260i | ||||
\(172\) | −489.454 | −0.216980 | ||||||||
\(173\) | 156.272 | − | 270.672i | 0.0686773 | − | 0.118953i | −0.829642 | − | 0.558296i | \(-0.811455\pi\) |
0.898319 | + | 0.439343i | \(0.144789\pi\) | |||||||
\(174\) | 3454.78 | + | 428.262i | 1.50521 | + | 0.186589i | ||||
\(175\) | 204.450 | + | 354.118i | 0.0883141 | + | 0.152965i | ||||
\(176\) | 642.620 | + | 1113.05i | 0.275224 | + | 0.476701i | ||||
\(177\) | 2972.91 | + | 368.528i | 1.26247 | + | 0.156499i | ||||
\(178\) | −2003.84 | + | 3470.75i | −0.843786 | + | 1.46148i | ||||
\(179\) | 4345.85 | 1.81466 | 0.907329 | − | 0.420421i | \(-0.138118\pi\) | ||||
0.907329 | + | 0.420421i | \(0.138118\pi\) | |||||||
\(180\) | 410.527 | + | 103.368i | 0.169994 | + | 0.0428033i | ||||
\(181\) | −110.995 | −0.0455812 | −0.0227906 | − | 0.999740i | \(-0.507255\pi\) | ||||
−0.0227906 | + | 0.999740i | \(0.507255\pi\) | |||||||
\(182\) | 219.674 | − | 380.486i | 0.0894687 | − | 0.154964i | ||||
\(183\) | 87.1418 | + | 205.957i | 0.0352006 | + | 0.0831956i | ||||
\(184\) | −1815.85 | − | 3145.14i | −0.727533 | − | 1.26012i | ||||
\(185\) | 2164.30 | + | 3748.67i | 0.860121 | + | 1.48977i | ||||
\(186\) | 22.3250 | − | 29.5549i | 0.00880080 | − | 0.0116509i | ||||
\(187\) | −959.122 | + | 1661.25i | −0.375069 | + | 0.649639i | ||||
\(188\) | −115.863 | −0.0449477 | ||||||||
\(189\) | 765.360 | − | 615.379i | 0.294559 | − | 0.236837i | ||||
\(190\) | 1772.92 | 0.676952 | ||||||||
\(191\) | −1102.94 | + | 1910.35i | −0.417833 | + | 0.723707i | −0.995721 | − | 0.0924083i | \(-0.970543\pi\) |
0.577889 | + | 0.816116i | \(0.303877\pi\) | |||||||
\(192\) | −1763.58 | + | 2334.72i | −0.662895 | + | 0.877571i | ||||
\(193\) | 219.259 | + | 379.767i | 0.0817750 | + | 0.141639i | 0.904012 | − | 0.427506i | \(-0.140608\pi\) |
−0.822237 | + | 0.569145i | \(0.807274\pi\) | |||||||
\(194\) | 2321.69 | + | 4021.29i | 0.859216 | + | 1.48821i | ||||
\(195\) | 657.958 | + | 1555.06i | 0.241627 | + | 0.571079i | ||||
\(196\) | 28.3645 | − | 49.1288i | 0.0103369 | − | 0.0179041i | ||||
\(197\) | 2536.01 | 0.917173 | 0.458587 | − | 0.888650i | \(-0.348356\pi\) | ||||
0.458587 | + | 0.888650i | \(0.348356\pi\) | |||||||
\(198\) | −1183.69 | + | 1220.07i | −0.424854 | + | 0.437911i | ||||
\(199\) | 2797.01 | 0.996356 | 0.498178 | − | 0.867075i | \(-0.334003\pi\) | ||||
0.498178 | + | 0.867075i | \(0.334003\pi\) | |||||||
\(200\) | 699.644 | − | 1211.82i | 0.247361 | − | 0.428443i | ||||
\(201\) | −5241.84 | − | 649.789i | −1.83946 | − | 0.228023i | ||||
\(202\) | −442.978 | − | 767.260i | −0.154296 | − | 0.267248i | ||||
\(203\) | 896.434 | + | 1552.67i | 0.309937 | + | 0.536827i | ||||
\(204\) | −475.797 | − | 58.9808i | −0.163296 | − | 0.0202426i | ||||
\(205\) | 1115.80 | − | 1932.62i | 0.380151 | − | 0.658441i | ||||
\(206\) | −1178.33 | −0.398534 | ||||||||
\(207\) | 2850.34 | − | 2937.95i | 0.957065 | − | 0.986480i | ||||
\(208\) | −1281.25 | −0.427109 | ||||||||
\(209\) | 602.287 | − | 1043.19i | 0.199335 | − | 0.345259i | ||||
\(210\) | −502.095 | − | 1186.69i | −0.164990 | − | 0.389948i | ||||
\(211\) | −944.079 | − | 1635.19i | −0.308024 | − | 0.533514i | 0.669906 | − | 0.742446i | \(-0.266334\pi\) |
−0.977930 | + | 0.208932i | \(0.933001\pi\) | |||||||
\(212\) | 112.868 | + | 195.493i | 0.0365651 | + | 0.0633327i | ||||
\(213\) | 1595.11 | − | 2111.68i | 0.513122 | − | 0.679296i | ||||
\(214\) | 760.154 | − | 1316.62i | 0.242818 | − | 0.420573i | ||||
\(215\) | −5725.58 | −1.81619 | ||||||||
\(216\) | −3133.30 | − | 1215.29i | −0.987010 | − | 0.382824i | ||||
\(217\) | 19.0756 | 0.00596743 | ||||||||
\(218\) | 1806.69 | − | 3129.28i | 0.561305 | − | 0.972210i | ||||
\(219\) | −3256.17 | + | 4310.67i | −1.00471 | + | 1.33008i | ||||
\(220\) | −188.694 | − | 326.827i | −0.0578260 | − | 0.100158i | ||||
\(221\) | −956.142 | − | 1656.09i | −0.291028 | − | 0.504075i | ||||
\(222\) | −1692.78 | − | 4000.85i | −0.511767 | − | 1.20955i | ||||
\(223\) | −674.874 | + | 1168.92i | −0.202659 | + | 0.351015i | −0.949384 | − | 0.314117i | \(-0.898292\pi\) |
0.746725 | + | 0.665132i | \(0.231625\pi\) | |||||||
\(224\) | −363.720 | −0.108491 | ||||||||
\(225\) | 1529.45 | + | 385.105i | 0.453170 | + | 0.114105i | ||||
\(226\) | 3923.02 | 1.15467 | ||||||||
\(227\) | −1242.53 | + | 2152.13i | −0.363303 | + | 0.629260i | −0.988502 | − | 0.151206i | \(-0.951684\pi\) |
0.625199 | + | 0.780465i | \(0.285018\pi\) | |||||||
\(228\) | 298.780 | + | 37.0374i | 0.0867859 | + | 0.0107582i | ||||
\(229\) | 931.009 | + | 1612.56i | 0.268659 | + | 0.465330i | 0.968516 | − | 0.248953i | \(-0.0800863\pi\) |
−0.699857 | + | 0.714283i | \(0.746753\pi\) | |||||||
\(230\) | −2685.39 | − | 4651.24i | −0.769868 | − | 1.33345i | ||||
\(231\) | −868.820 | − | 107.701i | −0.247464 | − | 0.0306761i | ||||
\(232\) | 3067.67 | − | 5313.35i | 0.868113 | − | 1.50362i | ||||
\(233\) | −4094.94 | −1.15137 | −0.575684 | − | 0.817672i | \(-0.695264\pi\) | ||||
−0.575684 | + | 0.817672i | \(0.695264\pi\) | |||||||
\(234\) | −463.322 | − | 1630.06i | −0.129437 | − | 0.455386i | ||||
\(235\) | −1355.35 | −0.376227 | ||||||||
\(236\) | 333.726 | − | 578.030i | 0.0920496 | − | 0.159435i | ||||
\(237\) | 1810.41 | + | 4278.85i | 0.496198 | + | 1.17275i | ||||
\(238\) | 729.643 | + | 1263.78i | 0.198722 | + | 0.344196i | ||||
\(239\) | 1061.36 | + | 1838.33i | 0.287254 | + | 0.497538i | 0.973153 | − | 0.230158i | \(-0.0739244\pi\) |
−0.685900 | + | 0.727696i | \(0.740591\pi\) | |||||||
\(240\) | −2264.92 | + | 2998.40i | −0.609166 | + | 0.806442i | ||||
\(241\) | −2644.98 | + | 4581.25i | −0.706964 | + | 1.22450i | 0.259014 | + | 0.965874i | \(0.416603\pi\) |
−0.965978 | + | 0.258624i | \(0.916731\pi\) | |||||||
\(242\) | −1966.21 | −0.522284 | ||||||||
\(243\) | 352.024 | − | 3771.60i | 0.0929315 | − | 0.995673i | ||||
\(244\) | 49.8270 | 0.0130731 | ||||||||
\(245\) | 331.805 | − | 574.703i | 0.0865234 | − | 0.149863i | ||||
\(246\) | −1349.93 | + | 1787.11i | −0.349873 | + | 0.463178i | ||||
\(247\) | 600.416 | + | 1039.95i | 0.154670 | + | 0.267897i | ||||
\(248\) | −32.6390 | − | 56.5325i | −0.00835718 | − | 0.0144751i | ||||
\(249\) | −29.2802 | − | 69.2028i | −0.00745203 | − | 0.0176127i | ||||
\(250\) | −1179.42 | + | 2042.81i | −0.298372 | + | 0.516795i | ||||
\(251\) | −4632.56 | −1.16496 | −0.582480 | − | 0.812845i | \(-0.697918\pi\) | ||||
−0.582480 | + | 0.812845i | \(0.697918\pi\) | |||||||
\(252\) | −59.8247 | − | 210.475i | −0.0149548 | − | 0.0526138i | ||||
\(253\) | −3649.07 | −0.906780 | ||||||||
\(254\) | 1187.86 | − | 2057.43i | 0.293437 | − | 0.508248i | ||||
\(255\) | −5565.82 | − | 689.951i | −1.36684 | − | 0.169437i | ||||
\(256\) | 869.621 | + | 1506.23i | 0.212310 | + | 0.367731i | ||||
\(257\) | −1578.23 | − | 2733.58i | −0.383065 | − | 0.663487i | 0.608434 | − | 0.793604i | \(-0.291798\pi\) |
−0.991499 | + | 0.130117i | \(0.958465\pi\) | |||||||
\(258\) | 5702.61 | + | 706.907i | 1.37608 | + | 0.170582i | ||||
\(259\) | 1118.66 | − | 1937.58i | 0.268379 | − | 0.464846i | ||||
\(260\) | 376.215 | 0.0897379 | ||||||||
\(261\) | 6706.03 | + | 1688.53i | 1.59039 | + | 0.400451i | ||||
\(262\) | −1621.42 | −0.382335 | ||||||||
\(263\) | 894.284 | − | 1548.95i | 0.209673 | − | 0.363164i | −0.741939 | − | 0.670468i | \(-0.766093\pi\) |
0.951611 | + | 0.307304i | \(0.0994268\pi\) | |||||||
\(264\) | 1167.40 | + | 2759.12i | 0.272154 | + | 0.643228i | ||||
\(265\) | 1320.32 | + | 2286.86i | 0.306062 | + | 0.530115i | ||||
\(266\) | −458.184 | − | 793.598i | −0.105613 | − | 0.182927i | ||||
\(267\) | −4798.50 | + | 6352.47i | −1.09986 | + | 1.45605i | ||||
\(268\) | −588.427 | + | 1019.18i | −0.134119 | + | 0.232301i | ||||
\(269\) | 5780.38 | 1.31017 | 0.655085 | − | 0.755555i | \(-0.272633\pi\) | ||||
0.655085 | + | 0.755555i | \(0.272633\pi\) | |||||||
\(270\) | −4633.73 | − | 1797.25i | −1.04444 | − | 0.405100i | ||||
\(271\) | 5745.97 | 1.28798 | 0.643991 | − | 0.765033i | \(-0.277277\pi\) | ||||
0.643991 | + | 0.765033i | \(0.277277\pi\) | |||||||
\(272\) | 2127.82 | − | 3685.50i | 0.474332 | − | 0.821567i | ||||
\(273\) | 526.042 | − | 696.400i | 0.116621 | − | 0.154388i | ||||
\(274\) | 997.362 | + | 1727.48i | 0.219901 | + | 0.380879i | ||||
\(275\) | −702.992 | − | 1217.62i | −0.154153 | − | 0.267001i | ||||
\(276\) | −355.387 | − | 839.947i | −0.0775065 | − | 0.183184i | ||||
\(277\) | −1746.81 | + | 3025.57i | −0.378902 | + | 0.656278i | −0.990903 | − | 0.134579i | \(-0.957032\pi\) |
0.612001 | + | 0.790857i | \(0.290365\pi\) | |||||||
\(278\) | 3641.51 | 0.785623 | ||||||||
\(279\) | 51.2336 | − | 52.8083i | 0.0109938 | − | 0.0113317i | ||||
\(280\) | −2270.92 | −0.484692 | ||||||||
\(281\) | −927.263 | + | 1606.07i | −0.196854 | + | 0.340961i | −0.947507 | − | 0.319736i | \(-0.896406\pi\) |
0.750653 | + | 0.660697i | \(0.229739\pi\) | |||||||
\(282\) | 1349.91 | + | 167.338i | 0.285057 | + | 0.0353362i | ||||
\(283\) | −2710.16 | − | 4694.13i | −0.569266 | − | 0.985997i | −0.996639 | − | 0.0819218i | \(-0.973894\pi\) |
0.427373 | − | 0.904075i | \(-0.359439\pi\) | |||||||
\(284\) | −294.820 | − | 510.643i | −0.0615998 | − | 0.106694i | ||||
\(285\) | 3495.09 | + | 433.259i | 0.726426 | + | 0.0900493i | ||||
\(286\) | −755.338 | + | 1308.28i | −0.156168 | + | 0.270491i | ||||
\(287\) | −1153.45 | −0.237233 | ||||||||
\(288\) | −976.888 | + | 1006.91i | −0.199874 | + | 0.206017i | ||||
\(289\) | 1438.63 | 0.292820 | ||||||||
\(290\) | 4536.66 | − | 7857.73i | 0.918628 | − | 1.59111i | ||||
\(291\) | 3594.23 | + | 8494.86i | 0.724047 | + | 1.71126i | ||||
\(292\) | 601.830 | + | 1042.40i | 0.120615 | + | 0.208911i | ||||
\(293\) | −707.626 | − | 1225.64i | −0.141092 | − | 0.244379i | 0.786816 | − | 0.617188i | \(-0.211728\pi\) |
−0.927908 | + | 0.372809i | \(0.878395\pi\) | |||||||
\(294\) | −401.429 | + | 531.431i | −0.0796320 | + | 0.105421i | ||||
\(295\) | 3903.89 | − | 6761.73i | 0.770485 | − | 1.33452i | ||||
\(296\) | −7656.29 | −1.50342 | ||||||||
\(297\) | −2631.66 | + | 2115.95i | −0.514155 | + | 0.413401i | ||||
\(298\) | 2726.28 | 0.529964 | ||||||||
\(299\) | 1818.87 | − | 3150.37i | 0.351799 | − | 0.609334i | ||||
\(300\) | 211.807 | − | 280.400i | 0.0407623 | − | 0.0539631i | ||||
\(301\) | 1479.69 | + | 2562.90i | 0.283349 | + | 0.490775i | ||||
\(302\) | −130.563 | − | 226.142i | −0.0248777 | − | 0.0430895i | ||||
\(303\) | −685.777 | − | 1620.81i | −0.130023 | − | 0.307305i | ||||
\(304\) | −1336.18 | + | 2314.33i | −0.252089 | + | 0.436632i | ||||
\(305\) | 582.870 | 0.109426 | ||||||||
\(306\) | 5458.31 | + | 1374.37i | 1.01971 | + | 0.256756i | ||||
\(307\) | 6596.15 | 1.22626 | 0.613131 | − | 0.789982i | \(-0.289910\pi\) | ||||
0.613131 | + | 0.789982i | \(0.289910\pi\) | |||||||
\(308\) | −97.5301 | + | 168.927i | −0.0180432 | + | 0.0312517i | ||||
\(309\) | −2322.94 | − | 287.956i | −0.427661 | − | 0.0530137i | ||||
\(310\) | −48.2687 | − | 83.6039i | −0.00884348 | − | 0.0153174i | ||||
\(311\) | 379.003 | + | 656.452i | 0.0691037 | + | 0.119691i | 0.898507 | − | 0.438959i | \(-0.144653\pi\) |
−0.829403 | + | 0.558650i | \(0.811319\pi\) | |||||||
\(312\) | −2963.93 | − | 367.416i | −0.537820 | − | 0.0666693i | ||||
\(313\) | −3552.76 | + | 6153.56i | −0.641578 | + | 1.11125i | 0.343503 | + | 0.939152i | \(0.388387\pi\) |
−0.985081 | + | 0.172094i | \(0.944947\pi\) | |||||||
\(314\) | 1290.73 | 0.231975 | ||||||||
\(315\) | −699.822 | − | 2462.11i | −0.125176 | − | 0.440394i | ||||
\(316\) | 1035.18 | 0.184283 | ||||||||
\(317\) | 2629.69 | − | 4554.75i | 0.465924 | − | 0.807005i | −0.533318 | − | 0.845915i | \(-0.679055\pi\) |
0.999243 | + | 0.0389100i | \(0.0123886\pi\) | |||||||
\(318\) | −1032.67 | − | 2440.69i | −0.182105 | − | 0.430400i | ||||
\(319\) | −3082.35 | − | 5338.78i | −0.540998 | − | 0.937036i | ||||
\(320\) | 3813.03 | + | 6604.36i | 0.666109 | + | 1.15373i | ||||
\(321\) | 1820.30 | − | 2409.81i | 0.316509 | − | 0.419010i | ||||
\(322\) | −1388.00 | + | 2404.09i | −0.240218 | + | 0.416070i | ||||
\(323\) | −3988.54 | −0.687085 | ||||||||
\(324\) | −743.352 | − | 399.682i | −0.127461 | − | 0.0685325i | ||||
\(325\) | 1401.62 | 0.239224 | ||||||||
\(326\) | −2844.41 | + | 4926.66i | −0.483243 | + | 0.837001i | ||||
\(327\) | 4326.40 | − | 5727.49i | 0.731653 | − | 0.968596i | ||||
\(328\) | 1973.60 | + | 3418.37i | 0.332237 | + | 0.575451i | ||||
\(329\) | 350.270 | + | 606.685i | 0.0586961 | + | 0.101665i | ||||
\(330\) | 1726.43 | + | 4080.37i | 0.287991 | + | 0.680657i | ||||
\(331\) | 2126.09 | − | 3682.50i | 0.353053 | − | 0.611507i | −0.633729 | − | 0.773555i | \(-0.718477\pi\) |
0.986783 | + | 0.162048i | \(0.0518100\pi\) | |||||||
\(332\) | −16.7422 | −0.00276761 | ||||||||
\(333\) | −2359.41 | − | 8300.87i | −0.388273 | − | 1.36602i | ||||
\(334\) | 6016.82 | 0.985706 | ||||||||
\(335\) | −6883.35 | + | 11922.3i | −1.12262 | + | 1.94443i | ||||
\(336\) | 1927.49 | + | 238.935i | 0.312956 | + | 0.0387946i | ||||
\(337\) | −1296.08 | − | 2244.87i | −0.209501 | − | 0.362867i | 0.742056 | − | 0.670338i | \(-0.233851\pi\) |
−0.951558 | + | 0.307471i | \(0.900517\pi\) | |||||||
\(338\) | 2120.43 | + | 3672.70i | 0.341232 | + | 0.591031i | ||||
\(339\) | 7733.77 | + | 958.694i | 1.23906 | + | 0.153596i | ||||
\(340\) | −624.796 | + | 1082.18i | −0.0996598 | + | 0.172616i | ||||
\(341\) | −65.5905 | −0.0104162 | ||||||||
\(342\) | −3427.58 | − | 863.041i | −0.541936 | − | 0.136456i | ||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 5063.62 | − | 8770.45i | 0.793640 | − | 1.37462i | ||||
\(345\) | −4157.28 | − | 9825.60i | −0.648755 | − | 1.53331i | ||||
\(346\) | 408.773 | + | 708.016i | 0.0635138 | + | 0.110009i | ||||
\(347\) | 245.989 | + | 426.066i | 0.0380559 | + | 0.0659148i | 0.884426 | − | 0.466680i | \(-0.154550\pi\) |
−0.846370 | + | 0.532595i | \(0.821217\pi\) | |||||||
\(348\) | 928.692 | − | 1229.45i | 0.143055 | − | 0.189383i | ||||
\(349\) | 5958.75 | − | 10320.9i | 0.913939 | − | 1.58299i | 0.105491 | − | 0.994420i | \(-0.466358\pi\) |
0.808448 | − | 0.588568i | \(-0.200308\pi\) | |||||||
\(350\) | −1069.59 | −0.163348 | ||||||||
\(351\) | −515.036 | − | 3326.69i | −0.0783208 | − | 0.505885i | ||||
\(352\) | 1250.63 | 0.189372 | ||||||||
\(353\) | −4039.98 | + | 6997.45i | −0.609140 | + | 1.05506i | 0.382242 | + | 0.924062i | \(0.375152\pi\) |
−0.991382 | + | 0.130999i | \(0.958181\pi\) | |||||||
\(354\) | −4723.06 | + | 6252.61i | −0.709118 | + | 0.938764i | ||||
\(355\) | −3448.77 | − | 5973.45i | −0.515611 | − | 0.893064i | ||||
\(356\) | 886.894 | + | 1536.15i | 0.132037 | + | 0.228695i | ||||
\(357\) | 1129.57 | + | 2669.70i | 0.167459 | + | 0.395785i | ||||
\(358\) | −5683.87 | + | 9844.76i | −0.839112 | + | 1.45338i | ||||
\(359\) | −6675.40 | −0.981376 | −0.490688 | − | 0.871335i | \(-0.663255\pi\) | ||||
−0.490688 | + | 0.871335i | \(0.663255\pi\) | |||||||
\(360\) | −6099.31 | + | 6286.77i | −0.892949 | + | 0.920394i | ||||
\(361\) | −4354.37 | −0.634840 | ||||||||
\(362\) | 145.169 | − | 251.440i | 0.0210771 | − | 0.0365066i | ||||
\(363\) | −3876.15 | − | 480.495i | −0.560454 | − | 0.0694751i | ||||
\(364\) | −97.2271 | − | 168.402i | −0.0140002 | − | 0.0242491i | ||||
\(365\) | 7040.14 | + | 12193.9i | 1.00958 | + | 1.74865i | ||||
\(366\) | −580.532 | − | 71.9639i | −0.0829095 | − | 0.0102776i | ||||
\(367\) | 5888.45 | − | 10199.1i | 0.837532 | − | 1.45065i | −0.0544197 | − | 0.998518i | \(-0.517331\pi\) |
0.891952 | − | 0.452130i | \(-0.149336\pi\) | |||||||
\(368\) | 8095.51 | 1.14676 | ||||||||
\(369\) | −3097.96 | + | 3193.18i | −0.437055 | + | 0.450488i | ||||
\(370\) | −11322.6 | −1.59091 | ||||||||
\(371\) | 682.433 | − | 1182.01i | 0.0954991 | − | 0.165409i | ||||
\(372\) | −6.38792 | − | 15.0977i | −0.000890318 | − | 0.00210424i | ||||
\(373\) | −741.638 | − | 1284.55i | −0.102950 | − | 0.178315i | 0.809949 | − | 0.586501i | \(-0.199495\pi\) |
−0.912899 | + | 0.408185i | \(0.866162\pi\) | |||||||
\(374\) | −2508.85 | − | 4345.45i | −0.346870 | − | 0.600796i | ||||
\(375\) | −2824.30 | + | 3738.94i | −0.388923 | + | 0.514874i | ||||
\(376\) | 1198.65 | − | 2076.12i | 0.164403 | − | 0.284755i | ||||
\(377\) | 6145.54 | 0.839553 | ||||||||
\(378\) | 393.030 | + | 2538.63i | 0.0534796 | + | 0.345432i | ||||
\(379\) | −13400.9 | −1.81625 | −0.908124 | − | 0.418701i | \(-0.862486\pi\) | ||||
−0.908124 | + | 0.418701i | \(0.862486\pi\) | |||||||
\(380\) | 392.344 | − | 679.561i | 0.0529654 | − | 0.0917387i | ||||
\(381\) | 2844.51 | − | 3765.70i | 0.382490 | − | 0.506359i | ||||
\(382\) | −2885.04 | − | 4997.04i | −0.386418 | − | 0.669296i | ||||
\(383\) | −5883.57 | − | 10190.6i | −0.784952 | − | 1.35958i | −0.929028 | − | 0.370010i | \(-0.879354\pi\) |
0.144076 | − | 0.989567i | \(-0.453979\pi\) | |||||||
\(384\) | −2140.68 | − | 5059.43i | −0.284482 | − | 0.672364i | ||||
\(385\) | −1140.90 | + | 1976.09i | −0.151027 | + | 0.261587i | ||||
\(386\) | −1147.06 | −0.151254 | ||||||||
\(387\) | 11069.3 | + | 2787.17i | 1.45396 | + | 0.366097i | ||||
\(388\) | 2055.15 | 0.268903 | ||||||||
\(389\) | −3900.97 | + | 6756.68i | −0.508450 | + | 0.880661i | 0.491502 | + | 0.870876i | \(0.336448\pi\) |
−0.999952 | + | 0.00978494i | \(0.996885\pi\) | |||||||
\(390\) | −4383.26 | − | 543.358i | −0.569115 | − | 0.0705487i | ||||
\(391\) | 6041.35 | + | 10463.9i | 0.781391 | + | 1.35341i | ||||
\(392\) | 586.886 | + | 1016.52i | 0.0756180 | + | 0.130974i | ||||
\(393\) | −3196.44 | − | 396.237i | −0.410278 | − | 0.0508589i | ||||
\(394\) | −3316.81 | + | 5744.88i | −0.424108 | + | 0.734576i | ||||
\(395\) | 12109.4 | 1.54251 | ||||||||
\(396\) | 205.704 | + | 723.708i | 0.0261036 | + | 0.0918377i | ||||
\(397\) | −6197.81 | −0.783525 | −0.391762 | − | 0.920066i | \(-0.628134\pi\) | ||||
−0.391762 | + | 0.920066i | \(0.628134\pi\) | |||||||
\(398\) | −3658.17 | + | 6336.14i | −0.460723 | + | 0.797995i | ||||
\(399\) | −709.318 | − | 1676.45i | −0.0889983 | − | 0.210345i | ||||
\(400\) | 1559.60 | + | 2701.30i | 0.194950 | + | 0.337662i | ||||
\(401\) | −500.722 | − | 867.276i | −0.0623563 | − | 0.108004i | 0.833162 | − | 0.553029i | \(-0.186528\pi\) |
−0.895518 | + | 0.445025i | \(0.853195\pi\) | |||||||
\(402\) | 8327.71 | − | 11024.6i | 1.03321 | − | 1.36781i | ||||
\(403\) | 32.6933 | − | 56.6265i | 0.00404112 | − | 0.00699943i | ||||
\(404\) | −392.122 | −0.0482891 | ||||||||
\(405\) | −8695.64 | − | 4675.43i | −1.06689 | − | 0.573640i | ||||
\(406\) | −4689.73 | −0.573270 | ||||||||
\(407\) | −3846.47 | + | 6662.27i | −0.468458 | + | 0.811392i | ||||
\(408\) | 5979.20 | − | 7915.55i | 0.725526 | − | 0.960485i | ||||
\(409\) | −5054.60 | − | 8754.82i | −0.611085 | − | 1.05843i | −0.991058 | − | 0.133433i | \(-0.957400\pi\) |
0.379973 | − | 0.924998i | \(-0.375933\pi\) | |||||||
\(410\) | 2918.68 | + | 5055.31i | 0.351569 | + | 0.608936i | ||||
\(411\) | 1544.02 | + | 3649.26i | 0.185307 | + | 0.437967i | ||||
\(412\) | −260.763 | + | 451.655i | −0.0311817 | + | 0.0540083i | ||||
\(413\) | −4035.61 | −0.480821 | ||||||||
\(414\) | 2927.48 | + | 10299.5i | 0.347531 | + | 1.22268i | ||||
\(415\) | −195.848 | −0.0231658 | ||||||||
\(416\) | −623.375 | + | 1079.72i | −0.0734699 | + | 0.127254i | ||||
\(417\) | 7178.80 | + | 889.899i | 0.843040 | + | 0.104505i | ||||
\(418\) | 1575.44 | + | 2728.75i | 0.184348 | + | 0.319300i | ||||
\(419\) | −178.252 | − | 308.741i | −0.0207832 | − | 0.0359976i | 0.855447 | − | 0.517891i | \(-0.173283\pi\) |
−0.876230 | + | 0.481893i | \(0.839949\pi\) | |||||||
\(420\) | −565.971 | − | 70.1590i | −0.0657537 | − | 0.00815097i | ||||
\(421\) | 1435.87 | − | 2487.00i | 0.166223 | − | 0.287907i | −0.770866 | − | 0.636998i | \(-0.780176\pi\) |
0.937089 | + | 0.349091i | \(0.113509\pi\) | |||||||
\(422\) | 4938.99 | 0.569731 | ||||||||
\(423\) | 2620.30 | + | 659.773i | 0.301189 | + | 0.0758375i | ||||
\(424\) | −4670.68 | −0.534972 | ||||||||
\(425\) | −2327.72 | + | 4031.74i | −0.265673 | + | 0.460160i | ||||
\(426\) | 2697.42 | + | 6375.28i | 0.306785 | + | 0.725078i | ||||
\(427\) | −150.634 | − | 260.906i | −0.0170719 | − | 0.0295694i | ||||
\(428\) | −336.442 | − | 582.735i | −0.0379966 | − | 0.0658121i | ||||
\(429\) | −1808.77 | + | 2394.54i | −0.203563 | + | 0.269486i | ||||
\(430\) | 7488.41 | − | 12970.3i | 0.839821 | − | 1.45461i | ||||
\(431\) | −3224.02 | −0.360314 | −0.180157 | − | 0.983638i | \(-0.557661\pi\) | ||||
−0.180157 | + | 0.983638i | \(0.557661\pi\) | |||||||
\(432\) | 5838.36 | − | 4694.27i | 0.650227 | − | 0.522808i | ||||
\(433\) | −14285.5 | −1.58549 | −0.792744 | − | 0.609555i | \(-0.791348\pi\) | ||||
−0.792744 | + | 0.609555i | \(0.791348\pi\) | |||||||
\(434\) | −24.9487 | + | 43.2123i | −0.00275939 | + | 0.00477940i | ||||
\(435\) | 10863.7 | − | 14381.9i | 1.19742 | − | 1.58520i | ||||
\(436\) | −799.638 | − | 1385.01i | −0.0878342 | − | 0.152133i | ||||
\(437\) | −3793.70 | − | 6570.88i | −0.415280 | − | 0.719286i | ||||
\(438\) | −5506.38 | − | 13014.2i | −0.600696 | − | 1.41973i | ||||
\(439\) | −1757.57 | + | 3044.19i | −0.191080 | + | 0.330960i | −0.945608 | − | 0.325307i | \(-0.894532\pi\) |
0.754528 | + | 0.656267i | \(0.227866\pi\) | |||||||
\(440\) | 7808.47 | 0.846032 | ||||||||
\(441\) | −921.238 | + | 949.552i | −0.0994750 | + | 0.102532i | ||||
\(442\) | 5002.10 | 0.538294 | ||||||||
\(443\) | 3991.41 | − | 6913.33i | 0.428076 | − | 0.741449i | −0.568626 | − | 0.822596i | \(-0.692525\pi\) |
0.996702 | + | 0.0811467i | \(0.0258582\pi\) | |||||||
\(444\) | −1908.14 | − | 236.537i | −0.203956 | − | 0.0252828i | ||||
\(445\) | 10374.8 | + | 17969.7i | 1.10520 | + | 1.91425i | ||||
\(446\) | −1765.32 | − | 3057.62i | −0.187422 | − | 0.324624i | ||||
\(447\) | 5374.54 | + | 666.240i | 0.568696 | + | 0.0704968i | ||||
\(448\) | 1970.84 | − | 3413.60i | 0.207843 | − | 0.359994i | ||||
\(449\) | 3502.50 | 0.368137 | 0.184068 | − | 0.982913i | \(-0.441073\pi\) | ||||
0.184068 | + | 0.982913i | \(0.441073\pi\) | |||||||
\(450\) | −2872.73 | + | 2961.02i | −0.300937 | + | 0.310187i | ||||
\(451\) | 3966.08 | 0.414092 | ||||||||
\(452\) | 868.161 | − | 1503.70i | 0.0903426 | − | 0.156478i | ||||
\(453\) | −202.126 | − | 477.719i | −0.0209640 | − | 0.0495479i | ||||
\(454\) | −3250.19 | − | 5629.49i | −0.335988 | − | 0.581949i | ||||
\(455\) | −1137.35 | − | 1969.95i | −0.117187 | − | 0.202973i | ||||
\(456\) | −3754.68 | + | 4970.62i | −0.385589 | + | 0.510461i | ||||
\(457\) | −6531.24 | + | 11312.4i | −0.668531 | + | 1.15793i | 0.309784 | + | 0.950807i | \(0.399743\pi\) |
−0.978315 | + | 0.207123i | \(0.933590\pi\) | |||||||
\(458\) | −4870.62 | −0.496919 | ||||||||
\(459\) | 10424.5 | + | 4043.28i | 1.06008 | + | 0.411164i | ||||
\(460\) | −2377.10 | −0.240941 | ||||||||
\(461\) | −3357.21 | + | 5814.86i | −0.339178 | + | 0.587473i | −0.984278 | − | 0.176625i | \(-0.943482\pi\) |
0.645101 | + | 0.764098i | \(0.276815\pi\) | |||||||
\(462\) | 1380.30 | − | 1827.30i | 0.138998 | − | 0.184012i | ||||
\(463\) | 3048.84 | + | 5280.74i | 0.306029 | + | 0.530058i | 0.977490 | − | 0.210982i | \(-0.0676661\pi\) |
−0.671461 | + | 0.741040i | \(0.734333\pi\) | |||||||
\(464\) | 6838.22 | + | 11844.1i | 0.684174 | + | 1.18502i | ||||
\(465\) | −74.7252 | − | 176.611i | −0.00745225 | − | 0.0176132i | ||||
\(466\) | 5355.72 | − | 9276.38i | 0.532401 | − | 0.922146i | ||||
\(467\) | −11929.4 | −1.18207 | −0.591033 | − | 0.806647i | \(-0.701280\pi\) | ||||
−0.591033 | + | 0.806647i | \(0.701280\pi\) | |||||||
\(468\) | −727.335 | − | 183.138i | −0.0718399 | − | 0.0180888i | ||||
\(469\) | 7115.59 | 0.700571 | ||||||||
\(470\) | 1772.64 | − | 3070.31i | 0.173970 | − | 0.301325i | ||||
\(471\) | 2544.53 | + | 315.425i | 0.248929 | + | 0.0308578i | ||||
\(472\) | 6905.08 | + | 11960.0i | 0.673373 | + | 1.16632i | ||||
\(473\) | −5087.85 | − | 8812.42i | −0.494587 | − | 0.856650i | ||||
\(474\) | −12060.8 | − | 1495.08i | −1.16872 | − | 0.144876i | ||||
\(475\) | 1461.71 | − | 2531.75i | 0.141195 | − | 0.244558i | ||||
\(476\) | 645.877 | 0.0621927 | ||||||||
\(477\) | −1439.34 | − | 5063.90i | −0.138162 | − | 0.486080i | ||||
\(478\) | −5552.55 | −0.531313 | ||||||||
\(479\) | 3745.00 | − | 6486.54i | 0.357231 | − | 0.618742i | −0.630266 | − | 0.776379i | \(-0.717054\pi\) |
0.987497 | + | 0.157637i | \(0.0503876\pi\) | |||||||
\(480\) | 1424.81 | + | 3367.50i | 0.135486 | + | 0.320218i | ||||
\(481\) | −3834.52 | − | 6641.58i | −0.363490 | − | 0.629584i | ||||
\(482\) | −6918.68 | − | 11983.5i | −0.653811 | − | 1.13243i | ||||
\(483\) | −3323.78 | + | 4400.17i | −0.313120 | + | 0.414523i | ||||
\(484\) | −435.120 | + | 753.650i | −0.0408640 | + | 0.0707785i | ||||
\(485\) | 24040.9 | 2.25081 | ||||||||
\(486\) | 8083.50 | + | 5730.28i | 0.754475 | + | 0.534837i | ||||
\(487\) | 14200.8 | 1.32135 | 0.660675 | − | 0.750672i | \(-0.270270\pi\) | ||||
0.660675 | + | 0.750672i | \(0.270270\pi\) | |||||||
\(488\) | −515.482 | + | 892.841i | −0.0478172 | + | 0.0828217i | ||||
\(489\) | −6811.37 | + | 9017.21i | −0.629899 | + | 0.833890i | ||||
\(490\) | 867.926 | + | 1503.29i | 0.0800181 | + | 0.138595i | ||||
\(491\) | −5395.93 | − | 9346.03i | −0.495957 | − | 0.859023i | 0.504032 | − | 0.863685i | \(-0.331849\pi\) |
−0.999989 | + | 0.00466183i | \(0.998516\pi\) | |||||||
\(492\) | 386.261 | + | 912.916i | 0.0353943 | + | 0.0836533i | ||||
\(493\) | −10206.2 | + | 17677.6i | −0.932378 | + | 1.61493i | ||||
\(494\) | −3141.10 | −0.286083 | ||||||||
\(495\) | 2406.31 | + | 8465.86i | 0.218496 | + | 0.768711i | ||||
\(496\) | 145.513 | 0.0131729 | ||||||||
\(497\) | −1782.57 | + | 3087.50i | −0.160883 | + | 0.278658i | ||||
\(498\) | 195.062 | + | 24.1803i | 0.0175521 | + | 0.00217579i | ||||
\(499\) | −3170.09 | − | 5490.75i | −0.284394 | − | 0.492585i | 0.688068 | − | 0.725646i | \(-0.258459\pi\) |
−0.972462 | + | 0.233061i | \(0.925126\pi\) | |||||||
\(500\) | 522.008 | + | 904.144i | 0.0466898 | + | 0.0808691i | ||||
\(501\) | 11861.4 | + | 1470.37i | 1.05775 | + | 0.131120i | ||||
\(502\) | 6058.87 | − | 10494.3i | 0.538686 | − | 0.933032i | ||||
\(503\) | 18901.4 | 1.67549 | 0.837747 | − | 0.546059i | \(-0.183873\pi\) | ||||
0.837747 | + | 0.546059i | \(0.183873\pi\) | |||||||
\(504\) | 4390.37 | + | 1105.47i | 0.388021 | + | 0.0977012i | ||||
\(505\) | −4587.00 | −0.404195 | ||||||||
\(506\) | 4772.57 | − | 8266.34i | 0.419302 | − | 0.726252i | ||||
\(507\) | 3282.66 | + | 7758.47i | 0.287551 | + | 0.679617i | ||||
\(508\) | −525.744 | − | 910.616i | −0.0459176 | − | 0.0795316i | ||||
\(509\) | 6838.35 | + | 11844.4i | 0.595491 | + | 1.03142i | 0.993477 | + | 0.114029i | \(0.0363757\pi\) |
−0.397987 | + | 0.917391i | \(0.630291\pi\) | |||||||
\(510\) | 8842.43 | − | 11706.0i | 0.767744 | − | 1.01638i | ||||
\(511\) | 3638.84 | − | 6302.65i | 0.315015 | − | 0.545622i | ||||
\(512\) | −13007.5 | −1.12277 | ||||||||
\(513\) | −6546.15 | − | 2539.00i | −0.563391 | − | 0.218518i | ||||
\(514\) | 8256.61 | 0.708528 | ||||||||
\(515\) | −3050.38 | + | 5283.40i | −0.261001 | + | 0.452067i | ||||
\(516\) | 1532.94 | − | 2029.38i | 0.130783 | − | 0.173136i | ||||
\(517\) | −1204.39 | − | 2086.06i | −0.102454 | − | 0.177456i | ||||
\(518\) | 2926.16 | + | 5068.26i | 0.248201 | + | 0.429897i | ||||
\(519\) | 632.825 | + | 1495.66i | 0.0535220 | + | 0.126498i | ||||
\(520\) | −3892.11 | + | 6741.33i | −0.328231 | + | 0.568513i | ||||
\(521\) | −10323.9 | −0.868139 | −0.434069 | − | 0.900879i | \(-0.642923\pi\) | ||||
−0.434069 | + | 0.900879i | \(0.642923\pi\) | |||||||
\(522\) | −12595.8 | + | 12982.9i | −1.05614 | + | 1.08860i | ||||
\(523\) | 9294.18 | 0.777067 | 0.388534 | − | 0.921435i | \(-0.372982\pi\) | ||||
0.388534 | + | 0.921435i | \(0.372982\pi\) | |||||||
\(524\) | −358.819 | + | 621.493i | −0.0299143 | + | 0.0518130i | ||||
\(525\) | −2108.57 | − | 261.382i | −0.175287 | − | 0.0217289i | ||||
\(526\) | 2339.24 | + | 4051.69i | 0.193909 | + | 0.335859i | ||||
\(527\) | 108.590 | + | 188.084i | 0.00897585 | + | 0.0155466i | ||||
\(528\) | −6627.58 | − | 821.569i | −0.546266 | − | 0.0677163i | ||||
\(529\) | −5408.95 | + | 9368.57i | −0.444559 | + | 0.769999i | ||||
\(530\) | −6907.30 | −0.566102 | ||||||||
\(531\) | −10838.9 | + | 11172.1i | −0.885819 | + | 0.913044i | ||||
\(532\) | −405.582 | −0.0330531 | ||||||||
\(533\) | −1976.88 | + | 3424.06i | −0.160653 | + | 0.278260i | ||||
\(534\) | −8114.54 | − | 19178.5i | −0.657585 | − | 1.55418i | ||||
\(535\) | −3935.66 | − | 6816.77i | −0.318044 | − | 0.550869i | ||||
\(536\) | −12175.1 | − | 21087.8i | −0.981124 | − | 1.69936i | ||||
\(537\) | −13610.9 | + | 18018.8i | −1.09377 | + | 1.44798i | ||||
\(538\) | −7560.08 | + | 13094.4i | −0.605833 | + | 1.04933i | ||||
\(539\) | 1179.39 | 0.0942485 | ||||||||
\(540\) | −1714.33 | + | 1378.38i | −0.136616 | + | 0.109845i | ||||
\(541\) | 4432.55 | 0.352256 | 0.176128 | − | 0.984367i | \(-0.443643\pi\) | ||||
0.176128 | + | 0.984367i | \(0.443643\pi\) | |||||||
\(542\) | −7515.08 | + | 13016.5i | −0.595572 | + | 1.03156i | ||||
\(543\) | 347.629 | − | 460.208i | 0.0274736 | − | 0.0363709i | ||||
\(544\) | −2070.53 | − | 3586.26i | −0.163186 | − | 0.282647i | ||||
\(545\) | −9354.07 | − | 16201.7i | −0.735201 | − | 1.27340i | ||||
\(546\) | 889.569 | + | 2102.47i | 0.0697253 | + | 0.164794i | ||||
\(547\) | −2164.18 | + | 3748.47i | −0.169166 | + | 0.293004i | −0.938127 | − | 0.346292i | \(-0.887441\pi\) |
0.768961 | + | 0.639296i | \(0.220774\pi\) | |||||||
\(548\) | 882.860 | 0.0688210 | ||||||||
\(549\) | −1126.86 | − | 283.737i | −0.0876017 | − | 0.0220575i | ||||
\(550\) | 3677.74 | 0.285126 | ||||||||
\(551\) | 6409.02 | − | 11100.8i | 0.495524 | − | 0.858272i | ||||
\(552\) | 18727.5 | + | 2321.50i | 1.44401 | + | 0.179003i | ||||
\(553\) | −3129.49 | − | 5420.44i | −0.240650 | − | 0.416819i | ||||
\(554\) | −4569.27 | − | 7914.21i | −0.350415 | − | 0.606936i | ||||
\(555\) | −22321.2 | − | 2766.98i | −1.70717 | − | 0.211625i | ||||
\(556\) | 805.862 | − | 1395.79i | 0.0614679 | − | 0.106466i | ||||
\(557\) | 6102.88 | 0.464250 | 0.232125 | − | 0.972686i | \(-0.425432\pi\) | ||||
0.232125 | + | 0.972686i | \(0.425432\pi\) | |||||||
\(558\) | 52.6202 | + | 185.128i | 0.00399209 | + | 0.0140450i | ||||
\(559\) | 10144.1 | 0.767530 | ||||||||
\(560\) | 2531.09 | − | 4383.98i | 0.190997 | − | 0.330816i | ||||
\(561\) | −3883.96 | − | 9179.63i | −0.292301 | − | 0.690846i | ||||
\(562\) | −2425.51 | − | 4201.11i | −0.182053 | − | 0.315326i | ||||
\(563\) | −2428.85 | − | 4206.89i | −0.181819 | − | 0.314919i | 0.760681 | − | 0.649126i | \(-0.224865\pi\) |
−0.942500 | + | 0.334207i | \(0.891532\pi\) | |||||||
\(564\) | 362.875 | − | 480.390i | 0.0270918 | − | 0.0358654i | ||||
\(565\) | 10155.6 | − | 17590.1i | 0.756197 | − | 1.30977i | ||||
\(566\) | 14178.3 | 1.05293 | ||||||||
\(567\) | 154.429 | + | 5100.66i | 0.0114381 | + | 0.377791i | ||||
\(568\) | 12200.2 | 0.901246 | ||||||||
\(569\) | −1501.30 | + | 2600.33i | −0.110611 | + | 0.191585i | −0.916017 | − | 0.401140i | \(-0.868614\pi\) |
0.805406 | + | 0.592724i | \(0.201948\pi\) | |||||||
\(570\) | −5552.66 | + | 7350.87i | −0.408027 | + | 0.540165i | ||||
\(571\) | −9682.85 | − | 16771.2i | −0.709658 | − | 1.22916i | −0.964984 | − | 0.262309i | \(-0.915516\pi\) |
0.255326 | − | 0.966855i | \(-0.417817\pi\) | |||||||
\(572\) | 334.311 | + | 579.044i | 0.0244375 | + | 0.0423270i | ||||
\(573\) | −4466.36 | − | 10556.1i | −0.325628 | − | 0.769612i | ||||
\(574\) | 1508.58 | − | 2612.94i | 0.109698 | − | 0.190003i | ||||
\(575\) | −8856.06 | −0.642301 | ||||||||
\(576\) | −4156.78 | − | 14624.4i | −0.300693 | − | 1.05790i | ||||
\(577\) | 9688.50 | 0.699025 | 0.349512 | − | 0.936932i | \(-0.386347\pi\) | ||||
0.349512 | + | 0.936932i | \(0.386347\pi\) | |||||||
\(578\) | −1881.56 | + | 3258.96i | −0.135402 | + | 0.234524i | ||||
\(579\) | −2261.29 | − | 280.315i | −0.162308 | − | 0.0201200i | ||||
\(580\) | −2007.92 | − | 3477.82i | −0.143749 | − | 0.248980i | ||||
\(581\) | 50.6140 | + | 87.6660i | 0.00361415 | + | 0.00625989i | ||||
\(582\) | −23944.5 | − | 2968.21i | −1.70538 | − | 0.211402i | ||||
\(583\) | −2346.52 | + | 4064.28i | −0.166694 | + | 0.288723i | ||||
\(584\) | −24904.8 | −1.76467 | ||||||||
\(585\) | −8508.29 | − | 2142.33i | −0.601324 | − | 0.151409i | ||||
\(586\) | 3701.98 | 0.260968 | ||||||||
\(587\) | 872.314 | − | 1510.89i | 0.0613360 | − | 0.106237i | −0.833727 | − | 0.552177i | \(-0.813797\pi\) |
0.895063 | + | 0.445940i | \(0.147131\pi\) | |||||||
\(588\) | 114.862 | + | 271.473i | 0.00805583 | + | 0.0190397i | ||||
\(589\) | −68.1900 | − | 118.109i | −0.00477033 | − | 0.00826245i | ||||
\(590\) | 10211.7 | + | 17687.2i | 0.712556 | + | 1.23418i | ||||
\(591\) | −7942.61 | + | 10514.8i | −0.552818 | + | 0.731846i | ||||
\(592\) | 8533.43 | − | 14780.3i | 0.592435 | − | 1.02613i | ||||
\(593\) | 20857.6 | 1.44438 | 0.722192 | − | 0.691692i | \(-0.243135\pi\) | ||||
0.722192 | + | 0.691692i | \(0.243135\pi\) | |||||||
\(594\) | −1351.42 | − | 8728.98i | −0.0933490 | − | 0.602954i | ||||
\(595\) | 7555.39 | 0.520573 | ||||||||
\(596\) | 603.324 | − | 1044.99i | 0.0414649 | − | 0.0718194i | ||||
\(597\) | −8760.06 | + | 11597.0i | −0.600545 | + | 0.795030i | ||||
\(598\) | 4757.75 | + | 8240.66i | 0.325349 | + | 0.563521i | ||||
\(599\) | −3598.35 | − | 6232.52i | −0.245450 | − | 0.425132i | 0.716808 | − | 0.697271i | \(-0.245602\pi\) |
−0.962258 | + | 0.272139i | \(0.912269\pi\) | |||||||
\(600\) | 2833.21 | + | 6696.20i | 0.192775 | + | 0.455619i | ||||
\(601\) | −5649.25 | + | 9784.79i | −0.383424 | + | 0.664110i | −0.991549 | − | 0.129731i | \(-0.958589\pi\) |
0.608125 | + | 0.793841i | \(0.291922\pi\) | |||||||
\(602\) | −7741.07 | −0.524091 | ||||||||
\(603\) | 19111.2 | − | 19698.6i | 1.29066 | − | 1.33033i | ||||
\(604\) | −115.574 | −0.00778583 | ||||||||
\(605\) | −5089.98 | + | 8816.11i | −0.342045 | + | 0.592439i | ||||
\(606\) | 4568.59 | + | 566.332i | 0.306248 | + | 0.0379631i | ||||
\(607\) | 9204.31 | + | 15942.3i | 0.615472 | + | 1.06603i | 0.990301 | + | 0.138935i | \(0.0443680\pi\) |
−0.374829 | + | 0.927094i | \(0.622299\pi\) | |||||||
\(608\) | 1300.20 | + | 2252.02i | 0.0867272 | + | 0.150216i | ||||
\(609\) | −9245.25 | − | 1146.06i | −0.615166 | − | 0.0762573i | ||||
\(610\) | −762.328 | + | 1320.39i | −0.0505996 | + | 0.0876411i | ||||
\(611\) | 2401.29 | 0.158995 | ||||||||
\(612\) | 1734.71 | − | 1788.03i | 0.114578 | − | 0.118099i | ||||
\(613\) | −8745.01 | −0.576195 | −0.288098 | − | 0.957601i | \(-0.593023\pi\) | ||||
−0.288098 | + | 0.957601i | \(0.593023\pi\) | |||||||
\(614\) | −8627.01 | + | 14942.4i | −0.567032 | + | 0.982129i | ||||
\(615\) | 4518.44 | + | 10679.2i | 0.296262 | + | 0.700206i | ||||
\(616\) | −2017.98 | − | 3495.25i | −0.131992 | − | 0.228616i | ||||
\(617\) | 14619.8 | + | 25322.2i | 0.953923 | + | 1.65224i | 0.736813 | + | 0.676096i | \(0.236330\pi\) |
0.217110 | + | 0.976147i | \(0.430337\pi\) | |||||||
\(618\) | 3690.45 | − | 4885.59i | 0.240213 | − | 0.318005i | ||||
\(619\) | −1289.82 | + | 2234.04i | −0.0837518 | + | 0.145062i | −0.904859 | − | 0.425712i | \(-0.860024\pi\) |
0.821107 | + | 0.570775i | \(0.193357\pi\) | |||||||
\(620\) | −42.7273 | −0.00276769 | ||||||||
\(621\) | 3254.24 | + | 21019.6i | 0.210287 | + | 1.35827i | ||||
\(622\) | −1982.77 | −0.127816 | ||||||||
\(623\) | 5362.42 | − | 9287.98i | 0.344849 | − | 0.597295i | ||||
\(624\) | 4012.78 | − | 5312.31i | 0.257436 | − | 0.340806i | ||||
\(625\) | 9757.28 | + | 16900.1i | 0.624466 | + | 1.08161i | ||||
\(626\) | −9293.21 | − | 16096.3i | −0.593341 | − | 1.02770i | ||||
\(627\) | 2438.96 | + | 5764.41i | 0.155347 | + | 0.367158i | ||||
\(628\) | 285.638 | − | 494.739i | 0.0181500 | − | 0.0314367i | ||||
\(629\) | 25472.6 | 1.61472 | ||||||||
\(630\) | 6492.77 | + | 1634.84i | 0.410600 | + | 0.103386i | ||||
\(631\) | 15166.5 | 0.956847 | 0.478424 | − | 0.878129i | \(-0.341208\pi\) | ||||
0.478424 | + | 0.878129i | \(0.341208\pi\) | |||||||
\(632\) | −10709.4 | + | 18549.2i | −0.674044 | + | 1.16748i | ||||
\(633\) | 9736.64 | + | 1206.97i | 0.611369 | + | 0.0757866i | ||||
\(634\) | 6878.67 | + | 11914.2i | 0.430894 | + | 0.746330i | ||||
\(635\) | −6150.10 | − | 10652.3i | −0.384345 | − | 0.665705i | ||||
\(636\) | −1164.05 | − | 144.298i | −0.0725748 | − | 0.00899652i | ||||
\(637\) | −587.863 | + | 1018.21i | −0.0365651 | + | 0.0633327i | ||||
\(638\) | 16125.4 | 1.00065 | ||||||||
\(639\) | 3759.68 | + | 13227.3i | 0.232755 | + | 0.818879i | ||||
\(640\) | −14318.5 | −0.884355 | ||||||||
\(641\) | 5784.05 | − | 10018.3i | 0.356406 | − | 0.617313i | −0.630952 | − | 0.775822i | \(-0.717335\pi\) |
0.987357 | + | 0.158509i | \(0.0506688\pi\) | |||||||
\(642\) | 3078.24 | + | 7275.33i | 0.189234 | + | 0.447250i | ||||
\(643\) | 26.3640 | + | 45.6638i | 0.00161694 | + | 0.00280063i | 0.866833 | − | 0.498599i | \(-0.166152\pi\) |
−0.865216 | + | 0.501400i | \(0.832819\pi\) | |||||||
\(644\) | 614.325 | + | 1064.04i | 0.0375898 | + | 0.0651074i | ||||
\(645\) | 17932.1 | − | 23739.4i | 1.09469 | − | 1.44921i | ||||
\(646\) | 5216.56 | − | 9035.35i | 0.317713 | − | 0.550296i | ||||
\(647\) | −13568.7 | −0.824484 | −0.412242 | − | 0.911074i | \(-0.635254\pi\) | ||||
−0.412242 | + | 0.911074i | \(0.635254\pi\) | |||||||
\(648\) | 14852.1 | − | 9185.10i | 0.900381 | − | 0.556829i | ||||
\(649\) | 13876.3 | 0.839277 | ||||||||
\(650\) | −1833.15 | + | 3175.12i | −0.110619 | + | 0.191597i | ||||
\(651\) | −59.7434 | + | 79.0911i | −0.00359682 | + | 0.00476164i | ||||
\(652\) | 1258.93 | + | 2180.53i | 0.0756188 | + | 0.130976i | ||||
\(653\) | 7707.15 | + | 13349.2i | 0.461875 | + | 0.799990i | 0.999054 | − | 0.0434774i | \(-0.0138437\pi\) |
−0.537180 | + | 0.843468i | \(0.680510\pi\) | |||||||
\(654\) | 7316.20 | + | 17291.6i | 0.437440 | + | 1.03388i | ||||
\(655\) | −4197.42 | + | 7270.15i | −0.250392 | + | 0.433692i | ||||
\(656\) | −8798.80 | −0.523682 | ||||||||
\(657\) | −7674.81 | − | 27001.5i | −0.455743 | − | 1.60339i | ||||
\(658\) | −1832.45 | −0.108566 | ||||||||
\(659\) | 9417.53 | − | 16311.6i | 0.556684 | − | 0.964206i | −0.441086 | − | 0.897465i | \(-0.645407\pi\) |
0.997770 | − | 0.0667409i | \(-0.0212601\pi\) | |||||||
\(660\) | 1946.07 | + | 241.238i | 0.114774 | + | 0.0142276i | ||||
\(661\) | −4509.40 | − | 7810.50i | −0.265348 | − | 0.459597i | 0.702307 | − | 0.711875i | \(-0.252154\pi\) |
−0.967655 | + | 0.252278i | \(0.918820\pi\) | |||||||
\(662\) | 5561.38 | + | 9632.59i | 0.326509 | + | 0.565531i | ||||
\(663\) | 9861.05 | + | 1222.40i | 0.577634 | + | 0.0716047i | ||||
\(664\) | 173.205 | − | 300.000i | 0.0101230 | − | 0.0175335i | ||||
\(665\) | −4744.46 | −0.276665 | ||||||||
\(666\) | 21890.0 | + | 5511.76i | 1.27360 | + | 0.320685i | ||||
\(667\) | −38830.4 | −2.25415 | ||||||||
\(668\) | 1331.52 | − | 2306.25i | 0.0771226 | − | 0.133580i | ||||
\(669\) | −2732.90 | − | 6459.13i | −0.157937 | − | 0.373280i | ||||
\(670\) | −18005.3 | − | 31186.0i | −1.03822 | − | 1.79824i | ||||
\(671\) | 517.949 | + | 897.114i | 0.0297991 | + | 0.0516136i | ||||
\(672\) | 1139.15 | − | 1508.06i | 0.0653922 | − | 0.0865693i | ||||
\(673\) | −11519.7 | + | 19952.8i | −0.659812 | + | 1.14283i | 0.320852 | + | 0.947129i | \(0.396031\pi\) |
−0.980664 | + | 0.195699i | \(0.937303\pi\) | |||||||
\(674\) | 6780.49 | 0.387500 | ||||||||
\(675\) | −6386.85 | + | 5135.27i | −0.364193 | + | 0.292825i | ||||
\(676\) | 1877.00 | 0.106793 | ||||||||
\(677\) | 14577.1 | − | 25248.3i | 0.827539 | − | 1.43334i | −0.0724245 | − | 0.997374i | \(-0.523074\pi\) |
0.899963 | − | 0.435965i | \(-0.143593\pi\) | |||||||
\(678\) | −12286.6 | + | 16265.6i | −0.695967 | + | 0.921354i | ||||
\(679\) | −6213.02 | − | 10761.3i | −0.351154 | − | 0.608217i | ||||
\(680\) | −12927.6 | − | 22391.2i | −0.729044 | − | 1.26274i | ||||
\(681\) | −5031.64 | − | 11892.1i | −0.283132 | − | 0.669174i | ||||
\(682\) | 85.7848 | − | 148.584i | 0.00481653 | − | 0.00834247i | ||||
\(683\) | −8818.55 | −0.494045 | −0.247022 | − | 0.969010i | \(-0.579452\pi\) | ||||
−0.247022 | + | 0.969010i | \(0.579452\pi\) | |||||||
\(684\) | −1089.32 | + | 1122.80i | −0.0608937 | + | 0.0627653i | ||||
\(685\) | 10327.6 | 0.576054 | ||||||||
\(686\) | 448.605 | − | 777.007i | 0.0249677 | − | 0.0432453i | ||||
\(687\) | −9601.84 | − | 1190.26i | −0.533236 | − | 0.0661010i | ||||
\(688\) | 11287.5 | + | 19550.5i | 0.625480 | + | 1.08336i | ||||
\(689\) | −2339.23 | − | 4051.66i | −0.129343 | − | 0.224029i | ||||
\(690\) | 27695.4 | + | 3433.18i | 1.52804 | + | 0.189419i | ||||
\(691\) | 4721.50 | − | 8177.88i | 0.259934 | − | 0.450219i | −0.706290 | − | 0.707923i | \(-0.749633\pi\) |
0.966224 | + | 0.257704i | \(0.0829659\pi\) | |||||||
\(692\) | 361.844 | 0.0198775 | ||||||||
\(693\) | 3167.64 | − | 3264.99i | 0.173634 | − | 0.178971i | ||||
\(694\) | −1286.90 | −0.0703894 | ||||||||
\(695\) | 9426.88 | − | 16327.8i | 0.514507 | − | 0.891152i | ||||
\(696\) | 12422.5 | + | 29360.2i | 0.676543 | + | 1.59899i | ||||
\(697\) | −6566.18 | − | 11373.0i | −0.356832 | − | 0.618051i | ||||
\(698\) | 15586.7 | + | 26997.0i | 0.845225 | + | 1.46397i | ||||
\(699\) | 12825.1 | − | 16978.5i | 0.693977 | − | 0.918719i | ||||
\(700\) | −236.699 | + | 409.975i | −0.0127805 | + | 0.0221365i | ||||
\(701\) | −11255.0 | −0.606411 | −0.303205 | − | 0.952925i | \(-0.598057\pi\) | ||||
−0.303205 | + | 0.952925i | \(0.598057\pi\) | |||||||
\(702\) | 8209.64 | + | 3184.21i | 0.441386 | + | 0.171197i | ||||
\(703\) | −15995.7 | −0.858162 | ||||||||
\(704\) | −6776.65 | + | 11737.5i | −0.362791 | + | 0.628372i | ||||
\(705\) | 4244.87 | − | 5619.55i | 0.226767 | − | 0.300205i | ||||
\(706\) | −10567.7 | − | 18303.7i | −0.563342 | − | 0.975737i | ||||
\(707\) | 1185.44 | + | 2053.24i | 0.0630595 | + | 0.109222i | ||||
\(708\) | 1351.42 | + | 3194.05i | 0.0717367 | + | 0.169548i | ||||
\(709\) | −11242.5 | + | 19472.6i | −0.595515 | + | 1.03146i | 0.397958 | + | 0.917403i | \(0.369719\pi\) |
−0.993474 | + | 0.114060i | \(0.963615\pi\) | |||||||
\(710\) | 18042.4 | 0.953689 | ||||||||
\(711\) | −23411.1 | − | 5894.76i | −1.23486 | − | 0.310929i | ||||
\(712\) | −36701.2 | −1.93179 | ||||||||
\(713\) | −206.572 | + | 357.792i | −0.0108502 | + | 0.0187930i | ||||
\(714\) | −7525.08 | − | 932.824i | −0.394424 | − | 0.0488937i | ||||
\(715\) | 3910.73 | + | 6773.59i | 0.204550 | + | 0.354291i | ||||
\(716\) | 2515.67 | + | 4357.27i | 0.131306 | + | 0.227428i | ||||
\(717\) | −10946.2 | − | 1356.91i | −0.570143 | − | 0.0706762i | ||||
\(718\) | 8730.66 | − | 15121.9i | 0.453796 | − | 0.785997i | ||||
\(719\) | −27322.6 | −1.41719 | −0.708595 | − | 0.705615i | \(-0.750671\pi\) | ||||
−0.708595 | + | 0.705615i | \(0.750671\pi\) | |||||||
\(720\) | −5338.42 | − | 18781.6i | −0.276321 | − | 0.972152i | ||||
\(721\) | 3153.30 | 0.162878 | ||||||||
\(722\) | 5695.02 | − | 9864.06i | 0.293555 | − | 0.508452i | ||||
\(723\) | −10710.9 | − | 25314.8i | −0.550956 | − | 1.30217i | ||||
\(724\) | −64.2514 | − | 111.287i | −0.00329818 | − | 0.00571262i | ||||
\(725\) | −7480.65 | − | 12956.9i | −0.383206 | − | 0.663732i | ||||
\(726\) | 6158.03 | − | 8152.30i | 0.314802 | − | 0.416750i | ||||
\(727\) | 388.538 | − | 672.967i | 0.0198213 | − | 0.0343315i | −0.855945 | − | 0.517068i | \(-0.827024\pi\) |
0.875766 | + | 0.482736i | \(0.160357\pi\) | |||||||
\(728\) | 4023.43 | 0.204833 | ||||||||
\(729\) | 14535.3 | + | 13272.0i | 0.738470 | + | 0.674286i | ||||
\(730\) | −36830.8 | −1.86736 | ||||||||
\(731\) | −16846.7 | + | 29179.4i | −0.852392 | + | 1.47639i | ||||
\(732\) | −156.055 | + | 206.593i | −0.00787972 | + | 0.0104315i | ||||
\(733\) | 12682.6 | + | 21966.9i | 0.639075 | + | 1.10691i | 0.985636 | + | 0.168883i | \(0.0540161\pi\) |
−0.346561 | + | 0.938028i | \(0.612651\pi\) | |||||||
\(734\) | 15402.8 | + | 26678.5i | 0.774563 | + | 1.34158i | ||||
\(735\) | 1343.64 | + | 3175.66i | 0.0674300 | + | 0.159369i | ||||
\(736\) | 3938.77 | − | 6822.15i | 0.197262 | − | 0.341668i | ||||
\(737\) | −24466.7 | −1.22285 | ||||||||
\(738\) | −3181.80 | − | 11194.2i | −0.158704 | − | 0.558353i | ||||
\(739\) | 851.804 | 0.0424007 | 0.0212004 | − | 0.999775i | \(-0.493251\pi\) | ||||
0.0212004 | + | 0.999775i | \(0.493251\pi\) | |||||||
\(740\) | −2505.68 | + | 4339.97i | −0.124474 | + | 0.215595i | ||||
\(741\) | −6192.31 | − | 767.611i | −0.306991 | − | 0.0380552i | ||||
\(742\) | 1785.09 | + | 3091.86i | 0.0883190 | + | 0.152973i | ||||
\(743\) | 16910.0 | + | 29289.0i | 0.834950 | + | 1.44618i | 0.894071 | + | 0.447926i | \(0.147837\pi\) |
−0.0591206 | + | 0.998251i | \(0.518830\pi\) | |||||||
\(744\) | 336.618 | + | 41.7279i | 0.0165874 | + | 0.00205621i | ||||
\(745\) | 7057.61 | − | 12224.1i | 0.347075 | − | 0.601152i | ||||
\(746\) | 3879.91 | 0.190420 | ||||||||
\(747\) | 378.632 | + | 95.3371i | 0.0185454 | + | 0.00466962i | ||||
\(748\) | −2220.82 | −0.108558 | ||||||||
\(749\) | −2034.23 | + | 3523.39i | −0.0992377 | + | 0.171885i | ||||
\(750\) | −4776.05 | − | 11288.1i | −0.232529 | − | 0.549575i | ||||
\(751\) | 376.630 | + | 652.341i | 0.0183001 | + | 0.0316968i | 0.875030 | − | 0.484068i | \(-0.160841\pi\) |
−0.856730 | + | 0.515765i | \(0.827508\pi\) | |||||||
\(752\) | 2671.95 | + | 4627.95i | 0.129569 | + | 0.224420i | ||||
\(753\) | 14508.9 | − | 19207.5i | 0.702169 | − | 0.929564i | ||||
\(754\) | −8037.67 | + | 13921.7i | −0.388216 | + | 0.672409i | ||||
\(755\) | −1351.97 | −0.0651699 | ||||||||
\(756\) | 1060.04 | + | 411.148i | 0.0509963 | + | 0.0197795i | ||||
\(757\) | −8507.90 | −0.408487 | −0.204244 | − | 0.978920i | \(-0.565473\pi\) | ||||
−0.204244 | + | 0.978920i | \(0.565473\pi\) | |||||||
\(758\) | 17526.9 | − | 30357.4i | 0.839847 | − | 1.45466i | ||||
\(759\) | 11428.7 | − | 15129.8i | 0.546553 | − | 0.723553i | ||||
\(760\) | 8117.95 | + | 14060.7i | 0.387459 | + | 0.671099i | ||||
\(761\) | −1839.97 | − | 3186.93i | −0.0876466 | − | 0.151808i | 0.818869 | − | 0.573980i | \(-0.194601\pi\) |
−0.906516 | + | 0.422172i | \(0.861268\pi\) | |||||||
\(762\) | 4810.24 | + | 11368.9i | 0.228683 | + | 0.540486i | ||||
\(763\) | −4834.84 | + | 8374.19i | −0.229401 | + | 0.397334i | ||||
\(764\) | −2553.83 | −0.120935 | ||||||||
\(765\) | 20292.5 | − | 20916.2i | 0.959053 | − | 0.988529i | ||||
\(766\) | 30780.2 | 1.45187 | ||||||||
\(767\) | −6916.57 | + | 11979.9i | −0.325610 | + | 0.563973i | ||||
\(768\) | −8968.72 | − | 1111.78i | −0.421394 | − | 0.0522369i | ||||
\(769\) | −10837.0 | − | 18770.3i | −0.508184 | − | 0.880201i | −0.999955 | − | 0.00947643i | \(-0.996984\pi\) |
0.491771 | − | 0.870725i | \(-0.336350\pi\) | |||||||
\(770\) | −2984.32 | − | 5169.00i | −0.139672 | − | 0.241919i | ||||
\(771\) | 16276.9 | + | 2017.72i | 0.760310 | + | 0.0942496i | ||||
\(772\) | −253.843 | + | 439.670i | −0.0118342 | + | 0.0204975i | ||||
\(773\) | 16219.4 | 0.754685 | 0.377342 | − | 0.926074i | \(-0.376838\pi\) | ||||
0.377342 | + | 0.926074i | \(0.376838\pi\) | |||||||
\(774\) | −20791.2 | + | 21430.2i | −0.965534 | + | 0.995209i | ||||
\(775\) | −159.184 | −0.00737812 | ||||||||
\(776\) | −21261.4 | + | 36825.9i | −0.983559 | + | 1.70357i | ||||
\(777\) | 4530.02 | + | 10706.6i | 0.209155 | + | 0.494332i | ||||
\(778\) | −10204.1 | − | 17673.9i | −0.470222 | − | 0.814449i | ||||
\(779\) | 4123.27 | + | 7141.72i | 0.189643 | + | 0.328471i | ||||
\(780\) | −1178.28 | + | 1559.86i | −0.0540887 | + | 0.0716052i | ||||
\(781\) | 6129.28 | − | 10616.2i | 0.280823 | − | 0.486400i | ||||
\(782\) | −31605.6 | −1.44529 | ||||||||
\(783\) | −28003.9 | + | 22516.2i | −1.27813 | + | 1.02767i | ||||
\(784\) | −2616.49 | −0.119191 | ||||||||
\(785\) | 3341.36 | − | 5787.40i | 0.151921 | − | 0.263135i | ||||
\(786\) | 5078.19 | − | 6722.74i | 0.230449 | − | 0.305079i | ||||
\(787\) | 12981.2 | + | 22484.0i | 0.587965 | + | 1.01838i | 0.994499 | + | 0.104749i | \(0.0334039\pi\) |
−0.406534 | + | 0.913636i | \(0.633263\pi\) | |||||||
\(788\) | 1468.01 | + | 2542.67i | 0.0663652 | + | 0.114948i | ||||
\(789\) | 3621.40 | + | 8559.08i | 0.163404 | + | 0.386199i | ||||
\(790\) | −15837.7 | + | 27431.7i | −0.713267 | + | 1.23541i | ||||
\(791\) | −10498.3 | −0.471905 | ||||||||
\(792\) | −15096.1 | − | 3801.10i | −0.677294 | − | 0.170538i | ||||
\(793\) | −1032.68 | −0.0462440 | ||||||||
\(794\) | 8106.03 | − | 14040.1i | 0.362308 | − | 0.627535i | ||||
\(795\) | −13616.9 | − | 1687.98i | −0.607475 | − | 0.0753038i | ||||
\(796\) | 1619.10 | + | 2804.36i | 0.0720948 | + | 0.124872i | ||||
\(797\) | −13877.2 | − | 24036.1i | −0.616759 | − | 1.06826i | −0.990073 | − | 0.140553i | \(-0.955112\pi\) |
0.373314 | − | 0.927705i | \(-0.378221\pi\) | |||||||
\(798\) | 4725.42 | + | 585.773i | 0.209622 | + | 0.0259851i | ||||
\(799\) | −3987.93 | + | 6907.29i | −0.176574 | + | 0.305835i | ||||
\(800\) | 3035.21 | 0.134138 | ||||||||
\(801\) | −11310.1 | − | 39791.1i | −0.498904 | − | 1.75524i | ||||
\(802\) | 2619.55 | 0.115336 | ||||||||
\(803\) | −12512.0 | + | 21671.4i | −0.549861 | + | 0.952387i | ||||
\(804\) | −2382.83 | − | 5631.75i | −0.104522 | − | 0.247036i | ||||
\(805\) | 7186.31 | + | 12447.1i | 0.314639 | + | 0.544970i | ||||
\(806\) | 85.5183 | + | 148.122i | 0.00373729 | + | 0.00647318i | ||||
\(807\) | −18103.8 | + | 23966.6i | −0.789693 | + | 1.04543i | ||||
\(808\) | 4056.67 | − | 7026.36i | 0.176625 | − | 0.305924i | ||||
\(809\) | −3816.68 | −0.165868 | −0.0829340 | − | 0.996555i | \(-0.526429\pi\) | ||||
−0.0829340 | + | 0.996555i | \(0.526429\pi\) | |||||||
\(810\) | 21964.3 | − | 13583.5i | 0.952773 | − | 0.589230i | ||||
\(811\) | 20419.0 | 0.884103 | 0.442051 | − | 0.896990i | \(-0.354251\pi\) | ||||
0.442051 | + | 0.896990i | \(0.354251\pi\) | |||||||
\(812\) | −1037.83 | + | 1797.58i | −0.0448532 | + | 0.0776880i | ||||
\(813\) | −17996.0 | + | 23824.0i | −0.776319 | + | 1.02773i | ||||
\(814\) | −10061.5 | − | 17427.0i | −0.433237 | − | 0.750388i | ||||
\(815\) | 14726.8 | + | 25507.6i | 0.632954 | + | 1.09631i | ||||
\(816\) | 8616.62 | + | 20365.1i | 0.369659 | + | 0.873679i | ||||
\(817\) | 10579.0 | − | 18323.4i | 0.453014 | − | 0.784644i | ||||
\(818\) | 26443.4 | 1.13028 | ||||||||
\(819\) | 1239.88 | + | 4362.16i | 0.0529000 | + | 0.186112i | ||||
\(820\) | 2583.60 | 0.110029 | ||||||||
\(821\) | 10976.3 | − | 19011.5i | 0.466597 | − | 0.808169i | −0.532675 | − | 0.846320i | \(-0.678813\pi\) |
0.999272 | + | 0.0381503i | \(0.0121466\pi\) | |||||||
\(822\) | −10286.2 | − | 1275.09i | −0.436461 | − | 0.0541046i | ||||
\(823\) | −5875.21 | − | 10176.2i | −0.248842 | − | 0.431007i | 0.714363 | − | 0.699775i | \(-0.246717\pi\) |
−0.963205 | + | 0.268769i | \(0.913383\pi\) | |||||||
\(824\) | −5395.41 | − | 9345.13i | −0.228105 | − | 0.395089i | ||||
\(825\) | 7250.22 | + | 898.752i | 0.305964 | + | 0.0379279i | ||||
\(826\) | 5278.11 | − | 9141.96i | 0.222335 | − | 0.385096i | ||||
\(827\) | −7326.79 | −0.308074 | −0.154037 | − | 0.988065i | \(-0.549228\pi\) | ||||
−0.154037 | + | 0.988065i | \(0.549228\pi\) | |||||||
\(828\) | 4595.64 | + | 1157.15i | 0.192886 | + | 0.0485674i | ||||
\(829\) | −13574.8 | −0.568725 | −0.284362 | − | 0.958717i | \(-0.591782\pi\) | ||||
−0.284362 | + | 0.958717i | \(0.591782\pi\) | |||||||
\(830\) | 256.147 | − | 443.659i | 0.0107120 | − | 0.0185538i | ||||
\(831\) | −7073.72 | − | 16718.5i | −0.295288 | − | 0.697906i | ||||
\(832\) | −6755.60 | − | 11701.0i | −0.281500 | − | 0.487573i | ||||
\(833\) | −1952.58 | − | 3381.97i | −0.0812159 | − | 0.140670i | ||||
\(834\) | −11405.0 | + | 15098.4i | −0.473527 | + | 0.626878i | ||||
\(835\) | 15575.9 | − | 26978.3i | 0.645541 | − | 1.11811i | ||||
\(836\) | 1394.58 | 0.0576943 | ||||||||
\(837\) | 58.4934 | + | 377.817i | 0.00241557 | + | 0.0156025i | ||||
\(838\) | 932.533 | 0.0384413 | ||||||||
\(839\) | 13920.6 | − | 24111.3i | 0.572818 | − | 0.992149i | −0.423457 | − | 0.905916i | \(-0.639184\pi\) |
0.996275 | − | 0.0862330i | \(-0.0274830\pi\) | |||||||
\(840\) | 7112.38 | − | 9415.71i | 0.292144 | − | 0.386753i | ||||
\(841\) | −20605.2 | − | 35689.3i | −0.844858 | − | 1.46334i | ||||
\(842\) | 3755.90 | + | 6505.42i | 0.153726 | + | 0.266261i | ||||
\(843\) | −3754.95 | − | 8874.72i | −0.153413 | − | 0.362588i | ||||
\(844\) | 1092.99 | − | 1893.12i | 0.0445763 | − | 0.0772084i | ||||
\(845\) | 21956.9 | 0.893895 | ||||||||
\(846\) | −4921.65 | + | 5072.91i | −0.200012 | + | 0.206159i | ||||
\(847\) | 5261.72 | 0.213453 | ||||||||
\(848\) | 5205.77 | − | 9016.66i | 0.210810 | − | 0.365134i | ||||
\(849\) | 27950.9 | + | 3464.85i | 1.12988 | + | 0.140063i | ||||
\(850\) | −6088.80 | − | 10546.1i | −0.245699 | − | 0.425563i | ||||
\(851\) | 24228.2 | + | 41964.5i | 0.975950 | + | 1.69039i | ||||
\(852\) | 3040.59 | + | 376.917i | 0.122264 | + | 0.0151561i | ||||
\(853\) | 10653.1 | − | 18451.7i | 0.427613 | − | 0.740648i | −0.569047 | − | 0.822305i | \(-0.692688\pi\) |
0.996661 | + | 0.0816568i | \(0.0260211\pi\) | |||||||
\(854\) | 788.049 | 0.0315767 | ||||||||
\(855\) | −12742.8 | + | 13134.4i | −0.509700 | + | 0.525366i | ||||
\(856\) | 13922.6 | 0.555916 | ||||||||
\(857\) | 1460.33 | − | 2529.37i | 0.0582077 | − | 0.100819i | −0.835453 | − | 0.549562i | \(-0.814795\pi\) |
0.893661 | + | 0.448743i | \(0.148128\pi\) | |||||||
\(858\) | −3058.74 | − | 7229.25i | −0.121706 | − | 0.287648i | ||||
\(859\) | 13786.5 | + | 23879.0i | 0.547602 | + | 0.948475i | 0.998438 | + | 0.0558681i | \(0.0177926\pi\) |
−0.450836 | + | 0.892607i | \(0.648874\pi\) | |||||||
\(860\) | −3314.35 | − | 5740.63i | −0.131417 | − | 0.227621i | ||||
\(861\) | 3612.52 | − | 4782.43i | 0.142990 | − | 0.189297i | ||||
\(862\) | 4216.64 | − | 7303.44i | 0.166612 | − | 0.288580i | ||||
\(863\) | 2361.13 | 0.0931329 | 0.0465664 | − | 0.998915i | \(-0.485172\pi\) | ||||
0.0465664 | + | 0.998915i | \(0.485172\pi\) | |||||||
\(864\) | −1115.31 | − | 7203.96i | −0.0439164 | − | 0.283662i | ||||
\(865\) | 4232.81 | 0.166381 | ||||||||
\(866\) | 18683.8 | − | 32361.2i | 0.733141 | − | 1.26984i | ||||
\(867\) | −4505.68 | + | 5964.84i | −0.176495 | + | 0.233652i | ||||
\(868\) | 11.0422 | + | 19.1257i | 0.000431794 | + | 0.000747890i | ||||
\(869\) | 10760.6 | + | 18638.0i | 0.420057 | + | 0.727560i | ||||
\(870\) | 18371.2 | + | 43419.8i | 0.715911 | + | 1.69203i | ||||
\(871\) | 12195.3 | − | 21122.9i | 0.474423 | − | 0.821725i | ||||
\(872\) | 33090.4 | 1.28507 | ||||||||
\(873\) | −46478.3 | − | 11702.9i | −1.80189 | − | 0.453705i | ||||
\(874\) | 19846.9 | 0.768114 | ||||||||
\(875\) | 3156.21 | − | 5466.71i | 0.121942 | − | 0.211210i | ||||
\(876\) | −6206.90 | − | 769.420i | −0.239397 | − | 0.0296761i | ||||
\(877\) | 22493.5 | + | 38959.8i | 0.866078 | + | 1.50009i | 0.865972 | + | 0.500092i | \(0.166700\pi\) |
0.000106172 | 1.00000i | \(0.499966\pi\) | ||||||||
\(878\) | −4597.39 | − | 7962.92i | −0.176714 | − | 0.306077i | ||||
\(879\) | 7298.01 | + | 904.676i | 0.280041 | + | 0.0347144i | ||||
\(880\) | −8703.04 | + | 15074.1i | −0.333386 | + | 0.577441i | ||||
\(881\) | −39465.4 | −1.50922 | −0.754610 | − | 0.656173i | \(-0.772174\pi\) | ||||
−0.754610 | + | 0.656173i | \(0.772174\pi\) | |||||||
\(882\) | −946.170 | − | 3328.81i | −0.0361215 | − | 0.127083i | ||||
\(883\) | −33583.8 | −1.27994 | −0.639968 | − | 0.768402i | \(-0.721052\pi\) | ||||
−0.639968 | + | 0.768402i | \(0.721052\pi\) | |||||||
\(884\) | 1106.96 | − | 1917.31i | 0.0421166 | − | 0.0729481i | ||||
\(885\) | 15808.8 | + | 37363.6i | 0.600460 | + | 1.41917i | ||||
\(886\) | 10440.6 | + | 18083.7i | 0.395891 | + | 0.685704i | ||||
\(887\) | −11710.5 | − | 20283.2i | −0.443293 | − | 0.767807i | 0.554638 | − | 0.832092i | \(-0.312857\pi\) |
−0.997932 | + | 0.0642850i | \(0.979523\pi\) | |||||||
\(888\) | 23979.0 | − | 31744.5i | 0.906174 | − | 1.19964i | ||||
\(889\) | −3178.80 | + | 5505.84i | −0.119925 | + | 0.207717i | ||||
\(890\) | −54276.1 | −2.04420 | ||||||||
\(891\) | −530.999 | − | 17538.4i | −0.0199653 | − | 0.659437i | ||||
\(892\) | −1562.65 | −0.0586563 | ||||||||
\(893\) | 2504.24 | − | 4337.48i | 0.0938425 | − | 0.162540i | ||||
\(894\) | −8538.54 | + | 11303.7i | −0.319431 | + | 0.422878i | ||||
\(895\) | 29428.0 | + | 50970.8i | 1.09907 | + | 1.90365i | ||||
\(896\) | 3700.39 | + | 6409.27i | 0.137970 | + | 0.238972i | ||||
\(897\) | 7365.51 | + | 17408.2i | 0.274166 | + | 0.647984i | ||||
\(898\) | −4580.88 | + | 7934.31i | −0.170229 | + | 0.294846i | ||||
\(899\) | −697.958 | −0.0258934 | ||||||||
\(900\) | 499.231 | + | 1756.39i | 0.0184900 | + | 0.0650515i | ||||
\(901\) | 15539.4 | 0.574576 | ||||||||
\(902\) | −5187.18 | + | 8984.47i | −0.191479 | + | 0.331652i | ||||
\(903\) | −15260.6 | − | 1891.74i | −0.562393 | − | 0.0697154i | ||||
\(904\) | 17963.0 | + | 31112.8i | 0.660886 | + | 1.14469i | ||||
\(905\) | −751.606 | − | 1301.82i | −0.0276069 | − | 0.0478165i | ||||
\(906\) | 1346.55 | + | 166.921i | 0.0493775 | + | 0.00612094i | ||||
\(907\) | −2380.08 | + | 4122.42i | −0.0871327 | + | 0.150918i | −0.906298 | − | 0.422639i | \(-0.861104\pi\) |
0.819165 | + | 0.573557i | \(0.194437\pi\) | |||||||
\(908\) | −2877.05 | −0.105152 | ||||||||
\(909\) | 8868.03 | + | 2232.91i | 0.323580 | + | 0.0814752i | ||||
\(910\) | 5950.11 | 0.216752 | ||||||||
\(911\) | 4403.96 | − | 7627.89i | 0.160164 | − | 0.277413i | −0.774763 | − | 0.632252i | \(-0.782131\pi\) |
0.934928 | + | 0.354839i | \(0.115464\pi\) | |||||||
\(912\) | −5410.86 | − | 12788.4i | −0.196460 | − | 0.464327i | ||||
\(913\) | −174.034 | − | 301.435i | −0.00630852 | − | 0.0109267i | ||||
\(914\) | −17084.2 | − | 29590.8i | −0.618268 | − | 1.07087i | ||||
\(915\) | −1825.51 | + | 2416.70i | −0.0659558 | + | 0.0873154i | ||||
\(916\) | −1077.86 | + | 1866.91i | −0.0388794 | + | 0.0673412i | ||||
\(917\) | 4339.05 | 0.156257 | ||||||||
\(918\) | −22793.4 | + | 18326.8i | −0.819494 | + | 0.658905i | ||||
\(919\) | 50540.1 | 1.81411 | 0.907054 | − | 0.421015i | \(-0.138326\pi\) | ||||
0.907054 | + | 0.421015i | \(0.138326\pi\) | |||||||
\(920\) | 24592.1 | − | 42594.8i | 0.881280 | − | 1.52642i | ||||
\(921\) | −20658.7 | + | 27349.0i | −0.739118 | + | 0.978479i | ||||
\(922\) | −8781.70 | − | 15210.4i | −0.313677 | − | 0.543304i | ||||
\(923\) | 6110.23 | + | 10583.2i | 0.217899 | + | 0.377412i | ||||
\(924\) | −394.948 | − | 933.448i | −0.0140615 | − | 0.0332340i | ||||
\(925\) | −9335.11 | + | 16168.9i | −0.331823 | + | 0.574735i | ||||
\(926\) | −15950.1 | −0.566041 | ||||||||
\(927\) | 8469.20 | − | 8729.50i | 0.300070 | − | 0.309293i | ||||
\(928\) | 13308.2 | 0.470757 | ||||||||
\(929\) | −2533.05 | + | 4387.36i | −0.0894580 | + | 0.154946i | −0.907282 | − | 0.420522i | \(-0.861847\pi\) |
0.817824 | + | 0.575468i | \(0.195180\pi\) | |||||||
\(930\) | 497.813 | + | 61.7099i | 0.0175526 | + | 0.00217586i | ||||
\(931\) | 1226.13 | + | 2123.73i | 0.0431632 | + | 0.0747608i | ||||
\(932\) | −2370.43 | − | 4105.71i | −0.0833112 | − | 0.144299i | ||||
\(933\) | −3908.79 | − | 484.542i | −0.137158 | − | 0.0170023i | ||||
\(934\) | 15602.2 | − | 27023.9i | 0.546597 | − | 0.946733i | ||||
\(935\) | −25978.9 | −0.908663 | ||||||||
\(936\) | 10806.2 | − | 11138.4i | 0.377364 | − | 0.388962i | ||||
\(937\) | −17496.0 | −0.609999 | −0.305000 | − | 0.952352i | \(-0.598656\pi\) | ||||
−0.305000 | + | 0.952352i | \(0.598656\pi\) | |||||||
\(938\) | −9306.39 | + | 16119.1i | −0.323949 | + | 0.561096i | ||||
\(939\) | −14386.9 | − | 34003.0i | −0.499999 | − | 1.18173i | ||||
\(940\) | −784.568 | − | 1358.91i | −0.0272232 | − | 0.0471519i | ||||
\(941\) | −15930.8 | − | 27592.9i | −0.551890 | − | 0.955902i | −0.998138 | − | 0.0609927i | \(-0.980573\pi\) |
0.446248 | − | 0.894909i | \(-0.352760\pi\) | |||||||
\(942\) | −4042.49 | + | 5351.64i | −0.139821 | + | 0.185102i | ||||
\(943\) | 12490.8 | − | 21634.8i | 0.431344 | − | 0.747110i | ||||
\(944\) | −30784.6 | −1.06139 | ||||||||
\(945\) | 12400.2 | + | 4809.57i | 0.426856 | + | 0.165561i | ||||
\(946\) | 26617.3 | 0.914803 | ||||||||
\(947\) | −6020.36 | + | 10427.6i | −0.206584 | + | 0.357814i | −0.950636 | − | 0.310307i | \(-0.899568\pi\) |
0.744052 | + | 0.668122i | \(0.232901\pi\) | |||||||
\(948\) | −3242.11 | + | 4292.06i | −0.111075 | + | 0.147046i | ||||
\(949\) | −12473.1 | − | 21604.1i | −0.426654 | − | 0.738986i | ||||
\(950\) | 3823.50 | + | 6622.49i | 0.130580 | + | 0.226171i | ||||
\(951\) | 10648.9 | + | 25168.4i | 0.363107 | + | 0.858193i | ||||
\(952\) | −6681.88 | + | 11573.4i | −0.227480 | + | 0.394007i | ||||
\(953\) | 56064.5 | 1.90567 | 0.952837 | − | 0.303482i | \(-0.0981494\pi\) | ||||
0.952837 | + | 0.303482i | \(0.0981494\pi\) | |||||||
\(954\) | 13353.9 | + | 3362.42i | 0.453195 | + | 0.114111i | ||||
\(955\) | −29874.4 | −1.01226 | ||||||||
\(956\) | −1228.77 | + | 2128.30i | −0.0415705 | + | 0.0720021i | ||||
\(957\) | 31789.4 | + | 3940.68i | 1.07378 | + | 0.133108i | ||||
\(958\) | 9796.08 | + | 16967.3i | 0.330373 | + | 0.572222i | ||||
\(959\) | −2669.01 | − | 4622.87i | −0.0898717 | − | 0.155662i | ||||
\(960\) | −39325.2 | − | 4874.83i | −1.32210 | − | 0.163890i | ||||
\(961\) | 14891.8 | − | 25793.3i | 0.499875 | − | 0.865810i | ||||
\(962\) | 20060.4 | 0.672323 | ||||||||
\(963\) | 4290.47 | + | 15094.7i | 0.143570 | + | 0.505109i | ||||
\(964\) | −6124.38 | −0.204619 | ||||||||
\(965\) | −2969.43 | + | 5143.21i | −0.0990563 | + | 0.171571i | ||||
\(966\) | −5620.70 | − | 13284.4i | −0.187208 | − | 0.442461i | ||||
\(967\) | −17575.4 | − | 30441.6i | −0.584476 | − | 1.01234i | −0.994941 | − | 0.100466i | \(-0.967967\pi\) |
0.410465 | − | 0.911877i | \(-0.365367\pi\) | |||||||
\(968\) | −9003.01 | − | 15593.7i | −0.298934 | − | 0.517768i | ||||
\(969\) | 12491.9 | − | 16537.3i | 0.414134 | − | 0.548251i | ||||
\(970\) | −31442.8 | + | 54460.5i | −1.04079 | + | 1.80270i | ||||
\(971\) | 5008.69 | 0.165537 | 0.0827685 | − | 0.996569i | \(-0.473624\pi\) | ||||
0.0827685 | + | 0.996569i | \(0.473624\pi\) | |||||||
\(972\) | 3985.29 | − | 1830.31i | 0.131511 | − | 0.0603983i | ||||
\(973\) | −9744.95 | −0.321078 | ||||||||
\(974\) | −18573.0 | + | 32169.3i | −0.611003 | + | 1.05829i | ||||
\(975\) | −4389.77 | + | 5811.39i | −0.144190 | + | 0.190885i | ||||
\(976\) | −1149.08 | − | 1990.26i | −0.0376855 | − | 0.0652731i | ||||
\(977\) | −7504.08 | − | 12997.4i | −0.245729 | − | 0.425614i | 0.716608 | − | 0.697476i | \(-0.245694\pi\) |
−0.962336 | + | 0.271862i | \(0.912361\pi\) | |||||||
\(978\) | −11518.4 | − | 27223.5i | −0.376604 | − | 0.890092i | ||||
\(979\) | −18438.4 | + | 31936.3i | −0.601935 | + | 1.04258i | ||||
\(980\) | 768.284 | 0.0250428 | ||||||||
\(981\) | 10197.3 | + | 35876.3i | 0.331882 | + | 1.16763i | ||||
\(982\) | 28229.1 | 0.917338 | ||||||||
\(983\) | 17493.7 | − | 30299.9i | 0.567611 | − | 0.983131i | −0.429191 | − | 0.903214i | \(-0.641201\pi\) |
0.996802 | − | 0.0799169i | \(-0.0254655\pi\) | |||||||
\(984\) | −20354.4 | − | 2523.18i | −0.659426 | − | 0.0817438i | ||||
\(985\) | 17172.7 | + | 29743.9i | 0.555499 | + | 0.962152i | ||||
\(986\) | −26697.0 | − | 46240.6i | −0.862278 | − | 1.49351i | ||||
\(987\) | −3612.46 | − | 447.808i | −0.116500 | − | 0.0144416i | ||||
\(988\) | −695.122 | + | 1203.99i | −0.0223834 | + | 0.0387692i | ||||
\(989\) | −64095.0 | −2.06077 | ||||||||
\(990\) | −22325.1 | − | 5621.31i | −0.716705 | − | 0.180462i | ||||
\(991\) | −34764.1 | −1.11435 | −0.557173 | − | 0.830396i | \(-0.688114\pi\) | ||||
−0.557173 | + | 0.830396i | \(0.688114\pi\) | |||||||
\(992\) | 70.7976 | − | 122.625i | 0.00226595 | − | 0.00392474i | ||||
\(993\) | 8609.61 | + | 20348.6i | 0.275144 | + | 0.650294i | ||||
\(994\) | −4662.79 | − | 8076.19i | −0.148787 | − | 0.257707i | ||||
\(995\) | 18940.0 | + | 32805.1i | 0.603457 | + | 1.04522i | ||||
\(996\) | 52.4353 | − | 69.4164i | 0.00166815 | − | 0.00220838i | ||||
\(997\) | 15164.0 | − | 26264.9i | 0.481695 | − | 0.834320i | −0.518085 | − | 0.855329i | \(-0.673355\pi\) |
0.999779 | + | 0.0210097i | \(0.00668810\pi\) | |||||||
\(998\) | 16584.4 | 0.526024 | ||||||||
\(999\) | 41806.6 | + | 16215.2i | 1.32403 | + | 0.513539i |
(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 | 63.4.f.b.43.3 | yes | 16 | |
3.2 | odd | 2 | 189.4.f.b.127.6 | 16 | |||
9.2 | odd | 6 | 567.4.a.g.1.3 | 8 | |||
9.4 | even | 3 | inner | 63.4.f.b.22.3 | ✓ | 16 | |
9.5 | odd | 6 | 189.4.f.b.64.6 | 16 | |||
9.7 | even | 3 | 567.4.a.i.1.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.f.b.22.3 | ✓ | 16 | 9.4 | even | 3 | inner | |
63.4.f.b.43.3 | yes | 16 | 1.1 | even | 1 | trivial | |
189.4.f.b.64.6 | 16 | 9.5 | odd | 6 | |||
189.4.f.b.127.6 | 16 | 3.2 | odd | 2 | |||
567.4.a.g.1.3 | 8 | 9.2 | odd | 6 | |||
567.4.a.i.1.6 | 8 | 9.7 | even | 3 |