Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1040,2,Mod(289,1040)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1040, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1040.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1040 = 2^{4} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1040.dh (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: | \(8.30444181021\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 8x^{10} + 54x^{8} - 78x^{6} + 92x^{4} - 10x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 65) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 529.6 | ||
Root | \(-0.286513 + 0.165418i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1040.529 |
Dual form | 1040.2.dh.a.289.6 |
$q$-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 \(\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(417\) | \(561\) | \(911\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.33117 | + | 1.34590i | 1.34590 | + | 0.777057i | 0.987666 | − | 0.156574i | \(-0.0500450\pi\) |
0.358236 | + | 0.933631i | \(0.383378\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.12291 | + | 0.702335i | −0.949392 | + | 0.314094i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.90420 | + | 1.67674i | −1.09768 | + | 0.633748i | −0.935611 | − | 0.353031i | \(-0.885151\pi\) |
−0.162072 | + | 0.986779i | \(0.551818\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.12291 | + | 3.67698i | 0.707635 | + | 1.22566i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.62291 | + | 2.81095i | −0.489324 | + | 0.847535i | −0.999925 | − | 0.0122837i | \(-0.996090\pi\) |
0.510600 | + | 0.859818i | \(0.329423\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.21648 | − | 3.39414i | −0.337391 | − | 0.941365i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.89413 | − | 1.21996i | −1.52186 | − | 0.314992i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.68772 | + | 0.974404i | −0.409332 | + | 0.236328i | −0.690503 | − | 0.723330i | \(-0.742611\pi\) |
0.281171 | + | 0.959658i | \(0.409277\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.622905 | + | 1.07890i | 0.142904 | + | 0.247517i | 0.928589 | − | 0.371110i | \(-0.121023\pi\) |
−0.785685 | + | 0.618627i | \(0.787689\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −9.02690 | −1.96983 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.33117 | − | 1.34590i | −0.486083 | − | 0.280640i | 0.236865 | − | 0.971543i | \(-0.423880\pi\) |
−0.722948 | + | 0.690903i | \(0.757213\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.01345 | − | 2.98198i | 0.802690 | − | 0.596396i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.35348i | 0.645377i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.50000 | − | 2.59808i | 0.278543 | − | 0.482451i | −0.692480 | − | 0.721437i | \(-0.743482\pi\) |
0.971023 | + | 0.238987i | \(0.0768152\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.78109 | −0.679105 | −0.339552 | − | 0.940587i | \(-0.610276\pi\) | ||||
−0.339552 | + | 0.940587i | \(0.610276\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.56654 | + | 4.36854i | −1.31717 | + | 0.760466i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.98770 | − | 5.59927i | 0.843076 | − | 0.946450i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.68772 | − | 0.974404i | −0.277459 | − | 0.160191i | 0.354813 | − | 0.934937i | \(-0.384544\pi\) |
−0.632273 | + | 0.774746i | \(0.717878\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.73236 | − | 9.54958i | 0.277399 | − | 1.52916i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.39055 | + | 2.40850i | −0.217167 | + | 0.376144i | −0.953941 | − | 0.299995i | \(-0.903015\pi\) |
0.736774 | + | 0.676139i | \(0.236348\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.56654 | + | 4.36854i | −1.15389 | + | 0.666197i | −0.949831 | − | 0.312763i | \(-0.898745\pi\) |
−0.204055 | + | 0.978959i | \(0.565412\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.08920 | − | 6.31489i | −1.05679 | − | 0.941368i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.86960i | 1.00203i | 0.865437 | + | 0.501017i | \(0.167041\pi\) | ||||
−0.865437 | + | 0.501017i | \(0.832959\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.12291 | − | 3.67698i | 0.303272 | − | 0.525283i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.24581 | −0.734560 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.8336i | 1.76282i | 0.472347 | + | 0.881412i | \(0.343407\pi\) | ||||
−0.472347 | + | 0.881412i | \(0.656593\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.47104 | − | 7.10721i | 0.198355 | − | 0.958336i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.35348i | 0.444179i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.26764 | + | 2.19562i | 0.165033 | + | 0.285845i | 0.936667 | − | 0.350221i | \(-0.113894\pi\) |
−0.771634 | + | 0.636067i | \(0.780560\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.74581 | + | 6.48793i | 0.479602 | + | 0.830695i | 0.999726 | − | 0.0233957i | \(-0.00744777\pi\) |
−0.520124 | + | 0.854090i | \(0.674114\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −12.3307 | − | 7.11911i | −1.55352 | − | 0.896924i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.96629 | + | 6.35106i | 0.615993 | + | 0.787752i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.47722 | − | 2.00758i | −0.424810 | − | 0.245264i | 0.272323 | − | 0.962206i | \(-0.412208\pi\) |
−0.697133 | + | 0.716942i | \(0.745541\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.62291 | − | 6.27506i | −0.436147 | − | 0.755428i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.62291 | + | 4.54300i | 0.311282 | + | 0.539155i | 0.978640 | − | 0.205581i | \(-0.0659084\pi\) |
−0.667359 | + | 0.744737i | \(0.732575\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.46493i | 0.639622i | 0.947481 | + | 0.319811i | \(0.103619\pi\) | ||||
−0.947481 | + | 0.319811i | \(0.896381\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 13.3695 | − | 1.54979i | 1.54378 | − | 0.178954i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 10.8848i | − | 1.24043i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.7811 | 1.55049 | 0.775247 | − | 0.631658i | \(-0.217625\pi\) | ||||
0.775247 | + | 0.631658i | \(0.217625\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.85526 | − | 3.21341i | 0.206140 | − | 0.357046i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.61955i | 0.946119i | 0.881031 | + | 0.473059i | \(0.156850\pi\) | ||||
−0.881031 | + | 0.473059i | \(0.843150\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.89851 | − | 3.25391i | 0.314387 | − | 0.352936i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.99351 | − | 4.03771i | 0.749783 | − | 0.432888i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.15819 | − | 8.93425i | 0.546767 | − | 0.947028i | −0.451726 | − | 0.892156i | \(-0.649192\pi\) |
0.998493 | − | 0.0548717i | \(-0.0174750\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.22398 | + | 7.81753i | 0.966936 | + | 0.819500i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.81438 | − | 5.08898i | −0.914008 | − | 0.527703i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.08012 | − | 1.85292i | −0.213416 | − | 0.190106i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.56055 | + | 2.63304i | −0.463054 | + | 0.267344i | −0.713328 | − | 0.700831i | \(-0.752813\pi\) |
0.250273 | + | 0.968175i | \(0.419479\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −13.7811 | −1.38505 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.85526 | + | 4.94546i | −0.284109 | + | 0.492092i | −0.972393 | − | 0.233350i | \(-0.925031\pi\) |
0.688283 | + | 0.725442i | \(0.258365\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 7.36863i | − | 0.726052i | −0.931779 | − | 0.363026i | \(-0.881744\pi\) | ||
0.931779 | − | 0.363026i | \(-0.118256\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 19.1633 | − | 6.33991i | 1.87014 | − | 0.618712i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.42568 | + | 4.28722i | 0.717868 | + | 0.414461i | 0.813967 | − | 0.580911i | \(-0.197303\pi\) |
−0.0960996 | + | 0.995372i | \(0.530637\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.49162 | 0.813350 | 0.406675 | − | 0.913573i | \(-0.366688\pi\) | ||||
0.406675 | + | 0.913573i | \(0.366688\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.62291 | − | 4.54300i | −0.248955 | − | 0.431203i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.35006 | − | 3.66621i | 0.597363 | − | 0.344888i | −0.170640 | − | 0.985333i | \(-0.554584\pi\) |
0.768004 | + | 0.640446i | \(0.221250\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.89413 | + | 1.21996i | 0.549630 | + | 0.113762i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.89771 | − | 11.6784i | 0.915044 | − | 1.07967i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.26764 | − | 5.65972i | 0.299544 | − | 0.518826i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.232358 | + | 0.402456i | 0.0211234 | + | 0.0365869i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.48321 | + | 3.74308i | −0.584571 | + | 0.337502i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.42583 | + | 9.14925i | −0.574744 | + | 0.818333i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.93599 | − | 4.58185i | −0.704205 | − | 0.406573i | 0.104707 | − | 0.994503i | \(-0.466610\pi\) |
−0.808912 | + | 0.587930i | \(0.799943\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −23.5185 | −2.07069 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.0000 | −0.873704 | −0.436852 | − | 0.899533i | \(-0.643907\pi\) | ||||
−0.436852 | + | 0.899533i | \(0.643907\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.61808 | − | 2.08890i | −0.313727 | − | 0.181130i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.35526 | − | 7.11911i | −0.202709 | − | 0.612716i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.5914 | − | 8.42435i | 1.24663 | − | 0.719741i | 0.276193 | − | 0.961102i | \(-0.410927\pi\) |
0.970435 | + | 0.241361i | \(0.0775938\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.513452 | + | 0.889325i | 0.0435505 | + | 0.0754316i | 0.886979 | − | 0.461810i | \(-0.152800\pi\) |
−0.843429 | + | 0.537241i | \(0.819466\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.24581 | + | 16.0142i | −0.778638 | + | 1.34864i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.5150 | + | 2.08890i | 0.962933 | + | 0.174682i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.35964 | + | 6.56897i | −0.112912 | + | 0.545523i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.89771 | − | 5.71445i | 0.816349 | − | 0.471319i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.92583 | + | 13.7279i | 0.649309 | + | 1.12464i | 0.983288 | + | 0.182056i | \(0.0582753\pi\) |
−0.333979 | + | 0.942581i | \(0.608391\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.5454 | −1.18369 | −0.591845 | − | 0.806052i | \(-0.701600\pi\) | ||||
−0.591845 | + | 0.806052i | \(0.701600\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.16573 | − | 4.13713i | −0.579315 | − | 0.334468i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.02690 | − | 2.65559i | 0.644736 | − | 0.213302i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.9210i | 0.871588i | 0.900047 | + | 0.435794i | \(0.143532\pi\) | ||||
−0.900047 | + | 0.435794i | \(0.856468\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −17.2727 | + | 29.9172i | −1.36982 | + | 2.37259i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.02690 | 0.711420 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.61808 | + | 2.08890i | −0.283390 | + | 0.163615i | −0.634957 | − | 0.772547i | \(-0.718982\pi\) |
0.351567 | + | 0.936163i | \(0.385649\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 12.9949 | − | 14.5882i | 1.01165 | − | 1.13569i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.90420 | − | 1.67674i | −0.224733 | − | 0.129750i | 0.383407 | − | 0.923580i | \(-0.374751\pi\) |
−0.608140 | + | 0.793830i | \(0.708084\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.0404 | + | 8.25780i | −0.772335 | + | 0.635215i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.64474 | + | 4.58082i | −0.202248 | + | 0.350304i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.56654 | + | 4.36854i | −0.575273 | + | 0.332134i | −0.759253 | − | 0.650796i | \(-0.774435\pi\) |
0.183979 | + | 0.982930i | \(0.441102\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.65585 | + | 15.3898i | −0.503135 | + | 1.16336i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.82449i | 0.512960i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.00507 | − | 15.5972i | 0.673071 | − | 1.16579i | −0.303958 | − | 0.952685i | \(-0.598308\pi\) |
0.977029 | − | 0.213107i | \(-0.0683584\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.04366 | 0.0775749 | 0.0387875 | − | 0.999247i | \(-0.487650\pi\) | ||||
0.0387875 | + | 0.999247i | \(0.487650\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 20.1660i | 1.49071i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.26722 | + | 0.883225i | 0.313732 | + | 0.0649360i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 6.32546i | − | 0.462564i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.62291 | − | 9.73916i | −0.409006 | − | 0.708419i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.7593 | + | 22.0997i | 0.923228 | + | 1.59908i | 0.794387 | + | 0.607412i | \(0.207792\pi\) |
0.128841 | + | 0.991665i | \(0.458874\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.1652 | − | 9.91035i | −1.23558 | − | 0.713362i | −0.267392 | − | 0.963588i | \(-0.586162\pi\) |
−0.968188 | + | 0.250225i | \(0.919495\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.02937 | + | 21.4895i | 0.216938 | + | 1.53890i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.7512 | − | 10.8260i | −1.33596 | − | 0.771319i | −0.349758 | − | 0.936840i | \(-0.613736\pi\) |
−0.986206 | + | 0.165521i | \(0.947070\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.11453 | − | 15.7868i | −0.646112 | − | 1.11910i | −0.984044 | − | 0.177928i | \(-0.943061\pi\) |
0.337932 | − | 0.941171i | \(-0.390273\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.40400 | − | 9.36000i | −0.381169 | − | 0.660204i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.0604i | 0.706104i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.26043 | − | 6.08964i | 0.0880321 | − | 0.425319i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 11.4289i | − | 0.794363i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.04366 | −0.279706 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.64981 | − | 16.7140i | 0.664320 | − | 1.15064i | −0.315149 | − | 0.949042i | \(-0.602054\pi\) |
0.979469 | − | 0.201594i | \(-0.0646122\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 14.1207i | 0.967534i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.9949 | − | 14.5882i | 0.886242 | − | 0.994910i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.9810 | − | 6.33991i | 0.745442 | − | 0.430381i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.35526 | + | 12.7397i | −0.497023 | + | 0.860868i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.36034 | + | 4.54300i | 0.360575 | + | 0.305596i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.7134 | − | 6.18537i | −0.717421 | − | 0.414203i | 0.0963818 | − | 0.995344i | \(-0.469273\pi\) |
−0.813803 | + | 0.581141i | \(0.802606\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 19.4849 | + | 8.42692i | 1.29899 | + | 0.561795i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.33715 | − | 3.08141i | 0.354239 | − | 0.204520i | −0.312311 | − | 0.949980i | \(-0.601103\pi\) |
0.666551 | + | 0.745460i | \(0.267770\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.9832 | 1.78310 | 0.891551 | − | 0.452920i | \(-0.149618\pi\) | ||||
0.891551 | + | 0.452920i | \(0.149618\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.6498 | − | 25.3742i | 0.963887 | − | 1.66950i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 0.824319i | − | 0.0540029i | −0.999635 | − | 0.0270015i | \(-0.991404\pi\) | ||
0.999635 | − | 0.0270015i | \(-0.00859588\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.82476 | − | 14.5835i | −0.314733 | − | 0.951323i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 32.1261 | + | 18.5480i | 2.08681 | + | 1.20482i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.00000 | 0.258738 | 0.129369 | − | 0.991596i | \(-0.458705\pi\) | ||||
0.129369 | + | 0.991596i | \(0.458705\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.3469 | − | 19.6534i | −0.730917 | − | 1.26599i | −0.956492 | − | 0.291760i | \(-0.905759\pi\) |
0.225575 | − | 0.974226i | \(-0.427574\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 17.3625 | − | 10.0242i | 1.11380 | − | 0.643054i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.92426 | + | 9.29687i | −0.122936 | + | 0.593955i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.90420 | − | 3.42669i | 0.184790 | − | 0.218035i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.6011 | + | 20.0936i | −0.735188 | + | 1.27338i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.51345 | + | 16.4778i | 0.600484 | + | 1.04007i | 0.992748 | + | 0.120216i | \(0.0383586\pi\) |
−0.392264 | + | 0.919853i | \(0.628308\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.56654 | − | 4.36854i | 0.475704 | − | 0.274648i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 11.1364 | − | 3.68431i | 0.697386 | − | 0.230721i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.82857 | + | 1.05573i | 0.114063 | + | 0.0658544i | 0.555946 | − | 0.831218i | \(-0.312356\pi\) |
−0.441883 | + | 0.897073i | \(0.645689\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.53528 | 0.406083 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.7374 | 0.788427 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −25.9092 | − | 14.9587i | −1.59763 | − | 0.922391i | −0.991943 | − | 0.126687i | \(-0.959566\pi\) |
−0.605685 | − | 0.795704i | \(-0.707101\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.01345 | − | 27.2444i | −0.553692 | − | 1.67361i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 24.0492 | − | 13.8848i | 1.47179 | − | 0.849738i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.29455 | + | 16.0986i | 0.566699 | + | 0.981551i | 0.996889 | + | 0.0788127i | \(0.0251129\pi\) |
−0.430191 | + | 0.902738i | \(0.641554\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.91238 | − | 5.04439i | 0.176914 | − | 0.306425i | −0.763908 | − | 0.645326i | \(-0.776722\pi\) |
0.940822 | + | 0.338901i | \(0.110055\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.9810 | + | 30.6386i | 0.664603 | + | 1.85433i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.86875 | + | 16.1211i | 0.112690 | + | 0.972139i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.7263 | + | 6.77017i | −0.704564 | + | 0.406780i | −0.809045 | − | 0.587747i | \(-0.800015\pi\) |
0.104481 | + | 0.994527i | \(0.466682\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.02690 | − | 13.9030i | −0.480558 | − | 0.832351i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.464716 | −0.0277226 | −0.0138613 | − | 0.999904i | \(-0.504412\pi\) | ||||
−0.0138613 | + | 0.999904i | \(0.504412\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.71259 | + | 5.03022i | 0.517910 | + | 0.299015i | 0.736079 | − | 0.676896i | \(-0.236675\pi\) |
−0.218169 | + | 0.975911i | \(0.570009\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.35526 | − | 7.11911i | −0.139514 | − | 0.421700i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 9.32634i | − | 0.550516i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.60107 | + | 11.4334i | −0.388298 | + | 0.672553i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.1752 | −0.830967 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.6481 | − | 6.72506i | 0.680492 | − | 0.392882i | −0.119548 | − | 0.992828i | \(-0.538145\pi\) |
0.800040 | + | 0.599946i | \(0.204811\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.23314 | − | 3.77079i | −0.246463 | − | 0.219544i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.42647 | − | 5.44238i | −0.546979 | − | 0.315799i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.73236 | + | 9.54958i | −0.100185 | + | 0.552266i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.6498 | − | 25.3742i | 0.844401 | − | 1.46255i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.3122 | + | 7.68581i | −0.764767 | + | 0.441538i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.5087 | − | 11.1425i | −0.716246 | − | 0.638015i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.6077i | 1.40444i | 0.711961 | + | 0.702219i | \(0.247807\pi\) | ||||
−0.711961 | + | 0.702219i | \(0.752193\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.91745 | − | 17.1775i | 0.564184 | − | 0.977196i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.43781 | −0.138236 | −0.0691178 | − | 0.997609i | \(-0.522018\pi\) | ||||
−0.0691178 | + | 0.997609i | \(0.522018\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 19.2965i | − | 1.09071i | −0.838207 | − | 0.545353i | \(-0.816396\pi\) | ||
0.838207 | − | 0.545353i | \(-0.183604\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 31.1768 | + | 6.45295i | 1.75662 | + | 0.363583i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 28.8217i | 1.61879i | 0.587265 | + | 0.809395i | \(0.300205\pi\) | ||||
−0.587265 | + | 0.809395i | \(0.699795\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.86872 | + | 8.43286i | 0.272596 | + | 0.472150i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.5404 | + | 19.9885i | 0.644120 | + | 1.11565i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.10258 | − | 1.21392i | −0.116990 | − | 0.0675445i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.0035 | − | 9.99470i | −0.832246 | − | 0.554406i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 19.7954 | + | 11.4289i | 1.09469 | + | 0.632019i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.5185 | − | 19.9507i | −0.635037 | − | 1.09992i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.48655 | − | 2.57478i | −0.0817081 | − | 0.141522i | 0.822276 | − | 0.569089i | \(-0.192704\pi\) |
−0.903984 | + | 0.427567i | \(0.859371\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 8.27427i | − | 0.453427i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.79180 | + | 1.81972i | 0.480347 | + | 0.0994218i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 1.90370i | − | 0.103701i | −0.998655 | − | 0.0518505i | \(-0.983488\pi\) | ||
0.998655 | − | 0.0518505i | \(-0.0165119\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 19.7374 | 1.07199 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.13636 | − | 10.6285i | 0.332302 | − | 0.575565i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 9.23611i | − | 0.498703i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.0983 | + | 10.7769i | 0.651349 | + | 0.580206i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.9420 | + | 6.31735i | −0.587396 | + | 0.339133i | −0.764067 | − | 0.645137i | \(-0.776800\pi\) |
0.176671 | + | 0.984270i | \(0.443467\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.48655 | − | 7.77093i | 0.240159 | − | 0.415968i | −0.720600 | − | 0.693351i | \(-0.756134\pi\) |
0.960760 | + | 0.277383i | \(0.0894670\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.3822 | − | 4.07944i | 0.607535 | − | 0.217744i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 29.6618 | + | 17.1252i | 1.57874 | + | 0.911484i | 0.995036 | + | 0.0995150i | \(0.0317291\pi\) |
0.583701 | + | 0.811969i | \(0.301604\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.75889 | − | 7.80221i | −0.464874 | − | 0.414098i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 15.2349 | − | 8.79585i | 0.806315 | − | 0.465526i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.4043 | 1.18245 | 0.591227 | − | 0.806505i | \(-0.298644\pi\) | ||||
0.591227 | + | 0.806505i | \(0.298644\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.72398 | − | 15.1104i | 0.459157 | − | 0.795283i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.25092i | 0.0656565i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.83821 | − | 11.6015i | −0.200901 | − | 0.607252i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.4273 | + | 6.59753i | 0.596498 | + | 0.344388i | 0.767663 | − | 0.640854i | \(-0.221420\pi\) |
−0.171165 | + | 0.985242i | \(0.554753\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −11.8080 | −0.614700 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −21.5185 | − | 37.2712i | −1.11719 | − | 1.93502i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.2168 | + | 7.63070i | −0.684338 | + | 0.395103i | −0.801488 | − | 0.598012i | \(-0.795958\pi\) |
0.117149 | + | 0.993114i | \(0.462624\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −27.2937 | + | 12.6799i | −1.40944 | + | 0.654788i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.6430 | − | 1.93070i | −0.548140 | − | 0.0994362i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.11453 | + | 15.7868i | −0.468182 | + | 0.810915i | −0.999339 | − | 0.0363588i | \(-0.988424\pi\) |
0.531157 | + | 0.847273i | \(0.321757\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.3334 | − | 21.3621i | −0.631861 | − | 1.09442i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.24784 | + | 0.720440i | −0.0637616 | + | 0.0368128i | −0.531542 | − | 0.847032i | \(-0.678387\pi\) |
0.467780 | + | 0.883845i | \(0.345054\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.64474 | + | 23.1073i | 0.389612 | + | 1.17766i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −32.1261 | − | 18.5480i | −1.63306 | − | 0.942848i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.7912 | 0.952754 | 0.476377 | − | 0.879241i | \(-0.341950\pi\) | ||||
0.476377 | + | 0.879241i | \(0.341950\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.24581 | 0.265292 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −23.3117 | − | 13.4590i | −1.17592 | − | 0.678918i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −29.2560 | + | 9.67894i | −1.47203 | + | 0.487000i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.8027 | − | 8.54634i | 0.742926 | − | 0.428928i | −0.0802063 | − | 0.996778i | \(-0.525558\pi\) |
0.823132 | + | 0.567850i | \(0.192225\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.62291 | − | 9.73916i | −0.281497 | − | 0.487568i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.1011 | + | 19.2276i | −0.554361 | + | 0.960182i | 0.443592 | + | 0.896229i | \(0.353704\pi\) |
−0.997953 | + | 0.0639527i | \(0.979629\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.59962 | + | 12.8336i | 0.229124 | + | 0.639285i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.68166 | + | 8.12478i | −0.0835623 | + | 0.403724i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.47801 | − | 3.16273i | 0.271535 | − | 0.156771i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.81638 | − | 8.34221i | −0.238155 | − | 0.412496i | 0.722030 | − | 0.691862i | \(-0.243209\pi\) |
−0.960185 | + | 0.279366i | \(0.909876\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 45.3534 | 2.23712 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.36296 | − | 4.25101i | −0.362308 | − | 0.209178i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.05381 | − | 18.2985i | −0.297170 | − | 0.898238i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.76423i | 0.135365i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.978168 | − | 1.69424i | 0.0477866 | − | 0.0827689i | −0.841143 | − | 0.540813i | \(-0.818117\pi\) |
0.888929 | + | 0.458044i | \(0.151450\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.0807 | −0.588778 | −0.294389 | − | 0.955686i | \(-0.595116\pi\) | ||||
−0.294389 | + | 0.955686i | \(0.595116\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −25.2594 | + | 14.5835i | −1.22815 | + | 0.709075i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.86792 | + | 8.94346i | −0.187622 | + | 0.433822i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21.7571 | − | 12.5615i | −1.05290 | − | 0.607893i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 24.0320 | + | 20.3676i | 1.16027 | + | 0.983359i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.2945 | − | 21.2948i | 0.592207 | − | 1.02573i | −0.401727 | − | 0.915759i | \(-0.631590\pi\) |
0.993934 | − | 0.109974i | \(-0.0350767\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −31.2400 | + | 18.0364i | −1.50130 | + | 0.866775i | −0.501299 | + | 0.865274i | \(0.667144\pi\) |
−0.999999 | + | 0.00150085i | \(0.999522\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.0107 | + | 13.4835i | −0.575871 | + | 0.646482i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 3.35348i | − | 0.160419i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.26764 | + | 2.19562i | −0.0605013 | + | 0.104791i | −0.894690 | − | 0.446688i | \(-0.852603\pi\) |
0.834188 | + | 0.551480i | \(0.185937\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.0269 | 0.858424 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.3579i | 0.919721i | 0.887991 | + | 0.459860i | \(0.152101\pi\) | ||||
−0.887991 | + | 0.459860i | \(0.847899\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.67552 | + | 22.5893i | −0.221641 | + | 1.07084i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 42.6696i | 2.01820i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.4040 | − | 21.4844i | −0.585381 | − | 1.01391i | −0.994828 | − | 0.101576i | \(-0.967612\pi\) |
0.409447 | − | 0.912334i | \(-0.365722\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.51345 | − | 7.81753i | −0.212530 | − | 0.368113i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −33.9079 | − | 19.5767i | −1.59313 | − | 0.919795i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −25.0722 | − | 10.1176i | −1.17540 | − | 0.474318i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.55363 | + | 3.78374i | 0.306566 | + | 0.176996i | 0.645389 | − | 0.763854i | \(-0.276695\pi\) |
−0.338823 | + | 0.940850i | \(0.610029\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.26764 | − | 5.65972i | −0.152520 | − | 0.264173i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.17164 | + | 10.6896i | 0.287442 | + | 0.497864i | 0.973198 | − | 0.229967i | \(-0.0738618\pi\) |
−0.685756 | + | 0.727831i | \(0.740528\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 22.8578i | − | 1.06229i | −0.847281 | − | 0.531146i | \(-0.821762\pi\) | ||
0.847281 | − | 0.531146i | \(-0.178238\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 22.2863 | + | 4.61279i | 1.03350 | + | 0.213913i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 15.2976i | − | 0.707889i | −0.935266 | − | 0.353945i | \(-0.884840\pi\) | ||
0.935266 | − | 0.353945i | \(-0.115160\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.4647 | 0.621743 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.6985 | + | 25.4586i | −0.677273 | + | 1.17307i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 28.3589i | − | 1.30394i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.71727 | + | 2.47264i | 0.262326 | + | 0.113452i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −47.1887 | + | 27.2444i | −2.16062 | + | 1.24744i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.1414 | + | 21.0296i | −0.554756 | + | 0.960866i | 0.443166 | + | 0.896439i | \(0.353855\pi\) |
−0.997922 | + | 0.0644264i | \(0.979478\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.25419 | + | 6.91369i | −0.0571861 | + | 0.315237i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 21.0433 | + | 12.1493i | 0.957501 | + | 0.552814i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.83235 | − | 8.79272i | 0.355649 | − | 0.399257i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.9462 | − | 18.4441i | 1.44762 | − | 0.835783i | 0.449280 | − | 0.893391i | \(-0.351681\pi\) |
0.998339 | + | 0.0576081i | \(0.0183474\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11.2458 | −0.508553 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.6767 | + | 30.6170i | −0.797739 | + | 1.38172i | 0.123346 | + | 0.992364i | \(0.460637\pi\) |
−0.921085 | + | 0.389361i | \(0.872696\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.84642i | 0.263310i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 29.2560 | − | 9.67894i | 1.31496 | − | 0.435036i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −15.2349 | − | 8.79585i | −0.683377 | − | 0.394548i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.2189 | 0.726058 | 0.363029 | − | 0.931778i | \(-0.381743\pi\) | ||||
0.363029 | + | 0.931778i | \(0.381743\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.51345 | − | 7.81753i | −0.201646 | − | 0.349261i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17.5270 | + | 10.1192i | −0.781489 | + | 0.451193i | −0.836958 | − | 0.547268i | \(-0.815668\pi\) |
0.0554688 | + | 0.998460i | \(0.482335\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.58808 | − | 12.5041i | 0.115168 | − | 0.556425i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −34.5200 | + | 5.73700i | −1.53309 | + | 0.254789i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.0185 | + | 17.3526i | −0.444063 | + | 0.769140i | −0.997986 | − | 0.0634276i | \(-0.979797\pi\) |
0.553923 | + | 0.832568i | \(0.313130\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.16326 | − | 15.8712i | −0.405359 | − | 0.702102i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.61808 | + | 2.08890i | −0.159742 | + | 0.0922271i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.17524 | + | 15.6429i | 0.228048 | + | 0.689308i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19.3101 | − | 11.1487i | −0.849259 | − | 0.490320i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −23.5185 | −1.03235 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.0269 | 0.702151 | 0.351076 | − | 0.936347i | \(-0.385816\pi\) | ||||
0.351076 | + | 0.936347i | \(0.385816\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.1654 | − | 5.86898i | −0.444501 | − | 0.256633i | 0.261004 | − | 0.965338i | \(-0.415946\pi\) |
−0.705505 | + | 0.708705i | \(0.749280\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −36.2291 | + | 26.9180i | −1.58117 | + | 1.17480i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.38142 | − | 3.68431i | 0.277979 | − | 0.160491i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.87709 | − | 13.6435i | −0.342482 | − | 0.593197i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.38217 | + | 9.32219i | −0.233566 | + | 0.404548i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.86635 | + | 1.78982i | 0.427359 | + | 0.0775258i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.7751 | − | 3.88605i | −0.811718 | − | 0.168008i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 41.9847 | − | 24.2399i | 1.81177 | − | 1.04603i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.89055 | + | 11.9348i | 0.296797 | + | 0.514067i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.8080 | −0.937599 | −0.468800 | − | 0.883305i | \(-0.655313\pi\) | ||||
−0.468800 | + | 0.883305i | \(0.655313\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.43296 | + | 1.40467i | 0.104408 | + | 0.0602801i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −18.0269 | + | 5.96396i | −0.772188 | + | 0.255468i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 6.30924i | − | 0.269764i | −0.990862 | − | 0.134882i | \(-0.956935\pi\) | ||
0.990862 | − | 0.134882i | \(-0.0430655\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −15.9040 | + | 27.5465i | −0.678766 | + | 1.17566i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.73743 | 0.159220 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −40.0230 | + | 23.1073i | −1.70195 | + | 0.982622i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.75889 | + | 7.80221i | 0.371794 | + | 0.331185i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 31.0364 | + | 17.9189i | 1.31506 | + | 0.759247i | 0.982929 | − | 0.183987i | \(-0.0589006\pi\) |
0.332126 | + | 0.943235i | \(0.392234\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.0320 | + | 20.3676i | 1.01644 | + | 0.861459i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.51345 | − | 14.7457i | 0.359438 | − | 0.622565i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.33196 | + | 2.50106i | −0.182570 | + | 0.105407i | −0.588500 | − | 0.808497i | \(-0.700281\pi\) |
0.405929 | + | 0.913904i | \(0.366948\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.9057 | + | 12.2429i | −0.458805 | + | 0.515062i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 12.4432i | 0.522564i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.58402 | + | 11.4039i | −0.276017 | + | 0.478075i | −0.970391 | − | 0.241539i | \(-0.922348\pi\) |
0.694375 | + | 0.719614i | \(0.255681\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.8349 | −0.830065 | −0.415032 | − | 0.909807i | \(-0.636230\pi\) | ||||
−0.415032 | + | 0.909807i | \(0.636230\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 68.6909i | 2.86960i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.3695 | + | 1.54979i | −0.557547 | + | 0.0646307i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 10.9210i | − | 0.454646i | −0.973819 | − | 0.227323i | \(-0.927003\pi\) | ||
0.973819 | − | 0.227323i | \(-0.0729972\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −26.6767 | − | 46.2054i | −1.10865 | − | 1.92023i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.4527 | − | 25.0329i | −0.599601 | − | 1.03854i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −36.0745 | − | 20.8276i | −1.49406 | − | 0.862593i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −12.8098 | + | 31.7436i | −0.529618 | + | 1.31244i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −35.0303 | − | 20.2247i | −1.44585 | − | 0.834764i | −0.447624 | − | 0.894222i | \(-0.647730\pi\) |
−0.998231 | + | 0.0594576i | \(0.981063\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.35526 | − | 4.07944i | −0.0970469 | − | 0.168090i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −29.1414 | − | 50.4744i | −1.19872 | − | 2.07624i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.47709i | 0.0606569i | 0.999540 | + | 0.0303284i | \(0.00965532\pi\) | ||||
−0.999540 | + | 0.0303284i | \(0.990345\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.96188 | + | 14.3100i | −0.121425 | + | 0.586654i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 49.0690i | − | 2.00826i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.27271 | 0.0928606 | 0.0464303 | − | 0.998922i | \(-0.485215\pi\) | ||||
0.0464303 | + | 0.998922i | \(0.485215\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.70215 | + | 6.41231i | −0.151014 | + | 0.261563i | −0.931600 | − | 0.363484i | \(-0.881587\pi\) |
0.780587 | + | 0.625048i | \(0.214920\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 17.0476i | − | 0.694231i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.775932 | − | 0.691182i | −0.0315461 | − | 0.0281006i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.26059 | + | 5.34661i | −0.375876 | + | 0.217012i | −0.676022 | − | 0.736881i | \(-0.736298\pi\) |
0.300146 | + | 0.953893i | \(0.402964\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −13.5404 | + | 23.4526i | −0.548683 | + | 0.950347i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23.3164 | − | 8.35673i | 0.943280 | − | 0.338077i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.26673 | − | 3.04075i | −0.212721 | − | 0.122815i | 0.389854 | − | 0.920877i | \(-0.372525\pi\) |
−0.602575 | + | 0.798062i | \(0.705859\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11.1343 | − | 12.4996i | 0.448980 | − | 0.504032i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.5732 | + | 15.9194i | −1.11006 | + | 0.640892i | −0.938844 | − | 0.344342i | \(-0.888102\pi\) |
−0.171213 | + | 0.985234i | \(0.554769\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.4043 | −1.06128 | −0.530639 | − | 0.847598i | \(-0.678048\pi\) | ||||
−0.530639 | + | 0.847598i | \(0.678048\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.51345 | − | 7.81753i | 0.181119 | − | 0.313707i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 34.5957i | 1.38605i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.21560 | − | 23.9361i | 0.288624 | − | 0.957443i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.42647 | − | 5.44238i | −0.376457 | − | 0.217348i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.79785 | 0.151430 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.5840 | + | 30.4564i | 0.700009 | + | 1.21245i | 0.968463 | + | 0.249158i | \(0.0801539\pi\) |
−0.268454 | + | 0.963293i | \(0.586513\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 44.9907 | − | 25.9754i | 1.78822 | − | 1.03243i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 20.0653 | + | 4.15310i | 0.796269 | + | 0.164811i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.0626 | − | 2.73247i | −0.596804 | − | 0.108264i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.1364 | + | 19.2887i | −0.440547 | + | 0.763051i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.76257 | − | 4.78491i | −0.109115 | − | 0.188993i | 0.806297 | − | 0.591511i | \(-0.201468\pi\) |
−0.915412 | + | 0.402518i | \(0.868135\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.8472 | − | 16.0776i | 1.09819 | − | 0.634039i | 0.162444 | − | 0.986718i | \(-0.448062\pi\) |
0.935744 | + | 0.352679i | \(0.114729\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 49.9276 | − | 16.5179i | 1.96590 | − | 0.650391i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.9376 | + | 6.89216i | 0.469314 | + | 0.270959i | 0.715953 | − | 0.698149i | \(-0.245993\pi\) |
−0.246638 | + | 0.969108i | \(0.579326\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.22905 | −0.323019 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 34.1316 | 1.33772 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.36296 | − | 4.25101i | −0.288135 | − | 0.166355i | 0.348965 | − | 0.937136i | \(-0.386533\pi\) |
−0.637100 | + | 0.770781i | \(0.719866\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 21.2291 | − | 7.02335i | 0.829488 | − | 0.274425i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −20.0944 | + | 11.6015i | −0.783959 | + | 0.452619i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.02183 | − | 3.50192i | −0.0787594 | − | 0.136415i | 0.823956 | − | 0.566654i | \(-0.191763\pi\) |
−0.902715 | + | 0.430239i | \(0.858429\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.6364 | + | 27.0830i | −0.608184 | + | 1.05341i | 0.383356 | + | 0.923601i | \(0.374768\pi\) |
−0.991540 | + | 0.129805i | \(0.958565\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.38142 | + | 17.8050i | 0.247834 | + | 0.691489i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.14794 | + | 1.89343i | 0.354742 | + | 0.0734241i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.99351 | + | 4.03771i | −0.270790 | + | 0.156341i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16.6498 | − | 28.8383i | −0.643719 | − | 1.11495i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −24.3164 | −0.938723 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.7768 | + | 16.0370i | 1.07072 | + | 0.618179i | 0.928377 | − | 0.371639i | \(-0.121204\pi\) |
0.142340 | + | 0.989818i | \(0.454537\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.0000 | + | 13.4590i | 0.384900 | + | 0.518038i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 14.2382i | − | 0.547220i | −0.961841 | − | 0.273610i | \(-0.911782\pi\) | ||
0.961841 | − | 0.273610i | \(-0.0882177\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.82983 | − | 15.2937i | 0.338858 | − | 0.586919i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.5891 | 0.635695 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.3302 | − | 12.8923i | 0.854440 | − | 0.493311i | −0.00770647 | − | 0.999970i | \(-0.502453\pi\) |
0.862146 | + | 0.506659i | \(0.169120\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −25.0595 | + | 28.1322i | −0.957473 | + | 1.07487i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 62.9025 | + | 36.3168i | 2.39988 | + | 1.38557i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 43.5589 | − | 15.6118i | 1.65946 | − | 0.594761i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.0218318 | + | 0.0378138i | −0.000830522 | + | 0.00143851i | −0.866440 | − | 0.499281i | \(-0.833598\pi\) |
0.865610 | + | 0.500719i | \(0.166931\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 40.0230 | − | 23.1073i | 1.52035 | − | 0.877774i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.71461 | − | 1.52734i | −0.0650390 | − | 0.0579352i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 5.41982i | − | 0.205290i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.10945 | − | 1.92163i | 0.0419634 | − | 0.0726827i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.5454 | −0.549373 | −0.274687 | − | 0.961534i | \(-0.588574\pi\) | ||||
−0.274687 | + | 0.961534i | \(0.588574\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 2.42785i | − | 0.0915679i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.38064 | − | 40.4903i | 0.315633 | − | 1.52495i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 19.1501i | − | 0.720214i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.81638 | + | 17.0025i | 0.368662 | + | 0.638541i | 0.989357 | − | 0.145511i | \(-0.0464827\pi\) |
−0.620695 | + | 0.784052i | \(0.713149\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 29.2560 | + | 50.6728i | 1.09718 | + | 1.90038i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.81438 | + | 5.08898i | 0.330101 | + | 0.190584i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −25.9124 | + | 3.65285i | −0.969067 | + | 0.136609i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.32468 | + | 5.38361i | 0.348237 | + | 0.201055i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23.7156 | − | 41.0766i | −0.884443 | − | 1.53190i | −0.846351 | − | 0.532625i | \(-0.821206\pi\) |
−0.0380914 | − | 0.999274i | \(-0.512128\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.3553 | + | 21.3999i | 0.460134 | + | 0.796976i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 61.0872i | − | 2.27186i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.72723 | − | 14.9002i | −0.0641477 | − | 0.553380i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.0951i | 1.26452i | 0.774757 | + | 0.632259i | \(0.217872\pi\) | ||||
−0.774757 | + | 0.632259i | \(0.782128\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 42.8349 | 1.58648 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.51345 | − | 14.7457i | 0.314881 | − | 0.545391i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 14.3920i | − | 0.531580i | −0.964031 | − | 0.265790i | \(-0.914367\pi\) | ||
0.964031 | − | 0.265790i | \(-0.0856327\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −16.9984 | + | 19.0827i | −0.626997 | + | 0.703877i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.2864 | − | 6.51621i | 0.415740 | − | 0.240028i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.2240 | − | 29.8328i | 0.633594 | − | 1.09742i | −0.353217 | − | 0.935541i | \(-0.614912\pi\) |
0.986811 | − | 0.161876i | \(-0.0517545\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.3822 | − | 4.07944i | 0.418134 | − | 0.149862i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35.2589 | + | 20.3567i | 1.29352 | + | 0.746816i | 0.979277 | − | 0.202526i | \(-0.0649150\pi\) |
0.314246 | + | 0.949342i | \(0.398248\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −26.4674 | − | 23.5765i | −0.969690 | − | 0.863777i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −31.6939 | + | 18.2985i | −1.15962 | + | 0.669507i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −28.7542 | −1.05066 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.2509 | − | 28.1474i | 0.593003 | − | 1.02711i | −0.400822 | − | 0.916156i | \(-0.631275\pi\) |
0.993825 | − | 0.110956i | \(-0.0353912\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 51.2167i | 1.86644i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 30.8786 | − | 10.2158i | 1.12379 | − | 0.371790i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.2864 | − | 6.51621i | −0.410211 | − | 0.236836i | 0.280669 | − | 0.959805i | \(-0.409444\pi\) |
−0.690881 | + | 0.722969i | \(0.742777\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 23.5185 | 0.853668 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.99493 | + | 3.45532i | 0.0723161 | + | 0.125255i | 0.899916 | − | 0.436063i | \(-0.143628\pi\) |
−0.827600 | + | 0.561318i | \(0.810294\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −24.6613 | + | 14.2382i | −0.892800 | + | 0.515458i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 18.1178 | + | 3.75001i | 0.655051 | + | 0.135582i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.91018 | − | 6.97348i | 0.213404 | − | 0.251798i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.33343 | − | 5.77367i | 0.120207 | − | 0.208204i | −0.799642 | − | 0.600476i | \(-0.794978\pi\) |
0.919849 | + | 0.392272i | \(0.128311\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.84181 | + | 4.92216i | 0.102345 | + | 0.177267i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 41.8593 | − | 24.1675i | 1.50557 | − | 0.869244i | 0.505595 | − | 0.862771i | \(-0.331273\pi\) |
0.999979 | − | 0.00647254i | \(-0.00206029\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.1752 | + | 11.2751i | −0.545111 | + | 0.405015i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 15.2349 | + | 8.79585i | 0.546548 | + | 0.315549i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.46472 | −0.124136 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.0269 | −0.609271 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.71259 | + | 5.03022i | 0.311363 | + | 0.179765i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.67017 | − | 23.1842i | −0.273760 | − | 0.827478i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.2151 | + | 13.9806i | −0.863176 | + | 0.498355i | −0.865074 | − | 0.501643i | \(-0.832729\pi\) |
0.00189876 | + | 0.999998i | \(0.499396\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −40.2658 | − | 69.7424i | −1.43350 | − | 2.48290i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.2945 | + | 21.2948i | −0.437144 | + | 0.757155i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.4642 | − | 20.6062i | 0.620174 | − | 0.731749i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 15.6564 | − | 75.6426i | 0.555277 | − | 2.68277i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −32.2529 | + | 18.6212i | −1.14246 | + | 0.659597i | −0.947038 | − | 0.321123i | \(-0.895940\pi\) |
−0.195418 | + | 0.980720i | \(0.562607\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.69377 | − | 11.5939i | −0.236808 | − | 0.410164i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 43.8014 | 1.54765 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15.3617 | − | 8.86907i | −0.542102 | − | 0.312983i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −19.1633 | + | 6.33991i | −0.675416 | + | 0.223452i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 50.0382i | 1.76143i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.26434 | − | 12.5822i | 0.255400 | − | 0.442367i | −0.709604 | − | 0.704601i | \(-0.751126\pi\) |
0.965004 | + | 0.262234i | \(0.0844594\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −44.0538 | −1.54694 | −0.773469 | − | 0.633834i | \(-0.781480\pi\) | ||||
−0.773469 | + | 0.633834i | \(0.781480\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.5785 | − | 7.83955i | 0.476219 | − | 0.274945i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.21373 | − | 6.97563i | 0.217657 | − | 0.244346i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.42647 | − | 5.44238i | −0.329790 | − | 0.190405i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.16326 | + | 50.5123i | −0.320190 | + | 1.76504i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.5135 | + | 23.4060i | −0.471623 | + | 0.816875i | −0.999473 | − | 0.0324629i | \(-0.989665\pi\) |
0.527850 | + | 0.849337i | \(0.322998\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.2914 | − | 19.7981i | 1.19532 | − | 0.690120i | 0.235814 | − | 0.971798i | \(-0.424225\pi\) |
0.959509 | + | 0.281679i | \(0.0908912\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −17.3410 | + | 40.0962i | −0.603737 | + | 1.39597i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 26.5639i | − | 0.923716i | −0.886954 | − | 0.461858i | \(-0.847183\pi\) | ||
0.886954 | − | 0.461858i | \(-0.152817\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.99162 | − | 12.1098i | 0.242829 | − | 0.420592i | −0.718690 | − | 0.695331i | \(-0.755258\pi\) |
0.961519 | + | 0.274738i | \(0.0885913\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −36.4480 | −1.26437 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.27427i | 0.286686i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.34297 | + | 1.51984i | 0.254114 | + | 0.0525962i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 12.6798i | − | 0.438278i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.19707 | − | 12.4657i | −0.248471 | − | 0.430364i | 0.714631 | − | 0.699502i | \(-0.246595\pi\) |
−0.963102 | + | 0.269138i | \(0.913261\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.0000 | + | 17.3205i | 0.344828 | + | 0.597259i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.08333 | − | 0.625462i | −0.0373119 | − | 0.0215421i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 15.5150 | − | 24.5822i | 0.533732 | − | 0.845654i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.34963 | − | 0.779207i | −0.0463737 | − | 0.0267739i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.5404 | + | 23.4526i | 0.464704 | + | 0.804891i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.62291 | + | 4.54300i | 0.0899120 | + | 0.155732i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 27.2633i | − | 0.933478i | −0.884395 | − | 0.466739i | \(-0.845429\pi\) | ||
0.884395 | − | 0.466739i | \(-0.154571\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.39726 | − | 11.5821i | 0.0819845 | − | 0.396101i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 50.6201i | 1.72915i | 0.502503 | + | 0.864575i | \(0.332413\pi\) | ||||
−0.502503 | + | 0.864575i | \(0.667587\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.27992 | 0.0436702 | 0.0218351 | − | 0.999762i | \(-0.493049\pi\) | ||||
0.0218351 | + | 0.999762i | \(0.493049\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.5523 | − | 21.7413i | 0.427782 | − | 0.740941i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 8.38448i | − | 0.285411i | −0.989765 | − | 0.142706i | \(-0.954420\pi\) | ||
0.989765 | − | 0.142706i | \(-0.0455802\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.9949 | − | 14.5882i | 0.441839 | − | 0.496015i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −30.7765 | + | 17.7688i | −1.04522 | + | 0.603460i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22.3654 | + | 38.7380i | −0.758695 | + | 1.31410i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.58402 | + | 14.2443i | −0.0875562 | + | 0.482651i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −19.3632 | − | 11.1794i | −0.655347 | − | 0.378365i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.32098 | − | 37.3456i | 0.112270 | − | 1.26251i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 48.3989 | − | 27.9431i | 1.63431 | − | 0.943572i | 0.651573 | − | 0.758586i | \(-0.274110\pi\) |
0.982741 | − | 0.184985i | \(-0.0592237\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 36.2051 | 1.22117 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.5975 | + | 21.8195i | −0.424420 | + | 0.735116i | −0.996366 | − | 0.0851746i | \(-0.972855\pi\) |
0.571946 | + | 0.820291i | \(0.306189\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.7868i | 1.03606i | 0.855363 | + | 0.518029i | \(0.173334\pi\) | ||||
−0.855363 | + | 0.518029i | \(0.826666\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.79307 | − | 14.4877i | −0.161117 | − | 0.487000i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10.8011 | + | 6.23603i | 0.362666 | + | 0.209385i | 0.670250 | − | 0.742136i | \(-0.266187\pi\) |
−0.307584 | + | 0.951521i | \(0.599520\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 30.7302 | 1.03066 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.02183 | + | 10.4301i | 0.201739 | + | 0.349422i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.41163 | + | 4.27911i | −0.248021 | + | 0.143195i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.16243 | + | 39.4360i | −0.272840 | + | 1.31820i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16.8912 | + | 19.9301i | −0.563981 | + | 0.665447i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.67164 | + | 9.82357i | −0.189160 | + | 0.327634i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.5051 | − | 21.6594i | −0.416604 | − | 0.721580i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 68.3024 | − | 39.4344i | 2.27296 | − | 1.31230i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.21560 | + | 0.733001i | −0.0736490 | + | 0.0243658i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.6807 | + | 19.4455i | 1.11835 | + | 0.645678i | 0.940979 | − | 0.338466i | \(-0.109908\pi\) |
0.177369 | + | 0.984144i | \(0.443241\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −24.2458 | −0.804183 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.165096 | −0.00546989 | −0.00273494 | − | 0.999996i | \(-0.500871\pi\) | ||||
−0.00273494 | + | 0.999996i | \(0.500871\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.2292 | − | 13.9887i | −0.801868 | − | 0.462959i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −14.1633 | − | 42.8105i | −0.468223 | − | 1.41527i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 29.0420 | − | 16.7674i | 0.959050 | − | 0.553708i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.447663 | − | 0.775375i | −0.0147670 | − | 0.0255773i | 0.858547 | − | 0.512734i | \(-0.171367\pi\) |
−0.873314 | + | 0.487157i | \(0.838034\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −33.1196 | + | 57.3648i | −1.09133 | + | 1.89024i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.2289 | − | 14.4290i | 0.402518 | − | 0.474935i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.67923 | + | 1.12201i | −0.318251 | + | 0.0368916i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 27.0943 | − | 15.6429i | 0.889893 | − | 0.513780i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.14474 | − | 10.6430i | −0.201602 | − | 0.349185i | 0.747443 | − | 0.664326i | \(-0.231282\pi\) |
−0.949045 | + | 0.315141i | \(0.897948\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.28947 | 0.173356 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.68295 | − | 3.28106i | −0.186052 | − | 0.107417i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.44259 | + | 13.4284i | 0.145288 | + | 0.439154i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.77242i | 0.188577i | 0.995545 | + | 0.0942884i | \(0.0300576\pi\) | ||||
−0.995545 | + | 0.0942884i | \(0.969942\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 25.9713 | − | 44.9835i | 0.847540 | − | 1.46798i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −55.8887 | −1.82192 | −0.910960 | − | 0.412495i | \(-0.864658\pi\) | ||||
−0.910960 | + | 0.412495i | \(0.864658\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.48321 | − | 3.74308i | 0.211122 | − | 0.121891i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 18.7770 | + | 16.7261i | 0.610817 | + | 0.544102i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.64231 | + | 0.948188i | 0.0533679 | + | 0.0308120i | 0.526447 | − | 0.850208i | \(-0.323524\pi\) |
−0.473079 | + | 0.881020i | \(0.656857\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.5487 | − | 6.64798i | 0.602117 | − | 0.215802i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −38.7912 | + | 67.1884i | −1.25789 | + | 2.17873i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.1438 | − | 16.8262i | 0.944059 | − | 0.545053i | 0.0528285 | − | 0.998604i | \(-0.483176\pi\) |
0.891230 | + | 0.453551i | \(0.149843\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −42.6081 | − | 37.9543i | −1.37877 | − | 1.22817i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 26.2113i | 0.847290i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −28.2509 | + | 48.9320i | −0.912269 | + | 1.58010i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.7033 | −0.538817 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 36.4054i | 1.17315i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 43.4005 | + | 8.98300i | 1.39711 | + | 0.289173i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 23.0493i | − | 0.741216i | −0.928789 | − | 0.370608i | \(-0.879149\pi\) | ||
0.928789 | − | 0.370608i | \(-0.120851\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.26764 | − | 5.65972i | −0.104972 | − | 0.181816i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.45964 | + | 12.9205i | 0.239391 | + | 0.414638i | 0.960540 | − | 0.278143i | \(-0.0897188\pi\) |
−0.721148 | + | 0.692781i | \(0.756385\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.98233 | − | 1.72185i | −0.0956092 | − | 0.0552000i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −21.5239 | − | 43.4926i | −0.689317 | − | 1.39288i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.2339 | − | 11.6821i | −0.647341 | − | 0.373742i | 0.140096 | − | 0.990138i | \(-0.455259\pi\) |
−0.787437 | + | 0.616396i | \(0.788592\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.7425 | + | 28.9989i | 0.535093 | + | 0.926808i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.0269 | + | 31.2235i | 0.575555 | + | 0.996890i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 5.31119i | − | 0.169401i | −0.996406 | − | 0.0847003i | \(-0.973007\pi\) | ||
0.996406 | − | 0.0847003i | \(-0.0269933\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 47.4104 | + | 9.81295i | 1.51062 | + | 0.312667i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 62.0112i | − | 1.97384i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 23.5185 | 0.747846 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.0440 | + | 20.8607i | −0.382589 | + | 0.662663i | −0.991432 | − | 0.130628i | \(-0.958301\pi\) |
0.608843 | + | 0.793291i | \(0.291634\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 8.00299i | − | 0.253967i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 30.4369 | + | 27.1125i | 0.964915 | + | 0.859523i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.6755 | + | 10.2050i | −0.559790 | + | 0.323195i | −0.753061 | − | 0.657951i | \(-0.771424\pi\) |
0.193271 | + | 0.981145i | \(0.438090\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.26764 | − | 5.65972i | 0.103384 | − | 0.179066i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))