Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(293,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.293");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.x (of order \(6\), 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: | \(14.0856109166\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 293.3 | ||
Root | \(1.68124 + 0.416458i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.293 |
Dual form | 1764.2.x.b.1469.3 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −0.647613 | − | 1.60642i | −0.373900 | − | 0.927469i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.349828 | + | 0.605920i | −0.156448 | + | 0.270975i | −0.933585 | − | 0.358355i | \(-0.883338\pi\) |
0.777137 | + | 0.629331i | \(0.216671\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.16119 | + | 2.08068i | −0.720398 | + | 0.693561i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.229685 | + | 0.132608i | −0.0692525 | + | 0.0399829i | −0.534226 | − | 0.845341i | \(-0.679397\pi\) |
0.464974 | + | 0.885324i | \(0.346064\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.13823 | − | 0.657156i | −0.315688 | − | 0.182262i | 0.333781 | − | 0.942651i | \(-0.391675\pi\) |
−0.649469 | + | 0.760388i | \(0.725009\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.19992 | + | 0.169570i | 0.309817 | + | 0.0437829i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.72784 | −0.904134 | −0.452067 | − | 0.891984i | \(-0.649313\pi\) | ||||
−0.452067 | + | 0.891984i | \(0.649313\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 0.441614i | − | 0.101313i | −0.998716 | − | 0.0506566i | \(-0.983869\pi\) | ||
0.998716 | − | 0.0506566i | \(-0.0161314\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.29949 | + | 2.48231i | 0.896507 | + | 0.517598i | 0.876065 | − | 0.482193i | \(-0.160160\pi\) |
0.0204414 | + | 0.999791i | \(0.493493\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.25524 | + | 3.90619i | 0.451048 | + | 0.781238i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.74208 | + | 2.12432i | 0.912613 | + | 0.408825i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.273287 | + | 0.157782i | −0.0507480 | + | 0.0292994i | −0.525159 | − | 0.851004i | \(-0.675994\pi\) |
0.474411 | + | 0.880303i | \(0.342661\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.85521 | + | 2.80316i | 0.872022 | + | 0.503462i | 0.868020 | − | 0.496530i | \(-0.165393\pi\) |
0.00400255 | + | 0.999992i | \(0.498726\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.361772 | + | 0.283092i | 0.0629764 | + | 0.0492799i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.702248 | 0.115449 | 0.0577244 | − | 0.998333i | \(-0.481616\pi\) | ||||
0.0577244 | + | 0.998333i | \(0.481616\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.318540 | + | 2.25406i | −0.0510072 | + | 0.360938i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.39354 | − | 9.34189i | 0.842330 | − | 1.45896i | −0.0455900 | − | 0.998960i | \(-0.514517\pi\) |
0.887920 | − | 0.459998i | \(-0.152150\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.73131 | + | 6.46283i | 0.569020 | + | 0.985572i | 0.996663 | + | 0.0816240i | \(0.0260106\pi\) |
−0.427643 | + | 0.903948i | \(0.640656\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.504680 | − | 2.03739i | −0.0752333 | − | 0.303716i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.50285 | − | 6.06712i | −0.510943 | − | 0.884980i | −0.999920 | − | 0.0126827i | \(-0.995963\pi\) |
0.488976 | − | 0.872297i | \(-0.337370\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.41420 | + | 5.98849i | 0.338055 | + | 0.838556i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.83712i | 1.35123i | 0.737254 | + | 0.675616i | \(0.236122\pi\) | ||||
−0.737254 | + | 0.675616i | \(0.763878\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.185561i | − | 0.0250210i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.709419 | + | 0.285995i | −0.0939648 | + | 0.0378809i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.73182 | + | 11.6598i | −0.876408 | + | 1.51798i | −0.0211522 | + | 0.999776i | \(0.506733\pi\) |
−0.855256 | + | 0.518206i | \(0.826600\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.89484 | − | 2.82604i | 0.626720 | − | 0.361837i | −0.152761 | − | 0.988263i | \(-0.548816\pi\) |
0.779481 | + | 0.626426i | \(0.215483\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.796368 | − | 0.459783i | 0.0987773 | − | 0.0570291i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.97060 | − | 5.14523i | 0.362916 | − | 0.628590i | −0.625523 | − | 0.780206i | \(-0.715114\pi\) |
0.988439 | + | 0.151616i | \(0.0484477\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.20324 | − | 8.51439i | 0.144853 | − | 1.02501i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.4323i | 1.59412i | 0.603900 | + | 0.797060i | \(0.293613\pi\) | ||||
−0.603900 | + | 0.797060i | \(0.706387\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.69241i | 0.900328i | 0.892946 | + | 0.450164i | \(0.148634\pi\) | ||||
−0.892946 | + | 0.450164i | \(0.851366\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.81448 | − | 6.15257i | 0.555928 | − | 0.710438i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.698360 | − | 1.20959i | −0.0785716 | − | 0.136090i | 0.824062 | − | 0.566499i | \(-0.191703\pi\) |
−0.902634 | + | 0.430409i | \(0.858369\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.341524 | − | 8.99352i | 0.0379471 | − | 0.999280i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.72399 | + | 6.45014i | 0.408761 | + | 0.707995i | 0.994751 | − | 0.102323i | \(-0.0326276\pi\) |
−0.585990 | + | 0.810318i | \(0.699294\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.30410 | − | 2.25877i | 0.141450 | − | 0.244998i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.430449 | + | 0.336832i | 0.0461490 | + | 0.0361122i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.1852 | 1.18563 | 0.592815 | − | 0.805339i | \(-0.298016\pi\) | ||||
0.592815 | + | 0.805339i | \(0.298016\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.35876 | − | 9.61489i | 0.140897 | − | 0.997018i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.267582 | + | 0.154489i | 0.0274534 | + | 0.0158502i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.18225 | − | 5.30138i | 0.932316 | − | 0.538273i | 0.0447729 | − | 0.998997i | \(-0.485744\pi\) |
0.887543 | + | 0.460724i | \(0.152410\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.220477 | − | 0.764493i | 0.0221588 | − | 0.0768345i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.75357 | − | 15.1616i | −0.871013 | − | 1.50864i | −0.860950 | − | 0.508690i | \(-0.830130\pi\) |
−0.0100634 | − | 0.999949i | \(-0.503203\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.39775 | + | 4.27110i | 0.728922 | + | 0.420844i | 0.818028 | − | 0.575179i | \(-0.195067\pi\) |
−0.0891054 | + | 0.996022i | \(0.528401\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 10.5019i | − | 1.01525i | −0.861577 | − | 0.507627i | \(-0.830523\pi\) | ||
0.861577 | − | 0.507627i | \(-0.169477\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.2422 | 1.36416 | 0.682078 | − | 0.731279i | \(-0.261076\pi\) | ||||
0.682078 | + | 0.731279i | \(0.261076\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.454785 | − | 1.12811i | −0.0431663 | − | 0.107075i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.3783 | + | 7.72396i | 1.25852 | + | 0.726609i | 0.972788 | − | 0.231699i | \(-0.0744284\pi\) |
0.285737 | + | 0.958308i | \(0.407762\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.00817 | + | 1.73677i | −0.280513 | + | 0.161954i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.82727 | − | 0.948048i | 0.353831 | − | 0.0876471i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.46483 | + | 9.46536i | −0.496803 | + | 0.860488i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −18.5000 | − | 2.61439i | −1.66809 | − | 0.235731i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.65406 | −0.595157 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.8304 | 1.93713 | 0.968566 | − | 0.248758i | \(-0.0800225\pi\) | ||||
0.968566 | + | 0.248758i | \(0.0800225\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.96559 | − | 10.1795i | 0.701331 | − | 0.896253i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.60461 | + | 4.51132i | −0.227566 | + | 0.394156i | −0.957086 | − | 0.289803i | \(-0.906410\pi\) |
0.729520 | + | 0.683959i | \(0.239743\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.94608 | + | 2.13017i | −0.253558 | + | 0.183336i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.33589 | − | 1.34863i | 0.199568 | − | 0.115221i | −0.396886 | − | 0.917868i | \(-0.629909\pi\) |
0.596454 | + | 0.802647i | \(0.296576\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.1448 | + | 5.85710i | 0.860470 | + | 0.496793i | 0.864170 | − | 0.503200i | \(-0.167844\pi\) |
−0.00369951 | + | 0.999993i | \(0.501178\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.47787 | + | 9.55621i | −0.629750 | + | 0.804778i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.348578 | 0.0291495 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 0.220786i | − | 0.0183353i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.3055 | − | 9.41399i | −1.33580 | − | 0.771224i | −0.349618 | − | 0.936892i | \(-0.613689\pi\) |
−0.986182 | + | 0.165668i | \(0.947022\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.00143 | − | 8.66273i | −0.407010 | − | 0.704963i | 0.587543 | − | 0.809193i | \(-0.300095\pi\) |
−0.994553 | + | 0.104230i | \(0.966762\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.05659 | − | 7.75645i | 0.651336 | − | 0.627072i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.39698 | + | 1.96125i | −0.272852 | + | 0.157531i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.218293 | + | 0.126032i | 0.0174217 | + | 0.0100584i | 0.508686 | − | 0.860952i | \(-0.330132\pi\) |
−0.491264 | + | 0.871011i | \(0.663465\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 15.8026 | − | 6.37065i | 1.25323 | − | 0.505225i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.59559 | −0.673259 | −0.336629 | − | 0.941637i | \(-0.609287\pi\) | ||||
−0.336629 | + | 0.941637i | \(0.609287\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.298089 | + | 0.120171i | −0.0232062 | + | 0.00935533i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.24437 | + | 3.88736i | −0.173674 | + | 0.300813i | −0.939702 | − | 0.341995i | \(-0.888897\pi\) |
0.766027 | + | 0.642808i | \(0.222231\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.63629 | − | 9.76234i | −0.433561 | − | 0.750949i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.918858 | + | 0.954413i | 0.0702668 | + | 0.0729858i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.56072 | − | 6.16736i | −0.270717 | − | 0.468895i | 0.698329 | − | 0.715777i | \(-0.253927\pi\) |
−0.969046 | + | 0.246882i | \(0.920594\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 23.0903 | + | 3.26308i | 1.73557 | + | 0.245268i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 25.5500i | 1.90970i | 0.297093 | + | 0.954848i | \(0.403983\pi\) | ||||
−0.297093 | + | 0.954848i | \(0.596017\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 0.943175i | − | 0.0701057i | −0.999385 | − | 0.0350528i | \(-0.988840\pi\) | ||
0.999385 | − | 0.0350528i | \(-0.0111599\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.70977 | − | 6.03301i | −0.569923 | − | 0.445973i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.245666 | + | 0.425506i | −0.0180617 | + | 0.0312838i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.856227 | − | 0.494343i | 0.0626135 | − | 0.0361499i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.57413 | − | 1.48617i | 0.186258 | − | 0.107536i | −0.403972 | − | 0.914771i | \(-0.632371\pi\) |
0.590229 | + | 0.807236i | \(0.299037\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.25721 | − | 16.0340i | 0.666348 | − | 1.15415i | −0.312570 | − | 0.949895i | \(-0.601190\pi\) |
0.978918 | − | 0.204254i | \(-0.0654769\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.25434 | − | 0.981542i | −0.0898255 | − | 0.0702897i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.1774i | 1.01010i | 0.863091 | + | 0.505048i | \(0.168525\pi\) | ||||
−0.863091 | + | 0.505048i | \(0.831475\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.7052i | 1.68042i | 0.542262 | + | 0.840209i | \(0.317568\pi\) | ||||
−0.542262 | + | 0.840209i | \(0.682432\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.1892 | − | 1.43992i | −0.718692 | − | 0.101564i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.77362 | + | 6.53611i | 0.263561 | + | 0.456502i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −14.4570 | + | 3.58112i | −1.00483 | + | 0.248905i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.0585617 | + | 0.101432i | 0.00405080 | + | 0.00701619i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.04004 | − | 5.26550i | 0.209285 | − | 0.362492i | −0.742205 | − | 0.670173i | \(-0.766220\pi\) |
0.951489 | + | 0.307681i | \(0.0995531\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 21.5780 | − | 8.69893i | 1.47850 | − | 0.596041i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.22127 | −0.356088 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.3573 | − | 4.98170i | 0.835027 | − | 0.336632i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.24313 | + | 2.44977i | 0.285424 | + | 0.164790i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.796137 | + | 0.459650i | −0.0533133 | + | 0.0307804i | −0.526420 | − | 0.850225i | \(-0.676466\pi\) |
0.473106 | + | 0.881005i | \(0.343133\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.0016 | − | 3.74960i | −0.866771 | − | 0.249973i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.00297 | − | 8.66540i | −0.332059 | − | 0.575143i | 0.650857 | − | 0.759201i | \(-0.274410\pi\) |
−0.982915 | + | 0.184058i | \(0.941077\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.38179 | − | 1.37513i | −0.157393 | − | 0.0908710i | 0.419235 | − | 0.907878i | \(-0.362298\pi\) |
−0.576628 | + | 0.817007i | \(0.695632\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.41451i | 0.420228i | 0.977677 | + | 0.210114i | \(0.0673836\pi\) | ||||
−0.977677 | + | 0.210114i | \(0.932616\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.90158 | 0.319744 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.49085 | + | 1.90521i | −0.0968414 | + | 0.123757i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.4288 | − | 6.59844i | −0.739270 | − | 0.426818i | 0.0825337 | − | 0.996588i | \(-0.473699\pi\) |
−0.821804 | + | 0.569770i | \(0.807032\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.20722 | + | 1.27434i | −0.142180 | + | 0.0820874i | −0.569402 | − | 0.822059i | \(-0.692825\pi\) |
0.427223 | + | 0.904146i | \(0.359492\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.6686 | + | 5.27569i | −0.940990 | + | 0.338436i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.290209 | + | 0.502657i | −0.0184656 | + | 0.0319833i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.94995 | − | 10.1595i | 0.503808 | − | 0.643832i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.7893 | −1.18597 | −0.592986 | − | 0.805213i | \(-0.702051\pi\) | ||||
−0.592986 | + | 0.805213i | \(0.702051\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.31670 | −0.0827804 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.47310 | − | 0.632131i | −0.280116 | − | 0.0395856i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.19727 | + | 12.4660i | −0.448953 | + | 0.777610i | −0.998318 | − | 0.0579725i | \(-0.981536\pi\) |
0.549365 | + | 0.835583i | \(0.314870\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.262331 | − | 0.909620i | 0.0162379 | − | 0.0563041i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.79810 | + | 3.92488i | −0.419189 | + | 0.242019i | −0.694730 | − | 0.719271i | \(-0.744476\pi\) |
0.275542 | + | 0.961289i | \(0.411143\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.96050 | − | 3.44130i | −0.366151 | − | 0.211397i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.24369 | − | 17.9682i | −0.443307 | − | 1.09964i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.4453 | −0.941719 | −0.470859 | − | 0.882208i | \(-0.656056\pi\) | ||||
−0.470859 | + | 0.882208i | \(0.656056\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.6411i | 0.767895i | 0.923355 | + | 0.383947i | \(0.125436\pi\) | ||||
−0.923355 | + | 0.383947i | \(0.874564\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.03599 | − | 0.598128i | −0.0624724 | − | 0.0360685i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.94531 | + | 10.2976i | 0.357219 | + | 0.618722i | 0.987495 | − | 0.157649i | \(-0.0503915\pi\) |
−0.630276 | + | 0.776371i | \(0.717058\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −16.3255 | + | 4.04399i | −0.977385 | + | 0.242107i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.75411 | + | 1.59009i | −0.164297 | + | 0.0948568i | −0.579894 | − | 0.814692i | \(-0.696906\pi\) |
0.415597 | + | 0.909549i | \(0.363573\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.0195 | + | 9.24889i | 0.952263 | + | 0.549789i | 0.893783 | − | 0.448499i | \(-0.148041\pi\) |
0.0584799 | + | 0.998289i | \(0.481375\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.0748846 | − | 0.529900i | 0.00443578 | − | 0.0313886i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.10322 | −0.182542 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.4628 | − | 11.3173i | −0.847824 | − | 0.663435i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.42975 | − | 2.47639i | 0.0835266 | − | 0.144672i | −0.821236 | − | 0.570589i | \(-0.806715\pi\) |
0.904762 | + | 0.425917i | \(0.140048\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.70995 | − | 8.15788i | −0.274224 | − | 0.474970i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.37088 | + | 0.140916i | −0.0795467 | + | 0.00817679i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.26254 | − | 5.65088i | −0.188677 | − | 0.326799i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −18.6871 | + | 23.8808i | −1.07354 | + | 1.37192i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.95451i | 0.226434i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.6746i | 1.23704i | 0.785771 | + | 0.618518i | \(0.212266\pi\) | ||||
−0.785771 | + | 0.618518i | \(0.787734\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.07031 | − | 14.6499i | 0.117776 | − | 0.833406i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.8462 | + | 20.5183i | −0.671738 | + | 1.16348i | 0.305673 | + | 0.952136i | \(0.401119\pi\) |
−0.977411 | + | 0.211348i | \(0.932215\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.6283 | + | 13.6418i | −1.33555 | + | 0.771081i | −0.986144 | − | 0.165890i | \(-0.946950\pi\) |
−0.349407 | + | 0.936971i | \(0.613617\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.2647 | − | 12.2772i | 1.19435 | − | 0.689556i | 0.235057 | − | 0.971982i | \(-0.424472\pi\) |
0.959289 | + | 0.282426i | \(0.0911391\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.0418465 | − | 0.0724802i | 0.00234295 | − | 0.00405811i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.8705 | + | 6.80115i | −0.941617 | + | 0.379603i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.64626i | 0.0916006i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 5.92818i | − | 0.328836i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.22344 | − | 22.8790i | −0.510057 | − | 1.26521i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.15579 | − | 14.1262i | −0.448283 | − | 0.776449i | 0.549991 | − | 0.835170i | \(-0.314631\pi\) |
−0.998274 | + | 0.0587215i | \(0.981298\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.51769 | + | 1.46115i | −0.0831691 | + | 0.0800708i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.07840 | + | 3.59989i | 0.113555 | + | 0.196683i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.6580 | − | 23.6563i | 0.743998 | − | 1.28864i | −0.206663 | − | 0.978412i | \(-0.566261\pi\) |
0.950661 | − | 0.310230i | \(-0.100406\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.74400 | − | 26.4934i | 0.203346 | − | 1.43892i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.48689 | −0.0805196 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.73811 | + | 3.70764i | 0.255091 | + | 0.199612i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.37986 | + | 3.10606i | 0.288806 | + | 0.166742i | 0.637403 | − | 0.770530i | \(-0.280009\pi\) |
−0.348597 | + | 0.937273i | \(0.613342\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.6529 | + | 14.2334i | −1.31964 | + | 0.761896i | −0.983671 | − | 0.179977i | \(-0.942398\pi\) |
−0.335971 | + | 0.941872i | \(0.609064\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.00155 | − | 5.53424i | −0.213587 | − | 0.295396i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.49346 | − | 2.58674i | −0.0794887 | − | 0.137678i | 0.823541 | − | 0.567257i | \(-0.191995\pi\) |
−0.903029 | + | 0.429579i | \(0.858662\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.13889 | − | 4.69899i | −0.431968 | − | 0.249397i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 30.7123i | 1.62094i | 0.585784 | + | 0.810468i | \(0.300787\pi\) | ||||
−0.585784 | + | 0.810468i | \(0.699213\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.8050 | 0.989736 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 18.7445 | + | 2.64894i | 0.983830 | + | 0.139033i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.66098 | − | 2.69102i | −0.243967 | − | 0.140854i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.4877 | − | 9.51918i | 0.860651 | − | 0.496897i | −0.00357920 | − | 0.999994i | \(-0.501139\pi\) |
0.864230 | + | 0.503096i | \(0.167806\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.78101 | + | 31.4119i | 0.405063 | + | 1.63524i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.05869 | + | 3.56576i | −0.106595 | + | 0.184628i | −0.914389 | − | 0.404837i | \(-0.867328\pi\) |
0.807794 | + | 0.589465i | \(0.200661\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.30926 | + | 10.6892i | 0.222529 | + | 0.551990i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.414750 | 0.0213607 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.2436 | −0.577546 | −0.288773 | − | 0.957398i | \(-0.593247\pi\) | ||||
−0.288773 | + | 0.957398i | \(0.593247\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.1376 | − | 35.0688i | −0.724293 | − | 1.79663i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.8046 | + | 27.3745i | −0.807580 | + | 1.39877i | 0.106956 | + | 0.994264i | \(0.465890\pi\) |
−0.914536 | + | 0.404505i | \(0.867444\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −21.5112 | − | 6.20374i | −1.09347 | − | 0.315354i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.4018 | + | 10.6243i | −0.933007 | + | 0.538672i | −0.887761 | − | 0.460304i | \(-0.847740\pi\) |
−0.0452458 | + | 0.998976i | \(0.514407\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.0278 | − | 9.25367i | −0.810562 | − | 0.467978i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.93387 | + | 1.26252i | 0.450654 | + | 0.0636857i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.977223 | 0.0491694 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.8939i | 1.19920i | 0.800300 | + | 0.599599i | \(0.204673\pi\) | ||||
−0.800300 | + | 0.599599i | \(0.795327\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.0121 | − | 12.7087i | −1.09923 | − | 0.634642i | −0.163213 | − | 0.986591i | \(-0.552186\pi\) |
−0.936019 | + | 0.351948i | \(0.885519\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.68423 | − | 6.38127i | −0.183524 | − | 0.317874i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.32987 | + | 3.35312i | 0.264844 | + | 0.166618i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.161295 | + | 0.0931240i | −0.00799512 | + | 0.00461598i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.3831 | + | 11.1908i | 0.958433 | + | 0.553351i | 0.895690 | − | 0.444678i | \(-0.146682\pi\) |
0.0627424 | + | 0.998030i | \(0.480015\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.67922 | − | 2.87904i | −0.181482 | − | 0.142013i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.21102 | −0.255799 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.83908 | − | 20.0900i | 0.139030 | − | 0.983810i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.04181 | + | 12.1968i | −0.344015 | + | 0.595851i | −0.985174 | − | 0.171556i | \(-0.945120\pi\) |
0.641159 | + | 0.767408i | \(0.278454\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.07639 | + | 13.9887i | 0.393619 | + | 0.681768i | 0.992924 | − | 0.118753i | \(-0.0378896\pi\) |
−0.599305 | + | 0.800521i | \(0.704556\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 20.1941 | + | 5.82390i | 0.981870 | + | 0.283168i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.40717 | − | 14.5617i | −0.407808 | − | 0.706344i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.225744 | − | 0.559964i | −0.0108990 | − | 0.0270353i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 8.26972i | − | 0.398338i | −0.979965 | − | 0.199169i | \(-0.936176\pi\) | ||
0.979965 | − | 0.199169i | \(-0.0638243\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 4.35102i | − | 0.209097i | −0.994520 | − | 0.104548i | \(-0.966660\pi\) | ||
0.994520 | − | 0.104548i | \(-0.0333397\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.354676 | + | 0.142984i | −0.0170054 | + | 0.00685556i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.09622 | − | 1.89872i | 0.0524395 | − | 0.0908279i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.0200 | − | 10.4039i | 0.860048 | − | 0.496549i | −0.00398054 | − | 0.999992i | \(-0.501267\pi\) |
0.864028 | + | 0.503443i | \(0.167934\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.7927 | − | 15.4688i | 1.27296 | − | 0.734945i | 0.297417 | − | 0.954748i | \(-0.403875\pi\) |
0.975544 | + | 0.219803i | \(0.0705414\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.91290 | + | 6.77734i | −0.185489 | + | 0.321277i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.56320 | + | 32.2902i | −0.215832 | + | 1.52727i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 20.9215i | − | 0.987346i | −0.869648 | − | 0.493673i | \(-0.835654\pi\) | ||
0.869648 | − | 0.493673i | \(-0.164346\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.86092i | 0.134715i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.6770 | + | 13.6445i | −0.501650 | + | 0.641075i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.15058 | − | 1.99286i | −0.0538217 | − | 0.0932218i | 0.837859 | − | 0.545886i | \(-0.183807\pi\) |
−0.891681 | + | 0.452664i | \(0.850474\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −17.6777 | − | 7.91911i | −0.825124 | − | 0.369633i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.92497 | − | 15.4585i | −0.415677 | − | 0.719974i | 0.579822 | − | 0.814743i | \(-0.303122\pi\) |
−0.995499 | + | 0.0947688i | \(0.969789\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.24034 | + | 10.8086i | −0.290013 | + | 0.502318i | −0.973813 | − | 0.227353i | \(-0.926993\pi\) |
0.683799 | + | 0.729670i | \(0.260326\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.35052 | + | 4.18686i | 0.248124 | + | 0.194161i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.85599 | −0.224708 | −0.112354 | − | 0.993668i | \(-0.535839\pi\) | ||||
−0.112354 | + | 0.993668i | \(0.535839\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.0610907 | − | 0.432291i | 0.00281491 | − | 0.0199189i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.71405 | − | 0.989607i | −0.0788121 | − | 0.0455022i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.72503 | − | 0.995945i | 0.0791497 | − | 0.0456971i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −20.4679 | − | 21.2599i | −0.937161 | − | 0.973425i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.40542 | − | 7.63041i | −0.201289 | − | 0.348642i | 0.747655 | − | 0.664087i | \(-0.231180\pi\) |
−0.948944 | + | 0.315445i | \(0.897846\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.799318 | − | 0.461486i | −0.0364458 | − | 0.0210420i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.41827i | 0.336847i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.32370 | −0.422497 | −0.211249 | − | 0.977432i | \(-0.567753\pi\) | ||||
−0.211249 | + | 0.977432i | \(0.567753\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.56662 | + | 13.8082i | 0.251731 | + | 0.624427i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.9192 | − | 15.5418i | −1.21485 | − | 0.701391i | −0.251034 | − | 0.967978i | \(-0.580771\pi\) |
−0.963811 | + | 0.266587i | \(0.914104\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.01877 | − | 0.588186i | 0.0458830 | − | 0.0264906i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.386092 | + | 0.401032i | 0.0173536 | + | 0.0180251i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.1694 | − | 19.3459i | 0.500010 | − | 0.866043i | −0.499990 | − | 0.866031i | \(-0.666663\pi\) |
1.00000 | 1.16519e-5i | \(-3.70891e-6\pi\) | ||||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.69823 | + | 1.08790i | 0.343932 | + | 0.0486039i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.2396 | 0.545738 | 0.272869 | − | 0.962051i | \(-0.412027\pi\) | ||||
0.272869 | + | 0.962051i | \(0.412027\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.2490 | 0.545072 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.0323 | + | 15.3765i | −0.534374 | + | 0.682894i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.05496 | − | 12.2195i | 0.312706 | − | 0.541622i | −0.666242 | − | 0.745736i | \(-0.732098\pi\) |
0.978947 | + | 0.204114i | \(0.0654314\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.938128 | − | 2.09417i | 0.0414193 | − | 0.0924597i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.17588 | + | 2.98830i | −0.228077 | + | 0.131680i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.60910 | + | 0.929015i | 0.0707682 | + | 0.0408580i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.60141 | + | 9.71409i | −0.333665 | + | 0.426401i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.63263 | 0.246770 | 0.123385 | − | 0.992359i | \(-0.460625\pi\) | ||||
0.123385 | + | 0.992359i | \(0.460625\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 38.3699i | − | 1.67780i | −0.544288 | − | 0.838899i | \(-0.683200\pi\) | ||
0.544288 | − | 0.838899i | \(-0.316800\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18.0995 | − | 10.4497i | −0.788425 | − | 0.455197i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.823769 | + | 1.42681i | 0.0358161 | + | 0.0620352i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.71167 | − | 39.2060i | −0.421451 | − | 1.70139i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.2782 | + | 7.08880i | −0.531826 | + | 0.307050i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.36329 | + | 3.67385i | 0.275109 | + | 0.158834i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 41.0441 | − | 16.5465i | 1.77118 | − | 0.714035i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.43346 | 0.276596 | 0.138298 | − | 0.990391i | \(-0.455837\pi\) | ||||
0.138298 | + | 0.990391i | \(0.455837\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.51514 | + | 0.610813i | −0.0650208 | + | 0.0262125i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.98232 | + | 8.62963i | −0.213419 | + | 0.369653i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.52889 | − | 11.3084i | −0.279155 | − | 0.483511i | 0.692020 | − | 0.721878i | \(-0.256721\pi\) |
−0.971175 | + | 0.238368i | \(0.923388\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.69862 | + | 16.2922i | −0.200532 | + | 0.695335i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.0696787 | + | 0.120687i | 0.00296841 | + | 0.00514144i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.842639 | + | 0.119080i | 0.0357680 | + | 0.00505468i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 29.4920i | − | 1.24962i | −0.780778 | − | 0.624809i | \(-0.785177\pi\) | ||
0.780778 | − | 0.624809i | \(-0.214823\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 9.80822i | − | 0.414844i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.34863 | − | 1.05532i | −0.0569391 | − | 0.0445557i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.25934 | + | 9.10944i | −0.221655 | + | 0.383917i | −0.955311 | − | 0.295604i | \(-0.904479\pi\) |
0.733656 | + | 0.679521i | \(0.237812\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.36020 | + | 5.40411i | −0.393787 | + | 0.227353i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22.8054 | − | 13.1667i | 0.956053 | − | 0.551977i | 0.0610967 | − | 0.998132i | \(-0.480540\pi\) |
0.894956 | + | 0.446155i | \(0.147207\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.0295 | − | 38.1562i | 0.921906 | − | 1.59679i | 0.125444 | − | 0.992101i | \(-0.459965\pi\) |
0.796463 | − | 0.604688i | \(-0.206702\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.05447 | − | 3.17268i | −0.169378 | − | 0.132540i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 22.3929i | 0.933847i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 14.0337i | − | 0.584229i | −0.956383 | − | 0.292115i | \(-0.905641\pi\) | ||
0.956383 | − | 0.292115i | \(-0.0943589\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −31.7524 | − | 4.48720i | −1.31959 | − | 0.186482i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.30448 | − | 2.25943i | −0.0540262 | − | 0.0935762i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.764443 | + | 2.65067i | −0.0316058 | + | 0.109592i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.52469 | − | 2.64085i | −0.0629308 | − | 0.108999i | 0.832843 | − | 0.553509i | \(-0.186711\pi\) |
−0.895774 | + | 0.444509i | \(0.853378\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.23791 | − | 2.14413i | 0.0510073 | − | 0.0883473i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 22.7749 | − | 9.18146i | 0.936834 | − | 0.377675i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26.6082 | 1.09267 | 0.546334 | − | 0.837568i | \(-0.316023\pi\) | ||||
0.546334 | + | 0.837568i | \(0.316023\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 38.0806 | − | 15.3518i | 1.55854 | − | 0.628308i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.86333 | + | 2.23050i | 0.157852 | + | 0.0911356i | 0.576845 | − | 0.816854i | \(-0.304284\pi\) |
−0.418993 | + | 0.907989i | \(0.637617\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.25019 | + | 3.03120i | −0.214160 | + | 0.123645i | −0.603243 | − | 0.797557i | \(-0.706125\pi\) |
0.389083 | + | 0.921203i | \(0.372792\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.28554 | + | 17.3007i | 0.174521 | + | 0.704539i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.82350 | − | 6.62250i | −0.155447 | − | 0.269243i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 39.2581 | + | 22.6657i | 1.59344 | + | 0.919971i | 0.992711 | + | 0.120516i | \(0.0384548\pi\) |
0.600725 | + | 0.799455i | \(0.294879\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.20768i | 0.372503i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −33.2588 | −1.34331 | −0.671654 | − | 0.740865i | \(-0.734416\pi\) | ||||
−0.671654 | + | 0.740865i | \(0.734416\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.05591 | − | 10.2949i | 0.324846 | − | 0.415131i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.3001 | + | 18.0711i | 1.26010 | + | 0.727516i | 0.973093 | − | 0.230414i | \(-0.0740079\pi\) |
0.287002 | + | 0.957930i | \(0.407341\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.9031 | + | 13.2231i | −0.920554 | + | 0.531482i | −0.883812 | − | 0.467843i | \(-0.845031\pi\) |
−0.0367423 | + | 0.999325i | \(0.511698\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.1153 | + | 20.9048i | 0.606556 | + | 0.838881i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.94843 | + | 15.4991i | −0.357937 | + | 0.619965i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.125017 | − | 0.159764i | 0.00499271 | − | 0.00638034i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.61787 | −0.104381 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.0484 | −1.27583 | −0.637914 | − | 0.770107i | \(-0.720203\pi\) | ||||
−0.637914 | + | 0.770107i | \(0.720203\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.4274 | − | 1.47358i | −0.414451 | − | 0.0585696i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.63687 | + | 13.2274i | −0.303060 | + | 0.524915i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −27.9483 | − | 29.0298i | −1.10562 | − | 1.14840i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.1444 | − | 12.2077i | 0.835153 | − | 0.482176i | −0.0204610 | − | 0.999791i | \(-0.506513\pi\) |
0.855614 | + | 0.517615i | \(0.173180\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.9014 | + | 18.4183i | 1.25807 | + | 0.726346i | 0.972699 | − | 0.232071i | \(-0.0745503\pi\) |
0.285370 | + | 0.958418i | \(0.407884\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.38136 | + | 8.38757i | 0.133141 | + | 0.330260i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.5694 | 1.04455 | 0.522276 | − | 0.852777i | \(-0.325083\pi\) | ||||
0.522276 | + | 0.852777i | \(0.325083\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 3.57078i | − | 0.140165i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −26.2767 | − | 15.1709i | −1.02829 | − | 0.593683i | −0.111794 | − | 0.993731i | \(-0.535660\pi\) |
−0.916494 | + | 0.400049i | \(0.868993\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.82233 | − | 3.15637i | −0.0712044 | − | 0.123330i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −16.0055 | − | 16.6248i | −0.624432 | − | 0.648595i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 40.9873 | − | 23.6640i | 1.59664 | − | 0.921820i | 0.604511 | − | 0.796597i | \(-0.293369\pi\) |
0.992129 | − | 0.125223i | \(-0.0399647\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.4187 | − | 17.5623i | −1.18315 | − | 0.683092i | −0.226409 | − | 0.974032i | \(-0.572699\pi\) |
−0.956741 | + | 0.290940i | \(0.906032\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.18747 | − | 8.40277i | 0.0461174 | − | 0.326337i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.56666 | −0.0606613 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.25398 | + | 0.981258i | 0.0484817 | + | 0.0379376i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.749513 | + | 1.29819i | −0.0289346 | + | 0.0501162i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.54758 | − | 4.41254i | −0.0982020 | − | 0.170091i | 0.812738 | − | 0.582629i | \(-0.197976\pi\) |
−0.910940 | + | 0.412538i | \(0.864642\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.39653 | + | 23.3143i | 0.0922425 | + | 0.897368i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.42072 | − | 14.5851i | −0.323635 | − | 0.560551i | 0.657601 | − | 0.753367i | \(-0.271571\pi\) |
−0.981235 | + | 0.192815i | \(0.938238\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.6803 | + | 13.6487i | −0.409271 | + | 0.523020i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.1929i | 0.696132i | 0.937470 | + | 0.348066i | \(0.113162\pi\) | ||||
−0.937470 | + | 0.348066i | \(0.886838\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.88715i | 0.0721042i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.666559 | + | 4.71672i | −0.0254308 | + | 0.179954i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.46452 | − | 11.1969i | 0.246279 | − | 0.426567i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.05405 | − | 1.76326i | 0.116182 | − | 0.0670775i | −0.440783 | − | 0.897614i | \(-0.645299\pi\) |
0.556965 | + | 0.830536i | \(0.311966\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.09786 | + | 4.09795i | −0.269237 | + | 0.155444i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.1063 | + | 34.8251i | −0.761579 | + | 1.31909i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.3044 | − | 4.15412i | 0.389749 | − | 0.157123i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.3502i | 0.504229i | 0.967697 | + | 0.252114i | \(0.0811259\pi\) | ||||
−0.967697 | + | 0.252114i | \(0.918874\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 0.310122i | − | 0.0116965i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.17433 | − | 7.87401i | −0.119552 | − | 0.296552i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.1447 | + | 36.6237i | 0.794107 | + | 1.37543i | 0.923405 | + | 0.383827i | \(0.125394\pi\) |
−0.129298 | + | 0.991606i | \(0.541273\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.02607 | + | 1.16110i | 0.150990 | + | 0.0435448i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.9166 | + | 24.1043i | 0.521182 | + | 0.902715i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.121942 | + | 0.211210i | −0.00456038 | + | 0.00789881i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.19843 | + | 22.6328i | −0.119448 | + | 0.845237i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 30.4069 | 1.13399 | 0.566994 | − | 0.823722i | \(-0.308106\pi\) | ||||
0.566994 | + | 0.823722i | \(0.308106\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.47655 | + | 2.72045i | 0.129294 | + | 0.101175i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.23265 | − | 0.711673i | −0.0457796 | − | 0.0264309i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.3671 | − | 6.56280i | 0.421583 | − | 0.243401i | −0.274171 | − | 0.961681i | \(-0.588404\pi\) |
0.695754 | + | 0.718280i | \(0.255070\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17.9746 | + | 20.1473i | 0.665724 | + | 0.746198i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.9097 | − | 24.0924i | −0.514470 | − | 0.891089i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32.7001 | − | 18.8794i | −1.20781 | − | 0.697327i | −0.245527 | − | 0.969390i | \(-0.578961\pi\) |
−0.962280 | + | 0.272063i | \(0.912294\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.57571i | 0.0580419i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.2430 | 0.965366 | 0.482683 | − | 0.875795i | \(-0.339662\pi\) | ||||
0.482683 | + | 0.875795i | \(0.339662\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.995424 | + | 0.140672i | 0.0365678 | + | 0.00516770i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.78379 | − | 5.07132i | −0.322246 | − | 0.186049i | 0.330147 | − | 0.943929i | \(-0.392902\pi\) |
−0.652393 | + | 0.757881i | \(0.726235\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.4082 | − | 6.58655i | 0.417966 | − | 0.241313i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −21.4690 | − | 6.19157i | −0.785508 | − | 0.226538i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.95369 | + | 6.84798i | −0.144272 | + | 0.249886i | −0.929101 | − | 0.369826i | \(-0.879417\pi\) |
0.784829 | + | 0.619712i | \(0.212751\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.1682 | + | 30.1836i | 0.443435 | + | 1.09995i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.99855 | 0.254703 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.8903 | 1.08638 | 0.543191 | − | 0.839609i | \(-0.317216\pi\) | ||||
0.543191 | + | 0.839609i | \(0.317216\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.852714 | + | 2.11518i | 0.0309516 | + | 0.0767763i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.05687 | − | 5.29465i | 0.110811 | − | 0.191931i | −0.805286 | − | 0.592886i | \(-0.797988\pi\) |
0.916098 | + | 0.400955i | \(0.131322\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.88137 | + | 7.59506i | 0.0680209 | + | 0.274600i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.3247 | − | 8.84771i | 0.553342 | − | 0.319472i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.79863 | + | 5.65724i | 0.353348 | + | 0.204005i | 0.666159 | − | 0.745810i | \(-0.267937\pi\) |
−0.312811 | + | 0.949815i | \(0.601271\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.6868 | + | 3.48870i | 0.889073 | + | 0.125642i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 38.4211 | 1.38191 | 0.690956 | − | 0.722896i | \(-0.257190\pi\) | ||||
0.690956 | + | 0.722896i | \(0.257190\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 25.2872i | 0.908343i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.12551 | − | 2.38186i | −0.147812 | − | 0.0853391i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.78124 | − | 3.08519i | −0.0637376 | − | 0.110397i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.63112 | + | 0.167667i | −0.0582916 | + | 0.00599193i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.152730 | + | 0.0881788i | −0.00545117 | + | 0.00314723i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −41.2747 | − | 23.8300i | −1.47129 | − | 0.849447i | −0.471806 | − | 0.881703i | \(-0.656398\pi\) |
−0.999480 | + | 0.0322557i | \(0.989731\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.7076 | + | 8.37882i | 0.381199 | + | 0.298294i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.42859 | −0.263797 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.66808 | + | 11.8037i | −0.0591608 | + | 0.418635i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.1359 | − | 26.2161i | 0.536139 | − | 0.928621i | −0.462968 | − | 0.886375i | \(-0.653215\pi\) |
0.999107 | − | 0.0422457i | \(-0.0134512\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.0581 | + | 22.6172i | 0.461961 | + | 0.800140i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −24.1734 | + | 23.2729i | −0.854126 | + | 0.822307i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.02008 | − | 1.76683i | −0.0359978 | − | 0.0623500i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.0026 | + | 24.8117i | 0.352108 | + | 0.873415i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.253310i | 0.00890590i | 0.999990 | + | 0.00445295i | \(0.00141742\pi\) | ||||
−0.999990 | + | 0.00445295i | \(0.998583\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 22.0629i | − | 0.774735i | −0.921925 | − | 0.387367i | \(-0.873385\pi\) | ||
0.921925 | − | 0.387367i | \(-0.126615\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20.3070 | − | 8.18657i | 0.712199 | − | 0.287116i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.00698 | − | 5.20824i | 0.105330 | − | 0.182437i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.85407 | − | 1.64780i | 0.0998514 | − | 0.0576492i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.2467 | + | 13.9988i | −0.846214 | + | 0.488562i | −0.859372 | − | 0.511352i | \(-0.829145\pi\) |
0.0131576 | + | 0.999913i | \(0.495812\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.4771 | + | 42.3955i | −0.853217 | + | 1.47782i | 0.0250719 | + | 0.999686i | \(0.492019\pi\) |
−0.878289 | + | 0.478130i | \(0.841315\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.289928 | + | 2.05159i | −0.0100940 | + | 0.0714272i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 0.641658i | − | 0.0223126i | −0.999938 | − | 0.0111563i | \(-0.996449\pi\) | ||
0.999938 | − | 0.0111563i | \(-0.00355124\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 11.0526i | − | 0.383871i | −0.981408 | − | 0.191936i | \(-0.938523\pi\) | ||
0.981408 | − | 0.191936i | \(-0.0614765\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.6920 | − | 16.2195i | 0.440281 | − | 0.562650i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.57029 | − | 2.71981i | −0.0543420 | − | 0.0941230i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 17.0690 | + | 23.6068i | 0.589991 | + | 0.815971i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.62330 | + | 8.00780i | 0.159614 | + | 0.276460i | 0.934730 | − | 0.355360i | \(-0.115642\pi\) |
−0.775115 | + | 0.631820i | \(0.782308\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.4502 | + | 25.0285i | −0.498283 | + | 0.863052i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.33796 | + | 3.39451i | 0.149407 | + | 0.116913i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.88693 | 0.271319 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.48317 | − | 31.7239i | 0.153862 | − | 1.08876i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.01931 | + | 1.74320i | 0.103501 | + | 0.0597561i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34.3256 | − | 19.8179i | 1.17529 | − | 0.678551i | 0.220366 | − | 0.975417i | \(-0.429275\pi\) |
0.954919 | + | 0.296866i | \(0.0959414\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.899740 | + | 0.222874i | −0.0307705 | + | 0.00762212i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.9260 | + | 20.6565i | 0.407385 | + | 0.705612i | 0.994596 | − | 0.103822i | \(-0.0331074\pi\) |
−0.587211 | + | 0.809434i | \(0.699774\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.62480 | − | 5.55688i | −0.328394 | − | 0.189598i | 0.326734 | − | 0.945116i | \(-0.394052\pi\) |
−0.655128 | + | 0.755518i | \(0.727385\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 44.7770i | 1.52423i | 0.647444 | + | 0.762113i | \(0.275838\pi\) | ||||
−0.647444 | + | 0.762113i | \(0.724162\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.98256 | 0.169412 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.00968 | + | 4.98508i | 0.0682525 | + | 0.169302i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.320805 | + | 0.185217i | 0.0108826 | + | 0.00628305i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.76244 | + | 3.90429i | −0.229136 | + | 0.132292i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.81415 | + | 30.5626i | −0.298314 | + | 1.03439i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.84096 | + | 3.18863i | −0.0621647 | + | 0.107672i | −0.895433 | − | 0.445197i | \(-0.853134\pi\) |
0.833268 | + | 0.552869i | \(0.186467\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.90406 | − | 0.693033i | −0.165410 | − | 0.0233754i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −17.3992 | −0.586194 | −0.293097 | − | 0.956083i | \(-0.594686\pi\) | ||||
−0.293097 | + | 0.956083i | \(0.594686\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.02834 | −0.0682592 | −0.0341296 | − | 0.999417i | \(-0.510866\pi\) | ||||
−0.0341296 | + | 0.999417i | \(0.510866\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.0548 | + | 12.8493i | −0.337988 | + | 0.431925i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23.1890 | + | 40.1645i | −0.778610 | + | 1.34859i | 0.154132 | + | 0.988050i | \(0.450742\pi\) |
−0.932743 | + | 0.360542i | \(0.882592\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.11417 | + | 2.11096i | 0.0373262 | + | 0.0707199i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.67932 | + | 1.54691i | −0.0896601 | + | 0.0517653i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.4812 | − | 8.93810i | −0.517481 | − | 0.298768i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.96484 | + | 8.90060i | −0.232549 | + | 0.297182i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.76915 | −0.0590046 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 36.6712i | − | 1.22169i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.571488 | + | 0.329949i | 0.0189969 | + | 0.0109679i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.01957 | − | 13.8903i | −0.266285 | − | 0.461220i | 0.701614 | − | 0.712557i | \(-0.252463\pi\) |
−0.967900 | + | 0.251337i | \(0.919130\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 50.4647 | + | 14.5538i | 1.67381 | + | 0.482720i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.7833 | − | 10.2672i | 0.589187 | − | 0.340167i | −0.175589 | − | 0.984464i | \(-0.556183\pi\) |
0.764776 | + | 0.644296i | \(0.222850\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.71069 | − | 0.987665i | −0.0566154 | − | 0.0326869i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.35261 | − | 2.56099i | 0.210011 | − | 0.0846637i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.4138 | 1.16819 | 0.584097 | − | 0.811684i | \(-0.301449\pi\) | ||||
0.584097 | + | 0.811684i | \(0.301449\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 34.8186 | − | 14.0368i | 1.14731 | − | 0.462527i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.82712 | − | 15.2890i | 0.290548 | − | 0.503244i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.58374 | + | 2.74311i | 0.0520730 | + | 0.0901930i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −24.8748 | + | 6.16171i | −0.816995 | + | 0.202377i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.8626 | − | 34.4030i | −0.651670 | − | 1.12873i | −0.982718 | − | 0.185111i | \(-0.940735\pi\) |
0.331048 | − | 0.943614i | \(-0.392598\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 40.6328 | + | 5.74216i | 1.33026 | + | 0.187990i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.691740i | 0.0226223i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 23.2142i | − | 0.758376i | −0.925320 | − | 0.379188i | \(-0.876203\pi\) | ||
0.925320 | − | 0.379188i | \(-0.123797\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 37.2165 | + | 29.1225i | 1.21452 | + | 0.950376i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.9616 | + | 31.1104i | −0.585531 | + | 1.01417i | 0.409278 | + | 0.912410i | \(0.365781\pi\) |
−0.994809 | + | 0.101760i | \(0.967553\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 46.3790 | − | 26.7769i | 1.51031 | − | 0.871977i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.7365 | − | 15.4363i | 0.868818 | − | 0.501612i | 0.00186277 | − | 0.999998i | \(-0.499407\pi\) |
0.866955 | + | 0.498386i | \(0.166074\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.05511 | − | 8.75571i | 0.164096 | − | 0.284222i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −33.4937 | − | 26.2093i | −1.08611 | − | 0.849894i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 30.4640i | − | 0.986826i | −0.869795 | − | 0.493413i | \(-0.835749\pi\) | ||
0.869795 | − | 0.493413i | \(-0.164251\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.07962i | 0.0672950i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.143534 | − | 0.0202840i | −0.00463980 | − | 0.000655689i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.215406 | + | 0.373095i | 0.00694859 | + | 0.0120353i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 21.8511 | + | 22.6966i | 0.704140 | + | 0.731387i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.47686 | + | 11.2182i | 0.208497 | + | 0.361128i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.75865 | + | 11.7063i | −0.217343 | + | 0.376450i | −0.953995 | − | 0.299823i | \(-0.903072\pi\) |
0.736652 | + | 0.676272i | \(0.236406\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.64460 | − | 1.06614i | 0.0849568 | − | 0.0342494i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33.2855 | 1.06818 | 0.534092 | − | 0.845427i | \(-0.320654\pi\) | ||||
0.534092 | + | 0.845427i | \(0.320654\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9.52317 | + | 3.83917i | −0.304986 | + | 0.122952i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −38.9127 | − | 22.4662i | −1.24493 | − | 0.718758i | −0.274833 | − | 0.961492i | \(-0.588623\pi\) |
−0.970093 | + | 0.242734i | \(0.921956\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.56907 | + | 1.48325i | −0.0821079 | + | 0.0474050i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −30.7802 | + | 29.6335i | −0.982736 | + | 0.946125i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.4474 | + | 23.2916i | 0.428907 | + | 0.742888i | 0.996776 | − | 0.0802305i | \(-0.0255656\pi\) |
−0.567870 | + | 0.823118i | \(0.692232\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.59035 | − | 4.95964i | −0.273711 | − | 0.158027i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 37.0492i | 1.17810i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −35.4401 | −1.12579 | −0.562896 | − | 0.826528i | \(-0.690313\pi\) | ||||
−0.562896 | + | 0.826528i | \(0.690313\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −17.4109 | + | 22.2500i | −0.552520 | + | 0.706082i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.3635 | − | 8.29275i | −0.455352 | − | 0.262898i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.1418 | + | 16.2477i | −0.891259 | + | 0.514568i | −0.874354 | − | 0.485289i | \(-0.838714\pi\) |
−0.0169046 | + | 0.999857i | \(0.505381\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.33011 | + | 1.49180i | 0.105360 | + | 0.0471984i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))