Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(529,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.529");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.q (of order \(3\), 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: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.309123.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 529.3 | ||
Root | \(0.500000 - 0.224437i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.529 |
Dual form | 1008.2.q.h.625.3 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.29418 | − | 1.15113i | 0.747196 | − | 0.664603i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.84981 | + | 3.20397i | −0.827262 | + | 1.43286i | 0.0729162 | + | 0.997338i | \(0.476769\pi\) |
−0.900178 | + | 0.435522i | \(0.856564\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.64400 | − | 0.0963576i | −0.999337 | − | 0.0364197i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.349814 | − | 2.97954i | 0.116605 | − | 0.993178i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.738550 | − | 1.27921i | −0.222681 | − | 0.385695i | 0.732940 | − | 0.680293i | \(-0.238148\pi\) |
−0.955621 | + | 0.294598i | \(0.904814\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.34981 | − | 2.33795i | −0.374371 | − | 0.648430i | 0.615862 | − | 0.787854i | \(-0.288808\pi\) |
−0.990233 | + | 0.139425i | \(0.955475\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.29418 | + | 6.27589i | 0.334156 | + | 1.62043i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.28799 | − | 5.69497i | 0.797455 | − | 1.38123i | −0.123813 | − | 0.992306i | \(-0.539512\pi\) |
0.921268 | − | 0.388927i | \(-0.127154\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.444368 | + | 0.769668i | 0.101945 | + | 0.176574i | 0.912486 | − | 0.409108i | \(-0.134160\pi\) |
−0.810541 | + | 0.585682i | \(0.800827\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.53273 | + | 2.91887i | −0.770905 | + | 0.636950i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.14400 | − | 5.44556i | 0.655568 | − | 1.13548i | −0.326182 | − | 0.945307i | \(-0.605762\pi\) |
0.981751 | − | 0.190171i | \(-0.0609043\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.34362 | − | 7.52338i | −0.868725 | − | 1.50468i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.97710 | − | 4.25874i | −0.572943 | − | 0.819595i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.25526 | − | 2.17417i | 0.233096 | − | 0.403734i | −0.725622 | − | 0.688094i | \(-0.758448\pi\) |
0.958718 | + | 0.284360i | \(0.0917810\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.81089 | −1.22327 | −0.611636 | − | 0.791139i | \(-0.709488\pi\) | ||||
−0.611636 | + | 0.791139i | \(0.709488\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.42835 | − | 0.805361i | −0.422721 | − | 0.140195i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.19963 | − | 8.29305i | 0.878898 | − | 1.40178i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.38874 | − | 2.40536i | −0.228307 | − | 0.395439i | 0.729000 | − | 0.684514i | \(-0.239986\pi\) |
−0.957306 | + | 0.289075i | \(0.906652\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.43818 | − | 1.47192i | −0.710677 | − | 0.235696i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.05563 | − | 3.56046i | −0.321036 | − | 0.556050i | 0.659666 | − | 0.751559i | \(-0.270698\pi\) |
−0.980702 | + | 0.195508i | \(0.937364\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.00618986 | + | 0.0107211i | −0.000943944 | + | 0.00163496i | −0.866497 | − | 0.499182i | \(-0.833634\pi\) |
0.865553 | + | 0.500817i | \(0.166967\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.89926 | + | 6.63238i | 1.32662 | + | 0.988697i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.98762 | 1.01925 | 0.509625 | − | 0.860397i | \(-0.329784\pi\) | ||||
0.509625 | + | 0.860397i | \(0.329784\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.98143 | + | 0.509538i | 0.997347 | + | 0.0727912i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.30037 | − | 11.1552i | −0.322116 | − | 1.56204i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.60507 | + | 2.78007i | −0.220474 | + | 0.381872i | −0.954952 | − | 0.296760i | \(-0.904094\pi\) |
0.734478 | + | 0.678632i | \(0.237427\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.46472 | 0.736863 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.46108 | + | 0.484566i | 0.193525 | + | 0.0641824i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.90978 | −0.899576 | −0.449788 | − | 0.893135i | \(-0.648501\pi\) | ||||
−0.449788 | + | 0.893135i | \(0.648501\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.73305 | −0.734042 | −0.367021 | − | 0.930213i | \(-0.619622\pi\) | ||||
−0.367021 | + | 0.930213i | \(0.619622\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.21201 | + | 7.84417i | −0.152699 | + | 0.988273i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.98762 | 1.23881 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.46472 | 1.15630 | 0.578150 | − | 0.815931i | \(-0.303775\pi\) | ||||
0.578150 | + | 0.815931i | \(0.303775\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.19963 | − | 10.6667i | −0.264804 | − | 1.28412i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.46472 | 0.648543 | 0.324271 | − | 0.945964i | \(-0.394881\pi\) | ||||
0.324271 | + | 0.945964i | \(0.394881\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.03273 | + | 10.4490i | −0.706078 | + | 1.22296i | 0.260223 | + | 0.965548i | \(0.416204\pi\) |
−0.966301 | + | 0.257414i | \(0.917130\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −14.2818 | − | 4.73656i | −1.64912 | − | 0.546931i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.82946 | + | 3.45338i | 0.208487 | + | 0.393549i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.4523 | −1.28849 | −0.644244 | − | 0.764820i | \(-0.722828\pi\) | ||||
−0.644244 | + | 0.764820i | \(0.722828\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.75526 | − | 2.08457i | −0.972807 | − | 0.231619i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.23855 | + | 3.87728i | −0.245713 | + | 0.425587i | −0.962332 | − | 0.271878i | \(-0.912355\pi\) |
0.716619 | + | 0.697465i | \(0.245689\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.1643 | + | 21.0693i | 1.31941 | + | 2.28528i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.878215 | − | 4.25874i | −0.0941546 | − | 0.456585i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.43818 | − | 7.68715i | −0.470446 | − | 0.814836i | 0.528983 | − | 0.848633i | \(-0.322574\pi\) |
−0.999429 | + | 0.0337963i | \(0.989240\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.34362 | + | 6.31159i | 0.350507 | + | 0.661634i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.81453 | + | 7.84020i | −0.914025 | + | 0.812991i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.28799 | −0.337341 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.58836 | + | 11.4114i | −0.668947 | + | 1.15865i | 0.309252 | + | 0.950980i | \(0.399921\pi\) |
−0.978199 | + | 0.207670i | \(0.933412\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.06979 | + | 1.75305i | −0.409030 | + | 0.176188i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.62729 | − | 4.55059i | −0.261425 | − | 0.452801i | 0.705196 | − | 0.709012i | \(-0.250859\pi\) |
−0.966621 | + | 0.256212i | \(0.917526\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.833104 | − | 1.44298i | 0.0820882 | − | 0.142181i | −0.822059 | − | 0.569403i | \(-0.807174\pi\) |
0.904147 | + | 0.427222i | \(0.140508\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.81708 | − | 16.7181i | −0.274919 | − | 1.63152i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.38255 | + | 9.32284i | 0.520350 | + | 0.901273i | 0.999720 | + | 0.0236602i | \(0.00753198\pi\) |
−0.479370 | + | 0.877613i | \(0.659135\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.0945538 | + | 0.163772i | −0.00905662 | + | 0.0156865i | −0.870518 | − | 0.492136i | \(-0.836216\pi\) |
0.861462 | + | 0.507823i | \(0.169550\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.56615 | − | 1.51436i | −0.433400 | − | 0.143737i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.78180 | − | 11.7464i | −0.637978 | − | 1.10501i | −0.985876 | − | 0.167478i | \(-0.946438\pi\) |
0.347897 | − | 0.937533i | \(-0.386896\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.6316 | + | 20.1466i | 1.08465 | + | 1.87868i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.43818 | + | 3.20397i | −0.687660 | + | 0.296207i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.24219 | + | 14.7407i | −0.847230 | + | 1.35127i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.40909 | − | 7.63676i | 0.400826 | − | 0.694251i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.75890 | − | 2.24159i | −0.609430 | − | 0.202117i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 13.6414 | 1.22013 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.85669 | 0.253490 | 0.126745 | − | 0.991935i | \(-0.459547\pi\) | ||||
0.126745 | + | 0.991935i | \(0.459547\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.00433060 | + | 0.0210004i | 0.000381288 | + | 0.00184898i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.0778435 | − | 0.134829i | 0.00680122 | − | 0.0117801i | −0.862605 | − | 0.505878i | \(-0.831168\pi\) |
0.869406 | + | 0.494098i | \(0.164502\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.10074 | − | 2.07782i | −0.0954466 | − | 0.180170i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 19.1520 | − | 1.66066i | 1.64834 | − | 0.142927i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.70582 | + | 2.95456i | 0.145738 | + | 0.252425i | 0.929648 | − | 0.368449i | \(-0.120111\pi\) |
−0.783910 | + | 0.620874i | \(0.786778\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.75526 | + | 11.7005i | 0.572974 | + | 0.992420i | 0.996259 | + | 0.0864229i | \(0.0275436\pi\) |
−0.423285 | + | 0.905997i | \(0.639123\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.04325 | − | 8.04364i | 0.761579 | − | 0.677396i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.99381 | + | 3.45338i | −0.166731 | + | 0.288786i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.64400 | + | 8.04364i | 0.385663 | + | 0.667988i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.62178 | − | 7.37708i | 0.793591 | − | 0.608451i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.166896 | + | 0.289073i | −0.0136727 | + | 0.0236818i | −0.872781 | − | 0.488112i | \(-0.837686\pi\) |
0.859108 | + | 0.511794i | \(0.171019\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.95489 | − | 17.2424i | −0.810117 | − | 1.40316i | −0.912781 | − | 0.408448i | \(-0.866070\pi\) |
0.102664 | − | 0.994716i | \(-0.467263\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −15.8182 | − | 11.7889i | −1.27882 | − | 0.953074i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.5989 | − | 21.8219i | 1.01197 | − | 1.75278i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.96286 | −0.555697 | −0.277848 | − | 0.960625i | \(-0.589621\pi\) | ||||
−0.277848 | + | 0.960625i | \(0.589621\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.12296 | + | 5.44556i | 0.0890561 | + | 0.431861i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.83743 | + | 14.0951i | −0.696487 | + | 1.11085i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.03706 | − | 6.99240i | −0.316207 | − | 0.547687i | 0.663486 | − | 0.748189i | \(-0.269076\pi\) |
−0.979693 | + | 0.200502i | \(0.935743\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.07234 | − | 6.29059i | 0.550581 | − | 0.489721i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.74288 | − | 16.8752i | −0.753927 | − | 1.30584i | −0.945906 | − | 0.324440i | \(-0.894824\pi\) |
0.191979 | − | 0.981399i | \(-0.438509\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.85600 | − | 4.94674i | 0.219693 | − | 0.380519i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.44870 | − | 1.05477i | 0.187257 | − | 0.0806602i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.5636 | 1.71548 | 0.857740 | − | 0.514085i | \(-0.171868\pi\) | ||||
0.857740 | + | 0.514085i | \(0.171868\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.7596 | + | 20.3103i | 0.813349 | + | 1.53532i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.94251 | + | 7.95403i | −0.672160 | + | 0.597861i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.166896 | + | 0.289073i | −0.0124744 | + | 0.0216063i | −0.872195 | − | 0.489158i | \(-0.837304\pi\) |
0.859721 | + | 0.510764i | \(0.170637\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.2422 | 1.72758 | 0.863789 | − | 0.503853i | \(-0.168085\pi\) | ||||
0.863789 | + | 0.503853i | \(0.168085\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.41961 | + | 6.59947i | −0.548473 | + | 0.487847i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.2756 | 0.755478 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.71339 | −0.710313 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 7.46108 | + | 11.5470i | 0.542714 | + | 0.839918i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.3214 | 1.18098 | 0.590488 | − | 0.807046i | \(-0.298935\pi\) | ||||
0.590488 | + | 0.807046i | \(0.298935\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.3214 | −1.03088 | −0.515439 | − | 0.856926i | \(-0.672371\pi\) | ||||
−0.515439 | + | 0.856926i | \(0.672371\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 12.9258 | − | 11.4970i | 0.925636 | − | 0.823319i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.42402 | 0.172704 | 0.0863520 | − | 0.996265i | \(-0.472479\pi\) | ||||
0.0863520 | + | 0.996265i | \(0.472479\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.05563 | − | 5.29251i | 0.216608 | − | 0.375176i | −0.737161 | − | 0.675717i | \(-0.763834\pi\) |
0.953769 | + | 0.300541i | \(0.0971673\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.2491 | − | 10.8951i | 0.863983 | − | 0.768481i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.52840 | + | 5.62755i | −0.247645 | + | 0.394977i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.2101 | 1.06232 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −15.1254 | − | 11.2726i | −1.05129 | − | 0.783499i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.656376 | − | 1.13688i | 0.0454025 | − | 0.0786394i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.72253 | − | 9.91171i | −0.393955 | − | 0.682350i | 0.599012 | − | 0.800740i | \(-0.295560\pi\) |
−0.992967 | + | 0.118390i | \(0.962227\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.07234 | − | 6.29059i | 0.484589 | − | 0.431024i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.0229002 | − | 0.0396643i | −0.00156178 | − | 0.00270508i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.0080 | + | 0.656281i | 1.22246 | + | 0.0445513i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.22067 | + | 20.4673i | 0.285206 | + | 1.38305i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −17.7527 | −1.19418 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.61126 | − | 6.25489i | 0.241828 | − | 0.418859i | −0.719407 | − | 0.694589i | \(-0.755586\pi\) |
0.961235 | + | 0.275730i | \(0.0889196\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −23.9356 | + | 10.3102i | −1.59571 | + | 0.687347i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.82760 | + | 11.8258i | 0.453164 | + | 0.784903i | 0.998581 | − | 0.0532622i | \(-0.0169619\pi\) |
−0.545417 | + | 0.838165i | \(0.683629\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.68725 | + | 15.0468i | −0.574070 | + | 0.994318i | 0.422073 | + | 0.906562i | \(0.361303\pi\) |
−0.996142 | + | 0.0877555i | \(0.972031\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.34294 | + | 2.36336i | 0.417335 | + | 0.155498i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.62110 | + | 13.2001i | 0.499275 | + | 0.864769i | 1.00000 | 0.000837426i | \(-0.000266561\pi\) | |
−0.500725 | + | 0.865606i | \(0.666933\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.9258 | + | 22.3881i | −0.843186 | + | 1.46044i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.8214 | + | 13.1831i | −0.962754 | + | 0.856334i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.47524 | − | 16.4116i | −0.612902 | − | 1.06158i | −0.990749 | − | 0.135710i | \(-0.956669\pi\) |
0.377846 | − | 0.925868i | \(-0.376665\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.2527 | + | 21.2223i | 0.789267 | + | 1.36705i | 0.926417 | + | 0.376500i | \(0.122872\pi\) |
−0.137150 | + | 0.990550i | \(0.543794\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.7305 | + | 7.38061i | −0.880812 | + | 0.473466i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.5469 | + | 21.4258i | −0.929367 | + | 1.36884i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.19963 | − | 2.07782i | 0.0763305 | − | 0.132208i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.56615 | + | 7.59476i | 0.0992509 | + | 0.481299i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.1236 | 0.765238 | 0.382619 | − | 0.923906i | \(-0.375022\pi\) | ||||
0.382619 | + | 0.923906i | \(0.375022\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.28799 | −0.583931 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 39.9963 | + | 13.2648i | 2.50466 | + | 0.830672i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.10439 | − | 7.10900i | 0.256025 | − | 0.443448i | −0.709149 | − | 0.705059i | \(-0.750921\pi\) |
0.965173 | + | 0.261611i | \(0.0842539\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.44004 | + | 6.49358i | 0.213754 | + | 0.403491i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.03892 | − | 4.50065i | −0.373800 | − | 0.278583i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.67309 | − | 4.62992i | −0.164830 | − | 0.285493i | 0.771765 | − | 0.635908i | \(-0.219374\pi\) |
−0.936595 | + | 0.350414i | \(0.886041\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.93818 | − | 10.2852i | −0.364779 | − | 0.631816i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.5927 | − | 4.83967i | −0.893058 | − | 0.296183i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.24219 | − | 16.0079i | 0.563506 | − | 0.976022i | −0.433681 | − | 0.901067i | \(-0.642785\pi\) |
0.997187 | − | 0.0749550i | \(-0.0238813\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.67742 | + | 6.36947i | 0.223387 | + | 0.386918i | 0.955834 | − | 0.293906i | \(-0.0949552\pi\) |
−0.732447 | + | 0.680824i | \(0.761622\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.5927 | + | 4.31941i | 0.701622 | + | 0.261422i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.41597 | + | 11.1128i | −0.386897 | + | 0.670126i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.54944 | + | 7.87987i | 0.273349 | + | 0.473455i | 0.969717 | − | 0.244230i | \(-0.0785351\pi\) |
−0.696368 | + | 0.717685i | \(0.745202\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.38255 | + | 20.2933i | −0.142639 | + | 1.21493i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00433 | − | 10.3998i | 0.358188 | − | 0.620400i | −0.629470 | − | 0.777025i | \(-0.716728\pi\) |
0.987658 | + | 0.156624i | \(0.0500612\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.84294 | −0.585102 | −0.292551 | − | 0.956250i | \(-0.594504\pi\) | ||||
−0.292551 | + | 0.956250i | \(0.594504\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.25526 | + | 3.78490i | −0.252060 | + | 0.224198i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.09201 | + | 9.61192i | 0.300572 | + | 0.567373i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.1218 | − | 22.7276i | −0.771870 | − | 1.33692i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.60940 | + | 22.3524i | 0.270208 | + | 1.31032i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.7101 | + | 18.5505i | 0.625694 | + | 1.08373i | 0.988406 | + | 0.151832i | \(0.0485173\pi\) |
−0.362713 | + | 0.931901i | \(0.618149\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.7818 | − | 22.1387i | 0.744185 | − | 1.28897i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.24907 | + | 6.95362i | −0.188530 | + | 0.403490i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −16.9752 | −0.981704 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.0173990 | − | 0.0277502i | 0.00100286 | − | 0.00159950i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.63849 | − | 2.86496i | −0.496269 | − | 0.164587i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.6051 | − | 18.3685i | 0.607245 | − | 1.05178i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.68725 | 0.324588 | 0.162294 | − | 0.986742i | \(-0.448111\pi\) | ||||
0.162294 | + | 0.986742i | \(0.448111\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.582863 | − | 2.82648i | −0.0331579 | − | 0.160793i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.7207 | 0.664618 | 0.332309 | − | 0.943171i | \(-0.392172\pi\) | ||||
0.332309 | + | 0.943171i | \(0.392172\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.7738 | −1.51334 | −0.756671 | − | 0.653796i | \(-0.773176\pi\) | ||||
−0.756671 | + | 0.653796i | \(0.773176\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −22.8905 | − | 18.3935i | −1.28973 | − | 1.03636i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.90249 | 0.106855 | 0.0534273 | − | 0.998572i | \(-0.482985\pi\) | ||||
0.0534273 | + | 0.998572i | \(0.482985\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.70829 | −0.207624 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.6978 | + | 5.86946i | 0.987793 | + | 0.327601i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.84431 | 0.325186 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.7262 | + | 20.3103i | −0.650451 | + | 1.12661i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.0661525 | + | 0.320794i | 0.00365824 | + | 0.0177400i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −18.4752 | − | 0.673310i | −1.01857 | − | 0.0371208i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.56732 | −0.306008 | −0.153004 | − | 0.988226i | \(-0.548895\pi\) | ||||
−0.153004 | + | 0.988226i | \(0.548895\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.65266 | + | 3.29636i | −0.419363 | + | 0.180639i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −17.5080 | + | 30.3247i | −0.956563 | + | 1.65682i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.8869 | − | 29.2489i | −0.919887 | − | 1.59329i | −0.799585 | − | 0.600553i | \(-0.794947\pi\) |
−0.120302 | − | 0.992737i | \(-0.538386\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −22.2985 | − | 7.39530i | −1.21109 | − | 0.401657i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.03018 | + | 8.71253i | 0.272400 | + | 0.471810i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.4098 | − | 2.01993i | −0.994035 | − | 0.109066i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 38.2447 | + | 12.6838i | 2.05902 | + | 0.682875i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 30.4065 | 1.63231 | 0.816154 | − | 0.577834i | \(-0.196102\pi\) | ||||
0.816154 | + | 0.577834i | \(0.196102\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.29782 | + | 10.9082i | −0.337115 | + | 0.583900i | −0.983889 | − | 0.178782i | \(-0.942784\pi\) |
0.646774 | + | 0.762682i | \(0.276118\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.93818 | + | 12.7088i | −0.316956 | + | 0.678346i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.76578 | + | 6.52252i | 0.200432 | + | 0.347159i | 0.948668 | − | 0.316274i | \(-0.102432\pi\) |
−0.748235 | + | 0.663433i | \(0.769099\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.1087 | + | 17.5088i | −0.536515 | + | 0.929271i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.00728 | + | 29.7160i | 0.265014 | + | 1.57274i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.44801 | + | 5.97213i | 0.181979 | + | 0.315197i | 0.942554 | − | 0.334053i | \(-0.108416\pi\) |
−0.760575 | + | 0.649250i | \(0.775083\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.10507 | − | 15.7705i | 0.479214 | − | 0.830024i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.08472 | − | 14.9588i | −0.161906 | − | 0.785132i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −22.3189 | − | 38.6574i | −1.16822 | − | 2.02342i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.5618 | + | 20.0257i | 0.603522 | + | 1.04533i | 0.992283 | + | 0.123992i | \(0.0395699\pi\) |
−0.388761 | + | 0.921339i | \(0.627097\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −11.3276 | + | 4.87933i | −0.589691 | + | 0.254008i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.51169 | − | 7.19583i | 0.234235 | − | 0.373589i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.5822 | + | 25.2571i | −0.755036 | + | 1.30776i | 0.190320 | + | 0.981722i | \(0.439047\pi\) |
−0.945356 | + | 0.326039i | \(0.894286\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 17.6545 | − | 15.7030i | 0.911675 | − | 0.810901i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.77747 | −0.349058 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.5622 | 0.696645 | 0.348322 | − | 0.937375i | \(-0.386751\pi\) | ||||
0.348322 | + | 0.937375i | \(0.386751\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.69708 | − | 3.28842i | 0.189407 | − | 0.168471i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.41783 | + | 2.45575i | −0.0724475 | + | 0.125483i | −0.899973 | − | 0.435945i | \(-0.856414\pi\) |
0.827526 | + | 0.561428i | \(0.189748\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14.4487 | − | 0.526567i | −0.736374 | − | 0.0268364i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.0297787 | + | 0.0221933i | 0.00151374 | + | 0.00112815i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.30401 | + | 16.1150i | 0.471732 | + | 0.817064i | 0.999477 | − | 0.0323388i | \(-0.0102956\pi\) |
−0.527745 | + | 0.849403i | \(0.676962\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −20.6749 | − | 35.8099i | −1.04557 | − | 1.81099i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.0544615 | − | 0.264101i | −0.00274722 | − | 0.0133221i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 21.1847 | − | 36.6930i | 1.06592 | − | 1.84622i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.2880 | − | 17.8193i | −0.516340 | − | 0.894326i | −0.999820 | − | 0.0189712i | \(-0.993961\pi\) |
0.483481 | − | 0.875355i | \(-0.339372\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.81639 | − | 1.42198i | −0.191059 | − | 0.0711879i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.37704 | − | 5.84921i | 0.168642 | − | 0.292096i | −0.769301 | − | 0.638887i | \(-0.779395\pi\) |
0.937942 | + | 0.346791i | \(0.112729\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.19344 | + | 15.9235i | 0.457958 | + | 0.793206i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 22.8745 | − | 24.1955i | 1.13664 | − | 1.20229i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.05130 | + | 3.55296i | −0.101679 | + | 0.176114i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.3214 | 0.757595 | 0.378798 | − | 0.925480i | \(-0.376338\pi\) | ||||
0.378798 | + | 0.925480i | \(0.376338\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.60872 | + | 1.86013i | 0.276658 | + | 0.0917534i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 18.2694 | + | 0.665809i | 0.898980 | + | 0.0327623i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.28180 | − | 14.3445i | −0.406538 | − | 0.704144i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 22.2112 | + | 7.36636i | 1.08769 | + | 0.360732i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.32141 | + | 7.48491i | 0.211115 | + | 0.365662i | 0.952064 | − | 0.305900i | \(-0.0989573\pi\) |
−0.740949 | + | 0.671561i | \(0.765624\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.5636 | − | 32.1531i | 0.904735 | − | 1.56705i | 0.0834618 | − | 0.996511i | \(-0.473402\pi\) |
0.821273 | − | 0.570536i | \(-0.193264\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.44437 | − | 20.8199i | 0.118849 | − | 1.01230i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −57.1272 | −2.77108 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.1582 | + | 0.552423i | 0.733555 | + | 0.0267336i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.39493 | + | 6.76443i | 0.0673476 | + | 0.326590i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.71015 | − | 8.15822i | 0.226880 | − | 0.392967i | −0.730002 | − | 0.683445i | \(-0.760481\pi\) |
0.956882 | + | 0.290478i | \(0.0938142\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.208771 | −0.0100329 | −0.00501645 | − | 0.999987i | \(-0.501597\pi\) | ||||
−0.00501645 | + | 0.999987i | \(0.501597\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 15.2694 | + | 5.06410i | 0.732113 | + | 0.242805i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.58836 | 0.267328 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.96796 | 0.475745 | 0.237872 | − | 0.971296i | \(-0.423550\pi\) | ||||
0.237872 | + | 0.971296i | \(0.423550\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.96039 | − | 20.6232i | 0.188590 | − | 0.982056i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.6996 | 0.745912 | 0.372956 | − | 0.927849i | \(-0.378344\pi\) | ||||
0.372956 | + | 0.927849i | \(0.378344\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 32.8392 | 1.55673 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.116765 | + | 0.566231i | 0.00552281 | + | 0.0267818i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.6253 | 1.58688 | 0.793439 | − | 0.608650i | \(-0.208288\pi\) | ||||
0.793439 | + | 0.608650i | \(0.208288\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.03637 | + | 5.25915i | −0.142977 | + | 0.247644i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −32.7316 | − | 10.8554i | −1.53786 | − | 0.510033i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −26.4072 | − | 0.962383i | −1.23799 | − | 0.0451172i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.7083 | 1.53003 | 0.765015 | − | 0.644013i | \(-0.222732\pi\) | ||||
0.765015 | + | 0.644013i | \(0.222732\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −34.0421 | + | 2.95178i | −1.58895 | + | 0.137778i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.07165 | + | 3.58821i | −0.0964865 | + | 0.167120i | −0.910228 | − | 0.414107i | \(-0.864094\pi\) |
0.813742 | + | 0.581227i | \(0.197427\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.34176 | + | 14.4484i | 0.387675 | + | 0.671472i | 0.992136 | − | 0.125162i | \(-0.0399451\pi\) |
−0.604462 | + | 0.796634i | \(0.706612\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.81453 | − | 42.7444i | −0.408764 | − | 1.98223i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.9585 | − | 25.9089i | −0.692198 | − | 1.19892i | −0.971116 | − | 0.238608i | \(-0.923309\pi\) |
0.278918 | − | 0.960315i | \(-0.410024\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −25.0247 | − | 0.911998i | −1.15553 | − | 0.0421121i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.01121 | + | 8.01514i | −0.415215 | + | 0.369318i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.0182861 | 0.000840794 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.86033 | − | 6.68630i | 0.177124 | − | 0.306788i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.72184 | + | 5.75488i | 0.353559 | + | 0.263498i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.47965 | − | 2.56283i | −0.0676068 | − | 0.117098i | 0.830241 | − | 0.557405i | \(-0.188203\pi\) |
−0.897847 | + | 0.440307i | \(0.854870\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.74907 | + | 6.49358i | −0.170943 | + | 0.296082i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.78799 | + | 28.4146i | 0.217861 | + | 1.29291i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −24.3745 | − | 42.2179i | −1.10679 | − | 1.91701i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.0309 | − | 24.3022i | 0.635800 | − | 1.10124i | −0.350546 | − | 0.936546i | \(-0.614004\pi\) |
0.986345 | − | 0.164691i | \(-0.0526628\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13.2738 | − | 4.40226i | −0.600263 | − | 0.199077i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.0734 | − | 29.5721i | −0.770513 | − | 1.33457i | −0.937282 | − | 0.348572i | \(-0.886667\pi\) |
0.166769 | − | 0.985996i | \(-0.446667\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.25457 | − | 14.2973i | −0.371767 | − | 0.643920i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.91164 | − | 16.2823i | 0.0859216 | − | 0.731836i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.4487 | − | 0.526567i | −0.648113 | − | 0.0236198i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.14035 | + | 1.97515i | −0.0510493 | + | 0.0884199i | −0.890421 | − | 0.455138i | \(-0.849590\pi\) |
0.839372 | + | 0.543558i | \(0.182923\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −32.0345 | − | 10.6242i | −1.43120 | − | 0.474656i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13.9890 | −0.623739 | −0.311869 | − | 0.950125i | \(-0.600955\pi\) | ||||
−0.311869 | + | 0.950125i | \(0.600955\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.4400 | 0.865067 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.99814 | − | 9.68961i | −0.0887405 | − | 0.430331i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.8090 | + | 22.1859i | −0.567750 | + | 0.983373i | 0.429038 | + | 0.903287i | \(0.358853\pi\) |
−0.996788 | + | 0.0800859i | \(0.974481\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.9574 | − | 27.0458i | 0.750149 | − | 1.19644i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.95489 | − | 4.18383i | 0.0863104 | − | 0.184720i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.08217 | + | 5.33848i | 0.135817 | + | 0.235242i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.16071 | − | 8.93861i | −0.226968 | − | 0.393119i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 29.2014 | − | 25.9736i | 1.28180 | − | 1.14011i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.9127 | + | 36.2219i | −0.916203 | + | 1.58691i | −0.111073 | + | 0.993812i | \(0.535429\pi\) |
−0.805130 | + | 0.593099i | \(0.797904\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.88323 | − | 13.6542i | −0.344710 | − | 0.597055i | 0.640591 | − | 0.767882i | \(-0.278689\pi\) |
−0.985301 | + | 0.170827i | \(0.945356\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 37.3046 | + | 13.8996i | 1.62811 | + | 0.606628i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −22.3942 | + | 38.7878i | −0.975505 | + | 1.68962i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.26942 | − | 14.3231i | −0.359540 | − | 0.622742i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.41714 | + | 20.5879i | −0.104895 | + | 0.893440i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.54944 | + | 9.61192i | −0.240373 | + | 0.416338i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −39.8268 | −1.72186 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.116765 | + | 0.566231i | 0.00503879 | + | 0.0244347i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.50433 | − | 9.30701i | −0.194015 | − | 0.400881i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.0963 | − | 36.5399i | −0.907002 | − | 1.57097i | −0.818207 | − | 0.574924i | \(-0.805031\pi\) |
−0.0887957 | − | 0.996050i | \(-0.528302\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 30.0796 | − | 26.7547i | 1.29084 | − | 1.14815i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.349814 | − | 0.605896i | −0.0149844 | − | 0.0259537i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.3356 | + | 35.2222i | −0.869486 | + | 1.50599i | −0.00696400 | + | 0.999976i | \(0.502217\pi\) |
−0.862522 | + | 0.506019i | \(0.831117\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.00550 | + | 17.0818i | −0.0855927 | + | 0.729034i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.23119 | 0.0950519 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 30.2799 | + | 1.10352i | 1.28763 | + | 0.0469264i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 13.2985 | − | 11.8285i | 0.564490 | − | 0.502093i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.68794 | − | 11.5838i | 0.283377 | − | 0.490823i | −0.688837 | − | 0.724916i | \(-0.741879\pi\) |
0.972214 | + | 0.234093i | \(0.0752119\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.0334206 | 0.00141354 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.5709 | + | 11.1813i | −0.530743 | + | 0.472076i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 32.7614 | 1.38073 | 0.690364 | − | 0.723463i | \(-0.257451\pi\) | ||||
0.690364 | + | 0.723463i | \(0.257451\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 50.1803 | 2.11110 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 22.9480 | + | 6.35522i | 0.963726 | + | 0.266894i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.7280 | −0.701272 | −0.350636 | − | 0.936512i | \(-0.614035\pi\) | ||||
−0.350636 | + | 0.936512i | \(0.614035\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.4734 | 1.14973 | 0.574863 | − | 0.818250i | \(-0.305055\pi\) | ||||
0.574863 | + | 0.818250i | \(0.305055\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21.1229 | − | 18.7880i | 0.882421 | − | 0.784881i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −54.6253 | −2.27803 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.41714 | − | 2.45455i | 0.0589962 | − | 0.102184i | −0.835019 | − | 0.550221i | \(-0.814543\pi\) |
0.894015 | + | 0.448037i | \(0.147877\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −18.5345 | + | 16.4858i | −0.770268 | + | 0.685125i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.29232 | − | 10.0358i | 0.261050 | − | 0.416356i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.74171 | 0.196382 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.49381 | − | 29.7585i | 0.144451 | − | 1.23036i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.34795 | − | 4.06678i | 0.0969105 | − | 0.167854i | −0.813494 | − | 0.581573i | \(-0.802437\pi\) |
0.910404 | + | 0.413720i | \(0.135771\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.02654 | − | 5.24212i | −0.124706 | − | 0.215998i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.13712 | − | 2.79035i | 0.129044 | − | 0.114780i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.636024 | + | 1.10163i | 0.0261184 | + | 0.0452383i | 0.878789 | − | 0.477210i | \(-0.158352\pi\) |
−0.852671 | + | 0.522449i | \(0.825019\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −30.1323 | − | 56.8792i | −1.23530 | − | 2.33182i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.13781 | − | 10.3669i | −0.0874946 | − | 0.424289i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −43.8516 | −1.79173 | −0.895864 | − | 0.444329i | \(-0.853442\pi\) | ||||
−0.895864 | + | 0.444329i | \(0.853442\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.71634 | + | 11.6330i | −0.273965 | + | 0.474522i | −0.969874 | − | 0.243609i | \(-0.921669\pi\) |
0.695908 | + | 0.718131i | \(0.255002\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.31089 | − | 28.2005i | 0.134830 | − | 1.14841i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 16.3120 | + | 28.2532i | 0.663177 | + | 1.14866i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.29232 | + | 3.97042i | −0.0930425 | + | 0.161154i | −0.908790 | − | 0.417254i | \(-0.862993\pi\) |
0.815747 | + | 0.578408i | \(0.196326\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.91164 | + | 11.3447i | 0.0774634 | + | 0.459711i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.43199 | − | 16.3367i | −0.381577 | − | 0.660911i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.0538 | + | 19.1457i | −0.446458 | + | 0.773287i | −0.998152 | − | 0.0607587i | \(-0.980648\pi\) |
0.551695 | + | 0.834046i | \(0.313981\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 19.6847 | − | 17.5088i | 0.793764 | − | 0.706023i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.00433 | + | 10.3998i | 0.241725 | + | 0.418680i | 0.961206 | − | 0.275832i | \(-0.0889534\pi\) |
−0.719481 | + | 0.694513i | \(0.755620\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.78180 | − | 15.2105i | −0.352970 | − | 0.611363i | 0.633798 | − | 0.773499i | \(-0.281495\pi\) |
−0.986768 | + | 0.162136i | \(0.948162\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −32.5512 | + | 2.82251i | −1.30624 | + | 0.113264i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.9938 | + | 20.7524i | 0.440458 | + | 0.831429i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.51602 | + | 6.08993i | −0.140641 | + | 0.243597i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.459219 | − | 2.22690i | −0.0183394 | − | 0.0889337i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18.2646 | −0.728258 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 44.9381 | 1.78896 | 0.894479 | − | 0.447110i | \(-0.147547\pi\) | ||||
0.894479 | + | 0.447110i | \(0.147547\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.8156 | − | 6.24020i | −0.747854 | − | 0.248026i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.28435 | + | 9.15276i | −0.209703 | + | 0.363216i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.23236 | − | 17.0100i | −0.326178 | − | 0.673960i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.91164 | − | 16.2823i | 0.0756232 | − | 0.644119i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.4920 | + | 25.1008i | 0.572398 | + | 0.991422i | 0.996319 | + | 0.0857228i | \(0.0273199\pi\) |
−0.423921 | + | 0.905699i | \(0.639347\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.03087 | − | 10.4458i | −0.237834 | − | 0.411941i | 0.722258 | − | 0.691623i | \(-0.243104\pi\) |
−0.960093 | + | 0.279682i | \(0.909771\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.0752956 | − | 0.0249718i | −0.00296476 | − | 0.000983262i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.8825 | + | 32.7055i | −0.742349 | + | 1.28579i | 0.209073 | + | 0.977900i | \(0.432955\pi\) |
−0.951423 | + | 0.307887i | \(0.900378\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.10322 | + | 8.83903i | 0.200319 | + | 0.346962i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 24.0611 | − | 19.8801i | 0.943027 | − | 0.779163i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.7040 | + | 32.3962i | −0.731942 | + | 1.26776i | 0.224109 | + | 0.974564i | \(0.428053\pi\) |
−0.956052 | + | 0.293198i | \(0.905281\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.287992 | + | 0.498817i | 0.0112528 | + | 0.0194904i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 29.0228 | + | 21.6299i | 1.13229 | + | 0.843864i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.9356 | + | 25.8693i | −0.581810 | + | 1.00772i | 0.413455 | + | 0.910524i | \(0.364322\pi\) |
−0.995265 | + | 0.0971993i | \(0.969012\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.60803 | 0.218127 | 0.109063 | − | 0.994035i | \(-0.465215\pi\) | ||||
0.109063 | + | 0.994035i | \(0.465215\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −22.9752 | + | 20.4356i | −0.892284 | + | 0.793654i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.69344 | + | 0.316823i | 0.337117 | + | 0.0122859i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.89307 | − | 13.6712i | −0.305621 | − | 0.529351i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.52654 | − | 12.2520i | −0.0976818 | − | 0.473689i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.23414 | + | 7.33375i | 0.163457 | + | 0.283116i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.72253 | + | 8.17966i | −0.182040 | + | 0.315303i | −0.942575 | − | 0.333994i | \(-0.891603\pi\) |
0.760535 | + | 0.649297i | \(0.224937\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −19.1087 | + | 40.8962i | −0.735495 | + | 1.57410i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.0617 | 0.425137 | 0.212569 | − | 0.977146i | \(-0.431817\pi\) | ||||
0.212569 | + | 0.977146i | \(0.431817\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.5192 | − | 29.5368i | 0.710701 | − | 1.13352i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 22.4491 | + | 7.44524i | 0.860252 | + | 0.285302i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.41961 | − | 7.65499i | 0.169112 | − | 0.292910i | −0.768996 | − | 0.639253i | \(-0.779243\pi\) |
0.938108 | + | 0.346343i | \(0.112577\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.6218 | −0.482254 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.07784 | + | 29.4734i | 0.231884 | + | 1.12448i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.66621 | 0.330156 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.0617 | −0.953394 | −0.476697 | − | 0.879068i | \(-0.658166\pi\) | ||||
−0.476697 | + | 0.879068i | \(0.658166\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.9294 | − | 4.24290i | 0.415175 | − | 0.161175i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −49.9839 | −1.89600 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −27.0356 | −1.02405 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 25.0581 | + | 8.31052i | 0.947785 | + | 0.314333i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −43.4858 | −1.64243 | −0.821217 | − | 0.570616i | \(-0.806705\pi\) | ||||
−0.821217 | + | 0.570616i | \(0.806705\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.23422 | − | 2.13773i | 0.0465495 | − | 0.0806260i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.04325 | + | 43.8536i | 0.340589 | + | 1.65162i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.50805 | + | 12.2849i | 0.244760 | + | 0.462021i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.7403 | −0.854031 | −0.427016 | − | 0.904244i | \(-0.640435\pi\) | ||||
−0.427016 | + | 0.904244i | \(0.640435\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.00619 | + | 34.1227i | −0.150244 | + | 1.27970i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −21.4134 | + | 37.0891i | −0.801939 | + | 1.38900i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.37636 | − | 12.7762i | −0.275860 | − | 0.477804i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −31.1545 | − | 10.3324i | −1.16349 | − | 0.385870i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.06182 | − | 10.4994i | −0.226068 | − | 0.391561i | 0.730571 | − | 0.682836i | \(-0.239254\pi\) |
−0.956639 | + | 0.291275i | \(0.905920\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.34176 | + | 3.73495i | −0.0872119 | + | 0.139097i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 40.2868 | + | 13.3611i | 1.49828 | + | 0.496905i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −21.8095 | −0.809985 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.0908 | + | 39.9945i | −0.856392 | + | 1.48331i | 0.0189562 | + | 0.999820i | \(0.493966\pi\) |
−0.875348 | + | 0.483494i | \(0.839368\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9.27375 | + | 25.3574i | −0.343472 | + | 0.939163i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.0407044 | + | 0.0705021i | 0.00150551 | + | 0.00260761i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.0149 | − | 31.2026i | 0.665394 | − | 1.15250i | −0.313785 | − | 0.949494i | \(-0.601597\pi\) |
0.979178 | − | 0.203002i | \(-0.0650696\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.83743 | + | 44.4741i | 0.215317 | + | 1.64045i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.99017 | − | 12.1073i | −0.257486 | − | 0.445979i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.2119 | + | 40.2042i | −0.853865 | + | 1.47894i | 0.0238296 | + | 0.999716i | \(0.492414\pi\) |
−0.877694 | + | 0.479221i | \(0.840919\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.839294 | − | 4.07000i | −0.0308322 | − | 0.149515i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.598884 | − | 1.03730i | −0.0219709 | − | 0.0380548i | 0.854831 | − | 0.518907i | \(-0.173661\pi\) |
−0.876802 | + | 0.480852i | \(0.840327\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.617454 | − | 1.06946i | −0.0226218 | − | 0.0391820i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.7694 | + | 8.02617i | 0.394033 | + | 0.293662i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −13.3331 | − | 25.1682i | −0.487181 | − | 0.919626i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.0600 | − | 41.6731i | 0.877961 | − | 1.52067i | 0.0243853 | − | 0.999703i | \(-0.492237\pi\) |
0.853575 | − | 0.520970i | \(-0.174430\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.6902 | − | 13.9559i | 0.571783 | − | 0.508580i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 73.6588 | 2.68072 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 49.6006 | 1.80276 | 0.901382 | − | 0.433025i | \(-0.142554\pi\) | ||||
0.901382 | + | 0.433025i | \(0.142554\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12.0204 | + | 10.6917i | −0.436311 | + | 0.388083i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.7701 | − | 32.5108i | 0.680416 | − | 1.17852i | −0.294438 | − | 0.955671i | \(-0.595132\pi\) |
0.974854 | − | 0.222845i | \(-0.0715342\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.265781 | − | 0.423902i | 0.00962191 | − | 0.0153463i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 67.0319 | − | 28.8738i | 2.42354 | − | 1.04393i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.32691 | + | 16.1547i | 0.336775 | + | 0.583312i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.4592 | − | 23.3121i | −0.485352 | − | 0.840654i | 0.514506 | − | 0.857486i | \(-0.327975\pi\) |
−0.999858 | + | 0.0168324i | \(0.994642\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.87154 | − | 13.9250i | −0.103416 | − | 0.501497i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25.1130 | − | 43.4971i | 0.903254 | − | 1.56448i | 0.0800089 | − | 0.996794i | \(-0.474505\pi\) |
0.823245 | − | 0.567687i | \(-0.192162\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29.5840 | + | 51.2409i | 1.06269 | + | 1.84063i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11.9270 | + | 4.44396i | 0.427878 | + | 0.159426i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.82691 | − | 3.16431i | 0.0654560 | − | 0.113373i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.03597 | − | 6.99050i | −0.144418 | − | 0.250140i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −12.9963 | + | 1.12691i | −0.464449 | + | 0.0402723i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.8800 | − | 22.3088i | 0.459707 | − | 0.796236i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.65892 | 0.0591342 | 0.0295671 | − | 0.999563i | \(-0.490587\pi\) | ||||
0.0295671 | + | 0.999563i | \(0.490587\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.78909 | − | 2.91490i | −0.312900 | − | 0.103773i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.7992 | + | 31.7110i | 0.597311 | + | 1.12751i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.73855 | + | 13.4036i | 0.274804 | + | 0.475974i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −19.5247 | − | 6.47536i | −0.692469 | − | 0.229657i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.3702 | − | 26.6219i | −0.544439 | − | 0.942996i | −0.998642 | − | 0.0520981i | \(-0.983409\pi\) |
0.454203 | − | 0.890898i | \(-0.349924\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.9752 | − | 39.7943i | 0.812806 | − | 1.40782i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −24.4567 | + | 10.5346i | −0.864134 | + | 0.372223i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17.8219 | 0.628921 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −28.8127 | − | 54.3882i | −1.01551 | − | 1.91693i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.46610 | − | 31.3561i | −0.227617 | − | 1.10379i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.44251 | + | 2.49850i | −0.0507159 | + | 0.0878425i | −0.890269 | − | 0.455435i | \(-0.849484\pi\) |
0.839553 | + | 0.543278i | \(0.182817\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.5461 | −1.00239 | −0.501195 | − | 0.865334i | \(-0.667106\pi\) | ||||
−0.501195 | + | 0.865334i | \(0.667106\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.0913 | + | 4.01008i | 0.424061 | + | 0.140640i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 29.8713 | 1.04634 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.0110023 | −0.000384922 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 19.9752 | − | 7.75456i | 0.697991 | − | 0.270966i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.96658 | 0.278036 | 0.139018 | − | 0.990290i | \(-0.455605\pi\) | ||||
0.139018 | + | 0.990290i | \(0.455605\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40.5461 | −1.41335 | −0.706675 | − | 0.707539i | \(-0.749806\pi\) | ||||
−0.706675 | + | 0.707539i | \(0.749806\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.48879 | + | 21.7676i | 0.156280 | + | 0.757849i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.22115 | −0.0424636 | −0.0212318 | − | 0.999775i | \(-0.506759\pi\) | ||||
−0.0212318 | + | 0.999775i | \(0.506759\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.07530 | + | 12.2548i | −0.245735 | + | 0.425626i | −0.962338 | − | 0.271856i | \(-0.912363\pi\) |
0.716603 | + | 0.697481i | \(0.245696\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.9585 | + | 4.96099i | 0.518906 | + | 0.172095i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 25.8567 | − | 38.0837i | 0.895881 | − | 1.31952i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 72.0901 | 2.49478 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 20.2767 | + | 29.0058i | 0.700866 | + | 1.00259i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.19599 | + | 2.07151i | −0.0412900 | + | 0.0715164i | −0.885932 | − | 0.463815i | \(-0.846480\pi\) |
0.844642 | + | 0.535332i | \(0.179813\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.3486 | + | 19.6564i | 0.391333 | + | 0.677808i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.20080 | − | 20.3710i | −0.144683 | − | 0.701614i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.5662 | + | 18.3011i | 0.363487 | + | 0.629577i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.3935 | + | 19.7667i | −0.425845 | + | 0.679193i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12.7385 | + | 11.3305i | −0.437186 | + | 0.388861i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.4647 | −0.598683 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.33998 | + | 14.4453i | −0.285556 | + | 0.494597i | −0.972744 | − | 0.231883i | \(-0.925511\pi\) |
0.687188 | + | 0.726479i | \(0.258845\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.15019 | + | 9.79669i | −0.0393355 | + | 0.335040i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.92580 | + | 11.9958i | 0.236581 | + | 0.409770i | 0.959731 | − | 0.280921i | \(-0.0906399\pi\) |
−0.723150 | + | 0.690691i | \(0.757307\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.2472 | − | 41.9974i | 0.827304 | − | 1.43293i | −0.0728414 | − | 0.997344i | \(-0.523207\pi\) |
0.900146 | − | 0.435589i | \(-0.143460\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17.6545 | + | 6.57802i | 0.601664 | + | 0.224178i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.96541 | − | 5.13624i | −0.100944 | − | 0.174840i | 0.811130 | − | 0.584866i | \(-0.198853\pi\) |
−0.912074 | + | 0.410026i | \(0.865520\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −41.7385 | + | 72.2932i | −1.41915 | + | 2.45804i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −43.1443 | − | 14.3088i | −1.46526 | − | 0.485953i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.45813 | + | 14.6499i | 0.286922 | + | 0.496964i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.7756 | − | 22.1280i | −0.432885 | − | 0.749779i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 31.6959 | + | 23.6221i | 1.07274 | + | 0.799488i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −36.0679 | − | 1.31446i | −1.21932 | − | 0.0444368i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.96472 | + | 3.40300i | −0.0663439 | + | 0.114911i | −0.897289 | − | 0.441443i | \(-0.854467\pi\) |
0.830945 | + | 0.556354i | \(0.187800\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 35.2149 | + | 11.6790i | 1.18777 | + | 0.393923i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37.6552 | 1.26864 | 0.634318 | − | 0.773072i | \(-0.281281\pi\) | ||||
0.634318 | + | 0.773072i | \(0.281281\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 53.2334 | 1.79145 | 0.895723 | − | 0.444613i | \(-0.146659\pi\) | ||||
0.895723 | + | 0.444613i | \(0.146659\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.94251 | − | 43.3650i | −0.300599 | − | 1.45770i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18.4938 | + | 32.0322i | −0.620961 | + | 1.07554i | 0.368346 | + | 0.929689i | \(0.379924\pi\) |
−0.989307 | + | 0.145848i | \(0.953409\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.55308 | − | 0.275264i | −0.253322 | − | 0.00923206i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.79961 | + | 12.7393i | 0.127292 | + | 0.426784i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.10507 | + | 5.37815i | 0.103907 | + | 0.179973i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.617454 | − | 1.06946i | −0.0206392 | − | 0.0357482i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −21.9691 | + | 19.5407i | −0.733525 | + | 0.652443i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.54944 | + | 14.8081i | −0.285140 | + | 0.493877i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.5549 | + | 18.2817i | 0.351636 | + | 0.609052i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.00942653 | − | 0.0559423i | −0.000313695 | − | 0.00186164i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −42.9937 | + | 74.4673i | −1.42916 | + | 2.47538i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.5080 | − | 33.7888i | −0.647752 | − | 1.12194i | −0.983659 | − | 0.180044i | \(-0.942376\pi\) |
0.335907 | − | 0.941895i | \(-0.390957\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −14.4777 | + | 6.23623i | −0.480195 | + | 0.206843i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.8090 | − | 22.1859i | 0.424382 | − | 0.735052i | −0.571980 | − | 0.820267i | \(-0.693825\pi\) |
0.996363 | + | 0.0852158i | \(0.0271580\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.61312 | 0.218862 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.41961 | − | 35.9800i | −0.245285 | − | 1.18946i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.218810 | + | 0.348986i | −0.00722574 | + | 0.0115245i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.3367 | − | 17.9038i | −0.340978 | − | 0.590591i | 0.643637 | − | 0.765331i | \(-0.277425\pi\) |
−0.984615 | + | 0.174740i | \(0.944091\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.36033 | − | 6.54674i | 0.242531 | − | 0.215723i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.37636 | − | 12.7762i | −0.242796 | − | 0.420535i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.0643 | + | 20.8960i | −0.396672 | + | 0.687055i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.00797 | − | 2.98704i | −0.131639 | − | 0.0981071i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.74033 | −0.122716 | −0.0613582 | − | 0.998116i | \(-0.519543\pi\) | ||||
−0.0613582 | + | 0.998116i | \(0.519543\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.71015 | + | 5.59980i | 0.0888215 | + | 0.183526i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15.1687 | − | 13.4920i | 0.496600 | − | 0.441707i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 17.9680 | − | 31.1214i | 0.587615 | − | 1.01778i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.1345 | −0.886445 | −0.443223 | − | 0.896412i | \(-0.646165\pi\) | ||||
−0.443223 | + | 0.896412i | \(0.646165\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −34.6501 | + | 30.8200i | −1.13076 | + | 1.00577i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.32870 | 0.206310 | 0.103155 | − | 0.994665i | \(-0.467106\pi\) | ||||
0.103155 | + | 0.994665i | \(0.467106\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −25.8516 | −0.841844 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −50.7977 | + | 2.54535i | −1.65245 | + | 0.0828004i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −31.2792 | −1.01644 | −0.508218 | − | 0.861228i | \(-0.669696\pi\) | ||||
−0.508218 | + | 0.861228i | \(0.669696\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 32.5723 | 1.05734 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.46217 | − | 2.19001i | 0.0798414 | − | 0.0710160i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.28937 | 0.138946 | 0.0694732 | − | 0.997584i | \(-0.477868\pi\) | ||||
0.0694732 | + | 0.997584i | \(0.477868\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −30.1916 | + | 52.2933i | −0.976977 | + | 1.69217i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.79920 | + | 4.26871i | −0.155136 | + | 0.137988i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.22548 | − | 7.97622i | −0.136448 | − | 0.257566i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.3883 | 0.496395 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 29.6606 | − | 12.7762i | 0.955800 | − | 0.411708i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 26.4920 | − | 45.8854i | 0.852806 | − | 1.47710i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.59201 | + | 13.1497i | 0.244142 | + | 0.422867i | 0.961890 | − | 0.273436i | \(-0.0881602\pi\) |
−0.717748 | + | 0.696303i | \(0.754827\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.56360 | − | 6.72755i | 0.242978 | − | 0.216120i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.62364 | − | 2.81223i | −0.0521052 | − | 0.0902489i | 0.838796 | − | 0.544445i | \(-0.183260\pi\) |
−0.890902 | + | 0.454196i | \(0.849926\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.7335 | − | 31.5869i | −0.536450 | − | 1.01263i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.20396 | + | 39.7836i | 0.262737 | + | 1.27409i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.5439 | 0.497295 | 0.248647 | − | 0.968594i | \(-0.420014\pi\) | ||||
0.248647 | + | 0.968594i | \(0.420014\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.55563 | + | 11.3547i | −0.209519 | + | 0.362897i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.454888 | + | 0.339016i | 0.0145235 | + | 0.0108240i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.19158 | + | 10.7241i | 0.197481 | + | 0.342047i | 0.947711 | − | 0.319130i | \(-0.103391\pi\) |
−0.750230 | + | 0.661177i | \(0.770057\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.48398 | + | 7.76648i | −0.142871 | + | 0.247461i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −24.6854 | + | 20.3960i | −0.785745 | + | 0.649211i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.0389218 | + | 0.0674145i | 0.00123764 | + | 0.00214366i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.32760 | − | 5.76358i | 0.105705 | − | 0.183086i | −0.808321 | − | 0.588742i | \(-0.799623\pi\) |
0.914026 | + | 0.405656i | \(0.132957\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.20513 | + | 6.40869i | −0.228648 | + | 0.203374i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.3047 | + | 19.5803i | 0.358383 | + | 0.620738i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.40104 | − | 4.15872i | −0.0760417 | − | 0.131708i | 0.825497 | − | 0.564406i | \(-0.190895\pi\) |
−0.901539 | + | 0.432698i | \(0.857562\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.10940 | + | 13.0753i | −0.193293 | + | 0.413683i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))