Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2646,2,Mod(1549,2646)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2646, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2646.1549");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2646.e (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: | \(21.1284163748\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2125.1 | ||
Root | \(0.500000 - 0.224437i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2646.2125 |
Dual form | 2646.2.e.o.1549.1 |
$q$-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 \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −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 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.84981 | − | 3.20397i | 0.584963 | − | 1.01318i | ||||
\(11\) | −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 | 0.990233 | − | 0.139425i | \(-0.0445253\pi\) |
−0.615862 | + | 0.787854i | \(0.711192\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 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 | \(0.800827\pi\) | |||||||
\(20\) | −1.84981 | + | 3.20397i | −0.413631 | + | 0.716430i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.738550 | + | 1.27921i | 0.157459 | + | 0.272728i | ||||
\(23\) | 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 | ||||
\(26\) | −1.34981 | − | 2.33795i | −0.264720 | − | 0.458509i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.25526 | + | 2.17417i | −0.233096 | + | 0.403734i | −0.958718 | − | 0.284360i | \(-0.908219\pi\) |
0.725622 | + | 0.688094i | \(0.241552\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.81089 | −1.22327 | −0.611636 | − | 0.791139i | \(-0.709488\pi\) | ||||
−0.611636 | + | 0.791139i | \(0.709488\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.28799 | + | 5.69497i | −0.563886 | + | 0.976679i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.38874 | − | 2.40536i | −0.228307 | − | 0.395439i | 0.729000 | − | 0.684514i | \(-0.239986\pi\) |
−0.957306 | + | 0.289075i | \(0.906652\pi\) | |||||||
\(38\) | −0.444368 | − | 0.769668i | −0.0720860 | − | 0.124857i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.84981 | − | 3.20397i | 0.292481 | − | 0.506592i | ||||
\(41\) | −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 | −0.865553 | − | 0.500817i | \(-0.833033\pi\) |
0.866497 | + | 0.499182i | \(0.166366\pi\) | |||||||
\(44\) | −0.738550 | − | 1.27921i | −0.111341 | − | 0.192848i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.14400 | + | 5.44556i | −0.463557 | + | 0.802904i | ||||
\(47\) | −6.98762 | −1.01925 | −0.509625 | − | 0.860397i | \(-0.670216\pi\) | ||||
−0.509625 | + | 0.860397i | \(0.670216\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.34362 | + | 7.52338i | 0.614281 | + | 1.06397i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.34981 | + | 2.33795i | 0.187186 | + | 0.324215i | ||||
\(53\) | 1.60507 | − | 2.78007i | 0.220474 | − | 0.381872i | −0.734478 | − | 0.678632i | \(-0.762573\pi\) |
0.954952 | + | 0.296760i | \(0.0959063\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.46472 | 0.736863 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.25526 | − | 2.17417i | 0.164824 | − | 0.285483i | ||||
\(59\) | 6.90978 | 0.899576 | 0.449788 | − | 0.893135i | \(-0.351499\pi\) | ||||
0.449788 | + | 0.893135i | \(0.351499\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.73305 | 0.734042 | 0.367021 | − | 0.930213i | \(-0.380378\pi\) | ||||
0.367021 | + | 0.930213i | \(0.380378\pi\) | |||||||
\(62\) | 6.81089 | 0.864984 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −9.98762 | −1.23881 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.46472 | −1.15630 | −0.578150 | − | 0.815931i | \(-0.696225\pi\) | ||||
−0.578150 | + | 0.815931i | \(0.696225\pi\) | |||||||
\(68\) | 3.28799 | − | 5.69497i | 0.398728 | − | 0.690616i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 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 | \(-0.583796\pi\) |
0.966301 | − | 0.257414i | \(-0.0828705\pi\) | |||||||
\(74\) | 1.38874 | + | 2.40536i | 0.161437 | + | 0.279618i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.444368 | + | 0.769668i | 0.0509725 | + | 0.0882870i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.4523 | 1.28849 | 0.644244 | − | 0.764820i | \(-0.277172\pi\) | ||||
0.644244 | + | 0.764820i | \(0.277172\pi\) | |||||||
\(80\) | −1.84981 | + | 3.20397i | −0.206816 | + | 0.358215i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.05563 | + | 3.56046i | 0.227007 | + | 0.393187i | ||||
\(83\) | 2.23855 | − | 3.87728i | 0.245713 | − | 0.425587i | −0.716619 | − | 0.697465i | \(-0.754311\pi\) |
0.962332 | + | 0.271878i | \(0.0876447\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.1643 | + | 21.0693i | 1.31941 | + | 2.28528i | ||||
\(86\) | −0.00618986 | + | 0.0107211i | −0.000667469 | + | 0.00115609i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.738550 | + | 1.27921i | 0.0787297 | + | 0.136364i | ||||
\(89\) | −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 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.14400 | − | 5.44556i | 0.327784 | − | 0.567739i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.98762 | 0.720718 | ||||||||
\(95\) | −3.28799 | −0.337341 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.58836 | − | 11.4114i | 0.668947 | − | 1.15865i | −0.309252 | − | 0.950980i | \(-0.600079\pi\) |
0.978199 | − | 0.207670i | \(-0.0665880\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.34362 | − | 7.52338i | −0.434362 | − | 0.752338i | ||||
\(101\) | −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 | \(0.140508\pi\) | |||||||
\(104\) | −1.34981 | − | 2.33795i | −0.132360 | − | 0.229255i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.60507 | + | 2.78007i | −0.155899 | + | 0.270024i | ||||
\(107\) | 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 | \(0.169550\pi\) | |||||||
\(110\) | −5.46472 | −0.521041 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.78180 | + | 11.7464i | 0.637978 | + | 1.10501i | 0.985876 | + | 0.167478i | \(0.0535624\pi\) |
−0.347897 | + | 0.937533i | \(0.613104\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.6316 | + | 20.1466i | 1.08465 | + | 1.87868i | ||||
\(116\) | −1.25526 | + | 2.17417i | −0.116548 | + | 0.201867i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.90978 | −0.636097 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.40909 | − | 7.63676i | 0.400826 | − | 0.694251i | ||||
\(122\) | −5.73305 | −0.519046 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.81089 | −0.611636 | ||||||||
\(125\) | 13.6414 | 1.22013 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.85669 | −0.253490 | −0.126745 | − | 0.991935i | \(-0.540453\pi\) | ||||
−0.126745 | + | 0.991935i | \(0.540453\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 9.98762 | 0.875972 | ||||||||
\(131\) | −0.0778435 | + | 0.134829i | −0.00680122 | + | 0.0117801i | −0.869406 | − | 0.494098i | \(-0.835498\pi\) |
0.862605 | + | 0.505878i | \(0.168832\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 9.46472 | 0.817627 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.28799 | + | 5.69497i | −0.281943 | + | 0.488340i | ||||
\(137\) | −1.70582 | − | 2.95456i | −0.145738 | − | 0.252425i | 0.783910 | − | 0.620874i | \(-0.213222\pi\) |
−0.929648 | + | 0.368449i | \(0.879889\pi\) | |||||||
\(138\) | 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 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.46472 | −0.458589 | ||||||||
\(143\) | 1.99381 | − | 3.45338i | 0.166731 | − | 0.288786i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.64400 | − | 8.04364i | −0.385663 | − | 0.667988i | ||||
\(146\) | −6.03273 | + | 10.4490i | −0.499272 | + | 0.864765i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.38874 | − | 2.40536i | −0.114153 | − | 0.197719i | ||||
\(149\) | 0.166896 | − | 0.289073i | 0.0136727 | − | 0.0236818i | −0.859108 | − | 0.511794i | \(-0.828981\pi\) |
0.872781 | + | 0.488112i | \(0.162314\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.95489 | + | 17.2424i | 0.810117 | + | 1.40316i | 0.912781 | + | 0.408448i | \(0.133930\pi\) |
−0.102664 | + | 0.994716i | \(0.532737\pi\) | |||||||
\(152\) | −0.444368 | − | 0.769668i | −0.0360430 | − | 0.0624283i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.5989 | − | 21.8219i | 1.01197 | − | 1.75278i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.96286 | 0.555697 | 0.277848 | − | 0.960625i | \(-0.410379\pi\) | ||||
0.277848 | + | 0.960625i | \(0.410379\pi\) | |||||||
\(158\) | −11.4523 | −0.911099 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.84981 | − | 3.20397i | 0.146241 | − | 0.253296i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.03706 | + | 6.99240i | 0.316207 | + | 0.547687i | 0.979693 | − | 0.200502i | \(-0.0642572\pi\) |
−0.663486 | + | 0.748189i | \(0.730924\pi\) | |||||||
\(164\) | −2.05563 | − | 3.56046i | −0.160518 | − | 0.278025i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.23855 | + | 3.87728i | −0.173745 | + | 0.300935i | ||||
\(167\) | 9.74288 | + | 16.8752i | 0.753927 | + | 1.30584i | 0.945906 | + | 0.324440i | \(0.105176\pi\) |
−0.191979 | + | 0.981399i | \(0.561491\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.85600 | − | 4.94674i | 0.219693 | − | 0.380519i | ||||
\(170\) | −12.1643 | − | 21.0693i | −0.932963 | − | 1.61594i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.00618986 | − | 0.0107211i | 0.000471972 | − | 0.000817480i | ||||
\(173\) | 22.5636 | 1.71548 | 0.857740 | − | 0.514085i | \(-0.171868\pi\) | ||||
0.857740 | + | 0.514085i | \(0.171868\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.738550 | − | 1.27921i | −0.0556703 | − | 0.0964238i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.43818 | + | 7.68715i | 0.332656 | + | 0.576176i | ||||
\(179\) | −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 | \(-0.831915\pi\) | ||||
−0.863789 | + | 0.503853i | \(0.831915\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.14400 | + | 5.44556i | −0.231778 | + | 0.401452i | ||||
\(185\) | 10.2756 | 0.755478 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.71339 | −0.710313 | ||||||||
\(188\) | −6.98762 | −0.509625 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.28799 | 0.238536 | ||||||||
\(191\) | 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 | \(0.672371\pi\) | |||||||
\(194\) | −6.58836 | + | 11.4114i | −0.473017 | + | 0.819289i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.42402 | −0.172704 | −0.0863520 | − | 0.996265i | \(-0.527521\pi\) | ||||
−0.0863520 | + | 0.996265i | \(0.527521\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.05563 | − | 5.29251i | 0.216608 | − | 0.375176i | −0.737161 | − | 0.675717i | \(-0.763834\pi\) |
0.953769 | + | 0.300541i | \(0.0971673\pi\) | |||||||
\(200\) | 4.34362 | + | 7.52338i | 0.307141 | + | 0.531983i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.62729 | + | 4.55059i | 0.184855 | + | 0.320179i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.2101 | 1.06232 | ||||||||
\(206\) | −0.833104 | + | 1.44298i | −0.0580451 | + | 0.100537i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.34981 | + | 2.33795i | 0.0935928 | + | 0.162107i | ||||
\(209\) | 0.656376 | − | 1.13688i | 0.0454025 | − | 0.0786394i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.72253 | + | 9.91171i | 0.393955 | + | 0.682350i | 0.992967 | − | 0.118390i | \(-0.0377732\pi\) |
−0.599012 | + | 0.800740i | \(0.704440\pi\) | |||||||
\(212\) | 1.60507 | − | 2.78007i | 0.110237 | − | 0.190936i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.38255 | − | 9.32284i | −0.367943 | − | 0.637296i | ||||
\(215\) | 0.0229002 | + | 0.0396643i | 0.00156178 | + | 0.00270508i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.0945538 | − | 0.163772i | 0.00640399 | − | 0.0110920i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5.46472 | 0.368431 | ||||||||
\(221\) | 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 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.78180 | − | 11.7464i | −0.451119 | − | 0.781361i | ||||
\(227\) | −6.82760 | − | 11.8258i | −0.453164 | − | 0.784903i | 0.545417 | − | 0.838165i | \(-0.316371\pi\) |
−0.998581 | + | 0.0532622i | \(0.983038\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.68725 | − | 15.0468i | 0.574070 | − | 0.994318i | −0.422073 | − | 0.906562i | \(-0.638697\pi\) |
0.996142 | − | 0.0877555i | \(-0.0279694\pi\) | |||||||
\(230\) | −11.6316 | − | 20.1466i | −0.766966 | − | 1.32842i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.25526 | − | 2.17417i | 0.0824119 | − | 0.142742i | ||||
\(233\) | −7.62110 | − | 13.2001i | −0.499275 | − | 0.864769i | 0.500725 | − | 0.865606i | \(-0.333067\pi\) |
−1.00000 | 0.000837426i | \(0.999733\pi\) | ||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.9258 | − | 22.3881i | 0.843186 | − | 1.46044i | ||||
\(236\) | 6.90978 | 0.449788 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 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 | \(-0.877128\pi\) |
0.137150 | − | 0.990550i | \(-0.456206\pi\) | |||||||
\(242\) | −4.40909 | + | 7.63676i | −0.283427 | + | 0.490910i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.73305 | 0.367021 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.19963 | + | 2.07782i | −0.0763305 | + | 0.132208i | ||||
\(248\) | 6.81089 | 0.432492 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −13.6414 | −0.862761 | ||||||||
\(251\) | −12.1236 | −0.765238 | −0.382619 | − | 0.923906i | \(-0.624978\pi\) | ||||
−0.382619 | + | 0.923906i | \(0.624978\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.28799 | −0.583931 | ||||||||
\(254\) | 2.85669 | 0.179245 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 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 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −9.98762 | −0.619406 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.0778435 | − | 0.134829i | 0.00480919 | − | 0.00832976i | ||||
\(263\) | −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 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −9.46472 | −0.578150 | ||||||||
\(269\) | 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 | \(0.761622\pi\) | |||||||
\(272\) | 3.28799 | − | 5.69497i | 0.199364 | − | 0.345308i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.70582 | + | 2.95456i | 0.103052 | + | 0.178492i | ||||
\(275\) | −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 | \(0.745202\pi\) | |||||||
\(278\) | −6.75526 | − | 11.7005i | −0.405154 | − | 0.701747i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.00433 | + | 10.3998i | −0.358188 | + | 0.620400i | −0.987658 | − | 0.156624i | \(-0.949939\pi\) |
0.629470 | + | 0.777025i | \(0.283272\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.84294 | −0.585102 | −0.292551 | − | 0.956250i | \(-0.594504\pi\) | ||||
−0.292551 | + | 0.956250i | \(0.594504\pi\) | |||||||
\(284\) | 5.46472 | 0.324271 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.99381 | + | 3.45338i | −0.117896 | + | 0.204203i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.1218 | − | 22.7276i | −0.771870 | − | 1.33692i | ||||
\(290\) | 4.64400 | + | 8.04364i | 0.272705 | + | 0.472339i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.03273 | − | 10.4490i | 0.353039 | − | 0.611481i | ||||
\(293\) | 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 | ||||
\(296\) | 1.38874 | + | 2.40536i | 0.0807186 | + | 0.139809i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.166896 | + | 0.289073i | −0.00966804 | + | 0.0167455i | ||||
\(299\) | 16.9752 | 0.981704 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −9.95489 | − | 17.2424i | −0.572839 | − | 0.992187i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.444368 | + | 0.769668i | 0.0254862 | + | 0.0441435i | ||||
\(305\) | −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 | 0 | ||||||||
\(310\) | −12.5989 | + | 21.8219i | −0.715569 | + | 1.23940i | ||||
\(311\) | −11.7207 | −0.664618 | −0.332309 | − | 0.943171i | \(-0.607828\pi\) | ||||
−0.332309 | + | 0.943171i | \(0.607828\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.7738 | 1.51334 | 0.756671 | − | 0.653796i | \(-0.226824\pi\) | ||||
0.756671 | + | 0.653796i | \(0.226824\pi\) | |||||||
\(314\) | −6.96286 | −0.392937 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.4523 | 0.644244 | ||||||||
\(317\) | −1.90249 | −0.106855 | −0.0534273 | − | 0.998572i | \(-0.517015\pi\) | ||||
−0.0534273 | + | 0.998572i | \(0.517015\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.70829 | 0.207624 | ||||||||
\(320\) | −1.84981 | + | 3.20397i | −0.103408 | + | 0.179107i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.84431 | 0.325186 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.7262 | − | 20.3103i | 0.650451 | − | 1.12661i | ||||
\(326\) | −4.03706 | − | 6.99240i | −0.223592 | − | 0.387273i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.05563 | + | 3.56046i | 0.113503 | + | 0.196593i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.56732 | 0.306008 | 0.153004 | − | 0.988226i | \(-0.451105\pi\) | ||||
0.153004 | + | 0.988226i | \(0.451105\pi\) | |||||||
\(332\) | 2.23855 | − | 3.87728i | 0.122856 | − | 0.212794i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −9.74288 | − | 16.8752i | −0.533107 | − | 0.923368i | ||||
\(335\) | 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 | \(-0.538386\pi\) | |||||||
\(338\) | −2.85600 | + | 4.94674i | −0.155346 | + | 0.269067i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 12.1643 | + | 21.0693i | 0.659704 | + | 1.14264i | ||||
\(341\) | 5.03018 | + | 8.71253i | 0.272400 | + | 0.471810i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −0.00618986 | + | 0.0107211i | −0.000333735 | + | 0.000578045i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −22.5636 | −1.21303 | ||||||||
\(347\) | 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 | −0.646774 | − | 0.762682i | \(-0.723882\pi\) |
0.983889 | + | 0.178782i | \(0.0572156\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.738550 | + | 1.27921i | 0.0393648 | + | 0.0681819i | ||||
\(353\) | 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 | ||||
\(356\) | −4.43818 | − | 7.68715i | −0.235223 | − | 0.407418i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.166896 | − | 0.289073i | 0.00882074 | − | 0.0152780i | ||||
\(359\) | 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 | ||||
\(362\) | 23.2422 | 1.22158 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 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 | \(0.627097\pi\) | |||||||
\(368\) | 3.14400 | − | 5.44556i | 0.163892 | − | 0.283869i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −10.2756 | −0.534204 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.5822 | + | 25.2571i | −0.755036 | + | 1.30776i | 0.190320 | + | 0.981722i | \(0.439047\pi\) |
−0.945356 | + | 0.326039i | \(0.894286\pi\) | |||||||
\(374\) | 9.71339 | 0.502267 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.98762 | 0.360359 | ||||||||
\(377\) | −6.77747 | −0.349058 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.5622 | −0.696645 | −0.348322 | − | 0.937375i | \(-0.613249\pi\) | ||||
−0.348322 | + | 0.937375i | \(0.613249\pi\) | |||||||
\(380\) | −3.28799 | −0.168670 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −16.3214 | −0.835076 | ||||||||
\(383\) | 1.41783 | − | 2.45575i | 0.0724475 | − | 0.125483i | −0.827526 | − | 0.561428i | \(-0.810252\pi\) |
0.899973 | + | 0.435945i | \(0.143586\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14.3214 | 0.728941 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.58836 | − | 11.4114i | 0.334474 | − | 0.579325i | ||||
\(389\) | −9.30401 | − | 16.1150i | −0.471732 | − | 0.817064i | 0.527745 | − | 0.849403i | \(-0.323038\pi\) |
−0.999477 | + | 0.0323388i | \(0.989704\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −20.6749 | − | 35.8099i | −1.04557 | − | 1.81099i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.42402 | 0.122120 | ||||||||
\(395\) | −21.1847 | + | 36.6930i | −1.06592 | + | 1.84622i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.2880 | + | 17.8193i | 0.516340 | + | 0.894326i | 0.999820 | + | 0.0189712i | \(0.00603907\pi\) |
−0.483481 | + | 0.875355i | \(0.660628\pi\) | |||||||
\(398\) | −3.05563 | + | 5.29251i | −0.153165 | + | 0.265290i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.34362 | − | 7.52338i | −0.217181 | − | 0.376169i | ||||
\(401\) | −3.37704 | + | 5.84921i | −0.168642 | + | 0.292096i | −0.937942 | − | 0.346791i | \(-0.887271\pi\) |
0.769301 | + | 0.638887i | \(0.220605\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.19344 | − | 15.9235i | −0.457958 | − | 0.793206i | ||||
\(404\) | −2.62729 | − | 4.55059i | −0.130712 | − | 0.226400i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.05130 | + | 3.55296i | −0.101679 | + | 0.176114i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.3214 | −0.757595 | −0.378798 | − | 0.925480i | \(-0.623662\pi\) | ||||
−0.378798 | + | 0.925480i | \(0.623662\pi\) | |||||||
\(410\) | −15.2101 | −0.751176 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.833104 | − | 1.44298i | 0.0410441 | − | 0.0710904i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.28180 | + | 14.3445i | 0.406538 | + | 0.704144i | ||||
\(416\) | −1.34981 | − | 2.33795i | −0.0661801 | − | 0.114627i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.656376 | + | 1.13688i | −0.0321044 | + | 0.0556064i | ||||
\(419\) | −4.32141 | − | 7.48491i | −0.211115 | − | 0.365662i | 0.740949 | − | 0.671561i | \(-0.234376\pi\) |
−0.952064 | + | 0.305900i | \(0.901043\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.5636 | − | 32.1531i | 0.904735 | − | 1.56705i | 0.0834618 | − | 0.996511i | \(-0.473402\pi\) |
0.821273 | − | 0.570536i | \(-0.193264\pi\) | |||||||
\(422\) | −5.72253 | − | 9.91171i | −0.278568 | − | 0.482494i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.60507 | + | 2.78007i | −0.0779493 | + | 0.135012i | ||||
\(425\) | −57.1272 | −2.77108 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 5.38255 | + | 9.32284i | 0.260175 | + | 0.450637i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.0229002 | − | 0.0396643i | −0.00110434 | − | 0.00191278i | ||||
\(431\) | 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 | \(-0.498403\pi\) | ||||
0.00501645 | + | 0.999987i | \(0.498403\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.0945538 | + | 0.163772i | −0.00452831 | + | 0.00784326i | ||||
\(437\) | 5.58836 | 0.267328 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.96796 | 0.475745 | 0.237872 | − | 0.971296i | \(-0.423550\pi\) | ||||
0.237872 | + | 0.971296i | \(0.423550\pi\) | |||||||
\(440\) | −5.46472 | −0.260520 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −17.7527 | −0.844410 | ||||||||
\(443\) | 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 | ||||||||
\(446\) | −3.61126 | + | 6.25489i | −0.170998 | + | 0.296178i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −33.6253 | −1.58688 | −0.793439 | − | 0.608650i | \(-0.791712\pi\) | ||||
−0.793439 | + | 0.608650i | \(0.791712\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.03637 | + | 5.25915i | −0.142977 | + | 0.247644i | ||||
\(452\) | 6.78180 | + | 11.7464i | 0.318989 | + | 0.552505i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.82760 | + | 11.8258i | 0.320435 | + | 0.555010i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.7083 | 1.53003 | 0.765015 | − | 0.644013i | \(-0.222732\pi\) | ||||
0.765015 | + | 0.644013i | \(0.222732\pi\) | |||||||
\(458\) | −8.68725 | + | 15.0468i | −0.405928 | + | 0.703089i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 11.6316 | + | 20.1466i | 0.542327 | + | 0.939338i | ||||
\(461\) | −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 | 0.604462 | − | 0.796634i | \(-0.293388\pi\) |
−0.992136 | + | 0.125162i | \(0.960055\pi\) | |||||||
\(464\) | −1.25526 | + | 2.17417i | −0.0582740 | + | 0.100934i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.62110 | + | 13.2001i | 0.353040 | + | 0.611484i | ||||
\(467\) | 14.9585 | + | 25.9089i | 0.692198 | + | 1.19892i | 0.971116 | + | 0.238608i | \(0.0766909\pi\) |
−0.278918 | + | 0.960315i | \(0.589976\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −12.9258 | + | 22.3881i | −0.596223 | + | 1.03269i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.90978 | −0.318048 | ||||||||
\(473\) | −0.0182861 | −0.000840794 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.86033 | − | 6.68630i | 0.177124 | − | 0.306788i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9.47524 | + | 16.4116i | 0.433387 | + | 0.750649i | ||||
\(479\) | 1.47965 | + | 2.56283i | 0.0676068 | + | 0.117098i | 0.897847 | − | 0.440307i | \(-0.145130\pi\) |
−0.830241 | + | 0.557405i | \(0.811797\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.74907 | − | 6.49358i | 0.170943 | − | 0.296082i | ||||
\(482\) | 12.2527 | + | 21.2223i | 0.558096 | + | 0.966650i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.40909 | − | 7.63676i | 0.200413 | − | 0.347126i | ||||
\(485\) | 24.3745 | + | 42.2179i | 1.10679 | + | 1.91701i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.0309 | + | 24.3022i | −0.635800 | + | 1.10124i | 0.350546 | + | 0.936546i | \(0.385996\pi\) |
−0.986345 | + | 0.164691i | \(0.947337\pi\) | |||||||
\(488\) | −5.73305 | −0.259523 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 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 | ||||
\(494\) | 1.19963 | − | 2.07782i | 0.0539738 | − | 0.0934854i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.81089 | −0.305818 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.14035 | − | 1.97515i | 0.0510493 | − | 0.0884199i | −0.839372 | − | 0.543558i | \(-0.817077\pi\) |
0.890421 | + | 0.455138i | \(0.150410\pi\) | |||||||
\(500\) | 13.6414 | 0.610064 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.1236 | 0.541105 | ||||||||
\(503\) | 13.9890 | 0.623739 | 0.311869 | − | 0.950125i | \(-0.399045\pi\) | ||||
0.311869 | + | 0.950125i | \(0.399045\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.4400 | 0.865067 | ||||||||
\(506\) | 9.28799 | 0.412902 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.85669 | −0.126745 | ||||||||
\(509\) | −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 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.10439 | + | 7.10900i | −0.181037 | + | 0.313565i | ||||
\(515\) | 3.08217 | + | 5.33848i | 0.135817 | + | 0.235242i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.16071 | + | 8.93861i | 0.226968 | + | 0.393119i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.98762 | 0.437986 | ||||||||
\(521\) | −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 | \(0.945356\pi\) | |||||||
\(524\) | −0.0778435 | + | 0.134829i | −0.00340061 | + | 0.00589003i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.67309 | + | 4.62992i | 0.116552 | + | 0.201874i | ||||
\(527\) | −22.3942 | + | 38.7878i | −0.975505 | + | 1.68962i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.26942 | − | 14.3231i | −0.359540 | − | 0.622742i | ||||
\(530\) | −5.93818 | − | 10.2852i | −0.257938 | − | 0.446762i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.54944 | − | 9.61192i | 0.240373 | − | 0.416338i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −39.8268 | −1.72186 | ||||||||
\(536\) | 9.46472 | 0.408814 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −9.24219 | + | 16.0079i | −0.398459 | + | 0.690152i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.0963 | − | 36.5399i | −0.907002 | − | 1.57097i | −0.818207 | − | 0.574924i | \(-0.805031\pi\) |
−0.0887957 | − | 0.996050i | \(-0.528302\pi\) | |||||||
\(542\) | −3.67742 | − | 6.36947i | −0.157959 | − | 0.273592i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.28799 | + | 5.69497i | −0.140971 | + | 0.244170i | ||||
\(545\) | −0.349814 | − | 0.605896i | −0.0149844 | − | 0.0259537i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.3356 | − | 35.2222i | 0.869486 | − | 1.50599i | 0.00696400 | − | 0.999976i | \(-0.497783\pi\) |
0.862522 | − | 0.506019i | \(-0.168883\pi\) | |||||||
\(548\) | −1.70582 | − | 2.95456i | −0.0728689 | − | 0.126213i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.41597 | − | 11.1128i | 0.273578 | − | 0.473851i | ||||
\(551\) | −2.23119 | −0.0950519 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −4.54944 | − | 7.87987i | −0.193287 | − | 0.334783i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.75526 | + | 11.7005i | 0.286487 | + | 0.496210i | ||||
\(557\) | −6.68794 | + | 11.5838i | −0.283377 | + | 0.490823i | −0.972214 | − | 0.234093i | \(-0.924788\pi\) |
0.688837 | + | 0.724916i | \(0.258121\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.0334206 | 0.00141354 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.00433 | − | 10.3998i | 0.253277 | − | 0.438689i | ||||
\(563\) | −32.7614 | −1.38073 | −0.690364 | − | 0.723463i | \(-0.742549\pi\) | ||||
−0.690364 | + | 0.723463i | \(0.742549\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −50.1803 | −2.11110 | ||||||||
\(566\) | 9.84294 | 0.413729 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.46472 | −0.229295 | ||||||||
\(569\) | 16.7280 | 0.701272 | 0.350636 | − | 0.936512i | \(-0.385965\pi\) | ||||
0.350636 | + | 0.936512i | \(0.385965\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.4734 | −1.14973 | −0.574863 | − | 0.818250i | \(-0.694945\pi\) | ||||
−0.574863 | + | 0.818250i | \(0.694945\pi\) | |||||||
\(572\) | 1.99381 | − | 3.45338i | 0.0833654 | − | 0.144393i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −54.6253 | −2.27803 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.41714 | + | 2.45455i | −0.0589962 | + | 0.102184i | −0.894015 | − | 0.448037i | \(-0.852123\pi\) |
0.835019 | + | 0.550221i | \(0.185457\pi\) | |||||||
\(578\) | 13.1218 | + | 22.7276i | 0.545794 | + | 0.945343i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.64400 | − | 8.04364i | −0.192831 | − | 0.333994i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.74171 | −0.196382 | ||||||||
\(584\) | −6.03273 | + | 10.4490i | −0.249636 | + | 0.432383i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.7101 | − | 18.5505i | −0.442432 | − | 0.766315i | ||||
\(587\) | −2.34795 | + | 4.06678i | −0.0969105 | + | 0.167854i | −0.910404 | − | 0.413720i | \(-0.864229\pi\) |
0.813494 | + | 0.581573i | \(0.197563\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.02654 | − | 5.24212i | −0.124706 | − | 0.215998i | ||||
\(590\) | 12.7818 | − | 22.1387i | 0.526218 | − | 0.911437i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.38874 | − | 2.40536i | −0.0570767 | − | 0.0988597i | ||||
\(593\) | 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 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.166896 | − | 0.289073i | 0.00683634 | − | 0.0118409i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −16.9752 | −0.694169 | ||||||||
\(599\) | −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 | −0.695908 | − | 0.718131i | \(-0.744998\pi\) |
0.969874 | + | 0.243609i | \(0.0783314\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 9.95489 | + | 17.2424i | 0.405059 | + | 0.701582i | ||||
\(605\) | 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 | \(0.196326\pi\) | |||||||
\(608\) | −0.444368 | − | 0.769668i | −0.0180215 | − | 0.0312142i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 10.6051 | − | 18.3685i | 0.429387 | − | 0.743720i | ||||
\(611\) | −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 | \(0.313981\pi\) | |||||||
\(614\) | −5.68725 | −0.229519 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.00433 | − | 10.3998i | −0.241725 | − | 0.418680i | 0.719481 | − | 0.694513i | \(-0.244380\pi\) |
−0.961206 | + | 0.275832i | \(0.911047\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.78180 | − | 15.2105i | −0.352970 | − | 0.611363i | 0.633798 | − | 0.773499i | \(-0.281495\pi\) |
−0.986768 | + | 0.162136i | \(0.948162\pi\) | |||||||
\(620\) | 12.5989 | − | 21.8219i | 0.505983 | − | 0.876389i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 11.7207 | 0.469956 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.51602 | + | 6.08993i | −0.140641 | + | 0.243597i | ||||
\(626\) | −26.7738 | −1.07009 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.96286 | 0.277848 | ||||||||
\(629\) | −18.2646 | −0.728258 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −44.9381 | −1.78896 | −0.894479 | − | 0.447110i | \(-0.852453\pi\) | ||||
−0.894479 | + | 0.447110i | \(0.852453\pi\) | |||||||
\(632\) | −11.4523 | −0.455550 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.90249 | 0.0755576 | ||||||||
\(635\) | 5.28435 | − | 9.15276i | 0.209703 | − | 0.363216i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −3.70829 | −0.146813 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.84981 | − | 3.20397i | 0.0731203 | − | 0.126648i | ||||
\(641\) | −14.4920 | − | 25.1008i | −0.572398 | − | 0.991422i | −0.996319 | − | 0.0857228i | \(-0.972680\pi\) |
0.423921 | − | 0.905699i | \(-0.360653\pi\) | |||||||
\(642\) | 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 | 0 | ||||||||
\(646\) | −5.84431 | −0.229941 | ||||||||
\(647\) | 18.8825 | − | 32.7055i | 0.742349 | − | 1.28579i | −0.209073 | − | 0.977900i | \(-0.567045\pi\) |
0.951423 | − | 0.307887i | \(-0.0996219\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.10322 | − | 8.83903i | −0.200319 | − | 0.346962i | ||||
\(650\) | −11.7262 | + | 20.3103i | −0.459938 | + | 0.796636i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.03706 | + | 6.99240i | 0.158104 | + | 0.273843i | ||||
\(653\) | 18.7040 | − | 32.3962i | 0.731942 | − | 1.26776i | −0.224109 | − | 0.974564i | \(-0.571947\pi\) |
0.956052 | − | 0.293198i | \(-0.0947194\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.287992 | − | 0.498817i | −0.0112528 | − | 0.0194904i | ||||
\(656\) | −2.05563 | − | 3.56046i | −0.0802589 | − | 0.139013i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 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 | \(-0.534785\pi\) | ||||
−0.109063 | + | 0.994035i | \(0.534785\pi\) | |||||||
\(662\) | −5.56732 | −0.216380 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.23855 | + | 3.87728i | −0.0868726 | + | 0.150468i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.89307 | + | 13.6712i | 0.305621 | + | 0.529351i | ||||
\(668\) | 9.74288 | + | 16.8752i | 0.376963 | + | 0.652920i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −17.5080 | + | 30.3247i | −0.676392 | + | 1.17155i | ||||
\(671\) | −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 | \(0.224937\pi\) | |||||||
\(674\) | 16.8869 | + | 29.2489i | 0.650458 | + | 1.12663i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.85600 | − | 4.94674i | 0.109846 | − | 0.190259i | ||||
\(677\) | 11.0617 | 0.425137 | 0.212569 | − | 0.977146i | \(-0.431817\pi\) | ||||
0.212569 | + | 0.977146i | \(0.431817\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −12.1643 | − | 21.0693i | −0.466481 | − | 0.807970i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5.03018 | − | 8.71253i | −0.192616 | − | 0.333620i | ||||
\(683\) | 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 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.00618986 | − | 0.0107211i | 0.000235986 | − | 0.000408740i | ||||
\(689\) | 8.66621 | 0.330156 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.0617 | −0.953394 | −0.476697 | − | 0.879068i | \(-0.658166\pi\) | ||||
−0.476697 | + | 0.879068i | \(0.658166\pi\) | |||||||
\(692\) | 22.5636 | 0.857740 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −30.4065 | −1.15422 | ||||||||
\(695\) | −49.9839 | −1.89600 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −27.0356 | −1.02405 | ||||||||
\(698\) | −6.29782 | + | 10.9082i | −0.238376 | + | 0.412880i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 43.4858 | 1.64243 | 0.821217 | − | 0.570616i | \(-0.193295\pi\) | ||||
0.821217 | + | 0.570616i | \(0.193295\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.23422 | − | 2.13773i | 0.0465495 | − | 0.0806260i | ||||
\(704\) | −0.738550 | − | 1.27921i | −0.0278351 | − | 0.0482119i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.76578 | − | 6.52252i | −0.141727 | − | 0.245478i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.7403 | −0.854031 | −0.427016 | − | 0.904244i | \(-0.640435\pi\) | ||||
−0.427016 | + | 0.904244i | \(0.640435\pi\) | |||||||
\(710\) | 10.1087 | − | 17.5088i | 0.379373 | − | 0.657094i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.43818 | + | 7.68715i | 0.166328 | + | 0.288088i | ||||
\(713\) | −21.4134 | + | 37.0891i | −0.801939 | + | 1.38900i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.37636 | + | 12.7762i | 0.275860 | + | 0.477804i | ||||
\(716\) | −0.166896 | + | 0.289073i | −0.00623721 | + | 0.0108032i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.44801 | − | 5.97213i | −0.128679 | − | 0.222878i | ||||
\(719\) | 6.06182 | + | 10.4994i | 0.226068 | + | 0.391561i | 0.956639 | − | 0.291275i | \(-0.0940796\pi\) |
−0.730571 | + | 0.682836i | \(0.760746\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −9.10507 | + | 15.7705i | −0.338856 | + | 0.586915i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −23.2422 | −0.863789 | ||||||||
\(725\) | 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 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −22.3189 | − | 38.6574i | −0.826058 | − | 1.43077i | ||||
\(731\) | −0.0407044 | − | 0.0705021i | −0.00150551 | − | 0.00260761i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.0149 | + | 31.2026i | −0.665394 | + | 1.15250i | 0.313785 | + | 0.949494i | \(0.398403\pi\) |
−0.979178 | + | 0.203002i | \(0.934930\pi\) | |||||||
\(734\) | −11.5618 | − | 20.0257i | −0.426755 | − | 0.739161i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.14400 | + | 5.44556i | −0.115889 | + | 0.200726i | ||||
\(737\) | 6.99017 | + | 12.1073i | 0.257486 | + | 0.445979i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.2119 | − | 40.2042i | 0.853865 | − | 1.47894i | −0.0238296 | − | 0.999716i | \(-0.507586\pi\) |
0.877694 | − | 0.479221i | \(-0.159081\pi\) | |||||||
\(740\) | 10.2756 | 0.377739 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 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 | ||||
\(746\) | 14.5822 | − | 25.2571i | 0.533891 | − | 0.924727i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −9.71339 | −0.355157 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.0600 | + | 41.6731i | −0.877961 | + | 1.52067i | −0.0243853 | + | 0.999703i | \(0.507763\pi\) |
−0.853575 | + | 0.520970i | \(0.825570\pi\) | |||||||
\(752\) | −6.98762 | −0.254812 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.77747 | 0.246821 | ||||||||
\(755\) | −73.6588 | −2.68072 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 49.6006 | 1.80276 | 0.901382 | − | 0.433025i | \(-0.142554\pi\) | ||||
0.901382 | + | 0.433025i | \(0.142554\pi\) | |||||||
\(758\) | 13.5622 | 0.492602 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.28799 | 0.119268 | ||||||||
\(761\) | 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 | 0 | ||||||||
\(764\) | 16.3214 | 0.590488 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.41783 | + | 2.45575i | −0.0512281 | + | 0.0887297i | ||||
\(767\) | 9.32691 | + | 16.1547i | 0.336775 | + | 0.583312i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.4592 | + | 23.3121i | 0.485352 | + | 0.840654i | 0.999858 | − | 0.0168324i | \(-0.00535818\pi\) |
−0.514506 | + | 0.857486i | \(0.672025\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −14.3214 | −0.515439 | ||||||||
\(773\) | 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 | ||||
\(776\) | −6.58836 | + | 11.4114i | −0.236508 | + | 0.409645i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.30401 | + | 16.1150i | 0.333565 | + | 0.577752i | ||||
\(779\) | 1.82691 | − | 3.16431i | 0.0654560 | − | 0.113373i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.03597 | − | 6.99050i | −0.144418 | − | 0.250140i | ||||
\(782\) | 20.6749 | + | 35.8099i | 0.739332 | + | 1.28056i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 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 | \(0.490587\pi\) | |||||||
\(788\) | −2.42402 | −0.0863520 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 21.1847 | − | 36.6930i | 0.753718 | − | 1.30548i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.73855 | + | 13.4036i | 0.274804 | + | 0.475974i | ||||
\(794\) | −10.2880 | − | 17.8193i | −0.365107 | − | 0.632384i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.05563 | − | 5.29251i | 0.108304 | − | 0.187588i | ||||
\(797\) | −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 | ||||
\(800\) | 4.34362 | + | 7.52338i | 0.153570 | + | 0.265992i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.37704 | − | 5.84921i | 0.119248 | − | 0.206543i | ||||
\(803\) | −17.8219 | −0.628921 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9.19344 | + | 15.9235i | 0.323825 | + | 0.560881i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.62729 | + | 4.55059i | 0.0924276 | + | 0.160089i | ||||
\(809\) | 1.44251 | − | 2.49850i | 0.0507159 | − | 0.0878425i | −0.839553 | − | 0.543278i | \(-0.817183\pi\) |
0.890269 | + | 0.455435i | \(0.150516\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.5461 | −1.00239 | −0.501195 | − | 0.865334i | \(-0.667106\pi\) | ||||
−0.501195 | + | 0.865334i | \(0.667106\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.05130 | − | 3.55296i | 0.0718981 | − | 0.124531i | ||||
\(815\) | −29.8713 | −1.04634 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.0110023 | 0.000384922 | ||||||||
\(818\) | 15.3214 | 0.535701 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 15.2101 | 0.531161 | ||||||||
\(821\) | −7.96658 | −0.278036 | −0.139018 | − | 0.990290i | \(-0.544395\pi\) | ||||
−0.139018 | + | 0.990290i | \(0.544395\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.5461 | 1.41335 | 0.706675 | − | 0.707539i | \(-0.250194\pi\) | ||||
0.706675 | + | 0.707539i | \(0.250194\pi\) | |||||||
\(824\) | −0.833104 | + | 1.44298i | −0.0290225 | + | 0.0502685i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 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 | −0.716603 | − | 0.697481i | \(-0.754304\pi\) |
0.962338 | + | 0.271856i | \(0.0876373\pi\) | |||||||
\(830\) | −8.28180 | − | 14.3445i | −0.287466 | − | 0.497905i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.34981 | + | 2.33795i | 0.0467964 | + | 0.0810537i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −72.0901 | −2.49478 | ||||||||
\(836\) | 0.656376 | − | 1.13688i | 0.0227012 | − | 0.0393197i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.32141 | + | 7.48491i | 0.149281 | + | 0.258562i | ||||
\(839\) | 1.19599 | − | 2.07151i | 0.0412900 | − | 0.0715164i | −0.844642 | − | 0.535332i | \(-0.820187\pi\) |
0.885932 | + | 0.463815i | \(0.153520\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.3486 | + | 19.6564i | 0.391333 | + | 0.677808i | ||||
\(842\) | −18.5636 | + | 32.1531i | −0.639744 | + | 1.10807i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.72253 | + | 9.91171i | 0.196978 | + | 0.341175i | ||||
\(845\) | 10.5662 | + | 18.3011i | 0.363487 | + | 0.629577i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.60507 | − | 2.78007i | 0.0551185 | − | 0.0954680i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 57.1272 | 1.95945 | ||||||||
\(851\) | −17.4647 | −0.598683 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.33998 | − | 14.4453i | 0.285556 | − | 0.494597i | −0.687188 | − | 0.726479i | \(-0.741155\pi\) |
0.972744 | + | 0.231883i | \(0.0744886\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.38255 | − | 9.32284i | −0.183972 | − | 0.318648i | ||||
\(857\) | 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 | \(-0.143460\pi\) | |||||||
\(860\) | 0.0229002 | + | 0.0396643i | 0.000780889 | + | 0.00135254i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.71015 | + | 8.15822i | −0.160428 | + | 0.277870i | ||||
\(863\) | −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 | ||||
\(866\) | −0.208771 | −0.00709433 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.45813 | − | 14.6499i | −0.286922 | − | 0.496964i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.7756 | − | 22.1280i | −0.432885 | − | 0.749779i | ||||
\(872\) | 0.0945538 | − | 0.163772i | 0.00320200 | − | 0.00554602i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.58836 | −0.189029 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.96472 | + | 3.40300i | −0.0663439 | + | 0.114911i | −0.897289 | − | 0.441443i | \(-0.854467\pi\) |
0.830945 | + | 0.556354i | \(0.187800\pi\) | |||||||
\(878\) | −9.96796 | −0.336402 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5.46472 | 0.184216 | ||||||||
\(881\) | 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 | \(-0.853341\pi\) | ||||
−0.895723 | + | 0.444613i | \(0.853341\pi\) | |||||||
\(884\) | 17.7527 | 0.597088 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.6996 | −0.527439 | ||||||||
\(887\) | 18.4938 | − | 32.0322i | 0.620961 | − | 1.07554i | −0.368346 | − | 0.929689i | \(-0.620076\pi\) |
0.989307 | − | 0.145848i | \(-0.0465910\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −32.8392 | −1.10077 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.61126 | − | 6.25489i | 0.120914 | − | 0.209429i | ||||
\(893\) | −3.10507 | − | 5.37815i | −0.103907 | − | 0.179973i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.617454 | − | 1.06946i | −0.0206392 | − | 0.0357482i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 33.6253 | 1.12209 | ||||||||
\(899\) | 8.54944 | − | 14.8081i | 0.285140 | − | 0.493877i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.5549 | − | 18.2817i | −0.351636 | − | 0.609052i | ||||
\(902\) | 3.03637 | − | 5.25915i | 0.101100 | − | 0.175111i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.78180 | − | 11.7464i | −0.225559 | − | 0.390680i | ||||
\(905\) | 42.9937 | − | 74.4673i | 1.42916 | − | 2.47538i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19.5080 | + | 33.7888i | 0.647752 | + | 1.12194i | 0.983659 | + | 0.180044i | \(0.0576239\pi\) |
−0.335907 | + | 0.941895i | \(0.609043\pi\) | |||||||
\(908\) | −6.82760 | − | 11.8258i | −0.226582 | − | 0.392451i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 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 | ||||||||
\(914\) | −32.7083 | −1.08189 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.68725 | − | 15.0468i | 0.287035 | − | 0.497159i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.3367 | + | 17.9038i | 0.340978 | + | 0.590591i | 0.984615 | − | 0.174740i | \(-0.0559086\pi\) |
−0.643637 | + | 0.765331i | \(0.722575\pi\) | |||||||
\(920\) | −11.6316 | − | 20.1466i | −0.383483 | − | 0.664212i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.07165 | − | 3.58821i | 0.0682263 | − | 0.118171i | ||||
\(923\) | 7.37636 | + | 12.7762i | 0.242796 | + | 0.420535i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.0643 | + | 20.8960i | −0.396672 | + | 0.687055i | ||||
\(926\) | 8.34176 | + | 14.4484i | 0.274127 | + | 0.474803i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.25526 | − | 2.17417i | 0.0412059 | − | 0.0713708i | ||||
\(929\) | −3.74033 | −0.122716 | −0.0613582 | − | 0.998116i | \(-0.519543\pi\) | ||||
−0.0613582 | + | 0.998116i | \(0.519543\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −7.62110 | − | 13.2001i | −0.249637 | − | 0.432384i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −14.9585 | − | 25.9089i | −0.489458 | − | 0.847766i | ||||
\(935\) | 17.9680 | − | 31.1214i | 0.587615 | − | 1.01778i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.1345 | 0.886445 | 0.443223 | − | 0.896412i | \(-0.353835\pi\) | ||||
0.443223 | + | 0.896412i | \(0.353835\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 12.9258 | − | 22.3881i | 0.421593 | − | 0.730221i | ||||
\(941\) | 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 | ||||||||
\(944\) | 6.90978 | 0.224894 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.0182861 | 0.000594531 | ||||||||
\(947\) | −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 | ||||||||
\(950\) | −3.86033 | + | 6.68630i | −0.125246 | + | 0.216932i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.28937 | −0.138946 | −0.0694732 | − | 0.997584i | \(-0.522132\pi\) | ||||
−0.0694732 | + | 0.997584i | \(0.522132\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −30.1916 | + | 52.2933i | −0.976977 | + | 1.69217i | ||||
\(956\) | −9.47524 | − | 16.4116i | −0.306451 | − | 0.530789i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.47965 | − | 2.56283i | −0.0478053 | − | 0.0828011i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.3883 | 0.496395 | ||||||||
\(962\) | −3.74907 | + | 6.49358i | −0.120875 | + | 0.209361i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −12.2527 | − | 21.2223i | −0.394633 | − | 0.683525i | ||||
\(965\) | 26.4920 | − | 45.8854i | 0.852806 | − | 1.47710i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.59201 | − | 13.1497i | −0.244142 | − | 0.422867i | 0.717748 | − | 0.696303i | \(-0.245173\pi\) |
−0.961890 | + | 0.273436i | \(0.911840\pi\) | |||||||
\(968\) | −4.40909 | + | 7.63676i | −0.141713 | + | 0.245455i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −24.3745 | − | 42.2179i | −0.782618 | − | 1.35553i | ||||
\(971\) | 1.62364 | + | 2.81223i | 0.0521052 | + | 0.0902489i | 0.890902 | − | 0.454196i | \(-0.150074\pi\) |
−0.838796 | + | 0.544445i | \(0.816740\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 14.0309 | − | 24.3022i | 0.449578 | − | 0.778692i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.73305 | 0.183510 | ||||||||
\(977\) | −15.5439 | −0.497295 | −0.248647 | − | 0.968594i | \(-0.579986\pi\) | ||||
−0.248647 | + | 0.968594i | \(0.579986\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.55563 | + | 11.3547i | −0.209519 | + | 0.362897i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 17.0734 | + | 29.5721i | 0.544835 | + | 0.943682i | ||||
\(983\) | −6.19158 | − | 10.7241i | −0.197481 | − | 0.342047i | 0.750230 | − | 0.661177i | \(-0.229943\pi\) |
−0.947711 | + | 0.319130i | \(0.896609\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.48398 | − | 7.76648i | 0.142871 | − | 0.247461i | ||||
\(986\) | −8.25457 | − | 14.2973i | −0.262879 | − | 0.455320i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.19963 | + | 2.07782i | −0.0381653 | + | 0.0661042i | ||||
\(989\) | −0.0389218 | − | 0.0674145i | −0.00123764 | − | 0.00214366i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.32760 | + | 5.76358i | −0.105705 | + | 0.183086i | −0.914026 | − | 0.405656i | \(-0.867043\pi\) |
0.808321 | + | 0.588742i | \(0.200377\pi\) | |||||||
\(992\) | 6.81089 | 0.216246 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.3047 | + | 19.5803i | 0.358383 | + | 0.620738i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.40104 | + | 4.15872i | 0.0760417 | + | 0.131708i | 0.901539 | − | 0.432698i | \(-0.142438\pi\) |
−0.825497 | + | 0.564406i | \(0.809105\pi\) | |||||||
\(998\) | −1.14035 | + | 1.97515i | −0.0360973 | + | 0.0625223i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))