Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [117,4,Mod(10,117)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(117, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("117.10");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 117 = 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 117.q (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.90322347067\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 70x^{8} + 1645x^{6} + 14700x^{4} + 44100x^{2} + 27648 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 82.2 | ||
Root | \(-3.27897i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 117.82 |
Dual form | 117.4.q.e.10.2 |
$q$-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 \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(92\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.83967 | − | 1.63949i | −1.00398 | − | 0.579646i | −0.0945542 | − | 0.995520i | \(-0.530143\pi\) |
−0.909422 | + | 0.415874i | \(0.863476\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.37583 | + | 2.38302i | 0.171979 | + | 0.297877i | ||||
\(5\) | − | 17.5414i | − | 1.56895i | −0.620160 | − | 0.784476i | \(-0.712932\pi\) | ||
0.620160 | − | 0.784476i | \(-0.287068\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 23.1228 | − | 13.3499i | 1.24851 | − | 0.720829i | 0.277700 | − | 0.960668i | \(-0.410428\pi\) |
0.970813 | + | 0.239838i | \(0.0770944\pi\) | |||||||
\(8\) | 17.2091i | 0.760544i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −28.7589 | + | 49.8119i | −0.909437 | + | 1.57519i | ||||
\(11\) | 18.5352 | + | 10.7013i | 0.508051 | + | 0.293324i | 0.732032 | − | 0.681270i | \(-0.238572\pi\) |
−0.223981 | + | 0.974594i | \(0.571905\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −8.67555 | − | 46.0623i | −0.185090 | − | 0.982722i | ||||
\(14\) | −87.5483 | −1.67130 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 39.2208 | − | 67.9325i | 0.612826 | − | 1.06144i | ||||
\(17\) | −41.9815 | − | 72.7141i | −0.598942 | − | 1.03740i | −0.992978 | − | 0.118302i | \(-0.962255\pi\) |
0.394036 | − | 0.919095i | \(-0.371078\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −66.7828 | + | 38.5571i | −0.806370 | + | 0.465558i | −0.845694 | − | 0.533669i | \(-0.820813\pi\) |
0.0393237 | + | 0.999227i | \(0.487480\pi\) | |||||||
\(20\) | 41.8015 | − | 24.1341i | 0.467354 | − | 0.269827i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −35.0892 | − | 60.7763i | −0.340048 | − | 0.588980i | ||||
\(23\) | −71.0597 | + | 123.079i | −0.644216 | + | 1.11581i | 0.340266 | + | 0.940329i | \(0.389483\pi\) |
−0.984482 | + | 0.175486i | \(0.943850\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −182.701 | −1.46161 | ||||||||
\(26\) | −50.8828 | + | 145.025i | −0.383805 | + | 1.09392i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 63.6263 | + | 36.7346i | 0.429437 | + | 0.247936i | ||||
\(29\) | 67.1115 | − | 116.241i | 0.429734 | − | 0.744322i | −0.567115 | − | 0.823639i | \(-0.691941\pi\) |
0.996849 | + | 0.0793167i | \(0.0252739\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 122.559i | 0.710074i | 0.934852 | + | 0.355037i | \(0.115532\pi\) | ||||
−0.934852 | + | 0.355037i | \(0.884468\pi\) | |||||||
\(32\) | −103.520 | + | 59.7675i | −0.571875 | + | 0.330172i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 275.312i | 1.38870i | ||||||||
\(35\) | −234.177 | − | 405.606i | −1.13095 | − | 1.95886i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −192.766 | − | 111.294i | −0.856502 | − | 0.494502i | 0.00633725 | − | 0.999980i | \(-0.497983\pi\) |
−0.862839 | + | 0.505478i | \(0.831316\pi\) | |||||||
\(38\) | 252.855 | 1.07944 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 301.873 | 1.19326 | ||||||||
\(41\) | 171.751 | + | 99.1604i | 0.654219 | + | 0.377713i | 0.790071 | − | 0.613016i | \(-0.210044\pi\) |
−0.135852 | + | 0.990729i | \(0.543377\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 77.3279 | + | 133.936i | 0.274242 | + | 0.475000i | 0.969944 | − | 0.243330i | \(-0.0782398\pi\) |
−0.695702 | + | 0.718331i | \(0.744907\pi\) | |||||||
\(44\) | 58.8928i | 0.201782i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 403.573 | − | 233.003i | 1.29356 | − | 0.746835i | ||||
\(47\) | − | 78.7956i | − | 0.244543i | −0.992497 | − | 0.122271i | \(-0.960982\pi\) | ||
0.992497 | − | 0.122271i | \(-0.0390178\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 184.942 | − | 320.329i | 0.539190 | − | 0.933905i | ||||
\(50\) | 518.811 | + | 299.536i | 1.46742 | + | 0.847216i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 97.8310 | − | 84.0481i | 0.260899 | − | 0.224142i | ||||
\(53\) | 477.088 | 1.23647 | 0.618237 | − | 0.785992i | \(-0.287847\pi\) | ||||
0.618237 | + | 0.785992i | \(0.287847\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 187.716 | − | 325.133i | 0.460210 | − | 0.797108i | ||||
\(56\) | 229.741 | + | 397.923i | 0.548222 | + | 0.949549i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −381.150 | + | 220.057i | −0.862887 | + | 0.498188i | ||||
\(59\) | −37.1769 | + | 21.4641i | −0.0820342 | + | 0.0473625i | −0.540456 | − | 0.841372i | \(-0.681748\pi\) |
0.458422 | + | 0.888735i | \(0.348415\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −248.269 | − | 430.015i | −0.521109 | − | 0.902587i | −0.999699 | − | 0.0245485i | \(-0.992185\pi\) |
0.478590 | − | 0.878039i | \(-0.341148\pi\) | |||||||
\(62\) | 200.934 | − | 348.028i | 0.411592 | − | 0.712897i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −235.581 | −0.460119 | ||||||||
\(65\) | −807.998 | + | 152.181i | −1.54184 | + | 0.290396i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 419.727 | + | 242.329i | 0.765340 | + | 0.441869i | 0.831210 | − | 0.555959i | \(-0.187649\pi\) |
−0.0658696 | + | 0.997828i | \(0.520982\pi\) | |||||||
\(68\) | 115.519 | − | 200.085i | 0.206011 | − | 0.356822i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1535.72i | 2.62219i | ||||||||
\(71\) | −331.196 | + | 191.216i | −0.553602 | + | 0.319622i | −0.750574 | − | 0.660787i | \(-0.770223\pi\) |
0.196971 | + | 0.980409i | \(0.436889\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 193.622i | − | 0.310435i | −0.987880 | − | 0.155217i | \(-0.950392\pi\) | ||
0.987880 | − | 0.155217i | \(-0.0496078\pi\) | |||||||
\(74\) | 364.929 | + | 632.076i | 0.573272 | + | 0.992936i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −183.764 | − | 106.096i | −0.277358 | − | 0.160133i | ||||
\(77\) | 571.447 | 0.845745 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1049.60 | 1.49480 | 0.747399 | − | 0.664375i | \(-0.231302\pi\) | ||||
0.747399 | + | 0.664375i | \(0.231302\pi\) | |||||||
\(80\) | −1191.63 | − | 687.989i | −1.66536 | − | 0.961493i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −325.144 | − | 563.166i | −0.437880 | − | 0.758431i | ||||
\(83\) | − | 861.900i | − | 1.13983i | −0.821704 | − | 0.569914i | \(-0.806976\pi\) | ||
0.821704 | − | 0.569914i | \(-0.193024\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1275.51 | + | 736.414i | −1.62763 | + | 0.939710i | ||||
\(86\) | − | 507.112i | − | 0.635853i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −184.160 | + | 318.974i | −0.223085 | + | 0.386395i | ||||
\(89\) | −838.005 | − | 483.823i | −0.998072 | − | 0.576237i | −0.0903946 | − | 0.995906i | \(-0.528813\pi\) |
−0.907677 | + | 0.419669i | \(0.862146\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −815.532 | − | 949.271i | −0.939461 | − | 1.09352i | ||||
\(92\) | −391.065 | −0.443167 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −129.184 | + | 223.754i | −0.141748 | + | 0.245515i | ||||
\(95\) | 676.345 | + | 1171.46i | 0.730438 | + | 1.26516i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 512.228 | − | 295.735i | 0.536174 | − | 0.309560i | −0.207353 | − | 0.978266i | \(-0.566485\pi\) |
0.743527 | + | 0.668706i | \(0.233152\pi\) | |||||||
\(98\) | −1050.35 | + | 606.421i | −1.08267 | + | 0.625079i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −251.366 | − | 435.379i | −0.251366 | − | 0.435379i | ||||
\(101\) | −127.555 | + | 220.932i | −0.125665 | + | 0.217659i | −0.921993 | − | 0.387207i | \(-0.873440\pi\) |
0.796328 | + | 0.604866i | \(0.206773\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 247.355 | 0.236627 | 0.118313 | − | 0.992976i | \(-0.462251\pi\) | ||||
0.118313 | + | 0.992976i | \(0.462251\pi\) | |||||||
\(104\) | 792.692 | − | 149.299i | 0.747403 | − | 0.140769i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1354.77 | − | 782.180i | −1.24139 | − | 0.716717i | ||||
\(107\) | 341.742 | − | 591.914i | 0.308761 | − | 0.534790i | −0.669331 | − | 0.742965i | \(-0.733419\pi\) |
0.978092 | + | 0.208175i | \(0.0667523\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1697.76i | 1.49189i | 0.666006 | + | 0.745946i | \(0.268002\pi\) | ||||
−0.666006 | + | 0.745946i | \(0.731998\pi\) | |||||||
\(110\) | −1066.10 | + | 615.515i | −0.924081 | + | 0.533518i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 2094.38i | − | 1.76697i | ||||||
\(113\) | −190.354 | − | 329.703i | −0.158469 | − | 0.274477i | 0.775848 | − | 0.630920i | \(-0.217323\pi\) |
−0.934317 | + | 0.356443i | \(0.883989\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2158.98 | + | 1246.49i | 1.75066 | + | 1.01074i | ||||
\(116\) | 369.337 | 0.295622 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 140.760 | 0.109814 | ||||||||
\(119\) | −1941.46 | − | 1120.90i | −1.49557 | − | 0.863469i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −436.465 | − | 755.979i | −0.327923 | − | 0.567979i | ||||
\(122\) | 1628.14i | 1.20824i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −292.061 | + | 168.621i | −0.211515 | + | 0.122118i | ||||
\(125\) | 1012.16i | 0.724241i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 61.6157 | − | 106.722i | 0.0430513 | − | 0.0745670i | −0.843697 | − | 0.536820i | \(-0.819625\pi\) |
0.886748 | + | 0.462253i | \(0.152959\pi\) | |||||||
\(128\) | 1497.14 | + | 864.372i | 1.03382 | + | 0.596878i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2543.95 | + | 892.556i | 1.71630 | + | 0.602172i | ||||
\(131\) | 1218.41 | 0.812616 | 0.406308 | − | 0.913736i | \(-0.366816\pi\) | ||||
0.406308 | + | 0.913736i | \(0.366816\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1029.47 | + | 1783.09i | −0.671176 | + | 1.16251i | ||||
\(134\) | −794.592 | − | 1376.27i | −0.512256 | − | 0.887253i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1251.35 | − | 722.465i | 0.788986 | − | 0.455521i | ||||
\(137\) | 2363.24 | − | 1364.41i | 1.47376 | − | 0.850875i | 0.474194 | − | 0.880420i | \(-0.342739\pi\) |
0.999563 | + | 0.0295456i | \(0.00940602\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1556.39 | − | 2695.75i | −0.949722 | − | 1.64497i | −0.746009 | − | 0.665936i | \(-0.768032\pi\) |
−0.203713 | − | 0.979031i | \(-0.565301\pi\) | |||||||
\(140\) | 644.377 | − | 1116.09i | 0.388999 | − | 0.673766i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1253.99 | 0.741071 | ||||||||
\(143\) | 332.123 | − | 946.612i | 0.194220 | − | 0.553564i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2039.02 | − | 1177.23i | −1.16780 | − | 0.674232i | ||||
\(146\) | −317.441 | + | 549.823i | −0.179942 | + | 0.311669i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 612.487i | − | 0.340176i | ||||||
\(149\) | −1186.95 | + | 685.286i | −0.652609 | + | 0.376784i | −0.789455 | − | 0.613809i | \(-0.789637\pi\) |
0.136846 | + | 0.990592i | \(0.456303\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2847.56i | 1.53464i | 0.641263 | + | 0.767321i | \(0.278411\pi\) | ||||
−0.641263 | + | 0.767321i | \(0.721589\pi\) | |||||||
\(152\) | −663.534 | − | 1149.27i | −0.354077 | − | 0.613280i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1622.72 | − | 936.879i | −0.849108 | − | 0.490233i | ||||
\(155\) | 2149.86 | 1.11407 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3354.00 | 1.70496 | 0.852479 | − | 0.522761i | \(-0.175098\pi\) | ||||
0.852479 | + | 0.522761i | \(0.175098\pi\) | |||||||
\(158\) | −2980.52 | − | 1720.80i | −1.50074 | − | 0.866454i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1048.41 | + | 1815.89i | 0.518024 | + | 0.897244i | ||||
\(161\) | 3794.57i | 1.85748i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1901.95 | − | 1098.09i | 0.913941 | − | 0.527664i | 0.0322438 | − | 0.999480i | \(-0.489735\pi\) |
0.881697 | + | 0.471816i | \(0.156401\pi\) | |||||||
\(164\) | 545.713i | 0.259836i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1413.07 | + | 2447.51i | −0.660697 | + | 1.14436i | ||||
\(167\) | −790.279 | − | 456.268i | −0.366189 | − | 0.211419i | 0.305603 | − | 0.952159i | \(-0.401142\pi\) |
−0.671792 | + | 0.740740i | \(0.734475\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2046.47 | + | 799.231i | −0.931484 | + | 0.363783i | ||||
\(170\) | 4829.37 | 2.17880 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −212.781 | + | 368.547i | −0.0943278 | + | 0.163381i | ||||
\(173\) | −449.818 | − | 779.108i | −0.197682 | − | 0.342396i | 0.750094 | − | 0.661331i | \(-0.230008\pi\) |
−0.947777 | + | 0.318935i | \(0.896675\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4224.56 | + | 2439.05i | −1.82484 | + | 1.05357i | ||||
\(176\) | 1453.93 | − | 839.427i | 0.622694 | − | 0.359512i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1586.44 | + | 2747.80i | 0.668027 | + | 1.15706i | ||||
\(179\) | −156.639 | + | 271.307i | −0.0654064 | + | 0.113287i | −0.896874 | − | 0.442286i | \(-0.854168\pi\) |
0.831468 | + | 0.555573i | \(0.187501\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2745.06 | 1.12728 | 0.563642 | − | 0.826019i | \(-0.309400\pi\) | ||||
0.563642 | + | 0.826019i | \(0.309400\pi\) | |||||||
\(182\) | 759.529 | + | 4032.67i | 0.309341 | + | 1.64243i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2118.08 | − | 1222.88i | −0.848626 | − | 0.489954i | ||||
\(185\) | −1952.25 | + | 3381.39i | −0.775849 | + | 1.34381i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1797.02i | − | 0.702735i | ||||||
\(188\) | 187.771 | − | 108.410i | 0.0728437 | − | 0.0420563i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 4435.44i | − | 1.69358i | ||||||
\(191\) | 44.9340 | + | 77.8279i | 0.0170226 | + | 0.0294839i | 0.874411 | − | 0.485186i | \(-0.161248\pi\) |
−0.857389 | + | 0.514670i | \(0.827915\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 735.215 | + | 424.477i | 0.274207 | + | 0.158314i | 0.630798 | − | 0.775947i | \(-0.282728\pi\) |
−0.356591 | + | 0.934261i | \(0.616061\pi\) | |||||||
\(194\) | −1939.41 | −0.717741 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1017.80 | 0.370918 | ||||||||
\(197\) | 3761.90 | + | 2171.93i | 1.36053 | + | 0.785501i | 0.989694 | − | 0.143198i | \(-0.0457386\pi\) |
0.370834 | + | 0.928699i | \(0.379072\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1664.20 | − | 2882.48i | −0.592825 | − | 1.02680i | −0.993850 | − | 0.110736i | \(-0.964679\pi\) |
0.401024 | − | 0.916067i | \(-0.368654\pi\) | |||||||
\(200\) | − | 3144.13i | − | 1.11162i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 724.429 | − | 418.249i | 0.252330 | − | 0.145683i | ||||
\(203\) | − | 3583.74i | − | 1.23906i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1739.41 | − | 3012.75i | 0.592614 | − | 1.02644i | ||||
\(206\) | −702.406 | − | 405.535i | −0.237568 | − | 0.137160i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3469.39 | − | 1217.25i | −1.15653 | − | 0.405775i | ||||
\(209\) | −1650.44 | −0.546236 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2299.94 | − | 3983.62i | 0.750401 | − | 1.29973i | −0.197228 | − | 0.980358i | \(-0.563194\pi\) |
0.947629 | − | 0.319375i | \(-0.103473\pi\) | |||||||
\(212\) | 656.394 | + | 1136.91i | 0.212648 | + | 0.368317i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1940.87 | + | 1120.56i | −0.619978 | + | 0.357944i | ||||
\(215\) | 2349.42 | − | 1356.44i | 0.745253 | − | 0.430272i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1636.16 | + | 2833.91i | 0.511842 | + | 0.886537i | ||||
\(218\) | 2783.46 | − | 4821.09i | 0.864769 | − | 1.49782i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1033.06 | 0.316587 | ||||||||
\(221\) | −2985.16 | + | 2564.60i | −0.908615 | + | 0.780604i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2190.68 | + | 1264.79i | 0.657842 | + | 0.379806i | 0.791454 | − | 0.611228i | \(-0.209324\pi\) |
−0.133612 | + | 0.991034i | \(0.542658\pi\) | |||||||
\(224\) | −1595.79 | + | 2763.98i | −0.475996 | + | 0.824449i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1248.33i | 0.367425i | ||||||||
\(227\) | −32.2742 | + | 18.6335i | −0.00943661 | + | 0.00544823i | −0.504711 | − | 0.863288i | \(-0.668401\pi\) |
0.495274 | + | 0.868737i | \(0.335068\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4094.45i | 1.18152i | 0.806846 | + | 0.590762i | \(0.201173\pi\) | ||||
−0.806846 | + | 0.590762i | \(0.798827\pi\) | |||||||
\(230\) | −4087.20 | − | 7079.23i | −1.17175 | − | 2.02953i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2000.40 | + | 1154.93i | 0.566089 | + | 0.326832i | ||||
\(233\) | 1466.04 | 0.412205 | 0.206103 | − | 0.978530i | \(-0.433922\pi\) | ||||
0.206103 | + | 0.978530i | \(0.433922\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1382.19 | −0.383676 | ||||||||
\(236\) | −102.298 | − | 59.0621i | −0.0282164 | − | 0.0162907i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3675.41 | + | 6365.99i | 1.00101 | + | 1.73381i | ||||
\(239\) | 5520.53i | 1.49412i | 0.664759 | + | 0.747058i | \(0.268534\pi\) | ||||
−0.664759 | + | 0.747058i | \(0.731466\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2308.50 | + | 1332.81i | −0.617028 | + | 0.356241i | −0.775711 | − | 0.631088i | \(-0.782609\pi\) |
0.158683 | + | 0.987330i | \(0.449275\pi\) | |||||||
\(242\) | 2862.31i | 0.760316i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 683.155 | − | 1183.26i | 0.179240 | − | 0.310453i | ||||
\(245\) | −5619.03 | − | 3244.15i | −1.46525 | − | 0.845963i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2355.40 | + | 2741.67i | 0.606764 | + | 0.706267i | ||||
\(248\) | −2109.14 | −0.540042 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1659.42 | − | 2874.20i | 0.419803 | − | 0.727121i | ||||
\(251\) | −789.605 | − | 1367.64i | −0.198564 | − | 0.343922i | 0.749499 | − | 0.662005i | \(-0.230294\pi\) |
−0.948063 | + | 0.318083i | \(0.896961\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2634.21 | + | 1520.86i | −0.654590 | + | 0.377927i | ||||
\(254\) | −349.937 | + | 202.036i | −0.0864449 | + | 0.0499090i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1891.93 | − | 3276.92i | −0.461897 | − | 0.800029i | ||||
\(257\) | 1331.96 | − | 2307.01i | 0.323288 | − | 0.559952i | −0.657876 | − | 0.753126i | \(-0.728545\pi\) |
0.981164 | + | 0.193174i | \(0.0618783\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5943.06 | −1.42581 | ||||||||
\(260\) | −1474.32 | − | 1716.09i | −0.351667 | − | 0.409337i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3459.88 | − | 1997.56i | −0.815847 | − | 0.471030i | ||||
\(263\) | −1218.47 | + | 2110.45i | −0.285680 | + | 0.494812i | −0.972774 | − | 0.231756i | \(-0.925553\pi\) |
0.687094 | + | 0.726569i | \(0.258886\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 8368.80i | − | 1.93997i | ||||||
\(266\) | 5846.72 | − | 3375.61i | 1.34769 | − | 0.778089i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1333.62i | 0.303970i | ||||||||
\(269\) | −1341.59 | − | 2323.70i | −0.304083 | − | 0.526687i | 0.672974 | − | 0.739666i | \(-0.265017\pi\) |
−0.977057 | + | 0.212980i | \(0.931683\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3340.38 | − | 1928.57i | −0.748759 | − | 0.432296i | 0.0764866 | − | 0.997071i | \(-0.475630\pi\) |
−0.825245 | + | 0.564775i | \(0.808963\pi\) | |||||||
\(272\) | −6586.20 | −1.46819 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8947.76 | −1.97282 | ||||||||
\(275\) | −3386.40 | − | 1955.14i | −0.742572 | − | 0.428724i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 552.453 | + | 956.877i | 0.119833 | + | 0.207557i | 0.919701 | − | 0.392619i | \(-0.128431\pi\) |
−0.799868 | + | 0.600175i | \(0.795097\pi\) | |||||||
\(278\) | 10206.7i | 2.20201i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6980.14 | − | 4029.98i | 1.48980 | − | 0.860134i | ||||
\(281\) | 4982.58i | 1.05778i | 0.848691 | + | 0.528890i | \(0.177391\pi\) | ||||
−0.848691 | + | 0.528890i | \(0.822609\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1292.43 | − | 2238.55i | 0.271473 | − | 0.470205i | −0.697766 | − | 0.716326i | \(-0.745822\pi\) |
0.969239 | + | 0.246120i | \(0.0791558\pi\) | |||||||
\(284\) | −911.342 | − | 526.164i | −0.190416 | − | 0.109937i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2495.08 | + | 2143.56i | −0.515864 | + | 0.443186i | ||||
\(287\) | 5295.14 | 1.08907 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1068.39 | + | 1850.51i | −0.217462 | + | 0.376655i | ||||
\(290\) | 3860.11 | + | 6685.90i | 0.781632 | + | 1.35383i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 461.404 | − | 266.392i | 0.0924714 | − | 0.0533884i | ||||
\(293\) | −80.1491 | + | 46.2741i | −0.0159807 | + | 0.00922649i | −0.507969 | − | 0.861375i | \(-0.669604\pi\) |
0.491988 | + | 0.870602i | \(0.336270\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 376.510 | + | 652.135i | 0.0743094 | + | 0.128708i | ||||
\(296\) | 1915.27 | − | 3317.34i | 0.376090 | − | 0.651407i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4494.07 | 0.873605 | ||||||||
\(299\) | 6285.78 | + | 2205.39i | 1.21577 | + | 0.426559i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3576.07 | + | 2064.65i | 0.684789 | + | 0.395363i | ||||
\(302\) | 4668.53 | − | 8086.14i | 0.889549 | − | 1.54074i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6048.96i | 1.14122i | ||||||||
\(305\) | −7543.07 | + | 4355.00i | −1.41612 | + | 0.817595i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3979.46i | 0.739803i | 0.929071 | + | 0.369901i | \(0.120609\pi\) | ||||
−0.929071 | + | 0.369901i | \(0.879391\pi\) | |||||||
\(308\) | 786.216 | + | 1361.77i | 0.145451 | + | 0.251928i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6104.91 | − | 3524.67i | −1.11850 | − | 0.645767i | ||||
\(311\) | 3450.91 | 0.629207 | 0.314604 | − | 0.949223i | \(-0.398128\pi\) | ||||
0.314604 | + | 0.949223i | \(0.398128\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6189.03 | −1.11765 | −0.558825 | − | 0.829285i | \(-0.688748\pi\) | ||||
−0.558825 | + | 0.829285i | \(0.688748\pi\) | |||||||
\(314\) | −9524.27 | − | 5498.84i | −1.71174 | − | 0.988272i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1444.07 | + | 2501.21i | 0.257075 | + | 0.445266i | ||||
\(317\) | − | 5437.78i | − | 0.963459i | −0.876320 | − | 0.481729i | \(-0.840009\pi\) | ||
0.876320 | − | 0.481729i | \(-0.159991\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2487.85 | − | 1436.36i | 0.436654 | − | 0.252102i | ||||
\(320\) | 4132.42i | 0.721904i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6221.15 | − | 10775.3i | 1.07668 | − | 1.86487i | ||||
\(323\) | 5607.28 | + | 3237.37i | 0.965937 | + | 0.557684i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1585.03 | + | 8415.63i | 0.270528 | + | 1.43635i | ||||
\(326\) | −7201.23 | −1.22343 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1706.46 | + | 2955.68i | −0.287268 | + | 0.497562i | ||||
\(329\) | −1051.92 | − | 1821.97i | −0.176274 | − | 0.305315i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5738.84 | − | 3313.32i | 0.952976 | − | 0.550201i | 0.0589722 | − | 0.998260i | \(-0.481218\pi\) |
0.894004 | + | 0.448058i | \(0.147884\pi\) | |||||||
\(332\) | 2053.92 | − | 1185.83i | 0.339529 | − | 0.196027i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1496.09 | + | 2591.30i | 0.245097 | + | 0.424520i | ||||
\(335\) | 4250.80 | − | 7362.60i | 0.693271 | − | 1.20078i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5538.63 | 0.895277 | 0.447638 | − | 0.894215i | \(-0.352265\pi\) | ||||
0.447638 | + | 0.894215i | \(0.352265\pi\) | |||||||
\(338\) | 7121.64 | + | 1085.60i | 1.14605 | + | 0.174701i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3509.77 | − | 2026.37i | −0.559836 | − | 0.323221i | ||||
\(341\) | −1311.54 | + | 2271.66i | −0.208281 | + | 0.360754i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 717.813i | − | 0.112998i | ||||||
\(344\) | −2304.92 | + | 1330.75i | −0.361259 | + | 0.208573i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2949.88i | 0.458343i | ||||||||
\(347\) | 4699.47 | + | 8139.72i | 0.727034 | + | 1.25926i | 0.958131 | + | 0.286329i | \(0.0924350\pi\) |
−0.231098 | + | 0.972931i | \(0.574232\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4985.99 | + | 2878.66i | 0.764739 | + | 0.441522i | 0.830995 | − | 0.556280i | \(-0.187772\pi\) |
−0.0662555 | + | 0.997803i | \(0.521105\pi\) | |||||||
\(350\) | 15995.2 | 2.44279 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2558.36 | −0.387389 | ||||||||
\(353\) | 2994.56 | + | 1728.91i | 0.451514 | + | 0.260682i | 0.708470 | − | 0.705741i | \(-0.249386\pi\) |
−0.256955 | + | 0.966423i | \(0.582719\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3354.20 | + | 5809.65i | 0.501472 | + | 0.868575i | ||||
\(356\) | − | 2662.64i | − | 0.396403i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 889.607 | − | 513.615i | 0.131333 | − | 0.0758251i | ||||
\(359\) | − | 7168.96i | − | 1.05394i | −0.849885 | − | 0.526968i | \(-0.823329\pi\) | ||
0.849885 | − | 0.526968i | \(-0.176671\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −456.203 | + | 790.167i | −0.0665116 | + | 0.115202i | ||||
\(362\) | −7795.07 | − | 4500.49i | −1.13177 | − | 0.653426i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1140.09 | − | 3249.47i | 0.164167 | − | 0.467907i | ||||
\(365\) | −3396.40 | −0.487057 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1955.05 | + | 3386.25i | −0.278073 | + | 0.481637i | −0.970906 | − | 0.239461i | \(-0.923029\pi\) |
0.692832 | + | 0.721099i | \(0.256363\pi\) | |||||||
\(368\) | 5574.04 | + | 9654.52i | 0.789584 | + | 1.36760i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 11087.5 | − | 6401.37i | 1.55787 | − | 0.899436i | ||||
\(371\) | 11031.6 | − | 6369.10i | 1.54375 | − | 0.891286i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5688.80 | − | 9853.28i | −0.789691 | − | 1.36778i | −0.926156 | − | 0.377140i | \(-0.876908\pi\) |
0.136466 | − | 0.990645i | \(-0.456426\pi\) | |||||||
\(374\) | −2946.20 | + | 5102.96i | −0.407337 | + | 0.705529i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1356.00 | 0.185986 | ||||||||
\(377\) | −5936.54 | − | 2082.86i | −0.811001 | − | 0.284543i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3492.00 | + | 2016.11i | 0.473278 | + | 0.273247i | 0.717611 | − | 0.696444i | \(-0.245236\pi\) |
−0.244333 | + | 0.969691i | \(0.578569\pi\) | |||||||
\(380\) | −1861.08 | + | 3223.48i | −0.251240 | + | 0.435161i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 294.675i | − | 0.0394682i | ||||||
\(383\) | 1724.22 | − | 995.480i | 0.230035 | − | 0.132811i | −0.380553 | − | 0.924759i | \(-0.624266\pi\) |
0.610588 | + | 0.791948i | \(0.290933\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 10024.0i | − | 1.32693i | ||||||
\(386\) | −1391.85 | − | 2410.75i | −0.183532 | − | 0.317886i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1409.48 | + | 813.765i | 0.184422 | + | 0.106476i | ||||
\(389\) | −11122.4 | −1.44969 | −0.724846 | − | 0.688911i | \(-0.758089\pi\) | ||||
−0.724846 | + | 0.688911i | \(0.758089\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11932.8 | 1.54339 | ||||||||
\(392\) | 5512.59 | + | 3182.70i | 0.710275 | + | 0.410078i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7121.71 | − | 12335.2i | −0.910625 | − | 1.57725i | ||||
\(395\) | − | 18411.4i | − | 2.34527i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9334.12 | + | 5389.06i | −1.18002 | + | 0.681282i | −0.956018 | − | 0.293308i | \(-0.905244\pi\) |
−0.223997 | + | 0.974590i | \(0.571911\pi\) | |||||||
\(398\) | 10913.8i | 1.37452i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7165.69 | + | 12411.3i | −0.895711 | + | 1.55142i | ||||
\(401\) | 4080.35 | + | 2355.79i | 0.508137 | + | 0.293373i | 0.732067 | − | 0.681232i | \(-0.238556\pi\) |
−0.223931 | + | 0.974605i | \(0.571889\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5645.36 | − | 1063.27i | 0.697805 | − | 0.131427i | ||||
\(404\) | −701.978 | −0.0864473 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5875.50 | + | 10176.7i | −0.718217 | + | 1.24399i | ||||
\(407\) | −2381.97 | − | 4125.69i | −0.290098 | − | 0.502465i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1026.05 | − | 592.388i | 0.124046 | − | 0.0716179i | −0.436693 | − | 0.899611i | \(-0.643850\pi\) |
0.560739 | + | 0.827993i | \(0.310517\pi\) | |||||||
\(410\) | −9878.73 | + | 5703.49i | −1.18994 | + | 0.687013i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 340.319 | + | 589.450i | 0.0406949 | + | 0.0704857i | ||||
\(413\) | −573.089 | + | 992.619i | −0.0682805 | + | 0.118265i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15118.9 | −1.78834 | ||||||||
\(416\) | 3651.13 | + | 4249.87i | 0.430315 | + | 0.500882i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4686.72 | + | 2705.88i | 0.548409 | + | 0.316624i | ||||
\(419\) | −3084.15 | + | 5341.91i | −0.359596 | + | 0.622838i | −0.987893 | − | 0.155135i | \(-0.950419\pi\) |
0.628298 | + | 0.777973i | \(0.283752\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 10328.8i | − | 1.19571i | −0.801603 | − | 0.597857i | \(-0.796019\pi\) | ||
0.801603 | − | 0.597857i | \(-0.203981\pi\) | |||||||
\(422\) | −13062.2 | + | 7541.45i | −1.50677 | + | 0.869934i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8210.27i | 0.940392i | ||||||||
\(425\) | 7670.06 | + | 13284.9i | 0.875418 | + | 1.51627i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11481.4 | − | 6628.77i | −1.30122 | − | 0.751261i | ||||
\(428\) | 1880.72 | 0.212402 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8895.46 | −0.997622 | ||||||||
\(431\) | −9796.87 | − | 5656.23i | −1.09489 | − | 0.632137i | −0.160018 | − | 0.987114i | \(-0.551155\pi\) |
−0.934875 | + | 0.354977i | \(0.884489\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5237.87 | − | 9072.27i | −0.581331 | − | 1.00689i | −0.995322 | − | 0.0966135i | \(-0.969199\pi\) |
0.413991 | − | 0.910281i | \(-0.364134\pi\) | |||||||
\(434\) | − | 10729.8i | − | 1.18675i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4045.80 | + | 2335.84i | −0.444400 | + | 0.256575i | ||||
\(437\) | − | 10959.4i | − | 1.19968i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1020.31 | + | 1767.23i | −0.110926 | + | 0.192130i | −0.916144 | − | 0.400849i | \(-0.868715\pi\) |
0.805218 | + | 0.592979i | \(0.202048\pi\) | |||||||
\(440\) | 5595.26 | + | 3230.42i | 0.606235 | + | 0.350010i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 12681.5 | − | 2388.49i | 1.36470 | − | 0.257033i | ||||
\(443\) | 4089.28 | 0.438572 | 0.219286 | − | 0.975661i | \(-0.429627\pi\) | ||||
0.219286 | + | 0.975661i | \(0.429627\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8486.93 | + | 14699.8i | −0.904088 | + | 1.56593i | ||||
\(446\) | −4147.21 | − | 7183.19i | −0.440306 | − | 0.762632i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5447.29 | + | 3144.99i | −0.574465 | + | 0.331667i | ||||
\(449\) | −13179.1 | + | 7608.96i | −1.38521 | + | 0.799753i | −0.992771 | − | 0.120025i | \(-0.961703\pi\) |
−0.392441 | + | 0.919777i | \(0.628369\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2122.29 | + | 3675.91i | 0.221585 | + | 0.383796i | ||||
\(452\) | 523.792 | − | 907.235i | 0.0545069 | − | 0.0944087i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 122.197 | 0.0126322 | ||||||||
\(455\) | −16651.5 | + | 14305.6i | −1.71568 | + | 1.47397i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −758.912 | − | 438.158i | −0.0776814 | − | 0.0448494i | 0.460656 | − | 0.887579i | \(-0.347614\pi\) |
−0.538338 | + | 0.842729i | \(0.680947\pi\) | |||||||
\(458\) | 6712.80 | − | 11626.9i | 0.684865 | − | 1.18622i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6859.84i | 0.695308i | ||||||||
\(461\) | 14110.5 | − | 8146.69i | 1.42558 | − | 0.823057i | 0.428808 | − | 0.903396i | \(-0.358934\pi\) |
0.996768 | + | 0.0803390i | \(0.0256003\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 11704.8i | − | 1.17488i | −0.809269 | − | 0.587438i | \(-0.800137\pi\) | ||
0.809269 | − | 0.587438i | \(-0.199863\pi\) | |||||||
\(464\) | −5264.34 | − | 9118.11i | −0.526704 | − | 0.912279i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4163.09 | − | 2403.56i | −0.413844 | − | 0.238933i | ||||
\(467\) | −15616.1 | −1.54738 | −0.773688 | − | 0.633567i | \(-0.781590\pi\) | ||||
−0.773688 | + | 0.633567i | \(0.781590\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12940.3 | 1.27405 | ||||||||
\(470\) | 3924.96 | + | 2266.07i | 0.385202 | + | 0.222396i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −369.378 | − | 639.782i | −0.0360212 | − | 0.0623906i | ||||
\(473\) | 3310.03i | 0.321766i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12201.3 | − | 7044.42i | 1.17860 | − | 0.680463i | ||||
\(476\) | − | 6168.70i | − | 0.593996i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9050.84 | − | 15676.5i | 0.866058 | − | 1.50006i | ||||
\(479\) | −8985.90 | − | 5188.01i | −0.857153 | − | 0.494877i | 0.00590498 | − | 0.999983i | \(-0.498120\pi\) |
−0.863058 | + | 0.505105i | \(0.831454\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3454.09 | + | 9844.79i | −0.327428 | + | 0.933230i | ||||
\(482\) | 8740.53 | 0.825976 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1201.01 | − | 2080.21i | 0.112792 | − | 0.195361i | ||||
\(485\) | −5187.61 | − | 8985.20i | −0.485685 | − | 0.841231i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3459.14 | + | 1997.13i | −0.321865 | + | 0.185829i | −0.652224 | − | 0.758027i | \(-0.726164\pi\) |
0.330358 | + | 0.943856i | \(0.392830\pi\) | |||||||
\(488\) | 7400.19 | − | 4272.50i | 0.686457 | − | 0.396326i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 10637.5 | + | 18424.6i | 0.980719 | + | 1.69865i | ||||
\(491\) | −6133.65 | + | 10623.8i | −0.563763 | + | 0.976467i | 0.433400 | + | 0.901202i | \(0.357314\pi\) |
−0.997164 | + | 0.0752653i | \(0.976020\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11269.8 | −1.02954 | ||||||||
\(494\) | −2193.66 | − | 11647.1i | −0.199792 | − | 1.06078i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8325.75 | + | 4806.88i | 0.753704 | + | 0.435151i | ||||
\(497\) | −5105.45 | + | 8842.90i | −0.460786 | + | 0.798105i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 3578.76i | − | 0.321056i | −0.987031 | − | 0.160528i | \(-0.948680\pi\) | ||
0.987031 | − | 0.160528i | \(-0.0513198\pi\) | |||||||
\(500\) | −2411.99 | + | 1392.56i | −0.215735 | + | 0.124554i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5178.19i | 0.460386i | ||||||||
\(503\) | −648.409 | − | 1123.08i | −0.0574774 | − | 0.0995537i | 0.835855 | − | 0.548950i | \(-0.184972\pi\) |
−0.893332 | + | 0.449397i | \(0.851639\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3875.45 | + | 2237.49i | 0.341496 | + | 0.197163i | ||||
\(506\) | 9973.72 | 0.876257 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 339.092 | 0.0296157 | ||||||||
\(509\) | 4095.09 | + | 2364.30i | 0.356604 | + | 0.205886i | 0.667590 | − | 0.744529i | \(-0.267326\pi\) |
−0.310986 | + | 0.950415i | \(0.600659\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2584.84 | − | 4477.08i | −0.223771 | − | 0.387582i | ||||
\(512\) | − | 1422.78i | − | 0.122810i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7564.64 | + | 4367.45i | −0.649148 | + | 0.374786i | ||||
\(515\) | − | 4338.95i | − | 0.371256i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 843.214 | − | 1460.49i | 0.0717302 | − | 0.124240i | ||||
\(518\) | 16876.4 | + | 9743.57i | 1.43148 | + | 0.826463i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2618.91 | − | 13904.9i | −0.220859 | − | 1.17264i | ||||
\(521\) | 9220.74 | 0.775370 | 0.387685 | − | 0.921792i | \(-0.373275\pi\) | ||||
0.387685 | + | 0.921792i | \(0.373275\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6051.33 | − | 10481.2i | 0.505939 | − | 0.876313i | −0.494037 | − | 0.869441i | \(-0.664479\pi\) |
0.999976 | − | 0.00687187i | \(-0.00218740\pi\) | |||||||
\(524\) | 1676.33 | + | 2903.48i | 0.139753 | + | 0.242059i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6920.10 | − | 3995.32i | 0.573632 | − | 0.331187i | ||||
\(527\) | 8911.78 | − | 5145.22i | 0.736629 | − | 0.425293i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4015.45 | − | 6954.97i | −0.330028 | − | 0.571626i | ||||
\(530\) | −13720.5 | + | 23764.7i | −1.12449 | + | 1.94768i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5665.52 | −0.461713 | ||||||||
\(533\) | 3077.52 | − | 8771.51i | 0.250098 | − | 0.712826i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10383.0 | − | 5994.63i | −0.839059 | − | 0.484431i | ||||
\(536\) | −4170.28 | + | 7223.14i | −0.336061 | + | 0.582075i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8798.08i | 0.705041i | ||||||||
\(539\) | 6855.87 | − | 3958.24i | 0.547873 | − | 0.316314i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12801.3i | 1.01732i | 0.860968 | + | 0.508659i | \(0.169859\pi\) | ||||
−0.860968 | + | 0.508659i | \(0.830141\pi\) | |||||||
\(542\) | 6323.73 | + | 10953.0i | 0.501157 | + | 0.868030i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8691.88 | + | 5018.26i | 0.685039 | + | 0.395508i | ||||
\(545\) | 29781.2 | 2.34071 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 400.693 | 0.0313207 | 0.0156603 | − | 0.999877i | \(-0.495015\pi\) | ||||
0.0156603 | + | 0.999877i | \(0.495015\pi\) | |||||||
\(548\) | 6502.84 | + | 3754.42i | 0.506912 | + | 0.292666i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6410.84 | + | 11103.9i | 0.497017 | + | 0.860858i | ||||
\(551\) | 10350.5i | 0.800265i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24269.7 | − | 14012.1i | 1.86628 | − | 1.07750i | ||||
\(554\) | − | 3622.96i | − | 0.277843i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4282.67 | − | 7417.81i | 0.326665 | − | 0.565801i | ||||
\(557\) | 12536.2 | + | 7237.77i | 0.953636 | + | 0.550582i | 0.894209 | − | 0.447650i | \(-0.147739\pi\) |
0.0594277 | + | 0.998233i | \(0.481072\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5498.53 | − | 4723.87i | 0.416034 | − | 0.357421i | ||||
\(560\) | −36738.5 | −2.77229 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8168.88 | − | 14148.9i | 0.613138 | − | 1.06199i | ||||
\(563\) | 7388.18 | + | 12796.7i | 0.553063 | + | 0.957934i | 0.998051 | + | 0.0623972i | \(0.0198746\pi\) |
−0.444988 | + | 0.895536i | \(0.646792\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5783.46 | + | 3339.08i | −0.430641 | + | 0.248631i | ||||
\(566\) | −7340.16 | + | 4237.84i | −0.545106 | + | 0.314717i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3290.67 | − | 5699.60i | −0.243087 | − | 0.421039i | ||||
\(569\) | 3434.44 | − | 5948.63i | 0.253039 | − | 0.438277i | −0.711322 | − | 0.702866i | \(-0.751903\pi\) |
0.964361 | + | 0.264590i | \(0.0852365\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3011.00 | −0.220677 | −0.110338 | − | 0.993894i | \(-0.535193\pi\) | ||||
−0.110338 | + | 0.993894i | \(0.535193\pi\) | |||||||
\(572\) | 2712.74 | − | 510.927i | 0.198296 | − | 0.0373478i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −15036.5 | − | 8681.32i | −1.09340 | − | 0.631274i | ||||
\(575\) | 12982.7 | − | 22486.7i | 0.941591 | − | 1.63088i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23106.6i | 1.66714i | 0.552411 | + | 0.833572i | \(0.313708\pi\) | ||||
−0.552411 | + | 0.833572i | \(0.686292\pi\) | |||||||
\(578\) | 6067.76 | − | 3503.22i | 0.436653 | − | 0.252102i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 6478.70i | − | 0.463816i | ||||||
\(581\) | −11506.3 | − | 19929.5i | −0.821622 | − | 1.42309i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8842.91 | + | 5105.46i | 0.628192 | + | 0.362687i | ||||
\(584\) | 3332.07 | 0.236099 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 303.463 | 0.0213924 | ||||||||
\(587\) | −2619.56 | − | 1512.40i | −0.184192 | − | 0.106343i | 0.405069 | − | 0.914286i | \(-0.367248\pi\) |
−0.589261 | + | 0.807943i | \(0.700581\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4725.53 | − | 8184.85i | −0.330580 | − | 0.572582i | ||||
\(590\) | − | 2469.13i | − | 0.172293i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −15120.9 | + | 8730.06i | −1.04977 | + | 0.606087i | ||||
\(593\) | 6396.07i | 0.442926i | 0.975169 | + | 0.221463i | \(0.0710832\pi\) | ||||
−0.975169 | + | 0.221463i | \(0.928917\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −19662.2 | + | 34055.9i | −1.35474 | + | 2.34648i | ||||
\(596\) | −3266.09 | − | 1885.68i | −0.224470 | − | 0.129598i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −14233.9 | − | 16568.1i | −0.973354 | − | 1.13297i | ||||
\(599\) | −12095.9 | −0.825084 | −0.412542 | − | 0.910939i | \(-0.635359\pi\) | ||||
−0.412542 | + | 0.910939i | \(0.635359\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5908.25 | − | 10233.4i | 0.401003 | − | 0.694557i | −0.592845 | − | 0.805317i | \(-0.701995\pi\) |
0.993847 | + | 0.110760i | \(0.0353285\pi\) | |||||||
\(602\) | −6769.92 | − | 11725.8i | −0.458341 | − | 0.793870i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6785.77 | + | 3917.77i | −0.457134 | + | 0.263927i | ||||
\(605\) | −13260.9 | + | 7656.21i | −0.891131 | + | 0.514495i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12582.0 | + | 21792.6i | 0.841329 | + | 1.45722i | 0.888771 | + | 0.458351i | \(0.151560\pi\) |
−0.0474421 | + | 0.998874i | \(0.515107\pi\) | |||||||
\(608\) | 4608.92 | − | 7982.89i | 0.307428 | − | 0.532482i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 28559.8 | 1.89566 | ||||||||
\(611\) | −3629.50 | + | 683.595i | −0.240318 | + | 0.0452623i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16959.4 | + | 9791.51i | 1.11743 | + | 0.645148i | 0.940743 | − | 0.339120i | \(-0.110129\pi\) |
0.176685 | + | 0.984267i | \(0.443462\pi\) | |||||||
\(614\) | 6524.26 | − | 11300.4i | 0.428824 | − | 0.742745i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9834.10i | 0.643226i | ||||||||
\(617\) | 17040.8 | − | 9838.54i | 1.11189 | − | 0.641952i | 0.172575 | − | 0.984996i | \(-0.444791\pi\) |
0.939319 | + | 0.343044i | \(0.111458\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 4394.05i | − | 0.285318i | −0.989772 | − | 0.142659i | \(-0.954435\pi\) | ||
0.989772 | − | 0.142659i | \(-0.0455652\pi\) | |||||||
\(620\) | 2957.85 | + | 5123.15i | 0.191597 | + | 0.331856i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −9799.47 | − | 5657.73i | −0.631709 | − | 0.364717i | ||||
\(623\) | −25836.0 | −1.66147 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5082.96 | −0.325310 | ||||||||
\(626\) | 17574.8 | + | 10146.8i | 1.12210 | + | 0.647842i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4614.55 | + | 7992.64i | 0.293218 | + | 0.507868i | ||||
\(629\) | 18689.1i | 1.18471i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20687.3 | + | 11943.8i | −1.30515 | + | 0.753529i | −0.981282 | − | 0.192574i | \(-0.938316\pi\) |
−0.323867 | + | 0.946102i | \(0.604983\pi\) | |||||||
\(632\) | 18062.7i | 1.13686i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8915.18 | + | 15441.5i | −0.558465 | + | 0.967290i | ||||
\(635\) | −1872.05 | − | 1080.83i | −0.116992 | − | 0.0675453i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16359.6 | − | 5739.83i | −1.01757 | − | 0.357018i | ||||
\(638\) | −9419.57 | −0.584521 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 15162.3 | − | 26261.9i | 0.936473 | − | 1.62202i | ||||
\(641\) | 2721.81 | + | 4714.31i | 0.167714 | + | 0.290490i | 0.937616 | − | 0.347673i | \(-0.113028\pi\) |
−0.769901 | + | 0.638163i | \(0.779695\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5056.73 | + | 2919.50i | −0.310137 | + | 0.179057i | −0.646988 | − | 0.762501i | \(-0.723971\pi\) |
0.336851 | + | 0.941558i | \(0.390638\pi\) | |||||||
\(644\) | −9042.52 | + | 5220.70i | −0.553300 | + | 0.319448i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10615.2 | − | 18386.1i | −0.646519 | − | 1.11980i | ||||
\(647\) | −4354.43 | + | 7542.09i | −0.264591 | + | 0.458285i | −0.967456 | − | 0.253038i | \(-0.918570\pi\) |
0.702866 | + | 0.711323i | \(0.251904\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −918.773 | −0.0555701 | ||||||||
\(650\) | 9296.34 | − | 26496.3i | 0.560973 | − | 1.59888i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5233.54 | + | 3021.59i | 0.314358 | + | 0.181495i | ||||
\(653\) | 1397.47 | − | 2420.48i | 0.0837475 | − | 0.145055i | −0.821109 | − | 0.570771i | \(-0.806644\pi\) |
0.904857 | + | 0.425716i | \(0.139978\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 21372.6i | − | 1.27495i | ||||||
\(656\) | 13472.4 | − | 7778.31i | 0.801844 | − | 0.462945i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6898.41i | 0.408705i | ||||||||
\(659\) | 15695.0 | + | 27184.5i | 0.927752 | + | 1.60691i | 0.787074 | + | 0.616859i | \(0.211595\pi\) |
0.140678 | + | 0.990055i | \(0.455072\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17837.7 | + | 10298.6i | 1.04963 | + | 0.606005i | 0.922546 | − | 0.385887i | \(-0.126104\pi\) |
0.127085 | + | 0.991892i | \(0.459438\pi\) | |||||||
\(662\) | −21728.6 | −1.27569 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14832.5 | 0.866889 | ||||||||
\(665\) | 31278.0 | + | 18058.4i | 1.82392 | + | 1.05304i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9537.85 | + | 16520.0i | 0.553684 | + | 0.959008i | ||||
\(668\) | − | 2511.00i | − | 0.145439i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −24141.8 | + | 13938.3i | −1.39206 | + | 0.803704i | ||||
\(671\) | − | 10627.2i | − | 0.611414i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8967.89 | + | 15532.8i | −0.513651 | + | 0.889669i | 0.486224 | + | 0.873834i | \(0.338374\pi\) |
−0.999875 | + | 0.0158347i | \(0.994959\pi\) | |||||||
\(674\) | −15727.9 | − | 9080.51i | −0.898837 | − | 0.518944i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4720.18 | − | 3777.16i | −0.268559 | − | 0.214904i | ||||
\(677\) | 24104.0 | 1.36838 | 0.684188 | − | 0.729305i | \(-0.260157\pi\) | ||||
0.684188 | + | 0.729305i | \(0.260157\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7896.09 | − | 13676.4i | 0.446280 | − | 0.772980i | ||||
\(680\) | −12673.1 | − | 21950.4i | −0.714691 | − | 1.23788i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 7448.70 | − | 4300.51i | 0.418219 | − | 0.241459i | ||||
\(683\) | −5840.69 | + | 3372.12i | −0.327215 | + | 0.188918i | −0.654604 | − | 0.755972i | \(-0.727165\pi\) |
0.327389 | + | 0.944890i | \(0.393831\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −23933.8 | − | 41454.5i | −1.33498 | − | 2.31225i | ||||
\(686\) | −1176.85 | + | 2038.36i | −0.0654988 | + | 0.113447i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 12131.5 | 0.672249 | ||||||||
\(689\) | −4139.00 | − | 21975.8i | −0.228858 | − | 1.21511i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26712.1 | + | 15422.2i | 1.47059 | + | 0.849043i | 0.999455 | − | 0.0330199i | \(-0.0105125\pi\) |
0.471131 | + | 0.882063i | \(0.343846\pi\) | |||||||
\(692\) | 1237.75 | − | 2143.85i | 0.0679945 | − | 0.117770i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 30818.9i | − | 1.68569i | ||||||
\(695\) | −47287.2 | + | 27301.3i | −2.58087 | + | 1.49007i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 16651.6i | − | 0.904913i | ||||||
\(698\) | −9439.06 | − | 16348.9i | −0.511853 | − | 0.886556i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −11624.6 | − | 6711.46i | −0.627669 | − | 0.362385i | ||||
\(701\) | −21007.6 | −1.13188 | −0.565940 | − | 0.824447i | \(-0.691486\pi\) | ||||
−0.565940 | + | 0.824447i | \(0.691486\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17164.6 | 0.920877 | ||||||||
\(704\) | −4366.53 | − | 2521.02i | −0.233764 | − | 0.134964i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5669.06 | − | 9819.10i | −0.302207 | − | 0.523437i | ||||
\(707\) | 6811.41i | 0.362333i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12785.5 | − | 7381.68i | 0.677246 | − | 0.391008i | −0.121570 | − | 0.992583i | \(-0.538793\pi\) |
0.798817 | + | 0.601574i | \(0.205460\pi\) | |||||||
\(710\) | − | 21996.7i | − | 1.16271i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8326.17 | − | 14421.4i | 0.438253 | − | 0.759077i | ||||
\(713\) | −15084.5 | − | 8709.02i | −0.792311 | − | 0.457441i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16604.9 | − | 5825.91i | −0.868515 | − | 0.304722i | ||||
\(716\) | −862.037 | −0.0449942 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −11753.4 | + | 20357.5i | −0.610910 | + | 1.05813i | ||||
\(719\) | 13093.1 | + | 22678.0i | 0.679126 | + | 1.17628i | 0.975245 | + | 0.221129i | \(0.0709742\pi\) |
−0.296119 | + | 0.955151i | \(0.595692\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5719.53 | − | 3302.17i | 0.295432 | − | 0.170568i | ||||
\(722\) | 2590.94 | − | 1495.88i | 0.133552 | − | 0.0771064i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3776.75 | + | 6541.52i | 0.193870 | + | 0.335792i | ||||
\(725\) | −12261.3 | + | 21237.3i | −0.628103 | + | 1.08791i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20044.0 | −1.02254 | −0.511272 | − | 0.859419i | \(-0.670825\pi\) | ||||
−0.511272 | + | 0.859419i | \(0.670825\pi\) | |||||||
\(728\) | 16336.1 | − | 14034.6i | 0.831672 | − | 0.714501i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 9644.68 | + | 5568.36i | 0.488994 | + | 0.282321i | ||||
\(731\) | 6492.68 | − | 11245.6i | 0.328509 | − | 0.568995i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25555.5i | 1.28774i | 0.765134 | + | 0.643871i | \(0.222673\pi\) | ||||
−0.765134 | + | 0.643871i | \(0.777327\pi\) | |||||||
\(734\) | 11103.4 | − | 6410.57i | 0.558358 | − | 0.322368i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 16988.2i | − | 0.850809i | ||||||
\(737\) | 5186.47 | + | 8983.23i | 0.259221 | + | 0.448985i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9620.24 | + | 5554.25i | 0.478872 | + | 0.276477i | 0.719946 | − | 0.694030i | \(-0.244166\pi\) |
−0.241074 | + | 0.970507i | \(0.577500\pi\) | |||||||
\(740\) | −10743.9 | −0.533720 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −41768.2 | −2.06652 | ||||||||
\(743\) | 24411.7 | + | 14094.1i | 1.20535 | + | 0.695911i | 0.961741 | − | 0.273962i | \(-0.0883342\pi\) |
0.243612 | + | 0.969873i | \(0.421667\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12020.9 | + | 20820.8i | 0.591155 | + | 1.02391i | ||||
\(746\) | 37306.8i | 1.83096i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4282.34 | − | 2472.41i | 0.209328 | − | 0.120856i | ||||
\(749\) | − | 18248.9i | − | 0.890256i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8588.28 | − | 14875.3i | 0.417298 | − | 0.722782i | −0.578369 | − | 0.815776i | \(-0.696310\pi\) |
0.995667 | + | 0.0929941i | \(0.0296438\pi\) | |||||||
\(752\) | −5352.78 | − | 3090.43i | −0.259569 | − | 0.149862i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 13443.0 | + | 15647.5i | 0.649291 | + | 0.755768i | ||||
\(755\) | 49950.2 | 2.40778 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2204.98 | − | 3819.14i | 0.105867 | − | 0.183367i | −0.808225 | − | 0.588874i | \(-0.799572\pi\) |
0.914092 | + | 0.405507i | \(0.132905\pi\) | |||||||
\(758\) | −6610.77 | − | 11450.2i | −0.316773 | − | 0.548667i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −20159.9 | + | 11639.3i | −0.962206 | + | 0.555530i | ||||
\(761\) | −28097.0 | + | 16221.8i | −1.33839 | + | 0.772721i | −0.986569 | − | 0.163346i | \(-0.947771\pi\) |
−0.351823 | + | 0.936067i | \(0.614438\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 22665.1 | + | 39257.0i | 1.07540 | + | 1.86265i | ||||
\(764\) | −123.643 | + | 214.157i | −0.00585505 | + | 0.0101413i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6528.30 | −0.307934 | ||||||||
\(767\) | 1311.21 | + | 1526.24i | 0.0617278 | + | 0.0718505i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27707.7 | − | 15997.1i | −1.29931 | − | 0.750155i | −0.319022 | − | 0.947747i | \(-0.603354\pi\) |
−0.980284 | + | 0.197593i | \(0.936688\pi\) | |||||||
\(770\) | −16434.2 | + | 28464.8i | −0.769152 | + | 1.33221i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2336.04i | 0.108907i | ||||||||
\(773\) | −7776.38 | + | 4489.70i | −0.361833 | + | 0.208904i | −0.669885 | − | 0.742465i | \(-0.733656\pi\) |
0.308051 | + | 0.951370i | \(0.400323\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 22391.7i | − | 1.03785i | ||||||
\(776\) | 5089.34 | + | 8815.00i | 0.235434 | + | 0.407784i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 31584.1 | + | 18235.1i | 1.45546 | + | 0.840308i | ||||
\(779\) | −15293.3 | −0.703390 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8185.04 | −0.375011 | ||||||||
\(782\) | −33885.2 | − | 19563.6i | −1.54953 | − | 0.894620i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −14507.2 | − | 25127.2i | −0.660859 | − | 1.14464i | ||||
\(785\) | − | 58833.9i | − | 2.67500i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10886.4 | + | 6285.27i | −0.493086 | + | 0.284683i | −0.725854 | − | 0.687849i | \(-0.758555\pi\) |
0.232768 | + | 0.972532i | \(0.425222\pi\) | |||||||
\(788\) | 11952.9i | 0.540360i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −30185.3 | + | 52282.5i | −1.35942 | + | 2.35459i | ||||
\(791\) | −8803.05 | − | 5082.44i | −0.395702 | − | 0.228459i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17653.6 | + | 15166.5i | −0.790540 | + | 0.679165i | ||||
\(794\) | 35341.2 | 1.57961 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4579.34 | − | 7931.65i | 0.203907 | − | 0.353178i | ||||
\(797\) | −18931.7 | − | 32790.6i | −0.841398 | − | 1.45734i | −0.888713 | − | 0.458464i | \(-0.848400\pi\) |
0.0473148 | − | 0.998880i | \(-0.484934\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5729.55 | + | 3307.96i | −0.253688 | + | 0.146467i | ||||
\(800\) | 18913.3 | − | 10919.6i | 0.835857 | − | 0.482582i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7724.58 | − | 13379.4i | −0.340105 | − | 0.589079i | ||||
\(803\) | 2072.00 | − | 3588.82i | 0.0910578 | − | 0.157717i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 66562.1 | 2.91429 | ||||||||
\(806\) | −17774.2 | − | 6236.16i | −0.776761 | − | 0.272530i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3802.04 | − | 2195.11i | −0.165539 | − | 0.0955739i | ||||
\(809\) | 1251.90 | − | 2168.35i | 0.0544058 | − | 0.0942336i | −0.837540 | − | 0.546376i | \(-0.816007\pi\) |
0.891946 | + | 0.452143i | \(0.149340\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5409.55i | 0.234223i | 0.993119 | + | 0.117112i | \(0.0373635\pi\) | ||||
−0.993119 | + | 0.117112i | \(0.962636\pi\) | |||||||
\(812\) | 8540.11 | − | 4930.64i | 0.369088 | − | 0.213093i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 15620.8i | 0.672617i | ||||||||
\(815\) | −19262.1 | − | 33362.9i | −0.827879 | − | 1.43393i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10328.3 | − | 5963.07i | −0.442280 | − | 0.255351i | ||||
\(818\) | −3884.85 | −0.166052 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9572.58 | 0.407669 | ||||||||
\(821\) | 27177.3 | + | 15690.8i | 1.15529 | + | 0.667007i | 0.950171 | − | 0.311730i | \(-0.100908\pi\) |
0.205119 | + | 0.978737i | \(0.434242\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16523.1 | − | 28618.8i | −0.699827 | − | 1.21214i | −0.968526 | − | 0.248912i | \(-0.919927\pi\) |
0.268699 | − | 0.963224i | \(-0.413406\pi\) | |||||||
\(824\) | 4256.76i | 0.179965i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3254.77 | − | 1879.14i | 0.137104 | − | 0.0791571i | ||||
\(827\) | 33653.7i | 1.41506i | 0.706684 | + | 0.707529i | \(0.250190\pi\) | ||||
−0.706684 | + | 0.707529i | \(0.749810\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6449.25 | − | 11170.4i | 0.270195 | − | 0.467992i | −0.698716 | − | 0.715399i | \(-0.746245\pi\) |
0.968912 | + | 0.247407i | \(0.0795784\pi\) | |||||||
\(830\) | 42932.8 | + | 24787.3i | 1.79545 | + | 1.03660i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2043.79 | + | 10851.4i | 0.0851632 | + | 0.452169i | ||||
\(833\) | −31056.6 | −1.29177 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8003.58 | + | 13862.6i | −0.331707 | + | 0.574533i | ||||
\(836\) | −2270.73 | − | 3933.03i | −0.0939414 | − | 0.162711i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 17516.0 | − | 10112.8i | 0.722051 | − | 0.416877i | ||||
\(839\) | 342.798 | − | 197.915i | 0.0141057 | − | 0.00814395i | −0.492931 | − | 0.870069i | \(-0.664074\pi\) |
0.507036 | + | 0.861925i | \(0.330741\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3186.59 | + | 5519.33i | 0.130657 | + | 0.226304i | ||||
\(842\) | −16934.0 | + | 29330.5i | −0.693091 | + | 1.20047i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 12657.4 | 0.516214 | ||||||||
\(845\) | 14019.6 | + | 35898.0i | 0.570758 | + | 1.46145i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20184.6 | − | 11653.6i | −0.818831 | − | 0.472752i | ||||
\(848\) | 18711.8 | − | 32409.8i | 0.757742 | − | 1.31245i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 50299.9i | − | 2.02973i | ||||||
\(851\) | 27395.8 | − | 15817.0i | 1.10354 | − | 0.637132i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 21248.9i | − | 0.852930i | −0.904504 | − | 0.426465i | \(-0.859759\pi\) | ||
0.904504 | − | 0.426465i | \(-0.140241\pi\) | |||||||
\(854\) | 21735.6 | + | 37647.1i | 0.870932 | + | 1.50850i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10186.3 | + | 5881.08i | 0.406731 | + | 0.234826i | ||||
\(857\) | −9920.37 | −0.395418 | −0.197709 | − | 0.980261i | \(-0.563350\pi\) | ||||
−0.197709 | + | 0.980261i | \(0.563350\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20946.3 | 0.831990 | 0.415995 | − | 0.909367i | \(-0.363433\pi\) | ||||
0.415995 | + | 0.909367i | \(0.363433\pi\) | |||||||
\(860\) | 6464.84 | + | 3732.47i | 0.256336 | + | 0.147996i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 18546.6 | + | 32123.7i | 0.732831 | + | 1.26930i | ||||
\(863\) | − | 11271.4i | − | 0.444594i | −0.974979 | − | 0.222297i | \(-0.928645\pi\) | ||
0.974979 | − | 0.222297i | \(-0.0713554\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13666.6 | + | 7890.44i | −0.537202 | + | 0.310154i | ||||
\(866\) | 34349.7i | 1.34786i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4502.17 | + | 7797.99i | −0.176053 | + | 0.304932i | ||||
\(869\) | 19454.5 | + | 11232.1i | 0.759435 | + | 0.438460i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7520.89 | − | 21435.9i | 0.292578 | − | 0.833902i | ||||
\(872\) | −29217.0 | −1.13465 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −17967.8 | + | 31121.2i | −0.695389 | + | 1.20445i | ||||
\(875\) | 13512.2 | + | 23403.9i | 0.522054 | + | 0.904224i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8172.12 | − | 4718.18i | 0.314656 | − | 0.181667i | −0.334352 | − | 0.942448i | \(-0.608518\pi\) |
0.649008 | + | 0.760782i | \(0.275184\pi\) | |||||||
\(878\) | 5794.69 | − | 3345.57i | 0.222735 | − | 0.128596i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −14724.7 | − | 25504.0i | −0.564057 | − | 0.976976i | ||||
\(881\) | 10171.5 | − | 17617.6i | 0.388974 | − | 0.673723i | −0.603337 | − | 0.797486i | \(-0.706163\pi\) |
0.992312 | + | 0.123763i | \(0.0394961\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −46521.9 | −1.77303 | −0.886515 | − | 0.462699i | \(-0.846881\pi\) | ||||
−0.886515 | + | 0.462699i | \(0.846881\pi\) | |||||||
\(884\) | −10218.6 | − | 3585.23i | −0.388787 | − | 0.136408i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11612.2 | − | 6704.32i | −0.440316 | − | 0.254217i | ||||
\(887\) | −9977.53 | + | 17281.6i | −0.377692 | + | 0.654181i | −0.990726 | − | 0.135875i | \(-0.956615\pi\) |
0.613034 | + | 0.790056i | \(0.289949\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 3290.27i | − | 0.124130i | ||||||
\(890\) | 48200.2 | − | 27828.4i | 1.81537 | − | 1.04810i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6960.57i | 0.261275i | ||||||||
\(893\) | 3038.13 | + | 5262.19i | 0.113849 | + | 0.197192i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4759.10 | + | 2747.67i | 0.177742 | + | 0.102619i | ||||
\(896\) | 46157.3 | 1.72099 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 49899.1 | 1.85429 | ||||||||
\(899\) | 14246.4 | + | 8225.14i | 0.528523 | + | 0.305143i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20028.9 | − | 34691.0i | −0.740575 | − | 1.28271i | ||||
\(902\) | − | 13917.9i | − | 0.513762i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5673.91 | − | 3275.83i | 0.208752 | − | 0.120523i | ||||
\(905\) | − | 48152.2i | − | 1.76866i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1326.97 | + | 2298.39i | −0.0485793 | + | 0.0841419i | −0.889293 | − | 0.457339i | \(-0.848803\pi\) |
0.840713 | + | 0.541481i | \(0.182136\pi\) | |||||||
\(908\) | −88.8078 | − | 51.2732i | −0.00324580 | − | 0.00187397i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 70738.8 | − | 13323.2i | 2.57689 | − | 0.485341i | ||||
\(911\) | −1797.50 | −0.0653720 | −0.0326860 | − | 0.999466i | \(-0.510406\pi\) | ||||
−0.0326860 | + | 0.999466i | \(0.510406\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9223.43 | − | 15975.5i | 0.334339 | − | 0.579091i | ||||
\(914\) | 1436.71 | + | 2488.45i | 0.0519936 | + | 0.0900555i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9757.14 | + | 5633.29i | −0.351949 | + | 0.203198i | ||||
\(917\) | 28173.0 | − | 16265.7i | 1.01456 | − | 0.585757i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24321.0 | + | 42125.2i | 0.872987 | + | 1.51206i | 0.858891 | + | 0.512158i | \(0.171154\pi\) |
0.0140961 | + | 0.999901i | \(0.495513\pi\) | |||||||
\(920\) | −21451.0 | + | 37154.2i | −0.768714 | + | 1.33145i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −53425.6 | −1.90833 | ||||||||
\(923\) | 11681.2 | + | 13596.7i | 0.416566 | + | 0.484878i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 35218.6 | + | 20333.5i | 1.25187 | + | 0.722768i | ||||
\(926\) | −19189.8 | + | 33237.8i | −0.681012 | + | 1.17955i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 16044.4i | 0.567545i | ||||||||
\(929\) | −32688.3 | + | 18872.6i | −1.15443 | + | 0.666513i | −0.949964 | − | 0.312359i | \(-0.898881\pi\) |
−0.204471 | + | 0.978873i | \(0.565547\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 28523.3i | 1.00410i | ||||||||
\(932\) | 2017.04 | + | 3493.61i | 0.0708908 | + | 0.122786i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 44344.5 | + | 25602.3i | 1.55353 | + | 0.896931i | ||||
\(935\) | −31522.3 | −1.10256 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2705.50 | 0.0943273 | 0.0471637 | − | 0.998887i | \(-0.484982\pi\) | ||||
0.0471637 | + | 0.998887i | \(0.484982\pi\) | |||||||
\(938\) | −36746.4 | − | 21215.5i | −1.27912 | − | 0.738498i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1901.66 | − | 3293.77i | −0.0659843 | − | 0.114288i | ||||
\(941\) | − | 5189.27i | − | 0.179772i | −0.995952 | − | 0.0898860i | \(-0.971350\pi\) | ||
0.995952 | − | 0.0898860i | \(-0.0286503\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24409.1 | + | 14092.6i | −0.842916 | + | 0.486658i | ||||
\(944\) | 3367.36i | 0.116100i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5426.75 | − | 9399.41i | 0.186511 | − | 0.323046i | ||||
\(947\) | 62.5886 | + | 36.1356i | 0.00214768 | + | 0.00123997i | 0.501073 | − | 0.865405i | \(-0.332939\pi\) |
−0.498926 | + | 0.866645i | \(0.666272\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8918.67 | + | 1679.78i | −0.305071 | + | 0.0574582i | ||||
\(950\) | −46196.9 | −1.57771 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 19289.7 | − | 33410.8i | 0.656706 | − | 1.13745i | ||||
\(953\) | −22347.5 | − | 38707.1i | −0.759609 | − | 1.31568i | −0.943050 | − | 0.332651i | \(-0.892057\pi\) |
0.183441 | − | 0.983031i | \(-0.441276\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1365.21 | − | 788.205i | 0.0462588 | − | 0.0267076i | ||||
\(956\) | −13155.5 | + | 7595.34i | −0.445063 | + | 0.256957i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 17011.4 | + | 29464.5i | 0.573708 | + | 0.993691i | ||||
\(959\) | 36429.7 | − | 63098.1i | 1.22667 | − | 2.12466i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14770.2 | 0.495795 | ||||||||
\(962\) | 25948.9 | − | 22293.1i | 0.869673 | − | 0.747149i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −6352.24 | − | 3667.47i | −0.212232 | − | 0.122532i | ||||
\(965\) | 7445.92 | − | 12896.7i | 0.248386 | − | 0.430217i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 17936.9i | − | 0.596496i | −0.954488 | − | 0.298248i | \(-0.903598\pi\) | ||
0.954488 | − | 0.298248i | \(-0.0964022\pi\) | |||||||
\(968\) | 13009.8 | − | 7511.18i | 0.431972 | − | 0.249399i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 34020.1i | 1.12610i | ||||||||
\(971\) | −20457.3 | − | 35433.1i | −0.676113 | − | 1.17106i | −0.976142 | − | 0.217132i | \(-0.930330\pi\) |
0.300029 | − | 0.953930i | \(-0.403004\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −71976.2 | − | 41555.5i | −2.37148 | − | 1.36918i | ||||
\(974\) | 13097.1 | 0.430860 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −38949.3 | −1.27740 | ||||||||
\(977\) | 20886.8 | + | 12059.0i | 0.683961 | + | 0.394885i | 0.801346 | − | 0.598202i | \(-0.204118\pi\) |
−0.117385 | + | 0.993086i | \(0.537451\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10355.1 | − | 17935.5i | −0.338048 | − | 0.585516i | ||||
\(980\) | − | 17853.6i | − | 0.581953i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 34835.2 | − | 20112.1i | 1.13201 | − | 0.653567i | ||||
\(983\) | − | 2928.61i | − | 0.0950235i | −0.998871 | − | 0.0475118i | \(-0.984871\pi\) | ||
0.998871 | − | 0.0475118i | \(-0.0151292\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 38098.7 | − | 65989.0i | 1.23241 | − | 2.13460i | ||||
\(986\) | 32002.5 | + | 18476.6i | 1.03364 | + | 0.596771i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3292.79 | + | 9385.05i | −0.106030 | + | 0.302205i | ||||
\(989\) | −21979.6 | −0.706683 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24904.9 | + | 43136.6i | −0.798317 | + | 1.38272i | 0.122395 | + | 0.992481i | \(0.460943\pi\) |
−0.920712 | + | 0.390244i | \(0.872391\pi\) | |||||||
\(992\) | −7325.06 | − | 12687.4i | −0.234447 | − | 0.406073i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 28995.6 | − | 16740.6i | 0.925238 | − | 0.534186i | ||||
\(995\) | −50562.8 | + | 29192.5i | −1.61100 | + | 0.930114i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20575.8 | + | 35638.4i | 0.653604 | + | 1.13208i | 0.982242 | + | 0.187620i | \(0.0600772\pi\) |
−0.328638 | + | 0.944456i | \(0.606589\pi\) | |||||||
\(998\) | −5867.33 | + | 10162.5i | −0.186099 | + | 0.322333i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 117.4.q.e.82.2 | 10 | ||
3.2 | odd | 2 | 39.4.j.c.4.4 | ✓ | 10 | ||
12.11 | even | 2 | 624.4.bv.h.433.5 | 10 | |||
13.6 | odd | 12 | 1521.4.a.bk.1.8 | 10 | |||
13.7 | odd | 12 | 1521.4.a.bk.1.3 | 10 | |||
13.10 | even | 6 | inner | 117.4.q.e.10.2 | 10 | ||
39.17 | odd | 6 | 507.4.b.i.337.8 | 10 | |||
39.20 | even | 12 | 507.4.a.r.1.8 | 10 | |||
39.23 | odd | 6 | 39.4.j.c.10.4 | yes | 10 | ||
39.32 | even | 12 | 507.4.a.r.1.3 | 10 | |||
39.35 | odd | 6 | 507.4.b.i.337.3 | 10 | |||
156.23 | even | 6 | 624.4.bv.h.49.1 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.j.c.4.4 | ✓ | 10 | 3.2 | odd | 2 | ||
39.4.j.c.10.4 | yes | 10 | 39.23 | odd | 6 | ||
117.4.q.e.10.2 | 10 | 13.10 | even | 6 | inner | ||
117.4.q.e.82.2 | 10 | 1.1 | even | 1 | trivial | ||
507.4.a.r.1.3 | 10 | 39.32 | even | 12 | |||
507.4.a.r.1.8 | 10 | 39.20 | even | 12 | |||
507.4.b.i.337.3 | 10 | 39.35 | odd | 6 | |||
507.4.b.i.337.8 | 10 | 39.17 | odd | 6 | |||
624.4.bv.h.49.1 | 10 | 156.23 | even | 6 | |||
624.4.bv.h.433.5 | 10 | 12.11 | even | 2 | |||
1521.4.a.bk.1.3 | 10 | 13.7 | odd | 12 | |||
1521.4.a.bk.1.8 | 10 | 13.6 | odd | 12 |