Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,4,Mod(136,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.136");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.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: | \(23.8957735523\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 2 x^{10} + 32 x^{9} + 583 x^{8} - 624 x^{7} + 594 x^{6} + 9450 x^{5} + 90513 x^{4} - 20304 x^{3} + 10368 x^{2} + 124416 x + 746496 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{9} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 271.1 | ||
Root | \(2.93142 - 2.93142i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 405.271 |
Dual form | 405.4.e.w.136.1 |
$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.61668 | − | 4.53223i | −0.925137 | − | 1.60238i | −0.791341 | − | 0.611375i | \(-0.790617\pi\) |
−0.133796 | − | 0.991009i | \(-0.542717\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −9.69405 | + | 16.7906i | −1.21176 | + | 2.09882i | ||||
\(5\) | −2.50000 | + | 4.33013i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −16.5090 | − | 28.5945i | −0.891403 | − | 1.54396i | −0.838194 | − | 0.545372i | \(-0.816388\pi\) |
−0.0532095 | − | 0.998583i | \(-0.516945\pi\) | |||||||
\(8\) | 59.5981 | 2.63389 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 26.1668 | 0.827468 | ||||||||
\(11\) | −3.04155 | − | 5.26813i | −0.0833694 | − | 0.144400i | 0.821326 | − | 0.570459i | \(-0.193235\pi\) |
−0.904695 | + | 0.426059i | \(0.859901\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 32.2254 | − | 55.8160i | 0.687516 | − | 1.19081i | −0.285123 | − | 0.958491i | \(-0.592034\pi\) |
0.972639 | − | 0.232322i | \(-0.0746322\pi\) | |||||||
\(14\) | −86.3977 | + | 149.645i | −1.64934 | + | 2.85674i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −78.3969 | − | 135.787i | −1.22495 | − | 2.12168i | ||||
\(17\) | −76.9845 | −1.09832 | −0.549162 | − | 0.835716i | \(-0.685053\pi\) | ||||
−0.549162 | + | 0.835716i | \(0.685053\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −118.716 | −1.43344 | −0.716720 | − | 0.697361i | \(-0.754357\pi\) | ||||
−0.716720 | + | 0.697361i | \(0.754357\pi\) | |||||||
\(20\) | −48.4703 | − | 83.9529i | −0.541914 | − | 0.938623i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −15.9176 | + | 27.5700i | −0.154256 | + | 0.267179i | ||||
\(23\) | −38.8002 | + | 67.2039i | −0.351757 | + | 0.609260i | −0.986557 | − | 0.163416i | \(-0.947749\pi\) |
0.634801 | + | 0.772676i | \(0.281082\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.5000 | − | 21.6506i | −0.100000 | − | 0.173205i | ||||
\(26\) | −337.294 | −2.54419 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 640.157 | 4.32065 | ||||||||
\(29\) | −31.4075 | − | 54.3993i | −0.201111 | − | 0.348334i | 0.747776 | − | 0.663951i | \(-0.231122\pi\) |
−0.948887 | + | 0.315617i | \(0.897789\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 53.4569 | − | 92.5901i | 0.309714 | − | 0.536441i | −0.668585 | − | 0.743635i | \(-0.733100\pi\) |
0.978300 | + | 0.207194i | \(0.0664332\pi\) | |||||||
\(32\) | −171.887 | + | 297.717i | −0.949550 | + | 1.64467i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 201.444 | + | 348.911i | 1.01610 | + | 1.75994i | ||||
\(35\) | 165.090 | 0.797295 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 108.268 | 0.481058 | 0.240529 | − | 0.970642i | \(-0.422679\pi\) | ||||
0.240529 | + | 0.970642i | \(0.422679\pi\) | |||||||
\(38\) | 310.642 | + | 538.048i | 1.32613 | + | 2.29692i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −148.995 | + | 258.067i | −0.588955 | + | 1.02010i | ||||
\(41\) | −71.3830 | + | 123.639i | −0.271906 | + | 0.470955i | −0.969350 | − | 0.245684i | \(-0.920987\pi\) |
0.697444 | + | 0.716640i | \(0.254321\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −169.784 | − | 294.075i | −0.602136 | − | 1.04293i | −0.992497 | − | 0.122268i | \(-0.960983\pi\) |
0.390361 | − | 0.920662i | \(-0.372350\pi\) | |||||||
\(44\) | 117.940 | 0.404093 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 406.111 | 1.30169 | ||||||||
\(47\) | 299.173 | + | 518.182i | 0.928486 | + | 1.60818i | 0.785857 | + | 0.618408i | \(0.212222\pi\) |
0.142629 | + | 0.989776i | \(0.454445\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −373.595 | + | 647.086i | −1.08920 | + | 1.88655i | ||||
\(50\) | −65.4171 | + | 113.306i | −0.185027 | + | 0.320477i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 624.789 | + | 1082.17i | 1.66620 | + | 2.88595i | ||||
\(53\) | 488.041 | 1.26486 | 0.632431 | − | 0.774617i | \(-0.282057\pi\) | ||||
0.632431 | + | 0.774617i | \(0.282057\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 30.4155 | 0.0745678 | ||||||||
\(56\) | −983.906 | − | 1704.18i | −2.34786 | − | 4.06661i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −164.367 | + | 284.691i | −0.372110 | + | 0.644514i | ||||
\(59\) | −121.413 | + | 210.294i | −0.267909 | + | 0.464033i | −0.968322 | − | 0.249706i | \(-0.919666\pi\) |
0.700412 | + | 0.713738i | \(0.252999\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 249.669 | + | 432.440i | 0.524047 | + | 0.907676i | 0.999608 | + | 0.0279936i | \(0.00891181\pi\) |
−0.475561 | + | 0.879683i | \(0.657755\pi\) | |||||||
\(62\) | −559.519 | −1.14611 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 544.744 | 1.06395 | ||||||||
\(65\) | 161.127 | + | 279.080i | 0.307466 | + | 0.532548i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 460.817 | − | 798.159i | 0.840266 | − | 1.45538i | −0.0494046 | − | 0.998779i | \(-0.515732\pi\) |
0.889670 | − | 0.456604i | \(-0.150934\pi\) | |||||||
\(68\) | 746.292 | − | 1292.62i | 1.33090 | − | 2.30519i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −431.989 | − | 748.226i | −0.737607 | − | 1.27757i | ||||
\(71\) | −60.6882 | −0.101442 | −0.0507209 | − | 0.998713i | \(-0.516152\pi\) | ||||
−0.0507209 | + | 0.998713i | \(0.516152\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −338.439 | −0.542621 | −0.271311 | − | 0.962492i | \(-0.587457\pi\) | ||||
−0.271311 | + | 0.962492i | \(0.587457\pi\) | |||||||
\(74\) | −283.303 | − | 490.695i | −0.445045 | − | 0.770840i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1150.84 | − | 1993.31i | 1.73698 | − | 3.00854i | ||||
\(77\) | −100.426 | + | 173.943i | −0.148631 | + | 0.257437i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 278.155 | + | 481.779i | 0.396138 | + | 0.686131i | 0.993246 | − | 0.116030i | \(-0.0370168\pi\) |
−0.597108 | + | 0.802161i | \(0.703683\pi\) | |||||||
\(80\) | 783.969 | 1.09563 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 747.147 | 1.00620 | ||||||||
\(83\) | 32.4210 | + | 56.1548i | 0.0428755 | + | 0.0742625i | 0.886667 | − | 0.462409i | \(-0.153015\pi\) |
−0.843791 | + | 0.536671i | \(0.819681\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 192.461 | − | 333.353i | 0.245592 | − | 0.425379i | ||||
\(86\) | −888.542 | + | 1539.00i | −1.11412 | + | 1.92971i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −181.271 | − | 313.970i | −0.219586 | − | 0.380333i | ||||
\(89\) | 941.159 | 1.12093 | 0.560465 | − | 0.828178i | \(-0.310623\pi\) | ||||
0.560465 | + | 0.828178i | \(0.310623\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2128.04 | −2.45142 | ||||||||
\(92\) | −752.262 | − | 1302.96i | −0.852487 | − | 1.47655i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1565.68 | − | 2711.84i | 1.71795 | − | 2.97558i | ||||
\(95\) | 296.790 | − | 514.056i | 0.320527 | − | 0.555169i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 521.085 | + | 902.546i | 0.545445 | + | 0.944738i | 0.998579 | + | 0.0532958i | \(0.0169726\pi\) |
−0.453134 | + | 0.891442i | \(0.649694\pi\) | |||||||
\(98\) | 3910.32 | 4.03064 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 484.703 | 0.484703 | ||||||||
\(101\) | −341.121 | − | 590.840i | −0.336068 | − | 0.582086i | 0.647622 | − | 0.761962i | \(-0.275764\pi\) |
−0.983689 | + | 0.179876i | \(0.942430\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −606.832 | + | 1051.06i | −0.580514 | + | 1.00548i | 0.414905 | + | 0.909865i | \(0.363815\pi\) |
−0.995418 | + | 0.0956144i | \(0.969518\pi\) | |||||||
\(104\) | 1920.57 | − | 3326.52i | 1.81084 | − | 3.13647i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1277.05 | − | 2211.91i | −1.17017 | − | 2.02679i | ||||
\(107\) | −1311.93 | −1.18532 | −0.592658 | − | 0.805454i | \(-0.701921\pi\) | ||||
−0.592658 | + | 0.805454i | \(0.701921\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −294.780 | −0.259035 | −0.129518 | − | 0.991577i | \(-0.541343\pi\) | ||||
−0.129518 | + | 0.991577i | \(0.541343\pi\) | |||||||
\(110\) | −79.5878 | − | 137.850i | −0.0689854 | − | 0.119486i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2588.51 | + | 4483.43i | −2.18385 | + | 3.78254i | ||||
\(113\) | −792.562 | + | 1372.76i | −0.659805 | + | 1.14282i | 0.320861 | + | 0.947126i | \(0.396028\pi\) |
−0.980666 | + | 0.195689i | \(0.937306\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −194.001 | − | 336.020i | −0.157310 | − | 0.272469i | ||||
\(116\) | 1217.86 | 0.974790 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1270.80 | 0.991412 | ||||||||
\(119\) | 1270.94 | + | 2201.33i | 0.979049 | + | 1.69576i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 646.998 | − | 1120.63i | 0.486099 | − | 0.841948i | ||||
\(122\) | 1306.61 | − | 2263.12i | 0.969631 | − | 1.67945i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1036.43 | + | 1795.15i | 0.750597 | + | 1.30007i | ||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −149.176 | −0.104230 | −0.0521149 | − | 0.998641i | \(-0.516596\pi\) | ||||
−0.0521149 | + | 0.998641i | \(0.516596\pi\) | |||||||
\(128\) | −50.3275 | − | 87.1698i | −0.0347528 | − | 0.0601937i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 843.235 | − | 1460.53i | 0.568897 | − | 0.985359i | ||||
\(131\) | −585.886 | + | 1014.78i | −0.390757 | + | 0.676810i | −0.992550 | − | 0.121842i | \(-0.961120\pi\) |
0.601793 | + | 0.798652i | \(0.294453\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1959.89 | + | 3394.62i | 1.27777 | + | 2.21317i | ||||
\(134\) | −4823.25 | −3.10944 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4588.13 | −2.89286 | ||||||||
\(137\) | 579.313 | + | 1003.40i | 0.361270 | + | 0.625739i | 0.988170 | − | 0.153361i | \(-0.0490098\pi\) |
−0.626900 | + | 0.779100i | \(0.715676\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −793.262 | + | 1373.97i | −0.484055 | + | 0.838408i | −0.999832 | − | 0.0183149i | \(-0.994170\pi\) |
0.515777 | + | 0.856723i | \(0.327503\pi\) | |||||||
\(140\) | −1600.39 | + | 2771.96i | −0.966128 | + | 1.67338i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 158.802 | + | 275.053i | 0.0938475 | + | 0.162549i | ||||
\(143\) | −392.061 | −0.229271 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 314.075 | 0.179879 | ||||||||
\(146\) | 885.588 | + | 1533.88i | 0.501999 | + | 0.869487i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1049.56 | + | 1817.88i | −0.582925 | + | 1.00966i | ||||
\(149\) | −258.555 | + | 447.830i | −0.142158 | + | 0.246226i | −0.928309 | − | 0.371809i | \(-0.878738\pi\) |
0.786151 | + | 0.618035i | \(0.212071\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −277.793 | − | 481.151i | −0.149712 | − | 0.259308i | 0.781409 | − | 0.624019i | \(-0.214501\pi\) |
−0.931121 | + | 0.364711i | \(0.881168\pi\) | |||||||
\(152\) | −7075.25 | −3.77552 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1051.13 | 0.550018 | ||||||||
\(155\) | 267.285 | + | 462.950i | 0.138508 | + | 0.239904i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −527.016 | + | 912.818i | −0.267901 | + | 0.464018i | −0.968320 | − | 0.249714i | \(-0.919663\pi\) |
0.700419 | + | 0.713732i | \(0.252997\pi\) | |||||||
\(158\) | 1455.69 | − | 2521.33i | 0.732964 | − | 1.26953i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −859.435 | − | 1488.58i | −0.424652 | − | 0.735519i | ||||
\(161\) | 2562.21 | 1.25423 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −635.916 | −0.305575 | −0.152788 | − | 0.988259i | \(-0.548825\pi\) | ||||
−0.152788 | + | 0.988259i | \(0.548825\pi\) | |||||||
\(164\) | −1383.98 | − | 2397.13i | −0.658968 | − | 1.14137i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 169.671 | − | 293.879i | 0.0793314 | − | 0.137406i | ||||
\(167\) | −682.557 | + | 1182.22i | −0.316274 | + | 0.547803i | −0.979708 | − | 0.200432i | \(-0.935765\pi\) |
0.663433 | + | 0.748236i | \(0.269099\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −978.448 | − | 1694.72i | −0.445356 | − | 0.771380i | ||||
\(170\) | −2014.44 | −0.908827 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6583.59 | 2.91857 | ||||||||
\(173\) | −567.465 | − | 982.878i | −0.249385 | − | 0.431947i | 0.713970 | − | 0.700176i | \(-0.246895\pi\) |
−0.963355 | + | 0.268229i | \(0.913562\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −412.726 | + | 714.862i | −0.178281 | + | 0.308791i | ||||
\(176\) | −476.897 | + | 826.009i | −0.204247 | + | 0.353766i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2462.72 | − | 4265.55i | −1.03701 | − | 1.79616i | ||||
\(179\) | 1813.33 | 0.757179 | 0.378589 | − | 0.925565i | \(-0.376409\pi\) | ||||
0.378589 | + | 0.925565i | \(0.376409\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2334.37 | 0.958634 | 0.479317 | − | 0.877642i | \(-0.340884\pi\) | ||||
0.479317 | + | 0.877642i | \(0.340884\pi\) | |||||||
\(182\) | 5568.40 | + | 9644.74i | 2.26790 | + | 3.92811i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2312.42 | + | 4005.23i | −0.926488 | + | 1.60472i | ||||
\(185\) | −270.670 | + | 468.814i | −0.107568 | + | 0.186313i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 234.153 | + | 405.564i | 0.0915665 | + | 0.158598i | ||||
\(188\) | −11600.8 | −4.50039 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3106.42 | −1.18612 | ||||||||
\(191\) | −221.322 | − | 383.341i | −0.0838444 | − | 0.145223i | 0.821054 | − | 0.570851i | \(-0.193387\pi\) |
−0.904898 | + | 0.425628i | \(0.860053\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1851.27 | − | 3206.49i | 0.690452 | − | 1.19590i | −0.281237 | − | 0.959638i | \(-0.590745\pi\) |
0.971690 | − | 0.236261i | \(-0.0759219\pi\) | |||||||
\(194\) | 2727.03 | − | 4723.35i | 1.00922 | − | 1.74802i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7243.31 | − | 12545.8i | −2.63969 | − | 4.57208i | ||||
\(197\) | 4491.92 | 1.62455 | 0.812274 | − | 0.583276i | \(-0.198229\pi\) | ||||
0.812274 | + | 0.583276i | \(0.198229\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2934.08 | −1.04518 | −0.522591 | − | 0.852584i | \(-0.675034\pi\) | ||||
−0.522591 | + | 0.852584i | \(0.675034\pi\) | |||||||
\(200\) | −744.976 | − | 1290.34i | −0.263389 | − | 0.456203i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1785.21 | + | 3092.08i | −0.621817 | + | 1.07702i | ||||
\(203\) | −1037.01 | + | 1796.16i | −0.358542 | + | 0.621013i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −356.915 | − | 618.195i | −0.121600 | − | 0.210618i | ||||
\(206\) | 6351.54 | 2.14822 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −10105.5 | −3.36869 | ||||||||
\(209\) | 361.082 | + | 625.412i | 0.119505 | + | 0.206989i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 336.970 | − | 583.649i | 0.109943 | − | 0.190427i | −0.805804 | − | 0.592182i | \(-0.798267\pi\) |
0.915747 | + | 0.401756i | \(0.131600\pi\) | |||||||
\(212\) | −4731.10 | + | 8194.50i | −1.53270 | + | 2.65472i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3432.90 | + | 5945.95i | 1.09658 | + | 1.89933i | ||||
\(215\) | 1697.84 | 0.538567 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3530.08 | −1.10432 | ||||||||
\(218\) | 771.347 | + | 1336.01i | 0.239643 | + | 0.415074i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −294.850 | + | 510.695i | −0.0903580 | + | 0.156505i | ||||
\(221\) | −2480.85 | + | 4296.97i | −0.755115 | + | 1.30790i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −89.2581 | − | 154.599i | −0.0268034 | − | 0.0464249i | 0.852313 | − | 0.523033i | \(-0.175199\pi\) |
−0.879116 | + | 0.476608i | \(0.841866\pi\) | |||||||
\(224\) | 11350.7 | 3.38573 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8295.53 | 2.44164 | ||||||||
\(227\) | −2526.05 | − | 4375.25i | −0.738590 | − | 1.27928i | −0.953130 | − | 0.302561i | \(-0.902158\pi\) |
0.214540 | − | 0.976715i | \(-0.431175\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −654.484 | + | 1133.60i | −0.188863 | + | 0.327120i | −0.944871 | − | 0.327442i | \(-0.893813\pi\) |
0.756009 | + | 0.654562i | \(0.227147\pi\) | |||||||
\(230\) | −1015.28 | + | 1758.51i | −0.291067 | + | 0.504143i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1871.82 | − | 3242.10i | −0.529704 | − | 0.917474i | ||||
\(233\) | −6591.30 | −1.85326 | −0.926632 | − | 0.375970i | \(-0.877309\pi\) | ||||
−0.926632 | + | 0.375970i | \(0.877309\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2991.73 | −0.830463 | ||||||||
\(236\) | −2353.97 | − | 4077.20i | −0.649282 | − | 1.12459i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6651.29 | − | 11520.4i | 1.81151 | − | 3.13762i | ||||
\(239\) | −792.252 | + | 1372.22i | −0.214421 | + | 0.371387i | −0.953093 | − | 0.302677i | \(-0.902120\pi\) |
0.738673 | + | 0.674064i | \(0.235453\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 837.234 | + | 1450.13i | 0.223780 | + | 0.387598i | 0.955953 | − | 0.293521i | \(-0.0948269\pi\) |
−0.732173 | + | 0.681119i | \(0.761494\pi\) | |||||||
\(242\) | −6771.95 | −1.79883 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −9681.23 | −2.54007 | ||||||||
\(245\) | −1867.98 | − | 3235.43i | −0.487105 | − | 0.843690i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3825.67 | + | 6626.25i | −0.985512 | + | 1.70696i | ||||
\(248\) | 3185.93 | − | 5518.19i | 0.815753 | − | 1.41293i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −327.085 | − | 566.528i | −0.0827468 | − | 0.143322i | ||||
\(251\) | −1200.75 | −0.301955 | −0.150978 | − | 0.988537i | \(-0.548242\pi\) | ||||
−0.150978 | + | 0.988537i | \(0.548242\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 472.052 | 0.117303 | ||||||||
\(254\) | 390.345 | + | 676.098i | 0.0964269 | + | 0.167016i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1915.60 | − | 3317.91i | 0.467675 | − | 0.810036i | ||||
\(257\) | 2603.34 | − | 4509.12i | 0.631876 | − | 1.09444i | −0.355292 | − | 0.934755i | \(-0.615619\pi\) |
0.987168 | − | 0.159686i | \(-0.0510481\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1787.40 | − | 3095.87i | −0.428817 | − | 0.742733i | ||||
\(260\) | −6247.89 | −1.49030 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6132.31 | 1.44601 | ||||||||
\(263\) | −3841.78 | − | 6654.16i | −0.900739 | − | 1.56012i | −0.826537 | − | 0.562882i | \(-0.809693\pi\) |
−0.0742011 | − | 0.997243i | \(-0.523641\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1220.10 | + | 2113.28i | −0.282832 | + | 0.489879i | ||||
\(266\) | 10256.8 | − | 17765.3i | 2.36423 | − | 4.09496i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8934.37 | + | 15474.8i | 2.03639 | + | 3.52714i | ||||
\(269\) | −624.277 | −0.141497 | −0.0707487 | − | 0.997494i | \(-0.522539\pi\) | ||||
−0.0707487 | + | 0.997494i | \(0.522539\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1462.51 | −0.327828 | −0.163914 | − | 0.986475i | \(-0.552412\pi\) | ||||
−0.163914 | + | 0.986475i | \(0.552412\pi\) | |||||||
\(272\) | 6035.35 | + | 10453.5i | 1.34539 | + | 2.33029i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3031.76 | − | 5251.15i | 0.668449 | − | 1.15779i | ||||
\(275\) | −76.0388 | + | 131.703i | −0.0166739 | + | 0.0288800i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2949.02 | + | 5107.85i | 0.639673 | + | 1.10795i | 0.985505 | + | 0.169649i | \(0.0542635\pi\) |
−0.345832 | + | 0.938297i | \(0.612403\pi\) | |||||||
\(278\) | 8302.86 | 1.79127 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 9839.06 | 2.09999 | ||||||||
\(281\) | 2636.45 | + | 4566.47i | 0.559707 | + | 0.969441i | 0.997521 | + | 0.0703753i | \(0.0224197\pi\) |
−0.437813 | + | 0.899066i | \(0.644247\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 559.632 | − | 969.311i | 0.117550 | − | 0.203603i | −0.801246 | − | 0.598335i | \(-0.795829\pi\) |
0.918796 | + | 0.394732i | \(0.129163\pi\) | |||||||
\(284\) | 588.315 | − | 1018.99i | 0.122923 | − | 0.212908i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1025.90 | + | 1776.91i | 0.212107 | + | 0.367380i | ||||
\(287\) | 4713.86 | 0.969513 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1013.62 | 0.206313 | ||||||||
\(290\) | −821.833 | − | 1423.46i | −0.166413 | − | 0.288235i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3280.85 | − | 5682.60i | 0.657525 | − | 1.13887i | ||||
\(293\) | 470.370 | − | 814.705i | 0.0937860 | − | 0.162442i | −0.815315 | − | 0.579017i | \(-0.803436\pi\) |
0.909101 | + | 0.416575i | \(0.136770\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −607.066 | − | 1051.47i | −0.119813 | − | 0.207522i | ||||
\(296\) | 6452.57 | 1.26705 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2706.22 | 0.526064 | ||||||||
\(299\) | 2500.70 | + | 4331.34i | 0.483676 | + | 0.837752i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5605.94 | + | 9709.77i | −1.07349 | + | 1.85934i | ||||
\(302\) | −1453.79 | + | 2518.04i | −0.277008 | + | 0.479791i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 9306.97 | + | 16120.1i | 1.75589 | + | 3.04130i | ||||
\(305\) | −2496.69 | −0.468722 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1931.88 | 0.359148 | 0.179574 | − | 0.983744i | \(-0.442528\pi\) | ||||
0.179574 | + | 0.983744i | \(0.442528\pi\) | |||||||
\(308\) | −1947.07 | − | 3372.43i | −0.360210 | − | 0.623902i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1398.80 | − | 2422.79i | 0.256279 | − | 0.443888i | ||||
\(311\) | 3149.08 | − | 5454.37i | 0.574174 | − | 0.994498i | −0.421957 | − | 0.906616i | \(-0.638657\pi\) |
0.996131 | − | 0.0878821i | \(-0.0280099\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 909.403 | + | 1575.13i | 0.164225 | + | 0.284446i | 0.936380 | − | 0.350988i | \(-0.114154\pi\) |
−0.772155 | + | 0.635435i | \(0.780821\pi\) | |||||||
\(314\) | 5516.13 | 0.991380 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10785.8 | −1.92009 | ||||||||
\(317\) | −1579.32 | − | 2735.46i | −0.279821 | − | 0.484665i | 0.691519 | − | 0.722358i | \(-0.256942\pi\) |
−0.971340 | + | 0.237694i | \(0.923609\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −191.055 | + | 330.917i | −0.0335330 | + | 0.0580808i | ||||
\(320\) | −1361.86 | + | 2358.81i | −0.237907 | + | 0.412068i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6704.50 | − | 11612.5i | −1.16033 | − | 2.00975i | ||||
\(323\) | 9139.31 | 1.57438 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1611.27 | −0.275006 | ||||||||
\(326\) | 1663.99 | + | 2882.12i | 0.282699 | + | 0.489649i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4254.29 | + | 7368.65i | −0.716171 | + | 1.24044i | ||||
\(329\) | 9878.10 | − | 17109.4i | 1.65531 | − | 2.86708i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 476.545 | + | 825.400i | 0.0791338 | + | 0.137064i | 0.902876 | − | 0.429900i | \(-0.141451\pi\) |
−0.823743 | + | 0.566964i | \(0.808118\pi\) | |||||||
\(332\) | −1257.16 | −0.207819 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7144.14 | 1.17039 | ||||||||
\(335\) | 2304.09 | + | 3990.79i | 0.375778 | + | 0.650867i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 284.447 | − | 492.676i | 0.0459786 | − | 0.0796373i | −0.842120 | − | 0.539290i | \(-0.818693\pi\) |
0.888099 | + | 0.459653i | \(0.152026\pi\) | |||||||
\(338\) | −5120.57 | + | 8869.09i | −0.824031 | + | 1.42726i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3731.46 | + | 6463.08i | 0.595197 | + | 1.03091i | ||||
\(341\) | −650.368 | −0.103283 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13345.6 | 2.10086 | ||||||||
\(344\) | −10118.8 | − | 17526.3i | −1.58596 | − | 2.74696i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2969.75 | + | 5143.76i | −0.461430 | + | 0.799220i | ||||
\(347\) | −4213.28 | + | 7297.61i | −0.651817 | + | 1.12898i | 0.330864 | + | 0.943678i | \(0.392660\pi\) |
−0.982682 | + | 0.185302i | \(0.940674\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3571.98 | − | 6186.85i | −0.547861 | − | 0.948924i | −0.998421 | − | 0.0561773i | \(-0.982109\pi\) |
0.450559 | − | 0.892746i | \(-0.351225\pi\) | |||||||
\(350\) | 4319.89 | 0.659736 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2091.21 | 0.316654 | ||||||||
\(353\) | −2650.35 | − | 4590.54i | −0.399614 | − | 0.692152i | 0.594064 | − | 0.804418i | \(-0.297522\pi\) |
−0.993678 | + | 0.112266i | \(0.964189\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 151.720 | − | 262.788i | 0.0226831 | − | 0.0392882i | ||||
\(356\) | −9123.65 | + | 15802.6i | −1.35829 | + | 2.35263i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4744.92 | − | 8218.44i | −0.700494 | − | 1.21329i | ||||
\(359\) | −9536.35 | −1.40198 | −0.700988 | − | 0.713173i | \(-0.747257\pi\) | ||||
−0.700988 | + | 0.713173i | \(0.747257\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7234.52 | 1.05475 | ||||||||
\(362\) | −6108.32 | − | 10579.9i | −0.886867 | − | 1.53610i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 20629.3 | − | 35731.0i | 2.97052 | − | 5.14509i | ||||
\(365\) | 846.098 | − | 1465.49i | 0.121334 | − | 0.210156i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 365.104 | + | 632.379i | 0.0519299 | + | 0.0899453i | 0.890822 | − | 0.454353i | \(-0.150129\pi\) |
−0.838892 | + | 0.544298i | \(0.816796\pi\) | |||||||
\(368\) | 12167.3 | 1.72354 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2833.03 | 0.398060 | ||||||||
\(371\) | −8057.09 | − | 13955.3i | −1.12750 | − | 1.95289i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6434.47 | + | 11144.8i | −0.893201 | + | 1.54707i | −0.0571863 | + | 0.998364i | \(0.518213\pi\) |
−0.836015 | + | 0.548707i | \(0.815120\pi\) | |||||||
\(374\) | 1225.41 | − | 2122.47i | 0.169423 | − | 0.293449i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 17830.1 | + | 30882.7i | 2.44553 | + | 4.23578i | ||||
\(377\) | −4048.47 | −0.553068 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4000.88 | −0.542246 | −0.271123 | − | 0.962545i | \(-0.587395\pi\) | ||||
−0.271123 | + | 0.962545i | \(0.587395\pi\) | |||||||
\(380\) | 5754.20 | + | 9966.57i | 0.776801 | + | 1.34546i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1158.26 | + | 2006.16i | −0.155135 | + | 0.268702i | ||||
\(383\) | 32.6599 | − | 56.5687i | 0.00435730 | − | 0.00754706i | −0.863839 | − | 0.503769i | \(-0.831946\pi\) |
0.868196 | + | 0.496222i | \(0.165280\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −502.131 | − | 869.716i | −0.0664700 | − | 0.115129i | ||||
\(386\) | −19376.7 | −2.55505 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −20205.7 | −2.64379 | ||||||||
\(389\) | −2959.89 | − | 5126.67i | −0.385790 | − | 0.668207i | 0.606089 | − | 0.795397i | \(-0.292738\pi\) |
−0.991878 | + | 0.127190i | \(0.959404\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2987.02 | − | 5173.66i | 0.386342 | − | 0.669165i | ||||
\(392\) | −22265.6 | + | 38565.1i | −2.86883 | + | 4.96896i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −11753.9 | − | 20358.4i | −1.50293 | − | 2.60315i | ||||
\(395\) | −2781.55 | −0.354317 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10228.7 | −1.29310 | −0.646551 | − | 0.762871i | \(-0.723789\pi\) | ||||
−0.646551 | + | 0.762871i | \(0.723789\pi\) | |||||||
\(398\) | 7677.54 | + | 13297.9i | 0.966936 | + | 1.67478i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1959.92 | + | 3394.68i | −0.244990 | + | 0.424335i | ||||
\(401\) | −6122.56 | + | 10604.6i | −0.762460 | + | 1.32062i | 0.179120 | + | 0.983827i | \(0.442675\pi\) |
−0.941579 | + | 0.336791i | \(0.890658\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3445.34 | − | 5967.50i | −0.425867 | − | 0.737623i | ||||
\(404\) | 13227.4 | 1.62893 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 10854.1 | 1.32680 | ||||||||
\(407\) | −329.303 | − | 570.370i | −0.0401055 | − | 0.0694648i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4916.47 | + | 8515.58i | −0.594386 | + | 1.02951i | 0.399247 | + | 0.916843i | \(0.369272\pi\) |
−0.993633 | + | 0.112664i | \(0.964062\pi\) | |||||||
\(410\) | −1867.87 | + | 3235.24i | −0.224994 | + | 0.389700i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −11765.3 | − | 20378.1i | −1.40688 | − | 2.43679i | ||||
\(413\) | 8017.65 | 0.955262 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −324.210 | −0.0383490 | ||||||||
\(416\) | 11078.2 | + | 19188.1i | 1.30566 | + | 2.26147i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1889.67 | − | 3273.01i | 0.221117 | − | 0.382986i | ||||
\(419\) | −6157.57 | + | 10665.2i | −0.717941 | + | 1.24351i | 0.243873 | + | 0.969807i | \(0.421582\pi\) |
−0.961814 | + | 0.273703i | \(0.911751\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2159.21 | + | 3739.86i | 0.249961 | + | 0.432945i | 0.963515 | − | 0.267656i | \(-0.0862489\pi\) |
−0.713554 | + | 0.700600i | \(0.752916\pi\) | |||||||
\(422\) | −3526.97 | −0.406849 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 29086.3 | 3.33150 | ||||||||
\(425\) | 962.307 | + | 1666.76i | 0.109832 | + | 0.190235i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8243.59 | − | 14278.3i | 0.934275 | − | 1.61821i | ||||
\(428\) | 12717.9 | − | 22028.0i | 1.43631 | − | 2.48777i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4442.71 | − | 7695.00i | −0.498248 | − | 0.862991i | ||||
\(431\) | 5265.39 | 0.588457 | 0.294228 | − | 0.955735i | \(-0.404937\pi\) | ||||
0.294228 | + | 0.955735i | \(0.404937\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5855.07 | 0.649831 | 0.324916 | − | 0.945743i | \(-0.394664\pi\) | ||||
0.324916 | + | 0.945743i | \(0.394664\pi\) | |||||||
\(434\) | 9237.11 | + | 15999.1i | 1.02165 | + | 1.76955i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2857.62 | − | 4949.54i | 0.313888 | − | 0.543669i | ||||
\(437\) | 4606.21 | − | 7978.19i | 0.504222 | − | 0.873338i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2011.35 | − | 3483.76i | −0.218671 | − | 0.378748i | 0.735731 | − | 0.677274i | \(-0.236839\pi\) |
−0.954402 | + | 0.298525i | \(0.903505\pi\) | |||||||
\(440\) | 1812.71 | 0.196403 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 25966.4 | 2.79434 | ||||||||
\(443\) | −3751.11 | − | 6497.12i | −0.402304 | − | 0.696811i | 0.591699 | − | 0.806159i | \(-0.298457\pi\) |
−0.994004 | + | 0.109347i | \(0.965124\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2352.90 | + | 4075.34i | −0.250647 | + | 0.434134i | ||||
\(446\) | −467.120 | + | 809.076i | −0.0495937 | + | 0.0858987i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8993.20 | − | 15576.7i | −0.948412 | − | 1.64270i | ||||
\(449\) | −18574.2 | −1.95227 | −0.976135 | − | 0.217166i | \(-0.930319\pi\) | ||||
−0.976135 | + | 0.217166i | \(0.930319\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 868.461 | 0.0906746 | ||||||||
\(452\) | −15366.3 | − | 26615.2i | −1.59905 | − | 2.76963i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −13219.8 | + | 22897.3i | −1.36659 | + | 2.36701i | ||||
\(455\) | 5320.09 | − | 9214.67i | 0.548153 | − | 0.949429i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7072.78 | − | 12250.4i | −0.723962 | − | 1.25394i | −0.959400 | − | 0.282049i | \(-0.908986\pi\) |
0.235438 | − | 0.971889i | \(-0.424347\pi\) | |||||||
\(458\) | 6850.31 | 0.698895 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7522.62 | 0.762487 | ||||||||
\(461\) | 2455.37 | + | 4252.83i | 0.248066 | + | 0.429662i | 0.962989 | − | 0.269541i | \(-0.0868718\pi\) |
−0.714923 | + | 0.699203i | \(0.753538\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4627.72 | + | 8015.45i | −0.464511 | + | 0.804557i | −0.999179 | − | 0.0405054i | \(-0.987103\pi\) |
0.534668 | + | 0.845062i | \(0.320437\pi\) | |||||||
\(464\) | −4924.49 | + | 8529.47i | −0.492702 | + | 0.853385i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 17247.3 | + | 29873.3i | 1.71452 | + | 2.96964i | ||||
\(467\) | −2825.10 | −0.279936 | −0.139968 | − | 0.990156i | \(-0.544700\pi\) | ||||
−0.139968 | + | 0.990156i | \(0.544700\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −30430.6 | −2.99606 | ||||||||
\(470\) | 7828.40 | + | 13559.2i | 0.768292 | + | 1.33072i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7236.00 | + | 12533.1i | −0.705644 | + | 1.22221i | ||||
\(473\) | −1032.82 | + | 1788.89i | −0.100399 | + | 0.173897i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1483.95 | + | 2570.28i | 0.143344 | + | 0.248279i | ||||
\(476\) | −49282.2 | −4.74547 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8292.29 | 0.793474 | ||||||||
\(479\) | −4586.74 | − | 7944.47i | −0.437523 | − | 0.757812i | 0.559975 | − | 0.828510i | \(-0.310811\pi\) |
−0.997498 | + | 0.0706977i | \(0.977477\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3488.98 | − | 6043.08i | 0.330735 | − | 0.572850i | ||||
\(482\) | 4381.55 | − | 7589.07i | 0.414054 | − | 0.717163i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 12544.1 | + | 21727.0i | 1.17807 | + | 2.04047i | ||||
\(485\) | −5210.85 | −0.487861 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13663.7 | 1.27138 | 0.635690 | − | 0.771945i | \(-0.280716\pi\) | ||||
0.635690 | + | 0.771945i | \(0.280716\pi\) | |||||||
\(488\) | 14879.8 | + | 25772.6i | 1.38028 | + | 2.39072i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −9775.81 | + | 16932.2i | −0.901277 | + | 1.56106i | ||||
\(491\) | 2925.16 | − | 5066.52i | 0.268860 | − | 0.465680i | −0.699707 | − | 0.714430i | \(-0.746686\pi\) |
0.968568 | + | 0.248750i | \(0.0800196\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2417.89 | + | 4187.91i | 0.220885 | + | 0.382584i | ||||
\(494\) | 40042.2 | 3.64694 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −16763.4 | −1.51754 | ||||||||
\(497\) | 1001.90 | + | 1735.35i | 0.0904255 | + | 0.156622i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1921.49 | + | 3328.11i | −0.172380 | + | 0.298571i | −0.939251 | − | 0.343230i | \(-0.888479\pi\) |
0.766872 | + | 0.641801i | \(0.221812\pi\) | |||||||
\(500\) | −1211.76 | + | 2098.82i | −0.108383 | + | 0.187725i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3141.98 | + | 5442.08i | 0.279350 | + | 0.483848i | ||||
\(503\) | 4242.88 | 0.376104 | 0.188052 | − | 0.982159i | \(-0.439783\pi\) | ||||
0.188052 | + | 0.982159i | \(0.439783\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3411.21 | 0.300588 | ||||||||
\(506\) | −1235.21 | − | 2139.44i | −0.108521 | − | 0.187964i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1446.12 | − | 2504.75i | 0.126301 | − | 0.218760i | ||||
\(509\) | −3682.80 | + | 6378.80i | −0.320702 | + | 0.555472i | −0.980633 | − | 0.195854i | \(-0.937252\pi\) |
0.659931 | + | 0.751326i | \(0.270585\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5587.30 | + | 9677.49i | 0.483694 | + | 0.837783i | ||||
\(512\) | −20855.3 | −1.80016 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −27248.5 | −2.33829 | ||||||||
\(515\) | −3034.16 | − | 5255.32i | −0.259614 | − | 0.449664i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1819.90 | − | 3152.16i | 0.154815 | − | 0.268147i | ||||
\(518\) | −9354.11 | + | 16201.8i | −0.793429 | + | 1.37426i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9602.85 | + | 16632.6i | 0.809832 | + | 1.40267i | ||||
\(521\) | −8717.87 | −0.733084 | −0.366542 | − | 0.930401i | \(-0.619458\pi\) | ||||
−0.366542 | + | 0.930401i | \(0.619458\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23515.4 | 1.96607 | 0.983037 | − | 0.183407i | \(-0.0587127\pi\) | ||||
0.983037 | + | 0.183407i | \(0.0587127\pi\) | |||||||
\(524\) | −11359.2 | − | 19674.7i | −0.947004 | − | 1.64026i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −20105.4 | + | 34823.6i | −1.66661 | + | 2.88666i | ||||
\(527\) | −4115.36 | + | 7128.00i | −0.340166 | + | 0.589185i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3072.59 | + | 5321.88i | 0.252535 | + | 0.437403i | ||||
\(530\) | 12770.5 | 1.04663 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −75997.0 | −6.19340 | ||||||||
\(533\) | 4600.69 | + | 7968.63i | 0.373880 | + | 0.647579i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3279.82 | − | 5680.81i | 0.265045 | − | 0.459071i | ||||
\(536\) | 27463.8 | − | 47568.8i | 2.21317 | − | 3.83332i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1633.53 | + | 2829.36i | 0.130905 | + | 0.226733i | ||||
\(539\) | 4545.24 | 0.363224 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3803.94 | 0.302300 | 0.151150 | − | 0.988511i | \(-0.451702\pi\) | ||||
0.151150 | + | 0.988511i | \(0.451702\pi\) | |||||||
\(542\) | 3826.94 | + | 6628.45i | 0.303286 | + | 0.525307i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 13232.6 | − | 22919.6i | 1.04291 | − | 1.80638i | ||||
\(545\) | 736.951 | − | 1276.44i | 0.0579221 | − | 0.100324i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8667.95 | − | 15013.3i | −0.677540 | − | 1.17353i | −0.975719 | − | 0.219024i | \(-0.929713\pi\) |
0.298179 | − | 0.954510i | \(-0.403621\pi\) | |||||||
\(548\) | −22463.6 | −1.75109 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 795.878 | 0.0617025 | ||||||||
\(551\) | 3728.57 | + | 6458.07i | 0.288280 | + | 0.499316i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9184.14 | − | 15907.4i | 0.706238 | − | 1.22324i | ||||
\(554\) | 15433.3 | − | 26731.2i | 1.18357 | − | 2.05000i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −15379.9 | − | 26638.7i | −1.17311 | − | 2.03189i | ||||
\(557\) | 7797.62 | 0.593170 | 0.296585 | − | 0.955006i | \(-0.404152\pi\) | ||||
0.296585 | + | 0.955006i | \(0.404152\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21885.4 | −1.65591 | ||||||||
\(560\) | −12942.6 | − | 22417.2i | −0.976648 | − | 1.69160i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 13797.5 | − | 23898.0i | 1.03561 | − | 1.79373i | ||||
\(563\) | 5767.81 | − | 9990.14i | 0.431766 | − | 0.747840i | −0.565260 | − | 0.824913i | \(-0.691224\pi\) |
0.997025 | + | 0.0770727i | \(0.0245574\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3962.81 | − | 6863.79i | −0.295074 | − | 0.511083i | ||||
\(566\) | −5857.52 | −0.435000 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3616.90 | −0.267186 | ||||||||
\(569\) | 5038.86 | + | 8727.56i | 0.371248 | + | 0.643020i | 0.989758 | − | 0.142757i | \(-0.0455967\pi\) |
−0.618510 | + | 0.785777i | \(0.712263\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8169.66 | − | 14150.3i | 0.598756 | − | 1.03708i | −0.394249 | − | 0.919004i | \(-0.628995\pi\) |
0.993005 | − | 0.118072i | \(-0.0376714\pi\) | |||||||
\(572\) | 3800.66 | − | 6582.93i | 0.277821 | − | 0.481200i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −12334.7 | − | 21364.3i | −0.896932 | − | 1.55353i | ||||
\(575\) | 1940.01 | 0.140703 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18648.6 | 1.34550 | 0.672748 | − | 0.739871i | \(-0.265114\pi\) | ||||
0.672748 | + | 0.739871i | \(0.265114\pi\) | |||||||
\(578\) | −2652.32 | − | 4593.95i | −0.190868 | − | 0.330593i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3044.65 | + | 5273.50i | −0.217970 | + | 0.377535i | ||||
\(581\) | 1070.48 | − | 1854.12i | 0.0764387 | − | 0.132396i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1484.40 | − | 2571.06i | −0.105451 | − | 0.182646i | ||||
\(584\) | −20170.3 | −1.42920 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4923.24 | −0.347060 | ||||||||
\(587\) | 9048.54 | + | 15672.5i | 0.636241 | + | 1.10200i | 0.986251 | + | 0.165255i | \(0.0528449\pi\) |
−0.350010 | + | 0.936746i | \(0.613822\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6346.20 | + | 10991.9i | −0.443957 | + | 0.768956i | ||||
\(590\) | −3177.00 | + | 5502.72i | −0.221686 | + | 0.383972i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −8487.87 | − | 14701.4i | −0.589273 | − | 1.02065i | ||||
\(593\) | 27154.1 | 1.88041 | 0.940207 | − | 0.340602i | \(-0.110631\pi\) | ||||
0.940207 | + | 0.340602i | \(0.110631\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12709.4 | −0.875688 | ||||||||
\(596\) | −5012.88 | − | 8682.57i | −0.344523 | − | 0.596731i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 13087.1 | − | 22667.5i | 0.894934 | − | 1.55007i | ||||
\(599\) | −1728.73 | + | 2994.25i | −0.117920 | + | 0.204243i | −0.918943 | − | 0.394390i | \(-0.870956\pi\) |
0.801023 | + | 0.598633i | \(0.204289\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1469.21 | + | 2544.75i | 0.0997179 | + | 0.172717i | 0.911568 | − | 0.411150i | \(-0.134873\pi\) |
−0.811850 | + | 0.583866i | \(0.801539\pi\) | |||||||
\(602\) | 58675.9 | 3.97251 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10771.8 | 0.725656 | ||||||||
\(605\) | 3234.99 | + | 5603.17i | 0.217390 | + | 0.376531i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3892.97 | − | 6742.82i | 0.260314 | − | 0.450877i | −0.706011 | − | 0.708201i | \(-0.749507\pi\) |
0.966325 | + | 0.257323i | \(0.0828405\pi\) | |||||||
\(608\) | 20405.8 | − | 35343.8i | 1.36112 | − | 2.35753i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6533.05 | + | 11315.6i | 0.433632 | + | 0.751073i | ||||
\(611\) | 38563.8 | 2.55339 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23893.4 | 1.57430 | 0.787151 | − | 0.616760i | \(-0.211555\pi\) | ||||
0.787151 | + | 0.616760i | \(0.211555\pi\) | |||||||
\(614\) | −5055.13 | − | 8755.74i | −0.332261 | − | 0.575493i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5985.21 | + | 10366.7i | −0.391479 | + | 0.678061i | ||||
\(617\) | 2440.23 | − | 4226.60i | 0.159222 | − | 0.275781i | −0.775366 | − | 0.631512i | \(-0.782435\pi\) |
0.934588 | + | 0.355731i | \(0.115768\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7941.77 | − | 13755.6i | −0.515681 | − | 0.893186i | −0.999834 | − | 0.0182030i | \(-0.994205\pi\) |
0.484153 | − | 0.874983i | \(-0.339128\pi\) | |||||||
\(620\) | −10364.3 | −0.671354 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −32960.6 | −2.12476 | ||||||||
\(623\) | −15537.6 | − | 26911.9i | −0.999200 | − | 1.73067i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −312.500 | + | 541.266i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 4759.24 | − | 8243.24i | 0.303862 | − | 0.526304i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10217.8 | − | 17697.8i | −0.649261 | − | 1.12455i | ||||
\(629\) | −8334.96 | −0.528357 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12862.4 | −0.811479 | −0.405740 | − | 0.913989i | \(-0.632986\pi\) | ||||
−0.405740 | + | 0.913989i | \(0.632986\pi\) | |||||||
\(632\) | 16577.5 | + | 28713.1i | 1.04338 | + | 1.80719i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8265.15 | + | 14315.7i | −0.517746 | + | 0.896763i | ||||
\(635\) | 372.939 | − | 645.949i | 0.0233065 | − | 0.0403680i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 24078.5 | + | 41705.2i | 1.49768 | + | 2.59407i | ||||
\(638\) | 1999.72 | 0.124090 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 503.275 | 0.0310839 | ||||||||
\(641\) | 14742.8 | + | 25535.3i | 0.908435 | + | 1.57346i | 0.816238 | + | 0.577715i | \(0.196056\pi\) |
0.0921970 | + | 0.995741i | \(0.470611\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7057.32 | − | 12223.6i | 0.432836 | − | 0.749694i | −0.564280 | − | 0.825583i | \(-0.690846\pi\) |
0.997116 | + | 0.0758891i | \(0.0241795\pi\) | |||||||
\(644\) | −24838.2 | + | 43021.1i | −1.51982 | + | 2.63240i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −23914.7 | − | 41421.4i | −1.45652 | − | 2.52276i | ||||
\(647\) | −13313.3 | −0.808962 | −0.404481 | − | 0.914546i | \(-0.632548\pi\) | ||||
−0.404481 | + | 0.914546i | \(0.632548\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1477.14 | 0.0893418 | ||||||||
\(650\) | 4216.18 | + | 7302.63i | 0.254419 | + | 0.440666i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6164.60 | − | 10677.4i | 0.370283 | − | 0.641349i | ||||
\(653\) | −5753.08 | + | 9964.62i | −0.344771 | + | 0.597160i | −0.985312 | − | 0.170763i | \(-0.945377\pi\) |
0.640541 | + | 0.767924i | \(0.278710\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2929.43 | − | 5073.92i | −0.174752 | − | 0.302679i | ||||
\(656\) | 22384.8 | 1.33229 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −103391. | −6.12556 | ||||||||
\(659\) | 12885.8 | + | 22318.9i | 0.761699 | + | 1.31930i | 0.941974 | + | 0.335686i | \(0.108968\pi\) |
−0.180275 | + | 0.983616i | \(0.557699\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3941.44 | + | 6826.77i | −0.231928 | + | 0.401710i | −0.958375 | − | 0.285511i | \(-0.907837\pi\) |
0.726448 | + | 0.687222i | \(0.241170\pi\) | |||||||
\(662\) | 2493.93 | − | 4319.62i | 0.146419 | − | 0.253605i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1932.23 | + | 3346.72i | 0.112929 | + | 0.195599i | ||||
\(665\) | −19598.9 | −1.14287 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4874.46 | 0.282968 | ||||||||
\(668\) | −13233.5 | − | 22921.1i | −0.766495 | − | 1.32761i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 12058.1 | − | 20885.3i | 0.695292 | − | 1.20428i | ||||
\(671\) | 1518.77 | − | 2630.58i | 0.0873790 | − | 0.151345i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9815.64 | + | 17001.2i | 0.562207 | + | 0.973771i | 0.997304 | + | 0.0733871i | \(0.0233808\pi\) |
−0.435097 | + | 0.900384i | \(0.643286\pi\) | |||||||
\(674\) | −2977.23 | −0.170146 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 37940.5 | 2.15865 | ||||||||
\(677\) | −299.163 | − | 518.166i | −0.0169834 | − | 0.0294161i | 0.857409 | − | 0.514636i | \(-0.172073\pi\) |
−0.874392 | + | 0.485220i | \(0.838740\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17205.2 | − | 29800.3i | 0.972423 | − | 1.68429i | ||||
\(680\) | 11470.3 | − | 19867.2i | 0.646863 | − | 1.12040i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1701.81 | + | 2947.62i | 0.0955507 | + | 0.165499i | ||||
\(683\) | −19041.9 | −1.06679 | −0.533394 | − | 0.845867i | \(-0.679084\pi\) | ||||
−0.533394 | + | 0.845867i | \(0.679084\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5793.13 | −0.323130 | ||||||||
\(686\) | −34921.2 | − | 60485.3i | −1.94358 | − | 3.36638i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −26621.1 | + | 46109.1i | −1.47517 | + | 2.55508i | ||||
\(689\) | 15727.3 | − | 27240.5i | 0.869612 | − | 1.50621i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13585.4 | + | 23530.6i | 0.747921 | + | 1.29544i | 0.948817 | + | 0.315825i | \(0.102281\pi\) |
−0.200896 | + | 0.979613i | \(0.564385\pi\) | |||||||
\(692\) | 22004.1 | 1.20877 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 44099.2 | 2.41208 | ||||||||
\(695\) | −3966.31 | − | 6869.85i | −0.216476 | − | 0.374947i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5495.39 | − | 9518.29i | 0.298641 | − | 0.517261i | ||||
\(698\) | −18693.5 | + | 32378.0i | −1.01369 | + | 1.75577i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −8001.96 | − | 13859.8i | −0.432065 | − | 0.748359i | ||||
\(701\) | −27091.0 | −1.45965 | −0.729824 | − | 0.683635i | \(-0.760398\pi\) | ||||
−0.729824 | + | 0.683635i | \(0.760398\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12853.2 | −0.689568 | ||||||||
\(704\) | −1656.87 | − | 2869.78i | −0.0887012 | − | 0.153635i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13870.2 | + | 24023.9i | −0.739395 | + | 1.28067i | ||||
\(707\) | −11263.2 | + | 19508.4i | −0.599144 | + | 1.03775i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2477.30 | + | 4290.81i | 0.131223 | + | 0.227284i | 0.924148 | − | 0.382034i | \(-0.124776\pi\) |
−0.792925 | + | 0.609319i | \(0.791443\pi\) | |||||||
\(710\) | −1588.02 | −0.0839398 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 56091.3 | 2.95240 | ||||||||
\(713\) | 4148.28 | + | 7185.03i | 0.217888 | + | 0.377393i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 980.152 | − | 1697.67i | 0.0512666 | − | 0.0887963i | ||||
\(716\) | −17578.6 | + | 30447.0i | −0.917516 | + | 1.58918i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 24953.6 | + | 43220.9i | 1.29702 | + | 2.24650i | ||||
\(719\) | −23414.3 | −1.21447 | −0.607235 | − | 0.794522i | \(-0.707721\pi\) | ||||
−0.607235 | + | 0.794522i | \(0.707721\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 40072.8 | 2.06989 | ||||||||
\(722\) | −18930.4 | − | 32788.5i | −0.975787 | − | 1.69011i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −22629.5 | + | 39195.5i | −1.16163 | + | 2.01200i | ||||
\(725\) | −785.186 | + | 1359.98i | −0.0402222 | + | 0.0696669i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15477.8 | − | 26808.4i | −0.789603 | − | 1.36763i | −0.926210 | − | 0.377007i | \(-0.876953\pi\) |
0.136607 | − | 0.990625i | \(-0.456380\pi\) | |||||||
\(728\) | −126827. | −6.45676 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −8855.88 | −0.449001 | ||||||||
\(731\) | 13070.8 | + | 22639.2i | 0.661340 | + | 1.14547i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7786.36 | + | 13486.4i | −0.392354 | + | 0.679578i | −0.992760 | − | 0.120118i | \(-0.961673\pi\) |
0.600405 | + | 0.799696i | \(0.295006\pi\) | |||||||
\(734\) | 1910.72 | − | 3309.47i | 0.0960846 | − | 0.166423i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −13338.5 | − | 23103.0i | −0.668021 | − | 1.15705i | ||||
\(737\) | −5606.40 | −0.280210 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30909.9 | −1.53862 | −0.769310 | − | 0.638876i | \(-0.779400\pi\) | ||||
−0.769310 | + | 0.638876i | \(0.779400\pi\) | |||||||
\(740\) | −5247.78 | − | 9089.42i | −0.260692 | − | 0.451532i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −42165.7 | + | 73033.1i | −2.08619 | + | 3.61338i | ||||
\(743\) | −17511.6 | + | 30331.0i | −0.864656 | + | 1.49763i | 0.00273301 | + | 0.999996i | \(0.499130\pi\) |
−0.867389 | + | 0.497631i | \(0.834203\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1292.77 | − | 2239.15i | −0.0635752 | − | 0.110115i | ||||
\(746\) | 67347.8 | 3.30533 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −9079.55 | −0.443825 | ||||||||
\(749\) | 21658.6 | + | 37513.8i | 1.05659 | + | 1.83007i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1805.39 | − | 3127.03i | 0.0877226 | − | 0.151940i | −0.818826 | − | 0.574043i | \(-0.805374\pi\) |
0.906548 | + | 0.422102i | \(0.138708\pi\) | |||||||
\(752\) | 46908.4 | − | 81247.7i | 2.27470 | − | 3.93989i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 10593.5 | + | 18348.6i | 0.511664 | + | 0.886227i | ||||
\(755\) | 2777.93 | 0.133906 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19982.2 | −0.959399 | −0.479700 | − | 0.877433i | \(-0.659254\pi\) | ||||
−0.479700 | + | 0.877433i | \(0.659254\pi\) | |||||||
\(758\) | 10469.0 | + | 18132.9i | 0.501652 | + | 0.868887i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 17688.1 | − | 30636.8i | 0.844232 | − | 1.46225i | ||||
\(761\) | −17578.7 | + | 30447.1i | −0.837354 | + | 1.45034i | 0.0547461 | + | 0.998500i | \(0.482565\pi\) |
−0.892100 | + | 0.451839i | \(0.850768\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4866.54 | + | 8429.09i | 0.230905 | + | 0.399939i | ||||
\(764\) | 8582.02 | 0.406396 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −341.843 | −0.0161244 | ||||||||
\(767\) | 7825.17 | + | 13553.6i | 0.368384 | + | 0.638060i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19520.6 | − | 33810.6i | 0.915384 | − | 1.58549i | 0.109045 | − | 0.994037i | \(-0.465221\pi\) |
0.806339 | − | 0.591454i | \(-0.201446\pi\) | |||||||
\(770\) | −2627.83 | + | 4551.54i | −0.122988 | + | 0.213021i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 35892.6 | + | 62167.8i | 1.67332 | + | 2.89828i | ||||
\(773\) | −18244.4 | −0.848907 | −0.424453 | − | 0.905450i | \(-0.639534\pi\) | ||||
−0.424453 | + | 0.905450i | \(0.639534\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2672.85 | −0.123886 | ||||||||
\(776\) | 31055.7 | + | 53790.0i | 1.43664 | + | 2.48834i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −15490.2 | + | 26829.7i | −0.713816 | + | 1.23637i | ||||
\(779\) | 8474.32 | − | 14677.9i | 0.389761 | − | 0.675086i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 184.586 | + | 319.713i | 0.00845713 | + | 0.0146482i | ||||
\(782\) | −31264.3 | −1.42968 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 117155. | 5.33686 | ||||||||
\(785\) | −2635.08 | − | 4564.09i | −0.119809 | − | 0.207515i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21444.1 | + | 37142.2i | −0.971282 | + | 1.68231i | −0.279587 | + | 0.960120i | \(0.590198\pi\) |
−0.691695 | + | 0.722190i | \(0.743136\pi\) | |||||||
\(788\) | −43544.9 | + | 75422.0i | −1.96856 | + | 3.40964i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7278.44 | + | 12606.6i | 0.327791 | + | 0.567751i | ||||
\(791\) | 52337.7 | 2.35261 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 32182.7 | 1.44116 | ||||||||
\(794\) | 26765.1 | + | 46358.6i | 1.19630 | + | 2.07205i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 28443.1 | − | 49264.9i | 1.26651 | − | 2.19365i | ||||
\(797\) | 5736.57 | − | 9936.03i | 0.254956 | − | 0.441596i | −0.709928 | − | 0.704274i | \(-0.751272\pi\) |
0.964883 | + | 0.262678i | \(0.0846058\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −23031.7 | − | 39892.0i | −1.01978 | − | 1.76631i | ||||
\(800\) | 8594.35 | 0.379820 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 64083.2 | 2.82152 | ||||||||
\(803\) | 1029.38 | + | 1782.94i | 0.0452380 | + | 0.0783545i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6405.53 | + | 11094.7i | −0.280454 | + | 0.485760i | ||||
\(806\) | −18030.7 | + | 31230.1i | −0.787971 | + | 1.36481i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −20330.2 | − | 35212.9i | −0.885165 | − | 1.53315i | ||||
\(809\) | 6454.45 | 0.280502 | 0.140251 | − | 0.990116i | \(-0.455209\pi\) | ||||
0.140251 | + | 0.990116i | \(0.455209\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11250.0 | −0.487102 | −0.243551 | − | 0.969888i | \(-0.578312\pi\) | ||||
−0.243551 | + | 0.969888i | \(0.578312\pi\) | |||||||
\(812\) | −20105.7 | − | 34824.1i | −0.868931 | − | 1.50503i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1723.36 | + | 2984.95i | −0.0742062 | + | 0.128529i | ||||
\(815\) | 1589.79 | − | 2753.60i | 0.0683288 | − | 0.118349i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20156.1 | + | 34911.4i | 0.863125 | + | 1.49498i | ||||
\(818\) | 51459.4 | 2.19955 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13839.8 | 0.589399 | ||||||||
\(821\) | −266.219 | − | 461.105i | −0.0113168 | − | 0.0196013i | 0.860312 | − | 0.509769i | \(-0.170269\pi\) |
−0.871628 | + | 0.490167i | \(0.836936\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16508.3 | − | 28593.3i | 0.699204 | − | 1.21106i | −0.269539 | − | 0.962989i | \(-0.586871\pi\) |
0.968743 | − | 0.248067i | \(-0.0797953\pi\) | |||||||
\(824\) | −36166.0 | + | 62641.4i | −1.52901 | + | 2.64832i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −20979.7 | − | 36337.8i | −0.883748 | − | 1.53070i | ||||
\(827\) | 36231.3 | 1.52344 | 0.761720 | − | 0.647906i | \(-0.224355\pi\) | ||||
0.761720 | + | 0.647906i | \(0.224355\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 36588.3 | 1.53289 | 0.766445 | − | 0.642310i | \(-0.222024\pi\) | ||||
0.766445 | + | 0.642310i | \(0.222024\pi\) | |||||||
\(830\) | 848.354 | + | 1469.39i | 0.0354781 | + | 0.0614498i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 17554.6 | − | 30405.4i | 0.731485 | − | 1.26697i | ||||
\(833\) | 28761.1 | − | 49815.6i | 1.19629 | − | 2.07204i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3412.78 | − | 5911.12i | −0.141442 | − | 0.244985i | ||||
\(836\) | −14001.4 | −0.579243 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 64449.7 | 2.65677 | ||||||||
\(839\) | 7663.38 | + | 13273.4i | 0.315339 | + | 0.546183i | 0.979509 | − | 0.201398i | \(-0.0645485\pi\) |
−0.664171 | + | 0.747581i | \(0.731215\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10221.6 | − | 17704.4i | 0.419109 | − | 0.725918i | ||||
\(842\) | 11299.9 | − | 19572.1i | 0.462496 | − | 0.801066i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6533.21 | + | 11315.8i | 0.266448 | + | 0.461502i | ||||
\(845\) | 9784.48 | 0.398339 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −42725.2 | −1.73324 | ||||||||
\(848\) | −38260.9 | − | 66269.9i | −1.54939 | − | 2.68363i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 5036.10 | − | 8722.78i | 0.203220 | − | 0.351987i | ||||
\(851\) | −4200.82 | + | 7276.04i | −0.169215 | + | 0.293090i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2286.65 | − | 3960.59i | −0.0917859 | − | 0.158978i | 0.816477 | − | 0.577378i | \(-0.195924\pi\) |
−0.908263 | + | 0.418400i | \(0.862591\pi\) | |||||||
\(854\) | −86283.4 | −3.45733 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −78188.3 | −3.12199 | ||||||||
\(857\) | 9784.58 | + | 16947.4i | 0.390006 | + | 0.675509i | 0.992450 | − | 0.122652i | \(-0.0391398\pi\) |
−0.602444 | + | 0.798161i | \(0.705806\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10948.5 | + | 18963.3i | −0.434875 | + | 0.753226i | −0.997285 | − | 0.0736324i | \(-0.976541\pi\) |
0.562410 | + | 0.826858i | \(0.309874\pi\) | |||||||
\(860\) | −16459.0 | + | 28507.8i | −0.652612 | + | 1.13036i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −13777.9 | − | 23863.9i | −0.544403 | − | 0.942934i | ||||
\(863\) | −13335.5 | −0.526008 | −0.263004 | − | 0.964795i | \(-0.584713\pi\) | ||||
−0.263004 | + | 0.964795i | \(0.584713\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5674.65 | 0.223057 | ||||||||
\(866\) | −15320.9 | − | 26536.5i | −0.601183 | − | 1.04128i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 34220.8 | − | 59272.2i | 1.33817 | − | 2.31778i | ||||
\(869\) | 1692.05 | − | 2930.71i | 0.0660516 | − | 0.114405i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29700.0 | − | 51441.9i | −1.15539 | − | 2.00120i | ||||
\(872\) | −17568.4 | −0.682270 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −48211.9 | −1.86590 | ||||||||
\(875\) | −2063.63 | − | 3574.31i | −0.0797295 | − | 0.138096i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10905.9 | − | 18889.5i | 0.419915 | − | 0.727314i | −0.576015 | − | 0.817439i | \(-0.695393\pi\) |
0.995931 | + | 0.0901245i | \(0.0287265\pi\) | |||||||
\(878\) | −10526.1 | + | 18231.8i | −0.404600 | + | 0.700788i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2384.48 | − | 4130.05i | −0.0913419 | − | 0.158209i | ||||
\(881\) | −3646.54 | −0.139450 | −0.0697248 | − | 0.997566i | \(-0.522212\pi\) | ||||
−0.0697248 | + | 0.997566i | \(0.522212\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9019.80 | 0.343760 | 0.171880 | − | 0.985118i | \(-0.445016\pi\) | ||||
0.171880 | + | 0.985118i | \(0.445016\pi\) | |||||||
\(884\) | −48099.1 | − | 83310.0i | −1.83003 | − | 3.16970i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −19630.9 | + | 34001.8i | −0.744373 | + | 1.28929i | ||||
\(887\) | −9865.97 | + | 17088.4i | −0.373469 | + | 0.646867i | −0.990097 | − | 0.140388i | \(-0.955165\pi\) |
0.616628 | + | 0.787255i | \(0.288498\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2462.74 | + | 4265.60i | 0.0929108 | + | 0.160926i | ||||
\(890\) | 24627.2 | 0.927533 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3461.09 | 0.129917 | ||||||||
\(893\) | −35516.6 | − | 61516.6i | −1.33093 | − | 2.30523i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4533.34 | + | 7851.97i | −0.169310 | + | 0.293254i | ||||
\(896\) | −1661.72 | + | 2878.18i | −0.0619576 | + | 0.107314i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 48602.7 | + | 84182.3i | 1.80612 | + | 3.12829i | ||||
\(899\) | −6715.78 | −0.249148 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −37571.6 | −1.38923 | ||||||||
\(902\) | −2272.49 | − | 3936.06i | −0.0838864 | − | 0.145296i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −47235.2 | + | 81813.7i | −1.73785 | + | 3.01005i | ||||
\(905\) | −5835.94 | + | 10108.1i | −0.214357 | + | 0.371277i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3853.07 | − | 6673.71i | −0.141057 | − | 0.244319i | 0.786838 | − | 0.617160i | \(-0.211717\pi\) |
−0.927895 | + | 0.372841i | \(0.878384\pi\) | |||||||
\(908\) | 97950.7 | 3.57997 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −55684.0 | −2.02847 | ||||||||
\(911\) | −12382.6 | − | 21447.2i | −0.450332 | − | 0.779998i | 0.548074 | − | 0.836430i | \(-0.315361\pi\) |
−0.998406 | + | 0.0564313i | \(0.982028\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 197.220 | − | 341.596i | 0.00714901 | − | 0.0123824i | ||||
\(914\) | −37014.4 | + | 64110.8i | −1.33953 | + | 2.32013i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −12689.2 | − | 21978.4i | −0.457711 | − | 0.792779i | ||||
\(917\) | 38689.6 | 1.39329 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4899.44 | −0.175862 | −0.0879312 | − | 0.996127i | \(-0.528026\pi\) | ||||
−0.0879312 | + | 0.996127i | \(0.528026\pi\) | |||||||
\(920\) | −11562.1 | − | 20026.1i | −0.414338 | − | 0.717654i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 12849.9 | − | 22256.6i | 0.458989 | − | 0.794993i | ||||
\(923\) | −1955.70 | + | 3387.37i | −0.0697428 | + | 0.120798i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1353.35 | − | 2344.07i | −0.0481058 | − | 0.0833217i | ||||
\(926\) | 48437.1 | 1.71894 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 21594.1 | 0.763860 | ||||||||
\(929\) | −6678.09 | − | 11566.8i | −0.235846 | − | 0.408498i | 0.723672 | − | 0.690144i | \(-0.242453\pi\) |
−0.959518 | + | 0.281646i | \(0.909120\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 44351.8 | − | 76819.6i | 1.56130 | − | 2.70425i | ||||
\(932\) | 63896.4 | − | 110672.i | 2.24570 | − | 3.88967i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7392.40 | + | 12804.0i | 0.258979 | + | 0.448565i | ||||
\(935\) | −2341.53 | −0.0818996 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4960.13 | 0.172935 | 0.0864677 | − | 0.996255i | \(-0.472442\pi\) | ||||
0.0864677 | + | 0.996255i | \(0.472442\pi\) | |||||||
\(938\) | 79627.1 | + | 137918.i | 2.77177 | + | 4.80084i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 29002.0 | − | 50232.9i | 1.00632 | − | 1.74300i | ||||
\(941\) | −27787.2 | + | 48128.8i | −0.962631 | + | 1.66733i | −0.246781 | + | 0.969071i | \(0.579373\pi\) |
−0.715850 | + | 0.698254i | \(0.753961\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5539.35 | − | 9594.44i | −0.191290 | − | 0.331323i | ||||
\(944\) | 38073.7 | 1.31270 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10810.2 | 0.371533 | ||||||||
\(947\) | 10472.8 | + | 18139.4i | 0.359366 | + | 0.622440i | 0.987855 | − | 0.155378i | \(-0.0496597\pi\) |
−0.628489 | + | 0.777818i | \(0.716326\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10906.3 | + | 18890.3i | −0.373061 | + | 0.646160i | ||||
\(950\) | 7766.06 | − | 13451.2i | 0.265226 | − | 0.459384i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 75745.6 | + | 131195.i | 2.57871 | + | 4.46645i | ||||
\(953\) | −26967.8 | −0.916656 | −0.458328 | − | 0.888783i | \(-0.651551\pi\) | ||||
−0.458328 | + | 0.888783i | \(0.651551\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2213.22 | 0.0749927 | ||||||||
\(956\) | −15360.3 | − | 26604.8i | −0.519651 | − | 0.900062i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −24004.1 | + | 41576.3i | −0.809537 | + | 1.40216i | ||||
\(959\) | 19127.8 | − | 33130.3i | 0.644075 | − | 1.11557i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9180.22 | + | 15900.6i | 0.308154 | + | 0.533738i | ||||
\(962\) | −36518.2 | −1.22390 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −32464.8 | −1.08467 | ||||||||
\(965\) | 9256.35 | + | 16032.5i | 0.308780 | + | 0.534822i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9253.25 | − | 16027.1i | 0.307719 | − | 0.532985i | −0.670144 | − | 0.742231i | \(-0.733768\pi\) |
0.977863 | + | 0.209246i | \(0.0671009\pi\) | |||||||
\(968\) | 38559.8 | − | 66787.6i | 1.28033 | − | 2.21760i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 13635.1 | + | 23616.7i | 0.451338 | + | 0.781740i | ||||
\(971\) | −56274.4 | −1.85987 | −0.929934 | − | 0.367726i | \(-0.880136\pi\) | ||||
−0.929934 | + | 0.367726i | \(0.880136\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 52383.9 | 1.72595 | ||||||||
\(974\) | −35753.6 | − | 61927.0i | −1.17620 | − | 2.03724i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 39146.6 | − | 67803.9i | 1.28386 | − | 2.22372i | ||||
\(977\) | −11582.8 | + | 20062.1i | −0.379292 | + | 0.656952i | −0.990959 | − | 0.134162i | \(-0.957166\pi\) |
0.611668 | + | 0.791115i | \(0.290499\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2862.59 | − | 4958.15i | −0.0934512 | − | 0.161862i | ||||
\(980\) | 72433.1 | 2.36101 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −30616.8 | −0.994931 | ||||||||
\(983\) | −1643.43 | − | 2846.50i | −0.0533237 | − | 0.0923594i | 0.838131 | − | 0.545468i | \(-0.183648\pi\) |
−0.891455 | + | 0.453109i | \(0.850315\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11229.8 | + | 19450.6i | −0.363260 | + | 0.629185i | ||||
\(986\) | 12653.7 | − | 21916.8i | 0.408697 | − | 0.707885i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −74172.5 | − | 128471.i | −2.38840 | − | 4.13683i | ||||
\(989\) | 26350.6 | 0.847221 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35155.7 | 1.12690 | 0.563450 | − | 0.826150i | \(-0.309474\pi\) | ||||
0.563450 | + | 0.826150i | \(0.309474\pi\) | |||||||
\(992\) | 18377.1 | + | 31830.1i | 0.588179 | + | 1.01876i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5243.32 | − | 9081.70i | 0.167312 | − | 0.289793i | ||||
\(995\) | 7335.19 | − | 12704.9i | 0.233710 | − | 0.404797i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6820.73 | + | 11813.9i | 0.216665 | + | 0.375274i | 0.953786 | − | 0.300486i | \(-0.0971488\pi\) |
−0.737122 | + | 0.675760i | \(0.763816\pi\) | |||||||
\(998\) | 20111.7 | 0.637900 | ||||||||
\(999\) | 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 | 405.4.e.w.271.1 | 12 | ||
3.2 | odd | 2 | 405.4.e.x.271.6 | 12 | |||
9.2 | odd | 6 | 405.4.e.x.136.6 | 12 | |||
9.4 | even | 3 | 405.4.a.l.1.6 | yes | 6 | ||
9.5 | odd | 6 | 405.4.a.k.1.1 | ✓ | 6 | ||
9.7 | even | 3 | inner | 405.4.e.w.136.1 | 12 | ||
45.4 | even | 6 | 2025.4.a.y.1.1 | 6 | |||
45.14 | odd | 6 | 2025.4.a.z.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
405.4.a.k.1.1 | ✓ | 6 | 9.5 | odd | 6 | ||
405.4.a.l.1.6 | yes | 6 | 9.4 | even | 3 | ||
405.4.e.w.136.1 | 12 | 9.7 | even | 3 | inner | ||
405.4.e.w.271.1 | 12 | 1.1 | even | 1 | trivial | ||
405.4.e.x.136.6 | 12 | 9.2 | odd | 6 | |||
405.4.e.x.271.6 | 12 | 3.2 | odd | 2 | |||
2025.4.a.y.1.1 | 6 | 45.4 | even | 6 | |||
2025.4.a.z.1.6 | 6 | 45.14 | odd | 6 |