Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [648,4,Mod(217,648)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(648, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("648.217");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 648 = 2^{3} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 648.i (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: | \(38.2332376837\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.897122304.10 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 8x^{6} + 51x^{4} - 104x^{2} + 169 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 433.3 | ||
Root | \(2.07341 - 1.19709i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 648.433 |
Dual form | 648.4.i.u.217.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(487\) | \(569\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.90171 | − | 5.02591i | 0.259537 | − | 0.449531i | −0.706581 | − | 0.707632i | \(-0.749763\pi\) |
0.966118 | + | 0.258101i | \(0.0830967\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 13.0614 | + | 22.6230i | 0.705249 | + | 1.22153i | 0.966602 | + | 0.256283i | \(0.0824979\pi\) |
−0.261353 | + | 0.965243i | \(0.584169\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 18.6230 | + | 32.2560i | 0.510458 | + | 0.884140i | 0.999927 | + | 0.0121186i | \(0.00385755\pi\) |
−0.489468 | + | 0.872021i | \(0.662809\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 15.1687 | − | 26.2729i | 0.323618 | − | 0.560522i | −0.657614 | − | 0.753355i | \(-0.728434\pi\) |
0.981232 | + | 0.192833i | \(0.0617675\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −48.4744 | −0.691575 | −0.345787 | − | 0.938313i | \(-0.612388\pi\) | ||||
−0.345787 | + | 0.938313i | \(0.612388\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 88.1865 | 1.06481 | 0.532404 | − | 0.846490i | \(-0.321289\pi\) | ||||
0.532404 | + | 0.846490i | \(0.321289\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −42.2630 | + | 73.2016i | −0.383149 | + | 0.663634i | −0.991511 | − | 0.130026i | \(-0.958494\pi\) |
0.608361 | + | 0.793660i | \(0.291827\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 45.6601 | + | 79.0857i | 0.365281 | + | 0.632685i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −88.3618 | − | 153.047i | −0.565806 | − | 0.980005i | −0.996974 | − | 0.0777332i | \(-0.975232\pi\) |
0.431168 | − | 0.902272i | \(-0.358102\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −77.6920 | + | 134.566i | −0.450126 | + | 0.779640i | −0.998393 | − | 0.0566624i | \(-0.981954\pi\) |
0.548268 | + | 0.836303i | \(0.315287\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 151.601 | 0.732152 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −258.310 | −1.14773 | −0.573864 | − | 0.818951i | \(-0.694556\pi\) | ||||
−0.573864 | + | 0.818951i | \(0.694556\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −110.143 | + | 190.774i | −0.419549 | + | 0.726680i | −0.995894 | − | 0.0905264i | \(-0.971145\pi\) |
0.576345 | + | 0.817206i | \(0.304478\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 23.8807 | + | 41.3626i | 0.0846925 | + | 0.146692i | 0.905260 | − | 0.424858i | \(-0.139676\pi\) |
−0.820568 | + | 0.571549i | \(0.806343\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −64.7495 | − | 112.149i | −0.200951 | − | 0.348057i | 0.747884 | − | 0.663829i | \(-0.231070\pi\) |
−0.948835 | + | 0.315772i | \(0.897736\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −169.700 | + | 293.928i | −0.494751 | + | 0.856934i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 577.029 | 1.49549 | 0.747746 | − | 0.663985i | \(-0.231136\pi\) | ||||
0.747746 | + | 0.663985i | \(0.231136\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 216.154 | 0.529931 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 121.758 | − | 210.891i | 0.268670 | − | 0.465350i | −0.699849 | − | 0.714291i | \(-0.746749\pi\) |
0.968519 | + | 0.248941i | \(0.0800827\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 343.816 | + | 595.507i | 0.721658 | + | 1.24995i | 0.960335 | + | 0.278849i | \(0.0899528\pi\) |
−0.238677 | + | 0.971099i | \(0.576714\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −88.0301 | − | 152.473i | −0.167981 | − | 0.290952i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −189.195 | + | 327.695i | −0.344982 | + | 0.597527i | −0.985351 | − | 0.170541i | \(-0.945448\pi\) |
0.640368 | + | 0.768068i | \(0.278782\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 332.826 | 0.556327 | 0.278163 | − | 0.960534i | \(-0.410274\pi\) | ||||
0.278163 | + | 0.960534i | \(0.410274\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1072.19 | 1.71904 | 0.859520 | − | 0.511103i | \(-0.170763\pi\) | ||||
0.859520 | + | 0.511103i | \(0.170763\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −486.484 | + | 842.615i | −0.720000 | + | 1.24708i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 630.104 | + | 1091.37i | 0.897370 | + | 1.55429i | 0.830843 | + | 0.556506i | \(0.187858\pi\) |
0.0665267 | + | 0.997785i | \(0.478808\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −613.047 | − | 1061.83i | −0.810731 | − | 1.40423i | −0.912353 | − | 0.409404i | \(-0.865737\pi\) |
0.101623 | − | 0.994823i | \(-0.467597\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −140.659 | + | 243.628i | −0.179489 | + | 0.310884i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1095.81 | −1.30512 | −0.652559 | − | 0.757738i | \(-0.726305\pi\) | ||||
−0.652559 | + | 0.757738i | \(0.726305\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 792.495 | 0.912923 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 255.892 | − | 443.217i | 0.276357 | − | 0.478665i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 564.300 | + | 977.397i | 0.590681 | + | 1.02309i | 0.994141 | + | 0.108092i | \(0.0344740\pi\) |
−0.403460 | + | 0.914997i | \(0.632193\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 617.823 | + | 1070.10i | 0.608670 | + | 1.05425i | 0.991460 | + | 0.130412i | \(0.0416300\pi\) |
−0.382790 | + | 0.923835i | \(0.625037\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −607.962 | + | 1053.02i | −0.581595 | + | 1.00735i | 0.413696 | + | 0.910415i | \(0.364238\pi\) |
−0.995291 | + | 0.0969365i | \(0.969096\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1779.08 | 1.60739 | 0.803694 | − | 0.595043i | \(-0.202865\pi\) | ||||
0.803694 | + | 0.595043i | \(0.202865\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −974.934 | −0.856714 | −0.428357 | − | 0.903610i | \(-0.640907\pi\) | ||||
−0.428357 | + | 0.903610i | \(0.640907\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −985.735 | + | 1707.34i | −0.820621 | + | 1.42136i | 0.0846002 | + | 0.996415i | \(0.473039\pi\) |
−0.905221 | + | 0.424942i | \(0.860295\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 245.270 | + | 424.820i | 0.198883 | + | 0.344475i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −633.143 | − | 1096.64i | −0.487732 | − | 0.844777i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −28.1310 | + | 48.7244i | −0.0211353 | + | 0.0366074i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1255.40 | 0.898290 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −604.990 | −0.422710 | −0.211355 | − | 0.977409i | \(-0.567788\pi\) | ||||
−0.211355 | + | 0.977409i | \(0.567788\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −704.848 | + | 1220.83i | −0.470098 | + | 0.814234i | −0.999415 | − | 0.0341899i | \(-0.989115\pi\) |
0.529317 | + | 0.848424i | \(0.322448\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1151.84 | + | 1995.04i | 0.750955 | + | 1.30069i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1131.77 | − | 1960.29i | −0.705795 | − | 1.22247i | −0.966404 | − | 0.257028i | \(-0.917257\pi\) |
0.260609 | − | 0.965444i | \(-0.416077\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −770.251 | + | 1334.11i | −0.470013 | + | 0.814087i | −0.999412 | − | 0.0342862i | \(-0.989084\pi\) |
0.529399 | + | 0.848373i | \(0.322418\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1129.94 | 0.660773 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1025.60 | −0.587390 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −306.517 | + | 530.903i | −0.168529 | + | 0.291901i | −0.937903 | − | 0.346898i | \(-0.887235\pi\) |
0.769374 | + | 0.638799i | \(0.220568\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1186.49 | − | 2055.06i | −0.639438 | − | 1.10754i | −0.985556 | − | 0.169348i | \(-0.945834\pi\) |
0.346118 | − | 0.938191i | \(-0.387500\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 450.879 | + | 780.946i | 0.233648 | + | 0.404691i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 884.031 | − | 1531.19i | 0.449385 | − | 0.778357i | −0.548962 | − | 0.835848i | \(-0.684977\pi\) |
0.998346 | + | 0.0574908i | \(0.0183100\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2208.05 | −1.08086 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2657.82 | 1.27715 | 0.638577 | − | 0.769558i | \(-0.279523\pi\) | ||||
0.638577 | + | 0.769558i | \(0.279523\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1676.26 | − | 2903.37i | 0.776724 | − | 1.34532i | −0.157097 | − | 0.987583i | \(-0.550214\pi\) |
0.933821 | − | 0.357742i | \(-0.116453\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 638.324 | + | 1105.61i | 0.290543 | + | 0.503236i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.21794 | − | 2.10954i | −0.000535251 | − | 0.000927083i | 0.865758 | − | 0.500463i | \(-0.166837\pi\) |
−0.866293 | + | 0.499536i | \(0.833504\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1192.77 | + | 2065.94i | −0.515228 | + | 0.892401i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1084.01 | 0.452642 | 0.226321 | − | 0.974053i | \(-0.427330\pi\) | ||||
0.226321 | + | 0.974053i | \(0.427330\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 869.840 | 0.357208 | 0.178604 | − | 0.983921i | \(-0.442842\pi\) | ||||
0.178604 | + | 0.983921i | \(0.442842\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −749.542 | + | 1298.24i | −0.297878 | + | 0.515939i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −902.738 | − | 1563.59i | −0.353020 | − | 0.611448i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 212.574 | + | 368.189i | 0.0805304 | + | 0.139483i | 0.903478 | − | 0.428635i | \(-0.141005\pi\) |
−0.822948 | + | 0.568117i | \(0.807672\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.854672 | − | 1.48034i | 0.000318760 | − | 0.000552108i | −0.865866 | − | 0.500276i | \(-0.833232\pi\) |
0.866185 | + | 0.499724i | \(0.166565\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3079.44 | −1.11371 | −0.556855 | − | 0.830610i | \(-0.687992\pi\) | ||||
−0.556855 | + | 0.830610i | \(0.687992\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3133.50 | 1.11622 | 0.558110 | − | 0.829767i | \(-0.311527\pi\) | ||||
0.558110 | + | 0.829767i | \(0.311527\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2308.25 | − | 3998.01i | 0.798068 | − | 1.38229i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 639.209 | + | 1107.14i | 0.217777 | + | 0.377201i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1642.30 | + | 2844.54i | 0.543540 | + | 0.941440i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1393.87 | − | 2414.26i | 0.454778 | − | 0.787699i | −0.543897 | − | 0.839152i | \(-0.683052\pi\) |
0.998675 | + | 0.0514532i | \(0.0163853\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 277.180 | 0.0879233 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4059.06 | −1.26980 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −735.291 | + | 1273.56i | −0.223806 | + | 0.387643i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 573.301 | + | 992.987i | 0.172157 | + | 0.298185i | 0.939174 | − | 0.343442i | \(-0.111593\pi\) |
−0.767016 | + | 0.641627i | \(0.778260\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 464.070 | + | 803.794i | 0.135689 | + | 0.235021i | 0.925861 | − | 0.377865i | \(-0.123342\pi\) |
−0.790171 | + | 0.612886i | \(0.790008\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1758.88 | − | 3046.47i | 0.507554 | − | 0.879110i | −0.492408 | − | 0.870365i | \(-0.663883\pi\) |
0.999962 | − | 0.00874485i | \(-0.00278361\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 976.524 | 0.274567 | 0.137284 | − | 0.990532i | \(-0.456163\pi\) | ||||
0.137284 | + | 0.990532i | \(0.456163\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −751.538 | −0.208617 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2270.49 | − | 3932.60i | 0.614500 | − | 1.06435i | −0.375972 | − | 0.926631i | \(-0.622691\pi\) |
0.990472 | − | 0.137714i | \(-0.0439755\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3610.19 | − | 6253.04i | −0.964951 | − | 1.67134i | −0.709748 | − | 0.704456i | \(-0.751191\pi\) |
−0.255203 | − | 0.966888i | \(-0.582142\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 984.839 | + | 1705.79i | 0.256812 | + | 0.444812i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1337.67 | − | 2316.91i | 0.344591 | − | 0.596849i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1285.44 | 0.323251 | 0.161626 | − | 0.986852i | \(-0.448326\pi\) | ||||
0.161626 | + | 0.986852i | \(0.448326\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3148.25 | −0.782327 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1302.25 | + | 2255.56i | −0.316078 | + | 0.547462i | −0.979666 | − | 0.200635i | \(-0.935699\pi\) |
0.663588 | + | 0.748098i | \(0.269033\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3373.89 | − | 5843.75i | −0.809433 | − | 1.40198i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2676.84 | − | 4636.43i | −0.627609 | − | 1.08705i | −0.988030 | − | 0.154261i | \(-0.950700\pi\) |
0.360421 | − | 0.932790i | \(-0.382633\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1674.37 | − | 2900.10i | 0.388136 | − | 0.672270i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7141.58 | −1.61870 | −0.809349 | − | 0.587328i | \(-0.800180\pi\) | ||||
−0.809349 | + | 0.587328i | \(0.800180\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6334.52 | −1.41991 | −0.709953 | − | 0.704249i | \(-0.751284\pi\) | ||||
−0.709953 | + | 0.704249i | \(0.751284\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1700.66 | + | 2945.62i | −0.372922 | + | 0.645919i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3545.09 | − | 6140.28i | −0.768967 | − | 1.33189i | −0.938124 | − | 0.346301i | \(-0.887438\pi\) |
0.169157 | − | 0.985589i | \(-0.445896\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3370.51 | + | 5837.89i | 0.715543 | + | 1.23936i | 0.962750 | + | 0.270394i | \(0.0871540\pi\) |
−0.247207 | + | 0.968963i | \(0.579513\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1779.83 | + | 3082.76i | −0.373852 | + | 0.647530i | −0.990154 | − | 0.139979i | \(-0.955296\pi\) |
0.616303 | + | 0.787509i | \(0.288630\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5754.50 | −1.18354 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2563.23 | −0.521725 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1077.71 | + | 1866.64i | −0.214881 | + | 0.372185i | −0.953236 | − | 0.302227i | \(-0.902270\pi\) |
0.738355 | + | 0.674413i | \(0.235603\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −706.612 | − | 1223.89i | −0.139459 | − | 0.241551i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1282.14 | + | 2220.74i | 0.247988 | + | 0.429527i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −623.831 | + | 1080.51i | −0.119458 | + | 0.206908i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3990.62 | 0.749187 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1552.85 | 0.288684 | 0.144342 | − | 0.989528i | \(-0.453893\pi\) | ||||
0.144342 | + | 0.989528i | \(0.453893\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4207.44 | − | 7287.50i | 0.767145 | − | 1.32873i | −0.171960 | − | 0.985104i | \(-0.555010\pi\) |
0.939105 | − | 0.343630i | \(-0.111657\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2852.13 | + | 4940.03i | 0.515053 | + | 0.892098i | 0.999847 | + | 0.0174701i | \(0.00556120\pi\) |
−0.484794 | + | 0.874628i | \(0.661105\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.181688 | − | 0.314692i | −3.21911e−5 | − | 5.57567e-5i | 0.866009 | − | 0.500028i | \(-0.166677\pi\) |
−0.866041 | + | 0.499972i | \(0.833344\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3291.12 | − | 5700.39i | 0.577641 | − | 1.00050i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4274.79 | −0.736395 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2770.41 | 0.472846 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1691.44 | − | 2929.66i | 0.283441 | − | 0.490933i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4467.17 | − | 7737.36i | −0.741806 | − | 1.28485i | −0.951672 | − | 0.307115i | \(-0.900636\pi\) |
0.209866 | − | 0.977730i | \(-0.432697\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1097.98 | + | 1901.75i | 0.179071 | + | 0.310161i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4762.05 | − | 8248.11i | 0.769749 | − | 1.33324i | −0.167950 | − | 0.985795i | \(-0.553715\pi\) |
0.937699 | − | 0.347448i | \(-0.112952\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5787.43 | −0.919081 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 94.0633 | 0.0148074 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4404.05 | − | 7628.04i | 0.681331 | − | 1.18010i | −0.293244 | − | 0.956038i | \(-0.594735\pi\) |
0.974575 | − | 0.224062i | \(-0.0719318\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1155.62 | − | 2001.59i | −0.177246 | − | 0.306998i | 0.763690 | − | 0.645583i | \(-0.223385\pi\) |
−0.940936 | + | 0.338584i | \(0.890052\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −82.8041 | − | 143.421i | −0.0124850 | − | 0.0216247i | 0.859715 | − | 0.510773i | \(-0.170641\pi\) |
−0.872200 | + | 0.489149i | \(0.837308\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 965.765 | − | 1672.75i | 0.144387 | − | 0.250086i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7007.10 | 1.03014 | 0.515071 | − | 0.857148i | \(-0.327766\pi\) | ||||
0.515071 | + | 0.857148i | \(0.327766\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 917.854 | 0.133817 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3111.17 | − | 5388.71i | 0.446154 | − | 0.772762i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1457.76 | − | 2524.91i | −0.207342 | − | 0.359126i | 0.743535 | − | 0.668698i | \(-0.233148\pi\) |
−0.950876 | + | 0.309571i | \(0.899815\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7536.80 | + | 13054.1i | 1.05469 | + | 1.82678i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2043.56 | + | 3539.54i | −0.283676 | + | 0.491342i | −0.972287 | − | 0.233789i | \(-0.924887\pi\) |
0.688611 | + | 0.725131i | \(0.258221\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5361.32 | −0.732419 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5785.10 | 0.784065 | 0.392032 | − | 0.919951i | \(-0.371772\pi\) | ||||
0.392032 | + | 0.919951i | \(0.371772\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6485.46 | + | 11233.1i | −0.865252 | + | 1.49866i | 0.00154474 | + | 0.999999i | \(0.499508\pi\) |
−0.866797 | + | 0.498662i | \(0.833825\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2823.27 | + | 4890.05i | 0.373733 | + | 0.647325i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2278.08 | − | 3945.75i | −0.296923 | − | 0.514286i | 0.678507 | − | 0.734594i | \(-0.262627\pi\) |
−0.975430 | + | 0.220307i | \(0.929294\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2048.67 | − | 3548.40i | 0.264976 | − | 0.458952i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7313.52 | 0.931603 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3193.40 | 0.403709 | 0.201854 | − | 0.979416i | \(-0.435303\pi\) | ||||
0.201854 | + | 0.979416i | \(0.435303\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7515.98 | − | 13018.1i | 0.935986 | − | 1.62117i | 0.163119 | − | 0.986606i | \(-0.447845\pi\) |
0.772867 | − | 0.634568i | \(-0.218822\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2356.97 | + | 4082.39i | 0.291337 | + | 0.504611i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4810.51 | − | 8332.04i | −0.585867 | − | 1.01475i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 316.934 | − | 548.947i | 0.0383164 | − | 0.0663659i | −0.846231 | − | 0.532816i | \(-0.821134\pi\) |
0.884548 | + | 0.466450i | \(0.154467\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6361.30 | 0.757916 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7115.54 | −0.841658 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6994.94 | + | 12115.6i | −0.815574 | + | 1.41261i | 0.0933417 | + | 0.995634i | \(0.470245\pi\) |
−0.908915 | + | 0.416981i | \(0.863088\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4426.72 | − | 7667.30i | −0.512458 | − | 0.887604i | −0.999896 | − | 0.0144458i | \(-0.995402\pi\) |
0.487437 | − | 0.873158i | \(-0.337932\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2213.35 | − | 3833.63i | −0.252619 | − | 0.437549i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8981.42 | + | 15556.3i | −1.01790 | + | 1.76305i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16509.1 | −1.84504 | −0.922522 | − | 0.385945i | \(-0.873875\pi\) | ||||
−0.922522 | + | 0.385945i | \(0.873875\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2218.19 | 0.246188 | 0.123094 | − | 0.992395i | \(-0.460718\pi\) | ||||
0.123094 | + | 0.992395i | \(0.460718\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3727.02 | + | 6455.39i | −0.407981 | + | 0.706643i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 722.909 | + | 1252.12i | 0.0785936 | + | 0.136128i | 0.902643 | − | 0.430389i | \(-0.141624\pi\) |
−0.824050 | + | 0.566517i | \(0.808290\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 492.812 | + | 853.576i | 0.0528538 | + | 0.0915454i | 0.891242 | − | 0.453528i | \(-0.149835\pi\) |
−0.838388 | + | 0.545074i | \(0.816502\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3179.72 | + | 5507.44i | −0.338726 | + | 0.586691i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6682.65 | 0.702391 | 0.351196 | − | 0.936302i | \(-0.385775\pi\) | ||||
0.351196 | + | 0.936302i | \(0.385775\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8204.79 | −0.856649 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2299.59 | − | 3983.01i | 0.236937 | − | 0.410388i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2382.72 | − | 4126.99i | −0.243893 | − | 0.422434i | 0.717927 | − | 0.696118i | \(-0.245091\pi\) |
−0.961820 | + | 0.273684i | \(0.911758\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4917.33 | − | 8517.06i | −0.496796 | − | 0.860476i | 0.503197 | − | 0.864172i | \(-0.332157\pi\) |
−0.999993 | + | 0.00369591i | \(0.998824\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2790.25 | − | 4832.86i | 0.280074 | − | 0.485102i | −0.691329 | − | 0.722540i | \(-0.742974\pi\) |
0.971403 | + | 0.237438i | \(0.0763077\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4459.02 | 0.441839 | 0.220920 | − | 0.975292i | \(-0.429094\pi\) | ||||
0.220920 | + | 0.975292i | \(0.429094\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9884.58 | −0.973193 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −889.461 | + | 1540.59i | −0.0864640 | + | 0.149760i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4026.61 | + | 6974.29i | 0.388954 | + | 0.673689i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5134.63 | − | 8893.44i | −0.489785 | − | 0.848333i | 0.510146 | − | 0.860088i | \(-0.329591\pi\) |
−0.999931 | + | 0.0117551i | \(0.996258\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3918.22 | + | 6786.55i | −0.371425 | + | 0.643327i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6549.75 | 0.613214 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −904.158 | −0.0841300 | −0.0420650 | − | 0.999115i | \(-0.513394\pi\) | ||||
−0.0420650 | + | 0.999115i | \(0.513394\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10263.5 | + | 17777.0i | −0.943354 | + | 1.63394i | −0.184340 | + | 0.982863i | \(0.559015\pi\) |
−0.759014 | + | 0.651074i | \(0.774319\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4283.28 | + | 7418.87i | 0.391297 | + | 0.677746i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4347.17 | + | 7529.52i | 0.392348 | + | 0.679567i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2087.14 | − | 3615.04i | 0.187241 | − | 0.324311i | −0.757088 | − | 0.653313i | \(-0.773379\pi\) |
0.944329 | + | 0.329001i | \(0.106712\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4835.95 | 0.428676 | 0.214338 | − | 0.976760i | \(-0.431241\pi\) | ||||
0.214338 | + | 0.976760i | \(0.431241\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7170.97 | 0.631889 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2602.27 | + | 4507.26i | −0.226608 | + | 0.392497i | −0.956801 | − | 0.290745i | \(-0.906097\pi\) |
0.730193 | + | 0.683241i | \(0.239430\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14004.2 | + | 24256.0i | 1.21235 | + | 2.09985i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3528.26 | + | 6111.12i | 0.301891 | + | 0.522890i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2411.66 | − | 4177.12i | 0.205154 | − | 0.355337i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12174.0 | 1.02371 | 0.511856 | − | 0.859071i | \(-0.328958\pi\) | ||||
0.511856 | + | 0.859071i | \(0.328958\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11583.5 | 0.968470 | 0.484235 | − | 0.874938i | \(-0.339098\pi\) | ||||
0.484235 | + | 0.874938i | \(0.339098\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3766.07 | − | 6523.03i | 0.311295 | − | 0.539179i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2511.19 | + | 4349.50i | 0.206393 | + | 0.357483i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3341.45 | + | 5787.57i | 0.271547 | + | 0.470333i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5162.39 | − | 8941.52i | 0.417177 | − | 0.722571i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12641.3 | −1.01020 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18249.3 | 1.45027 | 0.725137 | − | 0.688605i | \(-0.241777\pi\) | ||||
0.725137 | + | 0.688605i | \(0.241777\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2828.98 | + | 4899.93i | −0.222349 | + | 0.385119i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4805.00 | + | 8322.50i | 0.375588 | + | 0.650538i | 0.990415 | − | 0.138124i | \(-0.0441073\pi\) |
−0.614827 | + | 0.788662i | \(0.710774\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7792.32 | − | 13496.7i | −0.602475 | − | 1.04352i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16460.1 | + | 28509.7i | −1.26574 | + | 2.19232i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20247.0 | 1.54020 | 0.770101 | − | 0.637923i | \(-0.220206\pi\) | ||||
0.770101 | + | 0.637923i | \(0.220206\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1448.95 | 0.109632 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9172.09 | + | 15886.5i | −0.686603 | + | 1.18923i | 0.286327 | + | 0.958132i | \(0.407566\pi\) |
−0.972930 | + | 0.231099i | \(0.925768\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5720.64 | + | 9908.43i | 0.425963 | + | 0.737789i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11834.3 | − | 20497.6i | −0.871914 | − | 1.51020i | −0.860014 | − | 0.510271i | \(-0.829545\pi\) |
−0.0119007 | − | 0.999929i | \(-0.503788\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4425.57 | + | 7665.30i | −0.324351 | + | 0.561792i | −0.981381 | − | 0.192073i | \(-0.938479\pi\) |
0.657030 | + | 0.753864i | \(0.271812\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7718.93 | −0.559829 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16832.2 | 1.21444 | 0.607221 | − | 0.794533i | \(-0.292284\pi\) | ||||
0.607221 | + | 0.794533i | \(0.292284\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16014.5 | − | 27737.9i | 1.14353 | − | 1.98066i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10746.0 | + | 18612.6i | 0.763386 | + | 1.32222i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11649.3 | + | 20177.1i | 0.819109 | + | 1.41874i | 0.906340 | + | 0.422550i | \(0.138865\pi\) |
−0.0872307 | + | 0.996188i | \(0.527802\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6851.38 | + | 11866.9i | −0.479298 | + | 0.830168i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8720.33 | −0.603881 | −0.301940 | − | 0.953327i | \(-0.597634\pi\) | ||||
−0.301940 | + | 0.953327i | \(0.597634\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7348.79 | −0.506338 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −183.200 | + | 317.312i | −0.0124964 | + | 0.0216444i | −0.872206 | − | 0.489139i | \(-0.837311\pi\) |
0.859710 | + | 0.510783i | \(0.170645\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2943.48 | − | 5098.25i | −0.199779 | − | 0.346027i | 0.748678 | − | 0.662934i | \(-0.230689\pi\) |
−0.948457 | + | 0.316907i | \(0.897356\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 163.256 | + | 282.768i | 0.0109708 | + | 0.0190019i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9093.56 | − | 15750.5i | 0.608067 | − | 1.05320i | −0.383492 | − | 0.923544i | \(-0.625279\pi\) |
0.991559 | − | 0.129658i | \(-0.0413879\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3928.65 | −0.260125 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1998.47 | 0.131676 | 0.0658379 | − | 0.997830i | \(-0.479028\pi\) | ||||
0.0658379 | + | 0.997830i | \(0.479028\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7900.13 | + | 13683.4i | −0.515474 | + | 0.892827i | 0.484365 | + | 0.874866i | \(0.339051\pi\) |
−0.999839 | + | 0.0179609i | \(0.994283\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4883.43 | − | 8458.35i | −0.317095 | − | 0.549224i | 0.662786 | − | 0.748809i | \(-0.269374\pi\) |
−0.979881 | + | 0.199585i | \(0.936041\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14312.8 | − | 24790.5i | −0.920433 | − | 1.59424i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2064.71 | + | 3576.19i | −0.132142 | + | 0.228876i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12521.4 | 0.793739 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9966.80 | −0.628799 | −0.314399 | − | 0.949291i | \(-0.601803\pi\) | ||||
−0.314399 | + | 0.949291i | \(0.601803\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1755.51 | + | 3040.63i | −0.109709 | + | 0.190021i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5148.23 | + | 8917.00i | 0.320220 | + | 0.554638i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6355.26 | − | 11007.6i | −0.391603 | − | 0.678277i | 0.601058 | − | 0.799205i | \(-0.294746\pi\) |
−0.992661 | + | 0.120929i | \(0.961413\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6405.70 | + | 11095.0i | −0.392871 | + | 0.680473i | −0.992827 | − | 0.119560i | \(-0.961851\pi\) |
0.599956 | + | 0.800033i | \(0.295185\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3729.11 | 0.226594 | 0.113297 | − | 0.993561i | \(-0.463859\pi\) | ||||
0.113297 | + | 0.993561i | \(0.463859\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9069.97 | 0.548579 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1653.35 | − | 2863.68i | 0.0990820 | − | 0.171615i | −0.812223 | − | 0.583347i | \(-0.801743\pi\) |
0.911305 | + | 0.411732i | \(0.135076\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4090.53 | + | 7085.01i | 0.244016 | + | 0.422648i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8978.50 | + | 15551.2i | 0.530732 | + | 0.919256i | 0.999357 | + | 0.0358581i | \(0.0114164\pi\) |
−0.468624 | + | 0.883398i | \(0.655250\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4847.57 | + | 8396.23i | −0.285247 | + | 0.494063i | −0.972669 | − | 0.232195i | \(-0.925409\pi\) |
0.687422 | + | 0.726258i | \(0.258742\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 13369.2 | 0.779602 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14937.7 | 0.867153 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12805.8 | + | 22180.2i | −0.736752 | + | 1.27609i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10793.6 | − | 18695.1i | −0.618222 | − | 1.07079i | −0.989810 | − | 0.142394i | \(-0.954520\pi\) |
0.371588 | − | 0.928398i | \(-0.378813\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10336.2 | − | 17902.8i | −0.586782 | − | 1.01634i | −0.994651 | − | 0.103296i | \(-0.967061\pi\) |
0.407868 | − | 0.913041i | \(-0.366272\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14741.1 | + | 25532.3i | −0.833153 | + | 1.44306i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24403.9 | 1.36719 | 0.683594 | − | 0.729862i | \(-0.260416\pi\) | ||||
0.683594 | + | 0.729862i | \(0.260416\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13136.3 | −0.732719 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8752.76 | − | 15160.2i | 0.483968 | − | 0.838256i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2929.03 | + | 5073.24i | 0.161253 | + | 0.279298i | 0.935318 | − | 0.353808i | \(-0.115113\pi\) |
−0.774065 | + | 0.633106i | \(0.781780\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4470.09 | + | 7742.43i | 0.243972 | + | 0.422571i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5339.13 | − | 9247.65i | 0.290149 | − | 0.502553i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10530.8 | 0.567393 | 0.283697 | − | 0.958914i | \(-0.408439\pi\) | ||||
0.283697 | + | 0.958914i | \(0.408439\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22779.5 | −1.22211 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −16139.2 | + | 27954.0i | −0.858527 | + | 1.48701i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1888.39 | + | 3270.79i | 0.100028 | + | 0.173254i | 0.911696 | − | 0.410865i | \(-0.134773\pi\) |
−0.811668 | + | 0.584119i | \(0.801440\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6566.99 | − | 11374.4i | −0.344931 | − | 0.597437i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3278.77 | − | 5678.99i | 0.171495 | − | 0.297038i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7109.15 | 0.368743 | 0.184372 | − | 0.982857i | \(-0.440975\pi\) | ||||
0.184372 | + | 0.982857i | \(0.440975\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −31763.3 | −1.64068 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8069.22 | − | 13976.3i | 0.413356 | − | 0.715954i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1830.18 | − | 3169.96i | −0.0933667 | − | 0.161716i | 0.815559 | − | 0.578674i | \(-0.196430\pi\) |
−0.908926 | + | 0.416958i | \(0.863096\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1157.60 | − | 2005.03i | −0.0585712 | − | 0.101448i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18279.7 | − | 31661.3i | 0.921113 | − | 1.59541i | 0.123416 | − | 0.992355i | \(-0.460615\pi\) |
0.797697 | − | 0.603059i | \(-0.206052\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14093.5 | −0.704396 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15735.7 | 0.783285 | 0.391642 | − | 0.920118i | \(-0.371907\pi\) | ||||
0.391642 | + | 0.920118i | \(0.371907\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11847.1 | − | 20519.9i | 0.584966 | − | 1.01319i | −0.409914 | − | 0.912124i | \(-0.634441\pi\) |
0.994880 | − | 0.101066i | \(-0.0322254\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1778.85 | + | 3081.05i | 0.0874790 | + | 0.151518i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 23237.3 | + | 40248.2i | 1.13361 | + | 1.96347i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8643.50 | − | 14971.0i | 0.419981 | − | 0.727429i | −0.575956 | − | 0.817481i | \(-0.695370\pi\) |
0.995937 | + | 0.0900521i | \(0.0287034\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13771.4 | −0.663831 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18565.8 | 0.891394 | 0.445697 | − | 0.895184i | \(-0.352956\pi\) | ||||
0.445697 | + | 0.895184i | \(0.352956\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2968.73 | − | 5142.00i | 0.141415 | − | 0.244937i | −0.786615 | − | 0.617444i | \(-0.788168\pi\) |
0.928030 | + | 0.372507i | \(0.121502\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12734.0 | − | 22055.9i | −0.604196 | − | 1.04650i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3693.80 | − | 6397.86i | −0.173892 | − | 0.301191i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1244.77 | + | 2156.00i | −0.0583713 | + | 0.101102i | −0.893734 | − | 0.448596i | \(-0.851924\pi\) |
0.835363 | + | 0.549698i | \(0.185257\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16109.8 | −0.749584 | −0.374792 | − | 0.927109i | \(-0.622286\pi\) | ||||
−0.374792 | + | 0.927109i | \(0.622286\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14189.7 | −0.657690 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9713.15 | + | 16823.7i | −0.446739 | + | 0.773775i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6198.21 | + | 10735.6i | 0.283981 | + | 0.491870i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5130.41 | − | 8886.13i | −0.233264 | − | 0.404025i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7905.02 | + | 13691.9i | −0.358047 | + | 0.620156i | −0.987635 | − | 0.156773i | \(-0.949891\pi\) |
0.629587 | + | 0.776930i | \(0.283224\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −51500.2 | −2.31497 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20860.9 | 0.934164 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2092.58 | − | 3624.45i | 0.0930024 | − | 0.161085i | −0.815771 | − | 0.578375i | \(-0.803687\pi\) |
0.908773 | + | 0.417291i | \(0.137020\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3138.69 | + | 5436.38i | 0.138972 | + | 0.240707i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19967.3 | + | 34584.4i | 0.877498 | + | 1.51987i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6407.13 | + | 11097.5i | −0.280524 | + | 0.485881i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −35154.2 | −1.52776 | −0.763878 | − | 0.645360i | \(-0.776707\pi\) | ||||
−0.763878 | + | 0.645360i | \(0.776707\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3028.93 | −0.131147 | −0.0655734 | − | 0.997848i | \(-0.520888\pi\) | ||||
−0.0655734 | + | 0.997848i | \(0.520888\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7712.22 | − | 13358.0i | 0.331469 | − | 0.574121i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2105.96 | + | 3647.62i | 0.0901813 | + | 0.156199i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2398.99 | + | 4155.17i | 0.101980 | + | 0.176634i | 0.912500 | − | 0.409076i | \(-0.134149\pi\) |
−0.810521 | + | 0.585710i | \(0.800816\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20029.4 | − | 34691.9i | 0.848335 | − | 1.46936i | −0.0343587 | − | 0.999410i | \(-0.510939\pi\) |
0.882693 | − | 0.469949i | \(-0.155728\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22168.6 | 0.932139 | 0.466069 | − | 0.884748i | \(-0.345670\pi\) | ||||
0.466069 | + | 0.884748i | \(0.345670\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13091.9 | 0.548494 | 0.274247 | − | 0.961659i | \(-0.411571\pi\) | ||||
0.274247 | + | 0.961659i | \(0.411571\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8226.09 | − | 14248.0i | 0.342157 | − | 0.592634i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9728.04 | − | 16849.5i | −0.403177 | − | 0.698323i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −17395.2 | − | 30129.3i | −0.715790 | − | 1.23978i | −0.962654 | − | 0.270734i | \(-0.912733\pi\) |
0.246864 | − | 0.969050i | \(-0.420600\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3421.11 | + | 5925.54i | −0.140273 | + | 0.242960i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7408.93 | 0.301627 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1469.72 | −0.0596225 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10916.9 | − | 18908.7i | 0.439751 | − | 0.761671i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23990.4 | − | 41552.5i | −0.962971 | − | 1.66792i | −0.714970 | − | 0.699156i | \(-0.753559\pi\) |
−0.248002 | − | 0.968760i | \(-0.579774\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16007.7 | + | 27726.2i | 0.638055 | + | 1.10514i | 0.985859 | + | 0.167577i | \(0.0535942\pi\) |
−0.347804 | + | 0.937567i | \(0.613072\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16256.7 | − | 28157.5i | 0.645719 | − | 1.11842i | −0.338415 | − | 0.940997i | \(-0.609891\pi\) |
0.984135 | − | 0.177422i | \(-0.0567758\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −25867.1 | −1.02031 | −0.510154 | − | 0.860083i | \(-0.670411\pi\) | ||||
−0.510154 | + | 0.860083i | \(0.670411\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.1365 | −0.000555670 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −23468.8 | + | 40649.2i | −0.916140 | + | 1.58680i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5739.66 | + | 9941.38i | 0.223285 | + | 0.386740i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 16397.2 | + | 28400.9i | 0.633518 | + | 1.09728i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 287.352 | − | 497.708i | 0.0110641 | − | 0.0191635i | −0.860440 | − | 0.509551i | \(-0.829811\pi\) |
0.871504 | + | 0.490388i | \(0.163145\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28334.1 | 1.08354 | 0.541771 | − | 0.840526i | \(-0.317754\pi\) | ||||
0.541771 | + | 0.840526i | \(0.317754\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13424.9 | 0.511646 | 0.255823 | − | 0.966724i | \(-0.417654\pi\) | ||||
0.255823 | + | 0.966724i | \(0.417654\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21881.6 | − | 37900.0i | 0.828310 | − | 1.43467i | −0.0710540 | − | 0.997472i | \(-0.522636\pi\) |
0.899363 | − | 0.437202i | \(-0.144030\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7902.01 | − | 13686.7i | −0.298116 | − | 0.516352i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5710.03 | − | 9890.07i | −0.213974 | − | 0.370614i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3145.50 | − | 5448.16i | 0.117477 | − | 0.203477i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 27460.0 | 1.01874 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −27971.2 | −1.03424 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2524.02 | − | 4371.74i | 0.0927087 | − | 0.160576i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21398.6 | − | 37063.4i | −0.783383 | − | 1.35686i | −0.929961 | − | 0.367659i | \(-0.880159\pi\) |
0.146578 | − | 0.989199i | \(-0.453174\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1003.57 | − | 1738.24i | −0.0364982 | − | 0.0632167i | 0.847199 | − | 0.531275i | \(-0.178287\pi\) |
−0.883697 | + | 0.468058i | \(0.844954\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22833.5 | − | 39548.8i | 0.827688 | − | 1.43360i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −36825.2 | −1.32614 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −43558.3 | −1.56350 | −0.781750 | − | 0.623592i | \(-0.785673\pi\) | ||||
−0.781750 | + | 0.623592i | \(0.785673\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5048.52 | − | 8744.30i | 0.180037 | − | 0.311833i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11794.5 | − | 20428.6i | −0.419243 | − | 0.726151i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15754.0 | + | 27286.8i | 0.556376 | + | 0.963671i | 0.997795 | + | 0.0663701i | \(0.0211418\pi\) |
−0.441419 | + | 0.897301i | \(0.645525\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14965.2 | + | 25920.5i | −0.526815 | + | 0.912471i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −10477.9 | −0.366487 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20675.3 | −0.720846 | −0.360423 | − | 0.932789i | \(-0.617368\pi\) | ||||
−0.360423 | + | 0.932789i | \(0.617368\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 712.769 | − | 1234.55i | 0.0246925 | − | 0.0427686i | −0.853415 | − | 0.521232i | \(-0.825473\pi\) |
0.878108 | + | 0.478463i | \(0.158806\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9309.97 | − | 16125.3i | −0.321500 | − | 0.556854i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17830.9 | − | 30884.0i | −0.611853 | − | 1.05976i | −0.990928 | − | 0.134395i | \(-0.957091\pi\) |
0.379075 | − | 0.925366i | \(-0.376242\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16263.6 | − | 28169.4i | 0.556311 | − | 0.963560i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10384.9 | 0.352991 | 0.176496 | − | 0.984301i | \(-0.443524\pi\) | ||||
0.176496 | + | 0.984301i | \(0.443524\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2467.31 | 0.0836024 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 29565.0 | − | 51208.2i | 0.995521 | − | 1.72429i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2823.41 | + | 4890.29i | 0.0947739 | + | 0.164153i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.96002 | − | 8.59102i | −0.000165460 | − | 0.000286585i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4221.70 | − | 7312.19i | 0.140394 | − | 0.243169i | −0.787251 | − | 0.616632i | \(-0.788497\pi\) |
0.927645 | + | 0.373463i | \(0.121830\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6938.43 | −0.229315 | −0.114657 | − | 0.993405i | \(-0.536577\pi\) | ||||
−0.114657 | + | 0.993405i | \(0.536577\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −40242.2 | −1.32590 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19388.7 | + | 33582.3i | −0.634903 | + | 1.09969i | 0.351632 | + | 0.936138i | \(0.385627\pi\) |
−0.986536 | + | 0.163547i | \(0.947707\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −20407.2 | − | 35346.4i | −0.666208 | − | 1.15391i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3796.28 | + | 6575.34i | 0.123176 | + | 0.213348i | 0.921019 | − | 0.389519i | \(-0.127359\pi\) |
−0.797842 | + | 0.602866i | \(0.794025\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8935.64 | + | 15477.0i | −0.289049 | + | 0.500647i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4037.08 | −0.129799 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.96741 | 0.000191282 | 9.56412e−5 | − | 1.00000i | \(-0.499970\pi\) | ||||
9.56412e−5 | 1.00000i | \(0.499970\pi\) | ||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9092.51 | − | 15748.7i | 0.289700 | − | 0.501776i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17385.9 | − | 30113.2i | −0.552272 | − | 0.956564i | −0.998110 | − | 0.0614501i | \(-0.980427\pi\) |
0.445838 | − | 0.895114i | \(-0.352906\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 648.4.i.u.433.3 | 8 | ||
3.2 | odd | 2 | 648.4.i.v.433.2 | 8 | |||
9.2 | odd | 6 | 648.4.i.v.217.2 | 8 | |||
9.4 | even | 3 | 648.4.a.j.1.2 | yes | 4 | ||
9.5 | odd | 6 | 648.4.a.g.1.3 | ✓ | 4 | ||
9.7 | even | 3 | inner | 648.4.i.u.217.3 | 8 | ||
36.23 | even | 6 | 1296.4.a.x.1.3 | 4 | |||
36.31 | odd | 6 | 1296.4.a.bb.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
648.4.a.g.1.3 | ✓ | 4 | 9.5 | odd | 6 | ||
648.4.a.j.1.2 | yes | 4 | 9.4 | even | 3 | ||
648.4.i.u.217.3 | 8 | 9.7 | even | 3 | inner | ||
648.4.i.u.433.3 | 8 | 1.1 | even | 1 | trivial | ||
648.4.i.v.217.2 | 8 | 9.2 | odd | 6 | |||
648.4.i.v.433.2 | 8 | 3.2 | odd | 2 | |||
1296.4.a.x.1.3 | 4 | 36.23 | even | 6 | |||
1296.4.a.bb.1.2 | 4 | 36.31 | odd | 6 |