Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,3,Mod(445,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.445");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.s (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.6376500822\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 445.26 | ||
Character | \(\chi\) | \(=\) | 684.445 |
Dual form | 684.3.s.a.601.26 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | 1.44572 | + | 2.62867i | 0.481908 | + | 0.876222i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.78673 | − | 3.09471i | −0.357346 | − | 0.618942i | 0.630170 | − | 0.776457i | \(-0.282985\pi\) |
−0.987517 | + | 0.157515i | \(0.949652\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.11933 | + | 3.67079i | 0.302762 | + | 0.524399i | 0.976760 | − | 0.214334i | \(-0.0687580\pi\) |
−0.673999 | + | 0.738733i | \(0.735425\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.81977 | + | 7.60065i | −0.535530 | + | 0.844516i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8.61085 | − | 14.9144i | −0.782805 | − | 1.35586i | −0.930302 | − | 0.366795i | \(-0.880455\pi\) |
0.147497 | − | 0.989063i | \(-0.452878\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 19.3844i | − | 1.49111i | −0.666446 | − | 0.745553i | \(-0.732186\pi\) | ||
0.666446 | − | 0.745553i | \(-0.267814\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.55184 | − | 9.17081i | 0.370122 | − | 0.611387i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −16.5029 | + | 28.5838i | −0.970758 | + | 1.68140i | −0.277481 | + | 0.960731i | \(0.589500\pi\) |
−0.693277 | + | 0.720671i | \(0.743834\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.306057 | + | 18.9975i | −0.0161083 | + | 0.999870i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.58532 | + | 10.8780i | −0.313587 | + | 0.517998i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −33.6031 | −1.46100 | −0.730502 | − | 0.682910i | \(-0.760714\pi\) | ||||
−0.730502 | + | 0.682910i | \(0.760714\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.11519 | − | 10.5918i | 0.244608 | − | 0.423673i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −26.9476 | − | 1.68114i | −0.998060 | − | 0.0622645i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.310233 | + | 0.179113i | 0.0106977 | + | 0.00617632i | 0.505339 | − | 0.862921i | \(-0.331367\pi\) |
−0.494642 | + | 0.869097i | \(0.664701\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −43.6395 | − | 25.1953i | −1.40773 | − | 0.812751i | −0.412558 | − | 0.910931i | \(-0.635364\pi\) |
−0.995169 | + | 0.0981804i | \(0.968698\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 26.7562 | − | 44.1972i | 0.810793 | − | 1.33931i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.57335 | − | 13.1174i | 0.216381 | − | 0.374784i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 26.4325i | − | 0.714391i | −0.934030 | − | 0.357196i | \(-0.883733\pi\) | ||
0.934030 | − | 0.357196i | \(-0.116267\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 50.9550 | − | 28.0244i | 1.30654 | − | 0.718575i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −34.5685 | + | 19.9581i | −0.843134 | + | 0.486784i | −0.858328 | − | 0.513101i | \(-0.828497\pi\) |
0.0151941 | + | 0.999885i | \(0.495163\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 19.8505 | 0.461640 | 0.230820 | − | 0.972996i | \(-0.425859\pi\) | ||||
0.230820 | + | 0.972996i | \(0.425859\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 32.1334 | + | 1.33548i | 0.714076 | + | 0.0296773i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.57889 | + | 4.46676i | −0.0548699 | + | 0.0950375i | −0.892156 | − | 0.451728i | \(-0.850808\pi\) |
0.837286 | + | 0.546766i | \(0.184141\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15.5169 | − | 26.8760i | 0.316671 | − | 0.548490i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −98.9960 | − | 2.05627i | −1.94110 | − | 0.0403190i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 20.3465 | − | 11.7470i | 0.383896 | − | 0.221642i | −0.295616 | − | 0.955307i | \(-0.595525\pi\) |
0.679512 | + | 0.733664i | \(0.262192\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −30.7706 | + | 53.2962i | −0.559465 | + | 0.969021i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −50.3806 | + | 26.6606i | −0.883871 | + | 0.467731i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −23.0105 | + | 13.2851i | −0.390008 | + | 0.225171i | −0.682164 | − | 0.731200i | \(-0.738961\pi\) |
0.292156 | + | 0.956371i | \(0.405627\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 22.5456 | − | 39.0500i | 0.369599 | − | 0.640165i | −0.619904 | − | 0.784678i | \(-0.712828\pi\) |
0.989503 | + | 0.144513i | \(0.0461616\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −38.1151 | − | 1.58408i | −0.605001 | − | 0.0251441i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −59.9890 | + | 34.6347i | −0.922907 | + | 0.532841i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 79.5824i | 1.18780i | 0.804540 | + | 0.593899i | \(0.202412\pi\) | ||||
−0.804540 | + | 0.593899i | \(0.797588\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −48.5808 | − | 88.3314i | −0.704069 | − | 1.28016i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.79086 | − | 1.03395i | −0.0252234 | − | 0.0145627i | 0.487335 | − | 0.873215i | \(-0.337969\pi\) |
−0.512559 | + | 0.858652i | \(0.671302\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 18.0979 | − | 31.3466i | 0.247917 | − | 0.429405i | −0.715031 | − | 0.699093i | \(-0.753587\pi\) |
0.962948 | + | 0.269688i | \(0.0869206\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 36.6832 | + | 0.761956i | 0.489110 | + | 0.0101594i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 36.4985 | − | 63.2173i | 0.474007 | − | 0.821004i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 71.7472i | 0.908192i | 0.890953 | + | 0.454096i | \(0.150038\pi\) | ||||
−0.890953 | + | 0.454096i | \(0.849962\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −34.5396 | − | 73.2667i | −0.426415 | − | 0.904528i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −63.8891 | − | 110.659i | −0.769748 | − | 1.33324i | −0.937699 | − | 0.347447i | \(-0.887049\pi\) |
0.167951 | − | 0.985795i | \(-0.446285\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 117.945 | 1.38759 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.0223176 | + | 1.07445i | −0.000256524 | + | 0.0123500i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −35.6570 | + | 20.5866i | −0.400640 | + | 0.231310i | −0.686760 | − | 0.726884i | \(-0.740968\pi\) |
0.286120 | + | 0.958194i | \(0.407634\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 71.1560 | − | 41.0819i | 0.781934 | − | 0.451450i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.13935 | − | 151.139i | 0.0337564 | − | 1.62515i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 59.3387 | − | 32.9963i | 0.624617 | − | 0.347330i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 50.6357i | 0.522017i | 0.965336 | + | 0.261009i | \(0.0840551\pi\) | ||||
−0.965336 | + | 0.261009i | \(0.915945\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 154.862 | + | 6.43612i | 1.56426 | + | 0.0650113i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 72.5178 | − | 125.605i | 0.717998 | − | 1.24361i | −0.243794 | − | 0.969827i | \(-0.578392\pi\) |
0.961792 | − | 0.273782i | \(-0.0882747\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −120.942 | − | 69.8258i | −1.17419 | − | 0.677920i | −0.219528 | − | 0.975606i | \(-0.570452\pi\) |
−0.954664 | + | 0.297686i | \(0.903785\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 45.4303 | + | 0.943644i | 0.432670 | + | 0.00898709i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 24.8950i | − | 0.232664i | −0.993210 | − | 0.116332i | \(-0.962886\pi\) | ||
0.993210 | − | 0.116332i | \(-0.0371136\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −35.6302 | − | 20.5711i | −0.326882 | − | 0.188726i | 0.327574 | − | 0.944826i | \(-0.393769\pi\) |
−0.654456 | + | 0.756100i | \(0.727102\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 69.4822 | − | 38.2140i | 0.625965 | − | 0.344271i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 65.6579 | + | 37.9076i | 0.581043 | + | 0.335465i | 0.761548 | − | 0.648109i | \(-0.224440\pi\) |
−0.180505 | + | 0.983574i | \(0.557773\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 60.0397 | + | 103.992i | 0.522084 | + | 0.904277i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 147.334 | + | 93.4282i | 1.25926 | + | 0.798532i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −139.900 | −1.17563 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −87.7936 | + | 152.063i | −0.725567 | + | 1.25672i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −102.440 | − | 62.0151i | −0.832844 | − | 0.504188i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −133.041 | −1.06433 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.68080 | + | 3.85716i | −0.0526047 | + | 0.0303714i | −0.526072 | − | 0.850440i | \(-0.676336\pi\) |
0.473467 | + | 0.880812i | \(0.343002\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 28.6984 | + | 52.1804i | 0.222468 | + | 0.404499i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 52.3204 | + | 90.6216i | 0.399392 | + | 0.691768i | 0.993651 | − | 0.112506i | \(-0.0358878\pi\) |
−0.594259 | + | 0.804274i | \(0.702555\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −70.3846 | + | 39.1386i | −0.529208 | + | 0.294275i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 42.9455 | + | 86.3987i | 0.318115 | + | 0.639991i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −113.046 | + | 195.802i | −0.825154 | + | 1.42921i | 0.0766467 | + | 0.997058i | \(0.475579\pi\) |
−0.901801 | + | 0.432151i | \(0.857755\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −108.727 | −0.782211 | −0.391106 | − | 0.920346i | \(-0.627907\pi\) | ||||
−0.391106 | + | 0.920346i | \(0.627907\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.4700 | − | 0.321331i | −0.109716 | − | 0.00227894i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −289.107 | + | 166.916i | −2.02173 | + | 1.16725i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 1.28011i | − | 0.00882834i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 93.0811 | + | 1.93341i | 0.633205 | + | 0.0131525i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −42.2582 | − | 73.1934i | −0.283612 | − | 0.491231i | 0.688660 | − | 0.725085i | \(-0.258199\pi\) |
−0.972272 | + | 0.233854i | \(0.924866\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 129.120 | − | 74.5477i | 0.855102 | − | 0.493694i | −0.00726680 | − | 0.999974i | \(-0.502313\pi\) |
0.862369 | + | 0.506280i | \(0.168980\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −137.715 | − | 263.200i | −0.900101 | − | 1.72026i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 180.069i | 1.16173i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 111.891 | + | 193.800i | 0.712680 | + | 1.23440i | 0.963848 | + | 0.266454i | \(0.0858520\pi\) |
−0.251168 | + | 0.967943i | \(0.580815\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 60.2944 | + | 36.5011i | 0.379210 | + | 0.229567i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −71.2162 | − | 123.350i | −0.442336 | − | 0.766149i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 280.953 | 1.72364 | 0.861818 | − | 0.507218i | \(-0.169326\pi\) | ||||
0.861818 | + | 0.507218i | \(0.169326\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −184.583 | − | 3.83403i | −1.11869 | − | 0.0232365i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 90.9975i | − | 0.544895i | −0.962171 | − | 0.272448i | \(-0.912167\pi\) | ||
0.962171 | − | 0.272448i | \(-0.0878331\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −206.754 | −1.22340 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −142.918 | − | 93.8900i | −0.835780 | − | 0.549064i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 181.582i | − | 1.04961i | −0.851224 | − | 0.524803i | \(-0.824139\pi\) | ||
0.851224 | − | 0.524803i | \(-0.175861\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 51.8405 | 0.296231 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −68.1889 | − | 41.2803i | −0.385248 | − | 0.233222i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 285.526i | 1.59512i | 0.603241 | + | 0.797559i | \(0.293876\pi\) | ||||
−0.603241 | + | 0.797559i | \(0.706124\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −44.5028 | + | 25.6937i | −0.245872 | + | 0.141954i | −0.617873 | − | 0.786278i | \(-0.712005\pi\) |
0.372001 | + | 0.928232i | \(0.378672\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 135.244 | + | 2.80919i | 0.739039 | + | 0.0153508i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −81.8008 | + | 47.2277i | −0.442166 | + | 0.255285i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 568.416 | 3.03966 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −50.9398 | − | 102.482i | −0.269523 | − | 0.542233i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 186.020 | + | 322.197i | 0.973929 | + | 1.68689i | 0.683424 | + | 0.730021i | \(0.260490\pi\) |
0.290505 | + | 0.956874i | \(0.406177\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 72.0574 | − | 41.6024i | 0.373355 | − | 0.215556i | −0.301568 | − | 0.953445i | \(-0.597510\pi\) |
0.674923 | + | 0.737888i | \(0.264177\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −177.770 | − | 107.619i | −0.911643 | − | 0.551892i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −211.557 | −1.07390 | −0.536948 | − | 0.843615i | \(-0.680423\pi\) | ||||
−0.536948 | + | 0.843615i | \(0.680423\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 137.799 | + | 238.674i | 0.692456 | + | 1.19937i | 0.971031 | + | 0.238954i | \(0.0768046\pi\) |
−0.278575 | + | 0.960415i | \(0.589862\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −209.196 | + | 115.054i | −1.04077 | + | 0.572409i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.51840i | 0.00747982i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 123.529 | + | 71.3196i | 0.602581 | + | 0.347901i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 161.959 | − | 255.405i | 0.782412 | − | 1.23384i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 285.973 | − | 159.020i | 1.36829 | − | 0.760863i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −301.051 | + | 173.812i | −1.42678 | + | 0.823753i | −0.996865 | − | 0.0791156i | \(-0.974790\pi\) |
−0.429917 | + | 0.902869i | \(0.641457\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.128831 | − | 6.20238i | 0.000604841 | − | 0.0291191i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −35.4675 | − | 61.4316i | −0.164965 | − | 0.285728i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 213.589i | − | 0.984280i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 108.564 | + | 2.25501i | 0.495727 | + | 0.0102969i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 554.080 | + | 319.898i | 2.50715 | + | 1.44750i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 132.591i | − | 0.594577i | −0.954788 | − | 0.297289i | \(-0.903918\pi\) | ||
0.954788 | − | 0.297289i | \(-0.0960824\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 51.0308 | + | 97.5295i | 0.226804 | + | 0.433465i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 146.854 | − | 84.7865i | 0.646936 | − | 0.373509i | −0.140345 | − | 0.990103i | \(-0.544821\pi\) |
0.787281 | + | 0.616594i | \(0.211488\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −195.308 | + | 338.283i | −0.852872 | + | 1.47722i | 0.0257340 | + | 0.999669i | \(0.491808\pi\) |
−0.878606 | + | 0.477548i | \(0.841526\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 218.944 | + | 4.54774i | 0.947809 | + | 0.0196872i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −55.9875 | + | 96.9731i | −0.240290 | + | 0.416194i | −0.960797 | − | 0.277254i | \(-0.910576\pi\) |
0.720507 | + | 0.693447i | \(0.243909\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 18.4311 | 0.0784302 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −188.599 | + | 103.727i | −0.795778 | + | 0.437665i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −78.8759 | + | 136.617i | −0.330025 | + | 0.571619i | −0.982516 | − | 0.186177i | \(-0.940390\pi\) |
0.652492 | + | 0.757796i | \(0.273724\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 312.571 | + | 180.463i | 1.29697 | + | 0.748808i | 0.979880 | − | 0.199586i | \(-0.0639597\pi\) |
0.317094 | + | 0.948394i | \(0.397293\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 142.659 | − | 196.717i | 0.587074 | − | 0.809533i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −110.898 | −0.452644 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 368.255 | + | 5.93272i | 1.49091 | + | 0.0240191i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 198.520 | − | 327.926i | 0.797269 | − | 1.31697i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −95.8755 | − | 166.061i | −0.381974 | − | 0.661598i | 0.609370 | − | 0.792886i | \(-0.291422\pi\) |
−0.991344 | + | 0.131287i | \(0.958089\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 289.352 | + | 501.172i | 1.14368 | + | 1.98092i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 170.516 | + | 310.038i | 0.668688 | + | 1.21583i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 289.983i | − | 1.12834i | −0.825660 | − | 0.564169i | \(-0.809197\pi\) | ||
0.825660 | − | 0.564169i | \(-0.190803\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 97.0281 | − | 56.0192i | 0.374626 | − | 0.216290i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.85663 | + | 1.49469i | −0.0109449 | + | 0.00572678i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 58.9700 | 0.224221 | 0.112110 | − | 0.993696i | \(-0.464239\pi\) | ||||
0.112110 | + | 0.993696i | \(0.464239\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −72.7073 | − | 41.9776i | −0.274367 | − | 0.158406i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −105.665 | − | 63.9678i | −0.395750 | − | 0.239580i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −58.1708 | − | 33.5849i | −0.216248 | − | 0.124851i | 0.387964 | − | 0.921675i | \(-0.373179\pi\) |
−0.604212 | + | 0.796824i | \(0.706512\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.1126 | + | 34.8360i | −0.0742162 | + | 0.128546i | −0.900745 | − | 0.434348i | \(-0.856979\pi\) |
0.826529 | + | 0.562894i | \(0.190312\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 210.863 | + | 127.652i | 0.772390 | + | 0.467591i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −210.628 | −0.765920 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −62.3160 | − | 107.935i | −0.224968 | − | 0.389655i | 0.731342 | − | 0.682011i | \(-0.238894\pi\) |
−0.956310 | + | 0.292355i | \(0.905561\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 401.833 | − | 210.253i | 1.44026 | − | 0.753595i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −434.977 | − | 251.134i | −1.54796 | − | 0.893715i | −0.998298 | − | 0.0583272i | \(-0.981423\pi\) |
−0.549662 | − | 0.835387i | \(-0.685243\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 125.492 | + | 217.359i | 0.443435 | + | 0.768052i | 0.997942 | − | 0.0641272i | \(-0.0204263\pi\) |
−0.554507 | + | 0.832179i | \(0.687093\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 172.524 | + | 108.278i | 0.605346 | + | 0.379923i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −146.524 | − | 84.5958i | −0.510538 | − | 0.294759i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −400.191 | − | 693.150i | −1.38474 | − | 2.39844i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −133.104 | + | 73.2051i | −0.457403 | + | 0.251564i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 29.5654 | + | 17.0696i | 0.100906 | + | 0.0582580i | 0.549604 | − | 0.835426i | \(-0.314779\pi\) |
−0.448698 | + | 0.893684i | \(0.648112\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 82.2270 | + | 47.4738i | 0.278736 | + | 0.160928i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 206.969 | + | 416.385i | 0.696864 | + | 1.40197i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 651.375i | 2.17851i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 42.0699 | + | 72.8671i | 0.139767 | + | 0.242083i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 435.013 | + | 9.03576i | 1.43569 | + | 0.0298210i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −161.131 | −0.528299 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −174.403 | − | 100.692i | −0.568088 | − | 0.327986i | 0.188297 | − | 0.982112i | \(-0.439703\pi\) |
−0.756385 | + | 0.654126i | \(0.773036\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.70033 | − | 418.864i | 0.0281564 | − | 1.35555i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.4402 | − | 26.7432i | 0.0496470 | − | 0.0859911i | −0.840134 | − | 0.542379i | \(-0.817524\pi\) |
0.889781 | + | 0.456388i | \(0.150857\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 31.8993 | − | 55.2512i | 0.101915 | − | 0.176522i | −0.810559 | − | 0.585657i | \(-0.800836\pi\) |
0.912474 | + | 0.409136i | \(0.134170\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 63.1991 | + | 120.785i | 0.200632 | + | 0.383446i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 273.272 | + | 157.774i | 0.862056 | + | 0.497708i | 0.864700 | − | 0.502288i | \(-0.167508\pi\) |
−0.00264414 | + | 0.999997i | \(0.500842\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 6.16927i | − | 0.0193394i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 65.4407 | − | 35.9913i | 0.203865 | − | 0.112122i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −537.972 | − | 322.262i | −1.66555 | − | 0.997717i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −205.316 | − | 118.539i | −0.631741 | − | 0.364736i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.56317 | − | 123.400i | 0.00783844 | − | 0.377370i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −21.8621 | −0.0664501 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −67.2074 | + | 38.8022i | −0.203044 | + | 0.117227i | −0.598074 | − | 0.801441i | \(-0.704067\pi\) |
0.395031 | + | 0.918668i | \(0.370734\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 200.904 | + | 127.398i | 0.603315 | + | 0.382578i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 246.284 | − | 142.192i | 0.735177 | − | 0.424455i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 244.336 | − | 141.068i | 0.725033 | − | 0.418598i | −0.0915692 | − | 0.995799i | \(-0.529188\pi\) |
0.816602 | + | 0.577201i | \(0.195855\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.72331 | + | 227.397i | −0.0139331 | + | 0.670786i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 867.812i | 2.54490i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 339.236 | 0.989027 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −186.559 | + | 308.168i | −0.540751 | + | 0.893240i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −145.454 | − | 251.933i | −0.419175 | − | 0.726033i | 0.576681 | − | 0.816969i | \(-0.304347\pi\) |
−0.995857 | + | 0.0909362i | \(0.971014\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −195.221 | − | 338.133i | −0.559373 | − | 0.968863i | −0.997549 | − | 0.0699734i | \(-0.977709\pi\) |
0.438176 | − | 0.898889i | \(-0.355625\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −32.5879 | + | 522.363i | −0.0928429 | + | 1.48821i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −229.262 | − | 397.093i | −0.649467 | − | 1.12491i | −0.983250 | − | 0.182260i | \(-0.941659\pi\) |
0.333784 | − | 0.942650i | \(-0.391675\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.38958i | 0.0208157i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −202.257 | − | 367.751i | −0.566547 | − | 1.03012i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −34.1410 | + | 59.1339i | −0.0951002 | + | 0.164718i | −0.909650 | − | 0.415375i | \(-0.863650\pi\) |
0.814550 | + | 0.580093i | \(0.196984\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −360.813 | − | 11.6287i | −0.999481 | − | 0.0322123i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −526.648 | − | 10.9391i | −1.45082 | − | 0.0301354i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −129.345 | −0.354369 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −226.321 | + | 391.999i | −0.616678 | + | 1.06812i | 0.373410 | + | 0.927666i | \(0.378189\pi\) |
−0.990088 | + | 0.140451i | \(0.955145\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 14.9176 | − | 358.937i | 0.0404270 | − | 0.972728i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 86.2419 | + | 49.7918i | 0.232458 | + | 0.134210i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −180.571 | − | 104.253i | −0.484105 | − | 0.279498i | 0.238021 | − | 0.971260i | \(-0.423501\pi\) |
−0.722126 | + | 0.691762i | \(0.756835\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −192.341 | − | 349.721i | −0.512909 | − | 0.932590i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.47200 | − | 6.01368i | 0.00920955 | − | 0.0159514i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.5246i | 0.0699858i | 0.999388 | + | 0.0349929i | \(0.0111409\pi\) | ||||
−0.999388 | + | 0.0349929i | \(0.988859\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.7978 | − | 11.9852i | −0.0519627 | − | 0.0314572i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 99.1329 | − | 57.2344i | 0.258833 | − | 0.149437i | −0.364969 | − | 0.931020i | \(-0.618921\pi\) |
0.623802 | + | 0.781583i | \(0.285587\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −260.852 | −0.677538 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −95.6750 | + | 150.877i | −0.247222 | + | 0.389863i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −58.7477 | + | 101.754i | −0.151022 | + | 0.261579i | −0.931604 | − | 0.363476i | \(-0.881590\pi\) |
0.780581 | + | 0.625054i | \(0.214923\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 554.548 | − | 960.506i | 1.41828 | − | 2.45654i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −162.573 | + | 268.546i | −0.413672 | + | 0.683324i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 222.036 | − | 128.193i | 0.562118 | − | 0.324539i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 281.926 | − | 488.311i | 0.710142 | − | 1.23000i | −0.254662 | − | 0.967030i | \(-0.581964\pi\) |
0.964804 | − | 0.262971i | \(-0.0847024\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −204.639 | − | 128.434i | −0.512880 | − | 0.321890i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 491.130 | − | 283.554i | 1.22476 | − | 0.707117i | 0.258833 | − | 0.965922i | \(-0.416662\pi\) |
0.965929 | + | 0.258805i | \(0.0833288\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −488.395 | + | 845.925i | −1.21190 | + | 2.09907i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −165.026 | + | 237.798i | −0.407472 | + | 0.587155i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −394.226 | + | 227.606i | −0.968613 | + | 0.559229i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 175.230i | − | 0.428434i | −0.976786 | − | 0.214217i | \(-0.931280\pi\) | ||
0.976786 | − | 0.214217i | \(-0.0687200\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −678.131 | − | 14.0856i | −1.64995 | − | 0.0342716i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −97.5337 | − | 56.3111i | −0.236159 | − | 0.136346i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −228.305 | + | 395.436i | −0.550133 | + | 0.952858i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −157.190 | − | 285.808i | −0.376954 | − | 0.685391i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 37.2462 | − | 64.5122i | 0.0888930 | − | 0.153967i | −0.818150 | − | 0.575004i | \(-0.805000\pi\) |
0.907043 | + | 0.421037i | \(0.138334\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 61.2336i | 0.145448i | 0.997352 | + | 0.0727240i | \(0.0231692\pi\) | ||||
−0.997352 | + | 0.0727240i | \(0.976831\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −21.5206 | − | 41.1300i | −0.0508762 | − | 0.0972340i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 201.837 | + | 349.591i | 0.474910 | + | 0.822567i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 191.126 | 0.447602 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −856.735 | − | 518.652i | −1.99705 | − | 1.20898i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 462.163 | − | 266.830i | 1.07230 | − | 0.619095i | 0.143494 | − | 0.989651i | \(-0.454166\pi\) |
0.928810 | + | 0.370557i | \(0.120833\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −338.448 | + | 195.403i | −0.781635 | + | 0.451277i | −0.837010 | − | 0.547188i | \(-0.815698\pi\) |
0.0553741 | + | 0.998466i | \(0.482365\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.36498 | − | 1.85068i | 0.00773558 | − | 0.00425444i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.2845 | − | 638.376i | 0.0235343 | − | 1.46082i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 788.021i | 1.79504i | 0.440976 | + | 0.897519i | \(0.354632\pi\) | ||||
−0.440976 | + | 0.897519i | \(0.645368\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 129.487 | + | 247.474i | 0.293622 | + | 0.561166i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −255.045 | + | 441.750i | −0.575721 | + | 0.997179i | 0.420241 | + | 0.907412i | \(0.361945\pi\) |
−0.995963 | + | 0.0897663i | \(0.971388\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 127.419 | + | 73.5652i | 0.286334 | + | 0.165315i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 131.307 | − | 216.900i | 0.293752 | − | 0.485235i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 3.02812i | − | 0.00674414i | −0.999994 | − | 0.00337207i | \(-0.998927\pi\) | ||
0.999994 | − | 0.00337207i | \(-0.00107336\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 595.329 | + | 343.713i | 1.32002 | + | 0.762114i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 382.633 | + | 231.639i | 0.844666 | + | 0.511345i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −254.273 | − | 146.805i | −0.558842 | − | 0.322648i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −431.036 | − | 746.576i | −0.943186 | − | 1.63365i | −0.759343 | − | 0.650691i | \(-0.774479\pi\) |
−0.183843 | − | 0.982956i | \(-0.558854\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 492.767 | − | 742.522i | 1.07357 | − | 1.61770i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 394.550 | 0.855856 | 0.427928 | − | 0.903813i | \(-0.359244\pi\) | ||||
0.427928 | + | 0.903813i | \(0.359244\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −64.8349 | + | 112.297i | −0.140032 | + | 0.242543i | −0.927509 | − | 0.373802i | \(-0.878054\pi\) |
0.787476 | + | 0.616345i | \(0.211387\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −473.341 | + | 260.329i | −1.01794 | + | 0.559848i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 126.290 | 0.270428 | 0.135214 | − | 0.990816i | \(-0.456828\pi\) | ||||
0.135214 | + | 0.990816i | \(0.456828\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −292.130 | + | 168.662i | −0.622879 | + | 0.359620i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −347.674 | + | 574.305i | −0.738160 | + | 1.21933i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −170.930 | − | 296.059i | −0.361374 | − | 0.625918i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 199.347 | + | 119.415i | 0.419678 | + | 0.251400i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.78024 | + | 211.264i | −0.0184072 | + | 0.442902i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 140.257 | − | 242.932i | 0.292811 | − | 0.507164i | −0.681662 | − | 0.731667i | \(-0.738743\pi\) |
0.974473 | + | 0.224503i | \(0.0720759\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −512.377 | −1.06523 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 221.287 | − | 365.533i | 0.458151 | − | 0.756798i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 156.703 | − | 90.4723i | 0.323098 | − | 0.186541i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 783.264i | − | 1.60835i | −0.594396 | − | 0.804173i | \(-0.702609\pi\) | ||
0.594396 | − | 0.804173i | \(-0.297391\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 406.180 | + | 738.531i | 0.830633 | + | 1.51029i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 102.247 | + | 177.098i | 0.208243 | + | 0.360688i | 0.951161 | − | 0.308695i | \(-0.0998921\pi\) |
−0.742918 | + | 0.669382i | \(0.766559\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.2395 | + | 5.91177i | −0.0207698 | + | 0.0119914i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −256.778 | − | 490.751i | −0.518744 | − | 0.991417i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 8.76516i | − | 0.0176361i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −252.619 | − | 437.549i | −0.506251 | − | 0.876852i | −0.999974 | − | 0.00723259i | \(-0.997698\pi\) |
0.493723 | − | 0.869619i | \(-0.335636\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 239.202 | − | 131.557i | 0.477449 | − | 0.262589i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −340.083 | − | 589.040i | −0.676108 | − | 1.17105i | −0.976144 | − | 0.217126i | \(-0.930332\pi\) |
0.300035 | − | 0.953928i | \(-0.403002\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −518.279 | −1.02630 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −298.909 | − | 543.487i | −0.589564 | − | 1.07197i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 449.590i | − | 0.883280i | −0.897192 | − | 0.441640i | \(-0.854397\pi\) | ||
0.897192 | − | 0.441640i | \(-0.145603\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 153.422 | 0.300239 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 40.1850 | − | 511.424i | 0.0783334 | − | 0.996927i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 499.039i | 0.969008i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 88.8257 | 0.171810 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 477.318 | − | 262.517i | 0.919688 | − | 0.505813i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 725.604i | − | 1.39271i | −0.717696 | − | 0.696357i | \(-0.754803\pi\) | ||
0.717696 | − | 0.696357i | \(-0.245197\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −456.195 | + | 263.384i | −0.872265 | + | 0.503602i | −0.868100 | − | 0.496389i | \(-0.834659\pi\) |
−0.00416462 | + | 0.999991i | \(0.501326\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 74.9470 | + | 136.271i | 0.142756 | + | 0.259564i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1440.36 | − | 831.590i | 2.73312 | − | 1.57797i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 600.169 | 1.13454 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.92985 | − | 238.926i | 0.0187003 | − | 0.449954i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 386.876 | + | 670.089i | 0.725846 | + | 1.25720i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −77.0428 | + | 44.4807i | −0.144005 | + | 0.0831415i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −750.553 | + | 412.792i | −1.39768 | + | 0.768699i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −534.454 | −0.991565 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −241.845 | − | 418.888i | −0.447034 | − | 0.774286i | 0.551157 | − | 0.834401i | \(-0.314186\pi\) |
−0.998191 | + | 0.0601157i | \(0.980853\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −131.879 | − | 79.8371i | −0.242871 | − | 0.147030i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 147.020i | 0.269761i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −901.020 | − | 520.204i | −1.64720 | − | 0.951013i | −0.978177 | − | 0.207774i | \(-0.933378\pi\) |
−0.669026 | − | 0.743239i | \(-0.733289\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 188.141 | + | 359.573i | 0.342698 | + | 0.654960i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.49766 | + | 5.83885i | −0.00634784 | + | 0.0105968i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −263.369 | + | 152.056i | −0.476255 | + | 0.274966i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −242.407 | − | 146.749i | −0.436770 | − | 0.264412i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 321.105 | + | 556.170i | 0.576490 | + | 0.998510i | 0.995878 | + | 0.0907030i | \(0.0289114\pi\) |
−0.419388 | + | 0.907807i | \(0.637755\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 384.790i | − | 0.688354i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 821.772 | + | 1494.18i | 1.46483 | + | 2.66341i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17.8501 | − | 10.3058i | −0.0317053 | − | 0.0183051i | 0.484064 | − | 0.875033i | \(-0.339160\pi\) |
−0.515769 | + | 0.856728i | \(0.672494\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 270.923i | − | 0.479509i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 195.746 | − | 282.064i | 0.345231 | − | 0.497468i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −414.099 | + | 239.080i | −0.727767 | + | 0.420176i | −0.817605 | − | 0.575780i | \(-0.804698\pi\) |
0.0898379 | + | 0.995956i | \(0.471365\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −154.725 | + | 267.991i | −0.270972 | + | 0.469337i | −0.969111 | − | 0.246625i | \(-0.920678\pi\) |
0.698139 | + | 0.715962i | \(0.254012\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −578.014 | + | 954.793i | −1.00875 | + | 1.66631i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −205.489 | + | 355.918i | −0.357373 | + | 0.618988i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 684.624 | 1.18652 | 0.593262 | − | 0.805010i | \(-0.297840\pi\) | ||||
0.593262 | + | 0.805010i | \(0.297840\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 213.534 | + | 129.269i | 0.368798 | + | 0.223263i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 270.804 | − | 469.047i | 0.466100 | − | 0.807310i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −350.401 | − | 202.304i | −0.601031 | − | 0.347005i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 25.8874 | − | 622.886i | 0.0442520 | − | 1.06476i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 221.269 | 0.376949 | 0.188475 | − | 0.982078i | \(-0.439646\pi\) | ||||
0.188475 | + | 0.982078i | \(0.439646\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 492.004 | − | 821.332i | 0.835322 | − | 1.39445i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −305.853 | − | 556.114i | −0.517519 | − | 0.940971i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −173.199 | − | 299.989i | −0.292072 | − | 0.505883i | 0.682228 | − | 0.731140i | \(-0.261011\pi\) |
−0.974299 | + | 0.225257i | \(0.927678\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 249.964 | + | 432.951i | 0.420108 | + | 0.727649i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −428.177 | + | 707.284i | −0.717214 | + | 1.18473i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1126.11i | 1.87998i | 0.341207 | + | 0.939988i | \(0.389164\pi\) | ||||
−0.341207 | + | 0.939988i | \(0.610836\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.5616 | + | 8.40717i | −0.0242290 | + | 0.0139886i | −0.512066 | − | 0.858946i | \(-0.671120\pi\) |
0.487837 | + | 0.872935i | \(0.337786\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −604.878 | − | 383.569i | −1.00311 | − | 0.636101i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 627.454 | 1.03711 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −542.819 | − | 313.396i | −0.894265 | − | 0.516304i | −0.0189295 | − | 0.999821i | \(-0.506026\pi\) |
−0.875335 | + | 0.483517i | \(0.839359\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.99137 | + | 2.19519i | −0.00655398 | + | 0.00360458i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 86.5854 | + | 49.9901i | 0.141711 | + | 0.0818169i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −127.095 | + | 220.136i | −0.207333 | + | 0.359112i | −0.950874 | − | 0.309579i | \(-0.899812\pi\) |
0.743540 | + | 0.668691i | \(0.233145\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.88647 | + | 427.825i | −0.0144495 | + | 0.695651i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −617.018 | −1.00003 | −0.500015 | − | 0.866017i | \(-0.666672\pi\) | ||||
−0.500015 | + | 0.866017i | \(0.666672\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −373.018 | − | 646.086i | −0.602614 | − | 1.04376i | −0.992424 | − | 0.122863i | \(-0.960793\pi\) |
0.389810 | − | 0.920895i | \(-0.372541\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 905.524 | + | 56.4916i | 1.45817 | + | 0.0909687i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −151.138 | − | 87.2595i | −0.242597 | − | 0.140063i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 84.8292 | + | 146.928i | 0.135727 | + | 0.235086i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 831.449 | + | 521.828i | 1.32608 | + | 0.832262i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 755.542 | + | 436.212i | 1.20118 | + | 0.693501i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 423.895 | + | 734.207i | 0.671782 | + | 1.16356i | 0.977398 | + | 0.211406i | \(0.0678043\pi\) |
−0.305616 | + | 0.952155i | \(0.598862\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −892.130 | − | 540.079i | −1.40937 | − | 0.853205i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 23.8736 | + | 13.7834i | 0.0375962 | + | 0.0217062i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −520.974 | − | 300.785i | −0.817856 | − | 0.472189i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 16.4902 | − | 8.62827i | 0.0258063 | − | 0.0135028i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 736.317i | − | 1.14870i | −0.818609 | − | 0.574351i | \(-0.805255\pi\) | ||
0.818609 | − | 0.574351i | \(-0.194745\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 130.195 | + | 225.505i | 0.202481 | + | 0.350708i | 0.949327 | − | 0.314289i | \(-0.101766\pi\) |
−0.746846 | + | 0.664997i | \(0.768433\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 110.207 | − | 182.045i | 0.170863 | − | 0.282241i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −692.664 | −1.07058 | −0.535289 | − | 0.844669i | \(-0.679797\pi\) | ||||
−0.535289 | + | 0.844669i | \(0.679797\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 396.280 | + | 228.792i | 0.610600 | + | 0.352530i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 561.453 | − | 308.790i | 0.862448 | − | 0.474332i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 316.724 | − | 548.582i | 0.485029 | − | 0.840095i | −0.514823 | − | 0.857296i | \(-0.672142\pi\) |
0.999852 | + | 0.0172016i | \(0.00547572\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 186.965 | − | 323.833i | 0.285442 | − | 0.494401i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 151.026 | + | 288.639i | 0.229872 | + | 0.439329i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 577.022 | + | 333.144i | 0.875602 | + | 0.505529i | 0.869206 | − | 0.494450i | \(-0.164631\pi\) |
0.00639647 | + | 0.999980i | \(0.497964\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 46.6295i | − | 0.0705438i | −0.999378 | − | 0.0352719i | \(-0.988770\pi\) | ||
0.999378 | − | 0.0352719i | \(-0.0112297\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −39.8595 | + | 1918.97i | −0.0601199 | + | 2.89438i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 246.881 | + | 147.890i | 0.371249 | + | 0.222390i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.4248 | − | 6.01876i | −0.0156294 | − | 0.00902364i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 348.537 | − | 191.689i | 0.520982 | − | 0.286531i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −776.546 | −1.15730 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.1127 | − | 9.88002i | 0.0254275 | − | 0.0146806i | −0.487232 | − | 0.873272i | \(-0.661994\pi\) |
0.512660 | + | 0.858592i | \(0.328660\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −182.596 | + | 275.144i | −0.270513 | + | 0.407620i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −37.4947 | + | 21.6476i | −0.0553836 | + | 0.0319757i | −0.527436 | − | 0.849595i | \(-0.676847\pi\) |
0.472053 | + | 0.881570i | \(0.343513\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −185.873 | + | 107.314i | −0.273745 | + | 0.158047i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 435.186 | + | 263.454i | 0.639040 | + | 0.386863i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 1317.95i | − | 1.92965i | −0.262895 | − | 0.964825i | \(-0.584677\pi\) | ||
0.262895 | − | 0.964825i | \(-0.415323\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 807.932 | 1.17946 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1171.59 | − | 24.3355i | −1.70538 | − | 0.0354228i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −227.709 | − | 394.404i | −0.330492 | − | 0.572429i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −556.438 | − | 963.778i | −0.805264 | − | 1.39476i | −0.916113 | − | 0.400921i | \(-0.868690\pi\) |
0.110848 | − | 0.993837i | \(-0.464643\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 304.578 | + | 582.105i | 0.439506 | + | 0.839979i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 194.267 | + | 336.480i | 0.279520 | + | 0.484143i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 1317.47i | − | 1.89020i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −335.852 | − | 6.97607i | −0.480475 | − | 0.00998008i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −312.796 | + | 541.779i | −0.446214 | + | 0.772866i | −0.998136 | − | 0.0610303i | \(-0.980561\pi\) |
0.551922 | + | 0.833896i | \(0.313895\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 502.152 | + | 8.08985i | 0.714299 | + | 0.0115076i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 26.6463 | + | 48.4492i | 0.0377961 | + | 0.0687223i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 614.757 | 0.869529 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 658.564 | − | 1140.67i | 0.928863 | − | 1.60884i | 0.143635 | − | 0.989631i | \(-0.454121\pi\) |
0.785228 | − | 0.619207i | \(-0.212546\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −545.325 | − | 345.805i | −0.766983 | − | 0.486364i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1466.42 | + | 846.640i | 2.05669 | + | 1.18743i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1033.11 | + | 596.468i | 1.44491 | + | 0.834221i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −473.153 | − | 9.82798i | −0.659907 | − | 0.0137071i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 189.686 | − | 328.545i | 0.263819 | − | 0.456947i | −0.703435 | − | 0.710760i | \(-0.748351\pi\) |
0.967253 | + | 0.253812i | \(0.0816846\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 591.936i | − | 0.820993i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −22.4858 | + | 1082.54i | −0.0311007 | + | 1.49729i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.79427 | − | 2.19062i | 0.00523348 | − | 0.00302155i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −559.070 | −0.769010 | −0.384505 | − | 0.923123i | \(-0.625628\pi\) | ||||
−0.384505 | + | 0.923123i | \(0.625628\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 723.348 | + | 90.6055i | 0.992246 | + | 0.124287i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −327.591 | + | 567.404i | −0.448141 | + | 0.776203i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −700.738 | + | 1213.71i | −0.955986 | + | 1.65582i | −0.223891 | + | 0.974614i | \(0.571876\pi\) |
−0.732095 | + | 0.681202i | \(0.761457\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −160.327 | − | 291.513i | −0.218133 | − | 0.396617i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1186.93 | − | 685.273i | 1.61048 | − | 0.929814i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −149.513 | + | 258.964i | −0.202318 | + | 0.350425i | −0.949275 | − | 0.314448i | \(-0.898181\pi\) |
0.746957 | + | 0.664872i | \(0.231514\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 516.800 | + | 976.597i | 0.697436 | + | 1.31795i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 177.589 | − | 102.531i | 0.239016 | − | 0.137996i | −0.375709 | − | 0.926738i | \(-0.622601\pi\) |
0.614724 | + | 0.788742i | \(0.289267\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −151.008 | + | 261.554i | −0.202695 | + | 0.351079i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1149.01 | + | 47.7534i | 1.53817 | + | 0.0639269i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 91.3844 | − | 52.7608i | 0.122009 | − | 0.0704417i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 305.332i | − | 0.406567i | −0.979120 | − | 0.203284i | \(-0.934839\pi\) | ||
0.979120 | − | 0.203284i | \(-0.0651613\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 297.910 | − | 492.103i | 0.395631 | − | 0.653523i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −461.407 | − | 266.393i | −0.611135 | − | 0.352839i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −178.879 | + | 309.827i | −0.236300 | + | 0.409283i | −0.959650 | − | 0.281199i | \(-0.909268\pi\) |
0.723350 | + | 0.690482i | \(0.242601\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −899.090 | + | 1485.16i | −1.18457 | + | 1.95674i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −133.599 | + | 231.399i | −0.175557 | + | 0.304073i | −0.940354 | − | 0.340198i | \(-0.889506\pi\) |
0.764797 | + | 0.644271i | \(0.222839\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 174.388i | − | 0.228556i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −568.467 | + | 896.457i | −0.743094 | + | 1.17184i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 257.523 | + | 446.044i | 0.335754 | + | 0.581543i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −791.594 | −1.02938 | −0.514691 | − | 0.857376i | \(-0.672093\pi\) | ||||
−0.514691 | + | 0.857376i | \(0.672093\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 762.268 | − | 419.235i | 0.988674 | − | 0.543754i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −232.793 | + | 134.403i | −0.301155 | + | 0.173872i | −0.642962 | − | 0.765898i | \(-0.722295\pi\) |
0.341807 | + | 0.939770i | \(0.388961\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −533.728 | + | 308.148i | −0.688681 | + | 0.397610i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 287.532 | + | 174.066i | 0.370053 | + | 0.224023i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −368.575 | − | 662.825i | −0.473139 | − | 0.850866i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 35.6129i | 0.0455991i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.05893 | − | 5.34822i | −0.0102924 | − | 0.00683042i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 399.837 | − | 692.538i | 0.509347 | − | 0.882214i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 659.045 | + | 380.500i | 0.837414 | + | 0.483481i | 0.856384 | − | 0.516339i | \(-0.172706\pi\) |
−0.0189706 | + | 0.999820i | \(0.506039\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 85.2543 | + | 155.013i | 0.108054 | + | 0.196467i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 321.355i | 0.406264i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −756.961 | − | 437.031i | −0.954553 | − | 0.551112i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.23044 | − | 251.811i | 0.00657916 | − | 0.316744i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 69.0764 | + | 39.8813i | 0.0866705 | + | 0.0500392i | 0.542709 | − | 0.839921i | \(-0.317399\pi\) |
−0.456038 | + | 0.889960i | \(0.650732\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −85.1182 | − | 147.429i | −0.106531 | − | 0.184517i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.3873 | − | 370.238i | 0.0192101 | − | 0.462220i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −623.355 | −0.776283 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −254.488 | + | 440.786i | −0.316134 | + | 0.547561i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.18470 | − | 201.466i | 0.00518550 | − | 0.249648i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 783.760 | 0.968800 | 0.484400 | − | 0.874847i | \(-0.339038\pi\) | ||||
0.484400 | + | 0.874847i | \(0.339038\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1171.15 | + | 676.163i | −1.44408 | + | 0.833740i | −0.998119 | − | 0.0613126i | \(-0.980471\pi\) |
−0.445961 | + | 0.895052i | \(0.647138\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −120.649 | − | 2.50604i | −0.148400 | − | 0.00308246i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −501.987 | − | 869.466i | −0.615934 | − | 1.06683i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.07539 | + | 377.111i | −0.00743622 | + | 0.461580i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −30.7064 | + | 738.837i | −0.0374925 | + | 0.902121i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −355.115 | + | 615.078i | −0.432540 | + | 0.749181i | −0.997091 | − | 0.0762166i | \(-0.975716\pi\) |
0.564551 | + | 0.825398i | \(0.309049\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −649.981 | −0.789770 | −0.394885 | − | 0.918731i | \(-0.629216\pi\) | ||||
−0.394885 | + | 0.918731i | \(0.629216\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −304.510 | − | 553.671i | −0.369103 | − | 0.671116i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 414.480 | − | 239.300i | 0.501185 | − | 0.289359i | −0.228018 | − | 0.973657i | \(-0.573224\pi\) |
0.729203 | + | 0.684298i | \(0.239891\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 446.712i | 0.538857i | 0.963020 | + | 0.269429i | \(0.0868348\pi\) | ||||
−0.963020 | + | 0.269429i | \(0.913165\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 193.632 | − | 319.851i | 0.233011 | − | 0.384899i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 512.146 | + | 887.063i | 0.614821 | + | 1.06490i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −281.611 | + | 162.588i | −0.337258 | + | 0.194716i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1133.62 | + | 752.317i | 1.35439 | + | 0.898826i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 718.499i | 0.856375i | 0.903690 | + | 0.428187i | \(0.140848\pi\) | ||||
−0.903690 | + | 0.428187i | \(0.859152\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −420.436 | − | 728.216i | −0.499924 | − | 0.865893i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 31.2914 | − | 1506.48i | 0.0371191 | − | 1.78704i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 369.414 | + | 639.843i | 0.437176 | + | 0.757211i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −744.256 | −0.878696 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −389.937 | + | 644.117i | −0.459289 | + | 0.758678i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 888.214i | 1.04373i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.9836 | −0.0199104 | −0.00995519 | − | 0.999950i | \(-0.503169\pi\) | ||||
−0.00995519 | + | 0.999950i | \(0.503169\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −35.2055 | + | 610.047i | −0.0411760 | + | 0.713505i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 658.355i | 0.768209i | 0.923290 | + | 0.384105i | \(0.125490\pi\) | ||||
−0.923290 | + | 0.384105i | \(0.874510\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 795.978 | 0.926633 | 0.463317 | − | 0.886193i | \(-0.346659\pi\) | ||||
0.463317 | + | 0.886193i | \(0.346659\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.5407 | − | 507.466i | 0.0122424 | − | 0.589391i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 540.003i | 0.625727i | 0.949798 | + | 0.312864i | \(0.101288\pi\) | ||||
−0.949798 | + | 0.312864i | \(0.898712\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −561.943 | + | 324.438i | −0.649645 | + | 0.375073i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1243.50 | − | 2054.07i | 1.43425 | − | 2.36917i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1070.07 | − | 617.804i | 1.23138 | − | 0.710937i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1542.66 | 1.77113 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −384.864 | − | 244.052i | −0.440852 | − | 0.279556i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −281.959 | − | 488.367i | −0.322239 | − | 0.558133i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 986.530 | − | 569.573i | 1.12489 | − | 0.649457i | 0.182246 | − | 0.983253i | \(-0.441663\pi\) |
0.942645 | + | 0.333796i | \(0.108330\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.12688 | + | 102.396i | −0.00241966 | + | 0.116491i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 168.246 | 0.190972 | 0.0954861 | − | 0.995431i | \(-0.469559\pi\) | ||||
0.0954861 | + | 0.995431i | \(0.469559\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −301.318 | − | 521.897i | −0.341243 | − | 0.591050i | 0.643421 | − | 0.765513i | \(-0.277515\pi\) |
−0.984664 | + | 0.174463i | \(0.944181\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.91526 | + | 284.781i | −0.00668391 | + | 0.321787i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1187.26i | 1.33851i | 0.743033 | + | 0.669255i | \(0.233387\pi\) | ||||
−0.743033 | + | 0.669255i | \(0.766613\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −28.3177 | − | 16.3492i | −0.0318534 | − | 0.0183906i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −795.317 | + | 1146.03i | −0.892611 | + | 1.28623i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −84.0682 | − | 50.3596i | −0.0941413 | − | 0.0563937i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 883.620 | − | 510.158i | 0.987285 | − | 0.570009i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1712.25 | + | 941.708i | −1.90886 | + | 1.04984i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.02562 | − | 15.6328i | −0.0100396 | − | 0.0173891i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 775.441i | 0.860644i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −130.722 | + | 215.933i | −0.144764 | + | 0.239129i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 159.029 | + | 91.8155i | 0.175723 | + | 0.101454i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1006.71i | 1.10993i | 0.831873 | + | 0.554966i | \(0.187269\pi\) | ||||
−0.831873 | + | 0.554966i | \(0.812731\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 605.156 | + | 1156.57i | 0.665738 | + | 1.27235i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1111.24 | − | 641.574i | 1.21980 | − | 0.704253i | 0.254926 | − | 0.966961i | \(-0.417949\pi\) |
0.964875 | + | 0.262708i | \(0.0846156\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1100.28 | + | 1905.74i | −1.20513 | + | 2.08734i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −232.951 | − | 423.560i | −0.254591 | − | 0.462908i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −221.769 | + | 384.114i | −0.241841 | + | 0.418882i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 676.693 | 0.736336 | 0.368168 | − | 0.929759i | \(-0.379985\pi\) | ||||
0.368168 | + | 0.929759i | \(0.379985\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.5462 | − | 604.020i | 0.0136224 | − | 0.655830i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −20.0425 | + | 34.7147i | −0.0217145 | + | 0.0376107i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −279.968 | − | 161.640i | −0.302668 | − | 0.174746i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1113.63 | − | 582.691i | 1.20133 | − | 0.628577i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1699.03 | 1.82888 | 0.914440 | − | 0.404722i | \(-0.132632\pi\) | ||||
0.914440 | + | 0.404722i | \(0.132632\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 505.829 | + | 303.008i | 0.543317 | + | 0.325465i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 92.6213 | + | 1.92386i | 0.0992726 | + | 0.00206202i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1015.61 | − | 1759.08i | −1.08621 | − | 1.88137i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −440.942 | − | 763.734i | −0.470589 | − | 0.815084i | 0.528845 | − | 0.848718i | \(-0.322625\pi\) |
−0.999434 | + | 0.0336344i | \(0.989292\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 191.355 | + | 3.97468i | 0.203786 | + | 0.00423288i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1098.42i | − | 1.16729i | −0.812010 | − | 0.583644i | \(-0.801626\pi\) | ||
0.812010 | − | 0.583644i | \(-0.198374\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1161.61 | − | 670.655i | 1.23182 | − | 0.711193i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −226.136 | + | 340.751i | −0.239297 | + | 0.360584i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −337.114 | −0.355981 | −0.177990 | − | 0.984032i | \(-0.556960\pi\) | ||||
−0.177990 | + | 0.984032i | \(0.556960\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −607.633 | − | 350.817i | −0.640288 | − | 0.369670i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19.6587 | + | 946.437i | −0.0206716 | + | 0.995202i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −178.565 | − | 103.095i | −0.187372 | − | 0.108179i | 0.403380 | − | 0.915033i | \(-0.367835\pi\) |
−0.590752 | + | 0.806854i | \(0.701169\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 664.737 | − | 1151.36i | 0.696060 | − | 1.20561i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 16.2170 | − | 8.91906i | 0.0169456 | − | 0.00931981i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −958.330 | −0.999301 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 789.105 | + | 1366.77i | 0.821129 | + | 1.42224i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 189.218 | + | 119.988i | 0.196488 | + | 0.124598i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −257.494 | − | 148.664i | −0.266834 | − | 0.154056i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −395.091 | − | 684.318i | −0.408574 | − | 0.707671i | 0.586156 | − | 0.810198i | \(-0.300641\pi\) |
−0.994730 | + | 0.102527i | \(0.967307\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 69.3625 | − | 1880.05i | 0.0715815 | − | 1.94020i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −696.373 | − | 402.051i | −0.717171 | − | 0.414059i | 0.0965395 | − | 0.995329i | \(-0.469223\pi\) |
−0.813711 | + | 0.581270i | \(0.802556\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −230.429 | − | 399.116i | −0.236824 | − | 0.410191i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 14.7700 | − | 711.081i | 0.0151488 | − | 0.729314i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1248.86 | + | 721.028i | 1.27826 | + | 0.738002i | 0.976528 | − | 0.215391i | \(-0.0691027\pi\) |
0.301730 | + | 0.953394i | \(0.402436\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 614.074 | + | 354.536i | 0.627246 | + | 0.362141i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 328.083 | − | 171.664i | 0.334437 | − | 0.174989i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1749.25i | − | 1.77950i | −0.456445 | − | 0.889751i | \(-0.650878\pi\) | ||
0.456445 | − | 0.889751i | \(-0.349122\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 377.996 | + | 654.708i | 0.383752 | + | 0.664679i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −31.6065 | − | 57.4681i | −0.0320228 | − | 0.0582250i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −667.039 | −0.674458 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 306.985 | + | 177.238i | 0.309773 | + | 0.178847i | 0.646825 | − | 0.762639i | \(-0.276096\pi\) |
−0.337052 | + | 0.941486i | \(0.609430\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −199.161 | − | 120.569i | −0.200565 | − | 0.121419i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 492.418 | − | 852.894i | 0.494893 | − | 0.857180i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −640.147 | + | 1108.77i | −0.642073 | + | 1.11210i | 0.342896 | + | 0.939373i | \(0.388592\pi\) |
−0.984969 | + | 0.172730i | \(0.944741\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −44.4367 | + | 712.292i | −0.0444812 | + | 0.713005i |
(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 | 684.3.s.a.445.26 | ✓ | 80 | |
3.2 | odd | 2 | 2052.3.s.a.901.26 | 80 | |||
9.2 | odd | 6 | 2052.3.bl.a.1585.15 | 80 | |||
9.7 | even | 3 | 684.3.bl.a.673.40 | yes | 80 | ||
19.12 | odd | 6 | 684.3.bl.a.373.40 | yes | 80 | ||
57.50 | even | 6 | 2052.3.bl.a.145.15 | 80 | |||
171.88 | odd | 6 | inner | 684.3.s.a.601.26 | yes | 80 | |
171.164 | even | 6 | 2052.3.s.a.829.26 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.s.a.445.26 | ✓ | 80 | 1.1 | even | 1 | trivial | |
684.3.s.a.601.26 | yes | 80 | 171.88 | odd | 6 | inner | |
684.3.bl.a.373.40 | yes | 80 | 19.12 | odd | 6 | ||
684.3.bl.a.673.40 | yes | 80 | 9.7 | even | 3 | ||
2052.3.s.a.829.26 | 80 | 171.164 | even | 6 | |||
2052.3.s.a.901.26 | 80 | 3.2 | odd | 2 | |||
2052.3.bl.a.145.15 | 80 | 57.50 | even | 6 | |||
2052.3.bl.a.1585.15 | 80 | 9.2 | odd | 6 |