Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,3,Mod(139,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("483.139");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.g (of order \(2\), degree \(1\), 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: | \(13.1607967686\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 139.5 | ||
Character | \(\chi\) | \(=\) | 483.139 |
Dual form | 483.3.g.a.139.6 |
$q$-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 \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(346\) | \(442\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.29495 | −1.64747 | −0.823737 | − | 0.566971i | \(-0.808115\pi\) | ||||
−0.823737 | + | 0.566971i | \(0.808115\pi\) | |||||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | 6.85669 | 1.71417 | ||||||||
\(5\) | − | 6.17562i | − | 1.23512i | −0.786522 | − | 0.617562i | \(-0.788120\pi\) | ||
0.786522 | − | 0.617562i | \(-0.211880\pi\) | |||||||
\(6\) | − | 5.70702i | − | 0.951170i | ||||||
\(7\) | −6.91716 | + | 1.07376i | −0.988165 | + | 0.153394i | ||||
\(8\) | −9.41266 | −1.17658 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 20.3484i | 2.03484i | ||||||||
\(11\) | 18.6871 | 1.69883 | 0.849414 | − | 0.527727i | \(-0.176955\pi\) | ||||
0.849414 | + | 0.527727i | \(0.176955\pi\) | |||||||
\(12\) | 11.8761i | 0.989679i | ||||||||
\(13\) | 3.26619i | 0.251246i | 0.992078 | + | 0.125623i | \(0.0400929\pi\) | ||||
−0.992078 | + | 0.125623i | \(0.959907\pi\) | |||||||
\(14\) | 22.7917 | − | 3.53798i | 1.62798 | − | 0.252713i | ||||
\(15\) | 10.6965 | 0.713100 | ||||||||
\(16\) | 3.58748 | 0.224218 | ||||||||
\(17\) | 14.6408i | 0.861226i | 0.902537 | + | 0.430613i | \(0.141703\pi\) | ||||
−0.902537 | + | 0.430613i | \(0.858297\pi\) | |||||||
\(18\) | 9.88485 | 0.549158 | ||||||||
\(19\) | − | 21.5903i | − | 1.13633i | −0.822913 | − | 0.568167i | \(-0.807653\pi\) | ||
0.822913 | − | 0.568167i | \(-0.192347\pi\) | |||||||
\(20\) | − | 42.3444i | − | 2.11722i | ||||||
\(21\) | −1.85980 | − | 11.9809i | −0.0885621 | − | 0.570517i | ||||
\(22\) | −61.5731 | −2.79878 | ||||||||
\(23\) | −4.79583 | −0.208514 | ||||||||
\(24\) | − | 16.3032i | − | 0.679301i | ||||||
\(25\) | −13.1383 | −0.525533 | ||||||||
\(26\) | − | 10.7619i | − | 0.413921i | ||||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | −47.4288 | + | 7.36244i | −1.69389 | + | 0.262944i | ||||
\(29\) | 8.81655 | 0.304019 | 0.152010 | − | 0.988379i | \(-0.451426\pi\) | ||||
0.152010 | + | 0.988379i | \(0.451426\pi\) | |||||||
\(30\) | −35.2444 | −1.17481 | ||||||||
\(31\) | 13.8198i | 0.445800i | 0.974841 | + | 0.222900i | \(0.0715523\pi\) | ||||
−0.974841 | + | 0.222900i | \(0.928448\pi\) | |||||||
\(32\) | 25.8301 | 0.807190 | ||||||||
\(33\) | 32.3670i | 0.980819i | ||||||||
\(34\) | − | 48.2408i | − | 1.41885i | ||||||
\(35\) | 6.63113 | + | 42.7178i | 0.189461 | + | 1.22051i | ||||
\(36\) | −20.5701 | −0.571391 | ||||||||
\(37\) | −23.7342 | −0.641464 | −0.320732 | − | 0.947170i | \(-0.603929\pi\) | ||||
−0.320732 | + | 0.947170i | \(0.603929\pi\) | |||||||
\(38\) | 71.1391i | 1.87208i | ||||||||
\(39\) | −5.65721 | −0.145057 | ||||||||
\(40\) | 58.1291i | 1.45323i | ||||||||
\(41\) | − | 0.813534i | − | 0.0198423i | −0.999951 | − | 0.00992115i | \(-0.996842\pi\) | ||
0.999951 | − | 0.00992115i | \(-0.00315805\pi\) | |||||||
\(42\) | 6.12796 | + | 39.4763i | 0.145904 | + | 0.939913i | ||||
\(43\) | −55.9522 | −1.30121 | −0.650606 | − | 0.759415i | \(-0.725485\pi\) | ||||
−0.650606 | + | 0.759415i | \(0.725485\pi\) | |||||||
\(44\) | 128.132 | 2.91209 | ||||||||
\(45\) | 18.5269i | 0.411708i | ||||||||
\(46\) | 15.8020 | 0.343522 | ||||||||
\(47\) | − | 53.2456i | − | 1.13289i | −0.824101 | − | 0.566443i | \(-0.808319\pi\) | ||
0.824101 | − | 0.566443i | \(-0.191681\pi\) | |||||||
\(48\) | 6.21370i | 0.129452i | ||||||||
\(49\) | 46.6941 | − | 14.8547i | 0.952940 | − | 0.303157i | ||||
\(50\) | 43.2901 | 0.865803 | ||||||||
\(51\) | −25.3587 | −0.497229 | ||||||||
\(52\) | 22.3953i | 0.430678i | ||||||||
\(53\) | 9.55590 | 0.180300 | 0.0901500 | − | 0.995928i | \(-0.471265\pi\) | ||||
0.0901500 | + | 0.995928i | \(0.471265\pi\) | |||||||
\(54\) | 17.1211i | 0.317057i | ||||||||
\(55\) | − | 115.405i | − | 2.09827i | ||||||
\(56\) | 65.1089 | − | 10.1069i | 1.16266 | − | 0.180481i | ||||
\(57\) | 37.3956 | 0.656063 | ||||||||
\(58\) | −29.0501 | −0.500864 | ||||||||
\(59\) | − | 70.3769i | − | 1.19283i | −0.802677 | − | 0.596414i | \(-0.796592\pi\) | ||
0.802677 | − | 0.596414i | \(-0.203408\pi\) | |||||||
\(60\) | 73.3426 | 1.22238 | ||||||||
\(61\) | − | 73.6403i | − | 1.20722i | −0.797280 | − | 0.603609i | \(-0.793729\pi\) | ||
0.797280 | − | 0.603609i | \(-0.206271\pi\) | |||||||
\(62\) | − | 45.5355i | − | 0.734444i | ||||||
\(63\) | 20.7515 | − | 3.22128i | 0.329388 | − | 0.0511314i | ||||
\(64\) | −99.4588 | −1.55404 | ||||||||
\(65\) | 20.1708 | 0.310320 | ||||||||
\(66\) | − | 106.648i | − | 1.61587i | ||||||
\(67\) | 63.1408 | 0.942399 | 0.471200 | − | 0.882027i | \(-0.343821\pi\) | ||||
0.471200 | + | 0.882027i | \(0.343821\pi\) | |||||||
\(68\) | 100.388i | 1.47629i | ||||||||
\(69\) | − | 8.30662i | − | 0.120386i | ||||||
\(70\) | −21.8492 | − | 140.753i | −0.312132 | − | 2.01075i | ||||
\(71\) | 40.6288 | 0.572236 | 0.286118 | − | 0.958194i | \(-0.407635\pi\) | ||||
0.286118 | + | 0.958194i | \(0.407635\pi\) | |||||||
\(72\) | 28.2380 | 0.392194 | ||||||||
\(73\) | − | 17.4936i | − | 0.239639i | −0.992796 | − | 0.119819i | \(-0.961768\pi\) | ||
0.992796 | − | 0.119819i | \(-0.0382316\pi\) | |||||||
\(74\) | 78.2029 | 1.05680 | ||||||||
\(75\) | − | 22.7563i | − | 0.303417i | ||||||
\(76\) | − | 148.038i | − | 1.94787i | ||||||
\(77\) | −129.262 | + | 20.0655i | −1.67872 | + | 0.260590i | ||||
\(78\) | 18.6402 | 0.238977 | ||||||||
\(79\) | −30.8574 | −0.390600 | −0.195300 | − | 0.980744i | \(-0.562568\pi\) | ||||
−0.195300 | + | 0.980744i | \(0.562568\pi\) | |||||||
\(80\) | − | 22.1549i | − | 0.276937i | ||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 2.68056i | 0.0326897i | ||||||||
\(83\) | − | 140.993i | − | 1.69871i | −0.527821 | − | 0.849356i | \(-0.676991\pi\) | ||
0.527821 | − | 0.849356i | \(-0.323009\pi\) | |||||||
\(84\) | −12.7521 | − | 82.1491i | −0.151811 | − | 0.977966i | ||||
\(85\) | 90.4163 | 1.06372 | ||||||||
\(86\) | 184.360 | 2.14372 | ||||||||
\(87\) | 15.2707i | 0.175525i | ||||||||
\(88\) | −175.896 | −1.99881 | ||||||||
\(89\) | − | 117.309i | − | 1.31808i | −0.752110 | − | 0.659038i | \(-0.770964\pi\) | ||
0.752110 | − | 0.659038i | \(-0.229036\pi\) | |||||||
\(90\) | − | 61.0451i | − | 0.678279i | ||||||
\(91\) | −3.50710 | − | 22.5928i | −0.0385396 | − | 0.248272i | ||||
\(92\) | −32.8836 | −0.357430 | ||||||||
\(93\) | −23.9366 | −0.257383 | ||||||||
\(94\) | 175.442i | 1.86640i | ||||||||
\(95\) | −133.334 | −1.40351 | ||||||||
\(96\) | 44.7390i | 0.466032i | ||||||||
\(97\) | − | 62.3174i | − | 0.642447i | −0.947003 | − | 0.321224i | \(-0.895906\pi\) | ||
0.947003 | − | 0.321224i | \(-0.104094\pi\) | |||||||
\(98\) | −153.855 | + | 48.9455i | −1.56995 | + | 0.499444i | ||||
\(99\) | −56.0613 | −0.566276 | ||||||||
\(100\) | −90.0855 | −0.900855 | ||||||||
\(101\) | − | 166.315i | − | 1.64669i | −0.567544 | − | 0.823343i | \(-0.692106\pi\) | ||
0.567544 | − | 0.823343i | \(-0.307894\pi\) | |||||||
\(102\) | 83.5556 | 0.819172 | ||||||||
\(103\) | 92.5486i | 0.898530i | 0.893399 | + | 0.449265i | \(0.148314\pi\) | ||||
−0.893399 | + | 0.449265i | \(0.851686\pi\) | |||||||
\(104\) | − | 30.7436i | − | 0.295611i | ||||||
\(105\) | −73.9893 | + | 11.4855i | −0.704660 | + | 0.109385i | ||||
\(106\) | −31.4862 | −0.297040 | ||||||||
\(107\) | −14.0784 | −0.131574 | −0.0657869 | − | 0.997834i | \(-0.520956\pi\) | ||||
−0.0657869 | + | 0.997834i | \(0.520956\pi\) | |||||||
\(108\) | − | 35.6284i | − | 0.329893i | ||||||
\(109\) | 17.9547 | 0.164722 | 0.0823608 | − | 0.996603i | \(-0.473754\pi\) | ||||
0.0823608 | + | 0.996603i | \(0.473754\pi\) | |||||||
\(110\) | 380.252i | 3.45684i | ||||||||
\(111\) | − | 41.1088i | − | 0.370349i | ||||||
\(112\) | −24.8152 | + | 3.85209i | −0.221564 | + | 0.0343937i | ||||
\(113\) | 117.574 | 1.04048 | 0.520238 | − | 0.854022i | \(-0.325843\pi\) | ||||
0.520238 | + | 0.854022i | \(0.325843\pi\) | |||||||
\(114\) | −123.217 | −1.08085 | ||||||||
\(115\) | 29.6173i | 0.257541i | ||||||||
\(116\) | 60.4524 | 0.521141 | ||||||||
\(117\) | − | 9.79858i | − | 0.0837485i | ||||||
\(118\) | 231.888i | 1.96515i | ||||||||
\(119\) | −15.7207 | − | 101.273i | −0.132107 | − | 0.851034i | ||||
\(120\) | −100.683 | −0.839021 | ||||||||
\(121\) | 228.208 | 1.88602 | ||||||||
\(122\) | 242.641i | 1.98886i | ||||||||
\(123\) | 1.40908 | 0.0114560 | ||||||||
\(124\) | 94.7581i | 0.764178i | ||||||||
\(125\) | − | 73.2532i | − | 0.586026i | ||||||
\(126\) | −68.3750 | + | 10.6139i | −0.542659 | + | 0.0842377i | ||||
\(127\) | −30.7007 | −0.241738 | −0.120869 | − | 0.992668i | \(-0.538568\pi\) | ||||
−0.120869 | + | 0.992668i | \(0.538568\pi\) | |||||||
\(128\) | 224.391 | 1.75306 | ||||||||
\(129\) | − | 96.9120i | − | 0.751256i | ||||||
\(130\) | −66.4617 | −0.511244 | ||||||||
\(131\) | 106.463i | 0.812696i | 0.913718 | + | 0.406348i | \(0.133198\pi\) | ||||
−0.913718 | + | 0.406348i | \(0.866802\pi\) | |||||||
\(132\) | 221.931i | 1.68129i | ||||||||
\(133\) | 23.1828 | + | 149.344i | 0.174307 | + | 1.12289i | ||||
\(134\) | −208.046 | −1.55258 | ||||||||
\(135\) | −32.0895 | −0.237700 | ||||||||
\(136\) | − | 137.809i | − | 1.01330i | ||||||
\(137\) | 109.057 | 0.796033 | 0.398016 | − | 0.917378i | \(-0.369699\pi\) | ||||
0.398016 | + | 0.917378i | \(0.369699\pi\) | |||||||
\(138\) | 27.3699i | 0.198333i | ||||||||
\(139\) | 119.876i | 0.862418i | 0.902252 | + | 0.431209i | \(0.141913\pi\) | ||||
−0.902252 | + | 0.431209i | \(0.858087\pi\) | |||||||
\(140\) | 45.4676 | + | 292.903i | 0.324769 | + | 2.09216i | ||||
\(141\) | 92.2241 | 0.654072 | ||||||||
\(142\) | −133.870 | −0.942744 | ||||||||
\(143\) | 61.0357i | 0.426823i | ||||||||
\(144\) | −10.7624 | −0.0747392 | ||||||||
\(145\) | − | 54.4477i | − | 0.375501i | ||||||
\(146\) | 57.6407i | 0.394799i | ||||||||
\(147\) | 25.7291 | + | 80.8765i | 0.175028 | + | 0.550180i | ||||
\(148\) | −162.738 | −1.09958 | ||||||||
\(149\) | −57.1282 | −0.383411 | −0.191705 | − | 0.981453i | \(-0.561402\pi\) | ||||
−0.191705 | + | 0.981453i | \(0.561402\pi\) | |||||||
\(150\) | 74.9807i | 0.499871i | ||||||||
\(151\) | −177.338 | −1.17442 | −0.587211 | − | 0.809434i | \(-0.699774\pi\) | ||||
−0.587211 | + | 0.809434i | \(0.699774\pi\) | |||||||
\(152\) | 203.223i | 1.33699i | ||||||||
\(153\) | − | 43.9225i | − | 0.287075i | ||||||
\(154\) | 425.911 | − | 66.1147i | 2.76565 | − | 0.429316i | ||||
\(155\) | 85.3459 | 0.550618 | ||||||||
\(156\) | −38.7898 | −0.248652 | ||||||||
\(157\) | − | 278.100i | − | 1.77134i | −0.464318 | − | 0.885668i | \(-0.653701\pi\) | ||
0.464318 | − | 0.885668i | \(-0.346299\pi\) | |||||||
\(158\) | 101.674 | 0.643504 | ||||||||
\(159\) | 16.5513i | 0.104096i | ||||||||
\(160\) | − | 159.517i | − | 0.996981i | ||||||
\(161\) | 33.1735 | − | 5.14957i | 0.206047 | − | 0.0319849i | ||||
\(162\) | −29.6545 | −0.183053 | ||||||||
\(163\) | −271.093 | −1.66315 | −0.831574 | − | 0.555414i | \(-0.812560\pi\) | ||||
−0.831574 | + | 0.555414i | \(0.812560\pi\) | |||||||
\(164\) | − | 5.57816i | − | 0.0340132i | ||||||
\(165\) | 199.887 | 1.21143 | ||||||||
\(166\) | 464.565i | 2.79859i | ||||||||
\(167\) | − | 292.831i | − | 1.75348i | −0.480968 | − | 0.876738i | \(-0.659715\pi\) | ||
0.480968 | − | 0.876738i | \(-0.340285\pi\) | |||||||
\(168\) | 17.5057 | + | 112.772i | 0.104201 | + | 0.671261i | ||||
\(169\) | 158.332 | 0.936876 | ||||||||
\(170\) | −297.917 | −1.75245 | ||||||||
\(171\) | 64.7710i | 0.378778i | ||||||||
\(172\) | −383.647 | −2.23050 | ||||||||
\(173\) | 303.399i | 1.75375i | 0.480715 | + | 0.876877i | \(0.340377\pi\) | ||||
−0.480715 | + | 0.876877i | \(0.659623\pi\) | |||||||
\(174\) | − | 50.3162i | − | 0.289174i | ||||||
\(175\) | 90.8799 | − | 14.1074i | 0.519313 | − | 0.0806137i | ||||
\(176\) | 67.0397 | 0.380907 | ||||||||
\(177\) | 121.896 | 0.688680 | ||||||||
\(178\) | 386.526i | 2.17150i | ||||||||
\(179\) | −292.706 | −1.63523 | −0.817616 | − | 0.575764i | \(-0.804705\pi\) | ||||
−0.817616 | + | 0.575764i | \(0.804705\pi\) | |||||||
\(180\) | 127.033i | 0.705739i | ||||||||
\(181\) | 21.6285i | 0.119495i | 0.998214 | + | 0.0597473i | \(0.0190295\pi\) | ||||
−0.998214 | + | 0.0597473i | \(0.980971\pi\) | |||||||
\(182\) | 11.5557 | + | 74.4420i | 0.0634930 | + | 0.409022i | ||||
\(183\) | 127.549 | 0.696988 | ||||||||
\(184\) | 45.1416 | 0.245335 | ||||||||
\(185\) | 146.573i | 0.792288i | ||||||||
\(186\) | 78.8699 | 0.424032 | ||||||||
\(187\) | 273.595i | 1.46308i | ||||||||
\(188\) | − | 365.089i | − | 1.94196i | ||||||
\(189\) | 5.57941 | + | 35.9426i | 0.0295207 | + | 0.190172i | ||||
\(190\) | 439.328 | 2.31225 | ||||||||
\(191\) | 37.3713 | 0.195661 | 0.0978306 | − | 0.995203i | \(-0.468810\pi\) | ||||
0.0978306 | + | 0.995203i | \(0.468810\pi\) | |||||||
\(192\) | − | 172.268i | − | 0.897227i | ||||||
\(193\) | 50.5070 | 0.261694 | 0.130847 | − | 0.991403i | \(-0.458230\pi\) | ||||
0.130847 | + | 0.991403i | \(0.458230\pi\) | |||||||
\(194\) | 205.333i | 1.05842i | ||||||||
\(195\) | 34.9368i | 0.179163i | ||||||||
\(196\) | 320.167 | − | 101.854i | 1.63351 | − | 0.519664i | ||||
\(197\) | −168.711 | −0.856402 | −0.428201 | − | 0.903684i | \(-0.640852\pi\) | ||||
−0.428201 | + | 0.903684i | \(0.640852\pi\) | |||||||
\(198\) | 184.719 | 0.932926 | ||||||||
\(199\) | − | 268.488i | − | 1.34918i | −0.738191 | − | 0.674592i | \(-0.764320\pi\) | ||
0.738191 | − | 0.674592i | \(-0.235680\pi\) | |||||||
\(200\) | 123.667 | 0.618333 | ||||||||
\(201\) | 109.363i | 0.544095i | ||||||||
\(202\) | 548.001i | 2.71287i | ||||||||
\(203\) | −60.9855 | + | 9.46685i | −0.300421 | + | 0.0466347i | ||||
\(204\) | −173.877 | −0.852337 | ||||||||
\(205\) | −5.02408 | −0.0245077 | ||||||||
\(206\) | − | 304.943i | − | 1.48031i | ||||||
\(207\) | 14.3875 | 0.0695048 | ||||||||
\(208\) | 11.7174i | 0.0563336i | ||||||||
\(209\) | − | 403.461i | − | 1.93044i | ||||||
\(210\) | 243.791 | − | 37.8440i | 1.16091 | − | 0.180210i | ||||
\(211\) | −359.772 | −1.70508 | −0.852540 | − | 0.522661i | \(-0.824939\pi\) | ||||
−0.852540 | + | 0.522661i | \(0.824939\pi\) | |||||||
\(212\) | 65.5219 | 0.309066 | ||||||||
\(213\) | 70.3711i | 0.330381i | ||||||||
\(214\) | 46.3876 | 0.216765 | ||||||||
\(215\) | 345.539i | 1.60716i | ||||||||
\(216\) | 48.9096i | 0.226434i | ||||||||
\(217\) | −14.8391 | − | 95.5937i | −0.0683831 | − | 0.440524i | ||||
\(218\) | −59.1597 | −0.271375 | ||||||||
\(219\) | 30.2999 | 0.138356 | ||||||||
\(220\) | − | 791.294i | − | 3.59679i | ||||||
\(221\) | −47.8198 | −0.216379 | ||||||||
\(222\) | 135.451i | 0.610141i | ||||||||
\(223\) | 80.2136i | 0.359702i | 0.983694 | + | 0.179851i | \(0.0575616\pi\) | ||||
−0.983694 | + | 0.179851i | \(0.942438\pi\) | |||||||
\(224\) | −178.671 | + | 27.7353i | −0.797637 | + | 0.123818i | ||||
\(225\) | 39.4150 | 0.175178 | ||||||||
\(226\) | −387.400 | −1.71416 | ||||||||
\(227\) | 135.098i | 0.595146i | 0.954699 | + | 0.297573i | \(0.0961772\pi\) | ||||
−0.954699 | + | 0.297573i | \(0.903823\pi\) | |||||||
\(228\) | 256.410 | 1.12461 | ||||||||
\(229\) | − | 82.7151i | − | 0.361201i | −0.983557 | − | 0.180601i | \(-0.942196\pi\) | ||
0.983557 | − | 0.180601i | \(-0.0578042\pi\) | |||||||
\(230\) | − | 97.5874i | − | 0.424293i | ||||||
\(231\) | −34.7544 | − | 223.888i | −0.150452 | − | 0.969211i | ||||
\(232\) | −82.9872 | −0.357704 | ||||||||
\(233\) | −342.059 | −1.46806 | −0.734032 | − | 0.679115i | \(-0.762364\pi\) | ||||
−0.734032 | + | 0.679115i | \(0.762364\pi\) | |||||||
\(234\) | 32.2858i | 0.137974i | ||||||||
\(235\) | −328.825 | −1.39926 | ||||||||
\(236\) | − | 482.553i | − | 2.04472i | ||||||
\(237\) | − | 53.4466i | − | 0.225513i | ||||||
\(238\) | 51.7990 | + | 333.689i | 0.217643 | + | 1.40206i | ||||
\(239\) | 261.082 | 1.09239 | 0.546196 | − | 0.837658i | \(-0.316075\pi\) | ||||
0.546196 | + | 0.837658i | \(0.316075\pi\) | |||||||
\(240\) | 38.3735 | 0.159889 | ||||||||
\(241\) | 318.890i | 1.32319i | 0.749860 | + | 0.661597i | \(0.230121\pi\) | ||||
−0.749860 | + | 0.661597i | \(0.769879\pi\) | |||||||
\(242\) | −751.935 | −3.10717 | ||||||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | − | 504.929i | − | 2.06938i | ||||||
\(245\) | −91.7371 | − | 288.365i | −0.374437 | − | 1.17700i | ||||
\(246\) | −4.64286 | −0.0188734 | ||||||||
\(247\) | 70.5182 | 0.285499 | ||||||||
\(248\) | − | 130.081i | − | 0.524521i | ||||||
\(249\) | 244.207 | 0.980752 | ||||||||
\(250\) | 241.366i | 0.965463i | ||||||||
\(251\) | 233.834i | 0.931610i | 0.884887 | + | 0.465805i | \(0.154235\pi\) | ||||
−0.884887 | + | 0.465805i | \(0.845765\pi\) | |||||||
\(252\) | 142.286 | − | 22.0873i | 0.564629 | − | 0.0876481i | ||||
\(253\) | −89.6202 | −0.354230 | ||||||||
\(254\) | 101.157 | 0.398257 | ||||||||
\(255\) | 156.606i | 0.614140i | ||||||||
\(256\) | −341.523 | −1.33407 | ||||||||
\(257\) | − | 313.621i | − | 1.22031i | −0.792280 | − | 0.610157i | \(-0.791106\pi\) | ||
0.792280 | − | 0.610157i | \(-0.208894\pi\) | |||||||
\(258\) | 319.320i | 1.23767i | ||||||||
\(259\) | 164.173 | − | 25.4848i | 0.633872 | − | 0.0983968i | ||||
\(260\) | 138.305 | 0.531942 | ||||||||
\(261\) | −26.4497 | −0.101340 | ||||||||
\(262\) | − | 350.791i | − | 1.33890i | ||||||
\(263\) | 320.398 | 1.21824 | 0.609122 | − | 0.793077i | \(-0.291522\pi\) | ||||
0.609122 | + | 0.793077i | \(0.291522\pi\) | |||||||
\(264\) | − | 304.660i | − | 1.15402i | ||||||
\(265\) | − | 59.0136i | − | 0.222693i | ||||||
\(266\) | −76.3862 | − | 492.080i | −0.287166 | − | 1.84993i | ||||
\(267\) | 203.185 | 0.760991 | ||||||||
\(268\) | 432.937 | 1.61544 | ||||||||
\(269\) | − | 366.289i | − | 1.36167i | −0.732438 | − | 0.680834i | \(-0.761617\pi\) | ||
0.732438 | − | 0.680834i | \(-0.238383\pi\) | |||||||
\(270\) | 105.733 | 0.391605 | ||||||||
\(271\) | − | 37.5106i | − | 0.138416i | −0.997602 | − | 0.0692078i | \(-0.977953\pi\) | ||
0.997602 | − | 0.0692078i | \(-0.0220472\pi\) | |||||||
\(272\) | 52.5237i | 0.193102i | ||||||||
\(273\) | 39.1318 | − | 6.07448i | 0.143340 | − | 0.0222508i | ||||
\(274\) | −359.336 | −1.31144 | ||||||||
\(275\) | −245.517 | −0.892791 | ||||||||
\(276\) | − | 56.9560i | − | 0.206362i | ||||||
\(277\) | 125.818 | 0.454216 | 0.227108 | − | 0.973870i | \(-0.427073\pi\) | ||||
0.227108 | + | 0.973870i | \(0.427073\pi\) | |||||||
\(278\) | − | 394.986i | − | 1.42081i | ||||||
\(279\) | − | 41.4594i | − | 0.148600i | ||||||
\(280\) | −62.4166 | − | 402.088i | −0.222916 | − | 1.43603i | ||||
\(281\) | 523.002 | 1.86122 | 0.930609 | − | 0.366015i | \(-0.119278\pi\) | ||||
0.930609 | + | 0.366015i | \(0.119278\pi\) | |||||||
\(282\) | −303.874 | −1.07757 | ||||||||
\(283\) | 299.760i | 1.05922i | 0.848240 | + | 0.529612i | \(0.177662\pi\) | ||||
−0.848240 | + | 0.529612i | \(0.822338\pi\) | |||||||
\(284\) | 278.579 | 0.980912 | ||||||||
\(285\) | − | 230.941i | − | 0.810319i | ||||||
\(286\) | − | 201.110i | − | 0.703180i | ||||||
\(287\) | 0.873540 | + | 5.62734i | 0.00304369 | + | 0.0196075i | ||||
\(288\) | −77.4903 | −0.269063 | ||||||||
\(289\) | 74.6457 | 0.258290 | ||||||||
\(290\) | 179.402i | 0.618629i | ||||||||
\(291\) | 107.937 | 0.370917 | ||||||||
\(292\) | − | 119.949i | − | 0.410783i | ||||||
\(293\) | 517.985i | 1.76787i | 0.467613 | + | 0.883933i | \(0.345114\pi\) | ||||
−0.467613 | + | 0.883933i | \(0.654886\pi\) | |||||||
\(294\) | −84.7762 | − | 266.484i | −0.288354 | − | 0.906408i | ||||
\(295\) | −434.621 | −1.47329 | ||||||||
\(296\) | 223.402 | 0.754736 | ||||||||
\(297\) | − | 97.1011i | − | 0.326940i | ||||||
\(298\) | 188.234 | 0.631659 | ||||||||
\(299\) | − | 15.6641i | − | 0.0523883i | ||||||
\(300\) | − | 156.033i | − | 0.520109i | ||||||
\(301\) | 387.030 | − | 60.0791i | 1.28581 | − | 0.199598i | ||||
\(302\) | 584.319 | 1.93483 | ||||||||
\(303\) | 288.067 | 0.950715 | ||||||||
\(304\) | − | 77.4549i | − | 0.254786i | ||||||
\(305\) | −454.775 | −1.49107 | ||||||||
\(306\) | 144.723i | 0.472949i | ||||||||
\(307\) | 152.975i | 0.498291i | 0.968466 | + | 0.249146i | \(0.0801498\pi\) | ||||
−0.968466 | + | 0.249146i | \(0.919850\pi\) | |||||||
\(308\) | −886.308 | + | 137.583i | −2.87762 | + | 0.446697i | ||||
\(309\) | −160.299 | −0.518767 | ||||||||
\(310\) | −281.210 | −0.907130 | ||||||||
\(311\) | 115.037i | 0.369895i | 0.982748 | + | 0.184947i | \(0.0592115\pi\) | ||||
−0.982748 | + | 0.184947i | \(0.940788\pi\) | |||||||
\(312\) | 53.2494 | 0.170671 | ||||||||
\(313\) | − | 563.173i | − | 1.79928i | −0.436636 | − | 0.899638i | \(-0.643830\pi\) | ||
0.436636 | − | 0.899638i | \(-0.356170\pi\) | |||||||
\(314\) | 916.325i | 2.91823i | ||||||||
\(315\) | −19.8934 | − | 128.153i | −0.0631536 | − | 0.406836i | ||||
\(316\) | −211.580 | −0.669557 | ||||||||
\(317\) | −469.568 | −1.48129 | −0.740644 | − | 0.671897i | \(-0.765480\pi\) | ||||
−0.740644 | + | 0.671897i | \(0.765480\pi\) | |||||||
\(318\) | − | 54.5357i | − | 0.171496i | ||||||
\(319\) | 164.756 | 0.516476 | ||||||||
\(320\) | 614.220i | 1.91944i | ||||||||
\(321\) | − | 24.3845i | − | 0.0759642i | ||||||
\(322\) | −109.305 | + | 16.9676i | −0.339457 | + | 0.0526943i | ||||
\(323\) | 316.101 | 0.978640 | ||||||||
\(324\) | 61.7102 | 0.190464 | ||||||||
\(325\) | − | 42.9123i | − | 0.132038i | ||||||
\(326\) | 893.238 | 2.73999 | ||||||||
\(327\) | 31.0984i | 0.0951021i | ||||||||
\(328\) | 7.65753i | 0.0233461i | ||||||||
\(329\) | 57.1730 | + | 368.308i | 0.173778 | + | 1.11948i | ||||
\(330\) | −658.616 | −1.99581 | ||||||||
\(331\) | 306.543 | 0.926113 | 0.463057 | − | 0.886329i | \(-0.346753\pi\) | ||||
0.463057 | + | 0.886329i | \(0.346753\pi\) | |||||||
\(332\) | − | 966.746i | − | 2.91189i | ||||||
\(333\) | 71.2025 | 0.213821 | ||||||||
\(334\) | 964.862i | 2.88881i | ||||||||
\(335\) | − | 389.934i | − | 1.16398i | ||||||
\(336\) | −6.67201 | − | 42.9811i | −0.0198572 | − | 0.127920i | ||||
\(337\) | −185.669 | −0.550946 | −0.275473 | − | 0.961309i | \(-0.588834\pi\) | ||||
−0.275473 | + | 0.961309i | \(0.588834\pi\) | |||||||
\(338\) | −521.696 | −1.54348 | ||||||||
\(339\) | 203.644i | 0.600719i | ||||||||
\(340\) | 619.957 | 1.82340 | ||||||||
\(341\) | 258.252i | 0.757338i | ||||||||
\(342\) | − | 213.417i | − | 0.624027i | ||||||
\(343\) | −307.040 | + | 152.891i | −0.895160 | + | 0.445745i | ||||
\(344\) | 526.659 | 1.53099 | ||||||||
\(345\) | −51.2986 | −0.148692 | ||||||||
\(346\) | − | 999.686i | − | 2.88927i | ||||||
\(347\) | 27.6667 | 0.0797310 | 0.0398655 | − | 0.999205i | \(-0.487307\pi\) | ||||
0.0398655 | + | 0.999205i | \(0.487307\pi\) | |||||||
\(348\) | 104.707i | 0.300881i | ||||||||
\(349\) | − | 172.121i | − | 0.493184i | −0.969119 | − | 0.246592i | \(-0.920689\pi\) | ||
0.969119 | − | 0.246592i | \(-0.0793108\pi\) | |||||||
\(350\) | −299.445 | + | 46.4832i | −0.855556 | + | 0.132809i | ||||
\(351\) | 16.9716 | 0.0483522 | ||||||||
\(352\) | 482.690 | 1.37128 | ||||||||
\(353\) | 471.614i | 1.33602i | 0.744153 | + | 0.668009i | \(0.232853\pi\) | ||||
−0.744153 | + | 0.668009i | \(0.767147\pi\) | |||||||
\(354\) | −401.642 | −1.13458 | ||||||||
\(355\) | − | 250.908i | − | 0.706783i | ||||||
\(356\) | − | 804.350i | − | 2.25941i | ||||||
\(357\) | 175.410 | − | 27.2291i | 0.491344 | − | 0.0762720i | ||||
\(358\) | 964.453 | 2.69400 | ||||||||
\(359\) | 425.042 | 1.18396 | 0.591980 | − | 0.805952i | \(-0.298346\pi\) | ||||
0.591980 | + | 0.805952i | \(0.298346\pi\) | |||||||
\(360\) | − | 174.387i | − | 0.484409i | ||||||
\(361\) | −105.143 | −0.291255 | ||||||||
\(362\) | − | 71.2649i | − | 0.196864i | ||||||
\(363\) | 395.268i | 1.08889i | ||||||||
\(364\) | −24.0471 | − | 154.912i | −0.0660635 | − | 0.425581i | ||||
\(365\) | −108.034 | −0.295984 | ||||||||
\(366\) | −420.267 | −1.14827 | ||||||||
\(367\) | − | 383.085i | − | 1.04383i | −0.852998 | − | 0.521915i | \(-0.825218\pi\) | ||
0.852998 | − | 0.521915i | \(-0.174782\pi\) | |||||||
\(368\) | −17.2050 | −0.0467526 | ||||||||
\(369\) | 2.44060i | 0.00661410i | ||||||||
\(370\) | − | 482.952i | − | 1.30527i | ||||||
\(371\) | −66.0997 | + | 10.2607i | −0.178166 | + | 0.0276570i | ||||
\(372\) | −164.126 | −0.441199 | ||||||||
\(373\) | 711.450 | 1.90737 | 0.953686 | − | 0.300802i | \(-0.0972545\pi\) | ||||
0.953686 | + | 0.300802i | \(0.0972545\pi\) | |||||||
\(374\) | − | 901.482i | − | 2.41038i | ||||||
\(375\) | 126.878 | 0.338342 | ||||||||
\(376\) | 501.183i | 1.33293i | ||||||||
\(377\) | 28.7965i | 0.0763834i | ||||||||
\(378\) | −18.3839 | − | 118.429i | −0.0486346 | − | 0.313304i | ||||
\(379\) | 490.334 | 1.29376 | 0.646879 | − | 0.762592i | \(-0.276074\pi\) | ||||
0.646879 | + | 0.762592i | \(0.276074\pi\) | |||||||
\(380\) | −914.229 | −2.40587 | ||||||||
\(381\) | − | 53.1752i | − | 0.139568i | ||||||
\(382\) | −123.137 | −0.322347 | ||||||||
\(383\) | − | 187.274i | − | 0.488967i | −0.969653 | − | 0.244484i | \(-0.921382\pi\) | ||
0.969653 | − | 0.244484i | \(-0.0786184\pi\) | |||||||
\(384\) | 388.657i | 1.01213i | ||||||||
\(385\) | 123.917 | + | 798.271i | 0.321862 | + | 2.07343i | ||||
\(386\) | −166.418 | −0.431135 | ||||||||
\(387\) | 167.856 | 0.433738 | ||||||||
\(388\) | − | 427.291i | − | 1.10127i | ||||||
\(389\) | −673.049 | −1.73020 | −0.865101 | − | 0.501597i | \(-0.832746\pi\) | ||||
−0.865101 | + | 0.501597i | \(0.832746\pi\) | |||||||
\(390\) | − | 115.115i | − | 0.295167i | ||||||
\(391\) | − | 70.2150i | − | 0.179578i | ||||||
\(392\) | −439.516 | + | 139.822i | −1.12121 | + | 0.356690i | ||||
\(393\) | −184.400 | −0.469210 | ||||||||
\(394\) | 555.895 | 1.41090 | ||||||||
\(395\) | 190.564i | 0.482440i | ||||||||
\(396\) | −384.395 | −0.970696 | ||||||||
\(397\) | − | 499.360i | − | 1.25783i | −0.777473 | − | 0.628916i | \(-0.783499\pi\) | ||
0.777473 | − | 0.628916i | \(-0.216501\pi\) | |||||||
\(398\) | 884.653i | 2.22275i | ||||||||
\(399\) | −258.671 | + | 40.1538i | −0.648298 | + | 0.100636i | ||||
\(400\) | −47.1335 | −0.117834 | ||||||||
\(401\) | 523.213 | 1.30477 | 0.652385 | − | 0.757888i | \(-0.273768\pi\) | ||||
0.652385 | + | 0.757888i | \(0.273768\pi\) | |||||||
\(402\) | − | 360.346i | − | 0.896382i | ||||||
\(403\) | −45.1381 | −0.112005 | ||||||||
\(404\) | − | 1140.37i | − | 2.82271i | ||||||
\(405\) | − | 55.5806i | − | 0.137236i | ||||||
\(406\) | 200.944 | − | 31.1928i | 0.494936 | − | 0.0768295i | ||||
\(407\) | −443.523 | −1.08974 | ||||||||
\(408\) | 238.693 | 0.585031 | ||||||||
\(409\) | 118.910i | 0.290733i | 0.989378 | + | 0.145367i | \(0.0464361\pi\) | ||||
−0.989378 | + | 0.145367i | \(0.953564\pi\) | |||||||
\(410\) | 16.5541 | 0.0403759 | ||||||||
\(411\) | 188.891i | 0.459590i | ||||||||
\(412\) | 634.577i | 1.54024i | ||||||||
\(413\) | 75.5678 | + | 486.808i | 0.182973 | + | 1.17871i | ||||
\(414\) | −47.4061 | −0.114507 | ||||||||
\(415\) | −870.720 | −2.09812 | ||||||||
\(416\) | 84.3660i | 0.202803i | ||||||||
\(417\) | −207.632 | −0.497917 | ||||||||
\(418\) | 1329.38i | 3.18035i | ||||||||
\(419\) | − | 303.292i | − | 0.723848i | −0.932208 | − | 0.361924i | \(-0.882120\pi\) | ||
0.932208 | − | 0.361924i | \(-0.117880\pi\) | |||||||
\(420\) | −507.322 | + | 78.7523i | −1.20791 | + | 0.187505i | ||||
\(421\) | −104.240 | −0.247601 | −0.123801 | − | 0.992307i | \(-0.539508\pi\) | ||||
−0.123801 | + | 0.992307i | \(0.539508\pi\) | |||||||
\(422\) | 1185.43 | 2.80908 | ||||||||
\(423\) | 159.737i | 0.377629i | ||||||||
\(424\) | −89.9465 | −0.212138 | ||||||||
\(425\) | − | 192.356i | − | 0.452603i | ||||||
\(426\) | − | 231.869i | − | 0.544294i | ||||||
\(427\) | 79.0719 | + | 509.381i | 0.185180 | + | 1.19293i | ||||
\(428\) | −96.5313 | −0.225540 | ||||||||
\(429\) | −105.717 | −0.246426 | ||||||||
\(430\) | − | 1138.54i | − | 2.64776i | ||||||
\(431\) | −834.590 | −1.93640 | −0.968202 | − | 0.250171i | \(-0.919513\pi\) | ||||
−0.968202 | + | 0.250171i | \(0.919513\pi\) | |||||||
\(432\) | − | 18.6411i | − | 0.0431507i | ||||||
\(433\) | 743.715i | 1.71759i | 0.512321 | + | 0.858794i | \(0.328786\pi\) | ||||
−0.512321 | + | 0.858794i | \(0.671214\pi\) | |||||||
\(434\) | 48.8942 | + | 314.976i | 0.112659 | + | 0.725752i | ||||
\(435\) | 94.3062 | 0.216796 | ||||||||
\(436\) | 123.110 | 0.282361 | ||||||||
\(437\) | 103.544i | 0.236942i | ||||||||
\(438\) | −99.8366 | −0.227937 | ||||||||
\(439\) | − | 507.065i | − | 1.15505i | −0.816374 | − | 0.577523i | \(-0.804019\pi\) | ||
0.816374 | − | 0.577523i | \(-0.195981\pi\) | |||||||
\(440\) | 1086.26i | 2.46878i | ||||||||
\(441\) | −140.082 | + | 44.5641i | −0.317647 | + | 0.101052i | ||||
\(442\) | 157.564 | 0.356479 | ||||||||
\(443\) | −4.71685 | −0.0106475 | −0.00532376 | − | 0.999986i | \(-0.501695\pi\) | ||||
−0.00532376 | + | 0.999986i | \(0.501695\pi\) | |||||||
\(444\) | − | 281.870i | − | 0.634843i | ||||||
\(445\) | −724.455 | −1.62799 | ||||||||
\(446\) | − | 264.300i | − | 0.592600i | ||||||
\(447\) | − | 98.9489i | − | 0.221362i | ||||||
\(448\) | 687.972 | − | 106.795i | 1.53565 | − | 0.238381i | ||||
\(449\) | 512.840 | 1.14218 | 0.571092 | − | 0.820886i | \(-0.306520\pi\) | ||||
0.571092 | + | 0.820886i | \(0.306520\pi\) | |||||||
\(450\) | −129.870 | −0.288601 | ||||||||
\(451\) | − | 15.2026i | − | 0.0337087i | ||||||
\(452\) | 806.167 | 1.78356 | ||||||||
\(453\) | − | 307.158i | − | 0.678053i | ||||||
\(454\) | − | 445.142i | − | 0.980489i | ||||||
\(455\) | −139.524 | + | 21.6585i | −0.306647 | + | 0.0476012i | ||||
\(456\) | −351.992 | −0.771912 | ||||||||
\(457\) | 631.627 | 1.38212 | 0.691058 | − | 0.722800i | \(-0.257145\pi\) | ||||
0.691058 | + | 0.722800i | \(0.257145\pi\) | |||||||
\(458\) | 272.542i | 0.595070i | ||||||||
\(459\) | 76.0761 | 0.165743 | ||||||||
\(460\) | 203.076i | 0.441471i | ||||||||
\(461\) | 478.587i | 1.03815i | 0.854729 | + | 0.519075i | \(0.173724\pi\) | ||||
−0.854729 | + | 0.519075i | \(0.826276\pi\) | |||||||
\(462\) | 114.514 | + | 737.699i | 0.247866 | + | 1.59675i | ||||
\(463\) | 226.920 | 0.490108 | 0.245054 | − | 0.969509i | \(-0.421194\pi\) | ||||
0.245054 | + | 0.969509i | \(0.421194\pi\) | |||||||
\(464\) | 31.6292 | 0.0681664 | ||||||||
\(465\) | 147.823i | 0.317900i | ||||||||
\(466\) | 1127.07 | 2.41860 | ||||||||
\(467\) | − | 74.3726i | − | 0.159256i | −0.996825 | − | 0.0796281i | \(-0.974627\pi\) | ||
0.996825 | − | 0.0796281i | \(-0.0253733\pi\) | |||||||
\(468\) | − | 67.1858i | − | 0.143559i | ||||||
\(469\) | −436.754 | + | 67.7979i | −0.931246 | + | 0.144559i | ||||
\(470\) | 1083.46 | 2.30524 | ||||||||
\(471\) | 481.683 | 1.02268 | ||||||||
\(472\) | 662.434i | 1.40346i | ||||||||
\(473\) | −1045.58 | −2.21054 | ||||||||
\(474\) | 176.104i | 0.371527i | ||||||||
\(475\) | 283.661i | 0.597181i | ||||||||
\(476\) | −107.792 | − | 694.398i | −0.226454 | − | 1.45882i | ||||
\(477\) | −28.6677 | −0.0601000 | ||||||||
\(478\) | −860.251 | −1.79969 | ||||||||
\(479\) | 656.137i | 1.36981i | 0.728634 | + | 0.684903i | \(0.240155\pi\) | ||||
−0.728634 | + | 0.684903i | \(0.759845\pi\) | |||||||
\(480\) | 276.291 | 0.575607 | ||||||||
\(481\) | − | 77.5203i | − | 0.161165i | ||||||
\(482\) | − | 1050.73i | − | 2.17993i | ||||||
\(483\) | 8.91931 | + | 57.4582i | 0.0184665 | + | 0.118961i | ||||
\(484\) | 1564.75 | 3.23296 | ||||||||
\(485\) | −384.849 | −0.793503 | ||||||||
\(486\) | − | 51.3632i | − | 0.105686i | ||||||
\(487\) | −12.9840 | −0.0266613 | −0.0133306 | − | 0.999911i | \(-0.504243\pi\) | ||||
−0.0133306 | + | 0.999911i | \(0.504243\pi\) | |||||||
\(488\) | 693.152i | 1.42039i | ||||||||
\(489\) | − | 469.547i | − | 0.960219i | ||||||
\(490\) | 302.269 | + | 950.149i | 0.616876 | + | 1.93908i | ||||
\(491\) | 344.825 | 0.702291 | 0.351146 | − | 0.936321i | \(-0.385792\pi\) | ||||
0.351146 | + | 0.936321i | \(0.385792\pi\) | |||||||
\(492\) | 9.66165 | 0.0196375 | ||||||||
\(493\) | 129.082i | 0.261829i | ||||||||
\(494\) | −232.354 | −0.470352 | ||||||||
\(495\) | 346.214i | 0.699422i | ||||||||
\(496\) | 49.5782i | 0.0999561i | ||||||||
\(497\) | −281.035 | + | 43.6255i | −0.565464 | + | 0.0877776i | ||||
\(498\) | −804.650 | −1.61576 | ||||||||
\(499\) | −459.798 | −0.921438 | −0.460719 | − | 0.887546i | \(-0.652408\pi\) | ||||
−0.460719 | + | 0.887546i | \(0.652408\pi\) | |||||||
\(500\) | − | 502.275i | − | 1.00455i | ||||||
\(501\) | 507.197 | 1.01237 | ||||||||
\(502\) | − | 770.472i | − | 1.53480i | ||||||
\(503\) | 581.897i | 1.15685i | 0.815735 | + | 0.578426i | \(0.196333\pi\) | ||||
−0.815735 | + | 0.578426i | \(0.803667\pi\) | |||||||
\(504\) | −195.327 | + | 30.3208i | −0.387553 | + | 0.0601603i | ||||
\(505\) | −1027.10 | −2.03386 | ||||||||
\(506\) | 295.294 | 0.583585 | ||||||||
\(507\) | 274.239i | 0.540905i | ||||||||
\(508\) | −210.506 | −0.414381 | ||||||||
\(509\) | − | 151.503i | − | 0.297649i | −0.988864 | − | 0.148824i | \(-0.952451\pi\) | ||
0.988864 | − | 0.148824i | \(-0.0475489\pi\) | |||||||
\(510\) | − | 516.008i | − | 1.01178i | ||||||
\(511\) | 18.7840 | + | 121.006i | 0.0367592 | + | 0.236803i | ||||
\(512\) | 227.736 | 0.444797 | ||||||||
\(513\) | −112.187 | −0.218688 | ||||||||
\(514\) | 1033.36i | 2.01044i | ||||||||
\(515\) | 571.545 | 1.10980 | ||||||||
\(516\) | − | 664.496i | − | 1.28778i | ||||||
\(517\) | − | 995.007i | − | 1.92458i | ||||||
\(518\) | −540.942 | + | 83.9711i | −1.04429 | + | 0.162106i | ||||
\(519\) | −525.503 | −1.01253 | ||||||||
\(520\) | −189.861 | −0.365117 | ||||||||
\(521\) | − | 132.063i | − | 0.253479i | −0.991936 | − | 0.126740i | \(-0.959549\pi\) | ||
0.991936 | − | 0.126740i | \(-0.0404513\pi\) | |||||||
\(522\) | 87.1503 | 0.166955 | ||||||||
\(523\) | 624.639i | 1.19434i | 0.802115 | + | 0.597169i | \(0.203708\pi\) | ||||
−0.802115 | + | 0.597169i | \(0.796292\pi\) | |||||||
\(524\) | 729.986i | 1.39310i | ||||||||
\(525\) | 24.4347 | + | 157.409i | 0.0465423 | + | 0.299826i | ||||
\(526\) | −1055.70 | −2.00703 | ||||||||
\(527\) | −202.333 | −0.383934 | ||||||||
\(528\) | 116.116i | 0.219917i | ||||||||
\(529\) | 23.0000 | 0.0434783 | ||||||||
\(530\) | 194.447i | 0.366881i | ||||||||
\(531\) | 211.131i | 0.397609i | ||||||||
\(532\) | 158.958 | + | 1024.00i | 0.298792 | + | 1.92482i | ||||
\(533\) | 2.65716 | 0.00498529 | ||||||||
\(534\) | −669.483 | −1.25371 | ||||||||
\(535\) | 86.9429i | 0.162510i | ||||||||
\(536\) | −594.323 | −1.10881 | ||||||||
\(537\) | − | 506.983i | − | 0.944102i | ||||||
\(538\) | 1206.90i | 2.24331i | ||||||||
\(539\) | 872.578 | − | 277.592i | 1.61888 | − | 0.515013i | ||||
\(540\) | −220.028 | −0.407459 | ||||||||
\(541\) | −98.2510 | −0.181610 | −0.0908050 | − | 0.995869i | \(-0.528944\pi\) | ||||
−0.0908050 | + | 0.995869i | \(0.528944\pi\) | |||||||
\(542\) | 123.596i | 0.228036i | ||||||||
\(543\) | −37.4617 | −0.0689902 | ||||||||
\(544\) | 378.174i | 0.695173i | ||||||||
\(545\) | − | 110.881i | − | 0.203452i | ||||||
\(546\) | −128.937 | + | 20.0151i | −0.236149 | + | 0.0366577i | ||||
\(547\) | 92.3144 | 0.168765 | 0.0843824 | − | 0.996433i | \(-0.473108\pi\) | ||||
0.0843824 | + | 0.996433i | \(0.473108\pi\) | |||||||
\(548\) | 747.767 | 1.36454 | ||||||||
\(549\) | 220.921i | 0.402406i | ||||||||
\(550\) | 808.968 | 1.47085 | ||||||||
\(551\) | − | 190.352i | − | 0.345467i | ||||||
\(552\) | 78.1875i | 0.141644i | ||||||||
\(553\) | 213.446 | − | 33.1334i | 0.385978 | − | 0.0599158i | ||||
\(554\) | −414.563 | −0.748309 | ||||||||
\(555\) | −253.872 | −0.457428 | ||||||||
\(556\) | 821.954i | 1.47833i | ||||||||
\(557\) | −252.163 | −0.452717 | −0.226359 | − | 0.974044i | \(-0.572682\pi\) | ||||
−0.226359 | + | 0.974044i | \(0.572682\pi\) | |||||||
\(558\) | 136.607i | 0.244815i | ||||||||
\(559\) | − | 182.750i | − | 0.326924i | ||||||
\(560\) | 23.7891 | + | 153.249i | 0.0424805 | + | 0.273659i | ||||
\(561\) | −473.881 | −0.844707 | ||||||||
\(562\) | −1723.27 | −3.06631 | ||||||||
\(563\) | − | 603.228i | − | 1.07145i | −0.844391 | − | 0.535727i | \(-0.820038\pi\) | ||
0.844391 | − | 0.535727i | \(-0.179962\pi\) | |||||||
\(564\) | 632.353 | 1.12119 | ||||||||
\(565\) | − | 726.091i | − | 1.28512i | ||||||
\(566\) | − | 987.696i | − | 1.74505i | ||||||
\(567\) | −62.2544 | + | 9.66383i | −0.109796 | + | 0.0170438i | ||||
\(568\) | −382.425 | −0.673283 | ||||||||
\(569\) | 917.263 | 1.61206 | 0.806031 | − | 0.591874i | \(-0.201612\pi\) | ||||
0.806031 | + | 0.591874i | \(0.201612\pi\) | |||||||
\(570\) | 760.939i | 1.33498i | ||||||||
\(571\) | 65.0859 | 0.113986 | 0.0569929 | − | 0.998375i | \(-0.481849\pi\) | ||||
0.0569929 | + | 0.998375i | \(0.481849\pi\) | |||||||
\(572\) | 418.503i | 0.731649i | ||||||||
\(573\) | 64.7290i | 0.112965i | ||||||||
\(574\) | −2.87827 | − | 18.5418i | −0.00501441 | − | 0.0323028i | ||||
\(575\) | 63.0092 | 0.109581 | ||||||||
\(576\) | 298.376 | 0.518014 | ||||||||
\(577\) | 937.455i | 1.62471i | 0.583166 | + | 0.812353i | \(0.301814\pi\) | ||||
−0.583166 | + | 0.812353i | \(0.698186\pi\) | |||||||
\(578\) | −245.954 | −0.425526 | ||||||||
\(579\) | 87.4807i | 0.151089i | ||||||||
\(580\) | − | 373.331i | − | 0.643675i | ||||||
\(581\) | 151.393 | + | 975.271i | 0.260572 | + | 1.67861i | ||||
\(582\) | −355.647 | −0.611077 | ||||||||
\(583\) | 178.572 | 0.306299 | ||||||||
\(584\) | 164.662i | 0.281955i | ||||||||
\(585\) | −60.5123 | −0.103440 | ||||||||
\(586\) | − | 1706.73i | − | 2.91252i | ||||||
\(587\) | − | 601.022i | − | 1.02389i | −0.859019 | − | 0.511943i | \(-0.828926\pi\) | ||
0.859019 | − | 0.511943i | \(-0.171074\pi\) | |||||||
\(588\) | 176.417 | + | 554.546i | 0.300028 | + | 0.943105i | ||||
\(589\) | 298.374 | 0.506578 | ||||||||
\(590\) | 1432.05 | 2.42721 | ||||||||
\(591\) | − | 292.216i | − | 0.494444i | ||||||
\(592\) | −85.1459 | −0.143827 | ||||||||
\(593\) | 293.746i | 0.495356i | 0.968842 | + | 0.247678i | \(0.0796676\pi\) | ||||
−0.968842 | + | 0.247678i | \(0.920332\pi\) | |||||||
\(594\) | 319.943i | 0.538625i | ||||||||
\(595\) | −625.424 | + | 97.0853i | −1.05113 | + | 0.163169i | ||||
\(596\) | −391.710 | −0.657232 | ||||||||
\(597\) | 465.034 | 0.778951 | ||||||||
\(598\) | 51.6124i | 0.0863084i | ||||||||
\(599\) | 230.999 | 0.385641 | 0.192820 | − | 0.981234i | \(-0.438237\pi\) | ||||
0.192820 | + | 0.981234i | \(0.438237\pi\) | |||||||
\(600\) | 214.197i | 0.356995i | ||||||||
\(601\) | − | 361.950i | − | 0.602246i | −0.953585 | − | 0.301123i | \(-0.902639\pi\) | ||
0.953585 | − | 0.301123i | \(-0.0973614\pi\) | |||||||
\(602\) | −1275.24 | + | 197.958i | −2.11834 | + | 0.328833i | ||||
\(603\) | −189.422 | −0.314133 | ||||||||
\(604\) | −1215.95 | −2.01316 | ||||||||
\(605\) | − | 1409.33i | − | 2.32947i | ||||||
\(606\) | −949.165 | −1.56628 | ||||||||
\(607\) | − | 1104.05i | − | 1.81886i | −0.415859 | − | 0.909429i | \(-0.636519\pi\) | ||
0.415859 | − | 0.909429i | \(-0.363481\pi\) | |||||||
\(608\) | − | 557.681i | − | 0.917238i | ||||||
\(609\) | −16.3971 | − | 105.630i | −0.0269246 | − | 0.173448i | ||||
\(610\) | 1498.46 | 2.45649 | ||||||||
\(611\) | 173.910 | 0.284632 | ||||||||
\(612\) | − | 301.163i | − | 0.492097i | ||||||
\(613\) | −643.060 | −1.04904 | −0.524519 | − | 0.851399i | \(-0.675755\pi\) | ||||
−0.524519 | + | 0.851399i | \(0.675755\pi\) | |||||||
\(614\) | − | 504.046i | − | 0.820922i | ||||||
\(615\) | − | 8.70197i | − | 0.0141495i | ||||||
\(616\) | 1216.70 | − | 188.869i | 1.97516 | − | 0.306606i | ||||
\(617\) | 923.669 | 1.49703 | 0.748516 | − | 0.663117i | \(-0.230767\pi\) | ||||
0.748516 | + | 0.663117i | \(0.230767\pi\) | |||||||
\(618\) | 528.177 | 0.854655 | ||||||||
\(619\) | 1118.81i | 1.80745i | 0.428111 | + | 0.903726i | \(0.359179\pi\) | ||||
−0.428111 | + | 0.903726i | \(0.640821\pi\) | |||||||
\(620\) | 585.191 | 0.943856 | ||||||||
\(621\) | 24.9199i | 0.0401286i | ||||||||
\(622\) | − | 379.042i | − | 0.609393i | ||||||
\(623\) | 125.961 | + | 811.443i | 0.202185 | + | 1.30248i | ||||
\(624\) | −20.2951 | −0.0325242 | ||||||||
\(625\) | −780.843 | −1.24935 | ||||||||
\(626\) | 1855.63i | 2.96426i | ||||||||
\(627\) | 698.815 | 1.11454 | ||||||||
\(628\) | − | 1906.85i | − | 3.03638i | ||||||
\(629\) | − | 347.488i | − | 0.552446i | ||||||
\(630\) | 65.5477 | + | 422.259i | 0.104044 | + | 0.670252i | ||||
\(631\) | −704.827 | −1.11700 | −0.558500 | − | 0.829504i | \(-0.688623\pi\) | ||||
−0.558500 | + | 0.829504i | \(0.688623\pi\) | |||||||
\(632\) | 290.451 | 0.459574 | ||||||||
\(633\) | − | 623.144i | − | 0.984429i | ||||||
\(634\) | 1547.20 | 2.44039 | ||||||||
\(635\) | 189.596i | 0.298577i | ||||||||
\(636\) | 113.487i | 0.178439i | ||||||||
\(637\) | 48.5183 | + | 152.512i | 0.0761670 | + | 0.239422i | ||||
\(638\) | −542.862 | −0.850882 | ||||||||
\(639\) | −121.886 | −0.190745 | ||||||||
\(640\) | − | 1385.76i | − | 2.16524i | ||||||
\(641\) | 373.468 | 0.582633 | 0.291316 | − | 0.956627i | \(-0.405907\pi\) | ||||
0.291316 | + | 0.956627i | \(0.405907\pi\) | |||||||
\(642\) | 80.3457i | 0.125149i | ||||||||
\(643\) | − | 461.828i | − | 0.718239i | −0.933292 | − | 0.359119i | \(-0.883077\pi\) | ||
0.933292 | − | 0.359119i | \(-0.116923\pi\) | |||||||
\(644\) | 227.461 | − | 35.3090i | 0.353200 | − | 0.0548276i | ||||
\(645\) | −598.492 | −0.927894 | ||||||||
\(646\) | −1041.54 | −1.61229 | ||||||||
\(647\) | 362.430i | 0.560170i | 0.959975 | + | 0.280085i | \(0.0903627\pi\) | ||||
−0.959975 | + | 0.280085i | \(0.909637\pi\) | |||||||
\(648\) | −84.7140 | −0.130731 | ||||||||
\(649\) | − | 1315.14i | − | 2.02641i | ||||||
\(650\) | 141.394i | 0.217529i | ||||||||
\(651\) | 165.573 | − | 25.7021i | 0.254337 | − | 0.0394810i | ||||
\(652\) | −1858.80 | −2.85092 | ||||||||
\(653\) | 884.027 | 1.35379 | 0.676896 | − | 0.736078i | \(-0.263324\pi\) | ||||
0.676896 | + | 0.736078i | \(0.263324\pi\) | |||||||
\(654\) | − | 102.468i | − | 0.156678i | ||||||
\(655\) | 657.477 | 1.00378 | ||||||||
\(656\) | − | 2.91854i | − | 0.00444899i | ||||||
\(657\) | 52.4809i | 0.0798797i | ||||||||
\(658\) | −188.382 | − | 1213.56i | −0.286295 | − | 1.84431i | ||||
\(659\) | −911.585 | −1.38328 | −0.691642 | − | 0.722240i | \(-0.743113\pi\) | ||||
−0.691642 | + | 0.722240i | \(0.743113\pi\) | |||||||
\(660\) | 1370.56 | 2.07661 | ||||||||
\(661\) | − | 85.4704i | − | 0.129305i | −0.997908 | − | 0.0646523i | \(-0.979406\pi\) | ||
0.997908 | − | 0.0646523i | \(-0.0205938\pi\) | |||||||
\(662\) | −1010.05 | −1.52575 | ||||||||
\(663\) | − | 82.8263i | − | 0.124927i | ||||||
\(664\) | 1327.12i | 1.99868i | ||||||||
\(665\) | 922.291 | − | 143.168i | 1.38690 | − | 0.215291i | ||||
\(666\) | −234.609 | −0.352265 | ||||||||
\(667\) | −42.2827 | −0.0633923 | ||||||||
\(668\) | − | 2007.85i | − | 3.00576i | ||||||
\(669\) | −138.934 | −0.207674 | ||||||||
\(670\) | 1284.81i | 1.91763i | ||||||||
\(671\) | − | 1376.12i | − | 2.05086i | ||||||
\(672\) | −48.0389 | − | 309.467i | −0.0714865 | − | 0.460516i | ||||
\(673\) | 852.855 | 1.26724 | 0.633622 | − | 0.773643i | \(-0.281567\pi\) | ||||
0.633622 | + | 0.773643i | \(0.281567\pi\) | |||||||
\(674\) | 611.769 | 0.907669 | ||||||||
\(675\) | 68.2688i | 0.101139i | ||||||||
\(676\) | 1085.63 | 1.60597 | ||||||||
\(677\) | − | 585.534i | − | 0.864896i | −0.901659 | − | 0.432448i | \(-0.857650\pi\) | ||
0.901659 | − | 0.432448i | \(-0.142350\pi\) | |||||||
\(678\) | − | 670.996i | − | 0.989669i | ||||||
\(679\) | 66.9139 | + | 431.059i | 0.0985476 | + | 0.634844i | ||||
\(680\) | −851.059 | −1.25156 | ||||||||
\(681\) | −233.997 | −0.343608 | ||||||||
\(682\) | − | 850.928i | − | 1.24769i | ||||||
\(683\) | 165.791 | 0.242739 | 0.121370 | − | 0.992607i | \(-0.461271\pi\) | ||||
0.121370 | + | 0.992607i | \(0.461271\pi\) | |||||||
\(684\) | 444.115i | 0.649291i | ||||||||
\(685\) | − | 673.492i | − | 0.983200i | ||||||
\(686\) | 1011.68 | − | 503.767i | 1.47475 | − | 0.734354i | ||||
\(687\) | 143.267 | 0.208540 | ||||||||
\(688\) | −200.727 | −0.291755 | ||||||||
\(689\) | 31.2114i | 0.0452996i | ||||||||
\(690\) | 169.026 | 0.244966 | ||||||||
\(691\) | 188.310i | 0.272518i | 0.990673 | + | 0.136259i | \(0.0435080\pi\) | ||||
−0.990673 | + | 0.136259i | \(0.956492\pi\) | |||||||
\(692\) | 2080.32i | 3.00624i | ||||||||
\(693\) | 387.785 | − | 60.1964i | 0.559574 | − | 0.0868634i | ||||
\(694\) | −91.1602 | −0.131355 | ||||||||
\(695\) | 740.310 | 1.06519 | ||||||||
\(696\) | − | 143.738i | − | 0.206520i | ||||||
\(697\) | 11.9108 | 0.0170887 | ||||||||
\(698\) | 567.131i | 0.812509i | ||||||||
\(699\) | − | 592.463i | − | 0.847587i | ||||||
\(700\) | 623.135 | − | 96.7301i | 0.890193 | − | 0.138186i | ||||
\(701\) | 280.460 | 0.400085 | 0.200042 | − | 0.979787i | \(-0.435892\pi\) | ||||
0.200042 | + | 0.979787i | \(0.435892\pi\) | |||||||
\(702\) | −55.9207 | −0.0796591 | ||||||||
\(703\) | 512.429i | 0.728917i | ||||||||
\(704\) | −1858.60 | −2.64005 | ||||||||
\(705\) | − | 569.541i | − | 0.807860i | ||||||
\(706\) | − | 1553.95i | − | 2.20106i | ||||||
\(707\) | 178.583 | + | 1150.43i | 0.252592 | + | 1.62720i | ||||
\(708\) | 835.806 | 1.18052 | ||||||||
\(709\) | −1089.95 | −1.53731 | −0.768654 | − | 0.639665i | \(-0.779073\pi\) | ||||
−0.768654 | + | 0.639665i | \(0.779073\pi\) | |||||||
\(710\) | 826.729i | 1.16441i | ||||||||
\(711\) | 92.5723 | 0.130200 | ||||||||
\(712\) | 1104.19i | 1.55083i | ||||||||
\(713\) | − | 66.2774i | − | 0.0929557i | ||||||
\(714\) | −577.967 | + | 89.7186i | −0.809478 | + | 0.125656i | ||||
\(715\) | 376.933 | 0.527180 | ||||||||
\(716\) | −2007.00 | −2.80307 | ||||||||
\(717\) | 452.207i | 0.630693i | ||||||||
\(718\) | −1400.49 | −1.95055 | ||||||||
\(719\) | 686.206i | 0.954389i | 0.878798 | + | 0.477195i | \(0.158346\pi\) | ||||
−0.878798 | + | 0.477195i | \(0.841654\pi\) | |||||||
\(720\) | 66.4648i | 0.0923122i | ||||||||
\(721\) | −99.3749 | − | 640.173i | −0.137829 | − | 0.887896i | ||||
\(722\) | 346.441 | 0.479835 | ||||||||
\(723\) | −552.333 | −0.763946 | ||||||||
\(724\) | 148.300i | 0.204834i | ||||||||
\(725\) | −115.835 | −0.159772 | ||||||||
\(726\) | − | 1302.39i | − | 1.79392i | ||||||
\(727\) | 1325.91i | 1.82381i | 0.410402 | + | 0.911905i | \(0.365388\pi\) | ||||
−0.410402 | + | 0.911905i | \(0.634612\pi\) | |||||||
\(728\) | 33.0112 | + | 212.658i | 0.0453450 | + | 0.292113i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 355.967 | 0.487626 | ||||||||
\(731\) | − | 819.187i | − | 1.12064i | ||||||
\(732\) | 874.563 | 1.19476 | ||||||||
\(733\) | 96.6264i | 0.131823i | 0.997825 | + | 0.0659116i | \(0.0209955\pi\) | ||||
−0.997825 | + | 0.0659116i | \(0.979004\pi\) | |||||||
\(734\) | 1262.25i | 1.71968i | ||||||||
\(735\) | 499.463 | − | 158.893i | 0.679541 | − | 0.216181i | ||||
\(736\) | −123.877 | −0.168311 | ||||||||
\(737\) | 1179.92 | 1.60097 | ||||||||
\(738\) | − | 8.04167i | − | 0.0108966i | ||||||
\(739\) | 529.063 | 0.715917 | 0.357959 | − | 0.933737i | \(-0.383473\pi\) | ||||
0.357959 | + | 0.933737i | \(0.383473\pi\) | |||||||
\(740\) | 1005.01i | 1.35812i | ||||||||
\(741\) | 122.141i | 0.164833i | ||||||||
\(742\) | 217.795 | − | 33.8086i | 0.293524 | − | 0.0455642i | ||||
\(743\) | −205.001 | −0.275910 | −0.137955 | − | 0.990439i | \(-0.544053\pi\) | ||||
−0.137955 | + | 0.990439i | \(0.544053\pi\) | |||||||
\(744\) | 225.307 | 0.302832 | ||||||||
\(745\) | 352.802i | 0.473560i | ||||||||
\(746\) | −2344.19 | −3.14235 | ||||||||
\(747\) | 422.979i | 0.566237i | ||||||||
\(748\) | 1875.96i | 2.50797i | ||||||||
\(749\) | 97.3825 | − | 15.1168i | 0.130017 | − | 0.0201827i | ||||
\(750\) | −418.058 | −0.557410 | ||||||||
\(751\) | 607.228 | 0.808559 | 0.404279 | − | 0.914636i | \(-0.367522\pi\) | ||||
0.404279 | + | 0.914636i | \(0.367522\pi\) | |||||||
\(752\) | − | 191.018i | − | 0.254013i | ||||||
\(753\) | −405.012 | −0.537865 | ||||||||
\(754\) | − | 94.8832i | − | 0.125840i | ||||||
\(755\) | 1095.17i | 1.45056i | ||||||||
\(756\) | 38.2563 | + | 246.447i | 0.0506036 | + | 0.325989i | ||||
\(757\) | −650.858 | −0.859786 | −0.429893 | − | 0.902880i | \(-0.641449\pi\) | ||||
−0.429893 | + | 0.902880i | \(0.641449\pi\) | |||||||
\(758\) | −1615.63 | −2.13143 | ||||||||
\(759\) | − | 155.227i | − | 0.204515i | ||||||
\(760\) | 1255.03 | 1.65135 | ||||||||
\(761\) | − | 813.820i | − | 1.06941i | −0.845039 | − | 0.534704i | \(-0.820423\pi\) | ||
0.845039 | − | 0.534704i | \(-0.179577\pi\) | |||||||
\(762\) | 175.210i | 0.229934i | ||||||||
\(763\) | −124.195 | + | 19.2790i | −0.162772 | + | 0.0252673i | ||||
\(764\) | 256.244 | 0.335397 | ||||||||
\(765\) | −271.249 | −0.354574 | ||||||||
\(766\) | 617.060i | 0.805561i | ||||||||
\(767\) | 229.864 | 0.299693 | ||||||||
\(768\) | − | 591.535i | − | 0.770228i | ||||||
\(769\) | 506.793i | 0.659028i | 0.944151 | + | 0.329514i | \(0.106885\pi\) | ||||
−0.944151 | + | 0.329514i | \(0.893115\pi\) | |||||||
\(770\) | −408.299 | − | 2630.26i | −0.530259 | − | 3.41593i | ||||
\(771\) | 543.207 | 0.704549 | ||||||||
\(772\) | 346.311 | 0.448589 | ||||||||
\(773\) | − | 1390.41i | − | 1.79872i | −0.437207 | − | 0.899361i | \(-0.644032\pi\) | ||
0.437207 | − | 0.899361i | \(-0.355968\pi\) | |||||||
\(774\) | −553.079 | −0.714572 | ||||||||
\(775\) | − | 181.569i | − | 0.234283i | ||||||
\(776\) | 586.573i | 0.755893i | ||||||||
\(777\) | 44.1409 | + | 284.356i | 0.0568094 | + | 0.365966i | ||||
\(778\) | 2217.66 | 2.85047 | ||||||||
\(779\) | −17.5645 | −0.0225475 | ||||||||
\(780\) | 239.551i | 0.307117i | ||||||||
\(781\) | 759.234 | 0.972131 | ||||||||
\(782\) | 231.355i | 0.295850i | ||||||||
\(783\) | − | 45.8121i | − | 0.0585085i | ||||||
\(784\) | 167.514 | − | 53.2910i | 0.213666 | − | 0.0679732i | ||||
\(785\) | −1717.44 | −2.18782 | ||||||||
\(786\) | 607.588 | 0.773012 | ||||||||
\(787\) | 1146.86i | 1.45725i | 0.684912 | + | 0.728625i | \(0.259840\pi\) | ||||
−0.684912 | + | 0.728625i | \(0.740160\pi\) | |||||||
\(788\) | −1156.80 | −1.46802 | ||||||||
\(789\) | 554.946i | 0.703353i | ||||||||
\(790\) | − | 627.898i | − | 0.794808i | ||||||
\(791\) | −813.276 | + | 126.246i | −1.02816 | + | 0.159603i | ||||
\(792\) | 527.687 | 0.666271 | ||||||||
\(793\) | 240.523 | 0.303308 | ||||||||
\(794\) | 1645.36i | 2.07225i | ||||||||
\(795\) | 102.215 | 0.128572 | ||||||||
\(796\) | − | 1840.94i | − | 2.31273i | ||||||
\(797\) | − | 176.205i | − | 0.221085i | −0.993871 | − | 0.110543i | \(-0.964741\pi\) | ||
0.993871 | − | 0.110543i | \(-0.0352588\pi\) | |||||||
\(798\) | 852.308 | − | 132.305i | 1.06806 | − | 0.165796i | ||||
\(799\) | 779.561 | 0.975671 | ||||||||
\(800\) | −339.364 | −0.424205 | ||||||||
\(801\) | 351.926i | 0.439359i | ||||||||
\(802\) | −1723.96 | −2.14958 | ||||||||
\(803\) | − | 326.906i | − | 0.407106i | ||||||
\(804\) | 749.869i | 0.932672i | ||||||||
\(805\) | −31.8018 | − | 204.867i | −0.0395053 | − | 0.254493i | ||||
\(806\) | 148.728 | 0.184526 | ||||||||
\(807\) | 634.431 | 0.786160 | ||||||||
\(808\) | 1565.47i | 1.93746i | ||||||||
\(809\) | −162.123 | −0.200399 | −0.100200 | − | 0.994967i | \(-0.531948\pi\) | ||||
−0.100200 | + | 0.994967i | \(0.531948\pi\) | |||||||
\(810\) | 183.135i | 0.226093i | ||||||||
\(811\) | 776.407i | 0.957346i | 0.877993 | + | 0.478673i | \(0.158882\pi\) | ||||
−0.877993 | + | 0.478673i | \(0.841118\pi\) | |||||||
\(812\) | −418.159 | + | 64.9113i | −0.514974 | + | 0.0799400i | ||||
\(813\) | 64.9703 | 0.0799143 | ||||||||
\(814\) | 1461.39 | 1.79531 | ||||||||
\(815\) | 1674.17i | 2.05419i | ||||||||
\(816\) | −90.9738 | −0.111487 | ||||||||
\(817\) | 1208.03i | 1.47861i | ||||||||
\(818\) | − | 391.802i | − | 0.478975i | ||||||
\(819\) | 10.5213 | + | 67.7783i | 0.0128465 | + | 0.0827574i | ||||
\(820\) | −34.4486 | −0.0420105 | ||||||||
\(821\) | 537.716 | 0.654952 | 0.327476 | − | 0.944859i | \(-0.393802\pi\) | ||||
0.327476 | + | 0.944859i | \(0.393802\pi\) | |||||||
\(822\) | − | 622.388i | − | 0.757163i | ||||||
\(823\) | 531.113 | 0.645338 | 0.322669 | − | 0.946512i | \(-0.395420\pi\) | ||||
0.322669 | + | 0.946512i | \(0.395420\pi\) | |||||||
\(824\) | − | 871.129i | − | 1.05720i | ||||||
\(825\) | − | 425.249i | − | 0.515453i | ||||||
\(826\) | −248.992 | − | 1604.01i | −0.301443 | − | 1.94190i | ||||
\(827\) | 987.154 | 1.19366 | 0.596828 | − | 0.802369i | \(-0.296427\pi\) | ||||
0.596828 | + | 0.802369i | \(0.296427\pi\) | |||||||
\(828\) | 98.6507 | 0.119143 | ||||||||
\(829\) | − | 62.9942i | − | 0.0759882i | −0.999278 | − | 0.0379941i | \(-0.987903\pi\) | ||
0.999278 | − | 0.0379941i | \(-0.0120968\pi\) | |||||||
\(830\) | 2868.98 | 3.45660 | ||||||||
\(831\) | 217.923i | 0.262242i | ||||||||
\(832\) | − | 324.851i | − | 0.390446i | ||||||
\(833\) | 217.486 | + | 683.641i | 0.261087 | + | 0.820697i | ||||
\(834\) | 684.136 | 0.820306 | ||||||||
\(835\) | −1808.41 | −2.16576 | ||||||||
\(836\) | − | 2766.41i | − | 3.30910i | ||||||
\(837\) | 71.8098 | 0.0857942 | ||||||||
\(838\) | 999.334i | 1.19252i | ||||||||
\(839\) | − | 961.226i | − | 1.14568i | −0.819667 | − | 0.572840i | \(-0.805842\pi\) | ||
0.819667 | − | 0.572840i | \(-0.194158\pi\) | |||||||
\(840\) | 696.437 | − | 108.109i | 0.829091 | − | 0.128701i | ||||
\(841\) | −763.268 | −0.907572 | ||||||||
\(842\) | 343.466 | 0.407917 | ||||||||
\(843\) | 905.866i | 1.07457i | ||||||||
\(844\) | −2466.85 | −2.92280 | ||||||||
\(845\) | − | 977.799i | − | 1.15716i | ||||||
\(846\) | − | 526.325i | − | 0.622134i | ||||||
\(847\) | −1578.55 | + | 245.041i | −1.86370 | + | 0.289304i | ||||
\(848\) | 34.2816 | 0.0404264 | ||||||||
\(849\) | −519.200 | −0.611543 | ||||||||
\(850\) | 633.804i | 0.745652i | ||||||||
\(851\) | 113.825 | 0.133754 | ||||||||
\(852\) | 482.513i | 0.566330i | ||||||||
\(853\) | 244.370i | 0.286483i | 0.989688 | + | 0.143241i | \(0.0457525\pi\) | ||||
−0.989688 | + | 0.143241i | \(0.954247\pi\) | |||||||
\(854\) | −260.538 | − | 1678.39i | −0.305080 | − | 1.96532i | ||||
\(855\) | 400.002 | 0.467838 | ||||||||
\(856\) | 132.515 | 0.154808 | ||||||||
\(857\) | 622.245i | 0.726073i | 0.931775 | + | 0.363036i | \(0.118260\pi\) | ||||
−0.931775 | + | 0.363036i | \(0.881740\pi\) | |||||||
\(858\) | 348.332 | 0.405981 | ||||||||
\(859\) | 241.220i | 0.280815i | 0.990094 | + | 0.140407i | \(0.0448413\pi\) | ||||
−0.990094 | + | 0.140407i | \(0.955159\pi\) | |||||||
\(860\) | 2369.26i | 2.75495i | ||||||||
\(861\) | −9.74685 | + | 1.51302i | −0.0113204 | + | 0.00175728i | ||||
\(862\) | 2749.93 | 3.19018 | ||||||||
\(863\) | −696.263 | −0.806793 | −0.403397 | − | 0.915025i | \(-0.632170\pi\) | ||||
−0.403397 | + | 0.915025i | \(0.632170\pi\) | |||||||
\(864\) | − | 134.217i | − | 0.155344i | ||||||
\(865\) | 1873.68 | 2.16610 | ||||||||
\(866\) | − | 2450.50i | − | 2.82968i | ||||||
\(867\) | 129.290i | 0.149124i | ||||||||
\(868\) | −101.747 | − | 655.457i | −0.117220 | − | 0.755134i | ||||
\(869\) | −576.636 | −0.663563 | ||||||||
\(870\) | −310.734 | −0.357166 | ||||||||
\(871\) | 206.230i | 0.236774i | ||||||||
\(872\) | −169.001 | −0.193809 | ||||||||
\(873\) | 186.952i | 0.214149i | ||||||||
\(874\) | − | 341.171i | − | 0.390356i | ||||||
\(875\) | 78.6563 | + | 506.704i | 0.0898929 | + | 0.579090i | ||||
\(876\) | 207.757 | 0.237166 | ||||||||
\(877\) | −1025.59 | −1.16943 | −0.584717 | − | 0.811238i | \(-0.698794\pi\) | ||||
−0.584717 | + | 0.811238i | \(0.698794\pi\) | |||||||
\(878\) | 1670.75i | 1.90291i | ||||||||
\(879\) | −897.176 | −1.02068 | ||||||||
\(880\) | − | 414.012i | − | 0.470468i | ||||||
\(881\) | 1082.45i | 1.22866i | 0.789050 | + | 0.614329i | \(0.210573\pi\) | ||||
−0.789050 | + | 0.614329i | \(0.789427\pi\) | |||||||
\(882\) | 461.564 | − | 146.837i | 0.523315 | − | 0.166481i | ||||
\(883\) | −1023.34 | −1.15894 | −0.579468 | − | 0.814995i | \(-0.696739\pi\) | ||||
−0.579468 | + | 0.814995i | \(0.696739\pi\) | |||||||
\(884\) | −327.886 | −0.370911 | ||||||||
\(885\) | − | 752.786i | − | 0.850606i | ||||||
\(886\) | 15.5418 | 0.0175415 | ||||||||
\(887\) | 796.873i | 0.898391i | 0.893434 | + | 0.449195i | \(0.148289\pi\) | ||||
−0.893434 | + | 0.449195i | \(0.851711\pi\) | |||||||
\(888\) | 386.943i | 0.435747i | ||||||||
\(889\) | 212.362 | − | 32.9652i | 0.238877 | − | 0.0370812i | ||||
\(890\) | 2387.04 | 2.68207 | ||||||||
\(891\) | 168.184 | 0.188759 | ||||||||
\(892\) | 550.000i | 0.616592i | ||||||||
\(893\) | −1149.59 | −1.28734 | ||||||||
\(894\) | 326.032i | 0.364689i | ||||||||
\(895\) | 1807.65i | 2.01972i | ||||||||
\(896\) | −1552.15 | + | 240.942i | −1.73231 | + | 0.268909i | ||||
\(897\) | 27.1310 | 0.0302464 | ||||||||
\(898\) | −1689.78 | −1.88172 | ||||||||
\(899\) | 121.843i | 0.135532i | ||||||||
\(900\) | 270.257 | 0.300285 | ||||||||
\(901\) | 139.906i | 0.155279i | ||||||||
\(902\) | 50.0918i | 0.0555342i | ||||||||
\(903\) | 104.060 | + | 670.355i | 0.115238 | + | 0.742365i | ||||
\(904\) | −1106.68 | −1.22421 | ||||||||
\(905\) | 133.570 | 0.147591 | ||||||||
\(906\) | 1012.07i | 1.11707i | ||||||||
\(907\) | 527.672 | 0.581777 | 0.290889 | − | 0.956757i | \(-0.406049\pi\) | ||||
0.290889 | + | 0.956757i | \(0.406049\pi\) | |||||||
\(908\) | 926.327i | 1.02018i | ||||||||
\(909\) | 498.946i | 0.548895i | ||||||||
\(910\) | 459.726 | − | 71.3638i | 0.505193 | − | 0.0784218i | ||||
\(911\) | −1510.85 | −1.65845 | −0.829224 | − | 0.558916i | \(-0.811217\pi\) | ||||
−0.829224 | + | 0.558916i | \(0.811217\pi\) | |||||||
\(912\) | 134.156 | 0.147101 | ||||||||
\(913\) | − | 2634.75i | − | 2.88582i | ||||||
\(914\) | −2081.18 | −2.27700 | ||||||||
\(915\) | − | 787.693i | − | 0.860867i | ||||||
\(916\) | − | 567.152i | − | 0.619162i | ||||||
\(917\) | −114.316 | − | 736.423i | −0.124663 | − | 0.803078i | ||||
\(918\) | −250.667 | −0.273057 | ||||||||
\(919\) | −921.851 | −1.00310 | −0.501551 | − | 0.865128i | \(-0.667237\pi\) | ||||
−0.501551 | + | 0.865128i | \(0.667237\pi\) | |||||||
\(920\) | − | 278.777i | − | 0.303019i | ||||||
\(921\) | −264.961 | −0.287689 | ||||||||
\(922\) | − | 1576.92i | − | 1.71033i | ||||||
\(923\) | 132.701i | 0.143772i | ||||||||
\(924\) | −238.300 | − | 1535.13i | −0.257901 | − | 1.66140i | ||||
\(925\) | 311.827 | 0.337111 | ||||||||
\(926\) | −747.690 | −0.807440 | ||||||||
\(927\) | − | 277.646i | − | 0.299510i | ||||||
\(928\) | 227.732 | 0.245401 | ||||||||
\(929\) | 122.245i | 0.131588i | 0.997833 | + | 0.0657939i | \(0.0209580\pi\) | ||||
−0.997833 | + | 0.0657939i | \(0.979042\pi\) | |||||||
\(930\) | − | 487.071i | − | 0.523732i | ||||||
\(931\) | −320.718 | − | 1008.14i | −0.344488 | − | 1.08286i | ||||
\(932\) | −2345.39 | −2.51652 | ||||||||
\(933\) | −199.251 | −0.213559 | ||||||||
\(934\) | 245.054i | 0.262371i | ||||||||
\(935\) | 1689.62 | 1.80708 | ||||||||
\(936\) | 92.2307i | 0.0985371i | ||||||||
\(937\) | − | 1588.93i | − | 1.69576i | −0.530190 | − | 0.847879i | \(-0.677879\pi\) | ||
0.530190 | − | 0.847879i | \(-0.322121\pi\) | |||||||
\(938\) | 1439.08 | − | 223.391i | 1.53420 | − | 0.238157i | ||||
\(939\) | 975.445 | 1.03881 | ||||||||
\(940\) | −2254.65 | −2.39857 | ||||||||
\(941\) | − | 1132.07i | − | 1.20304i | −0.798856 | − | 0.601522i | \(-0.794561\pi\) | ||
0.798856 | − | 0.601522i | \(-0.205439\pi\) | |||||||
\(942\) | −1587.12 | −1.68484 | ||||||||
\(943\) | 3.90157i | 0.00413741i | ||||||||
\(944\) | − | 252.476i | − | 0.267453i | ||||||
\(945\) | 221.968 | − | 34.4564i | 0.234887 | − | 0.0364618i | ||||
\(946\) | 3445.15 | 3.64181 | ||||||||
\(947\) | 1190.19 | 1.25680 | 0.628399 | − | 0.777891i | \(-0.283710\pi\) | ||||
0.628399 | + | 0.777891i | \(0.283710\pi\) | |||||||
\(948\) | − | 366.467i | − | 0.386569i | ||||||
\(949\) | 57.1376 | 0.0602082 | ||||||||
\(950\) | − | 934.649i | − | 0.983841i | ||||||
\(951\) | − | 813.316i | − | 0.855222i | ||||||
\(952\) | 147.974 | + | 953.249i | 0.155435 | + | 1.00131i | ||||
\(953\) | 1525.03 | 1.60024 | 0.800121 | − | 0.599838i | \(-0.204768\pi\) | ||||
0.800121 | + | 0.599838i | \(0.204768\pi\) | |||||||
\(954\) | 94.4586 | 0.0990132 | ||||||||
\(955\) | − | 230.791i | − | 0.241666i | ||||||
\(956\) | 1790.16 | 1.87255 | ||||||||
\(957\) | 285.366i | 0.298188i | ||||||||
\(958\) | − | 2161.94i | − | 2.25672i | ||||||
\(959\) | −754.361 | + | 117.100i | −0.786612 | + | 0.122107i | ||||
\(960\) | −1063.86 | −1.10819 | ||||||||
\(961\) | 770.013 | 0.801262 | ||||||||
\(962\) | 255.426i | 0.265515i | ||||||||
\(963\) | 42.2352 | 0.0438579 | ||||||||
\(964\) | 2186.53i | 2.26818i | ||||||||
\(965\) | − | 311.912i | − | 0.323225i | ||||||
\(966\) | −29.3887 | − | 189.322i | −0.0304231 | − | 0.195985i | ||||
\(967\) | −678.121 | −0.701262 | −0.350631 | − | 0.936514i | \(-0.614033\pi\) | ||||
−0.350631 | + | 0.936514i | \(0.614033\pi\) | |||||||
\(968\) | −2148.05 | −2.21906 | ||||||||
\(969\) | 547.503i | 0.565018i | ||||||||
\(970\) | 1268.06 | 1.30728 | ||||||||
\(971\) | − | 1359.05i | − | 1.39964i | −0.714317 | − | 0.699822i | \(-0.753263\pi\) | ||
0.714317 | − | 0.699822i | \(-0.246737\pi\) | |||||||
\(972\) | 106.885i | 0.109964i | ||||||||
\(973\) | −128.718 | − | 829.202i | −0.132290 | − | 0.852212i | ||||
\(974\) | 42.7818 | 0.0439238 | ||||||||
\(975\) | 74.3263 | 0.0762321 | ||||||||
\(976\) | − | 264.183i | − | 0.270679i | ||||||
\(977\) | −116.477 | −0.119219 | −0.0596094 | − | 0.998222i | \(-0.518986\pi\) | ||||
−0.0596094 | + | 0.998222i | \(0.518986\pi\) | |||||||
\(978\) | 1547.13i | 1.58194i | ||||||||
\(979\) | − | 2192.16i | − | 2.23918i | ||||||
\(980\) | −629.013 | − | 1977.23i | −0.641850 | − | 2.01758i | ||||
\(981\) | −53.8640 | −0.0549072 | ||||||||
\(982\) | −1136.18 | −1.15701 | ||||||||
\(983\) | 225.983i | 0.229891i | 0.993372 | + | 0.114945i | \(0.0366693\pi\) | ||||
−0.993372 | + | 0.114945i | \(0.963331\pi\) | |||||||
\(984\) | −13.2632 | −0.0134789 | ||||||||
\(985\) | 1041.90i | 1.05776i | ||||||||
\(986\) | − | 425.318i | − | 0.431357i | ||||||
\(987\) | −637.929 | + | 99.0265i | −0.646331 | + | 0.100331i | ||||
\(988\) | 483.522 | 0.489395 | ||||||||
\(989\) | 268.337 | 0.271322 | ||||||||
\(990\) | − | 1140.76i | − | 1.15228i | ||||||
\(991\) | −313.193 | −0.316037 | −0.158019 | − | 0.987436i | \(-0.550511\pi\) | ||||
−0.158019 | + | 0.987436i | \(0.550511\pi\) | |||||||
\(992\) | 356.967i | 0.359845i | ||||||||
\(993\) | 530.949i | 0.534692i | ||||||||
\(994\) | 925.998 | − | 143.744i | 0.931587 | − | 0.144611i | ||||
\(995\) | −1658.08 | −1.66641 | ||||||||
\(996\) | 1674.45 | 1.68118 | ||||||||
\(997\) | − | 1777.33i | − | 1.78268i | −0.453336 | − | 0.891340i | \(-0.649766\pi\) | ||
0.453336 | − | 0.891340i | \(-0.350234\pi\) | |||||||
\(998\) | 1515.01 | 1.51805 | ||||||||
\(999\) | 123.326i | 0.123450i |
(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 | 483.3.g.a.139.5 | ✓ | 60 | |
7.6 | odd | 2 | inner | 483.3.g.a.139.6 | yes | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.3.g.a.139.5 | ✓ | 60 | 1.1 | even | 1 | trivial | |
483.3.g.a.139.6 | yes | 60 | 7.6 | odd | 2 | inner |