Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(461,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.461");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.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: | \(18.8011382409\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 461.20 | ||
Character | \(\chi\) | \(=\) | 690.461 |
Dual form | 690.3.g.a.461.19 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421i | 0.707107i | ||||||||
\(3\) | −2.91669 | + | 0.702099i | −0.972229 | + | 0.234033i | ||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 2.23607i | 0.447214i | ||||||||
\(6\) | −0.992918 | − | 4.12482i | −0.165486 | − | 0.687469i | ||||
\(7\) | −8.52828 | −1.21833 | −0.609163 | − | 0.793045i | \(-0.708494\pi\) | ||||
−0.609163 | + | 0.793045i | \(0.708494\pi\) | |||||||
\(8\) | − | 2.82843i | − | 0.353553i | ||||||
\(9\) | 8.01411 | − | 4.09561i | 0.890457 | − | 0.455067i | ||||
\(10\) | −3.16228 | −0.316228 | ||||||||
\(11\) | − | 11.2465i | − | 1.02241i | −0.859458 | − | 0.511206i | \(-0.829199\pi\) | ||
0.859458 | − | 0.511206i | \(-0.170801\pi\) | |||||||
\(12\) | 5.83337 | − | 1.40420i | 0.486114 | − | 0.117017i | ||||
\(13\) | 18.3730 | 1.41331 | 0.706653 | − | 0.707561i | \(-0.250204\pi\) | ||||
0.706653 | + | 0.707561i | \(0.250204\pi\) | |||||||
\(14\) | − | 12.0608i | − | 0.861486i | ||||||
\(15\) | −1.56994 | − | 6.52191i | −0.104663 | − | 0.434794i | ||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 0.800569i | 0.0470923i | 0.999723 | + | 0.0235462i | \(0.00749567\pi\) | ||||
−0.999723 | + | 0.0235462i | \(0.992504\pi\) | |||||||
\(18\) | 5.79206 | + | 11.3337i | 0.321781 | + | 0.629648i | ||||
\(19\) | 13.2492 | 0.697324 | 0.348662 | − | 0.937248i | \(-0.386636\pi\) | ||||
0.348662 | + | 0.937248i | \(0.386636\pi\) | |||||||
\(20\) | − | 4.47214i | − | 0.223607i | ||||||
\(21\) | 24.8743 | − | 5.98770i | 1.18449 | − | 0.285129i | ||||
\(22\) | 15.9050 | 0.722954 | ||||||||
\(23\) | 4.79583i | 0.208514i | ||||||||
\(24\) | 1.98584 | + | 8.24963i | 0.0827432 | + | 0.343735i | ||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 25.9833i | 0.999358i | ||||||||
\(27\) | −20.4991 | + | 17.5723i | −0.759227 | + | 0.650826i | ||||
\(28\) | 17.0566 | 0.609163 | ||||||||
\(29\) | 10.9760i | 0.378483i | 0.981931 | + | 0.189241i | \(0.0606029\pi\) | ||||
−0.981931 | + | 0.189241i | \(0.939397\pi\) | |||||||
\(30\) | 9.22337 | − | 2.22023i | 0.307446 | − | 0.0740078i | ||||
\(31\) | −42.6501 | −1.37581 | −0.687905 | − | 0.725801i | \(-0.741469\pi\) | ||||
−0.687905 | + | 0.725801i | \(0.741469\pi\) | |||||||
\(32\) | 5.65685i | 0.176777i | ||||||||
\(33\) | 7.89618 | + | 32.8026i | 0.239278 | + | 0.994018i | ||||
\(34\) | −1.13218 | −0.0332993 | ||||||||
\(35\) | − | 19.0698i | − | 0.544852i | ||||||
\(36\) | −16.0282 | + | 8.19121i | −0.445229 | + | 0.227534i | ||||
\(37\) | 42.8724 | 1.15871 | 0.579357 | − | 0.815074i | \(-0.303304\pi\) | ||||
0.579357 | + | 0.815074i | \(0.303304\pi\) | |||||||
\(38\) | 18.7371i | 0.493083i | ||||||||
\(39\) | −53.5882 | + | 12.8996i | −1.37406 | + | 0.330760i | ||||
\(40\) | 6.32456 | 0.158114 | ||||||||
\(41\) | − | 59.2804i | − | 1.44586i | −0.690919 | − | 0.722932i | \(-0.742794\pi\) | ||
0.690919 | − | 0.722932i | \(-0.257206\pi\) | |||||||
\(42\) | 8.46788 | + | 35.1776i | 0.201616 | + | 0.837562i | ||||
\(43\) | 10.6963 | 0.248750 | 0.124375 | − | 0.992235i | \(-0.460307\pi\) | ||||
0.124375 | + | 0.992235i | \(0.460307\pi\) | |||||||
\(44\) | 22.4931i | 0.511206i | ||||||||
\(45\) | 9.15805 | + | 17.9201i | 0.203512 | + | 0.398224i | ||||
\(46\) | −6.78233 | −0.147442 | ||||||||
\(47\) | 65.8685i | 1.40146i | 0.713428 | + | 0.700729i | \(0.247142\pi\) | ||||
−0.713428 | + | 0.700729i | \(0.752858\pi\) | |||||||
\(48\) | −11.6667 | + | 2.80840i | −0.243057 | + | 0.0585083i | ||||
\(49\) | 23.7316 | 0.484317 | ||||||||
\(50\) | − | 7.07107i | − | 0.141421i | ||||||
\(51\) | −0.562079 | − | 2.33501i | −0.0110212 | − | 0.0457845i | ||||
\(52\) | −36.7459 | −0.706653 | ||||||||
\(53\) | 68.3687i | 1.28998i | 0.764193 | + | 0.644988i | \(0.223138\pi\) | ||||
−0.764193 | + | 0.644988i | \(0.776862\pi\) | |||||||
\(54\) | −24.8510 | − | 28.9901i | −0.460203 | − | 0.536855i | ||||
\(55\) | 25.1480 | 0.457237 | ||||||||
\(56\) | 24.1216i | 0.430743i | ||||||||
\(57\) | −38.6436 | + | 9.30223i | −0.677959 | + | 0.163197i | ||||
\(58\) | −15.5224 | −0.267628 | ||||||||
\(59\) | 54.6341i | 0.926002i | 0.886358 | + | 0.463001i | \(0.153227\pi\) | ||||
−0.886358 | + | 0.463001i | \(0.846773\pi\) | |||||||
\(60\) | 3.13988 | + | 13.0438i | 0.0523314 | + | 0.217397i | ||||
\(61\) | 34.1922 | 0.560528 | 0.280264 | − | 0.959923i | \(-0.409578\pi\) | ||||
0.280264 | + | 0.959923i | \(0.409578\pi\) | |||||||
\(62\) | − | 60.3163i | − | 0.972844i | ||||||
\(63\) | −68.3466 | + | 34.9285i | −1.08487 | + | 0.554420i | ||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 41.0832i | 0.632049i | ||||||||
\(66\) | −46.3899 | + | 11.1669i | −0.702877 | + | 0.169195i | ||||
\(67\) | 54.8459 | 0.818595 | 0.409298 | − | 0.912401i | \(-0.365774\pi\) | ||||
0.409298 | + | 0.912401i | \(0.365774\pi\) | |||||||
\(68\) | − | 1.60114i | − | 0.0235462i | ||||||
\(69\) | −3.36715 | − | 13.9879i | −0.0487993 | − | 0.202724i | ||||
\(70\) | 26.9688 | 0.385268 | ||||||||
\(71\) | − | 32.3338i | − | 0.455405i | −0.973731 | − | 0.227703i | \(-0.926879\pi\) | ||
0.973731 | − | 0.227703i | \(-0.0731214\pi\) | |||||||
\(72\) | −11.5841 | − | 22.6673i | −0.160891 | − | 0.314824i | ||||
\(73\) | −39.7792 | −0.544920 | −0.272460 | − | 0.962167i | \(-0.587837\pi\) | ||||
−0.272460 | + | 0.962167i | \(0.587837\pi\) | |||||||
\(74\) | 60.6307i | 0.819334i | ||||||||
\(75\) | 14.5834 | − | 3.51050i | 0.194446 | − | 0.0468066i | ||||
\(76\) | −26.4983 | −0.348662 | ||||||||
\(77\) | 95.9136i | 1.24563i | ||||||||
\(78\) | −18.2429 | − | 75.7851i | −0.233883 | − | 0.971604i | ||||
\(79\) | 14.3142 | 0.181193 | 0.0905964 | − | 0.995888i | \(-0.471123\pi\) | ||||
0.0905964 | + | 0.995888i | \(0.471123\pi\) | |||||||
\(80\) | 8.94427i | 0.111803i | ||||||||
\(81\) | 47.4520 | − | 65.6453i | 0.585827 | − | 0.810436i | ||||
\(82\) | 83.8352 | 1.02238 | ||||||||
\(83\) | 42.0770i | 0.506952i | 0.967342 | + | 0.253476i | \(0.0815738\pi\) | ||||
−0.967342 | + | 0.253476i | \(0.918426\pi\) | |||||||
\(84\) | −49.7486 | + | 11.9754i | −0.592246 | + | 0.142564i | ||||
\(85\) | −1.79013 | −0.0210603 | ||||||||
\(86\) | 15.1268i | 0.175893i | ||||||||
\(87\) | −7.70625 | − | 32.0136i | −0.0885775 | − | 0.367972i | ||||
\(88\) | −31.8100 | −0.361477 | ||||||||
\(89\) | 77.1399i | 0.866740i | 0.901216 | + | 0.433370i | \(0.142676\pi\) | ||||
−0.901216 | + | 0.433370i | \(0.857324\pi\) | |||||||
\(90\) | −25.3429 | + | 12.9514i | −0.281587 | + | 0.143905i | ||||
\(91\) | −156.690 | −1.72187 | ||||||||
\(92\) | − | 9.59166i | − | 0.104257i | ||||||
\(93\) | 124.397 | − | 29.9446i | 1.33760 | − | 0.321985i | ||||
\(94\) | −93.1521 | −0.990980 | ||||||||
\(95\) | 29.6260i | 0.311853i | ||||||||
\(96\) | −3.97167 | − | 16.4993i | −0.0413716 | − | 0.171867i | ||||
\(97\) | 139.910 | 1.44237 | 0.721187 | − | 0.692740i | \(-0.243597\pi\) | ||||
0.721187 | + | 0.692740i | \(0.243597\pi\) | |||||||
\(98\) | 33.5615i | 0.342464i | ||||||||
\(99\) | −46.0614 | − | 90.1310i | −0.465266 | − | 0.910414i | ||||
\(100\) | 10.0000 | 0.100000 | ||||||||
\(101\) | 185.003i | 1.83171i | 0.401504 | + | 0.915857i | \(0.368488\pi\) | ||||
−0.401504 | + | 0.915857i | \(0.631512\pi\) | |||||||
\(102\) | 3.30220 | − | 0.794900i | 0.0323745 | − | 0.00779313i | ||||
\(103\) | −164.164 | −1.59383 | −0.796913 | − | 0.604093i | \(-0.793535\pi\) | ||||
−0.796913 | + | 0.604093i | \(0.793535\pi\) | |||||||
\(104\) | − | 51.9666i | − | 0.499679i | ||||||
\(105\) | 13.3889 | + | 55.6207i | 0.127513 | + | 0.529721i | ||||
\(106\) | −96.6880 | −0.912151 | ||||||||
\(107\) | 106.013i | 0.990772i | 0.868673 | + | 0.495386i | \(0.164973\pi\) | ||||
−0.868673 | + | 0.495386i | \(0.835027\pi\) | |||||||
\(108\) | 40.9983 | − | 35.1446i | 0.379614 | − | 0.325413i | ||||
\(109\) | 58.8011 | 0.539459 | 0.269730 | − | 0.962936i | \(-0.413066\pi\) | ||||
0.269730 | + | 0.962936i | \(0.413066\pi\) | |||||||
\(110\) | 35.5647i | 0.323315i | ||||||||
\(111\) | −125.045 | + | 30.1007i | −1.12653 | + | 0.271177i | ||||
\(112\) | −34.1131 | −0.304581 | ||||||||
\(113\) | 15.8528i | 0.140290i | 0.997537 | + | 0.0701450i | \(0.0223462\pi\) | ||||
−0.997537 | + | 0.0701450i | \(0.977654\pi\) | |||||||
\(114\) | −13.1553 | − | 54.6504i | −0.115398 | − | 0.479389i | ||||
\(115\) | −10.7238 | −0.0932505 | ||||||||
\(116\) | − | 21.9520i | − | 0.189241i | ||||||
\(117\) | 147.243 | − | 75.2484i | 1.25849 | − | 0.643149i | ||||
\(118\) | −77.2643 | −0.654782 | ||||||||
\(119\) | − | 6.82748i | − | 0.0573738i | ||||||
\(120\) | −18.4467 | + | 4.44047i | −0.153723 | + | 0.0370039i | ||||
\(121\) | −5.48447 | −0.0453262 | ||||||||
\(122\) | 48.3551i | 0.396353i | ||||||||
\(123\) | 41.6207 | + | 172.902i | 0.338380 | + | 1.40571i | ||||
\(124\) | 85.3002 | 0.687905 | ||||||||
\(125\) | − | 11.1803i | − | 0.0894427i | ||||||
\(126\) | −49.3963 | − | 96.6567i | −0.392034 | − | 0.767117i | ||||
\(127\) | 201.548 | 1.58699 | 0.793495 | − | 0.608577i | \(-0.208259\pi\) | ||||
0.793495 | + | 0.608577i | \(0.208259\pi\) | |||||||
\(128\) | − | 11.3137i | − | 0.0883883i | ||||||
\(129\) | −31.1976 | + | 7.50983i | −0.241842 | + | 0.0582158i | ||||
\(130\) | −58.1004 | −0.446926 | ||||||||
\(131\) | − | 137.815i | − | 1.05202i | −0.850477 | − | 0.526012i | \(-0.823687\pi\) | ||
0.850477 | − | 0.526012i | \(-0.176313\pi\) | |||||||
\(132\) | −15.7924 | − | 65.6052i | −0.119639 | − | 0.497009i | ||||
\(133\) | −112.993 | −0.849568 | ||||||||
\(134\) | 77.5638i | 0.578834i | ||||||||
\(135\) | −39.2929 | − | 45.8374i | −0.291058 | − | 0.339537i | ||||
\(136\) | 2.26435 | 0.0166496 | ||||||||
\(137\) | 12.5145i | 0.0913465i | 0.998956 | + | 0.0456733i | \(0.0145433\pi\) | ||||
−0.998956 | + | 0.0456733i | \(0.985457\pi\) | |||||||
\(138\) | 19.7819 | − | 4.76187i | 0.143347 | − | 0.0345063i | ||||
\(139\) | 271.132 | 1.95059 | 0.975296 | − | 0.220900i | \(-0.0708996\pi\) | ||||
0.975296 | + | 0.220900i | \(0.0708996\pi\) | |||||||
\(140\) | 38.1396i | 0.272426i | ||||||||
\(141\) | −46.2462 | − | 192.118i | −0.327987 | − | 1.36254i | ||||
\(142\) | 45.7268 | 0.322020 | ||||||||
\(143\) | − | 206.632i | − | 1.44498i | ||||||
\(144\) | 32.0565 | − | 16.3824i | 0.222614 | − | 0.113767i | ||||
\(145\) | −24.5431 | −0.169263 | ||||||||
\(146\) | − | 56.2562i | − | 0.385317i | ||||||
\(147\) | −69.2175 | + | 16.6619i | −0.470867 | + | 0.113346i | ||||
\(148\) | −85.7448 | −0.579357 | ||||||||
\(149\) | − | 83.1004i | − | 0.557721i | −0.960332 | − | 0.278861i | \(-0.910043\pi\) | ||
0.960332 | − | 0.278861i | \(-0.0899567\pi\) | |||||||
\(150\) | 4.96459 | + | 20.6241i | 0.0330973 | + | 0.137494i | ||||
\(151\) | 170.027 | 1.12601 | 0.563003 | − | 0.826455i | \(-0.309646\pi\) | ||||
0.563003 | + | 0.826455i | \(0.309646\pi\) | |||||||
\(152\) | − | 37.4743i | − | 0.246541i | ||||||
\(153\) | 3.27882 | + | 6.41585i | 0.0214302 | + | 0.0419337i | ||||
\(154\) | −135.642 | −0.880794 | ||||||||
\(155\) | − | 95.3685i | − | 0.615281i | ||||||
\(156\) | 107.176 | − | 25.7993i | 0.687028 | − | 0.165380i | ||||
\(157\) | 148.967 | 0.948833 | 0.474417 | − | 0.880300i | \(-0.342659\pi\) | ||||
0.474417 | + | 0.880300i | \(0.342659\pi\) | |||||||
\(158\) | 20.2434i | 0.128123i | ||||||||
\(159\) | −48.0016 | − | 199.410i | −0.301897 | − | 1.25415i | ||||
\(160\) | −12.6491 | −0.0790569 | ||||||||
\(161\) | − | 40.9002i | − | 0.254038i | ||||||
\(162\) | 92.8365 | + | 67.1073i | 0.573065 | + | 0.414243i | ||||
\(163\) | −233.872 | −1.43480 | −0.717398 | − | 0.696664i | \(-0.754667\pi\) | ||||
−0.717398 | + | 0.696664i | \(0.754667\pi\) | |||||||
\(164\) | 118.561i | 0.722932i | ||||||||
\(165\) | −73.3488 | + | 17.6564i | −0.444538 | + | 0.107008i | ||||
\(166\) | −59.5059 | −0.358469 | ||||||||
\(167\) | 140.840i | 0.843356i | 0.906746 | + | 0.421678i | \(0.138559\pi\) | ||||
−0.906746 | + | 0.421678i | \(0.861441\pi\) | |||||||
\(168\) | −16.9358 | − | 70.3552i | −0.100808 | − | 0.418781i | ||||
\(169\) | 168.566 | 0.997432 | ||||||||
\(170\) | − | 2.53162i | − | 0.0148919i | ||||||
\(171\) | 106.180 | − | 54.2633i | 0.620937 | − | 0.317330i | ||||
\(172\) | −21.3925 | −0.124375 | ||||||||
\(173\) | 112.577i | 0.650735i | 0.945588 | + | 0.325368i | \(0.105488\pi\) | ||||
−0.945588 | + | 0.325368i | \(0.894512\pi\) | |||||||
\(174\) | 45.2740 | − | 10.8983i | 0.260195 | − | 0.0626338i | ||||
\(175\) | 42.6414 | 0.243665 | ||||||||
\(176\) | − | 44.9861i | − | 0.255603i | ||||||
\(177\) | −38.3586 | − | 159.350i | −0.216715 | − | 0.900285i | ||||
\(178\) | −109.092 | −0.612878 | ||||||||
\(179\) | − | 265.456i | − | 1.48300i | −0.670954 | − | 0.741499i | \(-0.734115\pi\) | ||
0.670954 | − | 0.741499i | \(-0.265885\pi\) | |||||||
\(180\) | −18.3161 | − | 35.8402i | −0.101756 | − | 0.199112i | ||||
\(181\) | −181.424 | −1.00234 | −0.501172 | − | 0.865348i | \(-0.667098\pi\) | ||||
−0.501172 | + | 0.865348i | \(0.667098\pi\) | |||||||
\(182\) | − | 221.593i | − | 1.21754i | ||||||
\(183\) | −99.7279 | + | 24.0063i | −0.544961 | + | 0.131182i | ||||
\(184\) | 13.5647 | 0.0737210 | ||||||||
\(185\) | 95.8656i | 0.518192i | ||||||||
\(186\) | 42.3480 | + | 175.924i | 0.227678 | + | 0.945827i | ||||
\(187\) | 9.00363 | 0.0481477 | ||||||||
\(188\) | − | 131.737i | − | 0.700729i | ||||||
\(189\) | 174.822 | − | 149.861i | 0.924986 | − | 0.792918i | ||||
\(190\) | −41.8975 | −0.220513 | ||||||||
\(191\) | 192.654i | 1.00866i | 0.863511 | + | 0.504331i | \(0.168261\pi\) | ||||
−0.863511 | + | 0.504331i | \(0.831739\pi\) | |||||||
\(192\) | 23.3335 | − | 5.61679i | 0.121529 | − | 0.0292541i | ||||
\(193\) | 204.556 | 1.05988 | 0.529938 | − | 0.848036i | \(-0.322215\pi\) | ||||
0.529938 | + | 0.848036i | \(0.322215\pi\) | |||||||
\(194\) | 197.863i | 1.01991i | ||||||||
\(195\) | −28.8445 | − | 119.827i | −0.147920 | − | 0.614496i | ||||
\(196\) | −47.4631 | −0.242159 | ||||||||
\(197\) | 41.7064i | 0.211708i | 0.994382 | + | 0.105854i | \(0.0337576\pi\) | ||||
−0.994382 | + | 0.105854i | \(0.966242\pi\) | |||||||
\(198\) | 127.464 | − | 65.1406i | 0.643760 | − | 0.328993i | ||||
\(199\) | −7.69267 | −0.0386566 | −0.0193283 | − | 0.999813i | \(-0.506153\pi\) | ||||
−0.0193283 | + | 0.999813i | \(0.506153\pi\) | |||||||
\(200\) | 14.1421i | 0.0707107i | ||||||||
\(201\) | −159.968 | + | 38.5073i | −0.795862 | + | 0.191578i | ||||
\(202\) | −261.634 | −1.29522 | ||||||||
\(203\) | − | 93.6065i | − | 0.461116i | ||||||
\(204\) | 1.12416 | + | 4.67002i | 0.00551058 | + | 0.0228922i | ||||
\(205\) | 132.555 | 0.646610 | ||||||||
\(206\) | − | 232.163i | − | 1.12701i | ||||||
\(207\) | 19.6418 | + | 38.4343i | 0.0948881 | + | 0.185673i | ||||
\(208\) | 73.4919 | 0.353326 | ||||||||
\(209\) | − | 149.007i | − | 0.712953i | ||||||
\(210\) | −78.6595 | + | 18.9348i | −0.374569 | + | 0.0901655i | ||||
\(211\) | 348.331 | 1.65086 | 0.825429 | − | 0.564507i | \(-0.190934\pi\) | ||||
0.825429 | + | 0.564507i | \(0.190934\pi\) | |||||||
\(212\) | − | 136.737i | − | 0.644988i | ||||||
\(213\) | 22.7015 | + | 94.3074i | 0.106580 | + | 0.442758i | ||||
\(214\) | −149.924 | −0.700581 | ||||||||
\(215\) | 23.9176i | 0.111244i | ||||||||
\(216\) | 49.7020 | + | 57.9803i | 0.230102 | + | 0.268427i | ||||
\(217\) | 363.732 | 1.67618 | ||||||||
\(218\) | 83.1573i | 0.381455i | ||||||||
\(219\) | 116.023 | − | 27.9289i | 0.529787 | − | 0.127529i | ||||
\(220\) | −50.2960 | −0.228618 | ||||||||
\(221\) | 14.7088i | 0.0665558i | ||||||||
\(222\) | −42.5688 | − | 176.841i | −0.191751 | − | 0.796580i | ||||
\(223\) | 411.231 | 1.84409 | 0.922044 | − | 0.387086i | \(-0.126518\pi\) | ||||
0.922044 | + | 0.387086i | \(0.126518\pi\) | |||||||
\(224\) | − | 48.2432i | − | 0.215372i | ||||||
\(225\) | −40.0706 | + | 20.4780i | −0.178091 | + | 0.0910135i | ||||
\(226\) | −22.4192 | −0.0992000 | ||||||||
\(227\) | 97.7055i | 0.430421i | 0.976568 | + | 0.215210i | \(0.0690437\pi\) | ||||
−0.976568 | + | 0.215210i | \(0.930956\pi\) | |||||||
\(228\) | 77.2873 | − | 18.6045i | 0.338979 | − | 0.0815985i | ||||
\(229\) | 88.0463 | 0.384482 | 0.192241 | − | 0.981348i | \(-0.438425\pi\) | ||||
0.192241 | + | 0.981348i | \(0.438425\pi\) | |||||||
\(230\) | − | 15.1658i | − | 0.0659380i | ||||||
\(231\) | −67.3408 | − | 279.750i | −0.291519 | − | 1.21104i | ||||
\(232\) | 31.0448 | 0.133814 | ||||||||
\(233\) | 113.860i | 0.488671i | 0.969691 | + | 0.244336i | \(0.0785699\pi\) | ||||
−0.969691 | + | 0.244336i | \(0.921430\pi\) | |||||||
\(234\) | 106.417 | + | 208.233i | 0.454775 | + | 0.889885i | ||||
\(235\) | −147.286 | −0.626751 | ||||||||
\(236\) | − | 109.268i | − | 0.463001i | ||||||
\(237\) | −41.7501 | + | 10.0500i | −0.176161 | + | 0.0424051i | ||||
\(238\) | 9.65551 | 0.0405694 | ||||||||
\(239\) | − | 88.4422i | − | 0.370051i | −0.982734 | − | 0.185026i | \(-0.940763\pi\) | ||
0.982734 | − | 0.185026i | \(-0.0592368\pi\) | |||||||
\(240\) | −6.27977 | − | 26.0876i | −0.0261657 | − | 0.108698i | ||||
\(241\) | −297.884 | −1.23603 | −0.618017 | − | 0.786164i | \(-0.712064\pi\) | ||||
−0.618017 | + | 0.786164i | \(0.712064\pi\) | |||||||
\(242\) | − | 7.75622i | − | 0.0320505i | ||||||
\(243\) | −92.3131 | + | 224.783i | −0.379889 | + | 0.925032i | ||||
\(244\) | −68.3844 | −0.280264 | ||||||||
\(245\) | 53.0654i | 0.216593i | ||||||||
\(246\) | −244.521 | + | 58.8606i | −0.993988 | + | 0.239271i | ||||
\(247\) | 243.426 | 0.985532 | ||||||||
\(248\) | 120.633i | 0.486422i | ||||||||
\(249\) | −29.5422 | − | 122.725i | −0.118643 | − | 0.492873i | ||||
\(250\) | 15.8114 | 0.0632456 | ||||||||
\(251\) | − | 252.585i | − | 1.00632i | −0.864195 | − | 0.503158i | \(-0.832171\pi\) | ||
0.864195 | − | 0.503158i | \(-0.167829\pi\) | |||||||
\(252\) | 136.693 | − | 69.8569i | 0.542433 | − | 0.277210i | ||||
\(253\) | 53.9365 | 0.213188 | ||||||||
\(254\) | 285.032i | 1.12217i | ||||||||
\(255\) | 5.22124 | − | 1.25685i | 0.0204754 | − | 0.00492881i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − | 108.572i | − | 0.422460i | −0.977436 | − | 0.211230i | \(-0.932253\pi\) | ||
0.977436 | − | 0.211230i | \(-0.0677469\pi\) | |||||||
\(258\) | −10.6205 | − | 44.1201i | −0.0411648 | − | 0.171008i | ||||
\(259\) | −365.628 | −1.41169 | ||||||||
\(260\) | − | 82.1664i | − | 0.316025i | ||||||
\(261\) | 44.9534 | + | 87.9630i | 0.172235 | + | 0.337023i | ||||
\(262\) | 194.900 | 0.743893 | ||||||||
\(263\) | 411.174i | 1.56340i | 0.623655 | + | 0.781700i | \(0.285647\pi\) | ||||
−0.623655 | + | 0.781700i | \(0.714353\pi\) | |||||||
\(264\) | 92.7798 | − | 22.3338i | 0.351439 | − | 0.0845976i | ||||
\(265\) | −152.877 | −0.576895 | ||||||||
\(266\) | − | 159.796i | − | 0.600735i | ||||||
\(267\) | −54.1598 | − | 224.993i | −0.202846 | − | 0.842670i | ||||
\(268\) | −109.692 | −0.409298 | ||||||||
\(269\) | 270.452i | 1.00540i | 0.864462 | + | 0.502698i | \(0.167659\pi\) | ||||
−0.864462 | + | 0.502698i | \(0.832341\pi\) | |||||||
\(270\) | 64.8239 | − | 55.5685i | 0.240089 | − | 0.205809i | ||||
\(271\) | −138.939 | −0.512689 | −0.256345 | − | 0.966585i | \(-0.582518\pi\) | ||||
−0.256345 | + | 0.966585i | \(0.582518\pi\) | |||||||
\(272\) | 3.20228i | 0.0117731i | ||||||||
\(273\) | 457.015 | − | 110.012i | 1.67405 | − | 0.402974i | ||||
\(274\) | −17.6981 | −0.0645917 | ||||||||
\(275\) | 56.2327i | 0.204482i | ||||||||
\(276\) | 6.73430 | + | 27.9759i | 0.0243996 | + | 0.101362i | ||||
\(277\) | −64.2222 | −0.231849 | −0.115925 | − | 0.993258i | \(-0.536983\pi\) | ||||
−0.115925 | + | 0.993258i | \(0.536983\pi\) | |||||||
\(278\) | 383.439i | 1.37928i | ||||||||
\(279\) | −341.803 | + | 174.678i | −1.22510 | + | 0.626086i | ||||
\(280\) | −53.9376 | −0.192634 | ||||||||
\(281\) | 298.203i | 1.06122i | 0.847616 | + | 0.530611i | \(0.178037\pi\) | ||||
−0.847616 | + | 0.530611i | \(0.821963\pi\) | |||||||
\(282\) | 271.695 | − | 65.4020i | 0.963459 | − | 0.231922i | ||||
\(283\) | −118.877 | −0.420061 | −0.210031 | − | 0.977695i | \(-0.567356\pi\) | ||||
−0.210031 | + | 0.977695i | \(0.567356\pi\) | |||||||
\(284\) | 64.6675i | 0.227703i | ||||||||
\(285\) | −20.8004 | − | 86.4098i | −0.0729839 | − | 0.303192i | ||||
\(286\) | 292.222 | 1.02176 | ||||||||
\(287\) | 505.560i | 1.76153i | ||||||||
\(288\) | 23.1682 | + | 45.3347i | 0.0804453 | + | 0.157412i | ||||
\(289\) | 288.359 | 0.997782 | ||||||||
\(290\) | − | 34.7092i | − | 0.119687i | ||||||
\(291\) | −408.074 | + | 98.2309i | −1.40232 | + | 0.337563i | ||||
\(292\) | 79.5583 | 0.272460 | ||||||||
\(293\) | − | 338.920i | − | 1.15672i | −0.815781 | − | 0.578361i | \(-0.803692\pi\) | ||
0.815781 | − | 0.578361i | \(-0.196308\pi\) | |||||||
\(294\) | −23.5635 | − | 97.8883i | −0.0801479 | − | 0.332953i | ||||
\(295\) | −122.166 | −0.414120 | ||||||||
\(296\) | − | 121.261i | − | 0.409667i | ||||||
\(297\) | 197.627 | + | 230.544i | 0.665412 | + | 0.776243i | ||||
\(298\) | 117.522 | 0.394368 | ||||||||
\(299\) | 88.1137i | 0.294695i | ||||||||
\(300\) | −29.1669 | + | 7.02099i | −0.0972229 | + | 0.0234033i | ||||
\(301\) | −91.2207 | −0.303059 | ||||||||
\(302\) | 240.455i | 0.796207i | ||||||||
\(303\) | −129.891 | − | 539.596i | −0.428682 | − | 1.78085i | ||||
\(304\) | 52.9966 | 0.174331 | ||||||||
\(305\) | 76.4561i | 0.250676i | ||||||||
\(306\) | −9.07338 | + | 4.63695i | −0.0296516 | + | 0.0151534i | ||||
\(307\) | 194.037 | 0.632042 | 0.316021 | − | 0.948752i | \(-0.397653\pi\) | ||||
0.316021 | + | 0.948752i | \(0.397653\pi\) | |||||||
\(308\) | − | 191.827i | − | 0.622815i | ||||||
\(309\) | 478.815 | − | 115.260i | 1.54956 | − | 0.373008i | ||||
\(310\) | 134.871 | 0.435069 | ||||||||
\(311\) | − | 145.543i | − | 0.467985i | −0.972238 | − | 0.233992i | \(-0.924821\pi\) | ||
0.972238 | − | 0.233992i | \(-0.0751791\pi\) | |||||||
\(312\) | 36.4857 | + | 151.570i | 0.116941 | + | 0.485802i | ||||
\(313\) | −93.3372 | −0.298202 | −0.149101 | − | 0.988822i | \(-0.547638\pi\) | ||||
−0.149101 | + | 0.988822i | \(0.547638\pi\) | |||||||
\(314\) | 210.671i | 0.670926i | ||||||||
\(315\) | −78.1024 | − | 152.828i | −0.247944 | − | 0.485167i | ||||
\(316\) | −28.6285 | −0.0905964 | ||||||||
\(317\) | − | 282.185i | − | 0.890174i | −0.895487 | − | 0.445087i | \(-0.853173\pi\) | ||
0.895487 | − | 0.445087i | \(-0.146827\pi\) | |||||||
\(318\) | 282.008 | − | 67.8845i | 0.886819 | − | 0.213473i | ||||
\(319\) | 123.442 | 0.386966 | ||||||||
\(320\) | − | 17.8885i | − | 0.0559017i | ||||||
\(321\) | −74.4313 | − | 309.205i | −0.231873 | − | 0.963257i | ||||
\(322\) | 57.8416 | 0.179632 | ||||||||
\(323\) | 10.6069i | 0.0328386i | ||||||||
\(324\) | −94.9041 | + | 131.291i | −0.292914 | + | 0.405218i | ||||
\(325\) | −91.8648 | −0.282661 | ||||||||
\(326\) | − | 330.745i | − | 1.01455i | ||||||
\(327\) | −171.504 | + | 41.2842i | −0.524478 | + | 0.126251i | ||||
\(328\) | −167.670 | −0.511190 | ||||||||
\(329\) | − | 561.745i | − | 1.70743i | ||||||
\(330\) | −24.9699 | − | 103.731i | −0.0756664 | − | 0.314336i | ||||
\(331\) | −384.366 | −1.16123 | −0.580613 | − | 0.814179i | \(-0.697187\pi\) | ||||
−0.580613 | + | 0.814179i | \(0.697187\pi\) | |||||||
\(332\) | − | 84.1540i | − | 0.253476i | ||||||
\(333\) | 343.584 | − | 175.588i | 1.03178 | − | 0.527293i | ||||
\(334\) | −199.178 | −0.596343 | ||||||||
\(335\) | 122.639i | 0.366087i | ||||||||
\(336\) | 99.4973 | − | 23.9508i | 0.296123 | − | 0.0712821i | ||||
\(337\) | −267.563 | −0.793954 | −0.396977 | − | 0.917829i | \(-0.629941\pi\) | ||||
−0.396977 | + | 0.917829i | \(0.629941\pi\) | |||||||
\(338\) | 238.388i | 0.705291i | ||||||||
\(339\) | −11.1302 | − | 46.2376i | −0.0328325 | − | 0.136394i | ||||
\(340\) | 3.58025 | 0.0105302 | ||||||||
\(341\) | 479.666i | 1.40664i | ||||||||
\(342\) | 76.7400 | + | 150.162i | 0.224386 | + | 0.439069i | ||||
\(343\) | 215.496 | 0.628269 | ||||||||
\(344\) | − | 30.2536i | − | 0.0879465i | ||||||
\(345\) | 31.2780 | − | 7.52918i | 0.0906608 | − | 0.0218237i | ||||
\(346\) | −159.208 | −0.460139 | ||||||||
\(347\) | − | 518.074i | − | 1.49301i | −0.665380 | − | 0.746505i | \(-0.731730\pi\) | ||
0.665380 | − | 0.746505i | \(-0.268270\pi\) | |||||||
\(348\) | 15.4125 | + | 64.0271i | 0.0442888 | + | 0.183986i | ||||
\(349\) | −375.123 | −1.07485 | −0.537426 | − | 0.843311i | \(-0.680603\pi\) | ||||
−0.537426 | + | 0.843311i | \(0.680603\pi\) | |||||||
\(350\) | 60.3040i | 0.172297i | ||||||||
\(351\) | −376.630 | + | 322.855i | −1.07302 | + | 0.919816i | ||||
\(352\) | 63.6200 | 0.180739 | ||||||||
\(353\) | − | 101.654i | − | 0.287970i | −0.989580 | − | 0.143985i | \(-0.954008\pi\) | ||
0.989580 | − | 0.143985i | \(-0.0459918\pi\) | |||||||
\(354\) | 225.356 | − | 54.2472i | 0.636598 | − | 0.153241i | ||||
\(355\) | 72.3005 | 0.203663 | ||||||||
\(356\) | − | 154.280i | − | 0.433370i | ||||||
\(357\) | 4.79357 | + | 19.9136i | 0.0134274 | + | 0.0557804i | ||||
\(358\) | 375.412 | 1.04864 | ||||||||
\(359\) | − | 147.915i | − | 0.412019i | −0.978550 | − | 0.206010i | \(-0.933952\pi\) | ||
0.978550 | − | 0.206010i | \(-0.0660478\pi\) | |||||||
\(360\) | 50.6857 | − | 25.9029i | 0.140794 | − | 0.0719525i | ||||
\(361\) | −185.460 | −0.513739 | ||||||||
\(362\) | − | 256.573i | − | 0.708764i | ||||||
\(363\) | 15.9965 | − | 3.85064i | 0.0440674 | − | 0.0106078i | ||||
\(364\) | 313.380 | 0.860933 | ||||||||
\(365\) | − | 88.9489i | − | 0.243696i | ||||||
\(366\) | −33.9501 | − | 141.037i | −0.0927597 | − | 0.385346i | ||||
\(367\) | −398.761 | −1.08654 | −0.543271 | − | 0.839557i | \(-0.682814\pi\) | ||||
−0.543271 | + | 0.839557i | \(0.682814\pi\) | |||||||
\(368\) | 19.1833i | 0.0521286i | ||||||||
\(369\) | −242.789 | − | 475.080i | −0.657966 | − | 1.28748i | ||||
\(370\) | −135.574 | −0.366417 | ||||||||
\(371\) | − | 583.068i | − | 1.57161i | ||||||
\(372\) | −248.794 | + | 59.8892i | −0.668801 | + | 0.160992i | ||||
\(373\) | 349.777 | 0.937739 | 0.468869 | − | 0.883268i | \(-0.344662\pi\) | ||||
0.468869 | + | 0.883268i | \(0.344662\pi\) | |||||||
\(374\) | 12.7331i | 0.0340456i | ||||||||
\(375\) | 7.84971 | + | 32.6095i | 0.0209326 | + | 0.0869588i | ||||
\(376\) | 186.304 | 0.495490 | ||||||||
\(377\) | 201.662i | 0.534912i | ||||||||
\(378\) | 211.936 | + | 247.236i | 0.560678 | + | 0.654064i | ||||
\(379\) | −568.739 | −1.50063 | −0.750315 | − | 0.661080i | \(-0.770098\pi\) | ||||
−0.750315 | + | 0.661080i | \(0.770098\pi\) | |||||||
\(380\) | − | 59.2521i | − | 0.155926i | ||||||
\(381\) | −587.851 | + | 141.507i | −1.54292 | + | 0.371408i | ||||
\(382\) | −272.454 | −0.713231 | ||||||||
\(383\) | 116.352i | 0.303791i | 0.988397 | + | 0.151896i | \(0.0485378\pi\) | ||||
−0.988397 | + | 0.151896i | \(0.951462\pi\) | |||||||
\(384\) | 7.94335 | + | 32.9985i | 0.0206858 | + | 0.0859337i | ||||
\(385\) | −214.469 | −0.557063 | ||||||||
\(386\) | 289.286i | 0.749445i | ||||||||
\(387\) | 85.7210 | − | 43.8077i | 0.221501 | − | 0.113198i | ||||
\(388\) | −279.821 | −0.721187 | ||||||||
\(389\) | 718.880i | 1.84802i | 0.382368 | + | 0.924010i | \(0.375109\pi\) | ||||
−0.382368 | + | 0.924010i | \(0.624891\pi\) | |||||||
\(390\) | 169.461 | − | 40.7923i | 0.434515 | − | 0.104596i | ||||
\(391\) | −3.83939 | −0.00981942 | ||||||||
\(392\) | − | 67.1230i | − | 0.171232i | ||||||
\(393\) | 96.7599 | + | 401.963i | 0.246208 | + | 1.02281i | ||||
\(394\) | −58.9818 | −0.149700 | ||||||||
\(395\) | 32.0076i | 0.0810319i | ||||||||
\(396\) | 92.1227 | + | 180.262i | 0.232633 | + | 0.455207i | ||||
\(397\) | −187.368 | −0.471961 | −0.235980 | − | 0.971758i | \(-0.575830\pi\) | ||||
−0.235980 | + | 0.971758i | \(0.575830\pi\) | |||||||
\(398\) | − | 10.8791i | − | 0.0273344i | ||||||
\(399\) | 329.564 | − | 79.3320i | 0.825974 | − | 0.198827i | ||||
\(400\) | −20.0000 | −0.0500000 | ||||||||
\(401\) | − | 95.8953i | − | 0.239141i | −0.992826 | − | 0.119570i | \(-0.961848\pi\) | ||
0.992826 | − | 0.119570i | \(-0.0381517\pi\) | |||||||
\(402\) | −54.4575 | − | 226.229i | −0.135466 | − | 0.562759i | ||||
\(403\) | −783.609 | −1.94444 | ||||||||
\(404\) | − | 370.006i | − | 0.915857i | ||||||
\(405\) | 146.787 | + | 106.106i | 0.362438 | + | 0.261990i | ||||
\(406\) | 132.380 | 0.326058 | ||||||||
\(407\) | − | 482.166i | − | 1.18468i | ||||||
\(408\) | −6.60440 | + | 1.58980i | −0.0161873 | + | 0.00389657i | ||||
\(409\) | 678.263 | 1.65835 | 0.829173 | − | 0.558993i | \(-0.188812\pi\) | ||||
0.829173 | + | 0.558993i | \(0.188812\pi\) | |||||||
\(410\) | 187.461i | 0.457222i | ||||||||
\(411\) | −8.78640 | − | 36.5008i | −0.0213781 | − | 0.0888097i | ||||
\(412\) | 328.328 | 0.796913 | ||||||||
\(413\) | − | 465.935i | − | 1.12817i | ||||||
\(414\) | −54.3544 | + | 27.7777i | −0.131291 | + | 0.0670960i | ||||
\(415\) | −94.0870 | −0.226716 | ||||||||
\(416\) | 103.933i | 0.249839i | ||||||||
\(417\) | −790.808 | + | 190.362i | −1.89642 | + | 0.456503i | ||||
\(418\) | 210.728 | 0.504134 | ||||||||
\(419\) | 149.069i | 0.355774i | 0.984051 | + | 0.177887i | \(0.0569262\pi\) | ||||
−0.984051 | + | 0.177887i | \(0.943074\pi\) | |||||||
\(420\) | −26.7778 | − | 111.241i | −0.0637567 | − | 0.264860i | ||||
\(421\) | −61.2688 | −0.145532 | −0.0727658 | − | 0.997349i | \(-0.523183\pi\) | ||||
−0.0727658 | + | 0.997349i | \(0.523183\pi\) | |||||||
\(422\) | 492.614i | 1.16733i | ||||||||
\(423\) | 269.771 | + | 527.877i | 0.637757 | + | 1.24794i | ||||
\(424\) | 193.376 | 0.456075 | ||||||||
\(425\) | − | 4.00285i | − | 0.00941846i | ||||||
\(426\) | −133.371 | + | 32.1048i | −0.313077 | + | 0.0753633i | ||||
\(427\) | −291.601 | −0.682906 | ||||||||
\(428\) | − | 212.025i | − | 0.495386i | ||||||
\(429\) | 145.076 | + | 602.681i | 0.338173 | + | 1.40485i | ||||
\(430\) | −33.8245 | −0.0786617 | ||||||||
\(431\) | 325.729i | 0.755751i | 0.925856 | + | 0.377875i | \(0.123345\pi\) | ||||
−0.925856 | + | 0.377875i | \(0.876655\pi\) | |||||||
\(432\) | −81.9965 | + | 70.2892i | −0.189807 | + | 0.162706i | ||||
\(433\) | 406.666 | 0.939183 | 0.469592 | − | 0.882884i | \(-0.344401\pi\) | ||||
0.469592 | + | 0.882884i | \(0.344401\pi\) | |||||||
\(434\) | 514.395i | 1.18524i | ||||||||
\(435\) | 71.5845 | − | 17.2317i | 0.164562 | − | 0.0396131i | ||||
\(436\) | −117.602 | −0.269730 | ||||||||
\(437\) | 63.5407i | 0.145402i | ||||||||
\(438\) | 39.4975 | + | 164.082i | 0.0901769 | + | 0.374616i | ||||
\(439\) | 583.212 | 1.32850 | 0.664250 | − | 0.747510i | \(-0.268751\pi\) | ||||
0.664250 | + | 0.747510i | \(0.268751\pi\) | |||||||
\(440\) | − | 71.1293i | − | 0.161658i | ||||||
\(441\) | 190.187 | − | 97.1951i | 0.431264 | − | 0.220397i | ||||
\(442\) | −20.8014 | −0.0470621 | ||||||||
\(443\) | − | 203.714i | − | 0.459850i | −0.973208 | − | 0.229925i | \(-0.926152\pi\) | ||
0.973208 | − | 0.229925i | \(-0.0738482\pi\) | |||||||
\(444\) | 250.091 | − | 60.2013i | 0.563267 | − | 0.135589i | ||||
\(445\) | −172.490 | −0.387618 | ||||||||
\(446\) | 581.569i | 1.30397i | ||||||||
\(447\) | 58.3448 | + | 242.378i | 0.130525 | + | 0.542232i | ||||
\(448\) | 68.2262 | 0.152291 | ||||||||
\(449\) | 843.006i | 1.87752i | 0.344574 | + | 0.938759i | \(0.388023\pi\) | ||||
−0.344574 | + | 0.938759i | \(0.611977\pi\) | |||||||
\(450\) | −28.9603 | − | 56.6683i | −0.0643562 | − | 0.125930i | ||||
\(451\) | −666.699 | −1.47827 | ||||||||
\(452\) | − | 31.7055i | − | 0.0701450i | ||||||
\(453\) | −495.915 | + | 119.376i | −1.09474 | + | 0.263523i | ||||
\(454\) | −138.176 | −0.304353 | ||||||||
\(455\) | − | 350.369i | − | 0.770042i | ||||||
\(456\) | 26.3107 | + | 109.301i | 0.0576988 | + | 0.239695i | ||||
\(457\) | −209.735 | −0.458938 | −0.229469 | − | 0.973316i | \(-0.573699\pi\) | ||||
−0.229469 | + | 0.973316i | \(0.573699\pi\) | |||||||
\(458\) | 124.516i | 0.271870i | ||||||||
\(459\) | −14.0678 | − | 16.4110i | −0.0306489 | − | 0.0357538i | ||||
\(460\) | 21.4476 | 0.0466252 | ||||||||
\(461\) | 131.916i | 0.286153i | 0.989712 | + | 0.143076i | \(0.0456995\pi\) | ||||
−0.989712 | + | 0.143076i | \(0.954301\pi\) | |||||||
\(462\) | 395.626 | − | 95.2343i | 0.856333 | − | 0.206135i | ||||
\(463\) | −483.695 | −1.04470 | −0.522349 | − | 0.852732i | \(-0.674944\pi\) | ||||
−0.522349 | + | 0.852732i | \(0.674944\pi\) | |||||||
\(464\) | 43.9040i | 0.0946207i | ||||||||
\(465\) | 66.9581 | + | 278.160i | 0.143996 | + | 0.598193i | ||||
\(466\) | −161.023 | −0.345543 | ||||||||
\(467\) | 468.672i | 1.00358i | 0.864989 | + | 0.501790i | \(0.167325\pi\) | ||||
−0.864989 | + | 0.501790i | \(0.832675\pi\) | |||||||
\(468\) | −294.486 | + | 150.497i | −0.629244 | + | 0.321575i | ||||
\(469\) | −467.741 | −0.997316 | ||||||||
\(470\) | − | 208.294i | − | 0.443180i | ||||||
\(471\) | −434.489 | + | 104.589i | −0.922483 | + | 0.222058i | ||||
\(472\) | 154.529 | 0.327391 | ||||||||
\(473\) | − | 120.296i | − | 0.254325i | ||||||
\(474\) | −14.2129 | − | 59.0436i | −0.0299849 | − | 0.124565i | ||||
\(475\) | −66.2458 | −0.139465 | ||||||||
\(476\) | 13.6550i | 0.0286869i | ||||||||
\(477\) | 280.011 | + | 547.915i | 0.587026 | + | 1.14867i | ||||
\(478\) | 125.076 | 0.261666 | ||||||||
\(479\) | 661.943i | 1.38193i | 0.722890 | + | 0.690964i | \(0.242813\pi\) | ||||
−0.722890 | + | 0.690964i | \(0.757187\pi\) | |||||||
\(480\) | 36.8935 | − | 8.88093i | 0.0768614 | − | 0.0185019i | ||||
\(481\) | 787.693 | 1.63762 | ||||||||
\(482\) | − | 421.272i | − | 0.874009i | ||||||
\(483\) | 28.7160 | + | 119.293i | 0.0594534 | + | 0.246983i | ||||
\(484\) | 10.9689 | 0.0226631 | ||||||||
\(485\) | 312.849i | 0.645049i | ||||||||
\(486\) | −317.891 | − | 130.551i | −0.654096 | − | 0.268622i | ||||
\(487\) | −26.7852 | −0.0550003 | −0.0275002 | − | 0.999622i | \(-0.508755\pi\) | ||||
−0.0275002 | + | 0.999622i | \(0.508755\pi\) | |||||||
\(488\) | − | 96.7102i | − | 0.198177i | ||||||
\(489\) | 682.130 | − | 164.201i | 1.39495 | − | 0.335790i | ||||
\(490\) | −75.0458 | −0.153155 | ||||||||
\(491\) | − | 616.828i | − | 1.25627i | −0.778105 | − | 0.628135i | \(-0.783819\pi\) | ||
0.778105 | − | 0.628135i | \(-0.216181\pi\) | |||||||
\(492\) | −83.2415 | − | 345.805i | −0.169190 | − | 0.702855i | ||||
\(493\) | −8.78705 | −0.0178236 | ||||||||
\(494\) | 344.257i | 0.696876i | ||||||||
\(495\) | 201.539 | − | 102.996i | 0.407149 | − | 0.208073i | ||||
\(496\) | −170.600 | −0.343952 | ||||||||
\(497\) | 275.751i | 0.554832i | ||||||||
\(498\) | 173.560 | − | 41.7790i | 0.348514 | − | 0.0838936i | ||||
\(499\) | 985.407 | 1.97476 | 0.987382 | − | 0.158359i | \(-0.0506202\pi\) | ||||
0.987382 | + | 0.158359i | \(0.0506202\pi\) | |||||||
\(500\) | 22.3607i | 0.0447214i | ||||||||
\(501\) | −98.8839 | − | 410.787i | −0.197373 | − | 0.819935i | ||||
\(502\) | 357.209 | 0.711573 | ||||||||
\(503\) | − | 571.158i | − | 1.13550i | −0.823200 | − | 0.567752i | \(-0.807813\pi\) | ||
0.823200 | − | 0.567752i | \(-0.192187\pi\) | |||||||
\(504\) | 98.7926 | + | 193.313i | 0.196017 | + | 0.383558i | ||||
\(505\) | −413.680 | −0.819168 | ||||||||
\(506\) | 76.2777i | 0.150746i | ||||||||
\(507\) | −491.654 | + | 118.350i | −0.969732 | + | 0.233432i | ||||
\(508\) | −403.095 | −0.793495 | ||||||||
\(509\) | − | 885.134i | − | 1.73897i | −0.493962 | − | 0.869484i | \(-0.664452\pi\) | ||
0.493962 | − | 0.869484i | \(-0.335548\pi\) | |||||||
\(510\) | 1.77745 | + | 7.38395i | 0.00348520 | + | 0.0144783i | ||||
\(511\) | 339.248 | 0.663890 | ||||||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | −271.596 | + | 232.818i | −0.529427 | + | 0.453837i | ||||
\(514\) | 153.544 | 0.298724 | ||||||||
\(515\) | − | 367.082i | − | 0.712781i | ||||||
\(516\) | 62.3952 | − | 15.0197i | 0.120921 | − | 0.0291079i | ||||
\(517\) | 740.792 | 1.43287 | ||||||||
\(518\) | − | 517.076i | − | 0.998216i | ||||||
\(519\) | −79.0404 | − | 328.352i | −0.152294 | − | 0.632663i | ||||
\(520\) | 116.201 | 0.223463 | ||||||||
\(521\) | 578.831i | 1.11100i | 0.831516 | + | 0.555500i | \(0.187473\pi\) | ||||
−0.831516 | + | 0.555500i | \(0.812527\pi\) | |||||||
\(522\) | −124.398 | + | 63.5737i | −0.238311 | + | 0.121789i | ||||
\(523\) | −918.390 | −1.75600 | −0.878002 | − | 0.478657i | \(-0.841124\pi\) | ||||
−0.878002 | + | 0.478657i | \(0.841124\pi\) | |||||||
\(524\) | 275.630i | 0.526012i | ||||||||
\(525\) | −124.372 | + | 29.9385i | −0.236898 | + | 0.0570257i | ||||
\(526\) | −581.488 | −1.10549 | ||||||||
\(527\) | − | 34.1443i | − | 0.0647900i | ||||||
\(528\) | 31.5847 | + | 131.210i | 0.0598196 | + | 0.248505i | ||||
\(529\) | −23.0000 | −0.0434783 | ||||||||
\(530\) | − | 216.201i | − | 0.407926i | ||||||
\(531\) | 223.760 | + | 437.844i | 0.421393 | + | 0.824565i | ||||
\(532\) | 225.985 | 0.424784 | ||||||||
\(533\) | − | 1089.16i | − | 2.04345i | ||||||
\(534\) | 318.188 | − | 76.5936i | 0.595857 | − | 0.143434i | ||||
\(535\) | −237.051 | −0.443087 | ||||||||
\(536\) | − | 155.128i | − | 0.289417i | ||||||
\(537\) | 186.377 | + | 774.253i | 0.347070 | + | 1.44181i | ||||
\(538\) | −382.476 | −0.710922 | ||||||||
\(539\) | − | 266.898i | − | 0.495172i | ||||||
\(540\) | 78.5857 | + | 91.6749i | 0.145529 | + | 0.169768i | ||||
\(541\) | 635.953 | 1.17551 | 0.587757 | − | 0.809037i | \(-0.300011\pi\) | ||||
0.587757 | + | 0.809037i | \(0.300011\pi\) | |||||||
\(542\) | − | 196.489i | − | 0.362526i | ||||||
\(543\) | 529.158 | − | 127.378i | 0.974507 | − | 0.234582i | ||||
\(544\) | −4.52870 | −0.00832482 | ||||||||
\(545\) | 131.483i | 0.241254i | ||||||||
\(546\) | 155.580 | + | 646.317i | 0.284945 | + | 1.18373i | ||||
\(547\) | −147.805 | −0.270209 | −0.135105 | − | 0.990831i | \(-0.543137\pi\) | ||||
−0.135105 | + | 0.990831i | \(0.543137\pi\) | |||||||
\(548\) | − | 25.0289i | − | 0.0456733i | ||||||
\(549\) | 274.020 | − | 140.038i | 0.499126 | − | 0.255078i | ||||
\(550\) | −79.5250 | −0.144591 | ||||||||
\(551\) | 145.423i | 0.263925i | ||||||||
\(552\) | −39.5639 | + | 9.52374i | −0.0716736 | + | 0.0172531i | ||||
\(553\) | −122.076 | −0.220752 | ||||||||
\(554\) | − | 90.8239i | − | 0.163942i | ||||||
\(555\) | −67.3072 | − | 279.610i | −0.121274 | − | 0.503801i | ||||
\(556\) | −542.265 | −0.975296 | ||||||||
\(557\) | 301.911i | 0.542031i | 0.962575 | + | 0.271015i | \(0.0873594\pi\) | ||||
−0.962575 | + | 0.271015i | \(0.912641\pi\) | |||||||
\(558\) | −247.032 | − | 483.382i | −0.442709 | − | 0.866276i | ||||
\(559\) | 196.522 | 0.351560 | ||||||||
\(560\) | − | 76.2793i | − | 0.136213i | ||||||
\(561\) | −26.2608 | + | 6.32144i | −0.0468106 | + | 0.0112682i | ||||
\(562\) | −421.723 | −0.750397 | ||||||||
\(563\) | 1059.79i | 1.88240i | 0.337855 | + | 0.941198i | \(0.390299\pi\) | ||||
−0.337855 | + | 0.941198i | \(0.609701\pi\) | |||||||
\(564\) | 92.4924 | + | 384.235i | 0.163994 | + | 0.681268i | ||||
\(565\) | −35.4479 | −0.0627396 | ||||||||
\(566\) | − | 168.118i | − | 0.297028i | ||||||
\(567\) | −404.684 | + | 559.841i | −0.713729 | + | 0.987375i | ||||
\(568\) | −91.4537 | −0.161010 | ||||||||
\(569\) | − | 149.837i | − | 0.263335i | −0.991294 | − | 0.131667i | \(-0.957967\pi\) | ||
0.991294 | − | 0.131667i | \(-0.0420330\pi\) | |||||||
\(570\) | 122.202 | − | 29.4162i | 0.214389 | − | 0.0516074i | ||||
\(571\) | 1037.30 | 1.81665 | 0.908323 | − | 0.418271i | \(-0.137364\pi\) | ||||
0.908323 | + | 0.418271i | \(0.137364\pi\) | |||||||
\(572\) | 413.264i | 0.722490i | ||||||||
\(573\) | −135.262 | − | 561.912i | −0.236060 | − | 0.980649i | ||||
\(574\) | −714.970 | −1.24559 | ||||||||
\(575\) | − | 23.9792i | − | 0.0417029i | ||||||
\(576\) | −64.1129 | + | 32.7648i | −0.111307 | + | 0.0568834i | ||||
\(577\) | 580.551 | 1.00615 | 0.503077 | − | 0.864242i | \(-0.332201\pi\) | ||||
0.503077 | + | 0.864242i | \(0.332201\pi\) | |||||||
\(578\) | 407.801i | 0.705539i | ||||||||
\(579\) | −596.626 | + | 143.619i | −1.03044 | + | 0.248046i | ||||
\(580\) | 49.0862 | 0.0846314 | ||||||||
\(581\) | − | 358.844i | − | 0.617632i | ||||||
\(582\) | −138.919 | − | 577.104i | −0.238693 | − | 0.991588i | ||||
\(583\) | 768.911 | 1.31889 | ||||||||
\(584\) | 112.512i | 0.192658i | ||||||||
\(585\) | 168.261 | + | 329.245i | 0.287625 | + | 0.562813i | ||||
\(586\) | 479.305 | 0.817926 | ||||||||
\(587\) | 1007.65i | 1.71662i | 0.513136 | + | 0.858308i | \(0.328484\pi\) | ||||
−0.513136 | + | 0.858308i | \(0.671516\pi\) | |||||||
\(588\) | 138.435 | − | 33.3238i | 0.235434 | − | 0.0566732i | ||||
\(589\) | −565.078 | −0.959385 | ||||||||
\(590\) | − | 172.768i | − | 0.292827i | ||||||
\(591\) | −29.2820 | − | 121.644i | −0.0495466 | − | 0.205828i | ||||
\(592\) | 171.490 | 0.289678 | ||||||||
\(593\) | − | 181.266i | − | 0.305677i | −0.988251 | − | 0.152838i | \(-0.951159\pi\) | ||
0.988251 | − | 0.152838i | \(-0.0488414\pi\) | |||||||
\(594\) | −326.039 | + | 279.487i | −0.548887 | + | 0.470517i | ||||
\(595\) | 15.2667 | 0.0256583 | ||||||||
\(596\) | 166.201i | 0.278861i | ||||||||
\(597\) | 22.4371 | − | 5.40101i | 0.0375831 | − | 0.00904693i | ||||
\(598\) | −124.612 | −0.208381 | ||||||||
\(599\) | 75.2652i | 0.125651i | 0.998025 | + | 0.0628257i | \(0.0200112\pi\) | ||||
−0.998025 | + | 0.0628257i | \(0.979989\pi\) | |||||||
\(600\) | −9.92918 | − | 41.2482i | −0.0165486 | − | 0.0687469i | ||||
\(601\) | −206.231 | −0.343146 | −0.171573 | − | 0.985171i | \(-0.554885\pi\) | ||||
−0.171573 | + | 0.985171i | \(0.554885\pi\) | |||||||
\(602\) | − | 129.006i | − | 0.214295i | ||||||
\(603\) | 439.541 | − | 224.627i | 0.728924 | − | 0.372516i | ||||
\(604\) | −340.054 | −0.563003 | ||||||||
\(605\) | − | 12.2637i | − | 0.0202705i | ||||||
\(606\) | 763.104 | − | 183.693i | 1.25925 | − | 0.303124i | ||||
\(607\) | 649.464 | 1.06996 | 0.534978 | − | 0.844866i | \(-0.320320\pi\) | ||||
0.534978 | + | 0.844866i | \(0.320320\pi\) | |||||||
\(608\) | 74.9486i | 0.123271i | ||||||||
\(609\) | 65.7210 | + | 273.021i | 0.107916 | + | 0.448310i | ||||
\(610\) | −108.125 | −0.177255 | ||||||||
\(611\) | 1210.20i | 1.98069i | ||||||||
\(612\) | −6.55763 | − | 12.8317i | −0.0107151 | − | 0.0209668i | ||||
\(613\) | 230.058 | 0.375299 | 0.187650 | − | 0.982236i | \(-0.439913\pi\) | ||||
0.187650 | + | 0.982236i | \(0.439913\pi\) | |||||||
\(614\) | 274.410i | 0.446921i | ||||||||
\(615\) | −386.622 | + | 93.0668i | −0.628653 | + | 0.151328i | ||||
\(616\) | 271.285 | 0.440397 | ||||||||
\(617\) | − | 486.305i | − | 0.788176i | −0.919073 | − | 0.394088i | \(-0.871060\pi\) | ||
0.919073 | − | 0.394088i | \(-0.128940\pi\) | |||||||
\(618\) | 163.002 | + | 677.147i | 0.263757 | + | 1.09571i | ||||
\(619\) | −176.546 | −0.285211 | −0.142605 | − | 0.989780i | \(-0.545548\pi\) | ||||
−0.142605 | + | 0.989780i | \(0.545548\pi\) | |||||||
\(620\) | 190.737i | 0.307640i | ||||||||
\(621\) | −84.2738 | − | 98.3104i | −0.135707 | − | 0.158310i | ||||
\(622\) | 205.829 | 0.330915 | ||||||||
\(623\) | − | 657.870i | − | 1.05597i | ||||||
\(624\) | −214.353 | + | 51.5986i | −0.343514 | + | 0.0826900i | ||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | − | 131.999i | − | 0.210861i | ||||||
\(627\) | 104.618 | + | 434.607i | 0.166855 | + | 0.693153i | ||||
\(628\) | −297.934 | −0.474417 | ||||||||
\(629\) | 34.3223i | 0.0545665i | ||||||||
\(630\) | 216.131 | − | 110.454i | 0.343065 | − | 0.175323i | ||||
\(631\) | −594.149 | −0.941599 | −0.470800 | − | 0.882240i | \(-0.656035\pi\) | ||||
−0.470800 | + | 0.882240i | \(0.656035\pi\) | |||||||
\(632\) | − | 40.4868i | − | 0.0640613i | ||||||
\(633\) | −1015.97 | + | 244.563i | −1.60501 | + | 0.386355i | ||||
\(634\) | 399.070 | 0.629448 | ||||||||
\(635\) | 450.674i | 0.709724i | ||||||||
\(636\) | 96.0033 | + | 398.820i | 0.150949 | + | 0.627076i | ||||
\(637\) | 436.019 | 0.684488 | ||||||||
\(638\) | 174.573i | 0.273626i | ||||||||
\(639\) | −132.426 | − | 259.126i | −0.207240 | − | 0.405519i | ||||
\(640\) | 25.2982 | 0.0395285 | ||||||||
\(641\) | − | 457.503i | − | 0.713734i | −0.934155 | − | 0.356867i | \(-0.883845\pi\) | ||
0.934155 | − | 0.356867i | \(-0.116155\pi\) | |||||||
\(642\) | 437.282 | − | 105.262i | 0.681125 | − | 0.163959i | ||||
\(643\) | −713.769 | −1.11006 | −0.555030 | − | 0.831830i | \(-0.687293\pi\) | ||||
−0.555030 | + | 0.831830i | \(0.687293\pi\) | |||||||
\(644\) | 81.8004i | 0.127019i | ||||||||
\(645\) | −16.7925 | − | 69.7600i | −0.0260349 | − | 0.108155i | ||||
\(646\) | −15.0004 | −0.0232204 | ||||||||
\(647\) | 784.509i | 1.21253i | 0.795261 | + | 0.606267i | \(0.207334\pi\) | ||||
−0.795261 | + | 0.606267i | \(0.792666\pi\) | |||||||
\(648\) | −185.673 | − | 134.215i | −0.286532 | − | 0.207121i | ||||
\(649\) | 614.444 | 0.946755 | ||||||||
\(650\) | − | 129.917i | − | 0.199872i | ||||||
\(651\) | −1060.89 | + | 255.376i | −1.62963 | + | 0.392282i | ||||
\(652\) | 467.743 | 0.717398 | ||||||||
\(653\) | 400.746i | 0.613700i | 0.951758 | + | 0.306850i | \(0.0992750\pi\) | ||||
−0.951758 | + | 0.306850i | \(0.900725\pi\) | |||||||
\(654\) | −58.3847 | − | 242.544i | −0.0892732 | − | 0.370862i | ||||
\(655\) | 308.164 | 0.470479 | ||||||||
\(656\) | − | 237.122i | − | 0.361466i | ||||||
\(657\) | −318.795 | + | 162.920i | −0.485228 | + | 0.247975i | ||||
\(658\) | 794.427 | 1.20734 | ||||||||
\(659\) | − | 1057.28i | − | 1.60437i | −0.597073 | − | 0.802187i | \(-0.703670\pi\) | ||
0.597073 | − | 0.802187i | \(-0.296330\pi\) | |||||||
\(660\) | 146.698 | − | 35.3128i | 0.222269 | − | 0.0535042i | ||||
\(661\) | −266.071 | −0.402528 | −0.201264 | − | 0.979537i | \(-0.564505\pi\) | ||||
−0.201264 | + | 0.979537i | \(0.564505\pi\) | |||||||
\(662\) | − | 543.576i | − | 0.821111i | ||||||
\(663\) | −10.3271 | − | 42.9010i | −0.0155763 | − | 0.0647075i | ||||
\(664\) | 119.012 | 0.179234 | ||||||||
\(665\) | − | 252.659i | − | 0.379938i | ||||||
\(666\) | 248.320 | + | 485.901i | 0.372852 | + | 0.729582i | ||||
\(667\) | −52.6391 | −0.0789192 | ||||||||
\(668\) | − | 281.681i | − | 0.421678i | ||||||
\(669\) | −1199.43 | + | 288.725i | −1.79287 | + | 0.431577i | ||||
\(670\) | −173.438 | −0.258863 | ||||||||
\(671\) | − | 384.544i | − | 0.573091i | ||||||
\(672\) | 33.8715 | + | 140.710i | 0.0504041 | + | 0.209390i | ||||
\(673\) | −10.7379 | −0.0159552 | −0.00797761 | − | 0.999968i | \(-0.502539\pi\) | ||||
−0.00797761 | + | 0.999968i | \(0.502539\pi\) | |||||||
\(674\) | − | 378.391i | − | 0.561410i | ||||||
\(675\) | 102.496 | − | 87.8615i | 0.151845 | − | 0.130165i | ||||
\(676\) | −337.132 | −0.498716 | ||||||||
\(677\) | − | 245.177i | − | 0.362152i | −0.983469 | − | 0.181076i | \(-0.942042\pi\) | ||
0.983469 | − | 0.181076i | \(-0.0579581\pi\) | |||||||
\(678\) | 65.3898 | − | 15.7405i | 0.0964451 | − | 0.0232161i | ||||
\(679\) | −1193.19 | −1.75728 | ||||||||
\(680\) | 5.06324i | 0.00744595i | ||||||||
\(681\) | −68.5990 | − | 284.976i | −0.100733 | − | 0.418467i | ||||
\(682\) | −678.349 | −0.994647 | ||||||||
\(683\) | − | 965.369i | − | 1.41342i | −0.707501 | − | 0.706712i | \(-0.750178\pi\) | ||
0.707501 | − | 0.706712i | \(-0.249822\pi\) | |||||||
\(684\) | −212.361 | + | 108.527i | −0.310469 | + | 0.158665i | ||||
\(685\) | −27.9832 | −0.0408514 | ||||||||
\(686\) | 304.758i | 0.444253i | ||||||||
\(687\) | −256.803 | + | 61.8172i | −0.373804 | + | 0.0899814i | ||||
\(688\) | 42.7850 | 0.0621875 | ||||||||
\(689\) | 1256.14i | 1.82313i | ||||||||
\(690\) | 10.6479 | + | 44.2337i | 0.0154317 | + | 0.0641069i | ||||
\(691\) | −143.140 | −0.207148 | −0.103574 | − | 0.994622i | \(-0.533028\pi\) | ||||
−0.103574 | + | 0.994622i | \(0.533028\pi\) | |||||||
\(692\) | − | 225.154i | − | 0.325368i | ||||||
\(693\) | 392.824 | + | 768.662i | 0.566846 | + | 1.10918i | ||||
\(694\) | 732.668 | 1.05572 | ||||||||
\(695\) | 606.270i | 0.872332i | ||||||||
\(696\) | −90.5480 | + | 21.7966i | −0.130098 | + | 0.0313169i | ||||
\(697\) | 47.4581 | 0.0680891 | ||||||||
\(698\) | − | 530.504i | − | 0.760034i | ||||||
\(699\) | −79.9413 | − | 332.095i | −0.114365 | − | 0.475100i | ||||
\(700\) | −85.2828 | −0.121833 | ||||||||
\(701\) | − | 880.642i | − | 1.25627i | −0.778106 | − | 0.628133i | \(-0.783819\pi\) | ||
0.778106 | − | 0.628133i | \(-0.216181\pi\) | |||||||
\(702\) | −456.586 | − | 532.635i | −0.650408 | − | 0.758739i | ||||
\(703\) | 568.023 | 0.807999 | ||||||||
\(704\) | 89.9723i | 0.127801i | ||||||||
\(705\) | 429.588 | − | 103.410i | 0.609345 | − | 0.146680i | ||||
\(706\) | 143.760 | 0.203626 | ||||||||
\(707\) | − | 1577.76i | − | 2.23163i | ||||||
\(708\) | 76.7171 | + | 318.701i | 0.108357 | + | 0.450143i | ||||
\(709\) | 384.075 | 0.541713 | 0.270857 | − | 0.962620i | \(-0.412693\pi\) | ||||
0.270857 | + | 0.962620i | \(0.412693\pi\) | |||||||
\(710\) | 102.248i | 0.144012i | ||||||||
\(711\) | 114.716 | − | 58.6255i | 0.161344 | − | 0.0824549i | ||||
\(712\) | 218.184 | 0.306439 | ||||||||
\(713\) | − | 204.543i | − | 0.286876i | ||||||
\(714\) | −28.1621 | + | 6.77913i | −0.0394427 | + | 0.00949458i | ||||
\(715\) | 462.044 | 0.646215 | ||||||||
\(716\) | 530.913i | 0.741499i | ||||||||
\(717\) | 62.0952 | + | 257.958i | 0.0866042 | + | 0.359774i | ||||
\(718\) | 209.183 | 0.291342 | ||||||||
\(719\) | − | 366.200i | − | 0.509318i | −0.967031 | − | 0.254659i | \(-0.918037\pi\) | ||
0.967031 | − | 0.254659i | \(-0.0819632\pi\) | |||||||
\(720\) | 36.6322 | + | 71.6804i | 0.0508781 | + | 0.0995561i | ||||
\(721\) | 1400.04 | 1.94180 | ||||||||
\(722\) | − | 262.280i | − | 0.363268i | ||||||
\(723\) | 868.835 | − | 209.144i | 1.20171 | − | 0.289273i | ||||
\(724\) | 362.848 | 0.501172 | ||||||||
\(725\) | − | 54.8800i | − | 0.0756966i | ||||||
\(726\) | 5.44563 | + | 22.6224i | 0.00750087 | + | 0.0311604i | ||||
\(727\) | 46.5086 | 0.0639733 | 0.0319867 | − | 0.999488i | \(-0.489817\pi\) | ||||
0.0319867 | + | 0.999488i | \(0.489817\pi\) | |||||||
\(728\) | 443.186i | 0.608772i | ||||||||
\(729\) | 111.429 | − | 720.434i | 0.152851 | − | 0.988249i | ||||
\(730\) | 125.793 | 0.172319 | ||||||||
\(731\) | 8.56309i | 0.0117142i | ||||||||
\(732\) | 199.456 | − | 48.0126i | 0.272481 | − | 0.0655910i | ||||
\(733\) | −1189.43 | −1.62269 | −0.811344 | − | 0.584569i | \(-0.801264\pi\) | ||||
−0.811344 | + | 0.584569i | \(0.801264\pi\) | |||||||
\(734\) | − | 563.933i | − | 0.768301i | ||||||
\(735\) | −37.2572 | − | 154.775i | −0.0506900 | − | 0.210578i | ||||
\(736\) | −27.1293 | −0.0368605 | ||||||||
\(737\) | − | 616.826i | − | 0.836942i | ||||||
\(738\) | 671.865 | − | 343.356i | 0.910386 | − | 0.465252i | ||||
\(739\) | 91.0727 | 0.123238 | 0.0616189 | − | 0.998100i | \(-0.480374\pi\) | ||||
0.0616189 | + | 0.998100i | \(0.480374\pi\) | |||||||
\(740\) | − | 191.731i | − | 0.259096i | ||||||
\(741\) | −709.998 | + | 170.910i | −0.958163 | + | 0.230647i | ||||
\(742\) | 824.582 | 1.11130 | ||||||||
\(743\) | − | 1075.51i | − | 1.44753i | −0.690048 | − | 0.723764i | \(-0.742411\pi\) | ||
0.690048 | − | 0.723764i | \(-0.257589\pi\) | |||||||
\(744\) | −84.6961 | − | 351.848i | −0.113839 | − | 0.472913i | ||||
\(745\) | 185.818 | 0.249420 | ||||||||
\(746\) | 494.659i | 0.663081i | ||||||||
\(747\) | 172.331 | + | 337.210i | 0.230697 | + | 0.451419i | ||||
\(748\) | −18.0073 | −0.0240739 | ||||||||
\(749\) | − | 904.105i | − | 1.20708i | ||||||
\(750\) | −46.1169 | + | 11.1012i | −0.0614891 | + | 0.0148016i | ||||
\(751\) | 848.304 | 1.12957 | 0.564783 | − | 0.825240i | \(-0.308960\pi\) | ||||
0.564783 | + | 0.825240i | \(0.308960\pi\) | |||||||
\(752\) | 263.474i | 0.350364i | ||||||||
\(753\) | 177.340 | + | 736.712i | 0.235511 | + | 0.978369i | ||||
\(754\) | −285.193 | −0.378240 | ||||||||
\(755\) | 380.192i | 0.503566i | ||||||||
\(756\) | −349.645 | + | 299.723i | −0.462493 | + | 0.396459i | ||||
\(757\) | 244.126 | 0.322491 | 0.161245 | − | 0.986914i | \(-0.448449\pi\) | ||||
0.161245 | + | 0.986914i | \(0.448449\pi\) | |||||||
\(758\) | − | 804.318i | − | 1.06111i | ||||||
\(759\) | −157.316 | + | 37.8688i | −0.207267 | + | 0.0498930i | ||||
\(760\) | 83.7951 | 0.110257 | ||||||||
\(761\) | 926.253i | 1.21715i | 0.793495 | + | 0.608576i | \(0.208259\pi\) | ||||
−0.793495 | + | 0.608576i | \(0.791741\pi\) | |||||||
\(762\) | −200.120 | − | 831.348i | −0.262625 | − | 1.09101i | ||||
\(763\) | −501.472 | −0.657237 | ||||||||
\(764\) | − | 385.309i | − | 0.504331i | ||||||
\(765\) | −14.3463 | + | 7.33165i | −0.0187533 | + | 0.00958386i | ||||
\(766\) | −164.547 | −0.214813 | ||||||||
\(767\) | 1003.79i | 1.30872i | ||||||||
\(768\) | −46.6670 | + | 11.2336i | −0.0607643 | + | 0.0146271i | ||||
\(769\) | 39.9471 | 0.0519468 | 0.0259734 | − | 0.999663i | \(-0.491731\pi\) | ||||
0.0259734 | + | 0.999663i | \(0.491731\pi\) | |||||||
\(770\) | − | 303.305i | − | 0.393903i | ||||||
\(771\) | 76.2284 | + | 316.671i | 0.0988696 | + | 0.410728i | ||||
\(772\) | −409.112 | −0.529938 | ||||||||
\(773\) | − | 697.995i | − | 0.902969i | −0.892279 | − | 0.451485i | \(-0.850895\pi\) | ||
0.892279 | − | 0.451485i | \(-0.149105\pi\) | |||||||
\(774\) | 61.9534 | + | 121.228i | 0.0800431 | + | 0.156625i | ||||
\(775\) | 213.250 | 0.275162 | ||||||||
\(776\) | − | 395.726i | − | 0.509956i | ||||||
\(777\) | 1066.42 | − | 256.707i | 1.37249 | − | 0.330382i | ||||
\(778\) | −1016.65 | −1.30675 | ||||||||
\(779\) | − | 785.416i | − | 1.00824i | ||||||
\(780\) | 57.6890 | + | 239.654i | 0.0739602 | + | 0.307248i | ||||
\(781\) | −363.643 | −0.465612 | ||||||||
\(782\) | − | 5.42972i | − | 0.00694338i | ||||||
\(783\) | −192.874 | − | 224.999i | −0.246327 | − | 0.287355i | ||||
\(784\) | 94.9262 | 0.121079 | ||||||||
\(785\) | 333.100i | 0.424331i | ||||||||
\(786\) | −568.462 | + | 136.839i | −0.723234 | + | 0.174096i | ||||
\(787\) | 831.189 | 1.05615 | 0.528075 | − | 0.849198i | \(-0.322914\pi\) | ||||
0.528075 | + | 0.849198i | \(0.322914\pi\) | |||||||
\(788\) | − | 83.4128i | − | 0.105854i | ||||||
\(789\) | −288.685 | − | 1199.27i | −0.365887 | − | 1.51998i | ||||
\(790\) | −45.2656 | −0.0572982 | ||||||||
\(791\) | − | 135.197i | − | 0.170919i | ||||||
\(792\) | −254.929 | + | 130.281i | −0.321880 | + | 0.164496i | ||||
\(793\) | 628.212 | 0.792197 | ||||||||
\(794\) | − | 264.979i | − | 0.333727i | ||||||
\(795\) | 445.895 | − | 107.335i | 0.560874 | − | 0.135012i | ||||
\(796\) | 15.3853 | 0.0193283 | ||||||||
\(797\) | − | 797.786i | − | 1.00099i | −0.865740 | − | 0.500493i | \(-0.833152\pi\) | ||
0.865740 | − | 0.500493i | \(-0.166848\pi\) | |||||||
\(798\) | 112.192 | + | 466.074i | 0.140592 | + | 0.584052i | ||||
\(799\) | −52.7323 | −0.0659978 | ||||||||
\(800\) | − | 28.2843i | − | 0.0353553i | ||||||
\(801\) | 315.934 | + | 618.208i | 0.394425 | + | 0.771795i | ||||
\(802\) | 135.617 | 0.169098 | ||||||||
\(803\) | 447.378i | 0.557133i | ||||||||
\(804\) | 319.936 | − | 77.0145i | 0.397931 | − | 0.0957892i | ||||
\(805\) | 91.4556 | 0.113609 | ||||||||
\(806\) | − | 1108.19i | − | 1.37493i | ||||||
\(807\) | −189.884 | − | 788.822i | −0.235296 | − | 0.977475i | ||||
\(808\) | 523.268 | 0.647609 | ||||||||
\(809\) | − | 518.102i | − | 0.640423i | −0.947346 | − | 0.320211i | \(-0.896246\pi\) | ||
0.947346 | − | 0.320211i | \(-0.103754\pi\) | |||||||
\(810\) | −150.056 | + | 207.589i | −0.185255 | + | 0.256282i | ||||
\(811\) | 465.165 | 0.573570 | 0.286785 | − | 0.957995i | \(-0.407413\pi\) | ||||
0.286785 | + | 0.957995i | \(0.407413\pi\) | |||||||
\(812\) | 187.213i | 0.230558i | ||||||||
\(813\) | 405.241 | − | 97.5488i | 0.498451 | − | 0.119986i | ||||
\(814\) | 681.885 | 0.837697 | ||||||||
\(815\) | − | 522.953i | − | 0.641660i | ||||||
\(816\) | −2.24832 | − | 9.34004i | −0.00275529 | − | 0.0114461i | ||||
\(817\) | 141.716 | 0.173460 | ||||||||
\(818\) | 959.209i | 1.17263i | ||||||||
\(819\) | −1255.73 | + | 641.740i | −1.53325 | + | 0.783565i | ||||
\(820\) | −265.110 | −0.323305 | ||||||||
\(821\) | − | 539.166i | − | 0.656718i | −0.944553 | − | 0.328359i | \(-0.893504\pi\) | ||
0.944553 | − | 0.328359i | \(-0.106496\pi\) | |||||||
\(822\) | 51.6199 | − | 12.4258i | 0.0627979 | − | 0.0151166i | ||||
\(823\) | 253.501 | 0.308021 | 0.154010 | − | 0.988069i | \(-0.450781\pi\) | ||||
0.154010 | + | 0.988069i | \(0.450781\pi\) | |||||||
\(824\) | 464.326i | 0.563503i | ||||||||
\(825\) | −39.4809 | − | 164.013i | −0.0478556 | − | 0.198804i | ||||
\(826\) | 658.931 | 0.797738 | ||||||||
\(827\) | 478.558i | 0.578668i | 0.957228 | + | 0.289334i | \(0.0934338\pi\) | ||||
−0.957228 | + | 0.289334i | \(0.906566\pi\) | |||||||
\(828\) | −39.2837 | − | 76.8687i | −0.0474440 | − | 0.0928366i | ||||
\(829\) | −671.600 | −0.810133 | −0.405067 | − | 0.914287i | \(-0.632752\pi\) | ||||
−0.405067 | + | 0.914287i | \(0.632752\pi\) | |||||||
\(830\) | − | 133.059i | − | 0.160312i | ||||||
\(831\) | 187.316 | − | 45.0904i | 0.225410 | − | 0.0542604i | ||||
\(832\) | −146.984 | −0.176663 | ||||||||
\(833\) | 18.9988i | 0.0228076i | ||||||||
\(834\) | −269.212 | − | 1118.37i | −0.322797 | − | 1.34097i | ||||
\(835\) | −314.929 | −0.377160 | ||||||||
\(836\) | 298.014i | 0.356476i | ||||||||
\(837\) | 874.290 | − | 749.460i | 1.04455 | − | 0.895412i | ||||
\(838\) | −210.816 | −0.251570 | ||||||||
\(839\) | 1490.36i | 1.77636i | 0.459498 | + | 0.888179i | \(0.348030\pi\) | ||||
−0.459498 | + | 0.888179i | \(0.651970\pi\) | |||||||
\(840\) | 157.319 | − | 37.8695i | 0.187284 | − | 0.0450828i | ||||
\(841\) | 720.527 | 0.856751 | ||||||||
\(842\) | − | 86.6471i | − | 0.102906i | ||||||
\(843\) | −209.368 | − | 869.765i | −0.248361 | − | 1.03175i | ||||
\(844\) | −696.662 | −0.825429 | ||||||||
\(845\) | 376.925i | 0.446065i | ||||||||
\(846\) | −746.531 | + | 381.514i | −0.882425 | + | 0.450962i | ||||
\(847\) | 46.7731 | 0.0552221 | ||||||||
\(848\) | 273.475i | 0.322494i | ||||||||
\(849\) | 346.728 | − | 83.4637i | 0.408396 | − | 0.0983082i | ||||
\(850\) | 5.66088 | 0.00665986 | ||||||||
\(851\) | 205.609i | 0.241608i | ||||||||
\(852\) | −45.4030 | − | 188.615i | −0.0532899 | − | 0.221379i | ||||
\(853\) | 222.549 | 0.260901 | 0.130451 | − | 0.991455i | \(-0.458358\pi\) | ||||
0.130451 | + | 0.991455i | \(0.458358\pi\) | |||||||
\(854\) | − | 412.386i | − | 0.482887i | ||||||
\(855\) | 121.337 | + | 237.426i | 0.141914 | + | 0.277692i | ||||
\(856\) | 299.849 | 0.350291 | ||||||||
\(857\) | − | 1415.07i | − | 1.65119i | −0.564267 | − | 0.825593i | \(-0.690841\pi\) | ||
0.564267 | − | 0.825593i | \(-0.309159\pi\) | |||||||
\(858\) | −852.320 | + | 205.169i | −0.993380 | + | 0.239125i | ||||
\(859\) | 954.539 | 1.11122 | 0.555610 | − | 0.831443i | \(-0.312485\pi\) | ||||
0.555610 | + | 0.831443i | \(0.312485\pi\) | |||||||
\(860\) | − | 47.8351i | − | 0.0556222i | ||||||
\(861\) | −354.953 | − | 1474.56i | −0.412257 | − | 1.71261i | ||||
\(862\) | −460.650 | −0.534397 | ||||||||
\(863\) | − | 1414.59i | − | 1.63915i | −0.572969 | − | 0.819577i | \(-0.694208\pi\) | ||
0.572969 | − | 0.819577i | \(-0.305792\pi\) | |||||||
\(864\) | −99.4039 | − | 115.961i | −0.115051 | − | 0.134214i | ||||
\(865\) | −251.730 | −0.291018 | ||||||||
\(866\) | 575.113i | 0.664103i | ||||||||
\(867\) | −841.053 | + | 202.457i | −0.970073 | + | 0.233514i | ||||
\(868\) | −727.464 | −0.838092 | ||||||||
\(869\) | − | 160.985i | − | 0.185254i | ||||||
\(870\) | 24.3693 | + | 101.236i | 0.0280107 | + | 0.116363i | ||||
\(871\) | 1007.68 | 1.15693 | ||||||||
\(872\) | − | 166.315i | − | 0.190728i | ||||||
\(873\) | 1121.26 | − | 573.017i | 1.28437 | − | 0.656377i | ||||
\(874\) | −89.8602 | −0.102815 | ||||||||
\(875\) | 95.3491i | 0.108970i | ||||||||
\(876\) | −232.047 | + | 55.8579i | −0.264894 | + | 0.0637647i | ||||
\(877\) | −1052.66 | −1.20029 | −0.600147 | − | 0.799889i | \(-0.704891\pi\) | ||||
−0.600147 | + | 0.799889i | \(0.704891\pi\) | |||||||
\(878\) | 824.786i | 0.939392i | ||||||||
\(879\) | 237.955 | + | 988.522i | 0.270711 | + | 1.12460i | ||||
\(880\) | 100.592 | 0.114309 | ||||||||
\(881\) | 279.941i | 0.317754i | 0.987298 | + | 0.158877i | \(0.0507873\pi\) | ||||
−0.987298 | + | 0.158877i | \(0.949213\pi\) | |||||||
\(882\) | 137.455 | + | 268.966i | 0.155844 | + | 0.304950i | ||||
\(883\) | 545.266 | 0.617515 | 0.308758 | − | 0.951141i | \(-0.400087\pi\) | ||||
0.308758 | + | 0.951141i | \(0.400087\pi\) | |||||||
\(884\) | − | 29.4177i | − | 0.0332779i | ||||||
\(885\) | 356.319 | − | 85.7723i | 0.402620 | − | 0.0969179i | ||||
\(886\) | 288.095 | 0.325163 | ||||||||
\(887\) | 1247.29i | 1.40619i | 0.711098 | + | 0.703093i | \(0.248198\pi\) | ||||
−0.711098 | + | 0.703093i | \(0.751802\pi\) | |||||||
\(888\) | 85.1376 | + | 353.682i | 0.0958756 | + | 0.398290i | ||||
\(889\) | −1718.86 | −1.93347 | ||||||||
\(890\) | − | 243.938i | − | 0.274087i | ||||||
\(891\) | −738.282 | − | 533.671i | −0.828599 | − | 0.598957i | ||||
\(892\) | −822.463 | −0.922044 | ||||||||
\(893\) | 872.702i | 0.977270i | ||||||||
\(894\) | −342.774 | + | 82.5119i | −0.383416 | + | 0.0922952i | ||||
\(895\) | 593.579 | 0.663216 | ||||||||
\(896\) | 96.4865i | 0.107686i | ||||||||
\(897\) | −61.8645 | − | 257.000i | −0.0689683 | − | 0.286510i | ||||
\(898\) | −1192.19 | −1.32761 | ||||||||
\(899\) | − | 468.128i | − | 0.520720i | ||||||
\(900\) | 80.1411 | − | 40.9561i | 0.0890457 | − | 0.0455067i | ||||
\(901\) | −54.7339 | −0.0607479 | ||||||||
\(902\) | − | 942.855i | − | 1.04529i | ||||||
\(903\) | 266.062 | − | 64.0460i | 0.294642 | − | 0.0709258i | ||||
\(904\) | 44.8384 | 0.0496000 | ||||||||
\(905\) | − | 405.677i | − | 0.448262i | ||||||
\(906\) | −168.823 | − | 701.330i | −0.186339 | − | 0.774095i | ||||
\(907\) | −1507.05 | −1.66158 | −0.830789 | − | 0.556588i | \(-0.812110\pi\) | ||||
−0.830789 | + | 0.556588i | \(0.812110\pi\) | |||||||
\(908\) | − | 195.411i | − | 0.215210i | ||||||
\(909\) | 757.700 | + | 1482.64i | 0.833554 | + | 1.63106i | ||||
\(910\) | 495.497 | 0.544502 | ||||||||
\(911\) | − | 1565.44i | − | 1.71838i | −0.511656 | − | 0.859190i | \(-0.670968\pi\) | ||
0.511656 | − | 0.859190i | \(-0.329032\pi\) | |||||||
\(912\) | −154.575 | + | 37.2089i | −0.169490 | + | 0.0407992i | ||||
\(913\) | 473.220 | 0.518313 | ||||||||
\(914\) | − | 296.610i | − | 0.324518i | ||||||
\(915\) | −53.6798 | − | 222.998i | −0.0586664 | − | 0.243714i | ||||
\(916\) | −176.093 | −0.192241 | ||||||||
\(917\) | 1175.33i | 1.28171i | ||||||||
\(918\) | 23.2086 | − | 19.8949i | 0.0252817 | − | 0.0216720i | ||||
\(919\) | −250.103 | −0.272147 | −0.136073 | − | 0.990699i | \(-0.543448\pi\) | ||||
−0.136073 | + | 0.990699i | \(0.543448\pi\) | |||||||
\(920\) | 30.3315i | 0.0329690i | ||||||||
\(921\) | −565.945 | + | 136.233i | −0.614489 | + | 0.147919i | ||||
\(922\) | −186.558 | −0.202341 | ||||||||
\(923\) | − | 594.067i | − | 0.643626i | ||||||
\(924\) | 134.682 | + | 559.500i | 0.145759 | + | 0.605519i | ||||
\(925\) | −214.362 | −0.231743 | ||||||||
\(926\) | − | 684.049i | − | 0.738713i | ||||||
\(927\) | −1315.63 | + | 672.352i | −1.41923 | + | 0.725299i | ||||
\(928\) | −62.0897 | −0.0669070 | ||||||||
\(929\) | − | 1690.98i | − | 1.82021i | −0.414375 | − | 0.910106i | \(-0.636000\pi\) | ||
0.414375 | − | 0.910106i | \(-0.364000\pi\) | |||||||
\(930\) | −393.378 | + | 94.6931i | −0.422987 | + | 0.101821i | ||||
\(931\) | 314.423 | 0.337726 | ||||||||
\(932\) | − | 227.721i | − | 0.244336i | ||||||
\(933\) | 102.186 | + | 424.504i | 0.109524 | + | 0.454988i | ||||
\(934\) | −662.802 | −0.709638 | ||||||||
\(935\) | 20.1327i | 0.0215323i | ||||||||
\(936\) | −212.835 | − | 416.466i | −0.227388 | − | 0.444943i | ||||
\(937\) | −554.337 | −0.591608 | −0.295804 | − | 0.955249i | \(-0.595588\pi\) | ||||
−0.295804 | + | 0.955249i | \(0.595588\pi\) | |||||||
\(938\) | − | 661.486i | − | 0.705209i | ||||||
\(939\) | 272.235 | − | 65.5320i | 0.289921 | − | 0.0697891i | ||||
\(940\) | 294.573 | 0.313375 | ||||||||
\(941\) | − | 1116.35i | − | 1.18634i | −0.805077 | − | 0.593171i | \(-0.797876\pi\) | ||
0.805077 | − | 0.593171i | \(-0.202124\pi\) | |||||||
\(942\) | −147.912 | − | 614.461i | −0.157019 | − | 0.652294i | ||||
\(943\) | 284.299 | 0.301484 | ||||||||
\(944\) | 218.536i | 0.231500i | ||||||||
\(945\) | 335.100 | + | 390.915i | 0.354604 | + | 0.413666i | ||||
\(946\) | 170.124 | 0.179835 | ||||||||
\(947\) | − | 347.859i | − | 0.367328i | −0.982989 | − | 0.183664i | \(-0.941204\pi\) | ||
0.982989 | − | 0.183664i | \(-0.0587958\pi\) | |||||||
\(948\) | 83.5002 | − | 20.1000i | 0.0880804 | − | 0.0212026i | ||||
\(949\) | −730.862 | −0.770139 | ||||||||
\(950\) | − | 93.6857i | − | 0.0986166i | ||||||
\(951\) | 198.122 | + | 823.046i | 0.208330 | + | 0.865453i | ||||
\(952\) | −19.3110 | −0.0202847 | ||||||||
\(953\) | − | 321.261i | − | 0.337105i | −0.985693 | − | 0.168552i | \(-0.946091\pi\) | ||
0.985693 | − | 0.168552i | \(-0.0539092\pi\) | |||||||
\(954\) | −774.868 | + | 395.996i | −0.812231 | + | 0.415090i | ||||
\(955\) | −430.788 | −0.451087 | ||||||||
\(956\) | 176.884i | 0.185026i | ||||||||
\(957\) | −360.042 | + | 86.6685i | −0.376219 | + | 0.0905627i | ||||
\(958\) | −936.129 | −0.977170 | ||||||||
\(959\) | − | 106.727i | − | 0.111290i | ||||||
\(960\) | 12.5595 | + | 52.1753i | 0.0130828 | + | 0.0543492i | ||||
\(961\) | 858.030 | 0.892851 | ||||||||
\(962\) | 1113.97i | 1.15797i | ||||||||
\(963\) | 434.186 | + | 849.597i | 0.450868 | + | 0.882240i | ||||
\(964\) | 595.769 | 0.618017 | ||||||||
\(965\) | 457.401i | 0.473991i | ||||||||
\(966\) | −168.706 | + | 40.6105i | −0.174644 | + | 0.0420399i | ||||
\(967\) | −1469.81 | −1.51997 | −0.759985 | − | 0.649940i | \(-0.774794\pi\) | ||||
−0.759985 | + | 0.649940i | \(0.774794\pi\) | |||||||
\(968\) | 15.5124i | 0.0160252i | ||||||||
\(969\) | −7.44708 | − | 30.9369i | −0.00768532 | − | 0.0319266i | ||||
\(970\) | −442.435 | −0.456119 | ||||||||
\(971\) | 231.452i | 0.238365i | 0.992872 | + | 0.119182i | \(0.0380273\pi\) | ||||
−0.992872 | + | 0.119182i | \(0.961973\pi\) | |||||||
\(972\) | 184.626 | − | 449.565i | 0.189945 | − | 0.462516i | ||||
\(973\) | −2312.29 | −2.37646 | ||||||||
\(974\) | − | 37.8799i | − | 0.0388911i | ||||||
\(975\) | 267.941 | − | 64.4982i | 0.274811 | − | 0.0661520i | ||||
\(976\) | 136.769 | 0.140132 | ||||||||
\(977\) | − | 128.340i | − | 0.131362i | −0.997841 | − | 0.0656808i | \(-0.979078\pi\) | ||
0.997841 | − | 0.0656808i | \(-0.0209219\pi\) | |||||||
\(978\) | 232.215 | + | 964.678i | 0.237439 | + | 0.986378i | ||||
\(979\) | 867.556 | 0.886165 | ||||||||
\(980\) | − | 106.131i | − | 0.108297i | ||||||
\(981\) | 471.238 | − | 240.826i | 0.480365 | − | 0.245490i | ||||
\(982\) | 872.327 | 0.888316 | ||||||||
\(983\) | − | 547.128i | − | 0.556590i | −0.960496 | − | 0.278295i | \(-0.910231\pi\) | ||
0.960496 | − | 0.278295i | \(-0.0897692\pi\) | |||||||
\(984\) | 489.042 | − | 117.721i | 0.496994 | − | 0.119635i | ||||
\(985\) | −93.2584 | −0.0946785 | ||||||||
\(986\) | − | 12.4268i | − | 0.0126032i | ||||||
\(987\) | 394.401 | + | 1638.43i | 0.399595 | + | 1.66001i | ||||
\(988\) | −486.853 | −0.492766 | ||||||||
\(989\) | 51.2974i | 0.0518680i | ||||||||
\(990\) | 145.659 | + | 285.019i | 0.147130 | + | 0.287898i | ||||
\(991\) | −792.171 | −0.799365 | −0.399683 | − | 0.916654i | \(-0.630880\pi\) | ||||
−0.399683 | + | 0.916654i | \(0.630880\pi\) | |||||||
\(992\) | − | 241.265i | − | 0.243211i | ||||||
\(993\) | 1121.08 | − | 269.863i | 1.12898 | − | 0.271766i | ||||
\(994\) | −389.971 | −0.392325 | ||||||||
\(995\) | − | 17.2013i | − | 0.0172878i | ||||||
\(996\) | 59.0844 | + | 245.451i | 0.0593217 | + | 0.246436i | ||||
\(997\) | −74.0339 | −0.0742566 | −0.0371283 | − | 0.999311i | \(-0.511821\pi\) | ||||
−0.0371283 | + | 0.999311i | \(0.511821\pi\) | |||||||
\(998\) | 1393.58i | 1.39637i | ||||||||
\(999\) | −878.847 | + | 753.366i | −0.879726 | + | 0.754121i |
(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 | 690.3.g.a.461.20 | yes | 56 | |
3.2 | odd | 2 | inner | 690.3.g.a.461.19 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.g.a.461.19 | ✓ | 56 | 3.2 | odd | 2 | inner | |
690.3.g.a.461.20 | yes | 56 | 1.1 | even | 1 | trivial |