Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,4,Mod(55,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.55");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.b (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: | \(14.8684813214\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 358 x^{14} - 2828 x^{13} + 52557 x^{12} - 549972 x^{11} + 4434734 x^{10} - 37785264 x^{9} + 272741368 x^{8} - 1739202044 x^{7} + \cdots + 52705588025 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{26} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 55.2 | ||
Root | \(0.929907 - 12.9280i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.55 |
Dual form | 252.4.b.g.55.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.69547 | − | 0.856992i | −0.952993 | − | 0.302992i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 6.53113 | + | 4.62000i | 0.816391 | + | 0.577499i | ||||
\(5\) | 10.3049i | 0.921697i | 0.887479 | + | 0.460848i | \(0.152455\pi\) | ||||
−0.887479 | + | 0.460848i | \(0.847545\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 16.6272 | − | 8.15690i | 0.897786 | − | 0.440431i | ||||
\(8\) | −13.6452 | − | 18.0502i | −0.603037 | − | 0.797713i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 8.83121 | − | 27.7765i | 0.279267 | − | 0.878371i | ||||
\(11\) | − | 18.0502i | − | 0.494758i | −0.968919 | − | 0.247379i | \(-0.920431\pi\) | ||
0.968919 | − | 0.247379i | \(-0.0795693\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 49.0412i | − | 1.04628i | −0.852248 | − | 0.523138i | \(-0.824761\pi\) | ||
0.852248 | − | 0.523138i | \(-0.175239\pi\) | |||||||
\(14\) | −51.8086 | + | 7.73727i | −0.989031 | + | 0.147705i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 21.3113 | + | 60.3476i | 0.332989 | + | 0.942931i | ||||
\(17\) | 46.6928i | 0.666156i | 0.942899 | + | 0.333078i | \(0.108087\pi\) | ||||
−0.942899 | + | 0.333078i | \(0.891913\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 48.8465 | 0.589798 | 0.294899 | − | 0.955528i | \(-0.404714\pi\) | ||||
0.294899 | + | 0.955528i | \(0.404714\pi\) | |||||||
\(20\) | −47.6085 | + | 67.3025i | −0.532279 | + | 0.752465i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −15.4689 | + | 48.6538i | −0.149908 | + | 0.471501i | ||||
\(23\) | 33.7962i | 0.306391i | 0.988196 | + | 0.153195i | \(0.0489564\pi\) | ||||
−0.988196 | + | 0.153195i | \(0.951044\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 18.8094 | 0.150475 | ||||||||
\(26\) | −42.0280 | + | 132.189i | −0.317014 | + | 0.997094i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 146.279 | + | 23.5440i | 0.987294 | + | 0.158907i | ||||
\(29\) | −48.1829 | −0.308529 | −0.154264 | − | 0.988030i | \(-0.549301\pi\) | ||||
−0.154264 | + | 0.988030i | \(0.549301\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 152.751 | 0.884994 | 0.442497 | − | 0.896770i | \(-0.354093\pi\) | ||||
0.442497 | + | 0.896770i | \(0.354093\pi\) | |||||||
\(32\) | −5.72657 | − | 180.929i | −0.0316351 | − | 0.999499i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 40.0153 | − | 125.859i | 0.201840 | − | 0.634842i | ||||
\(35\) | 84.0559 | + | 171.342i | 0.405944 | + | 0.827487i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 37.6848 | 0.167442 | 0.0837209 | − | 0.996489i | \(-0.473320\pi\) | ||||
0.0837209 | + | 0.996489i | \(0.473320\pi\) | |||||||
\(38\) | −131.664 | − | 41.8611i | −0.562073 | − | 0.178704i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 186.005 | − | 140.612i | 0.735250 | − | 0.555817i | ||||
\(41\) | − | 409.288i | − | 1.55903i | −0.626385 | − | 0.779514i | \(-0.715466\pi\) | ||
0.626385 | − | 0.779514i | \(-0.284534\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 470.799i | 1.66968i | 0.550494 | + | 0.834839i | \(0.314440\pi\) | ||||
−0.550494 | + | 0.834839i | \(0.685560\pi\) | |||||||
\(44\) | 83.3918 | − | 117.888i | 0.285722 | − | 0.403916i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 28.9631 | − | 91.0966i | 0.0928341 | − | 0.291988i | ||||
\(47\) | 548.980 | 1.70377 | 0.851883 | − | 0.523733i | \(-0.175461\pi\) | ||||
0.851883 | + | 0.523733i | \(0.175461\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 209.930 | − | 271.253i | 0.612041 | − | 0.790826i | ||||
\(50\) | −50.7001 | − | 16.1195i | −0.143401 | − | 0.0455927i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 226.570 | − | 320.295i | 0.604224 | − | 0.854171i | ||||
\(53\) | 203.157 | 0.526523 | 0.263262 | − | 0.964724i | \(-0.415202\pi\) | ||||
0.263262 | + | 0.964724i | \(0.415202\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 186.005 | 0.456017 | ||||||||
\(56\) | −374.115 | − | 188.823i | −0.892736 | − | 0.450580i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 129.875 | + | 41.2923i | 0.294026 | + | 0.0934819i | ||||
\(59\) | 717.092 | 1.58233 | 0.791164 | − | 0.611604i | \(-0.209475\pi\) | ||||
0.791164 | + | 0.611604i | \(0.209475\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 493.466i | − | 1.03577i | −0.855451 | − | 0.517884i | \(-0.826720\pi\) | ||
0.855451 | − | 0.517884i | \(-0.173280\pi\) | |||||||
\(62\) | −411.735 | − | 130.906i | −0.843393 | − | 0.268147i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −139.619 | + | 492.596i | −0.272693 | + | 0.962101i | ||||
\(65\) | 505.364 | 0.964350 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 240.375i | − | 0.438305i | −0.975691 | − | 0.219152i | \(-0.929671\pi\) | ||
0.975691 | − | 0.219152i | \(-0.0703292\pi\) | |||||||
\(68\) | −215.720 | + | 304.956i | −0.384705 | + | 0.543844i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −79.7317 | − | 533.882i | −0.136139 | − | 0.911587i | ||||
\(71\) | 995.648i | 1.66425i | 0.554589 | + | 0.832125i | \(0.312876\pi\) | ||||
−0.554589 | + | 0.832125i | \(0.687124\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 790.766i | 1.26784i | 0.773399 | + | 0.633919i | \(0.218555\pi\) | ||||
−0.773399 | + | 0.633919i | \(0.781445\pi\) | |||||||
\(74\) | −101.578 | − | 32.2956i | −0.159571 | − | 0.0507336i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 319.023 | + | 225.671i | 0.481506 | + | 0.340608i | ||||
\(77\) | −147.234 | − | 300.125i | −0.217907 | − | 0.444187i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 214.111i | − | 0.304928i | −0.988309 | − | 0.152464i | \(-0.951279\pi\) | ||
0.988309 | − | 0.152464i | \(-0.0487209\pi\) | |||||||
\(80\) | −621.875 | + | 219.610i | −0.869096 | + | 0.306915i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −350.757 | + | 1103.23i | −0.472373 | + | 1.48574i | ||||
\(83\) | 885.204 | 1.17065 | 0.585324 | − | 0.810800i | \(-0.300967\pi\) | ||||
0.585324 | + | 0.810800i | \(0.300967\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −481.164 | −0.613994 | ||||||||
\(86\) | 403.471 | − | 1269.03i | 0.505900 | − | 1.59119i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −325.809 | + | 246.298i | −0.394675 | + | 0.298357i | ||||
\(89\) | 67.3025i | 0.0801579i | 0.999197 | + | 0.0400790i | \(0.0127609\pi\) | ||||
−0.999197 | + | 0.0400790i | \(0.987239\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −400.024 | − | 815.420i | −0.460813 | − | 0.939333i | ||||
\(92\) | −156.138 | + | 220.727i | −0.176941 | + | 0.250135i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1479.76 | − | 470.472i | −1.62368 | − | 0.516228i | ||||
\(95\) | 503.358i | 0.543615i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 934.837i | 0.978539i | 0.872133 | + | 0.489269i | \(0.162737\pi\) | ||||
−0.872133 | + | 0.489269i | \(0.837263\pi\) | |||||||
\(98\) | −798.322 | + | 551.247i | −0.822885 | + | 0.568208i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 122.846 | + | 86.8991i | 0.122846 | + | 0.0868991i | ||||
\(101\) | − | 643.394i | − | 0.633862i | −0.948449 | − | 0.316931i | \(-0.897348\pi\) | ||
0.948449 | − | 0.316931i | \(-0.102652\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −834.403 | −0.798215 | −0.399108 | − | 0.916904i | \(-0.630680\pi\) | ||||
−0.399108 | + | 0.916904i | \(0.630680\pi\) | |||||||
\(104\) | −885.204 | + | 669.176i | −0.834628 | + | 0.630943i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −547.603 | − | 174.104i | −0.501773 | − | 0.159533i | ||||
\(107\) | − | 1511.02i | − | 1.36520i | −0.730793 | − | 0.682599i | \(-0.760850\pi\) | ||
0.730793 | − | 0.682599i | \(-0.239150\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1347.35 | −1.18397 | −0.591983 | − | 0.805950i | \(-0.701655\pi\) | ||||
−0.591983 | + | 0.805950i | \(0.701655\pi\) | |||||||
\(110\) | −501.371 | − | 159.405i | −0.434581 | − | 0.138170i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 846.597 | + | 829.579i | 0.714249 | + | 0.699892i | ||||
\(113\) | −1677.23 | −1.39629 | −0.698145 | − | 0.715956i | \(-0.745991\pi\) | ||||
−0.698145 | + | 0.715956i | \(0.745991\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −348.266 | −0.282400 | ||||||||
\(116\) | −314.688 | − | 222.605i | −0.251880 | − | 0.178175i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1932.90 | − | 614.542i | −1.50795 | − | 0.479434i | ||||
\(119\) | 380.868 | + | 776.372i | 0.293396 | + | 0.598066i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1005.19 | 0.755215 | ||||||||
\(122\) | −422.896 | + | 1330.12i | −0.313830 | + | 0.987079i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 997.634 | + | 705.707i | 0.722502 | + | 0.511084i | ||||
\(125\) | 1481.94i | 1.06039i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 401.212i | − | 0.280329i | −0.990128 | − | 0.140164i | \(-0.955237\pi\) | ||
0.990128 | − | 0.140164i | \(-0.0447631\pi\) | |||||||
\(128\) | 798.489 | − | 1208.13i | 0.551384 | − | 0.834252i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1362.19 | − | 433.093i | −0.919018 | − | 0.292191i | ||||
\(131\) | −44.6445 | −0.0297756 | −0.0148878 | − | 0.999889i | \(-0.504739\pi\) | ||||
−0.0148878 | + | 0.999889i | \(0.504739\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 812.183 | − | 398.436i | 0.529513 | − | 0.259765i | ||||
\(134\) | −205.999 | + | 647.923i | −0.132803 | + | 0.417702i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 842.813 | − | 637.131i | 0.531402 | − | 0.401717i | ||||
\(137\) | 1481.82 | 0.924089 | 0.462044 | − | 0.886857i | \(-0.347116\pi\) | ||||
0.462044 | + | 0.886857i | \(0.347116\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1197.16 | −0.730517 | −0.365259 | − | 0.930906i | \(-0.619019\pi\) | ||||
−0.365259 | + | 0.930906i | \(0.619019\pi\) | |||||||
\(140\) | −242.618 | + | 1507.39i | −0.146464 | + | 0.909985i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 853.263 | − | 2683.74i | 0.504255 | − | 1.58602i | ||||
\(143\) | −885.204 | −0.517653 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 496.519i | − | 0.284370i | ||||||
\(146\) | 677.680 | − | 2131.49i | 0.384145 | − | 1.20824i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 246.125 | + | 174.104i | 0.136698 | + | 0.0966976i | ||||
\(149\) | 1198.40 | 0.658907 | 0.329453 | − | 0.944172i | \(-0.393136\pi\) | ||||
0.329453 | + | 0.944172i | \(0.393136\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3058.27i | 1.64820i | 0.566444 | + | 0.824100i | \(0.308319\pi\) | ||||
−0.566444 | + | 0.824100i | \(0.691681\pi\) | |||||||
\(152\) | −666.519 | − | 881.689i | −0.355670 | − | 0.470490i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 139.659 | + | 935.156i | 0.0730783 | + | 0.489331i | ||||
\(155\) | 1574.08i | 0.815697i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2265.06i | 1.15141i | 0.817658 | + | 0.575704i | \(0.195272\pi\) | ||||
−0.817658 | + | 0.575704i | \(0.804728\pi\) | |||||||
\(158\) | −183.491 | + | 577.129i | −0.0923910 | + | 0.290595i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1864.45 | − | 59.0116i | 0.921236 | − | 0.0291580i | ||||
\(161\) | 275.672 | + | 561.937i | 0.134944 | + | 0.275074i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 1497.01i | − | 0.719357i | −0.933076 | − | 0.359678i | \(-0.882886\pi\) | ||
0.933076 | − | 0.359678i | \(-0.117114\pi\) | |||||||
\(164\) | 1890.91 | − | 2673.12i | 0.900337 | − | 1.27278i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2386.04 | − | 758.613i | −1.11562 | − | 0.354697i | ||||
\(167\) | −672.447 | −0.311590 | −0.155795 | − | 0.987789i | \(-0.549794\pi\) | ||||
−0.155795 | + | 0.987789i | \(0.549794\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −208.043 | −0.0946940 | ||||||||
\(170\) | 1296.96 | + | 412.353i | 0.585132 | + | 0.186036i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2175.09 | + | 3074.85i | −0.964239 | + | 1.36311i | ||||
\(173\) | − | 2008.77i | − | 0.882798i | −0.897311 | − | 0.441399i | \(-0.854482\pi\) | ||
0.897311 | − | 0.441399i | \(-0.145518\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 312.748 | − | 153.426i | 0.135094 | − | 0.0662738i | ||||
\(176\) | 1089.29 | − | 384.673i | 0.466522 | − | 0.164749i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 57.6777 | − | 181.412i | 0.0242872 | − | 0.0763899i | ||||
\(179\) | − | 3724.04i | − | 1.55502i | −0.628872 | − | 0.777509i | \(-0.716483\pi\) | ||
0.628872 | − | 0.777509i | \(-0.283517\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2010.69i | − | 0.825710i | −0.910797 | − | 0.412855i | \(-0.864532\pi\) | ||
0.910797 | − | 0.412855i | \(-0.135468\pi\) | |||||||
\(182\) | 379.446 | + | 2540.76i | 0.154541 | + | 1.03480i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 610.027 | − | 461.155i | 0.244412 | − | 0.184765i | ||||
\(185\) | 388.338i | 0.154331i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 842.813 | 0.329586 | ||||||||
\(188\) | 3585.46 | + | 2536.28i | 1.39094 | + | 0.983923i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 431.374 | − | 1356.79i | 0.164711 | − | 0.518061i | ||||
\(191\) | − | 1167.67i | − | 0.442355i | −0.975234 | − | 0.221178i | \(-0.929010\pi\) | ||
0.975234 | − | 0.221178i | \(-0.0709901\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4481.71 | −1.67150 | −0.835752 | − | 0.549106i | \(-0.814968\pi\) | ||||
−0.835752 | + | 0.549106i | \(0.814968\pi\) | |||||||
\(194\) | 801.148 | − | 2519.83i | 0.296490 | − | 0.932541i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2624.27 | − | 801.715i | 0.956366 | − | 0.292170i | ||||
\(197\) | −4433.60 | −1.60346 | −0.801728 | − | 0.597689i | \(-0.796086\pi\) | ||||
−0.801728 | + | 0.597689i | \(0.796086\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2895.34 | 1.03138 | 0.515691 | − | 0.856775i | \(-0.327535\pi\) | ||||
0.515691 | + | 0.856775i | \(0.327535\pi\) | |||||||
\(200\) | −256.657 | − | 339.512i | −0.0907419 | − | 0.120036i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −551.383 | + | 1734.25i | −0.192055 | + | 0.604066i | ||||
\(203\) | −801.148 | + | 393.023i | −0.276993 | + | 0.135886i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4217.67 | 1.43695 | ||||||||
\(206\) | 2249.11 | + | 715.077i | 0.760693 | + | 0.241853i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2959.52 | − | 1045.13i | 0.986566 | − | 0.348398i | ||||
\(209\) | − | 881.689i | − | 0.291807i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 2313.24i | − | 0.754740i | −0.926063 | − | 0.377370i | \(-0.876828\pi\) | ||
0.926063 | − | 0.377370i | \(-0.123172\pi\) | |||||||
\(212\) | 1326.84 | + | 938.583i | 0.429849 | + | 0.304067i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1294.94 | + | 4072.92i | −0.413645 | + | 1.30102i | ||||
\(215\) | −4851.53 | −1.53894 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2539.82 | − | 1245.97i | 0.794536 | − | 0.389779i | ||||
\(218\) | 3631.73 | + | 1154.67i | 1.12831 | + | 0.358733i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1214.82 | + | 859.343i | 0.372288 | + | 0.263349i | ||||
\(221\) | 2289.87 | 0.696984 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4169.23 | 1.25198 | 0.625992 | − | 0.779830i | \(-0.284694\pi\) | ||||
0.625992 | + | 0.779830i | \(0.284694\pi\) | |||||||
\(224\) | −1571.03 | − | 2961.63i | −0.468612 | − | 0.883404i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4520.93 | + | 1437.38i | 1.33066 | + | 0.423066i | ||||
\(227\) | −3461.99 | −1.01225 | −0.506124 | − | 0.862461i | \(-0.668922\pi\) | ||||
−0.506124 | + | 0.862461i | \(0.668922\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 303.407i | 0.0875533i | 0.999041 | + | 0.0437766i | \(0.0139390\pi\) | ||||
−0.999041 | + | 0.0437766i | \(0.986061\pi\) | |||||||
\(230\) | 938.740 | + | 298.461i | 0.269125 | + | 0.0855649i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 657.463 | + | 869.710i | 0.186054 | + | 0.246117i | ||||
\(233\) | −2216.24 | −0.623137 | −0.311569 | − | 0.950224i | \(-0.600854\pi\) | ||||
−0.311569 | + | 0.950224i | \(0.600854\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5657.18i | 1.57035i | ||||||||
\(236\) | 4683.42 | + | 3312.96i | 1.29180 | + | 0.913794i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −361.275 | − | 2419.09i | −0.0983948 | − | 0.658850i | ||||
\(239\) | − | 1062.67i | − | 0.287609i | −0.989606 | − | 0.143805i | \(-0.954066\pi\) | ||
0.989606 | − | 0.143805i | \(-0.0459337\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 7334.62i | − | 1.96043i | −0.197926 | − | 0.980217i | \(-0.563421\pi\) | ||
0.197926 | − | 0.980217i | \(-0.436579\pi\) | |||||||
\(242\) | −2709.46 | − | 861.441i | −0.719714 | − | 0.228824i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2279.81 | − | 3222.89i | 0.598155 | − | 0.845591i | ||||
\(245\) | 2795.23 | + | 2163.30i | 0.728902 | + | 0.564116i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 2395.49i | − | 0.617092i | ||||||
\(248\) | −2084.31 | − | 2757.18i | −0.533684 | − | 0.705972i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1270.01 | − | 3994.52i | 0.321290 | − | 1.01054i | ||||
\(251\) | −5904.85 | −1.48490 | −0.742451 | − | 0.669900i | \(-0.766337\pi\) | ||||
−0.742451 | + | 0.669900i | \(0.766337\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 610.027 | 0.151589 | ||||||||
\(254\) | −343.835 | + | 1081.45i | −0.0849375 | + | 0.267151i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3187.66 | + | 2572.17i | −0.778237 | + | 0.627971i | ||||
\(257\) | 5814.10i | 1.41118i | 0.708620 | + | 0.705591i | \(0.249318\pi\) | ||||
−0.708620 | + | 0.705591i | \(0.750682\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 626.595 | − | 307.391i | 0.150327 | − | 0.0737466i | ||||
\(260\) | 3300.60 | + | 2334.78i | 0.787286 | + | 0.556911i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 120.338 | + | 38.2600i | 0.0283760 | + | 0.00902180i | ||||
\(263\) | − | 1699.79i | − | 0.398530i | −0.979946 | − | 0.199265i | \(-0.936144\pi\) | ||
0.979946 | − | 0.199265i | \(-0.0638555\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2093.51i | 0.485295i | ||||||||
\(266\) | −2530.67 | + | 377.939i | −0.583329 | + | 0.0871163i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1110.53 | − | 1569.92i | 0.253121 | − | 0.357828i | ||||
\(269\) | 5550.40i | 1.25804i | 0.777387 | + | 0.629022i | \(0.216545\pi\) | ||||
−0.777387 | + | 0.629022i | \(0.783455\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3741.78 | 0.838733 | 0.419367 | − | 0.907817i | \(-0.362252\pi\) | ||||
0.419367 | + | 0.907817i | \(0.362252\pi\) | |||||||
\(272\) | −2817.79 | + | 995.083i | −0.628139 | + | 0.221823i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3994.19 | − | 1269.91i | −0.880650 | − | 0.279992i | ||||
\(275\) | − | 339.512i | − | 0.0744486i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5697.37 | −1.23582 | −0.617910 | − | 0.786249i | \(-0.712020\pi\) | ||||
−0.617910 | + | 0.786249i | \(0.712020\pi\) | |||||||
\(278\) | 3226.91 | + | 1025.96i | 0.696178 | + | 0.221341i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1945.79 | − | 3855.21i | 0.415298 | − | 0.822832i | ||||
\(281\) | −6405.15 | −1.35978 | −0.679892 | − | 0.733312i | \(-0.737973\pi\) | ||||
−0.679892 | + | 0.733312i | \(0.737973\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7258.60 | −1.52466 | −0.762330 | − | 0.647188i | \(-0.775945\pi\) | ||||
−0.762330 | + | 0.647188i | \(0.775945\pi\) | |||||||
\(284\) | −4599.89 | + | 6502.71i | −0.961103 | + | 1.35868i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2386.04 | + | 758.613i | 0.493320 | + | 0.156845i | ||||
\(287\) | −3338.52 | − | 6805.34i | −0.686644 | − | 1.39967i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2732.79 | 0.556236 | ||||||||
\(290\) | −425.513 | + | 1338.35i | −0.0861619 | + | 0.271003i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3653.34 | + | 5164.60i | −0.732176 | + | 1.03505i | ||||
\(293\) | − | 2353.32i | − | 0.469224i | −0.972089 | − | 0.234612i | \(-0.924618\pi\) | ||
0.972089 | − | 0.234612i | \(-0.0753819\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7389.55i | 1.45843i | ||||||||
\(296\) | −514.216 | − | 680.218i | −0.100974 | − | 0.133571i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3230.27 | − | 1027.02i | −0.627934 | − | 0.199644i | ||||
\(299\) | 1657.41 | 0.320569 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3840.26 | + | 7828.09i | 0.735379 | + | 1.49901i | ||||
\(302\) | 2620.91 | − | 8243.47i | 0.499392 | − | 1.57072i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1040.98 | + | 2947.77i | 0.196396 | + | 0.556139i | ||||
\(305\) | 5085.11 | 0.954663 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5602.21 | −1.04148 | −0.520741 | − | 0.853714i | \(-0.674344\pi\) | ||||
−0.520741 | + | 0.853714i | \(0.674344\pi\) | |||||||
\(308\) | 424.974 | − | 2640.37i | 0.0786205 | − | 0.488471i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1348.97 | − | 4242.88i | 0.247150 | − | 0.777353i | ||||
\(311\) | 3081.12 | 0.561783 | 0.280891 | − | 0.959740i | \(-0.409370\pi\) | ||||
0.280891 | + | 0.959740i | \(0.409370\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5032.74i | 0.908841i | 0.890787 | + | 0.454420i | \(0.150154\pi\) | ||||
−0.890787 | + | 0.454420i | \(0.849846\pi\) | |||||||
\(314\) | 1941.14 | − | 6105.39i | 0.348868 | − | 1.09728i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 989.190 | − | 1398.38i | 0.176096 | − | 0.248941i | ||||
\(317\) | −6446.37 | −1.14216 | −0.571079 | − | 0.820895i | \(-0.693475\pi\) | ||||
−0.571079 | + | 0.820895i | \(0.693475\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 869.710i | 0.152647i | ||||||||
\(320\) | −5076.14 | − | 1438.75i | −0.886766 | − | 0.251340i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −261.490 | − | 1750.93i | −0.0452555 | − | 0.303030i | ||||
\(323\) | 2280.78i | 0.392898i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 922.434i | − | 0.157438i | ||||||
\(326\) | −1282.93 | + | 4035.16i | −0.217960 | + | 0.685542i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7387.73 | + | 5584.81i | −1.24366 | + | 0.940151i | ||||
\(329\) | 9128.02 | − | 4477.97i | 1.52962 | − | 0.750391i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 8175.39i | − | 1.35758i | −0.734331 | − | 0.678791i | \(-0.762504\pi\) | ||
0.734331 | − | 0.678791i | \(-0.237496\pi\) | |||||||
\(332\) | 5781.38 | + | 4089.64i | 0.955706 | + | 0.676048i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1812.56 | + | 576.282i | 0.296943 | + | 0.0944094i | ||||
\(335\) | 2477.03 | 0.403984 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5692.64 | −0.920172 | −0.460086 | − | 0.887874i | \(-0.652181\pi\) | ||||
−0.460086 | + | 0.887874i | \(0.652181\pi\) | |||||||
\(338\) | 560.773 | + | 178.291i | 0.0902427 | + | 0.0286916i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3142.54 | − | 2222.97i | −0.501259 | − | 0.354581i | ||||
\(341\) | − | 2757.18i | − | 0.437858i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1277.97 | − | 6222.57i | 0.201177 | − | 0.979555i | ||||
\(344\) | 8498.01 | − | 6424.13i | 1.33192 | − | 1.00688i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1721.50 | + | 5414.58i | −0.267481 | + | 0.841300i | ||||
\(347\) | 6701.89i | 1.03682i | 0.855132 | + | 0.518410i | \(0.173476\pi\) | ||||
−0.855132 | + | 0.518410i | \(0.826524\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 3914.14i | − | 0.600341i | −0.953886 | − | 0.300171i | \(-0.902956\pi\) | ||
0.953886 | − | 0.300171i | \(-0.0970436\pi\) | |||||||
\(350\) | −974.487 | + | 145.533i | −0.148824 | + | 0.0222259i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3265.80 | + | 103.366i | −0.494510 | + | 0.0156517i | ||||
\(353\) | − | 9853.62i | − | 1.48571i | −0.669453 | − | 0.742854i | \(-0.733472\pi\) | ||
0.669453 | − | 0.742854i | \(-0.266528\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10260.0 | −1.53393 | ||||||||
\(356\) | −310.937 | + | 439.561i | −0.0462911 | + | 0.0654402i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3191.48 | + | 10038.1i | −0.471159 | + | 1.48192i | ||||
\(359\) | 10120.4i | 1.48784i | 0.668270 | + | 0.743919i | \(0.267035\pi\) | ||||
−0.668270 | + | 0.743919i | \(0.732965\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4473.02 | −0.652138 | ||||||||
\(362\) | −1723.15 | + | 5419.76i | −0.250184 | + | 0.786896i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1154.63 | − | 7173.73i | 0.166261 | − | 1.03298i | ||||
\(365\) | −8148.75 | −1.16856 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4458.69 | 0.634173 | 0.317086 | − | 0.948397i | \(-0.397295\pi\) | ||||
0.317086 | + | 0.948397i | \(0.397295\pi\) | |||||||
\(368\) | −2039.52 | + | 720.240i | −0.288905 | + | 0.102025i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 332.803 | − | 1046.75i | 0.0467610 | − | 0.147076i | ||||
\(371\) | 3377.94 | − | 1657.13i | 0.472705 | − | 0.231897i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 829.392 | 0.115132 | 0.0575661 | − | 0.998342i | \(-0.481666\pi\) | ||||
0.0575661 | + | 0.998342i | \(0.481666\pi\) | |||||||
\(374\) | −2271.78 | − | 722.284i | −0.314093 | − | 0.0998621i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7490.92 | − | 9909.19i | −1.02743 | − | 1.35912i | ||||
\(377\) | 2362.95i | 0.322806i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 521.296i | − | 0.0706521i | −0.999376 | − | 0.0353261i | \(-0.988753\pi\) | ||
0.999376 | − | 0.0353261i | \(-0.0112470\pi\) | |||||||
\(380\) | −2325.51 | + | 3287.50i | −0.313937 | + | 0.443803i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1000.69 | + | 3147.43i | −0.134030 | + | 0.421562i | ||||
\(383\) | 12605.6 | 1.68177 | 0.840883 | − | 0.541217i | \(-0.182036\pi\) | ||||
0.840883 | + | 0.541217i | \(0.182036\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3092.75 | − | 1517.23i | 0.409406 | − | 0.200844i | ||||
\(386\) | 12080.3 | + | 3840.79i | 1.59293 | + | 0.506453i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4318.94 | + | 6105.54i | −0.565106 | + | 0.798871i | ||||
\(389\) | 11263.9 | 1.46812 | 0.734062 | − | 0.679082i | \(-0.237622\pi\) | ||||
0.734062 | + | 0.679082i | \(0.237622\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1578.04 | −0.204104 | ||||||||
\(392\) | −7760.71 | − | 87.9778i | −0.999936 | − | 0.0113356i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 11950.6 | + | 3799.56i | 1.52808 | + | 0.485835i | ||||
\(395\) | 2206.39 | 0.281051 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3304.08i | 0.417701i | 0.977948 | + | 0.208850i | \(0.0669721\pi\) | ||||
−0.977948 | + | 0.208850i | \(0.933028\pi\) | |||||||
\(398\) | −7804.30 | − | 2481.28i | −0.982900 | − | 0.312501i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 400.852 | + | 1135.10i | 0.0501064 | + | 0.141887i | ||||
\(401\) | −5752.87 | −0.716420 | −0.358210 | − | 0.933641i | \(-0.616613\pi\) | ||||
−0.358210 | + | 0.933641i | \(0.616613\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 7491.08i | − | 0.925949i | ||||||
\(404\) | 2972.48 | − | 4202.09i | 0.366055 | − | 0.517479i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2496.29 | − | 372.804i | 0.305145 | − | 0.0455713i | ||||
\(407\) | − | 680.218i | − | 0.0828432i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1731.71i | 0.209358i | 0.994506 | + | 0.104679i | \(0.0333815\pi\) | ||||
−0.994506 | + | 0.104679i | \(0.966618\pi\) | |||||||
\(410\) | −11368.6 | − | 3614.51i | −1.36940 | − | 0.435385i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5449.59 | − | 3854.94i | −0.651656 | − | 0.460969i | ||||
\(413\) | 11923.3 | − | 5849.25i | 1.42059 | − | 0.696907i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9121.92i | 1.07898i | ||||||||
\(416\) | −8872.97 | + | 280.838i | −1.04575 | + | 0.0330991i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −755.601 | + | 2376.57i | −0.0884154 | + | 0.278090i | ||||
\(419\) | 13882.1 | 1.61859 | 0.809293 | − | 0.587406i | \(-0.199851\pi\) | ||||
0.809293 | + | 0.587406i | \(0.199851\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3343.52 | −0.387062 | −0.193531 | − | 0.981094i | \(-0.561994\pi\) | ||||
−0.193531 | + | 0.981094i | \(0.561994\pi\) | |||||||
\(422\) | −1982.43 | + | 6235.28i | −0.228681 | + | 0.719262i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2772.11 | − | 3667.02i | −0.317513 | − | 0.420014i | ||||
\(425\) | 878.261i | 0.100240i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4025.15 | − | 8204.97i | −0.456184 | − | 0.929898i | ||||
\(428\) | 6980.92 | − | 9868.69i | 0.788401 | − | 1.11454i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 13077.2 | + | 4157.72i | 1.46660 | + | 0.466287i | ||||
\(431\) | − | 7075.93i | − | 0.790802i | −0.918509 | − | 0.395401i | \(-0.870606\pi\) | ||
0.918509 | − | 0.395401i | \(-0.129394\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4910.23i | 0.544967i | 0.962160 | + | 0.272483i | \(0.0878450\pi\) | ||||
−0.962160 | + | 0.272483i | \(0.912155\pi\) | |||||||
\(434\) | −7913.80 | + | 1181.87i | −0.875287 | + | 0.130718i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8799.69 | − | 6224.73i | −0.966580 | − | 0.683740i | ||||
\(437\) | 1650.83i | 0.180709i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13445.2 | 1.46174 | 0.730868 | − | 0.682518i | \(-0.239115\pi\) | ||||
0.730868 | + | 0.682518i | \(0.239115\pi\) | |||||||
\(440\) | −2538.07 | − | 3357.43i | −0.274995 | − | 0.363771i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6172.28 | − | 1962.40i | −0.664220 | − | 0.211181i | ||||
\(443\) | 14965.5i | 1.60504i | 0.596629 | + | 0.802518i | \(0.296507\pi\) | ||||
−0.596629 | + | 0.802518i | \(0.703493\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −693.545 | −0.0738813 | ||||||||
\(446\) | −11238.0 | − | 3573.00i | −1.19313 | − | 0.379342i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1696.58 | + | 9329.36i | 0.178919 | + | 0.983864i | ||||
\(449\) | −10908.7 | −1.14658 | −0.573291 | − | 0.819352i | \(-0.694334\pi\) | ||||
−0.573291 | + | 0.819352i | \(0.694334\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7387.73 | −0.771341 | ||||||||
\(452\) | −10954.2 | − | 7748.81i | −1.13992 | − | 0.806357i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9331.70 | + | 2966.90i | 0.964666 | + | 0.306704i | ||||
\(455\) | 8402.81 | − | 4122.21i | 0.865780 | − | 0.424730i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4804.83 | 0.491817 | 0.245908 | − | 0.969293i | \(-0.420914\pi\) | ||||
0.245908 | + | 0.969293i | \(0.420914\pi\) | |||||||
\(458\) | 260.017 | − | 817.825i | 0.0265280 | − | 0.0834376i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2274.57 | − | 1608.99i | −0.230548 | − | 0.163086i | ||||
\(461\) | 6090.11i | 0.615281i | 0.951503 | + | 0.307641i | \(0.0995394\pi\) | ||||
−0.951503 | + | 0.307641i | \(0.900461\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4149.32i | 0.416491i | 0.978077 | + | 0.208246i | \(0.0667753\pi\) | ||||
−0.978077 | + | 0.208246i | \(0.933225\pi\) | |||||||
\(464\) | −1026.84 | − | 2907.72i | −0.102737 | − | 0.290921i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5973.82 | + | 1899.30i | 0.593845 | + | 0.188806i | ||||
\(467\) | −6598.23 | −0.653810 | −0.326905 | − | 0.945057i | \(-0.606006\pi\) | ||||
−0.326905 | + | 0.945057i | \(0.606006\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1960.71 | − | 3996.77i | −0.193043 | − | 0.393504i | ||||
\(470\) | 4848.15 | − | 15248.8i | 0.475806 | − | 1.49654i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9784.84 | − | 12943.6i | −0.954203 | − | 1.26224i | ||||
\(473\) | 8498.01 | 0.826087 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 918.772 | 0.0887498 | ||||||||
\(476\) | −1099.33 | + | 6830.19i | −0.105857 | + | 0.657692i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −910.703 | + | 2864.41i | −0.0871435 | + | 0.274090i | ||||
\(479\) | 4494.37 | 0.428712 | 0.214356 | − | 0.976756i | \(-0.431235\pi\) | ||||
0.214356 | + | 0.976756i | \(0.431235\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 1848.11i | − | 0.175190i | ||||||
\(482\) | −6285.71 | + | 19770.3i | −0.593997 | + | 1.86828i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6565.03 | + | 4643.98i | 0.616550 | + | 0.436136i | ||||
\(485\) | −9633.38 | −0.901916 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12562.5i | 1.16892i | 0.811424 | + | 0.584458i | \(0.198693\pi\) | ||||
−0.811424 | + | 0.584458i | \(0.801307\pi\) | |||||||
\(488\) | −8907.15 | + | 6733.42i | −0.826245 | + | 0.624606i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5680.54 | − | 8226.62i | −0.523716 | − | 0.758451i | ||||
\(491\) | 12172.0i | 1.11877i | 0.828909 | + | 0.559383i | \(0.188962\pi\) | ||||
−0.828909 | + | 0.559383i | \(0.811038\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 2249.79i | − | 0.205528i | ||||||
\(494\) | −2052.92 | + | 6456.99i | −0.186974 | + | 0.588084i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3255.31 | + | 9218.13i | 0.294693 | + | 0.834488i | ||||
\(497\) | 8121.40 | + | 16554.9i | 0.732987 | + | 1.49414i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3482.57i | 0.312427i | 0.987723 | + | 0.156214i | \(0.0499288\pi\) | ||||
−0.987723 | + | 0.156214i | \(0.950071\pi\) | |||||||
\(500\) | −6846.55 | + | 9678.73i | −0.612374 | + | 0.865692i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 15916.3 | + | 5060.41i | 1.41510 | + | 0.449914i | ||||
\(503\) | 480.623 | 0.0426043 | 0.0213021 | − | 0.999773i | \(-0.493219\pi\) | ||||
0.0213021 | + | 0.999773i | \(0.493219\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6630.10 | 0.584229 | ||||||||
\(506\) | −1644.31 | − | 522.789i | −0.144464 | − | 0.0459304i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1853.60 | − | 2620.36i | 0.161890 | − | 0.228858i | ||||
\(509\) | − | 13977.8i | − | 1.21720i | −0.793476 | − | 0.608602i | \(-0.791731\pi\) | ||
0.793476 | − | 0.608602i | \(-0.208269\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6450.20 | + | 13148.3i | 0.558395 | + | 1.13825i | ||||
\(512\) | 10796.6 | − | 4201.41i | 0.931925 | − | 0.362652i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4982.64 | − | 15671.7i | 0.427577 | − | 1.34485i | ||||
\(515\) | − | 8598.43i | − | 0.735712i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 9909.19i | − | 0.842951i | ||||||
\(518\) | −1952.40 | + | 291.578i | −0.165605 | + | 0.0247320i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6895.78 | − | 9121.92i | −0.581538 | − | 0.769274i | ||||
\(521\) | − | 1574.54i | − | 0.132403i | −0.997806 | − | 0.0662015i | \(-0.978912\pi\) | ||
0.997806 | − | 0.0662015i | \(-0.0210880\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8049.27 | −0.672982 | −0.336491 | − | 0.941687i | \(-0.609240\pi\) | ||||
−0.336491 | + | 0.941687i | \(0.609240\pi\) | |||||||
\(524\) | −291.579 | − | 206.257i | −0.0243086 | − | 0.0171954i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1456.71 | + | 4581.73i | −0.120752 | + | 0.379797i | ||||
\(527\) | 7132.35i | 0.589545i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11024.8 | 0.906125 | ||||||||
\(530\) | 1794.12 | − | 5642.99i | 0.147041 | − | 0.462483i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7145.24 | + | 1150.04i | 0.582304 | + | 0.0937231i | ||||
\(533\) | −20072.0 | −1.63117 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15570.9 | 1.25830 | ||||||||
\(536\) | −4338.81 | + | 3279.95i | −0.349642 | + | 0.264314i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4756.65 | − | 14961.0i | 0.381178 | − | 1.19891i | ||||
\(539\) | −4896.18 | − | 3789.28i | −0.391268 | − | 0.302812i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4564.27 | −0.362723 | −0.181362 | − | 0.983416i | \(-0.558050\pi\) | ||||
−0.181362 | + | 0.983416i | \(0.558050\pi\) | |||||||
\(542\) | −10085.9 | − | 3206.67i | −0.799307 | − | 0.254130i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8448.06 | − | 267.389i | 0.665823 | − | 0.0210739i | ||||
\(545\) | − | 13884.2i | − | 1.09126i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 3464.95i | − | 0.270842i | −0.990788 | − | 0.135421i | \(-0.956761\pi\) | ||
0.990788 | − | 0.135421i | \(-0.0432387\pi\) | |||||||
\(548\) | 9677.94 | + | 6845.99i | 0.754418 | + | 0.533661i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −290.959 | + | 915.146i | −0.0225574 | + | 0.0709490i | ||||
\(551\) | −2353.57 | −0.181970 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1746.48 | − | 3560.07i | −0.134300 | − | 0.273760i | ||||
\(554\) | 15357.1 | + | 4882.60i | 1.17773 | + | 0.374444i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7818.81 | − | 5530.88i | −0.596388 | − | 0.421873i | ||||
\(557\) | 14056.1 | 1.06926 | 0.534629 | − | 0.845087i | \(-0.320451\pi\) | ||||
0.534629 | + | 0.845087i | \(0.320451\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23088.6 | 1.74695 | ||||||||
\(560\) | −8548.72 | + | 8724.08i | −0.645088 | + | 0.658321i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 17264.9 | + | 5489.17i | 1.29586 | + | 0.412004i | ||||
\(563\) | 13614.3 | 1.01914 | 0.509568 | − | 0.860430i | \(-0.329805\pi\) | ||||
0.509568 | + | 0.860430i | \(0.329805\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 17283.7i | − | 1.28696i | ||||||
\(566\) | 19565.3 | + | 6220.56i | 1.45299 | + | 0.461961i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 17971.6 | − | 13585.8i | 1.32759 | − | 1.00360i | ||||
\(569\) | −2692.70 | −0.198390 | −0.0991950 | − | 0.995068i | \(-0.531627\pi\) | ||||
−0.0991950 | + | 0.995068i | \(0.531627\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 8780.97i | − | 0.643559i | −0.946815 | − | 0.321779i | \(-0.895719\pi\) | ||
0.946815 | − | 0.321779i | \(-0.104281\pi\) | |||||||
\(572\) | −5781.38 | − | 4089.64i | −0.422608 | − | 0.298945i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3166.78 | + | 21204.7i | 0.230276 | + | 1.54193i | ||||
\(575\) | 635.684i | 0.0461041i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4486.99i | 0.323736i | 0.986812 | + | 0.161868i | \(0.0517519\pi\) | ||||
−0.986812 | + | 0.161868i | \(0.948248\pi\) | |||||||
\(578\) | −7366.15 | − | 2341.98i | −0.530089 | − | 0.168535i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2293.91 | − | 3242.83i | 0.164223 | − | 0.232157i | ||||
\(581\) | 14718.5 | − | 7220.52i | 1.05099 | − | 0.515589i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 3667.02i | − | 0.260502i | ||||||
\(584\) | 14273.5 | − | 10790.1i | 1.01137 | − | 0.764553i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2016.78 | + | 6343.31i | −0.142171 | + | 0.447167i | ||||
\(587\) | −5983.67 | −0.420737 | −0.210368 | − | 0.977622i | \(-0.567466\pi\) | ||||
−0.210368 | + | 0.977622i | \(0.567466\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7461.34 | 0.521968 | ||||||||
\(590\) | 6332.78 | − | 19918.3i | 0.441893 | − | 1.38987i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 803.112 | + | 2274.19i | 0.0557563 | + | 0.157886i | ||||
\(593\) | 594.936i | 0.0411992i | 0.999788 | + | 0.0205996i | \(0.00655751\pi\) | ||||
−0.999788 | + | 0.0205996i | \(0.993442\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8000.42 | + | 3924.80i | −0.551236 | + | 0.270422i | ||||
\(596\) | 7826.94 | + | 5536.62i | 0.537926 | + | 0.380518i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4467.49 | − | 1420.38i | −0.305500 | − | 0.0971301i | ||||
\(599\) | 13607.8i | 0.928213i | 0.885779 | + | 0.464107i | \(0.153625\pi\) | ||||
−0.885779 | + | 0.464107i | \(0.846375\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12594.1i | 0.854779i | 0.904068 | + | 0.427390i | \(0.140567\pi\) | ||||
−0.904068 | + | 0.427390i | \(0.859433\pi\) | |||||||
\(602\) | −3642.70 | − | 24391.5i | −0.246620 | − | 1.65136i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −14129.2 | + | 19973.9i | −0.951834 | + | 1.34558i | ||||
\(605\) | 10358.4i | 0.696079i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10949.8 | 0.732187 | 0.366094 | − | 0.930578i | \(-0.380695\pi\) | ||||
0.366094 | + | 0.930578i | \(0.380695\pi\) | |||||||
\(608\) | −279.723 | − | 8837.74i | −0.0186583 | − | 0.589503i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −13706.8 | − | 4357.90i | −0.909787 | − | 0.289256i | ||||
\(611\) | − | 26922.7i | − | 1.78261i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3150.93 | 0.207610 | 0.103805 | − | 0.994598i | \(-0.466898\pi\) | ||||
0.103805 | + | 0.994598i | \(0.466898\pi\) | |||||||
\(614\) | 15100.6 | + | 4801.05i | 0.992526 | + | 0.315562i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3408.28 | + | 6752.85i | −0.222928 | + | 0.441688i | ||||
\(617\) | −25804.8 | −1.68373 | −0.841865 | − | 0.539688i | \(-0.818542\pi\) | ||||
−0.841865 | + | 0.539688i | \(0.818542\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −727.458 | −0.0472359 | −0.0236179 | − | 0.999721i | \(-0.507519\pi\) | ||||
−0.0236179 | + | 0.999721i | \(0.507519\pi\) | |||||||
\(620\) | −7272.23 | + | 10280.5i | −0.471064 | + | 0.665927i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −8305.08 | − | 2640.50i | −0.535375 | − | 0.170216i | ||||
\(623\) | 548.980 | + | 1119.06i | 0.0353040 | + | 0.0719647i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12920.0 | −0.826883 | ||||||||
\(626\) | 4313.02 | − | 13565.6i | 0.275372 | − | 0.866119i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10464.5 | + | 14793.4i | −0.664938 | + | 0.940000i | ||||
\(629\) | 1759.61i | 0.111542i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 21044.9i | − | 1.32771i | −0.747862 | − | 0.663854i | \(-0.768920\pi\) | ||
0.747862 | − | 0.663854i | \(-0.231080\pi\) | |||||||
\(632\) | −3864.74 | + | 2921.58i | −0.243245 | + | 0.183883i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 17376.0 | + | 5524.49i | 1.08847 | + | 0.346066i | ||||
\(635\) | 4134.44 | 0.258378 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13302.6 | − | 10295.2i | −0.827423 | − | 0.640364i | ||||
\(638\) | 745.334 | − | 2344.28i | 0.0462509 | − | 0.145472i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 12449.6 | + | 8228.34i | 0.768927 | + | 0.508209i | ||||
\(641\) | 22930.9 | 1.41297 | 0.706486 | − | 0.707727i | \(-0.250279\pi\) | ||||
0.706486 | + | 0.707727i | \(0.250279\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26817.0 | −1.64473 | −0.822364 | − | 0.568962i | \(-0.807345\pi\) | ||||
−0.822364 | + | 0.568962i | \(0.807345\pi\) | |||||||
\(644\) | −795.697 | + | 4943.69i | −0.0486877 | + | 0.302498i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1954.61 | − | 6147.78i | 0.119045 | − | 0.374429i | ||||
\(647\) | −27901.0 | −1.69537 | −0.847683 | − | 0.530503i | \(-0.822003\pi\) | ||||
−0.847683 | + | 0.530503i | \(0.822003\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 12943.6i | − | 0.782870i | ||||||
\(650\) | −790.519 | + | 2486.39i | −0.0477026 | + | 0.150038i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6916.19 | − | 9777.19i | 0.415428 | − | 0.587276i | ||||
\(653\) | 9804.28 | 0.587552 | 0.293776 | − | 0.955874i | \(-0.405088\pi\) | ||||
0.293776 | + | 0.955874i | \(0.405088\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 460.057i | − | 0.0274441i | ||||||
\(656\) | 24699.6 | − | 8722.46i | 1.47005 | − | 0.519139i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −28441.9 | + | 4247.61i | −1.68508 | + | 0.251655i | ||||
\(659\) | 6511.96i | 0.384931i | 0.981304 | + | 0.192466i | \(0.0616484\pi\) | ||||
−0.981304 | + | 0.192466i | \(0.938352\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30763.5i | 1.81023i | 0.425165 | + | 0.905116i | \(0.360216\pi\) | ||||
−0.425165 | + | 0.905116i | \(0.639784\pi\) | |||||||
\(662\) | −7006.24 | + | 22036.5i | −0.411337 | + | 1.29377i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −12078.8 | − | 15978.1i | −0.705944 | − | 0.933841i | ||||
\(665\) | 4105.84 | + | 8369.45i | 0.239425 | + | 0.488050i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1628.40i | − | 0.0945304i | ||||||
\(668\) | −4391.84 | − | 3106.70i | −0.254379 | − | 0.179943i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6676.77 | − | 2122.80i | −0.384994 | − | 0.122404i | ||||
\(671\) | −8907.15 | −0.512454 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2596.57 | −0.148723 | −0.0743615 | − | 0.997231i | \(-0.523692\pi\) | ||||
−0.0743615 | + | 0.997231i | \(0.523692\pi\) | |||||||
\(674\) | 15344.3 | + | 4878.55i | 0.876917 | + | 0.278805i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1358.75 | − | 961.156i | −0.0773073 | − | 0.0546857i | ||||
\(677\) | 15954.7i | 0.905744i | 0.891576 | + | 0.452872i | \(0.149601\pi\) | ||||
−0.891576 | + | 0.452872i | \(0.850399\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7625.37 | + | 15543.8i | 0.430979 | + | 0.878519i | ||||
\(680\) | 6565.56 | + | 8685.09i | 0.370261 | + | 0.489791i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2362.88 | + | 7431.89i | −0.132668 | + | 0.417276i | ||||
\(683\) | − | 17296.4i | − | 0.969002i | −0.874791 | − | 0.484501i | \(-0.839001\pi\) | ||
0.874791 | − | 0.484501i | \(-0.160999\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15270.0i | 0.851730i | ||||||||
\(686\) | −8777.42 | + | 15677.6i | −0.488518 | + | 0.872554i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −28411.6 | + | 10033.3i | −1.57439 | + | 0.555985i | ||||
\(689\) | − | 9963.06i | − | 0.550889i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30696.5 | −1.68994 | −0.844970 | − | 0.534814i | \(-0.820382\pi\) | ||||
−0.844970 | + | 0.534814i | \(0.820382\pi\) | |||||||
\(692\) | 9280.51 | − | 13119.5i | 0.509815 | − | 0.720708i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5743.47 | − | 18064.7i | 0.314148 | − | 0.988081i | ||||
\(695\) | − | 12336.6i | − | 0.673315i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19110.8 | 1.03856 | ||||||||
\(698\) | −3354.39 | + | 10550.4i | −0.181899 | + | 0.572121i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2751.42 | + | 442.847i | 0.148563 | + | 0.0239115i | ||||
\(701\) | −27695.1 | −1.49219 | −0.746097 | − | 0.665837i | \(-0.768075\pi\) | ||||
−0.746097 | + | 0.665837i | \(0.768075\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1840.77 | 0.0987569 | ||||||||
\(704\) | 8891.45 | + | 2520.14i | 0.476007 | + | 0.134917i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8444.47 | + | 26560.1i | −0.450158 | + | 1.41587i | ||||
\(707\) | −5248.10 | − | 10697.9i | −0.279173 | − | 0.569073i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10901.1 | −0.577433 | −0.288716 | − | 0.957415i | \(-0.593228\pi\) | ||||
−0.288716 | + | 0.957415i | \(0.593228\pi\) | |||||||
\(710\) | 27655.6 | + | 8792.77i | 1.46183 | + | 0.464770i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1214.82 | − | 918.354i | 0.0639430 | − | 0.0483382i | ||||
\(713\) | 5162.39i | 0.271154i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 9121.92i | − | 0.477120i | ||||||
\(716\) | 17205.1 | − | 24322.2i | 0.898022 | − | 1.26950i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8673.10 | − | 27279.2i | 0.450804 | − | 1.41790i | ||||
\(719\) | −28539.3 | −1.48030 | −0.740150 | − | 0.672442i | \(-0.765245\pi\) | ||||
−0.740150 | + | 0.672442i | \(0.765245\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13873.8 | + | 6806.14i | −0.716627 | + | 0.351559i | ||||
\(722\) | 12056.9 | + | 3833.34i | 0.621483 | + | 0.197593i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9289.38 | − | 13132.1i | 0.476847 | − | 0.674102i | ||||
\(725\) | −906.288 | −0.0464258 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1103.93 | −0.0563169 | −0.0281584 | − | 0.999603i | \(-0.508964\pi\) | ||||
−0.0281584 | + | 0.999603i | \(0.508964\pi\) | |||||||
\(728\) | −9260.09 | + | 18347.1i | −0.471431 | + | 0.934049i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 21964.7 | + | 6983.42i | 1.11363 | + | 0.354066i | ||||
\(731\) | −21982.9 | −1.11227 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12729.3i | 0.641431i | 0.947176 | + | 0.320716i | \(0.103923\pi\) | ||||
−0.947176 | + | 0.320716i | \(0.896077\pi\) | |||||||
\(734\) | −12018.3 | − | 3821.06i | −0.604362 | − | 0.192150i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6114.70 | − | 193.536i | 0.306238 | − | 0.00969271i | ||||
\(737\) | −4338.81 | −0.216855 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 20655.8i | − | 1.02819i | −0.857732 | − | 0.514097i | \(-0.828127\pi\) | ||
0.857732 | − | 0.514097i | \(-0.171873\pi\) | |||||||
\(740\) | −1794.12 | + | 2536.28i | −0.0891259 | + | 0.125994i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −10525.3 | + | 1571.88i | −0.520748 | + | 0.0777702i | ||||
\(743\) | 30656.9i | 1.51372i | 0.653577 | + | 0.756860i | \(0.273268\pi\) | ||||
−0.653577 | + | 0.756860i | \(0.726732\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12349.4i | 0.607312i | ||||||||
\(746\) | −2235.60 | − | 710.783i | −0.109720 | − | 0.0348842i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5504.52 | + | 3893.79i | 0.269071 | + | 0.190336i | ||||
\(749\) | −12325.3 | − | 25124.2i | −0.601276 | − | 1.22566i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18986.0i | 0.922513i | 0.887267 | + | 0.461257i | \(0.152601\pi\) | ||||
−0.887267 | + | 0.461257i | \(0.847399\pi\) | |||||||
\(752\) | 11699.5 | + | 33129.6i | 0.567335 | + | 1.60653i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2025.03 | − | 6369.25i | 0.0978079 | − | 0.307632i | ||||
\(755\) | −31515.1 | −1.51914 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22252.7 | 1.06841 | 0.534206 | − | 0.845354i | \(-0.320611\pi\) | ||||
0.534206 | + | 0.845354i | \(0.320611\pi\) | |||||||
\(758\) | −446.746 | + | 1405.14i | −0.0214071 | + | 0.0673310i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 9085.71 | − | 6868.40i | 0.433649 | − | 0.327820i | ||||
\(761\) | 21595.4i | 1.02869i | 0.857583 | + | 0.514346i | \(0.171965\pi\) | ||||
−0.857583 | + | 0.514346i | \(0.828035\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22402.6 | + | 10990.2i | −1.06295 | + | 0.521456i | ||||
\(764\) | 5394.65 | − | 7626.23i | 0.255460 | − | 0.361135i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −33978.0 | − | 10802.9i | −1.60271 | − | 0.509562i | ||||
\(767\) | − | 35167.1i | − | 1.65555i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 37574.2i | − | 1.76198i | −0.473139 | − | 0.880988i | \(-0.656879\pi\) | ||
0.473139 | − | 0.880988i | \(-0.343121\pi\) | |||||||
\(770\) | −9636.67 | + | 1439.17i | −0.451015 | + | 0.0673561i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −29270.6 | − | 20705.5i | −1.36460 | − | 0.965293i | ||||
\(773\) | 31649.2i | 1.47263i | 0.676638 | + | 0.736315i | \(0.263436\pi\) | ||||
−0.676638 | + | 0.736315i | \(0.736564\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2873.14 | 0.133169 | ||||||||
\(776\) | 16874.0 | − | 12756.0i | 0.780593 | − | 0.590095i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −30361.4 | − | 9653.04i | −1.39911 | − | 0.444831i | ||||
\(779\) | − | 19992.3i | − | 0.919511i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17971.6 | 0.823401 | ||||||||
\(782\) | 4253.55 | + | 1352.37i | 0.194510 | + | 0.0618420i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 20843.4 | + | 6888.01i | 0.949497 | + | 0.313776i | ||||
\(785\) | −23341.1 | −1.06125 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13129.8 | −0.594698 | −0.297349 | − | 0.954769i | \(-0.596103\pi\) | ||||
−0.297349 | + | 0.954769i | \(0.596103\pi\) | |||||||
\(788\) | −28956.4 | − | 20483.2i | −1.30905 | − | 0.925995i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5947.25 | − | 1890.86i | −0.267840 | − | 0.0851565i | ||||
\(791\) | −27887.8 | + | 13681.0i | −1.25357 | + | 0.614970i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24200.2 | −1.08370 | ||||||||
\(794\) | 2831.57 | − | 8906.06i | 0.126560 | − | 0.398066i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 18909.8 | + | 13376.4i | 0.842011 | + | 0.595623i | ||||
\(797\) | 14391.2i | 0.639603i | 0.947485 | + | 0.319802i | \(0.103616\pi\) | ||||
−0.947485 | + | 0.319802i | \(0.896384\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25633.4i | 1.13497i | ||||||||
\(800\) | −107.713 | − | 3403.15i | −0.00476029 | − | 0.150399i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 15506.7 | + | 4930.16i | 0.682744 | + | 0.217070i | ||||
\(803\) | 14273.5 | 0.627273 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5790.70 | + | 2840.77i | −0.253534 | + | 0.124378i | ||||
\(806\) | −6419.80 | + | 20192.0i | −0.280555 | + | 0.882423i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −11613.4 | + | 8779.22i | −0.505640 | + | 0.382242i | ||||
\(809\) | 5116.40 | 0.222352 | 0.111176 | − | 0.993801i | \(-0.464538\pi\) | ||||
0.111176 | + | 0.993801i | \(0.464538\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9442.84 | −0.408857 | −0.204429 | − | 0.978881i | \(-0.565534\pi\) | ||||
−0.204429 | + | 0.978881i | \(0.565534\pi\) | |||||||
\(812\) | −7048.16 | − | 1134.42i | −0.304608 | − | 0.0490274i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −582.942 | + | 1833.51i | −0.0251009 | + | 0.0789490i | ||||
\(815\) | 15426.5 | 0.663029 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22996.9i | 0.984773i | ||||||||
\(818\) | 1484.06 | − | 4667.77i | 0.0634340 | − | 0.199517i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 27546.1 | + | 19485.6i | 1.17311 | + | 0.829838i | ||||
\(821\) | 8380.02 | 0.356230 | 0.178115 | − | 0.984010i | \(-0.443000\pi\) | ||||
0.178115 | + | 0.984010i | \(0.443000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 30980.2i | − | 1.31215i | −0.754694 | − | 0.656077i | \(-0.772215\pi\) | ||
0.754694 | − | 0.656077i | \(-0.227785\pi\) | |||||||
\(824\) | 11385.6 | + | 15061.1i | 0.481353 | + | 0.636747i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −37151.5 | + | 5548.34i | −1.56497 | + | 0.233718i | ||||
\(827\) | − | 21707.7i | − | 0.912760i | −0.889785 | − | 0.456380i | \(-0.849146\pi\) | ||
0.889785 | − | 0.456380i | \(-0.150854\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 40210.4i | − | 1.68464i | −0.538980 | − | 0.842319i | \(-0.681190\pi\) | ||
0.538980 | − | 0.842319i | \(-0.318810\pi\) | |||||||
\(830\) | 7817.41 | − | 24587.9i | 0.326923 | − | 1.02826i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 24157.5 | + | 6847.07i | 1.00662 | + | 0.285312i | ||||
\(833\) | 12665.6 | + | 9802.21i | 0.526814 | + | 0.407715i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 6929.49i | − | 0.287192i | ||||||
\(836\) | 4073.40 | − | 5758.43i | 0.168519 | − | 0.238229i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −37418.9 | − | 11896.9i | −1.54250 | − | 0.490419i | ||||
\(839\) | 1008.67 | 0.0415056 | 0.0207528 | − | 0.999785i | \(-0.493394\pi\) | ||||
0.0207528 | + | 0.999785i | \(0.493394\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22067.4 | −0.904810 | ||||||||
\(842\) | 9012.37 | + | 2865.37i | 0.368868 | + | 0.117277i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 10687.2 | − | 15108.1i | 0.435862 | − | 0.616163i | ||||
\(845\) | − | 2143.86i | − | 0.0872791i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16713.5 | − | 8199.24i | 0.678021 | − | 0.332620i | ||||
\(848\) | 4329.53 | + | 12260.0i | 0.175326 | + | 0.496475i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 752.662 | − | 2367.33i | 0.0303719 | − | 0.0955278i | ||||
\(851\) | 1273.60i | 0.0513027i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 41994.2i | 1.68564i | 0.538193 | + | 0.842821i | \(0.319107\pi\) | ||||
−0.538193 | + | 0.842821i | \(0.680893\pi\) | |||||||
\(854\) | 3818.08 | + | 25565.8i | 0.152988 | + | 1.02441i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −27274.3 | + | 20618.2i | −1.08904 | + | 0.823265i | ||||
\(857\) | − | 43337.5i | − | 1.72740i | −0.504007 | − | 0.863700i | \(-0.668141\pi\) | ||
0.504007 | − | 0.863700i | \(-0.331859\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25845.0 | 1.02657 | 0.513283 | − | 0.858219i | \(-0.328429\pi\) | ||||
0.513283 | + | 0.858219i | \(0.328429\pi\) | |||||||
\(860\) | −31686.0 | − | 22414.0i | −1.25638 | − | 0.888736i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6064.02 | + | 19073.0i | −0.239607 | + | 0.753629i | ||||
\(863\) | − | 4759.33i | − | 0.187728i | −0.995585 | − | 0.0938641i | \(-0.970078\pi\) | ||
0.995585 | − | 0.0938641i | \(-0.0299219\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20700.2 | 0.813672 | ||||||||
\(866\) | 4208.03 | − | 13235.4i | 0.165121 | − | 0.519349i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 22344.3 | + | 3596.36i | 0.873749 | + | 0.140632i | ||||
\(869\) | −3864.74 | −0.150866 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11788.3 | −0.458588 | ||||||||
\(872\) | 18384.8 | + | 24319.9i | 0.713976 | + | 0.944466i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1414.74 | − | 4449.75i | 0.0547534 | − | 0.172214i | ||||
\(875\) | 12088.0 | + | 24640.5i | 0.467028 | + | 0.952003i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4600.79 | −0.177147 | −0.0885734 | − | 0.996070i | \(-0.528231\pi\) | ||||
−0.0885734 | + | 0.996070i | \(0.528231\pi\) | |||||||
\(878\) | −36241.0 | − | 11522.4i | −1.39302 | − | 0.442895i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3964.01 | + | 11225.0i | 0.151849 | + | 0.429992i | ||||
\(881\) | 12349.2i | 0.472253i | 0.971722 | + | 0.236127i | \(0.0758780\pi\) | ||||
−0.971722 | + | 0.236127i | \(0.924122\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 20446.6i | − | 0.779257i | −0.920972 | − | 0.389629i | \(-0.872603\pi\) | ||
0.920972 | − | 0.389629i | \(-0.127397\pi\) | |||||||
\(884\) | 14955.4 | + | 10579.2i | 0.569011 | + | 0.402508i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12825.3 | − | 40339.0i | 0.486314 | − | 1.52959i | ||||
\(887\) | 12482.1 | 0.472502 | 0.236251 | − | 0.971692i | \(-0.424081\pi\) | ||||
0.236251 | + | 0.971692i | \(0.424081\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3272.64 | − | 6671.04i | −0.123466 | − | 0.251675i | ||||
\(890\) | 1869.43 | + | 594.362i | 0.0704084 | + | 0.0223855i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 27229.8 | + | 19261.8i | 1.02211 | + | 0.723020i | ||||
\(893\) | 26815.8 | 1.00488 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 38375.9 | 1.43326 | ||||||||
\(896\) | 3422.11 | − | 26601.0i | 0.127594 | − | 0.991826i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 29404.2 | + | 9348.71i | 1.09269 | + | 0.347406i | ||||
\(899\) | −7359.96 | −0.273046 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9485.95i | 0.350747i | ||||||||
\(902\) | 19913.4 | + | 6331.23i | 0.735083 | + | 0.233711i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 22886.1 | + | 30274.4i | 0.842015 | + | 1.11384i | ||||
\(905\) | 20719.9 | 0.761054 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 16244.3i | − | 0.594690i | −0.954770 | − | 0.297345i | \(-0.903899\pi\) | ||
0.954770 | − | 0.297345i | \(-0.0961011\pi\) | |||||||
\(908\) | −22610.7 | − | 15994.4i | −0.826391 | − | 0.584573i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −26182.2 | + | 3910.14i | −0.953772 | + | 0.142440i | ||||
\(911\) | 18806.3i | 0.683953i | 0.939709 | + | 0.341976i | \(0.111096\pi\) | ||||
−0.939709 | + | 0.341976i | \(0.888904\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 15978.1i | − | 0.579187i | ||||||
\(914\) | −12951.3 | − | 4117.70i | −0.468698 | − | 0.149017i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1401.74 | + | 1981.59i | −0.0505620 | + | 0.0714777i | ||||
\(917\) | −742.315 | + | 364.161i | −0.0267322 | + | 0.0131141i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42382.0i | 1.52128i | 0.649176 | + | 0.760639i | \(0.275114\pi\) | ||||
−0.649176 | + | 0.760639i | \(0.724886\pi\) | |||||||
\(920\) | 4752.14 | + | 6286.26i | 0.170297 | + | 0.225274i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 5219.17 | − | 16415.7i | 0.186426 | − | 0.586358i | ||||
\(923\) | 48827.8 | 1.74126 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 708.827 | 0.0251958 | ||||||||
\(926\) | 3555.94 | − | 11184.4i | 0.126194 | − | 0.396913i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 275.922 | + | 8717.66i | 0.00976034 | + | 0.308374i | ||||
\(929\) | − | 14960.7i | − | 0.528357i | −0.964474 | − | 0.264178i | \(-0.914899\pi\) | ||
0.964474 | − | 0.264178i | \(-0.0851008\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10254.4 | − | 13249.8i | 0.360980 | − | 0.466428i | ||||
\(932\) | −14474.6 | − | 10239.0i | −0.508724 | − | 0.359861i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 17785.3 | + | 5654.63i | 0.623077 | + | 0.198100i | ||||
\(935\) | 8685.09i | 0.303779i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 24321.2i | − | 0.847961i | −0.905671 | − | 0.423980i | \(-0.860633\pi\) | ||
0.905671 | − | 0.423980i | \(-0.139367\pi\) | |||||||
\(938\) | 1859.84 | + | 12453.5i | 0.0647399 | + | 0.433497i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −26136.1 | + | 36947.7i | −0.906879 | + | 1.28202i | ||||
\(941\) | 7556.97i | 0.261796i | 0.991396 | + | 0.130898i | \(0.0417861\pi\) | ||||
−0.991396 | + | 0.130898i | \(0.958214\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13832.4 | 0.477672 | ||||||||
\(944\) | 15282.1 | + | 43274.7i | 0.526898 | + | 1.49203i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −22906.1 | − | 7282.73i | −0.787255 | − | 0.250298i | ||||
\(947\) | 35766.4i | 1.22730i | 0.789579 | + | 0.613649i | \(0.210299\pi\) | ||||
−0.789579 | + | 0.613649i | \(0.789701\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 38780.1 | 1.32651 | ||||||||
\(950\) | −2476.52 | − | 787.380i | −0.0845779 | − | 0.0268905i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 8816.64 | − | 17468.5i | 0.300157 | − | 0.594702i | ||||
\(953\) | 7503.23 | 0.255040 | 0.127520 | − | 0.991836i | \(-0.459298\pi\) | ||||
0.127520 | + | 0.991836i | \(0.459298\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12032.7 | 0.407718 | ||||||||
\(956\) | 4909.55 | − | 6940.46i | 0.166094 | − | 0.234802i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −12114.5 | − | 3851.64i | −0.408560 | − | 0.129897i | ||||
\(959\) | 24638.5 | − | 12087.0i | 0.829634 | − | 0.406998i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6458.24 | −0.216785 | ||||||||
\(962\) | −1583.82 | + | 4981.53i | −0.0530814 | + | 0.166955i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 33885.9 | − | 47903.4i | 1.13215 | − | 1.60048i | ||||
\(965\) | − | 46183.5i | − | 1.54062i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41391.4i | 1.37648i | 0.725482 | + | 0.688241i | \(0.241617\pi\) | ||||
−0.725482 | + | 0.688241i | \(0.758383\pi\) | |||||||
\(968\) | −13716.0 | − | 18143.9i | −0.455422 | − | 0.602445i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 25966.5 | + | 8255.73i | 0.859520 | + | 0.273274i | ||||
\(971\) | −18250.3 | −0.603171 | −0.301586 | − | 0.953439i | \(-0.597516\pi\) | ||||
−0.301586 | + | 0.953439i | \(0.597516\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19905.5 | + | 9765.12i | −0.655848 | + | 0.321742i | ||||
\(974\) | 10766.0 | − | 33861.9i | 0.354173 | − | 1.11397i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 29779.4 | − | 10516.4i | 0.976657 | − | 0.344899i | ||||
\(977\) | −17959.5 | −0.588102 | −0.294051 | − | 0.955790i | \(-0.595004\pi\) | ||||
−0.294051 | + | 0.955790i | \(0.595004\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1214.82 | 0.0396588 | ||||||||
\(980\) | 8261.58 | + | 27042.8i | 0.269292 | + | 0.881480i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 10431.3 | − | 32809.2i | 0.338978 | − | 1.06618i | ||||
\(983\) | 47801.0 | 1.55098 | 0.775491 | − | 0.631359i | \(-0.217502\pi\) | ||||
0.775491 | + | 0.631359i | \(0.217502\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 45687.7i | − | 1.47790i | ||||||
\(986\) | −1928.05 | + | 6064.24i | −0.0622735 | + | 0.195867i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 11067.2 | − | 15645.3i | 0.356370 | − | 0.503788i | ||||
\(989\) | −15911.2 | −0.511574 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5324.87i | 0.170686i | 0.996352 | + | 0.0853431i | \(0.0271986\pi\) | ||||
−0.996352 | + | 0.0853431i | \(0.972801\pi\) | |||||||
\(992\) | −874.737 | − | 27637.0i | −0.0279969 | − | 0.884551i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −7703.60 | − | 51583.2i | −0.245818 | − | 1.64599i | ||||
\(995\) | 29836.1i | 0.950622i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 33227.4i | − | 1.05549i | −0.849403 | − | 0.527745i | \(-0.823038\pi\) | ||
0.849403 | − | 0.527745i | \(-0.176962\pi\) | |||||||
\(998\) | 2984.53 | − | 9387.16i | 0.0946631 | − | 0.297741i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 252.4.b.g.55.2 | yes | 16 | |
3.2 | odd | 2 | inner | 252.4.b.g.55.15 | yes | 16 | |
4.3 | odd | 2 | inner | 252.4.b.g.55.4 | yes | 16 | |
7.6 | odd | 2 | inner | 252.4.b.g.55.1 | ✓ | 16 | |
12.11 | even | 2 | inner | 252.4.b.g.55.13 | yes | 16 | |
21.20 | even | 2 | inner | 252.4.b.g.55.16 | yes | 16 | |
28.27 | even | 2 | inner | 252.4.b.g.55.3 | yes | 16 | |
84.83 | odd | 2 | inner | 252.4.b.g.55.14 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.4.b.g.55.1 | ✓ | 16 | 7.6 | odd | 2 | inner | |
252.4.b.g.55.2 | yes | 16 | 1.1 | even | 1 | trivial | |
252.4.b.g.55.3 | yes | 16 | 28.27 | even | 2 | inner | |
252.4.b.g.55.4 | yes | 16 | 4.3 | odd | 2 | inner | |
252.4.b.g.55.13 | yes | 16 | 12.11 | even | 2 | inner | |
252.4.b.g.55.14 | yes | 16 | 84.83 | odd | 2 | inner | |
252.4.b.g.55.15 | yes | 16 | 3.2 | odd | 2 | inner | |
252.4.b.g.55.16 | yes | 16 | 21.20 | even | 2 | inner |