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: | \( x^{16} - 4 x^{15} + 358 x^{14} - 2828 x^{13} + 52557 x^{12} - 549972 x^{11} + 4434734 x^{10} + \cdots + 52705588025 \) |
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 | 55.4 | ||
Root | \(0.929907 - 6.47387i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.55 |
Dual form | 252.4.b.g.55.1 |
$q$-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 | \(0.0795693\pi\) | ||||
−0.968919 | + | 0.247379i | \(0.920431\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 49.0412i | − | 1.04628i | −0.852248 | − | 0.523138i | \(-0.824761\pi\) | ||
0.852248 | − | 0.523138i | \(-0.175239\pi\) | |||||||
\(14\) | 37.8278 | − | 36.2361i | 0.722137 | − | 0.691750i | ||||
\(15\) | 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 | \(-0.595286\pi\) | ||||
−0.294899 | + | 0.955528i | \(0.595286\pi\) | |||||||
\(20\) | 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 | \(-0.951044\pi\) | ||
0.988196 | − | 0.153195i | \(-0.0489564\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 18.8094 | 0.150475 | ||||||||
\(26\) | 42.0280 | + | 132.189i | 0.317014 | + | 0.997094i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −70.9098 | + | 130.092i | −0.478596 | + | 0.878035i | ||||
\(29\) | −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 | \(-0.645907\pi\) | ||||
−0.442497 | + | 0.896770i | \(0.645907\pi\) | |||||||
\(32\) | −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 | \(-0.685560\pi\) | ||
0.550494 | − | 0.834839i | \(-0.314440\pi\) | |||||||
\(44\) | 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 | \(-0.824539\pi\) | ||||
−0.851883 | + | 0.523733i | \(0.824539\pi\) | |||||||
\(48\) | 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 | ||||||||
\(56\) | 79.6479 | − | 411.427i | 0.190061 | − | 0.981772i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 129.875 | − | 41.2923i | 0.294026 | − | 0.0934819i | ||||
\(59\) | −717.092 | −1.58233 | −0.791164 | − | 0.611604i | \(-0.790525\pi\) | ||||
−0.791164 | + | 0.611604i | \(0.790525\pi\) | |||||||
\(60\) | 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 | \(0.0703292\pi\) | ||||
−0.975691 | + | 0.219152i | \(0.929671\pi\) | |||||||
\(68\) | 215.720 | + | 304.956i | 0.384705 | + | 0.543844i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 373.409 | + | 389.811i | 0.637584 | + | 0.665591i | ||||
\(71\) | − | 995.648i | − | 1.66425i | −0.554589 | − | 0.832125i | \(-0.687124\pi\) | ||
0.554589 | − | 0.832125i | \(-0.312876\pi\) | |||||||
\(72\) | 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 | \(0.0487209\pi\) | ||||
−0.988309 | + | 0.152464i | \(0.951279\pi\) | |||||||
\(80\) | 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 | \(-0.699033\pi\) | ||||
−0.585324 | + | 0.810800i | \(0.699033\pi\) | |||||||
\(84\) | 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 | \(0.837263\pi\) | |||||||
\(98\) | −333.398 | + | 911.064i | −0.343656 | + | 0.939096i | ||||
\(99\) | 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 | \(-0.369320\pi\) | ||||
0.399108 | + | 0.916904i | \(0.369320\pi\) | |||||||
\(104\) | 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 | \(0.239150\pi\) | ||||
−0.730793 | + | 0.682599i | \(0.760850\pi\) | |||||||
\(108\) | 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 | ||||||||
\(112\) | 137.901 | + | 1177.25i | 0.116343 | + | 0.993209i | ||||
\(113\) | −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 | \(0.0447631\pi\) | ||||
−0.990128 | + | 0.140164i | \(0.955237\pi\) | |||||||
\(128\) | 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 | \(-0.495261\pi\) | ||||
0.0148878 | + | 0.999889i | \(0.495261\pi\) | |||||||
\(132\) | 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 | \(-0.380981\pi\) | ||||
0.365259 | + | 0.930906i | \(0.380981\pi\) | |||||||
\(140\) | −1340.58 | − | 730.717i | −0.809282 | − | 0.441121i | ||||
\(141\) | 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 | \(-0.691681\pi\) | ||
0.566444 | − | 0.824100i | \(-0.308319\pi\) | |||||||
\(152\) | 666.519 | − | 881.689i | 0.355670 | − | 0.470490i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 654.068 | + | 682.800i | 0.342249 | + | 0.357283i | ||||
\(155\) | − | 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 | \(0.117114\pi\) | ||||
−0.933076 | + | 0.359678i | \(0.882886\pi\) | |||||||
\(164\) | −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 | \(-0.450206\pi\) | ||||
0.155795 | + | 0.987789i | \(0.450206\pi\) | |||||||
\(168\) | 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 | \(0.283517\pi\) | ||||
−0.628872 | + | 0.777509i | \(0.716483\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2010.69i | − | 0.825710i | −0.910797 | − | 0.412855i | \(-0.864532\pi\) | ||
0.910797 | − | 0.412855i | \(-0.135468\pi\) | |||||||
\(182\) | −1777.06 | − | 1855.12i | −0.723762 | − | 0.755555i | ||||
\(183\) | 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 | \(0.0709901\pi\) | ||||
−0.975234 | + | 0.221178i | \(0.929010\pi\) | |||||||
\(192\) | 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 | ||||||||
\(196\) | 117.890 | − | 2741.47i | 0.0429630 | − | 0.999077i | ||||
\(197\) | −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 | \(-0.672465\pi\) | ||||
−0.515691 | + | 0.856775i | \(0.672465\pi\) | |||||||
\(200\) | −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 | \(0.123172\pi\) | ||||
−0.926063 | + | 0.377370i | \(0.876828\pi\) | |||||||
\(212\) | 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 | \(-0.715306\pi\) | ||||
−0.625992 | + | 0.779830i | \(0.715306\pi\) | |||||||
\(224\) | −1380.60 | − | 3055.06i | −0.411809 | − | 0.911270i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4520.93 | − | 1437.38i | 1.33066 | − | 0.423066i | ||||
\(227\) | 3461.99 | 1.01225 | 0.506124 | − | 0.862461i | \(-0.331078\pi\) | ||||
0.506124 | + | 0.862461i | \(0.331078\pi\) | |||||||
\(228\) | 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 | ||||||||
\(238\) | 1691.96 | + | 1766.29i | 0.460814 | + | 0.481056i | ||||
\(239\) | 1062.67i | 0.287609i | 0.989606 | + | 0.143805i | \(0.0459337\pi\) | ||||
−0.989606 | + | 0.143805i | \(0.954066\pi\) | |||||||
\(240\) | 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 | \(-0.233663\pi\) | ||||
0.742451 | + | 0.669900i | \(0.233663\pi\) | |||||||
\(252\) | 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 | \(0.0638555\pi\) | ||||
−0.979946 | + | 0.199265i | \(0.936144\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2093.51i | 0.485295i | ||||||||
\(266\) | −1847.76 | + | 1770.01i | −0.425915 | + | 0.407993i | ||||
\(267\) | 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 | \(-0.637748\pi\) | ||||
−0.419367 | + | 0.907817i | \(0.637748\pi\) | |||||||
\(272\) | 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 | ||||||||
\(280\) | 4239.71 | + | 820.762i | 0.904897 | + | 0.175178i | ||||
\(281\) | −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 | \(-0.224055\pi\) | ||||
0.762330 | + | 0.647188i | \(0.224055\pi\) | |||||||
\(284\) | −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 | \(-0.325656\pi\) | ||||
0.520741 | + | 0.853714i | \(0.325656\pi\) | |||||||
\(308\) | −2348.18 | − | 1279.94i | −0.434415 | − | 0.236789i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1348.97 | + | 4242.88i | 0.247150 | + | 0.777353i | ||||
\(311\) | −3081.12 | −0.561783 | −0.280891 | − | 0.959740i | \(-0.590630\pi\) | ||||
−0.280891 | + | 0.959740i | \(0.590630\pi\) | |||||||
\(312\) | 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 | ||||||||
\(322\) | −1224.64 | − | 1278.44i | −0.211946 | − | 0.221256i | ||||
\(323\) | − | 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 | \(0.237496\pi\) | ||||
−0.734331 | + | 0.678791i | \(0.762504\pi\) | |||||||
\(332\) | −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 | \(-0.826524\pi\) | ||
0.855132 | − | 0.518410i | \(-0.173476\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 3914.14i | − | 0.600341i | −0.953886 | − | 0.300171i | \(-0.902956\pi\) | ||
0.953886 | − | 0.300171i | \(-0.0970436\pi\) | |||||||
\(350\) | 711.517 | − | 681.577i | 0.108663 | − | 0.104091i | ||||
\(351\) | 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 | \(-0.732965\pi\) | ||
0.668270 | − | 0.743919i | \(-0.267035\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4473.02 | −0.652138 | ||||||||
\(362\) | 1723.15 | + | 5419.76i | 0.250184 | + | 0.786896i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6379.85 | + | 3477.50i | 0.918667 | + | 0.500744i | ||||
\(365\) | −8148.75 | −1.16856 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4458.69 | −0.634173 | −0.317086 | − | 0.948397i | \(-0.602705\pi\) | ||||
−0.317086 | + | 0.948397i | \(0.602705\pi\) | |||||||
\(368\) | −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 | \(0.0112470\pi\) | ||||
−0.999376 | + | 0.0353261i | \(0.988753\pi\) | |||||||
\(380\) | −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 | \(-0.817964\pi\) | ||||
−0.840883 | + | 0.541217i | \(0.817964\pi\) | |||||||
\(384\) | 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 | ||||||||
\(392\) | 2031.64 | + | 7490.57i | 0.261769 | + | 0.965130i | ||||
\(393\) | 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 | ||||||||
\(406\) | −1822.65 | + | 1745.96i | −0.222800 | + | 0.213425i | ||||
\(407\) | 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 | \(-0.800149\pi\) | ||||
−0.809293 | + | 0.587406i | \(0.800149\pi\) | |||||||
\(420\) | 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 | \(0.129394\pi\) | ||||
−0.918509 | + | 0.395401i | \(0.870606\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4910.23i | 0.544967i | 0.962160 | + | 0.272483i | \(0.0878450\pi\) | ||||
−0.962160 | + | 0.272483i | \(0.912155\pi\) | |||||||
\(434\) | −5778.23 | + | 5535.09i | −0.639087 | + | 0.612195i | ||||
\(435\) | 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 | \(-0.760885\pi\) | ||||
−0.730868 | + | 0.682518i | \(0.760885\pi\) | |||||||
\(440\) | 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 | \(-0.703493\pi\) | ||
0.596629 | − | 0.802518i | \(-0.296507\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −693.545 | −0.0738813 | ||||||||
\(446\) | 11238.0 | − | 3573.00i | 1.19313 | − | 0.379342i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6339.53 | + | 7051.65i | 0.668559 | + | 0.743659i | ||||
\(449\) | −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 | \(-0.933225\pi\) | ||
0.978077 | − | 0.208246i | \(-0.0667753\pi\) | |||||||
\(464\) | −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 | \(-0.393994\pi\) | ||||
0.326905 | + | 0.945057i | \(0.393994\pi\) | |||||||
\(468\) | 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 | ||||||||
\(476\) | −6074.33 | − | 3310.97i | −0.584909 | − | 0.318820i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −910.703 | − | 2864.41i | −0.0871435 | − | 0.274090i | ||||
\(479\) | −4494.37 | −0.428712 | −0.214356 | − | 0.976756i | \(-0.568765\pi\) | ||||
−0.214356 | + | 0.976756i | \(0.568765\pi\) | |||||||
\(480\) | 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 | \(-0.801307\pi\) | ||
0.811424 | − | 0.584458i | \(-0.198693\pi\) | |||||||
\(488\) | 8907.15 | + | 6733.42i | 0.826245 | + | 0.624606i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −9388.41 | − | 3435.63i | −0.865561 | − | 0.316747i | ||||
\(491\) | − | 12172.0i | − | 1.11877i | −0.828909 | − | 0.559383i | \(-0.811038\pi\) | ||
0.828909 | − | 0.559383i | \(-0.188962\pi\) | |||||||
\(492\) | 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 | \(-0.950071\pi\) | ||
0.987723 | − | 0.156214i | \(-0.0499288\pi\) | |||||||
\(500\) | 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 | \(-0.506781\pi\) | ||||
−0.0213021 | + | 0.999773i | \(0.506781\pi\) | |||||||
\(504\) | 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 | ||||||
\(518\) | 1425.54 | − | 1365.55i | 0.120916 | − | 0.115828i | ||||
\(519\) | 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 | \(-0.390760\pi\) | ||||
0.336491 | + | 0.941687i | \(0.390760\pi\) | |||||||
\(524\) | 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 | ||||||||
\(532\) | 3463.70 | − | 6354.52i | 0.282275 | − | 0.517863i | ||||
\(533\) | −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 | \(0.0432387\pi\) | ||||
−0.990788 | + | 0.135421i | \(0.956761\pi\) | |||||||
\(548\) | 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 | ||||||||
\(560\) | −12131.4 | + | 1421.06i | −0.915438 | + | 0.107233i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 17264.9 | − | 5489.17i | 1.29586 | − | 0.412004i | ||||
\(563\) | −13614.3 | −1.01914 | −0.509568 | − | 0.860430i | \(-0.670195\pi\) | ||||
−0.509568 | + | 0.860430i | \(0.670195\pi\) | |||||||
\(564\) | 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 | \(0.104281\pi\) | ||||
−0.946815 | + | 0.321779i | \(0.895719\pi\) | |||||||
\(572\) | 5781.38 | − | 4089.64i | 0.422608 | − | 0.298945i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −14831.0 | − | 15482.5i | −1.07846 | − | 1.12583i | ||||
\(575\) | − | 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 | \(-0.432534\pi\) | ||||
0.210368 | + | 0.977622i | \(0.432534\pi\) | |||||||
\(588\) | 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 | \(-0.846375\pi\) | ||
0.885779 | − | 0.464107i | \(-0.153625\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12594.1i | 0.854779i | 0.904068 | + | 0.427390i | \(0.140567\pi\) | ||||
−0.904068 | + | 0.427390i | \(0.859433\pi\) | |||||||
\(602\) | −17059.9 | − | 17809.3i | −1.15500 | − | 1.20574i | ||||
\(603\) | 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 | \(-0.619305\pi\) | ||||
−0.366094 | + | 0.930578i | \(0.619305\pi\) | |||||||
\(608\) | 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 | ||||||||
\(616\) | 7426.34 | + | 1437.66i | 0.485740 | + | 0.0940340i | ||||
\(617\) | −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 | \(-0.492481\pi\) | ||||
0.0236179 | + | 0.999721i | \(0.492481\pi\) | |||||||
\(620\) | −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 | \(0.231080\pi\) | ||||
−0.747862 | + | 0.663854i | \(0.768920\pi\) | |||||||
\(632\) | −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 | \(-0.192655\pi\) | ||||
0.822364 | + | 0.568962i | \(0.192655\pi\) | |||||||
\(644\) | 4396.60 | + | 2396.48i | 0.269022 | + | 0.146637i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1954.61 | + | 6147.78i | 0.119045 | + | 0.374429i | ||||
\(647\) | 27901.0 | 1.69537 | 0.847683 | − | 0.530503i | \(-0.177997\pi\) | ||||
0.847683 | + | 0.530503i | \(0.177997\pi\) | |||||||
\(648\) | 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 | ||||||||
\(658\) | −20766.7 | + | 19892.9i | −1.23035 | + | 1.17858i | ||||
\(659\) | − | 6511.96i | − | 0.384931i | −0.981304 | − | 0.192466i | \(-0.938352\pi\) | ||
0.981304 | − | 0.192466i | \(-0.0616484\pi\) | |||||||
\(660\) | 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 | \(0.160999\pi\) | ||||
−0.874791 | + | 0.484501i | \(0.839001\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15270.0i | 0.851730i | ||||||||
\(686\) | −1887.97 | − | 17868.0i | −0.105077 | − | 0.994464i | ||||
\(687\) | 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 | \(-0.179618\pi\) | ||||
0.844970 | + | 0.534814i | \(0.179618\pi\) | |||||||
\(692\) | −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 | ||||||||
\(700\) | −1333.77 | + | 2446.94i | −0.0720167 | + | 0.132122i | ||||
\(701\) | −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 | \(-0.234755\pi\) | ||||
0.740150 | + | 0.672442i | \(0.234755\pi\) | |||||||
\(720\) | 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 | \(-0.491036\pi\) | ||||
0.0281584 | + | 0.999603i | \(0.491036\pi\) | |||||||
\(728\) | −20176.9 | − | 3906.03i | −1.02721 | − | 0.198856i | ||||
\(729\) | 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 | \(0.171873\pi\) | ||||
−0.857732 | + | 0.514097i | \(0.828127\pi\) | |||||||
\(740\) | 1794.12 | + | 2536.28i | 0.0891259 | + | 0.125994i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7684.98 | − | 7361.61i | 0.380222 | − | 0.364223i | ||||
\(743\) | − | 30656.9i | − | 1.51372i | −0.653577 | − | 0.756860i | \(-0.726732\pi\) | ||
0.653577 | − | 0.756860i | \(-0.273268\pi\) | |||||||
\(744\) | 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 | \(-0.847399\pi\) | ||
0.887267 | − | 0.461257i | \(-0.152601\pi\) | |||||||
\(752\) | −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 | \(-0.343121\pi\) | |||||||
\(770\) | −7036.17 | + | 6740.10i | −0.329307 | + | 0.315450i | ||||
\(771\) | 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 | ||||||||
\(784\) | −11895.6 | − | 18449.5i | −0.541892 | − | 0.840448i | ||||
\(785\) | −23341.1 | −1.06125 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13129.8 | 0.594698 | 0.297349 | − | 0.954769i | \(-0.403897\pi\) | ||||
0.297349 | + | 0.954769i | \(0.403897\pi\) | |||||||
\(788\) | −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 | \(-0.434466\pi\) | ||||
0.204429 | + | 0.978881i | \(0.434466\pi\) | |||||||
\(812\) | 3416.64 | − | 6268.18i | 0.147661 | − | 0.270899i | ||||
\(813\) | 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 | \(0.227785\pi\) | ||||
−0.754694 | + | 0.656077i | \(0.772215\pi\) | |||||||
\(824\) | −11385.6 | + | 15061.1i | −0.481353 | + | 0.636747i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −27126.0 | + | 25984.6i | −1.14266 | + | 1.09458i | ||||
\(827\) | 21707.7i | 0.912760i | 0.889785 | + | 0.456380i | \(0.150854\pi\) | ||||
−0.889785 | + | 0.456380i | \(0.849146\pi\) | |||||||
\(828\) | 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 | \(-0.506606\pi\) | ||||
−0.0207528 | + | 0.999785i | \(0.506606\pi\) | |||||||
\(840\) | 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 | \(0.680893\pi\) | |||||||
\(854\) | −17881.3 | − | 18666.7i | −0.716492 | − | 0.747965i | ||||
\(855\) | 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 | \(-0.671571\pi\) | ||||
−0.513283 | + | 0.858219i | \(0.671571\pi\) | |||||||
\(860\) | 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 | \(0.0299219\pi\) | ||||
−0.995585 | + | 0.0938641i | \(0.970078\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20700.2 | 0.813672 | ||||||||
\(866\) | −4208.03 | − | 13235.4i | −0.165121 | − | 0.519349i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 10831.5 | − | 19871.6i | 0.423555 | − | 0.777056i | ||||
\(869\) | −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 | \(0.127397\pi\) | ||||
−0.920972 | + | 0.389629i | \(0.872603\pi\) | |||||||
\(884\) | 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 | \(-0.575919\pi\) | ||||
−0.236251 | + | 0.971692i | \(0.575919\pi\) | |||||||
\(888\) | 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 | ||||||||
\(896\) | −23131.2 | − | 13574.6i | −0.862455 | − | 0.506133i | ||||
\(897\) | 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 | \(0.0961011\pi\) | ||||
−0.954770 | + | 0.297345i | \(0.903899\pi\) | |||||||
\(908\) | 22610.7 | − | 15994.4i | 0.826391 | − | 0.584573i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 19116.8 | − | 18312.4i | 0.696392 | − | 0.667089i | ||||
\(911\) | − | 18806.3i | − | 0.683953i | −0.939709 | − | 0.341976i | \(-0.888904\pi\) | ||
0.939709 | − | 0.341976i | \(-0.111096\pi\) | |||||||
\(912\) | 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 | \(-0.724886\pi\) | ||
0.649176 | − | 0.760639i | \(-0.275114\pi\) | |||||||
\(920\) | −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 | \(-0.139367\pi\) | |||||||
\(938\) | 8710.24 | + | 9092.85i | 0.303198 | + | 0.316516i | ||||
\(939\) | 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 | \(-0.789701\pi\) | ||
0.789579 | − | 0.613649i | \(-0.210299\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 38780.1 | 1.32651 | ||||||||
\(950\) | 2476.52 | − | 787.380i | 0.0845779 | − | 0.0268905i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 19210.7 | + | 3718.98i | 0.654014 | + | 0.126610i | ||||
\(953\) | 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 | \(-0.758383\pi\) | ||
0.725482 | − | 0.688241i | \(-0.241617\pi\) | |||||||
\(968\) | −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 | \(-0.402484\pi\) | ||||
0.301586 | + | 0.953439i | \(0.402484\pi\) | |||||||
\(972\) | 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 | ||||||||
\(980\) | 28250.5 | + | 1214.85i | 0.920846 | + | 0.0395989i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 10431.3 | + | 32809.2i | 0.338978 | + | 1.06618i | ||||
\(983\) | −47801.0 | −1.55098 | −0.775491 | − | 0.631359i | \(-0.782498\pi\) | ||||
−0.775491 | + | 0.631359i | \(0.782498\pi\) | |||||||
\(984\) | 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 | \(-0.972801\pi\) | ||
0.996352 | − | 0.0853431i | \(-0.0271986\pi\) | |||||||
\(992\) | 874.737 | − | 27637.0i | 0.0279969 | − | 0.884551i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −36078.4 | − | 37663.2i | −1.15125 | − | 1.20182i | ||||
\(995\) | − | 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.55.4 | yes | 16 | |
3.2 | odd | 2 | inner | 252.4.b.g.55.13 | yes | 16 | |
4.3 | odd | 2 | inner | 252.4.b.g.55.2 | yes | 16 | |
7.6 | odd | 2 | inner | 252.4.b.g.55.3 | yes | 16 | |
12.11 | even | 2 | inner | 252.4.b.g.55.15 | yes | 16 | |
21.20 | even | 2 | inner | 252.4.b.g.55.14 | yes | 16 | |
28.27 | even | 2 | inner | 252.4.b.g.55.1 | ✓ | 16 | |
84.83 | odd | 2 | inner | 252.4.b.g.55.16 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.4.b.g.55.1 | ✓ | 16 | 28.27 | even | 2 | inner | |
252.4.b.g.55.2 | yes | 16 | 4.3 | odd | 2 | inner | |
252.4.b.g.55.3 | yes | 16 | 7.6 | odd | 2 | inner | |
252.4.b.g.55.4 | yes | 16 | 1.1 | even | 1 | trivial | |
252.4.b.g.55.13 | yes | 16 | 3.2 | odd | 2 | inner | |
252.4.b.g.55.14 | yes | 16 | 21.20 | even | 2 | inner | |
252.4.b.g.55.15 | yes | 16 | 12.11 | even | 2 | inner | |
252.4.b.g.55.16 | yes | 16 | 84.83 | odd | 2 | inner |