Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,4,Mod(193,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.193");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.q (of order \(3\), degree \(2\), not 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: | \(19.8246417619\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 193.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.193 |
Dual form | 336.4.q.a.289.1 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.50000 | + | 2.59808i | −0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.50000 | − | 6.06218i | −0.313050 | − | 0.542218i | 0.665971 | − | 0.745977i | \(-0.268017\pi\) |
−0.979021 | + | 0.203760i | \(0.934684\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 17.5000 | − | 6.06218i | 0.944911 | − | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.50000 | − | 7.79423i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.50000 | − | 6.06218i | 0.0959354 | − | 0.166165i | −0.814063 | − | 0.580776i | \(-0.802749\pi\) |
0.909999 | + | 0.414611i | \(0.136082\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −52.0000 | −1.10940 | −0.554700 | − | 0.832050i | \(-0.687167\pi\) | ||||
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 21.0000 | 0.361478 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −36.0000 | + | 62.3538i | −0.513605 | + | 0.889590i | 0.486271 | + | 0.873808i | \(0.338357\pi\) |
−0.999875 | + | 0.0157814i | \(0.994976\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 10.0000 | + | 17.3205i | 0.120745 | + | 0.209137i | 0.920062 | − | 0.391773i | \(-0.128138\pi\) |
−0.799317 | + | 0.600910i | \(0.794805\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −10.5000 | + | 54.5596i | −0.109109 | + | 0.566947i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −24.0000 | − | 41.5692i | −0.217580 | − | 0.376860i | 0.736487 | − | 0.676451i | \(-0.236483\pi\) |
−0.954068 | + | 0.299591i | \(0.903150\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 38.0000 | − | 65.8179i | 0.304000 | − | 0.526543i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −243.000 | −1.55600 | −0.777999 | − | 0.628265i | \(-0.783765\pi\) | ||||
−0.777999 | + | 0.628265i | \(0.783765\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 47.5000 | − | 82.2724i | 0.275202 | − | 0.476663i | −0.694984 | − | 0.719025i | \(-0.744589\pi\) |
0.970186 | + | 0.242362i | \(0.0779220\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 10.5000 | + | 18.1865i | 0.0553883 | + | 0.0959354i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −98.0000 | − | 84.8705i | −0.473286 | − | 0.409878i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −176.000 | − | 304.841i | −0.782006 | − | 1.35447i | −0.930771 | − | 0.365602i | \(-0.880863\pi\) |
0.148765 | − | 0.988873i | \(-0.452470\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 78.0000 | − | 135.100i | 0.320256 | − | 0.554700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −296.000 | −1.12750 | −0.563749 | − | 0.825946i | \(-0.690642\pi\) | ||||
−0.563749 | + | 0.825946i | \(0.690642\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −158.000 | −0.560344 | −0.280172 | − | 0.959950i | \(-0.590391\pi\) | ||||
−0.280172 | + | 0.959950i | \(0.590391\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −31.5000 | + | 54.5596i | −0.104350 | + | 0.180739i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −71.0000 | − | 122.976i | −0.220349 | − | 0.381656i | 0.734565 | − | 0.678539i | \(-0.237386\pi\) |
−0.954914 | + | 0.296882i | \(0.904053\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 269.500 | − | 212.176i | 0.785714 | − | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −108.000 | − | 187.061i | −0.296530 | − | 0.513605i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 187.500 | − | 324.760i | 0.485945 | − | 0.841682i | −0.513924 | − | 0.857836i | \(-0.671809\pi\) |
0.999870 | + | 0.0161535i | \(0.00514205\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −49.0000 | −0.120130 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −60.0000 | −0.139424 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 139.500 | − | 241.621i | 0.307820 | − | 0.533159i | −0.670066 | − | 0.742302i | \(-0.733734\pi\) |
0.977885 | + | 0.209143i | \(0.0670674\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −123.000 | − | 213.042i | −0.258173 | − | 0.447168i | 0.707580 | − | 0.706634i | \(-0.249787\pi\) |
−0.965752 | + | 0.259465i | \(0.916454\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −126.000 | − | 109.119i | −0.251976 | − | 0.218218i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 182.000 | + | 315.233i | 0.347297 | + | 0.601536i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −365.000 | + | 632.199i | −0.665550 | + | 1.15277i | 0.313586 | + | 0.949560i | \(0.398470\pi\) |
−0.979136 | + | 0.203207i | \(0.934864\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 144.000 | 0.251240 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −338.000 | −0.564975 | −0.282487 | − | 0.959271i | \(-0.591160\pi\) | ||||
−0.282487 | + | 0.959271i | \(0.591160\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 271.000 | − | 469.386i | 0.434495 | − | 0.752568i | −0.562759 | − | 0.826621i | \(-0.690260\pi\) |
0.997254 | + | 0.0740532i | \(0.0235935\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 114.000 | + | 197.454i | 0.175514 | + | 0.304000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 24.5000 | − | 127.306i | 0.0362602 | − | 0.188413i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −152.500 | − | 264.138i | −0.217185 | − | 0.376175i | 0.736761 | − | 0.676153i | \(-0.236354\pi\) |
−0.953946 | + | 0.299978i | \(0.903021\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −40.5000 | + | 70.1481i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1123.00 | −1.48512 | −0.742562 | − | 0.669778i | \(-0.766389\pi\) | ||||
−0.742562 | + | 0.669778i | \(0.766389\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 504.000 | 0.643135 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 364.500 | − | 631.333i | 0.449178 | − | 0.777999i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 213.000 | + | 368.927i | 0.253685 | + | 0.439395i | 0.964537 | − | 0.263946i | \(-0.0850240\pi\) |
−0.710853 | + | 0.703341i | \(0.751691\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −910.000 | + | 315.233i | −1.04828 | + | 0.363137i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 142.500 | + | 246.817i | 0.158888 | + | 0.275202i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 70.0000 | − | 121.244i | 0.0755984 | − | 0.130940i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −369.000 | −0.386250 | −0.193125 | − | 0.981174i | \(-0.561862\pi\) | ||||
−0.193125 | + | 0.981174i | \(0.561862\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −63.0000 | −0.0639570 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −635.000 | + | 1099.85i | −0.625593 | + | 1.08356i | 0.362833 | + | 0.931854i | \(0.381809\pi\) |
−0.988426 | + | 0.151704i | \(0.951524\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 916.000 | + | 1586.56i | 0.876273 | + | 1.51775i | 0.855400 | + | 0.517968i | \(0.173311\pi\) |
0.0208734 | + | 0.999782i | \(0.493355\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 367.500 | − | 127.306i | 0.341565 | − | 0.118322i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −499.500 | − | 865.159i | −0.451294 | − | 0.781665i | 0.547172 | − | 0.837020i | \(-0.315704\pi\) |
−0.998467 | + | 0.0553553i | \(0.982371\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 833.000 | − | 1442.80i | 0.731990 | − | 1.26784i | −0.224041 | − | 0.974580i | \(-0.571925\pi\) |
0.956031 | − | 0.293264i | \(-0.0947417\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1056.00 | 0.902983 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1832.00 | −1.52513 | −0.762567 | − | 0.646910i | \(-0.776061\pi\) | ||||
−0.762567 | + | 0.646910i | \(0.776061\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −168.000 | + | 290.985i | −0.136227 | + | 0.235952i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 234.000 | + | 405.300i | 0.184900 | + | 0.320256i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −252.000 | + | 1309.43i | −0.194124 | + | 1.00870i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 641.000 | + | 1110.24i | 0.481593 | + | 0.834143i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 444.000 | − | 769.031i | 0.325481 | − | 0.563749i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1407.00 | −1.00677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1931.00 | 1.34920 | 0.674601 | − | 0.738183i | \(-0.264316\pi\) | ||||
0.674601 | + | 0.738183i | \(0.264316\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 237.000 | − | 410.496i | 0.161757 | − | 0.280172i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 489.500 | + | 847.839i | 0.326472 | + | 0.565466i | 0.981809 | − | 0.189871i | \(-0.0608068\pi\) |
−0.655337 | + | 0.755336i | \(0.727473\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 280.000 | + | 242.487i | 0.182549 | + | 0.158092i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −94.5000 | − | 163.679i | −0.0602464 | − | 0.104350i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 243.000 | − | 420.888i | 0.151539 | − | 0.262474i | −0.780254 | − | 0.625463i | \(-0.784910\pi\) |
0.931794 | + | 0.362989i | \(0.118244\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2630.00 | 1.60485 | 0.802423 | − | 0.596755i | \(-0.203544\pi\) | ||||
0.802423 | + | 0.596755i | \(0.203544\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 426.000 | 0.254437 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −182.000 | + | 315.233i | −0.106431 | + | 0.184344i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 850.500 | + | 1473.11i | 0.487105 | + | 0.843690i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 147.000 | + | 1018.45i | 0.0824786 | + | 0.571429i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 939.000 | + | 1626.40i | 0.516281 | + | 0.894225i | 0.999821 | + | 0.0189029i | \(0.00601734\pi\) |
−0.483540 | + | 0.875322i | \(0.660649\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1051.50 | − | 1821.25i | 0.566688 | − | 0.981532i | −0.430203 | − | 0.902732i | \(-0.641558\pi\) |
0.996890 | − | 0.0787997i | \(-0.0251088\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 648.000 | 0.342403 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −665.000 | −0.344607 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −702.000 | + | 1215.90i | −0.356852 | + | 0.618085i | −0.987433 | − | 0.158038i | \(-0.949483\pi\) |
0.630581 | + | 0.776123i | \(0.282816\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 562.500 | + | 974.279i | 0.280561 | + | 0.485945i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −672.000 | − | 581.969i | −0.328950 | − | 0.284879i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −768.000 | − | 1330.22i | −0.369045 | − | 0.639205i | 0.620371 | − | 0.784308i | \(-0.286982\pi\) |
−0.989417 | + | 0.145103i | \(0.953649\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 73.5000 | − | 127.306i | 0.0346786 | − | 0.0600651i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3634.00 | 1.68388 | 0.841938 | − | 0.539574i | \(-0.181415\pi\) | ||||
0.841938 | + | 0.539574i | \(0.181415\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 507.000 | 0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 90.0000 | − | 155.885i | 0.0402484 | − | 0.0697122i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −429.000 | − | 743.050i | −0.188533 | − | 0.326549i | 0.756228 | − | 0.654308i | \(-0.227040\pi\) |
−0.944761 | + | 0.327759i | \(0.893707\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 266.000 | − | 1382.18i | 0.114901 | − | 0.597044i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 418.500 | + | 724.863i | 0.177720 | + | 0.307820i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1210.00 | + | 2095.78i | −0.505249 | + | 0.875118i | 0.494732 | + | 0.869046i | \(0.335266\pi\) |
−0.999982 | + | 0.00607215i | \(0.998067\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2672.00 | −1.09728 | −0.548641 | − | 0.836058i | \(-0.684855\pi\) | ||||
−0.548641 | + | 0.836058i | \(0.684855\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 738.000 | 0.298112 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1232.00 | + | 2133.89i | −0.489613 | + | 0.848035i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 252.000 | + | 436.477i | 0.0985458 | + | 0.170686i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 472.500 | − | 163.679i | 0.181848 | − | 0.0629941i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −856.000 | − | 1482.64i | −0.324283 | − | 0.561674i | 0.657084 | − | 0.753817i | \(-0.271790\pi\) |
−0.981367 | + | 0.192143i | \(0.938456\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1697.50 | − | 2940.16i | 0.633102 | − | 1.09657i | −0.353812 | − | 0.935317i | \(-0.615115\pi\) |
0.986914 | − | 0.161248i | \(-0.0515521\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1092.00 | −0.401024 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 510.000 | 0.184447 | 0.0922233 | − | 0.995738i | \(-0.470603\pi\) | ||||
0.0922233 | + | 0.995738i | \(0.470603\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 138.000 | − | 239.023i | 0.0491586 | − | 0.0851452i | −0.840399 | − | 0.541968i | \(-0.817679\pi\) |
0.889558 | + | 0.456823i | \(0.151013\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1095.00 | − | 1896.60i | −0.384255 | − | 0.665550i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4252.50 | + | 1473.11i | −1.47028 | + | 0.509320i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1036.00 | + | 1794.40i | 0.352963 | + | 0.611350i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −216.000 | + | 374.123i | −0.0725268 | + | 0.125620i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 140.000 | 0.0463349 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3198.00 | −1.04341 | −0.521705 | − | 0.853126i | \(-0.674704\pi\) | ||||
−0.521705 | + | 0.853126i | \(0.674704\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 507.000 | − | 878.150i | 0.163094 | − | 0.282487i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 553.000 | + | 957.824i | 0.175415 | + | 0.303828i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 332.500 | − | 1727.72i | 0.104016 | − | 0.540485i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 813.000 | + | 1408.16i | 0.250856 | + | 0.434495i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1872.00 | − | 3242.40i | 0.569793 | − | 0.986911i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5091.00 | 1.52878 | 0.764391 | − | 0.644752i | \(-0.223040\pi\) | ||||
0.764391 | + | 0.644752i | \(0.223040\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −684.000 | −0.202667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1947.50 | + | 3373.17i | −0.569428 | + | 0.986278i | 0.427195 | + | 0.904160i | \(0.359502\pi\) |
−0.996623 | + | 0.0821183i | \(0.973831\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3214.00 | + | 5566.81i | 0.927455 | + | 1.60640i | 0.787565 | + | 0.616231i | \(0.211341\pi\) |
0.139889 | + | 0.990167i | \(0.455325\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 294.000 | + | 254.611i | 0.0837393 | + | 0.0725204i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1912.00 | + | 3311.68i | 0.537593 | + | 0.931139i | 0.999033 | + | 0.0439676i | \(0.0139998\pi\) |
−0.461439 | + | 0.887172i | \(0.652667\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −497.000 | + | 860.829i | −0.137960 | + | 0.238955i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 915.000 | 0.250783 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −568.000 | −0.153727 | −0.0768637 | − | 0.997042i | \(-0.524491\pi\) | ||||
−0.0768637 | + | 0.997042i | \(0.524491\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1767.50 | + | 3061.40i | −0.472426 | + | 0.818266i | −0.999502 | − | 0.0315522i | \(-0.989955\pi\) |
0.527076 | + | 0.849818i | \(0.323288\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −121.500 | − | 210.444i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2229.50 | − | 891.140i | −0.581378 | − | 0.232379i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −520.000 | − | 900.666i | −0.133955 | − | 0.232016i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1684.50 | − | 2917.64i | 0.428718 | − | 0.742562i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4335.00 | −1.09013 | −0.545065 | − | 0.838394i | \(-0.683495\pi\) | ||||
−0.545065 | + | 0.838394i | \(0.683495\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −336.000 | −0.0834946 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −756.000 | + | 1309.43i | −0.185657 | + | 0.321568i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1787.00 | − | 3095.17i | −0.433735 | − | 0.751252i | 0.563456 | − | 0.826146i | \(-0.309471\pi\) |
−0.997191 | + | 0.0748943i | \(0.976138\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4928.00 | − | 4267.77i | −1.18228 | − | 1.02389i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1093.50 | + | 1894.00i | 0.259333 | + | 0.449178i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2733.00 | − | 4733.69i | 0.640776 | − | 1.10986i | −0.344484 | − | 0.938792i | \(-0.611946\pi\) |
0.985260 | − | 0.171064i | \(-0.0547205\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2625.00 | −0.608500 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1278.00 | −0.292930 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2907.50 | − | 5035.94i | 0.659009 | − | 1.14144i | −0.321864 | − | 0.946786i | \(-0.604309\pi\) |
0.980873 | − | 0.194651i | \(-0.0623574\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1618.50 | − | 2803.32i | −0.362793 | − | 0.628376i | 0.625626 | − | 0.780123i | \(-0.284843\pi\) |
−0.988419 | + | 0.151747i | \(0.951510\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 546.000 | − | 2837.10i | 0.121046 | − | 0.628971i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −266.000 | − | 460.726i | −0.0583287 | − | 0.101028i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1588.00 | − | 2750.50i | 0.344454 | − | 0.596611i | −0.640801 | − | 0.767707i | \(-0.721397\pi\) |
0.985254 | + | 0.171096i | \(0.0547308\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −855.000 | −0.183468 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3282.00 | −0.696753 | −0.348377 | − | 0.937355i | \(-0.613267\pi\) | ||||
−0.348377 | + | 0.937355i | \(0.613267\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1091.00 | − | 1889.67i | 0.229163 | − | 0.396923i | −0.728397 | − | 0.685155i | \(-0.759734\pi\) |
0.957560 | + | 0.288233i | \(0.0930677\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 210.000 | + | 363.731i | 0.0436468 | + | 0.0755984i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5180.00 | + | 1794.40i | −1.06539 | + | 0.369060i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −135.500 | − | 234.693i | −0.0275799 | − | 0.0477698i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 553.500 | − | 958.690i | 0.111501 | − | 0.193125i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3021.00 | 0.602351 | 0.301175 | − | 0.953569i | \(-0.402621\pi\) | ||||
0.301175 | + | 0.953569i | \(0.402621\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1953.00 | −0.385451 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 94.5000 | − | 163.679i | 0.0184628 | − | 0.0319785i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1248.00 | + | 2161.60i | 0.241384 | + | 0.418089i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2765.00 | + | 957.824i | −0.529475 | + | 0.183415i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1905.00 | − | 3299.56i | −0.361186 | − | 0.625593i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −861.000 | + | 1491.30i | −0.161642 | + | 0.279972i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1304.00 | 0.242421 | 0.121210 | − | 0.992627i | \(-0.461322\pi\) | ||||
0.121210 | + | 0.992627i | \(0.461322\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5496.00 | −1.01183 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3104.00 | − | 5376.29i | 0.565954 | − | 0.980261i | −0.431006 | − | 0.902349i | \(-0.641841\pi\) |
0.996960 | − | 0.0779121i | \(-0.0248254\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1668.50 | − | 2889.93i | −0.301307 | − | 0.521880i | 0.675125 | − | 0.737703i | \(-0.264090\pi\) |
−0.976432 | + | 0.215824i | \(0.930756\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −220.500 | + | 1145.75i | −0.0394405 | + | 0.204939i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4318.50 | − | 7479.86i | −0.765146 | − | 1.32527i | −0.940170 | − | 0.340707i | \(-0.889334\pi\) |
0.175024 | − | 0.984564i | \(-0.444000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −850.500 | + | 1473.11i | −0.149275 | + | 0.258553i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2997.00 | 0.521110 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1440.00 | −0.248061 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1976.00 | + | 3422.53i | −0.337258 | + | 0.584148i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2499.00 | + | 4328.39i | 0.422615 | + | 0.731990i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1988.00 | − | 1721.66i | −0.333137 | − | 0.288505i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 970.000 | + | 1680.09i | 0.161076 | + | 0.278991i | 0.935255 | − | 0.353975i | \(-0.115170\pi\) |
−0.774179 | + | 0.632967i | \(0.781837\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1584.00 | + | 2743.57i | −0.260669 | + | 0.451491i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5110.00 | 0.833400 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5527.00 | −0.893397 | −0.446699 | − | 0.894684i | \(-0.647400\pi\) | ||||
−0.446699 | + | 0.894684i | \(0.647400\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2748.00 | − | 4759.68i | 0.440268 | − | 0.762567i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −332.500 | − | 575.907i | −0.0528032 | − | 0.0914578i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3430.00 | − | 5346.84i | 0.539949 | − | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −504.000 | − | 872.954i | −0.0786506 | − | 0.136227i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4782.00 | − | 8282.67i | 0.739802 | − | 1.28137i | −0.212783 | − | 0.977100i | \(-0.568253\pi\) |
0.952584 | − | 0.304275i | \(-0.0984141\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −918.000 | −0.140801 | −0.0704003 | − | 0.997519i | \(-0.522428\pi\) | ||||
−0.0704003 | + | 0.997519i | \(0.522428\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1404.00 | −0.213504 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5740.00 | + | 9941.97i | −0.865466 | + | 1.49903i | 0.00111843 | + | 0.999999i | \(0.499644\pi\) |
−0.866584 | + | 0.499031i | \(0.833689\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1183.00 | + | 2049.02i | 0.176865 | + | 0.306339i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3024.00 | − | 2618.86i | −0.448311 | − | 0.388249i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1827.00 | + | 3164.46i | 0.268594 | + | 0.465219i | 0.968499 | − | 0.249017i | \(-0.0801076\pi\) |
−0.699905 | + | 0.714236i | \(0.746774\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3229.50 | − | 5593.66i | 0.470841 | − | 0.815521i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3846.00 | −0.556095 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3794.00 | −0.544074 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5033.50 | + | 8718.28i | −0.715931 | + | 1.24003i | 0.246669 | + | 0.969100i | \(0.420664\pi\) |
−0.962599 | + | 0.270928i | \(0.912669\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1332.00 | + | 2307.09i | 0.187916 | + | 0.325481i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1312.50 | − | 6819.95i | 0.183670 | − | 0.954378i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4400.00 | − | 7621.02i | −0.610786 | − | 1.05791i | −0.991108 | − | 0.133059i | \(-0.957520\pi\) |
0.380322 | − | 0.924854i | \(-0.375813\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2110.50 | − | 3655.49i | 0.290629 | − | 0.503384i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12636.0 | 1.72623 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1136.00 | −0.153964 | −0.0769821 | − | 0.997032i | \(-0.524528\pi\) | ||||
−0.0769821 | + | 0.997032i | \(0.524528\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2896.50 | + | 5016.89i | −0.389481 | + | 0.674601i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2145.00 | + | 3715.25i | 0.286173 | + | 0.495667i | 0.972893 | − | 0.231256i | \(-0.0742834\pi\) |
−0.686720 | + | 0.726922i | \(0.740950\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −857.500 | + | 297.047i | −0.113512 | + | 0.0393218i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 711.000 | + | 1231.49i | 0.0933906 | + | 0.161757i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 431.000 | − | 746.514i | 0.0561763 | − | 0.0973001i | −0.836570 | − | 0.547861i | \(-0.815442\pi\) |
0.892746 | + | 0.450560i | \(0.148776\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3456.00 | 0.447001 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2937.00 | −0.376977 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1067.50 | + | 1848.96i | −0.135979 | + | 0.235523i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4570.00 | + | 7915.47i | 0.577737 | + | 1.00067i | 0.995738 | + | 0.0922238i | \(0.0293975\pi\) |
−0.418001 | + | 0.908447i | \(0.637269\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1050.00 | + | 363.731i | −0.131744 | + | 0.0456374i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7116.00 | + | 12325.3i | 0.886175 | + | 1.53490i | 0.844361 | + | 0.535774i | \(0.179980\pi\) |
0.0418135 | + | 0.999125i | \(0.486686\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2470.00 | + | 4278.17i | −0.305309 | + | 0.528810i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 567.000 | 0.0695666 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2464.00 | −0.300088 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5000.50 | − | 8661.12i | 0.604545 | − | 1.04710i | −0.387578 | − | 0.921837i | \(-0.626688\pi\) |
0.992123 | − | 0.125266i | \(-0.0399783\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 729.000 | + | 1262.67i | 0.0874913 | + | 0.151539i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 976.500 | − | 5074.04i | 0.116345 | − | 0.604546i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3930.50 | + | 6807.83i | 0.464917 | + | 0.805260i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3945.00 | + | 6832.94i | −0.463279 | + | 0.802423i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10256.0 | 1.19580 | 0.597898 | − | 0.801572i | \(-0.296003\pi\) | ||||
0.597898 | + | 0.801572i | \(0.296003\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4502.00 | −0.521174 | −0.260587 | − | 0.965450i | \(-0.583916\pi\) | ||||
−0.260587 | + | 0.965450i | \(0.583916\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −639.000 | + | 1106.78i | −0.0734497 | + | 0.127219i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2736.00 | + | 4738.89i | 0.312272 | + | 0.540871i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3444.00 | − | 2982.59i | −0.390320 | − | 0.338027i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −546.000 | − | 945.700i | −0.0614479 | − | 0.106431i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6178.00 | − | 10700.6i | 0.690450 | − | 1.19589i | −0.281241 | − | 0.959637i | \(-0.590746\pi\) |
0.971691 | − | 0.236257i | \(-0.0759206\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 862.000 | 0.0956699 | 0.0478350 | − | 0.998855i | \(-0.484768\pi\) | ||||
0.0478350 | + | 0.998855i | \(0.484768\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5103.00 | −0.562460 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 480.000 | − | 831.384i | 0.0525435 | − | 0.0910080i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −682.500 | − | 1182.12i | −0.0742003 | − | 0.128519i | 0.826538 | − | 0.562881i | \(-0.190307\pi\) |
−0.900738 | + | 0.434362i | \(0.856974\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2866.50 | − | 1145.75i | −0.309524 | − | 0.123718i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4465.50 | + | 7734.47i | 0.478922 | + | 0.829517i | 0.999708 | − | 0.0241705i | \(-0.00769445\pi\) |
−0.520786 | + | 0.853687i | \(0.674361\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1491.00 | − | 2582.49i | 0.158832 | − | 0.275105i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5634.00 | −0.596150 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11228.0 | 1.18014 | 0.590069 | − | 0.807353i | \(-0.299100\pi\) | ||||
0.590069 | + | 0.807353i | \(0.299100\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1036.00 | + | 1794.40i | −0.108167 | + | 0.187351i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3154.50 | + | 5463.75i | 0.327177 | + | 0.566688i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5096.00 | + | 4413.27i | 0.525064 | + | 0.454719i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6075.50 | − | 10523.1i | −0.621882 | − | 1.07713i | −0.989135 | − | 0.147010i | \(-0.953035\pi\) |
0.367253 | − | 0.930121i | \(-0.380298\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −972.000 | + | 1683.55i | −0.0988433 | + | 0.171202i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18534.0 | 1.87248 | 0.936241 | − | 0.351358i | \(-0.114280\pi\) | ||||
0.936241 | + | 0.351358i | \(0.114280\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17096.0 | −1.71602 | −0.858011 | − | 0.513631i | \(-0.828300\pi\) | ||||
−0.858011 | + | 0.513631i | \(0.828300\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 997.500 | − | 1727.72i | 0.0994795 | − | 0.172304i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1070.00 | − | 1853.29i | −0.106025 | − | 0.183641i | 0.808131 | − | 0.589002i | \(-0.200479\pi\) |
−0.914157 | + | 0.405361i | \(0.867146\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2555.00 | + | 13276.2i | −0.251554 | + | 1.30711i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2106.00 | − | 3647.70i | −0.206028 | − | 0.356852i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −553.000 | + | 957.824i | −0.0537568 | + | 0.0931095i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1520.00 | 0.146826 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3375.00 | −0.323964 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6633.00 | + | 11488.7i | −0.632713 | + | 1.09589i | 0.354282 | + | 0.935139i | \(0.384725\pi\) |
−0.986995 | + | 0.160752i | \(0.948608\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9152.00 | + | 15851.7i | 0.867558 | + | 1.50265i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2520.00 | − | 872.954i | 0.237400 | − | 0.0822376i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1291.50 | + | 2236.94i | 0.120915 | + | 0.209432i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9591.50 | + | 16613.0i | −0.892469 | + | 1.54580i | −0.0555627 | + | 0.998455i | \(0.517695\pi\) |
−0.836906 | + | 0.547346i | \(0.815638\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4608.00 | 0.426137 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21693.0 | 1.99387 | 0.996936 | − | 0.0782185i | \(-0.0249232\pi\) | ||||
0.996936 | + | 0.0782185i | \(0.0249232\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8748.00 | − | 15152.0i | 0.799169 | − | 1.38420i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 220.500 | + | 381.917i | 0.0200217 | + | 0.0346786i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5915.00 | + | 2049.02i | −0.533851 | + | 0.184931i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9829.00 | + | 17024.3i | 0.881776 | + | 1.52728i | 0.849364 | + | 0.527807i | \(0.176986\pi\) |
0.0324122 | + | 0.999475i | \(0.489681\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5451.00 | + | 9441.41i | −0.486093 | + | 0.841938i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19436.0 | −1.72288 | −0.861440 | − | 0.507860i | \(-0.830437\pi\) | ||||
−0.861440 | + | 0.507860i | \(0.830437\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8890.00 | 0.783366 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −760.500 | + | 1317.22i | −0.0666173 | + | 0.115385i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1544.50 | − | 2675.15i | −0.134497 | − | 0.232955i | 0.790908 | − | 0.611934i | \(-0.209608\pi\) |
−0.925405 | + | 0.378980i | \(0.876275\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1897.00 | − | 9857.10i | 0.164224 | − | 0.853332i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 270.000 | + | 467.654i | 0.0232374 | + | 0.0402484i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6412.00 | − | 11105.9i | 0.548634 | − | 0.950262i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −994.000 | −0.0845572 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2574.00 | 0.217700 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −975.000 | + | 1688.75i | −0.0819876 | + | 0.142007i | −0.904104 | − | 0.427313i | \(-0.859460\pi\) |
0.822116 | + | 0.569320i | \(0.192793\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6566.00 | + | 11372.6i | 0.548970 | + | 0.950843i | 0.998345 | + | 0.0575005i | \(0.0183131\pi\) |
−0.449376 | + | 0.893343i | \(0.648354\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3192.00 | + | 2764.35i | 0.265353 | + | 0.229802i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3420.00 | + | 5923.61i | 0.282690 | + | 0.489633i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4931.50 | − | 8541.61i | 0.405318 | − | 0.702031i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2511.00 | −0.205213 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15392.0 | 1.25085 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3496.50 | + | 6056.12i | −0.282555 | + | 0.489399i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3630.00 | − | 6287.34i | −0.291706 | − | 0.505249i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −343.000 | − | 2376.37i | −0.0274101 | − | 0.189903i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1465.00 | − | 2537.45i | −0.116424 | − | 0.201652i | 0.801924 | − | 0.597426i | \(-0.203810\pi\) |
−0.918348 | + | 0.395774i | \(0.870476\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4008.00 | − | 6942.06i | 0.316758 | − | 0.548641i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11662.0 | −0.916597 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19824.0 | −1.54957 | −0.774783 | − | 0.632227i | \(-0.782141\pi\) | ||||
−0.774783 | + | 0.632227i | \(0.782141\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1107.00 | + | 1917.38i | −0.0860576 | + | 0.149056i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2430.00 | − | 4208.88i | −0.187879 | − | 0.325416i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4270.00 | − | 3697.93i | −0.328352 | − | 0.284362i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3696.00 | − | 6401.66i | −0.282678 | − | 0.489613i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9584.50 | − | 16600.8i | 0.729099 | − | 1.26284i | −0.228165 | − | 0.973622i | \(-0.573273\pi\) |
0.957264 | − | 0.289215i | \(-0.0933941\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8216.00 | 0.621645 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1512.00 | −0.113791 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3633.50 | − | 6293.41i | 0.271996 | − | 0.471111i | −0.697377 | − | 0.716705i | \(-0.745650\pi\) |
0.969373 | + | 0.245594i | \(0.0789829\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6412.00 | + | 11105.9i | 0.477442 | + | 0.826954i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −283.500 | + | 1473.11i | −0.0209980 | + | 0.109109i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2446.00 | + | 4236.60i | 0.180214 | + | 0.312139i | 0.941953 | − | 0.335744i | \(-0.108988\pi\) |
−0.761739 | + | 0.647883i | \(0.775654\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11063.0 | − | 19161.7i | 0.810809 | − | 1.40436i | −0.101489 | − | 0.994837i | \(-0.532361\pi\) |
0.912298 | − | 0.409526i | \(-0.134306\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5136.00 | 0.374449 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3648.00 | −0.264578 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 548.500 | − | 950.030i | 0.0395743 | − | 0.0685446i | −0.845560 | − | 0.533881i | \(-0.820733\pi\) |
0.885134 | + | 0.465336i | \(0.154066\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5092.50 | + | 8820.47i | 0.365522 | + | 0.633102i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −19652.5 | + | 6807.83i | −1.40331 | + | 0.486121i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1312.50 | − | 2273.32i | −0.0932388 | − | 0.161494i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1638.00 | − | 2837.10i | 0.115766 | − | 0.200512i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9969.00 | −0.700962 | −0.350481 | − | 0.936570i | \(-0.613982\pi\) | ||||
−0.350481 | + | 0.936570i | \(0.613982\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1900.00 | 0.132917 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −765.000 | + | 1325.02i | −0.0532452 | + | 0.0922233i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3212.00 | + | 5563.35i | 0.222430 | + | 0.385260i | 0.955545 | − | 0.294844i | \(-0.0952678\pi\) |
−0.733115 | + | 0.680104i | \(0.761934\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8820.00 | − | 3055.34i | 0.607705 | − | 0.210515i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 414.000 | + | 717.069i | 0.0283817 | + | 0.0491586i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8523.00 | − | 14762.3i | 0.581370 | − | 1.00696i | −0.413948 | − | 0.910301i | \(-0.635850\pi\) |
0.995317 | − | 0.0966609i | \(-0.0308162\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18877.0 | −1.28121 | −0.640606 | − | 0.767869i | \(-0.721317\pi\) | ||||
−0.640606 | + | 0.767869i | \(0.721317\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6570.00 | 0.443700 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4487.00 | − | 7771.71i | 0.301525 | − | 0.522256i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6891.50 | − | 11936.4i | −0.460819 | − | 0.798163i | 0.538183 | − | 0.842828i | \(-0.319111\pi\) |
−0.999002 | + | 0.0446657i | \(0.985778\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2551.50 | − | 13258.0i | 0.169773 | − | 0.882168i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3692.00 | + | 6394.73i | 0.244456 | + | 0.423409i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9096.00 | + | 15754.7i | −0.599321 | + | 1.03806i | 0.393600 | + | 0.919282i | \(0.371229\pi\) |
−0.992921 | + | 0.118773i | \(0.962104\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6216.00 | −0.407566 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13054.0 | −0.851757 | −0.425879 | − | 0.904780i | \(-0.640035\pi\) | ||||
−0.425879 | + | 0.904780i | \(0.640035\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3623.00 | − | 6275.22i | 0.235251 | − | 0.407468i | −0.724094 | − | 0.689701i | \(-0.757742\pi\) |
0.959346 | + | 0.282234i | \(0.0910753\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −648.000 | − | 1122.37i | −0.0418733 | − | 0.0725268i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5964.00 | + | 5164.98i | 0.383535 | + | 0.332151i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 174.500 | + | 302.243i | 0.0111680 | + | 0.0193435i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −210.000 | + | 363.731i | −0.0133757 | + | 0.0231675i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 25344.0 | 1.60657 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2817.00 | −0.177723 | −0.0888613 | − | 0.996044i | \(-0.528323\pi\) | ||||
−0.0888613 | + | 0.996044i | \(0.528323\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4797.00 | − | 8308.65i | 0.301206 | − | 0.521705i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6758.50 | − | 11706.1i | −0.422367 | − | 0.731561i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14014.0 | + | 11033.2i | −0.871672 | + | 0.686264i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1521.00 | + | 2634.45i | 0.0941625 | + | 0.163094i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7893.00 | + | 13671.1i | −0.486357 | + | 0.842395i | −0.999877 | − | 0.0156827i | \(-0.995008\pi\) |
0.513520 | + | 0.858078i | \(0.328341\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17426.0 | 1.06876 | 0.534381 | − | 0.845244i | \(-0.320545\pi\) | ||||
0.534381 | + | 0.845244i | \(0.320545\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3318.00 | −0.202552 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12917.0 | + | 22372.9i | −0.784884 | + | 1.35946i | 0.144185 | + | 0.989551i | \(0.453944\pi\) |
−0.929069 | + | 0.369907i | \(0.879389\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −976.500 | − | 1691.35i | −0.0590616 | − | 0.102298i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3990.00 | + | 3455.44i | 0.240216 | + | 0.208033i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13991.5 | − | 24234.0i | −0.838483 | − | 1.45230i | −0.891162 | − | 0.453684i | \(-0.850109\pi\) |
0.0526789 | − | 0.998612i | \(-0.483224\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3426.50 | − | 5934.87i | 0.204404 | − | 0.354038i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4878.00 | −0.289663 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28296.0 | 1.67262 | 0.836309 | − | 0.548258i | \(-0.184709\pi\) | ||||
0.836309 | + | 0.548258i | \(0.184709\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10627.0 | + | 18406.5i | −0.625329 | + | 1.08310i | 0.363148 | + | 0.931731i | \(0.381702\pi\) |
−0.988477 | + | 0.151370i | \(0.951631\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5616.00 | + | 9727.20i | 0.328970 | + | 0.569793i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 490.000 | − | 2546.11i | 0.0285735 | − | 0.148472i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5832.00 | + | 10101.3i | 0.338555 | + | 0.586394i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7636.50 | + | 13226.8i | −0.441322 | + | 0.764391i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1722.00 | −0.0990716 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28259.0 | −1.61858 | −0.809290 | − | 0.587409i | \(-0.800148\pi\) | ||||
−0.809290 | + | 0.587409i | \(0.800148\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1026.00 | − | 1777.08i | 0.0585048 | − | 0.101333i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15889.5 | − | 27521.4i | −0.902043 | − | 1.56238i | −0.824838 | − | 0.565369i | \(-0.808734\pi\) |
−0.0772049 | − | 0.997015i | \(-0.524600\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6457.50 | + | 2236.94i | −0.364972 | + | 0.126430i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5842.50 | − | 10119.5i | −0.328759 | − | 0.569428i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4873.50 | + | 8441.15i | −0.273030 | + | 0.472901i | −0.969636 | − | 0.244552i | \(-0.921359\pi\) |
0.696606 | + | 0.717453i | \(0.254692\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3402.00 | −0.189757 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19284.0 | −1.07093 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9750.00 | + | 16887.5i | −0.539108 | + | 0.933762i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12256.0 | − | 21228.0i | −0.674733 | − | 1.16867i | −0.976547 | − | 0.215304i | \(-0.930926\pi\) |
0.301814 | − | 0.953367i | \(-0.402408\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1102.50 | + | 381.917i | −0.0604336 | + | 0.0209348i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9205.00 | − | 15943.5i | −0.502396 | − | 0.870176i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10656.0 | − | 18456.7i | 0.579089 | − | 1.00301i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11472.0 | −0.620760 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14325.0 | 0.771823 | 0.385911 | − | 0.922536i | \(-0.373887\pi\) | ||||
0.385911 | + | 0.922536i | \(0.373887\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3520.00 | − | 6096.82i | 0.188847 | − | 0.327092i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1491.00 | − | 2582.49i | −0.0796515 | − | 0.137960i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4445.00 | + | 23096.9i | −0.236452 | + | 1.22864i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6039.00 | − | 10459.9i | −0.319886 | − | 0.554059i | 0.660578 | − | 0.750758i | \(-0.270311\pi\) |
−0.980464 | + | 0.196698i | \(0.936978\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1372.50 | + | 2377.24i | −0.0723949 | + | 0.125392i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4560.00 | −0.239514 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2548.00 | 0.133272 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 852.000 | − | 1475.71i | 0.0443773 | − | 0.0768637i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5329.00 | − | 9230.10i | −0.276409 | − | 0.478755i | 0.694081 | − | 0.719897i | \(-0.255811\pi\) |
−0.970490 | + | 0.241143i | \(0.922478\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 25648.0 | + | 22211.8i | 1.32480 | + | 1.14731i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5302.50 | − | 9184.20i | −0.272755 | − | 0.472426i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9234.00 | + | 15993.8i | −0.473024 | + | 0.819301i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19099.0 | −0.974337 | −0.487168 | − | 0.873308i | \(-0.661970\pi\) | ||||
−0.487168 | + | 0.873308i | \(0.661970\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5688.00 | − | 9851.90i | 0.287795 | − | 0.498476i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −703.000 | − | 1217.63i | −0.0354241 | − | 0.0613564i | 0.847770 | − | 0.530364i | \(-0.177945\pi\) |
−0.883194 | + | 0.469008i | \(0.844612\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5659.50 | − | 4455.70i | 0.284019 | − | 0.223607i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2555.00 | + | 4425.39i | 0.127700 | + | 0.221182i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3365.00 | − | 5828.35i | 0.167501 | − | 0.290121i | −0.770039 | − | 0.637996i | \(-0.779763\pi\) |
0.937541 | + | 0.347875i | \(0.113097\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3120.00 | 0.154678 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1166.00 | 0.0575725 | 0.0287863 | − | 0.999586i | \(-0.490836\pi\) | ||||
0.0287863 | + | 0.999586i | \(0.490836\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6573.00 | − | 11384.8i | 0.323243 | − | 0.559873i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5053.50 | + | 8752.92i | 0.247521 | + | 0.428718i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −13986.0 | − | 12112.2i | −0.682293 | − | 0.590883i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8483.50 | − | 14693.9i | −0.412207 | − | 0.713963i | 0.582924 | − | 0.812527i | \(-0.301909\pi\) |
−0.995131 | + | 0.0985636i | \(0.968575\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6502.50 | − | 11262.7i | 0.314694 | − | 0.545065i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −14721.0 | −0.709605 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11878.0 | 0.570295 | 0.285147 | − | 0.958484i | \(-0.407957\pi\) | ||||
0.285147 | + | 0.958484i | \(0.407957\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 504.000 | − | 872.954i | 0.0241028 | − | 0.0417473i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13662.0 | − | 23663.3i | −0.650785 | − | 1.12719i | −0.982933 | − | 0.183965i | \(-0.941107\pi\) |
0.332148 | − | 0.943227i | \(-0.392227\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5831.00 | − | 30298.8i | 0.276666 | − | 1.43760i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2268.00 | − | 3928.29i | −0.107189 | − | 0.185657i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7254.00 | + | 12564.3i | −0.341495 | + | 0.591487i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11971.0 | −0.561359 | −0.280680 | − | 0.959802i | \(-0.590560\pi\) | ||||
−0.280680 | + | 0.959802i | \(0.590560\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10722.0 | 0.500834 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 169.000 | − | 292.717i | 0.00786353 | − | 0.0136200i | −0.862067 | − | 0.506795i | \(-0.830830\pi\) |
0.869930 | + | 0.493175i | \(0.164164\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3610.00 | − | 6252.70i | −0.167323 | − | 0.289811i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 18480.0 | − | 6401.66i | 0.853238 | − | 0.295570i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2960.00 | − | 5126.87i | −0.136140 | − | 0.235801i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1183.00 | + | 2049.02i | −0.0542011 | + | 0.0938791i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6561.00 | −0.299452 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9828.00 | 0.446849 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7057.00 | − | 12223.1i | 0.319638 | − | 0.553629i | −0.660775 | − | 0.750584i | \(-0.729772\pi\) |
0.980412 | + | 0.196956i | \(0.0631055\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8199.00 | + | 14201.1i | 0.369952 | + | 0.640776i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −32060.0 | + | 11105.9i | −1.44112 | + | 0.499217i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6396.00 | + | 11078.2i | 0.286417 | + | 0.496089i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3937.50 | − | 6819.95i | 0.175659 | − | 0.304250i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1563.00 | 0.0694659 | 0.0347329 | − | 0.999397i | \(-0.488942\pi\) | ||||
0.0347329 | + | 0.999397i | \(0.488942\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10224.0 | 0.452690 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1917.00 | − | 3320.34i | 0.0845616 | − | 0.146465i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1897.00 | − | 3285.70i | −0.0833670 | − | 0.144396i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1176.00 | + | 6110.68i | −0.0514889 | + | 0.267544i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8722.50 | + | 15107.8i | 0.380479 | + | 0.659009i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15784.0 | − | 27338.7i | 0.685953 | − | 1.18811i | −0.287183 | − | 0.957876i | \(-0.592719\pi\) |
0.973136 | − | 0.230230i | \(-0.0739477\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2626.00 | −0.113701 | −0.0568504 | − | 0.998383i | \(-0.518106\pi\) | ||||
−0.0568504 | + | 0.998383i | \(0.518106\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9711.00 | 0.418917 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5376.00 | + | 9311.51i | −0.231059 | + | 0.400206i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1580.00 | − | 2736.64i | −0.0676588 | − | 0.117188i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6552.00 | + | 5674.20i | 0.279543 | + | 0.242091i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −180.500 | − | 312.635i | −0.00767295 | − | 0.0132899i | 0.862163 | − | 0.506630i | \(-0.169109\pi\) |
−0.869836 | + | 0.493340i | \(0.835776\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14772.0 | + | 25585.9i | −0.625662 | + | 1.08368i | 0.362751 | + | 0.931886i | \(0.381838\pi\) |
−0.988413 | + | 0.151792i | \(0.951496\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1596.00 | 0.0673522 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24163.0 | −1.01600 | −0.507999 | − | 0.861358i | \(-0.669615\pi\) | ||||
−0.507999 | + | 0.861358i | \(0.669615\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19598.0 | − | 33944.7i | 0.821070 | − | 1.42213i | −0.0838169 | − | 0.996481i | \(-0.526711\pi\) |
0.904886 | − | 0.425653i | \(-0.139956\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4764.00 | + | 8251.49i | 0.198870 | + | 0.344454i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3528.00 | + | 24442.7i | 0.146744 | + | 1.01667i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12719.0 | − | 22030.0i | −0.527137 | − | 0.913028i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1282.50 | − | 2221.36i | 0.0529626 | − | 0.0917339i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6528.00 | −0.268619 | −0.134310 | − | 0.990939i | \(-0.542882\pi\) | ||||
−0.134310 | + | 0.990939i | \(0.542882\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 34660.0 | 1.42113 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4923.00 | − | 8526.89i | 0.201135 | − | 0.348377i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1774.50 | − | 3073.52i | −0.0722422 | − | 0.125127i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17948.0 | + | 15543.4i | 0.728100 | + | 0.630553i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3273.00 | + | 5669.00i | 0.132308 | + | 0.229163i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8448.00 | + | 14632.4i | −0.340298 | + | 0.589414i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1046.00 | 0.0419864 | 0.0209932 | − | 0.999780i | \(-0.493317\pi\) | ||||
0.0209932 | + | 0.999780i | \(0.493317\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1260.00 | −0.0503989 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16455.0 | + | 28500.9i | −0.655883 | + | 1.13602i | 0.325788 | + | 0.945443i | \(0.394370\pi\) |
−0.981672 | + | 0.190581i | \(0.938963\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11341.0 | + | 19643.2i | 0.450466 | + | 0.780229i | 0.998415 | − | 0.0562823i | \(-0.0179247\pi\) |
−0.547949 | + | 0.836512i | \(0.684591\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3108.00 | − | 16149.6i | 0.123020 | − | 0.639231i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3725.00 | − | 6451.89i | −0.146930 | − | 0.254490i | 0.783161 | − | 0.621818i | \(-0.213606\pi\) |
−0.930091 | + | 0.367328i | \(0.880272\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3003.00 | + | 5201.35i | −0.118041 | + | 0.204452i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 813.000 | 0.0318465 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2135.00 | −0.0833428 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18980.0 | − | 32874.3i | 0.738361 | − | 1.27888i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1660.50 | + | 2876.07i | 0.0643750 | + | 0.111501i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −24622.5 | + | 8529.48i | −0.951306 | + | 0.329542i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5040.00 | − | 8729.54i | −0.194058 | − | 0.336118i | 0.752533 | − | 0.658554i | \(-0.228832\pi\) |
−0.946591 | + | 0.322436i | \(0.895498\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4531.50 | + | 7848.79i | −0.173884 | + | 0.301175i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32958.0 | −1.26037 | −0.630183 | − | 0.776446i | \(-0.717020\pi\) | ||||
−0.630183 | + | 0.776446i | \(0.717020\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19784.0 | 0.754003 | 0.377001 | − | 0.926213i | \(-0.376955\pi\) | ||||
0.377001 | + | 0.926213i | \(0.376955\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2929.50 | − | 5074.04i | 0.111270 | − | 0.192726i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5740.00 | − | 9941.97i | −0.217283 | − | 0.376346i | 0.736693 | − | 0.676227i | \(-0.236386\pi\) |
−0.953976 | + | 0.299881i | \(0.903053\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 33792.5 | − | 11706.1i | 1.27488 | − | 0.441630i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 283.500 | + | 491.036i | 0.0106595 | + | 0.0184628i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1420.00 | − | 2459.51i | 0.0532122 | − | 0.0921662i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16940.0 | 0.632672 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7488.00 | −0.278726 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11542.5 | + | 19992.2i | −0.428213 | + | 0.741688i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13500.0 | + | 23382.7i | 0.499168 | + | 0.864584i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1659.00 | − | 8620.42i | 0.0611385 | − | 0.317685i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9352.00 | + | 16198.1i | 0.343504 | + | 0.594966i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22676.0 | + | 39276.0i | −0.830148 | + | 1.43786i | 0.0677725 | + | 0.997701i | \(0.478411\pi\) |
−0.897920 | + | 0.440158i | \(0.854923\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11430.0 | 0.417062 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39906.0 | 1.45131 | 0.725656 | − | 0.688058i | \(-0.241537\pi\) | ||||
0.725656 | + | 0.688058i | \(0.241537\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3930.50 | + | 6807.83i | −0.142476 | + | 0.246776i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2583.00 | − | 4473.89i | −0.0933239 | − | 0.161642i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13706.0 | + | 11869.7i | 0.493579 | + | 0.427452i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8764.00 | + | 15179.7i | 0.314579 | + | 0.544866i | 0.979348 | − | 0.202183i | \(-0.0648035\pi\) |
−0.664769 | + | 0.747049i | \(0.731470\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1956.00 | + | 3387.89i | −0.0699809 | + | 0.121210i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 17576.0 | 0.626783 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −26752.0 | −0.950919 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8244.00 | − | 14279.0i | 0.292091 | − | 0.505917i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8533.00 | − | 14779.6i | −0.301355 | − | 0.521962i | 0.675088 | − | 0.737737i | \(-0.264106\pi\) |
−0.976443 | + | 0.215775i | \(0.930772\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6370.00 | + | 2546.11i | 0.224241 | + | 0.0896300i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9312.00 | + | 16128.9i | 0.326754 | + | 0.565954i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1764.00 | − | 3055.34i | 0.0616994 | − | 0.106867i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30821.0 | −1.07458 | −0.537288 | − | 0.843399i | \(-0.680551\pi\) | ||||
−0.537288 | + | 0.843399i | \(0.680551\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10011.0 | 0.347920 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2089.50 | + | 3619.12i | −0.0723866 | + | 0.125377i | −0.899947 | − | 0.436000i | \(-0.856395\pi\) |
0.827560 | + | 0.561377i | \(0.189728\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7104.00 | + | 12304.5i | 0.245321 | + | 0.424909i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2646.00 | − | 2291.50i | −0.0910840 | − | 0.0788811i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4888.00 | + | 8466.26i | 0.167728 | + | 0.290514i | 0.937621 | − | 0.347660i | \(-0.113024\pi\) |
−0.769893 | + | 0.638174i | \(0.779690\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14092.0 | + | 24408.1i | −0.482029 | + | 0.834899i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25911.0 | 0.883514 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14778.0 | 0.502315 | 0.251158 | − | 0.967946i | \(-0.419189\pi\) | ||||
0.251158 | + | 0.967946i | \(0.419189\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5992.00 | + | 10378.4i | −0.203033 | + | 0.351664i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2551.50 | − | 4419.33i | −0.0861842 | − | 0.149275i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1701.00 | − | 8838.66i | 0.0572765 | − | 0.297617i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10383.0 | + | 17983.9i | 0.348528 | + | 0.603668i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4495.50 | + | 7786.43i | −0.150431 | + | 0.260555i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −23765.0 | −0.792769 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8759.00 | −0.291283 | −0.145641 | − | 0.989337i | \(-0.546525\pi\) | ||||
−0.145641 | + | 0.989337i | \(0.546525\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2160.00 | − | 3741.23i | 0.0716091 | − | 0.124031i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16789.5 | − | 29080.3i | −0.554893 | − | 0.961102i | −0.997912 | − | 0.0645901i | \(-0.979426\pi\) |
0.443019 | − | 0.896512i | \(-0.353907\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 46025.0 | − | 15943.5i | 1.51644 | − | 0.525309i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5928.00 | − | 10267.6i | −0.194716 | − | 0.337258i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21317.0 | + | 36922.1i | −0.698046 | + | 1.20905i | 0.271097 | + | 0.962552i | \(0.412614\pi\) |
−0.969143 | + | 0.246500i | \(0.920720\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2982.00 | 0.0973495 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14994.0 | −0.487993 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14574.0 | − | 25242.9i | 0.472877 | − | 0.819048i | −0.526641 | − | 0.850088i | \(-0.676549\pi\) |
0.999518 | + | 0.0310404i | \(0.00988204\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1785.00 | − | 3091.71i | −0.0577409 | − | 0.100010i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7455.00 | − | 2582.49i | 0.240421 | − | 0.0832842i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3792.00 | + | 6567.94i | 0.121920 | + | 0.211171i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22398.5 | + | 38795.3i | −0.717974 | + | 1.24357i | 0.243828 | + | 0.969819i | \(0.421597\pi\) |
−0.961801 | + | 0.273748i | \(0.911737\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5820.00 | −0.185994 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1932.00 | −0.0615563 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5327.00 | + | 9226.63i | −0.169215 | + | 0.293090i | −0.938144 | − | 0.346245i | \(-0.887457\pi\) |
0.768929 | + | 0.639334i | \(0.220790\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4752.00 | − | 8230.71i | −0.150497 | − | 0.260669i |
(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 | 336.4.q.a.193.1 | 2 | ||
4.3 | odd | 2 | 168.4.q.a.25.1 | ✓ | 2 | ||
7.2 | even | 3 | inner | 336.4.q.a.289.1 | 2 | ||
7.3 | odd | 6 | 2352.4.a.c.1.1 | 1 | |||
7.4 | even | 3 | 2352.4.a.bg.1.1 | 1 | |||
12.11 | even | 2 | 504.4.s.e.361.1 | 2 | |||
28.3 | even | 6 | 1176.4.a.i.1.1 | 1 | |||
28.11 | odd | 6 | 1176.4.a.f.1.1 | 1 | |||
28.23 | odd | 6 | 168.4.q.a.121.1 | yes | 2 | ||
84.23 | even | 6 | 504.4.s.e.289.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.4.q.a.25.1 | ✓ | 2 | 4.3 | odd | 2 | ||
168.4.q.a.121.1 | yes | 2 | 28.23 | odd | 6 | ||
336.4.q.a.193.1 | 2 | 1.1 | even | 1 | trivial | ||
336.4.q.a.289.1 | 2 | 7.2 | even | 3 | inner | ||
504.4.s.e.289.1 | 2 | 84.23 | even | 6 | |||
504.4.s.e.361.1 | 2 | 12.11 | even | 2 | |||
1176.4.a.f.1.1 | 1 | 28.11 | odd | 6 | |||
1176.4.a.i.1.1 | 1 | 28.3 | even | 6 | |||
2352.4.a.c.1.1 | 1 | 7.3 | odd | 6 | |||
2352.4.a.bg.1.1 | 1 | 7.4 | even | 3 |