Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1800,3,Mod(1601,1800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1800.1601");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1800.l (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: | \(49.0464475849\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 360) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1601.1 | ||
Root | \(-1.58114 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1800.1601 |
Dual form | 1800.3.l.g.1601.2 |
$q$-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 \(\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1001\) | \(1351\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.83772 | 0.691103 | 0.345552 | − | 0.938400i | \(-0.387692\pi\) | ||||
0.345552 | + | 0.938400i | \(0.387692\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 14.8306i | − 1.34824i | −0.738623 | − | 0.674119i | \(-0.764523\pi\) | ||||
0.738623 | − | 0.674119i | \(-0.235477\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 20.1359 | 1.54892 | 0.774459 | − | 0.632624i | \(-0.218022\pi\) | ||||
0.774459 | + | 0.632624i | \(0.218022\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.57484i | 0.386755i | 0.981124 | + | 0.193378i | \(0.0619442\pi\) | ||||
−0.981124 | + | 0.193378i | \(0.938056\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 17.6754 | 0.930287 | 0.465143 | − | 0.885235i | \(-0.346003\pi\) | ||||
0.465143 | + | 0.885235i | \(0.346003\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 25.1891i | 1.09518i | 0.836747 | + | 0.547589i | \(0.184454\pi\) | ||||
−0.836747 | + | 0.547589i | \(0.815546\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 38.4133i | − 1.32460i | −0.749241 | − | 0.662298i | \(-0.769581\pi\) | ||||
0.749241 | − | 0.662298i | \(-0.230419\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −32.9737 | −1.06367 | −0.531833 | − | 0.846849i | \(-0.678497\pi\) | ||||
−0.531833 | + | 0.846849i | \(0.678497\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 44.7851 | 1.21041 | 0.605203 | − | 0.796071i | \(-0.293092\pi\) | ||||
0.605203 | + | 0.796071i | \(0.293092\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 21.2132i | 0.517395i | 0.965958 | + | 0.258698i | \(0.0832933\pi\) | ||||
−0.965958 | + | 0.258698i | \(0.916707\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −16.2719 | −0.378416 | −0.189208 | − | 0.981937i | \(-0.560592\pi\) | ||||
−0.189208 | + | 0.981937i | \(0.560592\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 24.0044i | 0.510732i | 0.966845 | + | 0.255366i | \(0.0821959\pi\) | ||||
−0.966845 | + | 0.255366i | \(0.917804\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −25.5964 | −0.522376 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 42.4264i | − 0.800498i | −0.916406 | − | 0.400249i | \(-0.868924\pi\) | ||||
0.916406 | − | 0.400249i | \(-0.131076\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 86.3848i | − 1.46415i | −0.681225 | − | 0.732075i | \(-0.738552\pi\) | ||||
0.681225 | − | 0.732075i | \(-0.261448\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −38.2719 | −0.627408 | −0.313704 | − | 0.949521i | \(-0.601570\pi\) | ||||
−0.313704 | + | 0.949521i | \(0.601570\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −37.2982 | −0.556690 | −0.278345 | − | 0.960481i | \(-0.589786\pi\) | ||||
−0.278345 | + | 0.960481i | \(0.589786\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 19.3400i | − 0.272394i | −0.990682 | − | 0.136197i | \(-0.956512\pi\) | ||||
0.990682 | − | 0.136197i | \(-0.0434881\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 108.974 | 1.49279 | 0.746395 | − | 0.665503i | \(-0.231783\pi\) | ||||
0.746395 | + | 0.665503i | \(0.231783\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 71.7464i | − 0.931772i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 119.570 | 1.51355 | 0.756773 | − | 0.653678i | \(-0.226775\pi\) | ||||
0.756773 | + | 0.653678i | \(0.226775\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 123.458i | − 1.48745i | −0.668486 | − | 0.743725i | \(-0.733057\pi\) | ||||
0.668486 | − | 0.743725i | \(-0.266943\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 63.0317i | 0.708221i | 0.935204 | + | 0.354110i | \(0.115216\pi\) | ||||
−0.935204 | + | 0.354110i | \(0.884784\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 97.4121 | 1.07046 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −109.623 | −1.13013 | −0.565066 | − | 0.825046i | \(-0.691149\pi\) | ||||
−0.565066 | + | 0.825046i | \(0.691149\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 140.696i | 1.39303i | 0.717544 | + | 0.696513i | \(0.245266\pi\) | ||||
−0.717544 | + | 0.696513i | \(0.754734\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 143.057 | 1.38890 | 0.694451 | − | 0.719540i | \(-0.255647\pi\) | ||||
0.694451 | + | 0.719540i | \(0.255647\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 88.5992i | 0.828030i | 0.910270 | + | 0.414015i | \(0.135874\pi\) | ||||
−0.910270 | + | 0.414015i | \(0.864126\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 213.517 | 1.95888 | 0.979438 | − | 0.201746i | \(-0.0646617\pi\) | ||||
0.979438 | + | 0.201746i | \(0.0646617\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 11.2392i | − 0.0994622i | −0.998763 | − | 0.0497311i | \(-0.984164\pi\) | ||||
0.998763 | − | 0.0497311i | \(-0.0158364\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 31.8072i | 0.267288i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −98.9473 | −0.817747 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 36.8377 | 0.290061 | 0.145030 | − | 0.989427i | \(-0.453672\pi\) | ||||
0.145030 | + | 0.989427i | \(0.453672\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.5432i | 0.0881161i | 0.999029 | + | 0.0440580i | \(0.0140286\pi\) | ||||
−0.999029 | + | 0.0440580i | \(0.985971\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 85.5089 | 0.642924 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 145.701i | − 1.06351i | −0.846897 | − | 0.531756i | \(-0.821532\pi\) | ||||
0.846897 | − | 0.531756i | \(-0.178468\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 182.649 | 1.31402 | 0.657011 | − | 0.753881i | \(-0.271820\pi\) | ||||
0.657011 | + | 0.753881i | \(0.271820\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 298.629i | − 2.08831i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 142.532i | − 0.956588i | −0.878200 | − | 0.478294i | \(-0.841255\pi\) | ||||
0.878200 | − | 0.478294i | \(-0.158745\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −230.438 | −1.52608 | −0.763041 | − | 0.646350i | \(-0.776295\pi\) | ||||
−0.763041 | + | 0.646350i | \(0.776295\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 164.136 | 1.04545 | 0.522726 | − | 0.852501i | \(-0.324915\pi\) | ||||
0.522726 | + | 0.852501i | \(0.324915\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 121.858i | 0.756881i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −222.763 | −1.36664 | −0.683322 | − | 0.730117i | \(-0.739465\pi\) | ||||
−0.683322 | + | 0.730117i | \(0.739465\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 236.180i | − 1.41425i | −0.707089 | − | 0.707125i | \(-0.749992\pi\) | ||||
0.707089 | − | 0.707125i | \(-0.250008\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 236.456 | 1.39915 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 204.106i | 1.17980i | 0.807476 | + | 0.589901i | \(0.200833\pi\) | ||||
−0.807476 | + | 0.589901i | \(0.799167\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 314.110i | − 1.75481i | −0.479753 | − | 0.877403i | \(-0.659274\pi\) | ||||
0.479753 | − | 0.877403i | \(-0.340726\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 304.763 | 1.68377 | 0.841887 | − | 0.539654i | \(-0.181445\pi\) | ||||
0.841887 | + | 0.539654i | \(0.181445\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 97.5089 | 0.521438 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 12.3062i | − 0.0644302i | −0.999481 | − | 0.0322151i | \(-0.989744\pi\) | ||||
0.999481 | − | 0.0322151i | \(-0.0102562\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 293.895 | 1.52277 | 0.761385 | − | 0.648300i | \(-0.224520\pi\) | ||||
0.761385 | + | 0.648300i | \(0.224520\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 160.346i | 0.813937i | 0.913442 | + | 0.406969i | \(0.133414\pi\) | ||||
−0.913442 | + | 0.406969i | \(0.866586\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −146.982 | −0.738604 | −0.369302 | − | 0.929309i | \(-0.620403\pi\) | ||||
−0.369302 | + | 0.929309i | \(0.620403\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 185.833i | − 0.915432i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 262.138i | − 1.25425i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −398.982 | −1.89091 | −0.945455 | − | 0.325751i | \(-0.894383\pi\) | ||||
−0.945455 | + | 0.325751i | \(0.894383\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −159.517 | −0.735103 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 132.391i | 0.599052i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 226.092 | 1.01386 | 0.506932 | − | 0.861986i | \(-0.330779\pi\) | ||||
0.506932 | + | 0.861986i | \(0.330779\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 153.504i | 0.676229i | 0.941105 | + | 0.338115i | \(0.109789\pi\) | ||||
−0.941105 | + | 0.338115i | \(0.890211\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 72.8071 | 0.317935 | 0.158967 | − | 0.987284i | \(-0.449183\pi\) | ||||
0.158967 | + | 0.987284i | \(0.449183\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.9856i | 0.0643160i | 0.999483 | + | 0.0321580i | \(0.0102380\pi\) | ||||
−0.999483 | + | 0.0321580i | \(0.989762\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 185.299i | − 0.775311i | −0.921804 | − | 0.387655i | \(-0.873285\pi\) | ||||
0.921804 | − | 0.387655i | \(-0.126715\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 134.930 | 0.559874 | 0.279937 | − | 0.960018i | \(-0.409686\pi\) | ||||
0.279937 | + | 0.960018i | \(0.409686\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 355.912 | 1.44094 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 388.419i | − 1.54748i | −0.633501 | − | 0.773742i | \(-0.718383\pi\) | ||||
0.633501 | − | 0.773742i | \(-0.281617\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 373.570 | 1.47656 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 260.227i | 1.01256i | 0.862370 | + | 0.506279i | \(0.168979\pi\) | ||||
−0.862370 | + | 0.506279i | \(0.831021\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 216.658 | 0.836516 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 243.673i | − 0.926512i | −0.886225 | − | 0.463256i | \(-0.846681\pi\) | ||||
0.886225 | − | 0.463256i | \(-0.153319\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 4.62110i | − 0.0171788i | −0.999963 | − | 0.00858941i | \(-0.997266\pi\) | ||||
0.999963 | − | 0.00858941i | \(-0.00273413\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −307.947 | −1.13634 | −0.568169 | − | 0.822912i | \(-0.692348\pi\) | ||||
−0.568169 | + | 0.822912i | \(0.692348\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −332.680 | −1.20101 | −0.600505 | − | 0.799621i | \(-0.705034\pi\) | ||||
−0.600505 | + | 0.799621i | \(0.705034\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 323.408i | − 1.15092i | −0.817831 | − | 0.575459i | \(-0.804823\pi\) | ||||
0.817831 | − | 0.575459i | \(-0.195177\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 181.737 | 0.642179 | 0.321090 | − | 0.947049i | \(-0.395951\pi\) | ||||
0.321090 | + | 0.947049i | \(0.395951\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 102.624i | 0.357573i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 245.772 | 0.850421 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 378.978i | 1.29344i | 0.762727 | + | 0.646720i | \(0.223860\pi\) | ||||
−0.762727 | + | 0.646720i | \(0.776140\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 507.206i | 1.69634i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −78.7189 | −0.261524 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.5438 | −0.0538885 | −0.0269443 | − | 0.999637i | \(-0.508578\pi\) | ||||
−0.0269443 | + | 0.999637i | \(0.508578\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 178.662i | 0.574476i | 0.957859 | + | 0.287238i | \(0.0927370\pi\) | ||||
−0.957859 | + | 0.287238i | \(0.907263\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −135.088 | −0.431590 | −0.215795 | − | 0.976439i | \(-0.569234\pi\) | ||||
−0.215795 | + | 0.976439i | \(0.569234\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 378.445i | − 1.19383i | −0.802304 | − | 0.596916i | \(-0.796393\pi\) | ||||
0.802304 | − | 0.596916i | \(-0.203607\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −569.693 | −1.78587 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 116.213i | 0.359793i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 116.127i | 0.352968i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 371.956 | 1.12373 | 0.561867 | − | 0.827228i | \(-0.310083\pi\) | ||||
0.561867 | + | 0.827228i | \(0.310083\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 193.956 | 0.575537 | 0.287768 | − | 0.957700i | \(-0.407087\pi\) | ||||
0.287768 | + | 0.957700i | \(0.407087\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 489.020i | 1.43408i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −360.877 | −1.05212 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 649.856i | 1.87278i | 0.350957 | + | 0.936392i | \(0.385856\pi\) | ||||
−0.350957 | + | 0.936392i | \(0.614144\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −343.675 | −0.984743 | −0.492372 | − | 0.870385i | \(-0.663870\pi\) | ||||
−0.492372 | + | 0.870385i | \(0.663870\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 461.195i | 1.30650i | 0.757142 | + | 0.653250i | \(0.226595\pi\) | ||||
−0.757142 | + | 0.653250i | \(0.773405\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 248.380i | − 0.691867i | −0.938259 | − | 0.345933i | \(-0.887562\pi\) | ||||
0.938259 | − | 0.345933i | \(-0.112438\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −48.5787 | −0.134567 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −59.6007 | −0.162400 | −0.0811999 | − | 0.996698i | \(-0.525875\pi\) | ||||
−0.0811999 | + | 0.996698i | \(0.525875\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 205.247i | − 0.553227i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −110.460 | −0.296141 | −0.148070 | − | 0.988977i | \(-0.547306\pi\) | ||||
−0.148070 | + | 0.988977i | \(0.547306\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 773.487i | − 2.05169i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 637.579 | 1.68227 | 0.841133 | − | 0.540829i | \(-0.181889\pi\) | ||||
0.841133 | + | 0.540829i | \(0.181889\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 574.728i | − 1.50060i | −0.661100 | − | 0.750298i | \(-0.729910\pi\) | ||||
0.661100 | − | 0.750298i | \(-0.270090\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 71.4364i | 0.183641i | 0.995776 | + | 0.0918206i | \(0.0292686\pi\) | ||||
−0.995776 | + | 0.0918206i | \(0.970731\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −165.614 | −0.423566 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −365.767 | −0.921328 | −0.460664 | − | 0.887575i | \(-0.652389\pi\) | ||||
−0.460664 | + | 0.887575i | \(0.652389\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 728.791i | 1.81743i | 0.417413 | + | 0.908717i | \(0.362937\pi\) | ||||
−0.417413 | + | 0.908717i | \(0.637063\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −663.956 | −1.64753 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 664.190i | − 1.63192i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −401.035 | −0.980525 | −0.490263 | − | 0.871575i | \(-0.663099\pi\) | ||||
−0.490263 | + | 0.871575i | \(0.663099\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 417.906i | − 1.01188i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 356.623i | 0.851130i | 0.904928 | + | 0.425565i | \(0.139925\pi\) | ||||
−0.904928 | + | 0.425565i | \(0.860075\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 272.719 | 0.647788 | 0.323894 | − | 0.946093i | \(-0.395008\pi\) | ||||
0.323894 | + | 0.946093i | \(0.395008\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −185.149 | −0.433604 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 469.680i | − 1.08974i | −0.838519 | − | 0.544872i | \(-0.816578\pi\) | ||||
0.838519 | − | 0.544872i | \(-0.183422\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −361.412 | −0.834670 | −0.417335 | − | 0.908753i | \(-0.637036\pi\) | ||||
−0.417335 | + | 0.908753i | \(0.637036\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 445.229i | 1.01883i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −250.105 | −0.569716 | −0.284858 | − | 0.958570i | \(-0.591946\pi\) | ||||
−0.284858 | + | 0.958570i | \(0.591946\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 356.319i | − 0.804333i | −0.915567 | − | 0.402166i | \(-0.868257\pi\) | ||||
0.915567 | − | 0.402166i | \(-0.131743\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 282.657i | 0.629525i | 0.949171 | + | 0.314762i | \(0.101925\pi\) | ||||
−0.949171 | + | 0.314762i | \(0.898075\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 314.605 | 0.697572 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 413.851 | 0.905581 | 0.452791 | − | 0.891617i | \(-0.350429\pi\) | ||||
0.452791 | + | 0.891617i | \(0.350429\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 177.453i | − 0.384931i | −0.981304 | − | 0.192465i | \(-0.938352\pi\) | ||||
0.981304 | − | 0.192465i | \(-0.0616483\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −267.101 | −0.576892 | −0.288446 | − | 0.957496i | \(-0.593139\pi\) | ||||
−0.288446 | + | 0.957496i | \(0.593139\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 260.525i | 0.557870i | 0.960310 | + | 0.278935i | \(0.0899814\pi\) | ||||
−0.960310 | + | 0.278935i | \(0.910019\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −180.438 | −0.384730 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 241.322i | 0.510195i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 149.746i | − 0.312621i | −0.987708 | − | 0.156311i | \(-0.950040\pi\) | ||||
0.987708 | − | 0.156311i | \(-0.0499601\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 901.789 | 1.87482 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −628.749 | −1.29107 | −0.645533 | − | 0.763732i | \(-0.723365\pi\) | ||||
−0.645533 | + | 0.763732i | \(0.723365\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 390.341i | − 0.794992i | −0.917604 | − | 0.397496i | \(-0.869879\pi\) | ||||
0.917604 | − | 0.397496i | \(-0.130121\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 252.561 | 0.512294 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 93.5615i | − 0.188253i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −254.097 | −0.509212 | −0.254606 | − | 0.967045i | \(-0.581946\pi\) | ||||
−0.254606 | + | 0.967045i | \(0.581946\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 830.503i | 1.65110i | 0.564330 | + | 0.825549i | \(0.309135\pi\) | ||||
−0.564330 | + | 0.825549i | \(0.690865\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 808.291i | 1.58800i | 0.607919 | + | 0.793999i | \(0.292005\pi\) | ||||
−0.607919 | + | 0.793999i | \(0.707995\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 527.184 | 1.03167 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 356.000 | 0.688588 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 591.948i | 1.13618i | 0.822968 | + | 0.568088i | \(0.192317\pi\) | ||||
−0.822968 | + | 0.568088i | \(0.807683\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −529.781 | −1.01297 | −0.506483 | − | 0.862250i | \(-0.669055\pi\) | ||||
−0.506483 | + | 0.862250i | \(0.669055\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 216.796i | − 0.411378i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −105.491 | −0.199416 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 427.148i | 0.801403i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 379.611i | 0.704288i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −413.307 | −0.763968 | −0.381984 | − | 0.924169i | \(-0.624759\pi\) | ||||
−0.381984 | + | 0.924169i | \(0.624759\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 691.851 | 1.26481 | 0.632405 | − | 0.774638i | \(-0.282068\pi\) | ||||
0.632405 | + | 0.774638i | \(0.282068\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 678.971i | − 1.23225i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 578.447 | 1.04602 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 111.996i | − 0.201069i | −0.994934 | − | 0.100535i | \(-0.967945\pi\) | ||||
0.994934 | − | 0.100535i | \(-0.0320553\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −327.650 | −0.586136 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 397.455i | 0.705960i | 0.935631 | + | 0.352980i | \(0.114832\pi\) | ||||
−0.935631 | + | 0.352980i | \(0.885168\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 340.056i | 0.597639i | 0.954310 | + | 0.298819i | \(0.0965928\pi\) | ||||
−0.954310 | + | 0.298819i | \(0.903407\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −547.412 | −0.958690 | −0.479345 | − | 0.877627i | \(-0.659126\pi\) | ||||
−0.479345 | + | 0.877627i | \(0.659126\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −140.974 | −0.244322 | −0.122161 | − | 0.992510i | \(-0.538982\pi\) | ||||
−0.122161 | + | 0.992510i | \(0.538982\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 597.257i | − 1.02798i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −629.210 | −1.07926 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 222.057i | 0.378291i | 0.981949 | + | 0.189145i | \(0.0605717\pi\) | ||||
−0.981949 | + | 0.189145i | \(0.939428\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −582.824 | −0.989515 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 948.975i | 1.60029i | 0.599804 | + | 0.800147i | \(0.295245\pi\) | ||||
−0.599804 | + | 0.800147i | \(0.704755\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.7951i | 0.0530804i | 0.999648 | + | 0.0265402i | \(0.00844900\pi\) | ||||
−0.999648 | + | 0.0265402i | \(0.991551\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −520.561 | −0.866158 | −0.433079 | − | 0.901356i | \(-0.642573\pi\) | ||||
−0.433079 | + | 0.901356i | \(0.642573\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −676.505 | −1.11451 | −0.557253 | − | 0.830343i | \(-0.688144\pi\) | ||||
−0.557253 | + | 0.830343i | \(0.688144\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 483.351i | 0.791082i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −479.820 | −0.782741 | −0.391370 | − | 0.920233i | \(-0.627999\pi\) | ||||
−0.391370 | + | 0.920233i | \(0.627999\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 514.687i | 0.834177i | 0.908866 | + | 0.417088i | \(0.136949\pi\) | ||||
−0.908866 | + | 0.417088i | \(0.863051\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −830.894 | −1.34232 | −0.671158 | − | 0.741314i | \(-0.734203\pi\) | ||||
−0.671158 | + | 0.741314i | \(0.734203\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 304.930i | 0.489454i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 294.454i | 0.468131i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −481.324 | −0.762795 | −0.381398 | − | 0.924411i | \(-0.624557\pi\) | ||||
−0.381398 | + | 0.924411i | \(0.624557\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −515.409 | −0.809119 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 1076.40i | − 1.67925i | −0.543163 | − | 0.839627i | \(-0.682774\pi\) | ||||
0.543163 | − | 0.839627i | \(-0.317226\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1021.36 | −1.58843 | −0.794214 | − | 0.607638i | \(-0.792117\pi\) | ||||
−0.794214 | + | 0.607638i | \(0.792117\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 972.866i | 1.50366i | 0.659359 | + | 0.751829i | \(0.270828\pi\) | ||||
−0.659359 | + | 0.751829i | \(0.729172\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1281.14 | −1.97402 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 309.260i | 0.473599i | 0.971559 | + | 0.236799i | \(0.0760984\pi\) | ||||
−0.971559 | + | 0.236799i | \(0.923902\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 294.758i | 0.447281i | 0.974672 | + | 0.223641i | \(0.0717942\pi\) | ||||
−0.974672 | + | 0.223641i | \(0.928206\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 232.552 | 0.351819 | 0.175909 | − | 0.984406i | \(-0.443713\pi\) | ||||
0.175909 | + | 0.984406i | \(0.443713\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 967.596 | 1.45067 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 567.596i | 0.845895i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −37.5174 | −0.0557466 | −0.0278733 | − | 0.999611i | \(-0.508873\pi\) | ||||
−0.0278733 | + | 0.999611i | \(0.508873\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 111.630i | − 0.164890i | −0.996596 | − | 0.0824448i | \(-0.973727\pi\) | ||||
0.996596 | − | 0.0824448i | \(-0.0262728\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −530.325 | −0.781038 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 80.5971i | − 0.118005i | −0.998258 | − | 0.0590023i | \(-0.981208\pi\) | ||||
0.998258 | − | 0.0590023i | \(-0.0187919\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 854.296i | − 1.23991i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 280.377 | 0.405756 | 0.202878 | − | 0.979204i | \(-0.434971\pi\) | ||||
0.202878 | + | 0.979204i | \(0.434971\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −139.473 | −0.200105 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 182.365i | − 0.260150i | −0.991504 | − | 0.130075i | \(-0.958478\pi\) | ||||
0.991504 | − | 0.130075i | \(-0.0415218\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 791.596 | 1.12603 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 680.646i | 0.962725i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −42.7374 | −0.0602784 | −0.0301392 | − | 0.999546i | \(-0.509595\pi\) | ||||
−0.0301392 | + | 0.999546i | \(0.509595\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 830.577i | − 1.16490i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 765.586i | − 1.06479i | −0.846495 | − | 0.532396i | \(-0.821292\pi\) | ||||
0.846495 | − | 0.532396i | \(-0.178708\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 692.070 | 0.959875 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −201.653 | −0.277377 | −0.138689 | − | 0.990336i | \(-0.544289\pi\) | ||||
−0.138689 | + | 0.990336i | \(0.544289\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 106.985i | − 0.146354i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −489.057 | −0.667199 | −0.333600 | − | 0.942715i | \(-0.608263\pi\) | ||||
−0.333600 | + | 0.942715i | \(0.608263\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 553.156i | 0.750551i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −760.306 | −1.02883 | −0.514415 | − | 0.857541i | \(-0.671991\pi\) | ||||
−0.514415 | + | 0.857541i | \(0.671991\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 771.776i | 1.03873i | 0.854553 | + | 0.519365i | \(0.173831\pi\) | ||||
−0.854553 | + | 0.519365i | \(0.826169\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 428.618i | 0.572254i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1366.53 | 1.81962 | 0.909809 | − | 0.415026i | \(-0.136228\pi\) | ||||
0.909809 | + | 0.415026i | \(0.136228\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.6271 | −0.0140384 | −0.00701919 | − | 0.999975i | \(-0.502234\pi\) | ||||
−0.00701919 | + | 0.999975i | \(0.502234\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 20.6052i | − 0.0270765i | −0.999908 | − | 0.0135383i | \(-0.995691\pi\) | ||||
0.999908 | − | 0.0135383i | \(-0.00430950\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1032.94 | 1.35379 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 1739.44i | − 2.26785i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1235.93 | 1.60719 | 0.803595 | − | 0.595177i | \(-0.202918\pi\) | ||||
0.803595 | + | 0.595177i | \(0.202918\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 54.0189i | − 0.0698822i | −0.999389 | − | 0.0349411i | \(-0.988876\pi\) | ||||
0.999389 | − | 0.0349411i | \(-0.0111244\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 374.953i | 0.481326i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −286.824 | −0.367253 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.0612 | −0.0356559 | −0.0178280 | − | 0.999841i | \(-0.505675\pi\) | ||||
−0.0178280 | + | 0.999841i | \(0.505675\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 54.3722i | − 0.0687386i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −770.641 | −0.971804 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 835.564i | − 1.04839i | −0.851599 | − | 0.524193i | \(-0.824367\pi\) | ||||
0.851599 | − | 0.524193i | \(-0.175633\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −157.825 | −0.197528 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 1616.15i | − 2.01264i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 793.187i | 0.980453i | 0.871595 | + | 0.490227i | \(0.163086\pi\) | ||||
−0.871595 | + | 0.490227i | \(0.836914\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 298.105 | 0.367577 | 0.183789 | − | 0.982966i | \(-0.441164\pi\) | ||||
0.183789 | + | 0.982966i | \(0.441164\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −287.613 | −0.352035 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 1143.48i | − 1.39280i | −0.717656 | − | 0.696398i | \(-0.754785\pi\) | ||||
0.717656 | − | 0.696398i | \(-0.245215\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 460.399 | 0.559416 | 0.279708 | − | 0.960085i | \(-0.409762\pi\) | ||||
0.279708 | + | 0.960085i | \(0.409762\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 250.204i | 0.302544i | 0.988492 | + | 0.151272i | \(0.0483370\pi\) | ||||
−0.988492 | + | 0.151272i | \(0.951663\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −171.815 | −0.207256 | −0.103628 | − | 0.994616i | \(-0.533045\pi\) | ||||
−0.103628 | + | 0.994616i | \(0.533045\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 168.292i | − 0.202032i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 915.442i | 1.09111i | 0.838075 | + | 0.545555i | \(0.183681\pi\) | ||||
−0.838075 | + | 0.545555i | \(0.816319\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −634.579 | −0.754553 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −478.680 | −0.565147 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1128.10i | 1.32561i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1242.33 | −1.45642 | −0.728211 | − | 0.685353i | \(-0.759648\pi\) | ||||
−0.728211 | + | 0.685353i | \(0.759648\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 716.993i | 0.836632i | 0.908302 | + | 0.418316i | \(0.137379\pi\) | ||||
−0.908302 | + | 0.418316i | \(0.862621\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 551.509 | 0.642036 | 0.321018 | − | 0.947073i | \(-0.395975\pi\) | ||||
0.321018 | + | 0.947073i | \(0.395975\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1513.33i | 1.75356i | 0.480887 | + | 0.876782i | \(0.340315\pi\) | ||||
−0.480887 | + | 0.876782i | \(0.659685\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 1773.30i | − 2.04062i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −751.035 | −0.862267 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 946.355 | 1.07908 | 0.539541 | − | 0.841959i | \(-0.318598\pi\) | ||||
0.539541 | + | 0.841959i | \(0.318598\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1239.83i | 1.40730i | 0.710547 | + | 0.703650i | \(0.248447\pi\) | ||||
−0.710547 | + | 0.703650i | \(0.751553\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1156.41 | 1.30964 | 0.654820 | − | 0.755785i | \(-0.272745\pi\) | ||||
0.654820 | + | 0.755785i | \(0.272745\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 1100.19i | − 1.24035i | −0.784464 | − | 0.620174i | \(-0.787062\pi\) | ||||
0.784464 | − | 0.620174i | \(-0.212938\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 178.211 | 0.200462 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 424.288i | 0.475127i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1266.63i | 1.40893i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 278.947 | 0.309597 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 570.430 | 0.628919 | 0.314460 | − | 0.949271i | \(-0.398177\pi\) | ||||
0.314460 | + | 0.949271i | \(0.398177\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1321.74i | − 1.45087i | −0.688290 | − | 0.725435i | \(-0.741638\pi\) | ||||
0.688290 | − | 0.725435i | \(-0.258362\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1830.96 | −2.00544 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 55.8428i | 0.0608973i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1748.03 | 1.90210 | 0.951048 | − | 0.309044i | \(-0.100009\pi\) | ||||
0.951048 | + | 0.309044i | \(0.100009\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 389.429i | − 0.421917i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 556.666i | 0.599210i | 0.954063 | + | 0.299605i | \(0.0968548\pi\) | ||||
−0.954063 | + | 0.299605i | \(0.903145\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −452.429 | −0.485960 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 117.701 | 0.125615 | 0.0628074 | − | 0.998026i | \(-0.479995\pi\) | ||||
0.0628074 | + | 0.998026i | \(0.479995\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1714.17i | 1.82165i | 0.412797 | + | 0.910823i | \(0.364552\pi\) | ||||
−0.412797 | + | 0.910823i | \(0.635448\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −534.342 | −0.566640 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1151.68i | − 1.21613i | −0.793886 | − | 0.608066i | \(-0.791946\pi\) | ||||
0.793886 | − | 0.608066i | \(-0.208054\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2194.29 | 2.31221 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 1272.18i | − 1.33493i | −0.744643 | − | 0.667463i | \(-0.767380\pi\) | ||||
0.744643 | − | 0.667463i | \(-0.232620\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 704.862i | − 0.734997i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 126.263 | 0.131387 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1358.70 | −1.40506 | −0.702532 | − | 0.711652i | \(-0.747947\pi\) | ||||
−0.702532 | + | 0.711652i | \(0.747947\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1818.71i | 1.87303i | 0.350632 | + | 0.936513i | \(0.385967\pi\) | ||||
−0.350632 | + | 0.936513i | \(0.614033\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 883.606 | 0.908125 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 594.974i | 0.608981i | 0.952515 | + | 0.304490i | \(0.0984862\pi\) | ||||
−0.952515 | + | 0.304490i | \(0.901514\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 934.799 | 0.954850 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1209.81i | 1.23073i | 0.788241 | + | 0.615366i | \(0.210992\pi\) | ||||
−0.788241 | + | 0.615366i | \(0.789008\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 409.874i | − 0.414433i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −236.596 | −0.238745 | −0.119373 | − | 0.992850i | \(-0.538088\pi\) | ||||
−0.119373 | + | 0.992850i | \(0.538088\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −614.355 | −0.616204 | −0.308102 | − | 0.951353i | \(-0.599694\pi\) | ||||
−0.308102 | + | 0.951353i | \(0.599694\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1800.3.l.g.1601.1 | 4 | ||
3.2 | odd | 2 | inner | 1800.3.l.g.1601.2 | 4 | ||
4.3 | odd | 2 | 3600.3.l.m.1601.4 | 4 | |||
5.2 | odd | 4 | 1800.3.c.b.449.5 | 8 | |||
5.3 | odd | 4 | 1800.3.c.b.449.3 | 8 | |||
5.4 | even | 2 | 360.3.l.a.161.4 | yes | 4 | ||
12.11 | even | 2 | 3600.3.l.m.1601.3 | 4 | |||
15.2 | even | 4 | 1800.3.c.b.449.6 | 8 | |||
15.8 | even | 4 | 1800.3.c.b.449.4 | 8 | |||
15.14 | odd | 2 | 360.3.l.a.161.2 | ✓ | 4 | ||
20.3 | even | 4 | 3600.3.c.l.449.6 | 8 | |||
20.7 | even | 4 | 3600.3.c.l.449.4 | 8 | |||
20.19 | odd | 2 | 720.3.l.d.161.3 | 4 | |||
40.19 | odd | 2 | 2880.3.l.h.1601.1 | 4 | |||
40.29 | even | 2 | 2880.3.l.a.1601.2 | 4 | |||
60.23 | odd | 4 | 3600.3.c.l.449.5 | 8 | |||
60.47 | odd | 4 | 3600.3.c.l.449.3 | 8 | |||
60.59 | even | 2 | 720.3.l.d.161.1 | 4 | |||
120.29 | odd | 2 | 2880.3.l.a.1601.4 | 4 | |||
120.59 | even | 2 | 2880.3.l.h.1601.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.3.l.a.161.2 | ✓ | 4 | 15.14 | odd | 2 | ||
360.3.l.a.161.4 | yes | 4 | 5.4 | even | 2 | ||
720.3.l.d.161.1 | 4 | 60.59 | even | 2 | |||
720.3.l.d.161.3 | 4 | 20.19 | odd | 2 | |||
1800.3.c.b.449.3 | 8 | 5.3 | odd | 4 | |||
1800.3.c.b.449.4 | 8 | 15.8 | even | 4 | |||
1800.3.c.b.449.5 | 8 | 5.2 | odd | 4 | |||
1800.3.c.b.449.6 | 8 | 15.2 | even | 4 | |||
1800.3.l.g.1601.1 | 4 | 1.1 | even | 1 | trivial | ||
1800.3.l.g.1601.2 | 4 | 3.2 | odd | 2 | inner | ||
2880.3.l.a.1601.2 | 4 | 40.29 | even | 2 | |||
2880.3.l.a.1601.4 | 4 | 120.29 | odd | 2 | |||
2880.3.l.h.1601.1 | 4 | 40.19 | odd | 2 | |||
2880.3.l.h.1601.3 | 4 | 120.59 | even | 2 | |||
3600.3.c.l.449.3 | 8 | 60.47 | odd | 4 | |||
3600.3.c.l.449.4 | 8 | 20.7 | even | 4 | |||
3600.3.c.l.449.5 | 8 | 60.23 | odd | 4 | |||
3600.3.c.l.449.6 | 8 | 20.3 | even | 4 | |||
3600.3.l.m.1601.3 | 4 | 12.11 | even | 2 | |||
3600.3.l.m.1601.4 | 4 | 4.3 | odd | 2 |