Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,3,Mod(305,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("684.305");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.6376500822\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 156x^{10} + 8721x^{8} + 208784x^{6} + 2024760x^{4} + 7117056x^{2} + 6533136 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 305.3 | ||
Root | \(-5.71859i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 684.305 |
Dual form | 684.3.e.a.305.10 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 5.71859i | − 1.14372i | −0.820352 | − | 0.571859i | \(-0.806222\pi\) | ||||
0.820352 | − | 0.571859i | \(-0.193778\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.91816 | 0.845452 | 0.422726 | − | 0.906258i | \(-0.361073\pi\) | ||||
0.422726 | + | 0.906258i | \(0.361073\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.41452i | 0.219502i | 0.993959 | + | 0.109751i | \(0.0350053\pi\) | ||||
−0.993959 | + | 0.109751i | \(0.964995\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 17.1103 | 1.31618 | 0.658088 | − | 0.752941i | \(-0.271365\pi\) | ||||
0.658088 | + | 0.752941i | \(0.271365\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 16.1412i | 0.949485i | 0.880125 | + | 0.474742i | \(0.157459\pi\) | ||||
−0.880125 | + | 0.474742i | \(0.842541\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.35890 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 15.9801i | − 0.694786i | −0.937720 | − | 0.347393i | \(-0.887067\pi\) | ||||
0.937720 | − | 0.347393i | \(-0.112933\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.70232 | −0.308093 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 31.2245i | − 1.07671i | −0.842719 | − | 0.538354i | \(-0.819046\pi\) | ||||
0.842719 | − | 0.538354i | \(-0.180954\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −13.5110 | −0.435839 | −0.217920 | − | 0.975967i | \(-0.569927\pi\) | ||||
−0.217920 | + | 0.975967i | \(0.569927\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 33.8436i | − 0.966959i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 45.7135 | 1.23550 | 0.617750 | − | 0.786375i | \(-0.288044\pi\) | ||||
0.617750 | + | 0.786375i | \(0.288044\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 30.3783i | − 0.740935i | −0.928845 | − | 0.370467i | \(-0.879197\pi\) | ||||
0.928845 | − | 0.370467i | \(-0.120803\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −21.0735 | −0.490081 | −0.245041 | − | 0.969513i | \(-0.578801\pi\) | ||||
−0.245041 | + | 0.969513i | \(0.578801\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 43.6245i | − 0.928182i | −0.885788 | − | 0.464091i | \(-0.846381\pi\) | ||||
0.885788 | − | 0.464091i | \(-0.153619\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −13.9754 | −0.285212 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 43.5224i | 0.821177i | 0.911821 | + | 0.410589i | \(0.134677\pi\) | ||||
−0.911821 | + | 0.410589i | \(0.865323\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13.8077 | 0.251048 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 86.2708i | − 1.46222i | −0.682261 | − | 0.731109i | \(-0.739003\pi\) | ||||
0.682261 | − | 0.731109i | \(-0.260997\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 112.834 | 1.84974 | 0.924870 | − | 0.380284i | \(-0.124174\pi\) | ||||
0.924870 | + | 0.380284i | \(0.124174\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 97.8468i | − 1.50534i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −41.3253 | −0.616796 | −0.308398 | − | 0.951257i | \(-0.599793\pi\) | ||||
−0.308398 | + | 0.951257i | \(0.599793\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 13.6014i | − 0.191569i | −0.995402 | − | 0.0957846i | \(-0.969464\pi\) | ||||
0.995402 | − | 0.0957846i | \(-0.0305360\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −21.7775 | −0.298322 | −0.149161 | − | 0.988813i | \(-0.547657\pi\) | ||||
−0.149161 | + | 0.988813i | \(0.547657\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 14.2895i | 0.185578i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 71.2807 | 0.902287 | 0.451143 | − | 0.892451i | \(-0.351016\pi\) | ||||
0.451143 | + | 0.892451i | \(0.351016\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 19.9149i | 0.239939i | 0.992778 | + | 0.119969i | \(0.0382796\pi\) | ||||
−0.992778 | + | 0.119969i | \(0.961720\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 92.3052 | 1.08594 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 20.3030i | − 0.228124i | −0.993474 | − | 0.114062i | \(-0.963614\pi\) | ||||
0.993474 | − | 0.114062i | \(-0.0363862\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 101.261 | 1.11276 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 24.9268i | − 0.262387i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 20.1043 | 0.207261 | 0.103631 | − | 0.994616i | \(-0.466954\pi\) | ||||
0.103631 | + | 0.994616i | \(0.466954\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 109.949i | − 1.08860i | −0.838890 | − | 0.544300i | \(-0.816795\pi\) | ||||
0.838890 | − | 0.544300i | \(-0.183205\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 96.5263 | 0.937148 | 0.468574 | − | 0.883424i | \(-0.344768\pi\) | ||||
0.468574 | + | 0.883424i | \(0.344768\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 158.697i | 1.48315i | 0.670872 | + | 0.741574i | \(0.265920\pi\) | ||||
−0.670872 | + | 0.741574i | \(0.734080\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −79.4341 | −0.728753 | −0.364376 | − | 0.931252i | \(-0.618718\pi\) | ||||
−0.364376 | + | 0.931252i | \(0.618718\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 27.4358i | 0.242795i | 0.992604 | + | 0.121397i | \(0.0387375\pi\) | ||||
−0.992604 | + | 0.121397i | \(0.961262\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −91.3836 | −0.794640 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 95.5265i | 0.802743i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 115.170 | 0.951819 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 98.9184i | − 0.791347i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −192.044 | −1.51216 | −0.756079 | − | 0.654480i | \(-0.772888\pi\) | ||||
−0.756079 | + | 0.654480i | \(0.772888\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 210.592i | 1.60757i | 0.594920 | + | 0.803785i | \(0.297184\pi\) | ||||
−0.594920 | + | 0.803785i | \(0.702816\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 25.7967 | 0.193960 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 136.988i | − 0.999915i | −0.866050 | − | 0.499957i | \(-0.833349\pi\) | ||||
0.866050 | − | 0.499957i | \(-0.166651\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −203.487 | −1.46394 | −0.731969 | − | 0.681338i | \(-0.761399\pi\) | ||||
−0.731969 | + | 0.681338i | \(0.761399\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 41.3131i | 0.288903i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −178.560 | −1.23145 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 100.061i | − 0.671552i | −0.941942 | − | 0.335776i | \(-0.891001\pi\) | ||||
0.941942 | − | 0.335776i | \(-0.108999\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.6662 | −0.143485 | −0.0717425 | − | 0.997423i | \(-0.522856\pi\) | ||||
−0.0717425 | + | 0.997423i | \(0.522856\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 77.2640i | 0.498478i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 150.489 | 0.958530 | 0.479265 | − | 0.877670i | \(-0.340903\pi\) | ||||
0.479265 | + | 0.877670i | \(0.340903\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 94.5727i | − 0.587408i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.2416 | −0.105777 | −0.0528884 | − | 0.998600i | \(-0.516843\pi\) | ||||
−0.0528884 | + | 0.998600i | \(0.516843\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 27.7925i | 0.166422i | 0.996532 | + | 0.0832110i | \(0.0265176\pi\) | ||||
−0.996532 | + | 0.0832110i | \(0.973482\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 123.762 | 0.732319 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 30.8921i | 0.178567i | 0.996006 | + | 0.0892836i | \(0.0284577\pi\) | ||||
−0.996006 | + | 0.0892836i | \(0.971542\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −45.5836 | −0.260478 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 200.232i | 1.11862i | 0.828960 | + | 0.559308i | \(0.188933\pi\) | ||||
−0.828960 | + | 0.559308i | \(0.811067\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −226.588 | −1.25187 | −0.625933 | − | 0.779877i | \(-0.715282\pi\) | ||||
−0.625933 | + | 0.779877i | \(0.715282\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 261.417i | − 1.41306i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −38.9733 | −0.208414 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.67013i | 0.0506290i | 0.999680 | + | 0.0253145i | \(0.00805871\pi\) | ||||
−0.999680 | + | 0.0253145i | \(0.991941\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.9769 | 0.119051 | 0.0595256 | − | 0.998227i | \(-0.481041\pi\) | ||||
0.0595256 | + | 0.998227i | \(0.481041\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 336.959i | 1.71045i | 0.518257 | + | 0.855225i | \(0.326581\pi\) | ||||
−0.518257 | + | 0.855225i | \(0.673419\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 101.008 | 0.507580 | 0.253790 | − | 0.967259i | \(-0.418323\pi\) | ||||
0.253790 | + | 0.967259i | \(0.418323\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 184.792i | − 0.910304i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −173.721 | −0.847421 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.5246i | 0.0503572i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.5805 | 0.0785805 | 0.0392902 | − | 0.999228i | \(-0.487490\pi\) | ||||
0.0392902 | + | 0.999228i | \(0.487490\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 120.511i | 0.560515i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −79.9604 | −0.368481 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 276.181i | 1.24969i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −292.950 | −1.31368 | −0.656839 | − | 0.754031i | \(-0.728107\pi\) | ||||
−0.656839 | + | 0.754031i | \(0.728107\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 395.334i | 1.74156i | 0.491675 | + | 0.870779i | \(0.336385\pi\) | ||||
−0.491675 | + | 0.870779i | \(0.663615\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 271.347 | 1.18492 | 0.592460 | − | 0.805600i | \(-0.298157\pi\) | ||||
0.592460 | + | 0.805600i | \(0.298157\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 78.1541i | 0.335425i | 0.985836 | + | 0.167713i | \(0.0536381\pi\) | ||||
−0.985836 | + | 0.167713i | \(0.946362\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −249.471 | −1.06158 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 376.765i | 1.57642i | 0.615405 | + | 0.788211i | \(0.288992\pi\) | ||||
−0.615405 | + | 0.788211i | \(0.711008\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −428.672 | −1.77872 | −0.889361 | − | 0.457206i | \(-0.848850\pi\) | ||||
−0.889361 | + | 0.457206i | \(0.848850\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 79.9194i | 0.326202i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 74.5820 | 0.301951 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 329.477i | 1.31266i | 0.754475 | + | 0.656329i | \(0.227892\pi\) | ||||
−0.754475 | + | 0.656329i | \(0.772108\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 38.5842 | 0.152507 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.5478i | 0.0527150i | 0.999653 | + | 0.0263575i | \(0.00839083\pi\) | ||||
−0.999653 | + | 0.0263575i | \(0.991609\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 270.540 | 1.04456 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 89.8023i | 0.341454i | 0.985318 | + | 0.170727i | \(0.0546115\pi\) | ||||
−0.985318 | + | 0.170727i | \(0.945388\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 248.887 | 0.939196 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 179.454i | − 0.667114i | −0.942730 | − | 0.333557i | \(-0.891751\pi\) | ||||
0.942730 | − | 0.333557i | \(-0.108249\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 279.633 | 1.03186 | 0.515928 | − | 0.856632i | \(-0.327447\pi\) | ||||
0.515928 | + | 0.856632i | \(0.327447\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 18.5974i | − 0.0676270i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −180.273 | −0.650804 | −0.325402 | − | 0.945576i | \(-0.605500\pi\) | ||||
−0.325402 | + | 0.945576i | \(0.605500\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 34.2781i | 0.121986i | 0.998138 | + | 0.0609931i | \(0.0194268\pi\) | ||||
−0.998138 | + | 0.0609931i | \(0.980573\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 234.711 | 0.829368 | 0.414684 | − | 0.909965i | \(-0.363892\pi\) | ||||
0.414684 | + | 0.909965i | \(0.363892\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 179.784i | − 0.626425i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 28.4603 | 0.0984787 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 502.963i | 1.71660i | 0.513150 | + | 0.858299i | \(0.328478\pi\) | ||||
−0.513150 | + | 0.858299i | \(0.671522\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −493.348 | −1.67237 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 273.424i | − 0.914461i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −124.716 | −0.414340 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 645.253i | − 2.11558i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −140.853 | −0.458805 | −0.229402 | − | 0.973332i | \(-0.573677\pi\) | ||||
−0.229402 | + | 0.973332i | \(0.573677\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 200.164i | − 0.643615i | −0.946805 | − | 0.321808i | \(-0.895710\pi\) | ||||
0.946805 | − | 0.321808i | \(-0.104290\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 136.384 | 0.435731 | 0.217865 | − | 0.975979i | \(-0.430091\pi\) | ||||
0.217865 | + | 0.975979i | \(0.430091\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 136.215i | 0.429700i | 0.976647 | + | 0.214850i | \(0.0689263\pi\) | ||||
−0.976647 | + | 0.214850i | \(0.931074\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 75.3923 | 0.236339 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 70.3580i | 0.217827i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −131.789 | −0.405505 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 258.177i | − 0.784733i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −572.123 | −1.72847 | −0.864235 | − | 0.503089i | \(-0.832197\pi\) | ||||
−0.864235 | + | 0.503089i | \(0.832197\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 236.323i | 0.705441i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 466.379 | 1.38391 | 0.691957 | − | 0.721938i | \(-0.256749\pi\) | ||||
0.691957 | + | 0.721938i | \(0.256749\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 32.6226i | − 0.0956675i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −372.698 | −1.08658 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 365.970i | − 1.05467i | −0.849658 | − | 0.527334i | \(-0.823192\pi\) | ||||
0.849658 | − | 0.527334i | \(-0.176808\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 498.969 | 1.42971 | 0.714855 | − | 0.699273i | \(-0.246493\pi\) | ||||
0.714855 | + | 0.699273i | \(0.246493\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 230.666i | − 0.653444i | −0.945120 | − | 0.326722i | \(-0.894056\pi\) | ||||
0.945120 | − | 0.326722i | \(-0.105944\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −77.7809 | −0.219101 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 80.5301i | − 0.224318i | −0.993690 | − | 0.112159i | \(-0.964223\pi\) | ||||
0.993690 | − | 0.112159i | \(-0.0357766\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.0000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 124.537i | 0.341197i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −225.261 | −0.613790 | −0.306895 | − | 0.951743i | \(-0.599290\pi\) | ||||
−0.306895 | + | 0.951743i | \(0.599290\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 257.573i | 0.694266i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.0567 | −0.0296427 | −0.0148214 | − | 0.999890i | \(-0.504718\pi\) | ||||
−0.0148214 | + | 0.999890i | \(0.504718\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 534.261i | − 1.41714i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −124.413 | −0.328267 | −0.164133 | − | 0.986438i | \(-0.552483\pi\) | ||||
−0.164133 | + | 0.986438i | \(0.552483\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 181.006i | 0.472601i | 0.971680 | + | 0.236301i | \(0.0759350\pi\) | ||||
−0.971680 | + | 0.236301i | \(0.924065\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 81.7160 | 0.212249 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 118.699i | − 0.305139i | −0.988293 | − | 0.152569i | \(-0.951245\pi\) | ||||
0.988293 | − | 0.152569i | \(-0.0487548\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 257.938 | 0.659689 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 407.625i | − 1.03196i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 307.471 | 0.774486 | 0.387243 | − | 0.921978i | \(-0.373427\pi\) | ||||
0.387243 | + | 0.921978i | \(0.373427\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 284.383i | 0.709185i | 0.935021 | + | 0.354593i | \(0.115380\pi\) | ||||
−0.935021 | + | 0.354593i | \(0.884620\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −231.177 | −0.573641 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 110.376i | 0.271194i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 172.237 | 0.421117 | 0.210559 | − | 0.977581i | \(-0.432472\pi\) | ||||
0.210559 | + | 0.977581i | \(0.432472\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 510.565i | − 1.23623i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 113.885 | 0.274422 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 149.429i | 0.356633i | 0.983973 | + | 0.178317i | \(0.0570651\pi\) | ||||
−0.983973 | + | 0.178317i | \(0.942935\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 42.9576 | 0.102037 | 0.0510185 | − | 0.998698i | \(-0.483753\pi\) | ||||
0.0510185 | + | 0.998698i | \(0.483753\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 124.325i | − 0.292530i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 667.771 | 1.56387 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 400.606i | 0.929480i | 0.885447 | + | 0.464740i | \(0.153852\pi\) | ||||
−0.885447 | + | 0.464740i | \(0.846148\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 428.936 | 0.990614 | 0.495307 | − | 0.868718i | \(-0.335056\pi\) | ||||
0.495307 | + | 0.868718i | \(0.335056\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 69.6556i | − 0.159395i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −101.286 | −0.230720 | −0.115360 | − | 0.993324i | \(-0.536802\pi\) | ||||
−0.115360 | + | 0.993324i | \(0.536802\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 762.277i | − 1.72071i | −0.509691 | − | 0.860357i | \(-0.670240\pi\) | ||||
0.509691 | − | 0.860357i | \(-0.329760\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −116.105 | −0.260909 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 447.630i | − 0.996949i | −0.866904 | − | 0.498474i | \(-0.833894\pi\) | ||||
0.866904 | − | 0.498474i | \(-0.166106\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 73.3491 | 0.162637 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 579.073i | − 1.27269i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 433.951 | 0.949565 | 0.474782 | − | 0.880103i | \(-0.342527\pi\) | ||||
0.474782 | + | 0.880103i | \(0.342527\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 517.149i | 1.12180i | 0.827884 | + | 0.560899i | \(0.189544\pi\) | ||||
−0.827884 | + | 0.560899i | \(0.810456\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 620.085 | 1.33928 | 0.669638 | − | 0.742688i | \(-0.266449\pi\) | ||||
0.669638 | + | 0.742688i | \(0.266449\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 551.719i | 1.18141i | 0.806887 | + | 0.590705i | \(0.201150\pi\) | ||||
−0.806887 | + | 0.590705i | \(0.798850\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −244.570 | −0.521471 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 50.8824i | − 0.107574i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −33.5737 | −0.0706814 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 728.217i | 1.52029i | 0.649755 | + | 0.760143i | \(0.274871\pi\) | ||||
−0.649755 | + | 0.760143i | \(0.725129\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 782.171 | 1.62613 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 114.968i | − 0.237048i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −588.424 | −1.20826 | −0.604131 | − | 0.796885i | \(-0.706480\pi\) | ||||
−0.604131 | + | 0.796885i | \(0.706480\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 181.398i | − 0.369446i | −0.982791 | − | 0.184723i | \(-0.940861\pi\) | ||||
0.982791 | − | 0.184723i | \(-0.0591387\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 504.003 | 1.02232 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 80.4953i | − 0.161962i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −360.725 | −0.722895 | −0.361448 | − | 0.932392i | \(-0.617717\pi\) | ||||
−0.361448 | + | 0.932392i | \(0.617717\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 875.415i | − 1.74039i | −0.492709 | − | 0.870194i | \(-0.663993\pi\) | ||||
0.492709 | − | 0.870194i | \(-0.336007\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −628.752 | −1.24505 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 99.8530i | 0.196175i | 0.995178 | + | 0.0980874i | \(0.0312725\pi\) | ||||
−0.995178 | + | 0.0980874i | \(0.968728\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −128.883 | −0.252217 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 551.995i | − 1.07183i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 105.332 | 0.203738 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 46.6446i | 0.0895290i | 0.998998 | + | 0.0447645i | \(0.0142538\pi\) | ||||
−0.998998 | + | 0.0447645i | \(0.985746\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 677.022 | 1.29450 | 0.647248 | − | 0.762279i | \(-0.275920\pi\) | ||||
0.647248 | + | 0.762279i | \(0.275920\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 218.085i | − 0.413823i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 273.637 | 0.517272 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 519.782i | − 0.975201i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 907.522 | 1.69630 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 33.7438i | − 0.0626045i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1007.63 | −1.86252 | −0.931262 | − | 0.364349i | \(-0.881292\pi\) | ||||
−0.931262 | + | 0.364349i | \(0.881292\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 454.251i | 0.833488i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 575.298 | 1.05173 | 0.525867 | − | 0.850567i | \(-0.323741\pi\) | ||||
0.525867 | + | 0.850567i | \(0.323741\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 136.105i | − 0.247014i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 421.850 | 0.762840 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 140.156i | − 0.251626i | −0.992054 | − | 0.125813i | \(-0.959846\pi\) | ||||
0.992054 | − | 0.125813i | \(-0.0401539\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −360.574 | −0.645033 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 157.113i | 0.279064i | 0.990218 | + | 0.139532i | \(0.0445598\pi\) | ||||
−0.990218 | + | 0.139532i | \(0.955440\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 156.894 | 0.277689 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 661.449i | − 1.16248i | −0.813733 | − | 0.581238i | \(-0.802568\pi\) | ||||
0.813733 | − | 0.581238i | \(-0.197432\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 496.494 | 0.869517 | 0.434759 | − | 0.900547i | \(-0.356834\pi\) | ||||
0.434759 | + | 0.900547i | \(0.356834\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 123.084i | 0.214059i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −700.475 | −1.21399 | −0.606997 | − | 0.794704i | \(-0.707626\pi\) | ||||
−0.606997 | + | 0.794704i | \(0.707626\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 117.860i | 0.202857i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −105.086 | −0.180250 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 318.368i | − 0.542364i | −0.962528 | − | 0.271182i | \(-0.912585\pi\) | ||||
0.962528 | − | 0.271182i | \(-0.0874145\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −58.8931 | −0.0999884 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 340.951i | 0.574959i | 0.957787 | + | 0.287479i | \(0.0928173\pi\) | ||||
−0.957787 | + | 0.287479i | \(0.907183\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 546.277 | 0.918113 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 993.451i | − 1.65852i | −0.558866 | − | 0.829258i | \(-0.688764\pi\) | ||||
0.558866 | − | 0.829258i | \(-0.311236\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −265.068 | −0.441044 | −0.220522 | − | 0.975382i | \(-0.570776\pi\) | ||||
−0.220522 | + | 0.975382i | \(0.570776\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 658.611i | − 1.08861i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −363.853 | −0.599429 | −0.299714 | − | 0.954029i | \(-0.596891\pi\) | ||||
−0.299714 | + | 0.954029i | \(0.596891\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 746.428i | − 1.22165i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −871.617 | −1.42189 | −0.710944 | − | 0.703249i | \(-0.751732\pi\) | ||||
−0.710944 | + | 0.703249i | \(0.751732\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 580.947i | − 0.941567i | −0.882249 | − | 0.470784i | \(-0.843971\pi\) | ||||
0.882249 | − | 0.470784i | \(-0.156029\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −766.583 | −1.23842 | −0.619211 | − | 0.785225i | \(-0.712548\pi\) | ||||
−0.619211 | + | 0.785225i | \(0.712548\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 120.156i | − 0.192868i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −758.232 | −1.21317 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 737.872i | 1.17309i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −828.521 | −1.31303 | −0.656514 | − | 0.754314i | \(-0.727970\pi\) | ||||
−0.656514 | + | 0.754314i | \(0.727970\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1098.22i | 1.72948i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −239.123 | −0.375389 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 892.171i | 1.39184i | 0.718118 | + | 0.695921i | \(0.245004\pi\) | ||||
−0.718118 | + | 0.695921i | \(0.754996\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1204.02 | 1.87251 | 0.936254 | − | 0.351323i | \(-0.114268\pi\) | ||||
0.936254 | + | 0.351323i | \(0.114268\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1181.91i | 1.82675i | 0.407117 | + | 0.913376i | \(0.366534\pi\) | ||||
−0.407117 | + | 0.913376i | \(0.633466\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 208.303 | 0.320959 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 891.748i | − 1.36562i | −0.730598 | − | 0.682808i | \(-0.760758\pi\) | ||||
0.730598 | − | 0.682808i | \(-0.239242\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1204.29 | 1.83861 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1111.12i | 1.68608i | 0.537854 | + | 0.843038i | \(0.319235\pi\) | ||||
−0.537854 | + | 0.843038i | \(0.680765\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −939.722 | −1.42167 | −0.710834 | − | 0.703360i | \(-0.751682\pi\) | ||||
−0.710834 | + | 0.703360i | \(0.751682\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 147.521i | − 0.221836i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −498.971 | −0.748082 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 272.440i | 0.406021i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 57.4396 | 0.0853485 | 0.0426743 | − | 0.999089i | \(-0.486412\pi\) | ||||
0.0426743 | + | 0.999089i | \(0.486412\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 975.447i | 1.44084i | 0.693539 | + | 0.720419i | \(0.256051\pi\) | ||||
−0.693539 | + | 0.720419i | \(0.743949\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 118.981 | 0.175229 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 933.409i | − 1.36663i | −0.730123 | − | 0.683316i | \(-0.760537\pi\) | ||||
0.730123 | − | 0.683316i | \(-0.239463\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −783.381 | −1.14362 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 744.681i | 1.08081i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 341.846 | 0.494712 | 0.247356 | − | 0.968925i | \(-0.420438\pi\) | ||||
0.247356 | + | 0.968925i | \(0.420438\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1163.66i | 1.67433i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 490.344 | 0.703506 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 796.464i | 1.13618i | 0.822965 | + | 0.568092i | \(0.192318\pi\) | ||||
−0.822965 | + | 0.568092i | \(0.807682\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 199.260 | 0.283443 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 650.694i | − 0.920359i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −84.7579 | −0.119546 | −0.0597728 | − | 0.998212i | \(-0.519038\pi\) | ||||
−0.0597728 | + | 0.998212i | \(0.519038\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 215.907i | 0.302815i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 236.253 | 0.330424 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 55.6567i | − 0.0774084i | −0.999251 | − | 0.0387042i | \(-0.987677\pi\) | ||||
0.999251 | − | 0.0387042i | \(-0.0123230\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 571.258 | 0.792313 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 240.501i | 0.331726i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1255.51 | −1.72698 | −0.863489 | − | 0.504368i | \(-0.831725\pi\) | ||||
−0.863489 | + | 0.504368i | \(0.831725\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 340.152i | − 0.465325i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −590.908 | −0.806150 | −0.403075 | − | 0.915167i | \(-0.632059\pi\) | ||||
−0.403075 | + | 0.915167i | \(0.632059\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 99.7809i | − 0.135388i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −429.402 | −0.581058 | −0.290529 | − | 0.956866i | \(-0.593831\pi\) | ||||
−0.290529 | + | 0.956866i | \(0.593831\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 212.103i | 0.285468i | 0.989761 | + | 0.142734i | \(0.0455893\pi\) | ||||
−0.989761 | + | 0.142734i | \(0.954411\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −572.210 | −0.768067 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 939.193i | 1.25393i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 828.843 | 1.10365 | 0.551826 | − | 0.833959i | \(-0.313931\pi\) | ||||
0.551826 | + | 0.833959i | \(0.313931\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 123.900i | 0.164106i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 430.874 | 0.569186 | 0.284593 | − | 0.958648i | \(-0.408142\pi\) | ||||
0.284593 | + | 0.958648i | \(0.408142\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 192.402i | − 0.252828i | −0.991978 | − | 0.126414i | \(-0.959653\pi\) | ||||
0.991978 | − | 0.126414i | \(-0.0403468\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −470.104 | −0.616125 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 1476.12i | − 1.92454i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 592.450 | 0.770416 | 0.385208 | − | 0.922830i | \(-0.374130\pi\) | ||||
0.385208 | + | 0.922830i | \(0.374130\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1372.66i | 1.77575i | 0.460081 | + | 0.887877i | \(0.347820\pi\) | ||||
−0.460081 | + | 0.887877i | \(0.652180\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 104.066 | 0.134279 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 132.416i | − 0.169982i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.8409 | 0.0420498 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 860.587i | − 1.09629i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −766.155 | −0.973514 | −0.486757 | − | 0.873537i | \(-0.661820\pi\) | ||||
−0.486757 | + | 0.873537i | \(0.661820\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 162.369i | 0.205271i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1930.62 | 2.43458 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 340.025i | 0.426631i | 0.976983 | + | 0.213315i | \(0.0684262\pi\) | ||||
−0.976983 | + | 0.213315i | \(0.931574\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 704.154 | 0.881294 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 52.5823i | − 0.0654823i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −540.823 | −0.671830 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1264.36i | 1.56287i | 0.623984 | + | 0.781437i | \(0.285513\pi\) | ||||
−0.623984 | + | 0.781437i | \(0.714487\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −906.142 | −1.11731 | −0.558657 | − | 0.829399i | \(-0.688683\pi\) | ||||
−0.558657 | + | 0.829399i | \(0.688683\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 98.5979i | 0.120979i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −91.8572 | −0.112432 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1093.41i | 1.33180i | 0.746041 | + | 0.665900i | \(0.231952\pi\) | ||||
−0.746041 | + | 0.665900i | \(0.768048\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1356.71 | 1.64849 | 0.824245 | − | 0.566233i | \(-0.191600\pi\) | ||||
0.824245 | + | 0.566233i | \(0.191600\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1606.81i | 1.94294i | 0.237166 | + | 0.971469i | \(0.423782\pi\) | ||||
−0.237166 | + | 0.971469i | \(0.576218\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1595.51 | −1.92462 | −0.962312 | − | 0.271946i | \(-0.912333\pi\) | ||||
−0.962312 | + | 0.271946i | \(0.912333\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 225.580i | − 0.270804i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 158.934 | 0.190340 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 614.374i | − 0.732270i | −0.930562 | − | 0.366135i | \(-0.880681\pi\) | ||||
0.930562 | − | 0.366135i | \(-0.119319\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −133.971 | −0.159300 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 707.744i | − 0.837567i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 681.595 | 0.804717 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 730.505i | − 0.858408i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1047.21 | −1.22768 | −0.613839 | − | 0.789431i | \(-0.710376\pi\) | ||||
−0.613839 | + | 0.789431i | \(0.710376\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 164.267i | 0.191677i | 0.995397 | + | 0.0958385i | \(0.0305532\pi\) | ||||
−0.995397 | + | 0.0958385i | \(0.969447\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −620.596 | −0.722464 | −0.361232 | − | 0.932476i | \(-0.617644\pi\) | ||||
−0.361232 | + | 0.932476i | \(0.617644\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 86.1854i | − 0.0998672i | −0.998753 | − | 0.0499336i | \(-0.984099\pi\) | ||||
0.998753 | − | 0.0499336i | \(-0.0159010\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 176.660 | 0.204231 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 172.109i | 0.198054i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −707.088 | −0.811812 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 585.415i | − 0.669046i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1408.22 | −1.60572 | −0.802860 | − | 0.596167i | \(-0.796689\pi\) | ||||
−0.802860 | + | 0.596167i | \(0.796689\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 675.980i | 0.767287i | 0.923481 | + | 0.383643i | \(0.125331\pi\) | ||||
−0.923481 | + | 0.383643i | \(0.874669\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 533.689 | 0.604404 | 0.302202 | − | 0.953244i | \(-0.402278\pi\) | ||||
0.302202 | + | 0.953244i | \(0.402278\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1403.05i | 1.58179i | 0.611954 | + | 0.790894i | \(0.290384\pi\) | ||||
−0.611954 | + | 0.790894i | \(0.709616\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1136.55 | −1.27846 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 190.155i | − 0.212939i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1145.05 | 1.27938 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 421.875i | 0.469271i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −702.505 | −0.779695 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1295.76i | 1.43178i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1071.75 | −1.18165 | −0.590823 | − | 0.806801i | \(-0.701197\pi\) | ||||
−0.590823 | + | 0.806801i | \(0.701197\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 706.802i | − 0.775853i | −0.921690 | − | 0.387926i | \(-0.873191\pi\) | ||||
0.921690 | − | 0.387926i | \(-0.126809\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −48.0849 | −0.0526670 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1246.32i | 1.35912i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1120.97 | −1.21978 | −0.609888 | − | 0.792487i | \(-0.708786\pi\) | ||||
−0.609888 | + | 0.792487i | \(0.708786\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 232.724i | − 0.252139i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −352.100 | −0.380649 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 1470.71i | − 1.58311i | −0.611099 | − | 0.791554i | \(-0.709272\pi\) | ||||
0.611099 | − | 0.791554i | \(-0.290728\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −60.9172 | −0.0654320 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 222.873i | 0.238367i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 877.866 | 0.936890 | 0.468445 | − | 0.883493i | \(-0.344814\pi\) | ||||
0.468445 | + | 0.883493i | \(0.344814\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1367.92i | 1.45369i | 0.686804 | + | 0.726843i | \(0.259013\pi\) | ||||
−0.686804 | + | 0.726843i | \(0.740987\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −485.448 | −0.514791 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 254.710i | 0.268965i | 0.990916 | + | 0.134483i | \(0.0429372\pi\) | ||||
−0.990916 | + | 0.134483i | \(0.957063\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −372.620 | −0.392645 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 1347.59i | − 1.41405i | −0.707188 | − | 0.707025i | \(-0.750037\pi\) | ||||
0.707188 | − | 0.707025i | \(-0.249963\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 55.2996 | 0.0579053 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 810.719i | − 0.845380i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −778.452 | −0.810044 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 131.395i | − 0.136161i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1086.76 | −1.12385 | −0.561924 | − | 0.827189i | \(-0.689939\pi\) | ||||
−0.561924 | + | 0.827189i | \(0.689939\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1004.02i | − 1.03401i | −0.855983 | − | 0.517005i | \(-0.827047\pi\) | ||||
0.855983 | − | 0.517005i | \(-0.172953\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1204.27 | −1.23769 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 765.973i | 0.784005i | 0.919964 | + | 0.392002i | \(0.128218\pi\) | ||||
−0.919964 | + | 0.392002i | \(0.871782\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 49.0220 | 0.0500736 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1779.64i | − 1.81042i | −0.424965 | − | 0.905210i | \(-0.639714\pi\) | ||||
0.424965 | − | 0.905210i | \(-0.360286\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1926.93 | 1.95627 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 336.756i | 0.340502i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 126.056 | 0.127201 | 0.0636004 | − | 0.997975i | \(-0.479742\pi\) | ||||
0.0636004 | + | 0.997975i | \(0.479742\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 577.626i | − 0.580529i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 587.955 | 0.589724 | 0.294862 | − | 0.955540i | \(-0.404726\pi\) | ||||
0.294862 | + | 0.955540i | \(0.404726\pi\) | |||||||
\(998\) | 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 | 684.3.e.a.305.3 | ✓ | 12 | |
3.2 | odd | 2 | inner | 684.3.e.a.305.10 | yes | 12 | |
4.3 | odd | 2 | 2736.3.h.c.305.3 | 12 | |||
12.11 | even | 2 | 2736.3.h.c.305.10 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.e.a.305.3 | ✓ | 12 | 1.1 | even | 1 | trivial | |
684.3.e.a.305.10 | yes | 12 | 3.2 | odd | 2 | inner | |
2736.3.h.c.305.3 | 12 | 4.3 | odd | 2 | |||
2736.3.h.c.305.10 | 12 | 12.11 | even | 2 |