Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(1469,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.1469");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.d (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: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1469.1 | ||
Character | \(\chi\) | \(=\) | 1470.1469 |
Dual form | 1470.2.d.h.1469.2 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.71521 | − | 0.240923i | −0.990279 | − | 0.139097i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.263182 | + | 2.22053i | −0.117699 | + | 0.993049i | ||||
\(6\) | −1.71521 | − | 0.240923i | −0.700233 | − | 0.0983566i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.88391 | + | 0.826470i | 0.961304 | + | 0.275490i | ||||
\(10\) | −0.263182 | + | 2.22053i | −0.0832255 | + | 0.702192i | ||||
\(11\) | 4.81031i | 1.45036i | 0.688557 | + | 0.725182i | \(0.258244\pi\) | ||||
−0.688557 | + | 0.725182i | \(0.741756\pi\) | |||||||
\(12\) | −1.71521 | − | 0.240923i | −0.495139 | − | 0.0695486i | ||||
\(13\) | −4.56331 | −1.26563 | −0.632817 | − | 0.774302i | \(-0.718101\pi\) | ||||
−0.632817 | + | 0.774302i | \(0.718101\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.986390 | − | 3.74527i | 0.254685 | − | 0.967024i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.16632i | 0.282875i | 0.989947 | + | 0.141438i | \(0.0451725\pi\) | ||||
−0.989947 | + | 0.141438i | \(0.954828\pi\) | |||||||
\(18\) | 2.88391 | + | 0.826470i | 0.679745 | + | 0.194801i | ||||
\(19\) | − | 4.61409i | − | 1.05854i | −0.848452 | − | 0.529272i | \(-0.822465\pi\) | ||
0.848452 | − | 0.529272i | \(-0.177535\pi\) | |||||||
\(20\) | −0.263182 | + | 2.22053i | −0.0588493 | + | 0.496525i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.81031i | 1.02556i | ||||||||
\(23\) | −3.85238 | −0.803278 | −0.401639 | − | 0.915798i | \(-0.631559\pi\) | ||||
−0.401639 | + | 0.915798i | \(0.631559\pi\) | |||||||
\(24\) | −1.71521 | − | 0.240923i | −0.350116 | − | 0.0491783i | ||||
\(25\) | −4.86147 | − | 1.16881i | −0.972294 | − | 0.233761i | ||||
\(26\) | −4.56331 | −0.894938 | ||||||||
\(27\) | −4.74741 | − | 2.11237i | −0.913639 | − | 0.406527i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1.96431i | − | 0.364764i | −0.983228 | − | 0.182382i | \(-0.941619\pi\) | ||
0.983228 | − | 0.182382i | \(-0.0583808\pi\) | |||||||
\(30\) | 0.986390 | − | 3.74527i | 0.180089 | − | 0.683789i | ||||
\(31\) | 5.57387i | 1.00110i | 0.865709 | + | 0.500548i | \(0.166868\pi\) | ||||
−0.865709 | + | 0.500548i | \(0.833132\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.15892 | − | 8.25071i | 0.201742 | − | 1.43626i | ||||
\(34\) | 1.16632i | 0.200023i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.88391 | + | 0.826470i | 0.480652 | + | 0.137745i | ||||
\(37\) | − | 8.98759i | − | 1.47755i | −0.673952 | − | 0.738775i | \(-0.735405\pi\) | ||
0.673952 | − | 0.738775i | \(-0.264595\pi\) | |||||||
\(38\) | − | 4.61409i | − | 0.748504i | ||||||
\(39\) | 7.82704 | + | 1.09941i | 1.25333 | + | 0.176046i | ||||
\(40\) | −0.263182 | + | 2.22053i | −0.0416127 | + | 0.351096i | ||||
\(41\) | 3.76181 | 0.587495 | 0.293748 | − | 0.955883i | \(-0.405097\pi\) | ||||
0.293748 | + | 0.955883i | \(0.405097\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.02444i | 0.613722i | 0.951754 | + | 0.306861i | \(0.0992786\pi\) | ||||
−0.951754 | + | 0.306861i | \(0.900721\pi\) | |||||||
\(44\) | 4.81031i | 0.725182i | ||||||||
\(45\) | −2.59419 | + | 6.18629i | −0.386719 | + | 0.922197i | ||||
\(46\) | −3.85238 | −0.568003 | ||||||||
\(47\) | 6.36970i | 0.929116i | 0.885543 | + | 0.464558i | \(0.153787\pi\) | ||||
−0.885543 | + | 0.464558i | \(0.846213\pi\) | |||||||
\(48\) | −1.71521 | − | 0.240923i | −0.247570 | − | 0.0347743i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.86147 | − | 1.16881i | −0.687516 | − | 0.165294i | ||||
\(51\) | 0.280995 | − | 2.00050i | 0.0393472 | − | 0.280125i | ||||
\(52\) | −4.56331 | −0.632817 | ||||||||
\(53\) | −10.0081 | −1.37472 | −0.687362 | − | 0.726315i | \(-0.741231\pi\) | ||||
−0.687362 | + | 0.726315i | \(0.741231\pi\) | |||||||
\(54\) | −4.74741 | − | 2.11237i | −0.646040 | − | 0.287458i | ||||
\(55\) | −10.6814 | − | 1.26599i | −1.44028 | − | 0.170706i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.11164 | + | 7.91414i | −0.147241 | + | 1.04825i | ||||
\(58\) | − | 1.96431i | − | 0.257927i | ||||||
\(59\) | −12.7078 | −1.65442 | −0.827209 | − | 0.561894i | \(-0.810073\pi\) | ||||
−0.827209 | + | 0.561894i | \(0.810073\pi\) | |||||||
\(60\) | 0.986390 | − | 3.74527i | 0.127342 | − | 0.483512i | ||||
\(61\) | 4.96802i | 0.636090i | 0.948076 | + | 0.318045i | \(0.103026\pi\) | ||||
−0.948076 | + | 0.318045i | \(0.896974\pi\) | |||||||
\(62\) | 5.57387i | 0.707882i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.20098 | − | 10.1329i | 0.148963 | − | 1.25684i | ||||
\(66\) | 1.15892 | − | 8.25071i | 0.142653 | − | 1.01559i | ||||
\(67\) | 12.5244i | 1.53010i | 0.643974 | + | 0.765048i | \(0.277285\pi\) | ||||
−0.643974 | + | 0.765048i | \(0.722715\pi\) | |||||||
\(68\) | 1.16632i | 0.141438i | ||||||||
\(69\) | 6.60766 | + | 0.928130i | 0.795469 | + | 0.111734i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.74047i | − | 0.325234i | −0.986689 | − | 0.162617i | \(-0.948006\pi\) | ||
0.986689 | − | 0.162617i | \(-0.0519935\pi\) | |||||||
\(72\) | 2.88391 | + | 0.826470i | 0.339872 | + | 0.0974004i | ||||
\(73\) | −13.9852 | −1.63685 | −0.818424 | − | 0.574615i | \(-0.805152\pi\) | ||||
−0.818424 | + | 0.574615i | \(0.805152\pi\) | |||||||
\(74\) | − | 8.98759i | − | 1.04479i | ||||||
\(75\) | 8.05686 | + | 3.17599i | 0.930327 | + | 0.366732i | ||||
\(76\) | − | 4.61409i | − | 0.529272i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 7.82704 | + | 1.09941i | 0.886238 | + | 0.124483i | ||||
\(79\) | −10.5162 | −1.18316 | −0.591581 | − | 0.806246i | \(-0.701496\pi\) | ||||
−0.591581 | + | 0.806246i | \(0.701496\pi\) | |||||||
\(80\) | −0.263182 | + | 2.22053i | −0.0294247 | + | 0.248262i | ||||
\(81\) | 7.63389 | + | 4.76693i | 0.848210 | + | 0.529659i | ||||
\(82\) | 3.76181 | 0.415422 | ||||||||
\(83\) | 3.54903i | 0.389557i | 0.980847 | + | 0.194778i | \(0.0623988\pi\) | ||||
−0.980847 | + | 0.194778i | \(0.937601\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.58985 | − | 0.306956i | −0.280909 | − | 0.0332940i | ||||
\(86\) | 4.02444i | 0.433967i | ||||||||
\(87\) | −0.473250 | + | 3.36922i | −0.0507377 | + | 0.361218i | ||||
\(88\) | 4.81031i | 0.512781i | ||||||||
\(89\) | 16.0060 | 1.69664 | 0.848318 | − | 0.529487i | \(-0.177616\pi\) | ||||
0.848318 | + | 0.529487i | \(0.177616\pi\) | |||||||
\(90\) | −2.59419 | + | 6.18629i | −0.273452 | + | 0.652092i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.85238 | −0.401639 | ||||||||
\(93\) | 1.34288 | − | 9.56038i | 0.139250 | − | 0.991365i | ||||
\(94\) | 6.36970i | 0.656984i | ||||||||
\(95\) | 10.2457 | + | 1.21435i | 1.05119 | + | 0.124589i | ||||
\(96\) | −1.71521 | − | 0.240923i | −0.175058 | − | 0.0245891i | ||||
\(97\) | 1.30193 | 0.132191 | 0.0660953 | − | 0.997813i | \(-0.478946\pi\) | ||||
0.0660953 | + | 0.997813i | \(0.478946\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.97558 | + | 13.8725i | −0.399561 | + | 1.39424i | ||||
\(100\) | −4.86147 | − | 1.16881i | −0.486147 | − | 0.116881i | ||||
\(101\) | 12.4689 | 1.24070 | 0.620351 | − | 0.784324i | \(-0.286990\pi\) | ||||
0.620351 | + | 0.784324i | \(0.286990\pi\) | |||||||
\(102\) | 0.280995 | − | 2.00050i | 0.0278226 | − | 0.198079i | ||||
\(103\) | −0.300347 | −0.0295941 | −0.0147970 | − | 0.999891i | \(-0.504710\pi\) | ||||
−0.0147970 | + | 0.999891i | \(0.504710\pi\) | |||||||
\(104\) | −4.56331 | −0.447469 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.0081 | −0.972076 | ||||||||
\(107\) | −13.5389 | −1.30886 | −0.654429 | − | 0.756123i | \(-0.727091\pi\) | ||||
−0.654429 | + | 0.756123i | \(0.727091\pi\) | |||||||
\(108\) | −4.74741 | − | 2.11237i | −0.456819 | − | 0.203263i | ||||
\(109\) | −14.8845 | −1.42567 | −0.712837 | − | 0.701330i | \(-0.752590\pi\) | ||||
−0.712837 | + | 0.701330i | \(0.752590\pi\) | |||||||
\(110\) | −10.6814 | − | 1.26599i | −1.01843 | − | 0.120707i | ||||
\(111\) | −2.16532 | + | 15.4156i | −0.205523 | + | 1.46319i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.49406 | 0.893126 | 0.446563 | − | 0.894752i | \(-0.352648\pi\) | ||||
0.446563 | + | 0.894752i | \(0.352648\pi\) | |||||||
\(114\) | −1.11164 | + | 7.91414i | −0.104115 | + | 0.741228i | ||||
\(115\) | 1.01388 | − | 8.55432i | 0.0945446 | − | 0.797694i | ||||
\(116\) | − | 1.96431i | − | 0.182382i | ||||||
\(117\) | −13.1602 | − | 3.77144i | −1.21666 | − | 0.348669i | ||||
\(118\) | −12.7078 | −1.16985 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.986390 | − | 3.74527i | 0.0900447 | − | 0.341895i | ||||
\(121\) | −12.1391 | −1.10355 | ||||||||
\(122\) | 4.96802i | 0.449784i | ||||||||
\(123\) | −6.45230 | − | 0.906307i | −0.581784 | − | 0.0817190i | ||||
\(124\) | 5.57387i | 0.500548i | ||||||||
\(125\) | 3.87481 | − | 10.4874i | 0.346574 | − | 0.938023i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.0483i | 1.24659i | 0.781988 | + | 0.623294i | \(0.214206\pi\) | ||||
−0.781988 | + | 0.623294i | \(0.785794\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0.969582 | − | 6.90277i | 0.0853670 | − | 0.607755i | ||||
\(130\) | 1.20098 | − | 10.1329i | 0.105333 | − | 0.888718i | ||||
\(131\) | 10.1222 | 0.884384 | 0.442192 | − | 0.896921i | \(-0.354201\pi\) | ||||
0.442192 | + | 0.896921i | \(0.354201\pi\) | |||||||
\(132\) | 1.15892 | − | 8.25071i | 0.100871 | − | 0.718132i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 12.5244i | 1.08194i | ||||||||
\(135\) | 5.94001 | − | 9.98580i | 0.511235 | − | 0.859441i | ||||
\(136\) | 1.16632i | 0.100012i | ||||||||
\(137\) | 17.8156 | 1.52209 | 0.761046 | − | 0.648698i | \(-0.224686\pi\) | ||||
0.761046 | + | 0.648698i | \(0.224686\pi\) | |||||||
\(138\) | 6.60766 | + | 0.928130i | 0.562481 | + | 0.0790076i | ||||
\(139\) | − | 16.7252i | − | 1.41861i | −0.704902 | − | 0.709305i | \(-0.749009\pi\) | ||
0.704902 | − | 0.709305i | \(-0.250991\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.53461 | − | 10.9254i | 0.129237 | − | 0.920084i | ||||
\(142\) | − | 2.74047i | − | 0.229975i | ||||||
\(143\) | − | 21.9509i | − | 1.83563i | ||||||
\(144\) | 2.88391 | + | 0.826470i | 0.240326 | + | 0.0688725i | ||||
\(145\) | 4.36181 | + | 0.516973i | 0.362229 | + | 0.0429322i | ||||
\(146\) | −13.9852 | −1.15743 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 8.98759i | − | 0.738775i | ||||||
\(149\) | 20.0263i | 1.64062i | 0.571921 | + | 0.820309i | \(0.306198\pi\) | ||||
−0.571921 | + | 0.820309i | \(0.693802\pi\) | |||||||
\(150\) | 8.05686 | + | 3.17599i | 0.657840 | + | 0.259319i | ||||
\(151\) | −3.80170 | −0.309378 | −0.154689 | − | 0.987963i | \(-0.549438\pi\) | ||||
−0.154689 | + | 0.987963i | \(0.549438\pi\) | |||||||
\(152\) | − | 4.61409i | − | 0.374252i | ||||||
\(153\) | −0.963932 | + | 3.36358i | −0.0779293 | + | 0.271929i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.3769 | − | 1.46694i | −0.994139 | − | 0.117828i | ||||
\(156\) | 7.82704 | + | 1.09941i | 0.626665 | + | 0.0880231i | ||||
\(157\) | 10.2291 | 0.816369 | 0.408185 | − | 0.912899i | \(-0.366162\pi\) | ||||
0.408185 | + | 0.912899i | \(0.366162\pi\) | |||||||
\(158\) | −10.5162 | −0.836621 | ||||||||
\(159\) | 17.1661 | + | 2.41119i | 1.36136 | + | 0.191220i | ||||
\(160\) | −0.263182 | + | 2.22053i | −0.0208064 | + | 0.175548i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 7.63389 | + | 4.76693i | 0.599775 | + | 0.374526i | ||||
\(163\) | 1.05739i | 0.0828212i | 0.999142 | + | 0.0414106i | \(0.0131852\pi\) | ||||
−0.999142 | + | 0.0414106i | \(0.986815\pi\) | |||||||
\(164\) | 3.76181 | 0.293748 | ||||||||
\(165\) | 18.0159 | + | 4.74484i | 1.40254 | + | 0.369386i | ||||
\(166\) | 3.54903i | 0.275458i | ||||||||
\(167\) | 1.75194i | 0.135569i | 0.997700 | + | 0.0677845i | \(0.0215930\pi\) | ||||
−0.997700 | + | 0.0677845i | \(0.978407\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.82377 | 0.601828 | ||||||||
\(170\) | −2.58985 | − | 0.306956i | −0.198633 | − | 0.0235424i | ||||
\(171\) | 3.81341 | − | 13.3066i | 0.291618 | − | 1.01758i | ||||
\(172\) | 4.02444i | 0.306861i | ||||||||
\(173\) | 0.127913i | 0.00972507i | 0.999988 | + | 0.00486254i | \(0.00154780\pi\) | ||||
−0.999988 | + | 0.00486254i | \(0.998452\pi\) | |||||||
\(174\) | −0.473250 | + | 3.36922i | −0.0358770 | + | 0.255420i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.81031i | 0.362591i | ||||||||
\(177\) | 21.7966 | + | 3.06161i | 1.63834 | + | 0.230125i | ||||
\(178\) | 16.0060 | 1.19970 | ||||||||
\(179\) | 6.24279i | 0.466608i | 0.972404 | + | 0.233304i | \(0.0749537\pi\) | ||||
−0.972404 | + | 0.233304i | \(0.925046\pi\) | |||||||
\(180\) | −2.59419 | + | 6.18629i | −0.193360 | + | 0.461099i | ||||
\(181\) | − | 1.20138i | − | 0.0892975i | −0.999003 | − | 0.0446488i | \(-0.985783\pi\) | ||
0.999003 | − | 0.0446488i | \(-0.0142169\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.19691 | − | 8.52122i | 0.0884784 | − | 0.629906i | ||||
\(184\) | −3.85238 | −0.284001 | ||||||||
\(185\) | 19.9572 | + | 2.36537i | 1.46728 | + | 0.173906i | ||||
\(186\) | 1.34288 | − | 9.56038i | 0.0984645 | − | 0.701001i | ||||
\(187\) | −5.61039 | −0.410272 | ||||||||
\(188\) | 6.36970i | 0.464558i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10.2457 | + | 1.21435i | 0.743301 | + | 0.0880979i | ||||
\(191\) | − | 21.8612i | − | 1.58182i | −0.611931 | − | 0.790911i | \(-0.709607\pi\) | ||
0.611931 | − | 0.790911i | \(-0.290393\pi\) | |||||||
\(192\) | −1.71521 | − | 0.240923i | −0.123785 | − | 0.0173872i | ||||
\(193\) | − | 16.1261i | − | 1.16078i | −0.814338 | − | 0.580391i | \(-0.802900\pi\) | ||
0.814338 | − | 0.580391i | \(-0.197100\pi\) | |||||||
\(194\) | 1.30193 | 0.0934729 | ||||||||
\(195\) | −4.50120 | + | 17.0908i | −0.322338 | + | 1.22390i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.4115 | 0.741786 | 0.370893 | − | 0.928676i | \(-0.379052\pi\) | ||||
0.370893 | + | 0.928676i | \(0.379052\pi\) | |||||||
\(198\) | −3.97558 | + | 13.8725i | −0.282532 | + | 0.985877i | ||||
\(199\) | 17.7968i | 1.26158i | 0.775953 | + | 0.630791i | \(0.217270\pi\) | ||||
−0.775953 | + | 0.630791i | \(0.782730\pi\) | |||||||
\(200\) | −4.86147 | − | 1.16881i | −0.343758 | − | 0.0826470i | ||||
\(201\) | 3.01741 | − | 21.4820i | 0.212832 | − | 1.51522i | ||||
\(202\) | 12.4689 | 0.877309 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.280995 | − | 2.00050i | 0.0196736 | − | 0.140063i | ||||
\(205\) | −0.990040 | + | 8.35319i | −0.0691474 | + | 0.583412i | ||||
\(206\) | −0.300347 | −0.0209262 | ||||||||
\(207\) | −11.1099 | − | 3.18388i | −0.772194 | − | 0.221295i | ||||
\(208\) | −4.56331 | −0.316408 | ||||||||
\(209\) | 22.1952 | 1.53527 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.89044 | 0.543200 | 0.271600 | − | 0.962410i | \(-0.412447\pi\) | ||||
0.271600 | + | 0.962410i | \(0.412447\pi\) | |||||||
\(212\) | −10.0081 | −0.687362 | ||||||||
\(213\) | −0.660244 | + | 4.70049i | −0.0452392 | + | 0.322073i | ||||
\(214\) | −13.5389 | −0.925503 | ||||||||
\(215\) | −8.93638 | − | 1.05916i | −0.609456 | − | 0.0722342i | ||||
\(216\) | −4.74741 | − | 2.11237i | −0.323020 | − | 0.143729i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −14.8845 | −1.00810 | ||||||||
\(219\) | 23.9877 | + | 3.36937i | 1.62094 | + | 0.227681i | ||||
\(220\) | −10.6814 | − | 1.26599i | −0.720141 | − | 0.0853529i | ||||
\(221\) | − | 5.32230i | − | 0.358016i | ||||||
\(222\) | −2.16532 | + | 15.4156i | −0.145327 | + | 1.03463i | ||||
\(223\) | 17.9707 | 1.20341 | 0.601704 | − | 0.798719i | \(-0.294489\pi\) | ||||
0.601704 | + | 0.798719i | \(0.294489\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.0541 | − | 7.38859i | −0.870271 | − | 0.492573i | ||||
\(226\) | 9.49406 | 0.631535 | ||||||||
\(227\) | 5.34178i | 0.354547i | 0.984162 | + | 0.177273i | \(0.0567277\pi\) | ||||
−0.984162 | + | 0.177273i | \(0.943272\pi\) | |||||||
\(228\) | −1.11164 | + | 7.91414i | −0.0736203 | + | 0.524127i | ||||
\(229\) | 3.53602i | 0.233667i | 0.993152 | + | 0.116834i | \(0.0372744\pi\) | ||||
−0.993152 | + | 0.116834i | \(0.962726\pi\) | |||||||
\(230\) | 1.01388 | − | 8.55432i | 0.0668532 | − | 0.564055i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 1.96431i | − | 0.128964i | ||||||
\(233\) | 5.24366 | 0.343524 | 0.171762 | − | 0.985138i | \(-0.445054\pi\) | ||||
0.171762 | + | 0.985138i | \(0.445054\pi\) | |||||||
\(234\) | −13.1602 | − | 3.77144i | −0.860307 | − | 0.246547i | ||||
\(235\) | −14.1441 | − | 1.67639i | −0.922658 | − | 0.109356i | ||||
\(236\) | −12.7078 | −0.827209 | ||||||||
\(237\) | 18.0375 | + | 2.53359i | 1.17166 | + | 0.164574i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.3376i | 1.57427i | 0.616780 | + | 0.787135i | \(0.288437\pi\) | ||||
−0.616780 | + | 0.787135i | \(0.711563\pi\) | |||||||
\(240\) | 0.986390 | − | 3.74527i | 0.0636712 | − | 0.241756i | ||||
\(241\) | 24.9383i | 1.60642i | 0.595698 | + | 0.803209i | \(0.296876\pi\) | ||||
−0.595698 | + | 0.803209i | \(0.703124\pi\) | |||||||
\(242\) | −12.1391 | −0.780331 | ||||||||
\(243\) | −11.9453 | − | 10.0155i | −0.766291 | − | 0.642494i | ||||
\(244\) | 4.96802i | 0.318045i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.45230 | − | 0.906307i | −0.411384 | − | 0.0577840i | ||||
\(247\) | 21.0555i | 1.33973i | ||||||||
\(248\) | 5.57387i | 0.353941i | ||||||||
\(249\) | 0.855045 | − | 6.08735i | 0.0541863 | − | 0.385770i | ||||
\(250\) | 3.87481 | − | 10.4874i | 0.245065 | − | 0.663282i | ||||
\(251\) | −8.21145 | −0.518302 | −0.259151 | − | 0.965837i | \(-0.583443\pi\) | ||||
−0.259151 | + | 0.965837i | \(0.583443\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 18.5312i | − | 1.16504i | ||||||
\(254\) | 14.0483i | 0.881471i | ||||||||
\(255\) | 4.36820 | + | 1.15045i | 0.273547 | + | 0.0720440i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 2.18021i | − | 0.135998i | −0.997685 | − | 0.0679990i | \(-0.978339\pi\) | ||
0.997685 | − | 0.0679990i | \(-0.0216615\pi\) | |||||||
\(258\) | 0.969582 | − | 6.90277i | 0.0603636 | − | 0.429748i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.20098 | − | 10.1329i | 0.0744817 | − | 0.628418i | ||||
\(261\) | 1.62345 | − | 5.66491i | 0.100489 | − | 0.350649i | ||||
\(262\) | 10.1222 | 0.625354 | ||||||||
\(263\) | 21.9316 | 1.35236 | 0.676179 | − | 0.736737i | \(-0.263634\pi\) | ||||
0.676179 | + | 0.736737i | \(0.263634\pi\) | |||||||
\(264\) | 1.15892 | − | 8.25071i | 0.0713264 | − | 0.507796i | ||||
\(265\) | 2.63396 | − | 22.2233i | 0.161803 | − | 1.36517i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −27.4537 | − | 3.85623i | −1.68014 | − | 0.235997i | ||||
\(268\) | 12.5244i | 0.765048i | ||||||||
\(269\) | −25.5632 | −1.55861 | −0.779307 | − | 0.626642i | \(-0.784429\pi\) | ||||
−0.779307 | + | 0.626642i | \(0.784429\pi\) | |||||||
\(270\) | 5.94001 | − | 9.98580i | 0.361498 | − | 0.607717i | ||||
\(271\) | 5.09869i | 0.309724i | 0.987936 | + | 0.154862i | \(0.0494932\pi\) | ||||
−0.987936 | + | 0.154862i | \(0.950507\pi\) | |||||||
\(272\) | 1.16632i | 0.0707188i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.8156 | 1.07628 | ||||||||
\(275\) | 5.62232 | − | 23.3852i | 0.339039 | − | 1.41018i | ||||
\(276\) | 6.60766 | + | 0.928130i | 0.397734 | + | 0.0558668i | ||||
\(277\) | 4.98773i | 0.299684i | 0.988710 | + | 0.149842i | \(0.0478764\pi\) | ||||
−0.988710 | + | 0.149842i | \(0.952124\pi\) | |||||||
\(278\) | − | 16.7252i | − | 1.00311i | ||||||
\(279\) | −4.60664 | + | 16.0746i | −0.275792 | + | 0.962358i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 18.3073i | − | 1.09212i | −0.837746 | − | 0.546060i | \(-0.816127\pi\) | ||
0.837746 | − | 0.546060i | \(-0.183873\pi\) | |||||||
\(282\) | 1.53461 | − | 10.9254i | 0.0913847 | − | 0.650598i | ||||
\(283\) | 5.04720 | 0.300025 | 0.150012 | − | 0.988684i | \(-0.452069\pi\) | ||||
0.150012 | + | 0.988684i | \(0.452069\pi\) | |||||||
\(284\) | − | 2.74047i | − | 0.162617i | ||||||
\(285\) | −17.2810 | − | 4.55129i | −1.02364 | − | 0.269595i | ||||
\(286\) | − | 21.9509i | − | 1.29799i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.88391 | + | 0.826470i | 0.169936 | + | 0.0487002i | ||||
\(289\) | 15.6397 | 0.919982 | ||||||||
\(290\) | 4.36181 | + | 0.516973i | 0.256134 | + | 0.0303577i | ||||
\(291\) | −2.23308 | − | 0.313665i | −0.130906 | − | 0.0183874i | ||||
\(292\) | −13.9852 | −0.818424 | ||||||||
\(293\) | − | 24.4169i | − | 1.42645i | −0.700934 | − | 0.713226i | \(-0.747233\pi\) | ||
0.700934 | − | 0.713226i | \(-0.252767\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.34447 | − | 28.2181i | 0.194723 | − | 1.64292i | ||||
\(296\) | − | 8.98759i | − | 0.522393i | ||||||
\(297\) | 10.1612 | − | 22.8365i | 0.589611 | − | 1.32511i | ||||
\(298\) | 20.0263i | 1.16009i | ||||||||
\(299\) | 17.5796 | 1.01666 | ||||||||
\(300\) | 8.05686 | + | 3.17599i | 0.465163 | + | 0.183366i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3.80170 | −0.218763 | ||||||||
\(303\) | −21.3868 | − | 3.00405i | −1.22864 | − | 0.172578i | ||||
\(304\) | − | 4.61409i | − | 0.264636i | ||||||
\(305\) | −11.0316 | − | 1.30749i | −0.631669 | − | 0.0748669i | ||||
\(306\) | −0.963932 | + | 3.36358i | −0.0551044 | + | 0.192283i | ||||
\(307\) | 15.1857 | 0.866691 | 0.433346 | − | 0.901228i | \(-0.357333\pi\) | ||||
0.433346 | + | 0.901228i | \(0.357333\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.515159 | + | 0.0723606i | 0.0293064 | + | 0.00411645i | ||||
\(310\) | −12.3769 | − | 1.46694i | −0.702962 | − | 0.0833168i | ||||
\(311\) | −11.0840 | −0.628518 | −0.314259 | − | 0.949337i | \(-0.601756\pi\) | ||||
−0.314259 | + | 0.949337i | \(0.601756\pi\) | |||||||
\(312\) | 7.82704 | + | 1.09941i | 0.443119 | + | 0.0622417i | ||||
\(313\) | 7.05798 | 0.398940 | 0.199470 | − | 0.979904i | \(-0.436078\pi\) | ||||
0.199470 | + | 0.979904i | \(0.436078\pi\) | |||||||
\(314\) | 10.2291 | 0.577260 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.5162 | −0.591581 | ||||||||
\(317\) | 1.09383 | 0.0614354 | 0.0307177 | − | 0.999528i | \(-0.490221\pi\) | ||||
0.0307177 | + | 0.999528i | \(0.490221\pi\) | |||||||
\(318\) | 17.1661 | + | 2.41119i | 0.962626 | + | 0.135213i | ||||
\(319\) | 9.44897 | 0.529041 | ||||||||
\(320\) | −0.263182 | + | 2.22053i | −0.0147123 | + | 0.124131i | ||||
\(321\) | 23.2222 | + | 3.26185i | 1.29614 | + | 0.182059i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.38152 | 0.299436 | ||||||||
\(324\) | 7.63389 | + | 4.76693i | 0.424105 | + | 0.264830i | ||||
\(325\) | 22.1844 | + | 5.33362i | 1.23057 | + | 0.295856i | ||||
\(326\) | 1.05739i | 0.0585635i | ||||||||
\(327\) | 25.5300 | + | 3.58602i | 1.41181 | + | 0.198307i | ||||
\(328\) | 3.76181 | 0.207711 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 18.0159 | + | 4.74484i | 0.991743 | + | 0.261195i | ||||
\(331\) | −13.3568 | −0.734154 | −0.367077 | − | 0.930191i | \(-0.619641\pi\) | ||||
−0.367077 | + | 0.930191i | \(0.619641\pi\) | |||||||
\(332\) | 3.54903i | 0.194778i | ||||||||
\(333\) | 7.42797 | − | 25.9194i | 0.407050 | − | 1.42037i | ||||
\(334\) | 1.75194i | 0.0958617i | ||||||||
\(335\) | −27.8107 | − | 3.29619i | −1.51946 | − | 0.180090i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 12.3715i | − | 0.673921i | −0.941519 | − | 0.336960i | \(-0.890601\pi\) | ||
0.941519 | − | 0.336960i | \(-0.109399\pi\) | |||||||
\(338\) | 7.82377 | 0.425557 | ||||||||
\(339\) | −16.2843 | − | 2.28734i | −0.884444 | − | 0.124231i | ||||
\(340\) | −2.58985 | − | 0.306956i | −0.140455 | − | 0.0166470i | ||||
\(341\) | −26.8121 | −1.45195 | ||||||||
\(342\) | 3.81341 | − | 13.3066i | 0.206205 | − | 0.719540i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.02444i | 0.216983i | ||||||||
\(345\) | −3.79995 | + | 14.4282i | −0.204583 | + | 0.776789i | ||||
\(346\) | 0.127913i | 0.00687666i | ||||||||
\(347\) | −2.96861 | −0.159363 | −0.0796817 | − | 0.996820i | \(-0.525390\pi\) | ||||
−0.0796817 | + | 0.996820i | \(0.525390\pi\) | |||||||
\(348\) | −0.473250 | + | 3.36922i | −0.0253688 | + | 0.180609i | ||||
\(349\) | 1.03511i | 0.0554080i | 0.999616 | + | 0.0277040i | \(0.00881959\pi\) | ||||
−0.999616 | + | 0.0277040i | \(0.991180\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 21.6639 | + | 9.63941i | 1.15633 | + | 0.514514i | ||||
\(352\) | 4.81031i | 0.256390i | ||||||||
\(353\) | 13.4155i | 0.714037i | 0.934097 | + | 0.357018i | \(0.116207\pi\) | ||||
−0.934097 | + | 0.357018i | \(0.883793\pi\) | |||||||
\(354\) | 21.7966 | + | 3.06161i | 1.15848 | + | 0.162723i | ||||
\(355\) | 6.08529 | + | 0.721243i | 0.322974 | + | 0.0382796i | ||||
\(356\) | 16.0060 | 0.848318 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.24279i | 0.329942i | ||||||||
\(359\) | 24.8666i | 1.31241i | 0.754584 | + | 0.656204i | \(0.227839\pi\) | ||||
−0.754584 | + | 0.656204i | \(0.772161\pi\) | |||||||
\(360\) | −2.59419 | + | 6.18629i | −0.136726 | + | 0.326046i | ||||
\(361\) | −2.28981 | −0.120516 | ||||||||
\(362\) | − | 1.20138i | − | 0.0631429i | ||||||
\(363\) | 20.8211 | + | 2.92459i | 1.09283 | + | 0.153501i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.68066 | − | 31.0546i | 0.192655 | − | 1.62547i | ||||
\(366\) | 1.19691 | − | 8.52122i | 0.0625637 | − | 0.445411i | ||||
\(367\) | 5.54367 | 0.289377 | 0.144689 | − | 0.989477i | \(-0.453782\pi\) | ||||
0.144689 | + | 0.989477i | \(0.453782\pi\) | |||||||
\(368\) | −3.85238 | −0.200819 | ||||||||
\(369\) | 10.8487 | + | 3.10902i | 0.564762 | + | 0.161849i | ||||
\(370\) | 19.9572 | + | 2.36537i | 1.03752 | + | 0.122970i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.34288 | − | 9.56038i | 0.0696249 | − | 0.495682i | ||||
\(373\) | − | 3.87531i | − | 0.200656i | −0.994954 | − | 0.100328i | \(-0.968011\pi\) | ||
0.994954 | − | 0.100328i | \(-0.0319892\pi\) | |||||||
\(374\) | −5.61039 | −0.290106 | ||||||||
\(375\) | −9.17280 | + | 17.0546i | −0.473681 | + | 0.880696i | ||||
\(376\) | 6.36970i | 0.328492i | ||||||||
\(377\) | 8.96377i | 0.461658i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.5126 | −0.848195 | −0.424098 | − | 0.905616i | \(-0.639409\pi\) | ||||
−0.424098 | + | 0.905616i | \(0.639409\pi\) | |||||||
\(380\) | 10.2457 | + | 1.21435i | 0.525593 | + | 0.0622946i | ||||
\(381\) | 3.38457 | − | 24.0959i | 0.173397 | − | 1.23447i | ||||
\(382\) | − | 21.8612i | − | 1.11852i | ||||||
\(383\) | 38.1711i | 1.95045i | 0.221214 | + | 0.975225i | \(0.428998\pi\) | ||||
−0.221214 | + | 0.975225i | \(0.571002\pi\) | |||||||
\(384\) | −1.71521 | − | 0.240923i | −0.0875291 | − | 0.0122946i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 16.1261i | − | 0.820797i | ||||||
\(387\) | −3.32608 | + | 11.6061i | −0.169074 | + | 0.589973i | ||||
\(388\) | 1.30193 | 0.0660953 | ||||||||
\(389\) | 10.2990i | 0.522181i | 0.965314 | + | 0.261090i | \(0.0840820\pi\) | ||||
−0.965314 | + | 0.261090i | \(0.915918\pi\) | |||||||
\(390\) | −4.50120 | + | 17.0908i | −0.227927 | + | 0.865427i | ||||
\(391\) | − | 4.49313i | − | 0.227227i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −17.3618 | − | 2.43868i | −0.875786 | − | 0.123015i | ||||
\(394\) | 10.4115 | 0.524522 | ||||||||
\(395\) | 2.76767 | − | 23.3514i | 0.139256 | − | 1.17494i | ||||
\(396\) | −3.97558 | + | 13.8725i | −0.199780 | + | 0.697120i | ||||
\(397\) | −9.95455 | −0.499605 | −0.249802 | − | 0.968297i | \(-0.580366\pi\) | ||||
−0.249802 | + | 0.968297i | \(0.580366\pi\) | |||||||
\(398\) | 17.7968i | 0.892074i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.86147 | − | 1.16881i | −0.243074 | − | 0.0584403i | ||||
\(401\) | 14.6489i | 0.731529i | 0.930707 | + | 0.365765i | \(0.119193\pi\) | ||||
−0.930707 | + | 0.365765i | \(0.880807\pi\) | |||||||
\(402\) | 3.01741 | − | 21.4820i | 0.150495 | − | 1.07142i | ||||
\(403\) | − | 25.4353i | − | 1.26702i | ||||||
\(404\) | 12.4689 | 0.620351 | ||||||||
\(405\) | −12.5942 | + | 15.6967i | −0.625811 | + | 0.779975i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 43.2331 | 2.14298 | ||||||||
\(408\) | 0.280995 | − | 2.00050i | 0.0139113 | − | 0.0990393i | ||||
\(409\) | − | 32.8807i | − | 1.62585i | −0.582371 | − | 0.812923i | \(-0.697875\pi\) | ||
0.582371 | − | 0.812923i | \(-0.302125\pi\) | |||||||
\(410\) | −0.990040 | + | 8.35319i | −0.0488946 | + | 0.412535i | ||||
\(411\) | −30.5576 | − | 4.29220i | −1.50730 | − | 0.211719i | ||||
\(412\) | −0.300347 | −0.0147970 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −11.1099 | − | 3.18388i | −0.546023 | − | 0.156479i | ||||
\(415\) | −7.88072 | − | 0.934042i | −0.386849 | − | 0.0458503i | ||||
\(416\) | −4.56331 | −0.223735 | ||||||||
\(417\) | −4.02948 | + | 28.6872i | −0.197325 | + | 1.40482i | ||||
\(418\) | 22.1952 | 1.08560 | ||||||||
\(419\) | −18.3939 | −0.898599 | −0.449299 | − | 0.893381i | \(-0.648326\pi\) | ||||
−0.449299 | + | 0.893381i | \(0.648326\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.4508 | −1.24040 | −0.620199 | − | 0.784444i | \(-0.712948\pi\) | ||||
−0.620199 | + | 0.784444i | \(0.712948\pi\) | |||||||
\(422\) | 7.89044 | 0.384101 | ||||||||
\(423\) | −5.26437 | + | 18.3697i | −0.255962 | + | 0.893163i | ||||
\(424\) | −10.0081 | −0.486038 | ||||||||
\(425\) | 1.36321 | − | 5.67005i | 0.0661252 | − | 0.275038i | ||||
\(426\) | −0.660244 | + | 4.70049i | −0.0319889 | + | 0.227740i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −13.5389 | −0.654429 | ||||||||
\(429\) | −5.28849 | + | 37.6505i | −0.255331 | + | 1.81778i | ||||
\(430\) | −8.93638 | − | 1.05916i | −0.430950 | − | 0.0510773i | ||||
\(431\) | 1.04891i | 0.0505243i | 0.999681 | + | 0.0252621i | \(0.00804204\pi\) | ||||
−0.999681 | + | 0.0252621i | \(0.991958\pi\) | |||||||
\(432\) | −4.74741 | − | 2.11237i | −0.228410 | − | 0.101632i | ||||
\(433\) | 27.5424 | 1.32360 | 0.661801 | − | 0.749679i | \(-0.269792\pi\) | ||||
0.661801 | + | 0.749679i | \(0.269792\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.35689 | − | 1.93758i | −0.352736 | − | 0.0928999i | ||||
\(436\) | −14.8845 | −0.712837 | ||||||||
\(437\) | 17.7752i | 0.850305i | ||||||||
\(438\) | 23.9877 | + | 3.36937i | 1.14617 | + | 0.160995i | ||||
\(439\) | − | 11.2089i | − | 0.534972i | −0.963562 | − | 0.267486i | \(-0.913807\pi\) | ||
0.963562 | − | 0.267486i | \(-0.0861929\pi\) | |||||||
\(440\) | −10.6814 | − | 1.26599i | −0.509217 | − | 0.0603536i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 5.32230i | − | 0.253156i | ||||||
\(443\) | 33.2580 | 1.58013 | 0.790067 | − | 0.613021i | \(-0.210046\pi\) | ||||
0.790067 | + | 0.613021i | \(0.210046\pi\) | |||||||
\(444\) | −2.16532 | + | 15.4156i | −0.102762 | + | 0.731593i | ||||
\(445\) | −4.21250 | + | 35.5418i | −0.199692 | + | 1.68484i | ||||
\(446\) | 17.9707 | 0.850938 | ||||||||
\(447\) | 4.82480 | − | 34.3494i | 0.228205 | − | 1.62467i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.45808i | 0.446354i | 0.974778 | + | 0.223177i | \(0.0716428\pi\) | ||||
−0.974778 | + | 0.223177i | \(0.928357\pi\) | |||||||
\(450\) | −13.0541 | − | 7.38859i | −0.615375 | − | 0.348302i | ||||
\(451\) | 18.0955i | 0.852082i | ||||||||
\(452\) | 9.49406 | 0.446563 | ||||||||
\(453\) | 6.52073 | + | 0.915920i | 0.306371 | + | 0.0430337i | ||||
\(454\) | 5.34178i | 0.250702i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.11164 | + | 7.91414i | −0.0520574 | + | 0.370614i | ||||
\(457\) | 14.7842i | 0.691577i | 0.938312 | + | 0.345789i | \(0.112389\pi\) | ||||
−0.938312 | + | 0.345789i | \(0.887611\pi\) | |||||||
\(458\) | 3.53602i | 0.165228i | ||||||||
\(459\) | 2.46371 | − | 5.53702i | 0.114996 | − | 0.258446i | ||||
\(460\) | 1.01388 | − | 8.55432i | 0.0472723 | − | 0.398847i | ||||
\(461\) | 14.8821 | 0.693130 | 0.346565 | − | 0.938026i | \(-0.387348\pi\) | ||||
0.346565 | + | 0.938026i | \(0.387348\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.24696i | 0.290321i | 0.989408 | + | 0.145161i | \(0.0463699\pi\) | ||||
−0.989408 | + | 0.145161i | \(0.953630\pi\) | |||||||
\(464\) | − | 1.96431i | − | 0.0911910i | ||||||
\(465\) | 20.8756 | + | 5.49801i | 0.968085 | + | 0.254964i | ||||
\(466\) | 5.24366 | 0.242908 | ||||||||
\(467\) | − | 16.4666i | − | 0.761985i | −0.924578 | − | 0.380993i | \(-0.875582\pi\) | ||
0.924578 | − | 0.380993i | \(-0.124418\pi\) | |||||||
\(468\) | −13.1602 | − | 3.77144i | −0.608329 | − | 0.174335i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −14.1441 | − | 1.67639i | −0.652418 | − | 0.0773262i | ||||
\(471\) | −17.5450 | − | 2.46442i | −0.808433 | − | 0.113555i | ||||
\(472\) | −12.7078 | −0.584925 | ||||||||
\(473\) | −19.3588 | −0.890119 | ||||||||
\(474\) | 18.0375 | + | 2.53359i | 0.828488 | + | 0.116372i | ||||
\(475\) | −5.39297 | + | 22.4313i | −0.247446 | + | 1.02922i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −28.8626 | − | 8.27142i | −1.32153 | − | 0.378723i | ||||
\(478\) | 24.3376i | 1.11318i | ||||||||
\(479\) | −20.0178 | −0.914635 | −0.457317 | − | 0.889304i | \(-0.651190\pi\) | ||||
−0.457317 | + | 0.889304i | \(0.651190\pi\) | |||||||
\(480\) | 0.986390 | − | 3.74527i | 0.0450223 | − | 0.170947i | ||||
\(481\) | 41.0131i | 1.87004i | ||||||||
\(482\) | 24.9383i | 1.13591i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12.1391 | −0.551777 | ||||||||
\(485\) | −0.342644 | + | 2.89096i | −0.0155587 | + | 0.131272i | ||||
\(486\) | −11.9453 | − | 10.0155i | −0.541849 | − | 0.454312i | ||||
\(487\) | − | 16.5821i | − | 0.751406i | −0.926740 | − | 0.375703i | \(-0.877401\pi\) | ||
0.926740 | − | 0.375703i | \(-0.122599\pi\) | |||||||
\(488\) | 4.96802i | 0.224892i | ||||||||
\(489\) | 0.254750 | − | 1.81365i | 0.0115202 | − | 0.0820161i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.5268i | 0.520197i | 0.965582 | + | 0.260098i | \(0.0837550\pi\) | ||||
−0.965582 | + | 0.260098i | \(0.916245\pi\) | |||||||
\(492\) | −6.45230 | − | 0.906307i | −0.290892 | − | 0.0408595i | ||||
\(493\) | 2.29103 | 0.103183 | ||||||||
\(494\) | 21.0555i | 0.947332i | ||||||||
\(495\) | −29.7580 | − | 12.4789i | −1.33752 | − | 0.560884i | ||||
\(496\) | 5.57387i | 0.250274i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.855045 | − | 6.08735i | 0.0383155 | − | 0.272781i | ||||
\(499\) | −16.9811 | −0.760180 | −0.380090 | − | 0.924950i | \(-0.624107\pi\) | ||||
−0.380090 | + | 0.924950i | \(0.624107\pi\) | |||||||
\(500\) | 3.87481 | − | 10.4874i | 0.173287 | − | 0.469011i | ||||
\(501\) | 0.422083 | − | 3.00495i | 0.0188573 | − | 0.134251i | ||||
\(502\) | −8.21145 | −0.366495 | ||||||||
\(503\) | − | 15.3592i | − | 0.684833i | −0.939548 | − | 0.342416i | \(-0.888755\pi\) | ||
0.939548 | − | 0.342416i | \(-0.111245\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.28159 | + | 27.6875i | −0.146029 | + | 1.23208i | ||||
\(506\) | − | 18.5312i | − | 0.823811i | ||||||
\(507\) | −13.4194 | − | 1.88493i | −0.595978 | − | 0.0837127i | ||||
\(508\) | 14.0483i | 0.623294i | ||||||||
\(509\) | −11.6509 | −0.516415 | −0.258208 | − | 0.966089i | \(-0.583132\pi\) | ||||
−0.258208 | + | 0.966089i | \(0.583132\pi\) | |||||||
\(510\) | 4.36820 | + | 1.15045i | 0.193427 | + | 0.0509428i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −9.74668 | + | 21.9050i | −0.430327 | + | 0.967127i | ||||
\(514\) | − | 2.18021i | − | 0.0961652i | ||||||
\(515\) | 0.0790459 | − | 0.666928i | 0.00348318 | − | 0.0293884i | ||||
\(516\) | 0.969582 | − | 6.90277i | 0.0426835 | − | 0.303878i | ||||
\(517\) | −30.6402 | −1.34756 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.0308173 | − | 0.219399i | 0.00135273 | − | 0.00963053i | ||||
\(520\) | 1.20098 | − | 10.1329i | 0.0526665 | − | 0.444359i | ||||
\(521\) | 28.6635 | 1.25577 | 0.627886 | − | 0.778306i | \(-0.283921\pi\) | ||||
0.627886 | + | 0.778306i | \(0.283921\pi\) | |||||||
\(522\) | 1.62345 | − | 5.66491i | 0.0710564 | − | 0.247946i | ||||
\(523\) | −19.6604 | −0.859689 | −0.429844 | − | 0.902903i | \(-0.641432\pi\) | ||||
−0.429844 | + | 0.902903i | \(0.641432\pi\) | |||||||
\(524\) | 10.1222 | 0.442192 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21.9316 | 0.956262 | ||||||||
\(527\) | −6.50094 | −0.283186 | ||||||||
\(528\) | 1.15892 | − | 8.25071i | 0.0504354 | − | 0.359066i | ||||
\(529\) | −8.15914 | −0.354745 | ||||||||
\(530\) | 2.63396 | − | 22.2233i | 0.114412 | − | 0.965319i | ||||
\(531\) | −36.6482 | − | 10.5026i | −1.59040 | − | 0.455776i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.1663 | −0.743554 | ||||||||
\(534\) | −27.4537 | − | 3.85623i | −1.18804 | − | 0.166875i | ||||
\(535\) | 3.56321 | − | 30.0636i | 0.154051 | − | 1.29976i | ||||
\(536\) | 12.5244i | 0.540970i | ||||||||
\(537\) | 1.50403 | − | 10.7077i | 0.0649039 | − | 0.462072i | ||||
\(538\) | −25.5632 | −1.10211 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 5.94001 | − | 9.98580i | 0.255618 | − | 0.429720i | ||||
\(541\) | 25.9929 | 1.11752 | 0.558762 | − | 0.829328i | \(-0.311277\pi\) | ||||
0.558762 | + | 0.829328i | \(0.311277\pi\) | |||||||
\(542\) | 5.09869i | 0.219008i | ||||||||
\(543\) | −0.289440 | + | 2.06062i | −0.0124210 | + | 0.0884295i | ||||
\(544\) | 1.16632i | 0.0500058i | ||||||||
\(545\) | 3.91733 | − | 33.0514i | 0.167800 | − | 1.41576i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.66375i | 0.113894i | 0.998377 | + | 0.0569468i | \(0.0181366\pi\) | ||||
−0.998377 | + | 0.0569468i | \(0.981863\pi\) | |||||||
\(548\) | 17.8156 | 0.761046 | ||||||||
\(549\) | −4.10592 | + | 14.3273i | −0.175236 | + | 0.611476i | ||||
\(550\) | 5.62232 | − | 23.3852i | 0.239736 | − | 0.997148i | ||||
\(551\) | −9.06352 | −0.386119 | ||||||||
\(552\) | 6.60766 | + | 0.928130i | 0.281241 | + | 0.0395038i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 4.98773i | 0.211908i | ||||||||
\(555\) | −33.6609 | − | 8.86527i | −1.42883 | − | 0.376310i | ||||
\(556\) | − | 16.7252i | − | 0.709305i | ||||||
\(557\) | −3.35036 | −0.141959 | −0.0709796 | − | 0.997478i | \(-0.522613\pi\) | ||||
−0.0709796 | + | 0.997478i | \(0.522613\pi\) | |||||||
\(558\) | −4.60664 | + | 16.0746i | −0.195015 | + | 0.680490i | ||||
\(559\) | − | 18.3648i | − | 0.776747i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.62301 | + | 1.35167i | 0.406284 | + | 0.0570677i | ||||
\(562\) | − | 18.3073i | − | 0.772246i | ||||||
\(563\) | 36.7092i | 1.54711i | 0.633730 | + | 0.773554i | \(0.281523\pi\) | ||||
−0.633730 | + | 0.773554i | \(0.718477\pi\) | |||||||
\(564\) | 1.53461 | − | 10.9254i | 0.0646187 | − | 0.460042i | ||||
\(565\) | −2.49867 | + | 21.0818i | −0.105120 | + | 0.886918i | ||||
\(566\) | 5.04720 | 0.212150 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 2.74047i | − | 0.114988i | ||||||
\(569\) | 33.4105i | 1.40064i | 0.713829 | + | 0.700320i | \(0.246959\pi\) | ||||
−0.713829 | + | 0.700320i | \(0.753041\pi\) | |||||||
\(570\) | −17.2810 | − | 4.55129i | −0.723821 | − | 0.190633i | ||||
\(571\) | 25.3007 | 1.05880 | 0.529401 | − | 0.848372i | \(-0.322417\pi\) | ||||
0.529401 | + | 0.848372i | \(0.322417\pi\) | |||||||
\(572\) | − | 21.9509i | − | 0.917814i | ||||||
\(573\) | −5.26688 | + | 37.4967i | −0.220027 | + | 1.56645i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.7282 | + | 4.50269i | 0.781022 | + | 0.187775i | ||||
\(576\) | 2.88391 | + | 0.826470i | 0.120163 | + | 0.0344363i | ||||
\(577\) | 5.59667 | 0.232992 | 0.116496 | − | 0.993191i | \(-0.462834\pi\) | ||||
0.116496 | + | 0.993191i | \(0.462834\pi\) | |||||||
\(578\) | 15.6397 | 0.650525 | ||||||||
\(579\) | −3.88515 | + | 27.6597i | −0.161462 | + | 1.14950i | ||||
\(580\) | 4.36181 | + | 0.516973i | 0.181114 | + | 0.0214661i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −2.23308 | − | 0.313665i | −0.0925642 | − | 0.0130018i | ||||
\(583\) | − | 48.1423i | − | 1.99385i | ||||||
\(584\) | −13.9852 | −0.578713 | ||||||||
\(585\) | 11.8381 | − | 28.2299i | 0.489445 | − | 1.16716i | ||||
\(586\) | − | 24.4169i | − | 1.00865i | ||||||
\(587\) | 39.5032i | 1.63047i | 0.579129 | + | 0.815236i | \(0.303393\pi\) | ||||
−0.579129 | + | 0.815236i | \(0.696607\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 25.7183 | 1.05971 | ||||||||
\(590\) | 3.34447 | − | 28.2181i | 0.137690 | − | 1.16172i | ||||
\(591\) | −17.8579 | − | 2.50837i | −0.734575 | − | 0.103180i | ||||
\(592\) | − | 8.98759i | − | 0.369388i | ||||||
\(593\) | 21.9019i | 0.899403i | 0.893179 | + | 0.449701i | \(0.148470\pi\) | ||||
−0.893179 | + | 0.449701i | \(0.851530\pi\) | |||||||
\(594\) | 10.1612 | − | 22.8365i | 0.416918 | − | 0.936993i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 20.0263i | 0.820309i | ||||||||
\(597\) | 4.28767 | − | 30.5253i | 0.175483 | − | 1.24932i | ||||
\(598\) | 17.5796 | 0.718884 | ||||||||
\(599\) | − | 32.9458i | − | 1.34613i | −0.739584 | − | 0.673065i | \(-0.764978\pi\) | ||
0.739584 | − | 0.673065i | \(-0.235022\pi\) | |||||||
\(600\) | 8.05686 | + | 3.17599i | 0.328920 | + | 0.129659i | ||||
\(601\) | 32.4903i | 1.32531i | 0.748927 | + | 0.662653i | \(0.230570\pi\) | ||||
−0.748927 | + | 0.662653i | \(0.769430\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.3510 | + | 36.1192i | −0.421526 | + | 1.47089i | ||||
\(604\) | −3.80170 | −0.154689 | ||||||||
\(605\) | 3.19479 | − | 26.9552i | 0.129887 | − | 1.09588i | ||||
\(606\) | −21.3868 | − | 3.00405i | −0.868780 | − | 0.122031i | ||||
\(607\) | 17.6501 | 0.716396 | 0.358198 | − | 0.933646i | \(-0.383391\pi\) | ||||
0.358198 | + | 0.933646i | \(0.383391\pi\) | |||||||
\(608\) | − | 4.61409i | − | 0.187126i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −11.0316 | − | 1.30749i | −0.446657 | − | 0.0529389i | ||||
\(611\) | − | 29.0669i | − | 1.17592i | ||||||
\(612\) | −0.963932 | + | 3.36358i | −0.0389647 | + | 0.135965i | ||||
\(613\) | 7.21302i | 0.291331i | 0.989334 | + | 0.145666i | \(0.0465323\pi\) | ||||
−0.989334 | + | 0.145666i | \(0.953468\pi\) | |||||||
\(614\) | 15.1857 | 0.612843 | ||||||||
\(615\) | 3.71061 | − | 14.0890i | 0.149626 | − | 0.568122i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27.1108 | 1.09144 | 0.545720 | − | 0.837968i | \(-0.316256\pi\) | ||||
0.545720 | + | 0.837968i | \(0.316256\pi\) | |||||||
\(618\) | 0.515159 | + | 0.0723606i | 0.0207227 | + | 0.00291077i | ||||
\(619\) | 32.0212i | 1.28704i | 0.765430 | + | 0.643520i | \(0.222527\pi\) | ||||
−0.765430 | + | 0.643520i | \(0.777473\pi\) | |||||||
\(620\) | −12.3769 | − | 1.46694i | −0.497069 | − | 0.0589138i | ||||
\(621\) | 18.2888 | + | 8.13768i | 0.733906 | + | 0.326554i | ||||
\(622\) | −11.0840 | −0.444429 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 7.82704 | + | 1.09941i | 0.313333 | + | 0.0440115i | ||||
\(625\) | 22.2678 | + | 11.3642i | 0.890712 | + | 0.454569i | ||||
\(626\) | 7.05798 | 0.282094 | ||||||||
\(627\) | −38.0695 | − | 5.34735i | −1.52035 | − | 0.213552i | ||||
\(628\) | 10.2291 | 0.408185 | ||||||||
\(629\) | 10.4824 | 0.417962 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.6088 | −1.05928 | −0.529641 | − | 0.848222i | \(-0.677673\pi\) | ||||
−0.529641 | + | 0.848222i | \(0.677673\pi\) | |||||||
\(632\) | −10.5162 | −0.418311 | ||||||||
\(633\) | −13.5338 | − | 1.90099i | −0.537920 | − | 0.0755577i | ||||
\(634\) | 1.09383 | 0.0434414 | ||||||||
\(635\) | −31.1947 | − | 3.69727i | −1.23792 | − | 0.146722i | ||||
\(636\) | 17.1661 | + | 2.41119i | 0.680680 | + | 0.0956101i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 9.44897 | 0.374088 | ||||||||
\(639\) | 2.26492 | − | 7.90328i | 0.0895988 | − | 0.312649i | ||||
\(640\) | −0.263182 | + | 2.22053i | −0.0104032 | + | 0.0877740i | ||||
\(641\) | − | 41.5662i | − | 1.64177i | −0.571096 | − | 0.820883i | \(-0.693482\pi\) | ||
0.571096 | − | 0.820883i | \(-0.306518\pi\) | |||||||
\(642\) | 23.2222 | + | 3.26185i | 0.916506 | + | 0.128735i | ||||
\(643\) | −13.9242 | −0.549116 | −0.274558 | − | 0.961571i | \(-0.588531\pi\) | ||||
−0.274558 | + | 0.961571i | \(0.588531\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 15.0726 | + | 3.96967i | 0.593483 | + | 0.156306i | ||||
\(646\) | 5.38152 | 0.211733 | ||||||||
\(647\) | 4.60509i | 0.181045i | 0.995894 | + | 0.0905223i | \(0.0288536\pi\) | ||||
−0.995894 | + | 0.0905223i | \(0.971146\pi\) | |||||||
\(648\) | 7.63389 | + | 4.76693i | 0.299888 | + | 0.187263i | ||||
\(649\) | − | 61.1286i | − | 2.39951i | ||||||
\(650\) | 22.1844 | + | 5.33362i | 0.870143 | + | 0.209202i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.05739i | 0.0414106i | ||||||||
\(653\) | −2.75937 | −0.107982 | −0.0539912 | − | 0.998541i | \(-0.517194\pi\) | ||||
−0.0539912 | + | 0.998541i | \(0.517194\pi\) | |||||||
\(654\) | 25.5300 | + | 3.58602i | 0.998304 | + | 0.140224i | ||||
\(655\) | −2.66399 | + | 22.4767i | −0.104091 | + | 0.878237i | ||||
\(656\) | 3.76181 | 0.146874 | ||||||||
\(657\) | −40.3322 | − | 11.5584i | −1.57351 | − | 0.450935i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.2287i | 1.41127i | 0.708576 | + | 0.705635i | \(0.249338\pi\) | ||||
−0.708576 | + | 0.705635i | \(0.750662\pi\) | |||||||
\(660\) | 18.0159 | + | 4.74484i | 0.701268 | + | 0.184693i | ||||
\(661\) | 9.32762i | 0.362803i | 0.983409 | + | 0.181401i | \(0.0580633\pi\) | ||||
−0.983409 | + | 0.181401i | \(0.941937\pi\) | |||||||
\(662\) | −13.3568 | −0.519125 | ||||||||
\(663\) | −1.28227 | + | 9.12887i | −0.0497991 | + | 0.354536i | ||||
\(664\) | 3.54903i | 0.137729i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.42797 | − | 25.9194i | 0.287828 | − | 1.00436i | ||||
\(667\) | 7.56729i | 0.293007i | ||||||||
\(668\) | 1.75194i | 0.0677845i | ||||||||
\(669\) | −30.8236 | − | 4.32957i | −1.19171 | − | 0.167391i | ||||
\(670\) | −27.8107 | − | 3.29619i | −1.07442 | − | 0.127343i | ||||
\(671\) | −23.8977 | −0.922562 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 50.4977i | 1.94654i | 0.229661 | + | 0.973271i | \(0.426238\pi\) | ||||
−0.229661 | + | 0.973271i | \(0.573762\pi\) | |||||||
\(674\) | − | 12.3715i | − | 0.476534i | ||||||
\(675\) | 20.6104 | + | 15.8180i | 0.793296 | + | 0.608837i | ||||
\(676\) | 7.82377 | 0.300914 | ||||||||
\(677\) | 26.8241i | 1.03093i | 0.856910 | + | 0.515467i | \(0.172381\pi\) | ||||
−0.856910 | + | 0.515467i | \(0.827619\pi\) | |||||||
\(678\) | −16.2843 | − | 2.28734i | −0.625396 | − | 0.0878448i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.58985 | − | 0.306956i | −0.0993164 | − | 0.0117712i | ||||
\(681\) | 1.28696 | − | 9.16230i | 0.0493165 | − | 0.351100i | ||||
\(682\) | −26.8121 | −1.02669 | ||||||||
\(683\) | −2.00337 | −0.0766570 | −0.0383285 | − | 0.999265i | \(-0.512203\pi\) | ||||
−0.0383285 | + | 0.999265i | \(0.512203\pi\) | |||||||
\(684\) | 3.81341 | − | 13.3066i | 0.145809 | − | 0.508791i | ||||
\(685\) | −4.68876 | + | 39.5601i | −0.179148 | + | 1.51151i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.851911 | − | 6.06504i | 0.0325024 | − | 0.231396i | ||||
\(688\) | 4.02444i | 0.153430i | ||||||||
\(689\) | 45.6702 | 1.73990 | ||||||||
\(690\) | −3.79995 | + | 14.4282i | −0.144662 | + | 0.549273i | ||||
\(691\) | − | 26.4071i | − | 1.00457i | −0.864702 | − | 0.502286i | \(-0.832492\pi\) | ||
0.864702 | − | 0.502286i | \(-0.167508\pi\) | |||||||
\(692\) | 0.127913i | 0.00486254i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.96861 | −0.112687 | ||||||||
\(695\) | 37.1386 | + | 4.40176i | 1.40875 | + | 0.166968i | ||||
\(696\) | −0.473250 | + | 3.36922i | −0.0179385 | + | 0.127710i | ||||
\(697\) | 4.38749i | 0.166188i | ||||||||
\(698\) | 1.03511i | 0.0391794i | ||||||||
\(699\) | −8.99400 | − | 1.26332i | −0.340184 | − | 0.0477832i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 14.6209i | − | 0.552222i | −0.961126 | − | 0.276111i | \(-0.910954\pi\) | ||
0.961126 | − | 0.276111i | \(-0.0890457\pi\) | |||||||
\(702\) | 21.6639 | + | 9.63941i | 0.817650 | + | 0.363816i | ||||
\(703\) | −41.4695 | −1.56405 | ||||||||
\(704\) | 4.81031i | 0.181295i | ||||||||
\(705\) | 23.8562 | + | 6.28301i | 0.898478 | + | 0.236632i | ||||
\(706\) | 13.4155i | 0.504900i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 21.7966 | + | 3.06161i | 0.819168 | + | 0.115062i | ||||
\(709\) | −20.7963 | −0.781022 | −0.390511 | − | 0.920598i | \(-0.627702\pi\) | ||||
−0.390511 | + | 0.920598i | \(0.627702\pi\) | |||||||
\(710\) | 6.08529 | + | 0.721243i | 0.228377 | + | 0.0270678i | ||||
\(711\) | −30.3277 | − | 8.69130i | −1.13738 | − | 0.325949i | ||||
\(712\) | 16.0060 | 0.599851 | ||||||||
\(713\) | − | 21.4727i | − | 0.804159i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 48.7426 | + | 5.77709i | 1.82287 | + | 0.216051i | ||||
\(716\) | 6.24279i | 0.233304i | ||||||||
\(717\) | 5.86351 | − | 41.7442i | 0.218977 | − | 1.55897i | ||||
\(718\) | 24.8666i | 0.928012i | ||||||||
\(719\) | 5.57749 | 0.208005 | 0.104003 | − | 0.994577i | \(-0.466835\pi\) | ||||
0.104003 | + | 0.994577i | \(0.466835\pi\) | |||||||
\(720\) | −2.59419 | + | 6.18629i | −0.0966798 | + | 0.230549i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −2.28981 | −0.0852180 | ||||||||
\(723\) | 6.00822 | − | 42.7745i | 0.223448 | − | 1.59080i | ||||
\(724\) | − | 1.20138i | − | 0.0446488i | ||||||
\(725\) | −2.29590 | + | 9.54946i | −0.0852676 | + | 0.354658i | ||||
\(726\) | 20.8211 | + | 2.92459i | 0.772745 | + | 0.108542i | ||||
\(727\) | −37.0725 | −1.37494 | −0.687471 | − | 0.726212i | \(-0.741279\pi\) | ||||
−0.687471 | + | 0.726212i | \(0.741279\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 18.0757 | + | 20.0566i | 0.669472 | + | 0.742837i | ||||
\(730\) | 3.68066 | − | 31.0546i | 0.136227 | − | 1.14938i | ||||
\(731\) | −4.69380 | −0.173607 | ||||||||
\(732\) | 1.19691 | − | 8.52122i | 0.0442392 | − | 0.314953i | ||||
\(733\) | −1.87554 | −0.0692748 | −0.0346374 | − | 0.999400i | \(-0.511028\pi\) | ||||
−0.0346374 | + | 0.999400i | \(0.511028\pi\) | |||||||
\(734\) | 5.54367 | 0.204621 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.85238 | −0.142001 | ||||||||
\(737\) | −60.2461 | −2.21919 | ||||||||
\(738\) | 10.8487 | + | 3.10902i | 0.399347 | + | 0.114445i | ||||
\(739\) | 21.1942 | 0.779642 | 0.389821 | − | 0.920891i | \(-0.372537\pi\) | ||||
0.389821 | + | 0.920891i | \(0.372537\pi\) | |||||||
\(740\) | 19.9572 | + | 2.36537i | 0.733640 | + | 0.0869528i | ||||
\(741\) | 5.07276 | − | 36.1147i | 0.186353 | − | 1.32671i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11.1477 | −0.408969 | −0.204484 | − | 0.978870i | \(-0.565552\pi\) | ||||
−0.204484 | + | 0.978870i | \(0.565552\pi\) | |||||||
\(744\) | 1.34288 | − | 9.56038i | 0.0492322 | − | 0.350500i | ||||
\(745\) | −44.4689 | − | 5.27056i | −1.62921 | − | 0.193098i | ||||
\(746\) | − | 3.87531i | − | 0.141885i | ||||||
\(747\) | −2.93317 | + | 10.2351i | −0.107319 | + | 0.374483i | ||||
\(748\) | −5.61039 | −0.205136 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −9.17280 | + | 17.0546i | −0.334943 | + | 0.622746i | ||||
\(751\) | 48.0203 | 1.75229 | 0.876143 | − | 0.482052i | \(-0.160108\pi\) | ||||
0.876143 | + | 0.482052i | \(0.160108\pi\) | |||||||
\(752\) | 6.36970i | 0.232279i | ||||||||
\(753\) | 14.0844 | + | 1.97833i | 0.513263 | + | 0.0720944i | ||||
\(754\) | 8.96377i | 0.326441i | ||||||||
\(755\) | 1.00054 | − | 8.44178i | 0.0364134 | − | 0.307228i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 26.1445i | − | 0.950239i | −0.879921 | − | 0.475120i | \(-0.842405\pi\) | ||
0.879921 | − | 0.475120i | \(-0.157595\pi\) | |||||||
\(758\) | −16.5126 | −0.599765 | ||||||||
\(759\) | −4.46459 | + | 31.7849i | −0.162054 | + | 1.15372i | ||||
\(760\) | 10.2457 | + | 1.21435i | 0.371651 | + | 0.0440489i | ||||
\(761\) | −0.650185 | −0.0235692 | −0.0117846 | − | 0.999931i | \(-0.503751\pi\) | ||||
−0.0117846 | + | 0.999931i | \(0.503751\pi\) | |||||||
\(762\) | 3.38457 | − | 24.0959i | 0.122610 | − | 0.872902i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 21.8612i | − | 0.790911i | ||||||
\(765\) | −7.21522 | − | 3.02567i | −0.260867 | − | 0.109393i | ||||
\(766\) | 38.1711i | 1.37918i | ||||||||
\(767\) | 57.9897 | 2.09389 | ||||||||
\(768\) | −1.71521 | − | 0.240923i | −0.0618924 | − | 0.00869358i | ||||
\(769\) | − | 14.2303i | − | 0.513159i | −0.966523 | − | 0.256580i | \(-0.917404\pi\) | ||
0.966523 | − | 0.256580i | \(-0.0825956\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.525265 | + | 3.73953i | −0.0189170 | + | 0.134676i | ||||
\(772\) | − | 16.1261i | − | 0.580391i | ||||||
\(773\) | − | 4.49715i | − | 0.161751i | −0.996724 | − | 0.0808756i | \(-0.974228\pi\) | ||
0.996724 | − | 0.0808756i | \(-0.0257716\pi\) | |||||||
\(774\) | −3.32608 | + | 11.6061i | −0.119553 | + | 0.417174i | ||||
\(775\) | 6.51477 | − | 27.0972i | 0.234017 | − | 0.973360i | ||||
\(776\) | 1.30193 | 0.0467364 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.2990i | 0.369237i | ||||||||
\(779\) | − | 17.3573i | − | 0.621890i | ||||||
\(780\) | −4.50120 | + | 17.0908i | −0.161169 | + | 0.611949i | ||||
\(781\) | 13.1825 | 0.471708 | ||||||||
\(782\) | − | 4.49313i | − | 0.160674i | ||||||
\(783\) | −4.14937 | + | 9.32540i | −0.148286 | + | 0.333263i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.69211 | + | 22.7139i | −0.0960855 | + | 0.810695i | ||||
\(786\) | −17.3618 | − | 2.43868i | −0.619274 | − | 0.0869850i | ||||
\(787\) | −39.8904 | −1.42194 | −0.710970 | − | 0.703223i | \(-0.751744\pi\) | ||||
−0.710970 | + | 0.703223i | \(0.751744\pi\) | |||||||
\(788\) | 10.4115 | 0.370893 | ||||||||
\(789\) | −37.6173 | − | 5.28383i | −1.33921 | − | 0.188109i | ||||
\(790\) | 2.76767 | − | 23.3514i | 0.0984692 | − | 0.830806i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −3.97558 | + | 13.8725i | −0.141266 | + | 0.492938i | ||||
\(793\) | − | 22.6706i | − | 0.805057i | ||||||
\(794\) | −9.95455 | −0.353274 | ||||||||
\(795\) | −9.87193 | + | 37.4832i | −0.350121 | + | 1.32939i | ||||
\(796\) | 17.7968i | 0.630791i | ||||||||
\(797\) | 10.5614i | 0.374105i | 0.982350 | + | 0.187052i | \(0.0598934\pi\) | ||||
−0.982350 | + | 0.187052i | \(0.940107\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.42914 | −0.262824 | ||||||||
\(800\) | −4.86147 | − | 1.16881i | −0.171879 | − | 0.0413235i | ||||
\(801\) | 46.1600 | + | 13.2285i | 1.63098 | + | 0.467406i | ||||
\(802\) | 14.6489i | 0.517269i | ||||||||
\(803\) | − | 67.2733i | − | 2.37402i | ||||||
\(804\) | 3.01741 | − | 21.4820i | 0.106416 | − | 0.757610i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 25.4353i | − | 0.895920i | ||||||
\(807\) | 43.8463 | + | 6.15877i | 1.54346 | + | 0.216799i | ||||
\(808\) | 12.4689 | 0.438654 | ||||||||
\(809\) | − | 31.1336i | − | 1.09460i | −0.836936 | − | 0.547300i | \(-0.815656\pi\) | ||
0.836936 | − | 0.547300i | \(-0.184344\pi\) | |||||||
\(810\) | −12.5942 | + | 15.6967i | −0.442515 | + | 0.551525i | ||||
\(811\) | 15.1367i | 0.531521i | 0.964039 | + | 0.265761i | \(0.0856231\pi\) | ||||
−0.964039 | + | 0.265761i | \(0.914377\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.22839 | − | 8.74535i | 0.0430817 | − | 0.306713i | ||||
\(814\) | 43.2331 | 1.51532 | ||||||||
\(815\) | −2.34796 | − | 0.278286i | −0.0822456 | − | 0.00974794i | ||||
\(816\) | 0.280995 | − | 2.00050i | 0.00983679 | − | 0.0700313i | ||||
\(817\) | 18.5691 | 0.649652 | ||||||||
\(818\) | − | 32.8807i | − | 1.14965i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.990040 | + | 8.35319i | −0.0345737 | + | 0.291706i | ||||
\(821\) | 48.4610i | 1.69130i | 0.533738 | + | 0.845650i | \(0.320787\pi\) | ||||
−0.533738 | + | 0.845650i | \(0.679213\pi\) | |||||||
\(822\) | −30.5576 | − | 4.29220i | −1.06582 | − | 0.149708i | ||||
\(823\) | − | 28.3716i | − | 0.988971i | −0.869186 | − | 0.494486i | \(-0.835356\pi\) | ||
0.869186 | − | 0.494486i | \(-0.164644\pi\) | |||||||
\(824\) | −0.300347 | −0.0104631 | ||||||||
\(825\) | −15.2775 | + | 38.7560i | −0.531895 | + | 1.34931i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.09153 | 0.0727296 | 0.0363648 | − | 0.999339i | \(-0.488422\pi\) | ||||
0.0363648 | + | 0.999339i | \(0.488422\pi\) | |||||||
\(828\) | −11.1099 | − | 3.18388i | −0.386097 | − | 0.110647i | ||||
\(829\) | − | 45.5410i | − | 1.58170i | −0.612008 | − | 0.790852i | \(-0.709638\pi\) | ||
0.612008 | − | 0.790852i | \(-0.290362\pi\) | |||||||
\(830\) | −7.88072 | − | 0.934042i | −0.273544 | − | 0.0324211i | ||||
\(831\) | 1.20166 | − | 8.55502i | 0.0416852 | − | 0.296770i | ||||
\(832\) | −4.56331 | −0.158204 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −4.02948 | + | 28.6872i | −0.139530 | + | 0.993357i | ||||
\(835\) | −3.89022 | − | 0.461078i | −0.134627 | − | 0.0159563i | ||||
\(836\) | 22.1952 | 0.767637 | ||||||||
\(837\) | 11.7741 | − | 26.4614i | 0.406973 | − | 0.914641i | ||||
\(838\) | −18.3939 | −0.635405 | ||||||||
\(839\) | −41.3972 | −1.42919 | −0.714595 | − | 0.699538i | \(-0.753389\pi\) | ||||
−0.714595 | + | 0.699538i | \(0.753389\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.1415 | 0.866947 | ||||||||
\(842\) | −25.4508 | −0.877094 | ||||||||
\(843\) | −4.41065 | + | 31.4009i | −0.151911 | + | 1.08150i | ||||
\(844\) | 7.89044 | 0.271600 | ||||||||
\(845\) | −2.05908 | + | 17.3729i | −0.0708344 | + | 0.597645i | ||||
\(846\) | −5.26437 | + | 18.3697i | −0.180993 | + | 0.631562i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −10.0081 | −0.343681 | ||||||||
\(849\) | −8.65702 | − | 1.21599i | −0.297108 | − | 0.0417326i | ||||
\(850\) | 1.36321 | − | 5.67005i | 0.0467576 | − | 0.194481i | ||||
\(851\) | 34.6236i | 1.18688i | ||||||||
\(852\) | −0.660244 | + | 4.70049i | −0.0226196 | + | 0.161036i | ||||
\(853\) | 9.62551 | 0.329571 | 0.164786 | − | 0.986329i | \(-0.447307\pi\) | ||||
0.164786 | + | 0.986329i | \(0.447307\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 28.5441 | + | 11.9698i | 0.976187 | + | 0.409360i | ||||
\(856\) | −13.5389 | −0.462751 | ||||||||
\(857\) | 11.8071i | 0.403321i | 0.979455 | + | 0.201661i | \(0.0646338\pi\) | ||||
−0.979455 | + | 0.201661i | \(0.935366\pi\) | |||||||
\(858\) | −5.28849 | + | 37.6505i | −0.180546 | + | 1.28537i | ||||
\(859\) | 37.9641i | 1.29532i | 0.761930 | + | 0.647659i | \(0.224252\pi\) | ||||
−0.761930 | + | 0.647659i | \(0.775748\pi\) | |||||||
\(860\) | −8.93638 | − | 1.05916i | −0.304728 | − | 0.0361171i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.04891i | 0.0357260i | ||||||||
\(863\) | −26.7170 | −0.909456 | −0.454728 | − | 0.890630i | \(-0.650264\pi\) | ||||
−0.454728 | + | 0.890630i | \(0.650264\pi\) | |||||||
\(864\) | −4.74741 | − | 2.11237i | −0.161510 | − | 0.0718644i | ||||
\(865\) | −0.284035 | − | 0.0336645i | −0.00965748 | − | 0.00114463i | ||||
\(866\) | 27.5424 | 0.935928 | ||||||||
\(867\) | −26.8254 | − | 3.76797i | −0.911038 | − | 0.127967i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 50.5860i | − | 1.71601i | ||||||
\(870\) | −7.35689 | − | 1.93758i | −0.249422 | − | 0.0656901i | ||||
\(871\) | − | 57.1525i | − | 1.93654i | ||||||
\(872\) | −14.8845 | −0.504052 | ||||||||
\(873\) | 3.75464 | + | 1.07600i | 0.127075 | + | 0.0364172i | ||||
\(874\) | 17.7752i | 0.601256i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 23.9877 | + | 3.36937i | 0.810468 | + | 0.113840i | ||||
\(877\) | − | 52.4373i | − | 1.77068i | −0.464942 | − | 0.885341i | \(-0.653925\pi\) | ||
0.464942 | − | 0.885341i | \(-0.346075\pi\) | |||||||
\(878\) | − | 11.2089i | − | 0.378282i | ||||||
\(879\) | −5.88261 | + | 41.8802i | −0.198415 | + | 1.41258i | ||||
\(880\) | −10.6814 | − | 1.26599i | −0.360071 | − | 0.0426764i | ||||
\(881\) | −33.9634 | −1.14426 | −0.572129 | − | 0.820164i | \(-0.693882\pi\) | ||||
−0.572129 | + | 0.820164i | \(0.693882\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 25.6542i | − | 0.863333i | −0.902033 | − | 0.431666i | \(-0.857926\pi\) | ||
0.902033 | − | 0.431666i | \(-0.142074\pi\) | |||||||
\(884\) | − | 5.32230i | − | 0.179008i | ||||||
\(885\) | −12.5349 | + | 47.5942i | −0.421355 | + | 1.59986i | ||||
\(886\) | 33.2580 | 1.11732 | ||||||||
\(887\) | − | 26.8939i | − | 0.903008i | −0.892269 | − | 0.451504i | \(-0.850888\pi\) | ||
0.892269 | − | 0.451504i | \(-0.149112\pi\) | |||||||
\(888\) | −2.16532 | + | 15.4156i | −0.0726634 | + | 0.517315i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −4.21250 | + | 35.5418i | −0.141203 | + | 1.19136i | ||||
\(891\) | −22.9304 | + | 36.7214i | −0.768199 | + | 1.23021i | ||||
\(892\) | 17.9707 | 0.601704 | ||||||||
\(893\) | 29.3904 | 0.983511 | ||||||||
\(894\) | 4.82480 | − | 34.3494i | 0.161366 | − | 1.14881i | ||||
\(895\) | −13.8623 | − | 1.64299i | −0.463365 | − | 0.0549191i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −30.1528 | − | 4.23534i | −1.00677 | − | 0.141414i | ||||
\(898\) | 9.45808i | 0.315620i | ||||||||
\(899\) | 10.9488 | 0.365164 | ||||||||
\(900\) | −13.0541 | − | 7.38859i | −0.435136 | − | 0.246286i | ||||
\(901\) | − | 11.6727i | − | 0.388875i | ||||||
\(902\) | 18.0955i | 0.602513i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9.49406 | 0.315768 | ||||||||
\(905\) | 2.66769 | + | 0.316181i | 0.0886769 | + | 0.0105102i | ||||
\(906\) | 6.52073 | + | 0.915920i | 0.216637 | + | 0.0304294i | ||||
\(907\) | 26.5074i | 0.880165i | 0.897957 | + | 0.440082i | \(0.145051\pi\) | ||||
−0.897957 | + | 0.440082i | \(0.854949\pi\) | |||||||
\(908\) | 5.34178i | 0.177273i | ||||||||
\(909\) | 35.9592 | + | 10.3052i | 1.19269 | + | 0.341801i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.71732i | 0.0900289i | 0.998986 | + | 0.0450145i | \(0.0143334\pi\) | ||||
−0.998986 | + | 0.0450145i | \(0.985667\pi\) | |||||||
\(912\) | −1.11164 | + | 7.91414i | −0.0368102 | + | 0.262064i | ||||
\(913\) | −17.0720 | −0.564999 | ||||||||
\(914\) | 14.7842i | 0.489019i | ||||||||
\(915\) | 18.6066 | + | 4.90041i | 0.615114 | + | 0.162002i | ||||
\(916\) | 3.53602i | 0.116834i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.46371 | − | 5.53702i | 0.0813147 | − | 0.182749i | ||||
\(919\) | 36.4031 | 1.20083 | 0.600414 | − | 0.799689i | \(-0.295002\pi\) | ||||
0.600414 | + | 0.799689i | \(0.295002\pi\) | |||||||
\(920\) | 1.01388 | − | 8.55432i | 0.0334266 | − | 0.282028i | ||||
\(921\) | −26.0466 | − | 3.65858i | −0.858266 | − | 0.120554i | ||||
\(922\) | 14.8821 | 0.490117 | ||||||||
\(923\) | 12.5056i | 0.411627i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.5047 | + | 43.6929i | −0.345394 | + | 1.43661i | ||||
\(926\) | 6.24696i | 0.205288i | ||||||||
\(927\) | −0.866174 | − | 0.248228i | −0.0284489 | − | 0.00815287i | ||||
\(928\) | − | 1.96431i | − | 0.0644818i | ||||||
\(929\) | 1.92528 | 0.0631665 | 0.0315833 | − | 0.999501i | \(-0.489945\pi\) | ||||
0.0315833 | + | 0.999501i | \(0.489945\pi\) | |||||||
\(930\) | 20.8756 | + | 5.49801i | 0.684539 | + | 0.180287i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 5.24366 | 0.171762 | ||||||||
\(933\) | 19.0115 | + | 2.67040i | 0.622408 | + | 0.0874251i | ||||
\(934\) | − | 16.4666i | − | 0.538805i | ||||||
\(935\) | 1.47655 | − | 12.4580i | 0.0482884 | − | 0.407420i | ||||
\(936\) | −13.1602 | − | 3.77144i | −0.430154 | − | 0.123273i | ||||
\(937\) | −28.5051 | −0.931220 | −0.465610 | − | 0.884990i | \(-0.654165\pi\) | ||||
−0.465610 | + | 0.884990i | \(0.654165\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.1059 | − | 1.70043i | −0.395062 | − | 0.0554915i | ||||
\(940\) | −14.1441 | − | 1.67639i | −0.461329 | − | 0.0546778i | ||||
\(941\) | −37.8130 | −1.23267 | −0.616334 | − | 0.787485i | \(-0.711383\pi\) | ||||
−0.616334 | + | 0.787485i | \(0.711383\pi\) | |||||||
\(942\) | −17.5450 | − | 2.46442i | −0.571648 | − | 0.0802953i | ||||
\(943\) | −14.4919 | −0.471922 | ||||||||
\(944\) | −12.7078 | −0.413605 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −19.3588 | −0.629409 | ||||||||
\(947\) | 43.7379 | 1.42129 | 0.710645 | − | 0.703551i | \(-0.248403\pi\) | ||||
0.710645 | + | 0.703551i | \(0.248403\pi\) | |||||||
\(948\) | 18.0375 | + | 2.53359i | 0.585830 | + | 0.0822872i | ||||
\(949\) | 63.8189 | 2.07165 | ||||||||
\(950\) | −5.39297 | + | 22.4313i | −0.174971 | + | 0.727766i | ||||
\(951\) | −1.87615 | − | 0.263529i | −0.0608382 | − | 0.00854550i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.44666 | −0.241221 | −0.120611 | − | 0.992700i | \(-0.538485\pi\) | ||||
−0.120611 | + | 0.992700i | \(0.538485\pi\) | |||||||
\(954\) | −28.8626 | − | 8.27142i | −0.934460 | − | 0.267797i | ||||
\(955\) | 48.5434 | + | 5.75348i | 1.57083 | + | 0.186178i | ||||
\(956\) | 24.3376i | 0.787135i | ||||||||
\(957\) | −16.2070 | − | 2.27648i | −0.523898 | − | 0.0735881i | ||||
\(958\) | −20.0178 | −0.646744 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.986390 | − | 3.74527i | 0.0318356 | − | 0.120878i | ||||
\(961\) | −0.0680375 | −0.00219476 | ||||||||
\(962\) | 41.0131i | 1.32232i | ||||||||
\(963\) | −39.0451 | − | 11.1895i | −1.25821 | − | 0.360578i | ||||
\(964\) | 24.9383i | 0.803209i | ||||||||
\(965\) | 35.8084 | + | 4.24410i | 1.15271 | + | 0.136622i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.99874i | 0.257222i | 0.991695 | + | 0.128611i | \(0.0410519\pi\) | ||||
−0.991695 | + | 0.128611i | \(0.958948\pi\) | |||||||
\(968\) | −12.1391 | −0.390166 | ||||||||
\(969\) | −9.23046 | − | 1.29654i | −0.296525 | − | 0.0416507i | ||||
\(970\) | −0.342644 | + | 2.89096i | −0.0110016 | + | 0.0928232i | ||||
\(971\) | 4.32616 | 0.138833 | 0.0694165 | − | 0.997588i | \(-0.477886\pi\) | ||||
0.0694165 | + | 0.997588i | \(0.477886\pi\) | |||||||
\(972\) | −11.9453 | − | 10.0155i | −0.383145 | − | 0.321247i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 16.5821i | − | 0.531324i | ||||||
\(975\) | −36.7659 | − | 14.4930i | −1.17745 | − | 0.464148i | ||||
\(976\) | 4.96802i | 0.159023i | ||||||||
\(977\) | −50.2866 | −1.60881 | −0.804405 | − | 0.594081i | \(-0.797516\pi\) | ||||
−0.804405 | + | 0.594081i | \(0.797516\pi\) | |||||||
\(978\) | 0.254750 | − | 1.81365i | 0.00814601 | − | 0.0579941i | ||||
\(979\) | 76.9940i | 2.46074i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −42.9255 | − | 12.3016i | −1.37051 | − | 0.392759i | ||||
\(982\) | 11.5268i | 0.367834i | ||||||||
\(983\) | − | 60.7315i | − | 1.93703i | −0.248948 | − | 0.968517i | \(-0.580085\pi\) | ||
0.248948 | − | 0.968517i | \(-0.419915\pi\) | |||||||
\(984\) | −6.45230 | − | 0.906307i | −0.205692 | − | 0.0288920i | ||||
\(985\) | −2.74011 | + | 23.1189i | −0.0873072 | + | 0.736630i | ||||
\(986\) | 2.29103 | 0.0729612 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 21.0555i | 0.669865i | ||||||||
\(989\) | − | 15.5037i | − | 0.492989i | ||||||
\(990\) | −29.7580 | − | 12.4789i | −0.945771 | − | 0.396605i | ||||
\(991\) | −25.5740 | −0.812384 | −0.406192 | − | 0.913788i | \(-0.633144\pi\) | ||||
−0.406192 | + | 0.913788i | \(0.633144\pi\) | |||||||
\(992\) | 5.57387i | 0.176971i | ||||||||
\(993\) | 22.9097 | + | 3.21796i | 0.727017 | + | 0.102119i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −39.5183 | − | 4.68380i | −1.25281 | − | 0.148487i | ||||
\(996\) | 0.855045 | − | 6.08735i | 0.0270931 | − | 0.192885i | ||||
\(997\) | 9.46618 | 0.299797 | 0.149898 | − | 0.988701i | \(-0.452105\pi\) | ||||
0.149898 | + | 0.988701i | \(0.452105\pi\) | |||||||
\(998\) | −16.9811 | −0.537528 | ||||||||
\(999\) | −18.9851 | + | 42.6677i | −0.600663 | + | 1.34995i |
(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 | 1470.2.d.h.1469.1 | yes | 24 | |
3.2 | odd | 2 | 1470.2.d.g.1469.2 | yes | 24 | ||
5.4 | even | 2 | 1470.2.d.g.1469.24 | yes | 24 | ||
7.6 | odd | 2 | inner | 1470.2.d.h.1469.24 | yes | 24 | |
15.14 | odd | 2 | inner | 1470.2.d.h.1469.23 | yes | 24 | |
21.20 | even | 2 | 1470.2.d.g.1469.23 | yes | 24 | ||
35.34 | odd | 2 | 1470.2.d.g.1469.1 | ✓ | 24 | ||
105.104 | even | 2 | inner | 1470.2.d.h.1469.2 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1470.2.d.g.1469.1 | ✓ | 24 | 35.34 | odd | 2 | ||
1470.2.d.g.1469.2 | yes | 24 | 3.2 | odd | 2 | ||
1470.2.d.g.1469.23 | yes | 24 | 21.20 | even | 2 | ||
1470.2.d.g.1469.24 | yes | 24 | 5.4 | even | 2 | ||
1470.2.d.h.1469.1 | yes | 24 | 1.1 | even | 1 | trivial | |
1470.2.d.h.1469.2 | yes | 24 | 105.104 | even | 2 | inner | |
1470.2.d.h.1469.23 | yes | 24 | 15.14 | odd | 2 | inner | |
1470.2.d.h.1469.24 | yes | 24 | 7.6 | odd | 2 | inner |