Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,2,Mod(419,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1045.419");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.34436701122\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 26 x^{18} + 281 x^{16} + 1640 x^{14} + 5623 x^{12} + 11551 x^{10} + 13894 x^{8} + 9095 x^{6} + 2753 x^{4} + 276 x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 419.13 | ||
Root | \(0.712399i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1045.419 |
Dual form | 1045.2.b.c.419.8 |
$q$-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 \(\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times\).
\(n\) | \(496\) | \(761\) | \(837\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.712399i | 0.503742i | 0.967761 | + | 0.251871i | \(0.0810459\pi\) | ||||
−0.967761 | + | 0.251871i | \(0.918954\pi\) | |||||||
\(3\) | − | 3.32227i | − | 1.91811i | −0.283216 | − | 0.959056i | \(-0.591401\pi\) | ||
0.283216 | − | 0.959056i | \(-0.408599\pi\) | |||||||
\(4\) | 1.49249 | 0.746244 | ||||||||
\(5\) | 1.31011 | − | 1.81207i | 0.585898 | − | 0.810385i | ||||
\(6\) | 2.36678 | 0.966234 | ||||||||
\(7\) | − | 2.70450i | − | 1.02221i | −0.859520 | − | 0.511103i | \(-0.829237\pi\) | ||
0.859520 | − | 0.511103i | \(-0.170763\pi\) | |||||||
\(8\) | 2.48804i | 0.879656i | ||||||||
\(9\) | −8.03747 | −2.67916 | ||||||||
\(10\) | 1.29092 | + | 0.933320i | 0.408225 | + | 0.295142i | ||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | − | 4.95845i | − | 1.43138i | ||||||
\(13\) | 3.93869i | 1.09240i | 0.837656 | + | 0.546198i | \(0.183925\pi\) | ||||
−0.837656 | + | 0.546198i | \(0.816075\pi\) | |||||||
\(14\) | 1.92668 | 0.514928 | ||||||||
\(15\) | −6.02020 | − | 4.35253i | −1.55441 | − | 1.12382i | ||||
\(16\) | 1.21250 | 0.303124 | ||||||||
\(17\) | − | 4.53720i | − | 1.10043i | −0.835023 | − | 0.550216i | \(-0.814545\pi\) | ||
0.835023 | − | 0.550216i | \(-0.185455\pi\) | |||||||
\(18\) | − | 5.72588i | − | 1.34960i | ||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 1.95532 | − | 2.70450i | 0.437223 | − | 0.604745i | ||||
\(21\) | −8.98508 | −1.96070 | ||||||||
\(22\) | 0.712399i | 0.151884i | ||||||||
\(23\) | − | 3.13766i | − | 0.654246i | −0.944982 | − | 0.327123i | \(-0.893921\pi\) | ||
0.944982 | − | 0.327123i | \(-0.106079\pi\) | |||||||
\(24\) | 8.26595 | 1.68728 | ||||||||
\(25\) | −1.56723 | − | 4.74803i | −0.313446 | − | 0.949606i | ||||
\(26\) | −2.80592 | −0.550285 | ||||||||
\(27\) | 16.7358i | 3.22081i | ||||||||
\(28\) | − | 4.03643i | − | 0.762814i | ||||||
\(29\) | 7.37268 | 1.36907 | 0.684536 | − | 0.728979i | \(-0.260005\pi\) | ||||
0.684536 | + | 0.728979i | \(0.260005\pi\) | |||||||
\(30\) | 3.10074 | − | 4.28878i | 0.566115 | − | 0.783021i | ||||
\(31\) | −6.00774 | −1.07902 | −0.539511 | − | 0.841979i | \(-0.681391\pi\) | ||||
−0.539511 | + | 0.841979i | \(0.681391\pi\) | |||||||
\(32\) | 5.83987i | 1.03235i | ||||||||
\(33\) | − | 3.32227i | − | 0.578333i | ||||||
\(34\) | 3.23229 | 0.554333 | ||||||||
\(35\) | −4.90076 | − | 3.54319i | −0.828379 | − | 0.598908i | ||||
\(36\) | −11.9958 | −1.99930 | ||||||||
\(37\) | − | 7.56844i | − | 1.24424i | −0.782920 | − | 0.622122i | \(-0.786271\pi\) | ||
0.782920 | − | 0.622122i | \(-0.213729\pi\) | |||||||
\(38\) | 0.712399i | 0.115566i | ||||||||
\(39\) | 13.0854 | 2.09534 | ||||||||
\(40\) | 4.50852 | + | 3.25961i | 0.712860 | + | 0.515389i | ||||
\(41\) | −0.108411 | −0.0169309 | −0.00846547 | − | 0.999964i | \(-0.502695\pi\) | ||||
−0.00846547 | + | 0.999964i | \(0.502695\pi\) | |||||||
\(42\) | − | 6.40096i | − | 0.987689i | ||||||
\(43\) | 3.35317i | 0.511354i | 0.966762 | + | 0.255677i | \(0.0822984\pi\) | ||||
−0.966762 | + | 0.255677i | \(0.917702\pi\) | |||||||
\(44\) | 1.49249 | 0.225001 | ||||||||
\(45\) | −10.5300 | + | 14.5645i | −1.56971 | + | 2.17115i | ||||
\(46\) | 2.23526 | 0.329571 | ||||||||
\(47\) | 7.06218i | 1.03013i | 0.857152 | + | 0.515063i | \(0.172231\pi\) | ||||
−0.857152 | + | 0.515063i | \(0.827769\pi\) | |||||||
\(48\) | − | 4.02824i | − | 0.581427i | ||||||
\(49\) | −0.314322 | −0.0449031 | ||||||||
\(50\) | 3.38249 | − | 1.11649i | 0.478356 | − | 0.157896i | ||||
\(51\) | −15.0738 | −2.11075 | ||||||||
\(52\) | 5.87844i | 0.815193i | ||||||||
\(53\) | 12.1616i | 1.67053i | 0.549847 | + | 0.835265i | \(0.314686\pi\) | ||||
−0.549847 | + | 0.835265i | \(0.685314\pi\) | |||||||
\(54\) | −11.9226 | −1.62246 | ||||||||
\(55\) | 1.31011 | − | 1.81207i | 0.176655 | − | 0.244340i | ||||
\(56\) | 6.72892 | 0.899189 | ||||||||
\(57\) | − | 3.32227i | − | 0.440045i | ||||||
\(58\) | 5.25228i | 0.689659i | ||||||||
\(59\) | −3.83960 | −0.499873 | −0.249937 | − | 0.968262i | \(-0.580410\pi\) | ||||
−0.249937 | + | 0.968262i | \(0.580410\pi\) | |||||||
\(60\) | −8.98508 | − | 6.49610i | −1.15997 | − | 0.838643i | ||||
\(61\) | −5.74344 | −0.735372 | −0.367686 | − | 0.929950i | \(-0.619850\pi\) | ||||
−0.367686 | + | 0.929950i | \(0.619850\pi\) | |||||||
\(62\) | − | 4.27991i | − | 0.543549i | ||||||
\(63\) | 21.7373i | 2.73865i | ||||||||
\(64\) | −1.73532 | −0.216915 | ||||||||
\(65\) | 7.13720 | + | 5.16011i | 0.885260 | + | 0.640033i | ||||
\(66\) | 2.36678 | 0.291330 | ||||||||
\(67\) | 15.8539i | 1.93686i | 0.249288 | + | 0.968430i | \(0.419804\pi\) | ||||
−0.249288 | + | 0.968430i | \(0.580196\pi\) | |||||||
\(68\) | − | 6.77171i | − | 0.821190i | ||||||
\(69\) | −10.4241 | −1.25492 | ||||||||
\(70\) | 2.52416 | − | 3.49129i | 0.301695 | − | 0.417289i | ||||
\(71\) | −7.83511 | −0.929856 | −0.464928 | − | 0.885348i | \(-0.653920\pi\) | ||||
−0.464928 | + | 0.885348i | \(0.653920\pi\) | |||||||
\(72\) | − | 19.9976i | − | 2.35674i | ||||||
\(73\) | − | 11.6635i | − | 1.36511i | −0.730834 | − | 0.682556i | \(-0.760868\pi\) | ||
0.730834 | − | 0.682556i | \(-0.239132\pi\) | |||||||
\(74\) | 5.39175 | 0.626778 | ||||||||
\(75\) | −15.7742 | + | 5.20676i | −1.82145 | + | 0.601225i | ||||
\(76\) | 1.49249 | 0.171200 | ||||||||
\(77\) | − | 2.70450i | − | 0.308206i | ||||||
\(78\) | 9.32200i | 1.05551i | ||||||||
\(79\) | 12.0695 | 1.35792 | 0.678962 | − | 0.734174i | \(-0.262430\pi\) | ||||
0.678962 | + | 0.734174i | \(0.262430\pi\) | |||||||
\(80\) | 1.58850 | − | 2.19714i | 0.177600 | − | 0.245647i | ||||
\(81\) | 31.4885 | 3.49872 | ||||||||
\(82\) | − | 0.0772318i | − | 0.00852882i | ||||||
\(83\) | 11.0121i | 1.20874i | 0.796705 | + | 0.604368i | \(0.206575\pi\) | ||||
−0.796705 | + | 0.604368i | \(0.793425\pi\) | |||||||
\(84\) | −13.4101 | −1.46316 | ||||||||
\(85\) | −8.22174 | − | 5.94422i | −0.891773 | − | 0.644741i | ||||
\(86\) | −2.38880 | −0.257591 | ||||||||
\(87\) | − | 24.4940i | − | 2.62603i | ||||||
\(88\) | 2.48804i | 0.265226i | ||||||||
\(89\) | 7.90725 | 0.838167 | 0.419084 | − | 0.907948i | \(-0.362351\pi\) | ||||
0.419084 | + | 0.907948i | \(0.362351\pi\) | |||||||
\(90\) | −10.3757 | − | 7.50153i | −1.09370 | − | 0.790730i | ||||
\(91\) | 10.6522 | 1.11665 | ||||||||
\(92\) | − | 4.68291i | − | 0.488228i | ||||||
\(93\) | 19.9593i | 2.06969i | ||||||||
\(94\) | −5.03109 | −0.518917 | ||||||||
\(95\) | 1.31011 | − | 1.81207i | 0.134414 | − | 0.185915i | ||||
\(96\) | 19.4016 | 1.98017 | ||||||||
\(97\) | − | 19.3959i | − | 1.96936i | −0.174382 | − | 0.984678i | \(-0.555793\pi\) | ||
0.174382 | − | 0.984678i | \(-0.444207\pi\) | |||||||
\(98\) | − | 0.223922i | − | 0.0226196i | ||||||
\(99\) | −8.03747 | −0.807796 | ||||||||
\(100\) | −2.33907 | − | 7.08638i | −0.233907 | − | 0.708638i | ||||
\(101\) | 6.19426 | 0.616352 | 0.308176 | − | 0.951329i | \(-0.400281\pi\) | ||||
0.308176 | + | 0.951329i | \(0.400281\pi\) | |||||||
\(102\) | − | 10.7385i | − | 1.06327i | ||||||
\(103\) | − | 14.1287i | − | 1.39215i | −0.717971 | − | 0.696073i | \(-0.754929\pi\) | ||
0.717971 | − | 0.696073i | \(-0.245071\pi\) | |||||||
\(104\) | −9.79963 | −0.960932 | ||||||||
\(105\) | −11.7714 | + | 16.2816i | −1.14877 | + | 1.58892i | ||||
\(106\) | −8.66394 | −0.841516 | ||||||||
\(107\) | 1.62430i | 0.157027i | 0.996913 | + | 0.0785134i | \(0.0250173\pi\) | ||||
−0.996913 | + | 0.0785134i | \(0.974983\pi\) | |||||||
\(108\) | 24.9780i | 2.40351i | ||||||||
\(109\) | 17.0381 | 1.63196 | 0.815978 | − | 0.578083i | \(-0.196199\pi\) | ||||
0.815978 | + | 0.578083i | \(0.196199\pi\) | |||||||
\(110\) | 1.29092 | + | 0.933320i | 0.123084 | + | 0.0889885i | ||||
\(111\) | −25.1444 | −2.38660 | ||||||||
\(112\) | − | 3.27920i | − | 0.309855i | ||||||
\(113\) | − | 0.922301i | − | 0.0867627i | −0.999059 | − | 0.0433814i | \(-0.986187\pi\) | ||
0.999059 | − | 0.0433814i | \(-0.0138131\pi\) | |||||||
\(114\) | 2.36678 | 0.221669 | ||||||||
\(115\) | −5.68567 | − | 4.11067i | −0.530191 | − | 0.383322i | ||||
\(116\) | 11.0036 | 1.02166 | ||||||||
\(117\) | − | 31.6571i | − | 2.92670i | ||||||
\(118\) | − | 2.73533i | − | 0.251807i | ||||||
\(119\) | −12.2708 | −1.12487 | ||||||||
\(120\) | 10.8293 | − | 14.9785i | 0.988575 | − | 1.36735i | ||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | − | 4.09162i | − | 0.370437i | ||||||
\(123\) | 0.360170i | 0.0324754i | ||||||||
\(124\) | −8.96648 | −0.805214 | ||||||||
\(125\) | −10.6570 | − | 3.38050i | −0.953194 | − | 0.302361i | ||||
\(126\) | −15.4856 | −1.37957 | ||||||||
\(127\) | 0.743724i | 0.0659948i | 0.999455 | + | 0.0329974i | \(0.0105053\pi\) | ||||
−0.999455 | + | 0.0329974i | \(0.989495\pi\) | |||||||
\(128\) | 10.4435i | 0.923084i | ||||||||
\(129\) | 11.1401 | 0.980835 | ||||||||
\(130\) | −3.67605 | + | 5.08453i | −0.322411 | + | 0.445943i | ||||
\(131\) | −4.73616 | −0.413801 | −0.206900 | − | 0.978362i | \(-0.566338\pi\) | ||||
−0.206900 | + | 0.978362i | \(0.566338\pi\) | |||||||
\(132\) | − | 4.95845i | − | 0.431577i | ||||||
\(133\) | − | 2.70450i | − | 0.234510i | ||||||
\(134\) | −11.2943 | −0.975677 | ||||||||
\(135\) | 30.3266 | + | 21.9257i | 2.61009 | + | 1.88707i | ||||
\(136\) | 11.2887 | 0.968002 | ||||||||
\(137\) | 2.26917i | 0.193869i | 0.995291 | + | 0.0969343i | \(0.0309037\pi\) | ||||
−0.995291 | + | 0.0969343i | \(0.969096\pi\) | |||||||
\(138\) | − | 7.42614i | − | 0.632155i | ||||||
\(139\) | −3.51232 | −0.297911 | −0.148955 | − | 0.988844i | \(-0.547591\pi\) | ||||
−0.148955 | + | 0.988844i | \(0.547591\pi\) | |||||||
\(140\) | −7.31432 | − | 5.28817i | −0.618173 | − | 0.446932i | ||||
\(141\) | 23.4625 | 1.97590 | ||||||||
\(142\) | − | 5.58172i | − | 0.468407i | ||||||
\(143\) | 3.93869i | 0.329370i | ||||||||
\(144\) | −9.74541 | −0.812117 | ||||||||
\(145\) | 9.65901 | − | 13.3598i | 0.802137 | − | 1.10947i | ||||
\(146\) | 8.30907 | 0.687664 | ||||||||
\(147\) | 1.04426i | 0.0861292i | ||||||||
\(148\) | − | 11.2958i | − | 0.928510i | ||||||
\(149\) | 12.8508 | 1.05278 | 0.526390 | − | 0.850243i | \(-0.323545\pi\) | ||||
0.526390 | + | 0.850243i | \(0.323545\pi\) | |||||||
\(150\) | −3.70929 | − | 11.2375i | −0.302862 | − | 0.917541i | ||||
\(151\) | 11.8967 | 0.968139 | 0.484069 | − | 0.875030i | \(-0.339158\pi\) | ||||
0.484069 | + | 0.875030i | \(0.339158\pi\) | |||||||
\(152\) | 2.48804i | 0.201807i | ||||||||
\(153\) | 36.4676i | 2.94823i | ||||||||
\(154\) | 1.92668 | 0.155256 | ||||||||
\(155\) | −7.87079 | + | 10.8865i | −0.632197 | + | 0.874423i | ||||
\(156\) | 19.5298 | 1.56363 | ||||||||
\(157\) | 5.21525i | 0.416222i | 0.978105 | + | 0.208111i | \(0.0667315\pi\) | ||||
−0.978105 | + | 0.208111i | \(0.933268\pi\) | |||||||
\(158\) | 8.59828i | 0.684043i | ||||||||
\(159\) | 40.4042 | 3.20427 | ||||||||
\(160\) | 10.5823 | + | 7.65086i | 0.836603 | + | 0.604854i | ||||
\(161\) | −8.48579 | −0.668774 | ||||||||
\(162\) | 22.4323i | 1.76245i | ||||||||
\(163\) | − | 7.87829i | − | 0.617075i | −0.951212 | − | 0.308538i | \(-0.900160\pi\) | ||
0.951212 | − | 0.308538i | \(-0.0998396\pi\) | |||||||
\(164\) | −0.161802 | −0.0126346 | ||||||||
\(165\) | −6.02020 | − | 4.35253i | −0.468672 | − | 0.338844i | ||||
\(166\) | −7.84502 | −0.608891 | ||||||||
\(167\) | 17.4388i | 1.34945i | 0.738068 | + | 0.674726i | \(0.235738\pi\) | ||||
−0.738068 | + | 0.674726i | \(0.764262\pi\) | |||||||
\(168\) | − | 22.3553i | − | 1.72475i | ||||||
\(169\) | −2.51325 | −0.193327 | ||||||||
\(170\) | 4.23465 | − | 5.85715i | 0.324783 | − | 0.449223i | ||||
\(171\) | −8.03747 | −0.614640 | ||||||||
\(172\) | 5.00457i | 0.381595i | ||||||||
\(173\) | − | 13.7948i | − | 1.04880i | −0.851473 | − | 0.524399i | \(-0.824290\pi\) | ||
0.851473 | − | 0.524399i | \(-0.175710\pi\) | |||||||
\(174\) | 17.4495 | 1.32284 | ||||||||
\(175\) | −12.8410 | + | 4.23858i | −0.970692 | + | 0.320406i | ||||
\(176\) | 1.21250 | 0.0913954 | ||||||||
\(177\) | 12.7562i | 0.958813i | ||||||||
\(178\) | 5.63312i | 0.422220i | ||||||||
\(179\) | 5.68388 | 0.424833 | 0.212417 | − | 0.977179i | \(-0.431867\pi\) | ||||
0.212417 | + | 0.977179i | \(0.431867\pi\) | |||||||
\(180\) | −15.7158 | + | 21.7373i | −1.17139 | + | 1.62020i | ||||
\(181\) | −18.5723 | −1.38047 | −0.690234 | − | 0.723586i | \(-0.742493\pi\) | ||||
−0.690234 | + | 0.723586i | \(0.742493\pi\) | |||||||
\(182\) | 7.58860i | 0.562504i | ||||||||
\(183\) | 19.0812i | 1.41053i | ||||||||
\(184\) | 7.80662 | 0.575512 | ||||||||
\(185\) | −13.7146 | − | 9.91548i | −1.00832 | − | 0.729001i | ||||
\(186\) | −14.2190 | −1.04259 | ||||||||
\(187\) | − | 4.53720i | − | 0.331793i | ||||||
\(188\) | 10.5402i | 0.768725i | ||||||||
\(189\) | 45.2620 | 3.29233 | ||||||||
\(190\) | 1.29092 | + | 0.933320i | 0.0936532 | + | 0.0677101i | ||||
\(191\) | −3.63564 | −0.263066 | −0.131533 | − | 0.991312i | \(-0.541990\pi\) | ||||
−0.131533 | + | 0.991312i | \(0.541990\pi\) | |||||||
\(192\) | 5.76520i | 0.416067i | ||||||||
\(193\) | − | 18.8353i | − | 1.35579i | −0.735158 | − | 0.677896i | \(-0.762892\pi\) | ||
0.735158 | − | 0.677896i | \(-0.237108\pi\) | |||||||
\(194\) | 13.8176 | 0.992047 | ||||||||
\(195\) | 17.1433 | − | 23.7117i | 1.22765 | − | 1.69803i | ||||
\(196\) | −0.469122 | −0.0335087 | ||||||||
\(197\) | − | 0.0627922i | − | 0.00447376i | −0.999997 | − | 0.00223688i | \(-0.999288\pi\) | ||
0.999997 | − | 0.00223688i | \(-0.000712021\pi\) | |||||||
\(198\) | − | 5.72588i | − | 0.406921i | ||||||
\(199\) | −6.95332 | −0.492908 | −0.246454 | − | 0.969155i | \(-0.579265\pi\) | ||||
−0.246454 | + | 0.969155i | \(0.579265\pi\) | |||||||
\(200\) | 11.8133 | − | 3.89934i | 0.835327 | − | 0.275725i | ||||
\(201\) | 52.6708 | 3.71511 | ||||||||
\(202\) | 4.41278i | 0.310482i | ||||||||
\(203\) | − | 19.9394i | − | 1.39947i | ||||||
\(204\) | −22.4974 | −1.57514 | ||||||||
\(205\) | −0.142030 | + | 0.196449i | −0.00991981 | + | 0.0137206i | ||||
\(206\) | 10.0653 | 0.701282 | ||||||||
\(207\) | 25.2188i | 1.75283i | ||||||||
\(208\) | 4.77565i | 0.331132i | ||||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | −11.5990 | − | 8.38595i | −0.800408 | − | 0.578685i | ||||
\(211\) | 19.3587 | 1.33271 | 0.666353 | − | 0.745637i | \(-0.267855\pi\) | ||||
0.666353 | + | 0.745637i | \(0.267855\pi\) | |||||||
\(212\) | 18.1511i | 1.24662i | ||||||||
\(213\) | 26.0303i | 1.78357i | ||||||||
\(214\) | −1.15715 | −0.0791009 | ||||||||
\(215\) | 6.07620 | + | 4.39302i | 0.414394 | + | 0.299602i | ||||
\(216\) | −41.6394 | −2.83321 | ||||||||
\(217\) | 16.2479i | 1.10298i | ||||||||
\(218\) | 12.1379i | 0.822084i | ||||||||
\(219\) | −38.7493 | −2.61844 | ||||||||
\(220\) | 1.95532 | − | 2.70450i | 0.131828 | − | 0.182337i | ||||
\(221\) | 17.8706 | 1.20211 | ||||||||
\(222\) | − | 17.9128i | − | 1.20223i | ||||||
\(223\) | 3.97309i | 0.266057i | 0.991112 | + | 0.133029i | \(0.0424703\pi\) | ||||
−0.991112 | + | 0.133029i | \(0.957530\pi\) | |||||||
\(224\) | 15.7939 | 1.05528 | ||||||||
\(225\) | 12.5966 | + | 38.1621i | 0.839771 | + | 2.54414i | ||||
\(226\) | 0.657046 | 0.0437060 | ||||||||
\(227\) | − | 3.15396i | − | 0.209336i | −0.994507 | − | 0.104668i | \(-0.966622\pi\) | ||
0.994507 | − | 0.104668i | \(-0.0333779\pi\) | |||||||
\(228\) | − | 4.95845i | − | 0.328381i | ||||||
\(229\) | −0.468155 | −0.0309365 | −0.0154683 | − | 0.999880i | \(-0.504924\pi\) | ||||
−0.0154683 | + | 0.999880i | \(0.504924\pi\) | |||||||
\(230\) | 2.92844 | − | 4.05046i | 0.193095 | − | 0.267080i | ||||
\(231\) | −8.98508 | −0.591175 | ||||||||
\(232\) | 18.3435i | 1.20431i | ||||||||
\(233\) | 15.5925i | 1.02150i | 0.859730 | + | 0.510749i | \(0.170632\pi\) | ||||
−0.859730 | + | 0.510749i | \(0.829368\pi\) | |||||||
\(234\) | 22.5524 | 1.47430 | ||||||||
\(235\) | 12.7972 | + | 9.25223i | 0.834798 | + | 0.603549i | ||||
\(236\) | −5.73056 | −0.373027 | ||||||||
\(237\) | − | 40.0981i | − | 2.60465i | ||||||
\(238\) | − | 8.74173i | − | 0.566642i | ||||||
\(239\) | −8.71766 | −0.563898 | −0.281949 | − | 0.959429i | \(-0.590981\pi\) | ||||
−0.281949 | + | 0.959429i | \(0.590981\pi\) | |||||||
\(240\) | −7.29948 | − | 5.27743i | −0.471179 | − | 0.340657i | ||||
\(241\) | −14.8860 | −0.958894 | −0.479447 | − | 0.877571i | \(-0.659163\pi\) | ||||
−0.479447 | + | 0.877571i | \(0.659163\pi\) | |||||||
\(242\) | 0.712399i | 0.0457947i | ||||||||
\(243\) | − | 54.4057i | − | 3.49013i | ||||||
\(244\) | −8.57201 | −0.548767 | ||||||||
\(245\) | −0.411796 | + | 0.569575i | −0.0263087 | + | 0.0363888i | ||||
\(246\) | −0.256585 | −0.0163592 | ||||||||
\(247\) | 3.93869i | 0.250613i | ||||||||
\(248\) | − | 14.9475i | − | 0.949168i | ||||||
\(249\) | 36.5852 | 2.31849 | ||||||||
\(250\) | 2.40826 | − | 7.59205i | 0.152312 | − | 0.480164i | ||||
\(251\) | 6.95702 | 0.439123 | 0.219562 | − | 0.975599i | \(-0.429537\pi\) | ||||
0.219562 | + | 0.975599i | \(0.429537\pi\) | |||||||
\(252\) | 32.4427i | 2.04370i | ||||||||
\(253\) | − | 3.13766i | − | 0.197263i | ||||||
\(254\) | −0.529828 | −0.0332443 | ||||||||
\(255\) | −19.7483 | + | 27.3148i | −1.23669 | + | 1.71052i | ||||
\(256\) | −10.9106 | −0.681911 | ||||||||
\(257\) | − | 17.2912i | − | 1.07859i | −0.842115 | − | 0.539297i | \(-0.818690\pi\) | ||
0.842115 | − | 0.539297i | \(-0.181310\pi\) | |||||||
\(258\) | 7.93623i | 0.494088i | ||||||||
\(259\) | −20.4689 | −1.27187 | ||||||||
\(260\) | 10.6522 | + | 7.70140i | 0.660620 | + | 0.477621i | ||||
\(261\) | −59.2576 | −3.66796 | ||||||||
\(262\) | − | 3.37404i | − | 0.208449i | ||||||
\(263\) | − | 8.88346i | − | 0.547778i | −0.961761 | − | 0.273889i | \(-0.911690\pi\) | ||
0.961761 | − | 0.273889i | \(-0.0883100\pi\) | |||||||
\(264\) | 8.26595 | 0.508734 | ||||||||
\(265\) | 22.0378 | + | 15.9331i | 1.35377 | + | 0.978761i | ||||
\(266\) | 1.92668 | 0.118132 | ||||||||
\(267\) | − | 26.2700i | − | 1.60770i | ||||||
\(268\) | 23.6617i | 1.44537i | ||||||||
\(269\) | 15.6372 | 0.953415 | 0.476707 | − | 0.879062i | \(-0.341830\pi\) | ||||
0.476707 | + | 0.879062i | \(0.341830\pi\) | |||||||
\(270\) | −15.6199 | + | 21.6046i | −0.950595 | + | 1.31481i | ||||
\(271\) | −6.18562 | −0.375750 | −0.187875 | − | 0.982193i | \(-0.560160\pi\) | ||||
−0.187875 | + | 0.982193i | \(0.560160\pi\) | |||||||
\(272\) | − | 5.50134i | − | 0.333568i | ||||||
\(273\) | − | 35.3894i | − | 2.14186i | ||||||
\(274\) | −1.61656 | −0.0976597 | ||||||||
\(275\) | −1.56723 | − | 4.74803i | −0.0945076 | − | 0.286317i | ||||
\(276\) | −15.5579 | −0.936475 | ||||||||
\(277\) | − | 13.5897i | − | 0.816524i | −0.912865 | − | 0.408262i | \(-0.866135\pi\) | ||
0.912865 | − | 0.408262i | \(-0.133865\pi\) | |||||||
\(278\) | − | 2.50217i | − | 0.150070i | ||||||
\(279\) | 48.2870 | 2.89087 | ||||||||
\(280\) | 8.81561 | − | 12.1933i | 0.526833 | − | 0.728689i | ||||
\(281\) | −9.70357 | −0.578866 | −0.289433 | − | 0.957198i | \(-0.593467\pi\) | ||||
−0.289433 | + | 0.957198i | \(0.593467\pi\) | |||||||
\(282\) | 16.7146i | 0.995342i | ||||||||
\(283\) | 1.54391i | 0.0917760i | 0.998947 | + | 0.0458880i | \(0.0146117\pi\) | ||||
−0.998947 | + | 0.0458880i | \(0.985388\pi\) | |||||||
\(284\) | −11.6938 | −0.693900 | ||||||||
\(285\) | −6.02020 | − | 4.35253i | −0.356606 | − | 0.257822i | ||||
\(286\) | −2.80592 | −0.165917 | ||||||||
\(287\) | 0.293197i | 0.0173069i | ||||||||
\(288\) | − | 46.9378i | − | 2.76583i | ||||||
\(289\) | −3.58614 | −0.210949 | ||||||||
\(290\) | 9.51753 | + | 6.88106i | 0.558889 | + | 0.404070i | ||||
\(291\) | −64.4384 | −3.77745 | ||||||||
\(292\) | − | 17.4077i | − | 1.01871i | ||||||
\(293\) | 22.2671i | 1.30086i | 0.759567 | + | 0.650430i | \(0.225411\pi\) | ||||
−0.759567 | + | 0.650430i | \(0.774589\pi\) | |||||||
\(294\) | −0.743930 | −0.0433869 | ||||||||
\(295\) | −5.03029 | + | 6.95764i | −0.292875 | + | 0.405090i | ||||
\(296\) | 18.8306 | 1.09451 | ||||||||
\(297\) | 16.7358i | 0.971111i | ||||||||
\(298\) | 9.15490i | 0.530329i | ||||||||
\(299\) | 12.3582 | 0.714696 | ||||||||
\(300\) | −23.5429 | + | 7.77103i | −1.35925 | + | 0.448661i | ||||
\(301\) | 9.06866 | 0.522709 | ||||||||
\(302\) | 8.47519i | 0.487692i | ||||||||
\(303\) | − | 20.5790i | − | 1.18223i | ||||||
\(304\) | 1.21250 | 0.0695415 | ||||||||
\(305\) | −7.52453 | + | 10.4075i | −0.430853 | + | 0.595934i | ||||
\(306\) | −25.9794 | −1.48515 | ||||||||
\(307\) | − | 10.2910i | − | 0.587340i | −0.955907 | − | 0.293670i | \(-0.905123\pi\) | ||
0.955907 | − | 0.293670i | \(-0.0948767\pi\) | |||||||
\(308\) | − | 4.03643i | − | 0.229997i | ||||||
\(309\) | −46.9394 | −2.67029 | ||||||||
\(310\) | −7.75551 | − | 5.60714i | −0.440483 | − | 0.318464i | ||||
\(311\) | 23.1134 | 1.31064 | 0.655320 | − | 0.755351i | \(-0.272534\pi\) | ||||
0.655320 | + | 0.755351i | \(0.272534\pi\) | |||||||
\(312\) | 32.5570i | 1.84318i | ||||||||
\(313\) | 8.71229i | 0.492448i | 0.969213 | + | 0.246224i | \(0.0791899\pi\) | ||||
−0.969213 | + | 0.246224i | \(0.920810\pi\) | |||||||
\(314\) | −3.71533 | −0.209668 | ||||||||
\(315\) | 39.3897 | + | 28.4783i | 2.21936 | + | 1.60457i | ||||
\(316\) | 18.0136 | 1.01334 | ||||||||
\(317\) | 18.3723i | 1.03189i | 0.856621 | + | 0.515946i | \(0.172560\pi\) | ||||
−0.856621 | + | 0.515946i | \(0.827440\pi\) | |||||||
\(318\) | 28.7839i | 1.61412i | ||||||||
\(319\) | 7.37268 | 0.412791 | ||||||||
\(320\) | −2.27346 | + | 3.14453i | −0.127090 | + | 0.175785i | ||||
\(321\) | 5.39635 | 0.301195 | ||||||||
\(322\) | − | 6.04527i | − | 0.336889i | ||||||
\(323\) | − | 4.53720i | − | 0.252456i | ||||||
\(324\) | 46.9962 | 2.61090 | ||||||||
\(325\) | 18.7010 | − | 6.17283i | 1.03734 | − | 0.342407i | ||||
\(326\) | 5.61248 | 0.310847 | ||||||||
\(327\) | − | 56.6052i | − | 3.13027i | ||||||
\(328\) | − | 0.269731i | − | 0.0148934i | ||||||
\(329\) | 19.0997 | 1.05300 | ||||||||
\(330\) | 3.10074 | − | 4.28878i | 0.170690 | − | 0.236090i | ||||
\(331\) | −4.86106 | −0.267188 | −0.133594 | − | 0.991036i | \(-0.542652\pi\) | ||||
−0.133594 | + | 0.991036i | \(0.542652\pi\) | |||||||
\(332\) | 16.4355i | 0.902013i | ||||||||
\(333\) | 60.8311i | 3.33352i | ||||||||
\(334\) | −12.4234 | −0.679775 | ||||||||
\(335\) | 28.7284 | + | 20.7703i | 1.56960 | + | 1.13480i | ||||
\(336\) | −10.8944 | −0.594337 | ||||||||
\(337\) | 17.0842i | 0.930634i | 0.885144 | + | 0.465317i | \(0.154060\pi\) | ||||
−0.885144 | + | 0.465317i | \(0.845940\pi\) | |||||||
\(338\) | − | 1.79044i | − | 0.0973870i | ||||||
\(339\) | −3.06413 | −0.166421 | ||||||||
\(340\) | −12.2708 | − | 8.87168i | −0.665480 | − | 0.481134i | ||||
\(341\) | −6.00774 | −0.325337 | ||||||||
\(342\) | − | 5.72588i | − | 0.309620i | ||||||
\(343\) | − | 18.0814i | − | 0.976305i | ||||||
\(344\) | −8.34285 | −0.449816 | ||||||||
\(345\) | −13.6567 | + | 18.8893i | −0.735255 | + | 1.01697i | ||||
\(346\) | 9.82738 | 0.528323 | ||||||||
\(347\) | 18.9161i | 1.01547i | 0.861513 | + | 0.507736i | \(0.169517\pi\) | ||||
−0.861513 | + | 0.507736i | \(0.830483\pi\) | |||||||
\(348\) | − | 36.5570i | − | 1.95966i | ||||||
\(349\) | −27.7295 | −1.48433 | −0.742163 | − | 0.670219i | \(-0.766200\pi\) | ||||
−0.742163 | + | 0.670219i | \(0.766200\pi\) | |||||||
\(350\) | −3.01956 | − | 9.14795i | −0.161402 | − | 0.488978i | ||||
\(351\) | −65.9171 | −3.51840 | ||||||||
\(352\) | 5.83987i | 0.311266i | ||||||||
\(353\) | − | 5.23456i | − | 0.278607i | −0.990250 | − | 0.139304i | \(-0.955514\pi\) | ||
0.990250 | − | 0.139304i | \(-0.0444864\pi\) | |||||||
\(354\) | −9.08748 | −0.482994 | ||||||||
\(355\) | −10.2648 | + | 14.1978i | −0.544801 | + | 0.753541i | ||||
\(356\) | 11.8015 | 0.625477 | ||||||||
\(357\) | 40.7670i | 2.15762i | ||||||||
\(358\) | 4.04919i | 0.214006i | ||||||||
\(359\) | −5.96494 | −0.314818 | −0.157409 | − | 0.987534i | \(-0.550314\pi\) | ||||
−0.157409 | + | 0.987534i | \(0.550314\pi\) | |||||||
\(360\) | −36.2371 | − | 26.1990i | −1.90986 | − | 1.38081i | ||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | − | 13.2309i | − | 0.695400i | ||||||
\(363\) | − | 3.32227i | − | 0.174374i | ||||||
\(364\) | 15.8983 | 0.833295 | ||||||||
\(365\) | −21.1352 | − | 15.2805i | −1.10627 | − | 0.799817i | ||||
\(366\) | −13.5934 | −0.710541 | ||||||||
\(367\) | 5.90016i | 0.307986i | 0.988072 | + | 0.153993i | \(0.0492133\pi\) | ||||
−0.988072 | + | 0.153993i | \(0.950787\pi\) | |||||||
\(368\) | − | 3.80440i | − | 0.198318i | ||||||
\(369\) | 0.871349 | 0.0453606 | ||||||||
\(370\) | 7.06378 | − | 9.77025i | 0.367228 | − | 0.507931i | ||||
\(371\) | 32.8912 | 1.70762 | ||||||||
\(372\) | 29.7891i | 1.54449i | ||||||||
\(373\) | 18.6800i | 0.967215i | 0.875285 | + | 0.483608i | \(0.160674\pi\) | ||||
−0.875285 | + | 0.483608i | \(0.839326\pi\) | |||||||
\(374\) | 3.23229 | 0.167138 | ||||||||
\(375\) | −11.2309 | + | 35.4055i | −0.579962 | + | 1.82833i | ||||
\(376\) | −17.5710 | −0.906156 | ||||||||
\(377\) | 29.0387i | 1.49557i | ||||||||
\(378\) | 32.2446i | 1.65848i | ||||||||
\(379\) | −13.2052 | −0.678306 | −0.339153 | − | 0.940731i | \(-0.610140\pi\) | ||||
−0.339153 | + | 0.940731i | \(0.610140\pi\) | |||||||
\(380\) | 1.95532 | − | 2.70450i | 0.100306 | − | 0.138738i | ||||
\(381\) | 2.47085 | 0.126585 | ||||||||
\(382\) | − | 2.59002i | − | 0.132517i | ||||||
\(383\) | 11.3980i | 0.582411i | 0.956661 | + | 0.291205i | \(0.0940563\pi\) | ||||
−0.956661 | + | 0.291205i | \(0.905944\pi\) | |||||||
\(384\) | 34.6961 | 1.77058 | ||||||||
\(385\) | −4.90076 | − | 3.54319i | −0.249766 | − | 0.180578i | ||||
\(386\) | 13.4182 | 0.682969 | ||||||||
\(387\) | − | 26.9510i | − | 1.37000i | ||||||
\(388\) | − | 28.9482i | − | 1.46962i | ||||||
\(389\) | −4.12316 | −0.209052 | −0.104526 | − | 0.994522i | \(-0.533333\pi\) | ||||
−0.104526 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(390\) | 16.8922 | + | 12.2128i | 0.855368 | + | 0.618421i | ||||
\(391\) | −14.2362 | −0.719953 | ||||||||
\(392\) | − | 0.782047i | − | 0.0394993i | ||||||
\(393\) | 15.7348i | 0.793716i | ||||||||
\(394\) | 0.0447330 | 0.00225362 | ||||||||
\(395\) | 15.8123 | − | 21.8708i | 0.795605 | − | 1.10044i | ||||
\(396\) | −11.9958 | −0.602813 | ||||||||
\(397\) | 20.5811i | 1.03293i | 0.856307 | + | 0.516467i | \(0.172753\pi\) | ||||
−0.856307 | + | 0.516467i | \(0.827247\pi\) | |||||||
\(398\) | − | 4.95354i | − | 0.248298i | ||||||
\(399\) | −8.98508 | −0.449816 | ||||||||
\(400\) | −1.90026 | − | 5.75697i | −0.0950131 | − | 0.287849i | ||||
\(401\) | 11.5597 | 0.577262 | 0.288631 | − | 0.957440i | \(-0.406800\pi\) | ||||
0.288631 | + | 0.957440i | \(0.406800\pi\) | |||||||
\(402\) | 37.5226i | 1.87146i | ||||||||
\(403\) | − | 23.6626i | − | 1.17872i | ||||||
\(404\) | 9.24486 | 0.459949 | ||||||||
\(405\) | 41.2533 | − | 57.0595i | 2.04989 | − | 2.83531i | ||||
\(406\) | 14.2048 | 0.704973 | ||||||||
\(407\) | − | 7.56844i | − | 0.375154i | ||||||
\(408\) | − | 37.5042i | − | 1.85674i | ||||||
\(409\) | 14.8227 | 0.732935 | 0.366468 | − | 0.930431i | \(-0.380567\pi\) | ||||
0.366468 | + | 0.930431i | \(0.380567\pi\) | |||||||
\(410\) | −0.139950 | − | 0.101182i | −0.00691162 | − | 0.00499702i | ||||
\(411\) | 7.53880 | 0.371862 | ||||||||
\(412\) | − | 21.0870i | − | 1.03888i | ||||||
\(413\) | 10.3842i | 0.510973i | ||||||||
\(414\) | −17.9658 | −0.882973 | ||||||||
\(415\) | 19.9548 | + | 14.4271i | 0.979542 | + | 0.708197i | ||||
\(416\) | −23.0014 | −1.12774 | ||||||||
\(417\) | 11.6689i | 0.571426i | ||||||||
\(418\) | 0.712399i | 0.0348446i | ||||||||
\(419\) | −4.58368 | −0.223927 | −0.111964 | − | 0.993712i | \(-0.535714\pi\) | ||||
−0.111964 | + | 0.993712i | \(0.535714\pi\) | |||||||
\(420\) | −17.5687 | + | 24.3001i | −0.857265 | + | 1.18573i | ||||
\(421\) | −5.07417 | −0.247300 | −0.123650 | − | 0.992326i | \(-0.539460\pi\) | ||||
−0.123650 | + | 0.992326i | \(0.539460\pi\) | |||||||
\(422\) | 13.7911i | 0.671340i | ||||||||
\(423\) | − | 56.7621i | − | 2.75987i | ||||||
\(424\) | −30.2587 | −1.46949 | ||||||||
\(425\) | −21.5427 | + | 7.11083i | −1.04498 | + | 0.344926i | ||||
\(426\) | −18.5440 | −0.898458 | ||||||||
\(427\) | 15.5331i | 0.751701i | ||||||||
\(428\) | 2.42424i | 0.117180i | ||||||||
\(429\) | 13.0854 | 0.631768 | ||||||||
\(430\) | −3.12958 | + | 4.32868i | −0.150922 | + | 0.208747i | ||||
\(431\) | −27.5096 | −1.32509 | −0.662546 | − | 0.749021i | \(-0.730524\pi\) | ||||
−0.662546 | + | 0.749021i | \(0.730524\pi\) | |||||||
\(432\) | 20.2921i | 0.976306i | ||||||||
\(433\) | − | 13.1720i | − | 0.633007i | −0.948591 | − | 0.316503i | \(-0.897491\pi\) | ||
0.948591 | − | 0.316503i | \(-0.102509\pi\) | |||||||
\(434\) | −11.5750 | −0.555618 | ||||||||
\(435\) | −44.3850 | − | 32.0898i | −2.12810 | − | 1.53859i | ||||
\(436\) | 25.4292 | 1.21784 | ||||||||
\(437\) | − | 3.13766i | − | 0.150094i | ||||||
\(438\) | − | 27.6050i | − | 1.31902i | ||||||
\(439\) | 12.4523 | 0.594317 | 0.297159 | − | 0.954828i | \(-0.403961\pi\) | ||||
0.297159 | + | 0.954828i | \(0.403961\pi\) | |||||||
\(440\) | 4.50852 | + | 3.25961i | 0.214935 | + | 0.155396i | ||||
\(441\) | 2.52635 | 0.120302 | ||||||||
\(442\) | 12.7310i | 0.605551i | ||||||||
\(443\) | − | 17.1036i | − | 0.812617i | −0.913736 | − | 0.406309i | \(-0.866816\pi\) | ||
0.913736 | − | 0.406309i | \(-0.133184\pi\) | |||||||
\(444\) | −37.5277 | −1.78099 | ||||||||
\(445\) | 10.3594 | − | 14.3285i | 0.491081 | − | 0.679238i | ||||
\(446\) | −2.83042 | −0.134024 | ||||||||
\(447\) | − | 42.6938i | − | 2.01935i | ||||||
\(448\) | 4.69317i | 0.221732i | ||||||||
\(449\) | −1.69279 | −0.0798876 | −0.0399438 | − | 0.999202i | \(-0.512718\pi\) | ||||
−0.0399438 | + | 0.999202i | \(0.512718\pi\) | |||||||
\(450\) | −27.1867 | + | 8.97377i | −1.28159 | + | 0.423028i | ||||
\(451\) | −0.108411 | −0.00510487 | ||||||||
\(452\) | − | 1.37652i | − | 0.0647462i | ||||||
\(453\) | − | 39.5240i | − | 1.85700i | ||||||
\(454\) | 2.24688 | 0.105451 | ||||||||
\(455\) | 13.9555 | − | 19.3025i | 0.654245 | − | 0.904917i | ||||
\(456\) | 8.26595 | 0.387089 | ||||||||
\(457\) | − | 16.2265i | − | 0.759044i | −0.925183 | − | 0.379522i | \(-0.876088\pi\) | ||
0.925183 | − | 0.379522i | \(-0.123912\pi\) | |||||||
\(458\) | − | 0.333513i | − | 0.0155840i | ||||||
\(459\) | 75.9337 | 3.54428 | ||||||||
\(460\) | −8.48579 | − | 6.13513i | −0.395652 | − | 0.286052i | ||||
\(461\) | 13.0705 | 0.608756 | 0.304378 | − | 0.952551i | \(-0.401551\pi\) | ||||
0.304378 | + | 0.952551i | \(0.401551\pi\) | |||||||
\(462\) | − | 6.40096i | − | 0.297799i | ||||||
\(463\) | − | 36.5814i | − | 1.70008i | −0.526718 | − | 0.850040i | \(-0.676578\pi\) | ||
0.526718 | − | 0.850040i | \(-0.323422\pi\) | |||||||
\(464\) | 8.93935 | 0.414999 | ||||||||
\(465\) | 36.1678 | + | 26.1489i | 1.67724 | + | 1.21263i | ||||
\(466\) | −11.1081 | −0.514572 | ||||||||
\(467\) | 5.78204i | 0.267561i | 0.991011 | + | 0.133781i | \(0.0427117\pi\) | ||||
−0.991011 | + | 0.133781i | \(0.957288\pi\) | |||||||
\(468\) | − | 47.2478i | − | 2.18403i | ||||||
\(469\) | 42.8768 | 1.97987 | ||||||||
\(470\) | −6.59128 | + | 9.11671i | −0.304033 | + | 0.420523i | ||||
\(471\) | 17.3264 | 0.798360 | ||||||||
\(472\) | − | 9.55309i | − | 0.439717i | ||||||
\(473\) | 3.35317i | 0.154179i | ||||||||
\(474\) | 28.5658 | 1.31207 | ||||||||
\(475\) | −1.56723 | − | 4.74803i | −0.0719095 | − | 0.217855i | ||||
\(476\) | −18.3141 | −0.839425 | ||||||||
\(477\) | − | 97.7488i | − | 4.47561i | ||||||
\(478\) | − | 6.21045i | − | 0.284059i | ||||||
\(479\) | −4.97976 | −0.227531 | −0.113765 | − | 0.993508i | \(-0.536291\pi\) | ||||
−0.113765 | + | 0.993508i | \(0.536291\pi\) | |||||||
\(480\) | 25.4182 | − | 35.1572i | 1.16018 | − | 1.60470i | ||||
\(481\) | 29.8097 | 1.35921 | ||||||||
\(482\) | − | 10.6048i | − | 0.483035i | ||||||
\(483\) | 28.1921i | 1.28278i | ||||||||
\(484\) | 1.49249 | 0.0678404 | ||||||||
\(485\) | −35.1468 | − | 25.4107i | −1.59594 | − | 1.15384i | ||||
\(486\) | 38.7585 | 1.75812 | ||||||||
\(487\) | 15.2998i | 0.693302i | 0.937994 | + | 0.346651i | \(0.112681\pi\) | ||||
−0.937994 | + | 0.346651i | \(0.887319\pi\) | |||||||
\(488\) | − | 14.2899i | − | 0.646874i | ||||||
\(489\) | −26.1738 | −1.18362 | ||||||||
\(490\) | −0.405764 | − | 0.293363i | −0.0183306 | − | 0.0132528i | ||||
\(491\) | 11.6615 | 0.526275 | 0.263138 | − | 0.964758i | \(-0.415243\pi\) | ||||
0.263138 | + | 0.964758i | \(0.415243\pi\) | |||||||
\(492\) | 0.537549i | 0.0242346i | ||||||||
\(493\) | − | 33.4513i | − | 1.50657i | ||||||
\(494\) | −2.80592 | −0.126244 | ||||||||
\(495\) | −10.5300 | + | 14.5645i | −0.473286 | + | 0.654625i | ||||
\(496\) | −7.28437 | −0.327078 | ||||||||
\(497\) | 21.1900i | 0.950504i | ||||||||
\(498\) | 26.0633i | 1.16792i | ||||||||
\(499\) | −21.2628 | −0.951855 | −0.475928 | − | 0.879484i | \(-0.657888\pi\) | ||||
−0.475928 | + | 0.879484i | \(0.657888\pi\) | |||||||
\(500\) | −15.9055 | − | 5.04535i | −0.711315 | − | 0.225635i | ||||
\(501\) | 57.9362 | 2.58840 | ||||||||
\(502\) | 4.95617i | 0.221205i | ||||||||
\(503\) | 26.1347i | 1.16529i | 0.812727 | + | 0.582645i | \(0.197982\pi\) | ||||
−0.812727 | + | 0.582645i | \(0.802018\pi\) | |||||||
\(504\) | −54.0834 | −2.40907 | ||||||||
\(505\) | 8.11515 | − | 11.2245i | 0.361120 | − | 0.499482i | ||||
\(506\) | 2.23526 | 0.0993695 | ||||||||
\(507\) | 8.34970i | 0.370823i | ||||||||
\(508\) | 1.11000i | 0.0492482i | ||||||||
\(509\) | 24.9546 | 1.10609 | 0.553046 | − | 0.833151i | \(-0.313465\pi\) | ||||
0.553046 | + | 0.833151i | \(0.313465\pi\) | |||||||
\(510\) | −19.4590 | − | 14.0687i | −0.861661 | − | 0.622971i | ||||
\(511\) | −31.5440 | −1.39542 | ||||||||
\(512\) | 13.1143i | 0.579576i | ||||||||
\(513\) | 16.7358i | 0.738904i | ||||||||
\(514\) | 12.3182 | 0.543333 | ||||||||
\(515\) | −25.6023 | − | 18.5102i | −1.12817 | − | 0.815656i | ||||
\(516\) | 16.6265 | 0.731942 | ||||||||
\(517\) | 7.06218i | 0.310595i | ||||||||
\(518\) | − | 14.5820i | − | 0.640696i | ||||||
\(519\) | −45.8300 | −2.01171 | ||||||||
\(520\) | −12.8386 | + | 17.7577i | −0.563009 | + | 0.778725i | ||||
\(521\) | −25.5480 | −1.11928 | −0.559640 | − | 0.828736i | \(-0.689060\pi\) | ||||
−0.559640 | + | 0.828736i | \(0.689060\pi\) | |||||||
\(522\) | − | 42.2151i | − | 1.84770i | ||||||
\(523\) | 16.6070i | 0.726172i | 0.931756 | + | 0.363086i | \(0.118277\pi\) | ||||
−0.931756 | + | 0.363086i | \(0.881723\pi\) | |||||||
\(524\) | −7.06867 | −0.308796 | ||||||||
\(525\) | 14.0817 | + | 42.6614i | 0.614575 | + | 1.86190i | ||||
\(526\) | 6.32857 | 0.275939 | ||||||||
\(527\) | 27.2583i | 1.18739i | ||||||||
\(528\) | − | 4.02824i | − | 0.175307i | ||||||
\(529\) | 13.1551 | 0.571962 | ||||||||
\(530\) | −11.3507 | + | 15.6997i | −0.493043 | + | 0.681952i | ||||
\(531\) | 30.8607 | 1.33924 | ||||||||
\(532\) | − | 4.03643i | − | 0.175002i | ||||||
\(533\) | − | 0.426996i | − | 0.0184953i | ||||||
\(534\) | 18.7147 | 0.809865 | ||||||||
\(535\) | 2.94335 | + | 2.12801i | 0.127252 | + | 0.0920017i | ||||
\(536\) | −39.4451 | −1.70377 | ||||||||
\(537\) | − | 18.8834i | − | 0.814878i | ||||||
\(538\) | 11.1399i | 0.480275i | ||||||||
\(539\) | −0.314322 | −0.0135388 | ||||||||
\(540\) | 45.2620 | + | 32.7239i | 1.94777 | + | 1.40821i | ||||
\(541\) | 33.1242 | 1.42412 | 0.712060 | − | 0.702119i | \(-0.247762\pi\) | ||||
0.712060 | + | 0.702119i | \(0.247762\pi\) | |||||||
\(542\) | − | 4.40663i | − | 0.189281i | ||||||
\(543\) | 61.7022i | 2.64789i | ||||||||
\(544\) | 26.4966 | 1.13603 | ||||||||
\(545\) | 22.3218 | − | 30.8743i | 0.956160 | − | 1.32251i | ||||
\(546\) | 25.2114 | 1.07895 | ||||||||
\(547\) | 29.8988i | 1.27838i | 0.769049 | + | 0.639189i | \(0.220730\pi\) | ||||
−0.769049 | + | 0.639189i | \(0.779270\pi\) | |||||||
\(548\) | 3.38672i | 0.144673i | ||||||||
\(549\) | 46.1627 | 1.97017 | ||||||||
\(550\) | 3.38249 | − | 1.11649i | 0.144230 | − | 0.0476074i | ||||
\(551\) | 7.37268 | 0.314087 | ||||||||
\(552\) | − | 25.9357i | − | 1.10390i | ||||||
\(553\) | − | 32.6419i | − | 1.38808i | ||||||
\(554\) | 9.68126 | 0.411318 | ||||||||
\(555\) | −32.9419 | + | 45.5635i | −1.39831 | + | 1.93406i | ||||
\(556\) | −5.24209 | −0.222314 | ||||||||
\(557\) | 18.2206i | 0.772030i | 0.922493 | + | 0.386015i | \(0.126149\pi\) | ||||
−0.922493 | + | 0.386015i | \(0.873851\pi\) | |||||||
\(558\) | 34.3996i | 1.45625i | ||||||||
\(559\) | −13.2071 | −0.558601 | ||||||||
\(560\) | −5.94215 | − | 4.29611i | −0.251102 | − | 0.181544i | ||||
\(561\) | −15.0738 | −0.636415 | ||||||||
\(562\) | − | 6.91281i | − | 0.291599i | ||||||
\(563\) | 46.4723i | 1.95858i | 0.202473 | + | 0.979288i | \(0.435102\pi\) | ||||
−0.202473 | + | 0.979288i | \(0.564898\pi\) | |||||||
\(564\) | 35.0175 | 1.47450 | ||||||||
\(565\) | −1.67128 | − | 1.20831i | −0.0703112 | − | 0.0508342i | ||||
\(566\) | −1.09988 | −0.0462314 | ||||||||
\(567\) | − | 85.1606i | − | 3.57641i | ||||||
\(568\) | − | 19.4941i | − | 0.817954i | ||||||
\(569\) | −33.2411 | −1.39354 | −0.696770 | − | 0.717295i | \(-0.745380\pi\) | ||||
−0.696770 | + | 0.717295i | \(0.745380\pi\) | |||||||
\(570\) | 3.10074 | − | 4.28878i | 0.129876 | − | 0.179637i | ||||
\(571\) | −25.3387 | −1.06039 | −0.530196 | − | 0.847875i | \(-0.677882\pi\) | ||||
−0.530196 | + | 0.847875i | \(0.677882\pi\) | |||||||
\(572\) | 5.87844i | 0.245790i | ||||||||
\(573\) | 12.0786i | 0.504589i | ||||||||
\(574\) | −0.208873 | −0.00871820 | ||||||||
\(575\) | −14.8977 | + | 4.91743i | −0.621276 | + | 0.205071i | ||||
\(576\) | 13.9476 | 0.581149 | ||||||||
\(577\) | − | 2.07211i | − | 0.0862632i | −0.999069 | − | 0.0431316i | \(-0.986267\pi\) | ||
0.999069 | − | 0.0431316i | \(-0.0137335\pi\) | |||||||
\(578\) | − | 2.55476i | − | 0.106264i | ||||||
\(579\) | −62.5758 | −2.60056 | ||||||||
\(580\) | 14.4160 | − | 19.9394i | 0.598590 | − | 0.827939i | ||||
\(581\) | 29.7823 | 1.23558 | ||||||||
\(582\) | − | 45.9058i | − | 1.90286i | ||||||
\(583\) | 12.1616i | 0.503684i | ||||||||
\(584\) | 29.0193 | 1.20083 | ||||||||
\(585\) | −57.3650 | − | 41.4742i | −2.37175 | − | 1.71475i | ||||
\(586\) | −15.8631 | −0.655297 | ||||||||
\(587\) | − | 8.27824i | − | 0.341679i | −0.985299 | − | 0.170840i | \(-0.945352\pi\) | ||
0.985299 | − | 0.170840i | \(-0.0546480\pi\) | |||||||
\(588\) | 1.55855i | 0.0642734i | ||||||||
\(589\) | −6.00774 | −0.247545 | ||||||||
\(590\) | −4.95661 | − | 3.58357i | −0.204061 | − | 0.147533i | ||||
\(591\) | −0.208612 | −0.00858117 | ||||||||
\(592\) | − | 9.17672i | − | 0.377161i | ||||||
\(593\) | 12.6945i | 0.521301i | 0.965433 | + | 0.260651i | \(0.0839371\pi\) | ||||
−0.965433 | + | 0.260651i | \(0.916063\pi\) | |||||||
\(594\) | −11.9226 | −0.489189 | ||||||||
\(595\) | −16.0761 | + | 22.2357i | −0.659058 | + | 0.911574i | ||||
\(596\) | 19.1797 | 0.785631 | ||||||||
\(597\) | 23.1008i | 0.945453i | ||||||||
\(598\) | 8.80400i | 0.360022i | ||||||||
\(599\) | 44.5906 | 1.82192 | 0.910962 | − | 0.412491i | \(-0.135341\pi\) | ||||
0.910962 | + | 0.412491i | \(0.135341\pi\) | |||||||
\(600\) | −12.9546 | − | 39.2470i | −0.528871 | − | 1.60225i | ||||
\(601\) | 48.0310 | 1.95922 | 0.979612 | − | 0.200900i | \(-0.0643865\pi\) | ||||
0.979612 | + | 0.200900i | \(0.0643865\pi\) | |||||||
\(602\) | 6.46050i | 0.263310i | ||||||||
\(603\) | − | 127.425i | − | 5.18915i | ||||||
\(604\) | 17.7557 | 0.722468 | ||||||||
\(605\) | 1.31011 | − | 1.81207i | 0.0532635 | − | 0.0736713i | ||||
\(606\) | 14.6604 | 0.595540 | ||||||||
\(607\) | 4.19205i | 0.170150i | 0.996375 | + | 0.0850751i | \(0.0271130\pi\) | ||||
−0.996375 | + | 0.0850751i | \(0.972887\pi\) | |||||||
\(608\) | 5.83987i | 0.236838i | ||||||||
\(609\) | −66.2440 | −2.68434 | ||||||||
\(610\) | −7.41431 | − | 5.36046i | −0.300197 | − | 0.217039i | ||||
\(611\) | −27.8157 | −1.12530 | ||||||||
\(612\) | 54.4274i | 2.20010i | ||||||||
\(613\) | − | 33.7644i | − | 1.36373i | −0.731477 | − | 0.681867i | \(-0.761168\pi\) | ||
0.731477 | − | 0.681867i | \(-0.238832\pi\) | |||||||
\(614\) | 7.33132 | 0.295868 | ||||||||
\(615\) | 0.652655 | + | 0.471862i | 0.0263176 | + | 0.0190273i | ||||
\(616\) | 6.72892 | 0.271116 | ||||||||
\(617\) | − | 4.33391i | − | 0.174477i | −0.996187 | − | 0.0872383i | \(-0.972196\pi\) | ||
0.996187 | − | 0.0872383i | \(-0.0278041\pi\) | |||||||
\(618\) | − | 33.4396i | − | 1.34514i | ||||||
\(619\) | −34.8040 | −1.39889 | −0.699445 | − | 0.714686i | \(-0.746570\pi\) | ||||
−0.699445 | + | 0.714686i | \(0.746570\pi\) | |||||||
\(620\) | −11.7471 | + | 16.2479i | −0.471773 | + | 0.652533i | ||||
\(621\) | 52.5112 | 2.10720 | ||||||||
\(622\) | 16.4660i | 0.660225i | ||||||||
\(623\) | − | 21.3852i | − | 0.856779i | ||||||
\(624\) | 15.8660 | 0.635148 | ||||||||
\(625\) | −20.0876 | + | 14.8825i | −0.803503 | + | 0.595301i | ||||
\(626\) | −6.20663 | −0.248067 | ||||||||
\(627\) | − | 3.32227i | − | 0.132679i | ||||||
\(628\) | 7.78369i | 0.310603i | ||||||||
\(629\) | −34.3395 | −1.36921 | ||||||||
\(630\) | −20.2879 | + | 28.0611i | −0.808288 | + | 1.11798i | ||||
\(631\) | −15.6712 | −0.623862 | −0.311931 | − | 0.950105i | \(-0.600976\pi\) | ||||
−0.311931 | + | 0.950105i | \(0.600976\pi\) | |||||||
\(632\) | 30.0294i | 1.19451i | ||||||||
\(633\) | − | 64.3147i | − | 2.55628i | ||||||
\(634\) | −13.0884 | −0.519808 | ||||||||
\(635\) | 1.34768 | + | 0.974359i | 0.0534812 | + | 0.0386662i | ||||
\(636\) | 60.3029 | 2.39116 | ||||||||
\(637\) | − | 1.23802i | − | 0.0490520i | ||||||
\(638\) | 5.25228i | 0.207940i | ||||||||
\(639\) | 62.9744 | 2.49123 | ||||||||
\(640\) | 18.9244 | + | 13.6821i | 0.748053 | + | 0.540833i | ||||
\(641\) | −41.6116 | −1.64356 | −0.821780 | − | 0.569805i | \(-0.807019\pi\) | ||||
−0.821780 | + | 0.569805i | \(0.807019\pi\) | |||||||
\(642\) | 3.84435i | 0.151724i | ||||||||
\(643\) | − | 38.0923i | − | 1.50221i | −0.660180 | − | 0.751107i | \(-0.729520\pi\) | ||
0.660180 | − | 0.751107i | \(-0.270480\pi\) | |||||||
\(644\) | −12.6649 | −0.499069 | ||||||||
\(645\) | 14.5948 | − | 20.1868i | 0.574670 | − | 0.794854i | ||||
\(646\) | 3.23229 | 0.127173 | ||||||||
\(647\) | 10.3871i | 0.408359i | 0.978934 | + | 0.204179i | \(0.0654526\pi\) | ||||
−0.978934 | + | 0.204179i | \(0.934547\pi\) | |||||||
\(648\) | 78.3447i | 3.07767i | ||||||||
\(649\) | −3.83960 | −0.150717 | ||||||||
\(650\) | 4.39752 | + | 13.3226i | 0.172485 | + | 0.522554i | ||||
\(651\) | 53.9800 | 2.11564 | ||||||||
\(652\) | − | 11.7583i | − | 0.460489i | ||||||
\(653\) | 38.8944i | 1.52205i | 0.648720 | + | 0.761027i | \(0.275305\pi\) | ||||
−0.648720 | + | 0.761027i | \(0.724695\pi\) | |||||||
\(654\) | 40.3255 | 1.57685 | ||||||||
\(655\) | −6.20489 | + | 8.58228i | −0.242445 | + | 0.335338i | ||||
\(656\) | −0.131448 | −0.00513218 | ||||||||
\(657\) | 93.7451i | 3.65735i | ||||||||
\(658\) | 13.6066i | 0.530440i | ||||||||
\(659\) | −15.3578 | −0.598253 | −0.299127 | − | 0.954213i | \(-0.596695\pi\) | ||||
−0.299127 | + | 0.954213i | \(0.596695\pi\) | |||||||
\(660\) | −8.98508 | − | 6.49610i | −0.349744 | − | 0.252860i | ||||
\(661\) | −0.608689 | −0.0236753 | −0.0118376 | − | 0.999930i | \(-0.503768\pi\) | ||||
−0.0118376 | + | 0.999930i | \(0.503768\pi\) | |||||||
\(662\) | − | 3.46301i | − | 0.134594i | ||||||
\(663\) | − | 59.3709i | − | 2.30577i | ||||||
\(664\) | −27.3986 | −1.06327 | ||||||||
\(665\) | −4.90076 | − | 3.54319i | −0.190043 | − | 0.137399i | ||||
\(666\) | −43.3360 | −1.67924 | ||||||||
\(667\) | − | 23.1329i | − | 0.895710i | ||||||
\(668\) | 26.0271i | 1.00702i | ||||||||
\(669\) | 13.1997 | 0.510328 | ||||||||
\(670\) | −14.7967 | + | 20.4661i | −0.571648 | + | 0.790674i | ||||
\(671\) | −5.74344 | −0.221723 | ||||||||
\(672\) | − | 52.4717i | − | 2.02414i | ||||||
\(673\) | 20.7131i | 0.798432i | 0.916857 | + | 0.399216i | \(0.130718\pi\) | ||||
−0.916857 | + | 0.399216i | \(0.869282\pi\) | |||||||
\(674\) | −12.1707 | −0.468799 | ||||||||
\(675\) | 79.4622 | − | 26.2289i | 3.05850 | − | 1.00955i | ||||
\(676\) | −3.75100 | −0.144269 | ||||||||
\(677\) | 18.6760i | 0.717776i | 0.933381 | + | 0.358888i | \(0.116844\pi\) | ||||
−0.933381 | + | 0.358888i | \(0.883156\pi\) | |||||||
\(678\) | − | 2.18288i | − | 0.0838331i | ||||||
\(679\) | −52.4562 | −2.01309 | ||||||||
\(680\) | 14.7895 | − | 20.4560i | 0.567151 | − | 0.784453i | ||||
\(681\) | −10.4783 | −0.401529 | ||||||||
\(682\) | − | 4.27991i | − | 0.163886i | ||||||
\(683\) | 44.6906i | 1.71004i | 0.518597 | + | 0.855019i | \(0.326455\pi\) | ||||
−0.518597 | + | 0.855019i | \(0.673545\pi\) | |||||||
\(684\) | −11.9958 | −0.458672 | ||||||||
\(685\) | 4.11191 | + | 2.97286i | 0.157108 | + | 0.113587i | ||||
\(686\) | 12.8812 | 0.491806 | ||||||||
\(687\) | 1.55534i | 0.0593397i | ||||||||
\(688\) | 4.06572i | 0.155004i | ||||||||
\(689\) | −47.9009 | −1.82488 | ||||||||
\(690\) | −13.4567 | − | 9.72905i | −0.512289 | − | 0.370379i | ||||
\(691\) | −33.2786 | −1.26598 | −0.632988 | − | 0.774162i | \(-0.718172\pi\) | ||||
−0.632988 | + | 0.774162i | \(0.718172\pi\) | |||||||
\(692\) | − | 20.5885i | − | 0.782659i | ||||||
\(693\) | 21.7373i | 0.825733i | ||||||||
\(694\) | −13.4758 | −0.511536 | ||||||||
\(695\) | −4.60152 | + | 6.36458i | −0.174545 | + | 0.241422i | ||||
\(696\) | 60.9422 | 2.31001 | ||||||||
\(697\) | 0.491881i | 0.0186313i | ||||||||
\(698\) | − | 19.7545i | − | 0.747717i | ||||||
\(699\) | 51.8025 | 1.95935 | ||||||||
\(700\) | −19.1651 | + | 6.32602i | −0.724373 | + | 0.239101i | ||||
\(701\) | 22.7497 | 0.859244 | 0.429622 | − | 0.903009i | \(-0.358647\pi\) | ||||
0.429622 | + | 0.903009i | \(0.358647\pi\) | |||||||
\(702\) | − | 46.9593i | − | 1.77236i | ||||||
\(703\) | − | 7.56844i | − | 0.285449i | ||||||
\(704\) | −1.73532 | −0.0654023 | ||||||||
\(705\) | 30.7384 | − | 42.5158i | 1.15767 | − | 1.60124i | ||||
\(706\) | 3.72909 | 0.140346 | ||||||||
\(707\) | − | 16.7524i | − | 0.630038i | ||||||
\(708\) | 19.0384i | 0.715509i | ||||||||
\(709\) | 11.0298 | 0.414233 | 0.207116 | − | 0.978316i | \(-0.433592\pi\) | ||||
0.207116 | + | 0.978316i | \(0.433592\pi\) | |||||||
\(710\) | −10.1145 | − | 7.31266i | −0.379590 | − | 0.274439i | ||||
\(711\) | −97.0081 | −3.63809 | ||||||||
\(712\) | 19.6736i | 0.737299i | ||||||||
\(713\) | 18.8502i | 0.705946i | ||||||||
\(714\) | −29.0424 | −1.08688 | ||||||||
\(715\) | 7.13720 | + | 5.16011i | 0.266916 | + | 0.192977i | ||||
\(716\) | 8.48313 | 0.317029 | ||||||||
\(717\) | 28.9624i | 1.08162i | ||||||||
\(718\) | − | 4.24942i | − | 0.158587i | ||||||
\(719\) | 8.03346 | 0.299598 | 0.149799 | − | 0.988717i | \(-0.452137\pi\) | ||||
0.149799 | + | 0.988717i | \(0.452137\pi\) | |||||||
\(720\) | −12.7675 | + | 17.6594i | −0.475818 | + | 0.658127i | ||||
\(721\) | −38.2112 | −1.42306 | ||||||||
\(722\) | 0.712399i | 0.0265127i | ||||||||
\(723\) | 49.4554i | 1.83927i | ||||||||
\(724\) | −27.7189 | −1.03017 | ||||||||
\(725\) | −11.5547 | − | 35.0057i | −0.429130 | − | 1.30008i | ||||
\(726\) | 2.36678 | 0.0878394 | ||||||||
\(727\) | 25.2120i | 0.935060i | 0.883977 | + | 0.467530i | \(0.154856\pi\) | ||||
−0.883977 | + | 0.467530i | \(0.845144\pi\) | |||||||
\(728\) | 26.5031i | 0.982270i | ||||||||
\(729\) | −86.2849 | −3.19574 | ||||||||
\(730\) | 10.8858 | − | 15.0567i | 0.402901 | − | 0.557272i | ||||
\(731\) | 15.2140 | 0.562710 | ||||||||
\(732\) | 28.4785i | 1.05260i | ||||||||
\(733\) | − | 10.9045i | − | 0.402766i | −0.979513 | − | 0.201383i | \(-0.935456\pi\) | ||
0.979513 | − | 0.201383i | \(-0.0645435\pi\) | |||||||
\(734\) | −4.20326 | −0.155145 | ||||||||
\(735\) | 1.89228 | + | 1.36810i | 0.0697978 | + | 0.0504630i | ||||
\(736\) | 18.3235 | 0.675413 | ||||||||
\(737\) | 15.8539i | 0.583985i | ||||||||
\(738\) | 0.620748i | 0.0228500i | ||||||||
\(739\) | 3.13455 | 0.115306 | 0.0576531 | − | 0.998337i | \(-0.481638\pi\) | ||||
0.0576531 | + | 0.998337i | \(0.481638\pi\) | |||||||
\(740\) | −20.4689 | − | 14.7987i | −0.752450 | − | 0.544012i | ||||
\(741\) | 13.0854 | 0.480703 | ||||||||
\(742\) | 23.4316i | 0.860202i | ||||||||
\(743\) | 18.0854i | 0.663489i | 0.943369 | + | 0.331744i | \(0.107637\pi\) | ||||
−0.943369 | + | 0.331744i | \(0.892363\pi\) | |||||||
\(744\) | −49.6597 | −1.82061 | ||||||||
\(745\) | 16.8360 | − | 23.2866i | 0.616822 | − | 0.853156i | ||||
\(746\) | −13.3076 | −0.487227 | ||||||||
\(747\) | − | 88.5095i | − | 3.23839i | ||||||
\(748\) | − | 6.77171i | − | 0.247598i | ||||||
\(749\) | 4.39291 | 0.160513 | ||||||||
\(750\) | −25.2228 | − | 8.00089i | −0.921008 | − | 0.292151i | ||||
\(751\) | −37.8934 | −1.38275 | −0.691374 | − | 0.722497i | \(-0.742994\pi\) | ||||
−0.691374 | + | 0.722497i | \(0.742994\pi\) | |||||||
\(752\) | 8.56288i | 0.312256i | ||||||||
\(753\) | − | 23.1131i | − | 0.842287i | ||||||
\(754\) | −20.6871 | −0.753380 | ||||||||
\(755\) | 15.5860 | − | 21.5577i | 0.567231 | − | 0.784565i | ||||
\(756\) | 67.5530 | 2.45688 | ||||||||
\(757\) | 33.0357i | 1.20070i | 0.799736 | + | 0.600351i | \(0.204973\pi\) | ||||
−0.799736 | + | 0.600351i | \(0.795027\pi\) | |||||||
\(758\) | − | 9.40737i | − | 0.341691i | ||||||
\(759\) | −10.4241 | −0.378372 | ||||||||
\(760\) | 4.50852 | + | 3.25961i | 0.163541 | + | 0.118238i | ||||
\(761\) | −39.4886 | −1.43146 | −0.715731 | − | 0.698376i | \(-0.753906\pi\) | ||||
−0.715731 | + | 0.698376i | \(0.753906\pi\) | |||||||
\(762\) | 1.76023i | 0.0637664i | ||||||||
\(763\) | − | 46.0796i | − | 1.66819i | ||||||
\(764\) | −5.42615 | −0.196311 | ||||||||
\(765\) | 66.0819 | + | 47.7765i | 2.38920 | + | 1.72736i | ||||
\(766\) | −8.11992 | −0.293385 | ||||||||
\(767\) | − | 15.1230i | − | 0.546059i | ||||||
\(768\) | 36.2479i | 1.30798i | ||||||||
\(769\) | −39.2949 | −1.41701 | −0.708505 | − | 0.705706i | \(-0.750630\pi\) | ||||
−0.708505 | + | 0.705706i | \(0.750630\pi\) | |||||||
\(770\) | 2.52416 | − | 3.49129i | 0.0909645 | − | 0.125817i | ||||
\(771\) | −57.4460 | −2.06887 | ||||||||
\(772\) | − | 28.1114i | − | 1.01175i | ||||||
\(773\) | − | 1.29918i | − | 0.0467281i | −0.999727 | − | 0.0233640i | \(-0.992562\pi\) | ||
0.999727 | − | 0.0233640i | \(-0.00743768\pi\) | |||||||
\(774\) | 19.1999 | 0.690125 | ||||||||
\(775\) | 9.41551 | + | 28.5249i | 0.338215 | + | 1.02465i | ||||
\(776\) | 48.2579 | 1.73236 | ||||||||
\(777\) | 68.0030i | 2.43959i | ||||||||
\(778\) | − | 2.93733i | − | 0.105308i | ||||||
\(779\) | −0.108411 | −0.00388422 | ||||||||
\(780\) | 25.5861 | − | 35.3894i | 0.916130 | − | 1.26714i | ||||
\(781\) | −7.83511 | −0.280362 | ||||||||
\(782\) | − | 10.1418i | − | 0.362671i | ||||||
\(783\) | 123.388i | 4.40952i | ||||||||
\(784\) | −0.381114 | −0.0136112 | ||||||||
\(785\) | 9.45041 | + | 6.83254i | 0.337300 | + | 0.243864i | ||||
\(786\) | −11.2095 | −0.399828 | ||||||||
\(787\) | 21.6621i | 0.772170i | 0.922463 | + | 0.386085i | \(0.126173\pi\) | ||||
−0.922463 | + | 0.386085i | \(0.873827\pi\) | |||||||
\(788\) | − | 0.0937165i | − | 0.00333851i | ||||||
\(789\) | −29.5132 | −1.05070 | ||||||||
\(790\) | 15.5807 | + | 11.2647i | 0.554338 | + | 0.400780i | ||||
\(791\) | −2.49436 | −0.0886893 | ||||||||
\(792\) | − | 19.9976i | − | 0.710583i | ||||||
\(793\) | − | 22.6216i | − | 0.803316i | ||||||
\(794\) | −14.6619 | −0.520332 | ||||||||
\(795\) | 52.9340 | − | 73.2155i | 1.87737 | − | 2.59669i | ||||
\(796\) | −10.3777 | −0.367830 | ||||||||
\(797\) | − | 31.7834i | − | 1.12582i | −0.826517 | − | 0.562912i | \(-0.809681\pi\) | ||
0.826517 | − | 0.562912i | \(-0.190319\pi\) | |||||||
\(798\) | − | 6.40096i | − | 0.226591i | ||||||
\(799\) | 32.0425 | 1.13358 | ||||||||
\(800\) | 27.7279 | − | 9.15242i | 0.980328 | − | 0.323587i | ||||
\(801\) | −63.5543 | −2.24558 | ||||||||
\(802\) | 8.23509i | 0.290791i | ||||||||
\(803\) | − | 11.6635i | − | 0.411597i | ||||||
\(804\) | 78.6106 | 2.77238 | ||||||||
\(805\) | −11.1173 | + | 15.3769i | −0.391834 | + | 0.541964i | ||||
\(806\) | 16.8572 | 0.593770 | ||||||||
\(807\) | − | 51.9509i | − | 1.82876i | ||||||
\(808\) | 15.4116i | 0.542178i | ||||||||
\(809\) | −26.2573 | −0.923157 | −0.461578 | − | 0.887099i | \(-0.652717\pi\) | ||||
−0.461578 | + | 0.887099i | \(0.652717\pi\) | |||||||
\(810\) | 40.6491 | + | 29.3888i | 1.42826 | + | 1.03262i | ||||
\(811\) | −36.5555 | −1.28364 | −0.641819 | − | 0.766856i | \(-0.721820\pi\) | ||||
−0.641819 | + | 0.766856i | \(0.721820\pi\) | |||||||
\(812\) | − | 29.7593i | − | 1.04435i | ||||||
\(813\) | 20.5503i | 0.720730i | ||||||||
\(814\) | 5.39175 | 0.188981 | ||||||||
\(815\) | −14.2761 | − | 10.3214i | −0.500068 | − | 0.361543i | ||||
\(816\) | −18.2769 | −0.639820 | ||||||||
\(817\) | 3.35317i | 0.117313i | ||||||||
\(818\) | 10.5597i | 0.369210i | ||||||||
\(819\) | −85.6165 | −2.99168 | ||||||||
\(820\) | −0.211978 | + | 0.293197i | −0.00740260 | + | 0.0102389i | ||||
\(821\) | 17.3018 | 0.603837 | 0.301919 | − | 0.953334i | \(-0.402373\pi\) | ||||
0.301919 | + | 0.953334i | \(0.402373\pi\) | |||||||
\(822\) | 5.37063i | 0.187322i | ||||||||
\(823\) | 27.8154i | 0.969582i | 0.874630 | + | 0.484791i | \(0.161104\pi\) | ||||
−0.874630 | + | 0.484791i | \(0.838896\pi\) | |||||||
\(824\) | 35.1529 | 1.22461 | ||||||||
\(825\) | −15.7742 | + | 5.20676i | −0.549188 | + | 0.181276i | ||||
\(826\) | −7.39769 | −0.257398 | ||||||||
\(827\) | 34.4103i | 1.19656i | 0.801285 | + | 0.598282i | \(0.204150\pi\) | ||||
−0.801285 | + | 0.598282i | \(0.795850\pi\) | |||||||
\(828\) | 37.6388i | 1.30804i | ||||||||
\(829\) | 2.94933 | 0.102434 | 0.0512172 | − | 0.998688i | \(-0.483690\pi\) | ||||
0.0512172 | + | 0.998688i | \(0.483690\pi\) | |||||||
\(830\) | −10.2778 | + | 14.2158i | −0.356749 | + | 0.493436i | ||||
\(831\) | −45.1485 | −1.56619 | ||||||||
\(832\) | − | 6.83488i | − | 0.236957i | ||||||
\(833\) | 1.42614i | 0.0494128i | ||||||||
\(834\) | −8.31288 | −0.287851 | ||||||||
\(835\) | 31.6003 | + | 22.8467i | 1.09357 | + | 0.790642i | ||||
\(836\) | 1.49249 | 0.0516188 | ||||||||
\(837\) | − | 100.544i | − | 3.47532i | ||||||
\(838\) | − | 3.26541i | − | 0.112802i | ||||||
\(839\) | −25.9837 | −0.897057 | −0.448528 | − | 0.893769i | \(-0.648052\pi\) | ||||
−0.448528 | + | 0.893769i | \(0.648052\pi\) | |||||||
\(840\) | −40.5094 | − | 29.2878i | −1.39771 | − | 1.01053i | ||||
\(841\) | 25.3563 | 0.874357 | ||||||||
\(842\) | − | 3.61483i | − | 0.124575i | ||||||
\(843\) | 32.2379i | 1.11033i | ||||||||
\(844\) | 28.8926 | 0.994524 | ||||||||
\(845\) | −3.29263 | + | 4.55420i | −0.113270 | + | 0.156669i | ||||
\(846\) | 40.4372 | 1.39026 | ||||||||
\(847\) | − | 2.70450i | − | 0.0929277i | ||||||
\(848\) | 14.7460i | 0.506378i | ||||||||
\(849\) | 5.12929 | 0.176037 | ||||||||
\(850\) | −5.06575 | − | 15.3470i | −0.173754 | − | 0.526398i | ||||
\(851\) | −23.7472 | −0.814042 | ||||||||
\(852\) | 38.8500i | 1.33098i | ||||||||
\(853\) | 31.9494i | 1.09393i | 0.837157 | + | 0.546963i | \(0.184216\pi\) | ||||
−0.837157 | + | 0.546963i | \(0.815784\pi\) | |||||||
\(854\) | −11.0658 | −0.378663 | ||||||||
\(855\) | −10.5300 | + | 14.5645i | −0.360117 | + | 0.498095i | ||||
\(856\) | −4.04132 | −0.138130 | ||||||||
\(857\) | 28.7090i | 0.980682i | 0.871531 | + | 0.490341i | \(0.163128\pi\) | ||||
−0.871531 | + | 0.490341i | \(0.836872\pi\) | |||||||
\(858\) | 9.32200i | 0.318248i | ||||||||
\(859\) | 18.4221 | 0.628552 | 0.314276 | − | 0.949332i | \(-0.398238\pi\) | ||||
0.314276 | + | 0.949332i | \(0.398238\pi\) | |||||||
\(860\) | 9.06866 | + | 6.55654i | 0.309239 | + | 0.223576i | ||||
\(861\) | 0.974080 | 0.0331966 | ||||||||
\(862\) | − | 19.5978i | − | 0.667504i | ||||||
\(863\) | − | 17.4004i | − | 0.592316i | −0.955139 | − | 0.296158i | \(-0.904294\pi\) | ||
0.955139 | − | 0.296158i | \(-0.0957055\pi\) | |||||||
\(864\) | −97.7350 | −3.32501 | ||||||||
\(865\) | −24.9972 | − | 18.0727i | −0.849929 | − | 0.614489i | ||||
\(866\) | 9.38373 | 0.318872 | ||||||||
\(867\) | 11.9141i | 0.404625i | ||||||||
\(868\) | 24.2498i | 0.823094i | ||||||||
\(869\) | 12.0695 | 0.409429 | ||||||||
\(870\) | 22.8607 | − | 31.6198i | 0.775052 | − | 1.07201i | ||||
\(871\) | −62.4434 | −2.11582 | ||||||||
\(872\) | 42.3916i | 1.43556i | ||||||||
\(873\) | 155.894i | 5.27621i | ||||||||
\(874\) | 2.23526 | 0.0756089 | ||||||||
\(875\) | −9.14255 | + | 28.8219i | −0.309075 | + | 0.974359i | ||||
\(876\) | −57.8329 | −1.95399 | ||||||||
\(877\) | 6.68555i | 0.225755i | 0.993609 | + | 0.112877i | \(0.0360067\pi\) | ||||
−0.993609 | + | 0.112877i | \(0.963993\pi\) | |||||||
\(878\) | 8.87102i | 0.299383i | ||||||||
\(879\) | 73.9774 | 2.49519 | ||||||||
\(880\) | 1.58850 | − | 2.19714i | 0.0535484 | − | 0.0740654i | ||||
\(881\) | −23.4701 | −0.790728 | −0.395364 | − | 0.918525i | \(-0.629382\pi\) | ||||
−0.395364 | + | 0.918525i | \(0.629382\pi\) | |||||||
\(882\) | 1.79977i | 0.0606014i | ||||||||
\(883\) | 20.8333i | 0.701096i | 0.936545 | + | 0.350548i | \(0.114005\pi\) | ||||
−0.936545 | + | 0.350548i | \(0.885995\pi\) | |||||||
\(884\) | 26.6716 | 0.897065 | ||||||||
\(885\) | 23.1152 | + | 16.7120i | 0.777007 | + | 0.561767i | ||||
\(886\) | 12.1846 | 0.409349 | ||||||||
\(887\) | − | 5.03263i | − | 0.168979i | −0.996424 | − | 0.0844896i | \(-0.973074\pi\) | ||
0.996424 | − | 0.0844896i | \(-0.0269260\pi\) | |||||||
\(888\) | − | 62.5604i | − | 2.09939i | ||||||
\(889\) | 2.01140 | 0.0674602 | ||||||||
\(890\) | 10.2076 | + | 7.37999i | 0.342160 | + | 0.247378i | ||||
\(891\) | 31.4885 | 1.05490 | ||||||||
\(892\) | 5.92978i | 0.198544i | ||||||||
\(893\) | 7.06218i | 0.236327i | ||||||||
\(894\) | 30.4150 | 1.01723 | ||||||||
\(895\) | 7.44650 | − | 10.2996i | 0.248909 | − | 0.344278i | ||||
\(896\) | 28.2444 | 0.943581 | ||||||||
\(897\) | − | 41.0574i | − | 1.37087i | ||||||
\(898\) | − | 1.20594i | − | 0.0402427i | ||||||
\(899\) | −44.2931 | −1.47726 | ||||||||
\(900\) | 18.8002 | + | 56.9565i | 0.626674 | + | 1.89855i | ||||
\(901\) | 55.1798 | 1.83830 | ||||||||
\(902\) | − | 0.0772318i | − | 0.00257154i | ||||||
\(903\) | − | 30.1285i | − | 1.00261i | ||||||
\(904\) | 2.29472 | 0.0763214 | ||||||||
\(905\) | −24.3317 | + | 33.6544i | −0.808814 | + | 1.11871i | ||||
\(906\) | 28.1568 | 0.935448 | ||||||||
\(907\) | − | 24.4295i | − | 0.811169i | −0.914058 | − | 0.405584i | \(-0.867068\pi\) | ||
0.914058 | − | 0.405584i | \(-0.132932\pi\) | |||||||
\(908\) | − | 4.70725i | − | 0.156215i | ||||||
\(909\) | −49.7862 | −1.65130 | ||||||||
\(910\) | 13.7511 | + | 9.94189i | 0.455845 | + | 0.329570i | ||||
\(911\) | −23.8703 | −0.790859 | −0.395430 | − | 0.918496i | \(-0.629404\pi\) | ||||
−0.395430 | + | 0.918496i | \(0.629404\pi\) | |||||||
\(912\) | − | 4.02824i | − | 0.133388i | ||||||
\(913\) | 11.0121i | 0.364448i | ||||||||
\(914\) | 11.5597 | 0.382362 | ||||||||
\(915\) | 34.5766 | + | 24.9985i | 1.14307 | + | 0.826425i | ||||
\(916\) | −0.698715 | −0.0230862 | ||||||||
\(917\) | 12.8090i | 0.422989i | ||||||||
\(918\) | 54.0950i | 1.78540i | ||||||||
\(919\) | 56.2979 | 1.85710 | 0.928548 | − | 0.371213i | \(-0.121058\pi\) | ||||
0.928548 | + | 0.371213i | \(0.121058\pi\) | |||||||
\(920\) | 10.2275 | − | 14.1462i | 0.337192 | − | 0.466386i | ||||
\(921\) | −34.1896 | −1.12658 | ||||||||
\(922\) | 9.31143i | 0.306656i | ||||||||
\(923\) | − | 30.8600i | − | 1.01577i | ||||||
\(924\) | −13.4101 | −0.441161 | ||||||||
\(925\) | −35.9352 | + | 11.8615i | −1.18154 | + | 0.390003i | ||||
\(926\) | 26.0605 | 0.856401 | ||||||||
\(927\) | 113.559i | 3.72977i | ||||||||
\(928\) | 43.0555i | 1.41336i | ||||||||
\(929\) | 52.6145 | 1.72623 | 0.863113 | − | 0.505011i | \(-0.168512\pi\) | ||||
0.863113 | + | 0.505011i | \(0.168512\pi\) | |||||||
\(930\) | −18.6284 | + | 25.7659i | −0.610850 | + | 0.844897i | ||||
\(931\) | −0.314322 | −0.0103015 | ||||||||
\(932\) | 23.2716i | 0.762288i | ||||||||
\(933\) | − | 76.7889i | − | 2.51396i | ||||||
\(934\) | −4.11912 | −0.134782 | ||||||||
\(935\) | −8.22174 | − | 5.94422i | −0.268880 | − | 0.194397i | ||||
\(936\) | 78.7642 | 2.57449 | ||||||||
\(937\) | 38.7016i | 1.26433i | 0.774835 | + | 0.632163i | \(0.217833\pi\) | ||||
−0.774835 | + | 0.632163i | \(0.782167\pi\) | |||||||
\(938\) | 30.5454i | 0.997342i | ||||||||
\(939\) | 28.9446 | 0.944571 | ||||||||
\(940\) | 19.0997 | + | 13.8088i | 0.622963 | + | 0.450395i | ||||
\(941\) | 13.4504 | 0.438471 | 0.219235 | − | 0.975672i | \(-0.429644\pi\) | ||||
0.219235 | + | 0.975672i | \(0.429644\pi\) | |||||||
\(942\) | 12.3433i | 0.402168i | ||||||||
\(943\) | 0.340156i | 0.0110770i | ||||||||
\(944\) | −4.65550 | −0.151524 | ||||||||
\(945\) | 59.2982 | − | 82.0182i | 1.92897 | − | 2.66805i | ||||
\(946\) | −2.38880 | −0.0776665 | ||||||||
\(947\) | − | 45.0879i | − | 1.46516i | −0.680681 | − | 0.732580i | \(-0.738316\pi\) | ||
0.680681 | − | 0.732580i | \(-0.261684\pi\) | |||||||
\(948\) | − | 59.8459i | − | 1.94370i | ||||||
\(949\) | 45.9389 | 1.49124 | ||||||||
\(950\) | 3.38249 | − | 1.11649i | 0.109742 | − | 0.0362238i | ||||
\(951\) | 61.0378 | 1.97929 | ||||||||
\(952\) | − | 30.5304i | − | 0.989496i | ||||||
\(953\) | 27.6756i | 0.896502i | 0.893908 | + | 0.448251i | \(0.147953\pi\) | ||||
−0.893908 | + | 0.448251i | \(0.852047\pi\) | |||||||
\(954\) | 69.6361 | 2.25455 | ||||||||
\(955\) | −4.76308 | + | 6.58805i | −0.154130 | + | 0.213184i | ||||
\(956\) | −13.0110 | −0.420806 | ||||||||
\(957\) | − | 24.4940i | − | 0.791779i | ||||||
\(958\) | − | 3.54757i | − | 0.114617i | ||||||
\(959\) | 6.13698 | 0.198173 | ||||||||
\(960\) | 10.4470 | + | 7.55304i | 0.337175 | + | 0.243773i | ||||
\(961\) | 5.09294 | 0.164288 | ||||||||
\(962\) | 21.2364i | 0.684689i | ||||||||
\(963\) | − | 13.0552i | − | 0.420699i | ||||||
\(964\) | −22.2172 | −0.715569 | ||||||||
\(965\) | −34.1309 | − | 24.6762i | −1.09871 | − | 0.794356i | ||||
\(966\) | −20.0840 | −0.646192 | ||||||||
\(967\) | 21.9186i | 0.704855i | 0.935839 | + | 0.352428i | \(0.114644\pi\) | ||||
−0.935839 | + | 0.352428i | \(0.885356\pi\) | |||||||
\(968\) | 2.48804i | 0.0799688i | ||||||||
\(969\) | −15.0738 | −0.484240 | ||||||||
\(970\) | 18.1026 | − | 25.0386i | 0.581239 | − | 0.803940i | ||||
\(971\) | 38.2300 | 1.22686 | 0.613429 | − | 0.789750i | \(-0.289790\pi\) | ||||
0.613429 | + | 0.789750i | \(0.289790\pi\) | |||||||
\(972\) | − | 81.1999i | − | 2.60449i | ||||||
\(973\) | 9.49906i | 0.304526i | ||||||||
\(974\) | −10.8996 | −0.349245 | ||||||||
\(975\) | −20.5078 | − | 62.1297i | −0.656775 | − | 1.98974i | ||||
\(976\) | −6.96390 | −0.222909 | ||||||||
\(977\) | − | 55.6928i | − | 1.78177i | −0.454227 | − | 0.890886i | \(-0.650085\pi\) | ||
0.454227 | − | 0.890886i | \(-0.349915\pi\) | |||||||
\(978\) | − | 18.6462i | − | 0.596239i | ||||||
\(979\) | 7.90725 | 0.252717 | ||||||||
\(980\) | −0.614600 | + | 0.850084i | −0.0196327 | + | 0.0271549i | ||||
\(981\) | −136.943 | −4.37226 | ||||||||
\(982\) | 8.30762i | 0.265107i | ||||||||
\(983\) | − | 55.0897i | − | 1.75709i | −0.477660 | − | 0.878545i | \(-0.658515\pi\) | ||
0.477660 | − | 0.878545i | \(-0.341485\pi\) | |||||||
\(984\) | −0.896119 | −0.0285672 | ||||||||
\(985\) | −0.113784 | − | 0.0822645i | −0.00362546 | − | 0.00262117i | ||||
\(986\) | 23.8306 | 0.758922 | ||||||||
\(987\) | − | 63.4543i | − | 2.01977i | ||||||
\(988\) | 5.87844i | 0.187018i | ||||||||
\(989\) | 10.5211 | 0.334552 | ||||||||
\(990\) | −10.3757 | − | 7.50153i | −0.329762 | − | 0.238414i | ||||
\(991\) | −39.1755 | −1.24445 | −0.622226 | − | 0.782838i | \(-0.713771\pi\) | ||||
−0.622226 | + | 0.782838i | \(0.713771\pi\) | |||||||
\(992\) | − | 35.0844i | − | 1.11393i | ||||||
\(993\) | 16.1497i | 0.512496i | ||||||||
\(994\) | −15.0958 | −0.478808 | ||||||||
\(995\) | −9.10961 | + | 12.5999i | −0.288794 | + | 0.399445i | ||||
\(996\) | 54.6030 | 1.73016 | ||||||||
\(997\) | − | 59.0338i | − | 1.86962i | −0.355148 | − | 0.934810i | \(-0.615569\pi\) | ||
0.355148 | − | 0.934810i | \(-0.384431\pi\) | |||||||
\(998\) | − | 15.1476i | − | 0.479489i | ||||||
\(999\) | 126.664 | 4.00747 |
(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 | 1045.2.b.c.419.13 | yes | 20 | |
5.2 | odd | 4 | 5225.2.a.ba.1.8 | 20 | |||
5.3 | odd | 4 | 5225.2.a.ba.1.13 | 20 | |||
5.4 | even | 2 | inner | 1045.2.b.c.419.8 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.2.b.c.419.8 | ✓ | 20 | 5.4 | even | 2 | inner | |
1045.2.b.c.419.13 | yes | 20 | 1.1 | even | 1 | trivial | |
5225.2.a.ba.1.8 | 20 | 5.2 | odd | 4 | |||
5225.2.a.ba.1.13 | 20 | 5.3 | odd | 4 |