Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(1009,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.1009");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.bb (of order \(6\), degree \(2\), 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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1009.6 | ||
Character | \(\chi\) | \(=\) | 1110.1009 |
Dual form | 1110.2.bb.e.1099.6 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −0.329099 | − | 2.21172i | −0.147177 | − | 0.989110i | ||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0.903939 | − | 0.521889i | 0.341657 | − | 0.197256i | −0.319348 | − | 0.947638i | \(-0.603464\pi\) |
0.661004 | + | 0.750382i | \(0.270130\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | −0.820851 | + | 2.07995i | −0.259576 | + | 0.657739i | ||||
\(11\) | 0.877352 | 0.264531 | 0.132266 | − | 0.991214i | \(-0.457775\pi\) | ||||
0.132266 | + | 0.991214i | \(0.457775\pi\) | |||||||
\(12\) | 0.866025 | + | 0.500000i | 0.250000 | + | 0.144338i | ||||
\(13\) | −3.82118 | + | 2.20616i | −1.05980 | + | 0.611878i | −0.925378 | − | 0.379045i | \(-0.876252\pi\) |
−0.134426 | + | 0.990924i | \(0.542919\pi\) | |||||||
\(14\) | −1.04378 | −0.278962 | ||||||||
\(15\) | −1.39087 | − | 1.75085i | −0.359120 | − | 0.452069i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −4.44494 | − | 2.56629i | −1.07806 | − | 0.622417i | −0.147686 | − | 0.989034i | \(-0.547182\pi\) |
−0.930372 | + | 0.366618i | \(0.880516\pi\) | |||||||
\(18\) | −0.866025 | + | 0.500000i | −0.204124 | + | 0.117851i | ||||
\(19\) | −1.51358 | − | 2.62160i | −0.347240 | − | 0.601437i | 0.638518 | − | 0.769607i | \(-0.279548\pi\) |
−0.985758 | + | 0.168170i | \(0.946214\pi\) | |||||||
\(20\) | 1.75085 | − | 1.39087i | 0.391503 | − | 0.311007i | ||||
\(21\) | 0.521889 | − | 0.903939i | 0.113886 | − | 0.197256i | ||||
\(22\) | −0.759809 | − | 0.438676i | −0.161992 | − | 0.0935260i | ||||
\(23\) | − | 7.11017i | − | 1.48257i | −0.671188 | − | 0.741287i | \(-0.734216\pi\) | ||
0.671188 | − | 0.741287i | \(-0.265784\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | −4.78339 | + | 1.45575i | −0.956678 | + | 0.291149i | ||||
\(26\) | 4.41232 | 0.865326 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0.903939 | + | 0.521889i | 0.170828 | + | 0.0986278i | ||||
\(29\) | 5.96130 | 1.10699 | 0.553493 | − | 0.832854i | \(-0.313294\pi\) | ||||
0.553493 | + | 0.832854i | \(0.313294\pi\) | |||||||
\(30\) | 0.329099 | + | 2.21172i | 0.0600850 | + | 0.403803i | ||||
\(31\) | −1.73335 | −0.311319 | −0.155660 | − | 0.987811i | \(-0.549750\pi\) | ||||
−0.155660 | + | 0.987811i | \(0.549750\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 0.759809 | − | 0.438676i | 0.132266 | − | 0.0763637i | ||||
\(34\) | 2.56629 | + | 4.44494i | 0.440115 | + | 0.762302i | ||||
\(35\) | −1.45176 | − | 1.82750i | −0.245392 | − | 0.308905i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −0.0184948 | − | 6.08273i | −0.00304052 | − | 0.999995i | ||||
\(38\) | 3.02716i | 0.491071i | ||||||||
\(39\) | −2.20616 | + | 3.82118i | −0.353268 | + | 0.611878i | ||||
\(40\) | −2.21172 | + | 0.329099i | −0.349703 | + | 0.0520351i | ||||
\(41\) | 3.12701 | + | 5.41615i | 0.488357 | + | 0.845860i | 0.999910 | − | 0.0133920i | \(-0.00426293\pi\) |
−0.511553 | + | 0.859252i | \(0.670930\pi\) | |||||||
\(42\) | −0.903939 | + | 0.521889i | −0.139481 | + | 0.0805293i | ||||
\(43\) | 1.46389i | 0.223241i | 0.993751 | + | 0.111621i | \(0.0356041\pi\) | ||||
−0.993751 | + | 0.111621i | \(0.964396\pi\) | |||||||
\(44\) | 0.438676 | + | 0.759809i | 0.0661329 | + | 0.114545i | ||||
\(45\) | −2.07995 | − | 0.820851i | −0.310061 | − | 0.122365i | ||||
\(46\) | −3.55509 | + | 6.15759i | −0.524169 | + | 0.907887i | ||||
\(47\) | 3.00050i | 0.437668i | 0.975762 | + | 0.218834i | \(0.0702254\pi\) | ||||
−0.975762 | + | 0.218834i | \(0.929775\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | −2.95526 | + | 5.11867i | −0.422180 | + | 0.731238i | ||||
\(50\) | 4.87041 | + | 1.13098i | 0.688780 | + | 0.159945i | ||||
\(51\) | −5.13258 | −0.718705 | ||||||||
\(52\) | −3.82118 | − | 2.20616i | −0.529902 | − | 0.305939i | ||||
\(53\) | −11.1687 | − | 6.44827i | −1.53414 | − | 0.885738i | −0.999164 | − | 0.0408730i | \(-0.986986\pi\) |
−0.534979 | − | 0.844865i | \(-0.679681\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | −0.288735 | − | 1.94045i | −0.0389331 | − | 0.261651i | ||||
\(56\) | −0.521889 | − | 0.903939i | −0.0697404 | − | 0.120794i | ||||
\(57\) | −2.62160 | − | 1.51358i | −0.347240 | − | 0.200479i | ||||
\(58\) | −5.16264 | − | 2.98065i | −0.677888 | − | 0.391379i | ||||
\(59\) | 4.32356 | − | 7.48863i | 0.562880 | − | 0.974937i | −0.434363 | − | 0.900738i | \(-0.643027\pi\) |
0.997243 | − | 0.0741992i | \(-0.0236401\pi\) | |||||||
\(60\) | 0.820851 | − | 2.07995i | 0.105971 | − | 0.268521i | ||||
\(61\) | 1.80822 | + | 3.13192i | 0.231518 | + | 0.401002i | 0.958255 | − | 0.285914i | \(-0.0922973\pi\) |
−0.726737 | + | 0.686916i | \(0.758964\pi\) | |||||||
\(62\) | 1.50113 | + | 0.866676i | 0.190643 | + | 0.110068i | ||||
\(63\) | − | 1.04378i | − | 0.131504i | ||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 6.13694 | + | 7.72532i | 0.761194 | + | 0.958208i | ||||
\(66\) | −0.877352 | −0.107995 | ||||||||
\(67\) | −2.30824 | + | 1.33266i | −0.281997 | + | 0.162811i | −0.634327 | − | 0.773065i | \(-0.718723\pi\) |
0.352330 | + | 0.935876i | \(0.385389\pi\) | |||||||
\(68\) | − | 5.13258i | − | 0.622417i | ||||||
\(69\) | −3.55509 | − | 6.15759i | −0.427982 | − | 0.741287i | ||||
\(70\) | 0.343506 | + | 2.30854i | 0.0410569 | + | 0.275924i | ||||
\(71\) | 0.582533 | + | 1.00898i | 0.0691340 | + | 0.119744i | 0.898520 | − | 0.438932i | \(-0.144643\pi\) |
−0.829386 | + | 0.558675i | \(0.811310\pi\) | |||||||
\(72\) | −0.866025 | − | 0.500000i | −0.102062 | − | 0.0589256i | ||||
\(73\) | 5.73680i | 0.671441i | 0.941962 | + | 0.335721i | \(0.108980\pi\) | ||||
−0.941962 | + | 0.335721i | \(0.891020\pi\) | |||||||
\(74\) | −3.02535 | + | 5.27705i | −0.351690 | + | 0.613445i | ||||
\(75\) | −3.41466 | + | 3.65241i | −0.394291 | + | 0.421744i | ||||
\(76\) | 1.51358 | − | 2.62160i | 0.173620 | − | 0.300718i | ||||
\(77\) | 0.793072 | − | 0.457881i | 0.0903790 | − | 0.0521803i | ||||
\(78\) | 3.82118 | − | 2.20616i | 0.432663 | − | 0.249798i | ||||
\(79\) | −5.03878 | − | 8.72742i | −0.566907 | − | 0.981911i | −0.996869 | − | 0.0790646i | \(-0.974807\pi\) |
0.429963 | − | 0.902847i | \(-0.358527\pi\) | |||||||
\(80\) | 2.07995 | + | 0.820851i | 0.232546 | + | 0.0917739i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | − | 6.25403i | − | 0.690642i | ||||||
\(83\) | −9.72771 | − | 5.61630i | −1.06776 | − | 0.616469i | −0.140188 | − | 0.990125i | \(-0.544771\pi\) |
−0.927567 | + | 0.373656i | \(0.878104\pi\) | |||||||
\(84\) | 1.04378 | 0.113886 | ||||||||
\(85\) | −4.21308 | + | 10.6755i | −0.456973 | + | 1.15792i | ||||
\(86\) | 0.731945 | − | 1.26777i | 0.0789277 | − | 0.136707i | ||||
\(87\) | 5.16264 | − | 2.98065i | 0.553493 | − | 0.319559i | ||||
\(88\) | − | 0.877352i | − | 0.0935260i | ||||||
\(89\) | 7.63676 | − | 13.2273i | 0.809495 | − | 1.40209i | −0.103719 | − | 0.994607i | \(-0.533074\pi\) |
0.913214 | − | 0.407480i | \(-0.133592\pi\) | |||||||
\(90\) | 1.39087 | + | 1.75085i | 0.146610 | + | 0.184556i | ||||
\(91\) | −2.30274 | + | 3.98846i | −0.241393 | + | 0.418105i | ||||
\(92\) | 6.15759 | − | 3.55509i | 0.641973 | − | 0.370643i | ||||
\(93\) | −1.50113 | + | 0.866676i | −0.155660 | + | 0.0898701i | ||||
\(94\) | 1.50025 | − | 2.59851i | 0.154739 | − | 0.268016i | ||||
\(95\) | −5.30012 | + | 4.21038i | −0.543781 | + | 0.431976i | ||||
\(96\) | 0.500000 | − | 0.866025i | 0.0510310 | − | 0.0883883i | ||||
\(97\) | − | 9.07922i | − | 0.921855i | −0.887438 | − | 0.460928i | \(-0.847517\pi\) | ||
0.887438 | − | 0.460928i | \(-0.152483\pi\) | |||||||
\(98\) | 5.11867 | − | 2.95526i | 0.517063 | − | 0.298527i | ||||
\(99\) | 0.438676 | − | 0.759809i | 0.0440886 | − | 0.0763637i | ||||
\(100\) | −3.65241 | − | 3.41466i | −0.365241 | − | 0.341466i | ||||
\(101\) | 1.97678 | 0.196697 | 0.0983486 | − | 0.995152i | \(-0.468644\pi\) | ||||
0.0983486 | + | 0.995152i | \(0.468644\pi\) | |||||||
\(102\) | 4.44494 | + | 2.56629i | 0.440115 | + | 0.254101i | ||||
\(103\) | 5.48507i | 0.540460i | 0.962796 | + | 0.270230i | \(0.0870998\pi\) | ||||
−0.962796 | + | 0.270230i | \(0.912900\pi\) | |||||||
\(104\) | 2.20616 | + | 3.82118i | 0.216332 | + | 0.374697i | ||||
\(105\) | −2.17101 | − | 0.856787i | −0.211869 | − | 0.0836138i | ||||
\(106\) | 6.44827 | + | 11.1687i | 0.626312 | + | 1.08480i | ||||
\(107\) | −0.205007 | + | 0.118361i | −0.0198188 | + | 0.0114424i | −0.509877 | − | 0.860248i | \(-0.670309\pi\) |
0.490058 | + | 0.871690i | \(0.336976\pi\) | |||||||
\(108\) | 0.866025 | − | 0.500000i | 0.0833333 | − | 0.0481125i | ||||
\(109\) | 3.39695 | − | 5.88369i | 0.325369 | − | 0.563555i | −0.656218 | − | 0.754571i | \(-0.727845\pi\) |
0.981587 | + | 0.191016i | \(0.0611783\pi\) | |||||||
\(110\) | −0.720175 | + | 1.82485i | −0.0686660 | + | 0.173993i | ||||
\(111\) | −3.05738 | − | 5.25856i | −0.290194 | − | 0.499120i | ||||
\(112\) | 1.04378i | 0.0986278i | ||||||||
\(113\) | 9.35427 | + | 5.40069i | 0.879976 | + | 0.508054i | 0.870650 | − | 0.491902i | \(-0.163698\pi\) |
0.00932533 | + | 0.999957i | \(0.497032\pi\) | |||||||
\(114\) | 1.51358 | + | 2.62160i | 0.141760 | + | 0.245535i | ||||
\(115\) | −15.7257 | + | 2.33995i | −1.46643 | + | 0.218201i | ||||
\(116\) | 2.98065 | + | 5.16264i | 0.276747 | + | 0.479339i | ||||
\(117\) | 4.41232i | 0.407919i | ||||||||
\(118\) | −7.48863 | + | 4.32356i | −0.689385 | + | 0.398016i | ||||
\(119\) | −5.35728 | −0.491101 | ||||||||
\(120\) | −1.75085 | + | 1.39087i | −0.159830 | + | 0.126968i | ||||
\(121\) | −10.2303 | −0.930023 | ||||||||
\(122\) | − | 3.61643i | − | 0.327416i | ||||||
\(123\) | 5.41615 | + | 3.12701i | 0.488357 | + | 0.281953i | ||||
\(124\) | −0.866676 | − | 1.50113i | −0.0778298 | − | 0.134805i | ||||
\(125\) | 4.79391 | + | 10.1004i | 0.428780 | + | 0.903409i | ||||
\(126\) | −0.521889 | + | 0.903939i | −0.0464936 | + | 0.0805293i | ||||
\(127\) | 2.96848 | + | 1.71385i | 0.263410 | + | 0.152080i | 0.625889 | − | 0.779912i | \(-0.284736\pi\) |
−0.362479 | + | 0.931992i | \(0.618070\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 0.731945 | + | 1.26777i | 0.0644442 | + | 0.111621i | ||||
\(130\) | −1.45209 | − | 9.75880i | −0.127357 | − | 0.855903i | ||||
\(131\) | −9.37585 | + | 16.2395i | −0.819172 | + | 1.41885i | 0.0871208 | + | 0.996198i | \(0.472233\pi\) |
−0.906293 | + | 0.422650i | \(0.861100\pi\) | |||||||
\(132\) | 0.759809 | + | 0.438676i | 0.0661329 | + | 0.0381818i | ||||
\(133\) | −2.73637 | − | 1.57985i | −0.237274 | − | 0.136990i | ||||
\(134\) | 2.66533 | 0.230249 | ||||||||
\(135\) | −2.21172 | + | 0.329099i | −0.190354 | + | 0.0283243i | ||||
\(136\) | −2.56629 | + | 4.44494i | −0.220058 | + | 0.381151i | ||||
\(137\) | − | 20.6333i | − | 1.76282i | −0.472348 | − | 0.881412i | \(-0.656593\pi\) | ||
0.472348 | − | 0.881412i | \(-0.343407\pi\) | |||||||
\(138\) | 7.11017i | 0.605258i | ||||||||
\(139\) | 3.04472 | − | 5.27361i | 0.258250 | − | 0.447302i | −0.707523 | − | 0.706690i | \(-0.750188\pi\) |
0.965773 | + | 0.259388i | \(0.0835209\pi\) | |||||||
\(140\) | 0.856787 | − | 2.17101i | 0.0724117 | − | 0.183484i | ||||
\(141\) | 1.50025 | + | 2.59851i | 0.126344 | + | 0.218834i | ||||
\(142\) | − | 1.16507i | − | 0.0977702i | ||||||
\(143\) | −3.35252 | + | 1.93558i | −0.280352 | + | 0.161861i | ||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | −1.96186 | − | 13.1847i | −0.162923 | − | 1.09493i | ||||
\(146\) | 2.86840 | − | 4.96821i | 0.237390 | − | 0.411172i | ||||
\(147\) | 5.91053i | 0.487492i | ||||||||
\(148\) | 5.25856 | − | 3.05738i | 0.432251 | − | 0.251315i | ||||
\(149\) | 10.4868 | 0.859109 | 0.429555 | − | 0.903041i | \(-0.358671\pi\) | ||||
0.429555 | + | 0.903041i | \(0.358671\pi\) | |||||||
\(150\) | 4.78339 | − | 1.45575i | 0.390562 | − | 0.118861i | ||||
\(151\) | −1.64176 | − | 2.84361i | −0.133604 | − | 0.231410i | 0.791459 | − | 0.611222i | \(-0.209322\pi\) |
−0.925063 | + | 0.379813i | \(0.875988\pi\) | |||||||
\(152\) | −2.62160 | + | 1.51358i | −0.212640 | + | 0.122768i | ||||
\(153\) | −4.44494 | + | 2.56629i | −0.359353 | + | 0.207472i | ||||
\(154\) | −0.915761 | −0.0737941 | ||||||||
\(155\) | 0.570444 | + | 3.83369i | 0.0458192 | + | 0.307929i | ||||
\(156\) | −4.41232 | −0.353268 | ||||||||
\(157\) | −4.20988 | − | 2.43057i | −0.335985 | − | 0.193981i | 0.322510 | − | 0.946566i | \(-0.395473\pi\) |
−0.658495 | + | 0.752585i | \(0.728807\pi\) | |||||||
\(158\) | 10.0776i | 0.801727i | ||||||||
\(159\) | −12.8965 | −1.02276 | ||||||||
\(160\) | −1.39087 | − | 1.75085i | −0.109958 | − | 0.138417i | ||||
\(161\) | −3.71072 | − | 6.42716i | −0.292446 | − | 0.506531i | ||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 18.1870 | + | 10.5002i | 1.42451 | + | 0.822443i | 0.996680 | − | 0.0814153i | \(-0.0259440\pi\) |
0.427832 | + | 0.903858i | \(0.359277\pi\) | |||||||
\(164\) | −3.12701 | + | 5.41615i | −0.244179 | + | 0.422930i | ||||
\(165\) | −1.22028 | − | 1.53611i | −0.0949986 | − | 0.119586i | ||||
\(166\) | 5.61630 | + | 9.72771i | 0.435909 | + | 0.755017i | ||||
\(167\) | 5.55334 | − | 3.20622i | 0.429731 | − | 0.248105i | −0.269501 | − | 0.963000i | \(-0.586859\pi\) |
0.699232 | + | 0.714895i | \(0.253525\pi\) | |||||||
\(168\) | −0.903939 | − | 0.521889i | −0.0697404 | − | 0.0402646i | ||||
\(169\) | 3.23427 | − | 5.60192i | 0.248790 | − | 0.430917i | ||||
\(170\) | 8.98640 | − | 7.13873i | 0.689225 | − | 0.547516i | ||||
\(171\) | −3.02716 | −0.231493 | ||||||||
\(172\) | −1.26777 | + | 0.731945i | −0.0966663 | + | 0.0558103i | ||||
\(173\) | −0.334462 | − | 0.193102i | −0.0254287 | − | 0.0146813i | 0.487232 | − | 0.873273i | \(-0.338007\pi\) |
−0.512660 | + | 0.858591i | \(0.671340\pi\) | |||||||
\(174\) | −5.96130 | −0.451925 | ||||||||
\(175\) | −3.56415 | + | 3.81231i | −0.269425 | + | 0.288183i | ||||
\(176\) | −0.438676 | + | 0.759809i | −0.0330664 | + | 0.0572727i | ||||
\(177\) | − | 8.64713i | − | 0.649958i | ||||||
\(178\) | −13.2273 | + | 7.63676i | −0.991425 | + | 0.572400i | ||||
\(179\) | −18.1446 | −1.35619 | −0.678094 | − | 0.734975i | \(-0.737194\pi\) | ||||
−0.678094 | + | 0.734975i | \(0.737194\pi\) | |||||||
\(180\) | −0.329099 | − | 2.21172i | −0.0245296 | − | 0.164852i | ||||
\(181\) | 2.94193 | + | 5.09557i | 0.218672 | + | 0.378750i | 0.954402 | − | 0.298524i | \(-0.0964943\pi\) |
−0.735730 | + | 0.677274i | \(0.763161\pi\) | |||||||
\(182\) | 3.98846 | − | 2.30274i | 0.295645 | − | 0.170691i | ||||
\(183\) | 3.13192 | + | 1.80822i | 0.231518 | + | 0.133667i | ||||
\(184\) | −7.11017 | −0.524169 | ||||||||
\(185\) | −13.4472 | + | 2.04273i | −0.988658 | + | 0.150184i | ||||
\(186\) | 1.73335 | 0.127096 | ||||||||
\(187\) | −3.89978 | − | 2.25154i | −0.285180 | − | 0.164649i | ||||
\(188\) | −2.59851 | + | 1.50025i | −0.189516 | + | 0.109417i | ||||
\(189\) | −0.521889 | − | 0.903939i | −0.0379619 | − | 0.0657519i | ||||
\(190\) | 6.69523 | − | 0.996236i | 0.485723 | − | 0.0722746i | ||||
\(191\) | 11.9257 | 0.862911 | 0.431455 | − | 0.902134i | \(-0.358000\pi\) | ||||
0.431455 | + | 0.902134i | \(0.358000\pi\) | |||||||
\(192\) | −0.866025 | + | 0.500000i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | 2.74542i | 0.197620i | 0.995106 | + | 0.0988099i | \(0.0315036\pi\) | ||||
−0.995106 | + | 0.0988099i | \(0.968496\pi\) | |||||||
\(194\) | −4.53961 | + | 7.86284i | −0.325925 | + | 0.564519i | ||||
\(195\) | 9.17741 | + | 3.62185i | 0.657208 | + | 0.259366i | ||||
\(196\) | −5.91053 | −0.422180 | ||||||||
\(197\) | 2.67557 | + | 1.54474i | 0.190627 | + | 0.110058i | 0.592276 | − | 0.805735i | \(-0.298230\pi\) |
−0.401649 | + | 0.915794i | \(0.631563\pi\) | |||||||
\(198\) | −0.759809 | + | 0.438676i | −0.0539973 | + | 0.0311753i | ||||
\(199\) | 21.7511 | 1.54189 | 0.770946 | − | 0.636900i | \(-0.219784\pi\) | ||||
0.770946 | + | 0.636900i | \(0.219784\pi\) | |||||||
\(200\) | 1.45575 | + | 4.78339i | 0.102937 | + | 0.338237i | ||||
\(201\) | −1.33266 | + | 2.30824i | −0.0939988 | + | 0.162811i | ||||
\(202\) | −1.71194 | − | 0.988392i | −0.120452 | − | 0.0695430i | ||||
\(203\) | 5.38865 | − | 3.11114i | 0.378209 | − | 0.218359i | ||||
\(204\) | −2.56629 | − | 4.44494i | −0.179676 | − | 0.311208i | ||||
\(205\) | 10.9499 | − | 8.69852i | 0.764773 | − | 0.607531i | ||||
\(206\) | 2.74254 | − | 4.75021i | 0.191082 | − | 0.330963i | ||||
\(207\) | −6.15759 | − | 3.55509i | −0.427982 | − | 0.247096i | ||||
\(208\) | − | 4.41232i | − | 0.305939i | ||||||
\(209\) | −1.32794 | − | 2.30007i | −0.0918558 | − | 0.159099i | ||||
\(210\) | 1.45176 | + | 1.82750i | 0.100181 | + | 0.126110i | ||||
\(211\) | 23.5364 | 1.62032 | 0.810158 | − | 0.586212i | \(-0.199381\pi\) | ||||
0.810158 | + | 0.586212i | \(0.199381\pi\) | |||||||
\(212\) | − | 12.8965i | − | 0.885738i | ||||||
\(213\) | 1.00898 | + | 0.582533i | 0.0691340 | + | 0.0399145i | ||||
\(214\) | 0.236722 | 0.0161820 | ||||||||
\(215\) | 3.23771 | − | 0.481765i | 0.220810 | − | 0.0328561i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −1.56684 | + | 0.904618i | −0.106364 | + | 0.0614095i | ||||
\(218\) | −5.88369 | + | 3.39695i | −0.398494 | + | 0.230070i | ||||
\(219\) | 2.86840 | + | 4.96821i | 0.193828 | + | 0.335721i | ||||
\(220\) | 1.53611 | − | 1.22028i | 0.103565 | − | 0.0822712i | ||||
\(221\) | 22.6466 | 1.52337 | ||||||||
\(222\) | 0.0184948 | + | 6.08273i | 0.00124129 | + | 0.408246i | ||||
\(223\) | 21.8135i | 1.46074i | 0.683051 | + | 0.730371i | \(0.260653\pi\) | ||||
−0.683051 | + | 0.730371i | \(0.739347\pi\) | |||||||
\(224\) | 0.521889 | − | 0.903939i | 0.0348702 | − | 0.0603970i | ||||
\(225\) | −1.13098 | + | 4.87041i | −0.0753987 | + | 0.324694i | ||||
\(226\) | −5.40069 | − | 9.35427i | −0.359249 | − | 0.622237i | ||||
\(227\) | 11.3937 | − | 6.57817i | 0.756229 | − | 0.436609i | −0.0717115 | − | 0.997425i | \(-0.522846\pi\) |
0.827940 | + | 0.560817i | \(0.189513\pi\) | |||||||
\(228\) | − | 3.02716i | − | 0.200479i | ||||||
\(229\) | −7.76074 | − | 13.4420i | −0.512844 | − | 0.888273i | −0.999889 | − | 0.0148955i | \(-0.995258\pi\) |
0.487045 | − | 0.873377i | \(-0.338075\pi\) | |||||||
\(230\) | 14.7888 | + | 5.83639i | 0.975146 | + | 0.384840i | ||||
\(231\) | 0.457881 | − | 0.793072i | 0.0301263 | − | 0.0521803i | ||||
\(232\) | − | 5.96130i | − | 0.391379i | ||||||
\(233\) | 20.8578i | 1.36644i | 0.730213 | + | 0.683220i | \(0.239421\pi\) | ||||
−0.730213 | + | 0.683220i | \(0.760579\pi\) | |||||||
\(234\) | 2.20616 | − | 3.82118i | 0.144221 | − | 0.249798i | ||||
\(235\) | 6.63626 | − | 0.987462i | 0.432902 | − | 0.0644149i | ||||
\(236\) | 8.64713 | 0.562880 | ||||||||
\(237\) | −8.72742 | − | 5.03878i | −0.566907 | − | 0.327304i | ||||
\(238\) | 4.63954 | + | 2.67864i | 0.300737 | + | 0.173630i | ||||
\(239\) | 1.58208 | − | 2.74024i | 0.102336 | − | 0.177251i | −0.810311 | − | 0.586001i | \(-0.800702\pi\) |
0.912647 | + | 0.408749i | \(0.134035\pi\) | |||||||
\(240\) | 2.21172 | − | 0.329099i | 0.142766 | − | 0.0212432i | ||||
\(241\) | −3.34456 | − | 5.79294i | −0.215442 | − | 0.373156i | 0.737967 | − | 0.674836i | \(-0.235786\pi\) |
−0.953409 | + | 0.301680i | \(0.902453\pi\) | |||||||
\(242\) | 8.85966 | + | 5.11513i | 0.569521 | + | 0.328813i | ||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | −1.80822 | + | 3.13192i | −0.115759 | + | 0.200501i | ||||
\(245\) | 12.2936 | + | 4.85166i | 0.785410 | + | 0.309961i | ||||
\(246\) | −3.12701 | − | 5.41615i | −0.199371 | − | 0.345321i | ||||
\(247\) | 11.5673 | + | 6.67840i | 0.736012 | + | 0.424937i | ||||
\(248\) | 1.73335i | 0.110068i | ||||||||
\(249\) | −11.2326 | −0.711837 | ||||||||
\(250\) | 0.898562 | − | 11.1442i | 0.0568300 | − | 0.704819i | ||||
\(251\) | −13.7418 | −0.867373 | −0.433686 | − | 0.901064i | \(-0.642787\pi\) | ||||
−0.433686 | + | 0.901064i | \(0.642787\pi\) | |||||||
\(252\) | 0.903939 | − | 0.521889i | 0.0569428 | − | 0.0328759i | ||||
\(253\) | − | 6.23812i | − | 0.392187i | ||||||
\(254\) | −1.71385 | − | 2.96848i | −0.107537 | − | 0.186259i | ||||
\(255\) | 1.68913 | + | 11.3518i | 0.105777 | + | 0.710878i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −0.431560 | − | 0.249162i | −0.0269200 | − | 0.0155423i | 0.486480 | − | 0.873692i | \(-0.338281\pi\) |
−0.513400 | + | 0.858150i | \(0.671614\pi\) | |||||||
\(258\) | − | 1.46389i | − | 0.0911379i | ||||||
\(259\) | −3.19123 | − | 5.48877i | −0.198294 | − | 0.341055i | ||||
\(260\) | −3.62185 | + | 9.17741i | −0.224618 | + | 0.569159i | ||||
\(261\) | 2.98065 | − | 5.16264i | 0.184498 | − | 0.319559i | ||||
\(262\) | 16.2395 | − | 9.37585i | 1.00328 | − | 0.579242i | ||||
\(263\) | 20.0619 | − | 11.5827i | 1.23707 | − | 0.714221i | 0.268574 | − | 0.963259i | \(-0.413448\pi\) |
0.968494 | + | 0.249038i | \(0.0801143\pi\) | |||||||
\(264\) | −0.438676 | − | 0.759809i | −0.0269986 | − | 0.0467630i | ||||
\(265\) | −10.5861 | + | 26.8242i | −0.650301 | + | 1.64780i | ||||
\(266\) | 1.57985 | + | 2.73637i | 0.0968665 | + | 0.167778i | ||||
\(267\) | − | 15.2735i | − | 0.934725i | ||||||
\(268\) | −2.30824 | − | 1.33266i | −0.140998 | − | 0.0814054i | ||||
\(269\) | 20.2746 | 1.23617 | 0.618083 | − | 0.786113i | \(-0.287910\pi\) | ||||
0.618083 | + | 0.786113i | \(0.287910\pi\) | |||||||
\(270\) | 2.07995 | + | 0.820851i | 0.126582 | + | 0.0499554i | ||||
\(271\) | −10.3687 | + | 17.9591i | −0.629852 | + | 1.09094i | 0.357729 | + | 0.933826i | \(0.383551\pi\) |
−0.987581 | + | 0.157111i | \(0.949782\pi\) | |||||||
\(272\) | 4.44494 | − | 2.56629i | 0.269514 | − | 0.155604i | ||||
\(273\) | 4.60548i | 0.278736i | ||||||||
\(274\) | −10.3167 | + | 17.8690i | −0.623252 | + | 1.07950i | ||||
\(275\) | −4.19671 | + | 1.27720i | −0.253071 | + | 0.0770182i | ||||
\(276\) | 3.55509 | − | 6.15759i | 0.213991 | − | 0.370643i | ||||
\(277\) | 9.85578 | − | 5.69024i | 0.592177 | − | 0.341893i | −0.173781 | − | 0.984784i | \(-0.555599\pi\) |
0.765958 | + | 0.642891i | \(0.222265\pi\) | |||||||
\(278\) | −5.27361 | + | 3.04472i | −0.316290 | + | 0.182610i | ||||
\(279\) | −0.866676 | + | 1.50113i | −0.0518865 | + | 0.0898701i | ||||
\(280\) | −1.82750 | + | 1.45176i | −0.109214 | + | 0.0867591i | ||||
\(281\) | 6.84750 | − | 11.8602i | 0.408488 | − | 0.707521i | −0.586233 | − | 0.810143i | \(-0.699390\pi\) |
0.994721 | + | 0.102621i | \(0.0327229\pi\) | |||||||
\(282\) | − | 3.00050i | − | 0.178677i | ||||||
\(283\) | 21.3150 | − | 12.3062i | 1.26704 | − | 0.731527i | 0.292615 | − | 0.956230i | \(-0.405474\pi\) |
0.974427 | + | 0.224703i | \(0.0721411\pi\) | |||||||
\(284\) | −0.582533 | + | 1.00898i | −0.0345670 | + | 0.0598718i | ||||
\(285\) | −2.48485 | + | 6.29636i | −0.147190 | + | 0.372964i | ||||
\(286\) | 3.87115 | 0.228906 | ||||||||
\(287\) | 5.65326 | + | 3.26391i | 0.333701 | + | 0.192663i | ||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | 4.67169 | + | 8.09161i | 0.274805 | + | 0.475977i | ||||
\(290\) | −4.89334 | + | 12.3992i | −0.287347 | + | 0.728108i | ||||
\(291\) | −4.53961 | − | 7.86284i | −0.266117 | − | 0.460928i | ||||
\(292\) | −4.96821 | + | 2.86840i | −0.290743 | + | 0.167860i | ||||
\(293\) | 20.6285 | − | 11.9099i | 1.20513 | − | 0.695782i | 0.243438 | − | 0.969916i | \(-0.421725\pi\) |
0.961691 | + | 0.274135i | \(0.0883914\pi\) | |||||||
\(294\) | 2.95526 | − | 5.11867i | 0.172354 | − | 0.298527i | ||||
\(295\) | −17.9856 | − | 7.09800i | −1.04716 | − | 0.413262i | ||||
\(296\) | −6.08273 | + | 0.0184948i | −0.353552 | + | 0.00107499i | ||||
\(297\) | − | 0.877352i | − | 0.0509091i | ||||||
\(298\) | −9.08180 | − | 5.24338i | −0.526095 | − | 0.303741i | ||||
\(299\) | 15.6862 | + | 27.1692i | 0.907154 | + | 1.57124i | ||||
\(300\) | −4.87041 | − | 1.13098i | −0.281193 | − | 0.0652972i | ||||
\(301\) | 0.763989 | + | 1.32327i | 0.0440356 | + | 0.0762719i | ||||
\(302\) | 3.28352i | 0.188945i | ||||||||
\(303\) | 1.71194 | − | 0.988392i | 0.0983486 | − | 0.0567816i | ||||
\(304\) | 3.02716 | 0.173620 | ||||||||
\(305\) | 6.33185 | − | 5.02998i | 0.362560 | − | 0.288016i | ||||
\(306\) | 5.13258 | 0.293410 | ||||||||
\(307\) | 11.6875i | 0.667039i | 0.942743 | + | 0.333520i | \(0.108236\pi\) | ||||
−0.942743 | + | 0.333520i | \(0.891764\pi\) | |||||||
\(308\) | 0.793072 | + | 0.457881i | 0.0451895 | + | 0.0260902i | ||||
\(309\) | 2.74254 | + | 4.75021i | 0.156017 | + | 0.270230i | ||||
\(310\) | 1.42282 | − | 3.60529i | 0.0808110 | − | 0.204767i | ||||
\(311\) | 9.68464 | − | 16.7743i | 0.549166 | − | 0.951183i | −0.449166 | − | 0.893448i | \(-0.648279\pi\) |
0.998332 | − | 0.0577348i | \(-0.0183878\pi\) | |||||||
\(312\) | 3.82118 | + | 2.20616i | 0.216332 | + | 0.124899i | ||||
\(313\) | 12.7904 | + | 7.38454i | 0.722956 | + | 0.417399i | 0.815840 | − | 0.578278i | \(-0.196275\pi\) |
−0.0928839 | + | 0.995677i | \(0.529609\pi\) | |||||||
\(314\) | 2.43057 | + | 4.20988i | 0.137165 | + | 0.237577i | ||||
\(315\) | −2.30854 | + | 0.343506i | −0.130072 | + | 0.0193544i | ||||
\(316\) | 5.03878 | − | 8.72742i | 0.283453 | − | 0.490956i | ||||
\(317\) | −5.38368 | − | 3.10827i | −0.302378 | − | 0.174578i | 0.341133 | − | 0.940015i | \(-0.389189\pi\) |
−0.643511 | + | 0.765437i | \(0.722523\pi\) | |||||||
\(318\) | 11.1687 | + | 6.44827i | 0.626312 | + | 0.361601i | ||||
\(319\) | 5.23016 | 0.292833 | ||||||||
\(320\) | 0.329099 | + | 2.21172i | 0.0183972 | + | 0.123639i | ||||
\(321\) | −0.118361 | + | 0.205007i | −0.00660627 | + | 0.0114424i | ||||
\(322\) | 7.42145i | 0.413581i | ||||||||
\(323\) | 15.5372i | 0.864511i | ||||||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | 15.0666 | − | 16.1156i | 0.835743 | − | 0.893932i | ||||
\(326\) | −10.5002 | − | 18.1870i | −0.581555 | − | 1.00728i | ||||
\(327\) | − | 6.79390i | − | 0.375703i | ||||||
\(328\) | 5.41615 | − | 3.12701i | 0.299057 | − | 0.172660i | ||||
\(329\) | 1.56593 | + | 2.71227i | 0.0863325 | + | 0.149532i | ||||
\(330\) | 0.288735 | + | 1.94045i | 0.0158944 | + | 0.106818i | ||||
\(331\) | −11.5832 | + | 20.0626i | −0.636668 | + | 1.10274i | 0.349491 | + | 0.936940i | \(0.386354\pi\) |
−0.986159 | + | 0.165801i | \(0.946979\pi\) | |||||||
\(332\) | − | 11.2326i | − | 0.616469i | ||||||
\(333\) | −5.27705 | − | 3.02535i | −0.289181 | − | 0.165788i | ||||
\(334\) | −6.41245 | −0.350874 | ||||||||
\(335\) | 3.70711 | + | 4.66660i | 0.202541 | + | 0.254964i | ||||
\(336\) | 0.521889 | + | 0.903939i | 0.0284714 | + | 0.0493139i | ||||
\(337\) | 10.2042 | − | 5.89139i | 0.555857 | − | 0.320924i | −0.195624 | − | 0.980679i | \(-0.562673\pi\) |
0.751481 | + | 0.659755i | \(0.229340\pi\) | |||||||
\(338\) | −5.60192 | + | 3.23427i | −0.304704 | + | 0.175921i | ||||
\(339\) | 10.8014 | 0.586650 | ||||||||
\(340\) | −11.3518 | + | 1.68913i | −0.615639 | + | 0.0916057i | ||||
\(341\) | −1.52076 | −0.0823538 | ||||||||
\(342\) | 2.62160 | + | 1.51358i | 0.141760 | + | 0.0818452i | ||||
\(343\) | 13.4757i | 0.727621i | ||||||||
\(344\) | 1.46389 | 0.0789277 | ||||||||
\(345\) | −12.4489 | + | 9.88930i | −0.670225 | + | 0.532422i | ||||
\(346\) | 0.193102 | + | 0.334462i | 0.0103812 | + | 0.0179808i | ||||
\(347\) | − | 20.6749i | − | 1.10988i | −0.831889 | − | 0.554942i | \(-0.812740\pi\) | ||
0.831889 | − | 0.554942i | \(-0.187260\pi\) | |||||||
\(348\) | 5.16264 | + | 2.98065i | 0.276747 | + | 0.159780i | ||||
\(349\) | 9.11242 | − | 15.7832i | 0.487777 | − | 0.844854i | −0.512124 | − | 0.858911i | \(-0.671141\pi\) |
0.999901 | + | 0.0140571i | \(0.00447465\pi\) | |||||||
\(350\) | 4.99280 | − | 1.51948i | 0.266876 | − | 0.0812195i | ||||
\(351\) | 2.20616 | + | 3.82118i | 0.117756 | + | 0.203959i | ||||
\(352\) | 0.759809 | − | 0.438676i | 0.0404979 | − | 0.0233815i | ||||
\(353\) | −24.8210 | − | 14.3304i | −1.32109 | − | 0.762731i | −0.337186 | − | 0.941438i | \(-0.609475\pi\) |
−0.983902 | + | 0.178707i | \(0.942808\pi\) | |||||||
\(354\) | −4.32356 | + | 7.48863i | −0.229795 | + | 0.398016i | ||||
\(355\) | 2.03986 | − | 1.62045i | 0.108265 | − | 0.0860046i | ||||
\(356\) | 15.2735 | 0.809495 | ||||||||
\(357\) | −4.63954 | + | 2.67864i | −0.245550 | + | 0.141769i | ||||
\(358\) | 15.7137 | + | 9.07228i | 0.830493 | + | 0.479485i | ||||
\(359\) | 23.0581 | 1.21696 | 0.608480 | − | 0.793569i | \(-0.291780\pi\) | ||||
0.608480 | + | 0.793569i | \(0.291780\pi\) | |||||||
\(360\) | −0.820851 | + | 2.07995i | −0.0432626 | + | 0.109623i | ||||
\(361\) | 4.91814 | − | 8.51846i | 0.258849 | − | 0.448340i | ||||
\(362\) | − | 5.88385i | − | 0.309248i | ||||||
\(363\) | −8.85966 | + | 5.11513i | −0.465012 | + | 0.268475i | ||||
\(364\) | −4.60548 | −0.241393 | ||||||||
\(365\) | 12.6882 | − | 1.88797i | 0.664130 | − | 0.0988211i | ||||
\(366\) | −1.80822 | − | 3.13192i | −0.0945170 | − | 0.163708i | ||||
\(367\) | 22.8357 | − | 13.1842i | 1.19201 | − | 0.688210i | 0.233251 | − | 0.972416i | \(-0.425063\pi\) |
0.958763 | + | 0.284207i | \(0.0917302\pi\) | |||||||
\(368\) | 6.15759 | + | 3.55509i | 0.320987 | + | 0.185322i | ||||
\(369\) | 6.25403 | 0.325572 | ||||||||
\(370\) | 12.6670 | + | 4.95455i | 0.658525 | + | 0.257575i | ||||
\(371\) | −13.4611 | −0.698867 | ||||||||
\(372\) | −1.50113 | − | 0.866676i | −0.0778298 | − | 0.0449351i | ||||
\(373\) | 23.6605 | − | 13.6604i | 1.22509 | − | 0.707308i | 0.259094 | − | 0.965852i | \(-0.416576\pi\) |
0.965999 | + | 0.258544i | \(0.0832427\pi\) | |||||||
\(374\) | 2.25154 | + | 3.89978i | 0.116424 | + | 0.201653i | ||||
\(375\) | 9.20186 | + | 6.35026i | 0.475182 | + | 0.327926i | ||||
\(376\) | 3.00050 | 0.154739 | ||||||||
\(377\) | −22.7792 | + | 13.1516i | −1.17319 | + | 0.677341i | ||||
\(378\) | 1.04378i | 0.0536862i | ||||||||
\(379\) | 2.47817 | − | 4.29231i | 0.127295 | − | 0.220481i | −0.795333 | − | 0.606173i | \(-0.792704\pi\) |
0.922628 | + | 0.385692i | \(0.126037\pi\) | |||||||
\(380\) | −6.29636 | − | 2.48485i | −0.322996 | − | 0.127470i | ||||
\(381\) | 3.42770 | 0.175607 | ||||||||
\(382\) | −10.3279 | − | 5.96283i | −0.528423 | − | 0.305085i | ||||
\(383\) | −30.3000 | + | 17.4937i | −1.54826 | + | 0.893886i | −0.549980 | + | 0.835178i | \(0.685365\pi\) |
−0.998275 | + | 0.0587078i | \(0.981302\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −1.27370 | − | 1.60336i | −0.0649138 | − | 0.0817150i | ||||
\(386\) | 1.37271 | − | 2.37760i | 0.0698691 | − | 0.121017i | ||||
\(387\) | 1.26777 | + | 0.731945i | 0.0644442 | + | 0.0372069i | ||||
\(388\) | 7.86284 | − | 4.53961i | 0.399175 | − | 0.230464i | ||||
\(389\) | −16.5222 | − | 28.6172i | −0.837707 | − | 1.45095i | −0.891807 | − | 0.452415i | \(-0.850563\pi\) |
0.0541006 | − | 0.998535i | \(-0.482771\pi\) | |||||||
\(390\) | −6.13694 | − | 7.72532i | −0.310756 | − | 0.391187i | ||||
\(391\) | −18.2468 | + | 31.6043i | −0.922779 | + | 1.59830i | ||||
\(392\) | 5.11867 | + | 2.95526i | 0.258532 | + | 0.149263i | ||||
\(393\) | 18.7517i | 0.945899i | ||||||||
\(394\) | −1.54474 | − | 2.67557i | −0.0778230 | − | 0.134793i | ||||
\(395\) | −17.6443 | + | 14.0165i | −0.887782 | + | 0.705248i | ||||
\(396\) | 0.877352 | 0.0440886 | ||||||||
\(397\) | − | 17.4364i | − | 0.875109i | −0.899192 | − | 0.437554i | \(-0.855845\pi\) | ||
0.899192 | − | 0.437554i | \(-0.144155\pi\) | |||||||
\(398\) | −18.8370 | − | 10.8755i | −0.944212 | − | 0.545141i | ||||
\(399\) | −3.15969 | −0.158182 | ||||||||
\(400\) | 1.13098 | − | 4.87041i | 0.0565490 | − | 0.243520i | ||||
\(401\) | −25.6014 | −1.27847 | −0.639237 | − | 0.769010i | \(-0.720750\pi\) | ||||
−0.639237 | + | 0.769010i | \(0.720750\pi\) | |||||||
\(402\) | 2.30824 | − | 1.33266i | 0.115125 | − | 0.0664672i | ||||
\(403\) | 6.62345 | − | 3.82405i | 0.329937 | − | 0.190489i | ||||
\(404\) | 0.988392 | + | 1.71194i | 0.0491743 | + | 0.0851724i | ||||
\(405\) | −1.75085 | + | 1.39087i | −0.0870006 | + | 0.0691127i | ||||
\(406\) | −6.22228 | −0.308807 | ||||||||
\(407\) | −0.0162264 | − | 5.33670i | −0.000804313 | − | 0.264530i | ||||
\(408\) | 5.13258i | 0.254101i | ||||||||
\(409\) | −3.56975 | + | 6.18298i | −0.176513 | + | 0.305729i | −0.940684 | − | 0.339285i | \(-0.889815\pi\) |
0.764171 | + | 0.645014i | \(0.223148\pi\) | |||||||
\(410\) | −13.8321 | + | 2.05819i | −0.683121 | + | 0.101647i | ||||
\(411\) | −10.3167 | − | 17.8690i | −0.508884 | − | 0.881412i | ||||
\(412\) | −4.75021 | + | 2.74254i | −0.234026 | + | 0.135115i | ||||
\(413\) | − | 9.02569i | − | 0.444125i | ||||||
\(414\) | 3.55509 | + | 6.15759i | 0.174723 | + | 0.302629i | ||||
\(415\) | −9.22028 | + | 23.3633i | −0.452606 | + | 1.14686i | ||||
\(416\) | −2.20616 | + | 3.82118i | −0.108166 | + | 0.187349i | ||||
\(417\) | − | 6.08944i | − | 0.298201i | ||||||
\(418\) | 2.65589i | 0.129904i | ||||||||
\(419\) | −10.8835 | + | 18.8507i | −0.531693 | + | 0.920919i | 0.467623 | + | 0.883928i | \(0.345111\pi\) |
−0.999316 | + | 0.0369911i | \(0.988223\pi\) | |||||||
\(420\) | −0.343506 | − | 2.30854i | −0.0167614 | − | 0.112645i | ||||
\(421\) | 31.9568 | 1.55748 | 0.778738 | − | 0.627349i | \(-0.215860\pi\) | ||||
0.778738 | + | 0.627349i | \(0.215860\pi\) | |||||||
\(422\) | −20.3832 | − | 11.7682i | −0.992237 | − | 0.572868i | ||||
\(423\) | 2.59851 | + | 1.50025i | 0.126344 | + | 0.0729447i | ||||
\(424\) | −6.44827 | + | 11.1687i | −0.313156 | + | 0.542402i | ||||
\(425\) | 24.9978 | + | 5.80485i | 1.21257 | + | 0.281576i | ||||
\(426\) | −0.582533 | − | 1.00898i | −0.0282238 | − | 0.0488851i | ||||
\(427\) | 3.26903 | + | 1.88738i | 0.158200 | + | 0.0913366i | ||||
\(428\) | −0.205007 | − | 0.118361i | −0.00990941 | − | 0.00572120i | ||||
\(429\) | −1.93558 | + | 3.35252i | −0.0934505 | + | 0.161861i | ||||
\(430\) | −3.04482 | − | 1.20164i | −0.146834 | − | 0.0579480i | ||||
\(431\) | 9.19553 | + | 15.9271i | 0.442933 | + | 0.767182i | 0.997906 | − | 0.0646862i | \(-0.0206046\pi\) |
−0.554973 | + | 0.831869i | \(0.687271\pi\) | |||||||
\(432\) | 0.866025 | + | 0.500000i | 0.0416667 | + | 0.0240563i | ||||
\(433\) | 15.3476i | 0.737559i | 0.929517 | + | 0.368780i | \(0.120224\pi\) | ||||
−0.929517 | + | 0.368780i | \(0.879776\pi\) | |||||||
\(434\) | 1.80924 | 0.0868461 | ||||||||
\(435\) | −8.29138 | − | 10.4374i | −0.397541 | − | 0.500434i | ||||
\(436\) | 6.79390 | 0.325369 | ||||||||
\(437\) | −18.6400 | + | 10.7618i | −0.891674 | + | 0.514808i | ||||
\(438\) | − | 5.73680i | − | 0.274115i | ||||||
\(439\) | −4.20538 | − | 7.28393i | −0.200712 | − | 0.347643i | 0.748046 | − | 0.663647i | \(-0.230992\pi\) |
−0.948758 | + | 0.316004i | \(0.897659\pi\) | |||||||
\(440\) | −1.94045 | + | 0.288735i | −0.0925075 | + | 0.0137649i | ||||
\(441\) | 2.95526 | + | 5.11867i | 0.140727 | + | 0.243746i | ||||
\(442\) | −19.6125 | − | 11.3233i | −0.932872 | − | 0.538594i | ||||
\(443\) | − | 25.4261i | − | 1.20803i | −0.796973 | − | 0.604014i | \(-0.793567\pi\) | ||
0.796973 | − | 0.604014i | \(-0.206433\pi\) | |||||||
\(444\) | 3.02535 | − | 5.27705i | 0.143577 | − | 0.250438i | ||||
\(445\) | −31.7682 | − | 12.5373i | −1.50596 | − | 0.594324i | ||||
\(446\) | 10.9068 | − | 18.8911i | 0.516450 | − | 0.894518i | ||||
\(447\) | 9.08180 | − | 5.24338i | 0.429555 | − | 0.248003i | ||||
\(448\) | −0.903939 | + | 0.521889i | −0.0427071 | + | 0.0246570i | ||||
\(449\) | −1.18209 | − | 2.04745i | −0.0557864 | − | 0.0966250i | 0.836784 | − | 0.547534i | \(-0.184433\pi\) |
−0.892570 | + | 0.450909i | \(0.851100\pi\) | |||||||
\(450\) | 3.41466 | − | 3.65241i | 0.160969 | − | 0.172176i | ||||
\(451\) | 2.74349 | + | 4.75186i | 0.129186 | + | 0.223757i | ||||
\(452\) | 10.8014i | 0.508054i | ||||||||
\(453\) | −2.84361 | − | 1.64176i | −0.133604 | − | 0.0771365i | ||||
\(454\) | −13.1563 | −0.617458 | ||||||||
\(455\) | 9.57919 | + | 3.78041i | 0.449079 | + | 0.177229i | ||||
\(456\) | −1.51358 | + | 2.62160i | −0.0708800 | + | 0.122768i | ||||
\(457\) | −4.33201 | + | 2.50109i | −0.202643 | + | 0.116996i | −0.597888 | − | 0.801580i | \(-0.703993\pi\) |
0.395245 | + | 0.918576i | \(0.370660\pi\) | |||||||
\(458\) | 15.5215i | 0.725272i | ||||||||
\(459\) | −2.56629 | + | 4.44494i | −0.119784 | + | 0.207472i | ||||
\(460\) | −9.88930 | − | 12.4489i | −0.461091 | − | 0.580432i | ||||
\(461\) | 3.31413 | − | 5.74025i | 0.154355 | − | 0.267350i | −0.778469 | − | 0.627683i | \(-0.784004\pi\) |
0.932824 | + | 0.360333i | \(0.117337\pi\) | |||||||
\(462\) | −0.793072 | + | 0.457881i | −0.0368971 | + | 0.0213025i | ||||
\(463\) | −2.10365 | + | 1.21454i | −0.0977651 | + | 0.0564447i | −0.548085 | − | 0.836422i | \(-0.684643\pi\) |
0.450320 | + | 0.892867i | \(0.351310\pi\) | |||||||
\(464\) | −2.98065 | + | 5.16264i | −0.138373 | + | 0.239670i | ||||
\(465\) | 2.41086 | + | 3.03485i | 0.111801 | + | 0.140738i | ||||
\(466\) | 10.4289 | − | 18.0634i | 0.483109 | − | 0.836770i | ||||
\(467\) | 10.9068i | 0.504706i | 0.967635 | + | 0.252353i | \(0.0812045\pi\) | ||||
−0.967635 | + | 0.252353i | \(0.918796\pi\) | |||||||
\(468\) | −3.82118 | + | 2.20616i | −0.176634 | + | 0.101980i | ||||
\(469\) | −1.39101 | + | 2.40929i | −0.0642307 | + | 0.111251i | ||||
\(470\) | −6.24090 | − | 2.46296i | −0.287871 | − | 0.113608i | ||||
\(471\) | −4.86115 | −0.223990 | ||||||||
\(472\) | −7.48863 | − | 4.32356i | −0.344692 | − | 0.199008i | ||||
\(473\) | 1.28435i | 0.0590543i | ||||||||
\(474\) | 5.03878 | + | 8.72742i | 0.231439 | + | 0.400864i | ||||
\(475\) | 11.0564 | + | 10.3367i | 0.507304 | + | 0.474282i | ||||
\(476\) | −2.67864 | − | 4.63954i | −0.122775 | − | 0.212653i | ||||
\(477\) | −11.1687 | + | 6.44827i | −0.511381 | + | 0.295246i | ||||
\(478\) | −2.74024 | + | 1.58208i | −0.125335 | + | 0.0723625i | ||||
\(479\) | −9.06499 | + | 15.7010i | −0.414190 | + | 0.717398i | −0.995343 | − | 0.0963964i | \(-0.969268\pi\) |
0.581153 | + | 0.813794i | \(0.302602\pi\) | |||||||
\(480\) | −2.07995 | − | 0.820851i | −0.0949364 | − | 0.0374665i | ||||
\(481\) | 13.4901 | + | 23.2024i | 0.615098 | + | 1.05794i | ||||
\(482\) | 6.68912i | 0.304681i | ||||||||
\(483\) | −6.42716 | − | 3.71072i | −0.292446 | − | 0.168844i | ||||
\(484\) | −5.11513 | − | 8.85966i | −0.232506 | − | 0.402712i | ||||
\(485\) | −20.0807 | + | 2.98796i | −0.911816 | + | 0.135676i | ||||
\(486\) | 0.500000 | + | 0.866025i | 0.0226805 | + | 0.0392837i | ||||
\(487\) | 26.7285i | 1.21118i | 0.795776 | + | 0.605591i | \(0.207063\pi\) | ||||
−0.795776 | + | 0.605591i | \(0.792937\pi\) | |||||||
\(488\) | 3.13192 | − | 1.80822i | 0.141775 | − | 0.0818541i | ||||
\(489\) | 21.0005 | 0.949675 | ||||||||
\(490\) | −8.22075 | − | 10.3485i | −0.371376 | − | 0.467496i | ||||
\(491\) | −35.4896 | −1.60162 | −0.800811 | − | 0.598917i | \(-0.795598\pi\) | ||||
−0.800811 | + | 0.598917i | \(0.795598\pi\) | |||||||
\(492\) | 6.25403i | 0.281953i | ||||||||
\(493\) | −26.4977 | − | 15.2984i | −1.19339 | − | 0.689007i | ||||
\(494\) | −6.67840 | − | 11.5673i | −0.300476 | − | 0.520439i | ||||
\(495\) | −1.82485 | − | 0.720175i | −0.0820209 | − | 0.0323694i | ||||
\(496\) | 0.866676 | − | 1.50113i | 0.0389149 | − | 0.0674026i | ||||
\(497\) | 1.05315 | + | 0.608036i | 0.0472402 | + | 0.0272741i | ||||
\(498\) | 9.72771 | + | 5.61630i | 0.435909 | + | 0.251672i | ||||
\(499\) | 4.80871 | + | 8.32892i | 0.215267 | + | 0.372854i | 0.953355 | − | 0.301851i | \(-0.0976044\pi\) |
−0.738088 | + | 0.674704i | \(0.764271\pi\) | |||||||
\(500\) | −6.35026 | + | 9.20186i | −0.283992 | + | 0.411519i | ||||
\(501\) | 3.20622 | − | 5.55334i | 0.143244 | − | 0.248105i | ||||
\(502\) | 11.9007 | + | 6.87089i | 0.531155 | + | 0.306663i | ||||
\(503\) | −34.5034 | − | 19.9206i | −1.53843 | − | 0.888214i | −0.998931 | − | 0.0462284i | \(-0.985280\pi\) |
−0.539500 | − | 0.841985i | \(-0.681387\pi\) | |||||||
\(504\) | −1.04378 | −0.0464936 | ||||||||
\(505\) | −0.650557 | − | 4.37209i | −0.0289494 | − | 0.194555i | ||||
\(506\) | −3.11906 | + | 5.40237i | −0.138659 | + | 0.240165i | ||||
\(507\) | − | 6.46854i | − | 0.287278i | ||||||
\(508\) | 3.42770i | 0.152080i | ||||||||
\(509\) | 0.416041 | − | 0.720604i | 0.0184407 | − | 0.0319402i | −0.856658 | − | 0.515885i | \(-0.827463\pi\) |
0.875098 | + | 0.483945i | \(0.160796\pi\) | |||||||
\(510\) | 4.21308 | − | 10.6755i | 0.186558 | − | 0.472720i | ||||
\(511\) | 2.99397 | + | 5.18572i | 0.132446 | + | 0.229403i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −2.62160 | + | 1.51358i | −0.115747 | + | 0.0668263i | ||||
\(514\) | 0.249162 | + | 0.431560i | 0.0109900 | + | 0.0190353i | ||||
\(515\) | 12.1314 | − | 1.80513i | 0.534575 | − | 0.0795436i | ||||
\(516\) | −0.731945 | + | 1.26777i | −0.0322221 | + | 0.0558103i | ||||
\(517\) | 2.63250i | 0.115777i | ||||||||
\(518\) | 0.0193044 | + | 6.34903i | 0.000848189 | + | 0.278960i | ||||
\(519\) | −0.386203 | −0.0169525 | ||||||||
\(520\) | 7.72532 | − | 6.13694i | 0.338778 | − | 0.269123i | ||||
\(521\) | −14.0682 | − | 24.3668i | −0.616337 | − | 1.06753i | −0.990148 | − | 0.140022i | \(-0.955283\pi\) |
0.373811 | − | 0.927505i | \(-0.378051\pi\) | |||||||
\(522\) | −5.16264 | + | 2.98065i | −0.225963 | + | 0.130460i | ||||
\(523\) | 3.62695 | − | 2.09402i | 0.158595 | − | 0.0915651i | −0.418602 | − | 0.908170i | \(-0.637480\pi\) |
0.577197 | + | 0.816605i | \(0.304146\pi\) | |||||||
\(524\) | −18.7517 | −0.819172 | ||||||||
\(525\) | −1.18049 | + | 5.08363i | −0.0515209 | + | 0.221868i | ||||
\(526\) | −23.1654 | −1.01006 | ||||||||
\(527\) | 7.70466 | + | 4.44829i | 0.335620 | + | 0.193770i | ||||
\(528\) | 0.877352i | 0.0381818i | ||||||||
\(529\) | −27.5546 | −1.19802 | ||||||||
\(530\) | 22.5800 | − | 17.9374i | 0.980811 | − | 0.779150i | ||||
\(531\) | −4.32356 | − | 7.48863i | −0.187627 | − | 0.324979i | ||||
\(532\) | − | 3.15969i | − | 0.136990i | ||||||
\(533\) | −23.8977 | − | 13.7974i | −1.03513 | − | 0.597630i | ||||
\(534\) | −7.63676 | + | 13.2273i | −0.330475 | + | 0.572400i | ||||
\(535\) | 0.329249 | + | 0.414466i | 0.0142347 | + | 0.0179189i | ||||
\(536\) | 1.33266 | + | 2.30824i | 0.0575623 | + | 0.0997008i | ||||
\(537\) | −15.7137 | + | 9.07228i | −0.678094 | + | 0.391498i | ||||
\(538\) | −17.5583 | − | 10.1373i | −0.756993 | − | 0.437050i | ||||
\(539\) | −2.59280 | + | 4.49087i | −0.111680 | + | 0.193435i | ||||
\(540\) | −1.39087 | − | 1.75085i | −0.0598534 | − | 0.0753448i | ||||
\(541\) | 39.4818 | 1.69746 | 0.848728 | − | 0.528830i | \(-0.177369\pi\) | ||||
0.848728 | + | 0.528830i | \(0.177369\pi\) | |||||||
\(542\) | 17.9591 | − | 10.3687i | 0.771408 | − | 0.445373i | ||||
\(543\) | 5.09557 | + | 2.94193i | 0.218672 | + | 0.126250i | ||||
\(544\) | −5.13258 | −0.220058 | ||||||||
\(545\) | −14.1310 | − | 5.57678i | −0.605305 | − | 0.238883i | ||||
\(546\) | 2.30274 | − | 3.98846i | 0.0985482 | − | 0.170691i | ||||
\(547\) | − | 22.8132i | − | 0.975420i | −0.873006 | − | 0.487710i | \(-0.837832\pi\) | ||
0.873006 | − | 0.487710i | \(-0.162168\pi\) | |||||||
\(548\) | 17.8690 | − | 10.3167i | 0.763325 | − | 0.440706i | ||||
\(549\) | 3.61643 | 0.154346 | ||||||||
\(550\) | 4.27306 | + | 0.992267i | 0.182204 | + | 0.0423104i | ||||
\(551\) | −9.02292 | − | 15.6282i | −0.384389 | − | 0.665782i | ||||
\(552\) | −6.15759 | + | 3.55509i | −0.262084 | + | 0.151315i | ||||
\(553\) | −9.10949 | − | 5.25937i | −0.387375 | − | 0.223651i | ||||
\(554\) | −11.3805 | −0.483510 | ||||||||
\(555\) | −10.6243 | + | 8.49265i | −0.450975 | + | 0.360493i | ||||
\(556\) | 6.08944 | 0.258250 | ||||||||
\(557\) | 4.86784 | + | 2.81045i | 0.206257 | + | 0.119082i | 0.599571 | − | 0.800322i | \(-0.295338\pi\) |
−0.393314 | + | 0.919404i | \(0.628671\pi\) | |||||||
\(558\) | 1.50113 | − | 0.866676i | 0.0635478 | − | 0.0366893i | ||||
\(559\) | −3.22957 | − | 5.59379i | −0.136596 | − | 0.236592i | ||||
\(560\) | 2.30854 | − | 0.343506i | 0.0975538 | − | 0.0145158i | ||||
\(561\) | −4.50308 | −0.190120 | ||||||||
\(562\) | −11.8602 | + | 6.84750i | −0.500293 | + | 0.288844i | ||||
\(563\) | 34.4290i | 1.45101i | 0.688218 | + | 0.725504i | \(0.258393\pi\) | ||||
−0.688218 | + | 0.725504i | \(0.741607\pi\) | |||||||
\(564\) | −1.50025 | + | 2.59851i | −0.0631720 | + | 0.109417i | ||||
\(565\) | 8.86632 | − | 22.4664i | 0.373009 | − | 0.945167i | ||||
\(566\) | −24.6124 | −1.03454 | ||||||||
\(567\) | −0.903939 | − | 0.521889i | −0.0379619 | − | 0.0219173i | ||||
\(568\) | 1.00898 | − | 0.582533i | 0.0423357 | − | 0.0244425i | ||||
\(569\) | −45.5928 | −1.91135 | −0.955675 | − | 0.294423i | \(-0.904872\pi\) | ||||
−0.955675 | + | 0.294423i | \(0.904872\pi\) | |||||||
\(570\) | 5.30012 | − | 4.21038i | 0.221998 | − | 0.176354i | ||||
\(571\) | −8.56659 | + | 14.8378i | −0.358501 | + | 0.620941i | −0.987711 | − | 0.156294i | \(-0.950045\pi\) |
0.629210 | + | 0.777235i | \(0.283379\pi\) | |||||||
\(572\) | −3.35252 | − | 1.93558i | −0.140176 | − | 0.0809305i | ||||
\(573\) | 10.3279 | − | 5.96283i | 0.431455 | − | 0.249101i | ||||
\(574\) | −3.26391 | − | 5.65326i | −0.136233 | − | 0.235962i | ||||
\(575\) | 10.3506 | + | 34.0107i | 0.431650 | + | 1.41834i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −18.3761 | − | 10.6094i | −0.765006 | − | 0.441677i | 0.0660839 | − | 0.997814i | \(-0.478949\pi\) |
−0.831090 | + | 0.556137i | \(0.812283\pi\) | |||||||
\(578\) | − | 9.34338i | − | 0.388633i | ||||||
\(579\) | 1.37271 | + | 2.37760i | 0.0570479 | + | 0.0988099i | ||||
\(580\) | 10.4374 | − | 8.29138i | 0.433388 | − | 0.344281i | ||||
\(581\) | −11.7243 | −0.486408 | ||||||||
\(582\) | 9.07922i | 0.376346i | ||||||||
\(583\) | −9.79891 | − | 5.65740i | −0.405829 | − | 0.234306i | ||||
\(584\) | 5.73680 | 0.237390 | ||||||||
\(585\) | 9.75880 | − | 1.45209i | 0.403477 | − | 0.0600365i | ||||
\(586\) | −23.8197 | −0.983984 | ||||||||
\(587\) | 1.16286 | − | 0.671378i | 0.0479964 | − | 0.0277107i | −0.475810 | − | 0.879548i | \(-0.657845\pi\) |
0.523806 | + | 0.851837i | \(0.324512\pi\) | |||||||
\(588\) | −5.11867 | + | 2.95526i | −0.211090 | + | 0.121873i | ||||
\(589\) | 2.62357 | + | 4.54416i | 0.108102 | + | 0.187239i | ||||
\(590\) | 12.0270 | + | 15.1399i | 0.495144 | + | 0.623298i | ||||
\(591\) | 3.08949 | 0.127084 | ||||||||
\(592\) | 5.27705 | + | 3.02535i | 0.216885 | + | 0.124341i | ||||
\(593\) | 8.07531i | 0.331613i | 0.986158 | + | 0.165807i | \(0.0530227\pi\) | ||||
−0.986158 | + | 0.165807i | \(0.946977\pi\) | |||||||
\(594\) | −0.438676 | + | 0.759809i | −0.0179991 | + | 0.0311753i | ||||
\(595\) | 1.76307 | + | 11.8488i | 0.0722790 | + | 0.485753i | ||||
\(596\) | 5.24338 | + | 9.08180i | 0.214777 | + | 0.372005i | ||||
\(597\) | 18.8370 | − | 10.8755i | 0.770946 | − | 0.445106i | ||||
\(598\) | − | 31.3723i | − | 1.28291i | ||||||
\(599\) | 2.05315 | + | 3.55616i | 0.0838894 | + | 0.145301i | 0.904917 | − | 0.425587i | \(-0.139932\pi\) |
−0.821028 | + | 0.570888i | \(0.806599\pi\) | |||||||
\(600\) | 3.65241 | + | 3.41466i | 0.149109 | + | 0.139403i | ||||
\(601\) | 10.6565 | − | 18.4576i | 0.434688 | − | 0.752902i | −0.562582 | − | 0.826741i | \(-0.690192\pi\) |
0.997270 | + | 0.0738397i | \(0.0235253\pi\) | |||||||
\(602\) | − | 1.52798i | − | 0.0622757i | ||||||
\(603\) | 2.66533i | 0.108541i | ||||||||
\(604\) | 1.64176 | − | 2.84361i | 0.0668022 | − | 0.115705i | ||||
\(605\) | 3.36676 | + | 22.6264i | 0.136878 | + | 0.919895i | ||||
\(606\) | −1.97678 | −0.0803013 | ||||||||
\(607\) | −17.5424 | − | 10.1281i | −0.712025 | − | 0.411088i | 0.0997855 | − | 0.995009i | \(-0.468184\pi\) |
−0.811810 | + | 0.583921i | \(0.801518\pi\) | |||||||
\(608\) | −2.62160 | − | 1.51358i | −0.106320 | − | 0.0613839i | ||||
\(609\) | 3.11114 | − | 5.38865i | 0.126070 | − | 0.218359i | ||||
\(610\) | −7.99853 | + | 1.19016i | −0.323851 | + | 0.0481883i | ||||
\(611\) | −6.61958 | − | 11.4655i | −0.267800 | − | 0.463843i | ||||
\(612\) | −4.44494 | − | 2.56629i | −0.179676 | − | 0.103736i | ||||
\(613\) | −1.40671 | − | 0.812164i | −0.0568165 | − | 0.0328030i | 0.471323 | − | 0.881961i | \(-0.343777\pi\) |
−0.528139 | + | 0.849158i | \(0.677110\pi\) | |||||||
\(614\) | 5.84373 | − | 10.1216i | 0.235834 | − | 0.408476i | ||||
\(615\) | 5.13362 | − | 13.0081i | 0.207008 | − | 0.524536i | ||||
\(616\) | −0.457881 | − | 0.793072i | −0.0184485 | − | 0.0319538i | ||||
\(617\) | 42.3655 | + | 24.4597i | 1.70557 | + | 0.984712i | 0.939882 | + | 0.341500i | \(0.110935\pi\) |
0.765689 | + | 0.643211i | \(0.222398\pi\) | |||||||
\(618\) | − | 5.48507i | − | 0.220642i | ||||||
\(619\) | 21.4035 | 0.860280 | 0.430140 | − | 0.902762i | \(-0.358464\pi\) | ||||
0.430140 | + | 0.902762i | \(0.358464\pi\) | |||||||
\(620\) | −3.03485 | + | 2.41086i | −0.121882 | + | 0.0968226i | ||||
\(621\) | −7.11017 | −0.285321 | ||||||||
\(622\) | −16.7743 | + | 9.68464i | −0.672588 | + | 0.388319i | ||||
\(623\) | − | 15.9422i | − | 0.638710i | ||||||
\(624\) | −2.20616 | − | 3.82118i | −0.0883170 | − | 0.152970i | ||||
\(625\) | 20.7616 | − | 13.9268i | 0.830464 | − | 0.557072i | ||||
\(626\) | −7.38454 | − | 12.7904i | −0.295145 | − | 0.511207i | ||||
\(627\) | −2.30007 | − | 1.32794i | −0.0918558 | − | 0.0530330i | ||||
\(628\) | − | 4.86115i | − | 0.193981i | ||||||
\(629\) | −15.5279 | + | 27.0849i | −0.619136 | + | 1.07994i | ||||
\(630\) | 2.17101 | + | 0.856787i | 0.0864951 | + | 0.0341352i | ||||
\(631\) | −6.88944 | + | 11.9329i | −0.274264 | + | 0.475040i | −0.969949 | − | 0.243307i | \(-0.921768\pi\) |
0.695685 | + | 0.718347i | \(0.255101\pi\) | |||||||
\(632\) | −8.72742 | + | 5.03878i | −0.347158 | + | 0.200432i | ||||
\(633\) | 20.3832 | − | 11.7682i | 0.810158 | − | 0.467745i | ||||
\(634\) | 3.10827 | + | 5.38368i | 0.123445 | + | 0.213813i | ||||
\(635\) | 2.81363 | − | 7.12946i | 0.111656 | − | 0.282924i | ||||
\(636\) | −6.44827 | − | 11.1687i | −0.255691 | − | 0.442869i | ||||
\(637\) | − | 26.0791i | − | 1.03329i | ||||||
\(638\) | −4.52945 | − | 2.61508i | −0.179323 | − | 0.103532i | ||||
\(639\) | 1.16507 | 0.0460893 | ||||||||
\(640\) | 0.820851 | − | 2.07995i | 0.0324470 | − | 0.0822174i | ||||
\(641\) | 4.64508 | − | 8.04552i | 0.183470 | − | 0.317779i | −0.759590 | − | 0.650402i | \(-0.774600\pi\) |
0.943060 | + | 0.332623i | \(0.107934\pi\) | |||||||
\(642\) | 0.205007 | − | 0.118361i | 0.00809100 | − | 0.00467134i | ||||
\(643\) | 50.2018i | 1.97977i | 0.141885 | + | 0.989883i | \(0.454684\pi\) | ||||
−0.141885 | + | 0.989883i | \(0.545316\pi\) | |||||||
\(644\) | 3.71072 | − | 6.42716i | 0.146223 | − | 0.253266i | ||||
\(645\) | 2.56306 | − | 2.03608i | 0.100920 | − | 0.0801704i | ||||
\(646\) | 7.76858 | − | 13.4556i | 0.305651 | − | 0.529403i | ||||
\(647\) | −12.4180 | + | 7.16955i | −0.488203 | + | 0.281864i | −0.723829 | − | 0.689980i | \(-0.757619\pi\) |
0.235626 | + | 0.971844i | \(0.424286\pi\) | |||||||
\(648\) | −0.866025 | + | 0.500000i | −0.0340207 | + | 0.0196419i | ||||
\(649\) | 3.79329 | − | 6.57016i | 0.148900 | − | 0.257902i | ||||
\(650\) | −21.1058 | + | 6.42322i | −0.827838 | + | 0.251939i | ||||
\(651\) | −0.904618 | + | 1.56684i | −0.0354548 | + | 0.0614095i | ||||
\(652\) | 21.0005i | 0.822443i | ||||||||
\(653\) | 16.4993 | − | 9.52590i | 0.645669 | − | 0.372777i | −0.141126 | − | 0.989992i | \(-0.545072\pi\) |
0.786795 | + | 0.617214i | \(0.211739\pi\) | |||||||
\(654\) | −3.39695 | + | 5.88369i | −0.132831 | + | 0.230070i | ||||
\(655\) | 39.0027 | + | 15.3924i | 1.52396 | + | 0.601429i | ||||
\(656\) | −6.25403 | −0.244179 | ||||||||
\(657\) | 4.96821 | + | 2.86840i | 0.193828 | + | 0.111907i | ||||
\(658\) | − | 3.13186i | − | 0.122093i | ||||||
\(659\) | −13.2234 | − | 22.9036i | −0.515111 | − | 0.892199i | −0.999846 | − | 0.0175378i | \(-0.994417\pi\) |
0.484735 | − | 0.874661i | \(-0.338916\pi\) | |||||||
\(660\) | 0.720175 | − | 1.82485i | 0.0280328 | − | 0.0710322i | ||||
\(661\) | −7.69031 | − | 13.3200i | −0.299119 | − | 0.518089i | 0.676816 | − | 0.736152i | \(-0.263359\pi\) |
−0.975935 | + | 0.218064i | \(0.930026\pi\) | |||||||
\(662\) | 20.0626 | − | 11.5832i | 0.779756 | − | 0.450192i | ||||
\(663\) | 19.6125 | − | 11.3233i | 0.761687 | − | 0.439760i | ||||
\(664\) | −5.61630 | + | 9.72771i | −0.217955 | + | 0.377508i | ||||
\(665\) | −2.59363 | + | 6.57201i | −0.100577 | + | 0.254851i | ||||
\(666\) | 3.05738 | + | 5.25856i | 0.118471 | + | 0.203765i | ||||
\(667\) | − | 42.3859i | − | 1.64119i | ||||||
\(668\) | 5.55334 | + | 3.20622i | 0.214865 | + | 0.124053i | ||||
\(669\) | 10.9068 | + | 18.8911i | 0.421680 | + | 0.730371i | ||||
\(670\) | −0.877156 | − | 5.89495i | −0.0338875 | − | 0.227742i | ||||
\(671\) | 1.58644 | + | 2.74780i | 0.0612439 | + | 0.106078i | ||||
\(672\) | − | 1.04378i | − | 0.0402646i | ||||||
\(673\) | 6.96587 | − | 4.02175i | 0.268515 | − | 0.155027i | −0.359698 | − | 0.933069i | \(-0.617120\pi\) |
0.628212 | + | 0.778042i | \(0.283787\pi\) | |||||||
\(674\) | −11.7828 | −0.453855 | ||||||||
\(675\) | 1.45575 | + | 4.78339i | 0.0560317 | + | 0.184113i | ||||
\(676\) | 6.46854 | 0.248790 | ||||||||
\(677\) | − | 8.07075i | − | 0.310184i | −0.987900 | − | 0.155092i | \(-0.950433\pi\) | ||
0.987900 | − | 0.155092i | \(-0.0495674\pi\) | |||||||
\(678\) | −9.35427 | − | 5.40069i | −0.359249 | − | 0.207412i | ||||
\(679\) | −4.73835 | − | 8.20706i | −0.181841 | − | 0.314958i | ||||
\(680\) | 10.6755 | + | 4.21308i | 0.409388 | + | 0.161564i | ||||
\(681\) | 6.57817 | − | 11.3937i | 0.252076 | − | 0.436609i | ||||
\(682\) | 1.31702 | + | 0.760380i | 0.0504312 | + | 0.0291164i | ||||
\(683\) | −39.8914 | − | 23.0313i | −1.52640 | − | 0.881269i | −0.999509 | − | 0.0313372i | \(-0.990023\pi\) |
−0.526893 | − | 0.849931i | \(-0.676643\pi\) | |||||||
\(684\) | −1.51358 | − | 2.62160i | −0.0578733 | − | 0.100239i | ||||
\(685\) | −45.6351 | + | 6.79040i | −1.74363 | + | 0.259448i | ||||
\(686\) | 6.73787 | − | 11.6703i | 0.257253 | − | 0.445575i | ||||
\(687\) | −13.4420 | − | 7.76074i | −0.512844 | − | 0.296091i | ||||
\(688\) | −1.26777 | − | 0.731945i | −0.0483331 | − | 0.0279052i | ||||
\(689\) | 56.9036 | 2.16786 | ||||||||
\(690\) | 15.7257 | − | 2.33995i | 0.598667 | − | 0.0890804i | ||||
\(691\) | 0.294937 | − | 0.510846i | 0.0112199 | − | 0.0194335i | −0.860361 | − | 0.509685i | \(-0.829762\pi\) |
0.871581 | + | 0.490252i | \(0.163095\pi\) | |||||||
\(692\) | − | 0.386203i | − | 0.0146813i | ||||||
\(693\) | − | 0.915761i | − | 0.0347869i | ||||||
\(694\) | −10.3374 | + | 17.9049i | −0.392403 | + | 0.679662i | ||||
\(695\) | −12.6657 | − | 4.99852i | −0.480439 | − | 0.189605i | ||||
\(696\) | −2.98065 | − | 5.16264i | −0.112981 | − | 0.195689i | ||||
\(697\) | − | 32.0993i | − | 1.21585i | ||||||
\(698\) | −15.7832 | + | 9.11242i | −0.597402 | + | 0.344910i | ||||
\(699\) | 10.4289 | + | 18.0634i | 0.394457 | + | 0.683220i | ||||
\(700\) | −5.08363 | − | 1.18049i | −0.192143 | − | 0.0446184i | ||||
\(701\) | 13.3161 | − | 23.0642i | 0.502942 | − | 0.871121i | −0.497052 | − | 0.867721i | \(-0.665584\pi\) |
0.999994 | − | 0.00340039i | \(-0.00108238\pi\) | |||||||
\(702\) | − | 4.41232i | − | 0.166532i | ||||||
\(703\) | −15.9185 | + | 9.25520i | −0.600378 | + | 0.349067i | ||||
\(704\) | −0.877352 | −0.0330664 | ||||||||
\(705\) | 5.25344 | − | 4.17330i | 0.197856 | − | 0.157176i | ||||
\(706\) | 14.3304 | + | 24.8210i | 0.539332 | + | 0.934151i | ||||
\(707\) | 1.78689 | − | 1.03166i | 0.0672030 | − | 0.0387997i | ||||
\(708\) | 7.48863 | − | 4.32356i | 0.281440 | − | 0.162489i | ||||
\(709\) | 32.8494 | 1.23369 | 0.616843 | − | 0.787086i | \(-0.288411\pi\) | ||||
0.616843 | + | 0.787086i | \(0.288411\pi\) | |||||||
\(710\) | −2.57680 | + | 0.383422i | −0.0967055 | + | 0.0143896i | ||||
\(711\) | −10.0776 | −0.377938 | ||||||||
\(712\) | −13.2273 | − | 7.63676i | −0.495713 | − | 0.286200i | ||||
\(713\) | 12.3244i | 0.461554i | ||||||||
\(714\) | 5.35728 | 0.200491 | ||||||||
\(715\) | 5.38426 | + | 6.77782i | 0.201360 | + | 0.253476i | ||||
\(716\) | −9.07228 | − | 15.7137i | −0.339047 | − | 0.587247i | ||||
\(717\) | − | 3.16415i | − | 0.118167i | ||||||
\(718\) | −19.9689 | − | 11.5291i | −0.745233 | − | 0.430260i | ||||
\(719\) | 0.522177 | − | 0.904437i | 0.0194739 | − | 0.0337298i | −0.856124 | − | 0.516770i | \(-0.827134\pi\) |
0.875598 | + | 0.483040i | \(0.160468\pi\) | |||||||
\(720\) | 1.75085 | − | 1.39087i | 0.0652505 | − | 0.0518345i | ||||
\(721\) | 2.86260 | + | 4.95817i | 0.106609 | + | 0.184652i | ||||
\(722\) | −8.51846 | + | 4.91814i | −0.317024 | + | 0.183034i | ||||
\(723\) | −5.79294 | − | 3.34456i | −0.215442 | − | 0.124385i | ||||
\(724\) | −2.94193 | + | 5.09557i | −0.109336 | + | 0.189375i | ||||
\(725\) | −28.5152 | + | 8.67815i | −1.05903 | + | 0.322298i | ||||
\(726\) | 10.2303 | 0.379680 | ||||||||
\(727\) | −4.42461 | + | 2.55455i | −0.164100 | + | 0.0947430i | −0.579801 | − | 0.814758i | \(-0.696870\pi\) |
0.415701 | + | 0.909501i | \(0.363536\pi\) | |||||||
\(728\) | 3.98846 | + | 2.30274i | 0.147822 | + | 0.0853453i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −11.9323 | − | 4.70906i | −0.441633 | − | 0.174290i | ||||
\(731\) | 3.75677 | − | 6.50691i | 0.138949 | − | 0.240667i | ||||
\(732\) | 3.61643i | 0.133667i | ||||||||
\(733\) | 16.8016 | − | 9.70040i | 0.620581 | − | 0.358293i | −0.156514 | − | 0.987676i | \(-0.550026\pi\) |
0.777095 | + | 0.629383i | \(0.216692\pi\) | |||||||
\(734\) | −26.3684 | −0.973276 | ||||||||
\(735\) | 13.0724 | − | 1.94515i | 0.482183 | − | 0.0717478i | ||||
\(736\) | −3.55509 | − | 6.15759i | −0.131042 | − | 0.226972i | ||||
\(737\) | −2.02514 | + | 1.16921i | −0.0745970 | + | 0.0430686i | ||||
\(738\) | −5.41615 | − | 3.12701i | −0.199371 | − | 0.115107i | ||||
\(739\) | −10.0534 | −0.369820 | −0.184910 | − | 0.982755i | \(-0.559199\pi\) | ||||
−0.184910 | + | 0.982755i | \(0.559199\pi\) | |||||||
\(740\) | −8.49265 | − | 10.6243i | −0.312196 | − | 0.390555i | ||||
\(741\) | 13.3568 | 0.490675 | ||||||||
\(742\) | 11.6577 | + | 6.73057i | 0.427967 | + | 0.247087i | ||||
\(743\) | 9.28566 | − | 5.36108i | 0.340658 | − | 0.196679i | −0.319905 | − | 0.947450i | \(-0.603651\pi\) |
0.660563 | + | 0.750771i | \(0.270318\pi\) | |||||||
\(744\) | 0.866676 | + | 1.50113i | 0.0317739 | + | 0.0550340i | ||||
\(745\) | −3.45118 | − | 23.1938i | −0.126442 | − | 0.849754i | ||||
\(746\) | −27.3208 | −1.00028 | ||||||||
\(747\) | −9.72771 | + | 5.61630i | −0.355918 | + | 0.205490i | ||||
\(748\) | − | 4.50308i | − | 0.164649i | ||||||
\(749\) | −0.123543 | + | 0.213982i | −0.00451416 | + | 0.00781875i | ||||
\(750\) | −4.79391 | − | 10.1004i | −0.175049 | − | 0.368815i | ||||
\(751\) | −32.1895 | −1.17461 | −0.587306 | − | 0.809365i | \(-0.699812\pi\) | ||||
−0.587306 | + | 0.809365i | \(0.699812\pi\) | |||||||
\(752\) | −2.59851 | − | 1.50025i | −0.0947579 | − | 0.0547085i | ||||
\(753\) | −11.9007 | + | 6.87089i | −0.433686 | + | 0.250389i | ||||
\(754\) | 26.3032 | 0.957905 | ||||||||
\(755\) | −5.74896 | + | 4.56693i | −0.209226 | + | 0.166208i | ||||
\(756\) | 0.521889 | − | 0.903939i | 0.0189809 | − | 0.0328759i | ||||
\(757\) | 7.21272 | + | 4.16427i | 0.262151 | + | 0.151353i | 0.625315 | − | 0.780372i | \(-0.284970\pi\) |
−0.363165 | + | 0.931725i | \(0.618304\pi\) | |||||||
\(758\) | −4.29231 | + | 2.47817i | −0.155904 | + | 0.0900110i | ||||
\(759\) | −3.11906 | − | 5.40237i | −0.113215 | − | 0.196094i | ||||
\(760\) | 4.21038 | + | 5.30012i | 0.152727 | + | 0.192256i | ||||
\(761\) | −23.8904 | + | 41.3795i | −0.866028 | + | 1.50000i | −5.16912e−6 | 1.00000i | \(0.500002\pi\) | |
−0.866023 | + | 0.500004i | \(0.833332\pi\) | |||||||
\(762\) | −2.96848 | − | 1.71385i | −0.107537 | − | 0.0620863i | ||||
\(763\) | − | 7.09133i | − | 0.256723i | ||||||
\(764\) | 5.96283 | + | 10.3279i | 0.215728 | + | 0.373651i | ||||
\(765\) | 7.13873 | + | 8.98640i | 0.258102 | + | 0.324904i | ||||
\(766\) | 34.9874 | 1.26415 | ||||||||
\(767\) | 38.1539i | 1.37766i | ||||||||
\(768\) | −0.866025 | − | 0.500000i | −0.0312500 | − | 0.0180422i | ||||
\(769\) | −13.1836 | −0.475414 | −0.237707 | − | 0.971337i | \(-0.576396\pi\) | ||||
−0.237707 | + | 0.971337i | \(0.576396\pi\) | |||||||
\(770\) | 0.301376 | + | 2.02540i | 0.0108608 | + | 0.0729905i | ||||
\(771\) | −0.498323 | −0.0179467 | ||||||||
\(772\) | −2.37760 | + | 1.37271i | −0.0855719 | + | 0.0494049i | ||||
\(773\) | −25.6873 | + | 14.8306i | −0.923908 | + | 0.533419i | −0.884880 | − | 0.465819i | \(-0.845760\pi\) |
−0.0390284 | + | 0.999238i | \(0.512426\pi\) | |||||||
\(774\) | −0.731945 | − | 1.26777i | −0.0263092 | − | 0.0455689i | ||||
\(775\) | 8.29130 | − | 2.52332i | 0.297832 | − | 0.0906404i | ||||
\(776\) | −9.07922 | −0.325925 | ||||||||
\(777\) | −5.50807 | − | 3.15780i | −0.197601 | − | 0.113285i | ||||
\(778\) | 33.0443i | 1.18470i | ||||||||
\(779\) | 9.46598 | − | 16.3956i | 0.339154 | − | 0.587432i | ||||
\(780\) | 1.45209 | + | 9.75880i | 0.0519931 | + | 0.349421i | ||||
\(781\) | 0.511086 | + | 0.885228i | 0.0182881 | + | 0.0316759i | ||||
\(782\) | 31.6043 | − | 18.2468i | 1.13017 | − | 0.652503i | ||||
\(783\) | − | 5.96130i | − | 0.213040i | ||||||
\(784\) | −2.95526 | − | 5.11867i | −0.105545 | − | 0.182809i | ||||
\(785\) | −3.99027 | + | 10.1110i | −0.142419 | + | 0.360875i | ||||
\(786\) | 9.37585 | − | 16.2395i | 0.334426 | − | 0.579242i | ||||
\(787\) | 46.8019i | 1.66831i | 0.551533 | + | 0.834153i | \(0.314043\pi\) | ||||
−0.551533 | + | 0.834153i | \(0.685957\pi\) | |||||||
\(788\) | 3.08949i | 0.110058i | ||||||||
\(789\) | 11.5827 | − | 20.0619i | 0.412356 | − | 0.714221i | ||||
\(790\) | 22.2887 | − | 3.31651i | 0.792996 | − | 0.117996i | ||||
\(791\) | 11.2743 | 0.400866 | ||||||||
\(792\) | −0.759809 | − | 0.438676i | −0.0269986 | − | 0.0155877i | ||||
\(793\) | −13.8190 | − | 7.97842i | −0.490728 | − | 0.283322i | ||||
\(794\) | −8.71821 | + | 15.1004i | −0.309398 | + | 0.535892i | ||||
\(795\) | 4.24424 | + | 28.5235i | 0.150528 | + | 1.01162i | ||||
\(796\) | 10.8755 | + | 18.8370i | 0.385473 | + | 0.667659i | ||||
\(797\) | 20.7986 | + | 12.0081i | 0.736726 | + | 0.425349i | 0.820878 | − | 0.571104i | \(-0.193485\pi\) |
−0.0841519 | + | 0.996453i | \(0.526818\pi\) | |||||||
\(798\) | 2.73637 | + | 1.57985i | 0.0968665 | + | 0.0559259i | ||||
\(799\) | 7.70016 | − | 13.3371i | 0.272412 | − | 0.471831i | ||||
\(800\) | −3.41466 | + | 3.65241i | −0.120727 | + | 0.129132i | ||||
\(801\) | −7.63676 | − | 13.2273i | −0.269832 | − | 0.467362i | ||||
\(802\) | 22.1715 | + | 12.8007i | 0.782902 | + | 0.452009i | ||||
\(803\) | 5.03319i | 0.177617i | ||||||||
\(804\) | −2.66533 | −0.0939988 | ||||||||
\(805\) | −12.9939 | + | 10.3222i | −0.457974 | + | 0.363811i | ||||
\(806\) | −7.64810 | −0.269393 | ||||||||
\(807\) | 17.5583 | − | 10.1373i | 0.618083 | − | 0.356850i | ||||
\(808\) | − | 1.97678i | − | 0.0695430i | ||||||
\(809\) | 21.6639 | + | 37.5229i | 0.761661 | + | 1.31923i | 0.941994 | + | 0.335629i | \(0.108949\pi\) |
−0.180334 | + | 0.983606i | \(0.557718\pi\) | |||||||
\(810\) | 2.21172 | − | 0.329099i | 0.0777118 | − | 0.0115634i | ||||
\(811\) | 21.8114 | + | 37.7784i | 0.765902 | + | 1.32658i | 0.939769 | + | 0.341811i | \(0.111040\pi\) |
−0.173867 | + | 0.984769i | \(0.555626\pi\) | |||||||
\(812\) | 5.38865 | + | 3.11114i | 0.189105 | + | 0.109180i | ||||
\(813\) | 20.7374i | 0.727291i | ||||||||
\(814\) | −2.65430 | + | 4.62983i | −0.0930330 | + | 0.162275i | ||||
\(815\) | 17.2383 | − | 43.6800i | 0.603830 | − | 1.53004i | ||||
\(816\) | 2.56629 | − | 4.44494i | 0.0898381 | − | 0.155604i | ||||
\(817\) | 3.83774 | − | 2.21572i | 0.134265 | − | 0.0775182i | ||||
\(818\) | 6.18298 | − | 3.56975i | 0.216183 | − | 0.124813i | ||||
\(819\) | 2.30274 | + | 3.98846i | 0.0804643 | + | 0.139368i | ||||
\(820\) | 13.0081 | + | 5.13362i | 0.454262 | + | 0.179274i | ||||
\(821\) | 3.25519 | + | 5.63816i | 0.113607 | + | 0.196773i | 0.917222 | − | 0.398376i | \(-0.130426\pi\) |
−0.803615 | + | 0.595149i | \(0.797093\pi\) | |||||||
\(822\) | 20.6333i | 0.719670i | ||||||||
\(823\) | −30.7094 | − | 17.7301i | −1.07046 | − | 0.618031i | −0.142154 | − | 0.989845i | \(-0.545403\pi\) |
−0.928307 | + | 0.371814i | \(0.878736\pi\) | |||||||
\(824\) | 5.48507 | 0.191082 | ||||||||
\(825\) | −2.99586 | + | 3.20445i | −0.104302 | + | 0.111564i | ||||
\(826\) | −4.51284 | + | 7.81648i | −0.157022 | + | 0.271970i | ||||
\(827\) | −12.9493 | + | 7.47628i | −0.450291 | + | 0.259976i | −0.707953 | − | 0.706259i | \(-0.750381\pi\) |
0.257662 | + | 0.966235i | \(0.417048\pi\) | |||||||
\(828\) | − | 7.11017i | − | 0.247096i | ||||||
\(829\) | 24.1406 | − | 41.8128i | 0.838439 | − | 1.45222i | −0.0527599 | − | 0.998607i | \(-0.516802\pi\) |
0.891199 | − | 0.453612i | \(-0.149865\pi\) | |||||||
\(830\) | 19.6666 | − | 15.6230i | 0.682639 | − | 0.542284i | ||||
\(831\) | 5.69024 | − | 9.85578i | 0.197392 | − | 0.341893i | ||||
\(832\) | 3.82118 | − | 2.20616i | 0.132476 | − | 0.0764848i | ||||
\(833\) | 26.2720 | − | 15.1681i | 0.910270 | − | 0.525544i | ||||
\(834\) | −3.04472 | + | 5.27361i | −0.105430 | + | 0.182610i | ||||
\(835\) | −8.91886 | − | 11.2273i | −0.308650 | − | 0.388535i | ||||
\(836\) | 1.32794 | − | 2.30007i | 0.0459279 | − | 0.0795495i | ||||
\(837\) | 1.73335i | 0.0599134i | ||||||||
\(838\) | 18.8507 | − | 10.8835i | 0.651188 | − | 0.375964i | ||||
\(839\) | −14.8588 | + | 25.7363i | −0.512984 | + | 0.888514i | 0.486903 | + | 0.873456i | \(0.338127\pi\) |
−0.999887 | + | 0.0150581i | \(0.995207\pi\) | |||||||
\(840\) | −0.856787 | + | 2.17101i | −0.0295619 | + | 0.0749070i | ||||
\(841\) | 6.53714 | 0.225419 | ||||||||
\(842\) | −27.6754 | − | 15.9784i | −0.953756 | − | 0.550651i | ||||
\(843\) | − | 13.6950i | − | 0.471681i | ||||||
\(844\) | 11.7682 | + | 20.3832i | 0.405079 | + | 0.701617i | ||||
\(845\) | −13.4543 | − | 5.30970i | −0.462840 | − | 0.182659i | ||||
\(846\) | −1.50025 | − | 2.59851i | −0.0515797 | − | 0.0893386i | ||||
\(847\) | −9.24753 | + | 5.33906i | −0.317749 | + | 0.183452i | ||||
\(848\) | 11.1687 | − | 6.44827i | 0.383536 | − | 0.221435i | ||||
\(849\) | 12.3062 | − | 21.3150i | 0.422348 | − | 0.731527i | ||||
\(850\) | −18.7463 | − | 17.5260i | −0.642992 | − | 0.601138i | ||||
\(851\) | −43.2493 | + | 0.131501i | −1.48257 | + | 0.00450780i | ||||
\(852\) | 1.16507i | 0.0399145i | ||||||||
\(853\) | −0.910252 | − | 0.525534i | −0.0311664 | − | 0.0179940i | 0.484336 | − | 0.874882i | \(-0.339061\pi\) |
−0.515502 | + | 0.856888i | \(0.672395\pi\) | |||||||
\(854\) | −1.88738 | − | 3.26903i | −0.0645847 | − | 0.111864i | ||||
\(855\) | 0.996236 | + | 6.69523i | 0.0340706 | + | 0.228972i | ||||
\(856\) | 0.118361 | + | 0.205007i | 0.00404550 | + | 0.00700701i | ||||
\(857\) | 30.7011i | 1.04873i | 0.851493 | + | 0.524365i | \(0.175697\pi\) | ||||
−0.851493 | + | 0.524365i | \(0.824303\pi\) | |||||||
\(858\) | 3.35252 | − | 1.93558i | 0.114453 | − | 0.0660795i | ||||
\(859\) | 31.0164 | 1.05827 | 0.529133 | − | 0.848539i | \(-0.322517\pi\) | ||||
0.529133 | + | 0.848539i | \(0.322517\pi\) | |||||||
\(860\) | 2.03608 | + | 2.56306i | 0.0694296 | + | 0.0873996i | ||||
\(861\) | 6.52782 | 0.222467 | ||||||||
\(862\) | − | 18.3911i | − | 0.626402i | ||||||
\(863\) | 24.2054 | + | 13.9750i | 0.823962 | + | 0.475715i | 0.851781 | − | 0.523898i | \(-0.175523\pi\) |
−0.0278186 | + | 0.999613i | \(0.508856\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | −0.317015 | + | 0.803285i | −0.0107788 | + | 0.0273125i | ||||
\(866\) | 7.67381 | − | 13.2914i | 0.260767 | − | 0.451661i | ||||
\(867\) | 8.09161 | + | 4.67169i | 0.274805 | + | 0.158659i | ||||
\(868\) | −1.56684 | − | 0.904618i | −0.0531822 | − | 0.0307047i | ||||
\(869\) | −4.42078 | − | 7.65701i | −0.149965 | − | 0.259746i | ||||
\(870\) | 1.96186 | + | 13.1847i | 0.0665132 | + | 0.447004i | ||||
\(871\) | 5.88013 | − | 10.1847i | 0.199241 | − | 0.345095i | ||||
\(872\) | −5.88369 | − | 3.39695i | −0.199247 | − | 0.115035i | ||||
\(873\) | −7.86284 | − | 4.53961i | −0.266117 | − | 0.153643i | ||||
\(874\) | 21.5237 | 0.728049 | ||||||||
\(875\) | 9.60470 | + | 6.62827i | 0.324698 | + | 0.224076i | ||||
\(876\) | −2.86840 | + | 4.96821i | −0.0969142 | + | 0.167860i | ||||
\(877\) | 20.1349i | 0.679908i | 0.940442 | + | 0.339954i | \(0.110412\pi\) | ||||
−0.940442 | + | 0.339954i | \(0.889588\pi\) | |||||||
\(878\) | 8.41076i | 0.283849i | ||||||||
\(879\) | 11.9099 | − | 20.6285i | 0.401710 | − | 0.695782i | ||||
\(880\) | 1.82485 | + | 0.720175i | 0.0615157 | + | 0.0242771i | ||||
\(881\) | 22.8164 | + | 39.5191i | 0.768703 | + | 1.33143i | 0.938266 | + | 0.345914i | \(0.112431\pi\) |
−0.169563 | + | 0.985519i | \(0.554236\pi\) | |||||||
\(882\) | − | 5.91053i | − | 0.199018i | ||||||
\(883\) | 13.5576 | − | 7.82751i | 0.456251 | − | 0.263417i | −0.254215 | − | 0.967148i | \(-0.581817\pi\) |
0.710467 | + | 0.703731i | \(0.248484\pi\) | |||||||
\(884\) | 11.3233 | + | 19.6125i | 0.380843 | + | 0.659640i | ||||
\(885\) | −19.1250 | + | 2.84576i | −0.642880 | + | 0.0956592i | ||||
\(886\) | −12.7130 | + | 22.0196i | −0.427103 | + | 0.739763i | ||||
\(887\) | 33.8991i | 1.13822i | 0.822261 | + | 0.569111i | \(0.192712\pi\) | ||||
−0.822261 | + | 0.569111i | \(0.807288\pi\) | |||||||
\(888\) | −5.25856 | + | 3.05738i | −0.176466 | + | 0.102599i | ||||
\(889\) | 3.57776 | 0.119994 | ||||||||
\(890\) | 21.2434 | + | 26.7417i | 0.712082 | + | 0.896384i | ||||
\(891\) | −0.438676 | − | 0.759809i | −0.0146962 | − | 0.0254546i | ||||
\(892\) | −18.8911 | + | 10.9068i | −0.632520 | + | 0.365185i | ||||
\(893\) | 7.86612 | − | 4.54151i | 0.263230 | − | 0.151976i | ||||
\(894\) | −10.4868 | −0.350730 | ||||||||
\(895\) | 5.97136 | + | 40.1307i | 0.199600 | + | 1.34142i | ||||
\(896\) | 1.04378 | 0.0348702 | ||||||||
\(897\) | 27.1692 | + | 15.6862i | 0.907154 | + | 0.523746i | ||||
\(898\) | 2.36419i | 0.0788939i | ||||||||
\(899\) | −10.3330 | −0.344626 | ||||||||
\(900\) | −4.78339 | + | 1.45575i | −0.159446 | + | 0.0485249i | ||||
\(901\) | 33.0963 | + | 57.3244i | 1.10260 | + | 1.90975i | ||||
\(902\) | − | 5.48698i | − | 0.182696i | ||||||
\(903\) | 1.32327 | + | 0.763989i | 0.0440356 | + | 0.0254240i | ||||
\(904\) | 5.40069 | − | 9.35427i | 0.179624 | − | 0.311118i | ||||
\(905\) | 10.3018 | − | 8.18365i | 0.342442 | − | 0.272034i | ||||
\(906\) | 1.64176 | + | 2.84361i | 0.0545438 | + | 0.0944725i | ||||
\(907\) | −35.3558 | + | 20.4127i | −1.17397 | + | 0.677791i | −0.954612 | − | 0.297853i | \(-0.903729\pi\) |
−0.219357 | + | 0.975645i | \(0.570396\pi\) | |||||||
\(908\) | 11.3937 | + | 6.57817i | 0.378114 | + | 0.218304i | ||||
\(909\) | 0.988392 | − | 1.71194i | 0.0327829 | − | 0.0567816i | ||||
\(910\) | −6.40561 | − | 8.06353i | −0.212344 | − | 0.267303i | ||||
\(911\) | −37.9616 | −1.25772 | −0.628862 | − | 0.777517i | \(-0.716479\pi\) | ||||
−0.628862 | + | 0.777517i | \(0.716479\pi\) | |||||||
\(912\) | 2.62160 | − | 1.51358i | 0.0868099 | − | 0.0501197i | ||||
\(913\) | −8.53462 | − | 4.92747i | −0.282455 | − | 0.163075i | ||||
\(914\) | 5.00217 | 0.165457 | ||||||||
\(915\) | 2.96855 | − | 7.52201i | 0.0981373 | − | 0.248670i | ||||
\(916\) | 7.76074 | − | 13.4420i | 0.256422 | − | 0.444136i | ||||
\(917\) | 19.5726i | 0.646345i | ||||||||
\(918\) | 4.44494 | − | 2.56629i | 0.146705 | − | 0.0847002i | ||||
\(919\) | −18.1870 | −0.599932 | −0.299966 | − | 0.953950i | \(-0.596975\pi\) | ||||
−0.299966 | + | 0.953950i | \(0.596975\pi\) | |||||||
\(920\) | 2.33995 | + | 15.7257i | 0.0771459 | + | 0.518461i | ||||
\(921\) | 5.84373 | + | 10.1216i | 0.192558 | + | 0.333520i | ||||
\(922\) | −5.74025 | + | 3.31413i | −0.189045 | + | 0.109145i | ||||
\(923\) | −4.45193 | − | 2.57032i | −0.146537 | − | 0.0846031i | ||||
\(924\) | 0.915761 | 0.0301263 | ||||||||
\(925\) | 8.94339 | + | 29.0692i | 0.294057 | + | 0.955788i | ||||
\(926\) | 2.42909 | 0.0798248 | ||||||||
\(927\) | 4.75021 | + | 2.74254i | 0.156017 | + | 0.0900767i | ||||
\(928\) | 5.16264 | − | 2.98065i | 0.169472 | − | 0.0978447i | ||||
\(929\) | −14.4907 | − | 25.0986i | −0.475424 | − | 0.823459i | 0.524180 | − | 0.851608i | \(-0.324372\pi\) |
−0.999604 | + | 0.0281490i | \(0.991039\pi\) | |||||||
\(930\) | −0.570444 | − | 3.83369i | −0.0187056 | − | 0.125712i | ||||
\(931\) | 17.8921 | 0.586391 | ||||||||
\(932\) | −18.0634 | + | 10.4289i | −0.591686 | + | 0.341610i | ||||
\(933\) | − | 19.3693i | − | 0.634122i | ||||||
\(934\) | 5.45340 | − | 9.44556i | 0.178441 | − | 0.309068i | ||||
\(935\) | −3.69635 | + | 9.36619i | −0.120884 | + | 0.306307i | ||||
\(936\) | 4.41232 | 0.144221 | ||||||||
\(937\) | 4.53863 | + | 2.62038i | 0.148271 | + | 0.0856041i | 0.572300 | − | 0.820044i | \(-0.306051\pi\) |
−0.424029 | + | 0.905648i | \(0.639385\pi\) | |||||||
\(938\) | 2.40929 | − | 1.39101i | 0.0786662 | − | 0.0454180i | ||||
\(939\) | 14.7691 | 0.481970 | ||||||||
\(940\) | 4.17330 | + | 5.25344i | 0.136118 | + | 0.171348i | ||||
\(941\) | 14.7595 | − | 25.5641i | 0.481145 | − | 0.833367i | −0.518621 | − | 0.855004i | \(-0.673554\pi\) |
0.999766 | + | 0.0216370i | \(0.00688782\pi\) | |||||||
\(942\) | 4.20988 | + | 2.43057i | 0.137165 | + | 0.0791923i | ||||
\(943\) | 38.5097 | − | 22.2336i | 1.25405 | − | 0.724026i | ||||
\(944\) | 4.32356 | + | 7.48863i | 0.140720 | + | 0.243734i | ||||
\(945\) | −1.82750 | + | 1.45176i | −0.0594487 | + | 0.0472257i | ||||
\(946\) | 0.642173 | − | 1.11228i | 0.0208789 | − | 0.0361632i | ||||
\(947\) | −12.2476 | − | 7.07114i | −0.397992 | − | 0.229781i | 0.287625 | − | 0.957743i | \(-0.407134\pi\) |
−0.685617 | + | 0.727962i | \(0.740468\pi\) | |||||||
\(948\) | − | 10.0776i | − | 0.327304i | ||||||
\(949\) | −12.6563 | − | 21.9213i | −0.410840 | − | 0.711596i | ||||
\(950\) | −4.40679 | − | 14.4801i | −0.142975 | − | 0.469797i | ||||
\(951\) | −6.21654 | −0.201585 | ||||||||
\(952\) | 5.35728i | 0.173630i | ||||||||
\(953\) | 49.4257 | + | 28.5359i | 1.60105 | + | 0.924369i | 0.991277 | + | 0.131796i | \(0.0420744\pi\) |
0.609777 | + | 0.792573i | \(0.291259\pi\) | |||||||
\(954\) | 12.8965 | 0.417541 | ||||||||
\(955\) | −3.92472 | − | 26.3762i | −0.127001 | − | 0.853514i | ||||
\(956\) | 3.16415 | 0.102336 | ||||||||
\(957\) | 4.52945 | − | 2.61508i | 0.146416 | − | 0.0845335i | ||||
\(958\) | 15.7010 | − | 9.06499i | 0.507277 | − | 0.292876i | ||||
\(959\) | −10.7683 | − | 18.6513i | −0.347727 | − | 0.602281i | ||||
\(960\) | 1.39087 | + | 1.75085i | 0.0448900 | + | 0.0565086i | ||||
\(961\) | −27.9955 | −0.903080 | ||||||||
\(962\) | −0.0816048 | − | 26.8389i | −0.00263104 | − | 0.865322i | ||||
\(963\) | 0.236722i | 0.00762827i | ||||||||
\(964\) | 3.34456 | − | 5.79294i | 0.107721 | − | 0.186578i | ||||
\(965\) | 6.07210 | − | 0.903515i | 0.195468 | − | 0.0290852i | ||||
\(966\) | 3.71072 | + | 6.42716i | 0.119391 | + | 0.206791i | ||||
\(967\) | 9.29892 | − | 5.36874i | 0.299033 | − | 0.172647i | −0.342975 | − | 0.939344i | \(-0.611435\pi\) |
0.642008 | + | 0.766698i | \(0.278101\pi\) | |||||||
\(968\) | 10.2303i | 0.328813i | ||||||||
\(969\) | 7.76858 | + | 13.4556i | 0.249563 | + | 0.432255i | ||||
\(970\) | 18.8844 | + | 7.45269i | 0.606340 | + | 0.239291i | ||||
\(971\) | 15.9497 | − | 27.6258i | 0.511852 | − | 0.886553i | −0.488054 | − | 0.872813i | \(-0.662293\pi\) |
0.999906 | − | 0.0137397i | \(-0.00437361\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | − | 6.35603i | − | 0.203765i | ||||||
\(974\) | 13.3642 | − | 23.1475i | 0.428218 | − | 0.741695i | ||||
\(975\) | 4.99024 | − | 21.4898i | 0.159816 | − | 0.688224i | ||||
\(976\) | −3.61643 | −0.115759 | ||||||||
\(977\) | −31.3706 | − | 18.1118i | −1.00363 | − | 0.579449i | −0.0943128 | − | 0.995543i | \(-0.530065\pi\) |
−0.909322 | + | 0.416094i | \(0.863399\pi\) | |||||||
\(978\) | −18.1870 | − | 10.5002i | −0.581555 | − | 0.335761i | ||||
\(979\) | 6.70013 | − | 11.6050i | 0.214137 | − | 0.370896i | ||||
\(980\) | 1.94515 | + | 13.0724i | 0.0621354 | + | 0.417583i | ||||
\(981\) | −3.39695 | − | 5.88369i | −0.108456 | − | 0.187852i | ||||
\(982\) | 30.7349 | + | 17.7448i | 0.980789 | + | 0.566259i | ||||
\(983\) | 23.8412 | + | 13.7647i | 0.760415 | + | 0.439026i | 0.829445 | − | 0.558589i | \(-0.188657\pi\) |
−0.0690299 | + | 0.997615i | \(0.521990\pi\) | |||||||
\(984\) | 3.12701 | − | 5.41615i | 0.0996855 | − | 0.172660i | ||||
\(985\) | 2.53601 | − | 6.42599i | 0.0808039 | − | 0.204749i | ||||
\(986\) | 15.2984 | + | 26.4977i | 0.487201 | + | 0.843858i | ||||
\(987\) | 2.71227 | + | 1.56593i | 0.0863325 | + | 0.0498441i | ||||
\(988\) | 13.3568i | 0.424937i | ||||||||
\(989\) | 10.4085 | 0.330972 | ||||||||
\(990\) | 1.22028 | + | 1.53611i | 0.0387830 | + | 0.0488209i | ||||
\(991\) | −14.9113 | −0.473673 | −0.236836 | − | 0.971550i | \(-0.576111\pi\) | ||||
−0.236836 | + | 0.971550i | \(0.576111\pi\) | |||||||
\(992\) | −1.50113 | + | 0.866676i | −0.0476608 | + | 0.0275170i | ||||
\(993\) | 23.1663i | 0.735161i | ||||||||
\(994\) | −0.608036 | − | 1.05315i | −0.0192857 | − | 0.0334038i | ||||
\(995\) | −7.15825 | − | 48.1072i | −0.226932 | − | 1.52510i | ||||
\(996\) | −5.61630 | − | 9.72771i | −0.177959 | − | 0.308234i | ||||
\(997\) | 4.22014 | + | 2.43650i | 0.133653 | + | 0.0771647i | 0.565336 | − | 0.824861i | \(-0.308747\pi\) |
−0.431683 | + | 0.902026i | \(0.642080\pi\) | |||||||
\(998\) | − | 9.61741i | − | 0.304434i | ||||||
\(999\) | −6.08273 | + | 0.0184948i | −0.192449 | + | 0.000585148i |
(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 | 1110.2.bb.e.1009.6 | ✓ | 40 | |
5.4 | even | 2 | inner | 1110.2.bb.e.1009.15 | yes | 40 | |
37.26 | even | 3 | inner | 1110.2.bb.e.1099.15 | yes | 40 | |
185.174 | even | 6 | inner | 1110.2.bb.e.1099.6 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.bb.e.1009.6 | ✓ | 40 | 1.1 | even | 1 | trivial | |
1110.2.bb.e.1009.15 | yes | 40 | 5.4 | even | 2 | inner | |
1110.2.bb.e.1099.6 | yes | 40 | 185.174 | even | 6 | inner | |
1110.2.bb.e.1099.15 | yes | 40 | 37.26 | even | 3 | inner |