Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(451,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.451");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.bj (of order \(6\), degree \(2\), not 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: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(84\) |
Relative dimension: | \(42\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 451.16 | ||
Character | \(\chi\) | \(=\) | 756.451 |
Dual form | 756.2.bj.b.523.15 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.667137 | + | 1.24697i | −0.471737 | + | 0.881739i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.10986 | − | 1.66380i | −0.554928 | − | 0.831899i | ||||
\(5\) | 0.627749 | + | 0.362431i | 0.280738 | + | 0.162084i | 0.633757 | − | 0.773532i | \(-0.281512\pi\) |
−0.353019 | + | 0.935616i | \(0.614845\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.64477 | + | 0.0721413i | −0.999628 | + | 0.0272668i | ||||
\(8\) | 2.81513 | − | 0.273973i | 0.995298 | − | 0.0968640i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.870735 | + | 0.540991i | −0.275351 | + | 0.171077i | ||||
\(11\) | 0.501838 | − | 0.289736i | 0.151310 | − | 0.0873588i | −0.422434 | − | 0.906394i | \(-0.638824\pi\) |
0.573743 | + | 0.819035i | \(0.305491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.35535 | + | 1.93721i | −0.930608 | + | 0.537287i | −0.887004 | − | 0.461762i | \(-0.847217\pi\) |
−0.0436041 | + | 0.999049i | \(0.513884\pi\) | |||||||
\(14\) | 1.67447 | − | 3.34607i | 0.447520 | − | 0.894274i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.53644 | + | 3.69315i | −0.384110 | + | 0.923287i | ||||
\(17\) | 3.20279 | + | 1.84913i | 0.776791 | + | 0.448480i | 0.835292 | − | 0.549807i | \(-0.185299\pi\) |
−0.0585009 | + | 0.998287i | \(0.518632\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.04363 | − | 3.53967i | −0.468841 | − | 0.812057i | 0.530525 | − | 0.847670i | \(-0.321995\pi\) |
−0.999366 | + | 0.0356130i | \(0.988662\pi\) | |||||||
\(20\) | −0.0936991 | − | 1.44669i | −0.0209517 | − | 0.323491i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.0264969 | + | 0.819070i | 0.00564915 | + | 0.174626i | ||||
\(23\) | −4.47089 | − | 2.58127i | −0.932244 | − | 0.538231i | −0.0447236 | − | 0.998999i | \(-0.514241\pi\) |
−0.887521 | + | 0.460768i | \(0.847574\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.23729 | − | 3.87510i | −0.447457 | − | 0.775019i | ||||
\(26\) | −0.177162 | − | 5.47641i | −0.0347442 | − | 1.07401i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.05534 | + | 4.32029i | 0.577405 | + | 0.816458i | ||||
\(29\) | −4.56967 | + | 7.91490i | −0.848566 | + | 1.46976i | 0.0339219 | + | 0.999424i | \(0.489200\pi\) |
−0.882488 | + | 0.470335i | \(0.844133\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.848671 | −0.152426 | −0.0762129 | − | 0.997092i | \(-0.524283\pi\) | ||||
−0.0762129 | + | 0.997092i | \(0.524283\pi\) | |||||||
\(32\) | −3.58022 | − | 4.37973i | −0.632899 | − | 0.774234i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.44251 | + | 2.76015i | −0.761884 | + | 0.473362i | ||||
\(35\) | −1.68640 | − | 0.913260i | −0.285053 | − | 0.154369i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.73892 | − | 3.01190i | −0.285877 | − | 0.495153i | 0.686945 | − | 0.726710i | \(-0.258951\pi\) |
−0.972821 | + | 0.231557i | \(0.925618\pi\) | |||||||
\(38\) | 5.77724 | − | 0.186894i | 0.937192 | − | 0.0303181i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.86649 | + | 0.848304i | 0.295118 | + | 0.134129i | ||||
\(41\) | 0.854749 | − | 0.493490i | 0.133489 | − | 0.0770701i | −0.431768 | − | 0.901985i | \(-0.642110\pi\) |
0.565258 | + | 0.824914i | \(0.308777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.9509 | − | 6.32252i | −1.67000 | − | 0.964175i | −0.967633 | − | 0.252360i | \(-0.918793\pi\) |
−0.702367 | − | 0.711815i | \(-0.747874\pi\) | |||||||
\(44\) | −1.03903 | − | 0.513391i | −0.156640 | − | 0.0773966i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.20145 | − | 3.85299i | 0.914354 | − | 0.568092i | ||||
\(47\) | −11.5806 | −1.68921 | −0.844603 | − | 0.535394i | \(-0.820163\pi\) | ||||
−0.844603 | + | 0.535394i | \(0.820163\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.98959 | − | 0.381594i | 0.998513 | − | 0.0545134i | ||||
\(50\) | 6.32470 | − | 0.204604i | 0.894447 | − | 0.0289353i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.94709 | + | 3.43260i | 0.963388 | + | 0.476016i | ||||
\(53\) | 2.70941 | − | 4.69284i | 0.372166 | − | 0.644611i | −0.617732 | − | 0.786388i | \(-0.711948\pi\) |
0.989899 | + | 0.141778i | \(0.0452818\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.420038 | 0.0566379 | ||||||||
\(56\) | −7.42559 | + | 0.927681i | −0.992286 | + | 0.123967i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.82102 | − | 10.9786i | −0.895644 | − | 1.44155i | ||||
\(59\) | 0.387839 | 0.0504924 | 0.0252462 | − | 0.999681i | \(-0.491963\pi\) | ||||
0.0252462 | + | 0.999681i | \(0.491963\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.891401i | 0.114132i | 0.998370 | + | 0.0570661i | \(0.0181746\pi\) | ||||
−0.998370 | + | 0.0570661i | \(0.981825\pi\) | |||||||
\(62\) | 0.566180 | − | 1.05827i | 0.0719050 | − | 0.134400i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.84988 | − | 1.54254i | 0.981235 | − | 0.192817i | ||||
\(65\) | −2.80843 | −0.348343 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.15867i | 0.385893i | 0.981209 | + | 0.192947i | \(0.0618044\pi\) | ||||
−0.981209 | + | 0.192947i | \(0.938196\pi\) | |||||||
\(68\) | −0.478055 | − | 7.38106i | −0.0579726 | − | 0.895085i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.26386 | − | 1.49361i | 0.270583 | − | 0.178521i | ||||
\(71\) | 7.56506i | 0.897807i | 0.893580 | + | 0.448904i | \(0.148185\pi\) | ||||
−0.893580 | + | 0.448904i | \(0.851815\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.1955 | − | 5.88637i | −1.19329 | − | 0.688947i | −0.234240 | − | 0.972179i | \(-0.575260\pi\) |
−0.959051 | + | 0.283232i | \(0.908593\pi\) | |||||||
\(74\) | 4.91584 | − | 0.159027i | 0.571454 | − | 0.0184865i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.62116 | + | 7.32871i | −0.415376 | + | 0.840661i | ||||
\(77\) | −1.30634 | + | 0.802489i | −0.148872 | + | 0.0914521i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.39987i | 0.382515i | 0.981540 | + | 0.191257i | \(0.0612565\pi\) | ||||
−0.981540 | + | 0.191257i | \(0.938743\pi\) | |||||||
\(80\) | −2.30301 | + | 1.76152i | −0.257485 | + | 0.196944i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.0451305 | + | 1.39507i | 0.00498383 | + | 0.154060i | ||||
\(83\) | 3.46587 | − | 6.00306i | 0.380428 | − | 0.658921i | −0.610695 | − | 0.791866i | \(-0.709110\pi\) |
0.991123 | + | 0.132945i | \(0.0424433\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.34037 | + | 2.32158i | 0.145383 | + | 0.251811i | ||||
\(86\) | 15.1897 | − | 9.43746i | 1.63795 | − | 1.01767i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.33336 | − | 0.953134i | 0.142136 | − | 0.101604i | ||||
\(89\) | 2.37662 | − | 1.37214i | 0.251921 | − | 0.145446i | −0.368723 | − | 0.929539i | \(-0.620205\pi\) |
0.620643 | + | 0.784093i | \(0.286871\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.73438 | − | 5.36554i | 0.915612 | − | 0.562462i | ||||
\(92\) | 0.667333 | + | 10.3035i | 0.0695743 | + | 1.07421i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.72586 | − | 14.4406i | 0.796861 | − | 1.48944i | ||||
\(95\) | − | 2.96270i | − | 0.303967i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.32750 | + | 5.38523i | 0.947064 | + | 0.546788i | 0.892168 | − | 0.451704i | \(-0.149184\pi\) |
0.0548963 | + | 0.998492i | \(0.482517\pi\) | |||||||
\(98\) | −4.18718 | + | 8.97037i | −0.422969 | + | 0.906144i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.96431 | + | 8.02319i | −0.396431 | + | 0.802319i | ||||
\(101\) | 8.28966 | − | 4.78604i | 0.824852 | − | 0.476229i | −0.0272346 | − | 0.999629i | \(-0.508670\pi\) |
0.852087 | + | 0.523400i | \(0.175337\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.35055 | − | 9.26743i | 0.527206 | − | 0.913147i | −0.472292 | − | 0.881442i | \(-0.656573\pi\) |
0.999497 | − | 0.0317044i | \(-0.0100935\pi\) | |||||||
\(104\) | −8.91500 | + | 6.37278i | −0.874188 | + | 0.624903i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.04427 | + | 6.50932i | 0.392814 | + | 0.632241i | ||||
\(107\) | 1.37590 | − | 0.794374i | 0.133013 | − | 0.0767950i | −0.432017 | − | 0.901865i | \(-0.642198\pi\) |
0.565030 | + | 0.825070i | \(0.308865\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.38392 | + | 7.59317i | −0.419903 | + | 0.727294i | −0.995929 | − | 0.0901375i | \(-0.971269\pi\) |
0.576026 | + | 0.817431i | \(0.304603\pi\) | |||||||
\(110\) | −0.280223 | + | 0.523774i | −0.0267182 | + | 0.0499399i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.79710 | − | 9.87836i | 0.358792 | − | 0.933417i | ||||
\(113\) | −3.31031 | − | 5.73363i | −0.311408 | − | 0.539375i | 0.667259 | − | 0.744825i | \(-0.267467\pi\) |
−0.978667 | + | 0.205451i | \(0.934134\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.87106 | − | 3.24078i | −0.174478 | − | 0.302204i | ||||
\(116\) | 18.2405 | − | 1.18139i | 1.69358 | − | 0.109690i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.258742 | + | 0.483623i | −0.0238191 | + | 0.0445211i | ||||
\(119\) | −8.60404 | − | 4.65947i | −0.788731 | − | 0.427133i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.33211 | + | 9.23548i | −0.484737 | + | 0.839589i | ||||
\(122\) | −1.11155 | − | 0.594687i | −0.100635 | − | 0.0538404i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.941902 | + | 1.41202i | 0.0845853 | + | 0.126803i | ||||
\(125\) | − | 6.86776i | − | 0.614271i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.20736i | 0.817021i | 0.912754 | + | 0.408511i | \(0.133952\pi\) | ||||
−0.912754 | + | 0.408511i | \(0.866048\pi\) | |||||||
\(128\) | −3.31345 | + | 10.8176i | −0.292871 | + | 0.956152i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.87361 | − | 3.50202i | 0.164326 | − | 0.307147i | ||||
\(131\) | −8.06936 | + | 13.9765i | −0.705023 | + | 1.22114i | 0.261660 | + | 0.965160i | \(0.415730\pi\) |
−0.966683 | + | 0.255976i | \(0.917603\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.66029 | + | 9.21418i | 0.490809 | + | 0.798971i | ||||
\(134\) | −3.93876 | − | 2.10727i | −0.340257 | − | 0.182040i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.52287 | + | 4.32806i | 0.816580 | + | 0.371128i | ||||
\(137\) | −1.14877 | − | 1.98972i | −0.0981457 | − | 0.169993i | 0.812771 | − | 0.582583i | \(-0.197958\pi\) |
−0.910917 | + | 0.412589i | \(0.864624\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.40486 | − | 5.89740i | −0.288797 | − | 0.500211i | 0.684726 | − | 0.728801i | \(-0.259922\pi\) |
−0.973523 | + | 0.228590i | \(0.926589\pi\) | |||||||
\(140\) | 0.352179 | + | 3.81941i | 0.0297645 | + | 0.322799i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.43338 | − | 5.04693i | −0.791632 | − | 0.423529i | ||||
\(143\) | −1.12256 | + | 1.94434i | −0.0938734 | + | 0.162594i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.73721 | + | 3.31238i | −0.476449 | + | 0.275078i | ||||
\(146\) | 14.1419 | − | 8.78642i | 1.17039 | − | 0.727169i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.08124 | + | 6.23598i | −0.253276 | + | 0.512594i | ||||
\(149\) | −5.94517 | + | 10.2973i | −0.487047 | + | 0.843590i | −0.999889 | − | 0.0148927i | \(-0.995259\pi\) |
0.512842 | + | 0.858483i | \(0.328593\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.9006 | − | 6.87083i | 0.968459 | − | 0.559140i | 0.0696928 | − | 0.997568i | \(-0.477798\pi\) |
0.898766 | + | 0.438428i | \(0.144465\pi\) | |||||||
\(152\) | −6.72285 | − | 9.40473i | −0.545295 | − | 0.762824i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.129167 | − | 2.16434i | −0.0104086 | − | 0.174407i | ||||
\(155\) | −0.532753 | − | 0.307585i | −0.0427917 | − | 0.0247058i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.3209i | 0.983317i | 0.870788 | + | 0.491659i | \(0.163609\pi\) | ||||
−0.870788 | + | 0.491659i | \(0.836391\pi\) | |||||||
\(158\) | −4.23952 | − | 2.26818i | −0.337278 | − | 0.180447i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.660129 | − | 4.04695i | −0.0521878 | − | 0.319940i | ||||
\(161\) | 12.0107 | + | 6.50432i | 0.946573 | + | 0.512612i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.96214 | + | 2.86489i | −0.388665 | + | 0.224396i | −0.681582 | − | 0.731742i | \(-0.738708\pi\) |
0.292917 | + | 0.956138i | \(0.405374\pi\) | |||||||
\(164\) | −1.76971 | − | 0.874427i | −0.138192 | − | 0.0682813i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.17341 | + | 8.32668i | 0.401534 | + | 0.646276i | ||||
\(167\) | 4.19478 | + | 7.26556i | 0.324601 | + | 0.562226i | 0.981432 | − | 0.191812i | \(-0.0614365\pi\) |
−0.656830 | + | 0.754039i | \(0.728103\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00560 | − | 1.74175i | 0.0773539 | − | 0.133981i | ||||
\(170\) | −3.78915 | + | 0.122579i | −0.290614 | + | 0.00940136i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.63456 | + | 25.2372i | 0.124634 | + | 1.92432i | ||||
\(173\) | 17.8687i | 1.35853i | 0.733891 | + | 0.679267i | \(0.237702\pi\) | ||||
−0.733891 | + | 0.679267i | \(0.762298\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.19666 | + | 10.0873i | 0.468423 | + | 0.762530i | ||||
\(176\) | 0.298995 | + | 2.29853i | 0.0225376 | + | 0.173258i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.125484 | + | 3.87897i | 0.00940546 | + | 0.290741i | ||||
\(179\) | 21.7765 | + | 12.5727i | 1.62765 | + | 0.939727i | 0.984790 | + | 0.173747i | \(0.0555874\pi\) |
0.642864 | + | 0.765980i | \(0.277746\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 21.3865i | − | 1.58965i | −0.606841 | − | 0.794824i | \(-0.707563\pi\) | ||
0.606841 | − | 0.794824i | \(-0.292437\pi\) | |||||||
\(182\) | 0.863626 | + | 14.4710i | 0.0640162 | + | 1.07266i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −13.2933 | − | 6.04169i | −0.979996 | − | 0.445400i | ||||
\(185\) | − | 2.52096i | − | 0.185344i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.14304 | 0.156715 | ||||||||
\(188\) | 12.8528 | + | 19.2678i | 0.937387 | + | 1.40525i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.69439 | + | 1.97653i | 0.268019 | + | 0.143393i | ||||
\(191\) | 0.399022i | 0.0288722i | 0.999896 | + | 0.0144361i | \(0.00459532\pi\) | ||||
−0.999896 | + | 0.0144361i | \(0.995405\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.1954 | −1.16577 | −0.582885 | − | 0.812554i | \(-0.698076\pi\) | ||||
−0.582885 | + | 0.812554i | \(0.698076\pi\) | |||||||
\(194\) | −12.9379 | + | 8.03840i | −0.928890 | + | 0.577123i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.39233 | − | 11.2057i | −0.599452 | − | 0.800411i | ||||
\(197\) | −23.4117 | −1.66801 | −0.834006 | − | 0.551756i | \(-0.813958\pi\) | ||||
−0.834006 | + | 0.551756i | \(0.813958\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.11333 | + | 10.5886i | −0.433362 | + | 0.750606i | −0.997160 | − | 0.0753071i | \(-0.976006\pi\) |
0.563798 | + | 0.825913i | \(0.309340\pi\) | |||||||
\(200\) | −7.35992 | − | 10.2959i | −0.520425 | − | 0.728032i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.437691 | + | 13.5299i | 0.0307959 | + | 0.951959i | ||||
\(203\) | 11.5147 | − | 21.2627i | 0.808175 | − | 1.49235i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.715424 | 0.0499674 | ||||||||
\(206\) | 7.98663 | + | 12.8546i | 0.556455 | + | 0.895623i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.99912 | − | 15.3682i | −0.138614 | − | 1.06560i | ||||
\(209\) | −2.05114 | − | 1.18423i | −0.141881 | − | 0.0819148i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.8107 | + | 6.81891i | −0.813082 | + | 0.469433i | −0.848025 | − | 0.529956i | \(-0.822208\pi\) |
0.0349433 | + | 0.999389i | \(0.488875\pi\) | |||||||
\(212\) | −10.8150 | + | 0.700462i | −0.742776 | + | 0.0481079i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.0726469 | + | 2.24565i | 0.00496604 | + | 0.153510i | ||||
\(215\) | −4.58296 | − | 7.93791i | −0.312555 | − | 0.541361i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.24454 | − | 0.0612242i | 0.152369 | − | 0.00415617i | ||||
\(218\) | −6.54376 | − | 10.5323i | −0.443199 | − | 0.713337i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.466181 | − | 0.698858i | −0.0314299 | − | 0.0471170i | ||||
\(221\) | −14.3287 | −0.963850 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.37599 | − | 14.5076i | 0.560898 | − | 0.971504i | −0.436520 | − | 0.899694i | \(-0.643789\pi\) |
0.997418 | − | 0.0718094i | \(-0.0228773\pi\) | |||||||
\(224\) | 9.78481 | + | 11.3251i | 0.653775 | + | 0.756689i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.35809 | − | 0.302734i | 0.622491 | − | 0.0201376i | ||||
\(227\) | 10.9841 | + | 19.0249i | 0.729037 | + | 1.26273i | 0.957291 | + | 0.289128i | \(0.0933652\pi\) |
−0.228253 | + | 0.973602i | \(0.573301\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.28647 | + | 1.89744i | 0.217176 | + | 0.125386i | 0.604642 | − | 0.796497i | \(-0.293316\pi\) |
−0.387466 | + | 0.921884i | \(0.626650\pi\) | |||||||
\(230\) | 5.28940 | − | 0.171112i | 0.348773 | − | 0.0112828i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.6957 | + | 23.5334i | −0.702209 | + | 1.54504i | ||||
\(233\) | 10.3989 | + | 18.0115i | 0.681256 | + | 1.17997i | 0.974598 | + | 0.223963i | \(0.0718995\pi\) |
−0.293341 | + | 0.956008i | \(0.594767\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.26972 | − | 4.19717i | −0.474224 | − | 0.273793i | ||||
\(236\) | −0.430446 | − | 0.645286i | −0.0280196 | − | 0.0420045i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 11.5503 | − | 7.62045i | 0.748694 | − | 0.493960i | ||||
\(239\) | −0.874254 | + | 0.504751i | −0.0565508 | + | 0.0326496i | −0.528009 | − | 0.849239i | \(-0.677061\pi\) |
0.471458 | + | 0.881888i | \(0.343728\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.5421 | − | 13.0147i | 1.45206 | − | 0.838349i | 0.453465 | − | 0.891274i | \(-0.350188\pi\) |
0.998598 | + | 0.0529249i | \(0.0168544\pi\) | |||||||
\(242\) | −7.95909 | − | 12.8103i | −0.511630 | − | 0.823477i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.48311 | − | 0.989326i | 0.0949464 | − | 0.0633351i | ||||
\(245\) | 4.52601 | + | 2.29370i | 0.289156 | + | 0.146539i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.7142 | + | 7.91790i | 0.872614 | + | 0.503804i | ||||
\(248\) | −2.38912 | + | 0.232513i | −0.151709 | + | 0.0147646i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 8.56388 | + | 4.58174i | 0.541627 | + | 0.289775i | ||||
\(251\) | −18.4201 | −1.16266 | −0.581332 | − | 0.813666i | \(-0.697468\pi\) | ||||
−0.581332 | + | 0.813666i | \(0.697468\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.99155 | −0.188077 | ||||||||
\(254\) | −11.4813 | − | 6.14258i | −0.720400 | − | 0.385419i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.2787 | − | 11.3486i | −0.704919 | − | 0.709288i | ||||
\(257\) | −10.8821 | − | 6.28280i | −0.678809 | − | 0.391910i | 0.120597 | − | 0.992702i | \(-0.461519\pi\) |
−0.799406 | + | 0.600791i | \(0.794852\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.81632 | + | 7.84032i | 0.299272 | + | 0.487174i | ||||
\(260\) | 3.11695 | + | 4.67265i | 0.193305 | + | 0.289786i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −12.0449 | − | 19.3865i | −0.744137 | − | 1.19770i | ||||
\(263\) | 8.60780 | − | 4.96972i | 0.530780 | − | 0.306446i | −0.210554 | − | 0.977582i | \(-0.567527\pi\) |
0.741334 | + | 0.671136i | \(0.234194\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.40166 | − | 1.96395i | 0.208962 | − | 0.120645i | ||||
\(266\) | −15.2660 | + | 0.911067i | −0.936017 | + | 0.0558611i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.25539 | − | 3.50567i | 0.321024 | − | 0.214143i | ||||
\(269\) | −6.20144 | − | 3.58040i | −0.378108 | − | 0.218301i | 0.298887 | − | 0.954289i | \(-0.403385\pi\) |
−0.676995 | + | 0.735988i | \(0.736718\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.11123 | + | 5.38881i | 0.188994 | + | 0.327347i | 0.944915 | − | 0.327316i | \(-0.106144\pi\) |
−0.755921 | + | 0.654663i | \(0.772811\pi\) | |||||||
\(272\) | −11.7500 | + | 8.98730i | −0.712450 | + | 0.544935i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.24750 | − | 0.105057i | 0.196189 | − | 0.00634670i | ||||
\(275\) | −2.24551 | − | 1.29645i | −0.135409 | − | 0.0781787i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.1171 | − | 22.7195i | −0.788130 | − | 1.36508i | −0.927111 | − | 0.374786i | \(-0.877716\pi\) |
0.138982 | − | 0.990295i | \(-0.455617\pi\) | |||||||
\(278\) | 9.62537 | − | 0.311381i | 0.577291 | − | 0.0186754i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.99763 | − | 2.10891i | −0.298666 | − | 0.126032i | ||||
\(281\) | 4.29087 | − | 7.43201i | 0.255972 | − | 0.443357i | −0.709187 | − | 0.705020i | \(-0.750938\pi\) |
0.965159 | + | 0.261664i | \(0.0842712\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.7140 | 1.70687 | 0.853435 | − | 0.521200i | \(-0.174515\pi\) | ||||
0.853435 | + | 0.521200i | \(0.174515\pi\) | |||||||
\(284\) | 12.5867 | − | 8.39612i | 0.746885 | − | 0.498218i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.67562 | − | 2.69694i | −0.0990815 | − | 0.159473i | ||||
\(287\) | −2.22501 | + | 1.36683i | −0.131338 | + | 0.0806813i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.66142 | − | 2.87767i | −0.0977307 | − | 0.169275i | ||||
\(290\) | −0.302923 | − | 9.36393i | −0.0177882 | − | 0.549869i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.52180 | + | 23.4962i | 0.0890565 | + | 1.37501i | ||||
\(293\) | 20.5937 | − | 11.8898i | 1.20310 | − | 0.694609i | 0.241855 | − | 0.970312i | \(-0.422244\pi\) |
0.961243 | + | 0.275704i | \(0.0889109\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.243466 | + | 0.140565i | 0.0141751 | + | 0.00818401i | ||||
\(296\) | −5.72046 | − | 8.00246i | −0.332495 | − | 0.465133i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −8.87419 | − | 14.2832i | −0.514068 | − | 0.827402i | ||||
\(299\) | 20.0019 | 1.15674 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 29.4188 | + | 15.9316i | 1.69567 | + | 0.918281i | ||||
\(302\) | 0.628349 | + | 19.4235i | 0.0361574 | + | 1.11770i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 16.2125 | − | 2.10893i | 0.929848 | − | 0.120956i | ||||
\(305\) | −0.323072 | + | 0.559576i | −0.0184990 | + | 0.0320412i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.4459 | −0.710323 | −0.355161 | − | 0.934805i | \(-0.615574\pi\) | ||||
−0.355161 | + | 0.934805i | \(0.615574\pi\) | |||||||
\(308\) | 2.78503 | + | 1.28284i | 0.158692 | + | 0.0730968i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.738967 | − | 0.459124i | 0.0419705 | − | 0.0260765i | ||||
\(311\) | 27.7490 | 1.57350 | 0.786752 | − | 0.617269i | \(-0.211761\pi\) | ||||
0.786752 | + | 0.617269i | \(0.211761\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 25.0450i | − | 1.41563i | −0.706400 | − | 0.707813i | \(-0.749682\pi\) | ||
0.706400 | − | 0.707813i | \(-0.250318\pi\) | |||||||
\(314\) | −15.3638 | − | 8.21975i | −0.867029 | − | 0.463867i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.65669 | − | 3.77336i | 0.318214 | − | 0.212268i | ||||
\(317\) | −19.1683 | −1.07660 | −0.538300 | − | 0.842754i | \(-0.680933\pi\) | ||||
−0.538300 | + | 0.842754i | \(0.680933\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.29600i | 0.296519i | ||||||||
\(320\) | 5.48682 | + | 1.87672i | 0.306722 | + | 0.104912i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −16.1234 | + | 10.6376i | −0.898524 | + | 0.592813i | ||||
\(323\) | − | 15.1158i | − | 0.841064i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.0138 | + | 8.66821i | 0.832815 | + | 0.480826i | ||||
\(326\) | −0.261999 | − | 8.09891i | −0.0145108 | − | 0.448557i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.27102 | − | 1.62341i | 0.125396 | − | 0.0896380i | ||||
\(329\) | 30.6280 | − | 0.835440i | 1.68858 | − | 0.0460593i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.75625i | 0.426322i | 0.977017 | + | 0.213161i | \(0.0683759\pi\) | ||||
−0.977017 | + | 0.213161i | \(0.931624\pi\) | |||||||
\(332\) | −13.8345 | + | 0.896028i | −0.759265 | + | 0.0491759i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −11.8584 | + | 0.383619i | −0.648863 | + | 0.0209907i | ||||
\(335\) | −1.14480 | + | 1.98285i | −0.0625472 | + | 0.108335i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.8555 | − | 29.1945i | −0.918175 | − | 1.59033i | −0.802185 | − | 0.597076i | \(-0.796329\pi\) |
−0.115990 | − | 0.993250i | \(-0.537004\pi\) | |||||||
\(338\) | 1.50103 | + | 2.41594i | 0.0816455 | + | 0.131410i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.37503 | − | 4.80672i | 0.128804 | − | 0.260681i | ||||
\(341\) | −0.425895 | + | 0.245891i | −0.0230635 | + | 0.0133157i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.4583 | + | 1.51347i | −0.996655 | + | 0.0817195i | ||||
\(344\) | −32.5604 | − | 14.7984i | −1.75554 | − | 0.797878i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −22.2817 | − | 11.9209i | −1.19787 | − | 0.640872i | ||||
\(347\) | 0.861953i | 0.0462721i | 0.999732 | + | 0.0231360i | \(0.00736509\pi\) | ||||
−0.999732 | + | 0.0231360i | \(0.992635\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.7538 | + | 17.1783i | 1.59268 | + | 0.919535i | 0.992845 | + | 0.119414i | \(0.0381015\pi\) |
0.599838 | + | 0.800122i | \(0.295232\pi\) | |||||||
\(350\) | −16.7126 | + | 0.997401i | −0.893325 | + | 0.0533133i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.06566 | − | 1.16060i | −0.163400 | − | 0.0618599i | ||||
\(353\) | 22.9489 | − | 13.2495i | 1.22145 | − | 0.705202i | 0.256220 | − | 0.966619i | \(-0.417523\pi\) |
0.965226 | + | 0.261416i | \(0.0841896\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.74181 | + | 4.74896i | −0.145520 | + | 0.252049i | ||||
\(356\) | −4.92066 | − | 2.43133i | −0.260795 | − | 0.128860i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −30.2057 | + | 18.7669i | −1.59642 | + | 0.991863i | ||||
\(359\) | 20.6811 | − | 11.9402i | 1.09150 | − | 0.630181i | 0.157528 | − | 0.987515i | \(-0.449648\pi\) |
0.933977 | + | 0.357334i | \(0.116314\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.14715 | − | 1.98692i | 0.0603761 | − | 0.104574i | ||||
\(362\) | 26.6683 | + | 14.2677i | 1.40165 | + | 0.749896i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −18.6211 | − | 8.57726i | −0.976009 | − | 0.449570i | ||||
\(365\) | −4.26680 | − | 7.39032i | −0.223335 | − | 0.386827i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.770528 | + | 1.33459i | 0.0402212 | + | 0.0696652i | 0.885435 | − | 0.464763i | \(-0.153860\pi\) |
−0.845214 | + | 0.534428i | \(0.820527\pi\) | |||||||
\(368\) | 16.4023 | − | 12.5457i | 0.855027 | − | 0.653989i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.14355 | + | 1.68182i | 0.163425 | + | 0.0874338i | ||||
\(371\) | −6.82722 | + | 12.6069i | −0.354451 | + | 0.654519i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.7744 | + | 27.3221i | −0.816770 | + | 1.41469i | 0.0912800 | + | 0.995825i | \(0.470904\pi\) |
−0.908050 | + | 0.418862i | \(0.862429\pi\) | |||||||
\(374\) | −1.42970 | + | 2.67230i | −0.0739282 | + | 0.138182i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −32.6009 | + | 3.17277i | −1.68126 | + | 0.163623i | ||||
\(377\) | − | 35.4097i | − | 1.82369i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.4907i | 1.10390i | 0.833876 | + | 0.551951i | \(0.186117\pi\) | ||||
−0.833876 | + | 0.551951i | \(0.813883\pi\) | |||||||
\(380\) | −4.92934 | + | 3.28817i | −0.252870 | + | 0.168680i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.497567 | − | 0.266202i | −0.0254578 | − | 0.0136201i | ||||
\(383\) | 2.12781 | − | 3.68547i | 0.108726 | − | 0.188319i | −0.806529 | − | 0.591195i | \(-0.798656\pi\) |
0.915254 | + | 0.402877i | \(0.131990\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.11090 | + | 0.0303021i | −0.0566168 | + | 0.00154434i | ||||
\(386\) | 10.8046 | − | 20.1951i | 0.549938 | − | 1.02791i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.39224 | − | 21.4959i | −0.0706803 | − | 1.09129i | ||||
\(389\) | −4.66309 | − | 8.07672i | −0.236428 | − | 0.409506i | 0.723259 | − | 0.690577i | \(-0.242643\pi\) |
−0.959687 | + | 0.281072i | \(0.909310\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.54621 | − | 16.5345i | −0.482773 | − | 0.836187i | ||||
\(392\) | 19.5720 | − | 2.98919i | 0.988537 | − | 0.150977i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 15.6188 | − | 29.1936i | 0.786863 | − | 1.47075i | ||||
\(395\) | −1.23222 | + | 2.13426i | −0.0619996 | + | 0.107386i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.08981 | + | 3.51595i | −0.305639 | + | 0.176461i | −0.644973 | − | 0.764205i | \(-0.723131\pi\) |
0.339334 | + | 0.940666i | \(0.389798\pi\) | |||||||
\(398\) | −9.12520 | − | 14.6872i | −0.457405 | − | 0.736201i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 17.7488 | − | 2.30878i | 0.887438 | − | 0.115439i | ||||
\(401\) | 2.90076 | − | 5.02426i | 0.144857 | − | 0.250899i | −0.784463 | − | 0.620176i | \(-0.787061\pi\) |
0.929320 | + | 0.369277i | \(0.120395\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.84759 | − | 1.64406i | 0.141849 | − | 0.0818964i | ||||
\(404\) | −17.1633 | − | 8.48050i | −0.853907 | − | 0.421921i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 18.8320 | + | 28.5436i | 0.934618 | + | 1.41660i | ||||
\(407\) | −1.74531 | − | 1.00766i | −0.0865119 | − | 0.0499477i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 23.0535i | − | 1.13992i | −0.821671 | − | 0.569961i | \(-0.806958\pi\) | ||
0.821671 | − | 0.569961i | \(-0.193042\pi\) | |||||||
\(410\) | −0.477286 | + | 0.892111i | −0.0235715 | + | 0.0440582i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −21.3575 | + | 1.38327i | −1.05221 | + | 0.0681490i | ||||
\(413\) | −1.02574 | + | 0.0279792i | −0.0504736 | + | 0.00137677i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.35139 | − | 2.51228i | 0.213601 | − | 0.123323i | ||||
\(416\) | 20.4974 | + | 7.75989i | 1.00497 | + | 0.380460i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.84509 | − | 1.76767i | 0.139158 | − | 0.0864594i | ||||
\(419\) | −7.60902 | − | 13.1792i | −0.371725 | − | 0.643847i | 0.618106 | − | 0.786095i | \(-0.287900\pi\) |
−0.989831 | + | 0.142248i | \(0.954567\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.47824 | + | 6.02448i | −0.169519 | + | 0.293615i | −0.938251 | − | 0.345956i | \(-0.887555\pi\) |
0.768732 | + | 0.639571i | \(0.220888\pi\) | |||||||
\(422\) | −0.623601 | − | 19.2767i | −0.0303564 | − | 0.938375i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.34163 | − | 13.9532i | 0.307977 | − | 0.677629i | ||||
\(425\) | − | 16.5482i | − | 0.802704i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.0643068 | − | 2.35755i | −0.00311203 | − | 0.114090i | ||||
\(428\) | −2.84872 | − | 1.40757i | −0.137698 | − | 0.0680375i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12.9558 | − | 0.419119i | 0.624783 | − | 0.0202117i | ||||
\(431\) | −27.3227 | − | 15.7748i | −1.31609 | − | 0.759845i | −0.332993 | − | 0.942929i | \(-0.608059\pi\) |
−0.983097 | + | 0.183084i | \(0.941392\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 9.13238i | − | 0.438874i | −0.975627 | − | 0.219437i | \(-0.929578\pi\) | ||
0.975627 | − | 0.219437i | \(-0.0704221\pi\) | |||||||
\(434\) | −1.42107 | + | 2.83971i | −0.0682136 | + | 0.136310i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 17.4990 | − | 1.13337i | 0.838051 | − | 0.0542786i | ||||
\(437\) | 21.1006i | 1.00938i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.1491 | −1.05712 | −0.528560 | − | 0.848896i | \(-0.677268\pi\) | ||||
−0.528560 | + | 0.848896i | \(0.677268\pi\) | |||||||
\(440\) | 1.18246 | − | 0.115079i | 0.0563716 | − | 0.00548617i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.55919 | − | 17.8674i | 0.454684 | − | 0.849864i | ||||
\(443\) | 12.4878i | 0.593313i | 0.954984 | + | 0.296656i | \(0.0958716\pi\) | ||||
−0.954984 | + | 0.296656i | \(0.904128\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.98922 | 0.0942983 | ||||||||
\(446\) | 12.5026 | + | 20.1232i | 0.592016 | + | 0.952860i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −20.6498 | + | 4.64595i | −0.975612 | + | 0.219500i | ||||
\(449\) | −23.2620 | −1.09780 | −0.548901 | − | 0.835888i | \(-0.684953\pi\) | ||||
−0.548901 | + | 0.835888i | \(0.684953\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.285964 | − | 0.495304i | 0.0134655 | − | 0.0233229i | ||||
\(452\) | −5.86563 | + | 11.8712i | −0.275896 | + | 0.558374i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −31.0514 | + | 1.00451i | −1.45731 | + | 0.0471440i | ||||
\(455\) | 7.42764 | − | 0.202604i | 0.348213 | − | 0.00949821i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.31974 | −0.248847 | −0.124423 | − | 0.992229i | \(-0.539708\pi\) | ||||
−0.124423 | + | 0.992229i | \(0.539708\pi\) | |||||||
\(458\) | −4.55857 | + | 2.83226i | −0.213008 | + | 0.132343i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.31539 | + | 6.70986i | −0.154581 | + | 0.312849i | ||||
\(461\) | −7.88185 | − | 4.55059i | −0.367094 | − | 0.211942i | 0.305094 | − | 0.952322i | \(-0.401312\pi\) |
−0.672188 | + | 0.740380i | \(0.734645\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.490550 | + | 0.283219i | −0.0227978 | + | 0.0131623i | −0.511356 | − | 0.859369i | \(-0.670856\pi\) |
0.488558 | + | 0.872532i | \(0.337523\pi\) | |||||||
\(464\) | −22.2099 | − | 29.0372i | −1.03107 | − | 1.34802i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −29.3972 | + | 0.951000i | −1.36180 | + | 0.0440542i | ||||
\(467\) | −4.77345 | − | 8.26785i | −0.220889 | − | 0.382591i | 0.734189 | − | 0.678945i | \(-0.237562\pi\) |
−0.955078 | + | 0.296354i | \(0.904229\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.227871 | − | 8.35395i | −0.0105221 | − | 0.385750i | ||||
\(470\) | 10.0836 | − | 6.26501i | 0.465124 | − | 0.288983i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.09182 | − | 0.106257i | 0.0502549 | − | 0.00489089i | ||||
\(473\) | −7.32745 | −0.336917 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.14438 | + | 15.8385i | −0.419573 | + | 0.726722i | ||||
\(476\) | 1.79682 | + | 19.4867i | 0.0823572 | + | 0.893172i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.0461603 | − | 1.42690i | −0.00211132 | − | 0.0652651i | ||||
\(479\) | −11.9617 | − | 20.7183i | −0.546545 | − | 0.946644i | −0.998508 | − | 0.0546071i | \(-0.982609\pi\) |
0.451963 | − | 0.892037i | \(-0.350724\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.6694 | + | 6.73732i | 0.532078 | + | 0.307195i | ||||
\(482\) | 1.19021 | + | 36.7918i | 0.0542128 | + | 1.67582i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 21.2838 | − | 1.37851i | 0.967447 | − | 0.0626593i | ||||
\(485\) | 3.90355 | + | 6.76115i | 0.177251 | + | 0.307008i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.0207 | − | 7.51748i | −0.590022 | − | 0.340650i | 0.175084 | − | 0.984553i | \(-0.443980\pi\) |
−0.765106 | + | 0.643904i | \(0.777314\pi\) | |||||||
\(488\) | 0.244220 | + | 2.50941i | 0.0110553 | + | 0.113596i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.87964 | + | 4.11358i | −0.265615 | + | 0.185832i | ||||
\(491\) | −13.4272 | + | 7.75218i | −0.605960 | + | 0.349851i | −0.771383 | − | 0.636372i | \(-0.780434\pi\) |
0.165423 | + | 0.986223i | \(0.447101\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −29.2714 | + | 16.8998i | −1.31832 | + | 0.761130i | ||||
\(494\) | −19.0226 | + | 11.8188i | −0.855869 | + | 0.531755i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.30393 | − | 3.13427i | 0.0585483 | − | 0.140733i | ||||
\(497\) | −0.545753 | − | 20.0078i | −0.0244804 | − | 0.897474i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.376114 | − | 0.217150i | −0.0168372 | − | 0.00972096i | 0.491558 | − | 0.870845i | \(-0.336428\pi\) |
−0.508395 | + | 0.861124i | \(0.669761\pi\) | |||||||
\(500\) | −11.4266 | + | 7.62222i | −0.511011 | + | 0.340876i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.2887 | − | 22.9692i | 0.548472 | − | 1.02517i | ||||
\(503\) | −16.6525 | −0.742496 | −0.371248 | − | 0.928534i | \(-0.621070\pi\) | ||||
−0.371248 | + | 0.928534i | \(0.621070\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.93844 | 0.308756 | ||||||||
\(506\) | 1.99577 | − | 3.73036i | 0.0887229 | − | 0.165835i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 15.3192 | − | 10.2188i | 0.679679 | − | 0.453388i | ||||
\(509\) | 9.83654 | + | 5.67913i | 0.435997 | + | 0.251723i | 0.701898 | − | 0.712277i | \(-0.252336\pi\) |
−0.265901 | + | 0.964000i | \(0.585670\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.3893 | + | 14.8326i | 1.21163 | + | 0.656154i | ||||
\(512\) | 21.6758 | − | 6.49309i | 0.957944 | − | 0.286957i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15.0943 | − | 9.37817i | 0.665782 | − | 0.413653i | ||||
\(515\) | 6.71761 | − | 3.87841i | 0.296013 | − | 0.170903i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.81159 | + | 3.35532i | −0.255593 | + | 0.147567i | ||||
\(518\) | −12.9898 | + | 0.775225i | −0.570738 | + | 0.0340614i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −7.90608 | + | 0.769433i | −0.346705 | + | 0.0337418i | ||||
\(521\) | 30.1497 | + | 17.4069i | 1.32088 | + | 0.762612i | 0.983869 | − | 0.178888i | \(-0.0572499\pi\) |
0.337013 | + | 0.941500i | \(0.390583\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.7500 | + | 20.3516i | 0.513791 | + | 0.889912i | 0.999872 | + | 0.0159982i | \(0.00509259\pi\) |
−0.486081 | + | 0.873914i | \(0.661574\pi\) | |||||||
\(524\) | 32.2099 | − | 2.08616i | 1.40710 | − | 0.0911345i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.454489 | + | 14.0491i | 0.0198167 | + | 0.612571i | ||||
\(527\) | −2.71812 | − | 1.56930i | −0.118403 | − | 0.0683600i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.82588 | + | 3.16252i | 0.0793862 | + | 0.137501i | ||||
\(530\) | 0.179607 | + | 5.55199i | 0.00780161 | + | 0.241163i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 9.04843 | − | 19.6440i | 0.392299 | − | 0.851674i | ||||
\(533\) | −1.91199 | + | 3.31167i | −0.0828175 | + | 0.143444i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.15162 | 0.0497890 | ||||||||
\(536\) | 0.865390 | + | 8.89206i | 0.0373791 | + | 0.384079i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8.60185 | − | 5.34437i | 0.370852 | − | 0.230412i | ||||
\(539\) | 3.39708 | − | 2.21664i | 0.146323 | − | 0.0954773i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.83947 | + | 6.65016i | 0.165072 | + | 0.285913i | 0.936681 | − | 0.350184i | \(-0.113881\pi\) |
−0.771609 | + | 0.636097i | \(0.780548\pi\) | |||||||
\(542\) | −8.79529 | + | 0.284527i | −0.377790 | + | 0.0122215i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.36799 | − | 20.6477i | −0.144402 | − | 0.885261i | ||||
\(545\) | −5.50400 | + | 3.17774i | −0.235766 | + | 0.136119i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.76933 | + | 2.17622i | 0.161165 | + | 0.0930485i | 0.578413 | − | 0.815744i | \(-0.303672\pi\) |
−0.417248 | + | 0.908792i | \(0.637006\pi\) | |||||||
\(548\) | −2.03553 | + | 4.11961i | −0.0869534 | + | 0.175981i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.11469 | − | 1.93517i | 0.132811 | − | 0.0825160i | ||||
\(551\) | 37.3549 | 1.59137 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.245271 | − | 8.99186i | −0.0104300 | − | 0.382373i | ||||
\(554\) | 37.0813 | − | 1.19958i | 1.57544 | − | 0.0509653i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.03316 | + | 12.2103i | −0.255863 | + | 0.517830i | ||||
\(557\) | −16.1918 | + | 28.0450i | −0.686068 | + | 1.18830i | 0.287032 | + | 0.957921i | \(0.407331\pi\) |
−0.973100 | + | 0.230384i | \(0.926002\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 48.9923 | 2.07215 | ||||||||
\(560\) | 5.96385 | − | 4.82495i | 0.252019 | − | 0.203891i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.40487 | + | 10.3088i | 0.270173 | + | 0.434848i | ||||
\(563\) | −15.0531 | −0.634411 | −0.317205 | − | 0.948357i | \(-0.602744\pi\) | ||||
−0.317205 | + | 0.948357i | \(0.602744\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 4.79904i | − | 0.201897i | ||||||
\(566\) | −19.1562 | + | 35.8054i | −0.805194 | + | 1.50501i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.07262 | + | 21.2966i | 0.0869652 | + | 0.893586i | ||||
\(569\) | 31.4512 | 1.31850 | 0.659252 | − | 0.751922i | \(-0.270873\pi\) | ||||
0.659252 | + | 0.751922i | \(0.270873\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 0.980970i | − | 0.0410523i | −0.999789 | − | 0.0205262i | \(-0.993466\pi\) | ||
0.999789 | − | 0.0205262i | \(-0.00653414\pi\) | |||||||
\(572\) | 4.48086 | − | 0.290215i | 0.187354 | − | 0.0121345i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.220002 | − | 3.68638i | −0.00918270 | − | 0.153867i | ||||
\(575\) | 23.1001i | 0.963343i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.71704 | − | 3.87808i | −0.279634 | − | 0.161447i | 0.353624 | − | 0.935388i | \(-0.384949\pi\) |
−0.633258 | + | 0.773941i | \(0.718283\pi\) | |||||||
\(578\) | 4.69675 | − | 0.151940i | 0.195359 | − | 0.00631986i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 11.8786 | + | 5.86929i | 0.493232 | + | 0.243709i | ||||
\(581\) | −8.73334 | + | 16.1267i | −0.362320 | + | 0.669049i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 3.14006i | − | 0.130048i | ||||||
\(584\) | −30.3143 | − | 13.7776i | −1.25441 | − | 0.570120i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.08734 | + | 33.6118i | 0.0449176 | + | 1.38849i | ||||
\(587\) | −9.68642 | + | 16.7774i | −0.399801 | + | 0.692476i | −0.993701 | − | 0.112063i | \(-0.964254\pi\) |
0.593900 | + | 0.804539i | \(0.297588\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.73437 | + | 3.00402i | 0.0714635 | + | 0.123778i | ||||
\(590\) | −0.337705 | + | 0.209818i | −0.0139031 | + | 0.00863806i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 13.7951 | − | 1.79449i | 0.566976 | − | 0.0737529i | ||||
\(593\) | −8.54276 | + | 4.93217i | −0.350809 | + | 0.202540i | −0.665042 | − | 0.746806i | \(-0.731586\pi\) |
0.314232 | + | 0.949346i | \(0.398253\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.71244 | − | 6.04335i | −0.152195 | − | 0.247753i | ||||
\(596\) | 23.7309 | − | 1.53700i | 0.972058 | − | 0.0629580i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −13.3440 | + | 24.9417i | −0.545677 | + | 1.01994i | ||||
\(599\) | 30.9174i | 1.26325i | 0.775274 | + | 0.631625i | \(0.217612\pi\) | ||||
−0.775274 | + | 0.631625i | \(0.782388\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.3705 | + | 7.71949i | 0.545396 | + | 0.314885i | 0.747263 | − | 0.664528i | \(-0.231368\pi\) |
−0.201867 | + | 0.979413i | \(0.564701\pi\) | |||||||
\(602\) | −39.4925 | + | 26.0557i | −1.60960 | + | 1.06195i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −24.6396 | − | 12.1746i | −1.00257 | − | 0.495377i | ||||
\(605\) | −6.69445 | + | 3.86504i | −0.272168 | + | 0.157136i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.56330 | + | 7.90387i | −0.185219 | + | 0.320808i | −0.943650 | − | 0.330945i | \(-0.892633\pi\) |
0.758432 | + | 0.651753i | \(0.225966\pi\) | |||||||
\(608\) | −8.18616 | + | 21.6234i | −0.331993 | + | 0.876943i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.482240 | − | 0.776174i | −0.0195253 | − | 0.0314264i | ||||
\(611\) | 38.8570 | − | 22.4341i | 1.57199 | − | 0.907587i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.5959 | + | 18.3526i | −0.427963 | + | 0.741253i | −0.996692 | − | 0.0812716i | \(-0.974102\pi\) |
0.568729 | + | 0.822525i | \(0.307435\pi\) | |||||||
\(614\) | 8.30309 | − | 15.5196i | 0.335086 | − | 0.626319i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.45766 | + | 2.61701i | −0.139313 | + | 0.105442i | ||||
\(617\) | 1.36130 | + | 2.35785i | 0.0548040 | + | 0.0949233i | 0.892126 | − | 0.451787i | \(-0.149213\pi\) |
−0.837322 | + | 0.546710i | \(0.815880\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.77457 | − | 16.9300i | −0.392873 | − | 0.680476i | 0.599954 | − | 0.800034i | \(-0.295185\pi\) |
−0.992827 | + | 0.119558i | \(0.961852\pi\) | |||||||
\(620\) | 0.0795197 | + | 1.22777i | 0.00319359 | + | 0.0493083i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −18.5124 | + | 34.6022i | −0.742281 | + | 1.38742i | ||||
\(623\) | −6.18661 | + | 3.80044i | −0.247861 | + | 0.152262i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.69734 | + | 15.0642i | −0.347894 | + | 0.602570i | ||||
\(626\) | 31.2303 | + | 16.7084i | 1.24821 | + | 0.667803i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 20.4995 | − | 13.6745i | 0.818020 | − | 0.545670i | ||||
\(629\) | − | 12.8620i | − | 0.512840i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 47.6971i | − | 1.89879i | −0.314080 | − | 0.949396i | \(-0.601696\pi\) | ||
0.314080 | − | 0.949396i | \(-0.398304\pi\) | |||||||
\(632\) | 0.931471 | + | 9.57106i | 0.0370519 | + | 0.380716i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 12.7879 | − | 23.9023i | 0.507872 | − | 0.949280i | ||||
\(635\) | −3.33704 | + | 5.77992i | −0.132426 | + | 0.229369i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −22.7133 | + | 14.8207i | −0.899935 | + | 0.587218i | ||||
\(638\) | −6.60393 | − | 3.53316i | −0.261452 | − | 0.139879i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −6.00066 | + | 5.58986i | −0.237197 | + | 0.220958i | ||||
\(641\) | −3.91165 | − | 6.77517i | −0.154501 | − | 0.267603i | 0.778376 | − | 0.627798i | \(-0.216044\pi\) |
−0.932877 | + | 0.360195i | \(0.882710\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.8295 | − | 36.0777i | −0.821435 | − | 1.42277i | −0.904614 | − | 0.426232i | \(-0.859841\pi\) |
0.0831794 | − | 0.996535i | \(-0.473493\pi\) | |||||||
\(644\) | −2.50825 | − | 27.2022i | −0.0988388 | − | 1.07192i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 18.8489 | + | 10.0843i | 0.741599 | + | 0.396761i | ||||
\(647\) | −9.38911 | + | 16.2624i | −0.369124 | + | 0.639342i | −0.989429 | − | 0.145019i | \(-0.953676\pi\) |
0.620305 | + | 0.784361i | \(0.287009\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.194632 | − | 0.112371i | 0.00763999 | − | 0.00441095i | ||||
\(650\) | −20.8252 | + | 12.9388i | −0.816833 | + | 0.507502i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.2739 | + | 5.07638i | 0.402355 | + | 0.198806i | ||||
\(653\) | 0.450392 | − | 0.780101i | 0.0176252 | − | 0.0305277i | −0.857078 | − | 0.515186i | \(-0.827723\pi\) |
0.874703 | + | 0.484658i | \(0.161056\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.1311 | + | 5.84917i | −0.395854 | + | 0.228546i | ||||
\(656\) | 0.509259 | + | 3.91493i | 0.0198832 | + | 0.152852i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −19.3913 | + | 38.7495i | −0.755953 | + | 1.51061i | ||||
\(659\) | −11.5880 | − | 6.69033i | −0.451404 | − | 0.260618i | 0.257019 | − | 0.966406i | \(-0.417260\pi\) |
−0.708423 | + | 0.705788i | \(0.750593\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.69061i | 0.0657571i | 0.999459 | + | 0.0328785i | \(0.0104674\pi\) | ||||
−0.999459 | + | 0.0328785i | \(0.989533\pi\) | |||||||
\(662\) | −9.67179 | − | 5.17449i | −0.375905 | − | 0.201112i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.11218 | − | 17.8489i | 0.314814 | − | 0.692672i | ||||
\(665\) | 0.213733 | + | 7.83566i | 0.00828822 | + | 0.303854i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 40.8609 | − | 23.5911i | 1.58214 | − | 0.913450i | ||||
\(668\) | 7.43283 | − | 15.0430i | 0.287585 | − | 0.582030i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.70881 | − | 2.75037i | −0.0660173 | − | 0.106256i | ||||
\(671\) | 0.258271 | + | 0.447339i | 0.00997045 | + | 0.0172693i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.6580 | − | 21.9243i | 0.487930 | − | 0.845119i | −0.511974 | − | 0.859001i | \(-0.671085\pi\) |
0.999904 | + | 0.0138817i | \(0.00441883\pi\) | |||||||
\(674\) | 47.6495 | − | 1.54146i | 1.83539 | − | 0.0593748i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.01399 | + | 0.259977i | −0.154384 | + | 0.00999913i | ||||
\(677\) | 32.9850i | 1.26772i | 0.773449 | + | 0.633859i | \(0.218530\pi\) | ||||
−0.773449 | + | 0.633859i | \(0.781470\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −25.0576 | − | 13.5698i | −0.961621 | − | 0.520761i | ||||
\(680\) | 4.40935 | + | 6.16833i | 0.169091 | + | 0.236544i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.0224871 | − | 0.695121i | −0.000861077 | − | 0.0266175i | ||||
\(683\) | −5.67586 | − | 3.27696i | −0.217181 | − | 0.125389i | 0.387463 | − | 0.921885i | \(-0.373351\pi\) |
−0.604644 | + | 0.796496i | \(0.706685\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 1.66539i | − | 0.0636314i | ||||||
\(686\) | 10.4270 | − | 24.0266i | 0.398104 | − | 0.917340i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 40.1755 | − | 30.7292i | 1.53168 | − | 1.17154i | ||||
\(689\) | 20.9948i | 0.799840i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.410768 | 0.0156264 | 0.00781318 | − | 0.999969i | \(-0.497513\pi\) | ||||
0.00781318 | + | 0.999969i | \(0.497513\pi\) | |||||||
\(692\) | 29.7299 | − | 19.8317i | 1.13016 | − | 0.753889i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.07483 | − | 0.575041i | −0.0407999 | − | 0.0218283i | ||||
\(695\) | − | 4.93611i | − | 0.187237i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.65011 | 0.138258 | ||||||||
\(698\) | −41.2707 | + | 25.6417i | −1.56212 | + | 0.970551i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 9.90587 | − | 21.5055i | 0.374407 | − | 0.812830i | ||||
\(701\) | −17.5496 | −0.662841 | −0.331420 | − | 0.943483i | \(-0.607528\pi\) | ||||
−0.331420 | + | 0.943483i | \(0.607528\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.10742 | + | 12.3104i | −0.268061 | + | 0.464296i | ||||
\(704\) | 3.49244 | − | 3.04850i | 0.131626 | − | 0.114895i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.21169 | + | 37.4558i | 0.0456027 | + | 1.40967i | ||||
\(707\) | −21.5790 | + | 13.2560i | −0.811560 | + | 0.498543i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.8431 | −0.632557 | −0.316279 | − | 0.948666i | \(-0.602433\pi\) | ||||
−0.316279 | + | 0.948666i | \(0.602433\pi\) | |||||||
\(710\) | −4.09263 | − | 6.58716i | −0.153594 | − | 0.247212i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.31454 | − | 4.51387i | 0.236648 | − | 0.169165i | ||||
\(713\) | 3.79431 | + | 2.19065i | 0.142098 | + | 0.0820404i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.40938 | + | 0.813704i | −0.0527077 | + | 0.0304308i | ||||
\(716\) | −3.25041 | − | 50.1856i | −0.121473 | − | 1.87552i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.09195 | + | 33.7544i | 0.0407513 | + | 1.25970i | ||||
\(719\) | 15.7871 | + | 27.3440i | 0.588759 | + | 1.01976i | 0.994395 | + | 0.105726i | \(0.0337166\pi\) |
−0.405636 | + | 0.914035i | \(0.632950\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.4824 | + | 24.8962i | −0.502111 | + | 0.927182i | ||||
\(722\) | 1.71231 | + | 2.75600i | 0.0637258 | + | 0.102568i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −35.5828 | + | 23.7359i | −1.32243 | + | 0.882139i | ||||
\(725\) | 40.8946 | 1.51879 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.8377 | + | 25.6997i | −0.550301 | + | 0.953150i | 0.447951 | + | 0.894058i | \(0.352154\pi\) |
−0.998253 | + | 0.0590918i | \(0.981180\pi\) | |||||||
\(728\) | 23.1184 | − | 17.4977i | 0.856824 | − | 0.648507i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 12.0620 | − | 0.390207i | 0.446436 | − | 0.0144422i | ||||
\(731\) | −23.3823 | − | 40.4994i | −0.864827 | − | 1.49792i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.7406 | − | 7.93312i | −0.507519 | − | 0.293016i | 0.224294 | − | 0.974522i | \(-0.427992\pi\) |
−0.731813 | + | 0.681505i | \(0.761326\pi\) | |||||||
\(734\) | −2.17824 | + | 0.0704661i | −0.0804004 | + | 0.00260095i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.70150 | + | 28.8228i | 0.173300 | + | 1.06242i | ||||
\(737\) | 0.915182 | + | 1.58514i | 0.0337112 | + | 0.0583894i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.242332 | + | 0.139910i | 0.00891432 | + | 0.00514668i | 0.504451 | − | 0.863441i | \(-0.331695\pi\) |
−0.495536 | + | 0.868587i | \(0.665028\pi\) | |||||||
\(740\) | −4.19436 | + | 2.79790i | −0.154188 | + | 0.102853i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11.1657 | − | 16.9239i | −0.409907 | − | 0.621295i | ||||
\(743\) | −8.28791 | + | 4.78503i | −0.304054 | + | 0.175546i | −0.644263 | − | 0.764804i | \(-0.722836\pi\) |
0.340209 | + | 0.940350i | \(0.389502\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.46415 | + | 4.30943i | −0.273465 | + | 0.157885i | ||||
\(746\) | −23.5461 | − | 37.8978i | −0.862084 | − | 1.38754i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.37847 | − | 3.56559i | −0.0869654 | − | 0.130371i | ||||
\(749\) | −3.58162 | + | 2.20019i | −0.130870 | + | 0.0803933i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.5319 | − | 14.7409i | −0.931674 | − | 0.537902i | −0.0443332 | − | 0.999017i | \(-0.514116\pi\) |
−0.887341 | + | 0.461115i | \(0.847450\pi\) | |||||||
\(752\) | 17.7929 | − | 42.7689i | 0.648841 | − | 1.55962i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 44.1548 | + | 23.6231i | 1.60802 | + | 0.860304i | ||||
\(755\) | 9.96081 | 0.362511 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.0636 | 0.983643 | 0.491821 | − | 0.870696i | \(-0.336331\pi\) | ||||
0.491821 | + | 0.870696i | \(0.336331\pi\) | |||||||
\(758\) | −26.7982 | − | 14.3372i | −0.973354 | − | 0.520752i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.811699 | − | 8.34038i | −0.0294434 | − | 0.302537i | ||||
\(761\) | −30.1287 | − | 17.3948i | −1.09216 | − | 0.630561i | −0.158012 | − | 0.987437i | \(-0.550509\pi\) |
−0.934152 | + | 0.356876i | \(0.883842\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.0467 | − | 20.3984i | 0.399916 | − | 0.738473i | ||||
\(764\) | 0.663892 | − | 0.442857i | 0.0240188 | − | 0.0160220i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.17612 | + | 5.11202i | 0.114758 | + | 0.184705i | ||||
\(767\) | −1.30134 | + | 0.751328i | −0.0469886 | + | 0.0271289i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.8103 | − | 23.5618i | 1.47166 | − | 0.849661i | 0.472164 | − | 0.881511i | \(-0.343473\pi\) |
0.999493 | + | 0.0318496i | \(0.0101398\pi\) | |||||||
\(770\) | 0.703339 | − | 1.40548i | 0.0253466 | − | 0.0506498i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 17.9746 | + | 26.9459i | 0.646919 | + | 0.969803i | ||||
\(773\) | −34.1954 | − | 19.7427i | −1.22992 | − | 0.710096i | −0.262909 | − | 0.964821i | \(-0.584682\pi\) |
−0.967014 | + | 0.254724i | \(0.918015\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.89872 | + | 3.28868i | 0.0682041 | + | 0.118133i | ||||
\(776\) | 27.7335 | + | 12.6046i | 0.995575 | + | 0.452480i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13.1823 | − | 0.426448i | 0.472609 | − | 0.0152889i | ||||
\(779\) | −3.49358 | − | 2.01702i | −0.125171 | − | 0.0722673i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.19187 | + | 3.79643i | 0.0784314 | + | 0.135847i | ||||
\(782\) | 26.9866 | − | 0.873017i | 0.965040 | − | 0.0312190i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −9.32981 | + | 26.3999i | −0.333208 | + | 0.942853i | ||||
\(785\) | −4.46549 | + | 7.73445i | −0.159380 | + | 0.276055i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.0153 | 1.10558 | 0.552788 | − | 0.833322i | \(-0.313564\pi\) | ||||
0.552788 | + | 0.833322i | \(0.313564\pi\) | |||||||
\(788\) | 25.9836 | + | 38.9522i | 0.925626 | + | 1.38762i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.83930 | − | 2.96038i | −0.0654393 | − | 0.105326i | ||||
\(791\) | 9.16864 | + | 14.9253i | 0.325999 | + | 0.530683i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.72684 | − | 2.99097i | −0.0613217 | − | 0.106212i | ||||
\(794\) | −0.321540 | − | 9.93942i | −0.0114110 | − | 0.352737i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 24.4022 | − | 1.58047i | 0.864913 | − | 0.0560184i | ||||
\(797\) | −8.30567 | + | 4.79528i | −0.294202 | + | 0.169857i | −0.639835 | − | 0.768512i | \(-0.720997\pi\) |
0.345633 | + | 0.938370i | \(0.387664\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −37.0903 | − | 21.4141i | −1.31216 | − | 0.757575i | ||||
\(800\) | −8.96189 | + | 23.6724i | −0.316851 | + | 0.836946i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4.32988 | + | 6.96902i | 0.152893 | + | 0.246085i | ||||
\(803\) | −6.82198 | −0.240742 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.18232 | + | 8.43612i | 0.182653 | + | 0.297334i | ||||
\(806\) | 0.150352 | + | 4.64767i | 0.00529592 | + | 0.163707i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 22.0252 | − | 15.7444i | 0.774844 | − | 0.553888i | ||||
\(809\) | 7.65189 | − | 13.2535i | 0.269026 | − | 0.465967i | −0.699584 | − | 0.714550i | \(-0.746632\pi\) |
0.968611 | + | 0.248583i | \(0.0799648\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.91368 | −0.277887 | −0.138943 | − | 0.990300i | \(-0.544371\pi\) | ||||
−0.138943 | + | 0.990300i | \(0.544371\pi\) | |||||||
\(812\) | −48.1565 | + | 4.44040i | −1.68996 | + | 0.155827i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.42088 | − | 1.50410i | 0.0848517 | − | 0.0527188i | ||||
\(815\) | −4.15331 | −0.145484 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 51.6836i | 1.80818i | ||||||||
\(818\) | 28.7470 | + | 15.3799i | 1.00511 | + | 0.537744i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.794018 | − | 1.19032i | −0.0277283 | − | 0.0415678i | ||||
\(821\) | −25.0583 | −0.874541 | −0.437271 | − | 0.899330i | \(-0.644055\pi\) | ||||
−0.437271 | + | 0.899330i | \(0.644055\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.5185i | 1.20324i | 0.798783 | + | 0.601619i | \(0.205478\pi\) | ||||
−0.798783 | + | 0.601619i | \(0.794522\pi\) | |||||||
\(824\) | 12.5235 | − | 27.5549i | 0.436275 | − | 0.959920i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.649423 | − | 1.29774i | 0.0225963 | − | 0.0451540i | ||||
\(827\) | 22.6614i | 0.788016i | 0.919107 | + | 0.394008i | \(0.128912\pi\) | ||||
−0.919107 | + | 0.394008i | \(0.871088\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.67197 | + | 4.42941i | 0.266458 | + | 0.153840i | 0.627277 | − | 0.778796i | \(-0.284169\pi\) |
−0.360819 | + | 0.932636i | \(0.617503\pi\) | |||||||
\(830\) | 0.229752 | + | 7.10207i | 0.00797480 | + | 0.246517i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −23.3509 | + | 20.3827i | −0.809547 | + | 0.706641i | ||||
\(833\) | 23.0918 | + | 11.7025i | 0.800084 | + | 0.405468i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.08127i | 0.210451i | ||||||||
\(836\) | 0.306158 | + | 4.72701i | 0.0105887 | + | 0.163487i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 21.5103 | − | 0.695858i | 0.743061 | − | 0.0240380i | ||||
\(839\) | 15.4881 | − | 26.8261i | 0.534707 | − | 0.926140i | −0.464470 | − | 0.885589i | \(-0.653755\pi\) |
0.999177 | − | 0.0405511i | \(-0.0129114\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.2637 | − | 47.2222i | −0.940129 | − | 1.62835i | ||||
\(842\) | −5.19187 | − | 8.35640i | −0.178924 | − | 0.287981i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 24.4534 | + | 12.0826i | 0.841722 | + | 0.415900i | ||||
\(845\) | 1.26253 | − | 0.728922i | 0.0434324 | − | 0.0250757i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.4359 | − | 24.8104i | 0.461664 | − | 0.852494i | ||||
\(848\) | 13.1685 | + | 17.2165i | 0.452208 | + | 0.591218i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 20.6350 | + | 11.0399i | 0.707775 | + | 0.378665i | ||||
\(851\) | 17.9545i | 0.615471i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.55084 | − | 4.35948i | −0.258536 | − | 0.149266i | 0.365131 | − | 0.930956i | \(-0.381024\pi\) |
−0.623666 | + | 0.781691i | \(0.714358\pi\) | |||||||
\(854\) | 2.98269 | + | 1.49262i | 0.102065 | + | 0.0510764i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.65569 | − | 2.61322i | 0.124949 | − | 0.0893181i | ||||
\(857\) | −39.9949 | + | 23.0911i | −1.36620 | + | 0.788776i | −0.990440 | − | 0.137941i | \(-0.955952\pi\) |
−0.375760 | + | 0.926717i | \(0.622618\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.4027 | + | 26.6783i | −0.525534 | + | 0.910252i | 0.474024 | + | 0.880512i | \(0.342801\pi\) |
−0.999558 | + | 0.0297395i | \(0.990532\pi\) | |||||||
\(860\) | −8.12066 | + | 16.4350i | −0.276912 | + | 0.560430i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 37.8987 | − | 23.5466i | 1.29083 | − | 0.802001i | ||||
\(863\) | −12.2843 | + | 7.09233i | −0.418161 | + | 0.241426i | −0.694290 | − | 0.719695i | \(-0.744282\pi\) |
0.276129 | + | 0.961121i | \(0.410948\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.47619 | + | 11.2171i | −0.220197 | + | 0.381392i | ||||
\(866\) | 11.3878 | + | 6.09255i | 0.386973 | + | 0.207033i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.59298 | − | 3.66651i | −0.0880114 | − | 0.124449i | ||||
\(869\) | 0.985065 | + | 1.70618i | 0.0334160 | + | 0.0578783i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.11903 | − | 10.5985i | −0.207335 | − | 0.359115i | ||||
\(872\) | −10.2610 | + | 22.5768i | −0.347480 | + | 0.764547i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −26.3118 | − | 14.0770i | −0.890010 | − | 0.476162i | ||||
\(875\) | 0.495449 | + | 18.1636i | 0.0167492 | + | 0.614043i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.4251 | − | 30.1812i | 0.588405 | − | 1.01915i | −0.406037 | − | 0.913857i | \(-0.633089\pi\) |
0.994442 | − | 0.105290i | \(-0.0335772\pi\) | |||||||
\(878\) | 14.7765 | − | 27.6192i | 0.498683 | − | 0.932103i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.645364 | + | 1.55126i | −0.0217552 | + | 0.0522931i | ||||
\(881\) | 23.0498i | 0.776567i | 0.921540 | + | 0.388283i | \(0.126932\pi\) | ||||
−0.921540 | + | 0.388283i | \(0.873068\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1.28738i | − | 0.0433239i | −0.999765 | − | 0.0216620i | \(-0.993104\pi\) | ||
0.999765 | − | 0.0216620i | \(-0.00689576\pi\) | |||||||
\(884\) | 15.9027 | + | 23.8400i | 0.534867 | + | 0.801825i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.5719 | − | 8.33107i | −0.523147 | − | 0.279888i | ||||
\(887\) | 2.51116 | − | 4.34946i | 0.0843165 | − | 0.146040i | −0.820783 | − | 0.571240i | \(-0.806463\pi\) |
0.905100 | + | 0.425199i | \(0.139796\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.664231 | − | 24.3513i | −0.0222776 | − | 0.816718i | ||||
\(890\) | −1.32709 | + | 2.48050i | −0.0444840 | + | 0.0831465i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −33.4339 | + | 2.16544i | −1.11945 | + | 0.0725043i | ||||
\(893\) | 23.6665 | + | 40.9916i | 0.791969 | + | 1.37173i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.11347 | + | 15.7850i | 0.304630 | + | 0.527634i | ||||
\(896\) | 7.98292 | − | 28.8491i | 0.266691 | − | 0.963782i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15.5189 | − | 29.0069i | 0.517874 | − | 0.967974i | ||||
\(899\) | 3.87815 | − | 6.71714i | 0.129343 | − | 0.224029i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.3554 | − | 10.0201i | 0.578191 | − | 0.333819i | ||||
\(902\) | 0.426851 | + | 0.687023i | 0.0142126 | + | 0.0228754i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10.8898 | − | 15.2340i | −0.362190 | − | 0.506674i | ||||
\(905\) | 7.75114 | − | 13.4254i | 0.257657 | − | 0.446274i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.9555 | − | 13.8307i | 0.795430 | − | 0.459242i | −0.0464409 | − | 0.998921i | \(-0.514788\pi\) |
0.841871 | + | 0.539680i | \(0.181455\pi\) | |||||||
\(908\) | 19.4629 | − | 39.3902i | 0.645900 | − | 1.30721i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.70262 | + | 9.39719i | −0.155890 | + | 0.311514i | ||||
\(911\) | 9.94522 | + | 5.74187i | 0.329500 | + | 0.190237i | 0.655619 | − | 0.755092i | \(-0.272408\pi\) |
−0.326119 | + | 0.945329i | \(0.605741\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 4.01675i | − | 0.132935i | ||||||
\(914\) | 3.54900 | − | 6.63354i | 0.117390 | − | 0.219418i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.490544 | − | 7.57390i | −0.0162080 | − | 0.250249i | ||||
\(917\) | 20.3333 | − | 37.5468i | 0.671464 | − | 1.23991i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23.5746 | + | 13.6108i | −0.777656 | + | 0.448980i | −0.835599 | − | 0.549340i | \(-0.814879\pi\) |
0.0579432 | + | 0.998320i | \(0.481546\pi\) | |||||||
\(920\) | −6.15517 | − | 8.61058i | −0.202930 | − | 0.283882i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 10.9327 | − | 6.79254i | 0.360050 | − | 0.223701i | ||||
\(923\) | −14.6551 | − | 25.3835i | −0.482380 | − | 0.835507i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.78093 | + | 13.4770i | −0.255835 | + | 0.443120i | ||||
\(926\) | −0.0259009 | − | 0.800646i | −0.000851156 | − | 0.0263109i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 51.0255 | − | 8.32316i | 1.67499 | − | 0.273221i | ||||
\(929\) | − | 28.0193i | − | 0.919284i | −0.888104 | − | 0.459642i | \(-0.847978\pi\) | ||
0.888104 | − | 0.459642i | \(-0.152022\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.6349 | − | 23.9610i | −0.512412 | − | 0.785291i | ||||
\(932\) | 18.4261 | − | 37.2918i | 0.603568 | − | 1.22153i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 13.4943 | − | 0.436540i | 0.441547 | − | 0.0142840i | ||||
\(935\) | 1.34529 | + | 0.776706i | 0.0439958 | + | 0.0254010i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 7.31723i | − | 0.239043i | −0.992832 | − | 0.119522i | \(-0.961864\pi\) | ||
0.992832 | − | 0.119522i | \(-0.0381361\pi\) | |||||||
\(938\) | 10.5691 | + | 5.28909i | 0.345094 | + | 0.172695i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.08509 | + | 16.7536i | 0.0353918 | + | 0.546442i | ||||
\(941\) | − | 17.3706i | − | 0.566266i | −0.959081 | − | 0.283133i | \(-0.908626\pi\) | ||
0.959081 | − | 0.283133i | \(-0.0913738\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.09532 | −0.165926 | ||||||||
\(944\) | −0.595892 | + | 1.43235i | −0.0193946 | + | 0.0466190i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.88842 | − | 9.13710i | 0.158936 | − | 0.297073i | ||||
\(947\) | 39.3196i | 1.27772i | 0.769324 | + | 0.638858i | \(0.220593\pi\) | ||||
−0.769324 | + | 0.638858i | \(0.779407\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 45.6126 | 1.48065 | ||||||||
\(950\) | −13.6496 | − | 21.9692i | −0.442851 | − | 0.712775i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −25.4980 | − | 10.7597i | −0.826396 | − | 0.348725i | ||||
\(953\) | 33.5157 | 1.08568 | 0.542840 | − | 0.839836i | \(-0.317349\pi\) | ||||
0.542840 | + | 0.839836i | \(0.317349\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.144618 | + | 0.250486i | −0.00467973 | + | 0.00810553i | ||||
\(956\) | 1.81010 | + | 0.894381i | 0.0585428 | + | 0.0289263i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 33.8152 | − | 1.09392i | 1.09252 | − | 0.0353430i | ||||
\(959\) | 3.18176 | + | 5.17947i | 0.102744 | + | 0.167254i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.2798 | −0.976766 | ||||||||
\(962\) | −16.1863 | + | 10.0566i | −0.521867 | + | 0.324239i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −46.6722 | − | 23.0610i | −1.50321 | − | 0.742746i | ||||
\(965\) | −10.1667 | − | 5.86972i | −0.327276 | − | 0.188953i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.2860 | − | 9.98006i | 0.555879 | − | 0.320937i | −0.195611 | − | 0.980682i | \(-0.562669\pi\) |
0.751490 | + | 0.659745i | \(0.229336\pi\) | |||||||
\(968\) | −12.4803 | + | 27.4599i | −0.401132 | + | 0.882594i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −11.0351 | + | 0.356987i | −0.354317 | + | 0.0114621i | ||||
\(971\) | −26.7791 | − | 46.3827i | −0.859381 | − | 1.48849i | −0.872520 | − | 0.488578i | \(-0.837516\pi\) |
0.0131389 | − | 0.999914i | \(-0.495818\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.43052 | + | 15.3516i | 0.302329 | + | 0.492150i | ||||
\(974\) | 18.0606 | − | 11.2211i | 0.578700 | − | 0.359549i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.29208 | − | 1.36959i | −0.105377 | − | 0.0438394i | ||||
\(977\) | −46.1501 | −1.47647 | −0.738236 | − | 0.674543i | \(-0.764341\pi\) | ||||
−0.738236 | + | 0.674543i | \(0.764341\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.795117 | − | 1.37718i | 0.0254121 | − | 0.0440150i | ||||
\(980\) | −1.20697 | − | 10.0760i | −0.0385552 | − | 0.321867i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.708950 | − | 21.9150i | −0.0226235 | − | 0.699336i | ||||
\(983\) | −14.9059 | − | 25.8179i | −0.475426 | − | 0.823462i | 0.524178 | − | 0.851609i | \(-0.324373\pi\) |
−0.999604 | + | 0.0281471i | \(0.991039\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.6966 | − | 8.48511i | −0.468274 | − | 0.270358i | ||||
\(986\) | −1.54552 | − | 47.7750i | −0.0492193 | − | 1.52147i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.04701 | − | 31.6054i | −0.0651240 | − | 1.00550i | ||||
\(989\) | 32.6402 | + | 56.5345i | 1.03790 | + | 1.79769i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.7638 | − | 20.0709i | −1.10431 | − | 0.637574i | −0.166960 | − | 0.985964i | \(-0.553395\pi\) |
−0.937350 | + | 0.348390i | \(0.886729\pi\) | |||||||
\(992\) | 3.03843 | + | 3.71695i | 0.0964702 | + | 0.118013i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 25.3132 | + | 12.6674i | 0.802886 | + | 0.401787i | ||||
\(995\) | −7.67527 | + | 4.43132i | −0.243323 | + | 0.140482i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.4866 | + | 22.7976i | −1.25055 | + | 0.722007i | −0.971219 | − | 0.238187i | \(-0.923447\pi\) |
−0.279333 | + | 0.960194i | \(0.590113\pi\) | |||||||
\(998\) | 0.521699 | − | 0.324134i | 0.0165141 | − | 0.0102603i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 756.2.bj.b.451.16 | 84 | ||
3.2 | odd | 2 | 252.2.bj.b.115.27 | yes | 84 | ||
4.3 | odd | 2 | inner | 756.2.bj.b.451.15 | 84 | ||
7.5 | odd | 6 | 756.2.n.b.19.42 | 84 | |||
9.4 | even | 3 | 756.2.n.b.199.13 | 84 | |||
9.5 | odd | 6 | 252.2.n.b.31.30 | yes | 84 | ||
12.11 | even | 2 | 252.2.bj.b.115.28 | yes | 84 | ||
21.5 | even | 6 | 252.2.n.b.187.1 | yes | 84 | ||
28.19 | even | 6 | 756.2.n.b.19.13 | 84 | |||
36.23 | even | 6 | 252.2.n.b.31.1 | ✓ | 84 | ||
36.31 | odd | 6 | 756.2.n.b.199.42 | 84 | |||
63.5 | even | 6 | 252.2.bj.b.103.27 | yes | 84 | ||
63.40 | odd | 6 | inner | 756.2.bj.b.523.16 | 84 | ||
84.47 | odd | 6 | 252.2.n.b.187.30 | yes | 84 | ||
252.103 | even | 6 | inner | 756.2.bj.b.523.15 | 84 | ||
252.131 | odd | 6 | 252.2.bj.b.103.28 | yes | 84 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.2.n.b.31.1 | ✓ | 84 | 36.23 | even | 6 | ||
252.2.n.b.31.30 | yes | 84 | 9.5 | odd | 6 | ||
252.2.n.b.187.1 | yes | 84 | 21.5 | even | 6 | ||
252.2.n.b.187.30 | yes | 84 | 84.47 | odd | 6 | ||
252.2.bj.b.103.27 | yes | 84 | 63.5 | even | 6 | ||
252.2.bj.b.103.28 | yes | 84 | 252.131 | odd | 6 | ||
252.2.bj.b.115.27 | yes | 84 | 3.2 | odd | 2 | ||
252.2.bj.b.115.28 | yes | 84 | 12.11 | even | 2 | ||
756.2.n.b.19.13 | 84 | 28.19 | even | 6 | |||
756.2.n.b.19.42 | 84 | 7.5 | odd | 6 | |||
756.2.n.b.199.13 | 84 | 9.4 | even | 3 | |||
756.2.n.b.199.42 | 84 | 36.31 | odd | 6 | |||
756.2.bj.b.451.15 | 84 | 4.3 | odd | 2 | inner | ||
756.2.bj.b.451.16 | 84 | 1.1 | even | 1 | trivial | ||
756.2.bj.b.523.15 | 84 | 252.103 | even | 6 | inner | ||
756.2.bj.b.523.16 | 84 | 63.40 | odd | 6 | inner |