Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [735,2,Mod(146,735)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(735, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("735.146");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 735 = 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 735.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.86900454856\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.856615824.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 146.6 | ||
Root | \(-1.07834i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 735.146 |
Dual form | 735.2.b.d.146.3 |
$q$-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 \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).
\(n\) | \(346\) | \(442\) | \(491\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.07834i | 0.762500i | 0.924472 | + | 0.381250i | \(0.124506\pi\) | ||||
−0.924472 | + | 0.381250i | \(0.875494\pi\) | |||||||
\(3\) | 0.812371 | + | 1.52972i | 0.469023 | + | 0.883186i | ||||
\(4\) | 0.837188 | 0.418594 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.64956 | + | 0.876010i | −0.673429 | + | 0.357630i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 3.05945i | 1.08168i | ||||||||
\(9\) | −1.68011 | + | 2.48541i | −0.560036 | + | 0.828469i | ||||
\(10\) | − | 1.07834i | − | 0.341000i | ||||||
\(11\) | 4.43975i | 1.33864i | 0.742976 | + | 0.669318i | \(0.233414\pi\) | ||||
−0.742976 | + | 0.669318i | \(0.766586\pi\) | |||||||
\(12\) | 0.680107 | + | 1.28067i | 0.196330 | + | 0.369696i | ||||
\(13\) | − | 0.955682i | − | 0.265059i | −0.991179 | − | 0.132529i | \(-0.957690\pi\) | ||
0.991179 | − | 0.132529i | \(-0.0423099\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.812371 | − | 1.52972i | −0.209753 | − | 0.394973i | ||||
\(16\) | −1.62474 | −0.406185 | ||||||||
\(17\) | 0.507522 | 0.123092 | 0.0615461 | − | 0.998104i | \(-0.480397\pi\) | ||||
0.0615461 | + | 0.998104i | \(0.480397\pi\) | |||||||
\(18\) | −2.68011 | − | 1.81172i | −0.631707 | − | 0.427027i | ||||
\(19\) | − | 5.09347i | − | 1.16852i | −0.811566 | − | 0.584261i | \(-0.801385\pi\) | ||
0.811566 | − | 0.584261i | \(-0.198615\pi\) | |||||||
\(20\) | −0.837188 | −0.187201 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.78755 | −1.02071 | ||||||||
\(23\) | − | 4.29713i | − | 0.896013i | −0.894030 | − | 0.448007i | \(-0.852134\pi\) | ||
0.894030 | − | 0.448007i | \(-0.147866\pi\) | |||||||
\(24\) | −4.68011 | + | 2.48541i | −0.955323 | + | 0.507331i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.03055 | 0.202107 | ||||||||
\(27\) | −5.16685 | − | 0.551027i | −0.994361 | − | 0.106045i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.89526i | 1.28042i | 0.768201 | + | 0.640209i | \(0.221152\pi\) | ||||
−0.768201 | + | 0.640209i | \(0.778848\pi\) | |||||||
\(30\) | 1.64956 | − | 0.876010i | 0.301167 | − | 0.159937i | ||||
\(31\) | 5.89355i | 1.05851i | 0.848462 | + | 0.529257i | \(0.177529\pi\) | ||||
−0.848462 | + | 0.529257i | \(0.822471\pi\) | |||||||
\(32\) | 4.36687i | 0.771961i | ||||||||
\(33\) | −6.79159 | + | 3.60673i | −1.18226 | + | 0.627851i | ||||
\(34\) | 0.547280i | 0.0938578i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.40656 | + | 2.08075i | −0.234427 | + | 0.346792i | ||||
\(37\) | 7.52707 | 1.23744 | 0.618721 | − | 0.785611i | \(-0.287651\pi\) | ||||
0.618721 | + | 0.785611i | \(0.287651\pi\) | |||||||
\(38\) | 5.49248 | 0.890998 | ||||||||
\(39\) | 1.46193 | − | 0.776369i | 0.234096 | − | 0.124318i | ||||
\(40\) | − | 3.05945i | − | 0.483741i | ||||||
\(41\) | −4.65529 | −0.727034 | −0.363517 | − | 0.931588i | \(-0.618424\pi\) | ||||
−0.363517 | + | 0.931588i | \(0.618424\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.492478 | −0.0751022 | −0.0375511 | − | 0.999295i | \(-0.511956\pi\) | ||||
−0.0375511 | + | 0.999295i | \(0.511956\pi\) | |||||||
\(44\) | 3.71691i | 0.560345i | ||||||||
\(45\) | 1.68011 | − | 2.48541i | 0.250456 | − | 0.370502i | ||||
\(46\) | 4.63376 | 0.683210 | ||||||||
\(47\) | −6.65933 | −0.971363 | −0.485682 | − | 0.874136i | \(-0.661429\pi\) | ||||
−0.485682 | + | 0.874136i | \(0.661429\pi\) | |||||||
\(48\) | −1.31989 | − | 2.48541i | −0.190510 | − | 0.358737i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.07834i | 0.152500i | ||||||||
\(51\) | 0.412296 | + | 0.776369i | 0.0577330 | + | 0.108713i | ||||
\(52\) | − | 0.800085i | − | 0.110952i | ||||||
\(53\) | − | 9.13231i | − | 1.25442i | −0.778850 | − | 0.627210i | \(-0.784197\pi\) | ||
0.778850 | − | 0.627210i | \(-0.215803\pi\) | |||||||
\(54\) | 0.594194 | − | 5.57161i | 0.0808595 | − | 0.758200i | ||||
\(55\) | − | 4.43975i | − | 0.598656i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.79159 | − | 4.13778i | 1.03202 | − | 0.548063i | ||||
\(58\) | −7.43542 | −0.976319 | ||||||||
\(59\) | 11.6288 | 1.51394 | 0.756969 | − | 0.653450i | \(-0.226679\pi\) | ||||
0.756969 | + | 0.653450i | \(0.226679\pi\) | |||||||
\(60\) | −0.680107 | − | 1.28067i | −0.0878014 | − | 0.165333i | ||||
\(61\) | − | 0.461313i | − | 0.0590651i | −0.999564 | − | 0.0295326i | \(-0.990598\pi\) | ||
0.999564 | − | 0.0295326i | \(-0.00940187\pi\) | |||||||
\(62\) | −6.35524 | −0.807116 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.95845 | −0.994806 | ||||||||
\(65\) | 0.955682i | 0.118538i | ||||||||
\(66\) | −3.88927 | − | 7.32363i | −0.478736 | − | 0.901477i | ||||
\(67\) | −3.70492 | −0.452628 | −0.226314 | − | 0.974054i | \(-0.572668\pi\) | ||||
−0.226314 | + | 0.974054i | \(0.572668\pi\) | |||||||
\(68\) | 0.424891 | 0.0515256 | ||||||||
\(69\) | 6.57342 | − | 3.49086i | 0.791346 | − | 0.420250i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.90386i | 0.938015i | 0.883194 | + | 0.469008i | \(0.155388\pi\) | ||||
−0.883194 | + | 0.469008i | \(0.844612\pi\) | |||||||
\(72\) | −7.60397 | − | 5.14020i | −0.896136 | − | 0.605778i | ||||
\(73\) | − | 6.31443i | − | 0.739048i | −0.929221 | − | 0.369524i | \(-0.879521\pi\) | ||
0.929221 | − | 0.369524i | \(-0.120479\pi\) | |||||||
\(74\) | 8.11672i | 0.943550i | ||||||||
\(75\) | 0.812371 | + | 1.52972i | 0.0938045 | + | 0.176637i | ||||
\(76\) | − | 4.26419i | − | 0.489136i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.837188 | + | 1.57645i | 0.0947928 | + | 0.178498i | ||||
\(79\) | 14.7610 | 1.66075 | 0.830374 | − | 0.557207i | \(-0.188127\pi\) | ||||
0.830374 | + | 0.557207i | \(0.188127\pi\) | |||||||
\(80\) | 1.62474 | 0.181652 | ||||||||
\(81\) | −3.35448 | − | 8.35149i | −0.372720 | − | 0.927944i | ||||
\(82\) | − | 5.01998i | − | 0.554364i | ||||||
\(83\) | 10.7916 | 1.18453 | 0.592266 | − | 0.805743i | \(-0.298234\pi\) | ||||
0.592266 | + | 0.805743i | \(0.298234\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.507522 | −0.0550485 | ||||||||
\(86\) | − | 0.531057i | − | 0.0572654i | ||||||
\(87\) | −10.5478 | + | 5.60151i | −1.13085 | + | 0.600545i | ||||
\(88\) | −13.5832 | −1.44797 | ||||||||
\(89\) | 7.15426 | 0.758350 | 0.379175 | − | 0.925325i | \(-0.376208\pi\) | ||||
0.379175 | + | 0.925325i | \(0.376208\pi\) | |||||||
\(90\) | 2.68011 | + | 1.81172i | 0.282508 | + | 0.190972i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 3.59750i | − | 0.375066i | ||||||
\(93\) | −9.01550 | + | 4.78775i | −0.934864 | + | 0.496467i | ||||
\(94\) | − | 7.18101i | − | 0.740664i | ||||||
\(95\) | 5.09347i | 0.522579i | ||||||||
\(96\) | −6.68011 | + | 3.54752i | −0.681786 | + | 0.362067i | ||||
\(97\) | − | 6.91148i | − | 0.701755i | −0.936421 | − | 0.350877i | \(-0.885883\pi\) | ||
0.936421 | − | 0.350877i | \(-0.114117\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −11.0346 | − | 7.45926i | −1.10902 | − | 0.749684i | ||||
\(100\) | 0.837188 | 0.0837188 | ||||||||
\(101\) | −2.39076 | −0.237890 | −0.118945 | − | 0.992901i | \(-0.537951\pi\) | ||||
−0.118945 | + | 0.992901i | \(0.537951\pi\) | |||||||
\(102\) | −0.837188 | + | 0.444595i | −0.0828939 | + | 0.0440214i | ||||
\(103\) | 14.9622i | 1.47427i | 0.675745 | + | 0.737135i | \(0.263822\pi\) | ||||
−0.675745 | + | 0.737135i | \(0.736178\pi\) | |||||||
\(104\) | 2.92386 | 0.286708 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.84772 | 0.956495 | ||||||||
\(107\) | − | 13.5614i | − | 1.31103i | −0.755181 | − | 0.655517i | \(-0.772451\pi\) | ||
0.755181 | − | 0.655517i | \(-0.227549\pi\) | |||||||
\(108\) | −4.32562 | − | 0.461313i | −0.416233 | − | 0.0443899i | ||||
\(109\) | 16.1213 | 1.54414 | 0.772068 | − | 0.635540i | \(-0.219222\pi\) | ||||
0.772068 | + | 0.635540i | \(0.219222\pi\) | |||||||
\(110\) | 4.78755 | 0.456475 | ||||||||
\(111\) | 6.11477 | + | 11.5143i | 0.580388 | + | 1.09289i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 5.05678i | − | 0.475702i | −0.971302 | − | 0.237851i | \(-0.923557\pi\) | ||
0.971302 | − | 0.237851i | \(-0.0764429\pi\) | |||||||
\(114\) | 4.46193 | + | 8.40197i | 0.417898 | + | 0.786917i | ||||
\(115\) | 4.29713i | 0.400709i | ||||||||
\(116\) | 5.77263i | 0.535975i | ||||||||
\(117\) | 2.37526 | + | 1.60565i | 0.219593 | + | 0.148442i | ||||
\(118\) | 12.5398i | 1.15438i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 4.68011 | − | 2.48541i | 0.427233 | − | 0.226885i | ||||
\(121\) | −8.71141 | −0.791947 | ||||||||
\(122\) | 0.497451 | 0.0450371 | ||||||||
\(123\) | −3.78182 | − | 7.12131i | −0.340995 | − | 0.642107i | ||||
\(124\) | 4.93401i | 0.443087i | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.05009 | 0.714330 | 0.357165 | − | 0.934041i | \(-0.383743\pi\) | ||||
0.357165 | + | 0.934041i | \(0.383743\pi\) | |||||||
\(128\) | 0.151850i | 0.0134218i | ||||||||
\(129\) | −0.400075 | − | 0.753355i | −0.0352246 | − | 0.0663292i | ||||
\(130\) | −1.03055 | −0.0903851 | ||||||||
\(131\) | 2.09927 | 0.183414 | 0.0917069 | − | 0.995786i | \(-0.470768\pi\) | ||||
0.0917069 | + | 0.995786i | \(0.470768\pi\) | |||||||
\(132\) | −5.68584 | + | 3.01951i | −0.494889 | + | 0.262814i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 3.99516i | − | 0.345129i | ||||||
\(135\) | 5.16685 | + | 0.551027i | 0.444692 | + | 0.0474249i | ||||
\(136\) | 1.55274i | 0.133146i | ||||||||
\(137\) | − | 4.94709i | − | 0.422659i | −0.977415 | − | 0.211329i | \(-0.932221\pi\) | ||
0.977415 | − | 0.211329i | \(-0.0677793\pi\) | |||||||
\(138\) | 3.76433 | + | 7.08836i | 0.320441 | + | 0.603402i | ||||
\(139\) | 10.7217i | 0.909406i | 0.890643 | + | 0.454703i | \(0.150255\pi\) | ||||
−0.890643 | + | 0.454703i | \(0.849745\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.40985 | − | 10.1869i | −0.455591 | − | 0.857895i | ||||
\(142\) | −8.52303 | −0.715236 | ||||||||
\(143\) | 4.24299 | 0.354817 | ||||||||
\(144\) | 2.72974 | − | 4.03814i | 0.227478 | − | 0.336512i | ||||
\(145\) | − | 6.89526i | − | 0.572620i | ||||||
\(146\) | 6.80909 | 0.563524 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.30157 | 0.517986 | ||||||||
\(149\) | 5.26356i | 0.431207i | 0.976481 | + | 0.215604i | \(0.0691719\pi\) | ||||
−0.976481 | + | 0.215604i | \(0.930828\pi\) | |||||||
\(150\) | −1.64956 | + | 0.876010i | −0.134686 | + | 0.0715259i | ||||
\(151\) | −7.00901 | −0.570385 | −0.285193 | − | 0.958470i | \(-0.592058\pi\) | ||||
−0.285193 | + | 0.958470i | \(0.592058\pi\) | |||||||
\(152\) | 15.5832 | 1.26396 | ||||||||
\(153\) | −0.852692 | + | 1.26140i | −0.0689360 | + | 0.101978i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 5.89355i | − | 0.473381i | ||||||
\(156\) | 1.22391 | − | 0.649966i | 0.0979912 | − | 0.0520389i | ||||
\(157\) | 2.90010i | 0.231453i | 0.993281 | + | 0.115727i | \(0.0369197\pi\) | ||||
−0.993281 | + | 0.115727i | \(0.963080\pi\) | |||||||
\(158\) | 15.9174i | 1.26632i | ||||||||
\(159\) | 13.9699 | − | 7.41883i | 1.10789 | − | 0.588351i | ||||
\(160\) | − | 4.36687i | − | 0.345232i | ||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 9.00573 | − | 3.61726i | 0.707557 | − | 0.284199i | ||||
\(163\) | −12.7586 | −0.999330 | −0.499665 | − | 0.866219i | \(-0.666544\pi\) | ||||
−0.499665 | + | 0.866219i | \(0.666544\pi\) | |||||||
\(164\) | −3.89735 | −0.304332 | ||||||||
\(165\) | 6.79159 | − | 3.60673i | 0.528725 | − | 0.280783i | ||||
\(166\) | 11.6370i | 0.903205i | ||||||||
\(167\) | 15.7766 | 1.22083 | 0.610413 | − | 0.792083i | \(-0.291003\pi\) | ||||
0.610413 | + | 0.792083i | \(0.291003\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0867 | 0.929744 | ||||||||
\(170\) | − | 0.547280i | − | 0.0419745i | ||||||
\(171\) | 12.6593 | + | 8.55757i | 0.968083 | + | 0.654414i | ||||
\(172\) | −0.412296 | −0.0314373 | ||||||||
\(173\) | −10.1733 | −0.773465 | −0.386732 | − | 0.922192i | \(-0.626396\pi\) | ||||
−0.386732 | + | 0.922192i | \(0.626396\pi\) | |||||||
\(174\) | −6.04032 | − | 11.3741i | −0.457916 | − | 0.862271i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 7.21345i | − | 0.543735i | ||||||
\(177\) | 9.44689 | + | 17.7888i | 0.710071 | + | 1.33709i | ||||
\(178\) | 7.71471i | 0.578242i | ||||||||
\(179\) | − | 5.26215i | − | 0.393312i | −0.980473 | − | 0.196656i | \(-0.936992\pi\) | ||
0.980473 | − | 0.196656i | \(-0.0630081\pi\) | |||||||
\(180\) | 1.40656 | − | 2.08075i | 0.104839 | − | 0.155090i | ||||
\(181\) | 9.71314i | 0.721972i | 0.932571 | + | 0.360986i | \(0.117560\pi\) | ||||
−0.932571 | + | 0.360986i | \(0.882440\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.705682 | − | 0.374757i | 0.0521655 | − | 0.0277029i | ||||
\(184\) | 13.1468 | 0.969198 | ||||||||
\(185\) | −7.52707 | −0.553401 | ||||||||
\(186\) | −5.16281 | − | 9.72176i | −0.378556 | − | 0.712834i | ||||
\(187\) | 2.25327i | 0.164776i | ||||||||
\(188\) | −5.57511 | −0.406607 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.49248 | −0.398466 | ||||||||
\(191\) | − | 9.59049i | − | 0.693943i | −0.937876 | − | 0.346972i | \(-0.887210\pi\) | ||
0.937876 | − | 0.346972i | \(-0.112790\pi\) | |||||||
\(192\) | −6.46521 | − | 12.1742i | −0.466586 | − | 0.878599i | ||||
\(193\) | 8.35166 | 0.601166 | 0.300583 | − | 0.953756i | \(-0.402819\pi\) | ||||
0.300583 | + | 0.953756i | \(0.402819\pi\) | |||||||
\(194\) | 7.45292 | 0.535088 | ||||||||
\(195\) | −1.46193 | + | 0.776369i | −0.104691 | + | 0.0555969i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.77574i | 0.126516i | 0.997997 | + | 0.0632580i | \(0.0201491\pi\) | ||||
−0.997997 | + | 0.0632580i | \(0.979851\pi\) | |||||||
\(198\) | 8.04360 | − | 11.8990i | 0.571634 | − | 0.845626i | ||||
\(199\) | − | 3.75858i | − | 0.266438i | −0.991087 | − | 0.133219i | \(-0.957469\pi\) | ||
0.991087 | − | 0.133219i | \(-0.0425314\pi\) | |||||||
\(200\) | 3.05945i | 0.216336i | ||||||||
\(201\) | −3.00977 | − | 5.66751i | −0.212293 | − | 0.399755i | ||||
\(202\) | − | 2.57805i | − | 0.181391i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.345169 | + | 0.649966i | 0.0241667 | + | 0.0455067i | ||||
\(205\) | 4.65529 | 0.325140 | ||||||||
\(206\) | −16.1343 | −1.12413 | ||||||||
\(207\) | 10.6801 | + | 7.21963i | 0.742319 | + | 0.501799i | ||||
\(208\) | 1.55274i | 0.107663i | ||||||||
\(209\) | 22.6137 | 1.56422 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.12126 | −0.627933 | −0.313967 | − | 0.949434i | \(-0.601658\pi\) | ||||
−0.313967 | + | 0.949434i | \(0.601658\pi\) | |||||||
\(212\) | − | 7.64546i | − | 0.525092i | ||||||
\(213\) | −12.0907 | + | 6.42086i | −0.828442 | + | 0.439950i | ||||
\(214\) | 14.6238 | 0.999663 | ||||||||
\(215\) | 0.492478 | 0.0335867 | ||||||||
\(216\) | 1.68584 | − | 15.8077i | 0.114707 | − | 1.07558i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 17.3842i | 1.17740i | ||||||||
\(219\) | 9.65933 | − | 5.12966i | 0.652717 | − | 0.346630i | ||||
\(220\) | − | 3.71691i | − | 0.250594i | ||||||
\(221\) | − | 0.485030i | − | 0.0326266i | ||||||
\(222\) | −12.4163 | + | 6.59379i | −0.833330 | + | 0.442546i | ||||
\(223\) | 11.7397i | 0.786146i | 0.919507 | + | 0.393073i | \(0.128588\pi\) | ||||
−0.919507 | + | 0.393073i | \(0.871412\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.68011 | + | 2.48541i | −0.112007 | + | 0.165694i | ||||
\(226\) | 5.45292 | 0.362723 | ||||||||
\(227\) | 24.2210 | 1.60760 | 0.803802 | − | 0.594897i | \(-0.202807\pi\) | ||||
0.803802 | + | 0.594897i | \(0.202807\pi\) | |||||||
\(228\) | 6.52303 | − | 3.46410i | 0.431998 | − | 0.229416i | ||||
\(229\) | − | 21.7088i | − | 1.43456i | −0.696788 | − | 0.717278i | \(-0.745388\pi\) | ||
0.696788 | − | 0.717278i | \(-0.254612\pi\) | |||||||
\(230\) | −4.63376 | −0.305541 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −21.0957 | −1.38500 | ||||||||
\(233\) | − | 10.9962i | − | 0.720388i | −0.932877 | − | 0.360194i | \(-0.882711\pi\) | ||
0.932877 | − | 0.360194i | \(-0.117289\pi\) | |||||||
\(234\) | −1.73143 | + | 2.56133i | −0.113187 | + | 0.167439i | ||||
\(235\) | 6.65933 | 0.434407 | ||||||||
\(236\) | 9.73547 | 0.633725 | ||||||||
\(237\) | 11.9914 | + | 22.5803i | 0.778928 | + | 1.46675i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 9.02649i | − | 0.583875i | −0.956437 | − | 0.291938i | \(-0.905700\pi\) | ||
0.956437 | − | 0.291938i | \(-0.0942999\pi\) | |||||||
\(240\) | 1.31989 | + | 2.48541i | 0.0851987 | + | 0.160432i | ||||
\(241\) | − | 5.08099i | − | 0.327295i | −0.986519 | − | 0.163648i | \(-0.947674\pi\) | ||
0.986519 | − | 0.163648i | \(-0.0523260\pi\) | |||||||
\(242\) | − | 9.39385i | − | 0.603859i | ||||||
\(243\) | 10.0504 | − | 11.9159i | 0.644733 | − | 0.764408i | ||||
\(244\) | − | 0.386206i | − | 0.0247243i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7.67917 | − | 4.07808i | 0.489606 | − | 0.260009i | ||||
\(247\) | −4.86774 | −0.309727 | ||||||||
\(248\) | −18.0310 | −1.14497 | ||||||||
\(249\) | 8.76678 | + | 16.5082i | 0.555572 | + | 1.04616i | ||||
\(250\) | − | 1.07834i | − | 0.0682001i | ||||||
\(251\) | −18.6748 | −1.17875 | −0.589373 | − | 0.807861i | \(-0.700625\pi\) | ||||
−0.589373 | + | 0.807861i | \(0.700625\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.0782 | 1.19944 | ||||||||
\(254\) | 8.68072i | 0.544677i | ||||||||
\(255\) | −0.412296 | − | 0.776369i | −0.0258190 | − | 0.0486181i | ||||
\(256\) | −16.0806 | −1.00504 | ||||||||
\(257\) | −12.0826 | −0.753694 | −0.376847 | − | 0.926276i | \(-0.622992\pi\) | ||||
−0.376847 | + | 0.926276i | \(0.622992\pi\) | |||||||
\(258\) | 0.812371 | − | 0.431416i | 0.0505760 | − | 0.0268588i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.800085i | 0.0496192i | ||||||||
\(261\) | −17.1375 | − | 11.5848i | −1.06079 | − | 0.717080i | ||||
\(262\) | 2.26372i | 0.139853i | ||||||||
\(263\) | − | 12.8878i | − | 0.794693i | −0.917669 | − | 0.397346i | \(-0.869931\pi\) | ||
0.917669 | − | 0.397346i | \(-0.130069\pi\) | |||||||
\(264\) | −11.0346 | − | 20.7785i | −0.679132 | − | 1.27883i | ||||
\(265\) | 9.13231i | 0.560993i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.81191 | + | 10.9440i | 0.355683 | + | 0.669764i | ||||
\(268\) | −3.10172 | −0.189467 | ||||||||
\(269\) | −0.466444 | −0.0284396 | −0.0142198 | − | 0.999899i | \(-0.504526\pi\) | ||||
−0.0142198 | + | 0.999899i | \(0.504526\pi\) | |||||||
\(270\) | −0.594194 | + | 5.57161i | −0.0361615 | + | 0.339078i | ||||
\(271\) | 23.2907i | 1.41481i | 0.706809 | + | 0.707404i | \(0.250134\pi\) | ||||
−0.706809 | + | 0.707404i | \(0.749866\pi\) | |||||||
\(272\) | −0.824593 | −0.0499983 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.33464 | 0.322277 | ||||||||
\(275\) | 4.43975i | 0.267727i | ||||||||
\(276\) | 5.50318 | − | 2.92251i | 0.331253 | − | 0.175914i | ||||
\(277\) | −13.8909 | −0.834621 | −0.417310 | − | 0.908764i | \(-0.637027\pi\) | ||||
−0.417310 | + | 0.908764i | \(0.637027\pi\) | |||||||
\(278\) | −11.5617 | −0.693422 | ||||||||
\(279\) | −14.6479 | − | 9.90180i | −0.876945 | − | 0.592805i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.85483i | 0.408925i | 0.978874 | + | 0.204462i | \(0.0655446\pi\) | ||||
−0.978874 | + | 0.204462i | \(0.934455\pi\) | |||||||
\(282\) | 10.9850 | − | 5.83364i | 0.654145 | − | 0.347388i | ||||
\(283\) | 4.43650i | 0.263723i | 0.991268 | + | 0.131861i | \(0.0420954\pi\) | ||||
−0.991268 | + | 0.131861i | \(0.957905\pi\) | |||||||
\(284\) | 6.61701i | 0.392647i | ||||||||
\(285\) | −7.79159 | + | 4.13778i | −0.461534 | + | 0.245101i | ||||
\(286\) | 4.57538i | 0.270548i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −10.8534 | − | 7.33681i | −0.639546 | − | 0.432326i | ||||
\(289\) | −16.7424 | −0.984848 | ||||||||
\(290\) | 7.43542 | 0.436623 | ||||||||
\(291\) | 10.5727 | − | 5.61469i | 0.619780 | − | 0.329139i | ||||
\(292\) | − | 5.28636i | − | 0.309361i | ||||||
\(293\) | −30.0822 | −1.75742 | −0.878709 | − | 0.477357i | \(-0.841595\pi\) | ||||
−0.878709 | + | 0.477357i | \(0.841595\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.6288 | −0.677054 | ||||||||
\(296\) | 23.0287i | 1.33851i | ||||||||
\(297\) | 2.44643 | − | 22.9396i | 0.141956 | − | 1.33109i | ||||
\(298\) | −5.67589 | −0.328796 | ||||||||
\(299\) | −4.10669 | −0.237496 | ||||||||
\(300\) | 0.680107 | + | 1.28067i | 0.0392660 | + | 0.0739392i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 7.55808i | − | 0.434919i | ||||||
\(303\) | −1.94219 | − | 3.65720i | −0.111576 | − | 0.210101i | ||||
\(304\) | 8.27557i | 0.474636i | ||||||||
\(305\) | 0.461313i | 0.0264147i | ||||||||
\(306\) | −1.36021 | − | 0.919490i | −0.0777582 | − | 0.0525637i | ||||
\(307\) | − | 32.8300i | − | 1.87371i | −0.349722 | − | 0.936853i | \(-0.613724\pi\) | ||
0.349722 | − | 0.936853i | \(-0.386276\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −22.8880 | + | 12.1549i | −1.30206 | + | 0.691466i | ||||
\(310\) | 6.35524 | 0.360953 | ||||||||
\(311\) | 16.4615 | 0.933444 | 0.466722 | − | 0.884404i | \(-0.345435\pi\) | ||||
0.466722 | + | 0.884404i | \(0.345435\pi\) | |||||||
\(312\) | 2.37526 | + | 4.47270i | 0.134473 | + | 0.253217i | ||||
\(313\) | 4.60844i | 0.260484i | 0.991482 | + | 0.130242i | \(0.0415755\pi\) | ||||
−0.991482 | + | 0.130242i | \(0.958425\pi\) | |||||||
\(314\) | −3.12729 | −0.176483 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.3578 | 0.695179 | ||||||||
\(317\) | 29.4302i | 1.65296i | 0.562964 | + | 0.826481i | \(0.309661\pi\) | ||||
−0.562964 | + | 0.826481i | \(0.690339\pi\) | |||||||
\(318\) | 8.00000 | + | 15.0643i | 0.448618 | + | 0.844763i | ||||
\(319\) | −30.6133 | −1.71401 | ||||||||
\(320\) | 7.95845 | 0.444891 | ||||||||
\(321\) | 20.7452 | − | 11.0169i | 1.15789 | − | 0.614904i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 2.58505i | − | 0.143836i | ||||||
\(324\) | −2.80833 | − | 6.99177i | −0.156018 | − | 0.388431i | ||||
\(325\) | − | 0.955682i | − | 0.0530117i | ||||||
\(326\) | − | 13.7581i | − | 0.761989i | ||||||
\(327\) | 13.0964 | + | 24.6611i | 0.724235 | + | 1.36376i | ||||
\(328\) | − | 14.2426i | − | 0.786417i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 3.88927 | + | 7.32363i | 0.214097 | + | 0.403153i | ||||
\(331\) | 2.65575 | 0.145973 | 0.0729866 | − | 0.997333i | \(-0.476747\pi\) | ||||
0.0729866 | + | 0.997333i | \(0.476747\pi\) | |||||||
\(332\) | 9.03459 | 0.495837 | ||||||||
\(333\) | −12.6463 | + | 18.7078i | −0.693012 | + | 1.02518i | ||||
\(334\) | 17.0125i | 0.930880i | ||||||||
\(335\) | 3.70492 | 0.202422 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.4599 | −1.16900 | −0.584499 | − | 0.811395i | \(-0.698709\pi\) | ||||
−0.584499 | + | 0.811395i | \(0.698709\pi\) | |||||||
\(338\) | 13.0335i | 0.708930i | ||||||||
\(339\) | 7.73547 | − | 4.10798i | 0.420133 | − | 0.223115i | ||||
\(340\) | −0.424891 | −0.0230430 | ||||||||
\(341\) | −26.1659 | −1.41696 | ||||||||
\(342\) | −9.22795 | + | 13.6510i | −0.498990 | + | 0.738163i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 1.50671i | − | 0.0812363i | ||||||
\(345\) | −6.57342 | + | 3.49086i | −0.353901 | + | 0.187942i | ||||
\(346\) | − | 10.9703i | − | 0.589767i | ||||||
\(347\) | − | 18.1637i | − | 0.975077i | −0.873102 | − | 0.487538i | \(-0.837895\pi\) | ||
0.873102 | − | 0.487538i | \(-0.162105\pi\) | |||||||
\(348\) | −8.83052 | + | 4.68951i | −0.473366 | + | 0.251384i | ||||
\(349\) | − | 13.1543i | − | 0.704135i | −0.935975 | − | 0.352067i | \(-0.885479\pi\) | ||
0.935975 | − | 0.352067i | \(-0.114521\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.526607 | + | 4.93787i | −0.0281082 | + | 0.263564i | ||||
\(352\) | −19.3878 | −1.03338 | ||||||||
\(353\) | −10.2941 | −0.547902 | −0.273951 | − | 0.961744i | \(-0.588331\pi\) | ||||
−0.273951 | + | 0.961744i | \(0.588331\pi\) | |||||||
\(354\) | −19.1824 | + | 10.1869i | −1.01953 | + | 0.541429i | ||||
\(355\) | − | 7.90386i | − | 0.419493i | ||||||
\(356\) | 5.98946 | 0.317441 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.67438 | 0.299900 | ||||||||
\(359\) | − | 11.8002i | − | 0.622790i | −0.950281 | − | 0.311395i | \(-0.899204\pi\) | ||
0.950281 | − | 0.311395i | \(-0.100796\pi\) | |||||||
\(360\) | 7.60397 | + | 5.14020i | 0.400764 | + | 0.270912i | ||||
\(361\) | −6.94340 | −0.365442 | ||||||||
\(362\) | −10.4741 | −0.550504 | ||||||||
\(363\) | −7.07690 | − | 13.3261i | −0.371441 | − | 0.699436i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.31443i | 0.330512i | ||||||||
\(366\) | 0.404115 | + | 0.760963i | 0.0211234 | + | 0.0397762i | ||||
\(367\) | 15.9739i | 0.833833i | 0.908945 | + | 0.416916i | \(0.136889\pi\) | ||||
−0.908945 | + | 0.416916i | \(0.863111\pi\) | |||||||
\(368\) | 6.98172i | 0.363948i | ||||||||
\(369\) | 7.82139 | − | 11.5703i | 0.407165 | − | 0.602325i | ||||
\(370\) | − | 8.11672i | − | 0.421968i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −7.54767 | + | 4.00825i | −0.391328 | + | 0.207818i | ||||
\(373\) | 5.31669 | 0.275288 | 0.137644 | − | 0.990482i | \(-0.456047\pi\) | ||||
0.137644 | + | 0.990482i | \(0.456047\pi\) | |||||||
\(374\) | −2.42979 | −0.125641 | ||||||||
\(375\) | −0.812371 | − | 1.52972i | −0.0419507 | − | 0.0789946i | ||||
\(376\) | − | 20.3739i | − | 1.05070i | ||||||
\(377\) | 6.58968 | 0.339386 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.0427 | 1.23499 | 0.617494 | − | 0.786575i | \(-0.288148\pi\) | ||||
0.617494 | + | 0.786575i | \(0.288148\pi\) | |||||||
\(380\) | 4.26419i | 0.218748i | ||||||||
\(381\) | 6.53966 | + | 12.3144i | 0.335037 | + | 0.630887i | ||||
\(382\) | 10.3418 | 0.529132 | ||||||||
\(383\) | 18.8011 | 0.960690 | 0.480345 | − | 0.877080i | \(-0.340512\pi\) | ||||
0.480345 | + | 0.877080i | \(0.340512\pi\) | |||||||
\(384\) | −0.232289 | + | 0.123359i | −0.0118539 | + | 0.00629512i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.00591i | 0.458389i | ||||||||
\(387\) | 0.827415 | − | 1.22401i | 0.0420599 | − | 0.0622198i | ||||
\(388\) | − | 5.78621i | − | 0.293750i | ||||||
\(389\) | − | 12.2172i | − | 0.619437i | −0.950828 | − | 0.309718i | \(-0.899765\pi\) | ||
0.950828 | − | 0.309718i | \(-0.100235\pi\) | |||||||
\(390\) | −0.837188 | − | 1.57645i | −0.0423926 | − | 0.0798268i | ||||
\(391\) | − | 2.18089i | − | 0.110292i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.70538 | + | 3.21130i | 0.0860252 | + | 0.161988i | ||||
\(394\) | −1.91484 | −0.0964685 | ||||||||
\(395\) | −14.7610 | −0.742709 | ||||||||
\(396\) | −9.23802 | − | 6.24480i | −0.464228 | − | 0.313813i | ||||
\(397\) | − | 18.7651i | − | 0.941792i | −0.882189 | − | 0.470896i | \(-0.843931\pi\) | ||
0.882189 | − | 0.470896i | \(-0.156069\pi\) | |||||||
\(398\) | 4.05302 | 0.203159 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.62474 | −0.0812371 | ||||||||
\(401\) | − | 23.9973i | − | 1.19837i | −0.800611 | − | 0.599184i | \(-0.795492\pi\) | ||
0.800611 | − | 0.599184i | \(-0.204508\pi\) | |||||||
\(402\) | 6.11149 | − | 3.24555i | 0.304813 | − | 0.161873i | ||||
\(403\) | 5.63236 | 0.280568 | ||||||||
\(404\) | −2.00152 | −0.0995792 | ||||||||
\(405\) | 3.35448 | + | 8.35149i | 0.166686 | + | 0.414989i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 33.4183i | 1.65648i | ||||||||
\(408\) | −2.37526 | + | 1.26140i | −0.117593 | + | 0.0624485i | ||||
\(409\) | − | 17.0828i | − | 0.844690i | −0.906435 | − | 0.422345i | \(-0.861207\pi\) | ||
0.906435 | − | 0.422345i | \(-0.138793\pi\) | |||||||
\(410\) | 5.01998i | 0.247919i | ||||||||
\(411\) | 7.56769 | − | 4.01888i | 0.373286 | − | 0.198237i | ||||
\(412\) | 12.5262i | 0.617120i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −7.78521 | + | 11.5168i | −0.382622 | + | 0.566018i | ||||
\(415\) | −10.7916 | −0.529739 | ||||||||
\(416\) | 4.17334 | 0.204615 | ||||||||
\(417\) | −16.4013 | + | 8.71003i | −0.803175 | + | 0.426532i | ||||
\(418\) | 24.3852i | 1.19272i | ||||||||
\(419\) | −39.6524 | −1.93714 | −0.968572 | − | 0.248732i | \(-0.919986\pi\) | ||||
−0.968572 | + | 0.248732i | \(0.919986\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.1423 | −1.66399 | −0.831997 | − | 0.554779i | \(-0.812803\pi\) | ||||
−0.831997 | + | 0.554779i | \(0.812803\pi\) | |||||||
\(422\) | − | 9.83580i | − | 0.478799i | ||||||
\(423\) | 11.1884 | − | 16.5511i | 0.543998 | − | 0.804744i | ||||
\(424\) | 27.9398 | 1.35688 | ||||||||
\(425\) | 0.507522 | 0.0246184 | ||||||||
\(426\) | −6.92386 | − | 13.0379i | −0.335462 | − | 0.631687i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 11.3535i | − | 0.548790i | ||||||
\(429\) | 3.44689 | + | 6.49061i | 0.166417 | + | 0.313369i | ||||
\(430\) | 0.531057i | 0.0256099i | ||||||||
\(431\) | 25.7708i | 1.24134i | 0.784073 | + | 0.620668i | \(0.213139\pi\) | ||||
−0.784073 | + | 0.620668i | \(0.786861\pi\) | |||||||
\(432\) | 8.39480 | + | 0.895277i | 0.403895 | + | 0.0430740i | ||||
\(433\) | 11.9120i | 0.572454i | 0.958162 | + | 0.286227i | \(0.0924011\pi\) | ||||
−0.958162 | + | 0.286227i | \(0.907599\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.5478 | − | 5.60151i | 0.505730 | − | 0.268572i | ||||
\(436\) | 13.4965 | 0.646366 | ||||||||
\(437\) | −21.8873 | −1.04701 | ||||||||
\(438\) | 5.53151 | + | 10.4160i | 0.264306 | + | 0.497697i | ||||
\(439\) | 16.7732i | 0.800542i | 0.916397 | + | 0.400271i | \(0.131084\pi\) | ||||
−0.916397 | + | 0.400271i | \(0.868916\pi\) | |||||||
\(440\) | 13.5832 | 0.647553 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.523026 | 0.0248778 | ||||||||
\(443\) | − | 2.39590i | − | 0.113833i | −0.998379 | − | 0.0569163i | \(-0.981873\pi\) | ||
0.998379 | − | 0.0569163i | \(-0.0181268\pi\) | |||||||
\(444\) | 5.11921 | + | 9.63965i | 0.242947 | + | 0.457478i | ||||
\(445\) | −7.15426 | −0.339144 | ||||||||
\(446\) | −12.6593 | −0.599437 | ||||||||
\(447\) | −8.05178 | + | 4.27596i | −0.380836 | + | 0.202246i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 25.4692i | − | 1.20196i | −0.799262 | − | 0.600982i | \(-0.794776\pi\) | ||
0.799262 | − | 0.600982i | \(-0.205224\pi\) | |||||||
\(450\) | −2.68011 | − | 1.81172i | −0.126341 | − | 0.0854054i | ||||
\(451\) | − | 20.6683i | − | 0.973234i | ||||||
\(452\) | − | 4.23347i | − | 0.199126i | ||||||
\(453\) | −5.69392 | − | 10.7219i | −0.267524 | − | 0.503757i | ||||
\(454\) | 26.1184i | 1.22580i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 12.6593 | + | 23.8380i | 0.592827 | + | 1.11632i | ||||
\(457\) | −3.44191 | −0.161006 | −0.0805029 | − | 0.996754i | \(-0.525653\pi\) | ||||
−0.0805029 | + | 0.996754i | \(0.525653\pi\) | |||||||
\(458\) | 23.4094 | 1.09385 | ||||||||
\(459\) | −2.62229 | − | 0.279659i | −0.122398 | − | 0.0130533i | ||||
\(460\) | 3.59750i | 0.167734i | ||||||||
\(461\) | −13.5376 | −0.630509 | −0.315254 | − | 0.949007i | \(-0.602090\pi\) | ||||
−0.315254 | + | 0.949007i | \(0.602090\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.13770 | −0.238769 | −0.119385 | − | 0.992848i | \(-0.538092\pi\) | ||||
−0.119385 | + | 0.992848i | \(0.538092\pi\) | |||||||
\(464\) | − | 11.2030i | − | 0.520087i | ||||||
\(465\) | 9.01550 | − | 4.78775i | 0.418084 | − | 0.222027i | ||||
\(466\) | 11.8577 | 0.549296 | ||||||||
\(467\) | −9.21788 | −0.426553 | −0.213276 | − | 0.976992i | \(-0.568413\pi\) | ||||
−0.213276 | + | 0.976992i | \(0.568413\pi\) | |||||||
\(468\) | 1.98854 | + | 1.34423i | 0.0919201 | + | 0.0621370i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 7.18101i | 0.331235i | ||||||||
\(471\) | −4.43635 | + | 2.35596i | −0.204416 | + | 0.108557i | ||||
\(472\) | 35.5776i | 1.63759i | ||||||||
\(473\) | − | 2.18648i | − | 0.100534i | ||||||
\(474\) | −24.3492 | + | 12.9308i | −1.11840 | + | 0.593933i | ||||
\(475\) | − | 5.09347i | − | 0.233704i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 22.6975 | + | 15.3433i | 1.03925 | + | 0.702520i | ||||
\(478\) | 9.73361 | 0.445205 | ||||||||
\(479\) | −20.6373 | −0.942943 | −0.471472 | − | 0.881881i | \(-0.656277\pi\) | ||||
−0.471472 | + | 0.881881i | \(0.656277\pi\) | |||||||
\(480\) | 6.68011 | − | 3.54752i | 0.304904 | − | 0.161921i | ||||
\(481\) | − | 7.19348i | − | 0.327995i | ||||||
\(482\) | 5.47902 | 0.249563 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.29309 | −0.331504 | ||||||||
\(485\) | 6.91148i | 0.313834i | ||||||||
\(486\) | 12.8494 | + | 10.8377i | 0.582861 | + | 0.491609i | ||||
\(487\) | 2.47498 | 0.112152 | 0.0560761 | − | 0.998426i | \(-0.482141\pi\) | ||||
0.0560761 | + | 0.998426i | \(0.482141\pi\) | |||||||
\(488\) | 1.41136 | 0.0638894 | ||||||||
\(489\) | −10.3647 | − | 19.5171i | −0.468709 | − | 0.882595i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 21.2827i | − | 0.960476i | −0.877138 | − | 0.480238i | \(-0.840550\pi\) | ||
0.877138 | − | 0.480238i | \(-0.159450\pi\) | |||||||
\(492\) | −3.16609 | − | 5.96187i | −0.142739 | − | 0.268782i | ||||
\(493\) | 3.49950i | 0.157609i | ||||||||
\(494\) | − | 5.24906i | − | 0.236167i | ||||||
\(495\) | 11.0346 | + | 7.45926i | 0.495968 | + | 0.335269i | ||||
\(496\) | − | 9.57550i | − | 0.429953i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −17.8014 | + | 9.45355i | −0.797698 | + | 0.423624i | ||||
\(499\) | 32.7379 | 1.46555 | 0.732775 | − | 0.680471i | \(-0.238225\pi\) | ||||
0.732775 | + | 0.680471i | \(0.238225\pi\) | |||||||
\(500\) | −0.837188 | −0.0374402 | ||||||||
\(501\) | 12.8164 | + | 24.1338i | 0.572595 | + | 1.07822i | ||||
\(502\) | − | 20.1378i | − | 0.898793i | ||||||
\(503\) | 0.675693 | 0.0301277 | 0.0150638 | − | 0.999887i | \(-0.495205\pi\) | ||||
0.0150638 | + | 0.999887i | \(0.495205\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.39076 | 0.106388 | ||||||||
\(506\) | 20.5727i | 0.914570i | ||||||||
\(507\) | 9.81886 | + | 18.4893i | 0.436071 | + | 0.821137i | ||||
\(508\) | 6.73944 | 0.299014 | ||||||||
\(509\) | −33.1038 | −1.46730 | −0.733649 | − | 0.679528i | \(-0.762184\pi\) | ||||
−0.733649 | + | 0.679528i | \(0.762184\pi\) | |||||||
\(510\) | 0.837188 | − | 0.444595i | 0.0370713 | − | 0.0196870i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 17.0367i | − | 0.752921i | ||||||
\(513\) | −2.80664 | + | 26.3172i | −0.123916 | + | 1.16193i | ||||
\(514\) | − | 13.0292i | − | 0.574692i | ||||||
\(515\) | − | 14.9622i | − | 0.659314i | ||||||
\(516\) | −0.334938 | − | 0.630699i | −0.0147448 | − | 0.0277650i | ||||
\(517\) | − | 29.5658i | − | 1.30030i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.26453 | − | 15.5624i | −0.362773 | − | 0.683114i | ||||
\(520\) | −2.92386 | −0.128220 | ||||||||
\(521\) | −42.9449 | −1.88145 | −0.940726 | − | 0.339169i | \(-0.889854\pi\) | ||||
−0.940726 | + | 0.339169i | \(0.889854\pi\) | |||||||
\(522\) | 12.4923 | − | 18.4800i | 0.546773 | − | 0.808849i | ||||
\(523\) | − | 38.1919i | − | 1.67001i | −0.550239 | − | 0.835007i | \(-0.685463\pi\) | ||
0.550239 | − | 0.835007i | \(-0.314537\pi\) | |||||||
\(524\) | 1.75748 | 0.0767759 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13.8974 | 0.605953 | ||||||||
\(527\) | 2.99111i | 0.130295i | ||||||||
\(528\) | 11.0346 | − | 5.86000i | 0.480219 | − | 0.255024i | ||||
\(529\) | 4.53469 | 0.197160 | ||||||||
\(530\) | −9.84772 | −0.427758 | ||||||||
\(531\) | −19.5376 | + | 28.9022i | −0.847859 | + | 1.25425i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.44898i | 0.192707i | ||||||||
\(534\) | −11.8014 | + | 6.26720i | −0.510695 | + | 0.271208i | ||||
\(535\) | 13.5614i | 0.586312i | ||||||||
\(536\) | − | 11.3350i | − | 0.489598i | ||||||
\(537\) | 8.04963 | − | 4.27482i | 0.347367 | − | 0.184472i | ||||
\(538\) | − | 0.502984i | − | 0.0216852i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 4.32562 | + | 0.461313i | 0.186145 | + | 0.0198518i | ||||
\(541\) | −0.409847 | −0.0176207 | −0.00881035 | − | 0.999961i | \(-0.502804\pi\) | ||||
−0.00881035 | + | 0.999961i | \(0.502804\pi\) | |||||||
\(542\) | −25.1152 | −1.07879 | ||||||||
\(543\) | −14.8584 | + | 7.89068i | −0.637636 | + | 0.338621i | ||||
\(544\) | 2.21628i | 0.0950224i | ||||||||
\(545\) | −16.1213 | −0.690559 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.9605 | −0.468638 | −0.234319 | − | 0.972160i | \(-0.575286\pi\) | ||||
−0.234319 | + | 0.972160i | \(0.575286\pi\) | |||||||
\(548\) | − | 4.14165i | − | 0.176922i | ||||||
\(549\) | 1.14655 | + | 0.775055i | 0.0489336 | + | 0.0330786i | ||||
\(550\) | −4.78755 | −0.204142 | ||||||||
\(551\) | 35.1208 | 1.49620 | ||||||||
\(552\) | 10.6801 | + | 20.1110i | 0.454576 | + | 0.855982i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 14.9790i | − | 0.636398i | ||||||
\(555\) | −6.11477 | − | 11.5143i | −0.259558 | − | 0.488756i | ||||
\(556\) | 8.97611i | 0.380672i | ||||||||
\(557\) | 6.01934i | 0.255048i | 0.991835 | + | 0.127524i | \(0.0407030\pi\) | ||||
−0.991835 | + | 0.127524i | \(0.959297\pi\) | |||||||
\(558\) | 10.6775 | − | 15.7953i | 0.452014 | − | 0.668670i | ||||
\(559\) | 0.470652i | 0.0199065i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.44689 | + | 1.83049i | −0.145528 | + | 0.0772835i | ||||
\(562\) | −7.39182 | −0.311805 | ||||||||
\(563\) | −14.8693 | −0.626667 | −0.313334 | − | 0.949643i | \(-0.601446\pi\) | ||||
−0.313334 | + | 0.949643i | \(0.601446\pi\) | |||||||
\(564\) | −4.52906 | − | 8.52837i | −0.190708 | − | 0.359109i | ||||
\(565\) | 5.05678i | 0.212740i | ||||||||
\(566\) | −4.78405 | −0.201089 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −24.1814 | −1.01463 | ||||||||
\(569\) | − | 5.26405i | − | 0.220681i | −0.993894 | − | 0.110340i | \(-0.964806\pi\) | ||
0.993894 | − | 0.110340i | \(-0.0351941\pi\) | |||||||
\(570\) | −4.46193 | − | 8.40197i | −0.186890 | − | 0.351920i | ||||
\(571\) | 45.7550 | 1.91479 | 0.957394 | − | 0.288786i | \(-0.0932517\pi\) | ||||
0.957394 | + | 0.288786i | \(0.0932517\pi\) | |||||||
\(572\) | 3.55218 | 0.148524 | ||||||||
\(573\) | 14.6708 | − | 7.79103i | 0.612881 | − | 0.325475i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 4.29713i | − | 0.179203i | ||||||
\(576\) | 13.3710 | − | 19.7800i | 0.557127 | − | 0.824165i | ||||
\(577\) | − | 5.03122i | − | 0.209452i | −0.994501 | − | 0.104726i | \(-0.966603\pi\) | ||
0.994501 | − | 0.104726i | \(-0.0333966\pi\) | |||||||
\(578\) | − | 18.0540i | − | 0.750947i | ||||||
\(579\) | 6.78465 | + | 12.7757i | 0.281960 | + | 0.530941i | ||||
\(580\) | − | 5.77263i | − | 0.239695i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 6.05453 | + | 11.4009i | 0.250968 | + | 0.472582i | ||||
\(583\) | 40.5452 | 1.67921 | ||||||||
\(584\) | 19.3187 | 0.799412 | ||||||||
\(585\) | −2.37526 | − | 1.60565i | −0.0982048 | − | 0.0663854i | ||||
\(586\) | − | 32.4387i | − | 1.34003i | ||||||
\(587\) | 18.5075 | 0.763887 | 0.381944 | − | 0.924186i | \(-0.375255\pi\) | ||||
0.381944 | + | 0.924186i | \(0.375255\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 30.0186 | 1.23690 | ||||||||
\(590\) | − | 12.5398i | − | 0.516254i | ||||||
\(591\) | −2.71639 | + | 1.44256i | −0.111737 | + | 0.0593389i | ||||
\(592\) | −12.2295 | −0.502631 | ||||||||
\(593\) | −18.5385 | −0.761286 | −0.380643 | − | 0.924722i | \(-0.624297\pi\) | ||||
−0.380643 | + | 0.924722i | \(0.624297\pi\) | |||||||
\(594\) | 24.7366 | + | 2.63807i | 1.01495 | + | 0.108241i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.40658i | 0.180501i | ||||||||
\(597\) | 5.74958 | − | 3.05336i | 0.235315 | − | 0.124966i | ||||
\(598\) | − | 4.42840i | − | 0.181091i | ||||||
\(599\) | − | 0.578987i | − | 0.0236568i | −0.999930 | − | 0.0118284i | \(-0.996235\pi\) | ||
0.999930 | − | 0.0118284i | \(-0.00376518\pi\) | |||||||
\(600\) | −4.68011 | + | 2.48541i | −0.191065 | + | 0.101466i | ||||
\(601\) | 29.8618i | 1.21809i | 0.793137 | + | 0.609044i | \(0.208447\pi\) | ||||
−0.793137 | + | 0.609044i | \(0.791553\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.22467 | − | 9.20824i | 0.253488 | − | 0.374988i | ||||
\(604\) | −5.86786 | −0.238760 | ||||||||
\(605\) | 8.71141 | 0.354169 | ||||||||
\(606\) | 3.94370 | − | 2.09433i | 0.160202 | − | 0.0850764i | ||||
\(607\) | − | 25.1099i | − | 1.01918i | −0.860417 | − | 0.509591i | \(-0.829797\pi\) | ||
0.860417 | − | 0.509591i | \(-0.170203\pi\) | |||||||
\(608\) | 22.2425 | 0.902053 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.497451 | −0.0201412 | ||||||||
\(611\) | 6.36420i | 0.257468i | ||||||||
\(612\) | −0.713863 | + | 1.05603i | −0.0288562 | + | 0.0426874i | ||||
\(613\) | −1.45986 | −0.0589634 | −0.0294817 | − | 0.999565i | \(-0.509386\pi\) | ||||
−0.0294817 | + | 0.999565i | \(0.509386\pi\) | |||||||
\(614\) | 35.4018 | 1.42870 | ||||||||
\(615\) | 3.78182 | + | 7.12131i | 0.152498 | + | 0.287159i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 6.56208i | − | 0.264179i | −0.991238 | − | 0.132090i | \(-0.957831\pi\) | ||
0.991238 | − | 0.132090i | \(-0.0421687\pi\) | |||||||
\(618\) | −13.1070 | − | 24.6810i | −0.527243 | − | 0.992817i | ||||
\(619\) | 21.0639i | 0.846629i | 0.905983 | + | 0.423315i | \(0.139133\pi\) | ||||
−0.905983 | + | 0.423315i | \(0.860867\pi\) | |||||||
\(620\) | − | 4.93401i | − | 0.198155i | ||||||
\(621\) | −2.36784 | + | 22.2026i | −0.0950179 | + | 0.890961i | ||||
\(622\) | 17.7510i | 0.711751i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −2.37526 | + | 1.26140i | −0.0950864 | + | 0.0504964i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −4.96945 | −0.198619 | ||||||||
\(627\) | 18.3707 | + | 34.5928i | 0.733657 | + | 1.38150i | ||||
\(628\) | 2.42793i | 0.0968850i | ||||||||
\(629\) | 3.82015 | 0.152319 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.5069 | 0.696937 | 0.348468 | − | 0.937321i | \(-0.386702\pi\) | ||||
0.348468 | + | 0.937321i | \(0.386702\pi\) | |||||||
\(632\) | 45.1606i | 1.79639i | ||||||||
\(633\) | −7.40985 | − | 13.9530i | −0.294515 | − | 0.554582i | ||||
\(634\) | −31.7357 | −1.26038 | ||||||||
\(635\) | −8.05009 | −0.319458 | ||||||||
\(636\) | 11.6954 | − | 6.21095i | 0.463754 | − | 0.246280i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 33.0114i | − | 1.30694i | ||||||
\(639\) | −19.6443 | − | 13.2793i | −0.777116 | − | 0.525322i | ||||
\(640\) | − | 0.151850i | − | 0.00600240i | ||||||
\(641\) | 11.5348i | 0.455597i | 0.973708 | + | 0.227798i | \(0.0731527\pi\) | ||||
−0.973708 | + | 0.227798i | \(0.926847\pi\) | |||||||
\(642\) | 11.8800 | + | 22.3704i | 0.468865 | + | 0.882889i | ||||
\(643\) | − | 17.3489i | − | 0.684173i | −0.939668 | − | 0.342087i | \(-0.888866\pi\) | ||
0.939668 | − | 0.342087i | \(-0.111134\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.400075 | + | 0.753355i | 0.0157529 | + | 0.0296633i | ||||
\(646\) | 2.78755 | 0.109675 | ||||||||
\(647\) | −7.86774 | −0.309313 | −0.154656 | − | 0.987968i | \(-0.549427\pi\) | ||||
−0.154656 | + | 0.987968i | \(0.549427\pi\) | |||||||
\(648\) | 25.5509 | − | 10.2629i | 1.00374 | − | 0.403163i | ||||
\(649\) | 51.6289i | 2.02661i | ||||||||
\(650\) | 1.03055 | 0.0404214 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.6813 | −0.418314 | ||||||||
\(653\) | 2.00359i | 0.0784065i | 0.999231 | + | 0.0392033i | \(0.0124820\pi\) | ||||
−0.999231 | + | 0.0392033i | \(0.987518\pi\) | |||||||
\(654\) | −26.5930 | + | 14.1224i | −1.03987 | + | 0.552229i | ||||
\(655\) | −2.09927 | −0.0820251 | ||||||||
\(656\) | 7.56365 | 0.295311 | ||||||||
\(657\) | 15.6939 | + | 10.6089i | 0.612278 | + | 0.413893i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 44.8494i | 1.74709i | 0.486747 | + | 0.873543i | \(0.338183\pi\) | ||||
−0.486747 | + | 0.873543i | \(0.661817\pi\) | |||||||
\(660\) | 5.68584 | − | 3.01951i | 0.221321 | − | 0.117534i | ||||
\(661\) | 12.0555i | 0.468905i | 0.972128 | + | 0.234453i | \(0.0753298\pi\) | ||||
−0.972128 | + | 0.234453i | \(0.924670\pi\) | |||||||
\(662\) | 2.86380i | 0.111305i | ||||||||
\(663\) | 0.741962 | − | 0.394024i | 0.0288154 | − | 0.0153026i | ||||
\(664\) | 33.0163i | 1.28128i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −20.1733 | − | 13.6370i | −0.781701 | − | 0.528421i | ||||
\(667\) | 29.6298 | 1.14727 | ||||||||
\(668\) | 13.2079 | 0.511030 | ||||||||
\(669\) | −17.9584 | + | 9.53697i | −0.694314 | + | 0.368720i | ||||
\(670\) | 3.99516i | 0.154346i | ||||||||
\(671\) | 2.04812 | 0.0790667 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.5641 | 0.445763 | 0.222882 | − | 0.974845i | \(-0.428454\pi\) | ||||
0.222882 | + | 0.974845i | \(0.428454\pi\) | |||||||
\(674\) | − | 23.1411i | − | 0.891361i | ||||||
\(675\) | −5.16685 | − | 0.551027i | −0.198872 | − | 0.0212091i | ||||
\(676\) | 10.1188 | 0.389185 | ||||||||
\(677\) | 21.4934 | 0.826058 | 0.413029 | − | 0.910718i | \(-0.364471\pi\) | ||||
0.413029 | + | 0.910718i | \(0.364471\pi\) | |||||||
\(678\) | 4.42979 | + | 8.34145i | 0.170125 | + | 0.320352i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − | 1.55274i | − | 0.0595447i | ||||||
\(681\) | 19.6764 | + | 37.0514i | 0.754002 | + | 1.41981i | ||||
\(682\) | − | 28.2157i | − | 1.08044i | ||||||
\(683\) | − | 17.3367i | − | 0.663372i | −0.943390 | − | 0.331686i | \(-0.892383\pi\) | ||
0.943390 | − | 0.331686i | \(-0.107617\pi\) | |||||||
\(684\) | 10.5982 | + | 7.16429i | 0.405234 | + | 0.273933i | ||||
\(685\) | 4.94709i | 0.189019i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 33.2084 | − | 17.6356i | 1.26698 | − | 0.672839i | ||||
\(688\) | 0.800149 | 0.0305054 | ||||||||
\(689\) | −8.72759 | −0.332495 | ||||||||
\(690\) | −3.76433 | − | 7.08836i | −0.143306 | − | 0.269849i | ||||
\(691\) | 13.5390i | 0.515048i | 0.966272 | + | 0.257524i | \(0.0829067\pi\) | ||||
−0.966272 | + | 0.257524i | \(0.917093\pi\) | |||||||
\(692\) | −8.51700 | −0.323768 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 19.5866 | 0.743496 | ||||||||
\(695\) | − | 10.7217i | − | 0.406699i | ||||||
\(696\) | −17.1375 | − | 32.2706i | −0.649596 | − | 1.22321i | ||||
\(697\) | −2.36266 | −0.0894922 | ||||||||
\(698\) | 14.1848 | 0.536903 | ||||||||
\(699\) | 16.8212 | − | 8.93303i | 0.636237 | − | 0.337878i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 41.8503i | − | 1.58066i | −0.612679 | − | 0.790332i | \(-0.709908\pi\) | ||
0.612679 | − | 0.790332i | \(-0.290092\pi\) | |||||||
\(702\) | −5.32469 | − | 0.567860i | −0.200968 | − | 0.0214325i | ||||
\(703\) | − | 38.3389i | − | 1.44598i | ||||||
\(704\) | − | 35.3335i | − | 1.33168i | ||||||
\(705\) | 5.40985 | + | 10.1869i | 0.203747 | + | 0.383662i | ||||
\(706\) | − | 11.1006i | − | 0.417775i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 7.90881 | + | 14.8926i | 0.297231 | + | 0.559697i | ||||
\(709\) | −45.4794 | −1.70802 | −0.854008 | − | 0.520261i | \(-0.825835\pi\) | ||||
−0.854008 | + | 0.520261i | \(0.825835\pi\) | |||||||
\(710\) | 8.52303 | 0.319863 | ||||||||
\(711\) | −24.8001 | + | 36.6872i | −0.930078 | + | 1.37588i | ||||
\(712\) | 21.8881i | 0.820290i | ||||||||
\(713\) | 25.3253 | 0.948442 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.24299 | −0.158679 | ||||||||
\(716\) | − | 4.40541i | − | 0.164638i | ||||||
\(717\) | 13.8080 | − | 7.33286i | 0.515670 | − | 0.273851i | ||||
\(718\) | 12.7246 | 0.474878 | ||||||||
\(719\) | 0.228621 | 0.00852614 | 0.00426307 | − | 0.999991i | \(-0.498643\pi\) | ||||
0.00426307 | + | 0.999991i | \(0.498643\pi\) | |||||||
\(720\) | −2.72974 | + | 4.03814i | −0.101731 | + | 0.150493i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 7.48733i | − | 0.278650i | ||||||
\(723\) | 7.77251 | − | 4.12765i | 0.289063 | − | 0.153509i | ||||
\(724\) | 8.13172i | 0.302213i | ||||||||
\(725\) | 6.89526i | 0.256084i | ||||||||
\(726\) | 14.3700 | − | 7.63129i | 0.533320 | − | 0.283224i | ||||
\(727\) | − | 19.2284i | − | 0.713140i | −0.934269 | − | 0.356570i | \(-0.883946\pi\) | ||
0.934269 | − | 0.356570i | \(-0.116054\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.3927 | + | 5.69415i | 0.977509 | + | 0.210895i | ||||
\(730\) | −6.80909 | −0.252016 | ||||||||
\(731\) | −0.249943 | −0.00924449 | ||||||||
\(732\) | 0.590788 | − | 0.313742i | 0.0218361 | − | 0.0115962i | ||||
\(733\) | 8.25651i | 0.304961i | 0.988306 | + | 0.152481i | \(0.0487261\pi\) | ||||
−0.988306 | + | 0.152481i | \(0.951274\pi\) | |||||||
\(734\) | −17.2253 | −0.635797 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 18.7650 | 0.691688 | ||||||||
\(737\) | − | 16.4489i | − | 0.605905i | ||||||
\(738\) | 12.4767 | + | 8.43410i | 0.459273 | + | 0.310463i | ||||
\(739\) | −10.3433 | −0.380485 | −0.190243 | − | 0.981737i | \(-0.560927\pi\) | ||||
−0.190243 | + | 0.981737i | \(0.560927\pi\) | |||||||
\(740\) | −6.30157 | −0.231650 | ||||||||
\(741\) | −3.95441 | − | 7.44629i | −0.145269 | − | 0.273546i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 37.7580i | − | 1.38521i | −0.721318 | − | 0.692604i | \(-0.756463\pi\) | ||
0.721318 | − | 0.692604i | \(-0.243537\pi\) | |||||||
\(744\) | −14.6479 | − | 27.5825i | −0.537017 | − | 1.01122i | ||||
\(745\) | − | 5.26356i | − | 0.192842i | ||||||
\(746\) | 5.73318i | 0.209907i | ||||||||
\(747\) | −18.1310 | + | 26.8215i | −0.663380 | + | 0.981347i | ||||
\(748\) | 1.88641i | 0.0689741i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.64956 | − | 0.876010i | 0.0602334 | − | 0.0319874i | ||||
\(751\) | −42.8883 | −1.56502 | −0.782509 | − | 0.622640i | \(-0.786060\pi\) | ||||
−0.782509 | + | 0.622640i | \(0.786060\pi\) | |||||||
\(752\) | 10.8197 | 0.394554 | ||||||||
\(753\) | −15.1709 | − | 28.5673i | −0.552858 | − | 1.04105i | ||||
\(754\) | 7.10590i | 0.258782i | ||||||||
\(755\) | 7.00901 | 0.255084 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30.1051 | −1.09419 | −0.547094 | − | 0.837071i | \(-0.684266\pi\) | ||||
−0.547094 | + | 0.837071i | \(0.684266\pi\) | |||||||
\(758\) | 25.9261i | 0.941679i | ||||||||
\(759\) | 15.4986 | + | 29.1844i | 0.562562 | + | 1.05932i | ||||
\(760\) | −15.5832 | −0.565262 | ||||||||
\(761\) | 37.7720 | 1.36924 | 0.684618 | − | 0.728902i | \(-0.259969\pi\) | ||||
0.684618 | + | 0.728902i | \(0.259969\pi\) | |||||||
\(762\) | −13.2791 | + | 7.05196i | −0.481051 | + | 0.255466i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 8.02904i | − | 0.290480i | ||||||
\(765\) | 0.852692 | − | 1.26140i | 0.0308291 | − | 0.0456060i | ||||
\(766\) | 20.2739i | 0.732526i | ||||||||
\(767\) | − | 11.1134i | − | 0.401282i | ||||||
\(768\) | −13.0634 | − | 24.5989i | −0.471386 | − | 0.887637i | ||||
\(769\) | 33.3656i | 1.20319i | 0.798800 | + | 0.601597i | \(0.205469\pi\) | ||||
−0.798800 | + | 0.601597i | \(0.794531\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.81558 | − | 18.4831i | −0.353499 | − | 0.665652i | ||||
\(772\) | 6.99191 | 0.251644 | ||||||||
\(773\) | 1.14671 | 0.0412443 | 0.0206222 | − | 0.999787i | \(-0.493435\pi\) | ||||
0.0206222 | + | 0.999787i | \(0.493435\pi\) | |||||||
\(774\) | 1.31989 | + | 0.892233i | 0.0474426 | + | 0.0320707i | ||||
\(775\) | 5.89355i | 0.211703i | ||||||||
\(776\) | 21.1453 | 0.759073 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13.1743 | 0.472321 | ||||||||
\(779\) | 23.7116i | 0.849555i | ||||||||
\(780\) | −1.22391 | + | 0.649966i | −0.0438230 | + | 0.0232725i | ||||
\(781\) | −35.0912 | −1.25566 | ||||||||
\(782\) | 2.35173 | 0.0840978 | ||||||||
\(783\) | 3.79948 | − | 35.6268i | 0.135782 | − | 1.27320i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 2.90010i | − | 0.103509i | ||||||
\(786\) | −3.46286 | + | 1.83898i | −0.123516 | + | 0.0655942i | ||||
\(787\) | − | 41.4786i | − | 1.47855i | −0.673403 | − | 0.739276i | \(-0.735168\pi\) | ||
0.673403 | − | 0.739276i | \(-0.264832\pi\) | |||||||
\(788\) | 1.48663i | 0.0529588i | ||||||||
\(789\) | 19.7147 | − | 10.4696i | 0.701862 | − | 0.372729i | ||||
\(790\) | − | 15.9174i | − | 0.566315i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 22.8212 | − | 33.7597i | 0.810916 | − | 1.19960i | ||||
\(793\) | −0.440869 | −0.0156557 | ||||||||
\(794\) | 20.2351 | 0.718117 | ||||||||
\(795\) | −13.9699 | + | 7.41883i | −0.495462 | + | 0.263119i | ||||
\(796\) | − | 3.14663i | − | 0.111529i | ||||||
\(797\) | −49.5086 | −1.75369 | −0.876843 | − | 0.480777i | \(-0.840355\pi\) | ||||
−0.876843 | + | 0.480777i | \(0.840355\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.37976 | −0.119567 | ||||||||
\(800\) | 4.36687i | 0.154392i | ||||||||
\(801\) | −12.0199 | + | 17.7812i | −0.424703 | + | 0.628269i | ||||
\(802\) | 25.8772 | 0.913756 | ||||||||
\(803\) | 28.0345 | 0.989317 | ||||||||
\(804\) | −2.51974 | − | 4.74477i | −0.0888645 | − | 0.167335i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.07359i | 0.213933i | ||||||||
\(807\) | −0.378925 | − | 0.713530i | −0.0133388 | − | 0.0251174i | ||||
\(808\) | − | 7.31441i | − | 0.257320i | ||||||
\(809\) | 25.1255i | 0.883367i | 0.897171 | + | 0.441683i | \(0.145619\pi\) | ||||
−0.897171 | + | 0.441683i | \(0.854381\pi\) | |||||||
\(810\) | −9.00573 | + | 3.61726i | −0.316429 | + | 0.127098i | ||||
\(811\) | − | 4.97517i | − | 0.174702i | −0.996178 | − | 0.0873509i | \(-0.972160\pi\) | ||
0.996178 | − | 0.0873509i | \(-0.0278401\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −35.6283 | + | 18.9207i | −1.24954 | + | 0.663577i | ||||
\(814\) | −36.0362 | −1.26307 | ||||||||
\(815\) | 12.7586 | 0.446914 | ||||||||
\(816\) | −0.669875 | − | 1.26140i | −0.0234503 | − | 0.0441578i | ||||
\(817\) | 2.50842i | 0.0877585i | ||||||||
\(818\) | 18.4210 | 0.644076 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.89735 | 0.136101 | ||||||||
\(821\) | 13.8573i | 0.483624i | 0.970323 | + | 0.241812i | \(0.0777417\pi\) | ||||
−0.970323 | + | 0.241812i | \(0.922258\pi\) | |||||||
\(822\) | 4.33371 | + | 8.16052i | 0.151155 | + | 0.284631i | ||||
\(823\) | 46.1558 | 1.60889 | 0.804446 | − | 0.594026i | \(-0.202462\pi\) | ||||
0.804446 | + | 0.594026i | \(0.202462\pi\) | |||||||
\(824\) | −45.7761 | −1.59469 | ||||||||
\(825\) | −6.79159 | + | 3.60673i | −0.236453 | + | 0.125570i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 18.6880i | − | 0.649844i | −0.945741 | − | 0.324922i | \(-0.894662\pi\) | ||
0.945741 | − | 0.324922i | \(-0.105338\pi\) | |||||||
\(828\) | 8.94125 | + | 6.04419i | 0.310730 | + | 0.210050i | ||||
\(829\) | − | 17.2579i | − | 0.599391i | −0.954035 | − | 0.299695i | \(-0.903115\pi\) | ||
0.954035 | − | 0.299695i | \(-0.0968851\pi\) | |||||||
\(830\) | − | 11.6370i | − | 0.403926i | ||||||
\(831\) | −11.2845 | − | 21.2492i | −0.391456 | − | 0.737126i | ||||
\(832\) | 7.60575i | 0.263682i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −9.39235 | − | 17.6861i | −0.325231 | − | 0.612421i | ||||
\(835\) | −15.7766 | −0.545970 | ||||||||
\(836\) | 18.9319 | 0.654775 | ||||||||
\(837\) | 3.24751 | − | 30.4511i | 0.112250 | − | 1.05254i | ||||
\(838\) | − | 42.7586i | − | 1.47707i | ||||||
\(839\) | 49.1689 | 1.69750 | 0.848750 | − | 0.528795i | \(-0.177356\pi\) | ||||
0.848750 | + | 0.528795i | \(0.177356\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.5446 | −0.639470 | ||||||||
\(842\) | − | 36.8170i | − | 1.26880i | ||||||
\(843\) | −10.4860 | + | 5.56866i | −0.361157 | + | 0.191795i | ||||
\(844\) | −7.63621 | −0.262849 | ||||||||
\(845\) | −12.0867 | −0.415794 | ||||||||
\(846\) | 17.8477 | + | 12.0649i | 0.613617 | + | 0.414798i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 14.8377i | 0.509527i | ||||||||
\(849\) | −6.78662 | + | 3.60409i | −0.232916 | + | 0.123692i | ||||
\(850\) | 0.547280i | 0.0187716i | ||||||||
\(851\) | − | 32.3448i | − | 1.10876i | ||||||
\(852\) | −10.1222 | + | 5.37547i | −0.346781 | + | 0.184160i | ||||
\(853\) | 8.86218i | 0.303435i | 0.988424 | + | 0.151718i | \(0.0484804\pi\) | ||||
−0.988424 | + | 0.151718i | \(0.951520\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12.6593 | − | 8.55757i | −0.432940 | − | 0.292663i | ||||
\(856\) | 41.4905 | 1.41812 | ||||||||
\(857\) | −0.983563 | −0.0335979 | −0.0167989 | − | 0.999859i | \(-0.505348\pi\) | ||||
−0.0167989 | + | 0.999859i | \(0.505348\pi\) | |||||||
\(858\) | −6.99907 | + | 3.71691i | −0.238944 | + | 0.126893i | ||||
\(859\) | 27.2791i | 0.930750i | 0.885114 | + | 0.465375i | \(0.154081\pi\) | ||||
−0.885114 | + | 0.465375i | \(0.845919\pi\) | |||||||
\(860\) | 0.412296 | 0.0140592 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −27.7897 | −0.946519 | ||||||||
\(863\) | 4.55257i | 0.154971i | 0.996993 | + | 0.0774857i | \(0.0246892\pi\) | ||||
−0.996993 | + | 0.0774857i | \(0.975311\pi\) | |||||||
\(864\) | 2.40627 | − | 22.5630i | 0.0818628 | − | 0.767608i | ||||
\(865\) | 10.1733 | 0.345904 | ||||||||
\(866\) | −12.8451 | −0.436496 | ||||||||
\(867\) | −13.6011 | − | 25.6113i | −0.461916 | − | 0.869804i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 65.5354i | 2.22314i | ||||||||
\(870\) | 6.04032 | + | 11.3741i | 0.204786 | + | 0.385619i | ||||
\(871\) | 3.54073i | 0.119973i | ||||||||
\(872\) | 49.3221i | 1.67026i | ||||||||
\(873\) | 17.1778 | + | 11.6120i | 0.581382 | + | 0.393008i | ||||
\(874\) | − | 23.6019i | − | 0.798346i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8.08667 | − | 4.29449i | 0.273223 | − | 0.145097i | ||||
\(877\) | 21.3568 | 0.721169 | 0.360584 | − | 0.932727i | \(-0.382577\pi\) | ||||
0.360584 | + | 0.932727i | \(0.382577\pi\) | |||||||
\(878\) | −18.0872 | −0.610414 | ||||||||
\(879\) | −24.4379 | − | 46.0174i | −0.824269 | − | 1.55213i | ||||
\(880\) | 7.21345i | 0.243165i | ||||||||
\(881\) | 33.2551 | 1.12039 | 0.560196 | − | 0.828360i | \(-0.310726\pi\) | ||||
0.560196 | + | 0.828360i | \(0.310726\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.0561 | 0.405721 | 0.202860 | − | 0.979208i | \(-0.434976\pi\) | ||||
0.202860 | + | 0.979208i | \(0.434976\pi\) | |||||||
\(884\) | − | 0.406061i | − | 0.0136573i | ||||||
\(885\) | −9.44689 | − | 17.7888i | −0.317554 | − | 0.597965i | ||||
\(886\) | 2.58359 | 0.0867974 | ||||||||
\(887\) | 23.4128 | 0.786123 | 0.393062 | − | 0.919512i | \(-0.371416\pi\) | ||||
0.393062 | + | 0.919512i | \(0.371416\pi\) | |||||||
\(888\) | −35.2275 | + | 18.7078i | −1.18216 | + | 0.627793i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 7.71471i | − | 0.258598i | ||||||
\(891\) | 37.0786 | − | 14.8931i | 1.24218 | − | 0.498937i | ||||
\(892\) | 9.82831i | 0.329076i | ||||||||
\(893\) | 33.9191i | 1.13506i | ||||||||
\(894\) | −4.61093 | − | 8.68254i | −0.154213 | − | 0.290388i | ||||
\(895\) | 5.26215i | 0.175894i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.33616 | − | 6.28210i | −0.111391 | − | 0.209753i | ||||
\(898\) | 27.4644 | 0.916498 | ||||||||
\(899\) | −40.6376 | −1.35534 | ||||||||
\(900\) | −1.40656 | + | 2.08075i | −0.0468855 | + | 0.0693584i | ||||
\(901\) | − | 4.63485i | − | 0.154409i | ||||||
\(902\) | 22.2875 | 0.742091 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 15.4709 | 0.514556 | ||||||||
\(905\) | − | 9.71314i | − | 0.322876i | ||||||
\(906\) | 11.5618 | − | 6.13997i | 0.384114 | − | 0.203987i | ||||
\(907\) | −41.5017 | −1.37804 | −0.689020 | − | 0.724742i | \(-0.741959\pi\) | ||||
−0.689020 | + | 0.724742i | \(0.741959\pi\) | |||||||
\(908\) | 20.2775 | 0.672933 | ||||||||
\(909\) | 4.01674 | − | 5.94201i | 0.133227 | − | 0.197084i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 57.6428i | 1.90979i | 0.296941 | + | 0.954896i | \(0.404034\pi\) | ||||
−0.296941 | + | 0.954896i | \(0.595966\pi\) | |||||||
\(912\) | −12.6593 | + | 6.72283i | −0.419192 | + | 0.222615i | ||||
\(913\) | 47.9120i | 1.58566i | ||||||||
\(914\) | − | 3.71154i | − | 0.122767i | ||||||
\(915\) | −0.705682 | + | 0.374757i | −0.0233291 | + | 0.0123891i | ||||
\(916\) | − | 18.1743i | − | 0.600496i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.301566 | − | 2.82772i | 0.00995318 | − | 0.0933286i | ||||
\(919\) | −10.9154 | −0.360065 | −0.180033 | − | 0.983661i | \(-0.557620\pi\) | ||||
−0.180033 | + | 0.983661i | \(0.557620\pi\) | |||||||
\(920\) | −13.1468 | −0.433438 | ||||||||
\(921\) | 50.2208 | − | 26.6701i | 1.65483 | − | 0.878811i | ||||
\(922\) | − | 14.5981i | − | 0.480763i | ||||||
\(923\) | 7.55357 | 0.248629 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.52707 | 0.247488 | ||||||||
\(926\) | − | 5.54017i | − | 0.182061i | ||||||
\(927\) | −37.1872 | − | 25.1381i | −1.22139 | − | 0.825644i | ||||
\(928\) | −30.1107 | −0.988433 | ||||||||
\(929\) | −40.4127 | −1.32590 | −0.662950 | − | 0.748664i | \(-0.730696\pi\) | ||||
−0.662950 | + | 0.748664i | \(0.730696\pi\) | |||||||
\(930\) | 5.16281 | + | 9.72176i | 0.169295 | + | 0.318789i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 9.20592i | − | 0.301550i | ||||||
\(933\) | 13.3728 | + | 25.1815i | 0.437806 | + | 0.824404i | ||||
\(934\) | − | 9.93999i | − | 0.325246i | ||||||
\(935\) | − | 2.25327i | − | 0.0736899i | ||||||
\(936\) | −4.91240 | + | 7.26698i | −0.160567 | + | 0.237529i | ||||
\(937\) | − | 5.67805i | − | 0.185494i | −0.995690 | − | 0.0927468i | \(-0.970435\pi\) | ||
0.995690 | − | 0.0927468i | \(-0.0295647\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.04963 | + | 3.74376i | −0.230056 | + | 0.122173i | ||||
\(940\) | 5.57511 | 0.181840 | ||||||||
\(941\) | 12.5927 | 0.410510 | 0.205255 | − | 0.978709i | \(-0.434198\pi\) | ||||
0.205255 | + | 0.978709i | \(0.434198\pi\) | |||||||
\(942\) | −2.54052 | − | 4.78389i | −0.0827746 | − | 0.155868i | ||||
\(943\) | 20.0044i | 0.651432i | ||||||||
\(944\) | −18.8938 | −0.614940 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.35776 | 0.0766575 | ||||||||
\(947\) | − | 31.3417i | − | 1.01847i | −0.860628 | − | 0.509234i | \(-0.829929\pi\) | ||
0.860628 | − | 0.509234i | \(-0.170071\pi\) | |||||||
\(948\) | 10.0391 | + | 18.9040i | 0.326054 | + | 0.613972i | ||||
\(949\) | −6.03459 | −0.195891 | ||||||||
\(950\) | 5.49248 | 0.178200 | ||||||||
\(951\) | −45.0200 | + | 23.9082i | −1.45987 | + | 0.775277i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 43.7751i | 1.41802i | 0.705200 | + | 0.709008i | \(0.250857\pi\) | ||||
−0.705200 | + | 0.709008i | \(0.749143\pi\) | |||||||
\(954\) | −16.5452 | + | 24.4756i | −0.535671 | + | 0.792426i | ||||
\(955\) | 9.59049i | 0.310341i | ||||||||
\(956\) | − | 7.55686i | − | 0.244406i | ||||||
\(957\) | −24.8693 | − | 46.8298i | −0.803911 | − | 1.51379i | ||||
\(958\) | − | 22.2540i | − | 0.718994i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 6.46521 | + | 12.1742i | 0.208664 | + | 0.392921i | ||||
\(961\) | −3.73396 | −0.120450 | ||||||||
\(962\) | 7.75701 | 0.250096 | ||||||||
\(963\) | 33.7057 | + | 22.7847i | 1.08615 | + | 0.734225i | ||||
\(964\) | − | 4.25374i | − | 0.137004i | ||||||
\(965\) | −8.35166 | −0.268849 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.3052 | 1.16750 | 0.583748 | − | 0.811935i | \(-0.301585\pi\) | ||||
0.583748 | + | 0.811935i | \(0.301585\pi\) | |||||||
\(968\) | − | 26.6521i | − | 0.856631i | ||||||
\(969\) | 3.95441 | − | 2.10002i | 0.127034 | − | 0.0674623i | ||||
\(970\) | −7.45292 | −0.239299 | ||||||||
\(971\) | −49.8257 | −1.59898 | −0.799492 | − | 0.600677i | \(-0.794898\pi\) | ||||
−0.799492 | + | 0.600677i | \(0.794898\pi\) | |||||||
\(972\) | 8.41406 | − | 9.97588i | 0.269881 | − | 0.319976i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 2.66887i | 0.0855161i | ||||||||
\(975\) | 1.46193 | − | 0.776369i | 0.0468192 | − | 0.0248637i | ||||
\(976\) | 0.749515i | 0.0239914i | ||||||||
\(977\) | 27.7554i | 0.887974i | 0.896033 | + | 0.443987i | \(0.146436\pi\) | ||||
−0.896033 | + | 0.443987i | \(0.853564\pi\) | |||||||
\(978\) | 21.0461 | − | 11.1767i | 0.672979 | − | 0.357390i | ||||
\(979\) | 31.7631i | 1.01515i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −27.0854 | + | 40.0679i | −0.864772 | + | 1.27927i | ||||
\(982\) | 22.9500 | 0.732363 | ||||||||
\(983\) | 42.0792 | 1.34212 | 0.671060 | − | 0.741403i | \(-0.265839\pi\) | ||||
0.671060 | + | 0.741403i | \(0.265839\pi\) | |||||||
\(984\) | 21.7873 | − | 11.5703i | 0.694552 | − | 0.368847i | ||||
\(985\) | − | 1.77574i | − | 0.0565797i | ||||||
\(986\) | −3.77364 | −0.120177 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.07521 | −0.129650 | ||||||||
\(989\) | 2.11624i | 0.0672925i | ||||||||
\(990\) | −8.04360 | + | 11.8990i | −0.255642 | + | 0.378176i | ||||
\(991\) | 5.72308 | 0.181799 | 0.0908997 | − | 0.995860i | \(-0.471026\pi\) | ||||
0.0908997 | + | 0.995860i | \(0.471026\pi\) | |||||||
\(992\) | −25.7364 | −0.817131 | ||||||||
\(993\) | 2.15745 | + | 4.06256i | 0.0684647 | + | 0.128922i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.75858i | 0.119155i | ||||||||
\(996\) | 7.33944 | + | 13.8204i | 0.232559 | + | 0.437917i | ||||
\(997\) | 11.1344i | 0.352629i | 0.984334 | + | 0.176315i | \(0.0564176\pi\) | ||||
−0.984334 | + | 0.176315i | \(0.943582\pi\) | |||||||
\(998\) | 35.3025i | 1.11748i | ||||||||
\(999\) | −38.8912 | − | 4.14762i | −1.23046 | − | 0.131225i |
(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 | 735.2.b.d.146.6 | 8 | ||
3.2 | odd | 2 | 735.2.b.c.146.3 | 8 | |||
7.2 | even | 3 | 735.2.s.l.521.3 | 8 | |||
7.3 | odd | 6 | 735.2.s.k.656.2 | 8 | |||
7.4 | even | 3 | 105.2.s.c.26.2 | ✓ | 8 | ||
7.5 | odd | 6 | 105.2.s.d.101.3 | yes | 8 | ||
7.6 | odd | 2 | 735.2.b.c.146.6 | 8 | |||
21.2 | odd | 6 | 735.2.s.k.521.2 | 8 | |||
21.5 | even | 6 | 105.2.s.c.101.2 | yes | 8 | ||
21.11 | odd | 6 | 105.2.s.d.26.3 | yes | 8 | ||
21.17 | even | 6 | 735.2.s.l.656.3 | 8 | |||
21.20 | even | 2 | inner | 735.2.b.d.146.3 | 8 | ||
35.4 | even | 6 | 525.2.t.g.26.3 | 8 | |||
35.12 | even | 12 | 525.2.q.e.374.6 | 16 | |||
35.18 | odd | 12 | 525.2.q.f.299.3 | 16 | |||
35.19 | odd | 6 | 525.2.t.f.101.2 | 8 | |||
35.32 | odd | 12 | 525.2.q.f.299.6 | 16 | |||
35.33 | even | 12 | 525.2.q.e.374.3 | 16 | |||
105.32 | even | 12 | 525.2.q.e.299.3 | 16 | |||
105.47 | odd | 12 | 525.2.q.f.374.3 | 16 | |||
105.53 | even | 12 | 525.2.q.e.299.6 | 16 | |||
105.68 | odd | 12 | 525.2.q.f.374.6 | 16 | |||
105.74 | odd | 6 | 525.2.t.f.26.2 | 8 | |||
105.89 | even | 6 | 525.2.t.g.101.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.s.c.26.2 | ✓ | 8 | 7.4 | even | 3 | ||
105.2.s.c.101.2 | yes | 8 | 21.5 | even | 6 | ||
105.2.s.d.26.3 | yes | 8 | 21.11 | odd | 6 | ||
105.2.s.d.101.3 | yes | 8 | 7.5 | odd | 6 | ||
525.2.q.e.299.3 | 16 | 105.32 | even | 12 | |||
525.2.q.e.299.6 | 16 | 105.53 | even | 12 | |||
525.2.q.e.374.3 | 16 | 35.33 | even | 12 | |||
525.2.q.e.374.6 | 16 | 35.12 | even | 12 | |||
525.2.q.f.299.3 | 16 | 35.18 | odd | 12 | |||
525.2.q.f.299.6 | 16 | 35.32 | odd | 12 | |||
525.2.q.f.374.3 | 16 | 105.47 | odd | 12 | |||
525.2.q.f.374.6 | 16 | 105.68 | odd | 12 | |||
525.2.t.f.26.2 | 8 | 105.74 | odd | 6 | |||
525.2.t.f.101.2 | 8 | 35.19 | odd | 6 | |||
525.2.t.g.26.3 | 8 | 35.4 | even | 6 | |||
525.2.t.g.101.3 | 8 | 105.89 | even | 6 | |||
735.2.b.c.146.3 | 8 | 3.2 | odd | 2 | |||
735.2.b.c.146.6 | 8 | 7.6 | odd | 2 | |||
735.2.b.d.146.3 | 8 | 21.20 | even | 2 | inner | ||
735.2.b.d.146.6 | 8 | 1.1 | even | 1 | trivial | ||
735.2.s.k.521.2 | 8 | 21.2 | odd | 6 | |||
735.2.s.k.656.2 | 8 | 7.3 | odd | 6 | |||
735.2.s.l.521.3 | 8 | 7.2 | even | 3 | |||
735.2.s.l.656.3 | 8 | 21.17 | even | 6 |