Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [640,2,Mod(129,640)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(640, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("640.129");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 640 = 2^{7} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 640.c (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: | \(5.11042572936\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 129.3 | ||
Root | \(0.403032 - 0.403032i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 640.129 |
Dual form | 640.2.c.d.129.4 |
$q$-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 \(\left(\mathbb{Z}/640\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 0.806063i | − | 0.465381i | −0.972551 | − | 0.232690i | \(-0.925247\pi\) | ||
0.972551 | − | 0.232690i | \(-0.0747529\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.48119 | + | 1.67513i | −0.662410 | + | 0.749141i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.15633i | − | 0.815014i | −0.913202 | − | 0.407507i | \(-0.866398\pi\) | ||
0.913202 | − | 0.407507i | \(-0.133602\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.35026 | 0.783421 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.387873 | 0.116948 | 0.0584741 | − | 0.998289i | \(-0.481377\pi\) | ||||
0.0584741 | + | 0.998289i | \(0.481377\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.962389i | 0.266919i | 0.991054 | + | 0.133459i | \(0.0426085\pi\) | ||||
−0.991054 | + | 0.133459i | \(0.957391\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.35026 | + | 1.19394i | 0.348636 | + | 0.308273i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.61213i | − | 0.390998i | −0.980704 | − | 0.195499i | \(-0.937367\pi\) | ||
0.980704 | − | 0.195499i | \(-0.0626327\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.31265 | 1.44822 | 0.724111 | − | 0.689684i | \(-0.242250\pi\) | ||||
0.724111 | + | 0.689684i | \(0.242250\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.73813 | −0.379292 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 6.15633i | − | 1.28368i | −0.766838 | − | 0.641841i | \(-0.778171\pi\) | ||
0.766838 | − | 0.641841i | \(-0.221829\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.612127 | − | 4.96239i | −0.122425 | − | 0.992478i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 4.31265i | − | 0.829970i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.92478 | 1.78254 | 0.891271 | − | 0.453470i | \(-0.149814\pi\) | ||||
0.891271 | + | 0.453470i | \(0.149814\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 0.312650i | − | 0.0544254i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.61213 | + | 3.19394i | 0.610561 | + | 0.539874i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.57452i | 1.08084i | 0.841394 | + | 0.540422i | \(0.181735\pi\) | ||||
−0.841394 | + | 0.540422i | \(0.818265\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.775746 | 0.124219 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.57452 | 0.714419 | 0.357210 | − | 0.934024i | \(-0.383728\pi\) | ||||
0.357210 | + | 0.934024i | \(0.383728\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 11.5066i | − | 1.75474i | −0.479816 | − | 0.877369i | \(-0.659297\pi\) | ||
0.479816 | − | 0.877369i | \(-0.340703\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.48119 | + | 3.93700i | −0.518946 | + | 0.586893i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.54420i | 0.662839i | 0.943483 | + | 0.331420i | \(0.107528\pi\) | ||||
−0.943483 | + | 0.331420i | \(0.892472\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.35026 | 0.335752 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.29948 | −0.181963 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 8.96239i | − | 1.23108i | −0.788106 | − | 0.615539i | \(-0.788938\pi\) | ||
0.788106 | − | 0.615539i | \(-0.211062\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.574515 | + | 0.649738i | −0.0774677 | + | 0.0876107i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 5.08840i | − | 0.673975i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.31265 | −0.821837 | −0.410919 | − | 0.911672i | \(-0.634792\pi\) | ||||
−0.410919 | + | 0.911672i | \(0.634792\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.261865 | 0.0335284 | 0.0167642 | − | 0.999859i | \(-0.494664\pi\) | ||||
0.0167642 | + | 0.999859i | \(0.494664\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 5.06793i | − | 0.638499i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.61213 | − | 1.42548i | −0.199960 | − | 0.176810i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.89446i | 1.20880i | 0.796681 | + | 0.604400i | \(0.206587\pi\) | ||||
−0.796681 | + | 0.604400i | \(0.793413\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.96239 | −0.597401 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.7005 | −1.26992 | −0.634959 | − | 0.772546i | \(-0.718983\pi\) | ||||
−0.634959 | + | 0.772546i | \(0.718983\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.0884i | 1.53188i | 0.642911 | + | 0.765940i | \(0.277726\pi\) | ||||
−0.642911 | + | 0.765940i | \(0.722274\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.00000 | + | 0.493413i | −0.461880 | + | 0.0569744i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 0.836381i | − | 0.0953144i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.92478 | 0.216554 | 0.108277 | − | 0.994121i | \(-0.465467\pi\) | ||||
0.108277 | + | 0.994121i | \(0.465467\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.57452 | 0.397168 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 2.88129i | − | 0.316262i | −0.987418 | − | 0.158131i | \(-0.949453\pi\) | ||
0.987418 | − | 0.158131i | \(-0.0505469\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.70052 | + | 2.38787i | 0.292913 | + | 0.259001i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.61213i | 0.172838i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.6253 | −1.12628 | −0.563140 | − | 0.826362i | \(-0.690407\pi\) | ||||
−0.563140 | + | 0.826362i | \(0.690407\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.07522 | 0.217542 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 8.00000i | − | 0.829561i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.35026 | + | 10.5745i | −0.959317 | + | 1.08492i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 9.61213i | − | 0.975964i | −0.872854 | − | 0.487982i | \(-0.837733\pi\) | ||
0.872854 | − | 0.487982i | \(-0.162267\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.911603 | 0.0916196 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.4010 | 1.13445 | 0.567223 | − | 0.823564i | \(-0.308018\pi\) | ||||
0.567223 | + | 0.823564i | \(0.308018\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 10.9321i | − | 1.07717i | −0.842572 | − | 0.538585i | \(-0.818959\pi\) | ||
0.842572 | − | 0.538585i | \(-0.181041\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.57452 | − | 2.91160i | 0.251247 | − | 0.284143i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.0435i | 1.06761i | 0.845606 | + | 0.533807i | \(0.179239\pi\) | ||||
−0.845606 | + | 0.533807i | \(0.820761\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.03761 | 0.482516 | 0.241258 | − | 0.970461i | \(-0.422440\pi\) | ||||
0.241258 | + | 0.970461i | \(0.422440\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.29948 | 0.503004 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 19.8496i | 1.86729i | 0.358201 | + | 0.933645i | \(0.383390\pi\) | ||||
−0.358201 | + | 0.933645i | \(0.616610\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.3127 | + | 9.11871i | 0.961660 | + | 0.850324i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.26187i | 0.209110i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.47627 | −0.318669 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8496 | −0.986323 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 3.68735i | − | 0.332477i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.21933 | + | 6.32487i | 0.824602 | + | 0.565713i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.7685i | 1.04428i | 0.852859 | + | 0.522141i | \(0.174866\pi\) | ||||
−0.852859 | + | 0.522141i | \(0.825134\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.27504 | −0.816622 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.0884 | −1.31828 | −0.659140 | − | 0.752021i | \(-0.729079\pi\) | ||||
−0.659140 | + | 0.752021i | \(0.729079\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 13.6121i | − | 1.18032i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.22425 | + | 6.38787i | 0.621765 | + | 0.549781i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.5501i | 1.58484i | 0.609976 | + | 0.792420i | \(0.291179\pi\) | ||||
−0.609976 | + | 0.792420i | \(0.708821\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.61213 | −0.645652 | −0.322826 | − | 0.946458i | \(-0.604633\pi\) | ||||
−0.322826 | + | 0.946458i | \(0.604633\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.66291 | 0.308473 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.373285i | 0.0312156i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.96239 | − | 3.35026i | 0.246013 | − | 0.278224i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 1.89446i | − | 0.156252i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.6629 | 1.11931 | 0.559655 | − | 0.828726i | \(-0.310934\pi\) | ||||
0.559655 | + | 0.828726i | \(0.310934\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.2243 | −1.23893 | −0.619466 | − | 0.785023i | \(-0.712651\pi\) | ||||
−0.619466 | + | 0.785023i | \(0.712651\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 3.78892i | − | 0.306316i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.7005 | + | 16.6253i | −1.18077 | + | 1.33538i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.42548i | 0.113766i | 0.998381 | + | 0.0568830i | \(0.0181162\pi\) | ||||
−0.998381 | + | 0.0568830i | \(0.981884\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.22425 | −0.572921 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13.2750 | −1.04622 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 8.80606i | − | 0.689744i | −0.938650 | − | 0.344872i | \(-0.887922\pi\) | ||
0.938650 | − | 0.344872i | \(-0.112078\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.523730 | + | 0.463096i | 0.0407723 | + | 0.0360520i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.4690i | 0.810114i | 0.914292 | + | 0.405057i | \(0.132748\pi\) | ||||
−0.914292 | + | 0.405057i | \(0.867252\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0738 | 0.928754 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 14.8364 | 1.13457 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 19.9756i | − | 1.51871i | −0.650674 | − | 0.759357i | \(-0.725514\pi\) | ||
0.650674 | − | 0.759357i | \(-0.274486\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.7005 | + | 1.31994i | −0.808884 | + | 0.0997784i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.08840i | 0.382467i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.2374 | −0.914668 | −0.457334 | − | 0.889295i | \(-0.651196\pi\) | ||||
−0.457334 | + | 0.889295i | \(0.651196\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.8496 | −1.02943 | −0.514715 | − | 0.857362i | \(-0.672102\pi\) | ||||
−0.514715 | + | 0.857362i | \(0.672102\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 0.211080i | − | 0.0156035i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11.0132 | − | 9.73813i | −0.809705 | − | 0.715962i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 0.625301i | − | 0.0457265i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.29948 | −0.676437 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.84955 | −0.278544 | −0.139272 | − | 0.990254i | \(-0.544476\pi\) | ||||
−0.139272 | + | 0.990254i | \(0.544476\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.61213i | 0.691896i | 0.938254 | + | 0.345948i | \(0.112443\pi\) | ||||
−0.938254 | + | 0.345948i | \(0.887557\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.14903 | + | 1.29948i | −0.0822838 | + | 0.0930574i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 9.58769i | − | 0.683095i | −0.939865 | − | 0.341547i | \(-0.889049\pi\) | ||
0.939865 | − | 0.341547i | \(-0.110951\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.29948 | 0.375670 | 0.187835 | − | 0.982201i | \(-0.439853\pi\) | ||||
0.187835 | + | 0.982201i | \(0.439853\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.97556 | 0.562553 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.31265i | 0.302689i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.77575 | + | 7.66291i | −0.473239 | + | 0.535201i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 14.4690i | − | 1.00566i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.44851 | 0.169367 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.0884 | −1.03873 | −0.519364 | − | 0.854553i | \(-0.673831\pi\) | ||||
−0.519364 | + | 0.854553i | \(0.673831\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.62530i | 0.590996i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 19.2750 | + | 17.0435i | 1.31455 | + | 1.16236i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 21.4010i | − | 1.45280i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.5501 | 0.712908 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.55149 | 0.104365 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 22.5296i | − | 1.50869i | −0.656476 | − | 0.754347i | \(-0.727954\pi\) | ||
0.656476 | − | 0.754347i | \(-0.272046\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.43866 | − | 11.6629i | −0.0959106 | − | 0.777527i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 2.35756i | − | 0.156476i | −0.996935 | − | 0.0782382i | \(-0.975071\pi\) | ||
0.996935 | − | 0.0782382i | \(-0.0249295\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.55149 | −0.234689 | −0.117345 | − | 0.993091i | \(-0.537438\pi\) | ||||
−0.117345 | + | 0.993091i | \(0.537438\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.674176 | −0.0443575 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.0884i | 0.857449i | 0.903435 | + | 0.428725i | \(0.141037\pi\) | ||||
−0.903435 | + | 0.428725i | \(0.858963\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.61213 | − | 6.73084i | −0.496560 | − | 0.439072i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 1.55149i | − | 0.100780i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.3258 | −0.991345 | −0.495673 | − | 0.868509i | \(-0.665078\pi\) | ||||
−0.495673 | + | 0.868509i | \(0.665078\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.12601 | 0.136948 | 0.0684741 | − | 0.997653i | \(-0.478187\pi\) | ||||
0.0684741 | + | 0.997653i | \(0.478187\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 15.8192i | − | 1.01480i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.48119 | + | 3.93700i | −0.222405 | + | 0.251525i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.07522i | 0.386557i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.32250 | −0.147182 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.6859 | 1.68440 | 0.842201 | − | 0.539164i | \(-0.181260\pi\) | ||||
0.842201 | + | 0.539164i | \(0.181260\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2.38787i | − | 0.150124i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.92478 | − | 2.17679i | 0.120534 | − | 0.136316i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 5.40105i | − | 0.336908i | −0.985710 | − | 0.168454i | \(-0.946123\pi\) | ||
0.985710 | − | 0.168454i | \(-0.0538775\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.1768 | 0.880903 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.70052 | −0.290955 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.4690i | 0.892195i | 0.894984 | + | 0.446098i | \(0.147187\pi\) | ||||
−0.894984 | + | 0.446098i | \(0.852813\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.0132 | + | 13.2750i | 0.922252 | + | 0.815479i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.56467i | 0.524149i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 28.1114 | 1.71398 | 0.856992 | − | 0.515330i | \(-0.172331\pi\) | ||||
0.856992 | + | 0.515330i | \(0.172331\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.8773 | 1.51119 | 0.755595 | − | 0.655039i | \(-0.227348\pi\) | ||||
0.755595 | + | 0.655039i | \(0.227348\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 1.67276i | − | 0.101240i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.237428 | − | 1.92478i | −0.0143174 | − | 0.116068i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.9756i | 1.20022i | 0.799919 | + | 0.600108i | \(0.204876\pi\) | ||||
−0.799919 | + | 0.600108i | \(0.795124\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 23.3258 | 1.39648 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.4993 | −0.864955 | −0.432478 | − | 0.901645i | \(-0.642361\pi\) | ||||
−0.432478 | + | 0.901645i | \(0.642361\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 8.80606i | − | 0.523466i | −0.965140 | − | 0.261733i | \(-0.915706\pi\) | ||
0.965140 | − | 0.261733i | \(-0.0842940\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.52373 | + | 7.53690i | 0.504902 | + | 0.446448i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 9.86414i | − | 0.582262i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.4010 | 0.847120 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.74798 | −0.454195 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.35026i | 0.195724i | 0.995200 | + | 0.0978622i | \(0.0312004\pi\) | ||||
−0.995200 | + | 0.0978622i | \(0.968800\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.35026 | − | 10.5745i | 0.544393 | − | 0.615672i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1.67276i | − | 0.0970634i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.92478 | 0.342639 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −24.8119 | −1.43014 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 9.18997i | − | 0.527950i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.387873 | + | 0.438658i | −0.0222096 | + | 0.0251175i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1.95509i | − | 0.111583i | −0.998442 | − | 0.0557916i | \(-0.982232\pi\) | ||
0.998442 | − | 0.0557916i | \(-0.0177682\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.81194 | −0.501294 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.77575 | −0.497627 | −0.248813 | − | 0.968551i | \(-0.580041\pi\) | ||||
−0.248813 | + | 0.968551i | \(0.580041\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 18.5501i | − | 1.04851i | −0.851561 | − | 0.524256i | \(-0.824343\pi\) | ||
0.851561 | − | 0.524256i | \(-0.175657\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.48944 | + | 7.50659i | 0.478326 | + | 0.422948i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.58769i | 0.538498i | 0.963071 | + | 0.269249i | \(0.0867755\pi\) | ||||
−0.963071 | + | 0.269249i | \(0.913224\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.775746 | −0.0434335 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.90175 | 0.496847 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 10.1768i | − | 0.566252i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.77575 | − | 0.589104i | 0.264911 | − | 0.0326776i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 4.06063i | − | 0.224554i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.79877 | 0.540224 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.0884 | 1.26905 | 0.634527 | − | 0.772901i | \(-0.281195\pi\) | ||||
0.634527 | + | 0.772901i | \(0.281195\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 15.4518i | 0.846755i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −16.5745 | − | 14.6556i | −0.905563 | − | 0.800722i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 4.77575i | − | 0.260151i | −0.991504 | − | 0.130076i | \(-0.958478\pi\) | ||
0.991504 | − | 0.130076i | \(-0.0415220\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.0000 | 0.869001 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.84955 | 0.208465 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 20.1622i | − | 1.08866i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.35026 | − | 8.31265i | 0.395725 | − | 0.447538i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.89446i | 0.101700i | 0.998706 | + | 0.0508500i | \(0.0161930\pi\) | ||||
−0.998706 | + | 0.0508500i | \(0.983807\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −31.4010 | −1.68086 | −0.840430 | − | 0.541921i | \(-0.817697\pi\) | ||||
−0.840430 | + | 0.541921i | \(0.817697\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.15045 | 0.221534 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 12.7757i | − | 0.679984i | −0.940428 | − | 0.339992i | \(-0.889576\pi\) | ||
0.940428 | − | 0.339992i | \(-0.110424\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.8496 | − | 17.9248i | 0.841207 | − | 0.951348i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.80209i | 0.148303i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.4749 | 0.869510 | 0.434755 | − | 0.900549i | \(-0.356835\pi\) | ||||
0.434755 | + | 0.900549i | \(0.356835\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20.8496 | 1.09734 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.74543i | 0.459016i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −21.9248 | − | 19.3865i | −1.14760 | − | 1.01473i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.0957i | 0.526991i | 0.964661 | + | 0.263495i | \(0.0848754\pi\) | ||||
−0.964661 | + | 0.263495i | \(0.915125\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.7513 | 0.559691 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.3258 | −1.00335 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 6.82653i | − | 0.353464i | −0.984259 | − | 0.176732i | \(-0.943447\pi\) | ||
0.984259 | − | 0.176732i | \(-0.0565527\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.09825 | − | 7.43136i | 0.263272 | − | 0.383754i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 1.92478i | − | 0.0991311i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.4617 | −0.999679 | −0.499840 | − | 0.866118i | \(-0.666608\pi\) | ||||
−0.499840 | + | 0.866118i | \(0.666608\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.48612 | 0.485989 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 5.90431i | − | 0.301696i | −0.988557 | − | 0.150848i | \(-0.951800\pi\) | ||
0.988557 | − | 0.150848i | \(-0.0482004\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.40105 | + | 1.23884i | 0.0714040 | + | 0.0631372i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 27.0435i | − | 1.37470i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.1866 | −0.719291 | −0.359646 | − | 0.933089i | \(-0.617102\pi\) | ||||
−0.359646 | + | 0.933089i | \(0.617102\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.92478 | −0.501918 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.1622i | 0.613502i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.85097 | + | 3.22425i | −0.143448 | + | 0.162230i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.1866i | 1.41465i | 0.706890 | + | 0.707324i | \(0.250098\pi\) | ||||
−0.706890 | + | 0.707324i | \(0.749902\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −10.9722 | −0.549299 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.62530 | 0.330852 | 0.165426 | − | 0.986222i | \(-0.447100\pi\) | ||||
0.165426 | + | 0.986222i | \(0.447100\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.55149i | 0.475794i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.29455 | + | 5.98778i | −0.263088 | + | 0.297535i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.55008i | 0.126403i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.6761 | −0.626792 | −0.313396 | − | 0.949623i | \(-0.601467\pi\) | ||||
−0.313396 | + | 0.949623i | \(0.601467\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.9525 | 0.737554 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.6121i | 0.669809i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.82653 | + | 4.26774i | 0.236925 | + | 0.209495i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.13586i | 0.300474i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.8364 | −0.724805 | −0.362402 | − | 0.932022i | \(-0.618043\pi\) | ||||
−0.362402 | + | 0.932022i | \(0.618043\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.261865 | 0.0127625 | 0.00638126 | − | 0.999980i | \(-0.497969\pi\) | ||||
0.00638126 | + | 0.999980i | \(0.497969\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.6801i | 0.519282i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.00000 | + | 0.986826i | −0.388057 | + | 0.0478681i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 0.564666i | − | 0.0273261i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.300891 | 0.0145272 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.52373 | 0.217900 | 0.108950 | − | 0.994047i | \(-0.465251\pi\) | ||||
0.108950 | + | 0.994047i | \(0.465251\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 15.6385i | − | 0.751537i | −0.926714 | − | 0.375769i | \(-0.877379\pi\) | ||
0.926714 | − | 0.375769i | \(-0.122621\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.70052 | − | 2.38787i | −0.129480 | − | 0.114490i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 38.8627i | − | 1.85906i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.3272 | 0.492892 | 0.246446 | − | 0.969156i | \(-0.420737\pi\) | ||||
0.246446 | + | 0.969156i | \(0.420737\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.52373 | 0.263035 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.1939i | 0.721886i | 0.932588 | + | 0.360943i | \(0.117545\pi\) | ||||
−0.932588 | + | 0.360943i | \(0.882455\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.7381 | − | 17.7988i | 0.746059 | − | 0.843743i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 11.0132i | − | 0.520905i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.6761 | −1.16454 | −0.582268 | − | 0.812997i | \(-0.697835\pi\) | ||||
−0.582268 | + | 0.812997i | \(0.697835\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.77433 | 0.0835500 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.2717i | 0.576575i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.07381 | + | 3.47627i | −0.144102 | + | 0.162970i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 8.37328i | − | 0.391686i | −0.980635 | − | 0.195843i | \(-0.937256\pi\) | ||
0.980635 | − | 0.195843i | \(-0.0627443\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.95254 | −0.324517 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.29806 | 0.386479 | 0.193240 | − | 0.981152i | \(-0.438101\pi\) | ||||
0.193240 | + | 0.981152i | \(0.438101\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.4676i | 1.83421i | 0.398642 | + | 0.917107i | \(0.369482\pi\) | ||||
−0.398642 | + | 0.917107i | \(0.630518\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13.4010 | + | 11.8496i | 0.621459 | + | 0.549510i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.41819i | 0.111901i | 0.998434 | + | 0.0559503i | \(0.0178188\pi\) | ||||
−0.998434 | + | 0.0559503i | \(0.982181\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21.3357 | 0.985190 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.14903 | 0.0529446 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 4.46310i | − | 0.205213i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.86414 | − | 31.3258i | −0.177299 | − | 1.43733i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 21.0640i | − | 0.964452i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.44851 | 0.294640 | 0.147320 | − | 0.989089i | \(-0.452935\pi\) | ||||
0.147320 | + | 0.989089i | \(0.452935\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.32724 | −0.288497 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.7005i | 0.486891i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.1016 | + | 14.2374i | 0.731135 | + | 0.646488i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 12.3331i | − | 0.558867i | −0.960165 | − | 0.279433i | \(-0.909853\pi\) | ||
0.960165 | − | 0.279433i | \(-0.0901466\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.09825 | −0.320994 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.3127 | −0.645921 | −0.322960 | − | 0.946412i | \(-0.604678\pi\) | ||||
−0.322960 | + | 0.946412i | \(0.604678\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.22425i | 0.145213i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.35026 | + | 1.52705i | −0.0606898 | + | 0.0686360i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 23.0738i | 1.03500i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.0606 | 0.629440 | 0.314720 | − | 0.949184i | \(-0.398089\pi\) | ||||
0.314720 | + | 0.949184i | \(0.398089\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.43866 | 0.377011 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.8700i | 1.42101i | 0.703690 | + | 0.710507i | \(0.251534\pi\) | ||||
−0.703690 | + | 0.710507i | \(0.748466\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.8872 | + | 19.0982i | −0.751469 | + | 0.849861i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 9.73226i | − | 0.432225i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −26.0000 | −1.15243 | −0.576215 | − | 0.817298i | \(-0.695471\pi\) | ||||
−0.576215 | + | 0.817298i | \(0.695471\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.2228 | 1.24850 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 27.2243i | − | 1.20198i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 18.3127 | + | 16.1925i | 0.806952 | + | 0.713528i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.76257i | 0.0775178i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.1016 | −0.706780 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.4010 | −0.849975 | −0.424988 | − | 0.905199i | \(-0.639722\pi\) | ||||
−0.424988 | + | 0.905199i | \(0.639722\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 7.75860i | − | 0.339260i | −0.985508 | − | 0.169630i | \(-0.945743\pi\) | ||
0.985508 | − | 0.169630i | \(-0.0542573\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.06396 | + | 8.62530i | 0.0464350 | + | 0.376439i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 16.0000i | − | 0.696971i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.9003 | −0.647841 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.8364 | −0.643844 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.40246i | 0.190692i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.4993 | − | 16.3576i | −0.799794 | − | 0.707199i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.86414i | 0.425669i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.911603 | 0.0392655 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.8496 | 1.11136 | 0.555680 | − | 0.831397i | \(-0.312458\pi\) | ||||
0.555680 | + | 0.831397i | \(0.312458\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.1636i | 0.479077i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.46168 | + | 8.43866i | −0.319623 | + | 0.361472i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.2677i | 1.63621i | 0.575068 | + | 0.818105i | \(0.304975\pi\) | ||||
−0.575068 | + | 0.818105i | \(0.695025\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.615452 | 0.0262668 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.6253 | −0.537856 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 4.15045i | − | 0.176495i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.84955 | + | 8.87732i | −0.333195 | + | 0.376821i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 37.5271i | − | 1.59007i | −0.606562 | − | 0.795036i | \(-0.707452\pi\) | ||
0.606562 | − | 0.795036i | \(-0.292548\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.0738 | 0.468372 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.504032 | −0.0212802 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 43.6688i | 1.84042i | 0.391425 | + | 0.920210i | \(0.371982\pi\) | ||||
−0.391425 | + | 0.920210i | \(0.628018\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −33.2506 | − | 29.4010i | −1.39886 | − | 1.23691i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 7.70782i | − | 0.323698i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.42407 | 0.353155 | 0.176578 | − | 0.984287i | \(-0.443497\pi\) | ||||
0.176578 | + | 0.984287i | \(0.443497\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.8627 | −1.04047 | −0.520236 | − | 0.854022i | \(-0.674156\pi\) | ||||
−0.520236 | + | 0.854022i | \(0.674156\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.10299i | 0.129629i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −30.5501 | + | 3.76845i | −1.27403 | + | 0.157155i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.0263i | 0.583924i | 0.956430 | + | 0.291962i | \(0.0943082\pi\) | ||||
−0.956430 | + | 0.291962i | \(0.905692\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.74798 | 0.321995 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.21299 | −0.257758 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 3.47627i | − | 0.143972i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.78892 | − | 3.35026i | −0.156653 | − | 0.138516i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 34.5804i | − | 1.42729i | −0.700510 | − | 0.713643i | \(-0.747044\pi\) | ||
0.700510 | − | 0.713643i | \(-0.252956\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 62.6516 | 2.58152 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.72829 | −0.317899 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 8.00000i | − | 0.328521i | −0.986417 | − | 0.164260i | \(-0.947476\pi\) | ||
0.986417 | − | 0.164260i | \(-0.0525237\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.14903 | − | 5.82321i | 0.211090 | − | 0.238728i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 4.27171i | − | 0.174830i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −42.3996 | −1.73240 | −0.866201 | − | 0.499696i | \(-0.833445\pi\) | ||||
−0.866201 | + | 0.499696i | \(0.833445\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.75131 | 0.112228 | 0.0561141 | − | 0.998424i | \(-0.482129\pi\) | ||||
0.0561141 | + | 0.998424i | \(0.482129\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 23.2546i | 0.946999i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 16.0703 | − | 18.1744i | 0.653351 | − | 0.738895i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.7948i | 1.53404i | 0.641621 | + | 0.767022i | \(0.278262\pi\) | ||||
−0.641621 | + | 0.767022i | \(0.721738\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.47627 | 0.140866 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.37328 | −0.176924 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.7659i | 0.757947i | 0.925407 | + | 0.378974i | \(0.123723\pi\) | ||||
−0.925407 | + | 0.378974i | \(0.876277\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.17679 | + | 5.46168i | 0.249072 | + | 0.220236i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.6107i | 0.749239i | 0.927179 | + | 0.374620i | \(0.122227\pi\) | ||||
−0.927179 | + | 0.374620i | \(0.877773\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.2097 | −0.772102 | −0.386051 | − | 0.922478i | \(-0.626161\pi\) | ||||
−0.386051 | + | 0.922478i | \(0.626161\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −26.5501 | −1.06542 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 22.9116i | 0.917934i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.2506 | + | 6.07522i | −0.970024 | + | 0.243009i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 1.97365i | − | 0.0788201i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.5990 | 0.422608 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.0263 | −1.03609 | −0.518046 | − | 0.855353i | \(-0.673341\pi\) | ||||
−0.518046 | + | 0.855353i | \(0.673341\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.1622i | 0.483404i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −19.7137 | − | 17.4314i | −0.782314 | − | 0.691743i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.26187i | 0.0896184i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −25.1490 | −0.994880 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.1735 | 0.441325 | 0.220663 | − | 0.975350i | \(-0.429178\pi\) | ||||
0.220663 | + | 0.975350i | \(0.429178\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 35.1451i | 1.38599i | 0.720944 | + | 0.692993i | \(0.243708\pi\) | ||||
−0.720944 | + | 0.692993i | \(0.756292\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13.7381 | − | 15.5369i | 0.540939 | − | 0.611765i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 6.93207i | − | 0.272528i | −0.990673 | − | 0.136264i | \(-0.956490\pi\) | ||
0.990673 | − | 0.136264i | \(-0.0435095\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.44851 | −0.0961123 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17.2506 | −0.676104 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 29.7381i | 1.16374i | 0.813281 | + | 0.581872i | \(0.197679\pi\) | ||||
−0.813281 | + | 0.581872i | \(0.802321\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.3488 | − | 25.2750i | 0.873242 | − | 0.987577i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 30.7612i | 1.20011i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.3879 | −0.950017 | −0.475008 | − | 0.879981i | \(-0.657555\pi\) | ||||
−0.475008 | + | 0.879981i | \(0.657555\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.1378 | 1.32781 | 0.663903 | − | 0.747819i | \(-0.268899\pi\) | ||||
0.663903 | + | 0.747819i | \(0.268899\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 1.25060i | − | 0.0485693i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 22.8021 | + | 20.1622i | 0.884227 | + | 0.781857i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.3127i | 0.476748i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −18.1603 | −0.702118 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.101570 | 0.00392108 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.6385i | 0.911196i | 0.890186 | + | 0.455598i | \(0.150575\pi\) | ||||
−0.890186 | + | 0.455598i | \(0.849425\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −21.4010 | + | 2.63989i | −0.823727 | + | 0.101609i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.88717i | 0.110963i | 0.998460 | + | 0.0554814i | \(0.0176694\pi\) | ||||
−0.998460 | + | 0.0554814i | \(0.982331\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20.7269 | −0.795424 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.90034 | −0.0728212 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.7440i | 0.525900i | 0.964809 | + | 0.262950i | \(0.0846954\pi\) | ||||
−0.964809 | + | 0.262950i | \(0.915305\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −31.0738 | − | 27.4763i | −1.18727 | − | 1.04981i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.86273i | 0.109220i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.62530 | 0.328598 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.5633 | 1.20072 | 0.600361 | − | 0.799729i | \(-0.295023\pi\) | ||||
0.600361 | + | 0.799729i | \(0.295023\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 1.96571i | − | 0.0746713i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11.2750 | − | 12.7513i | 0.427687 | − | 0.483685i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 7.37470i | − | 0.279337i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.5501 | 0.399041 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.8397 | 0.900413 | 0.450207 | − | 0.892924i | \(-0.351350\pi\) | ||||
0.450207 | + | 0.892924i | \(0.351350\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 41.5026i | 1.56530i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.42548 | + | 6.13586i | −0.204336 | + | 0.231090i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 24.5844i | − | 0.924590i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.8496 | −0.820577 | −0.410289 | − | 0.911956i | \(-0.634572\pi\) | ||||
−0.410289 | + | 0.911956i | \(0.634572\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.52373 | 0.169653 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 61.1002i | − | 2.28822i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.625301 | − | 0.552907i | −0.0233849 | − | 0.0206776i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.3536i | 0.461353i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33.9248 | 1.26518 | 0.632590 | − | 0.774487i | \(-0.281992\pi\) | ||||
0.632590 | + | 0.774487i | \(0.281992\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23.5731 | −0.877908 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 1.71370i | − | 0.0637331i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.22425 | + | 9.92478i | 0.0454676 | + | 0.368597i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 2.78163i | − | 0.103165i | −0.998669 | − | 0.0515824i | \(-0.983574\pi\) | ||
0.998669 | − | 0.0515824i | \(-0.0164265\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.02776 | −0.0751023 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.5501 | −0.686099 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 4.90175i | − | 0.181050i | −0.995894 | − | 0.0905252i | \(-0.971145\pi\) | ||
0.995894 | − | 0.0905252i | \(-0.0288546\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.17347 | + | 2.80606i | 0.117055 | + | 0.103503i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.83780i | 0.141367i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.9102 | 0.953122 | 0.476561 | − | 0.879141i | \(-0.341883\pi\) | ||||
0.476561 | + | 0.879141i | \(0.341883\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.89701 | 0.179896 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.06793i | 0.332670i | 0.986069 | + | 0.166335i | \(0.0531933\pi\) | ||||
−0.986069 | + | 0.166335i | \(0.946807\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.2374 | + | 22.8872i | −0.741442 | + | 0.838521i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 6.77178i | − | 0.247766i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 23.8134 | 0.870121 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.8496 | −0.432396 | −0.216198 | − | 0.976349i | \(-0.569366\pi\) | ||||
−0.216198 | + | 0.976349i | \(0.569366\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 21.5106i | − | 0.783888i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22.5501 | − | 25.5026i | 0.820681 | − | 0.928135i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 2.05079i | − | 0.0745371i | −0.999305 | − | 0.0372685i | \(-0.988134\pi\) | ||
0.999305 | − | 0.0372685i | \(-0.0118657\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.92478 | −0.0698650 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.0738 | 0.908925 | 0.454462 | − | 0.890766i | \(-0.349831\pi\) | ||||
0.454462 | + | 0.890766i | \(0.349831\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 10.8627i | − | 0.393257i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.34694 | + | 5.61213i | 0.229474 | + | 0.202907i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 6.07522i | − | 0.219364i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.7466 | 0.531775 | 0.265887 | − | 0.964004i | \(-0.414335\pi\) | ||||
0.265887 | + | 0.964004i | \(0.414335\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.35359 | −0.156791 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.8872i | 0.391584i | 0.980645 | + | 0.195792i | \(0.0627278\pi\) | ||||
−0.980645 | + | 0.195792i | \(0.937272\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.07522 | − | 49.2506i | −0.218228 | − | 1.76913i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 11.4274i | − | 0.409955i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 28.8773 | 1.03464 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.15045 | −0.148515 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.62530i | 0.308243i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.38787 | − | 2.11142i | −0.0852268 | − | 0.0753598i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.8178i | 1.31241i | 0.754581 | + | 0.656207i | \(0.227840\pi\) | ||||
−0.754581 | + | 0.656207i | \(0.772160\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.6629 | 0.415211 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 42.8021 | 1.52187 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.252016i | 0.00894935i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10.7005 | − | 12.1016i | 0.379508 | − | 0.429198i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.8119i | 0.453822i | 0.973915 | + | 0.226911i | \(0.0728627\pi\) | ||||
−0.973915 | + | 0.226911i | \(0.927137\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.32582 | 0.259169 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −24.9722 | −0.882351 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.07664i | 0.179151i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 19.6629 | − | 22.2374i | 0.693027 | − | 0.783766i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 22.6596i | − | 0.797655i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16.2981 | −0.573009 | −0.286505 | − | 0.958079i | \(-0.592493\pi\) | ||||
−0.286505 | + | 0.958079i | \(0.592493\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.21108 | −0.0776415 | −0.0388208 | − | 0.999246i | \(-0.512360\pi\) | ||||
−0.0388208 | + | 0.999246i | \(0.512360\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 20.0527i | − | 0.703279i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14.7513 | + | 13.0435i | 0.516716 | + | 0.456894i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 72.6371i | − | 2.54125i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.87732 | 0.170427 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −50.6615 | −1.76810 | −0.884049 | − | 0.467394i | \(-0.845193\pi\) | ||||
−0.884049 | + | 0.467394i | \(0.845193\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.917483i | 0.0319814i | 0.999872 | + | 0.0159907i | \(0.00509022\pi\) | ||||
−0.999872 | + | 0.0159907i | \(0.994910\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.55149 | + | 0.191382i | −0.0540160 | + | 0.00666305i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.5198i | 0.365808i | 0.983131 | + | 0.182904i | \(0.0585497\pi\) | ||||
−0.983131 | + | 0.182904i | \(0.941450\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −38.6907 | −1.34378 | −0.671891 | − | 0.740650i | \(-0.734518\pi\) | ||||
−0.671891 | + | 0.740650i | \(0.734518\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16.1016 | 0.558557 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 3.78892i | − | 0.131278i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17.5369 | − | 15.5066i | −0.606890 | − | 0.536628i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 42.8021i | − | 1.47946i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.0263 | 0.346148 | 0.173074 | − | 0.984909i | \(-0.444630\pi\) | ||||
0.173074 | + | 0.984909i | \(0.444630\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11.6873i | 0.402534i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −17.8837 | + | 20.2252i | −0.615216 | + | 0.695768i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23.3952i | 0.803867i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.09825 | −0.243611 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 40.4749 | 1.38746 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 49.5388i | 1.69618i | 0.529855 | + | 0.848088i | \(0.322246\pi\) | ||||
−0.529855 | + | 0.848088i | \(0.677754\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −21.9756 | + | 24.8529i | −0.751548 | + | 0.849951i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 43.4763i | 1.48512i | 0.669779 | + | 0.742561i | \(0.266389\pi\) | ||||
−0.669779 | + | 0.742561i | \(0.733611\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.5633 | −0.803968 | −0.401984 | − | 0.915647i | \(-0.631679\pi\) | ||||
−0.401984 | + | 0.915647i | \(0.631679\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.95112 | −0.270974 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 13.3317i | − | 0.453816i | −0.973916 | − | 0.226908i | \(-0.927138\pi\) | ||
0.973916 | − | 0.226908i | \(-0.0728617\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 33.4617 | + | 29.5877i | 1.13773 | + | 1.00601i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 11.6082i | − | 0.394234i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.746569 | 0.0253256 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.52232 | −0.322651 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 22.5910i | − | 0.764590i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 13.6385 | − | 19.8799i | 0.461065 | − | 0.672062i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 13.6483i | − | 0.460871i | −0.973088 | − | 0.230436i | \(-0.925985\pi\) | ||
0.973088 | − | 0.230436i | \(-0.0740151\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.70052 | 0.0910864 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.3028 | 0.549255 | 0.274628 | − | 0.961551i | \(-0.411445\pi\) | ||||
0.274628 | + | 0.961551i | \(0.411445\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 13.5818i | − | 0.457064i | −0.973536 | − | 0.228532i | \(-0.926607\pi\) | ||
0.973536 | − | 0.228532i | \(-0.0733926\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.52373 | − | 7.53690i | −0.286522 | − | 0.253350i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 37.0797i | − | 1.24501i | −0.782614 | − | 0.622507i | \(-0.786114\pi\) | ||
0.782614 | − | 0.622507i | \(-0.213886\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 25.3766 | 0.851104 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.38646 | 0.0464481 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 28.6859i | 0.959938i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.1260 | − | 20.4993i | 0.605886 | − | 0.685216i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 4.77575i | − | 0.159458i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −19.8496 | −0.662020 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.4485 | −0.481350 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 20.0000i | 0.665558i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.5139 | − | 23.1998i | 0.681904 | − | 0.771188i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 35.7294i | − | 1.18638i | −0.805064 | − | 0.593188i | \(-0.797869\pi\) | ||
0.805064 | − | 0.593188i | \(-0.202131\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 26.7954 | 0.888749 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.5237 | −0.679982 | −0.339991 | − | 0.940429i | \(-0.610424\pi\) | ||||
−0.339991 | + | 0.940429i | \(0.610424\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1.11757i | − | 0.0369863i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.353586 | + | 0.312650i | 0.0116892 | + | 0.0103359i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 32.5355i | 1.07442i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.9986 | 0.692679 | 0.346340 | − | 0.938109i | \(-0.387424\pi\) | ||||
0.346340 | + | 0.938109i | \(0.387424\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.57593 | −0.0519287 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 10.2981i | − | 0.338965i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 32.6253 | − | 4.02444i | 1.07271 | − | 0.132323i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 25.6932i | − | 0.843876i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 31.5271 | 1.03437 | 0.517185 | − | 0.855874i | \(-0.326980\pi\) | ||||
0.517185 | + | 0.855874i | \(0.326980\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.8364 | 0.486243 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.07381i | 0.231586i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.04746 | + | 0.926192i | 0.0342556 | + | 0.0302897i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 17.8641i | − | 0.583596i | −0.956480 | − | 0.291798i | \(-0.905746\pi\) | ||
0.956480 | − | 0.291798i | \(-0.0942535\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14.9525 | −0.487958 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −45.5487 | −1.48484 | −0.742422 | − | 0.669933i | \(-0.766323\pi\) | ||||
−0.742422 | + | 0.669933i | \(0.766323\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 28.1622i | − | 0.917088i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13.7743 | − | 15.5778i | 0.448079 | − | 0.506747i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 43.2057i | − | 1.40400i | −0.712179 | − | 0.701998i | \(-0.752291\pi\) | ||
0.712179 | − | 0.701998i | \(-0.247709\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.5961 | −0.408887 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.72829 | 0.250607 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 10.9722i | − | 0.355426i | −0.984082 | − | 0.177713i | \(-0.943130\pi\) | ||
0.984082 | − | 0.177713i | \(-0.0568698\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.70194 | − | 6.44851i | 0.184510 | − | 0.208669i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.625301i | 0.0202131i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 40.0000 | 1.29167 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 67.5012 | 2.17746 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 25.9551i | 0.836391i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −16.1016 | − | 14.2374i | −0.518328 | − | 0.458319i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.1417i | 1.41950i | 0.704452 | + | 0.709751i | \(0.251193\pi\) | ||||
−0.704452 | + | 0.709751i | \(0.748807\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.20314 | −0.263523 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.1886 | 0.647881 | 0.323941 | − | 0.946077i | \(-0.394992\pi\) | ||||
0.323941 | + | 0.946077i | \(0.394992\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.4142i | 0.526216i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.474855 | − | 3.84955i | −0.0152075 | − | 0.123284i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1.73340i | − | 0.0554562i | −0.999616 | − | 0.0277281i | \(-0.991173\pi\) | ||
0.999616 | − | 0.0277281i | \(-0.00882727\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.12127 | −0.131716 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.8397 | 0.378013 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 14.0059i | − | 0.446718i | −0.974736 | − | 0.223359i | \(-0.928298\pi\) | ||
0.974736 | − | 0.223359i | \(-0.0717023\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.0606 | + | 14.2012i | 0.511734 | + | 0.452489i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 7.89843i | − | 0.251410i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −70.8383 | −2.25253 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.8021 | −1.35965 | −0.679827 | − | 0.733373i | \(-0.737945\pi\) | ||||
−0.679827 | + | 0.733373i | \(0.737945\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 18.6107i | − | 0.590593i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.84955 | + | 8.87732i | −0.248848 | + | 0.281430i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.8872i | 1.35825i | 0.734023 | + | 0.679125i | \(0.237641\pi\) | ||||
−0.734023 | + | 0.679125i | \(0.762359\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 28.3536 | 0.897068 |
(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 | 640.2.c.d.129.3 | yes | 6 | |
4.3 | odd | 2 | 640.2.c.c.129.4 | yes | 6 | ||
5.2 | odd | 4 | 3200.2.a.bp.1.2 | 3 | |||
5.3 | odd | 4 | 3200.2.a.bv.1.2 | 3 | |||
5.4 | even | 2 | inner | 640.2.c.d.129.4 | yes | 6 | |
8.3 | odd | 2 | 640.2.c.b.129.3 | yes | 6 | ||
8.5 | even | 2 | 640.2.c.a.129.4 | yes | 6 | ||
16.3 | odd | 4 | 1280.2.f.j.129.4 | 6 | |||
16.5 | even | 4 | 1280.2.f.i.129.3 | 6 | |||
16.11 | odd | 4 | 1280.2.f.k.129.3 | 6 | |||
16.13 | even | 4 | 1280.2.f.l.129.4 | 6 | |||
20.3 | even | 4 | 3200.2.a.bo.1.2 | 3 | |||
20.7 | even | 4 | 3200.2.a.bu.1.2 | 3 | |||
20.19 | odd | 2 | 640.2.c.c.129.3 | yes | 6 | ||
40.3 | even | 4 | 3200.2.a.bt.1.2 | 3 | |||
40.13 | odd | 4 | 3200.2.a.bq.1.2 | 3 | |||
40.19 | odd | 2 | 640.2.c.b.129.4 | yes | 6 | ||
40.27 | even | 4 | 3200.2.a.br.1.2 | 3 | |||
40.29 | even | 2 | 640.2.c.a.129.3 | ✓ | 6 | ||
40.37 | odd | 4 | 3200.2.a.bs.1.2 | 3 | |||
80.19 | odd | 4 | 1280.2.f.k.129.4 | 6 | |||
80.29 | even | 4 | 1280.2.f.i.129.4 | 6 | |||
80.59 | odd | 4 | 1280.2.f.j.129.3 | 6 | |||
80.69 | even | 4 | 1280.2.f.l.129.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
640.2.c.a.129.3 | ✓ | 6 | 40.29 | even | 2 | ||
640.2.c.a.129.4 | yes | 6 | 8.5 | even | 2 | ||
640.2.c.b.129.3 | yes | 6 | 8.3 | odd | 2 | ||
640.2.c.b.129.4 | yes | 6 | 40.19 | odd | 2 | ||
640.2.c.c.129.3 | yes | 6 | 20.19 | odd | 2 | ||
640.2.c.c.129.4 | yes | 6 | 4.3 | odd | 2 | ||
640.2.c.d.129.3 | yes | 6 | 1.1 | even | 1 | trivial | |
640.2.c.d.129.4 | yes | 6 | 5.4 | even | 2 | inner | |
1280.2.f.i.129.3 | 6 | 16.5 | even | 4 | |||
1280.2.f.i.129.4 | 6 | 80.29 | even | 4 | |||
1280.2.f.j.129.3 | 6 | 80.59 | odd | 4 | |||
1280.2.f.j.129.4 | 6 | 16.3 | odd | 4 | |||
1280.2.f.k.129.3 | 6 | 16.11 | odd | 4 | |||
1280.2.f.k.129.4 | 6 | 80.19 | odd | 4 | |||
1280.2.f.l.129.3 | 6 | 80.69 | even | 4 | |||
1280.2.f.l.129.4 | 6 | 16.13 | even | 4 | |||
3200.2.a.bo.1.2 | 3 | 20.3 | even | 4 | |||
3200.2.a.bp.1.2 | 3 | 5.2 | odd | 4 | |||
3200.2.a.bq.1.2 | 3 | 40.13 | odd | 4 | |||
3200.2.a.br.1.2 | 3 | 40.27 | even | 4 | |||
3200.2.a.bs.1.2 | 3 | 40.37 | odd | 4 | |||
3200.2.a.bt.1.2 | 3 | 40.3 | even | 4 | |||
3200.2.a.bu.1.2 | 3 | 20.7 | even | 4 | |||
3200.2.a.bv.1.2 | 3 | 5.3 | odd | 4 |