Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [464,3,Mod(463,464)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(464, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("464.463");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 464 = 2^{4} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 464.h (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: | \(12.6430842663\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 58 x^{18} + 2256 x^{16} + 48540 x^{14} + 757617 x^{12} + 7081908 x^{10} + 46200312 x^{8} + \cdots + 529984 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{39}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 463.10 | ||
Root | \(-0.115536 - 0.200115i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 464.463 |
Dual form | 464.3.h.c.463.9 |
$q$-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 \(\left(\mathbb{Z}/464\mathbb{Z}\right)^\times\).
\(n\) | \(117\) | \(175\) | \(321\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | −0.231073 | −0.0770242 | −0.0385121 | − | 0.999258i | \(-0.512262\pi\) | ||||
−0.0385121 | + | 0.999258i | \(0.512262\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.30394 | 0.860789 | 0.430394 | − | 0.902641i | \(-0.358374\pi\) | ||||
0.430394 | + | 0.902641i | \(0.358374\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.80119i | 0.971599i | 0.874070 | + | 0.485799i | \(0.161471\pi\) | ||||
−0.874070 | + | 0.485799i | \(0.838529\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.94661 | −0.994067 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −19.6581 | −1.78710 | −0.893549 | − | 0.448966i | \(-0.851792\pi\) | ||||
−0.893549 | + | 0.448966i | \(0.851792\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −7.70811 | −0.592932 | −0.296466 | − | 0.955043i | \(-0.595808\pi\) | ||||
−0.296466 | + | 0.955043i | \(0.595808\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.994523 | −0.0663015 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 21.6001i | − | 1.27059i | −0.772268 | − | 0.635297i | \(-0.780878\pi\) | ||
0.772268 | − | 0.635297i | \(-0.219122\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.18543 | −0.378181 | −0.189090 | − | 0.981960i | \(-0.560554\pi\) | ||||
−0.189090 | + | 0.981960i | \(0.560554\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 1.57157i | − | 0.0748366i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 9.72519i | 0.422834i | 0.977396 | + | 0.211417i | \(0.0678079\pi\) | ||||
−0.977396 | + | 0.211417i | \(0.932192\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.47606 | −0.259043 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.14697 | 0.153591 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 14.1842 | − | 25.2945i | 0.489109 | − | 0.872222i | ||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.38352 | 0.109146 | 0.0545728 | − | 0.998510i | \(-0.482620\pi\) | ||||
0.0545728 | + | 0.998510i | \(0.482620\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.54244 | 0.137650 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 29.2719i | 0.836341i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 41.4808i | 1.12110i | 0.828120 | + | 0.560551i | \(0.189411\pi\) | ||||
−0.828120 | + | 0.560551i | \(0.810589\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.78113 | 0.0456701 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 24.1263i | − | 0.588446i | −0.955737 | − | 0.294223i | \(-0.904939\pi\) | ||
0.955737 | − | 0.294223i | \(-0.0950608\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −59.7926 | −1.39052 | −0.695262 | − | 0.718756i | \(-0.744712\pi\) | ||||
−0.695262 | + | 0.718756i | \(0.744712\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −38.5057 | −0.855682 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −51.6582 | −1.09911 | −0.549555 | − | 0.835457i | \(-0.685203\pi\) | ||||
−0.549555 | + | 0.835457i | \(0.685203\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.74381 | 0.0559961 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.99119i | 0.0978664i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −29.5243 | −0.557063 | −0.278531 | − | 0.960427i | \(-0.589848\pi\) | ||||
−0.278531 | + | 0.960427i | \(0.589848\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −84.6072 | −1.53831 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.66036 | 0.0291290 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 36.7723i | 0.623259i | 0.950204 | + | 0.311630i | \(0.100875\pi\) | ||||
−0.950204 | + | 0.311630i | \(0.899125\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 91.5419i | − | 1.50069i | −0.661049 | − | 0.750343i | \(-0.729888\pi\) | ||
0.661049 | − | 0.750343i | \(-0.270112\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 60.8476i | − | 0.965834i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −33.1753 | −0.510389 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 80.0439i | 1.19469i | 0.801986 | + | 0.597343i | \(0.203777\pi\) | ||||
−0.801986 | + | 0.597343i | \(0.796223\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 2.24722i | − | 0.0325685i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 112.333i | 1.58216i | 0.611715 | + | 0.791078i | \(0.290480\pi\) | ||||
−0.611715 | + | 0.791078i | \(0.709520\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 88.8678i | 1.21737i | 0.793413 | + | 0.608684i | \(0.208302\pi\) | ||||
−0.793413 | + | 0.608684i | \(0.791698\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.49644 | 0.0199525 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 133.698i | − | 1.73634i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 57.8571 | 0.732369 | 0.366184 | − | 0.930542i | \(-0.380664\pi\) | ||||
0.366184 | + | 0.930542i | \(0.380664\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 79.5612 | 0.982237 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 132.894i | − | 1.60114i | −0.599242 | − | 0.800568i | \(-0.704531\pi\) | ||
0.599242 | − | 0.800568i | \(-0.295469\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 92.9656i | − | 1.09371i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.27757 | + | 5.84485i | −0.0376732 | + | 0.0671822i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 24.3633i | 0.273744i | 0.990589 | + | 0.136872i | \(0.0437050\pi\) | ||||
−0.990589 | + | 0.136872i | \(0.956295\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 52.4243i | − | 0.576091i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.781838 | −0.00840686 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −30.9257 | −0.325534 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 116.255i | 1.19850i | 0.800561 | + | 0.599251i | \(0.204535\pi\) | ||||
−0.800561 | + | 0.599251i | \(0.795465\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 175.873 | 1.77649 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 130.349i | 1.29058i | 0.763938 | + | 0.645290i | \(0.223263\pi\) | ||||
−0.763938 | + | 0.645290i | \(0.776737\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 23.7727i | − | 0.230803i | −0.993319 | − | 0.115401i | \(-0.963185\pi\) | ||
0.993319 | − | 0.115401i | \(-0.0368155\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 6.76394i | − | 0.0644185i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 98.7482i | − | 0.922881i | −0.887171 | − | 0.461440i | \(-0.847333\pi\) | ||
0.887171 | − | 0.461440i | \(-0.152667\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −128.857 | −1.18217 | −0.591085 | − | 0.806609i | \(-0.701300\pi\) | ||||
−0.591085 | + | 0.806609i | \(0.701300\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 9.58506i | − | 0.0863519i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 187.341i | 1.65789i | 0.559333 | + | 0.828943i | \(0.311057\pi\) | ||||
−0.559333 | + | 0.828943i | \(0.688943\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 41.8567i | 0.363971i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 68.9614 | 0.589414 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 146.906 | 1.23451 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 265.440 | 2.19372 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.57492i | 0.0453245i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −135.471 | −1.08377 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 24.1239 | 0.189952 | 0.0949761 | − | 0.995480i | \(-0.469723\pi\) | ||||
0.0949761 | + | 0.995480i | \(0.469723\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 13.8164 | 0.107104 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −59.1156 | −0.451264 | −0.225632 | − | 0.974213i | \(-0.572445\pi\) | ||||
−0.225632 | + | 0.974213i | \(0.572445\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 48.8695i | − | 0.367440i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 17.8483 | 0.132210 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.4531i | 0.112796i | 0.998408 | + | 0.0563982i | \(0.0179616\pi\) | ||||
−0.998408 | + | 0.0563982i | \(0.982038\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 46.2451i | − | 0.332698i | −0.986067 | − | 0.166349i | \(-0.946802\pi\) | ||
0.986067 | − | 0.166349i | \(-0.0531979\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.9368 | 0.0846581 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 151.527 | 1.05963 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 61.0479 | − | 108.866i | 0.421020 | − | 0.750799i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.634019 | −0.00431306 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 160.675 | 1.07835 | 0.539177 | − | 0.842193i | \(-0.318735\pi\) | ||||
0.539177 | + | 0.842193i | \(0.318735\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 25.8590i | 0.171252i | 0.996327 | + | 0.0856260i | \(0.0272890\pi\) | ||||
−0.996327 | + | 0.0856260i | \(0.972711\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 193.247i | 1.26306i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 14.5625 | 0.0939514 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 147.491i | − | 0.939431i | −0.882818 | − | 0.469716i | \(-0.844356\pi\) | ||
0.882818 | − | 0.469716i | \(-0.155644\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.82226 | 0.0429073 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −66.1429 | −0.410825 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 97.0774 | 0.595567 | 0.297783 | − | 0.954633i | \(-0.403753\pi\) | ||||
0.297783 | + | 0.954633i | \(0.403753\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 19.5504 | 0.118487 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 190.831i | − | 1.14270i | −0.820707 | − | 0.571349i | \(-0.806420\pi\) | ||
0.820707 | − | 0.571349i | \(-0.193580\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −109.585 | −0.648432 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 64.2852 | 0.375937 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.7517 | −0.108391 | −0.0541956 | − | 0.998530i | \(-0.517259\pi\) | ||||
−0.0541956 | + | 0.998530i | \(0.517259\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 44.0449i | − | 0.251685i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 8.49707i | − | 0.0480060i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 309.856i | − | 1.73104i | −0.500876 | − | 0.865519i | \(-0.666989\pi\) | ||
0.500876 | − | 0.865519i | \(-0.333011\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −288.536 | −1.59412 | −0.797062 | − | 0.603897i | \(-0.793614\pi\) | ||||
−0.797062 | + | 0.603897i | \(0.793614\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 21.1528i | 0.115589i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 178.531i | 0.965032i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 424.616i | 2.27067i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 28.2043i | 0.149229i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 188.884 | 0.988921 | 0.494460 | − | 0.869200i | \(-0.335366\pi\) | ||||
0.494460 | + | 0.869200i | \(0.335366\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 188.056i | 0.974383i | 0.873295 | + | 0.487191i | \(0.161979\pi\) | ||||
−0.873295 | + | 0.487191i | \(0.838021\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.66589 | 0.0393123 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 177.823 | 0.902655 | 0.451327 | − | 0.892358i | \(-0.350951\pi\) | ||||
0.451327 | + | 0.892358i | \(0.350951\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 303.810i | − | 1.52669i | −0.645994 | − | 0.763343i | \(-0.723557\pi\) | ||
0.645994 | − | 0.763343i | \(-0.276443\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 18.4960i | − | 0.0920197i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 172.032 | + | 96.4693i | 0.847450 | + | 0.475218i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 103.838i | − | 0.506527i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 87.0075i | − | 0.420326i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 141.252 | 0.675846 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −98.5614 | −0.467116 | −0.233558 | − | 0.972343i | \(-0.575037\pi\) | ||||
−0.233558 | + | 0.972343i | \(0.575037\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 25.9571i | − | 0.121864i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −257.344 | −1.19695 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 23.0119i | 0.106046i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 20.5349i | − | 0.0937667i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 166.496i | 0.753375i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 72.7331i | 0.326157i | 0.986613 | + | 0.163079i | \(0.0521424\pi\) | ||||
−0.986613 | + | 0.163079i | \(0.947858\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 57.9388 | 0.257506 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 65.0082i | 0.286380i | 0.989695 | + | 0.143190i | \(0.0457359\pi\) | ||||
−0.989695 | + | 0.143190i | \(0.954264\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 218.440i | − | 0.953887i | −0.878934 | − | 0.476943i | \(-0.841745\pi\) | ||
0.878934 | − | 0.476943i | \(-0.158255\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 30.8940i | 0.133740i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 276.750 | 1.18777 | 0.593884 | − | 0.804551i | \(-0.297594\pi\) | ||||
0.593884 | + | 0.804551i | \(0.297594\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −222.334 | −0.946102 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.3692 | −0.0564101 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 272.798i | 1.14141i | 0.821154 | + | 0.570706i | \(0.193331\pi\) | ||||
−0.821154 | + | 0.570706i | \(0.806669\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.924675 | −0.00383683 | −0.00191841 | − | 0.999998i | \(-0.500611\pi\) | ||||
−0.00191841 | + | 0.999998i | \(0.500611\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −55.7071 | −0.229247 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11.8092 | 0.0482008 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 55.3861 | 0.224235 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 30.7082i | 0.123326i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 309.338 | 1.23242 | 0.616212 | − | 0.787580i | \(-0.288666\pi\) | ||||
0.616212 | + | 0.787580i | \(0.288666\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 191.179i | − | 0.755646i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 21.4818i | 0.0842423i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −94.6179 | −0.368163 | −0.184082 | − | 0.982911i | \(-0.558931\pi\) | ||||
−0.184082 | + | 0.982911i | \(0.558931\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −282.119 | −1.08926 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −126.900 | + | 226.299i | −0.486208 | + | 0.867048i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 155.836 | 0.592531 | 0.296265 | − | 0.955106i | \(-0.404259\pi\) | ||||
0.296265 | + | 0.955106i | \(0.404259\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −127.071 | −0.479513 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 5.62968i | − | 0.0210849i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 270.950i | − | 1.00725i | −0.863923 | − | 0.503625i | \(-0.831999\pi\) | ||
0.863923 | − | 0.503625i | \(-0.168001\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −390.591 | −1.44129 | −0.720647 | − | 0.693302i | \(-0.756155\pi\) | ||||
−0.720647 | + | 0.693302i | \(0.756155\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.1138i | 0.0443730i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 127.307 | 0.462934 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −320.161 | −1.15582 | −0.577909 | − | 0.816102i | \(-0.696131\pi\) | ||||
−0.577909 | + | 0.816102i | \(0.696131\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −30.2710 | −0.108498 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 40.6284 | 0.144585 | 0.0722925 | − | 0.997383i | \(-0.476969\pi\) | ||||
0.0722925 | + | 0.997383i | \(0.476969\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 106.865i | − | 0.377614i | −0.982014 | − | 0.188807i | \(-0.939538\pi\) | ||
0.982014 | − | 0.188807i | \(-0.0604621\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.14608 | 0.0250740 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 164.087 | 0.571733 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −177.564 | −0.614408 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 26.8632i | − | 0.0923136i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 79.8459i | 0.272512i | 0.990674 | + | 0.136256i | \(0.0435069\pi\) | ||||
−0.990674 | + | 0.136256i | \(0.956493\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 158.266i | 0.536495i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −81.5214 | −0.274483 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 74.9629i | − | 0.250712i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 406.661i | − | 1.35103i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 30.1200i | − | 0.0994059i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 393.991i | − | 1.29177i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −548.532 | −1.78675 | −0.893375 | − | 0.449312i | \(-0.851669\pi\) | ||||
−0.893375 | + | 0.449312i | \(0.851669\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.49322i | 0.0177774i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −559.013 | −1.79747 | −0.898735 | − | 0.438491i | \(-0.855513\pi\) | ||||
−0.898735 | + | 0.438491i | \(0.855513\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 31.9388 | 0.102041 | 0.0510204 | − | 0.998698i | \(-0.483753\pi\) | ||||
0.0510204 | + | 0.998698i | \(0.483753\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 261.885i | − | 0.831380i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 308.715i | 0.973866i | 0.873439 | + | 0.486933i | \(0.161884\pi\) | ||||
−0.873439 | + | 0.486933i | \(0.838116\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −278.833 | + | 497.240i | −0.874086 | + | 1.55875i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 22.8180i | 0.0710841i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 155.206i | 0.480514i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 49.9182 | 0.153594 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 29.7752 | 0.0910557 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 351.337i | − | 1.06789i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −214.596 | −0.648327 | −0.324164 | − | 0.946001i | \(-0.605083\pi\) | ||||
−0.324164 | + | 0.946001i | \(0.605083\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 371.112i | − | 1.11445i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 344.505i | 1.02837i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 243.746i | − | 0.723282i | −0.932317 | − | 0.361641i | \(-0.882217\pi\) | ||
0.932317 | − | 0.361641i | \(-0.117783\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 43.2894i | − | 0.127697i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −66.5134 | −0.195054 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 351.920i | 1.02600i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 9.67193i | − | 0.0280346i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 171.176i | 0.493304i | 0.969104 | + | 0.246652i | \(0.0793304\pi\) | ||||
−0.969104 | + | 0.246652i | \(0.920670\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.5336 | 0.0588356 | 0.0294178 | − | 0.999567i | \(-0.490635\pi\) | ||||
0.0294178 | + | 0.999567i | \(0.490635\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −31.9653 | −0.0910692 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 198.062 | 0.561083 | 0.280542 | − | 0.959842i | \(-0.409486\pi\) | ||||
0.280542 | + | 0.959842i | \(0.409486\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 483.475i | 1.36190i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −33.9460 | −0.0950869 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 237.929 | 0.662754 | 0.331377 | − | 0.943498i | \(-0.392487\pi\) | ||||
0.331377 | + | 0.943498i | \(0.392487\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −309.370 | −0.856979 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −61.3358 | −0.168969 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 382.482i | 1.04790i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −616.145 | −1.67887 | −0.839435 | − | 0.543460i | \(-0.817114\pi\) | ||||
−0.839435 | + | 0.543460i | \(0.817114\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 215.848i | 0.584954i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 200.800i | − | 0.541241i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 549.310 | 1.47268 | 0.736341 | − | 0.676611i | \(-0.236552\pi\) | ||||
0.736341 | + | 0.676611i | \(0.236552\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 31.3037 | 0.0834765 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −109.333 | + | 194.972i | −0.290008 | + | 0.517168i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −651.622 | −1.71932 | −0.859659 | − | 0.510868i | \(-0.829324\pi\) | ||||
−0.859659 | + | 0.510868i | \(0.829324\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.57438 | −0.0146309 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 449.975i | − | 1.17487i | −0.809272 | − | 0.587434i | \(-0.800138\pi\) | ||
0.809272 | − | 0.587434i | \(-0.199862\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 575.430i | − | 1.49462i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 534.940 | 1.38227 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 405.267i | 1.04182i | 0.853612 | + | 0.520909i | \(0.174407\pi\) | ||||
−0.853612 | + | 0.520909i | \(0.825593\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 210.065 | 0.537251 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.6600 | 0.0347583 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 249.014 | 0.630415 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −88.5209 | −0.222975 | −0.111487 | − | 0.993766i | \(-0.535561\pi\) | ||||
−0.111487 | + | 0.993766i | \(0.535561\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 11.2924i | 0.0283017i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −592.146 | −1.47667 | −0.738337 | − | 0.674432i | \(-0.764388\pi\) | ||||
−0.738337 | + | 0.674432i | \(0.764388\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −26.0805 | −0.0647159 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 342.427 | 0.845499 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 815.432i | − | 2.00352i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 771.560i | 1.88645i | 0.332148 | + | 0.943227i | \(0.392227\pi\) | ||||
−0.332148 | + | 0.943227i | \(0.607773\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 3.57079i | − | 0.00868805i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −250.095 | −0.605558 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 571.970i | − | 1.37824i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.6860i | 0.0256258i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 28.5209i | − | 0.0680689i | −0.999421 | − | 0.0340344i | \(-0.989164\pi\) | ||
0.999421 | − | 0.0340344i | \(-0.0108356\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 169.786i | − | 0.403292i | −0.979459 | − | 0.201646i | \(-0.935371\pi\) | ||
0.979459 | − | 0.201646i | \(-0.0646290\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 462.165 | 1.09259 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 139.884i | 0.329138i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 622.594 | 1.45806 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −35.0136 | −0.0816168 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 107.397i | − | 0.249181i | −0.992208 | − | 0.124591i | \(-0.960238\pi\) | ||
0.992208 | − | 0.124591i | \(-0.0397617\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 45.2546i | − | 0.104514i | −0.998634 | − | 0.0522570i | \(-0.983358\pi\) | ||
0.998634 | − | 0.0522570i | \(-0.0166415\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −14.1065 | + | 25.1559i | −0.0324287 | + | 0.0578297i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 69.8797i | − | 0.159908i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 769.460i | 1.75276i | 0.481624 | + | 0.876378i | \(0.340047\pi\) | ||||
−0.481624 | + | 0.876378i | \(0.659953\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −24.5478 | −0.0556639 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 389.900 | 0.880136 | 0.440068 | − | 0.897965i | \(-0.354954\pi\) | ||||
0.440068 | + | 0.897965i | \(0.354954\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 104.858i | 0.235636i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −37.1275 | −0.0830593 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 657.473i | − | 1.46431i | −0.681140 | − | 0.732153i | \(-0.738516\pi\) | ||
0.681140 | − | 0.732153i | \(-0.261484\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 474.276i | 1.05161i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 5.97531i | − | 0.0131905i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 225.631i | − | 0.495893i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 519.676 | 1.13715 | 0.568573 | − | 0.822633i | \(-0.307496\pi\) | ||||
0.568573 | + | 0.822633i | \(0.307496\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 89.5749i | − | 0.195152i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 190.635i | − | 0.413524i | −0.978391 | − | 0.206762i | \(-0.933707\pi\) | ||
0.978391 | − | 0.206762i | \(-0.0662926\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 246.775i | − | 0.532990i | −0.963836 | − | 0.266495i | \(-0.914134\pi\) | ||
0.963836 | − | 0.266495i | \(-0.0858657\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.36499 | −0.00723653 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −463.418 | −0.992330 | −0.496165 | − | 0.868228i | \(-0.665259\pi\) | ||||
−0.496165 | + | 0.868228i | \(0.665259\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −544.394 | −1.16075 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 34.0810i | 0.0723589i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1175.41 | 2.48500 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 46.5333 | 0.0979649 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 264.142 | 0.553758 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 335.918 | 0.701291 | 0.350646 | − | 0.936508i | \(-0.385962\pi\) | ||||
0.350646 | + | 0.936508i | \(0.385962\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 319.738i | − | 0.664737i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 15.2838 | 0.0316435 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 500.353i | 1.03166i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 235.047i | 0.482642i | 0.970445 | + | 0.241321i | \(0.0775806\pi\) | ||||
−0.970445 | + | 0.241321i | \(0.922419\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −22.4319 | −0.0458730 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −548.826 | −1.11777 | −0.558886 | − | 0.829245i | \(-0.688771\pi\) | ||||
−0.558886 | + | 0.829245i | \(0.688771\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −546.362 | − | 306.379i | −1.10824 | − | 0.621459i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 756.948 | 1.52919 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −763.999 | −1.53722 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 479.046i | 0.960011i | 0.877265 | + | 0.480006i | \(0.159365\pi\) | ||||
−0.877265 | + | 0.480006i | \(0.840635\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 44.0957i | 0.0880154i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 371.364 | 0.738297 | 0.369149 | − | 0.929370i | \(-0.379649\pi\) | ||||
0.369149 | + | 0.929370i | \(0.379649\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 561.013i | 1.11092i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 25.3221 | 0.0499449 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 212.182 | 0.416860 | 0.208430 | − | 0.978037i | \(-0.433165\pi\) | ||||
0.208430 | + | 0.978037i | \(0.433165\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −604.407 | −1.18279 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −29.7978 | −0.0580853 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 102.316i | − | 0.198673i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1015.50 | 1.96422 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.33300 | 0.00834874 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −171.625 | −0.329415 | −0.164707 | − | 0.986342i | \(-0.552668\pi\) | ||||
−0.164707 | + | 0.986342i | \(0.552668\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 889.718i | − | 1.70118i | −0.525829 | − | 0.850591i | \(-0.676245\pi\) | ||
0.525829 | − | 0.850591i | \(-0.323755\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 10.1776i | 0.0193859i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 73.0843i | − | 0.138680i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 434.421 | 0.821211 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 328.987i | − | 0.619562i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 185.968i | 0.348908i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 425.007i | − | 0.794405i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 71.5992i | 0.133332i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −53.9380 | −0.100071 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 336.328i | 0.621679i | 0.950462 | + | 0.310840i | \(0.100610\pi\) | ||||
−0.950462 | + | 0.310840i | \(0.899390\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 66.6729 | 0.122786 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −554.592 | −1.01760 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 360.971i | − | 0.659911i | −0.943997 | − | 0.329955i | \(-0.892966\pi\) | ||
0.943997 | − | 0.329955i | \(-0.107034\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 818.989i | 1.49178i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −101.919 | + | 181.752i | −0.184972 | + | 0.329858i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 393.497i | 0.711568i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 41.2536i | − | 0.0743308i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −440.285 | −0.790458 | −0.395229 | − | 0.918583i | \(-0.629335\pi\) | ||||
−0.395229 | + | 0.918583i | \(0.629335\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 460.888 | 0.824486 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 98.1171i | − | 0.174897i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1029.19 | 1.82804 | 0.914019 | − | 0.405671i | \(-0.132962\pi\) | ||||
0.914019 | + | 0.405671i | \(0.132962\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 806.306i | 1.42709i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 541.111i | 0.954340i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 176.077i | 0.309450i | 0.987958 | + | 0.154725i | \(0.0494492\pi\) | ||||
−0.987958 | + | 0.154725i | \(0.950551\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 367.028i | − | 0.642781i | −0.946947 | − | 0.321391i | \(-0.895850\pi\) | ||
0.946947 | − | 0.321391i | \(-0.104150\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −43.6459 | −0.0761708 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 62.9810i | − | 0.109532i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 777.390i | − | 1.34730i | −0.739053 | − | 0.673648i | \(-0.764726\pi\) | ||
0.739053 | − | 0.673648i | \(-0.235274\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 43.4545i | − | 0.0750510i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 903.840 | 1.55566 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 580.391 | 0.995525 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 296.806 | 0.507361 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 558.784i | 0.951932i | 0.879464 | + | 0.475966i | \(0.157901\pi\) | ||||
−0.879464 | + | 0.475966i | \(0.842099\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.3120 | −0.0412768 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −41.0900 | −0.0695262 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −678.701 | −1.14452 | −0.572261 | − | 0.820072i | \(-0.693933\pi\) | ||||
−0.572261 | + | 0.820072i | \(0.693933\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 632.277 | 1.06265 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 70.2022i | 0.117592i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −142.960 | −0.238664 | −0.119332 | − | 0.992854i | \(-0.538075\pi\) | ||||
−0.119332 | + | 0.992854i | \(0.538075\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 423.145i | − | 0.704068i | −0.935987 | − | 0.352034i | \(-0.885490\pi\) | ||
0.935987 | − | 0.352034i | \(-0.114510\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 716.121i | − | 1.18760i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1142.44 | 1.88833 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 908.045 | 1.49596 | 0.747978 | − | 0.663724i | \(-0.231025\pi\) | ||||
0.747978 | + | 0.663724i | \(0.231025\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −39.7520 | − | 22.2914i | −0.0652741 | − | 0.0366033i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 398.187 | 0.651697 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −372.883 | −0.608292 | −0.304146 | − | 0.952625i | \(-0.598371\pi\) | ||||
−0.304146 | + | 0.952625i | \(0.598371\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 23.9941i | 0.0390148i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 682.584i | 1.10630i | 0.833083 | + | 0.553148i | \(0.186573\pi\) | ||||
−0.833083 | + | 0.553148i | \(0.813427\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −368.152 | −0.594752 | −0.297376 | − | 0.954760i | \(-0.596112\pi\) | ||||
−0.297376 | + | 0.954760i | \(0.596112\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 40.3301i | 0.0649437i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −165.699 | −0.265970 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −421.159 | −0.673854 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −32.6394 | −0.0520564 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 895.988 | 1.42446 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 625.046i | 0.990564i | 0.868732 | + | 0.495282i | \(0.164935\pi\) | ||||
−0.868732 | + | 0.495282i | \(0.835065\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 22.7748 | 0.0359792 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 103.828 | 0.163509 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −21.1496 | −0.0332019 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 1005.00i | − | 1.57277i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 989.562i | − | 1.54378i | −0.635757 | − | 0.771889i | \(-0.719312\pi\) | ||
0.635757 | − | 0.771889i | \(-0.280688\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 405.454i | − | 0.630565i | −0.948998 | − | 0.315283i | \(-0.897901\pi\) | ||
0.948998 | − | 0.315283i | \(-0.102099\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 59.4651 | 0.0921939 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 1045.04i | − | 1.61521i | −0.589722 | − | 0.807606i | \(-0.700763\pi\) | ||
0.589722 | − | 0.807606i | \(-0.299237\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 722.872i | − | 1.11382i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 5.31743i | − | 0.00816809i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 539.784i | 0.826622i | 0.910590 | + | 0.413311i | \(0.135628\pi\) | ||||
−0.910590 | + | 0.413311i | \(0.864372\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −254.430 | −0.388443 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 795.065i | − | 1.21015i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 238.329 | 0.361652 | 0.180826 | − | 0.983515i | \(-0.442123\pi\) | ||||
0.180826 | + | 0.983515i | \(0.442123\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 69.9519 | 0.105827 | 0.0529137 | − | 0.998599i | \(-0.483149\pi\) | ||||
0.0529137 | + | 0.998599i | \(0.483149\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 38.4726i | − | 0.0580281i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 210.332i | − | 0.316288i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 245.993 | + | 137.944i | 0.368806 | + | 0.206812i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 16.8066i | − | 0.0251220i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1799.54i | 2.68187i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −829.767 | −1.23294 | −0.616469 | − | 0.787379i | \(-0.711437\pi\) | ||||
−0.616469 | + | 0.787379i | \(0.711437\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −26.8560 | −0.0397867 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 622.228i | 0.919095i | 0.888153 | + | 0.459548i | \(0.151988\pi\) | ||||
−0.888153 | + | 0.459548i | \(0.848012\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −790.670 | −1.16446 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 15.0216i | − | 0.0220581i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 900.254i | 1.31809i | 0.752105 | + | 0.659044i | \(0.229039\pi\) | ||||
−0.752105 | + | 0.659044i | \(0.770961\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 66.5093i | 0.0970939i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 50.4755i | 0.0734723i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 227.577 | 0.330300 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 574.448i | − | 0.831328i | −0.909518 | − | 0.415664i | \(-0.863549\pi\) | ||
0.909518 | − | 0.415664i | \(-0.136451\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1196.15i | 1.72604i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 199.036i | − | 0.286383i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −521.129 | −0.747675 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −63.9493 | −0.0914868 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −795.987 | −1.13550 | −0.567751 | − | 0.823200i | \(-0.692186\pi\) | ||||
−0.567751 | + | 0.823200i | \(0.692186\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 298.057i | − | 0.423979i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 51.3753 | 0.0728727 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −886.526 | −1.25393 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −360.327 | −0.508219 | −0.254109 | − | 0.967176i | \(-0.581782\pi\) | ||||
−0.254109 | + | 0.967176i | \(0.581782\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −517.625 | −0.728024 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 32.9054i | 0.0461506i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 652.162 | 0.912115 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 63.0360i | − | 0.0879164i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 554.656i | − | 0.771427i | −0.922619 | − | 0.385714i | \(-0.873955\pi\) | ||
0.922619 | − | 0.385714i | \(-0.126045\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 161.683 | 0.224248 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.213667 | 0.000295528 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −91.8576 | + | 163.808i | −0.126700 | + | 0.225943i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −888.134 | −1.22164 | −0.610821 | − | 0.791769i | \(-0.709161\pi\) | ||||
−0.610821 | + | 0.791769i | \(0.709161\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −703.178 | −0.964579 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1291.52i | 1.76679i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 320.351i | 0.437041i | 0.975832 | + | 0.218520i | \(0.0701230\pi\) | ||||
−0.975832 | + | 0.218520i | \(0.929877\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.72878 | −0.00371263 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1573.51i | − | 2.13502i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −889.912 | −1.20421 | −0.602106 | − | 0.798416i | \(-0.705671\pi\) | ||||
−0.602106 | + | 0.798416i | \(0.705671\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12.7982 | −0.0172715 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 81.5000 | 0.109690 | 0.0548452 | − | 0.998495i | \(-0.482533\pi\) | ||||
0.0548452 | + | 0.998495i | \(0.482533\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 691.535 | 0.928235 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1188.95i | 1.59164i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 671.606 | 0.896670 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1059.96 | −1.41140 | −0.705699 | − | 0.708512i | \(-0.749367\pi\) | ||||
−0.705699 | + | 0.708512i | \(0.749367\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −71.4796 | −0.0949264 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 111.296i | 0.147412i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 299.069i | 0.395071i | 0.980296 | + | 0.197536i | \(0.0632938\pi\) | ||||
−0.980296 | + | 0.197536i | \(0.936706\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 44.1761i | 0.0582030i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 67.2911 | 0.0884245 | 0.0442123 | − | 0.999022i | \(-0.485922\pi\) | ||||
0.0442123 | + | 0.999022i | \(0.485922\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 876.378i | − | 1.14860i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 831.726i | 1.08722i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 283.445i | − | 0.369550i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.8673i | 0.0375387i | 0.999824 | + | 0.0187694i | \(0.00597483\pi\) | ||||
−0.999824 | + | 0.0187694i | \(0.994025\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.8636 | 0.0283575 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 365.876i | − | 0.473320i | −0.971593 | − | 0.236660i | \(-0.923947\pi\) | ||
0.971593 | − | 0.236660i | \(-0.0760527\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.9119 | −0.0282734 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 65.1898 | 0.0838994 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 173.358i | 0.222539i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 2208.25i | − | 2.82747i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 58.8213 | − | 104.895i | 0.0751230 | − | 0.133966i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 634.792i | − | 0.808652i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1111.05i | 1.41175i | 0.708336 | + | 0.705875i | \(0.249446\pi\) | ||||
−0.708336 | + | 0.705875i | \(0.750554\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −36.0093 | −0.0456392 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1274.14 | −1.61080 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 705.615i | 0.889804i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 29.3626 | 0.0369341 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 530.802i | − | 0.665999i | −0.942927 | − | 0.333000i | \(-0.891939\pi\) | ||
0.942927 | − | 0.333000i | \(-0.108061\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1115.82i | 1.39652i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 217.968i | − | 0.272120i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 1746.97i | − | 2.17555i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −284.675 | −0.353634 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 62.6091i | 0.0775826i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1027.63i | 1.27025i | 0.772411 | + | 0.635123i | \(0.219050\pi\) | ||||
−0.772411 | + | 0.635123i | \(0.780950\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1073.28i | 1.32340i | 0.749768 | + | 0.661701i | \(0.230165\pi\) | ||||
−0.749768 | + | 0.661701i | \(0.769835\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 90.2548 | 0.111015 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 417.816 | 0.512657 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 429.635 | 0.525869 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 469.020i | 0.572674i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 681.241 | 0.829769 | 0.414885 | − | 0.909874i | \(-0.363822\pi\) | ||||
0.414885 | + | 0.909874i | \(0.363822\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 839.775 | 1.02038 | 0.510192 | − | 0.860061i | \(-0.329575\pi\) | ||||
0.510192 | + | 0.860061i | \(0.329575\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −29.4171 | −0.0356571 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1539.73 | −1.86183 | −0.930915 | − | 0.365237i | \(-0.880988\pi\) | ||||
−0.930915 | + | 0.365237i | \(0.880988\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 591.109i | − | 0.713039i | −0.934288 | − | 0.356519i | \(-0.883963\pi\) | ||
0.934288 | − | 0.356519i | \(-0.116037\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 73.9805 | 0.0890258 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 59.2665i | − | 0.0711483i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 821.324i | − | 0.983622i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 14.0313 | 0.0167638 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −249.139 | −0.296948 | −0.148474 | − | 0.988916i | \(-0.547436\pi\) | ||||
−0.148474 | + | 0.988916i | \(0.547436\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −438.618 | − | 717.562i | −0.521544 | − | 0.853224i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.38810 | −0.0111365 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −471.648 | −0.558163 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1805.31i | 2.13141i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 24.6935i | 0.0290854i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −403.408 | −0.474041 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 832.091i | − | 0.975488i | −0.872987 | − | 0.487744i | \(-0.837820\pi\) | ||
0.872987 | − | 0.487744i | \(-0.162180\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 276.680 | 0.323602 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −548.077 | −0.639530 | −0.319765 | − | 0.947497i | \(-0.603604\pi\) | ||||
−0.319765 | + | 0.947497i | \(0.603604\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 706.412 | 0.822365 | 0.411183 | − | 0.911553i | \(-0.365116\pi\) | ||||
0.411183 | + | 0.911553i | \(0.365116\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −37.9161 | −0.0440372 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 54.8305i | 0.0635348i | 0.999495 | + | 0.0317674i | \(0.0101136\pi\) | ||||
−0.999495 | + | 0.0317674i | \(0.989886\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −80.7062 | −0.0933020 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 41.0301 | 0.0473242 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1137.36 | −1.30881 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 616.987i | − | 0.708367i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 1040.08i | − | 1.19139i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 921.366i | − | 1.05299i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −802.388 | −0.914924 | −0.457462 | − | 0.889229i | \(-0.651241\pi\) | ||||
−0.457462 | + | 0.889229i | \(0.651241\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 18.4502i | − | 0.0209900i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 513.331i | 0.582669i | 0.956621 | + | 0.291334i | \(0.0940992\pi\) | ||||
−0.956621 | + | 0.291334i | \(0.905901\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1548.18i | 1.75332i | 0.481109 | + | 0.876661i | \(0.340234\pi\) | ||||
−0.481109 | + | 0.876661i | \(0.659766\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 36.5709i | − | 0.0413231i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 166.748 | 0.187991 | 0.0939954 | − | 0.995573i | \(-0.470036\pi\) | ||||
0.0939954 | + | 0.995573i | \(0.470036\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 164.071i | 0.184557i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1564.02 | −1.75535 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 371.186 | 0.415662 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1333.60i | − | 1.49006i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17.3219i | 0.0193109i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 47.9924 | − | 85.5842i | 0.0533842 | − | 0.0951993i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 637.728i | 0.707800i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 93.9681i | 0.104062i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1241.85 | −1.37220 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1350.48 | −1.48895 | −0.744476 | − | 0.667649i | \(-0.767301\pi\) | ||||
−0.744476 | + | 0.667649i | \(0.767301\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 1166.18i | − | 1.28292i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 885.235 | 0.971717 | 0.485859 | − | 0.874037i | \(-0.338507\pi\) | ||||
0.485859 | + | 0.874037i | \(0.338507\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2612.45i | 2.86139i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 91.0405i | 0.0994978i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 402.057i | − | 0.438448i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1362.45i | − | 1.48253i | −0.671212 | − | 0.741266i | \(-0.734226\pi\) | ||
0.671212 | − | 0.741266i | \(-0.265774\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 126.751 | 0.137623 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 865.876i | − | 0.938110i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 268.632i | − | 0.290413i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 212.685i | 0.229434i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 473.689 | 0.509891 | 0.254946 | − | 0.966955i | \(-0.417942\pi\) | ||||
0.254946 | + | 0.966955i | \(0.417942\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19.7155 | −0.0211767 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 129.173 | 0.138449 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1827.52i | 1.95457i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1762.54 | 1.88104 | 0.940521 | − | 0.339736i | \(-0.110338\pi\) | ||||
0.940521 | + | 0.339736i | \(0.110338\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.38017 | −0.00785961 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −197.827 | −0.210230 | −0.105115 | − | 0.994460i | \(-0.533521\pi\) | ||||
−0.105115 | + | 0.994460i | \(0.533521\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 234.633 | 0.248815 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 121.390i | 0.128455i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −397.069 | −0.419291 | −0.209646 | − | 0.977777i | \(-0.567231\pi\) | ||||
−0.209646 | + | 0.977777i | \(0.567231\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 685.003i | − | 0.721816i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 71.3356i | − | 0.0750112i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 46.1185 | 0.0483929 | 0.0241965 | − | 0.999707i | \(-0.492297\pi\) | ||||
0.0241965 | + | 0.999707i | \(0.492297\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 812.945 | 0.851252 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 64.4307 | − | 114.899i | 0.0673258 | − | 0.120061i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −105.100 | −0.109593 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −949.552 | −0.988087 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 883.462i | 0.917406i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 809.382i | 0.838738i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1575.16 | −1.62891 | −0.814457 | − | 0.580225i | \(-0.802965\pi\) | ||||
−0.814457 | + | 0.580225i | \(0.802965\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 35.8638i | − | 0.0370112i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 725.761 | 0.747437 | 0.373718 | − | 0.927542i | \(-0.378083\pi\) | ||||
0.373718 | + | 0.927542i | \(0.378083\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 314.522 | 0.323249 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −11.5347 | −0.0118305 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 512.873 | 0.524946 | 0.262473 | − | 0.964939i | \(-0.415462\pi\) | ||||
0.262473 | + | 0.964939i | \(0.415462\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 478.935i | − | 0.489208i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1152.83 | 1.17516 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 766.524 | 0.779780 | 0.389890 | − | 0.920861i | \(-0.372513\pi\) | ||||
0.389890 | + | 0.920861i | \(0.372513\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 765.340 | 0.776995 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 81.1844i | 0.0822537i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 581.494i | − | 0.587962i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 835.945i | 0.843537i | 0.906704 | + | 0.421768i | \(0.138590\pi\) | ||||
−0.906704 | + | 0.421768i | \(0.861410\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 49.5873 | 0.0499369 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 1307.58i | − | 1.31415i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 319.504i | 0.320465i | 0.987079 | + | 0.160233i | \(0.0512244\pi\) | ||||
−0.987079 | + | 0.160233i | \(0.948776\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 172.019i | 0.172192i |
(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 | 464.3.h.c.463.10 | yes | 20 | |
4.3 | odd | 2 | inner | 464.3.h.c.463.11 | yes | 20 | |
29.28 | even | 2 | inner | 464.3.h.c.463.12 | yes | 20 | |
116.115 | odd | 2 | inner | 464.3.h.c.463.9 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
464.3.h.c.463.9 | ✓ | 20 | 116.115 | odd | 2 | inner | |
464.3.h.c.463.10 | yes | 20 | 1.1 | even | 1 | trivial | |
464.3.h.c.463.11 | yes | 20 | 4.3 | odd | 2 | inner | |
464.3.h.c.463.12 | yes | 20 | 29.28 | even | 2 | inner |