Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1350,3,Mod(701,1350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1350, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1350.701");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.d (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: | \(36.7848356886\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 701.2 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1350.701 |
Dual form | 1350.3.d.l.701.4 |
$q$-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 \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1027\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.41421i | − 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.242641 | 0.0346630 | 0.0173315 | − | 0.999850i | \(-0.494483\pi\) | ||||
0.0173315 | + | 0.999850i | \(0.494483\pi\) | |||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.00000i | 0.272727i | 0.990659 | + | 0.136364i | \(0.0435416\pi\) | ||||
−0.990659 | + | 0.136364i | \(0.956458\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.48528 | −0.268099 | −0.134049 | − | 0.990975i | \(-0.542798\pi\) | ||||
−0.134049 | + | 0.990975i | \(0.542798\pi\) | |||||||
\(14\) | − 0.343146i | − 0.0245104i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − 7.75736i | − 0.456315i | −0.973624 | − | 0.228158i | \(-0.926730\pi\) | ||||
0.973624 | − | 0.228158i | \(-0.0732702\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.97056 | −0.472135 | −0.236067 | − | 0.971737i | \(-0.575859\pi\) | ||||
−0.236067 | + | 0.971737i | \(0.575859\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.24264 | 0.192847 | ||||||||
\(23\) | 6.51472i | 0.283249i | 0.989920 | + | 0.141624i | \(0.0452325\pi\) | ||||
−0.989920 | + | 0.141624i | \(0.954768\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.92893i | 0.189574i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.485281 | −0.0173315 | ||||||||
\(29\) | 7.02944i | 0.242394i | 0.992628 | + | 0.121197i | \(0.0386733\pi\) | ||||
−0.992628 | + | 0.121197i | \(0.961327\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 29.2132 | 0.942361 | 0.471181 | − | 0.882037i | \(-0.343828\pi\) | ||||
0.471181 | + | 0.882037i | \(0.343828\pi\) | |||||||
\(32\) | − 5.65685i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −10.9706 | −0.322664 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 36.4558 | 0.985293 | 0.492647 | − | 0.870230i | \(-0.336030\pi\) | ||||
0.492647 | + | 0.870230i | \(0.336030\pi\) | |||||||
\(38\) | 12.6863i | 0.333850i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 57.2132i | 1.39544i | 0.716369 | + | 0.697722i | \(0.245803\pi\) | ||||
−0.716369 | + | 0.697722i | \(0.754197\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.0294 | −0.256499 | −0.128249 | − | 0.991742i | \(-0.540936\pi\) | ||||
−0.128249 | + | 0.991742i | \(0.540936\pi\) | |||||||
\(44\) | − 6.00000i | − 0.136364i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 9.21320 | 0.200287 | ||||||||
\(47\) | − 6.51472i | − 0.138611i | −0.997595 | − | 0.0693055i | \(-0.977922\pi\) | ||||
0.997595 | − | 0.0693055i | \(-0.0220783\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −48.9411 | −0.998798 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.97056 | 0.134049 | ||||||||
\(53\) | 26.9117i | 0.507768i | 0.967235 | + | 0.253884i | \(0.0817081\pi\) | ||||
−0.967235 | + | 0.253884i | \(0.918292\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.686292i | 0.0122552i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.94113 | 0.171399 | ||||||||
\(59\) | 84.9411i | 1.43968i | 0.694140 | + | 0.719840i | \(0.255785\pi\) | ||||
−0.694140 | + | 0.719840i | \(0.744215\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 57.3675 | 0.940451 | 0.470226 | − | 0.882546i | \(-0.344173\pi\) | ||||
0.470226 | + | 0.882546i | \(0.344173\pi\) | |||||||
\(62\) | − 41.3137i | − 0.666350i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 97.0955 | 1.44919 | 0.724593 | − | 0.689177i | \(-0.242028\pi\) | ||||
0.724593 | + | 0.689177i | \(0.242028\pi\) | |||||||
\(68\) | 15.5147i | 0.228158i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 72.5147i | 1.02133i | 0.859779 | + | 0.510667i | \(0.170602\pi\) | ||||
−0.859779 | + | 0.510667i | \(0.829398\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 106.912 | 1.46454 | 0.732272 | − | 0.681012i | \(-0.238460\pi\) | ||||
0.732272 | + | 0.681012i | \(0.238460\pi\) | |||||||
\(74\) | − 51.5563i | − 0.696707i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 17.9411 | 0.236067 | ||||||||
\(77\) | 0.727922i | 0.00945353i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −78.1838 | −0.989668 | −0.494834 | − | 0.868988i | \(-0.664771\pi\) | ||||
−0.494834 | + | 0.868988i | \(0.664771\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 80.9117 | 0.986728 | ||||||||
\(83\) | − 25.8823i | − 0.311834i | −0.987770 | − | 0.155917i | \(-0.950167\pi\) | ||||
0.987770 | − | 0.155917i | \(-0.0498333\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 15.5980i | 0.181372i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.48528 | −0.0964237 | ||||||||
\(89\) | 31.7574i | 0.356824i | 0.983956 | + | 0.178412i | \(0.0570960\pi\) | ||||
−0.983956 | + | 0.178412i | \(0.942904\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.845671 | −0.00929309 | ||||||||
\(92\) | − 13.0294i | − 0.141624i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.21320 | −0.0980128 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 110.765 | 1.14190 | 0.570951 | − | 0.820984i | \(-0.306575\pi\) | ||||
0.570951 | + | 0.820984i | \(0.306575\pi\) | |||||||
\(98\) | 69.2132i | 0.706257i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 75.0366i | − 0.742936i | −0.928446 | − | 0.371468i | \(-0.878854\pi\) | ||||
0.928446 | − | 0.371468i | \(-0.121146\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 61.0955 | 0.593160 | 0.296580 | − | 0.955008i | \(-0.404154\pi\) | ||||
0.296580 | + | 0.955008i | \(0.404154\pi\) | |||||||
\(104\) | − 9.85786i | − 0.0947872i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 38.0589 | 0.359046 | ||||||||
\(107\) | − 33.8528i | − 0.316381i | −0.987409 | − | 0.158191i | \(-0.949434\pi\) | ||||
0.987409 | − | 0.158191i | \(-0.0505661\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.1472 | 0.175662 | 0.0878311 | − | 0.996135i | \(-0.472006\pi\) | ||||
0.0878311 | + | 0.996135i | \(0.472006\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.970563 | 0.00866574 | ||||||||
\(113\) | − 26.7868i | − 0.237051i | −0.992951 | − | 0.118526i | \(-0.962183\pi\) | ||||
0.992951 | − | 0.118526i | \(-0.0378168\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − 14.0589i | − 0.121197i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 120.125 | 1.01801 | ||||||||
\(119\) | − 1.88225i | − 0.0158172i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 112.000 | 0.925620 | ||||||||
\(122\) | − 81.1299i | − 0.665000i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −58.4264 | −0.471181 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 174.919 | 1.37731 | 0.688657 | − | 0.725087i | \(-0.258201\pi\) | ||||
0.688657 | + | 0.725087i | \(0.258201\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 149.735i | 1.14302i | 0.820597 | + | 0.571508i | \(0.193641\pi\) | ||||
−0.820597 | + | 0.571508i | \(0.806359\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.17662 | −0.0163656 | ||||||||
\(134\) | − 137.314i | − 1.02473i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 21.9411 | 0.161332 | ||||||||
\(137\) | 192.853i | 1.40768i | 0.710356 | + | 0.703842i | \(0.248534\pi\) | ||||
−0.710356 | + | 0.703842i | \(0.751466\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −117.095 | −0.842413 | −0.421207 | − | 0.906965i | \(-0.638393\pi\) | ||||
−0.421207 | + | 0.906965i | \(0.638393\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 102.551 | 0.722192 | ||||||||
\(143\) | − 10.4558i | − 0.0731178i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − 151.196i | − 1.03559i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −72.9117 | −0.492647 | ||||||||
\(149\) | 140.007i | 0.939645i | 0.882761 | + | 0.469823i | \(0.155682\pi\) | ||||
−0.882761 | + | 0.469823i | \(0.844318\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 130.912 | 0.866965 | 0.433482 | − | 0.901162i | \(-0.357285\pi\) | ||||
0.433482 | + | 0.901162i | \(0.357285\pi\) | |||||||
\(152\) | − 25.3726i | − 0.166925i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.02944 | 0.00668466 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 153.706 | 0.979017 | 0.489508 | − | 0.871999i | \(-0.337176\pi\) | ||||
0.489508 | + | 0.871999i | \(0.337176\pi\) | |||||||
\(158\) | 110.569i | 0.699801i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.58074i | 0.00981823i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 182.302 | 1.11841 | 0.559207 | − | 0.829028i | \(-0.311106\pi\) | ||||
0.559207 | + | 0.829028i | \(0.311106\pi\) | |||||||
\(164\) | − 114.426i | − 0.697722i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −36.6030 | −0.220500 | ||||||||
\(167\) | 31.7208i | 0.189945i | 0.995480 | + | 0.0949724i | \(0.0302763\pi\) | ||||
−0.995480 | + | 0.0949724i | \(0.969724\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −156.853 | −0.928123 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 22.0589 | 0.128249 | ||||||||
\(173\) | − 331.154i | − 1.91419i | −0.289779 | − | 0.957093i | \(-0.593582\pi\) | ||||
0.289779 | − | 0.957093i | \(-0.406418\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 12.0000i | 0.0681818i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 44.9117 | 0.252313 | ||||||||
\(179\) | 144.088i | 0.804963i | 0.915428 | + | 0.402481i | \(0.131852\pi\) | ||||
−0.915428 | + | 0.402481i | \(0.868148\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −46.6913 | −0.257963 | −0.128982 | − | 0.991647i | \(-0.541171\pi\) | ||||
−0.128982 | + | 0.991647i | \(0.541171\pi\) | |||||||
\(182\) | 1.19596i | 0.00657121i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −18.4264 | −0.100144 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 23.2721 | 0.124450 | ||||||||
\(188\) | 13.0294i | 0.0693055i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 298.441i | − 1.56252i | −0.624208 | − | 0.781258i | \(-0.714578\pi\) | ||||
0.624208 | − | 0.781258i | \(-0.285422\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −66.9117 | −0.346693 | −0.173346 | − | 0.984861i | \(-0.555458\pi\) | ||||
−0.173346 | + | 0.984861i | \(0.555458\pi\) | |||||||
\(194\) | − 156.645i | − 0.807447i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 97.8823 | 0.499399 | ||||||||
\(197\) | 122.059i | 0.619588i | 0.950804 | + | 0.309794i | \(0.100260\pi\) | ||||
−0.950804 | + | 0.309794i | \(0.899740\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 94.7868 | 0.476316 | 0.238158 | − | 0.971226i | \(-0.423456\pi\) | ||||
0.238158 | + | 0.971226i | \(0.423456\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −106.118 | −0.525335 | ||||||||
\(203\) | 1.70563i | 0.00840211i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − 86.4020i | − 0.419427i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −13.9411 | −0.0670246 | ||||||||
\(209\) | − 26.9117i | − 0.128764i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 165.706 | 0.785335 | 0.392667 | − | 0.919681i | \(-0.371552\pi\) | ||||
0.392667 | + | 0.919681i | \(0.371552\pi\) | |||||||
\(212\) | − 53.8234i | − 0.253884i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −47.8751 | −0.223715 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.08831 | 0.0326650 | ||||||||
\(218\) | − 27.0782i | − 0.124212i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 27.0366i | 0.122337i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −200.971 | −0.901213 | −0.450607 | − | 0.892723i | \(-0.648792\pi\) | ||||
−0.450607 | + | 0.892723i | \(0.648792\pi\) | |||||||
\(224\) | − 1.37258i | − 0.00612760i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −37.8823 | −0.167621 | ||||||||
\(227\) | 349.441i | 1.53939i | 0.638414 | + | 0.769693i | \(0.279591\pi\) | ||||
−0.638414 | + | 0.769693i | \(0.720409\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −172.515 | −0.753339 | −0.376670 | − | 0.926348i | \(-0.622931\pi\) | ||||
−0.376670 | + | 0.926348i | \(0.622931\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −19.8823 | −0.0856994 | ||||||||
\(233\) | − 148.243i | − 0.636235i | −0.948051 | − | 0.318117i | \(-0.896949\pi\) | ||||
0.948051 | − | 0.318117i | \(-0.103051\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − 169.882i | − 0.719840i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.66190 | −0.0111845 | ||||||||
\(239\) | 141.603i | 0.592481i | 0.955113 | + | 0.296241i | \(0.0957330\pi\) | ||||
−0.955113 | + | 0.296241i | \(0.904267\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 83.8528 | 0.347937 | 0.173968 | − | 0.984751i | \(-0.444341\pi\) | ||||
0.173968 | + | 0.984751i | \(0.444341\pi\) | |||||||
\(242\) | − 158.392i | − 0.654512i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −114.735 | −0.470226 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 31.2649 | 0.126579 | ||||||||
\(248\) | 82.6274i | 0.333175i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 202.529i | 0.806888i | 0.915004 | + | 0.403444i | \(0.132187\pi\) | ||||
−0.915004 | + | 0.403444i | \(0.867813\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −19.5442 | −0.0772496 | ||||||||
\(254\) | − 247.373i | − 0.973908i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − 39.8894i | − 0.155212i | −0.996984 | − | 0.0776058i | \(-0.975272\pi\) | ||||
0.996984 | − | 0.0776058i | \(-0.0247276\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.84567 | 0.0341532 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 211.757 | 0.808234 | ||||||||
\(263\) | − 295.014i | − 1.12173i | −0.827908 | − | 0.560864i | \(-0.810469\pi\) | ||||
0.827908 | − | 0.560864i | \(-0.189531\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.07821i | 0.0115722i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −194.191 | −0.724593 | ||||||||
\(269\) | 181.706i | 0.675486i | 0.941238 | + | 0.337743i | \(0.109663\pi\) | ||||
−0.941238 | + | 0.337743i | \(0.890337\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −261.823 | −0.966138 | −0.483069 | − | 0.875582i | \(-0.660478\pi\) | ||||
−0.483069 | + | 0.875582i | \(0.660478\pi\) | |||||||
\(272\) | − 31.0294i | − 0.114079i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 272.735 | 0.995383 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −305.882 | −1.10427 | −0.552134 | − | 0.833755i | \(-0.686186\pi\) | ||||
−0.552134 | + | 0.833755i | \(0.686186\pi\) | |||||||
\(278\) | 165.598i | 0.595676i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 558.323i | − 1.98691i | −0.114205 | − | 0.993457i | \(-0.536432\pi\) | ||||
0.114205 | − | 0.993457i | \(-0.463568\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.97056 | −0.0316981 | −0.0158491 | − | 0.999874i | \(-0.505045\pi\) | ||||
−0.0158491 | + | 0.999874i | \(0.505045\pi\) | |||||||
\(284\) | − 145.029i | − 0.510667i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −14.7868 | −0.0517021 | ||||||||
\(287\) | 13.8823i | 0.0483702i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 228.823 | 0.791776 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −213.823 | −0.732272 | ||||||||
\(293\) | 146.683i | 0.500626i | 0.968165 | + | 0.250313i | \(0.0805335\pi\) | ||||
−0.968165 | + | 0.250313i | \(0.919467\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 103.113i | 0.348354i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 198.000 | 0.664430 | ||||||||
\(299\) | − 22.7056i | − 0.0759386i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.67619 | −0.00889100 | ||||||||
\(302\) | − 185.137i | − 0.613037i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −35.8823 | −0.118034 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −343.640 | −1.11935 | −0.559674 | − | 0.828713i | \(-0.689074\pi\) | ||||
−0.559674 | + | 0.828713i | \(0.689074\pi\) | |||||||
\(308\) | − 1.45584i | − 0.00472677i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 512.044i | 1.64644i | 0.567720 | + | 0.823221i | \(0.307825\pi\) | ||||
−0.567720 | + | 0.823221i | \(0.692175\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −68.6173 | −0.219225 | −0.109612 | − | 0.993974i | \(-0.534961\pi\) | ||||
−0.109612 | + | 0.993974i | \(0.534961\pi\) | |||||||
\(314\) | − 217.373i | − 0.692269i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 156.368 | 0.494834 | ||||||||
\(317\) | 516.500i | 1.62934i | 0.579928 | + | 0.814668i | \(0.303081\pi\) | ||||
−0.579928 | + | 0.814668i | \(0.696919\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −21.0883 | −0.0661076 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.23550 | 0.00694254 | ||||||||
\(323\) | 69.5879i | 0.215442i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − 257.813i | − 0.790838i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −161.823 | −0.493364 | ||||||||
\(329\) | − 1.58074i | − 0.00480467i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −265.110 | −0.800936 | −0.400468 | − | 0.916311i | \(-0.631152\pi\) | ||||
−0.400468 | + | 0.916311i | \(0.631152\pi\) | |||||||
\(332\) | 51.7645i | 0.155917i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 44.8600 | 0.134311 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 72.4710 | 0.215047 | 0.107524 | − | 0.994203i | \(-0.465708\pi\) | ||||
0.107524 | + | 0.994203i | \(0.465708\pi\) | |||||||
\(338\) | 221.823i | 0.656282i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 87.6396i | 0.257008i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −23.7645 | −0.0692843 | ||||||||
\(344\) | − 31.1960i | − 0.0906859i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −468.323 | −1.35353 | ||||||||
\(347\) | − 529.706i | − 1.52653i | −0.646086 | − | 0.763265i | \(-0.723595\pi\) | ||||
0.646086 | − | 0.763265i | \(-0.276405\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 337.470 | 0.966963 | 0.483482 | − | 0.875355i | \(-0.339372\pi\) | ||||
0.483482 | + | 0.875355i | \(0.339372\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 16.9706 | 0.0482118 | ||||||||
\(353\) | − 490.087i | − 1.38835i | −0.719806 | − | 0.694175i | \(-0.755769\pi\) | ||||
0.719806 | − | 0.694175i | \(-0.244231\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − 63.5147i | − 0.178412i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 203.772 | 0.569195 | ||||||||
\(359\) | 370.955i | 1.03330i | 0.856196 | + | 0.516651i | \(0.172822\pi\) | ||||
−0.856196 | + | 0.516651i | \(0.827178\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −280.529 | −0.777089 | ||||||||
\(362\) | 66.0315i | 0.182408i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.69134 | 0.00464654 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −393.823 | −1.07309 | −0.536544 | − | 0.843872i | \(-0.680270\pi\) | ||||
−0.536544 | + | 0.843872i | \(0.680270\pi\) | |||||||
\(368\) | 26.0589i | 0.0708122i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.52987i | 0.0176007i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 90.1177 | 0.241603 | 0.120801 | − | 0.992677i | \(-0.461454\pi\) | ||||
0.120801 | + | 0.992677i | \(0.461454\pi\) | |||||||
\(374\) | − 32.9117i | − 0.0879992i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 18.4264 | 0.0490064 | ||||||||
\(377\) | − 24.4996i | − 0.0649856i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 327.051 | 0.862931 | 0.431466 | − | 0.902129i | \(-0.357997\pi\) | ||||
0.431466 | + | 0.902129i | \(0.357997\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −422.059 | −1.10487 | ||||||||
\(383\) | 468.338i | 1.22281i | 0.791316 | + | 0.611407i | \(0.209396\pi\) | ||||
−0.791316 | + | 0.611407i | \(0.790604\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 94.6274i | 0.245149i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −221.529 | −0.570951 | ||||||||
\(389\) | − 80.3818i | − 0.206637i | −0.994648 | − | 0.103319i | \(-0.967054\pi\) | ||||
0.994648 | − | 0.103319i | \(-0.0329461\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 50.5370 | 0.129251 | ||||||||
\(392\) | − 138.426i | − 0.353129i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 172.617 | 0.438115 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −489.632 | −1.23333 | −0.616664 | − | 0.787226i | \(-0.711516\pi\) | ||||
−0.616664 | + | 0.787226i | \(0.711516\pi\) | |||||||
\(398\) | − 134.049i | − 0.336806i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 263.418i | 0.656904i | 0.944521 | + | 0.328452i | \(0.106527\pi\) | ||||
−0.944521 | + | 0.328452i | \(0.893473\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −101.816 | −0.252646 | ||||||||
\(404\) | 150.073i | 0.371468i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.41212 | 0.00594119 | ||||||||
\(407\) | 109.368i | 0.268716i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 170.411 | 0.416653 | 0.208327 | − | 0.978059i | \(-0.433198\pi\) | ||||
0.208327 | + | 0.978059i | \(0.433198\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −122.191 | −0.296580 | ||||||||
\(413\) | 20.6102i | 0.0499036i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 19.7157i | 0.0473936i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −38.0589 | −0.0910499 | ||||||||
\(419\) | 353.647i | 0.844026i | 0.906590 | + | 0.422013i | \(0.138676\pi\) | ||||
−0.906590 | + | 0.422013i | \(0.861324\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −661.749 | −1.57185 | −0.785926 | − | 0.618321i | \(-0.787813\pi\) | ||||
−0.785926 | + | 0.618321i | \(0.787813\pi\) | |||||||
\(422\) | − 234.343i | − 0.555316i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −76.1177 | −0.179523 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.9197 | 0.0325988 | ||||||||
\(428\) | 67.7056i | 0.158191i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 757.544i | 1.75764i | 0.477151 | + | 0.878822i | \(0.341670\pi\) | ||||
−0.477151 | + | 0.878822i | \(0.658330\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −293.294 | −0.677354 | −0.338677 | − | 0.940903i | \(-0.609979\pi\) | ||||
−0.338677 | + | 0.940903i | \(0.609979\pi\) | |||||||
\(434\) | − 10.0244i | − 0.0230977i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −38.2944 | −0.0878311 | ||||||||
\(437\) | − 58.4407i | − 0.133732i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 441.831 | 1.00645 | 0.503224 | − | 0.864156i | \(-0.332147\pi\) | ||||
0.503224 | + | 0.864156i | \(0.332147\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 38.2355 | 0.0865057 | ||||||||
\(443\) | 46.3827i | 0.104701i | 0.998629 | + | 0.0523507i | \(0.0166714\pi\) | ||||
−0.998629 | + | 0.0523507i | \(0.983329\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 284.215i | 0.637254i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.94113 | −0.00433287 | ||||||||
\(449\) | 69.2132i | 0.154150i | 0.997025 | + | 0.0770748i | \(0.0245580\pi\) | ||||
−0.997025 | + | 0.0770748i | \(0.975442\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −171.640 | −0.380576 | ||||||||
\(452\) | 53.5736i | 0.118526i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 494.184 | 1.08851 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −189.382 | −0.414402 | −0.207201 | − | 0.978298i | \(-0.566435\pi\) | ||||
−0.207201 | + | 0.978298i | \(0.566435\pi\) | |||||||
\(458\) | 243.973i | 0.532691i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 615.058i | − 1.33418i | −0.744976 | − | 0.667091i | \(-0.767539\pi\) | ||||
0.744976 | − | 0.667091i | \(-0.232461\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 137.088 | 0.296087 | 0.148044 | − | 0.988981i | \(-0.452702\pi\) | ||||
0.148044 | + | 0.988981i | \(0.452702\pi\) | |||||||
\(464\) | 28.1177i | 0.0605986i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −209.647 | −0.449886 | ||||||||
\(467\) | − 337.118i | − 0.721880i | −0.932589 | − | 0.360940i | \(-0.882456\pi\) | ||||
0.932589 | − | 0.360940i | \(-0.117544\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.5593 | 0.0502331 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −240.250 | −0.509004 | ||||||||
\(473\) | − 33.0883i | − 0.0699541i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.76450i | 0.00790862i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 200.257 | 0.418948 | ||||||||
\(479\) | 227.647i | 0.475254i | 0.971356 | + | 0.237627i | \(0.0763696\pi\) | ||||
−0.971356 | + | 0.237627i | \(0.923630\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −127.059 | −0.264156 | ||||||||
\(482\) | − 118.586i | − 0.246029i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −224.000 | −0.462810 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −640.874 | −1.31596 | −0.657982 | − | 0.753034i | \(-0.728590\pi\) | ||||
−0.657982 | + | 0.753034i | \(0.728590\pi\) | |||||||
\(488\) | 162.260i | 0.332500i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 610.118i | 1.24260i | 0.783572 | + | 0.621301i | \(0.213396\pi\) | ||||
−0.783572 | + | 0.621301i | \(0.786604\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 54.5299 | 0.110608 | ||||||||
\(494\) | − 44.2153i | − 0.0895046i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 116.853 | 0.235590 | ||||||||
\(497\) | 17.5950i | 0.0354025i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 43.2935 | 0.0867605 | 0.0433803 | − | 0.999059i | \(-0.486187\pi\) | ||||
0.0433803 | + | 0.999059i | \(0.486187\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 286.419 | 0.570556 | ||||||||
\(503\) | 303.765i | 0.603906i | 0.953323 | + | 0.301953i | \(0.0976385\pi\) | ||||
−0.953323 | + | 0.301953i | \(0.902362\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 27.6396i | 0.0546237i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −349.838 | −0.688657 | ||||||||
\(509\) | − 40.2426i | − 0.0790622i | −0.999218 | − | 0.0395311i | \(-0.987414\pi\) | ||||
0.999218 | − | 0.0395311i | \(-0.0125864\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 25.9411 | 0.0507654 | ||||||||
\(512\) | − 22.6274i | − 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −56.4121 | −0.109751 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.5442 | 0.0378030 | ||||||||
\(518\) | − 12.5097i | − 0.0241499i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 88.5959i | − 0.170050i | −0.996379 | − | 0.0850248i | \(-0.972903\pi\) | ||||
0.996379 | − | 0.0850248i | \(-0.0270970\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −711.647 | −1.36070 | −0.680351 | − | 0.732887i | \(-0.738172\pi\) | ||||
−0.680351 | + | 0.732887i | \(0.738172\pi\) | |||||||
\(524\) | − 299.470i | − 0.571508i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −417.213 | −0.793181 | ||||||||
\(527\) | − 226.617i | − 0.430014i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 486.558 | 0.919770 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.35325 | 0.00818280 | ||||||||
\(533\) | − 199.404i | − 0.374117i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 274.627i | 0.512365i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 256.971 | 0.477640 | ||||||||
\(539\) | − 146.823i | − 0.272400i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 197.426 | 0.364929 | 0.182464 | − | 0.983212i | \(-0.441593\pi\) | ||||
0.182464 | + | 0.983212i | \(0.441593\pi\) | |||||||
\(542\) | 370.274i | 0.683163i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −43.8823 | −0.0806659 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −453.470 | −0.829013 | −0.414507 | − | 0.910046i | \(-0.636046\pi\) | ||||
−0.414507 | + | 0.910046i | \(0.636046\pi\) | |||||||
\(548\) | − 385.706i | − 0.703842i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 63.0580i | − 0.114443i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −18.9706 | −0.0343048 | ||||||||
\(554\) | 432.583i | 0.780835i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 234.191 | 0.421207 | ||||||||
\(557\) | 156.978i | 0.281827i | 0.990022 | + | 0.140914i | \(0.0450040\pi\) | ||||
−0.990022 | + | 0.140914i | \(0.954996\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 38.4407 | 0.0687669 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −789.588 | −1.40496 | ||||||||
\(563\) | 699.323i | 1.24214i | 0.783756 | + | 0.621068i | \(0.213301\pi\) | ||||
−0.783756 | + | 0.621068i | \(0.786699\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 12.6863i | 0.0224139i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −205.103 | −0.361096 | ||||||||
\(569\) | − 792.978i | − 1.39363i | −0.717249 | − | 0.696817i | \(-0.754599\pi\) | ||||
0.717249 | − | 0.696817i | \(-0.245401\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −327.418 | −0.573412 | −0.286706 | − | 0.958019i | \(-0.592560\pi\) | ||||
−0.286706 | + | 0.958019i | \(0.592560\pi\) | |||||||
\(572\) | 20.9117i | 0.0365589i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 19.6325 | 0.0342029 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −844.088 | −1.46289 | −0.731446 | − | 0.681900i | \(-0.761154\pi\) | ||||
−0.731446 | + | 0.681900i | \(0.761154\pi\) | |||||||
\(578\) | − 323.605i | − 0.559870i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 6.28009i | − 0.0108091i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −80.7351 | −0.138482 | ||||||||
\(584\) | 302.392i | 0.517794i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 207.442 | 0.353996 | ||||||||
\(587\) | − 304.471i | − 0.518690i | −0.965785 | − | 0.259345i | \(-0.916493\pi\) | ||||
0.965785 | − | 0.259345i | \(-0.0835067\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −262.059 | −0.444922 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 145.823 | 0.246323 | ||||||||
\(593\) | 403.882i | 0.681083i | 0.940229 | + | 0.340542i | \(0.110610\pi\) | ||||
−0.940229 | + | 0.340542i | \(0.889390\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − 280.014i | − 0.469823i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −32.1106 | −0.0536967 | ||||||||
\(599\) | 133.176i | 0.222330i | 0.993802 | + | 0.111165i | \(0.0354582\pi\) | ||||
−0.993802 | + | 0.111165i | \(0.964542\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −263.294 | −0.438094 | −0.219047 | − | 0.975714i | \(-0.570295\pi\) | ||||
−0.219047 | + | 0.975714i | \(0.570295\pi\) | |||||||
\(602\) | 3.78470i | 0.00628688i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −261.823 | −0.433482 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 613.449 | 1.01062 | 0.505312 | − | 0.862937i | \(-0.331377\pi\) | ||||
0.505312 | + | 0.862937i | \(0.331377\pi\) | |||||||
\(608\) | 50.7452i | 0.0834624i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 22.7056i | 0.0371614i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −712.838 | −1.16287 | −0.581434 | − | 0.813594i | \(-0.697508\pi\) | ||||
−0.581434 | + | 0.813594i | \(0.697508\pi\) | |||||||
\(614\) | 485.980i | 0.791498i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.05887 | −0.00334233 | ||||||||
\(617\) | 192.728i | 0.312363i | 0.987728 | + | 0.156181i | \(0.0499185\pi\) | ||||
−0.987728 | + | 0.156181i | \(0.950082\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −660.403 | −1.06689 | −0.533444 | − | 0.845836i | \(-0.679102\pi\) | ||||
−0.533444 | + | 0.845836i | \(0.679102\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 724.139 | 1.16421 | ||||||||
\(623\) | 7.70563i | 0.0123686i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 97.0395i | 0.155015i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −307.411 | −0.489508 | ||||||||
\(629\) | − 282.801i | − 0.449604i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −128.971 | −0.204391 | −0.102195 | − | 0.994764i | \(-0.532587\pi\) | ||||
−0.102195 | + | 0.994764i | \(0.532587\pi\) | |||||||
\(632\) | − 221.137i | − 0.349900i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 730.441 | 1.15211 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 170.574 | 0.267776 | ||||||||
\(638\) | 29.8234i | 0.0467451i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 526.773i | − 0.821798i | −0.911681 | − | 0.410899i | \(-0.865215\pi\) | ||||
0.911681 | − | 0.410899i | \(-0.134785\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 558.169 | 0.868071 | 0.434035 | − | 0.900896i | \(-0.357089\pi\) | ||||
0.434035 | + | 0.900896i | \(0.357089\pi\) | |||||||
\(644\) | − 3.16147i | − 0.00490912i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 98.4121 | 0.152341 | ||||||||
\(647\) | − 990.131i | − 1.53034i | −0.643827 | − | 0.765171i | \(-0.722654\pi\) | ||||
0.643827 | − | 0.765171i | \(-0.277346\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −254.823 | −0.392640 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −364.603 | −0.559207 | ||||||||
\(653\) | − 832.139i | − 1.27433i | −0.770726 | − | 0.637166i | \(-0.780106\pi\) | ||||
0.770726 | − | 0.637166i | \(-0.219894\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 228.853i | 0.348861i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.23550 | −0.00339741 | ||||||||
\(659\) | − 239.793i | − 0.363874i | −0.983310 | − | 0.181937i | \(-0.941763\pi\) | ||||
0.983310 | − | 0.181937i | \(-0.0582367\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1053.01 | 1.59306 | 0.796531 | − | 0.604597i | \(-0.206666\pi\) | ||||
0.796531 | + | 0.604597i | \(0.206666\pi\) | |||||||
\(662\) | 374.922i | 0.566347i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 73.2061 | 0.110250 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −45.7948 | −0.0686579 | ||||||||
\(668\) | − 63.4416i | − 0.0949724i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 172.103i | 0.256487i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 721.912 | 1.07268 | 0.536339 | − | 0.844003i | \(-0.319807\pi\) | ||||
0.536339 | + | 0.844003i | \(0.319807\pi\) | |||||||
\(674\) | − 102.489i | − 0.152062i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 313.706 | 0.464062 | ||||||||
\(677\) | 538.419i | 0.795302i | 0.917537 | + | 0.397651i | \(0.130174\pi\) | ||||
−0.917537 | + | 0.397651i | \(0.869826\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 26.8760 | 0.0395817 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 123.941 | 0.181732 | ||||||||
\(683\) | 335.412i | 0.491087i | 0.969386 | + | 0.245543i | \(0.0789663\pi\) | ||||
−0.969386 | + | 0.245543i | \(0.921034\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 33.6081i | 0.0489914i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −44.1177 | −0.0641246 | ||||||||
\(689\) | − 93.7948i | − 0.136132i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 225.477 | 0.326306 | 0.163153 | − | 0.986601i | \(-0.447834\pi\) | ||||
0.163153 | + | 0.986601i | \(0.447834\pi\) | |||||||
\(692\) | 662.309i | 0.957093i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −749.117 | −1.07942 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 443.823 | 0.636762 | ||||||||
\(698\) | − 477.255i | − 0.683746i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 709.684i | − 1.01239i | −0.862420 | − | 0.506194i | \(-0.831052\pi\) | ||||
0.862420 | − | 0.506194i | \(-0.168948\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −327.029 | −0.465191 | ||||||||
\(704\) | − 24.0000i | − 0.0340909i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −693.088 | −0.981711 | ||||||||
\(707\) | − 18.2069i | − 0.0257524i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 663.867 | 0.936343 | 0.468171 | − | 0.883638i | \(-0.344913\pi\) | ||||
0.468171 | + | 0.883638i | \(0.344913\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −89.8234 | −0.126156 | ||||||||
\(713\) | 190.316i | 0.266923i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − 288.177i | − 0.402481i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 524.610 | 0.730655 | ||||||||
\(719\) | − 402.161i | − 0.559334i | −0.960097 | − | 0.279667i | \(-0.909776\pi\) | ||||
0.960097 | − | 0.279667i | \(-0.0902241\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.8242 | 0.0205607 | ||||||||
\(722\) | 396.728i | 0.549485i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 93.3827 | 0.128982 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 643.294 | 0.884860 | 0.442430 | − | 0.896803i | \(-0.354116\pi\) | ||||
0.442430 | + | 0.896803i | \(0.354116\pi\) | |||||||
\(728\) | − 2.39192i | − 0.00328560i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 85.5593i | 0.117044i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 159.191 | 0.217177 | 0.108589 | − | 0.994087i | \(-0.465367\pi\) | ||||
0.108589 | + | 0.994087i | \(0.465367\pi\) | |||||||
\(734\) | 556.950i | 0.758788i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 36.8528 | 0.0500718 | ||||||||
\(737\) | 291.286i | 0.395233i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 115.272 | 0.155984 | 0.0779919 | − | 0.996954i | \(-0.475149\pi\) | ||||
0.0779919 | + | 0.996954i | \(0.475149\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.23463 | 0.0124456 | ||||||||
\(743\) | − 93.0732i | − 0.125267i | −0.998037 | − | 0.0626334i | \(-0.980050\pi\) | ||||
0.998037 | − | 0.0626334i | \(-0.0199499\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − 127.446i | − 0.170839i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −46.5442 | −0.0622248 | ||||||||
\(749\) | − 8.21407i | − 0.0109667i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 109.823 | 0.146236 | 0.0731181 | − | 0.997323i | \(-0.476705\pi\) | ||||
0.0731181 | + | 0.997323i | \(0.476705\pi\) | |||||||
\(752\) | − 26.0589i | − 0.0346528i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −34.6476 | −0.0459518 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 305.573 | 0.403663 | 0.201831 | − | 0.979420i | \(-0.435311\pi\) | ||||
0.201831 | + | 0.979420i | \(0.435311\pi\) | |||||||
\(758\) | − 462.520i | − 0.610184i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 1323.79i | − 1.73953i | −0.493462 | − | 0.869767i | \(-0.664269\pi\) | ||||
0.493462 | − | 0.869767i | \(-0.335731\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.64589 | 0.00608897 | ||||||||
\(764\) | 596.881i | 0.781258i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 662.330 | 0.864661 | ||||||||
\(767\) | − 296.044i | − 0.385976i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1383.79 | −1.79947 | −0.899735 | − | 0.436436i | \(-0.856241\pi\) | ||||
−0.899735 | + | 0.436436i | \(0.856241\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 133.823 | 0.173346 | ||||||||
\(773\) | − 1058.56i | − 1.36942i | −0.728818 | − | 0.684708i | \(-0.759930\pi\) | ||||
0.728818 | − | 0.684708i | \(-0.240070\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 313.289i | 0.403723i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −113.677 | −0.146114 | ||||||||
\(779\) | − 513.235i | − 0.658838i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −217.544 | −0.278546 | ||||||||
\(782\) | − 71.4701i | − 0.0913940i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −195.765 | −0.249700 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1092.76 | 1.38852 | 0.694259 | − | 0.719725i | \(-0.255732\pi\) | ||||
0.694259 | + | 0.719725i | \(0.255732\pi\) | |||||||
\(788\) | − 244.118i | − 0.309794i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 6.49957i | − 0.00821690i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −199.942 | −0.252134 | ||||||||
\(794\) | 692.444i | 0.872095i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −189.574 | −0.238158 | ||||||||
\(797\) | 464.029i | 0.582219i | 0.956690 | + | 0.291110i | \(0.0940244\pi\) | ||||
−0.956690 | + | 0.291110i | \(0.905976\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −50.5370 | −0.0632503 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 372.530 | 0.464501 | ||||||||
\(803\) | 320.735i | 0.399421i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 143.990i | 0.178648i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 212.235 | 0.262668 | ||||||||
\(809\) | − 1324.26i | − 1.63691i | −0.574567 | − | 0.818457i | \(-0.694830\pi\) | ||||
0.574567 | − | 0.818457i | \(-0.305170\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 527.433 | 0.650349 | 0.325174 | − | 0.945654i | \(-0.394577\pi\) | ||||
0.325174 | + | 0.945654i | \(0.394577\pi\) | |||||||
\(812\) | − 3.41125i | − 0.00420105i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 154.669 | 0.190011 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 98.9403 | 0.121102 | ||||||||
\(818\) | − 240.998i | − 0.294618i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 718.169i | − 0.874750i | −0.899279 | − | 0.437375i | \(-0.855908\pi\) | ||||
0.899279 | − | 0.437375i | \(-0.144092\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 864.617 | 1.05057 | 0.525284 | − | 0.850927i | \(-0.323959\pi\) | ||||
0.525284 | + | 0.850927i | \(0.323959\pi\) | |||||||
\(824\) | 172.804i | 0.209714i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 29.1472 | 0.0352872 | ||||||||
\(827\) | 555.323i | 0.671491i | 0.941953 | + | 0.335745i | \(0.108988\pi\) | ||||
−0.941953 | + | 0.335745i | \(0.891012\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −347.721 | −0.419446 | −0.209723 | − | 0.977761i | \(-0.567256\pi\) | ||||
−0.209723 | + | 0.977761i | \(0.567256\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 27.8823 | 0.0335123 | ||||||||
\(833\) | 379.654i | 0.455767i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 53.8234i | 0.0643820i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 500.132 | 0.596816 | ||||||||
\(839\) | − 529.721i | − 0.631372i | −0.948864 | − | 0.315686i | \(-0.897765\pi\) | ||||
0.948864 | − | 0.315686i | \(-0.102235\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 791.587 | 0.941245 | ||||||||
\(842\) | 935.855i | 1.11147i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −331.411 | −0.392667 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27.1758 | 0.0320847 | ||||||||
\(848\) | 107.647i | 0.126942i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 237.500i | 0.279083i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 917.043 | 1.07508 | 0.537540 | − | 0.843238i | \(-0.319354\pi\) | ||||
0.537540 | + | 0.843238i | \(0.319354\pi\) | |||||||
\(854\) | − 19.6854i | − 0.0230508i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 95.7502 | 0.111858 | ||||||||
\(857\) | − 287.294i | − 0.335232i | −0.985852 | − | 0.167616i | \(-0.946393\pi\) | ||||
0.985852 | − | 0.167616i | \(-0.0536068\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 82.5584 | 0.0961099 | 0.0480550 | − | 0.998845i | \(-0.484698\pi\) | ||||
0.0480550 | + | 0.998845i | \(0.484698\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1071.33 | 1.24284 | ||||||||
\(863\) | 1214.56i | 1.40737i | 0.710513 | + | 0.703684i | \(0.248463\pi\) | ||||
−0.710513 | + | 0.703684i | \(0.751537\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 414.781i | 0.478962i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −14.1766 | −0.0163325 | ||||||||
\(869\) | − 234.551i | − 0.269909i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −338.405 | −0.388525 | ||||||||
\(872\) | 54.1564i | 0.0621060i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −82.6476 | −0.0945625 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1489.63 | 1.69855 | 0.849277 | − | 0.527948i | \(-0.177038\pi\) | ||||
0.849277 | + | 0.527948i | \(0.177038\pi\) | |||||||
\(878\) | − 624.843i | − 0.711666i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 1438.94i | − 1.63330i | −0.577131 | − | 0.816652i | \(-0.695828\pi\) | ||||
0.577131 | − | 0.816652i | \(-0.304172\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 684.139 | 0.774790 | 0.387395 | − | 0.921914i | \(-0.373375\pi\) | ||||
0.387395 | + | 0.921914i | \(0.373375\pi\) | |||||||
\(884\) | − 54.0732i | − 0.0611687i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 65.5950 | 0.0740350 | ||||||||
\(887\) | − 1005.57i | − 1.13368i | −0.823828 | − | 0.566839i | \(-0.808166\pi\) | ||||
0.823828 | − | 0.566839i | \(-0.191834\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 42.4424 | 0.0477418 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 401.941 | 0.450607 | ||||||||
\(893\) | 58.4407i | 0.0654431i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.74517i | 0.00306380i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 97.8823 | 0.109000 | ||||||||
\(899\) | 205.352i | 0.228423i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 208.764 | 0.231702 | ||||||||
\(902\) | 242.735i | 0.269108i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 75.7645 | 0.0838103 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −73.4416 | −0.0809720 | −0.0404860 | − | 0.999180i | \(-0.512891\pi\) | ||||
−0.0404860 | + | 0.999180i | \(0.512891\pi\) | |||||||
\(908\) | − 698.881i | − 0.769693i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1557.69i | 1.70987i | 0.518738 | + | 0.854933i | \(0.326402\pi\) | ||||
−0.518738 | + | 0.854933i | \(0.673598\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 77.6468 | 0.0850457 | ||||||||
\(914\) | 267.826i | 0.293027i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 345.029 | 0.376670 | ||||||||
\(917\) | 36.3318i | 0.0396203i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −635.322 | −0.691319 | −0.345659 | − | 0.938360i | \(-0.612345\pi\) | ||||
−0.345659 | + | 0.938360i | \(0.612345\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −869.823 | −0.943409 | ||||||||
\(923\) | − 252.734i | − 0.273818i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − 193.872i | − 0.209365i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 39.7645 | 0.0428497 | ||||||||
\(929\) | − 1051.26i | − 1.13160i | −0.824542 | − | 0.565801i | \(-0.808567\pi\) | ||||
0.824542 | − | 0.565801i | \(-0.191433\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 439.029 | 0.471568 | ||||||||
\(932\) | 296.485i | 0.318117i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −476.756 | −0.510446 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 782.381 | 0.834985 | 0.417493 | − | 0.908680i | \(-0.362909\pi\) | ||||
0.417493 | + | 0.908680i | \(0.362909\pi\) | |||||||
\(938\) | − 33.3179i | − 0.0355201i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 1085.14i | − 1.15318i | −0.817035 | − | 0.576588i | \(-0.804384\pi\) | ||||
0.817035 | − | 0.576588i | \(-0.195616\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −372.728 | −0.395258 | ||||||||
\(944\) | 339.765i | 0.359920i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −46.7939 | −0.0494651 | ||||||||
\(947\) | − 1358.56i | − 1.43459i | −0.696769 | − | 0.717296i | \(-0.745380\pi\) | ||||
0.696769 | − | 0.717296i | \(-0.254620\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −372.617 | −0.392642 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.32381 | 0.00559224 | ||||||||
\(953\) | − 790.648i | − 0.829641i | −0.909903 | − | 0.414820i | \(-0.863844\pi\) | ||||
0.909903 | − | 0.414820i | \(-0.136156\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − 283.206i | − 0.296241i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 321.941 | 0.336055 | ||||||||
\(959\) | 46.7939i | 0.0487945i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −107.589 | −0.111955 | ||||||||
\(962\) | 179.688i | 0.186786i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −167.706 | −0.173968 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1062.23 | 1.09848 | 0.549242 | − | 0.835663i | \(-0.314917\pi\) | ||||
0.549242 | + | 0.835663i | \(0.314917\pi\) | |||||||
\(968\) | 316.784i | 0.327256i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 194.500i | 0.200309i | 0.994972 | + | 0.100155i | \(0.0319338\pi\) | ||||
−0.994972 | + | 0.100155i | \(0.968066\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −28.4121 | −0.0292005 | ||||||||
\(974\) | 906.333i | 0.930527i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 229.470 | 0.235113 | ||||||||
\(977\) | 715.882i | 0.732735i | 0.930470 | + | 0.366368i | \(0.119399\pi\) | ||||
−0.930470 | + | 0.366368i | \(0.880601\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −95.2721 | −0.0973157 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 862.837 | 0.878653 | ||||||||
\(983\) | 1679.98i | 1.70904i | 0.519420 | + | 0.854519i | \(0.326148\pi\) | ||||
−0.519420 | + | 0.854519i | \(0.673852\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − 77.1169i | − 0.0782118i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −62.5299 | −0.0632893 | ||||||||
\(989\) | − 71.8537i | − 0.0726529i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 655.294 | 0.661245 | 0.330622 | − | 0.943763i | \(-0.392741\pi\) | ||||
0.330622 | + | 0.943763i | \(0.392741\pi\) | |||||||
\(992\) | − 165.255i | − 0.166588i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 24.8831 | 0.0250333 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1169.57 | 1.17309 | 0.586546 | − | 0.809916i | \(-0.300487\pi\) | ||||
0.586546 | + | 0.809916i | \(0.300487\pi\) | |||||||
\(998\) | − 61.2263i | − 0.0613490i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1350.3.d.l.701.2 | ✓ | 4 | |
3.2 | odd | 2 | inner | 1350.3.d.l.701.4 | yes | 4 | |
5.2 | odd | 4 | 1350.3.b.f.1349.4 | 4 | |||
5.3 | odd | 4 | 1350.3.b.a.1349.1 | 4 | |||
5.4 | even | 2 | 1350.3.d.n.701.3 | yes | 4 | ||
15.2 | even | 4 | 1350.3.b.a.1349.2 | 4 | |||
15.8 | even | 4 | 1350.3.b.f.1349.3 | 4 | |||
15.14 | odd | 2 | 1350.3.d.n.701.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1350.3.b.a.1349.1 | 4 | 5.3 | odd | 4 | |||
1350.3.b.a.1349.2 | 4 | 15.2 | even | 4 | |||
1350.3.b.f.1349.3 | 4 | 15.8 | even | 4 | |||
1350.3.b.f.1349.4 | 4 | 5.2 | odd | 4 | |||
1350.3.d.l.701.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1350.3.d.l.701.4 | yes | 4 | 3.2 | odd | 2 | inner | |
1350.3.d.n.701.1 | yes | 4 | 15.14 | odd | 2 | ||
1350.3.d.n.701.3 | yes | 4 | 5.4 | even | 2 |