Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,6,Mod(161,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("320.161");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.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: | \(51.3228223402\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 343 x^{10} - 696 x^{9} + 44406 x^{8} + 179640 x^{7} - 2401691 x^{6} - 15554592 x^{5} + \cdots + 653157349 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{30} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.1 | ||
Root | \(10.0457 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.161 |
Dual form | 320.6.d.d.161.12 |
$q$-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 \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 30.0196i | − 1.92576i | −0.269928 | − | 0.962880i | \(-0.587000\pi\) | ||||
0.269928 | − | 0.962880i | \(-0.413000\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 25.0000i | − 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −45.4594 | −0.350654 | −0.175327 | − | 0.984510i | \(-0.556098\pi\) | ||||
−0.175327 | + | 0.984510i | \(0.556098\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −658.179 | −2.70855 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 142.717i | − 0.355625i | −0.984064 | − | 0.177813i | \(-0.943098\pi\) | ||||
0.984064 | − | 0.177813i | \(-0.0569021\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 897.074i | 1.47221i | 0.676867 | + | 0.736105i | \(0.263337\pi\) | ||||
−0.676867 | + | 0.736105i | \(0.736663\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −750.491 | −0.861226 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 11.4886 | 0.00964148 | 0.00482074 | − | 0.999988i | \(-0.498466\pi\) | ||||
0.00482074 | + | 0.999988i | \(0.498466\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1818.86i | 1.15588i | 0.816078 | + | 0.577942i | \(0.196144\pi\) | ||||
−0.816078 | + | 0.577942i | \(0.803856\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1364.67i | 0.675275i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3875.05 | 1.52742 | 0.763708 | − | 0.645562i | \(-0.223377\pi\) | ||||
0.763708 | + | 0.645562i | \(0.223377\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −625.000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 12463.5i | 3.29027i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 3463.55i | − 0.764763i | −0.924004 | − | 0.382382i | \(-0.875104\pi\) | ||||
0.924004 | − | 0.382382i | \(-0.124896\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1550.37 | 0.289755 | 0.144877 | − | 0.989450i | \(-0.453721\pi\) | ||||
0.144877 | + | 0.989450i | \(0.453721\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4284.30 | −0.684849 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1136.48i | 0.156817i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9610.99i | 1.15415i | 0.816690 | + | 0.577077i | \(0.195807\pi\) | ||||
−0.816690 | + | 0.577077i | \(0.804193\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 26929.8 | 2.83513 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −14807.5 | −1.37569 | −0.687847 | − | 0.725856i | \(-0.741444\pi\) | ||||
−0.687847 | + | 0.725856i | \(0.741444\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6324.64i | 0.521632i | 0.965388 | + | 0.260816i | \(0.0839916\pi\) | ||||
−0.965388 | + | 0.260816i | \(0.916008\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 16454.5i | 1.21130i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −29003.7 | −1.91517 | −0.957587 | − | 0.288145i | \(-0.906962\pi\) | ||||
−0.957587 | + | 0.288145i | \(0.906962\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −14740.4 | −0.877042 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 344.883i | − 0.0185672i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 32583.1i | − 1.59332i | −0.604429 | − | 0.796659i | \(-0.706599\pi\) | ||||
0.604429 | − | 0.796659i | \(-0.293401\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3567.91 | −0.159040 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 54601.4 | 2.22596 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 652.257i | 0.0243943i | 0.999926 | + | 0.0121972i | \(0.00388257\pi\) | ||||
−0.999926 | + | 0.0121972i | \(0.996117\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4715.33i | 0.162251i | 0.996704 | + | 0.0811255i | \(0.0258515\pi\) | ||||
−0.996704 | + | 0.0811255i | \(0.974149\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 29920.4 | 0.949765 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 22426.9 | 0.658393 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 46314.1i | 1.26045i | 0.776411 | + | 0.630226i | \(0.217038\pi\) | ||||
−0.776411 | + | 0.630226i | \(0.782962\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 116327.i | − 2.94144i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 52668.5 | 1.23995 | 0.619976 | − | 0.784621i | \(-0.287142\pi\) | ||||
0.619976 | + | 0.784621i | \(0.287142\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 69352.8 | 1.52320 | 0.761600 | − | 0.648048i | \(-0.224414\pi\) | ||||
0.761600 | + | 0.648048i | \(0.224414\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 18762.3i | 0.385152i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6487.80i | 0.124701i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −33288.8 | −0.600109 | −0.300054 | − | 0.953922i | \(-0.597005\pi\) | ||||
−0.300054 | + | 0.953922i | \(0.597005\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 214213. | 3.62771 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 55352.9i | − 0.881953i | −0.897519 | − | 0.440976i | \(-0.854632\pi\) | ||||
0.897519 | − | 0.440976i | \(-0.145368\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 287.214i | − 0.00431180i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −103975. | −1.47275 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 33235.3 | 0.444758 | 0.222379 | − | 0.974960i | \(-0.428618\pi\) | ||||
0.222379 | + | 0.974960i | \(0.428618\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 40780.4i | − 0.516236i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 46541.5i | − 0.557998i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 45471.4 | 0.516927 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −82468.3 | −0.889934 | −0.444967 | − | 0.895547i | \(-0.646785\pi\) | ||||
−0.444967 | + | 0.895547i | \(0.646785\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 93933.0i | 0.963231i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 36413.2i | 0.355185i | 0.984104 | + | 0.177593i | \(0.0568310\pi\) | ||||
−0.984104 | + | 0.177593i | \(0.943169\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −83074.5 | −0.771569 | −0.385785 | − | 0.922589i | \(-0.626069\pi\) | ||||
−0.385785 | + | 0.922589i | \(0.626069\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 34116.8 | 0.301992 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 30476.7i | 0.257340i | 0.991687 | + | 0.128670i | \(0.0410709\pi\) | ||||
−0.991687 | + | 0.128670i | \(0.958929\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 200282.i | 1.61464i | 0.590117 | + | 0.807318i | \(0.299082\pi\) | ||||
−0.590117 | + | 0.807318i | \(0.700918\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 288519. | 2.22263 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −24491.9 | −0.180437 | −0.0902186 | − | 0.995922i | \(-0.528757\pi\) | ||||
−0.0902186 | + | 0.995922i | \(0.528757\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 96876.1i | − 0.683081i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 590435.i | − 3.98756i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −522.263 | −0.00338082 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 140683. | 0.873531 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 444515.i | 2.64926i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 15625.0i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 133675. | 0.735431 | 0.367716 | − | 0.929938i | \(-0.380140\pi\) | ||||
0.367716 | + | 0.929938i | \(0.380140\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 189863. | 1.00454 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 227954.i | 1.16057i | 0.814415 | + | 0.580283i | \(0.197058\pi\) | ||||
−0.814415 | + | 0.580283i | \(0.802942\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 82684.1i | − 0.405315i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 311588. | 1.47145 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −354970. | −1.61581 | −0.807905 | − | 0.589313i | \(-0.799398\pi\) | ||||
−0.807905 | + | 0.589313i | \(0.799398\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 414105.i | 1.81792i | 0.416887 | + | 0.908958i | \(0.363121\pi\) | ||||
−0.416887 | + | 0.908958i | \(0.636879\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 870679.i | 3.68817i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 128027. | 0.523555 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −86588.9 | −0.342013 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 442503.i | 1.68897i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 233661.i | − 0.862224i | −0.902298 | − | 0.431112i | \(-0.858121\pi\) | ||||
0.902298 | − | 0.431112i | \(-0.141879\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 408202. | 1.45691 | 0.728455 | − | 0.685094i | \(-0.240239\pi\) | ||||
0.728455 | + | 0.685094i | \(0.240239\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7561.53 | −0.0261145 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 38759.2i | − 0.129582i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 342377.i | − 1.10855i | −0.832334 | − | 0.554275i | \(-0.812996\pi\) | ||||
0.832334 | − | 0.554275i | \(-0.187004\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −978132. | −3.06835 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −176157. | −0.535594 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 374906.i | − 1.10523i | −0.833436 | − | 0.552616i | \(-0.813630\pi\) | ||||
0.833436 | − | 0.552616i | \(-0.186370\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 107107.i | 0.306274i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −75465.0 | −0.209389 | −0.104695 | − | 0.994504i | \(-0.533387\pi\) | ||||
−0.104695 | + | 0.994504i | \(0.533387\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −433449. | −1.16740 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 1.19713e6i | − 3.13078i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 372218.i | 0.945545i | 0.881185 | + | 0.472772i | \(0.156747\pi\) | ||||
−0.881185 | + | 0.472772i | \(0.843253\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 28412.1 | 0.0701307 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 19580.5 | 0.0469776 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 235406.i | 0.549141i | 0.961567 | + | 0.274571i | \(0.0885357\pi\) | ||||
−0.961567 | + | 0.274571i | \(0.911464\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 625543.i | 1.41926i | 0.704577 | + | 0.709628i | \(0.251137\pi\) | ||||
−0.704577 | + | 0.709628i | \(0.748863\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 141553. | 0.312457 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 240275. | 0.516154 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 1639.61i | − 0.00342875i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 566584.i | − 1.15374i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 51939.4 | 0.103018 | 0.0515090 | − | 0.998673i | \(-0.483597\pi\) | ||||
0.0515090 | + | 0.998673i | \(0.483597\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −355320. | −0.686635 | −0.343318 | − | 0.939219i | \(-0.611551\pi\) | ||||
−0.343318 | + | 0.939219i | \(0.611551\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 673246.i | − 1.26791i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 125802.i | − 0.230953i | −0.993310 | − | 0.115476i | \(-0.963161\pi\) | ||||
0.993310 | − | 0.115476i | \(-0.0368394\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 593616. | 1.06261 | 0.531304 | − | 0.847181i | \(-0.321702\pi\) | ||||
0.531304 | + | 0.847181i | \(0.321702\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.39033e6 | 2.42733 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 157451.i | 0.268167i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 370187.i | 0.615229i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.55047e6 | −4.13709 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 259581. | 0.411062 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 316256.i | 0.489027i | 0.969646 | + | 0.244513i | \(0.0786282\pi\) | ||||
−0.969646 | + | 0.244513i | \(0.921372\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 1.58109e6i | − 2.38785i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 158116. | 0.233281 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −70478.7 | −0.101603 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 2.08195e6i | − 2.93332i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10306.1i | 0.0141943i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −154021. | −0.207405 | −0.103702 | − | 0.994608i | \(-0.533069\pi\) | ||||
−0.103702 | + | 0.994608i | \(0.533069\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 411362. | 0.541711 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 570137.i | 0.734370i | 0.930148 | + | 0.367185i | \(0.119678\pi\) | ||||
−0.930148 | + | 0.367185i | \(0.880322\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 80803.8i | − 0.101822i | −0.998703 | − | 0.0509111i | \(-0.983787\pi\) | ||||
0.998703 | − | 0.0509111i | \(-0.0162125\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 194762. | 0.240145 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −932668. | −1.12548 | −0.562739 | − | 0.826635i | \(-0.690252\pi\) | ||||
−0.562739 | + | 0.826635i | \(0.690252\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 725092.i | 0.856492i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 999317.i | 1.15567i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 483104. | 0.547074 | 0.273537 | − | 0.961861i | \(-0.411806\pi\) | ||||
0.273537 | + | 0.961861i | \(0.411806\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −194028. | −0.215190 | −0.107595 | − | 0.994195i | \(-0.534315\pi\) | ||||
−0.107595 | + | 0.994195i | \(0.534315\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 3.40196e6i | − 3.69584i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 368511.i | 0.392225i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.63165e6 | −1.70171 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.66167e6 | −1.69843 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 863008.i | − 0.864631i | −0.901723 | − | 0.432315i | \(-0.857697\pi\) | ||||
0.901723 | − | 0.432315i | \(-0.142303\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 553033.i | − 0.543188i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8622.07 | −0.00830350 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.00468e6 | −0.948841 | −0.474420 | − | 0.880298i | \(-0.657342\pi\) | ||||
−0.474420 | + | 0.880298i | \(0.657342\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 436910.i | − 0.404708i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.27964e6i | 2.07140i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.50898e6 | 1.34522 | 0.672611 | − | 0.739996i | \(-0.265173\pi\) | ||||
0.672611 | + | 0.739996i | \(0.265173\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −814577. | −0.712553 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 997711.i | − 0.856498i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 695284.i | − 0.585844i | −0.956136 | − | 0.292922i | \(-0.905372\pi\) | ||||
0.956136 | − | 0.292922i | \(-0.0946276\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −361686. | −0.299163 | −0.149582 | − | 0.988749i | \(-0.547793\pi\) | ||||
−0.149582 | + | 0.988749i | \(0.547793\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.22421e6 | −0.994147 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 89197.8i | 0.0711251i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.07506e6i | 1.62491i | 0.583020 | + | 0.812457i | \(0.301871\pi\) | ||||
−0.583020 | + | 0.812457i | \(0.698129\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.02042e6 | −0.784816 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.34117e6 | −1.01325 | −0.506626 | − | 0.862166i | \(-0.669108\pi\) | ||||
−0.506626 | + | 0.862166i | \(0.669108\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.41343e6i | 1.79130i | 0.444762 | + | 0.895649i | \(0.353288\pi\) | ||||
−0.444762 | + | 0.895649i | \(0.646712\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 1.36504e6i | − 0.995478i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 673139. | 0.482392 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.41973e6 | −0.999907 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.47567e6i | 1.71380i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.04581e6i | 1.39219i | 0.717952 | + | 0.696093i | \(0.245080\pi\) | ||||
−0.717952 | + | 0.696093i | \(0.754920\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16306.4 | 0.0109095 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.77875e6 | 1.17010 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.47620e6i | 2.24868i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 287514.i | − 0.182912i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.09311e6 | 0.684002 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 117883. | 0.0725609 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 454883.i | 0.275457i | 0.990470 | + | 0.137728i | \(0.0439801\pi\) | ||||
−0.990470 | + | 0.137728i | \(0.956020\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.49387e6i | 1.48586i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.36777e6 | −0.801884 | −0.400942 | − | 0.916103i | \(-0.631317\pi\) | ||||
−0.400942 | + | 0.916103i | \(0.631317\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 391986. | 0.226157 | 0.113078 | − | 0.993586i | \(-0.463929\pi\) | ||||
0.113078 | + | 0.993586i | \(0.463929\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 748010.i | − 0.424748i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 51502.5i | − 0.0287859i | −0.999896 | − | 0.0143930i | \(-0.995418\pi\) | ||||
0.999896 | − | 0.0143930i | \(-0.00458158\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −494307. | −0.271969 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 914898. | 0.495576 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20896.1i | 0.0111444i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 560671.i | − 0.294442i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.01238e6 | 3.10940 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.31849e6 | 0.671563 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 235665.i | 0.118229i | 0.998251 | + | 0.0591147i | \(0.0188278\pi\) | ||||
−0.998251 | + | 0.0591147i | \(0.981172\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 6.32575e6i | − 3.12609i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.15785e6 | 0.563692 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.60833e6 | −0.771435 | −0.385717 | − | 0.922617i | \(-0.626046\pi\) | ||||
−0.385717 | + | 0.922617i | \(0.626046\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 735237.i | 0.347479i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 221263.i | − 0.103044i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.43413e6 | 0.658192 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.90819e6 | −1.31545 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 266162.i | 0.118665i | 0.998238 | + | 0.0593324i | \(0.0188972\pi\) | ||||
−0.998238 | + | 0.0593324i | \(0.981103\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.43079e6i | 1.94723i | 0.228192 | + | 0.973616i | \(0.426719\pi\) | ||||
−0.228192 | + | 0.973616i | \(0.573281\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.11807e7 | −4.84397 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.80868e6 | −1.19968 | −0.599840 | − | 0.800120i | \(-0.704769\pi\) | ||||
−0.599840 | + | 0.800120i | \(0.704769\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 1.31671e6i | − 0.554523i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 15678.1i | 0.00651065i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.32643e6 | 0.952697 | 0.476348 | − | 0.879257i | \(-0.341960\pi\) | ||||
0.476348 | + | 0.879257i | \(0.341960\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −832139. | −0.336069 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 4.22325e6i | − 1.68221i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 1.73382e6i | − 0.681196i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.99596e6 | 1.16110 | 0.580552 | − | 0.814223i | \(-0.302837\pi\) | ||||
0.580552 | + | 0.814223i | \(0.302837\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.74598e6 | 3.72614 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.48121e6i | 0.558703i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.15331e6i | 0.429214i | 0.976700 | + | 0.214607i | \(0.0688471\pi\) | ||||
−0.976700 | + | 0.214607i | \(0.931153\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 469057. | 0.172245 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.10707e6 | 1.12589 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 2.98305e6i | − 1.06675i | −0.845879 | − | 0.533375i | \(-0.820923\pi\) | ||||
0.845879 | − | 0.533375i | \(-0.179077\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 4.01289e6i | − 1.41626i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.42628e6 | −1.19351 | −0.596755 | − | 0.802423i | \(-0.703544\pi\) | ||||
−0.596755 | + | 0.802423i | \(0.703544\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 162195. | 0.0557681 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 4.16274e6i | − 1.41287i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 578513.i | 0.193838i | 0.995292 | + | 0.0969191i | \(0.0308988\pi\) | ||||
−0.995292 | + | 0.0969191i | \(0.969101\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 44518.7 | 0.0147265 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.84311e6 | 2.23497 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 832219.i | 0.268377i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 2.80594e6i | − 0.893514i | −0.894655 | − | 0.446757i | \(-0.852579\pi\) | ||||
0.894655 | − | 0.446757i | \(-0.147421\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.48215e6 | −0.780540 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −333020. | −0.103421 | −0.0517106 | − | 0.998662i | \(-0.516467\pi\) | ||||
−0.0517106 | + | 0.998662i | \(0.516467\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.39079e6i | 0.426580i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 5.35532e6i | − 1.62236i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.37165e6 | 0.410447 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.51090e6 | −0.742201 | −0.371101 | − | 0.928593i | \(-0.621020\pi\) | ||||
−0.371101 | + | 0.928593i | \(0.621020\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.06561e7i | 3.11166i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 29651.2i | − 0.00855396i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.38382e6 | −0.394421 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.24313e7 | 3.50087 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.44535e6i | 0.402196i | 0.979571 | + | 0.201098i | \(0.0644510\pi\) | ||||
−0.979571 | + | 0.201098i | \(0.935549\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 1.66158e6i | − 0.456896i | −0.973556 | − | 0.228448i | \(-0.926635\pi\) | ||||
0.973556 | − | 0.228448i | \(-0.0733651\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.90896e7 | 5.18735 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7180.35 | −0.00192830 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 214356.i | − 0.0568939i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 3.84333e6i | − 1.00824i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.83017e6 | −0.733870 | −0.366935 | − | 0.930247i | \(-0.619593\pi\) | ||||
−0.366935 | + | 0.930247i | \(0.619593\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.79105e6 | −0.971717 | −0.485859 | − | 0.874037i | \(-0.661493\pi\) | ||||
−0.485859 | + | 0.874037i | \(0.661493\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.59937e6i | 0.658634i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.04815e6i | 1.76552i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 651598. | 0.161368 | 0.0806842 | − | 0.996740i | \(-0.474289\pi\) | ||||
0.0806842 | + | 0.996740i | \(0.474289\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.70185e6 | 2.37552 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 5.06806e6i | − 1.22697i | −0.789708 | − | 0.613483i | \(-0.789768\pi\) | ||||
0.789708 | − | 0.613483i | \(-0.210232\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 830882.i | − 0.198902i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.01441e6 | −1.66044 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.01985e6 | 0.941010 | 0.470505 | − | 0.882397i | \(-0.344072\pi\) | ||||
0.470505 | + | 0.882397i | \(0.344072\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.11327e6i | 0.489232i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 1.22541e7i | − 2.80566i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.01951e6 | −0.230868 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.13558e6 | −0.926288 | −0.463144 | − | 0.886283i | \(-0.653279\pi\) | ||||
−0.463144 | + | 0.886283i | \(0.653279\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 143188.i | 0.0317230i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 710960.i | − 0.155809i | −0.996961 | − | 0.0779046i | \(-0.975177\pi\) | ||||
0.996961 | − | 0.0779046i | \(-0.0248230\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.72786e6 | 0.374589 | 0.187295 | − | 0.982304i | \(-0.440028\pi\) | ||||
0.187295 | + | 0.982304i | \(0.440028\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.16354e6 | −0.249544 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.42693e6i | 0.514950i | 0.966285 | + | 0.257475i | \(0.0828905\pi\) | ||||
−0.966285 | + | 0.257475i | \(0.917110\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 2.10541e6i | − 0.441982i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.02780e7 | −2.13480 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 902630. | 0.185506 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 1.13679e6i | − 0.231177i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.14455e7i | 4.31559i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.40523e6 | 1.47469 | 0.737343 | − | 0.675519i | \(-0.236080\pi\) | ||||
0.737343 | + | 0.675519i | \(0.236080\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.62177e6 | −1.69916 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.28817e6i | 1.03143i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.06171e6i | 0.397991i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 920253. | 0.175827 | 0.0879133 | − | 0.996128i | \(-0.471980\pi\) | ||||
0.0879133 | + | 0.996128i | \(0.471980\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.12545e7 | −2.12841 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.74081e6i | 1.63624i | 0.575045 | + | 0.818122i | \(0.304984\pi\) | ||||
−0.575045 | + | 0.818122i | \(0.695016\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 39791.3i | − 0.00737345i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.34833e6 | 0.430770 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.39428e6 | −0.434794 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 5.85693e6i | − 1.05298i | −0.850182 | − | 0.526488i | \(-0.823508\pi\) | ||||
0.850182 | − | 0.526488i | \(-0.176492\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.26543e6i | 0.403234i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.54886e6 | −0.625416 | −0.312708 | − | 0.949849i | \(-0.601236\pi\) | ||||
−0.312708 | + | 0.949849i | \(0.601236\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 910329. | 0.158844 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.30120e7i | 2.24814i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.90600e6i | 0.497165i | 0.968611 | + | 0.248582i | \(0.0799647\pi\) | ||||
−0.968611 | + | 0.248582i | \(0.920035\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.15273e6 | −0.534115 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.26694e7 | −3.80317 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.07686e6i | 0.345056i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.13930e6i | 0.681084i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.11739e7 | 1.82089 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.04123e6 | 0.813658 | 0.406829 | − | 0.913504i | \(-0.366634\pi\) | ||||
0.406829 | + | 0.913504i | \(0.366634\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 7.90605e6i | − 1.26388i | −0.775018 | − | 0.631939i | \(-0.782259\pi\) | ||||
0.775018 | − | 0.631939i | \(-0.217741\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 852921.i | − 0.135055i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17811.5 | 0.00279366 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.57964e6 | 1.33300 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 429302.i | − 0.0660734i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 1.32834e7i | − 2.02531i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 761916. | 0.115086 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.06679e6 | 1.05751 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.10371e6i | 0.311898i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.78603e6i | 1.43752i | 0.695259 | + | 0.718759i | \(0.255289\pi\) | ||||
−0.695259 | + | 0.718759i | \(0.744711\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.87786e7 | 2.73315 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.00704e6 | 0.722087 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 2.64510e6i | − 0.377984i | −0.981979 | − | 0.188992i | \(-0.939478\pi\) | ||||
0.981979 | − | 0.188992i | \(-0.0605220\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 3.10353e6i | − 0.439466i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.29971e6 | 0.883978 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.51329e6 | 0.210430 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 7.21296e6i | − 0.993988i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 4.84707e6i | − 0.661975i | −0.943635 | − | 0.330987i | \(-0.892618\pi\) | ||||
0.943635 | − | 0.330987i | \(-0.107382\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.67367e6 | −0.767953 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −49220.5 | −0.00660296 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.18722e6i | 0.955631i | 0.878460 | + | 0.477815i | \(0.158571\pi\) | ||||
−0.878460 | + | 0.477815i | \(0.841429\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 612297.i | 0.0806940i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.73798e6 | −1.27207 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.30594e7 | −1.69100 | −0.845498 | − | 0.533979i | \(-0.820696\pi\) | ||||
−0.845498 | + | 0.533979i | \(0.820696\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 2.93976e6i | − 0.377330i | −0.982041 | − | 0.188665i | \(-0.939584\pi\) | ||||
0.982041 | − | 0.188665i | \(-0.0604161\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 1.55920e6i | − 0.198388i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.42190e6 | −0.305483 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.78611e6 | 0.598471 | 0.299236 | − | 0.954179i | \(-0.403268\pi\) | ||||
0.299236 | + | 0.954179i | \(0.403268\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.06666e7i | 1.32230i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.51631e6i | 0.309260i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.65014e6 | −0.566624 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.47609e7 | −1.78329 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.07501e6i | 0.248557i | 0.992247 | + | 0.124278i | \(0.0396616\pi\) | ||||
−0.992247 | + | 0.124278i | \(0.960338\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.81989e6i | 0.334923i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.77654e6 | −0.444759 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.08207e6 | 0.359920 | 0.179960 | − | 0.983674i | \(-0.442403\pi\) | ||||
0.179960 | + | 0.983674i | \(0.442403\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13056.6i | 0.00151195i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 1.78201e7i | − 2.04633i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.34954e7 | −1.53680 | −0.768400 | − | 0.639970i | \(-0.778947\pi\) | ||||
−0.768400 | + | 0.639970i | \(0.778947\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.69923e6 | −0.191897 | −0.0959483 | − | 0.995386i | \(-0.530588\pi\) | ||||
−0.0959483 | + | 0.995386i | \(0.530588\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 3.04830e7i | − 3.41401i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 3.51707e6i | − 0.390655i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.47300e7 | −1.62267 | −0.811335 | − | 0.584581i | \(-0.801259\pi\) | ||||
−0.811335 | + | 0.584581i | \(0.801259\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.72662e6 | 0.516426 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 2.60184e7i | − 2.81954i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.34059e6i | 0.574035i | 0.957925 | + | 0.287017i | \(0.0926638\pi\) | ||||
−0.957925 | + | 0.287017i | \(0.907336\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.11129e7 | 1.18478 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16763.1 | −0.00177272 | −0.000886361 | − | 1.00000i | \(-0.500282\pi\) | ||||
−0.000886361 | 1.00000i | \(0.500282\pi\) | ||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 1.20604e7i | − 1.26513i | −0.774507 | − | 0.632566i | \(-0.782002\pi\) | ||||
0.774507 | − | 0.632566i | \(-0.217998\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.82967e7i | 5.02561i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.51085e6 | −0.155956 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 7.79253e6i | − 0.791607i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 110417.i | 0.0111278i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.37030e6 | −0.936871 | −0.468436 | − | 0.883498i | \(-0.655182\pi\) | ||||
−0.468436 | + | 0.883498i | \(0.655182\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.49389e6 | 0.941749 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 3.34188e6i | − 0.328895i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 1.32233e7i | − 1.29119i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.46653e7 | −3.35848 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.24983e7 | 1.20145 | 0.600723 | − | 0.799457i | \(-0.294879\pi\) | ||||
0.600723 | + | 0.799457i | \(0.294879\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 8.90727e6i | − 0.849605i | −0.905286 | − | 0.424803i | \(-0.860344\pi\) | ||||
0.905286 | − | 0.424803i | \(-0.139656\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 4.74658e6i | − 0.449243i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.19736e6 | 0.394199 | 0.197100 | − | 0.980383i | \(-0.436848\pi\) | ||||
0.197100 | + | 0.980383i | \(0.436848\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 93087.9 | 0.00867524 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.11575e6i | 0.195664i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 7.16059e6i | − 0.657152i | −0.944477 | − | 0.328576i | \(-0.893431\pi\) | ||||
0.944477 | − | 0.328576i | \(-0.106569\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.69886e6 | 0.519021 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.56465e7 | −4.12567 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 6.13902e6i | − 0.550662i | −0.961349 | − | 0.275331i | \(-0.911213\pi\) | ||||
0.961349 | − | 0.275331i | \(-0.0887875\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 3.75445e6i | − 0.334228i | −0.985938 | − | 0.167114i | \(-0.946555\pi\) | ||||
0.985938 | − | 0.167114i | \(-0.0534448\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 309385. | 0.0273348 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.06710e6 | −0.181262 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 1.34214e7i | − 1.16811i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.62367e6i | 0.399412i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 672956. | 0.0577006 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.77234e7 | −1.50838 | −0.754188 | − | 0.656659i | \(-0.771969\pi\) | ||||
−0.754188 | + | 0.656659i | \(0.771969\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 7.78970e6i | − 0.658054i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 1.16984e7i | − 0.980969i | −0.871450 | − | 0.490485i | \(-0.836820\pi\) | ||||
0.871450 | − | 0.490485i | \(-0.163180\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.74896e6 | 0.312059 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.71153e7 | 1.41422 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.76343e7i | 1.44646i | 0.690608 | + | 0.723230i | \(0.257343\pi\) | ||||
−0.690608 | + | 0.723230i | \(0.742657\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.87425e6i | 0.722612i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.42570e6 | −0.196085 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.92294e7 | 2.34570 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 6.23688e6i | − 0.496903i | −0.968644 | − | 0.248452i | \(-0.920078\pi\) | ||||
0.968644 | − | 0.248452i | \(-0.0799217\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 4.27014e6i | − 0.337760i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.03526e7 | 0.812997 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −170117. | −0.0132637 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.79983e7i | 2.16740i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 1.52056e7i | − 1.16872i | −0.811496 | − | 0.584358i | \(-0.801346\pi\) | ||||
0.811496 | − | 0.584358i | \(-0.198654\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.74810e7 | −1.33407 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.17670e7 | 1.64940 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 1.65532e6i | − 0.124547i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.26475e7i | 1.69202i | 0.533170 | + | 0.846008i | \(0.321000\pi\) | ||||
−0.533170 | + | 0.846008i | \(0.679000\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.19100e7 | 1.62543 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.00774e6 | 0.442576 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 3.20068e6i | − 0.234141i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 1.45026e7i | − 1.05353i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.27400e7 | 0.919063 | 0.459532 | − | 0.888161i | \(-0.348017\pi\) | ||||
0.459532 | + | 0.888161i | \(0.348017\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.77652e6 | 0.270553 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.82465e6i | 0.414404i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.16472e6i | 0.152953i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.70816e7 | −1.19865 | −0.599325 | − | 0.800506i | \(-0.704564\pi\) | ||||
−0.599325 | + | 0.800506i | \(0.704564\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5.00719e7 | −3.48959 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 72661.0i | 0.00502931i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 9.13585e6i | − 0.628042i | −0.949416 | − | 0.314021i | \(-0.898324\pi\) | ||||
0.949416 | − | 0.314021i | \(-0.101676\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.10626e7 | 0.755332 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.60980e6 | 0.448249 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.83288e6i | 0.392891i | 0.980515 | + | 0.196446i | \(0.0629399\pi\) | ||||
−0.980515 | + | 0.196446i | \(0.937060\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.89815e7i | 3.27708i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.70851e6 | 0.179994 | 0.0899970 | − | 0.995942i | \(-0.471314\pi\) | ||||
0.0899970 | + | 0.995942i | \(0.471314\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.84152e6 | −0.385598 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.64321e7i | 2.38882i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 1.38545e6i | − 0.0902373i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.54490e7 | 0.999539 | 0.499769 | − | 0.866159i | \(-0.333418\pi\) | ||||
0.499769 | + | 0.866159i | \(0.333418\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.59072e7 | −1.66507 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 1.02050e7i | − 0.651550i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.16555e7i | 1.37350i | 0.726893 | + | 0.686750i | \(0.240963\pi\) | ||||
−0.726893 | + | 0.686750i | \(0.759037\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.66019e7 | −1.04605 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.80099e7 | 1.12732 | 0.563662 | − | 0.826006i | \(-0.309392\pi\) | ||||
0.563662 | + | 0.826006i | \(0.309392\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 9.10467e6i | − 0.566178i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 189038.i | 0.0116787i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −585123. | −0.0359136 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.00138e7 | −1.22043 | −0.610215 | − | 0.792236i | \(-0.708917\pi\) | ||||
−0.610215 | + | 0.792236i | \(0.708917\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.01600e7i | 1.82724i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.74507e6i | 0.345817i | 0.984938 | + | 0.172909i | \(0.0553166\pi\) | ||||
−0.984938 | + | 0.172909i | \(0.944683\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −968979. | −0.0579509 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.31159e7 | −0.779372 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 2.69327e7i | − 1.59014i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 7.51666e6i | − 0.440958i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.31681e7 | 2.51628 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.55941e6 | −0.495758 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 5.04447e6i | − 0.290321i | −0.989408 | − | 0.145160i | \(-0.953630\pi\) | ||||
0.989408 | − | 0.145160i | \(-0.0463698\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 4.52990e7i | − 2.59057i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.11339e6 | 0.0632709 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.23000e6 | −0.238868 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.44533e7i | 1.37221i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 963795.i | 0.0537451i | 0.999639 | + | 0.0268726i | \(0.00855483\pi\) | ||||
−0.999639 | + | 0.0268726i | \(0.991445\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −333211. | −0.0184651 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.18748e7 | −1.20465 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 9.89779e6i | − 0.541688i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.40393e6i | 0.239525i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.08722e7 | −1.12820 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.63331e6 | −0.356335 | −0.178168 | − | 0.984000i | \(-0.557017\pi\) | ||||
−0.178168 | + | 0.984000i | \(0.557017\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 3.04422e7i | − 1.62526i | −0.582779 | − | 0.812631i | \(-0.698035\pi\) | ||||
0.582779 | − | 0.812631i | \(-0.301965\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.08577e7i | 0.576117i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.37264e6 | −0.494274 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.15036e7 | −0.602947 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.68408e7i | 1.39825i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.68811e6i | 0.501627i | 0.968035 | + | 0.250814i | \(0.0806981\pi\) | ||||
−0.968035 | + | 0.250814i | \(0.919302\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.72636e6 | −0.449090 | −0.224545 | − | 0.974464i | \(-0.572090\pi\) | ||||
−0.224545 | + | 0.974464i | \(0.572090\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.67769e6 | 0.136970 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.23162e7i | 1.13464i | 0.823498 | + | 0.567319i | \(0.192019\pi\) | ||||
−0.823498 | + | 0.567319i | \(0.807981\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 3.36746e7i | − 1.70183i | −0.525302 | − | 0.850916i | \(-0.676048\pi\) | ||||
0.525302 | − | 0.850916i | \(-0.323952\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.22925e7 | 3.12920 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −169347. | −0.00845598 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.88662e6i | 0.0936417i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.93230e7i | 0.953370i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.64415e6 | 0.423952 | 0.211976 | − | 0.977275i | \(-0.432010\pi\) | ||||
0.211976 | + | 0.977275i | \(0.432010\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.51494e6 | 0.415137 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.02614e7i | 1.95128i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.08362e7i | 0.522079i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.39536e6 | −0.306307 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.24502e7 | 3.44961 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.72430e7i | 1.76287i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 2.91285e6i | − 0.137071i | −0.997649 | − | 0.0685355i | \(-0.978167\pi\) | ||||
0.997649 | − | 0.0685355i | \(-0.0218326\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.99283e7 | −1.40013 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.92591e7 | 1.82595 | 0.912973 | − | 0.408019i | \(-0.133780\pi\) | ||||
0.912973 | + | 0.408019i | \(0.133780\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 1.53343e7i | − 0.709059i | −0.935045 | − | 0.354529i | \(-0.884641\pi\) | ||||
0.935045 | − | 0.354529i | \(-0.115359\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 2.02074e7i | − 0.928972i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.19629e7 | 0.546774 | 0.273387 | − | 0.961904i | \(-0.411856\pi\) | ||||
0.273387 | + | 0.961904i | \(0.411856\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.30545e6 | 0.422861 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.26196e7i | 1.92558i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.75086e6i | 0.213414i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.15472e7 | −1.85565 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.42789e7 | 2.41044 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 710303.i | − 0.0313634i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 1.64985e7i | − 0.724346i | −0.932111 | − | 0.362173i | \(-0.882035\pi\) | ||||
0.932111 | − | 0.362173i | \(-0.117965\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.14146e7 | 2.68102 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.28694e7 | −0.558623 | −0.279312 | − | 0.960201i | \(-0.590106\pi\) | ||||
−0.279312 | + | 0.960201i | \(0.590106\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 2.00179e7i | − 0.864005i | −0.901872 | − | 0.432002i | \(-0.857807\pi\) | ||||
0.901872 | − | 0.432002i | \(-0.142193\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 489513.i | − 0.0210090i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.41401e7 | −1.45699 | −0.728493 | − | 0.685053i | \(-0.759779\pi\) | ||||
−0.728493 | + | 0.685053i | \(0.759779\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.07680e6 | −0.257882 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 3.05717e7i | − 1.29011i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 5.27535e7i | − 2.21372i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.88514e6 | 0.245583 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.04354e8 | 4.33041 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 5.36978e6i | − 0.221594i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 374333.i | − 0.0153619i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.63107e6 | −0.352245 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.56386e7 | 0.634710 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 2.89420e7i | − 1.16818i | −0.811688 | − | 0.584091i | \(-0.801451\pi\) | ||||
0.811688 | − | 0.584091i | \(-0.198549\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 2.39664e7i | − 0.962039i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.26460e7 | −1.30327 | −0.651634 | − | 0.758534i | \(-0.725916\pi\) | ||||
−0.651634 | + | 0.758534i | \(0.725916\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.89978e6 | −0.313645 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 3.53881e6i | − 0.139735i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 1.03627e7i | − 0.406957i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.68175e7 | 1.04744 | 0.523720 | − | 0.851890i | \(-0.324544\pi\) | ||||
0.523720 | + | 0.851890i | \(0.324544\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.36554e7 | 0.530464 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.72475e7i | 1.82547i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 6.00687e6i | − 0.230831i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.46779e7 | 2.08984 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.02792e6 | 0.0770923 | 0.0385462 | − | 0.999257i | \(-0.487727\pi\) | ||||
0.0385462 | + | 0.999257i | \(0.487727\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 2.68108e7i | − 1.01376i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.10599e7i | 1.54424i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −40990.2 | −0.00153339 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.18276e7 | −1.18428 | −0.592141 | − | 0.805834i | \(-0.701717\pi\) | ||||
−0.592141 | + | 0.805834i | \(0.701717\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 1.17673e7i | − 0.435523i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 4.36130e7i | − 1.60562i | −0.596237 | − | 0.802809i | \(-0.703338\pi\) | ||||
0.596237 | − | 0.802809i | \(-0.296662\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.73797e7 | −2.10126 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.41646e7 | −0.515970 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1.10000e7i | − 0.398582i | −0.979940 | − | 0.199291i | \(-0.936136\pi\) | ||||
0.979940 | − | 0.199291i | \(-0.0638638\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.22146e7i | 2.24247i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.54609e6 | −0.0554348 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.76840e7 | 0.987406 | 0.493703 | − | 0.869630i | \(-0.335643\pi\) | ||||
0.493703 | + | 0.869630i | \(0.335643\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 1.29848e6i | − 0.0460710i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.48389e7i | 0.523748i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.61367e7 | 0.566589 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.62255e7 | −0.916042 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 2.00591e7i | − 0.697020i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.88300e6i | 0.307073i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.67852e7 | 1.26505 | 0.632523 | − | 0.774541i | \(-0.282019\pi\) | ||||
0.632523 | + | 0.774541i | \(0.282019\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 627292. | 0.0214615 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.30736e6i | 0.112573i | 0.998415 | + | 0.0562865i | \(0.0179260\pi\) | ||||
−0.998415 | + | 0.0562865i | \(0.982074\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 1.88250e7i | − 0.637459i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.68312e7 | −0.567025 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.78379e7 | −1.60338 | −0.801689 | − | 0.597741i | \(-0.796065\pi\) | ||||
−0.801689 | + | 0.597741i | \(0.796065\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 4.74322e6i | − 0.158167i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 1.31821e8i | − 4.37333i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.03384e7 | 0.341248 | 0.170624 | − | 0.985336i | \(-0.445422\pi\) | ||||
0.170624 | + | 0.985336i | \(0.445422\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.14506e6 | −0.103285 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 3.95805e7i | − 1.29327i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.45083e7i | 0.796749i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.54794e7 | −1.14760 | −0.573802 | − | 0.818994i | \(-0.694532\pi\) | ||||
−0.573802 | + | 0.818994i | \(0.694532\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.07459e6 | 0.227682 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 1.48404e7i | − 0.475213i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.07614e7i | 0.980094i | 0.871696 | + | 0.490047i | \(0.163020\pi\) | ||||
−0.871696 | + | 0.490047i | \(0.836980\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.19787e8 | −3.79748 |
(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 | 320.6.d.d.161.1 | yes | 12 | |
4.3 | odd | 2 | 320.6.d.c.161.12 | yes | 12 | ||
8.3 | odd | 2 | 320.6.d.c.161.1 | ✓ | 12 | ||
8.5 | even | 2 | inner | 320.6.d.d.161.12 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
320.6.d.c.161.1 | ✓ | 12 | 8.3 | odd | 2 | ||
320.6.d.c.161.12 | yes | 12 | 4.3 | odd | 2 | ||
320.6.d.d.161.1 | yes | 12 | 1.1 | even | 1 | trivial | |
320.6.d.d.161.12 | yes | 12 | 8.5 | even | 2 | inner |