Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(17,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.bl (of order \(6\), degree \(2\), 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: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.4 | ||
Root | \(0.144868 + 1.25092i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 504.17 |
Dual form | 504.2.bl.a.89.4 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.144868 | − | 0.250919i | −0.0647871 | − | 0.112215i | 0.831812 | − | 0.555057i | \(-0.187304\pi\) |
−0.896600 | + | 0.442842i | \(0.853970\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.26907 | − | 1.36064i | −0.857627 | − | 0.514273i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.23077 | + | 3.01999i | 1.57714 | + | 0.910560i | 0.995256 | + | 0.0972858i | \(0.0310161\pi\) |
0.581880 | + | 0.813275i | \(0.302317\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.46050i | − | 1.51447i | −0.653142 | − | 0.757235i | \(-0.726550\pi\) | ||
0.653142 | − | 0.757235i | \(-0.273450\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.22666 | − | 3.85669i | 0.540045 | − | 0.935385i | −0.458856 | − | 0.888511i | \(-0.651741\pi\) |
0.998901 | − | 0.0468746i | \(-0.0149261\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.51739 | − | 2.03076i | 0.806944 | − | 0.465889i | −0.0389497 | − | 0.999241i | \(-0.512401\pi\) |
0.845893 | + | 0.533352i | \(0.179068\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.11743 | + | 0.645146i | −0.232999 | + | 0.134522i | −0.611955 | − | 0.790893i | \(-0.709617\pi\) |
0.378956 | + | 0.925415i | \(0.376283\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.45803 | − | 4.25743i | 0.491605 | − | 0.851485i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 0.377918i | − | 0.0701776i | −0.999384 | − | 0.0350888i | \(-0.988829\pi\) | ||
0.999384 | − | 0.0350888i | \(-0.0111714\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.09749 | − | 1.78834i | −0.556326 | − | 0.321195i | 0.195343 | − | 0.980735i | \(-0.437418\pi\) |
−0.751670 | + | 0.659540i | \(0.770751\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.0126942 | + | 0.766467i | −0.00214570 | + | 0.129557i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.01555 | + | 1.75898i | 0.166955 | + | 0.289174i | 0.937348 | − | 0.348395i | \(-0.113273\pi\) |
−0.770393 | + | 0.637569i | \(0.779940\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.50384 | 0.859556 | 0.429778 | − | 0.902935i | \(-0.358592\pi\) | ||||
0.429778 | + | 0.902935i | \(0.358592\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.45419 | −0.984254 | −0.492127 | − | 0.870523i | \(-0.663780\pi\) | ||||
−0.492127 | + | 0.870523i | \(0.663780\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.38833 | + | 9.33287i | 0.785969 | + | 1.36134i | 0.928418 | + | 0.371536i | \(0.121169\pi\) |
−0.142449 | + | 0.989802i | \(0.545498\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.29733 | + | 6.17475i | 0.471048 | + | 0.882108i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.77422 | − | 5.64315i | −1.34259 | − | 0.775146i | −0.355405 | − | 0.934713i | \(-0.615657\pi\) |
−0.987187 | + | 0.159567i | \(0.948990\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.75000i | − | 0.235970i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.790140 | − | 1.36856i | 0.102867 | − | 0.178172i | −0.809998 | − | 0.586433i | \(-0.800532\pi\) |
0.912865 | + | 0.408262i | \(0.133865\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.54984 | − | 5.51360i | 1.22273 | − | 0.705945i | 0.257233 | − | 0.966350i | \(-0.417189\pi\) |
0.965500 | + | 0.260405i | \(0.0838560\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.37015 | + | 0.791054i | −0.169946 | + | 0.0981182i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.04381 | + | 3.53999i | −0.249691 | + | 0.432478i | −0.963440 | − | 0.267924i | \(-0.913663\pi\) |
0.713749 | + | 0.700402i | \(0.246996\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 0.410536i | − | 0.0487216i | −0.999703 | − | 0.0243608i | \(-0.992245\pi\) | ||
0.999703 | − | 0.0243608i | \(-0.00775505\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.1149 | − | 6.41718i | −1.30090 | − | 0.751074i | −0.320340 | − | 0.947303i | \(-0.603797\pi\) |
−0.980558 | + | 0.196229i | \(0.937131\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.75986 | − | 13.9697i | −0.884319 | − | 1.59200i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.01355 | + | 10.4158i | 0.676577 | + | 1.17187i | 0.976005 | + | 0.217747i | \(0.0698707\pi\) |
−0.299428 | + | 0.954119i | \(0.596796\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.155917 | −0.0171142 | −0.00855708 | − | 0.999963i | \(-0.502724\pi\) | ||||
−0.00855708 | + | 0.999963i | \(0.502724\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.29029 | −0.139952 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.34409 | + | 5.79213i | 0.354473 | + | 0.613965i | 0.987028 | − | 0.160551i | \(-0.0513271\pi\) |
−0.632555 | + | 0.774516i | \(0.717994\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.42976 | + | 12.3902i | −0.778851 | + | 1.29885i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.01912 | − | 0.588387i | −0.104559 | − | 0.0603672i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.5090i | 1.67623i | 0.545494 | + | 0.838115i | \(0.316342\pi\) | ||||
−0.545494 | + | 0.838115i | \(0.683658\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.99552 | + | 10.3845i | −0.596577 | + | 1.03330i | 0.396746 | + | 0.917929i | \(0.370140\pi\) |
−0.993322 | + | 0.115373i | \(0.963194\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.100344 | + | 0.0579336i | −0.00988718 | + | 0.00570837i | −0.504935 | − | 0.863157i | \(-0.668484\pi\) |
0.495048 | + | 0.868865i | \(0.335150\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.1501 | + | 8.16957i | −1.36794 | + | 0.789782i | −0.990665 | − | 0.136318i | \(-0.956473\pi\) |
−0.377278 | + | 0.926100i | \(0.623140\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.454348 | − | 0.786954i | 0.0435187 | − | 0.0753766i | −0.843446 | − | 0.537215i | \(-0.819477\pi\) |
0.886964 | + | 0.461838i | \(0.152810\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 8.37176i | − | 0.787549i | −0.919207 | − | 0.393775i | \(-0.871169\pi\) | ||
0.919207 | − | 0.393775i | \(-0.128831\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.323760 | + | 0.186923i | 0.0301907 | + | 0.0174306i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.3000 | + | 5.72142i | −0.944200 | + | 0.524481i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.7406 | + | 22.0674i | 1.15824 | + | 2.00613i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.87305 | −0.256973 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.13280 | 0.544198 | 0.272099 | − | 0.962269i | \(-0.412282\pi\) | ||||
0.272099 | + | 0.962269i | \(0.412282\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.36514 | − | 12.7568i | −0.643495 | − | 1.11457i | −0.984647 | − | 0.174558i | \(-0.944150\pi\) |
0.341152 | − | 0.940008i | \(-0.389183\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.7443 | − | 0.177947i | −0.931651 | − | 0.0154299i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.7797 | + | 6.80101i | 1.00641 | + | 0.581050i | 0.910138 | − | 0.414306i | \(-0.135976\pi\) |
0.0962696 | + | 0.995355i | \(0.469309\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 17.3580i | − | 1.47229i | −0.676827 | − | 0.736143i | \(-0.736645\pi\) | ||
0.676827 | − | 0.736143i | \(-0.263355\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.4906 | − | 28.5626i | 1.37902 | − | 2.38853i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.0948270 | + | 0.0547484i | −0.00787495 | + | 0.00454661i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.3600 | + | 7.71339i | −1.09449 | + | 0.631905i | −0.934769 | − | 0.355257i | \(-0.884393\pi\) |
−0.159723 | + | 0.987162i | \(0.551060\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.68712 | + | 4.65423i | −0.218675 | + | 0.378756i | −0.954403 | − | 0.298521i | \(-0.903507\pi\) |
0.735728 | + | 0.677277i | \(0.236840\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.03630i | 0.0832373i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.03109 | − | 3.48205i | −0.481334 | − | 0.277898i | 0.239638 | − | 0.970862i | \(-0.422971\pi\) |
−0.720972 | + | 0.692964i | \(0.756304\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.41332 | + | 0.0565312i | 0.269008 | + | 0.00445528i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.00803 | + | 8.67416i | 0.392259 | + | 0.679413i | 0.992747 | − | 0.120221i | \(-0.0383603\pi\) |
−0.600488 | + | 0.799634i | \(0.705027\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.03254 | −0.466812 | −0.233406 | − | 0.972379i | \(-0.574987\pi\) | ||||
−0.233406 | + | 0.972379i | \(0.574987\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −16.8171 | −1.29362 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.18258 | + | 15.9047i | 0.698139 | + | 1.20921i | 0.969111 | + | 0.246625i | \(0.0793214\pi\) |
−0.270972 | + | 0.962587i | \(0.587345\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.3702 | + | 6.31591i | −0.859509 | + | 0.477438i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.83604 | + | 5.67884i | 0.735180 | + | 0.424457i | 0.820314 | − | 0.571913i | \(-0.193799\pi\) |
−0.0851340 | + | 0.996370i | \(0.527132\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 11.8647i | − | 0.881893i | −0.897533 | − | 0.440947i | \(-0.854643\pi\) | ||
0.897533 | − | 0.440947i | \(-0.145357\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.294241 | − | 0.509641i | 0.0216331 | − | 0.0374696i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 23.2943 | − | 13.4490i | 1.70345 | − | 0.983487i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.6310 | + | 6.71514i | −0.841587 | + | 0.485890i | −0.857803 | − | 0.513978i | \(-0.828171\pi\) |
0.0162166 | + | 0.999869i | \(0.494838\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.87792 | − | 4.98470i | 0.207157 | − | 0.358807i | −0.743661 | − | 0.668557i | \(-0.766912\pi\) |
0.950818 | + | 0.309751i | \(0.100246\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.66053i | 0.189555i | 0.995498 | + | 0.0947775i | \(0.0302140\pi\) | ||||
−0.995498 | + | 0.0947775i | \(0.969786\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.25552 | + | 4.18898i | 0.514330 | + | 0.296949i | 0.734612 | − | 0.678488i | \(-0.237364\pi\) |
−0.220282 | + | 0.975436i | \(0.570698\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.514209 | + | 0.857521i | −0.0360904 | + | 0.0601862i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.797333 | − | 1.38102i | −0.0556881 | − | 0.0964547i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 24.5315 | 1.69688 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.12240 | 0.490326 | 0.245163 | − | 0.969482i | \(-0.421159\pi\) | ||||
0.245163 | + | 0.969482i | \(0.421159\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.935008 | + | 1.61948i | 0.0637670 | + | 0.110448i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.59514 | + | 8.27243i | 0.311939 | + | 0.561569i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −21.0595 | − | 12.1587i | −1.41661 | − | 0.817882i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 13.6407i | − | 0.913449i | −0.889608 | − | 0.456725i | \(-0.849023\pi\) | ||
0.889608 | − | 0.456725i | \(-0.150977\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.59561 | − | 9.69188i | 0.371393 | − | 0.643272i | −0.618387 | − | 0.785874i | \(-0.712213\pi\) |
0.989780 | + | 0.142602i | \(0.0455468\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.40517 | − | 4.27538i | 0.489348 | − | 0.282525i | −0.234956 | − | 0.972006i | \(-0.575495\pi\) |
0.724304 | + | 0.689481i | \(0.242161\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.8863 | − | 6.28522i | 0.713186 | − | 0.411758i | −0.0990536 | − | 0.995082i | \(-0.531582\pi\) |
0.812240 | + | 0.583324i | \(0.198248\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.56120 | − | 2.70408i | 0.101841 | − | 0.176394i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 21.3263i | − | 1.37948i | −0.724056 | − | 0.689741i | \(-0.757725\pi\) | ||
0.724056 | − | 0.689741i | \(-0.242275\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.7751 | − | 10.2625i | −1.14499 | − | 0.661063i | −0.197332 | − | 0.980337i | \(-0.563228\pi\) |
−0.947663 | + | 0.319274i | \(0.896561\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.07169 | − | 1.72189i | 0.0684676 | − | 0.110008i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.0890 | − | 19.2067i | −0.705575 | − | 1.22209i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.9577 | −0.754764 | −0.377382 | − | 0.926058i | \(-0.623176\pi\) | ||||
−0.377382 | + | 0.926058i | \(0.623176\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.79333 | −0.489963 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.8581 | + | 27.4670i | 0.989199 | + | 1.71334i | 0.621541 | + | 0.783381i | \(0.286507\pi\) |
0.367658 | + | 0.929961i | \(0.380160\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.0889877 | − | 5.37303i | 0.00552943 | − | 0.333864i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.8678 | + | 12.0480i | 1.28676 | + | 0.742912i | 0.978075 | − | 0.208252i | \(-0.0667775\pi\) |
0.308686 | + | 0.951164i | \(0.400111\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.27006i | 0.200878i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.31897 | + | 7.48068i | −0.263332 | + | 0.456105i | −0.967125 | − | 0.254300i | \(-0.918155\pi\) |
0.703793 | + | 0.710405i | \(0.251488\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.1099 | − | 12.1878i | 1.28233 | − | 0.740356i | 0.305060 | − | 0.952333i | \(-0.401324\pi\) |
0.977275 | + | 0.211977i | \(0.0679902\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 25.7147 | − | 14.8464i | 1.55066 | − | 0.895272i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.9122 | − | 22.3646i | 0.775820 | − | 1.34376i | −0.158513 | − | 0.987357i | \(-0.550670\pi\) |
0.934333 | − | 0.356402i | \(-0.115997\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 29.9846i | 1.78873i | 0.447334 | + | 0.894367i | \(0.352374\pi\) | ||||
−0.447334 | + | 0.894367i | \(0.647626\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.8489 | − | 11.4597i | −1.17989 | − | 0.681211i | −0.223902 | − | 0.974612i | \(-0.571880\pi\) |
−0.955990 | + | 0.293401i | \(0.905213\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.4886 | − | 7.48873i | −0.737178 | − | 0.442046i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.41605 | − | 2.45267i | −0.0832972 | − | 0.144275i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 28.4782 | 1.66372 | 0.831858 | − | 0.554988i | \(-0.187277\pi\) | ||||
0.831858 | + | 0.554988i | \(0.187277\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.457865 | −0.0266579 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.52282 | + | 6.10171i | 0.203730 | + | 0.352871i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.6450 | + | 8.78181i | 0.844123 | + | 0.506175i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.76694 | − | 1.59749i | −0.158435 | − | 0.0914723i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.73643i | 0.327395i | 0.986511 | + | 0.163698i | \(0.0523422\pi\) | ||||
−0.986511 | + | 0.163698i | \(0.947658\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.71985 | + | 8.17502i | −0.267638 | + | 0.463563i | −0.968251 | − | 0.249978i | \(-0.919577\pi\) |
0.700613 | + | 0.713541i | \(0.252910\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.0870 | + | 5.82373i | −0.570150 | + | 0.329176i | −0.757209 | − | 0.653172i | \(-0.773438\pi\) |
0.187059 | + | 0.982349i | \(0.440104\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.90757 | + | 1.10133i | −0.107140 | + | 0.0618571i | −0.552612 | − | 0.833438i | \(-0.686369\pi\) |
0.445473 | + | 0.895296i | \(0.353036\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.14131 | − | 1.97680i | 0.0639009 | − | 0.110680i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 18.0873i | − | 1.00640i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −23.2477 | − | 13.4221i | −1.28955 | − | 0.744522i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.472155 | − | 28.5085i | 0.0260307 | − | 1.57172i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.5017 | + | 21.6535i | 0.687154 | + | 1.19019i | 0.972755 | + | 0.231837i | \(0.0744737\pi\) |
−0.285600 | + | 0.958349i | \(0.592193\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.18434 | 0.0647072 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.8462 | 0.645303 | 0.322651 | − | 0.946518i | \(-0.395426\pi\) | ||||
0.322651 | + | 0.946518i | \(0.395426\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.8015 | − | 18.7088i | −0.584935 | − | 1.01314i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.919731 | − | 18.4974i | 0.0496608 | − | 0.998766i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.2907 | − | 7.67341i | −0.713484 | − | 0.411930i | 0.0988655 | − | 0.995101i | \(-0.468479\pi\) |
−0.812350 | + | 0.583170i | \(0.801812\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.666155i | 0.0356585i | 0.999841 | + | 0.0178292i | \(0.00567552\pi\) | ||||
−0.999841 | + | 0.0178292i | \(0.994324\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.18680 | + | 7.25175i | −0.222841 | + | 0.385972i | −0.955669 | − | 0.294442i | \(-0.904866\pi\) |
0.732829 | + | 0.680413i | \(0.238200\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.103011 | + | 0.0594736i | −0.00546728 | + | 0.00315653i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.9438 | + | 14.4013i | −1.31649 | + | 0.760073i | −0.983161 | − | 0.182739i | \(-0.941504\pi\) |
−0.333324 | + | 0.942812i | \(0.608170\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.25200 | + | 2.16852i | −0.0658946 | + | 0.114133i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.71859i | 0.194640i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.5554 | + | 14.1770i | 1.28178 | + | 0.740036i | 0.977173 | − | 0.212443i | \(-0.0681419\pi\) |
0.304606 | + | 0.952478i | \(0.401475\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.5001 | + | 26.1038i | 0.752807 | + | 1.35524i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.87744 | + | 6.71593i | 0.200766 | + | 0.347737i | 0.948776 | − | 0.315951i | \(-0.102323\pi\) |
−0.748009 | + | 0.663688i | \(0.768990\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.06362 | −0.106282 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.3391 | −0.890652 | −0.445326 | − | 0.895368i | \(-0.646912\pi\) | ||||
−0.445326 | + | 0.895368i | \(0.646912\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.930503 | + | 1.61168i | 0.0475465 | + | 0.0823530i | 0.888819 | − | 0.458258i | \(-0.151526\pi\) |
−0.841273 | + | 0.540611i | \(0.818193\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.38112 | + | 3.97087i | −0.121353 | + | 0.202375i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.34272 | − | 2.50727i | −0.220184 | − | 0.127124i | 0.385851 | − | 0.922561i | \(-0.373908\pi\) |
−0.606036 | + | 0.795437i | \(0.707241\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.74609i | 0.290592i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.74235 | − | 3.01783i | 0.0876670 | − | 0.151844i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.0838 | + | 11.5954i | −1.00798 | + | 0.581955i | −0.910599 | − | 0.413292i | \(-0.864379\pi\) |
−0.0973778 | + | 0.995247i | \(0.531046\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.51104 | − | 0.872401i | 0.0754579 | − | 0.0435656i | −0.461796 | − | 0.886986i | \(-0.652795\pi\) |
0.537254 | + | 0.843420i | \(0.319462\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.76523 | + | 16.9139i | −0.486441 | + | 0.842540i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.2678i | 0.608090i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.7362 | + | 16.0135i | 1.37147 | + | 0.791816i | 0.991113 | − | 0.133026i | \(-0.0424694\pi\) |
0.380352 | + | 0.924842i | \(0.375803\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.65500 | + | 2.03027i | −0.179851 | + | 0.0999028i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.0225875 | + | 0.0391227i | 0.00110878 | + | 0.00192046i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.5506 | −0.808549 | −0.404274 | − | 0.914638i | \(-0.632476\pi\) | ||||
−0.404274 | + | 0.914638i | \(0.632476\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.2673 | 0.939029 | 0.469514 | − | 0.882925i | \(-0.344429\pi\) | ||||
0.469514 | + | 0.882925i | \(0.344429\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.9464 | − | 18.9597i | −0.530978 | − | 0.919681i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −29.1713 | − | 0.483132i | −1.41170 | − | 0.0233804i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.7026 | + | 17.7262i | 1.47889 | + | 0.853840i | 0.999715 | − | 0.0238778i | \(-0.00760125\pi\) |
0.479179 | + | 0.877717i | \(0.340935\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 10.7841i | − | 0.518251i | −0.965844 | − | 0.259125i | \(-0.916566\pi\) | ||
0.965844 | − | 0.259125i | \(-0.0834343\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.62028 | + | 4.53846i | −0.125345 | + | 0.217104i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −35.4313 | + | 20.4563i | −1.69104 | + | 0.976324i | −0.737364 | + | 0.675495i | \(0.763930\pi\) |
−0.953678 | + | 0.300829i | \(0.902737\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.84672 | + | 2.22090i | −0.182763 | + | 0.105518i | −0.588590 | − | 0.808432i | \(-0.700317\pi\) |
0.405827 | + | 0.913950i | \(0.366983\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.968906 | − | 1.67819i | 0.0459305 | − | 0.0795540i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 20.3226i | − | 0.959082i | −0.877519 | − | 0.479541i | \(-0.840803\pi\) | ||
0.877519 | − | 0.479541i | \(-0.159197\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28.7893 | + | 16.6215i | 1.35564 | + | 0.782677i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.18529 | + | 0.0693165i | 0.196209 | + | 0.00324961i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.324749 | − | 0.562482i | −0.0151911 | − | 0.0263118i | 0.858330 | − | 0.513098i | \(-0.171502\pi\) |
−0.873521 | + | 0.486786i | \(0.838169\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −35.7882 | −1.66682 | −0.833412 | − | 0.552652i | \(-0.813616\pi\) | ||||
−0.833412 | + | 0.552652i | \(0.813616\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.8281 | −0.782068 | −0.391034 | − | 0.920376i | \(-0.627883\pi\) | ||||
−0.391034 | + | 0.920376i | \(0.627883\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.6807 | − | 20.2315i | −0.540517 | − | 0.936203i | −0.998874 | − | 0.0474348i | \(-0.984895\pi\) |
0.458357 | − | 0.888768i | \(-0.348438\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.45419 | − | 5.25158i | 0.436554 | − | 0.242496i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −33.7604 | − | 19.4916i | −1.55230 | − | 0.896223i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 19.9667i | − | 0.916134i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.9020 | − | 32.7393i | 0.863657 | − | 1.49590i | −0.00471828 | − | 0.999989i | \(-0.501502\pi\) |
0.868375 | − | 0.495908i | \(-0.165165\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.60491 | − | 5.54540i | 0.437946 | − | 0.252848i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.14242 | − | 2.39163i | 0.188098 | − | 0.108598i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.1049 | + | 26.1624i | −0.684466 | + | 1.18553i | 0.289138 | + | 0.957287i | \(0.406631\pi\) |
−0.973604 | + | 0.228243i | \(0.926702\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.8318i | 1.75245i | 0.481899 | + | 0.876227i | \(0.339947\pi\) | ||||
−0.481899 | + | 0.876227i | \(0.660053\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.45751 | − | 0.841496i | −0.0656431 | − | 0.0378991i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.558590 | + | 0.931533i | −0.0250562 | + | 0.0417850i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.52542 | − | 6.10620i | −0.157819 | − | 0.273351i | 0.776263 | − | 0.630410i | \(-0.217113\pi\) |
−0.934082 | + | 0.357058i | \(0.883780\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.9561 | −0.577683 | −0.288842 | − | 0.957377i | \(-0.593270\pi\) | ||||
−0.288842 | + | 0.957377i | \(0.593270\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.47425 | 0.154602 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.964368 | − | 1.67033i | −0.0427449 | − | 0.0740363i | 0.843861 | − | 0.536561i | \(-0.180277\pi\) |
−0.886606 | + | 0.462525i | \(0.846944\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.4890 | + | 29.6843i | 0.729429 | + | 1.31316i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.0290733 | + | 0.0167855i | 0.00128112 | + | 0.000739657i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 65.0908i | 2.86269i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.43874 | + | 16.3484i | −0.413519 | + | 0.716235i | −0.995272 | − | 0.0971301i | \(-0.969034\pi\) |
0.581753 | + | 0.813366i | \(0.302367\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.87627 | + | 2.23797i | −0.169497 | + | 0.0978594i | −0.582349 | − | 0.812939i | \(-0.697866\pi\) |
0.412851 | + | 0.910798i | \(0.364533\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13.7941 | + | 7.96406i | −0.600883 | + | 0.346920i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.6676 | + | 18.4768i | −0.463808 | + | 0.803338i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 30.0537i | − | 1.30177i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.09981 | + | 2.36703i | 0.177250 | + | 0.102335i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.40009 | + | 42.2566i | −0.0603060 | + | 1.82012i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.637629 | − | 1.10441i | −0.0274138 | − | 0.0474821i | 0.851993 | − | 0.523553i | \(-0.175394\pi\) |
−0.879407 | + | 0.476071i | \(0.842061\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.263283 | −0.0112778 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.8770 | 1.32020 | 0.660102 | − | 0.751176i | \(-0.270513\pi\) | ||||
0.660102 | + | 0.751176i | \(0.270513\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.767462 | − | 1.32928i | −0.0326950 | − | 0.0566294i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.526940 | − | 31.8163i | 0.0224078 | − | 1.35297i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.0859 | + | 16.7927i | 1.23241 | + | 0.711531i | 0.967531 | − | 0.252751i | \(-0.0813355\pi\) |
0.264876 | + | 0.964282i | \(0.414669\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 35.2431i | 1.49062i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.4046 | + | 23.2175i | −0.564937 | + | 0.978499i | 0.432119 | + | 0.901817i | \(0.357766\pi\) |
−0.997056 | + | 0.0766823i | \(0.975567\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.10064 | + | 1.21280i | −0.0883745 | + | 0.0510231i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.7065 | − | 7.91345i | 0.574606 | − | 0.331749i | −0.184381 | − | 0.982855i | \(-0.559028\pi\) |
0.758987 | + | 0.651106i | \(0.225695\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.77658 | + | 6.54124i | −0.158045 | + | 0.273742i | −0.934164 | − | 0.356845i | \(-0.883852\pi\) |
0.776119 | + | 0.630587i | \(0.217186\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.34315i | 0.264527i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.7609 | + | 6.79013i | 0.489611 | + | 0.282677i | 0.724413 | − | 0.689366i | \(-0.242111\pi\) |
−0.234802 | + | 0.972043i | \(0.575444\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.353787 | + | 0.212147i | 0.0146776 | + | 0.00880134i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −34.0845 | − | 59.0360i | −1.41163 | − | 2.44502i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −25.7243 | −1.06176 | −0.530878 | − | 0.847449i | \(-0.678138\pi\) | ||||
−0.530878 | + | 0.847449i | \(0.678138\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.5268 | −0.598565 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.59806 | − | 11.4282i | −0.270950 | − | 0.469299i | 0.698156 | − | 0.715946i | \(-0.254004\pi\) |
−0.969105 | + | 0.246647i | \(0.920671\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.92776 | + | 1.75562i | 0.120026 | + | 0.0719734i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.8018 | − | 8.54581i | −0.604784 | − | 0.349172i | 0.166137 | − | 0.986103i | \(-0.446871\pi\) |
−0.770921 | + | 0.636930i | \(0.780204\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 10.7137i | − | 0.437019i | −0.975835 | − | 0.218510i | \(-0.929881\pi\) | ||
0.975835 | − | 0.218510i | \(-0.0701195\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.69143 | − | 6.39375i | 0.150078 | − | 0.259943i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.0938 | + | 8.13707i | −0.572050 | + | 0.330273i | −0.757968 | − | 0.652292i | \(-0.773808\pi\) |
0.185917 | + | 0.982565i | \(0.440474\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 50.9621 | − | 29.4230i | 2.06171 | − | 1.19033i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.76754 | − | 13.4538i | 0.313728 | − | 0.543393i | −0.665438 | − | 0.746453i | \(-0.731755\pi\) |
0.979166 | + | 0.203060i | \(0.0650886\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 3.18413i | − | 0.128188i | −0.997944 | − | 0.0640941i | \(-0.979584\pi\) | ||
0.997944 | − | 0.0640941i | \(-0.0204158\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.3325 | − | 13.4710i | −0.937811 | − | 0.541446i | −0.0485379 | − | 0.998821i | \(-0.515456\pi\) |
−0.889274 | + | 0.457376i | \(0.848789\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.293027 | − | 17.6928i | 0.0117399 | − | 0.708848i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.8739 | − | 20.5662i | −0.474957 | − | 0.822649i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.04512 | 0.360653 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.7789 | 0.787387 | 0.393693 | − | 0.919242i | \(-0.371197\pi\) | ||||
0.393693 | + | 0.919242i | \(0.371197\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.888449 | − | 1.53884i | −0.0352570 | − | 0.0610670i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 33.7173 | − | 18.0051i | 1.33593 | − | 0.713388i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −39.5884 | − | 22.8564i | −1.56365 | − | 0.902772i | −0.996883 | − | 0.0788925i | \(-0.974862\pi\) |
−0.566764 | − | 0.823880i | \(-0.691805\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 11.1743i | − | 0.440672i | −0.975424 | − | 0.220336i | \(-0.929285\pi\) | ||
0.975424 | − | 0.220336i | \(-0.0707155\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.35600 | + | 14.4730i | −0.328508 | + | 0.568993i | −0.982216 | − | 0.187754i | \(-0.939879\pi\) |
0.653708 | + | 0.756747i | \(0.273213\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.26608 | − | 4.77242i | 0.324472 | − | 0.187334i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 37.0979 | − | 21.4185i | 1.45175 | − | 0.838170i | 0.453173 | − | 0.891423i | \(-0.350292\pi\) |
0.998581 | + | 0.0532524i | \(0.0169588\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.13395 | + | 3.69611i | −0.0833804 | + | 0.144419i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 3.00672i | − | 0.117125i | −0.998284 | − | 0.0585627i | \(-0.981348\pi\) | ||
0.998284 | − | 0.0585627i | \(-0.0186518\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.0503 | + | 7.53461i | 0.507599 | + | 0.293062i | 0.731846 | − | 0.681470i | \(-0.238659\pi\) |
−0.224247 | + | 0.974532i | \(0.571992\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.51186 | + | 2.72174i | 0.0586275 | + | 0.105544i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.243812 | + | 0.422295i | 0.00944045 | + | 0.0163513i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 66.6040 | 2.57122 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.01408 | −0.231826 | −0.115913 | − | 0.993259i | \(-0.536979\pi\) | ||||
−0.115913 | + | 0.993259i | \(0.536979\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.93572 | + | 6.81687i | 0.151262 | + | 0.261994i | 0.931692 | − | 0.363250i | \(-0.118333\pi\) |
−0.780430 | + | 0.625244i | \(0.785000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 22.4627 | − | 37.4599i | 0.862039 | − | 1.43758i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.4955 | + | 7.79165i | 0.516393 | + | 0.298139i | 0.735457 | − | 0.677571i | \(-0.236967\pi\) |
−0.219065 | + | 0.975710i | \(0.570301\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 3.94101i | − | 0.150578i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −30.8144 | + | 53.3721i | −1.17394 | + | 2.03332i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.4535 | + | 14.1183i | −0.930256 | + | 0.537084i | −0.886893 | − | 0.461976i | \(-0.847141\pi\) |
−0.0433635 | + | 0.999059i | \(0.513807\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.35546 | + | 2.51462i | −0.165212 | + | 0.0953851i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.2552 | − | 21.2266i | 0.464199 | − | 0.804016i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.7937i | 0.634288i | 0.948377 | + | 0.317144i | \(0.102724\pi\) | ||||
−0.948377 | + | 0.317144i | \(0.897276\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.14414 | + | 4.12467i | 0.269446 | + | 0.155565i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 27.7338 | − | 15.4055i | 1.04304 | − | 0.579384i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.57291 | − | 6.18846i | −0.134183 | − | 0.232412i | 0.791102 | − | 0.611684i | \(-0.209508\pi\) |
−0.925285 | + | 0.379272i | \(0.876174\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.61496 | 0.172832 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.55589 | −0.357370 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.03223 | + | 12.1802i | 0.262258 | + | 0.454244i | 0.966842 | − | 0.255377i | \(-0.0821995\pi\) |
−0.704584 | + | 0.709621i | \(0.748866\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.306514 | + | 0.00507646i | 0.0114152 | + | 0.000189057i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.60896 | − | 0.928932i | −0.0597552 | − | 0.0344997i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 12.0721i | − | 0.447728i | −0.974620 | − | 0.223864i | \(-0.928133\pi\) | ||
0.974620 | − | 0.223864i | \(-0.0718672\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14.3713 | + | 24.8918i | −0.531542 | + | 0.920657i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.2754 | + | 12.2834i | −0.785827 | + | 0.453697i | −0.838491 | − | 0.544915i | \(-0.816562\pi\) |
0.0526646 | + | 0.998612i | \(0.483229\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −21.3814 | + | 12.3446i | −0.787595 | + | 0.454718i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.0963 | − | 33.0758i | 0.702470 | − | 1.21671i | −0.265126 | − | 0.964214i | \(-0.585414\pi\) |
0.967597 | − | 0.252501i | \(-0.0812530\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.94867i | 0.364981i | 0.983208 | + | 0.182491i | \(0.0584159\pi\) | ||||
−0.983208 | + | 0.182491i | \(0.941584\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.87088 | + | 2.23485i | 0.141818 | + | 0.0818786i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 43.2234 | + | 0.715862i | 1.57935 | + | 0.0261570i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.96469 | − | 3.40295i | −0.0716927 | − | 0.124175i | 0.827951 | − | 0.560801i | \(-0.189507\pi\) |
−0.899643 | + | 0.436626i | \(0.856173\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.55712 | 0.0566692 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.7492 | −0.390686 | −0.195343 | − | 0.980735i | \(-0.562582\pi\) | ||||
−0.195343 | + | 0.980735i | \(0.562582\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.24304 | − | 3.88506i | −0.0813102 | − | 0.140833i | 0.822503 | − | 0.568761i | \(-0.192577\pi\) |
−0.903813 | + | 0.427928i | \(0.859244\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.10171 | + | 1.16745i | −0.0760869 | + | 0.0422645i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.47303 | − | 4.31456i | −0.269836 | − | 0.155790i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 9.74739i | − | 0.351500i | −0.984435 | − | 0.175750i | \(-0.943765\pi\) | ||
0.984435 | − | 0.175750i | \(-0.0562350\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.4609 | − | 31.9752i | 0.663992 | − | 1.15007i | −0.315565 | − | 0.948904i | \(-0.602194\pi\) |
0.979557 | − | 0.201165i | \(-0.0644726\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.2274 | + | 8.79157i | −0.546986 | + | 0.315803i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 19.3591 | − | 11.1770i | 0.693613 | − | 0.400458i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.23981 | − | 2.14742i | 0.0443640 | − | 0.0768406i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.01776i | 0.0720169i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.7796 | + | 9.68771i | 0.598128 | + | 0.345330i | 0.768305 | − | 0.640084i | \(-0.221100\pi\) |
−0.170177 | + | 0.985414i | \(0.554434\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.3909 | + | 18.9961i | −0.405015 | + | 0.675423i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.1070 | − | 52.1469i | −1.06913 | − | 1.85179i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.8237 | 0.843880 | 0.421940 | − | 0.906624i | \(-0.361349\pi\) | ||||
0.421940 | + | 0.906624i | \(0.361349\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 47.9920 | 1.69783 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −38.7596 | − | 67.1336i | −1.36780 | − | 2.36909i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.480298 | − | 0.864659i | −0.0169283 | − | 0.0304752i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.6571 | + | 10.7717i | 0.655948 | + | 0.378712i | 0.790731 | − | 0.612163i | \(-0.209701\pi\) |
−0.134783 | + | 0.990875i | \(0.543034\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.36360i | 0.223456i | 0.993739 | + | 0.111728i | \(0.0356386\pi\) | ||||
−0.993739 | + | 0.111728i | \(0.964361\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.45101 | − | 2.51322i | 0.0508267 | − | 0.0880344i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.7019 | + | 13.1069i | −0.794238 | + | 0.458553i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.0269 | − | 5.78905i | 0.349942 | − | 0.202039i | −0.314717 | − | 0.949185i | \(-0.601910\pi\) |
0.664660 | + | 0.747146i | \(0.268576\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.91237 | − | 13.7046i | 0.275808 | − | 0.477714i | −0.694531 | − | 0.719463i | \(-0.744388\pi\) |
0.970339 | + | 0.241750i | \(0.0777213\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 12.6537i | − | 0.440011i | −0.975499 | − | 0.220006i | \(-0.929392\pi\) | ||
0.975499 | − | 0.220006i | \(-0.0706076\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.47709 | + | 4.31690i | 0.259690 | + | 0.149932i | 0.624193 | − | 0.781270i | \(-0.285428\pi\) |
−0.364503 | + | 0.931202i | \(0.618761\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 31.1562 | + | 1.03230i | 1.07950 | + | 0.0357669i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.873924 | + | 1.51368i | 0.0302434 | + | 0.0523831i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −33.7820 | −1.16628 | −0.583142 | − | 0.812371i | \(-0.698177\pi\) | ||||
−0.583142 | + | 0.812371i | \(0.698177\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.8572 | 0.995075 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.43626 | + | 4.21973i | 0.0838100 | + | 0.145163i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.11640 | − | 67.4079i | 0.0383601 | − | 2.31616i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.26960 | − | 1.31035i | −0.0778008 | − | 0.0449183i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.23446i | 0.0422671i | 0.999777 | + | 0.0211336i | \(0.00672752\pi\) | ||||
−0.999777 | + | 0.0211336i | \(0.993272\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.5237 | − | 30.3519i | 0.598597 | − | 1.03680i | −0.394431 | − | 0.918925i | \(-0.629058\pi\) |
0.993028 | − | 0.117875i | \(-0.0376082\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.5187 | − | 10.6918i | 0.631852 | − | 0.364800i | −0.149617 | − | 0.988744i | \(-0.547804\pi\) |
0.781469 | + | 0.623944i | \(0.214471\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.61471 | − | 2.66430i | 0.157087 | − | 0.0906940i | −0.419396 | − | 0.907803i | \(-0.637758\pi\) |
0.576483 | + | 0.817109i | \(0.304425\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.66053 | − | 4.60818i | 0.0904608 | − | 0.156683i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 72.6433i | 2.46426i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.3301 | + | 11.1602i | 0.654976 | + | 0.378150i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.51913 | + | 3.90917i | 0.220387 | + | 0.132154i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.76822 | − | 3.06264i | −0.0597085 | − | 0.103418i | 0.834626 | − | 0.550817i | \(-0.185684\pi\) |
−0.894335 | + | 0.447399i | \(0.852350\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −49.3358 | −1.66217 | −0.831083 | − | 0.556148i | \(-0.812279\pi\) | ||||
−0.831083 | + | 0.556148i | \(0.812279\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.9893 | −1.14383 | −0.571915 | − | 0.820313i | \(-0.693799\pi\) | ||||
−0.571915 | + | 0.820313i | \(0.693799\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.8153 | + | 32.5891i | 0.631757 | + | 1.09423i | 0.987192 | + | 0.159534i | \(0.0509991\pi\) |
−0.355436 | + | 0.934701i | \(0.615668\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13.9157 | − | 8.34452i | −0.466719 | − | 0.279866i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 37.9057 | + | 21.8849i | 1.26847 | + | 0.732349i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 3.29074i | − | 0.109997i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.675845 | + | 1.17060i | −0.0225407 | + | 0.0390417i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −43.5278 | + | 25.1308i | −1.45012 | + | 0.837227i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.97707 | + | 1.71881i | −0.0989613 | + | 0.0571353i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.75787 | − | 9.97293i | 0.191187 | − | 0.331146i | −0.754457 | − | 0.656350i | \(-0.772100\pi\) |
0.945644 | + | 0.325204i | \(0.105433\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 51.3469i | − | 1.70120i | −0.525815 | − | 0.850599i | \(-0.676240\pi\) | ||
0.525815 | − | 0.850599i | \(-0.323760\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.815568 | − | 0.470869i | −0.0269914 | − | 0.0155835i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.645373 | + | 38.9673i | −0.0213121 | + | 1.28681i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.49832 | − | 2.59517i | −0.0494251 | − | 0.0856068i | 0.840254 | − | 0.542192i | \(-0.182406\pi\) |
−0.889680 | + | 0.456586i | \(0.849072\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.24173 | −0.0737874 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.98497 | 0.328304 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18.7345 | − | 32.4491i | −0.614659 | − | 1.06462i | −0.990444 | − | 0.137914i | \(-0.955960\pi\) |
0.375785 | − | 0.926707i | \(-0.377373\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.1375 | + | 15.0229i | 0.791073 | + | 0.492355i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.74922 | − | 3.89667i | −0.220723 | − | 0.127435i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.97716i | 0.162597i | 0.996690 | + | 0.0812983i | \(0.0259067\pi\) | ||||
−0.996690 | + | 0.0812983i | \(0.974093\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.0429 | + | 29.5192i | −0.555584 | + | 0.962299i | 0.442274 | + | 0.896880i | \(0.354172\pi\) |
−0.997858 | + | 0.0654193i | \(0.979162\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.15014 | + | 3.55078i | −0.200276 | + | 0.115629i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.1735 | − | 15.1113i | 0.850524 | − | 0.491050i | −0.0103036 | − | 0.999947i | \(-0.503280\pi\) |
0.860828 | + | 0.508897i | \(0.169946\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −35.0410 | + | 60.6928i | −1.13748 | + | 1.97017i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20.5265i | 0.664917i | 0.943118 | + | 0.332459i | \(0.107878\pi\) | ||||
−0.943118 | + | 0.332459i | \(0.892122\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.36992 | + | 1.94562i | 0.109048 | + | 0.0629589i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.4752 | − | 31.4598i | −0.564304 | − | 1.01589i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.10369 | − | 15.7680i | −0.293667 | − | 0.508647i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.66768 | −0.0536845 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.8044 | −0.701181 | −0.350591 | − | 0.936529i | \(-0.614019\pi\) | ||||
−0.350591 | + | 0.936529i | \(0.614019\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.7817 | − | 30.7988i | −0.570642 | − | 0.988382i | −0.996500 | − | 0.0835915i | \(-0.973361\pi\) |
0.425858 | − | 0.904790i | \(-0.359972\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −23.6179 | + | 39.3864i | −0.757156 | + | 1.26267i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.92632 | + | 5.15362i | 0.285578 | + | 0.164879i | 0.635946 | − | 0.771733i | \(-0.280610\pi\) |
−0.350368 | + | 0.936612i | \(0.613943\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 40.3964i | 1.29108i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14.1069 | − | 24.4340i | 0.449942 | − | 0.779322i | −0.548440 | − | 0.836190i | \(-0.684778\pi\) |
0.998382 | + | 0.0568679i | \(0.0181114\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.667579 | − | 0.385427i | 0.0212708 | − | 0.0122807i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.21208 | − | 4.16389i | 0.229331 | − | 0.132404i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.2085 | + | 29.8061i | −0.546647 | + | 0.946821i | 0.451854 | + | 0.892092i | \(0.350763\pi\) |
−0.998501 | + | 0.0547288i | \(0.982571\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 2.42740i | − | 0.0769538i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.0269 | + | 23.6869i | 1.29934 | + | 0.750172i | 0.980289 | − | 0.197567i | \(-0.0633040\pi\) |
0.319047 | + | 0.947739i | \(0.396637\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 504.2.bl.a.17.4 | ✓ | 16 | |
3.2 | odd | 2 | inner | 504.2.bl.a.17.5 | yes | 16 | |
4.3 | odd | 2 | 1008.2.bt.d.17.4 | 16 | |||
7.2 | even | 3 | 3528.2.bl.a.1097.4 | 16 | |||
7.3 | odd | 6 | 3528.2.k.b.881.7 | 16 | |||
7.4 | even | 3 | 3528.2.k.b.881.9 | 16 | |||
7.5 | odd | 6 | inner | 504.2.bl.a.89.5 | yes | 16 | |
7.6 | odd | 2 | 3528.2.bl.a.521.5 | 16 | |||
12.11 | even | 2 | 1008.2.bt.d.17.5 | 16 | |||
21.2 | odd | 6 | 3528.2.bl.a.1097.5 | 16 | |||
21.5 | even | 6 | inner | 504.2.bl.a.89.4 | yes | 16 | |
21.11 | odd | 6 | 3528.2.k.b.881.8 | 16 | |||
21.17 | even | 6 | 3528.2.k.b.881.10 | 16 | |||
21.20 | even | 2 | 3528.2.bl.a.521.4 | 16 | |||
28.3 | even | 6 | 7056.2.k.h.881.8 | 16 | |||
28.11 | odd | 6 | 7056.2.k.h.881.10 | 16 | |||
28.19 | even | 6 | 1008.2.bt.d.593.5 | 16 | |||
84.11 | even | 6 | 7056.2.k.h.881.7 | 16 | |||
84.47 | odd | 6 | 1008.2.bt.d.593.4 | 16 | |||
84.59 | odd | 6 | 7056.2.k.h.881.9 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.bl.a.17.4 | ✓ | 16 | 1.1 | even | 1 | trivial | |
504.2.bl.a.17.5 | yes | 16 | 3.2 | odd | 2 | inner | |
504.2.bl.a.89.4 | yes | 16 | 21.5 | even | 6 | inner | |
504.2.bl.a.89.5 | yes | 16 | 7.5 | odd | 6 | inner | |
1008.2.bt.d.17.4 | 16 | 4.3 | odd | 2 | |||
1008.2.bt.d.17.5 | 16 | 12.11 | even | 2 | |||
1008.2.bt.d.593.4 | 16 | 84.47 | odd | 6 | |||
1008.2.bt.d.593.5 | 16 | 28.19 | even | 6 | |||
3528.2.k.b.881.7 | 16 | 7.3 | odd | 6 | |||
3528.2.k.b.881.8 | 16 | 21.11 | odd | 6 | |||
3528.2.k.b.881.9 | 16 | 7.4 | even | 3 | |||
3528.2.k.b.881.10 | 16 | 21.17 | even | 6 | |||
3528.2.bl.a.521.4 | 16 | 21.20 | even | 2 | |||
3528.2.bl.a.521.5 | 16 | 7.6 | odd | 2 | |||
3528.2.bl.a.1097.4 | 16 | 7.2 | even | 3 | |||
3528.2.bl.a.1097.5 | 16 | 21.2 | odd | 6 | |||
7056.2.k.h.881.7 | 16 | 84.11 | even | 6 | |||
7056.2.k.h.881.8 | 16 | 28.3 | even | 6 | |||
7056.2.k.h.881.9 | 16 | 84.59 | odd | 6 | |||
7056.2.k.h.881.10 | 16 | 28.11 | odd | 6 |