Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [125,2,Mod(124,125)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(125, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("125.124");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 125 = 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 125.b (of order \(2\), degree \(1\), not 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: | \(0.998130025266\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 124.1 | ||
Root | \(-1.61803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 125.124 |
Dual form | 125.2.b.b.124.4 |
$q$-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 \(\left(\mathbb{Z}/125\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.61803i | − 1.14412i | −0.820211 | − | 0.572061i | \(-0.806144\pi\) | ||||
0.820211 | − | 0.572061i | \(-0.193856\pi\) | |||||||
\(3\) | 0.381966i | 0.220528i | 0.993902 | + | 0.110264i | \(0.0351697\pi\) | ||||
−0.993902 | + | 0.110264i | \(0.964830\pi\) | |||||||
\(4\) | −0.618034 | −0.309017 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.618034 | 0.252311 | ||||||||
\(7\) | − 3.00000i | − 1.13389i | −0.823754 | − | 0.566947i | \(-0.808125\pi\) | ||||
0.823754 | − | 0.566947i | \(-0.191875\pi\) | |||||||
\(8\) | − 2.23607i | − 0.790569i | ||||||||
\(9\) | 2.85410 | 0.951367 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.00000 | −0.904534 | −0.452267 | − | 0.891883i | \(-0.649385\pi\) | ||||
−0.452267 | + | 0.891883i | \(0.649385\pi\) | |||||||
\(12\) | − 0.236068i | − 0.0681470i | ||||||||
\(13\) | 4.85410i | 1.34629i | 0.739512 | + | 0.673143i | \(0.235056\pi\) | ||||
−0.739512 | + | 0.673143i | \(0.764944\pi\) | |||||||
\(14\) | −4.85410 | −1.29731 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.85410 | −1.21353 | ||||||||
\(17\) | 4.23607i | 1.02740i | 0.857971 | + | 0.513699i | \(0.171725\pi\) | ||||
−0.857971 | + | 0.513699i | \(0.828275\pi\) | |||||||
\(18\) | − 4.61803i | − 1.08848i | ||||||||
\(19\) | 3.61803 | 0.830034 | 0.415017 | − | 0.909814i | \(-0.363776\pi\) | ||||
0.415017 | + | 0.909814i | \(0.363776\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.14590 | 0.250055 | ||||||||
\(22\) | 4.85410i | 1.03490i | ||||||||
\(23\) | 1.23607i | 0.257738i | 0.991662 | + | 0.128869i | \(0.0411347\pi\) | ||||
−0.991662 | + | 0.128869i | \(0.958865\pi\) | |||||||
\(24\) | 0.854102 | 0.174343 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 7.85410 | 1.54032 | ||||||||
\(27\) | 2.23607i | 0.430331i | ||||||||
\(28\) | 1.85410i | 0.350392i | ||||||||
\(29\) | −6.70820 | −1.24568 | −0.622841 | − | 0.782348i | \(-0.714022\pi\) | ||||
−0.622841 | + | 0.782348i | \(0.714022\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.09017 | 0.914222 | 0.457111 | − | 0.889410i | \(-0.348884\pi\) | ||||
0.457111 | + | 0.889410i | \(0.348884\pi\) | |||||||
\(32\) | 3.38197i | 0.597853i | ||||||||
\(33\) | − 1.14590i | − 0.199475i | ||||||||
\(34\) | 6.85410 | 1.17547 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.76393 | −0.293989 | ||||||||
\(37\) | 3.70820i | 0.609625i | 0.952412 | + | 0.304812i | \(0.0985938\pi\) | ||||
−0.952412 | + | 0.304812i | \(0.901406\pi\) | |||||||
\(38\) | − 5.85410i | − 0.949661i | ||||||||
\(39\) | −1.85410 | −0.296894 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.00000 | −0.468521 | −0.234261 | − | 0.972174i | \(-0.575267\pi\) | ||||
−0.234261 | + | 0.972174i | \(0.575267\pi\) | |||||||
\(42\) | − 1.85410i | − 0.286094i | ||||||||
\(43\) | 9.00000i | 1.37249i | 0.727372 | + | 0.686244i | \(0.240742\pi\) | ||||
−0.727372 | + | 0.686244i | \(0.759258\pi\) | |||||||
\(44\) | 1.85410 | 0.279516 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.00000 | 0.294884 | ||||||||
\(47\) | − 8.32624i | − 1.21451i | −0.794508 | − | 0.607253i | \(-0.792271\pi\) | ||||
0.794508 | − | 0.607253i | \(-0.207729\pi\) | |||||||
\(48\) | − 1.85410i | − 0.267617i | ||||||||
\(49\) | −2.00000 | −0.285714 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.61803 | −0.226570 | ||||||||
\(52\) | − 3.00000i | − 0.416025i | ||||||||
\(53\) | − 4.61803i | − 0.634336i | −0.948369 | − | 0.317168i | \(-0.897268\pi\) | ||||
0.948369 | − | 0.317168i | \(-0.102732\pi\) | |||||||
\(54\) | 3.61803 | 0.492352 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −6.70820 | −0.896421 | ||||||||
\(57\) | 1.38197i | 0.183046i | ||||||||
\(58\) | 10.8541i | 1.42521i | ||||||||
\(59\) | −4.14590 | −0.539750 | −0.269875 | − | 0.962895i | \(-0.586982\pi\) | ||||
−0.269875 | + | 0.962895i | \(0.586982\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.09017 | −0.779766 | −0.389883 | − | 0.920864i | \(-0.627485\pi\) | ||||
−0.389883 | + | 0.920864i | \(0.627485\pi\) | |||||||
\(62\) | − 8.23607i | − 1.04598i | ||||||||
\(63\) | − 8.56231i | − 1.07875i | ||||||||
\(64\) | −4.23607 | −0.529508 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.85410 | −0.228224 | ||||||||
\(67\) | − 13.8541i | − 1.69255i | −0.532748 | − | 0.846274i | \(-0.678841\pi\) | ||||
0.532748 | − | 0.846274i | \(-0.321159\pi\) | |||||||
\(68\) | − 2.61803i | − 0.317483i | ||||||||
\(69\) | −0.472136 | −0.0568385 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.00000 | −0.356034 | −0.178017 | − | 0.984027i | \(-0.556968\pi\) | ||||
−0.178017 | + | 0.984027i | \(0.556968\pi\) | |||||||
\(72\) | − 6.38197i | − 0.752122i | ||||||||
\(73\) | − 1.85410i | − 0.217006i | −0.994096 | − | 0.108503i | \(-0.965394\pi\) | ||||
0.994096 | − | 0.108503i | \(-0.0346057\pi\) | |||||||
\(74\) | 6.00000 | 0.697486 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.23607 | −0.256495 | ||||||||
\(77\) | 9.00000i | 1.02565i | ||||||||
\(78\) | 3.00000i | 0.339683i | ||||||||
\(79\) | −0.527864 | −0.0593893 | −0.0296947 | − | 0.999559i | \(-0.509453\pi\) | ||||
−0.0296947 | + | 0.999559i | \(0.509453\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.70820 | 0.856467 | ||||||||
\(82\) | 4.85410i | 0.536046i | ||||||||
\(83\) | − 0.472136i | − 0.0518237i | −0.999664 | − | 0.0259118i | \(-0.991751\pi\) | ||||
0.999664 | − | 0.0259118i | \(-0.00824891\pi\) | |||||||
\(84\) | −0.708204 | −0.0772714 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 14.5623 | 1.57029 | ||||||||
\(87\) | − 2.56231i | − 0.274708i | ||||||||
\(88\) | 6.70820i | 0.715097i | ||||||||
\(89\) | 13.4164 | 1.42214 | 0.711068 | − | 0.703123i | \(-0.248212\pi\) | ||||
0.711068 | + | 0.703123i | \(0.248212\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.5623 | 1.52654 | ||||||||
\(92\) | − 0.763932i | − 0.0796454i | ||||||||
\(93\) | 1.94427i | 0.201612i | ||||||||
\(94\) | −13.4721 | −1.38954 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.29180 | −0.131843 | ||||||||
\(97\) | 7.85410i | 0.797463i | 0.917068 | + | 0.398732i | \(0.130549\pi\) | ||||
−0.917068 | + | 0.398732i | \(0.869451\pi\) | |||||||
\(98\) | 3.23607i | 0.326892i | ||||||||
\(99\) | −8.56231 | −0.860544 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.00000 | −0.298511 | −0.149256 | − | 0.988799i | \(-0.547688\pi\) | ||||
−0.149256 | + | 0.988799i | \(0.547688\pi\) | |||||||
\(102\) | 2.61803i | 0.259224i | ||||||||
\(103\) | − 12.7082i | − 1.25218i | −0.779752 | − | 0.626088i | \(-0.784655\pi\) | ||||
0.779752 | − | 0.626088i | \(-0.215345\pi\) | |||||||
\(104\) | 10.8541 | 1.06433 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.47214 | −0.725758 | ||||||||
\(107\) | 0.0901699i | 0.00871706i | 0.999991 | + | 0.00435853i | \(0.00138737\pi\) | ||||
−0.999991 | + | 0.00435853i | \(0.998613\pi\) | |||||||
\(108\) | − 1.38197i | − 0.132980i | ||||||||
\(109\) | −5.32624 | −0.510161 | −0.255081 | − | 0.966920i | \(-0.582102\pi\) | ||||
−0.255081 | + | 0.966920i | \(0.582102\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.41641 | −0.134439 | ||||||||
\(112\) | 14.5623i | 1.37601i | ||||||||
\(113\) | − 2.05573i | − 0.193387i | −0.995314 | − | 0.0966933i | \(-0.969173\pi\) | ||||
0.995314 | − | 0.0966933i | \(-0.0308266\pi\) | |||||||
\(114\) | 2.23607 | 0.209427 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.14590 | 0.384937 | ||||||||
\(117\) | 13.8541i | 1.28081i | ||||||||
\(118\) | 6.70820i | 0.617540i | ||||||||
\(119\) | 12.7082 | 1.16496 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | 9.85410i | 0.892148i | ||||||||
\(123\) | − 1.14590i | − 0.103322i | ||||||||
\(124\) | −3.14590 | −0.282510 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −13.8541 | −1.23422 | ||||||||
\(127\) | − 9.70820i | − 0.861464i | −0.902480 | − | 0.430732i | \(-0.858255\pi\) | ||||
0.902480 | − | 0.430732i | \(-0.141745\pi\) | |||||||
\(128\) | 13.6180i | 1.20368i | ||||||||
\(129\) | −3.43769 | −0.302672 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.2705 | −1.07208 | −0.536040 | − | 0.844193i | \(-0.680080\pi\) | ||||
−0.536040 | + | 0.844193i | \(0.680080\pi\) | |||||||
\(132\) | 0.708204i | 0.0616412i | ||||||||
\(133\) | − 10.8541i | − 0.941170i | ||||||||
\(134\) | −22.4164 | −1.93648 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.47214 | 0.812229 | ||||||||
\(137\) | 5.61803i | 0.479981i | 0.970775 | + | 0.239991i | \(0.0771443\pi\) | ||||
−0.970775 | + | 0.239991i | \(0.922856\pi\) | |||||||
\(138\) | 0.763932i | 0.0650302i | ||||||||
\(139\) | 12.2361 | 1.03785 | 0.518925 | − | 0.854820i | \(-0.326332\pi\) | ||||
0.518925 | + | 0.854820i | \(0.326332\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.18034 | 0.267833 | ||||||||
\(142\) | 4.85410i | 0.407347i | ||||||||
\(143\) | − 14.5623i | − 1.21776i | ||||||||
\(144\) | −13.8541 | −1.15451 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.00000 | −0.248282 | ||||||||
\(147\) | − 0.763932i | − 0.0630081i | ||||||||
\(148\) | − 2.29180i | − 0.188384i | ||||||||
\(149\) | 15.0000 | 1.22885 | 0.614424 | − | 0.788976i | \(-0.289388\pi\) | ||||
0.614424 | + | 0.788976i | \(0.289388\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.0902 | −1.71629 | −0.858147 | − | 0.513404i | \(-0.828384\pi\) | ||||
−0.858147 | + | 0.513404i | \(0.828384\pi\) | |||||||
\(152\) | − 8.09017i | − 0.656199i | ||||||||
\(153\) | 12.0902i | 0.977432i | ||||||||
\(154\) | 14.5623 | 1.17346 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.14590 | 0.0917453 | ||||||||
\(157\) | − 12.2705i | − 0.979293i | −0.871921 | − | 0.489647i | \(-0.837126\pi\) | ||||
0.871921 | − | 0.489647i | \(-0.162874\pi\) | |||||||
\(158\) | 0.854102i | 0.0679487i | ||||||||
\(159\) | 1.76393 | 0.139889 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.70820 | 0.292247 | ||||||||
\(162\) | − 12.4721i | − 0.979904i | ||||||||
\(163\) | 19.8541i | 1.55509i | 0.628825 | + | 0.777547i | \(0.283536\pi\) | ||||
−0.628825 | + | 0.777547i | \(0.716464\pi\) | |||||||
\(164\) | 1.85410 | 0.144781 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.763932 | −0.0592926 | ||||||||
\(167\) | 9.23607i | 0.714708i | 0.933969 | + | 0.357354i | \(0.116321\pi\) | ||||
−0.933969 | + | 0.357354i | \(0.883679\pi\) | |||||||
\(168\) | − 2.56231i | − 0.197686i | ||||||||
\(169\) | −10.5623 | −0.812485 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.3262 | 0.789667 | ||||||||
\(172\) | − 5.56231i | − 0.424122i | ||||||||
\(173\) | 0.0557281i | 0.00423693i | 0.999998 | + | 0.00211846i | \(0.000674329\pi\) | ||||
−0.999998 | + | 0.00211846i | \(0.999326\pi\) | |||||||
\(174\) | −4.14590 | −0.314300 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 14.5623 | 1.09768 | ||||||||
\(177\) | − 1.58359i | − 0.119030i | ||||||||
\(178\) | − 21.7082i | − 1.62710i | ||||||||
\(179\) | −6.70820 | −0.501395 | −0.250697 | − | 0.968066i | \(-0.580660\pi\) | ||||
−0.250697 | + | 0.968066i | \(0.580660\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.1803 | 1.35133 | 0.675667 | − | 0.737207i | \(-0.263856\pi\) | ||||
0.675667 | + | 0.737207i | \(0.263856\pi\) | |||||||
\(182\) | − 23.5623i | − 1.74655i | ||||||||
\(183\) | − 2.32624i | − 0.171960i | ||||||||
\(184\) | 2.76393 | 0.203760 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.14590 | 0.230668 | ||||||||
\(187\) | − 12.7082i | − 0.929316i | ||||||||
\(188\) | 5.14590i | 0.375303i | ||||||||
\(189\) | 6.70820 | 0.487950 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.0000 | 0.868290 | 0.434145 | − | 0.900843i | \(-0.357051\pi\) | ||||
0.434145 | + | 0.900843i | \(0.357051\pi\) | |||||||
\(192\) | − 1.61803i | − 0.116772i | ||||||||
\(193\) | − 15.2705i | − 1.09920i | −0.835429 | − | 0.549598i | \(-0.814781\pi\) | ||||
0.835429 | − | 0.549598i | \(-0.185219\pi\) | |||||||
\(194\) | 12.7082 | 0.912396 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.23607 | 0.0882906 | ||||||||
\(197\) | − 4.05573i | − 0.288959i | −0.989508 | − | 0.144479i | \(-0.953849\pi\) | ||||
0.989508 | − | 0.144479i | \(-0.0461507\pi\) | |||||||
\(198\) | 13.8541i | 0.984568i | ||||||||
\(199\) | −16.1803 | −1.14699 | −0.573497 | − | 0.819208i | \(-0.694414\pi\) | ||||
−0.573497 | + | 0.819208i | \(0.694414\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.29180 | 0.373255 | ||||||||
\(202\) | 4.85410i | 0.341533i | ||||||||
\(203\) | 20.1246i | 1.41247i | ||||||||
\(204\) | 1.00000 | 0.0700140 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −20.5623 | −1.43264 | ||||||||
\(207\) | 3.52786i | 0.245204i | ||||||||
\(208\) | − 23.5623i | − 1.63375i | ||||||||
\(209\) | −10.8541 | −0.750794 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.18034 | −0.287786 | −0.143893 | − | 0.989593i | \(-0.545962\pi\) | ||||
−0.143893 | + | 0.989593i | \(0.545962\pi\) | |||||||
\(212\) | 2.85410i | 0.196021i | ||||||||
\(213\) | − 1.14590i | − 0.0785156i | ||||||||
\(214\) | 0.145898 | 0.00997338 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 5.00000 | 0.340207 | ||||||||
\(217\) | − 15.2705i | − 1.03663i | ||||||||
\(218\) | 8.61803i | 0.583687i | ||||||||
\(219\) | 0.708204 | 0.0478560 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.5623 | −1.38317 | ||||||||
\(222\) | 2.29180i | 0.153815i | ||||||||
\(223\) | − 1.85410i | − 0.124160i | −0.998071 | − | 0.0620799i | \(-0.980227\pi\) | ||||
0.998071 | − | 0.0620799i | \(-0.0197734\pi\) | |||||||
\(224\) | 10.1459 | 0.677901 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.32624 | −0.221258 | ||||||||
\(227\) | − 6.61803i | − 0.439254i | −0.975584 | − | 0.219627i | \(-0.929516\pi\) | ||||
0.975584 | − | 0.219627i | \(-0.0704841\pi\) | |||||||
\(228\) | − 0.854102i | − 0.0565643i | ||||||||
\(229\) | 1.38197 | 0.0913229 | 0.0456614 | − | 0.998957i | \(-0.485460\pi\) | ||||
0.0456614 | + | 0.998957i | \(0.485460\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.43769 | −0.226184 | ||||||||
\(232\) | 15.0000i | 0.984798i | ||||||||
\(233\) | 26.8885i | 1.76153i | 0.473556 | + | 0.880764i | \(0.342970\pi\) | ||||
−0.473556 | + | 0.880764i | \(0.657030\pi\) | |||||||
\(234\) | 22.4164 | 1.46541 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.56231 | 0.166792 | ||||||||
\(237\) | − 0.201626i | − 0.0130970i | ||||||||
\(238\) | − 20.5623i | − 1.33286i | ||||||||
\(239\) | −25.8541 | −1.67236 | −0.836181 | − | 0.548453i | \(-0.815217\pi\) | ||||
−0.836181 | + | 0.548453i | \(0.815217\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.1803 | −1.23551 | −0.617757 | − | 0.786369i | \(-0.711959\pi\) | ||||
−0.617757 | + | 0.786369i | \(0.711959\pi\) | |||||||
\(242\) | 3.23607i | 0.208022i | ||||||||
\(243\) | 9.65248i | 0.619207i | ||||||||
\(244\) | 3.76393 | 0.240961 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.85410 | −0.118213 | ||||||||
\(247\) | 17.5623i | 1.11746i | ||||||||
\(248\) | − 11.3820i | − 0.722756i | ||||||||
\(249\) | 0.180340 | 0.0114286 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.27051 | 0.395791 | 0.197896 | − | 0.980223i | \(-0.436589\pi\) | ||||
0.197896 | + | 0.980223i | \(0.436589\pi\) | |||||||
\(252\) | 5.29180i | 0.333352i | ||||||||
\(253\) | − 3.70820i | − 0.233133i | ||||||||
\(254\) | −15.7082 | −0.985620 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.5623 | 0.847644 | ||||||||
\(257\) | 29.3607i | 1.83147i | 0.401784 | + | 0.915734i | \(0.368390\pi\) | ||||
−0.401784 | + | 0.915734i | \(0.631610\pi\) | |||||||
\(258\) | 5.56231i | 0.346294i | ||||||||
\(259\) | 11.1246 | 0.691250 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −19.1459 | −1.18510 | ||||||||
\(262\) | 19.8541i | 1.22659i | ||||||||
\(263\) | − 16.3262i | − 1.00672i | −0.864077 | − | 0.503359i | \(-0.832097\pi\) | ||||
0.864077 | − | 0.503359i | \(-0.167903\pi\) | |||||||
\(264\) | −2.56231 | −0.157699 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −17.5623 | −1.07681 | ||||||||
\(267\) | 5.12461i | 0.313621i | ||||||||
\(268\) | 8.56231i | 0.523026i | ||||||||
\(269\) | −2.56231 | −0.156227 | −0.0781133 | − | 0.996944i | \(-0.524890\pi\) | ||||
−0.0781133 | + | 0.996944i | \(0.524890\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.0902 | 1.22039 | 0.610195 | − | 0.792251i | \(-0.291091\pi\) | ||||
0.610195 | + | 0.792251i | \(0.291091\pi\) | |||||||
\(272\) | − 20.5623i | − 1.24677i | ||||||||
\(273\) | 5.56231i | 0.336646i | ||||||||
\(274\) | 9.09017 | 0.549157 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.291796 | 0.0175641 | ||||||||
\(277\) | 5.29180i | 0.317953i | 0.987282 | + | 0.158977i | \(0.0508194\pi\) | ||||
−0.987282 | + | 0.158977i | \(0.949181\pi\) | |||||||
\(278\) | − 19.7984i | − 1.18743i | ||||||||
\(279\) | 14.5279 | 0.869760 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.0000 | 0.715860 | 0.357930 | − | 0.933748i | \(-0.383483\pi\) | ||||
0.357930 | + | 0.933748i | \(0.383483\pi\) | |||||||
\(282\) | − 5.14590i | − 0.306434i | ||||||||
\(283\) | 15.7082i | 0.933756i | 0.884322 | + | 0.466878i | \(0.154621\pi\) | ||||
−0.884322 | + | 0.466878i | \(0.845379\pi\) | |||||||
\(284\) | 1.85410 | 0.110021 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −23.5623 | −1.39327 | ||||||||
\(287\) | 9.00000i | 0.531253i | ||||||||
\(288\) | 9.65248i | 0.568778i | ||||||||
\(289\) | −0.944272 | −0.0555454 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.00000 | −0.175863 | ||||||||
\(292\) | 1.14590i | 0.0670586i | ||||||||
\(293\) | 21.3607i | 1.24790i | 0.781463 | + | 0.623952i | \(0.214474\pi\) | ||||
−0.781463 | + | 0.623952i | \(0.785526\pi\) | |||||||
\(294\) | −1.23607 | −0.0720889 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 8.29180 | 0.481951 | ||||||||
\(297\) | − 6.70820i | − 0.389249i | ||||||||
\(298\) | − 24.2705i | − 1.40595i | ||||||||
\(299\) | −6.00000 | −0.346989 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 27.0000 | 1.55625 | ||||||||
\(302\) | 34.1246i | 1.96365i | ||||||||
\(303\) | − 1.14590i | − 0.0658301i | ||||||||
\(304\) | −17.5623 | −1.00727 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 19.5623 | 1.11830 | ||||||||
\(307\) | 6.27051i | 0.357877i | 0.983860 | + | 0.178938i | \(0.0572663\pi\) | ||||
−0.983860 | + | 0.178938i | \(0.942734\pi\) | |||||||
\(308\) | − 5.56231i | − 0.316942i | ||||||||
\(309\) | 4.85410 | 0.276140 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.2705 | 1.20614 | 0.603070 | − | 0.797688i | \(-0.293944\pi\) | ||||
0.603070 | + | 0.797688i | \(0.293944\pi\) | |||||||
\(312\) | 4.14590i | 0.234715i | ||||||||
\(313\) | − 19.4164i | − 1.09748i | −0.835993 | − | 0.548740i | \(-0.815108\pi\) | ||||
0.835993 | − | 0.548740i | \(-0.184892\pi\) | |||||||
\(314\) | −19.8541 | −1.12043 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.326238 | 0.0183523 | ||||||||
\(317\) | − 26.9443i | − 1.51334i | −0.653796 | − | 0.756671i | \(-0.726825\pi\) | ||||
0.653796 | − | 0.756671i | \(-0.273175\pi\) | |||||||
\(318\) | − 2.85410i | − 0.160050i | ||||||||
\(319\) | 20.1246 | 1.12676 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.0344419 | −0.00192236 | ||||||||
\(322\) | − 6.00000i | − 0.334367i | ||||||||
\(323\) | 15.3262i | 0.852775i | ||||||||
\(324\) | −4.76393 | −0.264663 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 32.1246 | 1.77922 | ||||||||
\(327\) | − 2.03444i | − 0.112505i | ||||||||
\(328\) | 6.70820i | 0.370399i | ||||||||
\(329\) | −24.9787 | −1.37712 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.0902 | −1.15922 | −0.579610 | − | 0.814894i | \(-0.696795\pi\) | ||||
−0.579610 | + | 0.814894i | \(0.696795\pi\) | |||||||
\(332\) | 0.291796i | 0.0160144i | ||||||||
\(333\) | 10.5836i | 0.579977i | ||||||||
\(334\) | 14.9443 | 0.817714 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −5.56231 | −0.303449 | ||||||||
\(337\) | − 29.8328i | − 1.62510i | −0.582894 | − | 0.812549i | \(-0.698080\pi\) | ||||
0.582894 | − | 0.812549i | \(-0.301920\pi\) | |||||||
\(338\) | 17.0902i | 0.929583i | ||||||||
\(339\) | 0.785218 | 0.0426472 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.2705 | −0.826944 | ||||||||
\(342\) | − 16.7082i | − 0.903476i | ||||||||
\(343\) | − 15.0000i | − 0.809924i | ||||||||
\(344\) | 20.1246 | 1.08505 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.0901699 | 0.00484757 | ||||||||
\(347\) | 15.9443i | 0.855933i | 0.903795 | + | 0.427967i | \(0.140770\pi\) | ||||
−0.903795 | + | 0.427967i | \(0.859230\pi\) | |||||||
\(348\) | 1.58359i | 0.0848894i | ||||||||
\(349\) | 17.3607 | 0.929296 | 0.464648 | − | 0.885496i | \(-0.346181\pi\) | ||||
0.464648 | + | 0.885496i | \(0.346181\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.8541 | −0.579349 | ||||||||
\(352\) | − 10.1459i | − 0.540778i | ||||||||
\(353\) | − 3.88854i | − 0.206966i | −0.994631 | − | 0.103483i | \(-0.967001\pi\) | ||||
0.994631 | − | 0.103483i | \(-0.0329988\pi\) | |||||||
\(354\) | −2.56231 | −0.136185 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −8.29180 | −0.439464 | ||||||||
\(357\) | 4.85410i | 0.256906i | ||||||||
\(358\) | 10.8541i | 0.573657i | ||||||||
\(359\) | 10.8541 | 0.572858 | 0.286429 | − | 0.958102i | \(-0.407532\pi\) | ||||
0.286429 | + | 0.958102i | \(0.407532\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.90983 | −0.311044 | ||||||||
\(362\) | − 29.4164i | − 1.54609i | ||||||||
\(363\) | − 0.763932i | − 0.0400960i | ||||||||
\(364\) | −9.00000 | −0.471728 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.76393 | −0.196744 | ||||||||
\(367\) | 1.14590i | 0.0598154i | 0.999553 | + | 0.0299077i | \(0.00952133\pi\) | ||||
−0.999553 | + | 0.0299077i | \(0.990479\pi\) | |||||||
\(368\) | − 6.00000i | − 0.312772i | ||||||||
\(369\) | −8.56231 | −0.445736 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.8541 | −0.719269 | ||||||||
\(372\) | − 1.20163i | − 0.0623014i | ||||||||
\(373\) | − 1.85410i | − 0.0960018i | −0.998847 | − | 0.0480009i | \(-0.984715\pi\) | ||||
0.998847 | − | 0.0480009i | \(-0.0152850\pi\) | |||||||
\(374\) | −20.5623 | −1.06325 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −18.6180 | −0.960152 | ||||||||
\(377\) | − 32.5623i | − 1.67704i | ||||||||
\(378\) | − 10.8541i | − 0.558275i | ||||||||
\(379\) | 7.56231 | 0.388450 | 0.194225 | − | 0.980957i | \(-0.437781\pi\) | ||||
0.194225 | + | 0.980957i | \(0.437781\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.70820 | 0.189977 | ||||||||
\(382\) | − 19.4164i | − 0.993430i | ||||||||
\(383\) | − 35.4721i | − 1.81254i | −0.422698 | − | 0.906271i | \(-0.638917\pi\) | ||||
0.422698 | − | 0.906271i | \(-0.361083\pi\) | |||||||
\(384\) | −5.20163 | −0.265444 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −24.7082 | −1.25761 | ||||||||
\(387\) | 25.6869i | 1.30574i | ||||||||
\(388\) | − 4.85410i | − 0.246430i | ||||||||
\(389\) | −1.58359 | −0.0802913 | −0.0401457 | − | 0.999194i | \(-0.512782\pi\) | ||||
−0.0401457 | + | 0.999194i | \(0.512782\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.23607 | −0.264799 | ||||||||
\(392\) | 4.47214i | 0.225877i | ||||||||
\(393\) | − 4.68692i | − 0.236424i | ||||||||
\(394\) | −6.56231 | −0.330604 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 5.29180 | 0.265923 | ||||||||
\(397\) | − 16.4164i | − 0.823916i | −0.911203 | − | 0.411958i | \(-0.864845\pi\) | ||||
0.911203 | − | 0.411958i | \(-0.135155\pi\) | |||||||
\(398\) | 26.1803i | 1.31230i | ||||||||
\(399\) | 4.14590 | 0.207555 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.0000 | 0.599251 | 0.299626 | − | 0.954057i | \(-0.403138\pi\) | ||||
0.299626 | + | 0.954057i | \(0.403138\pi\) | |||||||
\(402\) | − 8.56231i | − 0.427049i | ||||||||
\(403\) | 24.7082i | 1.23080i | ||||||||
\(404\) | 1.85410 | 0.0922450 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 32.5623 | 1.61604 | ||||||||
\(407\) | − 11.1246i | − 0.551427i | ||||||||
\(408\) | 3.61803i | 0.179119i | ||||||||
\(409\) | 22.7639 | 1.12560 | 0.562802 | − | 0.826592i | \(-0.309723\pi\) | ||||
0.562802 | + | 0.826592i | \(0.309723\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.14590 | −0.105849 | ||||||||
\(412\) | 7.85410i | 0.386944i | ||||||||
\(413\) | 12.4377i | 0.612019i | ||||||||
\(414\) | 5.70820 | 0.280543 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −16.4164 | −0.804881 | ||||||||
\(417\) | 4.67376i | 0.228875i | ||||||||
\(418\) | 17.5623i | 0.859000i | ||||||||
\(419\) | 6.70820 | 0.327717 | 0.163859 | − | 0.986484i | \(-0.447606\pi\) | ||||
0.163859 | + | 0.986484i | \(0.447606\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.90983 | 0.434239 | 0.217119 | − | 0.976145i | \(-0.430334\pi\) | ||||
0.217119 | + | 0.976145i | \(0.430334\pi\) | |||||||
\(422\) | 6.76393i | 0.329263i | ||||||||
\(423\) | − 23.7639i | − 1.15544i | ||||||||
\(424\) | −10.3262 | −0.501486 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.85410 | −0.0898315 | ||||||||
\(427\) | 18.2705i | 0.884172i | ||||||||
\(428\) | − 0.0557281i | − 0.00269372i | ||||||||
\(429\) | 5.56231 | 0.268551 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.2705 | −0.591050 | −0.295525 | − | 0.955335i | \(-0.595495\pi\) | ||||
−0.295525 | + | 0.955335i | \(0.595495\pi\) | |||||||
\(432\) | − 10.8541i | − 0.522218i | ||||||||
\(433\) | − 14.2918i | − 0.686820i | −0.939186 | − | 0.343410i | \(-0.888418\pi\) | ||||
0.939186 | − | 0.343410i | \(-0.111582\pi\) | |||||||
\(434\) | −24.7082 | −1.18603 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.29180 | 0.157648 | ||||||||
\(437\) | 4.47214i | 0.213931i | ||||||||
\(438\) | − 1.14590i | − 0.0547531i | ||||||||
\(439\) | −30.1246 | −1.43777 | −0.718885 | − | 0.695129i | \(-0.755347\pi\) | ||||
−0.718885 | + | 0.695129i | \(0.755347\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.70820 | −0.271819 | ||||||||
\(442\) | 33.2705i | 1.58252i | ||||||||
\(443\) | − 7.18034i | − 0.341148i | −0.985345 | − | 0.170574i | \(-0.945438\pi\) | ||||
0.985345 | − | 0.170574i | \(-0.0545622\pi\) | |||||||
\(444\) | 0.875388 | 0.0415441 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.00000 | −0.142054 | ||||||||
\(447\) | 5.72949i | 0.270996i | ||||||||
\(448\) | 12.7082i | 0.600406i | ||||||||
\(449\) | 39.2705 | 1.85329 | 0.926645 | − | 0.375938i | \(-0.122679\pi\) | ||||
0.926645 | + | 0.375938i | \(0.122679\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.00000 | 0.423793 | ||||||||
\(452\) | 1.27051i | 0.0597598i | ||||||||
\(453\) | − 8.05573i | − 0.378491i | ||||||||
\(454\) | −10.7082 | −0.502561 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.09017 | 0.144710 | ||||||||
\(457\) | − 18.0000i | − 0.842004i | −0.907060 | − | 0.421002i | \(-0.861678\pi\) | ||||
0.907060 | − | 0.421002i | \(-0.138322\pi\) | |||||||
\(458\) | − 2.23607i | − 0.104485i | ||||||||
\(459\) | −9.47214 | −0.442121 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 36.2705 | 1.68929 | 0.844643 | − | 0.535330i | \(-0.179813\pi\) | ||||
0.844643 | + | 0.535330i | \(0.179813\pi\) | |||||||
\(462\) | 5.56231i | 0.258782i | ||||||||
\(463\) | 14.1246i | 0.656426i | 0.944604 | + | 0.328213i | \(0.106446\pi\) | ||||
−0.944604 | + | 0.328213i | \(0.893554\pi\) | |||||||
\(464\) | 32.5623 | 1.51167 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 43.5066 | 2.01540 | ||||||||
\(467\) | 39.2361i | 1.81563i | 0.419372 | + | 0.907814i | \(0.362250\pi\) | ||||
−0.419372 | + | 0.907814i | \(0.637750\pi\) | |||||||
\(468\) | − 8.56231i | − 0.395793i | ||||||||
\(469\) | −41.5623 | −1.91917 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.68692 | 0.215962 | ||||||||
\(472\) | 9.27051i | 0.426710i | ||||||||
\(473\) | − 27.0000i | − 1.24146i | ||||||||
\(474\) | −0.326238 | −0.0149846 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −7.85410 | −0.359992 | ||||||||
\(477\) | − 13.1803i | − 0.603486i | ||||||||
\(478\) | 41.8328i | 1.91339i | ||||||||
\(479\) | 32.5623 | 1.48781 | 0.743905 | − | 0.668286i | \(-0.232972\pi\) | ||||
0.743905 | + | 0.668286i | \(0.232972\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.0000 | −0.820729 | ||||||||
\(482\) | 31.0344i | 1.41358i | ||||||||
\(483\) | 1.41641i | 0.0644488i | ||||||||
\(484\) | 1.23607 | 0.0561849 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 15.6180 | 0.708448 | ||||||||
\(487\) | 3.70820i | 0.168035i | 0.996464 | + | 0.0840174i | \(0.0267751\pi\) | ||||
−0.996464 | + | 0.0840174i | \(0.973225\pi\) | |||||||
\(488\) | 13.6180i | 0.616459i | ||||||||
\(489\) | −7.58359 | −0.342942 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 36.2705 | 1.63687 | 0.818433 | − | 0.574603i | \(-0.194843\pi\) | ||||
0.818433 | + | 0.574603i | \(0.194843\pi\) | |||||||
\(492\) | 0.708204i | 0.0319283i | ||||||||
\(493\) | − 28.4164i | − 1.27981i | ||||||||
\(494\) | 28.4164 | 1.27851 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −24.7082 | −1.10943 | ||||||||
\(497\) | 9.00000i | 0.403705i | ||||||||
\(498\) | − 0.291796i | − 0.0130757i | ||||||||
\(499\) | −42.3607 | −1.89632 | −0.948162 | − | 0.317787i | \(-0.897060\pi\) | ||||
−0.948162 | + | 0.317787i | \(0.897060\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.52786 | −0.157613 | ||||||||
\(502\) | − 10.1459i | − 0.452834i | ||||||||
\(503\) | − 25.7984i | − 1.15029i | −0.818051 | − | 0.575146i | \(-0.804945\pi\) | ||||
0.818051 | − | 0.575146i | \(-0.195055\pi\) | |||||||
\(504\) | −19.1459 | −0.852826 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −6.00000 | −0.266733 | ||||||||
\(507\) | − 4.03444i | − 0.179176i | ||||||||
\(508\) | 6.00000i | 0.266207i | ||||||||
\(509\) | −13.4164 | −0.594672 | −0.297336 | − | 0.954773i | \(-0.596098\pi\) | ||||
−0.297336 | + | 0.954773i | \(0.596098\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.56231 | −0.246062 | ||||||||
\(512\) | 5.29180i | 0.233867i | ||||||||
\(513\) | 8.09017i | 0.357190i | ||||||||
\(514\) | 47.5066 | 2.09543 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.12461 | 0.0935308 | ||||||||
\(517\) | 24.9787i | 1.09856i | ||||||||
\(518\) | − 18.0000i | − 0.790875i | ||||||||
\(519\) | −0.0212862 | −0.000934362 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.27051 | 0.274716 | 0.137358 | − | 0.990521i | \(-0.456139\pi\) | ||||
0.137358 | + | 0.990521i | \(0.456139\pi\) | |||||||
\(522\) | 30.9787i | 1.35590i | ||||||||
\(523\) | 37.4164i | 1.63611i | 0.575143 | + | 0.818053i | \(0.304946\pi\) | ||||
−0.575143 | + | 0.818053i | \(0.695054\pi\) | |||||||
\(524\) | 7.58359 | 0.331291 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −26.4164 | −1.15181 | ||||||||
\(527\) | 21.5623i | 0.939269i | ||||||||
\(528\) | 5.56231i | 0.242068i | ||||||||
\(529\) | 21.4721 | 0.933571 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.8328 | −0.513500 | ||||||||
\(532\) | 6.70820i | 0.290838i | ||||||||
\(533\) | − 14.5623i | − 0.630763i | ||||||||
\(534\) | 8.29180 | 0.358821 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −30.9787 | −1.33808 | ||||||||
\(537\) | − 2.56231i | − 0.110572i | ||||||||
\(538\) | 4.14590i | 0.178742i | ||||||||
\(539\) | 6.00000 | 0.258438 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.1803 | −1.46953 | −0.734764 | − | 0.678323i | \(-0.762707\pi\) | ||||
−0.734764 | + | 0.678323i | \(0.762707\pi\) | |||||||
\(542\) | − 32.5066i | − 1.39628i | ||||||||
\(543\) | 6.94427i | 0.298007i | ||||||||
\(544\) | −14.3262 | −0.614232 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 9.00000 | 0.385164 | ||||||||
\(547\) | − 22.1459i | − 0.946890i | −0.880823 | − | 0.473445i | \(-0.843010\pi\) | ||||
0.880823 | − | 0.473445i | \(-0.156990\pi\) | |||||||
\(548\) | − 3.47214i | − 0.148322i | ||||||||
\(549\) | −17.3820 | −0.741844 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −24.2705 | −1.03396 | ||||||||
\(552\) | 1.05573i | 0.0449348i | ||||||||
\(553\) | 1.58359i | 0.0673412i | ||||||||
\(554\) | 8.56231 | 0.363778 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.56231 | −0.320713 | ||||||||
\(557\) | − 40.3607i | − 1.71014i | −0.518515 | − | 0.855068i | \(-0.673515\pi\) | ||||
0.518515 | − | 0.855068i | \(-0.326485\pi\) | |||||||
\(558\) | − 23.5066i | − 0.995113i | ||||||||
\(559\) | −43.6869 | −1.84776 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.85410 | 0.204940 | ||||||||
\(562\) | − 19.4164i | − 0.819032i | ||||||||
\(563\) | − 7.05573i | − 0.297363i | −0.988885 | − | 0.148682i | \(-0.952497\pi\) | ||||
0.988885 | − | 0.148682i | \(-0.0475030\pi\) | |||||||
\(564\) | −1.96556 | −0.0827649 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 25.4164 | 1.06833 | ||||||||
\(567\) | − 23.1246i | − 0.971142i | ||||||||
\(568\) | 6.70820i | 0.281470i | ||||||||
\(569\) | −26.8328 | −1.12489 | −0.562445 | − | 0.826835i | \(-0.690139\pi\) | ||||
−0.562445 | + | 0.826835i | \(0.690139\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.0000 | −0.544033 | −0.272017 | − | 0.962293i | \(-0.587691\pi\) | ||||
−0.272017 | + | 0.962293i | \(0.587691\pi\) | |||||||
\(572\) | 9.00000i | 0.376309i | ||||||||
\(573\) | 4.58359i | 0.191482i | ||||||||
\(574\) | 14.5623 | 0.607819 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −12.0902 | −0.503757 | ||||||||
\(577\) | 29.5623i | 1.23069i | 0.788256 | + | 0.615347i | \(0.210984\pi\) | ||||
−0.788256 | + | 0.615347i | \(0.789016\pi\) | |||||||
\(578\) | 1.52786i | 0.0635508i | ||||||||
\(579\) | 5.83282 | 0.242404 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.41641 | −0.0587625 | ||||||||
\(582\) | 4.85410i | 0.201209i | ||||||||
\(583\) | 13.8541i | 0.573778i | ||||||||
\(584\) | −4.14590 | −0.171558 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 34.5623 | 1.42776 | ||||||||
\(587\) | − 2.47214i | − 0.102036i | −0.998698 | − | 0.0510180i | \(-0.983753\pi\) | ||||
0.998698 | − | 0.0510180i | \(-0.0162466\pi\) | |||||||
\(588\) | 0.472136i | 0.0194706i | ||||||||
\(589\) | 18.4164 | 0.758835 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.54915 | 0.0637235 | ||||||||
\(592\) | − 18.0000i | − 0.739795i | ||||||||
\(593\) | 41.3607i | 1.69848i | 0.528007 | + | 0.849240i | \(0.322939\pi\) | ||||
−0.528007 | + | 0.849240i | \(0.677061\pi\) | |||||||
\(594\) | −10.8541 | −0.445349 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9.27051 | −0.379735 | ||||||||
\(597\) | − 6.18034i | − 0.252944i | ||||||||
\(598\) | 9.70820i | 0.396998i | ||||||||
\(599\) | 24.2705 | 0.991666 | 0.495833 | − | 0.868418i | \(-0.334863\pi\) | ||||
0.495833 | + | 0.868418i | \(0.334863\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.639320 | −0.0260784 | −0.0130392 | − | 0.999915i | \(-0.504151\pi\) | ||||
−0.0130392 | + | 0.999915i | \(0.504151\pi\) | |||||||
\(602\) | − 43.6869i | − 1.78055i | ||||||||
\(603\) | − 39.5410i | − 1.61023i | ||||||||
\(604\) | 13.0344 | 0.530364 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.85410 | −0.0753177 | ||||||||
\(607\) | 30.5410i | 1.23962i | 0.784751 | + | 0.619811i | \(0.212791\pi\) | ||||
−0.784751 | + | 0.619811i | \(0.787209\pi\) | |||||||
\(608\) | 12.2361i | 0.496238i | ||||||||
\(609\) | −7.68692 | −0.311490 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 40.4164 | 1.63507 | ||||||||
\(612\) | − 7.47214i | − 0.302043i | ||||||||
\(613\) | − 4.41641i | − 0.178377i | −0.996015 | − | 0.0891885i | \(-0.971573\pi\) | ||||
0.996015 | − | 0.0891885i | \(-0.0284274\pi\) | |||||||
\(614\) | 10.1459 | 0.409455 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 20.1246 | 0.810844 | ||||||||
\(617\) | − 25.7639i | − 1.03722i | −0.855012 | − | 0.518608i | \(-0.826450\pi\) | ||||
0.855012 | − | 0.518608i | \(-0.173550\pi\) | |||||||
\(618\) | − 7.85410i | − 0.315938i | ||||||||
\(619\) | 20.5279 | 0.825085 | 0.412542 | − | 0.910938i | \(-0.364641\pi\) | ||||
0.412542 | + | 0.910938i | \(0.364641\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.76393 | −0.110913 | ||||||||
\(622\) | − 34.4164i | − 1.37997i | ||||||||
\(623\) | − 40.2492i | − 1.61255i | ||||||||
\(624\) | 9.00000 | 0.360288 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −31.4164 | −1.25565 | ||||||||
\(627\) | − 4.14590i | − 0.165571i | ||||||||
\(628\) | 7.58359i | 0.302618i | ||||||||
\(629\) | −15.7082 | −0.626327 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.00000 | 0.0796187 | 0.0398094 | − | 0.999207i | \(-0.487325\pi\) | ||||
0.0398094 | + | 0.999207i | \(0.487325\pi\) | |||||||
\(632\) | 1.18034i | 0.0469514i | ||||||||
\(633\) | − 1.59675i | − 0.0634650i | ||||||||
\(634\) | −43.5967 | −1.73145 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.09017 | −0.0432281 | ||||||||
\(637\) | − 9.70820i | − 0.384653i | ||||||||
\(638\) | − 32.5623i | − 1.28915i | ||||||||
\(639\) | −8.56231 | −0.338720 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.72949 | −0.344794 | −0.172397 | − | 0.985028i | \(-0.555151\pi\) | ||||
−0.172397 | + | 0.985028i | \(0.555151\pi\) | |||||||
\(642\) | 0.0557281i | 0.00219941i | ||||||||
\(643\) | 18.2705i | 0.720519i | 0.932852 | + | 0.360259i | \(0.117312\pi\) | ||||
−0.932852 | + | 0.360259i | \(0.882688\pi\) | |||||||
\(644\) | −2.29180 | −0.0903094 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 24.7984 | 0.975679 | ||||||||
\(647\) | − 20.2361i | − 0.795562i | −0.917480 | − | 0.397781i | \(-0.869780\pi\) | ||||
0.917480 | − | 0.397781i | \(-0.130220\pi\) | |||||||
\(648\) | − 17.2361i | − 0.677097i | ||||||||
\(649\) | 12.4377 | 0.488222 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.83282 | 0.228606 | ||||||||
\(652\) | − 12.2705i | − 0.480550i | ||||||||
\(653\) | 4.65248i | 0.182065i | 0.995848 | + | 0.0910327i | \(0.0290168\pi\) | ||||
−0.995848 | + | 0.0910327i | \(0.970983\pi\) | |||||||
\(654\) | −3.29180 | −0.128719 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 14.5623 | 0.568563 | ||||||||
\(657\) | − 5.29180i | − 0.206453i | ||||||||
\(658\) | 40.4164i | 1.57560i | ||||||||
\(659\) | 25.8541 | 1.00713 | 0.503566 | − | 0.863957i | \(-0.332021\pi\) | ||||
0.503566 | + | 0.863957i | \(0.332021\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.3607 | 0.558566 | 0.279283 | − | 0.960209i | \(-0.409903\pi\) | ||||
0.279283 | + | 0.960209i | \(0.409903\pi\) | |||||||
\(662\) | 34.1246i | 1.32629i | ||||||||
\(663\) | − 7.85410i | − 0.305028i | ||||||||
\(664\) | −1.05573 | −0.0409702 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 17.1246 | 0.663565 | ||||||||
\(667\) | − 8.29180i | − 0.321060i | ||||||||
\(668\) | − 5.70820i | − 0.220857i | ||||||||
\(669\) | 0.708204 | 0.0273807 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.2705 | 0.705325 | ||||||||
\(672\) | 3.87539i | 0.149496i | ||||||||
\(673\) | 31.6869i | 1.22144i | 0.791846 | + | 0.610720i | \(0.209120\pi\) | ||||
−0.791846 | + | 0.610720i | \(0.790880\pi\) | |||||||
\(674\) | −48.2705 | −1.85931 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.52786 | 0.251072 | ||||||||
\(677\) | 4.11146i | 0.158016i | 0.996874 | + | 0.0790080i | \(0.0251753\pi\) | ||||
−0.996874 | + | 0.0790080i | \(0.974825\pi\) | |||||||
\(678\) | − 1.27051i | − 0.0487936i | ||||||||
\(679\) | 23.5623 | 0.904238 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.52786 | 0.0968680 | ||||||||
\(682\) | 24.7082i | 0.946126i | ||||||||
\(683\) | 43.0689i | 1.64799i | 0.566601 | + | 0.823993i | \(0.308258\pi\) | ||||
−0.566601 | + | 0.823993i | \(0.691742\pi\) | |||||||
\(684\) | −6.38197 | −0.244021 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −24.2705 | −0.926652 | ||||||||
\(687\) | 0.527864i | 0.0201393i | ||||||||
\(688\) | − 43.6869i | − 1.66555i | ||||||||
\(689\) | 22.4164 | 0.853997 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.8197 | 0.982226 | 0.491113 | − | 0.871096i | \(-0.336590\pi\) | ||||
0.491113 | + | 0.871096i | \(0.336590\pi\) | |||||||
\(692\) | − 0.0344419i | − 0.00130928i | ||||||||
\(693\) | 25.6869i | 0.975765i | ||||||||
\(694\) | 25.7984 | 0.979293 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.72949 | −0.217176 | ||||||||
\(697\) | − 12.7082i | − 0.481358i | ||||||||
\(698\) | − 28.0902i | − 1.06323i | ||||||||
\(699\) | −10.2705 | −0.388466 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.72949 | 0.103091 | 0.0515457 | − | 0.998671i | \(-0.483585\pi\) | ||||
0.0515457 | + | 0.998671i | \(0.483585\pi\) | |||||||
\(702\) | 17.5623i | 0.662847i | ||||||||
\(703\) | 13.4164i | 0.506009i | ||||||||
\(704\) | 12.7082 | 0.478958 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.29180 | −0.236795 | ||||||||
\(707\) | 9.00000i | 0.338480i | ||||||||
\(708\) | 0.978714i | 0.0367823i | ||||||||
\(709\) | 17.0344 | 0.639742 | 0.319871 | − | 0.947461i | \(-0.396360\pi\) | ||||
0.319871 | + | 0.947461i | \(0.396360\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.50658 | −0.0565011 | ||||||||
\(712\) | − 30.0000i | − 1.12430i | ||||||||
\(713\) | 6.29180i | 0.235630i | ||||||||
\(714\) | 7.85410 | 0.293932 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.14590 | 0.154939 | ||||||||
\(717\) | − 9.87539i | − 0.368803i | ||||||||
\(718\) | − 17.5623i | − 0.655419i | ||||||||
\(719\) | −47.5623 | −1.77377 | −0.886887 | − | 0.461986i | \(-0.847137\pi\) | ||||
−0.886887 | + | 0.461986i | \(0.847137\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −38.1246 | −1.41983 | ||||||||
\(722\) | 9.56231i | 0.355872i | ||||||||
\(723\) | − 7.32624i | − 0.272466i | ||||||||
\(724\) | −11.2361 | −0.417585 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.23607 | −0.0458748 | ||||||||
\(727\) | 38.8328i | 1.44023i | 0.693855 | + | 0.720115i | \(0.255911\pi\) | ||||
−0.693855 | + | 0.720115i | \(0.744089\pi\) | |||||||
\(728\) | − 32.5623i | − 1.20684i | ||||||||
\(729\) | 19.4377 | 0.719915 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −38.1246 | −1.41009 | ||||||||
\(732\) | 1.43769i | 0.0531387i | ||||||||
\(733\) | − 23.5623i | − 0.870294i | −0.900360 | − | 0.435147i | \(-0.856696\pi\) | ||||
0.900360 | − | 0.435147i | \(-0.143304\pi\) | |||||||
\(734\) | 1.85410 | 0.0684362 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.18034 | −0.154089 | ||||||||
\(737\) | 41.5623i | 1.53097i | ||||||||
\(738\) | 13.8541i | 0.509977i | ||||||||
\(739\) | −17.7639 | −0.653457 | −0.326728 | − | 0.945118i | \(-0.605946\pi\) | ||||
−0.326728 | + | 0.945118i | \(0.605946\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.70820 | −0.246432 | ||||||||
\(742\) | 22.4164i | 0.822932i | ||||||||
\(743\) | 25.9098i | 0.950539i | 0.879840 | + | 0.475270i | \(0.157650\pi\) | ||||
−0.879840 | + | 0.475270i | \(0.842350\pi\) | |||||||
\(744\) | 4.34752 | 0.159388 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.00000 | −0.109838 | ||||||||
\(747\) | − 1.34752i | − 0.0493033i | ||||||||
\(748\) | 7.85410i | 0.287174i | ||||||||
\(749\) | 0.270510 | 0.00988421 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.3607 | −0.560519 | −0.280260 | − | 0.959924i | \(-0.590421\pi\) | ||||
−0.280260 | + | 0.959924i | \(0.590421\pi\) | |||||||
\(752\) | 40.4164i | 1.47383i | ||||||||
\(753\) | 2.39512i | 0.0872831i | ||||||||
\(754\) | −52.6869 | −1.91874 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.14590 | −0.150785 | ||||||||
\(757\) | 27.0000i | 0.981332i | 0.871348 | + | 0.490666i | \(0.163246\pi\) | ||||
−0.871348 | + | 0.490666i | \(0.836754\pi\) | |||||||
\(758\) | − 12.2361i | − 0.444434i | ||||||||
\(759\) | 1.41641 | 0.0514123 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.0000 | −0.652499 | −0.326250 | − | 0.945284i | \(-0.605785\pi\) | ||||
−0.326250 | + | 0.945284i | \(0.605785\pi\) | |||||||
\(762\) | − 6.00000i | − 0.217357i | ||||||||
\(763\) | 15.9787i | 0.578468i | ||||||||
\(764\) | −7.41641 | −0.268316 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −57.3951 | −2.07377 | ||||||||
\(767\) | − 20.1246i | − 0.726658i | ||||||||
\(768\) | 5.18034i | 0.186929i | ||||||||
\(769\) | 12.8885 | 0.464773 | 0.232386 | − | 0.972624i | \(-0.425347\pi\) | ||||
0.232386 | + | 0.972624i | \(0.425347\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.2148 | −0.403890 | ||||||||
\(772\) | 9.43769i | 0.339670i | ||||||||
\(773\) | 21.2361i | 0.763808i | 0.924202 | + | 0.381904i | \(0.124732\pi\) | ||||
−0.924202 | + | 0.381904i | \(0.875268\pi\) | |||||||
\(774\) | 41.5623 | 1.49393 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 17.5623 | 0.630450 | ||||||||
\(777\) | 4.24922i | 0.152440i | ||||||||
\(778\) | 2.56231i | 0.0918631i | ||||||||
\(779\) | −10.8541 | −0.388889 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.00000 | 0.322045 | ||||||||
\(782\) | 8.47214i | 0.302963i | ||||||||
\(783\) | − 15.0000i | − 0.536056i | ||||||||
\(784\) | 9.70820 | 0.346722 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −7.58359 | −0.270498 | ||||||||
\(787\) | − 11.2918i | − 0.402509i | −0.979539 | − | 0.201255i | \(-0.935498\pi\) | ||||
0.979539 | − | 0.201255i | \(-0.0645018\pi\) | |||||||
\(788\) | 2.50658i | 0.0892931i | ||||||||
\(789\) | 6.23607 | 0.222010 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.16718 | −0.219280 | ||||||||
\(792\) | 19.1459i | 0.680320i | ||||||||
\(793\) | − 29.5623i | − 1.04979i | ||||||||
\(794\) | −26.5623 | −0.942661 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10.0000 | 0.354441 | ||||||||
\(797\) | 35.2148i | 1.24737i | 0.781675 | + | 0.623686i | \(0.214366\pi\) | ||||
−0.781675 | + | 0.623686i | \(0.785634\pi\) | |||||||
\(798\) | − 6.70820i | − 0.237468i | ||||||||
\(799\) | 35.2705 | 1.24778 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 38.2918 | 1.35297 | ||||||||
\(802\) | − 19.4164i | − 0.685617i | ||||||||
\(803\) | 5.56231i | 0.196290i | ||||||||
\(804\) | −3.27051 | −0.115342 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 39.9787 | 1.40819 | ||||||||
\(807\) | − 0.978714i | − 0.0344524i | ||||||||
\(808\) | 6.70820i | 0.235994i | ||||||||
\(809\) | 5.12461 | 0.180172 | 0.0900859 | − | 0.995934i | \(-0.471286\pi\) | ||||
0.0900859 | + | 0.995934i | \(0.471286\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.8197 | −0.415044 | −0.207522 | − | 0.978230i | \(-0.566540\pi\) | ||||
−0.207522 | + | 0.978230i | \(0.566540\pi\) | |||||||
\(812\) | − 12.4377i | − 0.436477i | ||||||||
\(813\) | 7.67376i | 0.269131i | ||||||||
\(814\) | −18.0000 | −0.630900 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 7.85410 | 0.274949 | ||||||||
\(817\) | 32.5623i | 1.13921i | ||||||||
\(818\) | − 36.8328i | − 1.28783i | ||||||||
\(819\) | 41.5623 | 1.45230 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.2705 | 0.742346 | 0.371173 | − | 0.928564i | \(-0.378956\pi\) | ||||
0.371173 | + | 0.928564i | \(0.378956\pi\) | |||||||
\(822\) | 3.47214i | 0.121105i | ||||||||
\(823\) | 22.4164i | 0.781387i | 0.920521 | + | 0.390693i | \(0.127765\pi\) | ||||
−0.920521 | + | 0.390693i | \(0.872235\pi\) | |||||||
\(824\) | −28.4164 | −0.989932 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 20.1246 | 0.700225 | ||||||||
\(827\) | − 31.6180i | − 1.09947i | −0.835340 | − | 0.549733i | \(-0.814729\pi\) | ||||
0.835340 | − | 0.549733i | \(-0.185271\pi\) | |||||||
\(828\) | − 2.18034i | − 0.0757720i | ||||||||
\(829\) | −6.25735 | −0.217327 | −0.108663 | − | 0.994079i | \(-0.534657\pi\) | ||||
−0.108663 | + | 0.994079i | \(0.534657\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.02129 | −0.0701176 | ||||||||
\(832\) | − 20.5623i | − 0.712870i | ||||||||
\(833\) | − 8.47214i | − 0.293542i | ||||||||
\(834\) | 7.56231 | 0.261861 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.70820 | 0.232008 | ||||||||
\(837\) | 11.3820i | 0.393418i | ||||||||
\(838\) | − 10.8541i | − 0.374949i | ||||||||
\(839\) | −29.3951 | −1.01483 | −0.507416 | − | 0.861701i | \(-0.669399\pi\) | ||||
−0.507416 | + | 0.861701i | \(0.669399\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.0000 | 0.551724 | ||||||||
\(842\) | − 14.4164i | − 0.496822i | ||||||||
\(843\) | 4.58359i | 0.157867i | ||||||||
\(844\) | 2.58359 | 0.0889309 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −38.4508 | −1.32197 | ||||||||
\(847\) | 6.00000i | 0.206162i | ||||||||
\(848\) | 22.4164i | 0.769783i | ||||||||
\(849\) | −6.00000 | −0.205919 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.58359 | −0.157124 | ||||||||
\(852\) | 0.708204i | 0.0242627i | ||||||||
\(853\) | 5.83282i | 0.199712i | 0.995002 | + | 0.0998559i | \(0.0318382\pi\) | ||||
−0.995002 | + | 0.0998559i | \(0.968162\pi\) | |||||||
\(854\) | 29.5623 | 1.01160 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.201626 | 0.00689144 | ||||||||
\(857\) | − 34.1803i | − 1.16758i | −0.811905 | − | 0.583789i | \(-0.801569\pi\) | ||||
0.811905 | − | 0.583789i | \(-0.198431\pi\) | |||||||
\(858\) | − 9.00000i | − 0.307255i | ||||||||
\(859\) | 25.1246 | 0.857241 | 0.428620 | − | 0.903485i | \(-0.359000\pi\) | ||||
0.428620 | + | 0.903485i | \(0.359000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.43769 | −0.117156 | ||||||||
\(862\) | 19.8541i | 0.676233i | ||||||||
\(863\) | 6.76393i | 0.230247i | 0.993351 | + | 0.115123i | \(0.0367264\pi\) | ||||
−0.993351 | + | 0.115123i | \(0.963274\pi\) | |||||||
\(864\) | −7.56231 | −0.257275 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −23.1246 | −0.785806 | ||||||||
\(867\) | − 0.360680i | − 0.0122493i | ||||||||
\(868\) | 9.43769i | 0.320336i | ||||||||
\(869\) | 1.58359 | 0.0537197 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 67.2492 | 2.27865 | ||||||||
\(872\) | 11.9098i | 0.403318i | ||||||||
\(873\) | 22.4164i | 0.758680i | ||||||||
\(874\) | 7.23607 | 0.244764 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.437694 | −0.0147883 | ||||||||
\(877\) | − 18.9787i | − 0.640866i | −0.947271 | − | 0.320433i | \(-0.896172\pi\) | ||||
0.947271 | − | 0.320433i | \(-0.103828\pi\) | |||||||
\(878\) | 48.7426i | 1.64498i | ||||||||
\(879\) | −8.15905 | −0.275198 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 45.5410 | 1.53432 | 0.767158 | − | 0.641458i | \(-0.221670\pi\) | ||||
0.767158 | + | 0.641458i | \(0.221670\pi\) | |||||||
\(882\) | 9.23607i | 0.310995i | ||||||||
\(883\) | − 17.8328i | − 0.600122i | −0.953920 | − | 0.300061i | \(-0.902993\pi\) | ||||
0.953920 | − | 0.300061i | \(-0.0970070\pi\) | |||||||
\(884\) | 12.7082 | 0.427423 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11.6180 | −0.390315 | ||||||||
\(887\) | − 42.4721i | − 1.42607i | −0.701126 | − | 0.713037i | \(-0.747319\pi\) | ||||
0.701126 | − | 0.713037i | \(-0.252681\pi\) | |||||||
\(888\) | 3.16718i | 0.106284i | ||||||||
\(889\) | −29.1246 | −0.976808 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −23.1246 | −0.774704 | ||||||||
\(892\) | 1.14590i | 0.0383675i | ||||||||
\(893\) | − 30.1246i | − 1.00808i | ||||||||
\(894\) | 9.27051 | 0.310052 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 40.8541 | 1.36484 | ||||||||
\(897\) | − 2.29180i | − 0.0765208i | ||||||||
\(898\) | − 63.5410i | − 2.12039i | ||||||||
\(899\) | −34.1459 | −1.13883 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.5623 | 0.651715 | ||||||||
\(902\) | − 14.5623i | − 0.484872i | ||||||||
\(903\) | 10.3131i | 0.343198i | ||||||||
\(904\) | −4.59675 | −0.152886 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −13.0344 | −0.433040 | ||||||||
\(907\) | − 42.2705i | − 1.40357i | −0.712389 | − | 0.701785i | \(-0.752387\pi\) | ||||
0.712389 | − | 0.701785i | \(-0.247613\pi\) | |||||||
\(908\) | 4.09017i | 0.135737i | ||||||||
\(909\) | −8.56231 | −0.283994 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.5410 | −1.21066 | −0.605329 | − | 0.795975i | \(-0.706958\pi\) | ||||
−0.605329 | + | 0.795975i | \(0.706958\pi\) | |||||||
\(912\) | − 6.70820i | − 0.222131i | ||||||||
\(913\) | 1.41641i | 0.0468763i | ||||||||
\(914\) | −29.1246 | −0.963357 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.854102 | −0.0282203 | ||||||||
\(917\) | 36.8115i | 1.21562i | ||||||||
\(918\) | 15.3262i | 0.505841i | ||||||||
\(919\) | 24.0689 | 0.793959 | 0.396980 | − | 0.917827i | \(-0.370058\pi\) | ||||
0.396980 | + | 0.917827i | \(0.370058\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.39512 | −0.0789219 | ||||||||
\(922\) | − 58.6869i | − 1.93275i | ||||||||
\(923\) | − 14.5623i | − 0.479324i | ||||||||
\(924\) | 2.12461 | 0.0698946 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 22.8541 | 0.751032 | ||||||||
\(927\) | − 36.2705i | − 1.19128i | ||||||||
\(928\) | − 22.6869i | − 0.744735i | ||||||||
\(929\) | −36.7082 | −1.20436 | −0.602179 | − | 0.798361i | \(-0.705700\pi\) | ||||
−0.602179 | + | 0.798361i | \(0.705700\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.23607 | −0.237153 | ||||||||
\(932\) | − 16.6180i | − 0.544342i | ||||||||
\(933\) | 8.12461i | 0.265988i | ||||||||
\(934\) | 63.4853 | 2.07730 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 30.9787 | 1.01257 | ||||||||
\(937\) | 9.43769i | 0.308316i | 0.988046 | + | 0.154158i | \(0.0492665\pi\) | ||||
−0.988046 | + | 0.154158i | \(0.950734\pi\) | |||||||
\(938\) | 67.2492i | 2.19576i | ||||||||
\(939\) | 7.41641 | 0.242025 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.2705 | −0.888993 | −0.444497 | − | 0.895781i | \(-0.646617\pi\) | ||||
−0.444497 | + | 0.895781i | \(0.646617\pi\) | |||||||
\(942\) | − 7.58359i | − 0.247087i | ||||||||
\(943\) | − 3.70820i | − 0.120756i | ||||||||
\(944\) | 20.1246 | 0.655000 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −43.6869 | −1.42038 | ||||||||
\(947\) | − 22.5967i | − 0.734296i | −0.930163 | − | 0.367148i | \(-0.880334\pi\) | ||||
0.930163 | − | 0.367148i | \(-0.119666\pi\) | |||||||
\(948\) | 0.124612i | 0.00404720i | ||||||||
\(949\) | 9.00000 | 0.292152 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.2918 | 0.333734 | ||||||||
\(952\) | − 28.4164i | − 0.920981i | ||||||||
\(953\) | − 13.1591i | − 0.426264i | −0.977023 | − | 0.213132i | \(-0.931634\pi\) | ||||
0.977023 | − | 0.213132i | \(-0.0683664\pi\) | |||||||
\(954\) | −21.3262 | −0.690462 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 15.9787 | 0.516789 | ||||||||
\(957\) | 7.68692i | 0.248483i | ||||||||
\(958\) | − 52.6869i | − 1.70224i | ||||||||
\(959\) | 16.8541 | 0.544247 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.09017 | −0.164199 | ||||||||
\(962\) | 29.1246i | 0.939015i | ||||||||
\(963\) | 0.257354i | 0.00829312i | ||||||||
\(964\) | 11.8541 | 0.381795 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.29180 | 0.0737373 | ||||||||
\(967\) | 16.1459i | 0.519217i | 0.965714 | + | 0.259609i | \(0.0835935\pi\) | ||||
−0.965714 | + | 0.259609i | \(0.916406\pi\) | |||||||
\(968\) | 4.47214i | 0.143740i | ||||||||
\(969\) | −5.85410 | −0.188061 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −51.5410 | −1.65403 | −0.827015 | − | 0.562180i | \(-0.809963\pi\) | ||||
−0.827015 | + | 0.562180i | \(0.809963\pi\) | |||||||
\(972\) | − 5.96556i | − 0.191345i | ||||||||
\(973\) | − 36.7082i | − 1.17681i | ||||||||
\(974\) | 6.00000 | 0.192252 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 29.5623 | 0.946266 | ||||||||
\(977\) | 23.3820i | 0.748055i | 0.927418 | + | 0.374028i | \(0.122024\pi\) | ||||
−0.927418 | + | 0.374028i | \(0.877976\pi\) | |||||||
\(978\) | 12.2705i | 0.392368i | ||||||||
\(979\) | −40.2492 | −1.28637 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.2016 | −0.485351 | ||||||||
\(982\) | − 58.6869i | − 1.87277i | ||||||||
\(983\) | 5.25735i | 0.167684i | 0.996479 | + | 0.0838418i | \(0.0267190\pi\) | ||||
−0.996479 | + | 0.0838418i | \(0.973281\pi\) | |||||||
\(984\) | −2.56231 | −0.0816833 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −45.9787 | −1.46426 | ||||||||
\(987\) | − 9.54102i | − 0.303694i | ||||||||
\(988\) | − 10.8541i | − 0.345315i | ||||||||
\(989\) | −11.1246 | −0.353742 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.8197 | −0.851955 | −0.425977 | − | 0.904734i | \(-0.640070\pi\) | ||||
−0.425977 | + | 0.904734i | \(0.640070\pi\) | |||||||
\(992\) | 17.2148i | 0.546570i | ||||||||
\(993\) | − 8.05573i | − 0.255641i | ||||||||
\(994\) | 14.5623 | 0.461888 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.111456 | −0.00353162 | ||||||||
\(997\) | 52.8541i | 1.67391i | 0.547275 | + | 0.836953i | \(0.315665\pi\) | ||||
−0.547275 | + | 0.836953i | \(0.684335\pi\) | |||||||
\(998\) | 68.5410i | 2.16963i | ||||||||
\(999\) | −8.29180 | −0.262341 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))