Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [845,2,Mod(339,845)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(845, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("845.339");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 845 = 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 845.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.74735897080\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.49843600.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 8x^{4} + 10x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 65) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 339.1 | ||
Root | \(-2.54574i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 845.339 |
Dual form | 845.2.b.e.339.6 |
$q$-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 \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).
\(n\) | \(171\) | \(677\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.54574i | − | 1.80011i | −0.435777 | − | 0.900055i | \(-0.643526\pi\) | ||
0.435777 | − | 0.900055i | \(-0.356474\pi\) | |||||||
\(3\) | − | 2.15293i | − | 1.24299i | −0.783417 | − | 0.621496i | \(-0.786525\pi\) | ||
0.783417 | − | 0.621496i | \(-0.213475\pi\) | |||||||
\(4\) | −4.48079 | −2.24039 | ||||||||
\(5\) | 0.817544 | − | 2.08125i | 0.365617 | − | 0.930765i | ||||
\(6\) | −5.48079 | −2.23752 | ||||||||
\(7\) | − | 2.93855i | − | 1.11067i | −0.831627 | − | 0.555334i | \(-0.812590\pi\) | ||
0.831627 | − | 0.555334i | \(-0.187410\pi\) | |||||||
\(8\) | 6.31544i | 2.23284i | ||||||||
\(9\) | −1.63509 | −0.545030 | ||||||||
\(10\) | −5.29833 | − | 2.08125i | −1.67548 | − | 0.658151i | ||||
\(11\) | 0.635089 | 0.191487 | 0.0957433 | − | 0.995406i | \(-0.469477\pi\) | ||||
0.0957433 | + | 0.995406i | \(0.469477\pi\) | |||||||
\(12\) | 9.64680i | 2.78479i | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −7.48079 | −1.99932 | ||||||||
\(15\) | −4.48079 | − | 1.76011i | −1.15693 | − | 0.454459i | ||||
\(16\) | 7.11588 | 1.77897 | ||||||||
\(17\) | 1.22396i | 0.296853i | 0.988923 | + | 0.148427i | \(0.0474209\pi\) | ||||
−0.988923 | + | 0.148427i | \(0.952579\pi\) | |||||||
\(18\) | 4.16251i | 0.981113i | ||||||||
\(19\) | 1.36491 | 0.313132 | 0.156566 | − | 0.987667i | \(-0.449958\pi\) | ||||
0.156566 | + | 0.987667i | \(0.449958\pi\) | |||||||
\(20\) | −3.66324 | + | 9.32566i | −0.819126 | + | 2.08528i | ||||
\(21\) | −6.32648 | −1.38055 | ||||||||
\(22\) | − | 1.61677i | − | 0.344697i | ||||||
\(23\) | 2.15293i | 0.448916i | 0.974484 | + | 0.224458i | \(0.0720612\pi\) | ||||
−0.974484 | + | 0.224458i | \(0.927939\pi\) | |||||||
\(24\) | 13.5967 | 2.77541 | ||||||||
\(25\) | −3.66324 | − | 3.40304i | −0.732648 | − | 0.680607i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 2.93855i | − | 0.565525i | ||||||
\(28\) | 13.1670i | 2.48833i | ||||||||
\(29\) | −3.00000 | −0.557086 | −0.278543 | − | 0.960424i | \(-0.589851\pi\) | ||||
−0.278543 | + | 0.960424i | \(0.589851\pi\) | |||||||
\(30\) | −4.48079 | + | 11.4069i | −0.818076 | + | 2.08261i | ||||
\(31\) | 8.96157 | 1.60955 | 0.804773 | − | 0.593583i | \(-0.202287\pi\) | ||||
0.804773 | + | 0.593583i | \(0.202287\pi\) | |||||||
\(32\) | − | 5.48429i | − | 0.969495i | ||||||
\(33\) | − | 1.36730i | − | 0.238016i | ||||||
\(34\) | 3.11588 | 0.534368 | ||||||||
\(35\) | −6.11588 | − | 2.40240i | −1.03377 | − | 0.406079i | ||||
\(36\) | 7.32648 | 1.22108 | ||||||||
\(37\) | 1.22396i | 0.201217i | 0.994926 | + | 0.100609i | \(0.0320790\pi\) | ||||
−0.994926 | + | 0.100609i | \(0.967921\pi\) | |||||||
\(38\) | − | 3.47471i | − | 0.563672i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 13.1440 | + | 5.16315i | 2.07825 | + | 0.816366i | ||||
\(41\) | 9.96157 | 1.55574 | 0.777868 | − | 0.628427i | \(-0.216301\pi\) | ||||
0.777868 | + | 0.628427i | \(0.216301\pi\) | |||||||
\(42\) | 16.1056i | 2.48514i | ||||||||
\(43\) | − | 1.36730i | − | 0.208511i | −0.994551 | − | 0.104256i | \(-0.966754\pi\) | ||
0.994551 | − | 0.104256i | \(-0.0332460\pi\) | |||||||
\(44\) | −2.84570 | −0.429005 | ||||||||
\(45\) | −1.33676 | + | 3.40304i | −0.199272 | + | 0.507295i | ||||
\(46\) | 5.48079 | 0.808098 | ||||||||
\(47\) | − | 6.16379i | − | 0.899081i | −0.893260 | − | 0.449540i | \(-0.851588\pi\) | ||
0.893260 | − | 0.449540i | \(-0.148412\pi\) | |||||||
\(48\) | − | 15.3200i | − | 2.21124i | ||||||
\(49\) | −1.63509 | −0.233584 | ||||||||
\(50\) | −8.66324 | + | 9.32566i | −1.22517 | + | 1.31885i | ||||
\(51\) | 2.63509 | 0.368986 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.642285i | 0.0882246i | 0.999027 | + | 0.0441123i | \(0.0140459\pi\) | ||||
−0.999027 | + | 0.0441123i | \(0.985954\pi\) | |||||||
\(54\) | −7.48079 | −1.01801 | ||||||||
\(55\) | 0.519213 | − | 1.32178i | 0.0700107 | − | 0.178229i | ||||
\(56\) | 18.5582 | 2.47995 | ||||||||
\(57\) | − | 2.93855i | − | 0.389221i | ||||||
\(58\) | 7.63722i | 1.00282i | ||||||||
\(59\) | 7.59666 | 0.989001 | 0.494501 | − | 0.869177i | \(-0.335351\pi\) | ||||
0.494501 | + | 0.869177i | \(0.335351\pi\) | |||||||
\(60\) | 20.0774 | + | 7.88669i | 2.59199 | + | 1.01817i | ||||
\(61\) | −2.27018 | −0.290666 | −0.145333 | − | 0.989383i | \(-0.546425\pi\) | ||||
−0.145333 | + | 0.989383i | \(0.546425\pi\) | |||||||
\(62\) | − | 22.8138i | − | 2.89736i | ||||||
\(63\) | 4.80479i | 0.605347i | ||||||||
\(64\) | 0.270178 | 0.0337722 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.48079 | −0.428455 | ||||||||
\(67\) | 8.03003i | 0.981024i | 0.871434 | + | 0.490512i | \(0.163190\pi\) | ||||
−0.871434 | + | 0.490512i | \(0.836810\pi\) | |||||||
\(68\) | − | 5.48429i | − | 0.665068i | ||||||
\(69\) | 4.63509 | 0.557999 | ||||||||
\(70\) | −6.11588 | + | 15.5694i | −0.730987 | + | 1.86090i | ||||
\(71\) | −2.63509 | −0.312728 | −0.156364 | − | 0.987700i | \(-0.549977\pi\) | ||||
−0.156364 | + | 0.987700i | \(0.549977\pi\) | |||||||
\(72\) | − | 10.3263i | − | 1.21697i | ||||||
\(73\) | 10.3263i | 1.20860i | 0.796756 | + | 0.604301i | \(0.206547\pi\) | ||||
−0.796756 | + | 0.604301i | \(0.793453\pi\) | |||||||
\(74\) | 3.11588 | 0.362213 | ||||||||
\(75\) | −7.32648 | + | 7.88669i | −0.845990 | + | 0.910676i | ||||
\(76\) | −6.11588 | −0.701539 | ||||||||
\(77\) | − | 1.86624i | − | 0.212678i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.03843 | −0.116832 | −0.0584161 | − | 0.998292i | \(-0.518605\pi\) | ||||
−0.0584161 | + | 0.998292i | \(0.518605\pi\) | |||||||
\(80\) | 5.81754 | − | 14.8099i | 0.650421 | − | 1.65580i | ||||
\(81\) | −11.2318 | −1.24797 | ||||||||
\(82\) | − | 25.3596i | − | 2.80050i | ||||||
\(83\) | − | 11.8452i | − | 1.30018i | −0.759855 | − | 0.650092i | \(-0.774730\pi\) | ||
0.759855 | − | 0.650092i | \(-0.225270\pi\) | |||||||
\(84\) | 28.3476 | 3.09298 | ||||||||
\(85\) | 2.54737 | + | 1.00064i | 0.276301 | + | 0.108535i | ||||
\(86\) | −3.48079 | −0.375343 | ||||||||
\(87\) | 6.45878i | 0.692454i | ||||||||
\(88\) | 4.01086i | 0.427559i | ||||||||
\(89\) | −12.5582 | −1.33117 | −0.665585 | − | 0.746322i | \(-0.731818\pi\) | ||||
−0.665585 | + | 0.746322i | \(0.731818\pi\) | |||||||
\(90\) | 8.66324 | + | 3.40304i | 0.913186 | + | 0.358712i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 9.64680i | − | 1.00575i | ||||||
\(93\) | − | 19.2936i | − | 2.00065i | ||||||
\(94\) | −15.6914 | −1.61844 | ||||||||
\(95\) | 1.11588 | − | 2.84073i | 0.114486 | − | 0.291453i | ||||
\(96\) | −11.8073 | −1.20507 | ||||||||
\(97\) | − | 14.7838i | − | 1.50107i | −0.660832 | − | 0.750534i | \(-0.729797\pi\) | ||
0.660832 | − | 0.750534i | \(-0.270203\pi\) | |||||||
\(98\) | 4.16251i | 0.420477i | ||||||||
\(99\) | −1.03843 | −0.104366 | ||||||||
\(100\) | 16.4142 | + | 15.2483i | 1.64142 | + | 1.52483i | ||||
\(101\) | 13.2318 | 1.31661 | 0.658304 | − | 0.752752i | \(-0.271274\pi\) | ||||
0.658304 | + | 0.752752i | \(0.271274\pi\) | |||||||
\(102\) | − | 6.70825i | − | 0.664216i | ||||||
\(103\) | 10.9686i | 1.08077i | 0.841419 | + | 0.540383i | \(0.181721\pi\) | ||||
−0.841419 | + | 0.540383i | \(0.818279\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.17218 | + | 13.1670i | −0.504753 | + | 1.28497i | ||||
\(106\) | 1.63509 | 0.158814 | ||||||||
\(107\) | 10.6736i | 1.03186i | 0.856632 | + | 0.515928i | \(0.172553\pi\) | ||||
−0.856632 | + | 0.515928i | \(0.827447\pi\) | |||||||
\(108\) | 13.1670i | 1.26700i | ||||||||
\(109\) | −3.27018 | −0.313226 | −0.156613 | − | 0.987660i | \(-0.550058\pi\) | ||||
−0.156613 | + | 0.987660i | \(0.550058\pi\) | |||||||
\(110\) | −3.36491 | − | 1.32178i | −0.320832 | − | 0.126027i | ||||
\(111\) | 2.63509 | 0.250112 | ||||||||
\(112\) | − | 20.9104i | − | 1.97584i | ||||||
\(113\) | − | 5.52981i | − | 0.520201i | −0.965582 | − | 0.260100i | \(-0.916244\pi\) | ||
0.965582 | − | 0.260100i | \(-0.0837556\pi\) | |||||||
\(114\) | −7.48079 | −0.700640 | ||||||||
\(115\) | 4.48079 | + | 1.76011i | 0.417836 | + | 0.164131i | ||||
\(116\) | 13.4424 | 1.24809 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 19.3391i | − | 1.78031i | ||||||
\(119\) | 3.59666 | 0.329705 | ||||||||
\(120\) | 11.1159 | − | 28.2981i | 1.01474 | − | 2.58325i | ||||
\(121\) | −10.5967 | −0.963333 | ||||||||
\(122\) | 5.77928i | 0.523231i | ||||||||
\(123\) | − | 21.4465i | − | 1.93377i | ||||||
\(124\) | −40.1549 | −3.60602 | ||||||||
\(125\) | −10.0774 | + | 4.84201i | −0.901354 | + | 0.433082i | ||||
\(126\) | 12.2318 | 1.08969 | ||||||||
\(127\) | 17.2317i | 1.52907i | 0.644584 | + | 0.764534i | \(0.277031\pi\) | ||||
−0.644584 | + | 0.764534i | \(0.722969\pi\) | |||||||
\(128\) | − | 11.6564i | − | 1.03029i | ||||||
\(129\) | −2.94369 | −0.259178 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.0000 | 0.873704 | 0.436852 | − | 0.899533i | \(-0.356093\pi\) | ||||
0.436852 | + | 0.899533i | \(0.356093\pi\) | |||||||
\(132\) | 6.12658i | 0.533250i | ||||||||
\(133\) | − | 4.01086i | − | 0.347786i | ||||||
\(134\) | 20.4424 | 1.76595 | ||||||||
\(135\) | −6.11588 | − | 2.40240i | −0.526371 | − | 0.206765i | ||||
\(136\) | −7.72982 | −0.662827 | ||||||||
\(137\) | − | 8.67231i | − | 0.740926i | −0.928847 | − | 0.370463i | \(-0.879199\pi\) | ||
0.928847 | − | 0.370463i | \(-0.120801\pi\) | |||||||
\(138\) | − | 11.7997i | − | 1.00446i | ||||||
\(139\) | −14.3265 | −1.21516 | −0.607578 | − | 0.794260i | \(-0.707859\pi\) | ||||
−0.607578 | + | 0.794260i | \(0.707859\pi\) | |||||||
\(140\) | 27.4039 | + | 10.7646i | 2.31606 | + | 0.909777i | ||||
\(141\) | −13.2702 | −1.11755 | ||||||||
\(142\) | 6.70825i | 0.562944i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −11.6351 | −0.969591 | ||||||||
\(145\) | −2.45263 | + | 6.24376i | −0.203680 | + | 0.518516i | ||||
\(146\) | 26.2881 | 2.17562 | ||||||||
\(147\) | 3.52022i | 0.290343i | ||||||||
\(148\) | − | 5.48429i | − | 0.450806i | ||||||
\(149\) | −17.1549 | −1.40538 | −0.702692 | − | 0.711494i | \(-0.748019\pi\) | ||||
−0.702692 | + | 0.711494i | \(0.748019\pi\) | |||||||
\(150\) | 20.0774 | + | 18.6513i | 1.63932 | + | 1.52287i | ||||
\(151\) | 21.3828 | 1.74011 | 0.870053 | − | 0.492957i | \(-0.164084\pi\) | ||||
0.870053 | + | 0.492957i | \(0.164084\pi\) | |||||||
\(152\) | 8.62001i | 0.699175i | ||||||||
\(153\) | − | 2.00128i | − | 0.161794i | ||||||
\(154\) | −4.75096 | −0.382844 | ||||||||
\(155\) | 7.32648 | − | 18.6513i | 0.588477 | − | 1.49811i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.3646i | 1.46566i | 0.680413 | + | 0.732829i | \(0.261800\pi\) | ||||
−0.680413 | + | 0.732829i | \(0.738200\pi\) | |||||||
\(158\) | 2.64356i | 0.210311i | ||||||||
\(159\) | 1.38279 | 0.109662 | ||||||||
\(160\) | −11.4142 | − | 4.48365i | −0.902372 | − | 0.354464i | ||||
\(161\) | 6.32648 | 0.498597 | ||||||||
\(162\) | 28.5931i | 2.24649i | ||||||||
\(163\) | 4.01086i | 0.314155i | 0.987586 | + | 0.157078i | \(0.0502072\pi\) | ||||
−0.987586 | + | 0.157078i | \(0.949793\pi\) | |||||||
\(164\) | −44.6357 | −3.48546 | ||||||||
\(165\) | −2.84570 | − | 1.11783i | −0.221537 | − | 0.0870228i | ||||
\(166\) | −30.1549 | −2.34047 | ||||||||
\(167\) | 2.93855i | 0.227392i | 0.993516 | + | 0.113696i | \(0.0362690\pi\) | ||||
−0.993516 | + | 0.113696i | \(0.963731\pi\) | |||||||
\(168\) | − | 39.9545i | − | 3.08256i | ||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 2.54737 | − | 6.48493i | 0.195374 | − | 0.497371i | ||||
\(171\) | −2.23175 | −0.170666 | ||||||||
\(172\) | 6.12658i | 0.467147i | ||||||||
\(173\) | 1.36730i | 0.103954i | 0.998648 | + | 0.0519769i | \(0.0165522\pi\) | ||||
−0.998648 | + | 0.0519769i | \(0.983448\pi\) | |||||||
\(174\) | 16.4424 | 1.24649 | ||||||||
\(175\) | −10.0000 | + | 10.7646i | −0.755929 | + | 0.813729i | ||||
\(176\) | 4.51921 | 0.340649 | ||||||||
\(177\) | − | 16.3550i | − | 1.22932i | ||||||
\(178\) | 31.9700i | 2.39625i | ||||||||
\(179\) | −7.78613 | −0.581963 | −0.290981 | − | 0.956729i | \(-0.593982\pi\) | ||||
−0.290981 | + | 0.956729i | \(0.593982\pi\) | |||||||
\(180\) | 5.98973 | − | 15.2483i | 0.446448 | − | 1.13654i | ||||
\(181\) | −3.86684 | −0.287420 | −0.143710 | − | 0.989620i | \(-0.545903\pi\) | ||||
−0.143710 | + | 0.989620i | \(0.545903\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.88752i | 0.361296i | ||||||||
\(184\) | −13.5967 | −1.00236 | ||||||||
\(185\) | 2.54737 | + | 1.00064i | 0.187286 | + | 0.0735685i | ||||
\(186\) | −49.1165 | −3.60139 | ||||||||
\(187\) | 0.777322i | 0.0568434i | ||||||||
\(188\) | 27.6186i | 2.01429i | ||||||||
\(189\) | −8.63509 | −0.628110 | ||||||||
\(190\) | −7.23175 | − | 2.84073i | −0.524646 | − | 0.206088i | ||||
\(191\) | 4.94369 | 0.357713 | 0.178857 | − | 0.983875i | \(-0.442760\pi\) | ||||
0.178857 | + | 0.983875i | \(0.442760\pi\) | |||||||
\(192\) | − | 0.581673i | − | 0.0419786i | ||||||
\(193\) | − | 4.95644i | − | 0.356772i | −0.983961 | − | 0.178386i | \(-0.942912\pi\) | ||
0.983961 | − | 0.178386i | \(-0.0570876\pi\) | |||||||
\(194\) | −37.6357 | −2.70208 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.32648 | 0.523320 | ||||||||
\(197\) | 6.74546i | 0.480594i | 0.970699 | + | 0.240297i | \(0.0772449\pi\) | ||||
−0.970699 | + | 0.240297i | \(0.922755\pi\) | |||||||
\(198\) | 2.64356i | 0.187870i | ||||||||
\(199\) | −5.17544 | −0.366878 | −0.183439 | − | 0.983031i | \(-0.558723\pi\) | ||||
−0.183439 | + | 0.983031i | \(0.558723\pi\) | |||||||
\(200\) | 21.4917 | − | 23.1350i | 1.51969 | − | 1.63589i | ||||
\(201\) | 17.2881 | 1.21941 | ||||||||
\(202\) | − | 33.6846i | − | 2.37004i | ||||||
\(203\) | 8.81566i | 0.618738i | ||||||||
\(204\) | −11.8073 | −0.826674 | ||||||||
\(205\) | 8.14403 | − | 20.7326i | 0.568804 | − | 1.44803i | ||||
\(206\) | 27.9231 | 1.94550 | ||||||||
\(207\) | − | 3.52022i | − | 0.244673i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.866840 | 0.0599606 | ||||||||
\(210\) | 33.5198 | + | 13.1670i | 2.31309 | + | 0.908611i | ||||
\(211\) | −14.0179 | −0.965031 | −0.482515 | − | 0.875888i | \(-0.660277\pi\) | ||||
−0.482515 | + | 0.875888i | \(0.660277\pi\) | |||||||
\(212\) | − | 2.87794i | − | 0.197658i | ||||||
\(213\) | 5.67315i | 0.388718i | ||||||||
\(214\) | 27.1722 | 1.85745 | ||||||||
\(215\) | −2.84570 | − | 1.11783i | −0.194075 | − | 0.0762352i | ||||
\(216\) | 18.5582 | 1.26273 | ||||||||
\(217\) | − | 26.3341i | − | 1.78767i | ||||||
\(218\) | 8.32502i | 0.563841i | ||||||||
\(219\) | 22.2318 | 1.50228 | ||||||||
\(220\) | −2.32648 | + | 5.92262i | −0.156852 | + | 0.399303i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | − | 6.70825i | − | 0.450228i | ||||||
\(223\) | 0.00830491i | 0.000556138i | 1.00000 | 0.000278069i | \(8.85121e-5\pi\) | |||||
−1.00000 | 0.000278069i | \(0.999911\pi\) | ||||||||
\(224\) | −16.1159 | −1.07679 | ||||||||
\(225\) | 5.98973 | + | 5.56427i | 0.399315 | + | 0.370951i | ||||
\(226\) | −14.0774 | −0.936418 | ||||||||
\(227\) | 11.2636i | 0.747589i | 0.927511 | + | 0.373795i | \(0.121944\pi\) | ||||
−0.927511 | + | 0.373795i | \(0.878056\pi\) | |||||||
\(228\) | 13.1670i | 0.872008i | ||||||||
\(229\) | −16.5404 | −1.09302 | −0.546509 | − | 0.837453i | \(-0.684043\pi\) | ||||
−0.546509 | + | 0.837453i | \(0.684043\pi\) | |||||||
\(230\) | 4.48079 | − | 11.4069i | 0.295454 | − | 0.752150i | ||||
\(231\) | −4.01788 | −0.264357 | ||||||||
\(232\) | − | 18.9463i | − | 1.24389i | ||||||
\(233\) | 6.94941i | 0.455271i | 0.973746 | + | 0.227636i | \(0.0730995\pi\) | ||||
−0.973746 | + | 0.227636i | \(0.926900\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.8284 | − | 5.03917i | −0.836833 | − | 0.328719i | ||||
\(236\) | −34.0390 | −2.21575 | ||||||||
\(237\) | 2.23566i | 0.145221i | ||||||||
\(238\) | − | 9.15616i | − | 0.593506i | ||||||
\(239\) | 4.00000 | 0.258738 | 0.129369 | − | 0.991596i | \(-0.458705\pi\) | ||||
0.129369 | + | 0.991596i | \(0.458705\pi\) | |||||||
\(240\) | −31.8847 | − | 12.5247i | −2.05815 | − | 0.808469i | ||||
\(241\) | −19.7721 | −1.27363 | −0.636817 | − | 0.771015i | \(-0.719749\pi\) | ||||
−0.636817 | + | 0.771015i | \(0.719749\pi\) | |||||||
\(242\) | 26.9763i | 1.73410i | ||||||||
\(243\) | 15.3655i | 0.985695i | ||||||||
\(244\) | 10.1722 | 0.651207 | ||||||||
\(245\) | −1.33676 | + | 3.40304i | −0.0854023 | + | 0.217412i | ||||
\(246\) | −54.5973 | −3.48099 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 56.5962i | 3.59386i | ||||||||
\(249\) | −25.5019 | −1.61612 | ||||||||
\(250\) | 12.3265 | + | 25.6546i | 0.779595 | + | 1.62254i | ||||
\(251\) | 3.67352 | 0.231870 | 0.115935 | − | 0.993257i | \(-0.463014\pi\) | ||||
0.115935 | + | 0.993257i | \(0.463014\pi\) | |||||||
\(252\) | − | 21.5293i | − | 1.35622i | ||||||
\(253\) | 1.36730i | 0.0859614i | ||||||||
\(254\) | 43.8674 | 2.75249 | ||||||||
\(255\) | 2.15430 | − | 5.48429i | 0.134908 | − | 0.343440i | ||||
\(256\) | −29.1338 | −1.82086 | ||||||||
\(257\) | 13.2648i | 0.827439i | 0.910404 | + | 0.413719i | \(0.135771\pi\) | ||||
−0.910404 | + | 0.413719i | \(0.864229\pi\) | |||||||
\(258\) | 7.49387i | 0.466548i | ||||||||
\(259\) | 3.59666 | 0.223486 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.90527 | 0.303628 | ||||||||
\(262\) | − | 25.4574i | − | 1.57276i | ||||||
\(263\) | − | 30.2705i | − | 1.86656i | −0.359152 | − | 0.933279i | \(-0.616934\pi\) | ||
0.359152 | − | 0.933279i | \(-0.383066\pi\) | |||||||
\(264\) | 8.63509 | 0.531453 | ||||||||
\(265\) | 1.33676 | + | 0.525096i | 0.0821164 | + | 0.0322564i | ||||
\(266\) | −10.2106 | −0.626053 | ||||||||
\(267\) | 27.0369i | 1.65463i | ||||||||
\(268\) | − | 35.9809i | − | 2.19788i | ||||||
\(269\) | 22.2496 | 1.35658 | 0.678292 | − | 0.734792i | \(-0.262720\pi\) | ||||
0.678292 | + | 0.734792i | \(0.262720\pi\) | |||||||
\(270\) | −6.11588 | + | 15.5694i | −0.372200 | + | 0.947525i | ||||
\(271\) | 11.8284 | 0.718525 | 0.359262 | − | 0.933237i | \(-0.383028\pi\) | ||||
0.359262 | + | 0.933237i | \(0.383028\pi\) | |||||||
\(272\) | 8.70953i | 0.528093i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −22.0774 | −1.33375 | ||||||||
\(275\) | −2.32648 | − | 2.16123i | −0.140292 | − | 0.130327i | ||||
\(276\) | −20.7688 | −1.25014 | ||||||||
\(277\) | 16.7851i | 1.00852i | 0.863553 | + | 0.504259i | \(0.168234\pi\) | ||||
−0.863553 | + | 0.504259i | \(0.831766\pi\) | |||||||
\(278\) | 36.4715i | 2.18741i | ||||||||
\(279\) | −14.6530 | −0.877250 | ||||||||
\(280\) | 15.1722 | − | 38.6244i | 0.906711 | − | 2.30825i | ||||
\(281\) | 10.5967 | 0.632144 | 0.316072 | − | 0.948735i | \(-0.397636\pi\) | ||||
0.316072 | + | 0.948735i | \(0.397636\pi\) | |||||||
\(282\) | 33.7824i | 2.01171i | ||||||||
\(283\) | 8.81566i | 0.524036i | 0.965063 | + | 0.262018i | \(0.0843880\pi\) | ||||
−0.965063 | + | 0.262018i | \(0.915612\pi\) | |||||||
\(284\) | 11.8073 | 0.700633 | ||||||||
\(285\) | −6.11588 | − | 2.40240i | −0.362273 | − | 0.142306i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 29.2726i | − | 1.72791i | ||||||
\(288\) | 8.96730i | 0.528403i | ||||||||
\(289\) | 15.5019 | 0.911878 | ||||||||
\(290\) | 15.8950 | + | 6.24376i | 0.933386 | + | 0.366646i | ||||
\(291\) | −31.8284 | −1.86581 | ||||||||
\(292\) | − | 46.2699i | − | 2.70774i | ||||||
\(293\) | − | 28.2526i | − | 1.65053i | −0.564742 | − | 0.825267i | \(-0.691024\pi\) | ||
0.564742 | − | 0.825267i | \(-0.308976\pi\) | |||||||
\(294\) | 8.96157 | 0.522650 | ||||||||
\(295\) | 6.21061 | − | 15.8106i | 0.361596 | − | 0.920528i | ||||
\(296\) | −7.72982 | −0.449287 | ||||||||
\(297\) | − | 1.86624i | − | 0.108290i | ||||||
\(298\) | 43.6719i | 2.52984i | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 32.8284 | − | 35.3386i | 1.89535 | − | 2.04027i | ||||
\(301\) | −4.01788 | −0.231587 | ||||||||
\(302\) | − | 54.4350i | − | 3.13238i | ||||||
\(303\) | − | 28.4870i | − | 1.63653i | ||||||
\(304\) | 9.71254 | 0.557052 | ||||||||
\(305\) | −1.85597 | + | 4.72482i | −0.106273 | + | 0.270542i | ||||
\(306\) | −5.09473 | −0.291247 | ||||||||
\(307\) | − | 12.7219i | − | 0.726077i | −0.931774 | − | 0.363039i | \(-0.881739\pi\) | ||
0.931774 | − | 0.363039i | \(-0.118261\pi\) | |||||||
\(308\) | 8.36223i | 0.476482i | ||||||||
\(309\) | 23.6145 | 1.34338 | ||||||||
\(310\) | −47.4814 | − | 18.6513i | −2.69676 | − | 1.05932i | ||||
\(311\) | 27.9231 | 1.58338 | 0.791688 | − | 0.610925i | \(-0.209202\pi\) | ||||
0.791688 | + | 0.610925i | \(0.209202\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 24.5807i | − | 1.38938i | −0.719307 | − | 0.694692i | \(-0.755540\pi\) | ||
0.719307 | − | 0.694692i | \(-0.244460\pi\) | |||||||
\(314\) | 46.7516 | 2.63834 | ||||||||
\(315\) | 10.0000 | + | 3.92813i | 0.563436 | + | 0.221325i | ||||
\(316\) | 4.65297 | 0.261750 | ||||||||
\(317\) | 0.234377i | 0.0131639i | 0.999978 | + | 0.00658196i | \(0.00209512\pi\) | ||||
−0.999978 | + | 0.00658196i | \(0.997905\pi\) | |||||||
\(318\) | − | 3.52022i | − | 0.197404i | ||||||
\(319\) | −1.90527 | −0.106674 | ||||||||
\(320\) | 0.220882 | − | 0.562309i | 0.0123477 | − | 0.0314340i | ||||
\(321\) | 22.9795 | 1.28259 | ||||||||
\(322\) | − | 16.1056i | − | 0.897529i | ||||||
\(323\) | 1.67059i | 0.0929543i | ||||||||
\(324\) | 50.3271 | 2.79595 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 10.2106 | 0.565513 | ||||||||
\(327\) | 7.04045i | 0.389338i | ||||||||
\(328\) | 62.9117i | 3.47372i | ||||||||
\(329\) | −18.1126 | −0.998581 | ||||||||
\(330\) | −2.84570 | + | 7.24440i | −0.156651 | + | 0.398791i | ||||
\(331\) | 18.3265 | 1.00731 | 0.503657 | − | 0.863904i | \(-0.331987\pi\) | ||||
0.503657 | + | 0.863904i | \(0.331987\pi\) | |||||||
\(332\) | 53.0760i | 2.91292i | ||||||||
\(333\) | − | 2.00128i | − | 0.109669i | ||||||
\(334\) | 7.48079 | 0.409330 | ||||||||
\(335\) | 16.7125 | + | 6.56491i | 0.913103 | + | 0.358679i | ||||
\(336\) | −45.0185 | −2.45596 | ||||||||
\(337\) | − | 21.2949i | − | 1.16001i | −0.814614 | − | 0.580003i | \(-0.803051\pi\) | ||
0.814614 | − | 0.580003i | \(-0.196949\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.9053 | −0.646605 | ||||||||
\(340\) | −11.4142 | − | 4.48365i | −0.619022 | − | 0.243160i | ||||
\(341\) | 5.69140 | 0.308206 | ||||||||
\(342\) | 5.68146i | 0.307218i | ||||||||
\(343\) | − | 15.7651i | − | 0.851234i | ||||||
\(344\) | 8.63509 | 0.465573 | ||||||||
\(345\) | 3.78939 | − | 9.64680i | 0.204014 | − | 0.519366i | ||||
\(346\) | 3.48079 | 0.187128 | ||||||||
\(347\) | − | 3.81521i | − | 0.204811i | −0.994743 | − | 0.102406i | \(-0.967346\pi\) | ||
0.994743 | − | 0.102406i | \(-0.0326540\pi\) | |||||||
\(348\) | − | 28.9404i | − | 1.55137i | ||||||
\(349\) | 24.3265 | 1.30217 | 0.651083 | − | 0.759006i | \(-0.274315\pi\) | ||||
0.651083 | + | 0.759006i | \(0.274315\pi\) | |||||||
\(350\) | 27.4039 | + | 25.4574i | 1.46480 | + | 1.36075i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 3.48301i | − | 0.185645i | ||||||
\(353\) | − | 27.0591i | − | 1.44021i | −0.693866 | − | 0.720104i | \(-0.744094\pi\) | ||
0.693866 | − | 0.720104i | \(-0.255906\pi\) | |||||||
\(354\) | −41.6357 | −2.21291 | ||||||||
\(355\) | −2.15430 | + | 5.48429i | −0.114338 | + | 0.291076i | ||||
\(356\) | 56.2708 | 2.98235 | ||||||||
\(357\) | − | 7.74335i | − | 0.409821i | ||||||
\(358\) | 19.8215i | 1.04760i | ||||||||
\(359\) | 27.0039 | 1.42521 | 0.712605 | − | 0.701566i | \(-0.247515\pi\) | ||||
0.712605 | + | 0.701566i | \(0.247515\pi\) | |||||||
\(360\) | −21.4917 | − | 8.44221i | −1.13271 | − | 0.444943i | ||||
\(361\) | −17.1370 | −0.901948 | ||||||||
\(362\) | 9.84396i | 0.517387i | ||||||||
\(363\) | 22.8138i | 1.19742i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 21.4917 | + | 8.44221i | 1.12492 | + | 0.441885i | ||||
\(366\) | 12.4424 | 0.650373 | ||||||||
\(367\) | − | 6.94111i | − | 0.362323i | −0.983453 | − | 0.181161i | \(-0.942014\pi\) | ||
0.983453 | − | 0.181161i | \(-0.0579857\pi\) | |||||||
\(368\) | 15.3200i | 0.798608i | ||||||||
\(369\) | −16.2881 | −0.847922 | ||||||||
\(370\) | 2.54737 | − | 6.48493i | 0.132431 | − | 0.337135i | ||||
\(371\) | 1.88739 | 0.0979882 | ||||||||
\(372\) | 86.4505i | 4.48225i | ||||||||
\(373\) | − | 2.31288i | − | 0.119756i | −0.998206 | − | 0.0598781i | \(-0.980929\pi\) | ||
0.998206 | − | 0.0598781i | \(-0.0190712\pi\) | |||||||
\(374\) | 1.97886 | 0.102324 | ||||||||
\(375\) | 10.4245 | + | 21.6960i | 0.538318 | + | 1.12038i | ||||
\(376\) | 38.9270 | 2.00751 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 21.9827i | 1.13067i | ||||||||
\(379\) | 5.17544 | 0.265845 | 0.132922 | − | 0.991126i | \(-0.457564\pi\) | ||||
0.132922 | + | 0.991126i | \(0.457564\pi\) | |||||||
\(380\) | −5.00000 | + | 12.7287i | −0.256495 | + | 0.652968i | ||||
\(381\) | 37.0986 | 1.90062 | ||||||||
\(382\) | − | 12.5854i | − | 0.643923i | ||||||
\(383\) | − | 20.6609i | − | 1.05572i | −0.849331 | − | 0.527861i | \(-0.822994\pi\) | ||
0.849331 | − | 0.527861i | \(-0.177006\pi\) | |||||||
\(384\) | −25.0953 | −1.28064 | ||||||||
\(385\) | −3.88412 | − | 1.52574i | −0.197953 | − | 0.0777587i | ||||
\(386\) | −12.6178 | −0.642229 | ||||||||
\(387\) | 2.23566i | 0.113645i | ||||||||
\(388\) | 66.2430i | 3.36298i | ||||||||
\(389\) | −19.7477 | −1.00125 | −0.500624 | − | 0.865665i | \(-0.666896\pi\) | ||||
−0.500624 | + | 0.865665i | \(0.666896\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.63509 | −0.133262 | ||||||||
\(392\) | − | 10.3263i | − | 0.521557i | ||||||
\(393\) | − | 21.5293i | − | 1.08601i | ||||||
\(394\) | 17.1722 | 0.865122 | ||||||||
\(395\) | −0.848960 | + | 2.16123i | −0.0427158 | + | 0.108743i | ||||
\(396\) | 4.65297 | 0.233820 | ||||||||
\(397\) | 9.38902i | 0.471222i | 0.971847 | + | 0.235611i | \(0.0757091\pi\) | ||||
−0.971847 | + | 0.235611i | \(0.924291\pi\) | |||||||
\(398\) | 13.1753i | 0.660420i | ||||||||
\(399\) | −8.63509 | −0.432295 | ||||||||
\(400\) | −26.0672 | − | 24.2156i | −1.30336 | − | 1.21078i | ||||
\(401\) | −24.5019 | −1.22357 | −0.611784 | − | 0.791025i | \(-0.709548\pi\) | ||||
−0.611784 | + | 0.791025i | \(0.709548\pi\) | |||||||
\(402\) | − | 44.0109i | − | 2.19506i | ||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −59.2887 | −2.94972 | ||||||||
\(405\) | −9.18246 | + | 23.3761i | −0.456280 | + | 1.16157i | ||||
\(406\) | 22.4424 | 1.11380 | ||||||||
\(407\) | 0.777322i | 0.0385304i | ||||||||
\(408\) | 16.6417i | 0.823889i | ||||||||
\(409\) | 36.1165 | 1.78584 | 0.892922 | − | 0.450211i | \(-0.148651\pi\) | ||||
0.892922 | + | 0.450211i | \(0.148651\pi\) | |||||||
\(410\) | −52.7797 | − | 20.7326i | −2.60660 | − | 1.02391i | ||||
\(411\) | −18.6708 | −0.920965 | ||||||||
\(412\) | − | 49.1479i | − | 2.42134i | ||||||
\(413\) | − | 22.3232i | − | 1.09845i | ||||||
\(414\) | −8.96157 | −0.440437 | ||||||||
\(415\) | −24.6530 | − | 9.68401i | −1.21017 | − | 0.475370i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 30.8439i | 1.51043i | ||||||||
\(418\) | − | 2.20675i | − | 0.107936i | ||||||
\(419\) | 6.86684 | 0.335467 | 0.167734 | − | 0.985832i | \(-0.446355\pi\) | ||||
0.167734 | + | 0.985832i | \(0.446355\pi\) | |||||||
\(420\) | 23.1754 | − | 58.9986i | 1.13085 | − | 2.87884i | ||||
\(421\) | −33.9795 | −1.65606 | −0.828029 | − | 0.560686i | \(-0.810538\pi\) | ||||
−0.828029 | + | 0.560686i | \(0.810538\pi\) | |||||||
\(422\) | 35.6859i | 1.73716i | ||||||||
\(423\) | 10.0783i | 0.490026i | ||||||||
\(424\) | −4.05631 | −0.196992 | ||||||||
\(425\) | 4.16517 | − | 4.48365i | 0.202040 | − | 0.217489i | ||||
\(426\) | 14.4424 | 0.699735 | ||||||||
\(427\) | 6.67104i | 0.322834i | ||||||||
\(428\) | − | 47.8261i | − | 2.31176i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.84570 | + | 7.24440i | −0.137232 | + | 0.349356i | ||||
\(431\) | 16.2496 | 0.782717 | 0.391359 | − | 0.920238i | \(-0.372005\pi\) | ||||
0.391359 | + | 0.920238i | \(0.372005\pi\) | |||||||
\(432\) | − | 20.9104i | − | 1.00605i | ||||||
\(433\) | − | 0.256261i | − | 0.0123151i | −0.999981 | − | 0.00615756i | \(-0.998040\pi\) | ||
0.999981 | − | 0.00615756i | \(-0.00196002\pi\) | |||||||
\(434\) | −67.0396 | −3.21800 | ||||||||
\(435\) | 13.4424 | + | 5.28034i | 0.644512 | + | 0.253173i | ||||
\(436\) | 14.6530 | 0.701750 | ||||||||
\(437\) | 2.93855i | 0.140570i | ||||||||
\(438\) | − | 56.5962i | − | 2.70427i | ||||||
\(439\) | 7.59666 | 0.362569 | 0.181284 | − | 0.983431i | \(-0.441975\pi\) | ||||
0.181284 | + | 0.983431i | \(0.441975\pi\) | |||||||
\(440\) | 8.34763 | + | 3.27906i | 0.397957 | + | 0.156323i | ||||
\(441\) | 2.67352 | 0.127310 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 4.32246i | − | 0.205366i | −0.994714 | − | 0.102683i | \(-0.967257\pi\) | ||
0.994714 | − | 0.102683i | \(-0.0327428\pi\) | |||||||
\(444\) | −11.8073 | −0.560348 | ||||||||
\(445\) | −10.2669 | + | 26.1369i | −0.486698 | + | 1.23901i | ||||
\(446\) | 0.0211421 | 0.00100111 | ||||||||
\(447\) | 36.9332i | 1.74688i | ||||||||
\(448\) | − | 0.793931i | − | 0.0375097i | ||||||
\(449\) | 3.28806 | 0.155173 | 0.0775865 | − | 0.996986i | \(-0.475279\pi\) | ||||
0.0775865 | + | 0.996986i | \(0.475279\pi\) | |||||||
\(450\) | 14.1652 | − | 15.2483i | 0.667753 | − | 0.718811i | ||||
\(451\) | 6.32648 | 0.297903 | ||||||||
\(452\) | 24.7779i | 1.16545i | ||||||||
\(453\) | − | 46.0356i | − | 2.16294i | ||||||
\(454\) | 28.6741 | 1.34574 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 18.5582 | 0.869069 | ||||||||
\(457\) | 15.4261i | 0.721602i | 0.932643 | + | 0.360801i | \(0.117497\pi\) | ||||
−0.932643 | + | 0.360801i | \(0.882503\pi\) | |||||||
\(458\) | 42.1074i | 1.96755i | ||||||||
\(459\) | 3.59666 | 0.167878 | ||||||||
\(460\) | −20.0774 | − | 7.88669i | −0.936116 | − | 0.367719i | ||||
\(461\) | −25.8847 | −1.20557 | −0.602786 | − | 0.797903i | \(-0.705943\pi\) | ||||
−0.602786 | + | 0.797903i | \(0.705943\pi\) | |||||||
\(462\) | 10.2285i | 0.475872i | ||||||||
\(463\) | 7.04045i | 0.327197i | 0.986527 | + | 0.163599i | \(0.0523102\pi\) | ||||
−0.986527 | + | 0.163599i | \(0.947690\pi\) | |||||||
\(464\) | −21.3476 | −0.991039 | ||||||||
\(465\) | −40.1549 | − | 15.7734i | −1.86214 | − | 0.731473i | ||||
\(466\) | 17.6914 | 0.819538 | ||||||||
\(467\) | 18.8113i | 0.870482i | 0.900314 | + | 0.435241i | \(0.143337\pi\) | ||||
−0.900314 | + | 0.435241i | \(0.856663\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.5967 | 1.08959 | ||||||||
\(470\) | −12.8284 | + | 32.6578i | −0.591731 | + | 1.50639i | ||||
\(471\) | 39.5377 | 1.82180 | ||||||||
\(472\) | 47.9762i | 2.20828i | ||||||||
\(473\) | − | 0.868356i | − | 0.0399271i | ||||||
\(474\) | 5.69140 | 0.261414 | ||||||||
\(475\) | −5.00000 | − | 4.64484i | −0.229416 | − | 0.213120i | ||||
\(476\) | −16.1159 | −0.738670 | ||||||||
\(477\) | − | 1.05019i | − | 0.0480850i | ||||||
\(478\) | − | 10.1830i | − | 0.465758i | ||||||
\(479\) | −19.4775 | −0.889951 | −0.444975 | − | 0.895543i | \(-0.646788\pi\) | ||||
−0.444975 | + | 0.895543i | \(0.646788\pi\) | |||||||
\(480\) | −9.65297 | + | 24.5739i | −0.440596 | + | 1.12164i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 50.3346i | 2.29268i | ||||||||
\(483\) | − | 13.6205i | − | 0.619752i | ||||||
\(484\) | 47.4814 | 2.15824 | ||||||||
\(485\) | −30.7688 | − | 12.0864i | −1.39714 | − | 0.548816i | ||||
\(486\) | 39.1165 | 1.77436 | ||||||||
\(487\) | 32.3241i | 1.46474i | 0.680905 | + | 0.732372i | \(0.261587\pi\) | ||||
−0.680905 | + | 0.732372i | \(0.738413\pi\) | |||||||
\(488\) | − | 14.3372i | − | 0.649013i | ||||||
\(489\) | 8.63509 | 0.390492 | ||||||||
\(490\) | 8.66324 | + | 3.40304i | 0.391365 | + | 0.153734i | ||||
\(491\) | 28.6708 | 1.29390 | 0.646949 | − | 0.762534i | \(-0.276045\pi\) | ||||
0.646949 | + | 0.762534i | \(0.276045\pi\) | |||||||
\(492\) | 96.0973i | 4.33240i | ||||||||
\(493\) | − | 3.67187i | − | 0.165373i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.848960 | + | 2.16123i | −0.0381579 | + | 0.0971401i | ||||
\(496\) | 63.7694 | 2.86333 | ||||||||
\(497\) | 7.74335i | 0.347337i | ||||||||
\(498\) | 64.9213i | 2.90919i | ||||||||
\(499\) | 28.9616 | 1.29650 | 0.648249 | − | 0.761428i | \(-0.275502\pi\) | ||||
0.648249 | + | 0.761428i | \(0.275502\pi\) | |||||||
\(500\) | 45.1549 | − | 21.6960i | 2.01939 | − | 0.970275i | ||||
\(501\) | 6.32648 | 0.282646 | ||||||||
\(502\) | − | 9.35181i | − | 0.417392i | ||||||
\(503\) | 28.1093i | 1.25333i | 0.779289 | + | 0.626665i | \(0.215581\pi\) | ||||
−0.779289 | + | 0.626665i | \(0.784419\pi\) | |||||||
\(504\) | −30.3444 | −1.35165 | ||||||||
\(505\) | 10.8175 | − | 27.5386i | 0.481374 | − | 1.22545i | ||||
\(506\) | 3.48079 | 0.154740 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 77.2116i | − | 3.42571i | ||||||
\(509\) | 21.1126 | 0.935800 | 0.467900 | − | 0.883781i | \(-0.345011\pi\) | ||||
0.467900 | + | 0.883781i | \(0.345011\pi\) | |||||||
\(510\) | −13.9616 | − | 5.48429i | −0.618229 | − | 0.242848i | ||||
\(511\) | 30.3444 | 1.34236 | ||||||||
\(512\) | 50.8542i | 2.24746i | ||||||||
\(513\) | − | 4.01086i | − | 0.177084i | ||||||
\(514\) | 33.7688 | 1.48948 | ||||||||
\(515\) | 22.8284 | + | 8.96730i | 1.00594 | + | 0.395147i | ||||
\(516\) | 13.1901 | 0.580660 | ||||||||
\(517\) | − | 3.91455i | − | 0.172162i | ||||||
\(518\) | − | 9.15616i | − | 0.402299i | ||||||
\(519\) | 2.94369 | 0.129214 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.673516 | 0.0295073 | 0.0147536 | − | 0.999891i | \(-0.495304\pi\) | ||||
0.0147536 | + | 0.999891i | \(0.495304\pi\) | |||||||
\(522\) | − | 12.4875i | − | 0.546564i | ||||||
\(523\) | 29.8626i | 1.30580i | 0.757444 | + | 0.652900i | \(0.226448\pi\) | ||||
−0.757444 | + | 0.652900i | \(0.773552\pi\) | |||||||
\(524\) | −44.8079 | −1.95744 | ||||||||
\(525\) | 23.1754 | + | 21.5293i | 1.01146 | + | 0.939614i | ||||
\(526\) | −77.0608 | −3.36001 | ||||||||
\(527\) | 10.9686i | 0.477799i | ||||||||
\(528\) | − | 9.72953i | − | 0.423423i | ||||||
\(529\) | 18.3649 | 0.798474 | ||||||||
\(530\) | 1.33676 | − | 3.40304i | 0.0580650 | − | 0.147818i | ||||
\(531\) | −12.4212 | −0.539035 | ||||||||
\(532\) | 17.9718i | 0.779177i | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 68.8290 | 2.97852 | ||||||||
\(535\) | 22.2145 | + | 8.72614i | 0.960415 | + | 0.377264i | ||||
\(536\) | −50.7131 | −2.19047 | ||||||||
\(537\) | 16.7630i | 0.723375i | ||||||||
\(538\) | − | 56.6418i | − | 2.44200i | ||||||
\(539\) | −1.03843 | −0.0447282 | ||||||||
\(540\) | 27.4039 | + | 10.7646i | 1.17928 | + | 0.463236i | ||||
\(541\) | −6.28806 | −0.270345 | −0.135172 | − | 0.990822i | \(-0.543159\pi\) | ||||
−0.135172 | + | 0.990822i | \(0.543159\pi\) | |||||||
\(542\) | − | 30.1121i | − | 1.29342i | ||||||
\(543\) | 8.32502i | 0.357261i | ||||||||
\(544\) | 6.71254 | 0.287798 | ||||||||
\(545\) | −2.67352 | + | 6.80607i | −0.114521 | + | 0.291540i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 3.03789i | − | 0.129891i | −0.997889 | − | 0.0649454i | \(-0.979313\pi\) | ||
0.997889 | − | 0.0649454i | \(-0.0206873\pi\) | |||||||
\(548\) | 38.8588i | 1.65997i | ||||||||
\(549\) | 3.71194 | 0.158422 | ||||||||
\(550\) | −5.50193 | + | 5.92262i | −0.234603 | + | 0.252541i | ||||
\(551\) | −4.09473 | −0.174442 | ||||||||
\(552\) | 29.2726i | 1.24592i | ||||||||
\(553\) | 3.05147i | 0.129762i | ||||||||
\(554\) | 42.7304 | 1.81544 | ||||||||
\(555\) | 2.15430 | − | 5.48429i | 0.0914450 | − | 0.232795i | ||||
\(556\) | 64.1939 | 2.72243 | ||||||||
\(557\) | − | 20.6996i | − | 0.877071i | −0.898714 | − | 0.438536i | \(-0.855497\pi\) | ||
0.898714 | − | 0.438536i | \(-0.144503\pi\) | |||||||
\(558\) | 37.3026i | 1.57915i | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −43.5198 | − | 17.0952i | −1.83905 | − | 0.722402i | ||||
\(561\) | 1.67352 | 0.0706559 | ||||||||
\(562\) | − | 26.9763i | − | 1.13793i | ||||||
\(563\) | − | 10.9603i | − | 0.461921i | −0.972963 | − | 0.230960i | \(-0.925813\pi\) | ||
0.972963 | − | 0.230960i | \(-0.0741868\pi\) | |||||||
\(564\) | 59.4608 | 2.50375 | ||||||||
\(565\) | −11.5089 | − | 4.52086i | −0.484185 | − | 0.190194i | ||||
\(566\) | 22.4424 | 0.943323 | ||||||||
\(567\) | 33.0051i | 1.38608i | ||||||||
\(568\) | − | 16.6417i | − | 0.698272i | ||||||
\(569\) | −42.7131 | −1.79063 | −0.895314 | − | 0.445436i | \(-0.853049\pi\) | ||||
−0.895314 | + | 0.445436i | \(0.853049\pi\) | |||||||
\(570\) | −6.11588 | + | 15.5694i | −0.256166 | + | 0.652131i | ||||
\(571\) | −23.6145 | −0.988238 | −0.494119 | − | 0.869394i | \(-0.664509\pi\) | ||||
−0.494119 | + | 0.869394i | \(0.664509\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 10.6434i | − | 0.444635i | ||||||
\(574\) | −74.5204 | −3.11042 | ||||||||
\(575\) | 7.32648 | − | 7.88669i | 0.305536 | − | 0.328898i | ||||
\(576\) | −0.441765 | −0.0184069 | ||||||||
\(577\) | 18.3646i | 0.764530i | 0.924053 | + | 0.382265i | \(0.124856\pi\) | ||||
−0.924053 | + | 0.382265i | \(0.875144\pi\) | |||||||
\(578\) | − | 39.4639i | − | 1.64148i | ||||||
\(579\) | −10.6708 | −0.443465 | ||||||||
\(580\) | 10.9897 | − | 27.9770i | 0.456324 | − | 1.16168i | ||||
\(581\) | −34.8079 | −1.44407 | ||||||||
\(582\) | 81.0268i | 3.35867i | ||||||||
\(583\) | 0.407908i | 0.0168938i | ||||||||
\(584\) | −65.2151 | −2.69862 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −71.9237 | −2.97114 | ||||||||
\(587\) | 0.702897i | 0.0290116i | 0.999895 | + | 0.0145058i | \(0.00461751\pi\) | ||||
−0.999895 | + | 0.0145058i | \(0.995382\pi\) | |||||||
\(588\) | − | 15.7734i | − | 0.650483i | ||||||
\(589\) | 12.2318 | 0.504001 | ||||||||
\(590\) | −40.2496 | − | 15.8106i | −1.65705 | − | 0.650912i | ||||
\(591\) | 14.5225 | 0.597375 | ||||||||
\(592\) | 8.70953i | 0.357959i | ||||||||
\(593\) | − | 37.1593i | − | 1.52595i | −0.646428 | − | 0.762975i | \(-0.723738\pi\) | ||
0.646428 | − | 0.762975i | \(-0.276262\pi\) | |||||||
\(594\) | −4.75096 | −0.194934 | ||||||||
\(595\) | 2.94043 | − | 7.48557i | 0.120546 | − | 0.306878i | ||||
\(596\) | 76.8674 | 3.14861 | ||||||||
\(597\) | 11.1423i | 0.456026i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.6914 | 0.641133 | 0.320567 | − | 0.947226i | \(-0.396127\pi\) | ||||
0.320567 | + | 0.947226i | \(0.396127\pi\) | |||||||
\(600\) | −49.8079 | − | 46.2699i | −2.03340 | − | 1.88896i | ||||
\(601\) | 12.0039 | 0.489648 | 0.244824 | − | 0.969568i | \(-0.421270\pi\) | ||||
0.244824 | + | 0.969568i | \(0.421270\pi\) | |||||||
\(602\) | 10.2285i | 0.416881i | ||||||||
\(603\) | − | 13.1298i | − | 0.534687i | ||||||
\(604\) | −95.8117 | −3.89852 | ||||||||
\(605\) | −8.66324 | + | 22.0544i | −0.352211 | + | 0.896637i | ||||
\(606\) | −72.5204 | −2.94594 | ||||||||
\(607\) | 38.6865i | 1.57024i | 0.619345 | + | 0.785119i | \(0.287398\pi\) | ||||
−0.619345 | + | 0.785119i | \(0.712602\pi\) | |||||||
\(608\) | − | 7.48557i | − | 0.303580i | ||||||
\(609\) | 18.9795 | 0.769086 | ||||||||
\(610\) | 12.0282 | + | 4.72482i | 0.487006 | + | 0.191302i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 8.96730i | 0.362482i | ||||||||
\(613\) | − | 17.2840i | − | 0.698095i | −0.937105 | − | 0.349047i | \(-0.886505\pi\) | ||
0.937105 | − | 0.349047i | \(-0.113495\pi\) | |||||||
\(614\) | −32.3866 | −1.30702 | ||||||||
\(615\) | −44.6357 | − | 17.5335i | −1.79988 | − | 0.707018i | ||||
\(616\) | 11.7861 | 0.474877 | ||||||||
\(617\) | − | 26.4691i | − | 1.06561i | −0.846240 | − | 0.532803i | \(-0.821139\pi\) | ||
0.846240 | − | 0.532803i | \(-0.178861\pi\) | |||||||
\(618\) | − | 60.1165i | − | 2.41824i | ||||||
\(619\) | −31.0039 | −1.24615 | −0.623075 | − | 0.782162i | \(-0.714117\pi\) | ||||
−0.623075 | + | 0.782162i | \(0.714117\pi\) | |||||||
\(620\) | −32.8284 | + | 83.5726i | −1.31842 | + | 3.35636i | ||||
\(621\) | 6.32648 | 0.253873 | ||||||||
\(622\) | − | 71.0850i | − | 2.85025i | ||||||
\(623\) | 36.9030i | 1.47849i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.83869 | + | 24.9323i | 0.0735475 | + | 0.997292i | ||||
\(626\) | −62.5761 | −2.50104 | ||||||||
\(627\) | − | 1.86624i | − | 0.0745305i | ||||||
\(628\) | − | 82.2880i | − | 3.28365i | ||||||
\(629\) | −1.49807 | −0.0597320 | ||||||||
\(630\) | 10.0000 | − | 25.4574i | 0.398410 | − | 1.01425i | ||||
\(631\) | 20.7131 | 0.824577 | 0.412288 | − | 0.911053i | \(-0.364730\pi\) | ||||
0.412288 | + | 0.911053i | \(0.364730\pi\) | |||||||
\(632\) | − | 6.55812i | − | 0.260868i | ||||||
\(633\) | 30.1795i | 1.19953i | ||||||||
\(634\) | 0.596662 | 0.0236965 | ||||||||
\(635\) | 35.8636 | + | 14.0877i | 1.42320 | + | 0.559053i | ||||
\(636\) | −6.19599 | −0.245687 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.85031i | 0.192026i | ||||||||
\(639\) | 4.30860 | 0.170446 | ||||||||
\(640\) | −24.2599 | − | 9.52961i | −0.958957 | − | 0.376691i | ||||
\(641\) | 21.1895 | 0.836934 | 0.418467 | − | 0.908232i | \(-0.362568\pi\) | ||||
0.418467 | + | 0.908232i | \(0.362568\pi\) | |||||||
\(642\) | − | 58.4997i | − | 2.30880i | ||||||
\(643\) | − | 11.5336i | − | 0.454843i | −0.973796 | − | 0.227421i | \(-0.926971\pi\) | ||
0.973796 | − | 0.227421i | \(-0.0730294\pi\) | |||||||
\(644\) | −28.3476 | −1.11705 | ||||||||
\(645\) | −2.40660 | + | 6.12658i | −0.0947598 | + | 0.241234i | ||||
\(646\) | 4.25289 | 0.167328 | ||||||||
\(647\) | − | 34.8464i | − | 1.36995i | −0.728565 | − | 0.684977i | \(-0.759812\pi\) | ||
0.728565 | − | 0.684977i | \(-0.240188\pi\) | |||||||
\(648\) | − | 70.9334i | − | 2.78653i | ||||||
\(649\) | 4.82456 | 0.189380 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −56.6953 | −2.22206 | ||||||||
\(652\) | − | 17.9718i | − | 0.703831i | ||||||
\(653\) | − | 22.3232i | − | 0.873574i | −0.899565 | − | 0.436787i | \(-0.856116\pi\) | ||
0.899565 | − | 0.436787i | \(-0.143884\pi\) | |||||||
\(654\) | 17.9231 | 0.700850 | ||||||||
\(655\) | 8.17544 | − | 20.8125i | 0.319441 | − | 0.813214i | ||||
\(656\) | 70.8853 | 2.76761 | ||||||||
\(657\) | − | 16.8844i | − | 0.658724i | ||||||
\(658\) | 46.1100i | 1.79755i | ||||||||
\(659\) | 0.866840 | 0.0337673 | 0.0168836 | − | 0.999857i | \(-0.494626\pi\) | ||||
0.0168836 | + | 0.999857i | \(0.494626\pi\) | |||||||
\(660\) | 12.7510 | + | 5.00875i | 0.496331 | + | 0.194965i | ||||
\(661\) | −13.3086 | −0.517645 | −0.258822 | − | 0.965925i | \(-0.583334\pi\) | ||||
−0.258822 | + | 0.965925i | \(0.583334\pi\) | |||||||
\(662\) | − | 46.6544i | − | 1.81328i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 74.8079 | 2.90311 | ||||||||
\(665\) | −8.34763 | − | 3.27906i | −0.323707 | − | 0.127156i | ||||
\(666\) | −5.09473 | −0.197417 | ||||||||
\(667\) | − | 6.45878i | − | 0.250085i | ||||||
\(668\) | − | 13.1670i | − | 0.509448i | ||||||
\(669\) | 0.0178799 | 0.000691275 | ||||||||
\(670\) | 16.7125 | − | 42.5458i | 0.645662 | − | 1.64369i | ||||
\(671\) | −1.44176 | −0.0556587 | ||||||||
\(672\) | 34.6963i | 1.33844i | ||||||||
\(673\) | 5.51320i | 0.212518i | 0.994338 | + | 0.106259i | \(0.0338873\pi\) | ||||
−0.994338 | + | 0.106259i | \(0.966113\pi\) | |||||||
\(674\) | −54.2112 | −2.08814 | ||||||||
\(675\) | −10.0000 | + | 10.7646i | −0.384900 | + | 0.414331i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 4.80479i | − | 0.184663i | −0.995728 | − | 0.0923316i | \(-0.970568\pi\) | ||
0.995728 | − | 0.0923316i | \(-0.0294320\pi\) | |||||||
\(678\) | 30.3077i | 1.16396i | ||||||||
\(679\) | −43.4430 | −1.66719 | ||||||||
\(680\) | −6.31947 | + | 16.0877i | −0.242341 | + | 0.616936i | ||||
\(681\) | 24.2496 | 0.929248 | ||||||||
\(682\) | − | 14.4888i | − | 0.554805i | ||||||
\(683\) | 11.7625i | 0.450080i | 0.974350 | + | 0.225040i | \(0.0722513\pi\) | ||||
−0.974350 | + | 0.225040i | \(0.927749\pi\) | |||||||
\(684\) | 10.0000 | 0.382360 | ||||||||
\(685\) | −18.0493 | − | 7.09000i | −0.689628 | − | 0.270895i | ||||
\(686\) | −40.1338 | −1.53231 | ||||||||
\(687\) | 35.6102i | 1.35861i | ||||||||
\(688\) | − | 9.72953i | − | 0.370935i | ||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −24.5582 | − | 9.64680i | −0.934916 | − | 0.367247i | ||||
\(691\) | −4.86684 | −0.185143 | −0.0925717 | − | 0.995706i | \(-0.529509\pi\) | ||||
−0.0925717 | + | 0.995706i | \(0.529509\pi\) | |||||||
\(692\) | − | 6.12658i | − | 0.232897i | ||||||
\(693\) | 3.05147i | 0.115916i | ||||||||
\(694\) | −9.71254 | −0.368683 | ||||||||
\(695\) | −11.7125 | + | 29.8171i | −0.444282 | + | 1.13103i | ||||
\(696\) | −40.7900 | −1.54614 | ||||||||
\(697\) | 12.1925i | 0.461825i | ||||||||
\(698\) | − | 61.9289i | − | 2.34404i | ||||||
\(699\) | 14.9616 | 0.565899 | ||||||||
\(700\) | 44.8079 | − | 48.2340i | 1.69358 | − | 1.82307i | ||||
\(701\) | 21.3828 | 0.807617 | 0.403808 | − | 0.914844i | \(-0.367686\pi\) | ||||
0.403808 | + | 0.914844i | \(0.367686\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.67059i | 0.0630076i | ||||||||
\(704\) | 0.171587 | 0.00646692 | ||||||||
\(705\) | −10.8490 | + | 27.6186i | −0.408595 | + | 1.04018i | ||||
\(706\) | −68.8853 | −2.59253 | ||||||||
\(707\) | − | 38.8822i | − | 1.46232i | ||||||
\(708\) | 73.2835i | 2.75416i | ||||||||
\(709\) | −26.1165 | −0.980825 | −0.490412 | − | 0.871491i | \(-0.663154\pi\) | ||||
−0.490412 | + | 0.871491i | \(0.663154\pi\) | |||||||
\(710\) | 13.9616 | + | 5.48429i | 0.523969 | + | 0.205822i | ||||
\(711\) | 1.69792 | 0.0636770 | ||||||||
\(712\) | − | 79.3107i | − | 2.97229i | ||||||
\(713\) | 19.2936i | 0.722551i | ||||||||
\(714\) | −19.7125 | −0.737723 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 34.8880 | 1.30383 | ||||||||
\(717\) | − | 8.61170i | − | 0.321610i | ||||||
\(718\) | − | 68.7448i | − | 2.56553i | ||||||
\(719\) | −36.6774 | −1.36784 | −0.683918 | − | 0.729559i | \(-0.739725\pi\) | ||||
−0.683918 | + | 0.729559i | \(0.739725\pi\) | |||||||
\(720\) | −9.51220 | + | 24.2156i | −0.354499 | + | 0.902462i | ||||
\(721\) | 32.2318 | 1.20037 | ||||||||
\(722\) | 43.6264i | 1.62361i | ||||||||
\(723\) | 42.5679i | 1.58312i | ||||||||
\(724\) | 17.3265 | 0.643934 | ||||||||
\(725\) | 10.9897 | + | 10.2091i | 0.408148 | + | 0.379157i | ||||
\(726\) | 58.0780 | 2.15548 | ||||||||
\(727\) | − | 26.2596i | − | 0.973916i | −0.873425 | − | 0.486958i | \(-0.838107\pi\) | ||
0.873425 | − | 0.486958i | \(-0.161893\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.614542 | −0.0227608 | ||||||||
\(730\) | 21.4917 | − | 54.7121i | 0.795442 | − | 2.02499i | ||||
\(731\) | 1.67352 | 0.0618972 | ||||||||
\(732\) | − | 21.9000i | − | 0.809446i | ||||||
\(733\) | 31.7811i | 1.17386i | 0.809637 | + | 0.586931i | \(0.199664\pi\) | ||||
−0.809637 | + | 0.586931i | \(0.800336\pi\) | |||||||
\(734\) | −17.6703 | −0.652221 | ||||||||
\(735\) | 7.32648 | + | 2.87794i | 0.270241 | + | 0.106154i | ||||
\(736\) | 11.8073 | 0.435222 | ||||||||
\(737\) | 5.09978i | 0.187853i | ||||||||
\(738\) | 41.4651i | 1.52635i | ||||||||
\(739\) | −34.1370 | −1.25575 | −0.627875 | − | 0.778314i | \(-0.716075\pi\) | ||||
−0.627875 | + | 0.778314i | \(0.716075\pi\) | |||||||
\(740\) | −11.4142 | − | 4.48365i | −0.419595 | − | 0.164822i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 4.80479i | − | 0.176390i | ||||||
\(743\) | 3.12062i | 0.114485i | 0.998360 | + | 0.0572423i | \(0.0182307\pi\) | ||||
−0.998360 | + | 0.0572423i | \(0.981769\pi\) | |||||||
\(744\) | 121.847 | 4.46715 | ||||||||
\(745\) | −14.0249 | + | 35.7037i | −0.513832 | + | 1.30808i | ||||
\(746\) | −5.88798 | −0.215574 | ||||||||
\(747\) | 19.3680i | 0.708639i | ||||||||
\(748\) | − | 3.48301i | − | 0.127352i | ||||||
\(749\) | 31.3649 | 1.14605 | ||||||||
\(750\) | 55.2323 | − | 26.5380i | 2.01680 | − | 0.969031i | ||||
\(751\) | 1.48405 | 0.0541537 | 0.0270769 | − | 0.999633i | \(-0.491380\pi\) | ||||
0.0270769 | + | 0.999633i | \(0.491380\pi\) | |||||||
\(752\) | − | 43.8607i | − | 1.59944i | ||||||
\(753\) | − | 7.90881i | − | 0.288213i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17.4814 | − | 44.5030i | 0.636213 | − | 1.61963i | ||||
\(756\) | 38.6920 | 1.40721 | ||||||||
\(757\) | 5.09978i | 0.185355i | 0.995696 | + | 0.0926774i | \(0.0295425\pi\) | ||||
−0.995696 | + | 0.0926774i | \(0.970457\pi\) | |||||||
\(758\) | − | 13.1753i | − | 0.478550i | ||||||
\(759\) | 2.94369 | 0.106849 | ||||||||
\(760\) | 17.9404 | + | 7.04724i | 0.650768 | + | 0.255630i | ||||
\(761\) | 29.7861 | 1.07975 | 0.539873 | − | 0.841746i | \(-0.318472\pi\) | ||||
0.539873 | + | 0.841746i | \(0.318472\pi\) | |||||||
\(762\) | − | 94.4433i | − | 3.42132i | ||||||
\(763\) | 9.60959i | 0.347890i | ||||||||
\(764\) | −22.1516 | −0.801418 | ||||||||
\(765\) | −4.16517 | − | 1.63613i | −0.150592 | − | 0.0591546i | ||||
\(766\) | −52.5973 | −1.90042 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 62.7228i | 2.26331i | ||||||||
\(769\) | 19.0986 | 0.688713 | 0.344356 | − | 0.938839i | \(-0.388097\pi\) | ||||
0.344356 | + | 0.938839i | \(0.388097\pi\) | |||||||
\(770\) | −3.88412 | + | 9.88797i | −0.139974 | + | 0.356338i | ||||
\(771\) | 28.5582 | 1.02850 | ||||||||
\(772\) | 22.2088i | 0.799311i | ||||||||
\(773\) | 49.2306i | 1.77070i | 0.464923 | + | 0.885351i | \(0.346082\pi\) | ||||
−0.464923 | + | 0.885351i | \(0.653918\pi\) | |||||||
\(774\) | 5.69140 | 0.204573 | ||||||||
\(775\) | −32.8284 | − | 30.4966i | −1.17923 | − | 1.09547i | ||||
\(776\) | 93.3661 | 3.35165 | ||||||||
\(777\) | − | 7.74335i | − | 0.277791i | ||||||
\(778\) | 50.2725i | 1.80236i | ||||||||
\(779\) | 13.5967 | 0.487151 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.67352 | −0.0598831 | ||||||||
\(782\) | 6.70825i | 0.239886i | ||||||||
\(783\) | 8.81566i | 0.315046i | ||||||||
\(784\) | −11.6351 | −0.415539 | ||||||||
\(785\) | 38.2215 | + | 15.0139i | 1.36418 | + | 0.535869i | ||||
\(786\) | −54.8079 | −1.95493 | ||||||||
\(787\) | 9.78335i | 0.348739i | 0.984680 | + | 0.174369i | \(0.0557887\pi\) | ||||
−0.984680 | + | 0.174369i | \(0.944211\pi\) | |||||||
\(788\) | − | 30.2250i | − | 1.07672i | ||||||
\(789\) | −65.1701 | −2.32012 | ||||||||
\(790\) | 5.50193 | + | 2.16123i | 0.195750 | + | 0.0768931i | ||||
\(791\) | −16.2496 | −0.577770 | ||||||||
\(792\) | − | 6.55812i | − | 0.233033i | ||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 23.9020 | 0.848250 | ||||||||
\(795\) | 1.13049 | − | 2.87794i | 0.0400945 | − | 0.102070i | ||||
\(796\) | 23.1901 | 0.821950 | ||||||||
\(797\) | 16.5371i | 0.585775i | 0.956147 | + | 0.292887i | \(0.0946161\pi\) | ||||
−0.956147 | + | 0.292887i | \(0.905384\pi\) | |||||||
\(798\) | 21.9827i | 0.778178i | ||||||||
\(799\) | 7.54421 | 0.266895 | ||||||||
\(800\) | −18.6632 | + | 20.0903i | −0.659845 | + | 0.710299i | ||||
\(801\) | 20.5338 | 0.725527 | ||||||||
\(802\) | 62.3755i | 2.20256i | ||||||||
\(803\) | 6.55812i | 0.231431i | ||||||||
\(804\) | −77.4641 | −2.73195 | ||||||||
\(805\) | 5.17218 | − | 13.1670i | 0.182295 | − | 0.464077i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 47.9018i | − | 1.68622i | ||||||
\(808\) | 83.5643i | 2.93978i | ||||||||
\(809\) | 31.8424 | 1.11952 | 0.559760 | − | 0.828655i | \(-0.310893\pi\) | ||||
0.559760 | + | 0.828655i | \(0.310893\pi\) | |||||||
\(810\) | 59.5095 | + | 23.3761i | 2.09095 | + | 0.821354i | ||||
\(811\) | −13.3470 | −0.468678 | −0.234339 | − | 0.972155i | \(-0.575293\pi\) | ||||
−0.234339 | + | 0.972155i | \(0.575293\pi\) | |||||||
\(812\) | − | 39.5011i | − | 1.38622i | ||||||
\(813\) | − | 25.4657i | − | 0.893121i | ||||||
\(814\) | 1.97886 | 0.0693589 | ||||||||
\(815\) | 8.34763 | + | 3.27906i | 0.292405 | + | 0.114860i | ||||
\(816\) | 18.7510 | 0.656415 | ||||||||
\(817\) | − | 1.86624i | − | 0.0652915i | ||||||
\(818\) | − | 91.9431i | − | 3.21472i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −36.4917 | + | 92.8982i | −1.27434 | + | 3.24415i | ||||
\(821\) | −11.6735 | −0.407409 | −0.203704 | − | 0.979032i | \(-0.565298\pi\) | ||||
−0.203704 | + | 0.979032i | \(0.565298\pi\) | |||||||
\(822\) | 47.5311i | 1.65784i | ||||||||
\(823\) | − | 32.4317i | − | 1.13050i | −0.824920 | − | 0.565249i | \(-0.808780\pi\) | ||
0.824920 | − | 0.565249i | \(-0.191220\pi\) | |||||||
\(824\) | −69.2714 | −2.41318 | ||||||||
\(825\) | −4.65297 | + | 5.00875i | −0.161996 | + | 0.174382i | ||||
\(826\) | −56.8290 | −1.97733 | ||||||||
\(827\) | − | 27.3319i | − | 0.950425i | −0.879871 | − | 0.475212i | \(-0.842371\pi\) | ||
0.879871 | − | 0.475212i | \(-0.157629\pi\) | |||||||
\(828\) | 15.7734i | 0.548163i | ||||||||
\(829\) | −3.54036 | −0.122962 | −0.0614808 | − | 0.998108i | \(-0.519582\pi\) | ||||
−0.0614808 | + | 0.998108i | \(0.519582\pi\) | |||||||
\(830\) | −24.6530 | + | 62.7600i | −0.855717 | + | 2.17843i | ||||
\(831\) | 36.1370 | 1.25358 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 2.00128i | − | 0.0693402i | ||||||
\(834\) | 78.5204 | 2.71894 | ||||||||
\(835\) | 6.11588 | + | 2.40240i | 0.211649 | + | 0.0831384i | ||||
\(836\) | −3.88412 | −0.134335 | ||||||||
\(837\) | − | 26.3341i | − | 0.910238i | ||||||
\(838\) | − | 17.4812i | − | 0.603877i | ||||||
\(839\) | 44.7900 | 1.54632 | 0.773161 | − | 0.634210i | \(-0.218674\pi\) | ||||
0.773161 | + | 0.634210i | \(0.218674\pi\) | |||||||
\(840\) | −83.1555 | − | 32.6646i | −2.86914 | − | 1.12704i | ||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | 86.5028i | 2.98108i | ||||||||
\(843\) | − | 22.8138i | − | 0.785750i | ||||||
\(844\) | 62.8111 | 2.16205 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 25.6568 | 0.882100 | ||||||||
\(847\) | 31.1388i | 1.06994i | ||||||||
\(848\) | 4.57042i | 0.156949i | ||||||||
\(849\) | 18.9795 | 0.651373 | ||||||||
\(850\) | −11.4142 | − | 10.6034i | −0.391504 | − | 0.363695i | ||||
\(851\) | −2.63509 | −0.0903297 | ||||||||
\(852\) | − | 25.4202i | − | 0.870881i | ||||||
\(853\) | − | 31.3732i | − | 1.07420i | −0.843519 | − | 0.537099i | \(-0.819520\pi\) | ||
0.843519 | − | 0.537099i | \(-0.180480\pi\) | |||||||
\(854\) | 16.9827 | 0.581137 | ||||||||
\(855\) | −1.82456 | + | 4.64484i | −0.0623985 | + | 0.158850i | ||||
\(856\) | −67.4084 | −2.30397 | ||||||||
\(857\) | − | 21.2813i | − | 0.726955i | −0.931603 | − | 0.363478i | \(-0.881589\pi\) | ||
0.931603 | − | 0.363478i | \(-0.118411\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −56.8502 | −1.93970 | −0.969851 | − | 0.243698i | \(-0.921639\pi\) | ||||
−0.969851 | + | 0.243698i | \(0.921639\pi\) | |||||||
\(860\) | 12.7510 | + | 5.00875i | 0.434804 | + | 0.170797i | ||||
\(861\) | −63.0217 | −2.14778 | ||||||||
\(862\) | − | 41.3673i | − | 1.40898i | ||||||
\(863\) | 32.8011i | 1.11656i | 0.829651 | + | 0.558282i | \(0.188539\pi\) | ||||
−0.829651 | + | 0.558282i | \(0.811461\pi\) | |||||||
\(864\) | −16.1159 | −0.548273 | ||||||||
\(865\) | 2.84570 | + | 1.11783i | 0.0967566 | + | 0.0380073i | ||||
\(866\) | −0.652374 | −0.0221686 | ||||||||
\(867\) | − | 33.3745i | − | 1.13346i | ||||||
\(868\) | 117.997i | 4.00509i | ||||||||
\(869\) | −0.659493 | −0.0223718 | ||||||||
\(870\) | 13.4424 | − | 34.2207i | 0.455739 | − | 1.16019i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | − | 20.6526i | − | 0.699385i | ||||||
\(873\) | 24.1728i | 0.818126i | ||||||||
\(874\) | 7.48079 | 0.253041 | ||||||||
\(875\) | 14.2285 | + | 29.6131i | 0.481011 | + | 1.00111i | ||||
\(876\) | −99.6157 | −3.36570 | ||||||||
\(877\) | 36.0651i | 1.21783i | 0.793235 | + | 0.608916i | \(0.208395\pi\) | ||||
−0.793235 | + | 0.608916i | \(0.791605\pi\) | |||||||
\(878\) | − | 19.3391i | − | 0.652664i | ||||||
\(879\) | −60.8257 | −2.05160 | ||||||||
\(880\) | 3.69466 | − | 9.40563i | 0.124547 | − | 0.317064i | ||||
\(881\) | −46.0396 | −1.55111 | −0.775557 | − | 0.631277i | \(-0.782531\pi\) | ||||
−0.775557 | + | 0.631277i | \(0.782531\pi\) | |||||||
\(882\) | − | 6.80607i | − | 0.229172i | ||||||
\(883\) | − | 0.802236i | − | 0.0269974i | −0.999909 | − | 0.0134987i | \(-0.995703\pi\) | ||
0.999909 | − | 0.0134987i | \(-0.00429690\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −34.0390 | − | 13.3710i | −1.14421 | − | 0.449461i | ||||
\(886\) | −11.0039 | −0.369682 | ||||||||
\(887\) | 8.22568i | 0.276191i | 0.990419 | + | 0.138096i | \(0.0440981\pi\) | ||||
−0.990419 | + | 0.138096i | \(0.955902\pi\) | |||||||
\(888\) | 16.6417i | 0.558460i | ||||||||
\(889\) | 50.6363 | 1.69829 | ||||||||
\(890\) | 66.5377 | + | 26.1369i | 2.23035 | + | 0.876110i | ||||
\(891\) | −7.13316 | −0.238970 | ||||||||
\(892\) | − | 0.0372125i | − | 0.00124597i | ||||||
\(893\) | − | 8.41302i | − | 0.281531i | ||||||
\(894\) | 94.0223 | 3.14458 | ||||||||
\(895\) | −6.36551 | + | 16.2049i | −0.212775 | + | 0.541671i | ||||
\(896\) | −34.2529 | −1.14431 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 8.37054i | − | 0.279328i | ||||||
\(899\) | −26.8847 | −0.896656 | ||||||||
\(900\) | −26.8387 | − | 24.9323i | −0.894623 | − | 0.831076i | ||||
\(901\) | −0.786129 | −0.0261897 | ||||||||
\(902\) | − | 16.1056i | − | 0.536257i | ||||||
\(903\) | 8.65020i | 0.287861i | ||||||||
\(904\) | 34.9231 | 1.16153 | ||||||||
\(905\) | −3.16131 | + | 8.04788i | −0.105086 | + | 0.267521i | ||||
\(906\) | −117.195 | −3.89353 | ||||||||
\(907\) | − | 30.4359i | − | 1.01061i | −0.862941 | − | 0.505305i | \(-0.831380\pi\) | ||
0.862941 | − | 0.505305i | \(-0.168620\pi\) | |||||||
\(908\) | − | 50.4697i | − | 1.67489i | ||||||
\(909\) | −21.6351 | −0.717591 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43.6145 | 1.44501 | 0.722507 | − | 0.691363i | \(-0.242990\pi\) | ||||
0.722507 | + | 0.691363i | \(0.242990\pi\) | |||||||
\(912\) | − | 20.9104i | − | 0.692412i | ||||||
\(913\) | − | 7.52278i | − | 0.248968i | ||||||
\(914\) | 39.2708 | 1.29896 | ||||||||
\(915\) | 10.1722 | + | 3.99577i | 0.336282 | + | 0.132096i | ||||
\(916\) | 74.1138 | 2.44879 | ||||||||
\(917\) | − | 29.3855i | − | 0.970395i | ||||||
\(918\) | − | 9.15616i | − | 0.302198i | ||||||
\(919\) | 37.0217 | 1.22123 | 0.610617 | − | 0.791926i | \(-0.290921\pi\) | ||||
0.610617 | + | 0.791926i | \(0.290921\pi\) | |||||||
\(920\) | −11.1159 | + | 28.2981i | −0.366480 | + | 0.932961i | ||||
\(921\) | −27.3893 | −0.902509 | ||||||||
\(922\) | 65.8957i | 2.17016i | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 18.0033 | 0.592264 | ||||||||
\(925\) | 4.16517 | − | 4.48365i | 0.136950 | − | 0.147422i | ||||
\(926\) | 17.9231 | 0.588991 | ||||||||
\(927\) | − | 17.9346i | − | 0.589050i | ||||||
\(928\) | 16.4529i | 0.540092i | ||||||||
\(929\) | −4.76825 | −0.156441 | −0.0782206 | − | 0.996936i | \(-0.524924\pi\) | ||||
−0.0782206 | + | 0.996936i | \(0.524924\pi\) | |||||||
\(930\) | −40.1549 | + | 102.224i | −1.31673 | + | 3.35205i | ||||
\(931\) | −2.23175 | −0.0731427 | ||||||||
\(932\) | − | 31.1388i | − | 1.01999i | ||||||
\(933\) | − | 60.1165i | − | 1.96812i | ||||||
\(934\) | 47.8886 | 1.56696 | ||||||||
\(935\) | 1.61780 | + | 0.635495i | 0.0529079 | + | 0.0207829i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.6264i | 1.42521i | 0.701565 | + | 0.712606i | \(0.252485\pi\) | ||||
−0.701565 | + | 0.712606i | \(0.747515\pi\) | |||||||
\(938\) | − | 60.0709i | − | 1.96139i | ||||||
\(939\) | −52.9205 | −1.72699 | ||||||||
\(940\) | 57.4814 | + | 22.5794i | 1.87484 | + | 0.736460i | ||||
\(941\) | −18.2675 | −0.595504 | −0.297752 | − | 0.954643i | \(-0.596237\pi\) | ||||
−0.297752 | + | 0.954643i | \(0.596237\pi\) | |||||||
\(942\) | − | 100.653i | − | 3.27944i | ||||||
\(943\) | 21.4465i | 0.698395i | ||||||||
\(944\) | 54.0569 | 1.75940 | ||||||||
\(945\) | −7.05957 | + | 17.9718i | −0.229648 | + | 0.584623i | ||||
\(946\) | −2.21061 | −0.0718731 | ||||||||
\(947\) | 19.9829i | 0.649358i | 0.945824 | + | 0.324679i | \(0.105256\pi\) | ||||
−0.945824 | + | 0.324679i | \(0.894744\pi\) | |||||||
\(948\) | − | 10.0175i | − | 0.325353i | ||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −11.8246 | + | 12.7287i | −0.383639 | + | 0.412973i | ||||
\(951\) | 0.504596 | 0.0163626 | ||||||||
\(952\) | 22.7145i | 0.736181i | ||||||||
\(953\) | 39.8635i | 1.29130i | 0.763632 | + | 0.645652i | \(0.223414\pi\) | ||||
−0.763632 | + | 0.645652i | \(0.776586\pi\) | |||||||
\(954\) | −2.67352 | −0.0865583 | ||||||||
\(955\) | 4.04169 | − | 10.2891i | 0.130786 | − | 0.332947i | ||||
\(956\) | −17.9231 | −0.579676 | ||||||||
\(957\) | 4.10190i | 0.132596i | ||||||||
\(958\) | 49.5847i | 1.60201i | ||||||||
\(959\) | −25.4840 | −0.822923 | ||||||||
\(960\) | −1.21061 | − | 0.475543i | −0.0390722 | − | 0.0153481i | ||||
\(961\) | 49.3098 | 1.59064 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 17.4523i | − | 0.562392i | ||||||
\(964\) | 88.5946 | 2.85344 | ||||||||
\(965\) | −10.3156 | − | 4.05211i | −0.332071 | − | 0.130442i | ||||
\(966\) | −34.6741 | −1.11562 | ||||||||
\(967\) | 43.8607i | 1.41047i | 0.708975 | + | 0.705233i | \(0.249158\pi\) | ||||
−0.708975 | + | 0.705233i | \(0.750842\pi\) | |||||||
\(968\) | − | 66.9225i | − | 2.15097i | ||||||
\(969\) | 3.59666 | 0.115541 | ||||||||
\(970\) | −30.7688 | + | 78.3294i | −0.987928 | + | 2.51501i | ||||
\(971\) | 60.9795 | 1.95692 | 0.978462 | − | 0.206428i | \(-0.0661838\pi\) | ||||
0.978462 | + | 0.206428i | \(0.0661838\pi\) | |||||||
\(972\) | − | 68.8494i | − | 2.20835i | ||||||
\(973\) | 42.0991i | 1.34964i | ||||||||
\(974\) | 82.2887 | 2.63670 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −16.1543 | −0.517087 | ||||||||
\(977\) | − | 51.3697i | − | 1.64346i | −0.569875 | − | 0.821731i | \(-0.693008\pi\) | ||
0.569875 | − | 0.821731i | \(-0.306992\pi\) | |||||||
\(978\) | − | 21.9827i | − | 0.702929i | ||||||
\(979\) | −7.97560 | −0.254901 | ||||||||
\(980\) | 5.98973 | − | 15.2483i | 0.191335 | − | 0.487088i | ||||
\(981\) | 5.34703 | 0.170718 | ||||||||
\(982\) | − | 72.9885i | − | 2.32916i | ||||||
\(983\) | 37.3026i | 1.18977i | 0.803811 | + | 0.594885i | \(0.202802\pi\) | ||||
−0.803811 | + | 0.594885i | \(0.797198\pi\) | |||||||
\(984\) | 135.444 | 4.31780 | ||||||||
\(985\) | 14.0390 | + | 5.51471i | 0.447320 | + | 0.175713i | ||||
\(986\) | −9.34763 | −0.297689 | ||||||||
\(987\) | 38.9951i | 1.24123i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.94369 | 0.0936040 | ||||||||
\(990\) | 5.50193 | + | 2.16123i | 0.174863 | + | 0.0686884i | ||||
\(991\) | −51.5621 | −1.63792 | −0.818962 | − | 0.573848i | \(-0.805450\pi\) | ||||
−0.818962 | + | 0.573848i | \(0.805450\pi\) | |||||||
\(992\) | − | 49.1479i | − | 1.56045i | ||||||
\(993\) | − | 39.4556i | − | 1.25208i | ||||||
\(994\) | 19.7125 | 0.625244 | ||||||||
\(995\) | −4.23116 | + | 10.7714i | −0.134137 | + | 0.341477i | ||||
\(996\) | 114.269 | 3.62074 | ||||||||
\(997\) | 22.9489i | 0.726798i | 0.931634 | + | 0.363399i | \(0.118384\pi\) | ||||
−0.931634 | + | 0.363399i | \(0.881616\pi\) | |||||||
\(998\) | − | 73.7286i | − | 2.33384i | ||||||
\(999\) | 3.59666 | 0.113793 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))