Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [36,3,Mod(5,36)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(36, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("36.5");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 36 = 2^{2} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 36.g (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.980928951697\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 5.1 | ||
Root | \(-1.18614 + 1.26217i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 36.5 |
Dual form | 36.3.g.a.29.1 |
$q$-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 \(\left(\mathbb{Z}/36\mathbb{Z}\right)^\times\).
\(n\) | \(19\) | \(29\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.686141 | + | 2.92048i | −0.228714 | + | 0.973494i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.55842 | + | 3.78651i | 1.31168 | + | 0.757301i | 0.982375 | − | 0.186921i | \(-0.0598508\pi\) |
0.329309 | + | 0.944222i | \(0.393184\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.55842 | − | 7.89542i | −0.651203 | − | 1.12792i | −0.982831 | − | 0.184507i | \(-0.940931\pi\) |
0.331628 | − | 0.943410i | \(-0.392402\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.05842 | − | 4.00772i | −0.895380 | − | 0.445302i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.383156 | + | 0.221215i | −0.0348324 | + | 0.0201105i | −0.517315 | − | 0.855795i | \(-0.673068\pi\) |
0.482483 | + | 0.875906i | \(0.339735\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.55842 | − | 9.62747i | 0.427571 | − | 0.740575i | −0.569086 | − | 0.822278i | \(-0.692703\pi\) |
0.996657 | + | 0.0817036i | \(0.0260361\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −15.5584 | + | 16.5557i | −1.03723 | + | 1.10371i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 8.01544i | − | 0.471497i | −0.971814 | − | 0.235748i | \(-0.924246\pi\) | ||
0.971814 | − | 0.235748i | \(-0.0757541\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.11684 | −0.427202 | −0.213601 | − | 0.976921i | \(-0.568519\pi\) | ||||
−0.213601 | + | 0.976921i | \(0.568519\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 26.1861 | − | 7.89542i | 1.24696 | − | 0.375972i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 20.4416 | + | 11.8020i | 0.888764 | + | 0.513128i | 0.873538 | − | 0.486756i | \(-0.161820\pi\) |
0.0152262 | + | 0.999884i | \(0.495153\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 16.1753 | + | 28.0164i | 0.647011 | + | 1.12066i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 17.2337 | − | 20.7846i | 0.638285 | − | 0.769800i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −45.9090 | + | 26.5055i | −1.58307 | + | 0.913984i | −0.588659 | + | 0.808381i | \(0.700344\pi\) |
−0.994408 | + | 0.105603i | \(0.966323\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −14.6753 | + | 25.4183i | −0.473396 | + | 0.819945i | −0.999536 | − | 0.0304523i | \(-0.990305\pi\) |
0.526141 | + | 0.850398i | \(0.323639\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.383156 | − | 1.27078i | −0.0116108 | − | 0.0385086i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 69.0420i | − | 1.97263i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 18.4674 | 0.499118 | 0.249559 | − | 0.968360i | \(-0.419714\pi\) | ||||
0.249559 | + | 0.968360i | \(0.419714\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 24.3030 | + | 22.8391i | 0.623153 | + | 0.585617i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −38.9674 | − | 22.4978i | −0.950424 | − | 0.548727i | −0.0572112 | − | 0.998362i | \(-0.518221\pi\) |
−0.893213 | + | 0.449635i | \(0.851554\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.5000 | − | 19.9186i | −0.267442 | − | 0.463223i | 0.700759 | − | 0.713398i | \(-0.252845\pi\) |
−0.968200 | + | 0.250176i | \(0.919512\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −37.6753 | − | 56.7976i | −0.837228 | − | 1.26217i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.32473 | + | 4.22894i | −0.155845 | + | 0.0899774i | −0.575895 | − | 0.817524i | \(-0.695346\pi\) |
0.420049 | + | 0.907501i | \(0.362013\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −17.0584 | + | 29.5461i | −0.348131 | + | 0.602981i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 23.4090 | + | 5.49972i | 0.458999 | + | 0.107838i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 60.5841i | 1.14310i | 0.820569 | + | 0.571548i | \(0.193657\pi\) | ||||
−0.820569 | + | 0.571548i | \(0.806343\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.35053 | −0.0609188 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.56930 | − | 23.7051i | 0.0977070 | − | 0.415879i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 65.9674 | + | 38.0863i | 1.11809 | + | 0.645530i | 0.940913 | − | 0.338649i | \(-0.109970\pi\) |
0.177178 | + | 0.984179i | \(0.443303\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.67527 | − | 4.63370i | −0.0438568 | − | 0.0759622i | 0.843264 | − | 0.537500i | \(-0.180631\pi\) |
−0.887121 | + | 0.461538i | \(0.847298\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.09105 | + | 81.8935i | 0.0808103 | + | 1.29990i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 72.9090 | − | 42.0940i | 1.12168 | − | 0.647600i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 54.8505 | − | 95.0039i | 0.818665 | − | 1.41797i | −0.0880017 | − | 0.996120i | \(-0.528048\pi\) |
0.906666 | − | 0.421848i | \(-0.138619\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −48.4932 | + | 51.6014i | −0.702800 | + | 0.747847i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.0309i | 0.225787i | 0.993607 | + | 0.112894i | \(0.0360119\pi\) | ||||
−0.993607 | + | 0.112894i | \(0.963988\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.35053 | −0.0595963 | −0.0297982 | − | 0.999556i | \(-0.509486\pi\) | ||||
−0.0297982 | + | 0.999556i | \(0.509486\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −92.9198 | + | 28.0164i | −1.23893 | + | 0.373552i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.49317 | + | 2.01678i | 0.0453659 | + | 0.0261920i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.792110 | − | 1.37197i | −0.0100267 | − | 0.0173668i | 0.860969 | − | 0.508658i | \(-0.169858\pi\) |
−0.870995 | + | 0.491291i | \(0.836525\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 48.8763 | + | 64.5918i | 0.603411 | + | 0.797430i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.32473 | + | 4.22894i | −0.0882498 | + | 0.0509511i | −0.543475 | − | 0.839425i | \(-0.682892\pi\) |
0.455226 | + | 0.890376i | \(0.349559\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 30.3505 | − | 52.5687i | 0.357065 | − | 0.618455i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −45.9090 | − | 152.263i | −0.527689 | − | 1.75015i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 64.1236i | 0.720489i | 0.932858 | + | 0.360245i | \(0.117307\pi\) | ||||
−0.932858 | + | 0.360245i | \(0.882693\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −101.351 | −1.11374 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −64.1644 | − | 60.2994i | −0.689940 | − | 0.648380i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −53.2337 | − | 30.7345i | −0.560355 | − | 0.323521i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −57.6168 | − | 99.7953i | −0.593988 | − | 1.02882i | −0.993689 | − | 0.112172i | \(-0.964219\pi\) |
0.399701 | − | 0.916646i | \(-0.369114\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.97420 | − | 0.247063i | 0.0401435 | − | 0.00249558i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 114.558 | − | 66.1403i | 1.13424 | − | 0.654855i | 0.189244 | − | 0.981930i | \(-0.439396\pi\) |
0.944998 | + | 0.327075i | \(0.106063\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −62.6753 | + | 108.557i | −0.608498 | + | 1.05395i | 0.382990 | + | 0.923752i | \(0.374894\pi\) |
−0.991488 | + | 0.130197i | \(0.958439\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 201.636 | + | 47.3725i | 1.92034 | + | 0.451167i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 36.5378i | 0.341475i | 0.985317 | + | 0.170737i | \(0.0546149\pi\) | ||||
−0.985317 | + | 0.170737i | \(0.945385\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 134.701 | 1.23579 | 0.617895 | − | 0.786261i | \(-0.287986\pi\) | ||||
0.617895 | + | 0.786261i | \(0.287986\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.6712 | + | 53.9336i | −0.114155 | + | 0.485889i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −164.727 | − | 95.1051i | −1.45776 | − | 0.841638i | −0.458859 | − | 0.888509i | \(-0.651742\pi\) |
−0.998901 | + | 0.0468711i | \(0.985075\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 89.3763 | + | 154.804i | 0.777185 | + | 1.34612i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −83.3763 | + | 55.3056i | −0.712618 | + | 0.472697i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −63.2853 | + | 36.5378i | −0.531809 | + | 0.307040i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −60.4021 | + | 104.620i | −0.499191 | + | 0.864624i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 92.4416 | − | 98.3668i | 0.751558 | − | 0.799730i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 55.6657i | 0.445325i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 184.103 | 1.44963 | 0.724816 | − | 0.688943i | \(-0.241925\pi\) | ||||
0.724816 | + | 0.688943i | \(0.241925\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 66.0625 | − | 19.9186i | 0.512112 | − | 0.154408i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −109.194 | − | 63.0433i | −0.833544 | − | 0.481247i | 0.0215207 | − | 0.999768i | \(-0.493149\pi\) |
−0.855064 | + | 0.518522i | \(0.826483\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 37.0000 | + | 64.0859i | 0.278195 | + | 0.481849i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 191.727 | − | 71.0588i | 1.42020 | − | 0.526361i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 107.617 | − | 62.1326i | 0.785524 | − | 0.453523i | −0.0528602 | − | 0.998602i | \(-0.516834\pi\) |
0.838385 | + | 0.545079i | \(0.183500\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.3832 | + | 23.1803i | −0.0962817 | + | 0.166765i | −0.910143 | − | 0.414295i | \(-0.864028\pi\) |
0.813861 | + | 0.581059i | \(0.197362\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.32473 | − | 24.2934i | −0.0519485 | − | 0.172294i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.91843i | 0.0343946i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −401.454 | −2.76865 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −74.5842 | − | 70.0916i | −0.507376 | − | 0.476813i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 69.8437 | + | 40.3243i | 0.468750 | + | 0.270633i | 0.715716 | − | 0.698391i | \(-0.246100\pi\) |
−0.246966 | + | 0.969024i | \(0.579434\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −49.9742 | − | 86.5579i | −0.330955 | − | 0.573231i | 0.651744 | − | 0.758439i | \(-0.274037\pi\) |
−0.982699 | + | 0.185208i | \(0.940704\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −32.1237 | + | 64.5918i | −0.209959 | + | 0.422169i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −192.493 | + | 111.136i | −1.24189 | + | 0.717006i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 34.7269 | − | 60.1487i | 0.221190 | − | 0.383113i | −0.733979 | − | 0.679172i | \(-0.762339\pi\) |
0.955170 | + | 0.296059i | \(0.0956725\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −176.935 | − | 41.5692i | −1.11280 | − | 0.261442i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 215.193i | − | 1.33660i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 162.467 | 0.996732 | 0.498366 | − | 0.866967i | \(-0.333934\pi\) | ||||
0.498366 | + | 0.866967i | \(0.333934\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.29894 | − | 9.78517i | 0.0139329 | − | 0.0593040i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 83.7269 | + | 48.3397i | 0.501358 | + | 0.289459i | 0.729274 | − | 0.684221i | \(-0.239858\pi\) |
−0.227916 | + | 0.973681i | \(0.573191\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 22.7079 | + | 39.3312i | 0.134366 | + | 0.232729i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 65.4090 | + | 32.5301i | 0.382509 | + | 0.190234i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −24.2731 | + | 14.0141i | −0.140307 | + | 0.0810064i | −0.568510 | − | 0.822676i | \(-0.692480\pi\) |
0.428203 | + | 0.903682i | \(0.359147\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 147.467 | − | 255.421i | 0.842671 | − | 1.45955i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −156.493 | + | 166.524i | −0.884142 | + | 0.940813i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 35.6012i | − | 0.198889i | −0.995043 | − | 0.0994447i | \(-0.968293\pi\) | ||
0.995043 | − | 0.0994447i | \(-0.0317067\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.6358 | −0.108485 | −0.0542426 | − | 0.998528i | \(-0.517274\pi\) | ||||
−0.0542426 | + | 0.998528i | \(0.517274\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.3682 | − | 4.63370i | 0.0839794 | − | 0.0253207i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 121.117 | + | 69.9268i | 0.654686 | + | 0.377983i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.77314 | + | 3.07117i | 0.00948202 | + | 0.0164233i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −242.662 | − | 41.3222i | −1.28392 | − | 0.218636i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 188.662 | − | 108.924i | 0.987757 | − | 0.570282i | 0.0831540 | − | 0.996537i | \(-0.473501\pi\) |
0.904603 | + | 0.426255i | \(0.140167\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24.5000 | − | 42.4352i | 0.126943 | − | 0.219872i | −0.795548 | − | 0.605891i | \(-0.792817\pi\) |
0.922491 | + | 0.386019i | \(0.126150\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 72.9090 | + | 241.812i | 0.373892 | + | 1.24006i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 359.965i | 1.82723i | 0.406575 | + | 0.913617i | \(0.366723\pi\) | ||||
−0.406575 | + | 0.913617i | \(0.633277\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −61.0652 | −0.306861 | −0.153430 | − | 0.988159i | \(-0.549032\pi\) | ||||
−0.153430 | + | 0.988159i | \(0.549032\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 239.822 | + | 225.376i | 1.19314 | + | 1.12127i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 418.545 | + | 241.647i | 2.06180 | + | 1.19038i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −170.376 | − | 295.100i | −0.831104 | − | 1.43951i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −117.428 | − | 177.029i | −0.567285 | − | 0.855214i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.11002 | − | 1.79557i | 0.0148805 | − | 0.00859124i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −193.493 | + | 335.140i | −0.917029 | + | 1.58834i | −0.113126 | + | 0.993581i | \(0.536087\pi\) |
−0.803903 | + | 0.594761i | \(0.797247\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −46.8179 | − | 10.9994i | −0.219802 | − | 0.0516406i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 174.179i | − | 0.810136i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 267.584 | 1.23311 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.98508 | − | 12.7056i | 0.0136305 | − | 0.0580167i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −77.1684 | − | 44.5532i | −0.349178 | − | 0.201598i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −51.3763 | − | 88.9864i | −0.230387 | − | 0.399042i | 0.727535 | − | 0.686071i | \(-0.240666\pi\) |
−0.957922 | + | 0.287028i | \(0.907333\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −18.0652 | − | 290.594i | −0.0802900 | − | 1.29153i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −293.552 | + | 169.482i | −1.29318 | + | 0.746617i | −0.979216 | − | 0.202818i | \(-0.934990\pi\) |
−0.313962 | + | 0.949435i | \(0.601657\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 148.376 | − | 256.995i | 0.647932 | − | 1.12225i | −0.335685 | − | 0.941974i | \(-0.608968\pi\) |
0.983616 | − | 0.180276i | \(-0.0576991\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.28679 | + | 8.81795i | −0.0358736 | + | 0.0381729i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 346.537i | − | 1.48728i | −0.668578 | − | 0.743642i | \(-0.733097\pi\) | ||
0.668578 | − | 0.743642i | \(-0.266903\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −64.0516 | −0.272560 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.55033 | − | 1.37197i | 0.0191997 | − | 0.00578892i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −140.026 | − | 80.8439i | −0.585882 | − | 0.338259i | 0.177586 | − | 0.984105i | \(-0.443171\pi\) |
−0.763468 | + | 0.645846i | \(0.776505\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 162.370 | + | 281.232i | 0.673732 | + | 1.16694i | 0.976838 | + | 0.213982i | \(0.0686433\pi\) |
−0.303105 | + | 0.952957i | \(0.598023\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −222.175 | + | 98.4233i | −0.914302 | + | 0.405034i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −223.753 | + | 129.184i | −0.913276 | + | 0.527280i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −45.1168 | + | 78.1447i | −0.182659 | + | 0.316375i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.32473 | − | 24.2934i | −0.0294166 | − | 0.0975638i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 384.012i | − | 1.52993i | −0.644074 | − | 0.764963i | \(-0.722757\pi\) | ||
0.644074 | − | 0.764963i | \(-0.277243\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.4431 | −0.0412770 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 132.701 | + | 124.708i | 0.520396 | + | 0.489050i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.2011 | − | 6.46694i | −0.0435839 | − | 0.0251632i | 0.478050 | − | 0.878333i | \(-0.341344\pi\) |
−0.521634 | + | 0.853170i | \(0.674677\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −84.1821 | − | 145.808i | −0.325027 | − | 0.562964i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 476.181 | − | 29.6026i | 1.82445 | − | 0.113420i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −42.8437 | + | 24.7358i | −0.162904 | + | 0.0940526i | −0.579236 | − | 0.815160i | \(-0.696649\pi\) |
0.416332 | + | 0.909213i | \(0.363316\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −229.402 | + | 397.336i | −0.865668 | + | 1.49938i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −187.272 | − | 43.9978i | −0.701392 | − | 0.164786i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.4434i | 0.0797154i | 0.999205 | + | 0.0398577i | \(0.0126905\pi\) | ||||
−0.999205 | + | 0.0398577i | \(0.987310\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −326.907 | −1.20630 | −0.603150 | − | 0.797628i | \(-0.706088\pi\) | ||||
−0.603150 | + | 0.797628i | \(0.706088\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 69.5407 | − | 295.992i | 0.254728 | − | 1.08422i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12.3953 | − | 7.15643i | −0.0450738 | − | 0.0260234i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 238.727 | + | 413.487i | 0.861830 | + | 1.49273i | 0.870161 | + | 0.492768i | \(0.164015\pi\) |
−0.00833105 | + | 0.999965i | \(0.502652\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 220.129 | − | 146.017i | 0.788993 | − | 0.523359i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −103.064 | + | 59.5039i | −0.366775 | + | 0.211758i | −0.672049 | − | 0.740507i | \(-0.734585\pi\) |
0.305274 | + | 0.952265i | \(0.401252\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 195.675 | − | 338.920i | 0.691432 | − | 1.19760i | −0.279937 | − | 0.960018i | \(-0.590313\pi\) |
0.971369 | − | 0.237577i | \(-0.0763532\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 126.285 | − | 134.380i | 0.443106 | − | 0.471508i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 410.218i | 1.42933i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 224.753 | 0.777691 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 330.984 | − | 99.7953i | 1.13740 | − | 0.342939i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 62.0910 | + | 35.8483i | 0.211915 | + | 0.122349i | 0.602201 | − | 0.798345i | \(-0.294291\pi\) |
−0.390286 | + | 0.920694i | \(0.627624\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 288.428 | + | 499.572i | 0.977722 | + | 1.69346i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.00532 | + | 11.7761i | −0.00675192 | + | 0.0396502i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 227.246 | − | 131.200i | 0.760020 | − | 0.438797i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −104.844 | + | 181.595i | −0.348318 | + | 0.603304i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 114.558 | + | 379.947i | 0.378081 | + | 1.25395i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 40.5196i | − | 0.132851i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −172.351 | −0.561402 | −0.280701 | − | 0.959795i | \(-0.590567\pi\) | ||||
−0.280701 | + | 0.959795i | \(0.590567\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −274.034 | − | 257.527i | −0.886841 | − | 0.833421i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −524.246 | − | 302.673i | −1.68568 | − | 0.973227i | −0.957763 | − | 0.287559i | \(-0.907156\pi\) |
−0.727915 | − | 0.685667i | \(-0.759511\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −163.734 | − | 283.595i | −0.523111 | − | 0.906055i | −0.999638 | − | 0.0268949i | \(-0.991438\pi\) |
0.476527 | − | 0.879160i | \(-0.341895\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −276.701 | + | 556.369i | −0.878416 | + | 1.76625i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −59.7921 | + | 34.5210i | −0.188619 | + | 0.108899i | −0.591336 | − | 0.806425i | \(-0.701399\pi\) |
0.402717 | + | 0.915325i | \(0.368066\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.7269 | − | 20.3115i | 0.0367613 | − | 0.0636725i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −106.708 | − | 25.0701i | −0.332423 | − | 0.0780999i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 65.0601i | 0.201424i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 359.636 | 1.10657 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −92.4239 | + | 393.392i | −0.282642 | + | 1.20303i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 66.7785 | + | 38.5546i | 0.202974 | + | 0.117187i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −254.895 | − | 441.492i | −0.770076 | − | 1.33381i | −0.937521 | − | 0.347930i | \(-0.886885\pi\) |
0.167444 | − | 0.985882i | \(-0.446449\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −148.818 | − | 74.0121i | −0.446901 | − | 0.222259i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 719.466 | − | 415.384i | 2.14766 | − | 1.23995i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 168.720 | − | 292.232i | 0.500653 | − | 0.867156i | −0.499347 | − | 0.866402i | \(-0.666427\pi\) |
1.00000 | 0.000754096i | \(-0.000240036\pi\) | ||||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 390.778 | − | 415.826i | 1.15274 | − | 1.22663i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 12.9856i | − | 0.0380808i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −135.687 | −0.395590 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −513.428 | + | 154.804i | −1.48820 | + | 0.448708i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 186.407 | + | 107.622i | 0.537197 | + | 0.310151i | 0.743942 | − | 0.668244i | \(-0.232954\pi\) |
−0.206745 | + | 0.978395i | \(0.566287\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −181.012 | − | 313.522i | −0.518659 | − | 0.898345i | −0.999765 | − | 0.0216818i | \(-0.993098\pi\) |
0.481105 | − | 0.876663i | \(-0.340235\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −104.311 | − | 281.446i | −0.297183 | − | 0.801842i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −506.486 | + | 292.420i | −1.43481 | + | 0.828385i | −0.997482 | − | 0.0709189i | \(-0.977407\pi\) |
−0.437323 | + | 0.899304i | \(0.644074\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −60.7011 | + | 105.137i | −0.170989 | + | 0.296161i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −63.2853 | − | 209.894i | −0.177270 | − | 0.587937i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 393.693i | 1.09664i | 0.836269 | + | 0.548319i | \(0.184732\pi\) | ||||
−0.836269 | + | 0.548319i | \(0.815268\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −295.117 | −0.817498 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −264.095 | − | 248.187i | −0.727535 | − | 0.683711i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −28.5326 | − | 16.4733i | −0.0781716 | − | 0.0451324i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −190.428 | − | 329.831i | −0.518877 | − | 0.898722i | −0.999759 | − | 0.0219364i | \(-0.993017\pi\) |
0.480882 | − | 0.876785i | \(-0.340316\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 223.851 | + | 337.467i | 0.606641 | + | 0.914546i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 478.337 | − | 276.168i | 1.28932 | − | 0.744388i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −66.4416 | + | 115.080i | −0.178128 | + | 0.308526i | −0.941239 | − | 0.337741i | \(-0.890337\pi\) |
0.763112 | + | 0.646267i | \(0.223671\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −162.571 | − | 38.1945i | −0.433522 | − | 0.101852i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 589.316i | 1.56317i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 507.622 | 1.33937 | 0.669686 | − | 0.742644i | \(-0.266429\pi\) | ||||
0.669686 | + | 0.742644i | \(0.266429\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −126.321 | + | 537.670i | −0.331550 | + | 1.41121i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 287.466 | + | 165.968i | 0.750564 | + | 0.433338i | 0.825898 | − | 0.563820i | \(-0.190669\pi\) |
−0.0753339 | + | 0.997158i | \(0.524002\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15.2731 | + | 26.4539i | 0.0396705 | + | 0.0687113i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.8437 | + | 206.601i | 0.0331879 | + | 0.533853i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 296.662 | − | 171.278i | 0.762626 | − | 0.440302i | −0.0676116 | − | 0.997712i | \(-0.521538\pi\) |
0.830238 | + | 0.557409i | \(0.188205\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 94.5979 | − | 163.848i | 0.241938 | − | 0.419049i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 259.039 | − | 275.643i | 0.659133 | − | 0.701382i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 11.9973i | − | 0.0303730i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.8043 | −0.0624792 | −0.0312396 | − | 0.999512i | \(-0.509945\pi\) | ||||
−0.0312396 | + | 0.999512i | \(0.509945\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −212.549 | + | 64.0859i | −0.532704 | + | 0.160616i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 52.0842 | + | 30.0708i | 0.129886 | + | 0.0749896i | 0.563535 | − | 0.826092i | \(-0.309441\pi\) |
−0.433649 | + | 0.901082i | \(0.642774\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 163.143 | + | 282.571i | 0.404820 | + | 0.701170i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 75.9742 | + | 608.691i | 0.187591 | + | 1.50294i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.07589 | + | 4.08526i | −0.0173855 | + | 0.0100375i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 240.720 | − | 416.939i | 0.588558 | − | 1.01941i | −0.405864 | − | 0.913933i | \(-0.633029\pi\) |
0.994422 | − | 0.105478i | \(-0.0336373\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 107.617 | + | 356.925i | 0.261841 | + | 0.868430i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 694.453i | − | 1.68149i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −64.0516 | −0.154341 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −58.5149 | − | 54.9902i | −0.140324 | − | 0.131871i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −479.531 | − | 276.857i | −1.14447 | − | 0.660758i | −0.196933 | − | 0.980417i | \(-0.563098\pi\) |
−0.947533 | + | 0.319659i | \(0.896432\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 190.947 | + | 330.730i | 0.453556 | + | 0.785581i | 0.998604 | − | 0.0528233i | \(-0.0168220\pi\) |
−0.545048 | + | 0.838405i | \(0.683489\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 75.9742 | − | 4.72306i | 0.179608 | − | 0.0111656i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 224.564 | − | 129.652i | 0.528385 | − | 0.305063i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −24.3900 | + | 42.2447i | −0.0571194 | + | 0.0989337i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −14.3642 | − | 3.37474i | −0.0334829 | − | 0.00786652i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 821.321i | 1.90562i | 0.303570 | + | 0.952809i | \(0.401821\pi\) | ||||
−0.303570 | + | 0.952809i | \(0.598179\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −199.155 | −0.459942 | −0.229971 | − | 0.973198i | \(-0.573863\pi\) | ||||
−0.229971 | + | 0.973198i | \(0.573863\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 275.454 | − | 1172.44i | 0.633227 | − | 2.69526i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −165.921 | − | 95.7946i | −0.379682 | − | 0.219210i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 240.830 | + | 417.130i | 0.548588 | + | 0.950182i | 0.998372 | + | 0.0570445i | \(0.0181677\pi\) |
−0.449784 | + | 0.893137i | \(0.648499\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 255.876 | − | 169.729i | 0.580218 | − | 0.384873i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −467.902 | + | 270.143i | −1.05621 | + | 0.609805i | −0.924382 | − | 0.381468i | \(-0.875419\pi\) |
−0.131830 | + | 0.991272i | \(0.542085\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −242.804 | + | 420.549i | −0.545628 | + | 0.945055i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −165.689 | + | 176.309i | −0.370669 | + | 0.394428i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 300.318i | 0.668859i | 0.942421 | + | 0.334429i | \(0.108544\pi\) | ||||
−0.942421 | + | 0.334429i | \(0.891456\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.9074 | 0.0441407 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 287.080 | − | 86.5579i | 0.633731 | − | 0.191077i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −664.700 | − | 383.764i | −1.46088 | − | 0.843438i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −77.8505 | − | 134.841i | −0.170351 | − | 0.295057i | 0.768191 | − | 0.640220i | \(-0.221157\pi\) |
−0.938543 | + | 0.345163i | \(0.887824\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −166.598 | − | 138.136i | −0.362958 | − | 0.300949i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 261.143 | − | 150.771i | 0.566470 | − | 0.327052i | −0.189268 | − | 0.981925i | \(-0.560612\pi\) |
0.755738 | + | 0.654874i | \(0.227278\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −119.390 | + | 206.790i | −0.257862 | + | 0.446630i | −0.965669 | − | 0.259776i | \(-0.916351\pi\) |
0.707807 | + | 0.706406i | \(0.249685\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −192.493 | − | 638.428i | −0.413964 | − | 1.37296i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 423.152i | − | 0.906107i | −0.891483 | − | 0.453054i | \(-0.850335\pi\) | ||
0.891483 | − | 0.453054i | \(-0.149665\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1000.13 | −2.13247 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 151.836 | + | 142.690i | 0.322369 | + | 0.302950i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.81259 | + | 5.08795i | 0.0186313 | + | 0.0107568i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −131.292 | − | 227.405i | −0.276404 | − | 0.478747i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 242.804 | − | 488.212i | 0.509024 | − | 1.02351i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −379.284 | + | 218.980i | −0.791824 | + | 0.457160i | −0.840604 | − | 0.541650i | \(-0.817800\pi\) |
0.0487802 | + | 0.998810i | \(0.484467\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 102.649 | − | 177.794i | 0.213408 | − | 0.369634i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 628.467 | + | 147.653i | 1.30117 | + | 0.305699i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 872.666i | − | 1.79931i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 401.945 | 0.825350 | 0.412675 | − | 0.910878i | \(-0.364595\pi\) | ||||
0.412675 | + | 0.910878i | \(0.364595\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −111.475 | + | 474.483i | −0.227966 | + | 0.970313i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −241.084 | − | 139.190i | −0.491007 | − | 0.283483i | 0.233985 | − | 0.972240i | \(-0.424823\pi\) |
−0.724992 | + | 0.688757i | \(0.758157\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 212.454 | + | 367.981i | 0.430941 | + | 0.746411i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 27.0000 | + | 13.4280i | 0.0545455 | + | 0.0271273i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 126.571 | − | 73.0756i | 0.254669 | − | 0.147033i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −272.655 | + | 472.252i | −0.546402 | + | 0.946397i | 0.452115 | + | 0.891960i | \(0.350670\pi\) |
−0.998517 | + | 0.0544369i | \(0.982664\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −198.624 | + | 211.355i | −0.396454 | + | 0.421866i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 306.460i | − | 0.609264i | −0.952470 | − | 0.304632i | \(-0.901466\pi\) | ||
0.952470 | − | 0.304632i | \(-0.0985335\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1001.76 | 1.98369 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −130.447 | + | 39.3312i | −0.257292 | + | 0.0775764i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 480.208 | + | 277.248i | 0.943434 | + | 0.544692i | 0.891035 | − | 0.453934i | \(-0.149980\pi\) |
0.0523989 | + | 0.998626i | \(0.483313\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.8316 | + | 34.3493i | 0.0388093 | + | 0.0672197i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −139.883 | + | 168.705i | −0.272677 | + | 0.328860i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −822.102 | + | 474.641i | −1.59631 | + | 0.921632i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.87101 | − | 3.24069i | 0.00361898 | − | 0.00626825i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −24.2731 | − | 80.5049i | −0.0467691 | − | 0.155115i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 154.167i | 0.295905i | 0.988994 | + | 0.147953i | \(0.0472683\pi\) | ||||
−0.988994 | + | 0.147953i | \(0.952732\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 480.598 | 0.918925 | 0.459463 | − | 0.888197i | \(-0.348042\pi\) | ||||
0.459463 | + | 0.888197i | \(0.348042\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 644.769 | + | 605.930i | 1.22813 | + | 1.15415i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 203.739 | + | 117.629i | 0.386602 | + | 0.223204i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.0721 | + | 24.3735i | 0.0266013 | + | 0.0460748i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −378.954 | − | 571.294i | −0.713660 | − | 1.07588i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −433.194 | + | 250.105i | −0.812747 | + | 0.469240i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −138.351 | + | 239.630i | −0.258599 | + | 0.447907i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 103.973 | + | 24.4274i | 0.193618 | + | 0.0454887i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 15.0943i | − | 0.0280043i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −300.543 | −0.555533 | −0.277766 | − | 0.960649i | \(-0.589594\pi\) | ||||
−0.277766 | + | 0.960649i | \(0.589594\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.4729 | − | 57.3460i | 0.0248120 | − | 0.105610i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 883.426 | + | 510.046i | 1.62097 | + | 0.935865i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 50.6032 | + | 87.6473i | 0.0925104 | + | 0.160233i | 0.908567 | − | 0.417739i | \(-0.137178\pi\) |
−0.816056 | + | 0.577972i | \(0.803844\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.98785 | + | 48.0620i | 0.00544236 | + | 0.0875446i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 372.636 | − | 215.141i | 0.676290 | − | 0.390456i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.22154 | + | 12.5081i | −0.0130588 | + | 0.0226186i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −287.323 | + | 305.740i | −0.517700 | + | 0.550883i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 433.041i | − | 0.777452i | −0.921353 | − | 0.388726i | \(-0.872915\pi\) | ||
0.921353 | − | 0.388726i | \(-0.127085\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −255.687 | −0.457401 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.1859 | + | 3.07117i | −0.0181567 | + | 0.00547445i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 902.201 | + | 520.886i | 1.60249 | + | 0.925197i | 0.990988 | + | 0.133954i | \(0.0427673\pi\) |
0.611501 | + | 0.791244i | \(0.290566\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −720.232 | − | 1247.48i | −1.27475 | − | 2.20793i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 287.181 | − | 680.336i | 0.506491 | − | 1.19989i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 257.445 | − | 148.636i | 0.452452 | − | 0.261223i | −0.256413 | − | 0.966567i | \(-0.582541\pi\) |
0.708865 | + | 0.705344i | \(0.249207\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 339.524 | − | 588.073i | 0.594613 | − | 1.02990i | −0.398988 | − | 0.916956i | \(-0.630638\pi\) |
0.993601 | − | 0.112945i | \(-0.0360282\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 188.662 | + | 625.720i | 0.329252 | + | 1.09201i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 763.599i | 1.32800i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −148.351 | −0.257107 | −0.128553 | − | 0.991703i | \(-0.541033\pi\) | ||||
−0.128553 | + | 0.991703i | \(0.541033\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 107.121 | + | 100.668i | 0.185010 | + | 0.173866i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 66.7785 | + | 38.5546i | 0.114937 | + | 0.0663590i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.4021 | − | 23.2132i | −0.0229882 | − | 0.0398168i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −756.232 | + | 47.0124i | −1.29270 | + | 0.0803631i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 456.497 | − | 263.559i | 0.777678 | − | 0.448993i | −0.0579287 | − | 0.998321i | \(-0.518450\pi\) |
0.835607 | + | 0.549328i | \(0.185116\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 119.117 | − | 206.316i | 0.202236 | − | 0.350283i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1051.27 | − | 246.987i | −1.77880 | − | 0.417913i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 473.848i | − | 0.799069i | −0.916718 | − | 0.399534i | \(-0.869172\pi\) | ||
0.916718 | − | 0.399534i | \(-0.130828\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −553.402 | −0.930088 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 41.8993 | − | 178.340i | 0.0701832 | − | 0.298727i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −601.414 | − | 347.227i | −1.00403 | − | 0.579677i | −0.0945922 | − | 0.995516i | \(-0.530155\pi\) |
−0.909438 | + | 0.415839i | \(0.863488\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −93.3559 | − | 161.697i | −0.155334 | − | 0.269047i | 0.777846 | − | 0.628454i | \(-0.216312\pi\) |
−0.933181 | + | 0.359408i | \(0.882979\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −822.758 | + | 545.756i | −1.36444 | + | 0.905068i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −792.285 | + | 457.426i | −1.30956 | + | 0.756076i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 411.194 | − | 712.209i | 0.677420 | − | 1.17333i | −0.298335 | − | 0.954461i | \(-0.596431\pi\) |
0.975755 | − | 0.218865i | \(-0.0702355\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −992.906 | + | 1056.55i | −1.63039 | + | 1.73489i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 94.0249i | 0.153887i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −482.206 | −0.786634 | −0.393317 | − | 0.919403i | \(-0.628672\pi\) | ||||
−0.393317 | + | 0.919403i | \(0.628672\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 978.737 | − | 295.100i | 1.59144 | − | 0.479838i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −595.916 | − | 344.052i | −0.965828 | − | 0.557621i | −0.0678661 | − | 0.997694i | \(-0.521619\pi\) |
−0.897962 | + | 0.440073i | \(0.854952\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 380.253 | + | 658.617i | 0.614302 | + | 1.06400i | 0.990507 | + | 0.137465i | \(0.0438955\pi\) |
−0.376205 | + | 0.926536i | \(0.622771\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 597.583 | − | 221.479i | 0.962291 | − | 0.356649i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 506.282 | − | 292.302i | 0.812652 | − | 0.469185i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 193.603 | − | 335.331i | 0.309765 | − | 0.536529i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.11002 | + | 10.3148i | 0.00496016 | + | 0.0164510i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 148.024i | − | 0.235333i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1008.08 | 1.59758 | 0.798792 | − | 0.601607i | \(-0.205473\pi\) | ||||
0.798792 | + | 0.601607i | \(0.205473\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −846.007 | − | 795.046i | −1.33650 | − | 1.25600i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1207.43 | + | 697.108i | 1.90146 | + | 1.09781i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 189.636 | + | 328.459i | 0.297701 | + | 0.515634i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 64.2473 | − | 129.184i | 0.100544 | − | 0.202165i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −488.095 | + | 281.802i | −0.761458 | + | 0.439628i | −0.829819 | − | 0.558032i | \(-0.811556\pi\) |
0.0683607 | + | 0.997661i | \(0.478223\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 288.500 | − | 499.697i | 0.448678 | − | 0.777133i | −0.549622 | − | 0.835413i | \(-0.685228\pi\) |
0.998300 | + | 0.0582801i | \(0.0185617\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 508.687 | + | 119.512i | 0.788663 | + | 0.185289i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 1024.52i | − | 1.58349i | −0.610853 | − | 0.791744i | \(-0.709173\pi\) | ||
0.610853 | − | 0.791744i | \(-0.290827\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −33.7011 | −0.0519277 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −183.600 | + | 781.475i | −0.282028 | + | 1.20042i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 345.885 | + | 199.697i | 0.529686 | + | 0.305814i | 0.740888 | − | 0.671628i | \(-0.234405\pi\) |
−0.211203 | + | 0.977442i | \(0.567738\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −477.428 | − | 826.929i | −0.728898 | − | 1.26249i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 35.0584 | + | 17.4357i | 0.0533614 | + | 0.0265384i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −646.308 | + | 373.146i | −0.980741 | + | 0.566231i | −0.902494 | − | 0.430703i | \(-0.858266\pi\) |
−0.0782470 | + | 0.996934i | \(0.524932\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −475.624 | + | 823.804i | −0.719552 | + | 1.24630i | 0.241626 | + | 0.970369i | \(0.422319\pi\) |
−0.961178 | + | 0.275931i | \(0.911014\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 183.065 | − | 194.799i | 0.276117 | − | 0.293815i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 560.403i | 0.842711i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1251.27 | −1.87596 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 295.135 | − | 88.9864i | 0.441158 | − | 0.133014i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.05009 | + | 1.18362i | 0.00305527 | + | 0.00176396i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 172.115 | + | 298.113i | 0.255743 | + | 0.442961i | 0.965097 | − | 0.261892i | \(-0.0843464\pi\) |
−0.709354 | + | 0.704853i | \(0.751013\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 861.069 | + | 146.629i | 1.27566 | + | 0.217228i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 853.610 | − | 492.832i | 1.26087 | − | 0.727965i | 0.287628 | − | 0.957742i | \(-0.407133\pi\) |
0.973243 | + | 0.229778i | \(0.0737999\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −525.284 | + | 909.818i | −0.773614 | + | 1.33994i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −293.552 | − | 973.600i | −0.431060 | − | 1.42966i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 166.658i | 0.244009i | 0.992530 | + | 0.122004i | \(0.0389322\pi\) | ||||
−0.992530 | + | 0.122004i | \(0.961068\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 941.062 | 1.37381 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 648.743 | + | 609.665i | 0.944313 | + | 0.887431i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 583.272 | + | 336.752i | 0.846548 | + | 0.488755i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 449.077 | + | 777.825i | 0.649895 | + | 1.12565i | 0.983148 | + | 0.182813i | \(0.0585204\pi\) |
−0.333253 | + | 0.942838i | \(0.608146\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −20.0668 | − | 30.2518i | −0.0289564 | − | 0.0436534i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −175.545 | + | 101.351i | −0.252582 | + | 0.145829i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −180.330 | + | 312.341i | −0.258723 | + | 0.448122i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1012.06 | + | 237.773i | 1.44786 | + | 0.340162i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 730.549i | 1.04215i | 0.853510 | + | 0.521076i | \(0.174469\pi\) | ||||
−0.853510 | + | 0.521076i | \(0.825531\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −149.897 | −0.213224 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 43.9484 | − | 187.061i | 0.0623382 | − | 0.265335i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1044.41 | − | 602.991i | −1.47724 | − | 0.852887i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 114.961 | + | 199.118i | 0.162145 | + | 0.280843i | 0.935638 | − | 0.352962i | \(-0.114826\pi\) |
−0.773493 | + | 0.633805i | \(0.781492\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.884663 | + | 14.2305i | 0.00124425 | + | 0.0200148i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −599.971 | + | 346.394i | −0.841474 | + | 0.485825i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.6237 | + | 32.2571i | −0.0260471 | + | 0.0451149i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 332.181 | − | 353.472i | 0.463292 | − | 0.492988i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 907.095i | − | 1.26161i | −0.775943 | − | 0.630803i | \(-0.782725\pi\) | ||
0.775943 | − | 0.630803i | \(-0.217275\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1142.80 | 1.58502 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −932.742 | + | 281.232i | −1.29010 | + | 0.388980i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1485.18 | − | 857.469i | −2.04852 | − | 1.18272i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −107.871 | − | 186.838i | −0.148378 | − | 0.256999i | 0.782250 | − | 0.622965i | \(-0.214072\pi\) |
−0.930628 | + | 0.365966i | \(0.880739\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −135.000 | − | 716.391i | −0.185185 | − | 0.982704i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −159.656 | + | 92.1776i | −0.218408 | + | 0.126098i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −314.634 | + | 544.963i | −0.429242 | + | 0.743469i | −0.996806 | − | 0.0798604i | \(-0.974553\pi\) |
0.567564 | + | 0.823329i | \(0.307886\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −223.753 | − | 742.104i | −0.304425 | − | 1.00966i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 48.5351i | 0.0658549i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 547.649 | 0.741068 | 0.370534 | − | 0.928819i | \(-0.379175\pi\) | ||||
0.370534 | + | 0.928819i | \(0.379175\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −197.264 | − | 185.381i | −0.266213 | − | 0.250177i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −462.583 | − | 267.072i | −0.622588 | − | 0.359451i | 0.155288 | − | 0.987869i | \(-0.450369\pi\) |
−0.777876 | + | 0.628418i | \(0.783703\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 305.376 | + | 528.927i | 0.409901 | + | 0.709970i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 75.9742 | − | 4.72306i | 0.101706 | − | 0.00632271i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 288.481 | − | 166.555i | 0.385155 | − | 0.222369i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 225.545 | − | 390.655i | 0.300326 | − | 0.520180i | −0.675884 | − | 0.737008i | \(-0.736238\pi\) |
0.976210 | + | 0.216828i | \(0.0695712\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1121.50 | + | 263.486i | 1.48937 | + | 0.349915i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 756.911i | − | 1.00253i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −352.391 | −0.465511 | −0.232755 | − | 0.972535i | \(-0.574774\pi\) | ||||
−0.232755 | + | 0.972535i | \(0.574774\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.16543 | − | 30.4988i | 0.00944061 | − | 0.0401829i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −929.923 | − | 536.891i | −1.22197 | − | 0.705507i | −0.256636 | − | 0.966508i | \(-0.582614\pi\) |
−0.965339 | + | 0.261001i | \(0.915947\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −614.024 | − | 1063.52i | −0.804750 | − | 1.39387i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −455.258 | + | 301.984i | −0.595108 | + | 0.394750i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 733.349 | − | 423.399i | 0.956126 | − | 0.552020i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −177.988 | + | 308.284i | −0.231454 | + | 0.400889i | −0.958236 | − | 0.285978i | \(-0.907681\pi\) |
0.726782 | + | 0.686868i | \(0.241015\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26.5721 | − | 28.2753i | 0.0344644 | − | 0.0366735i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 370.790i | 0.479677i | 0.970813 | + | 0.239838i | \(0.0770945\pi\) | ||||
−0.970813 | + | 0.239838i | \(0.922906\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −949.505 | −1.22517 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 483.589 | − | 145.808i | 0.622380 | − | 0.187655i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 316.292 | + | 182.611i | 0.406023 | + | 0.234418i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.54628 | − | 6.14233i | −0.00454069 | − | 0.00786470i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −240.273 | + | 1410.99i | −0.306862 | + | 1.80203i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 455.507 | − | 262.987i | 0.580263 | − | 0.335015i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −576.531 | + | 998.581i | −0.732568 | + | 1.26885i | 0.223214 | + | 0.974769i | \(0.428345\pi\) |
−0.955782 | + | 0.294076i | \(0.904988\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −42.8437 | − | 142.096i | −0.0543013 | − | 0.180097i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1734.12i | 2.19231i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −59.4810 | −0.0750076 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1003.01 | − | 942.593i | −1.26165 | − | 1.18565i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −761.882 | − | 439.873i | −0.955937 | − | 0.551910i | −0.0610167 | − | 0.998137i | \(-0.519434\pi\) |
−0.894920 | + | 0.446226i | \(0.852768\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 33.8968 | + | 58.7110i | 0.0424240 | + | 0.0734806i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 256.989 | − | 516.735i | 0.320836 | − | 0.645112i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.66693 | − | 0.962404i | 0.00207588 | − | 0.00119851i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 814.830 | − | 1411.33i | 1.01221 | − | 1.75320i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −62.6252 | − | 14.7132i | −0.0776025 | − | 0.0182320i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 884.508i | 1.09334i | 0.837350 | + | 0.546668i | \(0.184104\pi\) | ||||
−0.837350 | + | 0.546668i | \(0.815896\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −961.464 | −1.18553 | −0.592765 | − | 0.805376i | \(-0.701964\pi\) | ||||
−0.592765 | + | 0.805376i | \(0.701964\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 224.304 | − | 954.727i | 0.275897 | − | 1.17433i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1065.53 | + | 615.184i | 1.30740 | + | 0.754827i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 93.3437 | + | 161.676i | 0.114252 | + | 0.197890i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 816.725 | + | 406.185i | 0.997223 | + | 0.495952i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 778.064 | − | 449.215i | 0.947702 | − | 0.547156i | 0.0553360 | − | 0.998468i | \(-0.482377\pi\) |
0.892366 | + | 0.451312i | \(0.149044\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −108.091 | + | 187.219i | −0.131338 | + | 0.227484i | −0.924193 | − | 0.381927i | \(-0.875261\pi\) |
0.792855 | + | 0.609411i | \(0.208594\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 29.4051 | − | 31.2899i | 0.0356426 | − | 0.0379272i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 113.883i | 0.137706i | 0.997627 | + | 0.0688528i | \(0.0219339\pi\) | ||||
−0.997627 | + | 0.0688528i | \(0.978066\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 101.326 | 0.122227 | 0.0611135 | − | 0.998131i | \(-0.480535\pi\) | ||||
0.0611135 | + | 0.998131i | \(0.480535\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1371.38 | + | 413.487i | −1.65028 | + | 0.497578i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 236.825 | + | 136.731i | 0.284303 | + | 0.164143i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 366.077 | + | 634.065i | 0.438416 | + | 0.759359i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 275.401 | + | 743.071i | 0.329033 | + | 0.887779i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 60.4689 | − | 34.9117i | 0.0720726 | − | 0.0416111i | −0.463531 | − | 0.886081i | \(-0.653418\pi\) |
0.535603 | + | 0.844470i | \(0.320084\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 984.588 | − | 1705.36i | 1.17073 | − | 2.02777i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −103.064 | − | 341.824i | −0.122258 | − | 0.405485i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 343.934i | 0.407023i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1101.35 | 1.30030 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 855.547 | + | 804.012i | 1.00771 | + | 0.947011i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 377.502 | + | 217.951i | 0.443598 | + | 0.256112i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 573.325 | + | 993.028i | 0.672127 | + | 1.16416i | 0.977300 | + | 0.211862i | \(0.0679527\pi\) |
−0.305172 | + | 0.952297i | \(0.598714\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 305.804 | + | 461.017i | 0.357666 | + | 0.539201i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 217.871 | − | 125.788i | 0.254225 | − | 0.146777i | −0.367472 | − | 0.930035i | \(-0.619777\pi\) |
0.621697 | + | 0.783258i | \(0.286443\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 244.266 | − | 423.082i | 0.284361 | − | 0.492528i | −0.688093 | − | 0.725623i | \(-0.741552\pi\) |
0.972454 | + | 0.233095i | \(0.0748852\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1198.03 | − | 281.467i | −1.39145 | − | 0.326908i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 596.889i | − | 0.691644i | −0.938300 | − | 0.345822i | \(-0.887600\pi\) | ||
0.938300 | − | 0.345822i | \(-0.112400\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −212.258 | −0.245385 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −154.212 | + | 656.386i | −0.177868 | + | 0.757077i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.607003 | + | 0.350454i | 0.000698508 | + | 0.000403284i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −609.765 | − | 1056.14i | −0.700074 | − | 1.21256i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 64.3490 | + | 1035.10i | 0.0737102 | + | 1.18569i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 439.504 | − | 253.748i | 0.502290 | − | 0.289997i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −358.208 | + | 620.434i | −0.408447 | + | 0.707451i | −0.994716 | − | 0.102666i | \(-0.967263\pi\) |
0.586269 | + | 0.810116i | \(0.300596\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −147.297 | + | 156.739i | −0.167574 | + | 0.178315i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1200.86i | 1.36306i | 0.731790 | + | 0.681531i | \(0.238685\pi\) | ||||
−0.731790 | + | 0.681531i | \(0.761315\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.8938 | 0.0259273 | 0.0129636 | − | 0.999916i | \(-0.495873\pi\) | ||||
0.0129636 | + | 0.999916i | \(0.495873\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1656.89 | + | 499.572i | −1.87219 | + | 0.564488i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 521.857 | + | 301.294i | 0.588340 | + | 0.339678i | 0.764441 | − | 0.644694i | \(-0.223015\pi\) |
−0.176101 | + | 0.984372i | \(0.556349\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −839.220 | − | 1453.57i | −0.944005 | − | 1.63506i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −33.0160 | − | 13.9366i | −0.0370549 | − | 0.0156415i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 59.4537 | − | 34.3256i | 0.0665775 | − | 0.0384385i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 134.804 | − | 233.488i | 0.150619 | − | 0.260880i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 227.246 | + | 753.689i | 0.253340 | + | 0.840233i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 1555.90i | − | 1.73071i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 485.609 | 0.538966 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −458.406 | − | 430.794i | −0.507648 | − | 0.477069i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −128.780 | − | 74.3511i | −0.142298 | − | 0.0821560i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −211.473 | − | 366.281i | −0.233156 | − | 0.403838i | 0.725579 | − | 0.688139i | \(-0.241572\pi\) |
−0.958735 | + | 0.284300i | \(0.908239\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1188.23 | + | 73.8684i | −1.30719 | + | 0.0812634i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 125.376 | − | 72.3861i | 0.137625 | − | 0.0794578i | −0.429607 | − | 0.903016i | \(-0.641348\pi\) |
0.567232 | + | 0.823558i | \(0.308014\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.87101 | − | 3.24069i | 0.00204930 | − | 0.00354949i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 118.337 | + | 27.8022i | 0.129330 | + | 0.0303849i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1149.51i | 1.25356i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −869.093 | −0.945694 | −0.472847 | − | 0.881145i | \(-0.656774\pi\) | ||||
−0.472847 | + | 0.881145i | \(0.656774\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 118.257 | − | 503.347i | 0.128400 | − | 0.546522i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 154.337 | + | 89.1064i | 0.167212 | + | 0.0965400i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 298.715 | + | 517.389i | 0.322935 | + | 0.559340i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 940.129 | − | 623.611i | 1.01416 | − | 0.672720i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 82.2838 | − | 47.5066i | 0.0885724 | − | 0.0511373i | −0.455060 | − | 0.890461i | \(-0.650382\pi\) |
0.543632 | + | 0.839324i | \(0.317049\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 138.461 | − | 239.821i | 0.148722 | − | 0.257595i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1243.66 | − | 1323.37i | 1.33297 | − | 1.41841i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 26.8560i | 0.0287230i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1555.55 | −1.66014 | −0.830071 | − | 0.557657i | \(-0.811700\pi\) | ||||
−0.830071 | + | 0.557657i | \(0.811700\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 940.578 | − | 283.595i | 1.00168 | − | 0.302018i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 335.246 | + | 193.554i | 0.356265 | + | 0.205690i | 0.667441 | − | 0.744662i | \(-0.267389\pi\) |
−0.311176 | + | 0.950352i | \(0.600723\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −531.036 | − | 919.782i | −0.563135 | − | 0.975379i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1435.01 | − | 1189.85i | −1.51853 | − | 1.25910i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −839.861 | + | 484.894i | −0.886865 | + | 0.512032i | −0.872916 | − | 0.487871i | \(-0.837774\pi\) |
−0.0139492 | + | 0.999903i | \(0.504440\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −24.1821 | + | 41.8846i | −0.0254817 | + | 0.0441355i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −59.7921 | − | 198.308i | −0.0628729 | − | 0.208526i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1294.65i | − | 1.35850i | −0.733909 | − | 0.679248i | \(-0.762306\pi\) | ||
0.733909 | − | 0.679248i | \(-0.237694\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1649.76 | 1.72750 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 51.2731 | + | 48.1846i | 0.0535769 | + | 0.0503497i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −981.126 | − | 566.453i | −1.02307 | − | 0.590671i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 49.7731 | + | 86.2096i | 0.0517931 | + | 0.0897082i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 146.433 | − | 294.437i | 0.152059 | − | 0.305750i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 321.363 | − | 185.539i | 0.333018 | − | 0.192268i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −412.036 | + | 713.668i | −0.426098 | + | 0.738023i | −0.996522 | − | 0.0833272i | \(-0.973445\pi\) |
0.570425 | + | 0.821350i | \(0.306779\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −190.007 | − | 44.6404i | −0.196085 | − | 0.0460685i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1518.35i | 1.56370i | 0.623469 | + | 0.781848i | \(0.285723\pi\) | ||||
−0.623469 | + | 0.781848i | \(0.714277\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 244.024 | 0.250796 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −246.761 | + | 1050.31i | −0.253088 | + | 1.07724i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −321.497 | − | 185.616i | −0.329065 | − | 0.189986i | 0.326361 | − | 0.945245i | \(-0.394178\pi\) |
−0.655426 | + | 0.755259i | \(0.727511\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.1851 | − | 24.5693i | −0.0144894 | − | 0.0250963i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1085.48 | − | 539.844i | −1.10650 | − | 0.550300i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −808.039 | + | 466.522i | −0.822014 | + | 0.474590i | −0.851110 | − | 0.524987i | \(-0.824070\pi\) |
0.0290967 | + | 0.999577i | \(0.490737\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1363.01 | + | 2360.80i | −1.38377 | + | 2.39676i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −158.417 | + | 168.571i | −0.160504 | + | 0.170792i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 542.890i | − | 0.548928i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1615.53 | 1.63020 | 0.815099 | − | 0.579321i | \(-0.196682\pi\) | ||||
0.815099 | + | 0.579321i | \(0.196682\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1464.26 | − | 441.492i | 1.47458 | − | 0.444604i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −400.492 | − | 231.224i | −0.402504 | − | 0.232386i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −519.376 | − | 899.586i | −0.520939 | − | 0.902293i | −0.999704 | − | 0.0243496i | \(-0.992249\pi\) |
0.478764 | − | 0.877943i | \(-0.341085\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 318.261 | − | 383.837i | 0.318580 | − | 0.384221i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))