Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(449,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.7 | ||
Character | \(\chi\) | \(=\) | 1050.449 |
Dual form | 1050.3.c.b.449.8 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | −0.236961 | − | 2.99063i | −0.0789868 | − | 0.996876i | ||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.335113 | + | 4.22939i | 0.0558521 | + | 0.704898i | ||||
\(7\) | − | 2.64575i | − | 0.377964i | ||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | −8.88770 | + | 1.41732i | −0.987522 | + | 0.157480i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 9.89436i | 0.899488i | 0.893158 | + | 0.449744i | \(0.148485\pi\) | ||||
−0.893158 | + | 0.449744i | \(0.851515\pi\) | |||||||
\(12\) | −0.473921 | − | 5.98125i | −0.0394934 | − | 0.498438i | ||||
\(13\) | − | 6.33097i | − | 0.486998i | −0.969901 | − | 0.243499i | \(-0.921705\pi\) | ||
0.969901 | − | 0.243499i | \(-0.0782952\pi\) | |||||||
\(14\) | 3.74166i | 0.267261i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | −5.17268 | −0.304275 | −0.152138 | − | 0.988359i | \(-0.548616\pi\) | ||||
−0.152138 | + | 0.988359i | \(0.548616\pi\) | |||||||
\(18\) | 12.5691 | − | 2.00439i | 0.698284 | − | 0.111355i | ||||
\(19\) | −10.2878 | −0.541464 | −0.270732 | − | 0.962655i | \(-0.587266\pi\) | ||||
−0.270732 | + | 0.962655i | \(0.587266\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.91246 | + | 0.626939i | −0.376784 | + | 0.0298542i | ||||
\(22\) | − | 13.9927i | − | 0.636034i | ||||||
\(23\) | 15.2580 | 0.663390 | 0.331695 | − | 0.943387i | \(-0.392380\pi\) | ||||
0.331695 | + | 0.943387i | \(0.392380\pi\) | |||||||
\(24\) | 0.670226 | + | 8.45877i | 0.0279261 | + | 0.352449i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 8.95334i | 0.344359i | ||||||||
\(27\) | 6.34471 | + | 26.2439i | 0.234989 | + | 0.971998i | ||||
\(28\) | − | 5.29150i | − | 0.188982i | ||||||
\(29\) | 15.1060i | 0.520898i | 0.965488 | + | 0.260449i | \(0.0838706\pi\) | ||||
−0.965488 | + | 0.260449i | \(0.916129\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −13.0380 | −0.420581 | −0.210290 | − | 0.977639i | \(-0.567441\pi\) | ||||
−0.210290 | + | 0.977639i | \(0.567441\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | 29.5904 | − | 2.34457i | 0.896677 | − | 0.0710477i | ||||
\(34\) | 7.31527 | 0.215155 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −17.7754 | + | 2.83464i | −0.493761 | + | 0.0787401i | ||||
\(37\) | 35.8403i | 0.968657i | 0.874886 | + | 0.484328i | \(0.160936\pi\) | ||||
−0.874886 | + | 0.484328i | \(0.839064\pi\) | |||||||
\(38\) | 14.5492 | 0.382873 | ||||||||
\(39\) | −18.9336 | + | 1.50019i | −0.485476 | + | 0.0384664i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 63.0675i | 1.53823i | 0.639109 | + | 0.769116i | \(0.279303\pi\) | ||||
−0.639109 | + | 0.769116i | \(0.720697\pi\) | |||||||
\(42\) | 11.1899 | − | 0.886625i | 0.266426 | − | 0.0211101i | ||||
\(43\) | − | 19.0241i | − | 0.442422i | −0.975226 | − | 0.221211i | \(-0.928999\pi\) | ||
0.975226 | − | 0.221211i | \(-0.0710009\pi\) | |||||||
\(44\) | 19.7887i | 0.449744i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −21.5780 | −0.469087 | ||||||||
\(47\) | −10.0367 | −0.213547 | −0.106774 | − | 0.994283i | \(-0.534052\pi\) | ||||
−0.106774 | + | 0.994283i | \(0.534052\pi\) | |||||||
\(48\) | −0.947842 | − | 11.9625i | −0.0197467 | − | 0.249219i | ||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.22572 | + | 15.4696i | 0.0240337 | + | 0.303325i | ||||
\(52\) | − | 12.6619i | − | 0.243499i | ||||||
\(53\) | 72.2509 | 1.36323 | 0.681613 | − | 0.731713i | \(-0.261279\pi\) | ||||
0.681613 | + | 0.731713i | \(0.261279\pi\) | |||||||
\(54\) | −8.97278 | − | 37.1145i | −0.166163 | − | 0.687306i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 7.48331i | 0.133631i | ||||||||
\(57\) | 2.43781 | + | 30.7670i | 0.0427686 | + | 0.539773i | ||||
\(58\) | − | 21.3632i | − | 0.368331i | ||||||
\(59\) | 0.266801i | 0.00452205i | 0.999997 | + | 0.00226102i | \(0.000719707\pi\) | ||||
−0.999997 | + | 0.00226102i | \(0.999280\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −17.6626 | −0.289551 | −0.144775 | − | 0.989465i | \(-0.546246\pi\) | ||||
−0.144775 | + | 0.989465i | \(0.546246\pi\) | |||||||
\(62\) | 18.4385 | 0.297395 | ||||||||
\(63\) | 3.74988 | + | 23.5146i | 0.0595219 | + | 0.373248i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −41.8471 | + | 3.31573i | −0.634047 | + | 0.0502383i | ||||
\(67\) | − | 5.55641i | − | 0.0829315i | −0.999140 | − | 0.0414657i | \(-0.986797\pi\) | ||
0.999140 | − | 0.0414657i | \(-0.0132027\pi\) | |||||||
\(68\) | −10.3454 | −0.152138 | ||||||||
\(69\) | −3.61554 | − | 45.6309i | −0.0523991 | − | 0.661317i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 139.562i | 1.96566i | 0.184505 | + | 0.982832i | \(0.440932\pi\) | ||||
−0.184505 | + | 0.982832i | \(0.559068\pi\) | |||||||
\(72\) | 25.1382 | − | 4.00879i | 0.349142 | − | 0.0556776i | ||||
\(73\) | − | 32.7875i | − | 0.449144i | −0.974458 | − | 0.224572i | \(-0.927902\pi\) | ||
0.974458 | − | 0.224572i | \(-0.0720984\pi\) | |||||||
\(74\) | − | 50.6858i | − | 0.684944i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −20.5757 | −0.270732 | ||||||||
\(77\) | 26.1780 | 0.339974 | ||||||||
\(78\) | 26.7761 | − | 2.12159i | 0.343283 | − | 0.0271999i | ||||
\(79\) | −2.91874 | −0.0369461 | −0.0184730 | − | 0.999829i | \(-0.505880\pi\) | ||||
−0.0184730 | + | 0.999829i | \(0.505880\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 76.9824 | − | 25.1934i | 0.950400 | − | 0.311030i | ||||
\(82\) | − | 89.1909i | − | 1.08769i | ||||||
\(83\) | −88.5027 | −1.06630 | −0.533149 | − | 0.846021i | \(-0.678991\pi\) | ||||
−0.533149 | + | 0.846021i | \(0.678991\pi\) | |||||||
\(84\) | −15.8249 | + | 1.25388i | −0.188392 | + | 0.0149271i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 26.9042i | 0.312839i | ||||||||
\(87\) | 45.1766 | − | 3.57954i | 0.519271 | − | 0.0411441i | ||||
\(88\) | − | 27.9855i | − | 0.318017i | ||||||
\(89\) | − | 146.550i | − | 1.64663i | −0.567588 | − | 0.823313i | \(-0.692123\pi\) | ||
0.567588 | − | 0.823313i | \(-0.307877\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −16.7502 | −0.184068 | ||||||||
\(92\) | 30.5159 | 0.331695 | ||||||||
\(93\) | 3.08949 | + | 38.9918i | 0.0332203 | + | 0.419267i | ||||
\(94\) | 14.1941 | 0.151001 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.34045 | + | 16.9175i | 0.0139630 | + | 0.176224i | ||||
\(97\) | 167.535i | 1.72716i | 0.504210 | + | 0.863581i | \(0.331784\pi\) | ||||
−0.504210 | + | 0.863581i | \(0.668216\pi\) | |||||||
\(98\) | 9.89949 | 0.101015 | ||||||||
\(99\) | −14.0235 | − | 87.9381i | −0.141651 | − | 0.888264i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 77.9574i | 0.771856i | 0.922529 | + | 0.385928i | \(0.126119\pi\) | ||||
−0.922529 | + | 0.385928i | \(0.873881\pi\) | |||||||
\(102\) | −1.73343 | − | 21.8773i | −0.0169944 | − | 0.214483i | ||||
\(103\) | − | 17.0241i | − | 0.165283i | −0.996579 | − | 0.0826415i | \(-0.973664\pi\) | ||
0.996579 | − | 0.0826415i | \(-0.0263356\pi\) | |||||||
\(104\) | 17.9067i | 0.172180i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −102.178 | −0.963946 | ||||||||
\(107\) | 189.549 | 1.77149 | 0.885745 | − | 0.464173i | \(-0.153648\pi\) | ||||
0.885745 | + | 0.464173i | \(0.153648\pi\) | |||||||
\(108\) | 12.6894 | + | 52.4879i | 0.117495 | + | 0.485999i | ||||
\(109\) | 77.0791 | 0.707148 | 0.353574 | − | 0.935407i | \(-0.384966\pi\) | ||||
0.353574 | + | 0.935407i | \(0.384966\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 107.185 | − | 8.49274i | 0.965631 | − | 0.0765112i | ||||
\(112\) | − | 10.5830i | − | 0.0944911i | ||||||
\(113\) | −22.2664 | −0.197048 | −0.0985239 | − | 0.995135i | \(-0.531412\pi\) | ||||
−0.0985239 | + | 0.995135i | \(0.531412\pi\) | |||||||
\(114\) | −3.44758 | − | 43.5112i | −0.0302419 | − | 0.381677i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 30.2121i | 0.260449i | ||||||||
\(117\) | 8.97302 | + | 56.2678i | 0.0766925 | + | 0.480921i | ||||
\(118\) | − | 0.377313i | − | 0.00319757i | ||||||
\(119\) | 13.6856i | 0.115005i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 23.1016 | 0.190922 | ||||||||
\(122\) | 24.9787 | 0.204743 | ||||||||
\(123\) | 188.611 | − | 14.9445i | 1.53343 | − | 0.121500i | ||||
\(124\) | −26.0760 | −0.210290 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −5.30313 | − | 33.2547i | −0.0420883 | − | 0.263926i | ||||
\(127\) | − | 128.979i | − | 1.01559i | −0.861479 | − | 0.507793i | \(-0.830462\pi\) | ||
0.861479 | − | 0.507793i | \(-0.169538\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | −56.8941 | + | 4.50797i | −0.441040 | + | 0.0349455i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 38.6800i | 0.295267i | 0.989042 | + | 0.147634i | \(0.0471657\pi\) | ||||
−0.989042 | + | 0.147634i | \(0.952834\pi\) | |||||||
\(132\) | 59.1807 | − | 4.68915i | 0.448339 | − | 0.0355238i | ||||
\(133\) | 27.2190i | 0.204654i | ||||||||
\(134\) | 7.85795i | 0.0586414i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 14.6305 | 0.107578 | ||||||||
\(137\) | 187.436 | 1.36814 | 0.684072 | − | 0.729414i | \(-0.260207\pi\) | ||||
0.684072 | + | 0.729414i | \(0.260207\pi\) | |||||||
\(138\) | 5.11314 | + | 64.5318i | 0.0370517 | + | 0.467622i | ||||
\(139\) | 199.427 | 1.43472 | 0.717362 | − | 0.696701i | \(-0.245350\pi\) | ||||
0.717362 | + | 0.696701i | \(0.245350\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.37831 | + | 30.0161i | 0.0168674 | + | 0.212880i | ||||
\(142\) | − | 197.371i | − | 1.38993i | ||||||
\(143\) | 62.6409 | 0.438048 | ||||||||
\(144\) | −35.5508 | + | 5.66928i | −0.246881 | + | 0.0393700i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 46.3685i | 0.317593i | ||||||||
\(147\) | 1.65872 | + | 20.9344i | 0.0112838 | + | 0.142411i | ||||
\(148\) | 71.6806i | 0.484328i | ||||||||
\(149\) | 178.869i | 1.20047i | 0.799825 | + | 0.600233i | \(0.204925\pi\) | ||||
−0.799825 | + | 0.600233i | \(0.795075\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 237.977 | 1.57600 | 0.788002 | − | 0.615672i | \(-0.211115\pi\) | ||||
0.788002 | + | 0.615672i | \(0.211115\pi\) | |||||||
\(152\) | 29.0984 | 0.191437 | ||||||||
\(153\) | 45.9732 | − | 7.33135i | 0.300479 | − | 0.0479173i | ||||
\(154\) | −37.0213 | −0.240398 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −37.8671 | + | 3.00038i | −0.242738 | + | 0.0192332i | ||||
\(157\) | 213.542i | 1.36014i | 0.733148 | + | 0.680069i | \(0.238050\pi\) | ||||
−0.733148 | + | 0.680069i | \(0.761950\pi\) | |||||||
\(158\) | 4.12772 | 0.0261248 | ||||||||
\(159\) | −17.1206 | − | 216.076i | −0.107677 | − | 1.35897i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 40.3688i | − | 0.250738i | ||||||
\(162\) | −108.870 | + | 35.6289i | −0.672034 | + | 0.219932i | ||||
\(163\) | − | 68.2021i | − | 0.418418i | −0.977871 | − | 0.209209i | \(-0.932911\pi\) | ||
0.977871 | − | 0.209209i | \(-0.0670888\pi\) | |||||||
\(164\) | 126.135i | 0.769116i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 125.162 | 0.753986 | ||||||||
\(167\) | 75.9689 | 0.454903 | 0.227452 | − | 0.973789i | \(-0.426961\pi\) | ||||
0.227452 | + | 0.973789i | \(0.426961\pi\) | |||||||
\(168\) | 22.3798 | − | 1.77325i | 0.133213 | − | 0.0105551i | ||||
\(169\) | 128.919 | 0.762833 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 91.4351 | − | 14.5812i | 0.534708 | − | 0.0852699i | ||||
\(172\) | − | 38.0483i | − | 0.221211i | ||||||
\(173\) | −182.168 | −1.05299 | −0.526497 | − | 0.850177i | \(-0.676495\pi\) | ||||
−0.526497 | + | 0.850177i | \(0.676495\pi\) | |||||||
\(174\) | −63.8893 | + | 5.06223i | −0.367180 | + | 0.0290933i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 39.5775i | 0.224872i | ||||||||
\(177\) | 0.797901 | − | 0.0632212i | 0.00450792 | − | 0.000357182i | ||||
\(178\) | 207.253i | 1.16434i | ||||||||
\(179\) | 253.745i | 1.41757i | 0.705424 | + | 0.708786i | \(0.250757\pi\) | ||||
−0.705424 | + | 0.708786i | \(0.749243\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −260.351 | −1.43840 | −0.719202 | − | 0.694801i | \(-0.755493\pi\) | ||||
−0.719202 | + | 0.694801i | \(0.755493\pi\) | |||||||
\(182\) | 23.6883 | 0.130156 | ||||||||
\(183\) | 4.18534 | + | 52.8223i | 0.0228707 | + | 0.288646i | ||||
\(184\) | −43.1560 | −0.234544 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4.36920 | − | 55.1427i | −0.0234903 | − | 0.296466i | ||||
\(187\) | − | 51.1804i | − | 0.273692i | ||||||
\(188\) | −20.0734 | −0.106774 | ||||||||
\(189\) | 69.4350 | − | 16.7865i | 0.367381 | − | 0.0888176i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 48.4377i | 0.253600i | 0.991928 | + | 0.126800i | \(0.0404707\pi\) | ||||
−0.991928 | + | 0.126800i | \(0.959529\pi\) | |||||||
\(192\) | −1.89568 | − | 23.9250i | −0.00987336 | − | 0.124609i | ||||
\(193\) | − | 103.284i | − | 0.535149i | −0.963537 | − | 0.267574i | \(-0.913778\pi\) | ||
0.963537 | − | 0.267574i | \(-0.0862221\pi\) | |||||||
\(194\) | − | 236.930i | − | 1.22129i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | −330.940 | −1.67990 | −0.839950 | − | 0.542664i | \(-0.817416\pi\) | ||||
−0.839950 | + | 0.542664i | \(0.817416\pi\) | |||||||
\(198\) | 19.8322 | + | 124.363i | 0.100163 | + | 0.628097i | ||||
\(199\) | 254.131 | 1.27704 | 0.638521 | − | 0.769605i | \(-0.279547\pi\) | ||||
0.638521 | + | 0.769605i | \(0.279547\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.6172 | + | 1.31665i | −0.0826724 | + | 0.00655050i | ||||
\(202\) | − | 110.248i | − | 0.545785i | ||||||
\(203\) | 39.9669 | 0.196881 | ||||||||
\(204\) | 2.45144 | + | 30.9391i | 0.0120169 | + | 0.151662i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 24.0758i | 0.116873i | ||||||||
\(207\) | −135.608 | + | 21.6254i | −0.655112 | + | 0.104471i | ||||
\(208\) | − | 25.3239i | − | 0.121749i | ||||||
\(209\) | − | 101.791i | − | 0.487041i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 115.082 | 0.545413 | 0.272707 | − | 0.962097i | \(-0.412081\pi\) | ||||
0.272707 | + | 0.962097i | \(0.412081\pi\) | |||||||
\(212\) | 144.502 | 0.681613 | ||||||||
\(213\) | 417.378 | − | 33.0707i | 1.95952 | − | 0.155262i | ||||
\(214\) | −268.063 | −1.25263 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −17.9456 | − | 74.2291i | −0.0830813 | − | 0.343653i | ||||
\(217\) | 34.4953i | 0.158965i | ||||||||
\(218\) | −109.006 | −0.500029 | ||||||||
\(219\) | −98.0552 | + | 7.76934i | −0.447741 | + | 0.0354765i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 32.7481i | 0.148181i | ||||||||
\(222\) | −151.582 | + | 12.0105i | −0.682804 | + | 0.0541016i | ||||
\(223\) | 304.920i | 1.36735i | 0.729784 | + | 0.683677i | \(0.239620\pi\) | ||||
−0.729784 | + | 0.683677i | \(0.760380\pi\) | |||||||
\(224\) | 14.9666i | 0.0668153i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 31.4894 | 0.139334 | ||||||||
\(227\) | −205.433 | −0.904990 | −0.452495 | − | 0.891767i | \(-0.649466\pi\) | ||||
−0.452495 | + | 0.891767i | \(0.649466\pi\) | |||||||
\(228\) | 4.87562 | + | 61.5341i | 0.0213843 | + | 0.269886i | ||||
\(229\) | 313.595 | 1.36941 | 0.684706 | − | 0.728820i | \(-0.259931\pi\) | ||||
0.684706 | + | 0.728820i | \(0.259931\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.20316 | − | 78.2887i | −0.0268535 | − | 0.338912i | ||||
\(232\) | − | 42.7264i | − | 0.184165i | ||||||
\(233\) | −252.829 | −1.08510 | −0.542552 | − | 0.840022i | \(-0.682542\pi\) | ||||
−0.542552 | + | 0.840022i | \(0.682542\pi\) | |||||||
\(234\) | −12.6898 | − | 79.5746i | −0.0542298 | − | 0.340063i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.533601i | 0.00226102i | ||||||||
\(237\) | 0.691627 | + | 8.72887i | 0.00291826 | + | 0.0368307i | ||||
\(238\) | − | 19.3544i | − | 0.0813210i | ||||||
\(239\) | 197.651i | 0.826990i | 0.910506 | + | 0.413495i | \(0.135692\pi\) | ||||
−0.910506 | + | 0.413495i | \(0.864308\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −330.829 | −1.37274 | −0.686368 | − | 0.727254i | \(-0.740796\pi\) | ||||
−0.686368 | + | 0.727254i | \(0.740796\pi\) | |||||||
\(242\) | −32.6706 | −0.135002 | ||||||||
\(243\) | −93.5860 | − | 224.256i | −0.385128 | − | 0.922863i | ||||
\(244\) | −35.3252 | −0.144775 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −266.737 | + | 21.1347i | −1.08430 | + | 0.0859136i | ||||
\(247\) | 65.1319i | 0.263692i | ||||||||
\(248\) | 36.8770 | 0.148698 | ||||||||
\(249\) | 20.9717 | + | 264.679i | 0.0842235 | + | 1.06297i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 17.1119i | − | 0.0681750i | −0.999419 | − | 0.0340875i | \(-0.989148\pi\) | ||
0.999419 | − | 0.0340875i | \(-0.0108525\pi\) | |||||||
\(252\) | 7.49976 | + | 47.0293i | 0.0297609 | + | 0.186624i | ||||
\(253\) | 150.968i | 0.596711i | ||||||||
\(254\) | 182.404i | 0.718127i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −43.8481 | −0.170615 | −0.0853075 | − | 0.996355i | \(-0.527187\pi\) | ||||
−0.0853075 | + | 0.996355i | \(0.527187\pi\) | |||||||
\(258\) | 80.4604 | − | 6.37523i | 0.311862 | − | 0.0247102i | ||||
\(259\) | 94.8245 | 0.366118 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −21.4101 | − | 134.258i | −0.0820311 | − | 0.514399i | ||||
\(262\) | − | 54.7018i | − | 0.208786i | ||||||
\(263\) | −244.864 | −0.931042 | −0.465521 | − | 0.885037i | \(-0.654133\pi\) | ||||
−0.465521 | + | 0.885037i | \(0.654133\pi\) | |||||||
\(264\) | −83.6942 | + | 6.63146i | −0.317023 | + | 0.0251191i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 38.4935i | − | 0.144712i | ||||||
\(267\) | −438.275 | + | 34.7265i | −1.64148 | + | 0.130062i | ||||
\(268\) | − | 11.1128i | − | 0.0414657i | ||||||
\(269\) | 250.644i | 0.931762i | 0.884847 | + | 0.465881i | \(0.154263\pi\) | ||||
−0.884847 | + | 0.465881i | \(0.845737\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 274.065 | 1.01131 | 0.505656 | − | 0.862735i | \(-0.331251\pi\) | ||||
0.505656 | + | 0.862735i | \(0.331251\pi\) | |||||||
\(272\) | −20.6907 | −0.0760688 | ||||||||
\(273\) | 3.96913 | + | 50.0935i | 0.0145389 | + | 0.183493i | ||||
\(274\) | −265.074 | −0.967424 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −7.23107 | − | 91.2618i | −0.0261995 | − | 0.330659i | ||||
\(277\) | − | 208.404i | − | 0.752361i | −0.926546 | − | 0.376181i | \(-0.877237\pi\) | ||
0.926546 | − | 0.376181i | \(-0.122763\pi\) | |||||||
\(278\) | −282.032 | −1.01450 | ||||||||
\(279\) | 115.878 | − | 18.4790i | 0.415333 | − | 0.0662331i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 239.837i | 0.853514i | 0.904366 | + | 0.426757i | \(0.140344\pi\) | ||||
−0.904366 | + | 0.426757i | \(0.859656\pi\) | |||||||
\(282\) | −3.36343 | − | 42.4491i | −0.0119271 | − | 0.150529i | ||||
\(283\) | − | 306.227i | − | 1.08207i | −0.840999 | − | 0.541036i | \(-0.818032\pi\) | ||
0.840999 | − | 0.541036i | \(-0.181968\pi\) | |||||||
\(284\) | 279.124i | 0.982832i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −88.5876 | −0.309747 | ||||||||
\(287\) | 166.861 | 0.581397 | ||||||||
\(288\) | 50.2764 | − | 8.01758i | 0.174571 | − | 0.0278388i | ||||
\(289\) | −262.243 | −0.907417 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 501.034 | − | 39.6991i | 1.72177 | − | 0.136423i | ||||
\(292\) | − | 65.5750i | − | 0.224572i | ||||||
\(293\) | −409.157 | −1.39644 | −0.698220 | − | 0.715883i | \(-0.746024\pi\) | ||||
−0.698220 | + | 0.715883i | \(0.746024\pi\) | |||||||
\(294\) | −2.34579 | − | 29.6057i | −0.00797888 | − | 0.100700i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 101.372i | − | 0.342472i | ||||||
\(297\) | −259.667 | + | 62.7769i | −0.874300 | + | 0.211370i | ||||
\(298\) | − | 252.959i | − | 0.848857i | ||||||
\(299\) | − | 96.5977i | − | 0.323069i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −50.3331 | −0.167220 | ||||||||
\(302\) | −336.550 | −1.11440 | ||||||||
\(303\) | 233.142 | − | 18.4728i | 0.769444 | − | 0.0609665i | ||||
\(304\) | −41.1513 | −0.135366 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −65.0159 | + | 10.3681i | −0.212470 | + | 0.0338826i | ||||
\(307\) | 61.0085i | 0.198725i | 0.995051 | + | 0.0993623i | \(0.0316803\pi\) | ||||
−0.995051 | + | 0.0993623i | \(0.968320\pi\) | |||||||
\(308\) | 52.3561 | 0.169987 | ||||||||
\(309\) | −50.9129 | + | 4.03405i | −0.164767 | + | 0.0130552i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 332.103i | − | 1.06786i | −0.845530 | − | 0.533928i | \(-0.820715\pi\) | ||
0.845530 | − | 0.533928i | \(-0.179285\pi\) | |||||||
\(312\) | 53.5522 | − | 4.24318i | 0.171642 | − | 0.0135999i | ||||
\(313\) | − | 269.682i | − | 0.861603i | −0.902447 | − | 0.430802i | \(-0.858231\pi\) | ||
0.902447 | − | 0.430802i | \(-0.141769\pi\) | |||||||
\(314\) | − | 301.993i | − | 0.961762i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.83748 | −0.0184730 | ||||||||
\(317\) | 221.234 | 0.697899 | 0.348949 | − | 0.937142i | \(-0.386539\pi\) | ||||
0.348949 | + | 0.937142i | \(0.386539\pi\) | |||||||
\(318\) | 24.2122 | + | 305.577i | 0.0761390 | + | 0.960934i | ||||
\(319\) | −149.465 | −0.468542 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −44.9157 | − | 566.871i | −0.139924 | − | 1.76595i | ||||
\(322\) | 57.0901i | 0.177298i | ||||||||
\(323\) | 53.2156 | 0.164754 | ||||||||
\(324\) | 153.965 | − | 50.3869i | 0.475200 | − | 0.155515i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 96.4523i | 0.295866i | ||||||||
\(327\) | −18.2647 | − | 230.515i | −0.0558553 | − | 0.704938i | ||||
\(328\) | − | 178.382i | − | 0.543847i | ||||||
\(329\) | 26.5547i | 0.0807132i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 151.066 | 0.456391 | 0.228196 | − | 0.973615i | \(-0.426717\pi\) | ||||
0.228196 | + | 0.973615i | \(0.426717\pi\) | |||||||
\(332\) | −177.005 | −0.533149 | ||||||||
\(333\) | −50.7972 | − | 318.538i | −0.152544 | − | 0.956570i | ||||
\(334\) | −107.436 | −0.321665 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −31.6498 | + | 2.50775i | −0.0941959 | + | 0.00746356i | ||||
\(337\) | 386.598i | 1.14717i | 0.819144 | + | 0.573587i | \(0.194449\pi\) | ||||
−0.819144 | + | 0.573587i | \(0.805551\pi\) | |||||||
\(338\) | −182.319 | −0.539405 | ||||||||
\(339\) | 5.27626 | + | 66.5905i | 0.0155642 | + | 0.196432i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 129.003i | − | 0.378307i | ||||||
\(342\) | −129.309 | + | 20.6209i | −0.378096 | + | 0.0602949i | ||||
\(343\) | 18.5203i | 0.0539949i | ||||||||
\(344\) | 53.8084i | 0.156420i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 257.624 | 0.744579 | ||||||||
\(347\) | −101.455 | −0.292378 | −0.146189 | − | 0.989257i | \(-0.546701\pi\) | ||||
−0.146189 | + | 0.989257i | \(0.546701\pi\) | |||||||
\(348\) | 90.3531 | − | 7.15907i | 0.259635 | − | 0.0205721i | ||||
\(349\) | −201.227 | −0.576581 | −0.288290 | − | 0.957543i | \(-0.593087\pi\) | ||||
−0.288290 | + | 0.957543i | \(0.593087\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 166.150 | − | 40.1682i | 0.473361 | − | 0.114439i | ||||
\(352\) | − | 55.9710i | − | 0.159008i | ||||||
\(353\) | −324.605 | −0.919560 | −0.459780 | − | 0.888033i | \(-0.652072\pi\) | ||||
−0.459780 | + | 0.888033i | \(0.652072\pi\) | |||||||
\(354\) | −1.12840 | + | 0.0894083i | −0.00318758 | + | 0.000252566i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 293.099i | − | 0.823313i | ||||||
\(357\) | 40.9286 | − | 3.24295i | 0.114646 | − | 0.00908390i | ||||
\(358\) | − | 358.850i | − | 1.00237i | ||||||
\(359\) | 71.5032i | 0.199173i | 0.995029 | + | 0.0995866i | \(0.0317520\pi\) | ||||
−0.995029 | + | 0.0995866i | \(0.968248\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −255.161 | −0.706816 | ||||||||
\(362\) | 368.192 | 1.01711 | ||||||||
\(363\) | −5.47416 | − | 69.0882i | −0.0150803 | − | 0.190326i | ||||
\(364\) | −33.5003 | −0.0920339 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −5.91896 | − | 74.7020i | −0.0161720 | − | 0.204104i | ||||
\(367\) | 120.662i | 0.328780i | 0.986395 | + | 0.164390i | \(0.0525656\pi\) | ||||
−0.986395 | + | 0.164390i | \(0.947434\pi\) | |||||||
\(368\) | 61.0319 | 0.165847 | ||||||||
\(369\) | −89.3869 | − | 560.525i | −0.242241 | − | 1.51904i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 191.158i | − | 0.515251i | ||||||
\(372\) | 6.17898 | + | 77.9836i | 0.0166102 | + | 0.209633i | ||||
\(373\) | − | 336.650i | − | 0.902547i | −0.892386 | − | 0.451273i | \(-0.850970\pi\) | ||
0.892386 | − | 0.451273i | \(-0.149030\pi\) | |||||||
\(374\) | 72.3800i | 0.193529i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 28.3881 | 0.0755003 | ||||||||
\(377\) | 95.6359 | 0.253676 | ||||||||
\(378\) | −98.1958 | + | 23.7397i | −0.259777 | + | 0.0628035i | ||||
\(379\) | 190.311 | 0.502141 | 0.251071 | − | 0.967969i | \(-0.419217\pi\) | ||||
0.251071 | + | 0.967969i | \(0.419217\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −385.729 | + | 30.5630i | −1.01241 | + | 0.0802179i | ||||
\(382\) | − | 68.5012i | − | 0.179322i | ||||||
\(383\) | −608.518 | −1.58882 | −0.794409 | − | 0.607383i | \(-0.792219\pi\) | ||||
−0.794409 | + | 0.607383i | \(0.792219\pi\) | |||||||
\(384\) | 2.68090 | + | 33.8351i | 0.00698152 | + | 0.0881122i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 146.065i | 0.378407i | ||||||||
\(387\) | 26.9633 | + | 169.081i | 0.0696726 | + | 0.436901i | ||||
\(388\) | 335.069i | 0.863581i | ||||||||
\(389\) | − | 72.7694i | − | 0.187068i | −0.995616 | − | 0.0935339i | \(-0.970184\pi\) | ||
0.995616 | − | 0.0935339i | \(-0.0298164\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −78.9245 | −0.201853 | ||||||||
\(392\) | 19.7990 | 0.0505076 | ||||||||
\(393\) | 115.678 | − | 9.16564i | 0.294345 | − | 0.0233222i | ||||
\(394\) | 468.020 | 1.18787 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −28.0470 | − | 175.876i | −0.0708257 | − | 0.444132i | ||||
\(397\) | 188.473i | 0.474744i | 0.971419 | + | 0.237372i | \(0.0762860\pi\) | ||||
−0.971419 | + | 0.237372i | \(0.923714\pi\) | |||||||
\(398\) | −359.396 | −0.903004 | ||||||||
\(399\) | 81.4020 | − | 6.44984i | 0.204015 | − | 0.0161650i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 675.476i | − | 1.68448i | −0.539104 | − | 0.842240i | \(-0.681237\pi\) | ||
0.539104 | − | 0.842240i | \(-0.318763\pi\) | |||||||
\(402\) | 23.5002 | − | 1.86202i | 0.0584582 | − | 0.00463190i | ||||
\(403\) | 82.5432i | 0.204822i | ||||||||
\(404\) | 155.915i | 0.385928i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −56.5217 | −0.139216 | ||||||||
\(407\) | −354.617 | −0.871295 | ||||||||
\(408\) | −3.46686 | − | 43.7545i | −0.00849721 | − | 0.107241i | ||||
\(409\) | −658.803 | −1.61077 | −0.805383 | − | 0.592755i | \(-0.798040\pi\) | ||||
−0.805383 | + | 0.592755i | \(0.798040\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −44.4149 | − | 560.550i | −0.108065 | − | 1.36387i | ||||
\(412\) | − | 34.0483i | − | 0.0826415i | ||||||
\(413\) | 0.705888 | 0.00170917 | ||||||||
\(414\) | 191.779 | − | 30.5830i | 0.463234 | − | 0.0738719i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 35.8134i | 0.0860898i | ||||||||
\(417\) | −47.2562 | − | 596.410i | −0.113324 | − | 1.43024i | ||||
\(418\) | 143.955i | 0.344390i | ||||||||
\(419\) | − | 499.544i | − | 1.19223i | −0.802899 | − | 0.596115i | \(-0.796710\pi\) | ||
0.802899 | − | 0.596115i | \(-0.203290\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −322.054 | −0.764974 | −0.382487 | − | 0.923961i | \(-0.624932\pi\) | ||||
−0.382487 | + | 0.923961i | \(0.624932\pi\) | |||||||
\(422\) | −162.751 | −0.385665 | ||||||||
\(423\) | 89.2033 | − | 14.2252i | 0.210883 | − | 0.0336294i | ||||
\(424\) | −204.357 | −0.481973 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −590.262 | + | 46.7690i | −1.38559 | + | 0.109786i | ||||
\(427\) | 46.7309i | 0.109440i | ||||||||
\(428\) | 379.099 | 0.885745 | ||||||||
\(429\) | −14.8434 | − | 187.336i | −0.0346001 | − | 0.436680i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 188.011i | 0.436221i | 0.975924 | + | 0.218110i | \(0.0699893\pi\) | ||||
−0.975924 | + | 0.218110i | \(0.930011\pi\) | |||||||
\(432\) | 25.3789 | + | 104.976i | 0.0587473 | + | 0.242999i | ||||
\(433\) | 450.861i | 1.04125i | 0.853785 | + | 0.520625i | \(0.174301\pi\) | ||||
−0.853785 | + | 0.520625i | \(0.825699\pi\) | |||||||
\(434\) | − | 48.7837i | − | 0.112405i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 154.158 | 0.353574 | ||||||||
\(437\) | −156.971 | −0.359202 | ||||||||
\(438\) | 138.671 | − | 10.9875i | 0.316600 | − | 0.0250856i | ||||
\(439\) | 25.6728 | 0.0584801 | 0.0292400 | − | 0.999572i | \(-0.490691\pi\) | ||||
0.0292400 | + | 0.999572i | \(0.490691\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 62.2139 | − | 9.92125i | 0.141075 | − | 0.0224972i | ||||
\(442\) | − | 46.3128i | − | 0.104780i | ||||||
\(443\) | −128.613 | −0.290322 | −0.145161 | − | 0.989408i | \(-0.546370\pi\) | ||||
−0.145161 | + | 0.989408i | \(0.546370\pi\) | |||||||
\(444\) | 214.370 | − | 16.9855i | 0.482815 | − | 0.0382556i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 431.222i | − | 0.966866i | ||||||
\(447\) | 534.931 | − | 42.3850i | 1.19671 | − | 0.0948210i | ||||
\(448\) | − | 21.1660i | − | 0.0472456i | ||||||
\(449\) | 746.161i | 1.66183i | 0.556401 | + | 0.830914i | \(0.312182\pi\) | ||||
−0.556401 | + | 0.830914i | \(0.687818\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −624.013 | −1.38362 | ||||||||
\(452\) | −44.5328 | −0.0985239 | ||||||||
\(453\) | −56.3911 | − | 711.700i | −0.124484 | − | 1.57108i | ||||
\(454\) | 290.526 | 0.639925 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.89516 | − | 87.0224i | −0.0151210 | − | 0.190838i | ||||
\(457\) | 861.637i | 1.88542i | 0.333612 | + | 0.942710i | \(0.391732\pi\) | ||||
−0.333612 | + | 0.942710i | \(0.608268\pi\) | |||||||
\(458\) | −443.491 | −0.968320 | ||||||||
\(459\) | −32.8192 | − | 135.752i | −0.0715014 | − | 0.295755i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 119.284i | − | 0.258750i | −0.991596 | − | 0.129375i | \(-0.958703\pi\) | ||
0.991596 | − | 0.129375i | \(-0.0412972\pi\) | |||||||
\(462\) | 8.77259 | + | 110.717i | 0.0189883 | + | 0.239647i | ||||
\(463\) | 815.164i | 1.76061i | 0.474406 | + | 0.880306i | \(0.342663\pi\) | ||||
−0.474406 | + | 0.880306i | \(0.657337\pi\) | |||||||
\(464\) | 60.4242i | 0.130225i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 357.555 | 0.767285 | ||||||||
\(467\) | 396.290 | 0.848587 | 0.424293 | − | 0.905525i | \(-0.360523\pi\) | ||||
0.424293 | + | 0.905525i | \(0.360523\pi\) | |||||||
\(468\) | 17.9460 | + | 112.536i | 0.0383462 | + | 0.240460i | ||||
\(469\) | −14.7009 | −0.0313452 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 638.623 | − | 50.6009i | 1.35589 | − | 0.107433i | ||||
\(472\) | − | 0.754626i | − | 0.00159878i | ||||||
\(473\) | 188.232 | 0.397953 | ||||||||
\(474\) | −0.978108 | − | 12.3445i | −0.00206352 | − | 0.0260432i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 27.3712i | 0.0575026i | ||||||||
\(477\) | −642.145 | + | 102.403i | −1.34622 | + | 0.214681i | ||||
\(478\) | − | 279.520i | − | 0.584770i | ||||||
\(479\) | 757.324i | 1.58105i | 0.612429 | + | 0.790526i | \(0.290193\pi\) | ||||
−0.612429 | + | 0.790526i | \(0.709807\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 226.904 | 0.471734 | ||||||||
\(482\) | 467.864 | 0.970671 | ||||||||
\(483\) | −120.728 | + | 9.56581i | −0.249954 | + | 0.0198050i | ||||
\(484\) | 46.2031 | 0.0954610 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 132.351 | + | 317.146i | 0.272326 | + | 0.652563i | ||||
\(487\) | − | 286.196i | − | 0.587672i | −0.955856 | − | 0.293836i | \(-0.905068\pi\) | ||
0.955856 | − | 0.293836i | \(-0.0949319\pi\) | |||||||
\(488\) | 49.9574 | 0.102372 | ||||||||
\(489\) | −203.967 | + | 16.1612i | −0.417110 | + | 0.0330495i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 825.348i | 1.68095i | 0.541848 | + | 0.840476i | \(0.317725\pi\) | ||||
−0.541848 | + | 0.840476i | \(0.682275\pi\) | |||||||
\(492\) | 377.223 | − | 29.8890i | 0.766713 | − | 0.0607501i | ||||
\(493\) | − | 78.1387i | − | 0.158496i | ||||||
\(494\) | − | 92.1104i | − | 0.186458i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −52.1520 | −0.105145 | ||||||||
\(497\) | 369.247 | 0.742951 | ||||||||
\(498\) | −29.6584 | − | 374.312i | −0.0595550 | − | 0.751631i | ||||
\(499\) | −384.354 | −0.770249 | −0.385125 | − | 0.922865i | \(-0.625842\pi\) | ||||
−0.385125 | + | 0.922865i | \(0.625842\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.0016 | − | 227.195i | −0.0359314 | − | 0.453482i | ||||
\(502\) | 24.1999i | 0.0482070i | ||||||||
\(503\) | 84.4100 | 0.167813 | 0.0839066 | − | 0.996474i | \(-0.473260\pi\) | ||||
0.0839066 | + | 0.996474i | \(0.473260\pi\) | |||||||
\(504\) | −10.6063 | − | 66.5095i | −0.0210442 | − | 0.131963i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 213.501i | − | 0.421938i | ||||||
\(507\) | −30.5487 | − | 385.548i | −0.0602538 | − | 0.760450i | ||||
\(508\) | − | 257.959i | − | 0.507793i | ||||||
\(509\) | 111.260i | 0.218585i | 0.994010 | + | 0.109293i | \(0.0348585\pi\) | ||||
−0.994010 | + | 0.109293i | \(0.965141\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −86.7476 | −0.169760 | ||||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | −65.2733 | − | 269.993i | −0.127238 | − | 0.526302i | ||||
\(514\) | 62.0105 | 0.120643 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −113.788 | + | 9.01594i | −0.220520 | + | 0.0174727i | ||||
\(517\) | − | 99.3069i | − | 0.192083i | ||||||
\(518\) | −134.102 | −0.258884 | ||||||||
\(519\) | 43.1666 | + | 544.796i | 0.0831726 | + | 1.04970i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 227.355i | 0.436383i | 0.975906 | + | 0.218191i | \(0.0700157\pi\) | ||||
−0.975906 | + | 0.218191i | \(0.929984\pi\) | |||||||
\(522\) | 30.2785 | + | 189.870i | 0.0580048 | + | 0.363735i | ||||
\(523\) | 957.094i | 1.83001i | 0.403446 | + | 0.915004i | \(0.367812\pi\) | ||||
−0.403446 | + | 0.915004i | \(0.632188\pi\) | |||||||
\(524\) | 77.3601i | 0.147634i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 346.290 | 0.658346 | ||||||||
\(527\) | 67.4414 | 0.127972 | ||||||||
\(528\) | 118.361 | − | 9.37829i | 0.224169 | − | 0.0177619i | ||||
\(529\) | −296.195 | −0.559914 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.378142 | − | 2.37124i | −0.000712132 | − | 0.00446562i | ||||
\(532\) | 54.4381i | 0.102327i | ||||||||
\(533\) | 399.279 | 0.749116 | ||||||||
\(534\) | 619.815 | − | 49.1107i | 1.16070 | − | 0.0919676i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 15.7159i | 0.0293207i | ||||||||
\(537\) | 758.857 | − | 60.1276i | 1.41314 | − | 0.111969i | ||||
\(538\) | − | 354.464i | − | 0.658855i | ||||||
\(539\) | − | 69.2605i | − | 0.128498i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −179.389 | −0.331587 | −0.165793 | − | 0.986161i | \(-0.553019\pi\) | ||||
−0.165793 | + | 0.986161i | \(0.553019\pi\) | |||||||
\(542\) | −387.587 | −0.715105 | ||||||||
\(543\) | 61.6930 | + | 778.614i | 0.113615 | + | 1.43391i | ||||
\(544\) | 29.2611 | 0.0537888 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −5.61320 | − | 70.8429i | −0.0102806 | − | 0.129749i | ||||
\(547\) | − | 182.706i | − | 0.334014i | −0.985956 | − | 0.167007i | \(-0.946590\pi\) | ||
0.985956 | − | 0.167007i | \(-0.0534102\pi\) | |||||||
\(548\) | 374.872 | 0.684072 | ||||||||
\(549\) | 156.980 | − | 25.0336i | 0.285938 | − | 0.0455985i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 155.408i | − | 0.282048i | ||||||
\(552\) | 10.2263 | + | 129.064i | 0.0185259 | + | 0.233811i | ||||
\(553\) | 7.72226i | 0.0139643i | ||||||||
\(554\) | 294.728i | 0.532000i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 398.853 | 0.717362 | ||||||||
\(557\) | −591.471 | −1.06189 | −0.530943 | − | 0.847407i | \(-0.678162\pi\) | ||||
−0.530943 | + | 0.847407i | \(0.678162\pi\) | |||||||
\(558\) | −163.876 | + | 26.1333i | −0.293685 | + | 0.0468339i | ||||
\(559\) | −120.441 | −0.215458 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −153.061 | + | 12.1277i | −0.272837 | + | 0.0216181i | ||||
\(562\) | − | 339.181i | − | 0.603526i | ||||||
\(563\) | −97.5678 | −0.173300 | −0.0866499 | − | 0.996239i | \(-0.527616\pi\) | ||||
−0.0866499 | + | 0.996239i | \(0.527616\pi\) | |||||||
\(564\) | 4.75661 | + | 60.0321i | 0.00843371 | + | 0.106440i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 433.070i | 0.765141i | ||||||||
\(567\) | −66.6556 | − | 203.676i | −0.117558 | − | 0.359217i | ||||
\(568\) | − | 394.741i | − | 0.694967i | ||||||
\(569\) | − | 604.562i | − | 1.06250i | −0.847215 | − | 0.531250i | \(-0.821723\pi\) | ||
0.847215 | − | 0.531250i | \(-0.178277\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 651.161 | 1.14039 | 0.570194 | − | 0.821510i | \(-0.306868\pi\) | ||||
0.570194 | + | 0.821510i | \(0.306868\pi\) | |||||||
\(572\) | 125.282 | 0.219024 | ||||||||
\(573\) | 144.859 | − | 11.4778i | 0.252808 | − | 0.0200311i | ||||
\(574\) | −235.977 | −0.411110 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −71.1016 | + | 11.3386i | −0.123440 | + | 0.0196850i | ||||
\(577\) | 18.4946i | 0.0320531i | 0.999872 | + | 0.0160265i | \(0.00510162\pi\) | ||||
−0.999872 | + | 0.0160265i | \(0.994898\pi\) | |||||||
\(578\) | 370.868 | 0.641640 | ||||||||
\(579\) | −308.883 | + | 24.4742i | −0.533477 | + | 0.0422697i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 234.156i | 0.403023i | ||||||||
\(582\) | −708.569 | + | 56.1430i | −1.21747 | + | 0.0964657i | ||||
\(583\) | 714.877i | 1.22620i | ||||||||
\(584\) | 92.7371i | 0.158796i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 578.635 | 0.987432 | ||||||||
\(587\) | 704.219 | 1.19969 | 0.599846 | − | 0.800115i | \(-0.295228\pi\) | ||||
0.599846 | + | 0.800115i | \(0.295228\pi\) | |||||||
\(588\) | 3.31745 | + | 41.8688i | 0.00564192 | + | 0.0712054i | ||||
\(589\) | 134.133 | 0.227729 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 78.4198 | + | 989.719i | 0.132690 | + | 1.67465i | ||||
\(592\) | 143.361i | 0.242164i | ||||||||
\(593\) | 730.470 | 1.23182 | 0.615911 | − | 0.787816i | \(-0.288788\pi\) | ||||
0.615911 | + | 0.787816i | \(0.288788\pi\) | |||||||
\(594\) | 367.225 | − | 88.7799i | 0.618224 | − | 0.149461i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 357.739i | 0.600233i | ||||||||
\(597\) | −60.2191 | − | 760.012i | −0.100869 | − | 1.27305i | ||||
\(598\) | 136.610i | 0.228444i | ||||||||
\(599\) | − | 486.764i | − | 0.812627i | −0.913734 | − | 0.406314i | \(-0.866814\pi\) | ||
0.913734 | − | 0.406314i | \(-0.133186\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 486.097 | 0.808814 | 0.404407 | − | 0.914579i | \(-0.367478\pi\) | ||||
0.404407 | + | 0.914579i | \(0.367478\pi\) | |||||||
\(602\) | 71.1818 | 0.118242 | ||||||||
\(603\) | 7.87522 | + | 49.3837i | 0.0130601 | + | 0.0818967i | ||||
\(604\) | 475.953 | 0.788002 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −329.712 | + | 26.1245i | −0.544079 | + | 0.0431098i | ||||
\(607\) | − | 815.911i | − | 1.34417i | −0.740474 | − | 0.672085i | \(-0.765399\pi\) | ||
0.740474 | − | 0.672085i | \(-0.234601\pi\) | |||||||
\(608\) | 58.1967 | 0.0957183 | ||||||||
\(609\) | −9.47057 | − | 119.526i | −0.0155510 | − | 0.196266i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 63.5421i | 0.103997i | ||||||||
\(612\) | 91.9464 | − | 14.6627i | 0.150239 | − | 0.0239587i | ||||
\(613\) | − | 387.354i | − | 0.631899i | −0.948776 | − | 0.315949i | \(-0.897677\pi\) | ||
0.948776 | − | 0.315949i | \(-0.102323\pi\) | |||||||
\(614\) | − | 86.2790i | − | 0.140520i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −74.0426 | −0.120199 | ||||||||
\(617\) | −1021.58 | −1.65572 | −0.827860 | − | 0.560935i | \(-0.810442\pi\) | ||||
−0.827860 | + | 0.560935i | \(0.810442\pi\) | |||||||
\(618\) | 72.0017 | − | 5.70501i | 0.116508 | − | 0.00923141i | ||||
\(619\) | 529.302 | 0.855091 | 0.427546 | − | 0.903994i | \(-0.359378\pi\) | ||||
0.427546 | + | 0.903994i | \(0.359378\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 96.8074 | + | 400.429i | 0.155890 | + | 0.644813i | ||||
\(622\) | 469.665i | 0.755089i | ||||||||
\(623\) | −387.734 | −0.622366 | ||||||||
\(624\) | −75.7343 | + | 6.00076i | −0.121369 | + | 0.00961660i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 381.388i | 0.609246i | ||||||||
\(627\) | −304.420 | + | 24.1206i | −0.485519 | + | 0.0384698i | ||||
\(628\) | 427.083i | 0.680069i | ||||||||
\(629\) | − | 185.390i | − | 0.294738i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −504.590 | −0.799667 | −0.399833 | − | 0.916588i | \(-0.630932\pi\) | ||||
−0.399833 | + | 0.916588i | \(0.630932\pi\) | |||||||
\(632\) | 8.25545 | 0.0130624 | ||||||||
\(633\) | −27.2699 | − | 344.168i | −0.0430805 | − | 0.543709i | ||||
\(634\) | −312.872 | −0.493489 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −34.2412 | − | 432.151i | −0.0538384 | − | 0.679483i | ||||
\(637\) | 44.3168i | 0.0695711i | ||||||||
\(638\) | 211.375 | 0.331309 | ||||||||
\(639\) | −197.804 | − | 1240.39i | −0.309553 | − | 1.94114i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1067.75i | 1.66575i | 0.553459 | + | 0.832877i | \(0.313308\pi\) | ||||
−0.553459 | + | 0.832877i | \(0.686692\pi\) | |||||||
\(642\) | 63.5204 | + | 801.677i | 0.0989414 | + | 1.24872i | ||||
\(643\) | 575.185i | 0.894534i | 0.894401 | + | 0.447267i | \(0.147603\pi\) | ||||
−0.894401 | + | 0.447267i | \(0.852397\pi\) | |||||||
\(644\) | − | 80.7376i | − | 0.125369i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −75.2583 | −0.116499 | ||||||||
\(647\) | −998.983 | −1.54402 | −0.772012 | − | 0.635608i | \(-0.780749\pi\) | ||||
−0.772012 | + | 0.635608i | \(0.780749\pi\) | |||||||
\(648\) | −217.739 | + | 71.2578i | −0.336017 | + | 0.109966i | ||||
\(649\) | −2.63982 | −0.00406752 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 103.163 | − | 8.17402i | 0.158468 | − | 0.0125561i | ||||
\(652\) | − | 136.404i | − | 0.209209i | ||||||
\(653\) | 473.061 | 0.724442 | 0.362221 | − | 0.932092i | \(-0.382019\pi\) | ||||
0.362221 | + | 0.932092i | \(0.382019\pi\) | |||||||
\(654\) | 25.8302 | + | 325.997i | 0.0394957 | + | 0.498467i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 252.270i | 0.384558i | ||||||||
\(657\) | 46.4704 | + | 291.405i | 0.0707312 | + | 0.443539i | ||||
\(658\) | − | 37.5539i | − | 0.0570729i | ||||||
\(659\) | 732.225i | 1.11111i | 0.831478 | + | 0.555557i | \(0.187495\pi\) | ||||
−0.831478 | + | 0.555557i | \(0.812505\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −682.586 | −1.03266 | −0.516328 | − | 0.856391i | \(-0.672701\pi\) | ||||
−0.516328 | + | 0.856391i | \(0.672701\pi\) | |||||||
\(662\) | −213.639 | −0.322717 | ||||||||
\(663\) | 97.9373 | − | 7.76000i | 0.147718 | − | 0.0117044i | ||||
\(664\) | 250.324 | 0.376993 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 71.8381 | + | 450.481i | 0.107865 | + | 0.676397i | ||||
\(667\) | 230.488i | 0.345559i | ||||||||
\(668\) | 151.938 | 0.227452 | ||||||||
\(669\) | 911.902 | − | 72.2540i | 1.36308 | − | 0.108003i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 174.760i | − | 0.260447i | ||||||
\(672\) | 44.7596 | − | 3.54650i | 0.0666066 | − | 0.00527753i | ||||
\(673\) | 621.860i | 0.924012i | 0.886877 | + | 0.462006i | \(0.152870\pi\) | ||||
−0.886877 | + | 0.462006i | \(0.847130\pi\) | |||||||
\(674\) | − | 546.732i | − | 0.811175i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 257.838 | 0.381417 | ||||||||
\(677\) | 1249.46 | 1.84559 | 0.922794 | − | 0.385293i | \(-0.125900\pi\) | ||||
0.922794 | + | 0.385293i | \(0.125900\pi\) | |||||||
\(678\) | −7.46175 | − | 94.1732i | −0.0110055 | − | 0.138898i | ||||
\(679\) | 443.255 | 0.652806 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 48.6795 | + | 614.373i | 0.0714823 | + | 0.902163i | ||||
\(682\) | 182.437i | 0.267503i | ||||||||
\(683\) | 161.483 | 0.236432 | 0.118216 | − | 0.992988i | \(-0.462282\pi\) | ||||
0.118216 | + | 0.992988i | \(0.462282\pi\) | |||||||
\(684\) | 182.870 | − | 29.1623i | 0.267354 | − | 0.0426349i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 26.1916i | − | 0.0381802i | ||||||
\(687\) | −74.3097 | − | 937.846i | −0.108165 | − | 1.36513i | ||||
\(688\) | − | 76.0965i | − | 0.110605i | ||||||
\(689\) | − | 457.419i | − | 0.663888i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −520.487 | −0.753237 | −0.376619 | − | 0.926368i | \(-0.622913\pi\) | ||||
−0.376619 | + | 0.926368i | \(0.622913\pi\) | |||||||
\(692\) | −364.336 | −0.526497 | ||||||||
\(693\) | −232.662 | + | 37.1027i | −0.335732 | + | 0.0535392i | ||||
\(694\) | 143.479 | 0.206742 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −127.779 | + | 10.1245i | −0.183590 | + | 0.0145466i | ||||
\(697\) | − | 326.228i | − | 0.468046i | ||||||
\(698\) | 284.578 | 0.407704 | ||||||||
\(699\) | 59.9106 | + | 756.118i | 0.0857090 | + | 1.08171i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1017.26i | 1.45115i | 0.688142 | + | 0.725576i | \(0.258427\pi\) | ||||
−0.688142 | + | 0.725576i | \(0.741573\pi\) | |||||||
\(702\) | −234.971 | + | 56.8064i | −0.334717 | + | 0.0809208i | ||||
\(703\) | − | 368.719i | − | 0.524493i | ||||||
\(704\) | 79.1549i | 0.112436i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 459.060 | 0.650227 | ||||||||
\(707\) | 206.256 | 0.291734 | ||||||||
\(708\) | 1.59580 | − | 0.126442i | 0.00225396 | − | 0.000178591i | ||||
\(709\) | −1317.44 | −1.85817 | −0.929086 | − | 0.369863i | \(-0.879405\pi\) | ||||
−0.929086 | + | 0.369863i | \(0.879405\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 25.9409 | − | 4.13679i | 0.0364851 | − | 0.00581828i | ||||
\(712\) | 414.505i | 0.582170i | ||||||||
\(713\) | −198.933 | −0.279009 | ||||||||
\(714\) | −57.8818 | + | 4.58623i | −0.0810669 | + | 0.00642329i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 507.491i | 0.708786i | ||||||||
\(717\) | 591.099 | − | 46.8354i | 0.824406 | − | 0.0653213i | ||||
\(718\) | − | 101.121i | − | 0.140837i | ||||||
\(719\) | − | 8.42284i | − | 0.0117147i | −0.999983 | − | 0.00585733i | \(-0.998136\pi\) | ||
0.999983 | − | 0.00585733i | \(-0.00186446\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −45.0417 | −0.0624711 | ||||||||
\(722\) | 360.852 | 0.499795 | ||||||||
\(723\) | 78.3935 | + | 989.388i | 0.108428 | + | 1.36845i | ||||
\(724\) | −520.703 | −0.719202 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 7.74163 | + | 97.7054i | 0.0106634 | + | 0.134580i | ||||
\(727\) | − | 540.554i | − | 0.743541i | −0.928325 | − | 0.371770i | \(-0.878751\pi\) | ||
0.928325 | − | 0.371770i | \(-0.121249\pi\) | |||||||
\(728\) | 47.3766 | 0.0650778 | ||||||||
\(729\) | −648.489 | + | 333.021i | −0.889560 | + | 0.456818i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 98.4058i | 0.134618i | ||||||||
\(732\) | 8.37068 | + | 105.645i | 0.0114354 | + | 0.144323i | ||||
\(733\) | − | 581.326i | − | 0.793078i | −0.918018 | − | 0.396539i | \(-0.870211\pi\) | ||
0.918018 | − | 0.396539i | \(-0.129789\pi\) | |||||||
\(734\) | − | 170.642i | − | 0.232483i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −86.3121 | −0.117272 | ||||||||
\(737\) | 54.9771 | 0.0745959 | ||||||||
\(738\) | 126.412 | + | 792.702i | 0.171290 | + | 1.07412i | ||||
\(739\) | 886.532 | 1.19964 | 0.599819 | − | 0.800136i | \(-0.295239\pi\) | ||||
0.599819 | + | 0.800136i | \(0.295239\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 194.785 | − | 15.4337i | 0.262868 | − | 0.0208282i | ||||
\(742\) | 270.338i | 0.364337i | ||||||||
\(743\) | 1466.84 | 1.97421 | 0.987106 | − | 0.160066i | \(-0.0511706\pi\) | ||||
0.987106 | + | 0.160066i | \(0.0511706\pi\) | |||||||
\(744\) | −8.73840 | − | 110.285i | −0.0117452 | − | 0.148233i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 476.095i | 0.638197i | ||||||||
\(747\) | 786.586 | − | 125.437i | 1.05299 | − | 0.167921i | ||||
\(748\) | − | 102.361i | − | 0.136846i | ||||||
\(749\) | − | 501.500i | − | 0.669560i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −578.835 | −0.770752 | −0.385376 | − | 0.922760i | \(-0.625928\pi\) | ||||
−0.385376 | + | 0.922760i | \(0.625928\pi\) | |||||||
\(752\) | −40.1469 | −0.0533868 | ||||||||
\(753\) | −51.1754 | + | 4.05485i | −0.0679620 | + | 0.00538493i | ||||
\(754\) | −135.250 | −0.179376 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 138.870 | − | 33.5731i | 0.183690 | − | 0.0444088i | ||||
\(757\) | 318.935i | 0.421314i | 0.977560 | + | 0.210657i | \(0.0675603\pi\) | ||||
−0.977560 | + | 0.210657i | \(0.932440\pi\) | |||||||
\(758\) | −269.141 | −0.355067 | ||||||||
\(759\) | 451.488 | − | 35.7734i | 0.594846 | − | 0.0471323i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1038.56i | − | 1.36473i | −0.731010 | − | 0.682367i | \(-0.760951\pi\) | ||
0.731010 | − | 0.682367i | \(-0.239049\pi\) | |||||||
\(762\) | 545.503 | − | 43.2226i | 0.715884 | − | 0.0567226i | ||||
\(763\) | − | 203.932i | − | 0.267277i | ||||||
\(764\) | 96.8753i | 0.126800i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 860.574 | 1.12346 | ||||||||
\(767\) | 1.68911 | 0.00220223 | ||||||||
\(768\) | −3.79137 | − | 47.8500i | −0.00493668 | − | 0.0623047i | ||||
\(769\) | −1061.13 | −1.37989 | −0.689943 | − | 0.723863i | \(-0.742365\pi\) | ||||
−0.689943 | + | 0.723863i | \(0.742365\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.3903 | + | 131.133i | 0.0134763 | + | 0.170082i | ||||
\(772\) | − | 206.567i | − | 0.267574i | ||||||
\(773\) | 413.194 | 0.534533 | 0.267266 | − | 0.963623i | \(-0.413880\pi\) | ||||
0.267266 | + | 0.963623i | \(0.413880\pi\) | |||||||
\(774\) | −38.1319 | − | 239.116i | −0.0492660 | − | 0.308936i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 473.860i | − | 0.610644i | ||||||
\(777\) | −22.4697 | − | 283.585i | −0.0289185 | − | 0.364974i | ||||
\(778\) | 102.911i | 0.132277i | ||||||||
\(779\) | − | 648.828i | − | 0.832898i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1380.88 | −1.76809 | ||||||||
\(782\) | 111.616 | 0.142732 | ||||||||
\(783\) | −396.442 | + | 95.8435i | −0.506312 | + | 0.122406i | ||||
\(784\) | −28.0000 | −0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −163.593 | + | 12.9622i | −0.208133 | + | 0.0164913i | ||||
\(787\) | − | 470.548i | − | 0.597901i | −0.954269 | − | 0.298951i | \(-0.903363\pi\) | ||
0.954269 | − | 0.298951i | \(-0.0966366\pi\) | |||||||
\(788\) | −661.881 | −0.839950 | ||||||||
\(789\) | 58.0231 | + | 732.297i | 0.0735401 | + | 0.928133i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 58.9113i | 0.0744770i | ||||||||
\(792\) | 39.6644 | + | 248.727i | 0.0500813 | + | 0.314049i | ||||
\(793\) | 111.821i | 0.141011i | ||||||||
\(794\) | − | 266.542i | − | 0.335695i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 508.262 | 0.638521 | ||||||||
\(797\) | 1377.25 | 1.72805 | 0.864023 | − | 0.503453i | \(-0.167937\pi\) | ||||
0.864023 | + | 0.503453i | \(0.167937\pi\) | |||||||
\(798\) | −115.120 | + | 9.12144i | −0.144260 | + | 0.0114304i | ||||
\(799\) | 51.9167 | 0.0649771 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 207.708 | + | 1302.49i | 0.259311 | + | 1.62608i | ||||
\(802\) | 955.267i | 1.19111i | ||||||||
\(803\) | 324.411 | 0.403999 | ||||||||
\(804\) | −33.2343 | + | 2.63330i | −0.0413362 | + | 0.00327525i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 116.734i | − | 0.144831i | ||||||
\(807\) | 749.583 | − | 59.3927i | 0.928851 | − | 0.0735969i | ||||
\(808\) | − | 220.497i | − | 0.272892i | ||||||
\(809\) | 48.7456i | 0.0602541i | 0.999546 | + | 0.0301271i | \(0.00959119\pi\) | ||||
−0.999546 | + | 0.0301271i | \(0.990409\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −154.380 | −0.190357 | −0.0951786 | − | 0.995460i | \(-0.530342\pi\) | ||||
−0.0951786 | + | 0.995460i | \(0.530342\pi\) | |||||||
\(812\) | 79.9337 | 0.0984405 | ||||||||
\(813\) | −64.9427 | − | 819.627i | −0.0798803 | − | 1.00815i | ||||
\(814\) | 501.504 | 0.616099 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.90288 | + | 61.8782i | 0.00600844 | + | 0.0758311i | ||||
\(817\) | 195.717i | 0.239556i | ||||||||
\(818\) | 931.688 | 1.13898 | ||||||||
\(819\) | 148.870 | − | 23.7404i | 0.181771 | − | 0.0289870i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 882.281i | − | 1.07464i | −0.843378 | − | 0.537321i | \(-0.819436\pi\) | ||
0.843378 | − | 0.537321i | \(-0.180564\pi\) | |||||||
\(822\) | 62.8121 | + | 792.738i | 0.0764138 | + | 0.964402i | ||||
\(823\) | − | 342.633i | − | 0.416323i | −0.978095 | − | 0.208161i | \(-0.933252\pi\) | ||
0.978095 | − | 0.208161i | \(-0.0667479\pi\) | |||||||
\(824\) | 48.1516i | 0.0584364i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.998277 | −0.00120857 | ||||||||
\(827\) | −380.344 | −0.459908 | −0.229954 | − | 0.973202i | \(-0.573858\pi\) | ||||
−0.229954 | + | 0.973202i | \(0.573858\pi\) | |||||||
\(828\) | −271.216 | + | 43.2509i | −0.327556 | + | 0.0522353i | ||||
\(829\) | 273.732 | 0.330196 | 0.165098 | − | 0.986277i | \(-0.447206\pi\) | ||||
0.165098 | + | 0.986277i | \(0.447206\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −623.259 | + | 49.3835i | −0.750010 | + | 0.0594266i | ||||
\(832\) | − | 50.6478i | − | 0.0608747i | ||||||
\(833\) | 36.2088 | 0.0434679 | ||||||||
\(834\) | 66.8304 | + | 843.452i | 0.0801324 | + | 1.01133i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 203.583i | − | 0.243520i | ||||||
\(837\) | −82.7223 | − | 342.168i | −0.0988320 | − | 0.408803i | ||||
\(838\) | 706.463i | 0.843034i | ||||||||
\(839\) | − | 1377.92i | − | 1.64234i | −0.570683 | − | 0.821171i | \(-0.693321\pi\) | ||
0.570683 | − | 0.821171i | \(-0.306679\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 612.807 | 0.728665 | ||||||||
\(842\) | 455.453 | 0.540918 | ||||||||
\(843\) | 717.264 | − | 56.8320i | 0.850847 | − | 0.0674164i | ||||
\(844\) | 230.164 | 0.272707 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −126.153 | + | 20.1175i | −0.149116 | + | 0.0237796i | ||||
\(847\) | − | 61.1210i | − | 0.0721618i | ||||||
\(848\) | 289.004 | 0.340806 | ||||||||
\(849\) | −915.809 | + | 72.5636i | −1.07869 | + | 0.0854695i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 546.850i | 0.642597i | ||||||||
\(852\) | 834.756 | − | 66.1414i | 0.979761 | − | 0.0776308i | ||||
\(853\) | − | 580.625i | − | 0.680685i | −0.940301 | − | 0.340343i | \(-0.889457\pi\) | ||
0.940301 | − | 0.340343i | \(-0.110543\pi\) | |||||||
\(854\) | − | 66.0874i | − | 0.0773857i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −536.126 | −0.626316 | ||||||||
\(857\) | −714.979 | −0.834281 | −0.417141 | − | 0.908842i | \(-0.636968\pi\) | ||||
−0.417141 | + | 0.908842i | \(0.636968\pi\) | |||||||
\(858\) | 20.9918 | + | 264.933i | 0.0244659 | + | 0.308779i | ||||
\(859\) | 975.849 | 1.13603 | 0.568015 | − | 0.823019i | \(-0.307712\pi\) | ||||
0.568015 | + | 0.823019i | \(0.307712\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −39.5395 | − | 499.019i | −0.0459227 | − | 0.579581i | ||||
\(862\) | − | 265.888i | − | 0.308455i | ||||||
\(863\) | −485.722 | −0.562830 | −0.281415 | − | 0.959586i | \(-0.590804\pi\) | ||||
−0.281415 | + | 0.959586i | \(0.590804\pi\) | |||||||
\(864\) | −35.8911 | − | 148.458i | −0.0415406 | − | 0.171827i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 637.614i | − | 0.736275i | ||||||
\(867\) | 62.1413 | + | 784.272i | 0.0716740 | + | 0.904581i | ||||
\(868\) | 68.9906i | 0.0794823i | ||||||||
\(869\) | − | 28.8791i | − | 0.0332326i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −35.1775 | −0.0403874 | ||||||||
\(872\) | −218.013 | −0.250014 | ||||||||
\(873\) | −237.450 | − | 1489.00i | −0.271994 | − | 1.70561i | ||||
\(874\) | 221.991 | 0.253994 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −196.110 | + | 15.5387i | −0.223870 | + | 0.0177382i | ||||
\(877\) | − | 499.530i | − | 0.569589i | −0.958589 | − | 0.284795i | \(-0.908075\pi\) | ||
0.958589 | − | 0.284795i | \(-0.0919254\pi\) | |||||||
\(878\) | −36.3068 | −0.0413517 | ||||||||
\(879\) | 96.9540 | + | 1223.64i | 0.110300 | + | 1.39208i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 74.9416i | 0.0850643i | 0.999095 | + | 0.0425321i | \(0.0135425\pi\) | ||||
−0.999095 | + | 0.0425321i | \(0.986458\pi\) | |||||||
\(882\) | −87.9837 | + | 14.0308i | −0.0997548 | + | 0.0159079i | ||||
\(883\) | 493.010i | 0.558335i | 0.960242 | + | 0.279168i | \(0.0900585\pi\) | ||||
−0.960242 | + | 0.279168i | \(0.909941\pi\) | |||||||
\(884\) | 65.4962i | 0.0740907i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 181.886 | 0.205289 | ||||||||
\(887\) | 1423.57 | 1.60492 | 0.802461 | − | 0.596705i | \(-0.203524\pi\) | ||||
0.802461 | + | 0.596705i | \(0.203524\pi\) | |||||||
\(888\) | −303.165 | + | 24.0211i | −0.341402 | + | 0.0270508i | ||||
\(889\) | −341.247 | −0.383855 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 249.273 | + | 761.692i | 0.279768 | + | 0.854873i | ||||
\(892\) | 609.840i | 0.683677i | ||||||||
\(893\) | 103.256 | 0.115628 | ||||||||
\(894\) | −756.507 | + | 59.9414i | −0.846205 | + | 0.0670485i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 29.9333i | 0.0334077i | ||||||||
\(897\) | −288.888 | + | 22.8898i | −0.322060 | + | 0.0255182i | ||||
\(898\) | − | 1055.23i | − | 1.17509i | ||||||
\(899\) | − | 196.953i | − | 0.219080i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −373.731 | −0.414796 | ||||||||
\(902\) | 882.488 | 0.978368 | ||||||||
\(903\) | 11.9270 | + | 150.528i | 0.0132082 | + | 0.166697i | ||||
\(904\) | 62.9789 | 0.0696669 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 79.7490 | + | 1006.50i | 0.0880232 | + | 1.11092i | ||||
\(907\) | 1109.55i | 1.22331i | 0.791123 | + | 0.611657i | \(0.209497\pi\) | ||||
−0.791123 | + | 0.611657i | \(0.790503\pi\) | |||||||
\(908\) | −410.866 | −0.452495 | ||||||||
\(909\) | −110.491 | − | 692.862i | −0.121552 | − | 0.762225i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 201.238i | 0.220898i | 0.993882 | + | 0.110449i | \(0.0352288\pi\) | ||||
−0.993882 | + | 0.110449i | \(0.964771\pi\) | |||||||
\(912\) | 9.75123 | + | 123.068i | 0.0106921 | + | 0.134943i | ||||
\(913\) | − | 875.678i | − | 0.959122i | ||||||
\(914\) | − | 1218.54i | − | 1.33319i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 627.190 | 0.684706 | ||||||||
\(917\) | 102.338 | 0.111601 | ||||||||
\(918\) | 46.4133 | + | 191.982i | 0.0505592 | + | 0.209130i | ||||
\(919\) | 267.388 | 0.290956 | 0.145478 | − | 0.989362i | \(-0.453528\pi\) | ||||
0.145478 | + | 0.989362i | \(0.453528\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 182.454 | − | 14.4566i | 0.198104 | − | 0.0156966i | ||||
\(922\) | 168.693i | 0.182964i | ||||||||
\(923\) | 883.563 | 0.957273 | ||||||||
\(924\) | −12.4063 | − | 156.577i | −0.0134268 | − | 0.169456i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 1152.82i | − | 1.24494i | ||||||
\(927\) | 24.1287 | + | 151.306i | 0.0260288 | + | 0.163221i | ||||
\(928\) | − | 85.4527i | − | 0.0920827i | ||||||
\(929\) | 599.465i | 0.645280i | 0.946522 | + | 0.322640i | \(0.104570\pi\) | ||||
−0.946522 | + | 0.322640i | \(0.895430\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 72.0148 | 0.0773521 | ||||||||
\(932\) | −505.659 | −0.542552 | ||||||||
\(933\) | −993.198 | + | 78.6954i | −1.06452 | + | 0.0843466i | ||||
\(934\) | −560.439 | −0.600041 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −25.3795 | − | 159.149i | −0.0271149 | − | 0.170031i | ||||
\(937\) | 804.479i | 0.858569i | 0.903169 | + | 0.429285i | \(0.141234\pi\) | ||||
−0.903169 | + | 0.429285i | \(0.858766\pi\) | |||||||
\(938\) | 20.7902 | 0.0221644 | ||||||||
\(939\) | −806.518 | + | 63.9040i | −0.858912 | + | 0.0680553i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 832.160i | − | 0.884336i | −0.896932 | − | 0.442168i | \(-0.854209\pi\) | ||
0.896932 | − | 0.442168i | \(-0.145791\pi\) | |||||||
\(942\) | −903.149 | + | 71.5605i | −0.958757 | + | 0.0759666i | ||||
\(943\) | 962.282i | 1.02045i | ||||||||
\(944\) | 1.06720i | 0.00113051i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −266.200 | −0.281395 | ||||||||
\(947\) | 293.644 | 0.310078 | 0.155039 | − | 0.987908i | \(-0.450450\pi\) | ||||
0.155039 | + | 0.987908i | \(0.450450\pi\) | |||||||
\(948\) | 1.38325 | + | 17.4577i | 0.00145913 | + | 0.0184153i | ||||
\(949\) | −207.577 | −0.218732 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −52.4237 | − | 661.628i | −0.0551248 | − | 0.695718i | ||||
\(952\) | − | 38.7088i | − | 0.0406605i | ||||||
\(953\) | 1309.64 | 1.37422 | 0.687112 | − | 0.726551i | \(-0.258878\pi\) | ||||
0.687112 | + | 0.726551i | \(0.258878\pi\) | |||||||
\(954\) | 908.130 | − | 144.819i | 0.951918 | − | 0.151802i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 395.301i | 0.413495i | ||||||||
\(957\) | 35.4172 | + | 446.993i | 0.0370086 | + | 0.467078i | ||||
\(958\) | − | 1071.02i | − | 1.11797i | ||||||
\(959\) | − | 495.908i | − | 0.517110i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −791.011 | −0.823112 | ||||||||
\(962\) | −320.891 | −0.333566 | ||||||||
\(963\) | −1684.66 | + | 268.652i | −1.74938 | + | 0.278974i | ||||
\(964\) | −661.659 | −0.686368 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 170.735 | − | 13.5281i | 0.176744 | − | 0.0140042i | ||||
\(967\) | − | 1512.04i | − | 1.56364i | −0.623503 | − | 0.781821i | \(-0.714291\pi\) | ||
0.623503 | − | 0.781821i | \(-0.285709\pi\) | |||||||
\(968\) | −65.3411 | −0.0675011 | ||||||||
\(969\) | −12.6100 | − | 159.148i | −0.0130134 | − | 0.164239i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1169.63i | − | 1.20456i | −0.798283 | − | 0.602282i | \(-0.794258\pi\) | ||
0.798283 | − | 0.602282i | \(-0.205742\pi\) | |||||||
\(972\) | −187.172 | − | 448.512i | −0.192564 | − | 0.461432i | ||||
\(973\) | − | 527.633i | − | 0.542274i | ||||||
\(974\) | 404.742i | 0.415547i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −70.6504 | −0.0723877 | ||||||||
\(977\) | 497.435 | 0.509145 | 0.254573 | − | 0.967054i | \(-0.418065\pi\) | ||||
0.254573 | + | 0.967054i | \(0.418065\pi\) | |||||||
\(978\) | 288.453 | − | 22.8554i | 0.294942 | − | 0.0233695i | ||||
\(979\) | 1450.02 | 1.48112 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −685.056 | + | 109.246i | −0.698324 | + | 0.111362i | ||||
\(982\) | − | 1167.22i | − | 1.18861i | ||||||
\(983\) | −634.120 | −0.645087 | −0.322543 | − | 0.946555i | \(-0.604538\pi\) | ||||
−0.322543 | + | 0.946555i | \(0.604538\pi\) | |||||||
\(984\) | −533.474 | + | 42.2695i | −0.542148 | + | 0.0429568i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 110.505i | 0.112074i | ||||||||
\(987\) | 79.4151 | − | 6.29240i | 0.0804611 | − | 0.00637528i | ||||
\(988\) | 130.264i | 0.131846i | ||||||||
\(989\) | − | 290.270i | − | 0.293498i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1453.55 | −1.46675 | −0.733375 | − | 0.679824i | \(-0.762056\pi\) | ||||
−0.733375 | + | 0.679824i | \(0.762056\pi\) | |||||||
\(992\) | 73.7540 | 0.0743488 | ||||||||
\(993\) | −35.7966 | − | 451.781i | −0.0360489 | − | 0.454965i | ||||
\(994\) | −522.194 | −0.525346 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 41.9433 | + | 529.357i | 0.0421118 | + | 0.531483i | ||||
\(997\) | − | 1390.83i | − | 1.39501i | −0.716579 | − | 0.697506i | \(-0.754293\pi\) | ||
0.716579 | − | 0.697506i | \(-0.245707\pi\) | |||||||
\(998\) | 543.559 | 0.544649 | ||||||||
\(999\) | −940.591 | + | 227.396i | −0.941533 | + | 0.227624i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1050.3.c.b.449.7 | 32 | ||
3.2 | odd | 2 | inner | 1050.3.c.b.449.25 | 32 | ||
5.2 | odd | 4 | 1050.3.e.b.701.1 | ✓ | 16 | ||
5.3 | odd | 4 | 1050.3.e.c.701.16 | yes | 16 | ||
5.4 | even | 2 | inner | 1050.3.c.b.449.26 | 32 | ||
15.2 | even | 4 | 1050.3.e.b.701.9 | yes | 16 | ||
15.8 | even | 4 | 1050.3.e.c.701.8 | yes | 16 | ||
15.14 | odd | 2 | inner | 1050.3.c.b.449.8 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.3.c.b.449.7 | 32 | 1.1 | even | 1 | trivial | ||
1050.3.c.b.449.8 | 32 | 15.14 | odd | 2 | inner | ||
1050.3.c.b.449.25 | 32 | 3.2 | odd | 2 | inner | ||
1050.3.c.b.449.26 | 32 | 5.4 | even | 2 | inner | ||
1050.3.e.b.701.1 | ✓ | 16 | 5.2 | odd | 4 | ||
1050.3.e.b.701.9 | yes | 16 | 15.2 | even | 4 | ||
1050.3.e.c.701.8 | yes | 16 | 15.8 | even | 4 | ||
1050.3.e.c.701.16 | yes | 16 | 5.3 | odd | 4 |