Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2013,2,Mod(1,2013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2013, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2013 = 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2013.a (trivial) |
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: | yes |
Analytic conductor: | \(16.0738859269\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 4 x^{12} - 11 x^{11} + 57 x^{10} + 28 x^{9} - 290 x^{8} + 51 x^{7} + 644 x^{6} - 259 x^{5} - 640 x^{4} + 274 x^{3} + 256 x^{2} - 74 x - 35 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.33467\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2013.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.33467 | −1.65086 | −0.825431 | − | 0.564503i | \(-0.809068\pi\) | ||||
−0.825431 | + | 0.564503i | \(0.809068\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 3.45069 | 1.72534 | ||||||||
\(5\) | 0.0293558 | 0.0131283 | 0.00656416 | − | 0.999978i | \(-0.497911\pi\) | ||||
0.00656416 | + | 0.999978i | \(0.497911\pi\) | |||||||
\(6\) | −2.33467 | −0.953125 | ||||||||
\(7\) | −2.70286 | −1.02159 | −0.510793 | − | 0.859703i | \(-0.670648\pi\) | ||||
−0.510793 | + | 0.859703i | \(0.670648\pi\) | |||||||
\(8\) | −3.38688 | −1.19744 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.0685361 | −0.0216730 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 3.45069 | 0.996128 | ||||||||
\(13\) | 2.89225 | 0.802167 | 0.401084 | − | 0.916041i | \(-0.368634\pi\) | ||||
0.401084 | + | 0.916041i | \(0.368634\pi\) | |||||||
\(14\) | 6.31030 | 1.68650 | ||||||||
\(15\) | 0.0293558 | 0.00757963 | ||||||||
\(16\) | 1.00587 | 0.251467 | ||||||||
\(17\) | 7.17621 | 1.74049 | 0.870243 | − | 0.492623i | \(-0.163962\pi\) | ||||
0.870243 | + | 0.492623i | \(0.163962\pi\) | |||||||
\(18\) | −2.33467 | −0.550287 | ||||||||
\(19\) | 4.17563 | 0.957956 | 0.478978 | − | 0.877827i | \(-0.341007\pi\) | ||||
0.478978 | + | 0.877827i | \(0.341007\pi\) | |||||||
\(20\) | 0.101298 | 0.0226508 | ||||||||
\(21\) | −2.70286 | −0.589813 | ||||||||
\(22\) | −2.33467 | −0.497753 | ||||||||
\(23\) | −2.06467 | −0.430513 | −0.215256 | − | 0.976558i | \(-0.569059\pi\) | ||||
−0.215256 | + | 0.976558i | \(0.569059\pi\) | |||||||
\(24\) | −3.38688 | −0.691343 | ||||||||
\(25\) | −4.99914 | −0.999828 | ||||||||
\(26\) | −6.75246 | −1.32427 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −9.32674 | −1.76259 | ||||||||
\(29\) | 4.39436 | 0.816012 | 0.408006 | − | 0.912979i | \(-0.366224\pi\) | ||||
0.408006 | + | 0.912979i | \(0.366224\pi\) | |||||||
\(30\) | −0.0685361 | −0.0125129 | ||||||||
\(31\) | −4.71288 | −0.846457 | −0.423229 | − | 0.906023i | \(-0.639103\pi\) | ||||
−0.423229 | + | 0.906023i | \(0.639103\pi\) | |||||||
\(32\) | 4.42539 | 0.782305 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | −16.7541 | −2.87330 | ||||||||
\(35\) | −0.0793448 | −0.0134117 | ||||||||
\(36\) | 3.45069 | 0.575114 | ||||||||
\(37\) | −2.29994 | −0.378108 | −0.189054 | − | 0.981967i | \(-0.560542\pi\) | ||||
−0.189054 | + | 0.981967i | \(0.560542\pi\) | |||||||
\(38\) | −9.74873 | −1.58145 | ||||||||
\(39\) | 2.89225 | 0.463131 | ||||||||
\(40\) | −0.0994245 | −0.0157204 | ||||||||
\(41\) | −2.67070 | −0.417094 | −0.208547 | − | 0.978012i | \(-0.566873\pi\) | ||||
−0.208547 | + | 0.978012i | \(0.566873\pi\) | |||||||
\(42\) | 6.31030 | 0.973700 | ||||||||
\(43\) | −8.92207 | −1.36060 | −0.680301 | − | 0.732932i | \(-0.738151\pi\) | ||||
−0.680301 | + | 0.732932i | \(0.738151\pi\) | |||||||
\(44\) | 3.45069 | 0.520211 | ||||||||
\(45\) | 0.0293558 | 0.00437610 | ||||||||
\(46\) | 4.82032 | 0.710717 | ||||||||
\(47\) | 10.7872 | 1.57348 | 0.786738 | − | 0.617287i | \(-0.211768\pi\) | ||||
0.786738 | + | 0.617287i | \(0.211768\pi\) | |||||||
\(48\) | 1.00587 | 0.145184 | ||||||||
\(49\) | 0.305477 | 0.0436396 | ||||||||
\(50\) | 11.6713 | 1.65058 | ||||||||
\(51\) | 7.17621 | 1.00487 | ||||||||
\(52\) | 9.98027 | 1.38401 | ||||||||
\(53\) | −4.86692 | −0.668523 | −0.334261 | − | 0.942480i | \(-0.608487\pi\) | ||||
−0.334261 | + | 0.942480i | \(0.608487\pi\) | |||||||
\(54\) | −2.33467 | −0.317708 | ||||||||
\(55\) | 0.0293558 | 0.00395834 | ||||||||
\(56\) | 9.15427 | 1.22329 | ||||||||
\(57\) | 4.17563 | 0.553076 | ||||||||
\(58\) | −10.2594 | −1.34712 | ||||||||
\(59\) | −0.181028 | −0.0235678 | −0.0117839 | − | 0.999931i | \(-0.503751\pi\) | ||||
−0.0117839 | + | 0.999931i | \(0.503751\pi\) | |||||||
\(60\) | 0.101298 | 0.0130775 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | 11.0030 | 1.39738 | ||||||||
\(63\) | −2.70286 | −0.340529 | ||||||||
\(64\) | −12.3436 | −1.54294 | ||||||||
\(65\) | 0.0849045 | 0.0105311 | ||||||||
\(66\) | −2.33467 | −0.287378 | ||||||||
\(67\) | 14.4055 | 1.75991 | 0.879955 | − | 0.475057i | \(-0.157573\pi\) | ||||
0.879955 | + | 0.475057i | \(0.157573\pi\) | |||||||
\(68\) | 24.7628 | 3.00294 | ||||||||
\(69\) | −2.06467 | −0.248557 | ||||||||
\(70\) | 0.185244 | 0.0221409 | ||||||||
\(71\) | 4.73226 | 0.561616 | 0.280808 | − | 0.959764i | \(-0.409398\pi\) | ||||
0.280808 | + | 0.959764i | \(0.409398\pi\) | |||||||
\(72\) | −3.38688 | −0.399147 | ||||||||
\(73\) | 7.51871 | 0.879999 | 0.439999 | − | 0.897998i | \(-0.354979\pi\) | ||||
0.439999 | + | 0.897998i | \(0.354979\pi\) | |||||||
\(74\) | 5.36960 | 0.624204 | ||||||||
\(75\) | −4.99914 | −0.577251 | ||||||||
\(76\) | 14.4088 | 1.65280 | ||||||||
\(77\) | −2.70286 | −0.308020 | ||||||||
\(78\) | −6.75246 | −0.764566 | ||||||||
\(79\) | 11.1725 | 1.25701 | 0.628503 | − | 0.777807i | \(-0.283668\pi\) | ||||
0.628503 | + | 0.777807i | \(0.283668\pi\) | |||||||
\(80\) | 0.0295280 | 0.00330133 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 6.23522 | 0.688564 | ||||||||
\(83\) | 12.9734 | 1.42402 | 0.712008 | − | 0.702171i | \(-0.247786\pi\) | ||||
0.712008 | + | 0.702171i | \(0.247786\pi\) | |||||||
\(84\) | −9.32674 | −1.01763 | ||||||||
\(85\) | 0.210663 | 0.0228496 | ||||||||
\(86\) | 20.8301 | 2.24617 | ||||||||
\(87\) | 4.39436 | 0.471125 | ||||||||
\(88\) | −3.38688 | −0.361042 | ||||||||
\(89\) | −10.1884 | −1.07997 | −0.539983 | − | 0.841676i | \(-0.681569\pi\) | ||||
−0.539983 | + | 0.841676i | \(0.681569\pi\) | |||||||
\(90\) | −0.0685361 | −0.00722434 | ||||||||
\(91\) | −7.81737 | −0.819483 | ||||||||
\(92\) | −7.12452 | −0.742783 | ||||||||
\(93\) | −4.71288 | −0.488702 | ||||||||
\(94\) | −25.1846 | −2.59759 | ||||||||
\(95\) | 0.122579 | 0.0125763 | ||||||||
\(96\) | 4.42539 | 0.451664 | ||||||||
\(97\) | −16.7207 | −1.69773 | −0.848867 | − | 0.528606i | \(-0.822715\pi\) | ||||
−0.848867 | + | 0.528606i | \(0.822715\pi\) | |||||||
\(98\) | −0.713188 | −0.0720429 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −17.2505 | −1.72505 | ||||||||
\(101\) | 1.97502 | 0.196522 | 0.0982610 | − | 0.995161i | \(-0.468672\pi\) | ||||
0.0982610 | + | 0.995161i | \(0.468672\pi\) | |||||||
\(102\) | −16.7541 | −1.65890 | ||||||||
\(103\) | 8.68750 | 0.856005 | 0.428003 | − | 0.903777i | \(-0.359217\pi\) | ||||
0.428003 | + | 0.903777i | \(0.359217\pi\) | |||||||
\(104\) | −9.79571 | −0.960548 | ||||||||
\(105\) | −0.0793448 | −0.00774325 | ||||||||
\(106\) | 11.3627 | 1.10364 | ||||||||
\(107\) | −6.12215 | −0.591851 | −0.295925 | − | 0.955211i | \(-0.595628\pi\) | ||||
−0.295925 | + | 0.955211i | \(0.595628\pi\) | |||||||
\(108\) | 3.45069 | 0.332043 | ||||||||
\(109\) | −3.59659 | −0.344491 | −0.172245 | − | 0.985054i | \(-0.555102\pi\) | ||||
−0.172245 | + | 0.985054i | \(0.555102\pi\) | |||||||
\(110\) | −0.0685361 | −0.00653466 | ||||||||
\(111\) | −2.29994 | −0.218301 | ||||||||
\(112\) | −2.71872 | −0.256895 | ||||||||
\(113\) | 6.81766 | 0.641352 | 0.320676 | − | 0.947189i | \(-0.396090\pi\) | ||||
0.320676 | + | 0.947189i | \(0.396090\pi\) | |||||||
\(114\) | −9.74873 | −0.913052 | ||||||||
\(115\) | −0.0606100 | −0.00565191 | ||||||||
\(116\) | 15.1636 | 1.40790 | ||||||||
\(117\) | 2.89225 | 0.267389 | ||||||||
\(118\) | 0.422640 | 0.0389072 | ||||||||
\(119\) | −19.3963 | −1.77806 | ||||||||
\(120\) | −0.0994245 | −0.00907617 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −2.33467 | −0.211371 | ||||||||
\(123\) | −2.67070 | −0.240809 | ||||||||
\(124\) | −16.2627 | −1.46043 | ||||||||
\(125\) | −0.293533 | −0.0262544 | ||||||||
\(126\) | 6.31030 | 0.562166 | ||||||||
\(127\) | 5.40526 | 0.479639 | 0.239819 | − | 0.970817i | \(-0.422912\pi\) | ||||
0.239819 | + | 0.970817i | \(0.422912\pi\) | |||||||
\(128\) | 19.9674 | 1.76488 | ||||||||
\(129\) | −8.92207 | −0.785544 | ||||||||
\(130\) | −0.198224 | −0.0173854 | ||||||||
\(131\) | 19.3818 | 1.69340 | 0.846698 | − | 0.532075i | \(-0.178587\pi\) | ||||
0.846698 | + | 0.532075i | \(0.178587\pi\) | |||||||
\(132\) | 3.45069 | 0.300344 | ||||||||
\(133\) | −11.2862 | −0.978635 | ||||||||
\(134\) | −33.6321 | −2.90537 | ||||||||
\(135\) | 0.0293558 | 0.00252654 | ||||||||
\(136\) | −24.3049 | −2.08413 | ||||||||
\(137\) | 15.7164 | 1.34275 | 0.671373 | − | 0.741119i | \(-0.265705\pi\) | ||||
0.671373 | + | 0.741119i | \(0.265705\pi\) | |||||||
\(138\) | 4.82032 | 0.410333 | ||||||||
\(139\) | 1.57642 | 0.133711 | 0.0668553 | − | 0.997763i | \(-0.478703\pi\) | ||||
0.0668553 | + | 0.997763i | \(0.478703\pi\) | |||||||
\(140\) | −0.273794 | −0.0231398 | ||||||||
\(141\) | 10.7872 | 0.908447 | ||||||||
\(142\) | −11.0483 | −0.927150 | ||||||||
\(143\) | 2.89225 | 0.241862 | ||||||||
\(144\) | 1.00587 | 0.0838222 | ||||||||
\(145\) | 0.129000 | 0.0107129 | ||||||||
\(146\) | −17.5537 | −1.45276 | ||||||||
\(147\) | 0.305477 | 0.0251953 | ||||||||
\(148\) | −7.93637 | −0.652366 | ||||||||
\(149\) | 1.10490 | 0.0905172 | 0.0452586 | − | 0.998975i | \(-0.485589\pi\) | ||||
0.0452586 | + | 0.998975i | \(0.485589\pi\) | |||||||
\(150\) | 11.6713 | 0.952961 | ||||||||
\(151\) | −15.0032 | −1.22095 | −0.610473 | − | 0.792037i | \(-0.709021\pi\) | ||||
−0.610473 | + | 0.792037i | \(0.709021\pi\) | |||||||
\(152\) | −14.1424 | −1.14710 | ||||||||
\(153\) | 7.17621 | 0.580162 | ||||||||
\(154\) | 6.31030 | 0.508498 | ||||||||
\(155\) | −0.138350 | −0.0111126 | ||||||||
\(156\) | 9.98027 | 0.799061 | ||||||||
\(157\) | −9.75971 | −0.778910 | −0.389455 | − | 0.921046i | \(-0.627337\pi\) | ||||
−0.389455 | + | 0.921046i | \(0.627337\pi\) | |||||||
\(158\) | −26.0842 | −2.07514 | ||||||||
\(159\) | −4.86692 | −0.385972 | ||||||||
\(160\) | 0.129911 | 0.0102703 | ||||||||
\(161\) | 5.58052 | 0.439806 | ||||||||
\(162\) | −2.33467 | −0.183429 | ||||||||
\(163\) | 21.3224 | 1.67010 | 0.835050 | − | 0.550174i | \(-0.185439\pi\) | ||||
0.835050 | + | 0.550174i | \(0.185439\pi\) | |||||||
\(164\) | −9.21577 | −0.719630 | ||||||||
\(165\) | 0.0293558 | 0.00228535 | ||||||||
\(166\) | −30.2886 | −2.35085 | ||||||||
\(167\) | 19.0985 | 1.47789 | 0.738943 | − | 0.673768i | \(-0.235325\pi\) | ||||
0.738943 | + | 0.673768i | \(0.235325\pi\) | |||||||
\(168\) | 9.15427 | 0.706267 | ||||||||
\(169\) | −4.63486 | −0.356528 | ||||||||
\(170\) | −0.491829 | −0.0377216 | ||||||||
\(171\) | 4.17563 | 0.319319 | ||||||||
\(172\) | −30.7873 | −2.34751 | ||||||||
\(173\) | −17.4746 | −1.32857 | −0.664285 | − | 0.747479i | \(-0.731264\pi\) | ||||
−0.664285 | + | 0.747479i | \(0.731264\pi\) | |||||||
\(174\) | −10.2594 | −0.777762 | ||||||||
\(175\) | 13.5120 | 1.02141 | ||||||||
\(176\) | 1.00587 | 0.0758200 | ||||||||
\(177\) | −0.181028 | −0.0136069 | ||||||||
\(178\) | 23.7865 | 1.78288 | ||||||||
\(179\) | 15.9382 | 1.19127 | 0.595637 | − | 0.803253i | \(-0.296900\pi\) | ||||
0.595637 | + | 0.803253i | \(0.296900\pi\) | |||||||
\(180\) | 0.101298 | 0.00755028 | ||||||||
\(181\) | 7.41273 | 0.550984 | 0.275492 | − | 0.961303i | \(-0.411159\pi\) | ||||
0.275492 | + | 0.961303i | \(0.411159\pi\) | |||||||
\(182\) | 18.2510 | 1.35285 | ||||||||
\(183\) | 1.00000 | 0.0739221 | ||||||||
\(184\) | 6.99277 | 0.515514 | ||||||||
\(185\) | −0.0675166 | −0.00496392 | ||||||||
\(186\) | 11.0030 | 0.806780 | ||||||||
\(187\) | 7.17621 | 0.524776 | ||||||||
\(188\) | 37.2233 | 2.71479 | ||||||||
\(189\) | −2.70286 | −0.196604 | ||||||||
\(190\) | −0.286182 | −0.0207618 | ||||||||
\(191\) | 11.6075 | 0.839886 | 0.419943 | − | 0.907550i | \(-0.362050\pi\) | ||||
0.419943 | + | 0.907550i | \(0.362050\pi\) | |||||||
\(192\) | −12.3436 | −0.890819 | ||||||||
\(193\) | 20.4885 | 1.47479 | 0.737396 | − | 0.675460i | \(-0.236055\pi\) | ||||
0.737396 | + | 0.675460i | \(0.236055\pi\) | |||||||
\(194\) | 39.0374 | 2.80272 | ||||||||
\(195\) | 0.0849045 | 0.00608013 | ||||||||
\(196\) | 1.05411 | 0.0752933 | ||||||||
\(197\) | 7.27132 | 0.518060 | 0.259030 | − | 0.965869i | \(-0.416597\pi\) | ||||
0.259030 | + | 0.965869i | \(0.416597\pi\) | |||||||
\(198\) | −2.33467 | −0.165918 | ||||||||
\(199\) | −10.0401 | −0.711723 | −0.355862 | − | 0.934539i | \(-0.615813\pi\) | ||||
−0.355862 | + | 0.934539i | \(0.615813\pi\) | |||||||
\(200\) | 16.9315 | 1.19724 | ||||||||
\(201\) | 14.4055 | 1.01608 | ||||||||
\(202\) | −4.61103 | −0.324431 | ||||||||
\(203\) | −11.8774 | −0.833627 | ||||||||
\(204\) | 24.7628 | 1.73375 | ||||||||
\(205\) | −0.0784007 | −0.00547574 | ||||||||
\(206\) | −20.2825 | −1.41315 | ||||||||
\(207\) | −2.06467 | −0.143504 | ||||||||
\(208\) | 2.90922 | 0.201718 | ||||||||
\(209\) | 4.17563 | 0.288835 | ||||||||
\(210\) | 0.185244 | 0.0127830 | ||||||||
\(211\) | −7.36422 | −0.506974 | −0.253487 | − | 0.967339i | \(-0.581577\pi\) | ||||
−0.253487 | + | 0.967339i | \(0.581577\pi\) | |||||||
\(212\) | −16.7942 | −1.15343 | ||||||||
\(213\) | 4.73226 | 0.324249 | ||||||||
\(214\) | 14.2932 | 0.977063 | ||||||||
\(215\) | −0.261915 | −0.0178624 | ||||||||
\(216\) | −3.38688 | −0.230448 | ||||||||
\(217\) | 12.7383 | 0.864730 | ||||||||
\(218\) | 8.39685 | 0.568706 | ||||||||
\(219\) | 7.51871 | 0.508068 | ||||||||
\(220\) | 0.101298 | 0.00682949 | ||||||||
\(221\) | 20.7554 | 1.39616 | ||||||||
\(222\) | 5.36960 | 0.360384 | ||||||||
\(223\) | 1.02663 | 0.0687482 | 0.0343741 | − | 0.999409i | \(-0.489056\pi\) | ||||
0.0343741 | + | 0.999409i | \(0.489056\pi\) | |||||||
\(224\) | −11.9612 | −0.799193 | ||||||||
\(225\) | −4.99914 | −0.333276 | ||||||||
\(226\) | −15.9170 | −1.05878 | ||||||||
\(227\) | 21.6433 | 1.43651 | 0.718257 | − | 0.695778i | \(-0.244940\pi\) | ||||
0.718257 | + | 0.695778i | \(0.244940\pi\) | |||||||
\(228\) | 14.4088 | 0.954246 | ||||||||
\(229\) | 9.88816 | 0.653428 | 0.326714 | − | 0.945123i | \(-0.394059\pi\) | ||||
0.326714 | + | 0.945123i | \(0.394059\pi\) | |||||||
\(230\) | 0.141504 | 0.00933052 | ||||||||
\(231\) | −2.70286 | −0.177835 | ||||||||
\(232\) | −14.8832 | −0.977127 | ||||||||
\(233\) | −24.8039 | −1.62496 | −0.812480 | − | 0.582989i | \(-0.801883\pi\) | ||||
−0.812480 | + | 0.582989i | \(0.801883\pi\) | |||||||
\(234\) | −6.75246 | −0.441422 | ||||||||
\(235\) | 0.316667 | 0.0206571 | ||||||||
\(236\) | −0.624670 | −0.0406626 | ||||||||
\(237\) | 11.1725 | 0.725733 | ||||||||
\(238\) | 45.2840 | 2.93533 | ||||||||
\(239\) | 15.9365 | 1.03084 | 0.515422 | − | 0.856936i | \(-0.327635\pi\) | ||||
0.515422 | + | 0.856936i | \(0.327635\pi\) | |||||||
\(240\) | 0.0295280 | 0.00190602 | ||||||||
\(241\) | −10.6415 | −0.685481 | −0.342740 | − | 0.939430i | \(-0.611355\pi\) | ||||
−0.342740 | + | 0.939430i | \(0.611355\pi\) | |||||||
\(242\) | −2.33467 | −0.150078 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 3.45069 | 0.220908 | ||||||||
\(245\) | 0.00896753 | 0.000572914 0 | ||||||||
\(246\) | 6.23522 | 0.397543 | ||||||||
\(247\) | 12.0770 | 0.768441 | ||||||||
\(248\) | 15.9619 | 1.01358 | ||||||||
\(249\) | 12.9734 | 0.822156 | ||||||||
\(250\) | 0.685302 | 0.0433423 | ||||||||
\(251\) | −24.6375 | −1.55510 | −0.777552 | − | 0.628819i | \(-0.783539\pi\) | ||||
−0.777552 | + | 0.628819i | \(0.783539\pi\) | |||||||
\(252\) | −9.32674 | −0.587529 | ||||||||
\(253\) | −2.06467 | −0.129805 | ||||||||
\(254\) | −12.6195 | −0.791818 | ||||||||
\(255\) | 0.210663 | 0.0131922 | ||||||||
\(256\) | −21.9301 | −1.37063 | ||||||||
\(257\) | 8.56747 | 0.534424 | 0.267212 | − | 0.963638i | \(-0.413898\pi\) | ||||
0.267212 | + | 0.963638i | \(0.413898\pi\) | |||||||
\(258\) | 20.8301 | 1.29683 | ||||||||
\(259\) | 6.21643 | 0.386270 | ||||||||
\(260\) | 0.292979 | 0.0181698 | ||||||||
\(261\) | 4.39436 | 0.272004 | ||||||||
\(262\) | −45.2501 | −2.79556 | ||||||||
\(263\) | −7.12601 | −0.439408 | −0.219704 | − | 0.975567i | \(-0.570509\pi\) | ||||
−0.219704 | + | 0.975567i | \(0.570509\pi\) | |||||||
\(264\) | −3.38688 | −0.208448 | ||||||||
\(265\) | −0.142872 | −0.00877658 | ||||||||
\(266\) | 26.3495 | 1.61559 | ||||||||
\(267\) | −10.1884 | −0.623519 | ||||||||
\(268\) | 49.7088 | 3.03645 | ||||||||
\(269\) | 14.1919 | 0.865295 | 0.432648 | − | 0.901563i | \(-0.357579\pi\) | ||||
0.432648 | + | 0.901563i | \(0.357579\pi\) | |||||||
\(270\) | −0.0685361 | −0.00417098 | ||||||||
\(271\) | 29.2260 | 1.77535 | 0.887677 | − | 0.460466i | \(-0.152318\pi\) | ||||
0.887677 | + | 0.460466i | \(0.152318\pi\) | |||||||
\(272\) | 7.21830 | 0.437674 | ||||||||
\(273\) | −7.81737 | −0.473129 | ||||||||
\(274\) | −36.6927 | −2.21669 | ||||||||
\(275\) | −4.99914 | −0.301459 | ||||||||
\(276\) | −7.12452 | −0.428846 | ||||||||
\(277\) | −13.9600 | −0.838774 | −0.419387 | − | 0.907808i | \(-0.637755\pi\) | ||||
−0.419387 | + | 0.907808i | \(0.637755\pi\) | |||||||
\(278\) | −3.68043 | −0.220738 | ||||||||
\(279\) | −4.71288 | −0.282152 | ||||||||
\(280\) | 0.268731 | 0.0160597 | ||||||||
\(281\) | −5.84690 | −0.348797 | −0.174398 | − | 0.984675i | \(-0.555798\pi\) | ||||
−0.174398 | + | 0.984675i | \(0.555798\pi\) | |||||||
\(282\) | −25.1846 | −1.49972 | ||||||||
\(283\) | 25.6344 | 1.52380 | 0.761902 | − | 0.647692i | \(-0.224266\pi\) | ||||
0.761902 | + | 0.647692i | \(0.224266\pi\) | |||||||
\(284\) | 16.3296 | 0.968981 | ||||||||
\(285\) | 0.122579 | 0.00726096 | ||||||||
\(286\) | −6.75246 | −0.399281 | ||||||||
\(287\) | 7.21855 | 0.426098 | ||||||||
\(288\) | 4.42539 | 0.260768 | ||||||||
\(289\) | 34.4979 | 2.02929 | ||||||||
\(290\) | −0.301172 | −0.0176855 | ||||||||
\(291\) | −16.7207 | −0.980187 | ||||||||
\(292\) | 25.9447 | 1.51830 | ||||||||
\(293\) | 1.56499 | 0.0914279 | 0.0457140 | − | 0.998955i | \(-0.485444\pi\) | ||||
0.0457140 | + | 0.998955i | \(0.485444\pi\) | |||||||
\(294\) | −0.713188 | −0.0415940 | ||||||||
\(295\) | −0.00531422 | −0.000309406 0 | ||||||||
\(296\) | 7.78961 | 0.452762 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | −2.57959 | −0.149431 | ||||||||
\(299\) | −5.97154 | −0.345343 | ||||||||
\(300\) | −17.2505 | −0.995956 | ||||||||
\(301\) | 24.1151 | 1.38997 | ||||||||
\(302\) | 35.0276 | 2.01561 | ||||||||
\(303\) | 1.97502 | 0.113462 | ||||||||
\(304\) | 4.20013 | 0.240894 | ||||||||
\(305\) | 0.0293558 | 0.00168091 | ||||||||
\(306\) | −16.7541 | −0.957767 | ||||||||
\(307\) | 8.60524 | 0.491127 | 0.245563 | − | 0.969381i | \(-0.421027\pi\) | ||||
0.245563 | + | 0.969381i | \(0.421027\pi\) | |||||||
\(308\) | −9.32674 | −0.531440 | ||||||||
\(309\) | 8.68750 | 0.494215 | ||||||||
\(310\) | 0.323002 | 0.0183453 | ||||||||
\(311\) | −31.7733 | −1.80170 | −0.900850 | − | 0.434130i | \(-0.857056\pi\) | ||||
−0.900850 | + | 0.434130i | \(0.857056\pi\) | |||||||
\(312\) | −9.79571 | −0.554573 | ||||||||
\(313\) | 26.8892 | 1.51987 | 0.759934 | − | 0.650000i | \(-0.225231\pi\) | ||||
0.759934 | + | 0.650000i | \(0.225231\pi\) | |||||||
\(314\) | 22.7857 | 1.28587 | ||||||||
\(315\) | −0.0793448 | −0.00447057 | ||||||||
\(316\) | 38.5529 | 2.16877 | ||||||||
\(317\) | −21.6911 | −1.21830 | −0.609148 | − | 0.793057i | \(-0.708488\pi\) | ||||
−0.609148 | + | 0.793057i | \(0.708488\pi\) | |||||||
\(318\) | 11.3627 | 0.637186 | ||||||||
\(319\) | 4.39436 | 0.246037 | ||||||||
\(320\) | −0.362355 | −0.0202562 | ||||||||
\(321\) | −6.12215 | −0.341705 | ||||||||
\(322\) | −13.0287 | −0.726059 | ||||||||
\(323\) | 29.9652 | 1.66731 | ||||||||
\(324\) | 3.45069 | 0.191705 | ||||||||
\(325\) | −14.4588 | −0.802029 | ||||||||
\(326\) | −49.7808 | −2.75710 | ||||||||
\(327\) | −3.59659 | −0.198892 | ||||||||
\(328\) | 9.04535 | 0.499446 | ||||||||
\(329\) | −29.1564 | −1.60744 | ||||||||
\(330\) | −0.0685361 | −0.00377279 | ||||||||
\(331\) | −3.16662 | −0.174053 | −0.0870265 | − | 0.996206i | \(-0.527736\pi\) | ||||
−0.0870265 | + | 0.996206i | \(0.527736\pi\) | |||||||
\(332\) | 44.7672 | 2.45692 | ||||||||
\(333\) | −2.29994 | −0.126036 | ||||||||
\(334\) | −44.5887 | −2.43979 | ||||||||
\(335\) | 0.422884 | 0.0231046 | ||||||||
\(336\) | −2.71872 | −0.148318 | ||||||||
\(337\) | 29.0756 | 1.58385 | 0.791924 | − | 0.610619i | \(-0.209079\pi\) | ||||
0.791924 | + | 0.610619i | \(0.209079\pi\) | |||||||
\(338\) | 10.8209 | 0.588578 | ||||||||
\(339\) | 6.81766 | 0.370285 | ||||||||
\(340\) | 0.726933 | 0.0394235 | ||||||||
\(341\) | −4.71288 | −0.255217 | ||||||||
\(342\) | −9.74873 | −0.527151 | ||||||||
\(343\) | 18.0944 | 0.977005 | ||||||||
\(344\) | 30.2179 | 1.62924 | ||||||||
\(345\) | −0.0606100 | −0.00326313 | ||||||||
\(346\) | 40.7975 | 2.19329 | ||||||||
\(347\) | −5.76588 | −0.309529 | −0.154764 | − | 0.987951i | \(-0.549462\pi\) | ||||
−0.154764 | + | 0.987951i | \(0.549462\pi\) | |||||||
\(348\) | 15.1636 | 0.812852 | ||||||||
\(349\) | −29.8833 | −1.59961 | −0.799807 | − | 0.600257i | \(-0.795065\pi\) | ||||
−0.799807 | + | 0.600257i | \(0.795065\pi\) | |||||||
\(350\) | −31.5461 | −1.68621 | ||||||||
\(351\) | 2.89225 | 0.154377 | ||||||||
\(352\) | 4.42539 | 0.235874 | ||||||||
\(353\) | 8.68646 | 0.462334 | 0.231167 | − | 0.972914i | \(-0.425746\pi\) | ||||
0.231167 | + | 0.972914i | \(0.425746\pi\) | |||||||
\(354\) | 0.422640 | 0.0224631 | ||||||||
\(355\) | 0.138919 | 0.00737307 | ||||||||
\(356\) | −35.1569 | −1.86331 | ||||||||
\(357\) | −19.3963 | −1.02656 | ||||||||
\(358\) | −37.2104 | −1.96663 | ||||||||
\(359\) | −0.320645 | −0.0169230 | −0.00846150 | − | 0.999964i | \(-0.502693\pi\) | ||||
−0.00846150 | + | 0.999964i | \(0.502693\pi\) | |||||||
\(360\) | −0.0994245 | −0.00524013 | ||||||||
\(361\) | −1.56409 | −0.0823205 | ||||||||
\(362\) | −17.3063 | −0.909598 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | −26.9753 | −1.41389 | ||||||||
\(365\) | 0.220718 | 0.0115529 | ||||||||
\(366\) | −2.33467 | −0.122035 | ||||||||
\(367\) | −14.7522 | −0.770060 | −0.385030 | − | 0.922904i | \(-0.625809\pi\) | ||||
−0.385030 | + | 0.922904i | \(0.625809\pi\) | |||||||
\(368\) | −2.07678 | −0.108260 | ||||||||
\(369\) | −2.67070 | −0.139031 | ||||||||
\(370\) | 0.157629 | 0.00819474 | ||||||||
\(371\) | 13.1546 | 0.682954 | ||||||||
\(372\) | −16.2627 | −0.843180 | ||||||||
\(373\) | −7.54533 | −0.390683 | −0.195341 | − | 0.980735i | \(-0.562581\pi\) | ||||
−0.195341 | + | 0.980735i | \(0.562581\pi\) | |||||||
\(374\) | −16.7541 | −0.866333 | ||||||||
\(375\) | −0.293533 | −0.0151580 | ||||||||
\(376\) | −36.5349 | −1.88415 | ||||||||
\(377\) | 12.7096 | 0.654578 | ||||||||
\(378\) | 6.31030 | 0.324567 | ||||||||
\(379\) | −5.90833 | −0.303491 | −0.151745 | − | 0.988420i | \(-0.548489\pi\) | ||||
−0.151745 | + | 0.988420i | \(0.548489\pi\) | |||||||
\(380\) | 0.422982 | 0.0216985 | ||||||||
\(381\) | 5.40526 | 0.276920 | ||||||||
\(382\) | −27.0996 | −1.38654 | ||||||||
\(383\) | 28.3128 | 1.44672 | 0.723358 | − | 0.690473i | \(-0.242598\pi\) | ||||
0.723358 | + | 0.690473i | \(0.242598\pi\) | |||||||
\(384\) | 19.9674 | 1.01895 | ||||||||
\(385\) | −0.0793448 | −0.00404378 | ||||||||
\(386\) | −47.8338 | −2.43468 | ||||||||
\(387\) | −8.92207 | −0.453534 | ||||||||
\(388\) | −57.6981 | −2.92918 | ||||||||
\(389\) | −16.1105 | −0.816833 | −0.408417 | − | 0.912796i | \(-0.633919\pi\) | ||||
−0.408417 | + | 0.912796i | \(0.633919\pi\) | |||||||
\(390\) | −0.198224 | −0.0100375 | ||||||||
\(391\) | −14.8165 | −0.749302 | ||||||||
\(392\) | −1.03461 | −0.0522559 | ||||||||
\(393\) | 19.3818 | 0.977682 | ||||||||
\(394\) | −16.9761 | −0.855245 | ||||||||
\(395\) | 0.327978 | 0.0165024 | ||||||||
\(396\) | 3.45069 | 0.173404 | ||||||||
\(397\) | −12.9139 | −0.648128 | −0.324064 | − | 0.946035i | \(-0.605049\pi\) | ||||
−0.324064 | + | 0.946035i | \(0.605049\pi\) | |||||||
\(398\) | 23.4403 | 1.17496 | ||||||||
\(399\) | −11.2862 | −0.565015 | ||||||||
\(400\) | −5.02846 | −0.251423 | ||||||||
\(401\) | 21.6181 | 1.07956 | 0.539778 | − | 0.841808i | \(-0.318508\pi\) | ||||
0.539778 | + | 0.841808i | \(0.318508\pi\) | |||||||
\(402\) | −33.6321 | −1.67741 | ||||||||
\(403\) | −13.6308 | −0.679000 | ||||||||
\(404\) | 6.81518 | 0.339068 | ||||||||
\(405\) | 0.0293558 | 0.00145870 | ||||||||
\(406\) | 27.7297 | 1.37620 | ||||||||
\(407\) | −2.29994 | −0.114004 | ||||||||
\(408\) | −24.3049 | −1.20327 | ||||||||
\(409\) | −10.5185 | −0.520108 | −0.260054 | − | 0.965594i | \(-0.583740\pi\) | ||||
−0.260054 | + | 0.965594i | \(0.583740\pi\) | |||||||
\(410\) | 0.183040 | 0.00903969 | ||||||||
\(411\) | 15.7164 | 0.775235 | ||||||||
\(412\) | 29.9779 | 1.47690 | ||||||||
\(413\) | 0.489294 | 0.0240766 | ||||||||
\(414\) | 4.82032 | 0.236906 | ||||||||
\(415\) | 0.380845 | 0.0186949 | ||||||||
\(416\) | 12.7993 | 0.627539 | ||||||||
\(417\) | 1.57642 | 0.0771978 | ||||||||
\(418\) | −9.74873 | −0.476826 | ||||||||
\(419\) | 5.19468 | 0.253777 | 0.126888 | − | 0.991917i | \(-0.459501\pi\) | ||||
0.126888 | + | 0.991917i | \(0.459501\pi\) | |||||||
\(420\) | −0.273794 | −0.0133598 | ||||||||
\(421\) | −22.0265 | −1.07351 | −0.536753 | − | 0.843740i | \(-0.680349\pi\) | ||||
−0.536753 | + | 0.843740i | \(0.680349\pi\) | |||||||
\(422\) | 17.1930 | 0.836943 | ||||||||
\(423\) | 10.7872 | 0.524492 | ||||||||
\(424\) | 16.4837 | 0.800517 | ||||||||
\(425\) | −35.8748 | −1.74019 | ||||||||
\(426\) | −11.0483 | −0.535290 | ||||||||
\(427\) | −2.70286 | −0.130801 | ||||||||
\(428\) | −21.1256 | −1.02115 | ||||||||
\(429\) | 2.89225 | 0.139639 | ||||||||
\(430\) | 0.611484 | 0.0294884 | ||||||||
\(431\) | −0.844284 | −0.0406677 | −0.0203339 | − | 0.999793i | \(-0.506473\pi\) | ||||
−0.0203339 | + | 0.999793i | \(0.506473\pi\) | |||||||
\(432\) | 1.00587 | 0.0483948 | ||||||||
\(433\) | 28.8544 | 1.38665 | 0.693326 | − | 0.720624i | \(-0.256144\pi\) | ||||
0.693326 | + | 0.720624i | \(0.256144\pi\) | |||||||
\(434\) | −29.7397 | −1.42755 | ||||||||
\(435\) | 0.129000 | 0.00618508 | ||||||||
\(436\) | −12.4107 | −0.594365 | ||||||||
\(437\) | −8.62129 | −0.412412 | ||||||||
\(438\) | −17.5537 | −0.838749 | ||||||||
\(439\) | −21.6203 | −1.03188 | −0.515941 | − | 0.856624i | \(-0.672557\pi\) | ||||
−0.515941 | + | 0.856624i | \(0.672557\pi\) | |||||||
\(440\) | −0.0994245 | −0.00473987 | ||||||||
\(441\) | 0.305477 | 0.0145465 | ||||||||
\(442\) | −48.4571 | −2.30487 | ||||||||
\(443\) | −3.90144 | −0.185363 | −0.0926815 | − | 0.995696i | \(-0.529544\pi\) | ||||
−0.0926815 | + | 0.995696i | \(0.529544\pi\) | |||||||
\(444\) | −7.93637 | −0.376644 | ||||||||
\(445\) | −0.299088 | −0.0141781 | ||||||||
\(446\) | −2.39684 | −0.113494 | ||||||||
\(447\) | 1.10490 | 0.0522601 | ||||||||
\(448\) | 33.3629 | 1.57625 | ||||||||
\(449\) | −7.16531 | −0.338152 | −0.169076 | − | 0.985603i | \(-0.554078\pi\) | ||||
−0.169076 | + | 0.985603i | \(0.554078\pi\) | |||||||
\(450\) | 11.6713 | 0.550192 | ||||||||
\(451\) | −2.67070 | −0.125759 | ||||||||
\(452\) | 23.5256 | 1.10655 | ||||||||
\(453\) | −15.0032 | −0.704914 | ||||||||
\(454\) | −50.5299 | −2.37149 | ||||||||
\(455\) | −0.229485 | −0.0107584 | ||||||||
\(456\) | −14.1424 | −0.662276 | ||||||||
\(457\) | 3.35821 | 0.157091 | 0.0785453 | − | 0.996911i | \(-0.474972\pi\) | ||||
0.0785453 | + | 0.996911i | \(0.474972\pi\) | |||||||
\(458\) | −23.0856 | −1.07872 | ||||||||
\(459\) | 7.17621 | 0.334957 | ||||||||
\(460\) | −0.209146 | −0.00975148 | ||||||||
\(461\) | −41.2484 | −1.92113 | −0.960565 | − | 0.278055i | \(-0.910310\pi\) | ||||
−0.960565 | + | 0.278055i | \(0.910310\pi\) | |||||||
\(462\) | 6.31030 | 0.293582 | ||||||||
\(463\) | 18.7387 | 0.870862 | 0.435431 | − | 0.900222i | \(-0.356596\pi\) | ||||
0.435431 | + | 0.900222i | \(0.356596\pi\) | |||||||
\(464\) | 4.42014 | 0.205200 | ||||||||
\(465\) | −0.138350 | −0.00641584 | ||||||||
\(466\) | 57.9091 | 2.68259 | ||||||||
\(467\) | −24.4499 | −1.13141 | −0.565704 | − | 0.824608i | \(-0.691396\pi\) | ||||
−0.565704 | + | 0.824608i | \(0.691396\pi\) | |||||||
\(468\) | 9.98027 | 0.461338 | ||||||||
\(469\) | −38.9361 | −1.79790 | ||||||||
\(470\) | −0.739314 | −0.0341020 | ||||||||
\(471\) | −9.75971 | −0.449704 | ||||||||
\(472\) | 0.613119 | 0.0282211 | ||||||||
\(473\) | −8.92207 | −0.410237 | ||||||||
\(474\) | −26.0842 | −1.19809 | ||||||||
\(475\) | −20.8746 | −0.957791 | ||||||||
\(476\) | −66.9306 | −3.06776 | ||||||||
\(477\) | −4.86692 | −0.222841 | ||||||||
\(478\) | −37.2064 | −1.70178 | ||||||||
\(479\) | −34.9779 | −1.59818 | −0.799089 | − | 0.601212i | \(-0.794685\pi\) | ||||
−0.799089 | + | 0.601212i | \(0.794685\pi\) | |||||||
\(480\) | 0.129911 | 0.00592959 | ||||||||
\(481\) | −6.65201 | −0.303306 | ||||||||
\(482\) | 24.8445 | 1.13163 | ||||||||
\(483\) | 5.58052 | 0.253922 | ||||||||
\(484\) | 3.45069 | 0.156849 | ||||||||
\(485\) | −0.490851 | −0.0222884 | ||||||||
\(486\) | −2.33467 | −0.105903 | ||||||||
\(487\) | 11.8692 | 0.537847 | 0.268923 | − | 0.963162i | \(-0.413332\pi\) | ||||
0.268923 | + | 0.963162i | \(0.413332\pi\) | |||||||
\(488\) | −3.38688 | −0.153317 | ||||||||
\(489\) | 21.3224 | 0.964233 | ||||||||
\(490\) | −0.0209362 | −0.000945802 0 | ||||||||
\(491\) | 34.2782 | 1.54695 | 0.773477 | − | 0.633824i | \(-0.218516\pi\) | ||||
0.773477 | + | 0.633824i | \(0.218516\pi\) | |||||||
\(492\) | −9.21577 | −0.415479 | ||||||||
\(493\) | 31.5348 | 1.42026 | ||||||||
\(494\) | −28.1958 | −1.26859 | ||||||||
\(495\) | 0.0293558 | 0.00131945 | ||||||||
\(496\) | −4.74052 | −0.212856 | ||||||||
\(497\) | −12.7907 | −0.573740 | ||||||||
\(498\) | −30.2886 | −1.35727 | ||||||||
\(499\) | 22.9767 | 1.02858 | 0.514289 | − | 0.857617i | \(-0.328056\pi\) | ||||
0.514289 | + | 0.857617i | \(0.328056\pi\) | |||||||
\(500\) | −1.01289 | −0.0452978 | ||||||||
\(501\) | 19.0985 | 0.853258 | ||||||||
\(502\) | 57.5204 | 2.56726 | ||||||||
\(503\) | −31.8586 | −1.42051 | −0.710253 | − | 0.703946i | \(-0.751420\pi\) | ||||
−0.710253 | + | 0.703946i | \(0.751420\pi\) | |||||||
\(504\) | 9.15427 | 0.407763 | ||||||||
\(505\) | 0.0579784 | 0.00258000 | ||||||||
\(506\) | 4.82032 | 0.214289 | ||||||||
\(507\) | −4.63486 | −0.205841 | ||||||||
\(508\) | 18.6518 | 0.827542 | ||||||||
\(509\) | −14.4168 | −0.639012 | −0.319506 | − | 0.947584i | \(-0.603517\pi\) | ||||
−0.319506 | + | 0.947584i | \(0.603517\pi\) | |||||||
\(510\) | −0.491829 | −0.0217786 | ||||||||
\(511\) | −20.3221 | −0.898995 | ||||||||
\(512\) | 11.2648 | 0.497840 | ||||||||
\(513\) | 4.17563 | 0.184359 | ||||||||
\(514\) | −20.0022 | −0.882261 | ||||||||
\(515\) | 0.255029 | 0.0112379 | ||||||||
\(516\) | −30.7873 | −1.35533 | ||||||||
\(517\) | 10.7872 | 0.474421 | ||||||||
\(518\) | −14.5133 | −0.637678 | ||||||||
\(519\) | −17.4746 | −0.767050 | ||||||||
\(520\) | −0.287561 | −0.0126104 | ||||||||
\(521\) | 5.61958 | 0.246198 | 0.123099 | − | 0.992394i | \(-0.460717\pi\) | ||||
0.123099 | + | 0.992394i | \(0.460717\pi\) | |||||||
\(522\) | −10.2594 | −0.449041 | ||||||||
\(523\) | 13.6790 | 0.598142 | 0.299071 | − | 0.954231i | \(-0.403323\pi\) | ||||
0.299071 | + | 0.954231i | \(0.403323\pi\) | |||||||
\(524\) | 66.8805 | 2.92169 | ||||||||
\(525\) | 13.5120 | 0.589712 | ||||||||
\(526\) | 16.6369 | 0.725402 | ||||||||
\(527\) | −33.8206 | −1.47325 | ||||||||
\(528\) | 1.00587 | 0.0437747 | ||||||||
\(529\) | −18.7371 | −0.814659 | ||||||||
\(530\) | 0.333560 | 0.0144889 | ||||||||
\(531\) | −0.181028 | −0.00785594 | ||||||||
\(532\) | −38.9450 | −1.68848 | ||||||||
\(533\) | −7.72436 | −0.334579 | ||||||||
\(534\) | 23.7865 | 1.02934 | ||||||||
\(535\) | −0.179721 | −0.00777000 | ||||||||
\(536\) | −48.7896 | −2.10739 | ||||||||
\(537\) | 15.9382 | 0.687783 | ||||||||
\(538\) | −33.1334 | −1.42848 | ||||||||
\(539\) | 0.305477 | 0.0131578 | ||||||||
\(540\) | 0.101298 | 0.00435916 | ||||||||
\(541\) | 7.06159 | 0.303602 | 0.151801 | − | 0.988411i | \(-0.451493\pi\) | ||||
0.151801 | + | 0.988411i | \(0.451493\pi\) | |||||||
\(542\) | −68.2331 | −2.93086 | ||||||||
\(543\) | 7.41273 | 0.318111 | ||||||||
\(544\) | 31.7575 | 1.36159 | ||||||||
\(545\) | −0.105581 | −0.00452258 | ||||||||
\(546\) | 18.2510 | 0.781070 | ||||||||
\(547\) | −21.3505 | −0.912881 | −0.456441 | − | 0.889754i | \(-0.650876\pi\) | ||||
−0.456441 | + | 0.889754i | \(0.650876\pi\) | |||||||
\(548\) | 54.2325 | 2.31670 | ||||||||
\(549\) | 1.00000 | 0.0426790 | ||||||||
\(550\) | 11.6713 | 0.497668 | ||||||||
\(551\) | 18.3492 | 0.781704 | ||||||||
\(552\) | 6.99277 | 0.297632 | ||||||||
\(553\) | −30.1978 | −1.28414 | ||||||||
\(554\) | 32.5919 | 1.38470 | ||||||||
\(555\) | −0.0675166 | −0.00286592 | ||||||||
\(556\) | 5.43975 | 0.230697 | ||||||||
\(557\) | 12.8162 | 0.543039 | 0.271520 | − | 0.962433i | \(-0.412474\pi\) | ||||
0.271520 | + | 0.962433i | \(0.412474\pi\) | |||||||
\(558\) | 11.0030 | 0.465795 | ||||||||
\(559\) | −25.8049 | −1.09143 | ||||||||
\(560\) | −0.0798102 | −0.00337260 | ||||||||
\(561\) | 7.17621 | 0.302980 | ||||||||
\(562\) | 13.6506 | 0.575815 | ||||||||
\(563\) | −30.0977 | −1.26846 | −0.634232 | − | 0.773142i | \(-0.718684\pi\) | ||||
−0.634232 | + | 0.773142i | \(0.718684\pi\) | |||||||
\(564\) | 37.2233 | 1.56738 | ||||||||
\(565\) | 0.200138 | 0.00841986 | ||||||||
\(566\) | −59.8478 | −2.51559 | ||||||||
\(567\) | −2.70286 | −0.113510 | ||||||||
\(568\) | −16.0276 | −0.672502 | ||||||||
\(569\) | 33.1992 | 1.39178 | 0.695891 | − | 0.718148i | \(-0.255010\pi\) | ||||
0.695891 | + | 0.718148i | \(0.255010\pi\) | |||||||
\(570\) | −0.286182 | −0.0119868 | ||||||||
\(571\) | −21.8687 | −0.915177 | −0.457589 | − | 0.889164i | \(-0.651287\pi\) | ||||
−0.457589 | + | 0.889164i | \(0.651287\pi\) | |||||||
\(572\) | 9.98027 | 0.417296 | ||||||||
\(573\) | 11.6075 | 0.484908 | ||||||||
\(574\) | −16.8529 | −0.703428 | ||||||||
\(575\) | 10.3216 | 0.430439 | ||||||||
\(576\) | −12.3436 | −0.514315 | ||||||||
\(577\) | −10.2833 | −0.428101 | −0.214050 | − | 0.976823i | \(-0.568666\pi\) | ||||
−0.214050 | + | 0.976823i | \(0.568666\pi\) | |||||||
\(578\) | −80.5413 | −3.35008 | ||||||||
\(579\) | 20.4885 | 0.851472 | ||||||||
\(580\) | 0.445139 | 0.0184834 | ||||||||
\(581\) | −35.0654 | −1.45476 | ||||||||
\(582\) | 39.0374 | 1.61815 | ||||||||
\(583\) | −4.86692 | −0.201567 | ||||||||
\(584\) | −25.4650 | −1.05375 | ||||||||
\(585\) | 0.0849045 | 0.00351037 | ||||||||
\(586\) | −3.65374 | −0.150935 | ||||||||
\(587\) | −21.6507 | −0.893622 | −0.446811 | − | 0.894628i | \(-0.647440\pi\) | ||||
−0.446811 | + | 0.894628i | \(0.647440\pi\) | |||||||
\(588\) | 1.05411 | 0.0434706 | ||||||||
\(589\) | −19.6792 | −0.810869 | ||||||||
\(590\) | 0.0124069 | 0.000510786 0 | ||||||||
\(591\) | 7.27132 | 0.299102 | ||||||||
\(592\) | −2.31343 | −0.0950815 | ||||||||
\(593\) | −12.8896 | −0.529312 | −0.264656 | − | 0.964343i | \(-0.585258\pi\) | ||||
−0.264656 | + | 0.964343i | \(0.585258\pi\) | |||||||
\(594\) | −2.33467 | −0.0957927 | ||||||||
\(595\) | −0.569394 | −0.0233429 | ||||||||
\(596\) | 3.81268 | 0.156173 | ||||||||
\(597\) | −10.0401 | −0.410914 | ||||||||
\(598\) | 13.9416 | 0.570114 | ||||||||
\(599\) | −22.2972 | −0.911039 | −0.455520 | − | 0.890226i | \(-0.650547\pi\) | ||||
−0.455520 | + | 0.890226i | \(0.650547\pi\) | |||||||
\(600\) | 16.9315 | 0.691224 | ||||||||
\(601\) | −7.06663 | −0.288254 | −0.144127 | − | 0.989559i | \(-0.546037\pi\) | ||||
−0.144127 | + | 0.989559i | \(0.546037\pi\) | |||||||
\(602\) | −56.3009 | −2.29465 | ||||||||
\(603\) | 14.4055 | 0.586637 | ||||||||
\(604\) | −51.7715 | −2.10655 | ||||||||
\(605\) | 0.0293558 | 0.00119348 | ||||||||
\(606\) | −4.61103 | −0.187310 | ||||||||
\(607\) | −10.6898 | −0.433886 | −0.216943 | − | 0.976184i | \(-0.569609\pi\) | ||||
−0.216943 | + | 0.976184i | \(0.569609\pi\) | |||||||
\(608\) | 18.4788 | 0.749414 | ||||||||
\(609\) | −11.8774 | −0.481295 | ||||||||
\(610\) | −0.0685361 | −0.00277495 | ||||||||
\(611\) | 31.1994 | 1.26219 | ||||||||
\(612\) | 24.7628 | 1.00098 | ||||||||
\(613\) | 24.7225 | 0.998533 | 0.499267 | − | 0.866448i | \(-0.333603\pi\) | ||||
0.499267 | + | 0.866448i | \(0.333603\pi\) | |||||||
\(614\) | −20.0904 | −0.810782 | ||||||||
\(615\) | −0.0784007 | −0.00316142 | ||||||||
\(616\) | 9.15427 | 0.368836 | ||||||||
\(617\) | 47.5636 | 1.91484 | 0.957420 | − | 0.288700i | \(-0.0932230\pi\) | ||||
0.957420 | + | 0.288700i | \(0.0932230\pi\) | |||||||
\(618\) | −20.2825 | −0.815880 | ||||||||
\(619\) | 19.1635 | 0.770246 | 0.385123 | − | 0.922865i | \(-0.374159\pi\) | ||||
0.385123 | + | 0.922865i | \(0.374159\pi\) | |||||||
\(620\) | −0.477403 | −0.0191730 | ||||||||
\(621\) | −2.06467 | −0.0828523 | ||||||||
\(622\) | 74.1803 | 2.97436 | ||||||||
\(623\) | 27.5378 | 1.10328 | ||||||||
\(624\) | 2.90922 | 0.116462 | ||||||||
\(625\) | 24.9871 | 0.999483 | ||||||||
\(626\) | −62.7775 | −2.50909 | ||||||||
\(627\) | 4.17563 | 0.166759 | ||||||||
\(628\) | −33.6777 | −1.34389 | ||||||||
\(629\) | −16.5048 | −0.658091 | ||||||||
\(630\) | 0.185244 | 0.00738029 | ||||||||
\(631\) | 4.32941 | 0.172351 | 0.0861755 | − | 0.996280i | \(-0.472535\pi\) | ||||
0.0861755 | + | 0.996280i | \(0.472535\pi\) | |||||||
\(632\) | −37.8399 | −1.50519 | ||||||||
\(633\) | −7.36422 | −0.292701 | ||||||||
\(634\) | 50.6417 | 2.01124 | ||||||||
\(635\) | 0.158676 | 0.00629685 | ||||||||
\(636\) | −16.7942 | −0.665934 | ||||||||
\(637\) | 0.883518 | 0.0350062 | ||||||||
\(638\) | −10.2594 | −0.406173 | ||||||||
\(639\) | 4.73226 | 0.187205 | ||||||||
\(640\) | 0.586158 | 0.0231699 | ||||||||
\(641\) | 28.9219 | 1.14234 | 0.571172 | − | 0.820830i | \(-0.306489\pi\) | ||||
0.571172 | + | 0.820830i | \(0.306489\pi\) | |||||||
\(642\) | 14.2932 | 0.564108 | ||||||||
\(643\) | −33.7472 | −1.33086 | −0.665430 | − | 0.746460i | \(-0.731752\pi\) | ||||
−0.665430 | + | 0.746460i | \(0.731752\pi\) | |||||||
\(644\) | 19.2566 | 0.758817 | ||||||||
\(645\) | −0.261915 | −0.0103129 | ||||||||
\(646\) | −69.9589 | −2.75250 | ||||||||
\(647\) | −43.6251 | −1.71508 | −0.857540 | − | 0.514418i | \(-0.828008\pi\) | ||||
−0.857540 | + | 0.514418i | \(0.828008\pi\) | |||||||
\(648\) | −3.38688 | −0.133049 | ||||||||
\(649\) | −0.181028 | −0.00710597 | ||||||||
\(650\) | 33.7565 | 1.32404 | ||||||||
\(651\) | 12.7383 | 0.499252 | ||||||||
\(652\) | 73.5770 | 2.88150 | ||||||||
\(653\) | 13.5296 | 0.529455 | 0.264727 | − | 0.964323i | \(-0.414718\pi\) | ||||
0.264727 | + | 0.964323i | \(0.414718\pi\) | |||||||
\(654\) | 8.39685 | 0.328343 | ||||||||
\(655\) | 0.568968 | 0.0222314 | ||||||||
\(656\) | −2.68637 | −0.104885 | ||||||||
\(657\) | 7.51871 | 0.293333 | ||||||||
\(658\) | 68.0705 | 2.65367 | ||||||||
\(659\) | −3.51759 | −0.137026 | −0.0685129 | − | 0.997650i | \(-0.521825\pi\) | ||||
−0.0685129 | + | 0.997650i | \(0.521825\pi\) | |||||||
\(660\) | 0.101298 | 0.00394301 | ||||||||
\(661\) | −43.5404 | −1.69353 | −0.846763 | − | 0.531971i | \(-0.821452\pi\) | ||||
−0.846763 | + | 0.531971i | \(0.821452\pi\) | |||||||
\(662\) | 7.39301 | 0.287337 | ||||||||
\(663\) | 20.7554 | 0.806074 | ||||||||
\(664\) | −43.9393 | −1.70518 | ||||||||
\(665\) | −0.331315 | −0.0128478 | ||||||||
\(666\) | 5.36960 | 0.208068 | ||||||||
\(667\) | −9.07289 | −0.351304 | ||||||||
\(668\) | 65.9030 | 2.54986 | ||||||||
\(669\) | 1.02663 | 0.0396918 | ||||||||
\(670\) | −0.987296 | −0.0381426 | ||||||||
\(671\) | 1.00000 | 0.0386046 | ||||||||
\(672\) | −11.9612 | −0.461414 | ||||||||
\(673\) | 31.6788 | 1.22113 | 0.610563 | − | 0.791968i | \(-0.290943\pi\) | ||||
0.610563 | + | 0.791968i | \(0.290943\pi\) | |||||||
\(674\) | −67.8819 | −2.61471 | ||||||||
\(675\) | −4.99914 | −0.192417 | ||||||||
\(676\) | −15.9935 | −0.615133 | ||||||||
\(677\) | 0.472792 | 0.0181709 | 0.00908543 | − | 0.999959i | \(-0.497108\pi\) | ||||
0.00908543 | + | 0.999959i | \(0.497108\pi\) | |||||||
\(678\) | −15.9170 | −0.611288 | ||||||||
\(679\) | 45.1939 | 1.73438 | ||||||||
\(680\) | −0.713490 | −0.0273611 | ||||||||
\(681\) | 21.6433 | 0.829372 | ||||||||
\(682\) | 11.0030 | 0.421327 | ||||||||
\(683\) | 1.89167 | 0.0723828 | 0.0361914 | − | 0.999345i | \(-0.488477\pi\) | ||||
0.0361914 | + | 0.999345i | \(0.488477\pi\) | |||||||
\(684\) | 14.4088 | 0.550934 | ||||||||
\(685\) | 0.461369 | 0.0176280 | ||||||||
\(686\) | −42.2444 | −1.61290 | ||||||||
\(687\) | 9.88816 | 0.377257 | ||||||||
\(688\) | −8.97441 | −0.342146 | ||||||||
\(689\) | −14.0764 | −0.536267 | ||||||||
\(690\) | 0.141504 | 0.00538698 | ||||||||
\(691\) | 47.6079 | 1.81109 | 0.905545 | − | 0.424250i | \(-0.139462\pi\) | ||||
0.905545 | + | 0.424250i | \(0.139462\pi\) | |||||||
\(692\) | −60.2994 | −2.29224 | ||||||||
\(693\) | −2.70286 | −0.102673 | ||||||||
\(694\) | 13.4614 | 0.510989 | ||||||||
\(695\) | 0.0462772 | 0.00175539 | ||||||||
\(696\) | −14.8832 | −0.564145 | ||||||||
\(697\) | −19.1655 | −0.725946 | ||||||||
\(698\) | 69.7676 | 2.64074 | ||||||||
\(699\) | −24.8039 | −0.938172 | ||||||||
\(700\) | 46.6257 | 1.76228 | ||||||||
\(701\) | 29.5010 | 1.11424 | 0.557119 | − | 0.830433i | \(-0.311907\pi\) | ||||
0.557119 | + | 0.830433i | \(0.311907\pi\) | |||||||
\(702\) | −6.75246 | −0.254855 | ||||||||
\(703\) | −9.60370 | −0.362211 | ||||||||
\(704\) | −12.3436 | −0.465215 | ||||||||
\(705\) | 0.316667 | 0.0119264 | ||||||||
\(706\) | −20.2800 | −0.763249 | ||||||||
\(707\) | −5.33822 | −0.200764 | ||||||||
\(708\) | −0.624670 | −0.0234766 | ||||||||
\(709\) | −24.1831 | −0.908215 | −0.454107 | − | 0.890947i | \(-0.650042\pi\) | ||||
−0.454107 | + | 0.890947i | \(0.650042\pi\) | |||||||
\(710\) | −0.324331 | −0.0121719 | ||||||||
\(711\) | 11.1725 | 0.419002 | ||||||||
\(712\) | 34.5068 | 1.29320 | ||||||||
\(713\) | 9.73052 | 0.364411 | ||||||||
\(714\) | 45.2840 | 1.69471 | ||||||||
\(715\) | 0.0849045 | 0.00317525 | ||||||||
\(716\) | 54.9976 | 2.05536 | ||||||||
\(717\) | 15.9365 | 0.595158 | ||||||||
\(718\) | 0.748601 | 0.0279375 | ||||||||
\(719\) | 5.78255 | 0.215653 | 0.107826 | − | 0.994170i | \(-0.465611\pi\) | ||||
0.107826 | + | 0.994170i | \(0.465611\pi\) | |||||||
\(720\) | 0.0295280 | 0.00110044 | ||||||||
\(721\) | −23.4811 | −0.874484 | ||||||||
\(722\) | 3.65163 | 0.135900 | ||||||||
\(723\) | −10.6415 | −0.395763 | ||||||||
\(724\) | 25.5790 | 0.950636 | ||||||||
\(725\) | −21.9680 | −0.815872 | ||||||||
\(726\) | −2.33467 | −0.0866478 | ||||||||
\(727\) | 11.9924 | 0.444774 | 0.222387 | − | 0.974958i | \(-0.428615\pi\) | ||||
0.222387 | + | 0.974958i | \(0.428615\pi\) | |||||||
\(728\) | 26.4765 | 0.981283 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.515304 | −0.0190722 | ||||||||
\(731\) | −64.0266 | −2.36811 | ||||||||
\(732\) | 3.45069 | 0.127541 | ||||||||
\(733\) | 6.07851 | 0.224515 | 0.112257 | − | 0.993679i | \(-0.464192\pi\) | ||||
0.112257 | + | 0.993679i | \(0.464192\pi\) | |||||||
\(734\) | 34.4416 | 1.27126 | ||||||||
\(735\) | 0.00896753 | 0.000330772 0 | ||||||||
\(736\) | −9.13695 | −0.336792 | ||||||||
\(737\) | 14.4055 | 0.530633 | ||||||||
\(738\) | 6.23522 | 0.229521 | ||||||||
\(739\) | 27.1397 | 0.998350 | 0.499175 | − | 0.866501i | \(-0.333636\pi\) | ||||
0.499175 | + | 0.866501i | \(0.333636\pi\) | |||||||
\(740\) | −0.232979 | −0.00856446 | ||||||||
\(741\) | 12.0770 | 0.443659 | ||||||||
\(742\) | −30.7117 | −1.12746 | ||||||||
\(743\) | 1.32191 | 0.0484963 | 0.0242482 | − | 0.999706i | \(-0.492281\pi\) | ||||
0.0242482 | + | 0.999706i | \(0.492281\pi\) | |||||||
\(744\) | 15.9619 | 0.585193 | ||||||||
\(745\) | 0.0324353 | 0.00118834 | ||||||||
\(746\) | 17.6159 | 0.644963 | ||||||||
\(747\) | 12.9734 | 0.474672 | ||||||||
\(748\) | 24.7628 | 0.905419 | ||||||||
\(749\) | 16.5473 | 0.604627 | ||||||||
\(750\) | 0.685302 | 0.0250237 | ||||||||
\(751\) | 5.66385 | 0.206677 | 0.103338 | − | 0.994646i | \(-0.467048\pi\) | ||||
0.103338 | + | 0.994646i | \(0.467048\pi\) | |||||||
\(752\) | 10.8505 | 0.395677 | ||||||||
\(753\) | −24.6375 | −0.897840 | ||||||||
\(754\) | −29.6728 | −1.08062 | ||||||||
\(755\) | −0.440432 | −0.0160290 | ||||||||
\(756\) | −9.32674 | −0.339210 | ||||||||
\(757\) | −43.1109 | −1.56689 | −0.783447 | − | 0.621459i | \(-0.786540\pi\) | ||||
−0.783447 | + | 0.621459i | \(0.786540\pi\) | |||||||
\(758\) | 13.7940 | 0.501021 | ||||||||
\(759\) | −2.06467 | −0.0749427 | ||||||||
\(760\) | −0.415160 | −0.0150594 | ||||||||
\(761\) | 15.5334 | 0.563086 | 0.281543 | − | 0.959549i | \(-0.409154\pi\) | ||||
0.281543 | + | 0.959549i | \(0.409154\pi\) | |||||||
\(762\) | −12.6195 | −0.457156 | ||||||||
\(763\) | 9.72109 | 0.351927 | ||||||||
\(764\) | 40.0537 | 1.44909 | ||||||||
\(765\) | 0.210663 | 0.00761655 | ||||||||
\(766\) | −66.1011 | −2.38833 | ||||||||
\(767\) | −0.523579 | −0.0189053 | ||||||||
\(768\) | −21.9301 | −0.791334 | ||||||||
\(769\) | −44.5062 | −1.60493 | −0.802467 | − | 0.596697i | \(-0.796479\pi\) | ||||
−0.802467 | + | 0.596697i | \(0.796479\pi\) | |||||||
\(770\) | 0.185244 | 0.00667573 | ||||||||
\(771\) | 8.56747 | 0.308550 | ||||||||
\(772\) | 70.6993 | 2.54452 | ||||||||
\(773\) | −3.75321 | −0.134993 | −0.0674967 | − | 0.997719i | \(-0.521501\pi\) | ||||
−0.0674967 | + | 0.997719i | \(0.521501\pi\) | |||||||
\(774\) | 20.8301 | 0.748722 | ||||||||
\(775\) | 23.5603 | 0.846312 | ||||||||
\(776\) | 56.6311 | 2.03294 | ||||||||
\(777\) | 6.21643 | 0.223013 | ||||||||
\(778\) | 37.6126 | 1.34848 | ||||||||
\(779\) | −11.1519 | −0.399558 | ||||||||
\(780\) | 0.292979 | 0.0104903 | ||||||||
\(781\) | 4.73226 | 0.169334 | ||||||||
\(782\) | 34.5916 | 1.23699 | ||||||||
\(783\) | 4.39436 | 0.157042 | ||||||||
\(784\) | 0.307269 | 0.0109739 | ||||||||
\(785\) | −0.286504 | −0.0102258 | ||||||||
\(786\) | −45.2501 | −1.61402 | ||||||||
\(787\) | −44.9918 | −1.60379 | −0.801893 | − | 0.597468i | \(-0.796174\pi\) | ||||
−0.801893 | + | 0.597468i | \(0.796174\pi\) | |||||||
\(788\) | 25.0910 | 0.893832 | ||||||||
\(789\) | −7.12601 | −0.253693 | ||||||||
\(790\) | −0.765721 | −0.0272431 | ||||||||
\(791\) | −18.4272 | −0.655196 | ||||||||
\(792\) | −3.38688 | −0.120347 | ||||||||
\(793\) | 2.89225 | 0.102707 | ||||||||
\(794\) | 30.1496 | 1.06997 | ||||||||
\(795\) | −0.142872 | −0.00506716 | ||||||||
\(796\) | −34.6452 | −1.22797 | ||||||||
\(797\) | 43.6737 | 1.54700 | 0.773501 | − | 0.633795i | \(-0.218504\pi\) | ||||
0.773501 | + | 0.633795i | \(0.218504\pi\) | |||||||
\(798\) | 26.3495 | 0.932762 | ||||||||
\(799\) | 77.4112 | 2.73861 | ||||||||
\(800\) | −22.1231 | −0.782170 | ||||||||
\(801\) | −10.1884 | −0.359989 | ||||||||
\(802\) | −50.4711 | −1.78220 | ||||||||
\(803\) | 7.51871 | 0.265330 | ||||||||
\(804\) | 49.7088 | 1.75309 | ||||||||
\(805\) | 0.163821 | 0.00577392 | ||||||||
\(806\) | 31.8235 | 1.12094 | ||||||||
\(807\) | 14.1919 | 0.499578 | ||||||||
\(808\) | −6.68916 | −0.235324 | ||||||||
\(809\) | −21.0958 | −0.741690 | −0.370845 | − | 0.928695i | \(-0.620932\pi\) | ||||
−0.370845 | + | 0.928695i | \(0.620932\pi\) | |||||||
\(810\) | −0.0685361 | −0.00240811 | ||||||||
\(811\) | 47.7913 | 1.67818 | 0.839090 | − | 0.543992i | \(-0.183088\pi\) | ||||
0.839090 | + | 0.543992i | \(0.183088\pi\) | |||||||
\(812\) | −40.9851 | −1.43829 | ||||||||
\(813\) | 29.2260 | 1.02500 | ||||||||
\(814\) | 5.36960 | 0.188204 | ||||||||
\(815\) | 0.625936 | 0.0219256 | ||||||||
\(816\) | 7.21830 | 0.252691 | ||||||||
\(817\) | −37.2553 | −1.30340 | ||||||||
\(818\) | 24.5573 | 0.858626 | ||||||||
\(819\) | −7.81737 | −0.273161 | ||||||||
\(820\) | −0.270536 | −0.00944753 | ||||||||
\(821\) | 8.42000 | 0.293860 | 0.146930 | − | 0.989147i | \(-0.453061\pi\) | ||||
0.146930 | + | 0.989147i | \(0.453061\pi\) | |||||||
\(822\) | −36.6927 | −1.27981 | ||||||||
\(823\) | 21.4926 | 0.749186 | 0.374593 | − | 0.927189i | \(-0.377782\pi\) | ||||
0.374593 | + | 0.927189i | \(0.377782\pi\) | |||||||
\(824\) | −29.4235 | −1.02502 | ||||||||
\(825\) | −4.99914 | −0.174048 | ||||||||
\(826\) | −1.14234 | −0.0397471 | ||||||||
\(827\) | 32.0863 | 1.11575 | 0.557875 | − | 0.829925i | \(-0.311617\pi\) | ||||
0.557875 | + | 0.829925i | \(0.311617\pi\) | |||||||
\(828\) | −7.12452 | −0.247594 | ||||||||
\(829\) | −43.5722 | −1.51332 | −0.756662 | − | 0.653806i | \(-0.773171\pi\) | ||||
−0.756662 | + | 0.653806i | \(0.773171\pi\) | |||||||
\(830\) | −0.889147 | −0.0308627 | ||||||||
\(831\) | −13.9600 | −0.484266 | ||||||||
\(832\) | −35.7007 | −1.23770 | ||||||||
\(833\) | 2.19217 | 0.0759541 | ||||||||
\(834\) | −3.68043 | −0.127443 | ||||||||
\(835\) | 0.560652 | 0.0194022 | ||||||||
\(836\) | 14.4088 | 0.498339 | ||||||||
\(837\) | −4.71288 | −0.162901 | ||||||||
\(838\) | −12.1279 | −0.418951 | ||||||||
\(839\) | −9.71778 | −0.335495 | −0.167748 | − | 0.985830i | \(-0.553649\pi\) | ||||
−0.167748 | + | 0.985830i | \(0.553649\pi\) | |||||||
\(840\) | 0.268731 | 0.00927209 | ||||||||
\(841\) | −9.68959 | −0.334124 | ||||||||
\(842\) | 51.4246 | 1.77221 | ||||||||
\(843\) | −5.84690 | −0.201378 | ||||||||
\(844\) | −25.4116 | −0.874704 | ||||||||
\(845\) | −0.136060 | −0.00468061 | ||||||||
\(846\) | −25.1846 | −0.865864 | ||||||||
\(847\) | −2.70286 | −0.0928715 | ||||||||
\(848\) | −4.89547 | −0.168111 | ||||||||
\(849\) | 25.6344 | 0.879769 | ||||||||
\(850\) | 83.7559 | 2.87281 | ||||||||
\(851\) | 4.74861 | 0.162780 | ||||||||
\(852\) | 16.3296 | 0.559441 | ||||||||
\(853\) | 10.1506 | 0.347551 | 0.173776 | − | 0.984785i | \(-0.444403\pi\) | ||||
0.173776 | + | 0.984785i | \(0.444403\pi\) | |||||||
\(854\) | 6.31030 | 0.215934 | ||||||||
\(855\) | 0.122579 | 0.00419211 | ||||||||
\(856\) | 20.7350 | 0.708707 | ||||||||
\(857\) | 1.00340 | 0.0342754 | 0.0171377 | − | 0.999853i | \(-0.494545\pi\) | ||||
0.0171377 | + | 0.999853i | \(0.494545\pi\) | |||||||
\(858\) | −6.75246 | −0.230525 | ||||||||
\(859\) | −30.9914 | −1.05741 | −0.528706 | − | 0.848805i | \(-0.677323\pi\) | ||||
−0.528706 | + | 0.848805i | \(0.677323\pi\) | |||||||
\(860\) | −0.903785 | −0.0308188 | ||||||||
\(861\) | 7.21855 | 0.246008 | ||||||||
\(862\) | 1.97113 | 0.0671368 | ||||||||
\(863\) | −36.5669 | −1.24475 | −0.622377 | − | 0.782718i | \(-0.713833\pi\) | ||||
−0.622377 | + | 0.782718i | \(0.713833\pi\) | |||||||
\(864\) | 4.42539 | 0.150555 | ||||||||
\(865\) | −0.512981 | −0.0174419 | ||||||||
\(866\) | −67.3655 | −2.28917 | ||||||||
\(867\) | 34.4979 | 1.17161 | ||||||||
\(868\) | 43.9558 | 1.49196 | ||||||||
\(869\) | 11.1725 | 0.379002 | ||||||||
\(870\) | −0.301172 | −0.0102107 | ||||||||
\(871\) | 41.6643 | 1.41174 | ||||||||
\(872\) | 12.1812 | 0.412507 | ||||||||
\(873\) | −16.7207 | −0.565911 | ||||||||
\(874\) | 20.1279 | 0.680836 | ||||||||
\(875\) | 0.793379 | 0.0268211 | ||||||||
\(876\) | 25.9447 | 0.876591 | ||||||||
\(877\) | 4.64834 | 0.156963 | 0.0784816 | − | 0.996916i | \(-0.474993\pi\) | ||||
0.0784816 | + | 0.996916i | \(0.474993\pi\) | |||||||
\(878\) | 50.4763 | 1.70349 | ||||||||
\(879\) | 1.56499 | 0.0527859 | ||||||||
\(880\) | 0.0295280 | 0.000995389 0 | ||||||||
\(881\) | −29.7857 | −1.00351 | −0.501753 | − | 0.865011i | \(-0.667311\pi\) | ||||
−0.501753 | + | 0.865011i | \(0.667311\pi\) | |||||||
\(882\) | −0.713188 | −0.0240143 | ||||||||
\(883\) | −43.9469 | −1.47893 | −0.739466 | − | 0.673194i | \(-0.764922\pi\) | ||||
−0.739466 | + | 0.673194i | \(0.764922\pi\) | |||||||
\(884\) | 71.6204 | 2.40886 | ||||||||
\(885\) | −0.00531422 | −0.000178635 0 | ||||||||
\(886\) | 9.10858 | 0.306009 | ||||||||
\(887\) | −31.7216 | −1.06511 | −0.532554 | − | 0.846396i | \(-0.678767\pi\) | ||||
−0.532554 | + | 0.846396i | \(0.678767\pi\) | |||||||
\(888\) | 7.78961 | 0.261402 | ||||||||
\(889\) | −14.6097 | −0.489993 | ||||||||
\(890\) | 0.698272 | 0.0234061 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 3.54258 | 0.118614 | ||||||||
\(893\) | 45.0434 | 1.50732 | ||||||||
\(894\) | −2.57959 | −0.0862742 | ||||||||
\(895\) | 0.467878 | 0.0156394 | ||||||||
\(896\) | −53.9691 | −1.80298 | ||||||||
\(897\) | −5.97154 | −0.199384 | ||||||||
\(898\) | 16.7286 | 0.558242 | ||||||||
\(899\) | −20.7101 | −0.690720 | ||||||||
\(900\) | −17.2505 | −0.575015 | ||||||||
\(901\) | −34.9260 | −1.16355 | ||||||||
\(902\) | 6.23522 | 0.207610 | ||||||||
\(903\) | 24.1151 | 0.802502 | ||||||||
\(904\) | −23.0906 | −0.767981 | ||||||||
\(905\) | 0.217607 | 0.00723349 | ||||||||
\(906\) | 35.0276 | 1.16372 | ||||||||
\(907\) | −43.3090 | −1.43805 | −0.719026 | − | 0.694983i | \(-0.755412\pi\) | ||||
−0.719026 | + | 0.694983i | \(0.755412\pi\) | |||||||
\(908\) | 74.6841 | 2.47848 | ||||||||
\(909\) | 1.97502 | 0.0655074 | ||||||||
\(910\) | 0.535772 | 0.0177607 | ||||||||
\(911\) | −39.7332 | −1.31642 | −0.658210 | − | 0.752834i | \(-0.728686\pi\) | ||||
−0.658210 | + | 0.752834i | \(0.728686\pi\) | |||||||
\(912\) | 4.20013 | 0.139080 | ||||||||
\(913\) | 12.9734 | 0.429357 | ||||||||
\(914\) | −7.84032 | −0.259335 | ||||||||
\(915\) | 0.0293558 | 0.000970473 0 | ||||||||
\(916\) | 34.1209 | 1.12739 | ||||||||
\(917\) | −52.3864 | −1.72995 | ||||||||
\(918\) | −16.7541 | −0.552967 | ||||||||
\(919\) | −47.8215 | −1.57749 | −0.788744 | − | 0.614722i | \(-0.789268\pi\) | ||||
−0.788744 | + | 0.614722i | \(0.789268\pi\) | |||||||
\(920\) | 0.205278 | 0.00676783 | ||||||||
\(921\) | 8.60524 | 0.283552 | ||||||||
\(922\) | 96.3015 | 3.17152 | ||||||||
\(923\) | 13.6869 | 0.450510 | ||||||||
\(924\) | −9.32674 | −0.306827 | ||||||||
\(925\) | 11.4977 | 0.378043 | ||||||||
\(926\) | −43.7487 | −1.43767 | ||||||||
\(927\) | 8.68750 | 0.285335 | ||||||||
\(928\) | 19.4467 | 0.638371 | ||||||||
\(929\) | 33.7455 | 1.10715 | 0.553576 | − | 0.832798i | \(-0.313263\pi\) | ||||
0.553576 | + | 0.832798i | \(0.313263\pi\) | |||||||
\(930\) | 0.323002 | 0.0105917 | ||||||||
\(931\) | 1.27556 | 0.0418048 | ||||||||
\(932\) | −85.5907 | −2.80362 | ||||||||
\(933\) | −31.7733 | −1.04021 | ||||||||
\(934\) | 57.0826 | 1.86780 | ||||||||
\(935\) | 0.210663 | 0.00688943 | ||||||||
\(936\) | −9.79571 | −0.320183 | ||||||||
\(937\) | 28.0948 | 0.917817 | 0.458908 | − | 0.888484i | \(-0.348241\pi\) | ||||
0.458908 | + | 0.888484i | \(0.348241\pi\) | |||||||
\(938\) | 90.9029 | 2.96808 | ||||||||
\(939\) | 26.8892 | 0.877497 | ||||||||
\(940\) | 1.09272 | 0.0356406 | ||||||||
\(941\) | −2.34219 | −0.0763531 | −0.0381765 | − | 0.999271i | \(-0.512155\pi\) | ||||
−0.0381765 | + | 0.999271i | \(0.512155\pi\) | |||||||
\(942\) | 22.7857 | 0.742398 | ||||||||
\(943\) | 5.51412 | 0.179564 | ||||||||
\(944\) | −0.182090 | −0.00592652 | ||||||||
\(945\) | −0.0793448 | −0.00258108 | ||||||||
\(946\) | 20.8301 | 0.677245 | ||||||||
\(947\) | 0.361908 | 0.0117604 | 0.00588021 | − | 0.999983i | \(-0.498128\pi\) | ||||
0.00588021 | + | 0.999983i | \(0.498128\pi\) | |||||||
\(948\) | 38.5529 | 1.25214 | ||||||||
\(949\) | 21.7460 | 0.705906 | ||||||||
\(950\) | 48.7352 | 1.58118 | ||||||||
\(951\) | −21.6911 | −0.703383 | ||||||||
\(952\) | 65.6929 | 2.12912 | ||||||||
\(953\) | 20.2966 | 0.657473 | 0.328736 | − | 0.944422i | \(-0.393377\pi\) | ||||
0.328736 | + | 0.944422i | \(0.393377\pi\) | |||||||
\(954\) | 11.3627 | 0.367879 | ||||||||
\(955\) | 0.340746 | 0.0110263 | ||||||||
\(956\) | 54.9918 | 1.77856 | ||||||||
\(957\) | 4.39436 | 0.142050 | ||||||||
\(958\) | 81.6618 | 2.63837 | ||||||||
\(959\) | −42.4794 | −1.37173 | ||||||||
\(960\) | −0.362355 | −0.0116950 | ||||||||
\(961\) | −8.78880 | −0.283510 | ||||||||
\(962\) | 15.5303 | 0.500716 | ||||||||
\(963\) | −6.12215 | −0.197284 | ||||||||
\(964\) | −36.7206 | −1.18269 | ||||||||
\(965\) | 0.601455 | 0.0193615 | ||||||||
\(966\) | −13.0287 | −0.419191 | ||||||||
\(967\) | −18.7607 | −0.603303 | −0.301651 | − | 0.953418i | \(-0.597538\pi\) | ||||
−0.301651 | + | 0.953418i | \(0.597538\pi\) | |||||||
\(968\) | −3.38688 | −0.108858 | ||||||||
\(969\) | 29.9652 | 0.962621 | ||||||||
\(970\) | 1.14598 | 0.0367950 | ||||||||
\(971\) | 56.5296 | 1.81412 | 0.907061 | − | 0.420999i | \(-0.138320\pi\) | ||||
0.907061 | + | 0.420999i | \(0.138320\pi\) | |||||||
\(972\) | 3.45069 | 0.110681 | ||||||||
\(973\) | −4.26086 | −0.136597 | ||||||||
\(974\) | −27.7108 | −0.887911 | ||||||||
\(975\) | −14.4588 | −0.463052 | ||||||||
\(976\) | 1.00587 | 0.0321970 | ||||||||
\(977\) | 3.17054 | 0.101435 | 0.0507173 | − | 0.998713i | \(-0.483849\pi\) | ||||
0.0507173 | + | 0.998713i | \(0.483849\pi\) | |||||||
\(978\) | −49.7808 | −1.59181 | ||||||||
\(979\) | −10.1884 | −0.325622 | ||||||||
\(980\) | 0.0309441 | 0.000988474 0 | ||||||||
\(981\) | −3.59659 | −0.114830 | ||||||||
\(982\) | −80.0284 | −2.55381 | ||||||||
\(983\) | −40.8147 | −1.30179 | −0.650893 | − | 0.759169i | \(-0.725606\pi\) | ||||
−0.650893 | + | 0.759169i | \(0.725606\pi\) | |||||||
\(984\) | 9.04535 | 0.288355 | ||||||||
\(985\) | 0.213455 | 0.00680125 | ||||||||
\(986\) | −73.6235 | −2.34465 | ||||||||
\(987\) | −29.1564 | −0.928058 | ||||||||
\(988\) | 41.6739 | 1.32582 | ||||||||
\(989\) | 18.4211 | 0.585757 | ||||||||
\(990\) | −0.0685361 | −0.00217822 | ||||||||
\(991\) | −56.3255 | −1.78924 | −0.894619 | − | 0.446829i | \(-0.852553\pi\) | ||||
−0.894619 | + | 0.446829i | \(0.852553\pi\) | |||||||
\(992\) | −20.8563 | −0.662188 | ||||||||
\(993\) | −3.16662 | −0.100490 | ||||||||
\(994\) | 29.8620 | 0.947164 | ||||||||
\(995\) | −0.294735 | −0.00934372 | ||||||||
\(996\) | 44.7672 | 1.41850 | ||||||||
\(997\) | −44.4996 | −1.40932 | −0.704658 | − | 0.709547i | \(-0.748900\pi\) | ||||
−0.704658 | + | 0.709547i | \(0.748900\pi\) | |||||||
\(998\) | −53.6430 | −1.69804 | ||||||||
\(999\) | −2.29994 | −0.0727669 |
(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 | 2013.2.a.g.1.1 | ✓ | 13 | |
3.2 | odd | 2 | 6039.2.a.h.1.13 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.2.a.g.1.1 | ✓ | 13 | 1.1 | even | 1 | trivial | |
6039.2.a.h.1.13 | 13 | 3.2 | odd | 2 |