Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, 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("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 3 x^{13} - 36 x^{12} + 108 x^{11} + 434 x^{10} - 1239 x^{9} - 2404 x^{8} + 6204 x^{7} + 6361 x^{6} - 14618 x^{5} - 7015 x^{4} + 15763 x^{3} + 1118 x^{2} + \cdots + 1552 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-1.02849\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.02849 | 0.459954 | 0.229977 | − | 0.973196i | \(-0.426135\pi\) | ||||
0.229977 | + | 0.973196i | \(0.426135\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −4.96874 | −1.87801 | −0.939004 | − | 0.343906i | \(-0.888250\pi\) | ||||
−0.939004 | + | 0.343906i | \(0.888250\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.02849 | −0.325236 | ||||||||
\(11\) | 4.09511 | 1.23472 | 0.617361 | − | 0.786680i | \(-0.288202\pi\) | ||||
0.617361 | + | 0.786680i | \(0.288202\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 4.96874 | 1.32795 | ||||||||
\(15\) | −1.02849 | −0.265554 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.459045 | 0.111335 | 0.0556674 | − | 0.998449i | \(-0.482271\pi\) | ||||
0.0556674 | + | 0.998449i | \(0.482271\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 2.05940 | 0.472459 | 0.236230 | − | 0.971697i | \(-0.424088\pi\) | ||||
0.236230 | + | 0.971697i | \(0.424088\pi\) | |||||||
\(20\) | 1.02849 | 0.229977 | ||||||||
\(21\) | 4.96874 | 1.08427 | ||||||||
\(22\) | −4.09511 | −0.873081 | ||||||||
\(23\) | 7.97226 | 1.66233 | 0.831165 | − | 0.556025i | \(-0.187674\pi\) | ||||
0.831165 | + | 0.556025i | \(0.187674\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −3.94221 | −0.788443 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −4.96874 | −0.939004 | ||||||||
\(29\) | 3.58639 | 0.665975 | 0.332988 | − | 0.942931i | \(-0.391943\pi\) | ||||
0.332988 | + | 0.942931i | \(0.391943\pi\) | |||||||
\(30\) | 1.02849 | 0.187775 | ||||||||
\(31\) | −9.09347 | −1.63324 | −0.816618 | − | 0.577179i | \(-0.804154\pi\) | ||||
−0.816618 | + | 0.577179i | \(0.804154\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −4.09511 | −0.712868 | ||||||||
\(34\) | −0.459045 | −0.0787256 | ||||||||
\(35\) | −5.11029 | −0.863797 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −6.55603 | −1.07780 | −0.538902 | − | 0.842368i | \(-0.681161\pi\) | ||||
−0.538902 | + | 0.842368i | \(0.681161\pi\) | |||||||
\(38\) | −2.05940 | −0.334079 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −1.02849 | −0.162618 | ||||||||
\(41\) | 5.24275 | 0.818779 | 0.409390 | − | 0.912360i | \(-0.365742\pi\) | ||||
0.409390 | + | 0.912360i | \(0.365742\pi\) | |||||||
\(42\) | −4.96874 | −0.766693 | ||||||||
\(43\) | 8.24715 | 1.25768 | 0.628840 | − | 0.777535i | \(-0.283530\pi\) | ||||
0.628840 | + | 0.777535i | \(0.283530\pi\) | |||||||
\(44\) | 4.09511 | 0.617361 | ||||||||
\(45\) | 1.02849 | 0.153318 | ||||||||
\(46\) | −7.97226 | −1.17545 | ||||||||
\(47\) | 1.59375 | 0.232473 | 0.116236 | − | 0.993222i | \(-0.462917\pi\) | ||||
0.116236 | + | 0.993222i | \(0.462917\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 17.6884 | 2.52691 | ||||||||
\(50\) | 3.94221 | 0.557513 | ||||||||
\(51\) | −0.459045 | −0.0642792 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | 5.49115 | 0.754267 | 0.377133 | − | 0.926159i | \(-0.376910\pi\) | ||||
0.377133 | + | 0.926159i | \(0.376910\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 4.21177 | 0.567915 | ||||||||
\(56\) | 4.96874 | 0.663976 | ||||||||
\(57\) | −2.05940 | −0.272774 | ||||||||
\(58\) | −3.58639 | −0.470916 | ||||||||
\(59\) | −2.90936 | −0.378767 | −0.189383 | − | 0.981903i | \(-0.560649\pi\) | ||||
−0.189383 | + | 0.981903i | \(0.560649\pi\) | |||||||
\(60\) | −1.02849 | −0.132777 | ||||||||
\(61\) | −9.24844 | −1.18414 | −0.592071 | − | 0.805886i | \(-0.701689\pi\) | ||||
−0.592071 | + | 0.805886i | \(0.701689\pi\) | |||||||
\(62\) | 9.09347 | 1.15487 | ||||||||
\(63\) | −4.96874 | −0.626003 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.02849 | 0.127568 | ||||||||
\(66\) | 4.09511 | 0.504074 | ||||||||
\(67\) | −1.92754 | −0.235487 | −0.117743 | − | 0.993044i | \(-0.537566\pi\) | ||||
−0.117743 | + | 0.993044i | \(0.537566\pi\) | |||||||
\(68\) | 0.459045 | 0.0556674 | ||||||||
\(69\) | −7.97226 | −0.959747 | ||||||||
\(70\) | 5.11029 | 0.610797 | ||||||||
\(71\) | 12.7767 | 1.51632 | 0.758160 | − | 0.652069i | \(-0.226099\pi\) | ||||
0.758160 | + | 0.652069i | \(0.226099\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −1.18160 | −0.138296 | −0.0691481 | − | 0.997606i | \(-0.522028\pi\) | ||||
−0.0691481 | + | 0.997606i | \(0.522028\pi\) | |||||||
\(74\) | 6.55603 | 0.762123 | ||||||||
\(75\) | 3.94221 | 0.455208 | ||||||||
\(76\) | 2.05940 | 0.236230 | ||||||||
\(77\) | −20.3476 | −2.31882 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | 10.7487 | 1.20933 | 0.604663 | − | 0.796481i | \(-0.293308\pi\) | ||||
0.604663 | + | 0.796481i | \(0.293308\pi\) | |||||||
\(80\) | 1.02849 | 0.114988 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.24275 | −0.578964 | ||||||||
\(83\) | −16.0640 | −1.76325 | −0.881627 | − | 0.471946i | \(-0.843552\pi\) | ||||
−0.881627 | + | 0.471946i | \(0.843552\pi\) | |||||||
\(84\) | 4.96874 | 0.542134 | ||||||||
\(85\) | 0.472123 | 0.0512089 | ||||||||
\(86\) | −8.24715 | −0.889313 | ||||||||
\(87\) | −3.58639 | −0.384501 | ||||||||
\(88\) | −4.09511 | −0.436540 | ||||||||
\(89\) | 15.5497 | 1.64827 | 0.824133 | − | 0.566396i | \(-0.191663\pi\) | ||||
0.824133 | + | 0.566396i | \(0.191663\pi\) | |||||||
\(90\) | −1.02849 | −0.108412 | ||||||||
\(91\) | −4.96874 | −0.520866 | ||||||||
\(92\) | 7.97226 | 0.831165 | ||||||||
\(93\) | 9.09347 | 0.942949 | ||||||||
\(94\) | −1.59375 | −0.164383 | ||||||||
\(95\) | 2.11807 | 0.217309 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −15.5491 | −1.57877 | −0.789386 | − | 0.613897i | \(-0.789601\pi\) | ||||
−0.789386 | + | 0.613897i | \(0.789601\pi\) | |||||||
\(98\) | −17.6884 | −1.78680 | ||||||||
\(99\) | 4.09511 | 0.411574 | ||||||||
\(100\) | −3.94221 | −0.394221 | ||||||||
\(101\) | −11.6401 | −1.15824 | −0.579118 | − | 0.815244i | \(-0.696603\pi\) | ||||
−0.579118 | + | 0.815244i | \(0.696603\pi\) | |||||||
\(102\) | 0.459045 | 0.0454523 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 5.11029 | 0.498713 | ||||||||
\(106\) | −5.49115 | −0.533347 | ||||||||
\(107\) | 10.8455 | 1.04848 | 0.524239 | − | 0.851571i | \(-0.324350\pi\) | ||||
0.524239 | + | 0.851571i | \(0.324350\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −16.0922 | −1.54136 | −0.770679 | − | 0.637224i | \(-0.780083\pi\) | ||||
−0.770679 | + | 0.637224i | \(0.780083\pi\) | |||||||
\(110\) | −4.21177 | −0.401577 | ||||||||
\(111\) | 6.55603 | 0.622270 | ||||||||
\(112\) | −4.96874 | −0.469502 | ||||||||
\(113\) | −14.8459 | −1.39658 | −0.698291 | − | 0.715814i | \(-0.746056\pi\) | ||||
−0.698291 | + | 0.715814i | \(0.746056\pi\) | |||||||
\(114\) | 2.05940 | 0.192881 | ||||||||
\(115\) | 8.19937 | 0.764595 | ||||||||
\(116\) | 3.58639 | 0.332988 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 2.90936 | 0.267828 | ||||||||
\(119\) | −2.28088 | −0.209088 | ||||||||
\(120\) | 1.02849 | 0.0938877 | ||||||||
\(121\) | 5.76995 | 0.524541 | ||||||||
\(122\) | 9.24844 | 0.837314 | ||||||||
\(123\) | −5.24275 | −0.472722 | ||||||||
\(124\) | −9.09347 | −0.816618 | ||||||||
\(125\) | −9.19696 | −0.822601 | ||||||||
\(126\) | 4.96874 | 0.442651 | ||||||||
\(127\) | 0.472953 | 0.0419678 | 0.0209839 | − | 0.999780i | \(-0.493320\pi\) | ||||
0.0209839 | + | 0.999780i | \(0.493320\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −8.24715 | −0.726121 | ||||||||
\(130\) | −1.02849 | −0.0902044 | ||||||||
\(131\) | 5.27085 | 0.460517 | 0.230258 | − | 0.973130i | \(-0.426043\pi\) | ||||
0.230258 | + | 0.973130i | \(0.426043\pi\) | |||||||
\(132\) | −4.09511 | −0.356434 | ||||||||
\(133\) | −10.2326 | −0.887282 | ||||||||
\(134\) | 1.92754 | 0.166514 | ||||||||
\(135\) | −1.02849 | −0.0885181 | ||||||||
\(136\) | −0.459045 | −0.0393628 | ||||||||
\(137\) | −3.17885 | −0.271587 | −0.135794 | − | 0.990737i | \(-0.543358\pi\) | ||||
−0.135794 | + | 0.990737i | \(0.543358\pi\) | |||||||
\(138\) | 7.97226 | 0.678644 | ||||||||
\(139\) | −0.950817 | −0.0806473 | −0.0403236 | − | 0.999187i | \(-0.512839\pi\) | ||||
−0.0403236 | + | 0.999187i | \(0.512839\pi\) | |||||||
\(140\) | −5.11029 | −0.431898 | ||||||||
\(141\) | −1.59375 | −0.134218 | ||||||||
\(142\) | −12.7767 | −1.07220 | ||||||||
\(143\) | 4.09511 | 0.342451 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 3.68855 | 0.306318 | ||||||||
\(146\) | 1.18160 | 0.0977901 | ||||||||
\(147\) | −17.6884 | −1.45891 | ||||||||
\(148\) | −6.55603 | −0.538902 | ||||||||
\(149\) | 6.42360 | 0.526242 | 0.263121 | − | 0.964763i | \(-0.415248\pi\) | ||||
0.263121 | + | 0.964763i | \(0.415248\pi\) | |||||||
\(150\) | −3.94221 | −0.321880 | ||||||||
\(151\) | 12.5514 | 1.02142 | 0.510710 | − | 0.859753i | \(-0.329383\pi\) | ||||
0.510710 | + | 0.859753i | \(0.329383\pi\) | |||||||
\(152\) | −2.05940 | −0.167040 | ||||||||
\(153\) | 0.459045 | 0.0371116 | ||||||||
\(154\) | 20.3476 | 1.63965 | ||||||||
\(155\) | −9.35253 | −0.751213 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | −16.7227 | −1.33462 | −0.667309 | − | 0.744781i | \(-0.732554\pi\) | ||||
−0.667309 | + | 0.744781i | \(0.732554\pi\) | |||||||
\(158\) | −10.7487 | −0.855123 | ||||||||
\(159\) | −5.49115 | −0.435476 | ||||||||
\(160\) | −1.02849 | −0.0813091 | ||||||||
\(161\) | −39.6121 | −3.12187 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 10.3522 | 0.810850 | 0.405425 | − | 0.914128i | \(-0.367123\pi\) | ||||
0.405425 | + | 0.914128i | \(0.367123\pi\) | |||||||
\(164\) | 5.24275 | 0.409390 | ||||||||
\(165\) | −4.21177 | −0.327886 | ||||||||
\(166\) | 16.0640 | 1.24681 | ||||||||
\(167\) | −11.8605 | −0.917797 | −0.458898 | − | 0.888489i | \(-0.651756\pi\) | ||||
−0.458898 | + | 0.888489i | \(0.651756\pi\) | |||||||
\(168\) | −4.96874 | −0.383347 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −0.472123 | −0.0362101 | ||||||||
\(171\) | 2.05940 | 0.157486 | ||||||||
\(172\) | 8.24715 | 0.628840 | ||||||||
\(173\) | 24.8743 | 1.89116 | 0.945581 | − | 0.325388i | \(-0.105495\pi\) | ||||
0.945581 | + | 0.325388i | \(0.105495\pi\) | |||||||
\(174\) | 3.58639 | 0.271883 | ||||||||
\(175\) | 19.5878 | 1.48070 | ||||||||
\(176\) | 4.09511 | 0.308681 | ||||||||
\(177\) | 2.90936 | 0.218681 | ||||||||
\(178\) | −15.5497 | −1.16550 | ||||||||
\(179\) | 7.75139 | 0.579366 | 0.289683 | − | 0.957123i | \(-0.406450\pi\) | ||||
0.289683 | + | 0.957123i | \(0.406450\pi\) | |||||||
\(180\) | 1.02849 | 0.0766590 | ||||||||
\(181\) | 17.7205 | 1.31715 | 0.658577 | − | 0.752513i | \(-0.271159\pi\) | ||||
0.658577 | + | 0.752513i | \(0.271159\pi\) | |||||||
\(182\) | 4.96874 | 0.368308 | ||||||||
\(183\) | 9.24844 | 0.683664 | ||||||||
\(184\) | −7.97226 | −0.587723 | ||||||||
\(185\) | −6.74279 | −0.495740 | ||||||||
\(186\) | −9.09347 | −0.666766 | ||||||||
\(187\) | 1.87984 | 0.137468 | ||||||||
\(188\) | 1.59375 | 0.116236 | ||||||||
\(189\) | 4.96874 | 0.361423 | ||||||||
\(190\) | −2.11807 | −0.153661 | ||||||||
\(191\) | 19.3541 | 1.40042 | 0.700209 | − | 0.713938i | \(-0.253090\pi\) | ||||
0.700209 | + | 0.713938i | \(0.253090\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −3.45493 | −0.248691 | −0.124346 | − | 0.992239i | \(-0.539683\pi\) | ||||
−0.124346 | + | 0.992239i | \(0.539683\pi\) | |||||||
\(194\) | 15.5491 | 1.11636 | ||||||||
\(195\) | −1.02849 | −0.0736515 | ||||||||
\(196\) | 17.6884 | 1.26346 | ||||||||
\(197\) | −8.07696 | −0.575459 | −0.287730 | − | 0.957712i | \(-0.592900\pi\) | ||||
−0.287730 | + | 0.957712i | \(0.592900\pi\) | |||||||
\(198\) | −4.09511 | −0.291027 | ||||||||
\(199\) | 10.6009 | 0.751477 | 0.375739 | − | 0.926726i | \(-0.377389\pi\) | ||||
0.375739 | + | 0.926726i | \(0.377389\pi\) | |||||||
\(200\) | 3.94221 | 0.278757 | ||||||||
\(201\) | 1.92754 | 0.135958 | ||||||||
\(202\) | 11.6401 | 0.818996 | ||||||||
\(203\) | −17.8198 | −1.25071 | ||||||||
\(204\) | −0.459045 | −0.0321396 | ||||||||
\(205\) | 5.39210 | 0.376601 | ||||||||
\(206\) | 1.00000 | 0.0696733 | ||||||||
\(207\) | 7.97226 | 0.554110 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | 8.43348 | 0.583356 | ||||||||
\(210\) | −5.11029 | −0.352644 | ||||||||
\(211\) | −6.54374 | −0.450490 | −0.225245 | − | 0.974302i | \(-0.572318\pi\) | ||||
−0.225245 | + | 0.974302i | \(0.572318\pi\) | |||||||
\(212\) | 5.49115 | 0.377133 | ||||||||
\(213\) | −12.7767 | −0.875448 | ||||||||
\(214\) | −10.8455 | −0.741385 | ||||||||
\(215\) | 8.48210 | 0.578474 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 45.1831 | 3.06723 | ||||||||
\(218\) | 16.0922 | 1.08990 | ||||||||
\(219\) | 1.18160 | 0.0798453 | ||||||||
\(220\) | 4.21177 | 0.283958 | ||||||||
\(221\) | 0.459045 | 0.0308787 | ||||||||
\(222\) | −6.55603 | −0.440012 | ||||||||
\(223\) | −5.38319 | −0.360485 | −0.180243 | − | 0.983622i | \(-0.557688\pi\) | ||||
−0.180243 | + | 0.983622i | \(0.557688\pi\) | |||||||
\(224\) | 4.96874 | 0.331988 | ||||||||
\(225\) | −3.94221 | −0.262814 | ||||||||
\(226\) | 14.8459 | 0.987532 | ||||||||
\(227\) | −5.14503 | −0.341488 | −0.170744 | − | 0.985315i | \(-0.554617\pi\) | ||||
−0.170744 | + | 0.985315i | \(0.554617\pi\) | |||||||
\(228\) | −2.05940 | −0.136387 | ||||||||
\(229\) | 14.1375 | 0.934231 | 0.467116 | − | 0.884196i | \(-0.345293\pi\) | ||||
0.467116 | + | 0.884196i | \(0.345293\pi\) | |||||||
\(230\) | −8.19937 | −0.540650 | ||||||||
\(231\) | 20.3476 | 1.33877 | ||||||||
\(232\) | −3.58639 | −0.235458 | ||||||||
\(233\) | −8.36084 | −0.547737 | −0.273869 | − | 0.961767i | \(-0.588303\pi\) | ||||
−0.273869 | + | 0.961767i | \(0.588303\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | 1.63916 | 0.106927 | ||||||||
\(236\) | −2.90936 | −0.189383 | ||||||||
\(237\) | −10.7487 | −0.698205 | ||||||||
\(238\) | 2.28088 | 0.147847 | ||||||||
\(239\) | 17.7749 | 1.14976 | 0.574882 | − | 0.818236i | \(-0.305048\pi\) | ||||
0.574882 | + | 0.818236i | \(0.305048\pi\) | |||||||
\(240\) | −1.02849 | −0.0663886 | ||||||||
\(241\) | −1.63447 | −0.105285 | −0.0526426 | − | 0.998613i | \(-0.516764\pi\) | ||||
−0.0526426 | + | 0.998613i | \(0.516764\pi\) | |||||||
\(242\) | −5.76995 | −0.370906 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −9.24844 | −0.592071 | ||||||||
\(245\) | 18.1923 | 1.16226 | ||||||||
\(246\) | 5.24275 | 0.334265 | ||||||||
\(247\) | 2.05940 | 0.131037 | ||||||||
\(248\) | 9.09347 | 0.577436 | ||||||||
\(249\) | 16.0640 | 1.01802 | ||||||||
\(250\) | 9.19696 | 0.581667 | ||||||||
\(251\) | −18.7438 | −1.18310 | −0.591549 | − | 0.806269i | \(-0.701483\pi\) | ||||
−0.591549 | + | 0.806269i | \(0.701483\pi\) | |||||||
\(252\) | −4.96874 | −0.313001 | ||||||||
\(253\) | 32.6473 | 2.05252 | ||||||||
\(254\) | −0.472953 | −0.0296757 | ||||||||
\(255\) | −0.472123 | −0.0295655 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −21.6529 | −1.35067 | −0.675334 | − | 0.737512i | \(-0.736000\pi\) | ||||
−0.675334 | + | 0.737512i | \(0.736000\pi\) | |||||||
\(258\) | 8.24715 | 0.513445 | ||||||||
\(259\) | 32.5752 | 2.02412 | ||||||||
\(260\) | 1.02849 | 0.0637841 | ||||||||
\(261\) | 3.58639 | 0.221992 | ||||||||
\(262\) | −5.27085 | −0.325634 | ||||||||
\(263\) | 16.9718 | 1.04653 | 0.523264 | − | 0.852170i | \(-0.324714\pi\) | ||||
0.523264 | + | 0.852170i | \(0.324714\pi\) | |||||||
\(264\) | 4.09511 | 0.252037 | ||||||||
\(265\) | 5.64758 | 0.346928 | ||||||||
\(266\) | 10.2326 | 0.627403 | ||||||||
\(267\) | −15.5497 | −0.951627 | ||||||||
\(268\) | −1.92754 | −0.117743 | ||||||||
\(269\) | 5.09786 | 0.310822 | 0.155411 | − | 0.987850i | \(-0.450330\pi\) | ||||
0.155411 | + | 0.987850i | \(0.450330\pi\) | |||||||
\(270\) | 1.02849 | 0.0625918 | ||||||||
\(271\) | −25.2640 | −1.53468 | −0.767338 | − | 0.641242i | \(-0.778419\pi\) | ||||
−0.767338 | + | 0.641242i | \(0.778419\pi\) | |||||||
\(272\) | 0.459045 | 0.0278337 | ||||||||
\(273\) | 4.96874 | 0.300722 | ||||||||
\(274\) | 3.17885 | 0.192041 | ||||||||
\(275\) | −16.1438 | −0.973508 | ||||||||
\(276\) | −7.97226 | −0.479874 | ||||||||
\(277\) | 30.4540 | 1.82981 | 0.914903 | − | 0.403675i | \(-0.132267\pi\) | ||||
0.914903 | + | 0.403675i | \(0.132267\pi\) | |||||||
\(278\) | 0.950817 | 0.0570262 | ||||||||
\(279\) | −9.09347 | −0.544412 | ||||||||
\(280\) | 5.11029 | 0.305398 | ||||||||
\(281\) | −21.9475 | −1.30928 | −0.654638 | − | 0.755943i | \(-0.727179\pi\) | ||||
−0.654638 | + | 0.755943i | \(0.727179\pi\) | |||||||
\(282\) | 1.59375 | 0.0949066 | ||||||||
\(283\) | −14.0193 | −0.833360 | −0.416680 | − | 0.909053i | \(-0.636807\pi\) | ||||
−0.416680 | + | 0.909053i | \(0.636807\pi\) | |||||||
\(284\) | 12.7767 | 0.758160 | ||||||||
\(285\) | −2.11807 | −0.125464 | ||||||||
\(286\) | −4.09511 | −0.242149 | ||||||||
\(287\) | −26.0498 | −1.53767 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −16.7893 | −0.987605 | ||||||||
\(290\) | −3.68855 | −0.216599 | ||||||||
\(291\) | 15.5491 | 0.911504 | ||||||||
\(292\) | −1.18160 | −0.0691481 | ||||||||
\(293\) | 32.0087 | 1.86997 | 0.934985 | − | 0.354688i | \(-0.115413\pi\) | ||||
0.934985 | + | 0.354688i | \(0.115413\pi\) | |||||||
\(294\) | 17.6884 | 1.03161 | ||||||||
\(295\) | −2.99224 | −0.174215 | ||||||||
\(296\) | 6.55603 | 0.381061 | ||||||||
\(297\) | −4.09511 | −0.237623 | ||||||||
\(298\) | −6.42360 | −0.372109 | ||||||||
\(299\) | 7.97226 | 0.461048 | ||||||||
\(300\) | 3.94221 | 0.227604 | ||||||||
\(301\) | −40.9780 | −2.36193 | ||||||||
\(302\) | −12.5514 | −0.722253 | ||||||||
\(303\) | 11.6401 | 0.668708 | ||||||||
\(304\) | 2.05940 | 0.118115 | ||||||||
\(305\) | −9.51191 | −0.544650 | ||||||||
\(306\) | −0.459045 | −0.0262419 | ||||||||
\(307\) | 8.88019 | 0.506819 | 0.253409 | − | 0.967359i | \(-0.418448\pi\) | ||||
0.253409 | + | 0.967359i | \(0.418448\pi\) | |||||||
\(308\) | −20.3476 | −1.15941 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 9.35253 | 0.531188 | ||||||||
\(311\) | 3.26270 | 0.185011 | 0.0925053 | − | 0.995712i | \(-0.470512\pi\) | ||||
0.0925053 | + | 0.995712i | \(0.470512\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | 15.9412 | 0.901050 | 0.450525 | − | 0.892764i | \(-0.351237\pi\) | ||||
0.450525 | + | 0.892764i | \(0.351237\pi\) | |||||||
\(314\) | 16.7227 | 0.943717 | ||||||||
\(315\) | −5.11029 | −0.287932 | ||||||||
\(316\) | 10.7487 | 0.604663 | ||||||||
\(317\) | 31.6414 | 1.77716 | 0.888578 | − | 0.458725i | \(-0.151694\pi\) | ||||
0.888578 | + | 0.458725i | \(0.151694\pi\) | |||||||
\(318\) | 5.49115 | 0.307928 | ||||||||
\(319\) | 14.6867 | 0.822295 | ||||||||
\(320\) | 1.02849 | 0.0574942 | ||||||||
\(321\) | −10.8455 | −0.605339 | ||||||||
\(322\) | 39.6121 | 2.20750 | ||||||||
\(323\) | 0.945359 | 0.0526012 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −3.94221 | −0.218675 | ||||||||
\(326\) | −10.3522 | −0.573358 | ||||||||
\(327\) | 16.0922 | 0.889903 | ||||||||
\(328\) | −5.24275 | −0.289482 | ||||||||
\(329\) | −7.91895 | −0.436586 | ||||||||
\(330\) | 4.21177 | 0.231851 | ||||||||
\(331\) | 23.7022 | 1.30279 | 0.651396 | − | 0.758738i | \(-0.274184\pi\) | ||||
0.651396 | + | 0.758738i | \(0.274184\pi\) | |||||||
\(332\) | −16.0640 | −0.881627 | ||||||||
\(333\) | −6.55603 | −0.359268 | ||||||||
\(334\) | 11.8605 | 0.648980 | ||||||||
\(335\) | −1.98246 | −0.108313 | ||||||||
\(336\) | 4.96874 | 0.271067 | ||||||||
\(337\) | −28.6757 | −1.56207 | −0.781033 | − | 0.624490i | \(-0.785307\pi\) | ||||
−0.781033 | + | 0.624490i | \(0.785307\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | 14.8459 | 0.806316 | ||||||||
\(340\) | 0.472123 | 0.0256044 | ||||||||
\(341\) | −37.2388 | −2.01659 | ||||||||
\(342\) | −2.05940 | −0.111360 | ||||||||
\(343\) | −53.1079 | −2.86756 | ||||||||
\(344\) | −8.24715 | −0.444657 | ||||||||
\(345\) | −8.19937 | −0.441439 | ||||||||
\(346\) | −24.8743 | −1.33725 | ||||||||
\(347\) | 11.0875 | 0.595208 | 0.297604 | − | 0.954689i | \(-0.403812\pi\) | ||||
0.297604 | + | 0.954689i | \(0.403812\pi\) | |||||||
\(348\) | −3.58639 | −0.192250 | ||||||||
\(349\) | −1.21549 | −0.0650636 | −0.0325318 | − | 0.999471i | \(-0.510357\pi\) | ||||
−0.0325318 | + | 0.999471i | \(0.510357\pi\) | |||||||
\(350\) | −19.5878 | −1.04701 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −4.09511 | −0.218270 | ||||||||
\(353\) | 35.0241 | 1.86415 | 0.932074 | − | 0.362269i | \(-0.117998\pi\) | ||||
0.932074 | + | 0.362269i | \(0.117998\pi\) | |||||||
\(354\) | −2.90936 | −0.154631 | ||||||||
\(355\) | 13.1407 | 0.697437 | ||||||||
\(356\) | 15.5497 | 0.824133 | ||||||||
\(357\) | 2.28088 | 0.120717 | ||||||||
\(358\) | −7.75139 | −0.409674 | ||||||||
\(359\) | −1.78365 | −0.0941373 | −0.0470687 | − | 0.998892i | \(-0.514988\pi\) | ||||
−0.0470687 | + | 0.998892i | \(0.514988\pi\) | |||||||
\(360\) | −1.02849 | −0.0542061 | ||||||||
\(361\) | −14.7589 | −0.776782 | ||||||||
\(362\) | −17.7205 | −0.931369 | ||||||||
\(363\) | −5.76995 | −0.302844 | ||||||||
\(364\) | −4.96874 | −0.260433 | ||||||||
\(365\) | −1.21526 | −0.0636098 | ||||||||
\(366\) | −9.24844 | −0.483424 | ||||||||
\(367\) | 28.0568 | 1.46455 | 0.732276 | − | 0.681008i | \(-0.238458\pi\) | ||||
0.732276 | + | 0.681008i | \(0.238458\pi\) | |||||||
\(368\) | 7.97226 | 0.415583 | ||||||||
\(369\) | 5.24275 | 0.272926 | ||||||||
\(370\) | 6.74279 | 0.350541 | ||||||||
\(371\) | −27.2841 | −1.41652 | ||||||||
\(372\) | 9.09347 | 0.471475 | ||||||||
\(373\) | 11.2886 | 0.584501 | 0.292251 | − | 0.956342i | \(-0.405596\pi\) | ||||
0.292251 | + | 0.956342i | \(0.405596\pi\) | |||||||
\(374\) | −1.87984 | −0.0972043 | ||||||||
\(375\) | 9.19696 | 0.474929 | ||||||||
\(376\) | −1.59375 | −0.0821915 | ||||||||
\(377\) | 3.58639 | 0.184708 | ||||||||
\(378\) | −4.96874 | −0.255564 | ||||||||
\(379\) | 27.1091 | 1.39250 | 0.696250 | − | 0.717799i | \(-0.254850\pi\) | ||||
0.696250 | + | 0.717799i | \(0.254850\pi\) | |||||||
\(380\) | 2.11807 | 0.108655 | ||||||||
\(381\) | −0.472953 | −0.0242301 | ||||||||
\(382\) | −19.3541 | −0.990244 | ||||||||
\(383\) | −14.4162 | −0.736632 | −0.368316 | − | 0.929701i | \(-0.620066\pi\) | ||||
−0.368316 | + | 0.929701i | \(0.620066\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −20.9272 | −1.06655 | ||||||||
\(386\) | 3.45493 | 0.175851 | ||||||||
\(387\) | 8.24715 | 0.419226 | ||||||||
\(388\) | −15.5491 | −0.789386 | ||||||||
\(389\) | −15.2367 | −0.772531 | −0.386266 | − | 0.922388i | \(-0.626235\pi\) | ||||
−0.386266 | + | 0.922388i | \(0.626235\pi\) | |||||||
\(390\) | 1.02849 | 0.0520795 | ||||||||
\(391\) | 3.65963 | 0.185075 | ||||||||
\(392\) | −17.6884 | −0.893399 | ||||||||
\(393\) | −5.27085 | −0.265879 | ||||||||
\(394\) | 8.07696 | 0.406911 | ||||||||
\(395\) | 11.0549 | 0.556234 | ||||||||
\(396\) | 4.09511 | 0.205787 | ||||||||
\(397\) | −31.4044 | −1.57614 | −0.788071 | − | 0.615585i | \(-0.788920\pi\) | ||||
−0.788071 | + | 0.615585i | \(0.788920\pi\) | |||||||
\(398\) | −10.6009 | −0.531375 | ||||||||
\(399\) | 10.2326 | 0.512272 | ||||||||
\(400\) | −3.94221 | −0.197111 | ||||||||
\(401\) | −8.39107 | −0.419030 | −0.209515 | − | 0.977805i | \(-0.567189\pi\) | ||||
−0.209515 | + | 0.977805i | \(0.567189\pi\) | |||||||
\(402\) | −1.92754 | −0.0961372 | ||||||||
\(403\) | −9.09347 | −0.452978 | ||||||||
\(404\) | −11.6401 | −0.579118 | ||||||||
\(405\) | 1.02849 | 0.0511060 | ||||||||
\(406\) | 17.8198 | 0.884383 | ||||||||
\(407\) | −26.8477 | −1.33079 | ||||||||
\(408\) | 0.459045 | 0.0227261 | ||||||||
\(409\) | −14.6020 | −0.722022 | −0.361011 | − | 0.932562i | \(-0.617568\pi\) | ||||
−0.361011 | + | 0.932562i | \(0.617568\pi\) | |||||||
\(410\) | −5.39210 | −0.266297 | ||||||||
\(411\) | 3.17885 | 0.156801 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | 14.4559 | 0.711327 | ||||||||
\(414\) | −7.97226 | −0.391815 | ||||||||
\(415\) | −16.5216 | −0.811016 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | 0.950817 | 0.0465617 | ||||||||
\(418\) | −8.43348 | −0.412495 | ||||||||
\(419\) | −34.2605 | −1.67373 | −0.836867 | − | 0.547406i | \(-0.815615\pi\) | ||||
−0.836867 | + | 0.547406i | \(0.815615\pi\) | |||||||
\(420\) | 5.11029 | 0.249357 | ||||||||
\(421\) | 35.7527 | 1.74248 | 0.871239 | − | 0.490858i | \(-0.163317\pi\) | ||||
0.871239 | + | 0.490858i | \(0.163317\pi\) | |||||||
\(422\) | 6.54374 | 0.318544 | ||||||||
\(423\) | 1.59375 | 0.0774909 | ||||||||
\(424\) | −5.49115 | −0.266674 | ||||||||
\(425\) | −1.80965 | −0.0877811 | ||||||||
\(426\) | 12.7767 | 0.619035 | ||||||||
\(427\) | 45.9531 | 2.22383 | ||||||||
\(428\) | 10.8455 | 0.524239 | ||||||||
\(429\) | −4.09511 | −0.197714 | ||||||||
\(430\) | −8.48210 | −0.409043 | ||||||||
\(431\) | −7.35529 | −0.354292 | −0.177146 | − | 0.984185i | \(-0.556686\pi\) | ||||
−0.177146 | + | 0.984185i | \(0.556686\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −15.3502 | −0.737684 | −0.368842 | − | 0.929492i | \(-0.620246\pi\) | ||||
−0.368842 | + | 0.929492i | \(0.620246\pi\) | |||||||
\(434\) | −45.1831 | −2.16886 | ||||||||
\(435\) | −3.68855 | −0.176853 | ||||||||
\(436\) | −16.0922 | −0.770679 | ||||||||
\(437\) | 16.4181 | 0.785383 | ||||||||
\(438\) | −1.18160 | −0.0564592 | ||||||||
\(439\) | 28.9661 | 1.38248 | 0.691238 | − | 0.722627i | \(-0.257066\pi\) | ||||
0.691238 | + | 0.722627i | \(0.257066\pi\) | |||||||
\(440\) | −4.21177 | −0.200788 | ||||||||
\(441\) | 17.6884 | 0.842304 | ||||||||
\(442\) | −0.459045 | −0.0218346 | ||||||||
\(443\) | 19.1078 | 0.907838 | 0.453919 | − | 0.891043i | \(-0.350026\pi\) | ||||
0.453919 | + | 0.891043i | \(0.350026\pi\) | |||||||
\(444\) | 6.55603 | 0.311135 | ||||||||
\(445\) | 15.9927 | 0.758126 | ||||||||
\(446\) | 5.38319 | 0.254902 | ||||||||
\(447\) | −6.42360 | −0.303826 | ||||||||
\(448\) | −4.96874 | −0.234751 | ||||||||
\(449\) | 13.3828 | 0.631575 | 0.315787 | − | 0.948830i | \(-0.397731\pi\) | ||||
0.315787 | + | 0.948830i | \(0.397731\pi\) | |||||||
\(450\) | 3.94221 | 0.185838 | ||||||||
\(451\) | 21.4696 | 1.01097 | ||||||||
\(452\) | −14.8459 | −0.698291 | ||||||||
\(453\) | −12.5514 | −0.589717 | ||||||||
\(454\) | 5.14503 | 0.241468 | ||||||||
\(455\) | −5.11029 | −0.239574 | ||||||||
\(456\) | 2.05940 | 0.0964403 | ||||||||
\(457\) | 28.3863 | 1.32786 | 0.663928 | − | 0.747796i | \(-0.268888\pi\) | ||||
0.663928 | + | 0.747796i | \(0.268888\pi\) | |||||||
\(458\) | −14.1375 | −0.660601 | ||||||||
\(459\) | −0.459045 | −0.0214264 | ||||||||
\(460\) | 8.19937 | 0.382298 | ||||||||
\(461\) | 21.3334 | 0.993594 | 0.496797 | − | 0.867867i | \(-0.334509\pi\) | ||||
0.496797 | + | 0.867867i | \(0.334509\pi\) | |||||||
\(462\) | −20.3476 | −0.946654 | ||||||||
\(463\) | 17.6985 | 0.822519 | 0.411259 | − | 0.911518i | \(-0.365089\pi\) | ||||
0.411259 | + | 0.911518i | \(0.365089\pi\) | |||||||
\(464\) | 3.58639 | 0.166494 | ||||||||
\(465\) | 9.35253 | 0.433713 | ||||||||
\(466\) | 8.36084 | 0.387309 | ||||||||
\(467\) | 2.08932 | 0.0966821 | 0.0483411 | − | 0.998831i | \(-0.484607\pi\) | ||||
0.0483411 | + | 0.998831i | \(0.484607\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | 9.57747 | 0.442246 | ||||||||
\(470\) | −1.63916 | −0.0756086 | ||||||||
\(471\) | 16.7227 | 0.770542 | ||||||||
\(472\) | 2.90936 | 0.133914 | ||||||||
\(473\) | 33.7730 | 1.55289 | ||||||||
\(474\) | 10.7487 | 0.493705 | ||||||||
\(475\) | −8.11860 | −0.372507 | ||||||||
\(476\) | −2.28088 | −0.104544 | ||||||||
\(477\) | 5.49115 | 0.251422 | ||||||||
\(478\) | −17.7749 | −0.813006 | ||||||||
\(479\) | 42.6843 | 1.95030 | 0.975148 | − | 0.221552i | \(-0.0711124\pi\) | ||||
0.975148 | + | 0.221552i | \(0.0711124\pi\) | |||||||
\(480\) | 1.02849 | 0.0469438 | ||||||||
\(481\) | −6.55603 | −0.298929 | ||||||||
\(482\) | 1.63447 | 0.0744479 | ||||||||
\(483\) | 39.6121 | 1.80241 | ||||||||
\(484\) | 5.76995 | 0.262270 | ||||||||
\(485\) | −15.9921 | −0.726162 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −10.8026 | −0.489512 | −0.244756 | − | 0.969585i | \(-0.578708\pi\) | ||||
−0.244756 | + | 0.969585i | \(0.578708\pi\) | |||||||
\(488\) | 9.24844 | 0.418657 | ||||||||
\(489\) | −10.3522 | −0.468145 | ||||||||
\(490\) | −18.1923 | −0.821844 | ||||||||
\(491\) | −3.24078 | −0.146254 | −0.0731271 | − | 0.997323i | \(-0.523298\pi\) | ||||
−0.0731271 | + | 0.997323i | \(0.523298\pi\) | |||||||
\(492\) | −5.24275 | −0.236361 | ||||||||
\(493\) | 1.64631 | 0.0741462 | ||||||||
\(494\) | −2.05940 | −0.0926569 | ||||||||
\(495\) | 4.21177 | 0.189305 | ||||||||
\(496\) | −9.09347 | −0.408309 | ||||||||
\(497\) | −63.4843 | −2.84766 | ||||||||
\(498\) | −16.0640 | −0.719846 | ||||||||
\(499\) | 42.1087 | 1.88504 | 0.942521 | − | 0.334146i | \(-0.108448\pi\) | ||||
0.942521 | + | 0.334146i | \(0.108448\pi\) | |||||||
\(500\) | −9.19696 | −0.411300 | ||||||||
\(501\) | 11.8605 | 0.529890 | ||||||||
\(502\) | 18.7438 | 0.836577 | ||||||||
\(503\) | 33.9257 | 1.51267 | 0.756336 | − | 0.654183i | \(-0.226988\pi\) | ||||
0.756336 | + | 0.654183i | \(0.226988\pi\) | |||||||
\(504\) | 4.96874 | 0.221325 | ||||||||
\(505\) | −11.9717 | −0.532735 | ||||||||
\(506\) | −32.6473 | −1.45135 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 0.472953 | 0.0209839 | ||||||||
\(509\) | 15.7968 | 0.700181 | 0.350090 | − | 0.936716i | \(-0.386151\pi\) | ||||
0.350090 | + | 0.936716i | \(0.386151\pi\) | |||||||
\(510\) | 0.472123 | 0.0209059 | ||||||||
\(511\) | 5.87108 | 0.259721 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −2.05940 | −0.0909248 | ||||||||
\(514\) | 21.6529 | 0.955066 | ||||||||
\(515\) | −1.02849 | −0.0453206 | ||||||||
\(516\) | −8.24715 | −0.363061 | ||||||||
\(517\) | 6.52660 | 0.287039 | ||||||||
\(518\) | −32.5752 | −1.43127 | ||||||||
\(519\) | −24.8743 | −1.09186 | ||||||||
\(520\) | −1.02849 | −0.0451022 | ||||||||
\(521\) | 4.30005 | 0.188388 | 0.0941942 | − | 0.995554i | \(-0.469973\pi\) | ||||
0.0941942 | + | 0.995554i | \(0.469973\pi\) | |||||||
\(522\) | −3.58639 | −0.156972 | ||||||||
\(523\) | −12.3676 | −0.540796 | −0.270398 | − | 0.962749i | \(-0.587155\pi\) | ||||
−0.270398 | + | 0.962749i | \(0.587155\pi\) | |||||||
\(524\) | 5.27085 | 0.230258 | ||||||||
\(525\) | −19.5878 | −0.854883 | ||||||||
\(526\) | −16.9718 | −0.740008 | ||||||||
\(527\) | −4.17432 | −0.181836 | ||||||||
\(528\) | −4.09511 | −0.178217 | ||||||||
\(529\) | 40.5569 | 1.76334 | ||||||||
\(530\) | −5.64758 | −0.245315 | ||||||||
\(531\) | −2.90936 | −0.126256 | ||||||||
\(532\) | −10.2326 | −0.443641 | ||||||||
\(533\) | 5.24275 | 0.227089 | ||||||||
\(534\) | 15.5497 | 0.672902 | ||||||||
\(535\) | 11.1545 | 0.482251 | ||||||||
\(536\) | 1.92754 | 0.0832572 | ||||||||
\(537\) | −7.75139 | −0.334497 | ||||||||
\(538\) | −5.09786 | −0.219784 | ||||||||
\(539\) | 72.4360 | 3.12004 | ||||||||
\(540\) | −1.02849 | −0.0442591 | ||||||||
\(541\) | 33.6022 | 1.44467 | 0.722336 | − | 0.691542i | \(-0.243068\pi\) | ||||
0.722336 | + | 0.691542i | \(0.243068\pi\) | |||||||
\(542\) | 25.2640 | 1.08518 | ||||||||
\(543\) | −17.7205 | −0.760459 | ||||||||
\(544\) | −0.459045 | −0.0196814 | ||||||||
\(545\) | −16.5507 | −0.708953 | ||||||||
\(546\) | −4.96874 | −0.212643 | ||||||||
\(547\) | 24.7409 | 1.05785 | 0.528923 | − | 0.848670i | \(-0.322596\pi\) | ||||
0.528923 | + | 0.848670i | \(0.322596\pi\) | |||||||
\(548\) | −3.17885 | −0.135794 | ||||||||
\(549\) | −9.24844 | −0.394714 | ||||||||
\(550\) | 16.1438 | 0.688374 | ||||||||
\(551\) | 7.38581 | 0.314646 | ||||||||
\(552\) | 7.97226 | 0.339322 | ||||||||
\(553\) | −53.4077 | −2.27112 | ||||||||
\(554\) | −30.4540 | −1.29387 | ||||||||
\(555\) | 6.74279 | 0.286216 | ||||||||
\(556\) | −0.950817 | −0.0403236 | ||||||||
\(557\) | 4.47790 | 0.189735 | 0.0948674 | − | 0.995490i | \(-0.469757\pi\) | ||||
0.0948674 | + | 0.995490i | \(0.469757\pi\) | |||||||
\(558\) | 9.09347 | 0.384957 | ||||||||
\(559\) | 8.24715 | 0.348817 | ||||||||
\(560\) | −5.11029 | −0.215949 | ||||||||
\(561\) | −1.87984 | −0.0793670 | ||||||||
\(562\) | 21.9475 | 0.925798 | ||||||||
\(563\) | −3.44667 | −0.145260 | −0.0726298 | − | 0.997359i | \(-0.523139\pi\) | ||||
−0.0726298 | + | 0.997359i | \(0.523139\pi\) | |||||||
\(564\) | −1.59375 | −0.0671091 | ||||||||
\(565\) | −15.2688 | −0.642363 | ||||||||
\(566\) | 14.0193 | 0.589275 | ||||||||
\(567\) | −4.96874 | −0.208668 | ||||||||
\(568\) | −12.7767 | −0.536100 | ||||||||
\(569\) | −15.1304 | −0.634301 | −0.317151 | − | 0.948375i | \(-0.602726\pi\) | ||||
−0.317151 | + | 0.948375i | \(0.602726\pi\) | |||||||
\(570\) | 2.11807 | 0.0887162 | ||||||||
\(571\) | 14.3366 | 0.599970 | 0.299985 | − | 0.953944i | \(-0.403018\pi\) | ||||
0.299985 | + | 0.953944i | \(0.403018\pi\) | |||||||
\(572\) | 4.09511 | 0.171225 | ||||||||
\(573\) | −19.3541 | −0.808531 | ||||||||
\(574\) | 26.0498 | 1.08730 | ||||||||
\(575\) | −31.4283 | −1.31065 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −29.2586 | −1.21805 | −0.609025 | − | 0.793151i | \(-0.708439\pi\) | ||||
−0.609025 | + | 0.793151i | \(0.708439\pi\) | |||||||
\(578\) | 16.7893 | 0.698342 | ||||||||
\(579\) | 3.45493 | 0.143582 | ||||||||
\(580\) | 3.68855 | 0.153159 | ||||||||
\(581\) | 79.8179 | 3.31141 | ||||||||
\(582\) | −15.5491 | −0.644531 | ||||||||
\(583\) | 22.4869 | 0.931311 | ||||||||
\(584\) | 1.18160 | 0.0488951 | ||||||||
\(585\) | 1.02849 | 0.0425227 | ||||||||
\(586\) | −32.0087 | −1.32227 | ||||||||
\(587\) | −34.5674 | −1.42675 | −0.713374 | − | 0.700783i | \(-0.752834\pi\) | ||||
−0.713374 | + | 0.700783i | \(0.752834\pi\) | |||||||
\(588\) | −17.6884 | −0.729457 | ||||||||
\(589\) | −18.7271 | −0.771637 | ||||||||
\(590\) | 2.99224 | 0.123189 | ||||||||
\(591\) | 8.07696 | 0.332242 | ||||||||
\(592\) | −6.55603 | −0.269451 | ||||||||
\(593\) | 44.3419 | 1.82090 | 0.910452 | − | 0.413615i | \(-0.135734\pi\) | ||||
0.910452 | + | 0.413615i | \(0.135734\pi\) | |||||||
\(594\) | 4.09511 | 0.168025 | ||||||||
\(595\) | −2.34585 | −0.0961707 | ||||||||
\(596\) | 6.42360 | 0.263121 | ||||||||
\(597\) | −10.6009 | −0.433865 | ||||||||
\(598\) | −7.97226 | −0.326010 | ||||||||
\(599\) | −5.66048 | −0.231281 | −0.115641 | − | 0.993291i | \(-0.536892\pi\) | ||||
−0.115641 | + | 0.993291i | \(0.536892\pi\) | |||||||
\(600\) | −3.94221 | −0.160940 | ||||||||
\(601\) | 27.2086 | 1.10986 | 0.554931 | − | 0.831896i | \(-0.312745\pi\) | ||||
0.554931 | + | 0.831896i | \(0.312745\pi\) | |||||||
\(602\) | 40.9780 | 1.67014 | ||||||||
\(603\) | −1.92754 | −0.0784957 | ||||||||
\(604\) | 12.5514 | 0.510710 | ||||||||
\(605\) | 5.93432 | 0.241264 | ||||||||
\(606\) | −11.6401 | −0.472848 | ||||||||
\(607\) | 27.1662 | 1.10264 | 0.551321 | − | 0.834293i | \(-0.314124\pi\) | ||||
0.551321 | + | 0.834293i | \(0.314124\pi\) | |||||||
\(608\) | −2.05940 | −0.0835198 | ||||||||
\(609\) | 17.8198 | 0.722096 | ||||||||
\(610\) | 9.51191 | 0.385126 | ||||||||
\(611\) | 1.59375 | 0.0644763 | ||||||||
\(612\) | 0.459045 | 0.0185558 | ||||||||
\(613\) | 2.06093 | 0.0832401 | 0.0416200 | − | 0.999134i | \(-0.486748\pi\) | ||||
0.0416200 | + | 0.999134i | \(0.486748\pi\) | |||||||
\(614\) | −8.88019 | −0.358375 | ||||||||
\(615\) | −5.39210 | −0.217430 | ||||||||
\(616\) | 20.3476 | 0.819826 | ||||||||
\(617\) | 3.32466 | 0.133846 | 0.0669229 | − | 0.997758i | \(-0.478682\pi\) | ||||
0.0669229 | + | 0.997758i | \(0.478682\pi\) | |||||||
\(618\) | −1.00000 | −0.0402259 | ||||||||
\(619\) | −10.2630 | −0.412506 | −0.206253 | − | 0.978499i | \(-0.566127\pi\) | ||||
−0.206253 | + | 0.978499i | \(0.566127\pi\) | |||||||
\(620\) | −9.35253 | −0.375607 | ||||||||
\(621\) | −7.97226 | −0.319916 | ||||||||
\(622\) | −3.26270 | −0.130822 | ||||||||
\(623\) | −77.2625 | −3.09546 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | 10.2521 | 0.410084 | ||||||||
\(626\) | −15.9412 | −0.637138 | ||||||||
\(627\) | −8.43348 | −0.336801 | ||||||||
\(628\) | −16.7227 | −0.667309 | ||||||||
\(629\) | −3.00951 | −0.119997 | ||||||||
\(630\) | 5.11029 | 0.203599 | ||||||||
\(631\) | −32.1948 | −1.28165 | −0.640827 | − | 0.767685i | \(-0.721409\pi\) | ||||
−0.640827 | + | 0.767685i | \(0.721409\pi\) | |||||||
\(632\) | −10.7487 | −0.427561 | ||||||||
\(633\) | 6.54374 | 0.260090 | ||||||||
\(634\) | −31.6414 | −1.25664 | ||||||||
\(635\) | 0.486426 | 0.0193032 | ||||||||
\(636\) | −5.49115 | −0.217738 | ||||||||
\(637\) | 17.6884 | 0.700840 | ||||||||
\(638\) | −14.6867 | −0.581450 | ||||||||
\(639\) | 12.7767 | 0.505440 | ||||||||
\(640\) | −1.02849 | −0.0406546 | ||||||||
\(641\) | 13.5087 | 0.533560 | 0.266780 | − | 0.963757i | \(-0.414040\pi\) | ||||
0.266780 | + | 0.963757i | \(0.414040\pi\) | |||||||
\(642\) | 10.8455 | 0.428039 | ||||||||
\(643\) | −19.4901 | −0.768613 | −0.384307 | − | 0.923205i | \(-0.625559\pi\) | ||||
−0.384307 | + | 0.923205i | \(0.625559\pi\) | |||||||
\(644\) | −39.6121 | −1.56093 | ||||||||
\(645\) | −8.48210 | −0.333982 | ||||||||
\(646\) | −0.945359 | −0.0371946 | ||||||||
\(647\) | 44.1340 | 1.73509 | 0.867544 | − | 0.497361i | \(-0.165697\pi\) | ||||
0.867544 | + | 0.497361i | \(0.165697\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −11.9142 | −0.467672 | ||||||||
\(650\) | 3.94221 | 0.154626 | ||||||||
\(651\) | −45.1831 | −1.77087 | ||||||||
\(652\) | 10.3522 | 0.405425 | ||||||||
\(653\) | −41.1137 | −1.60890 | −0.804452 | − | 0.594017i | \(-0.797541\pi\) | ||||
−0.804452 | + | 0.594017i | \(0.797541\pi\) | |||||||
\(654\) | −16.0922 | −0.629257 | ||||||||
\(655\) | 5.42101 | 0.211816 | ||||||||
\(656\) | 5.24275 | 0.204695 | ||||||||
\(657\) | −1.18160 | −0.0460987 | ||||||||
\(658\) | 7.91895 | 0.308713 | ||||||||
\(659\) | 46.5601 | 1.81372 | 0.906861 | − | 0.421429i | \(-0.138471\pi\) | ||||
0.906861 | + | 0.421429i | \(0.138471\pi\) | |||||||
\(660\) | −4.21177 | −0.163943 | ||||||||
\(661\) | −37.4969 | −1.45846 | −0.729230 | − | 0.684269i | \(-0.760122\pi\) | ||||
−0.729230 | + | 0.684269i | \(0.760122\pi\) | |||||||
\(662\) | −23.7022 | −0.921214 | ||||||||
\(663\) | −0.459045 | −0.0178278 | ||||||||
\(664\) | 16.0640 | 0.623405 | ||||||||
\(665\) | −10.5241 | −0.408109 | ||||||||
\(666\) | 6.55603 | 0.254041 | ||||||||
\(667\) | 28.5916 | 1.10707 | ||||||||
\(668\) | −11.8605 | −0.458898 | ||||||||
\(669\) | 5.38319 | 0.208126 | ||||||||
\(670\) | 1.98246 | 0.0765889 | ||||||||
\(671\) | −37.8734 | −1.46209 | ||||||||
\(672\) | −4.96874 | −0.191673 | ||||||||
\(673\) | 11.2045 | 0.431903 | 0.215951 | − | 0.976404i | \(-0.430715\pi\) | ||||
0.215951 | + | 0.976404i | \(0.430715\pi\) | |||||||
\(674\) | 28.6757 | 1.10455 | ||||||||
\(675\) | 3.94221 | 0.151736 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −49.1615 | −1.88943 | −0.944716 | − | 0.327890i | \(-0.893662\pi\) | ||||
−0.944716 | + | 0.327890i | \(0.893662\pi\) | |||||||
\(678\) | −14.8459 | −0.570152 | ||||||||
\(679\) | 77.2595 | 2.96495 | ||||||||
\(680\) | −0.472123 | −0.0181051 | ||||||||
\(681\) | 5.14503 | 0.197158 | ||||||||
\(682\) | 37.2388 | 1.42595 | ||||||||
\(683\) | −20.0565 | −0.767440 | −0.383720 | − | 0.923449i | \(-0.625357\pi\) | ||||
−0.383720 | + | 0.923449i | \(0.625357\pi\) | |||||||
\(684\) | 2.05940 | 0.0787432 | ||||||||
\(685\) | −3.26940 | −0.124918 | ||||||||
\(686\) | 53.1079 | 2.02767 | ||||||||
\(687\) | −14.1375 | −0.539379 | ||||||||
\(688\) | 8.24715 | 0.314420 | ||||||||
\(689\) | 5.49115 | 0.209196 | ||||||||
\(690\) | 8.19937 | 0.312145 | ||||||||
\(691\) | 15.0158 | 0.571227 | 0.285614 | − | 0.958345i | \(-0.407803\pi\) | ||||
0.285614 | + | 0.958345i | \(0.407803\pi\) | |||||||
\(692\) | 24.8743 | 0.945581 | ||||||||
\(693\) | −20.3476 | −0.772940 | ||||||||
\(694\) | −11.0875 | −0.420876 | ||||||||
\(695\) | −0.977904 | −0.0370940 | ||||||||
\(696\) | 3.58639 | 0.135942 | ||||||||
\(697\) | 2.40666 | 0.0911587 | ||||||||
\(698\) | 1.21549 | 0.0460069 | ||||||||
\(699\) | 8.36084 | 0.316236 | ||||||||
\(700\) | 19.5878 | 0.740351 | ||||||||
\(701\) | 38.1436 | 1.44066 | 0.720331 | − | 0.693630i | \(-0.243990\pi\) | ||||
0.720331 | + | 0.693630i | \(0.243990\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | −13.5015 | −0.509218 | ||||||||
\(704\) | 4.09511 | 0.154340 | ||||||||
\(705\) | −1.63916 | −0.0617342 | ||||||||
\(706\) | −35.0241 | −1.31815 | ||||||||
\(707\) | 57.8368 | 2.17518 | ||||||||
\(708\) | 2.90936 | 0.109341 | ||||||||
\(709\) | 5.87299 | 0.220565 | 0.110282 | − | 0.993900i | \(-0.464824\pi\) | ||||
0.110282 | + | 0.993900i | \(0.464824\pi\) | |||||||
\(710\) | −13.1407 | −0.493162 | ||||||||
\(711\) | 10.7487 | 0.403109 | ||||||||
\(712\) | −15.5497 | −0.582750 | ||||||||
\(713\) | −72.4955 | −2.71498 | ||||||||
\(714\) | −2.28088 | −0.0853597 | ||||||||
\(715\) | 4.21177 | 0.157511 | ||||||||
\(716\) | 7.75139 | 0.289683 | ||||||||
\(717\) | −17.7749 | −0.663816 | ||||||||
\(718\) | 1.78365 | 0.0665651 | ||||||||
\(719\) | −5.49463 | −0.204915 | −0.102458 | − | 0.994737i | \(-0.532671\pi\) | ||||
−0.102458 | + | 0.994737i | \(0.532671\pi\) | |||||||
\(720\) | 1.02849 | 0.0383295 | ||||||||
\(721\) | 4.96874 | 0.185046 | ||||||||
\(722\) | 14.7589 | 0.549268 | ||||||||
\(723\) | 1.63447 | 0.0607864 | ||||||||
\(724\) | 17.7205 | 0.658577 | ||||||||
\(725\) | −14.1383 | −0.525083 | ||||||||
\(726\) | 5.76995 | 0.214143 | ||||||||
\(727\) | 16.2167 | 0.601446 | 0.300723 | − | 0.953712i | \(-0.402772\pi\) | ||||
0.300723 | + | 0.953712i | \(0.402772\pi\) | |||||||
\(728\) | 4.96874 | 0.184154 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.21526 | 0.0449789 | ||||||||
\(731\) | 3.78582 | 0.140024 | ||||||||
\(732\) | 9.24844 | 0.341832 | ||||||||
\(733\) | −35.8501 | −1.32415 | −0.662076 | − | 0.749436i | \(-0.730325\pi\) | ||||
−0.662076 | + | 0.749436i | \(0.730325\pi\) | |||||||
\(734\) | −28.0568 | −1.03559 | ||||||||
\(735\) | −18.1923 | −0.671033 | ||||||||
\(736\) | −7.97226 | −0.293861 | ||||||||
\(737\) | −7.89351 | −0.290761 | ||||||||
\(738\) | −5.24275 | −0.192988 | ||||||||
\(739\) | 11.4133 | 0.419846 | 0.209923 | − | 0.977718i | \(-0.432679\pi\) | ||||
0.209923 | + | 0.977718i | \(0.432679\pi\) | |||||||
\(740\) | −6.74279 | −0.247870 | ||||||||
\(741\) | −2.05940 | −0.0756540 | ||||||||
\(742\) | 27.2841 | 1.00163 | ||||||||
\(743\) | −39.2609 | −1.44034 | −0.720172 | − | 0.693795i | \(-0.755937\pi\) | ||||
−0.720172 | + | 0.693795i | \(0.755937\pi\) | |||||||
\(744\) | −9.09347 | −0.333383 | ||||||||
\(745\) | 6.60660 | 0.242047 | ||||||||
\(746\) | −11.2886 | −0.413305 | ||||||||
\(747\) | −16.0640 | −0.587752 | ||||||||
\(748\) | 1.87984 | 0.0687338 | ||||||||
\(749\) | −53.8887 | −1.96905 | ||||||||
\(750\) | −9.19696 | −0.335825 | ||||||||
\(751\) | −27.9898 | −1.02136 | −0.510681 | − | 0.859770i | \(-0.670607\pi\) | ||||
−0.510681 | + | 0.859770i | \(0.670607\pi\) | |||||||
\(752\) | 1.59375 | 0.0581182 | ||||||||
\(753\) | 18.7438 | 0.683062 | ||||||||
\(754\) | −3.58639 | −0.130608 | ||||||||
\(755\) | 12.9090 | 0.469806 | ||||||||
\(756\) | 4.96874 | 0.180711 | ||||||||
\(757\) | 34.3539 | 1.24862 | 0.624308 | − | 0.781179i | \(-0.285381\pi\) | ||||
0.624308 | + | 0.781179i | \(0.285381\pi\) | |||||||
\(758\) | −27.1091 | −0.984647 | ||||||||
\(759\) | −32.6473 | −1.18502 | ||||||||
\(760\) | −2.11807 | −0.0768305 | ||||||||
\(761\) | −34.5760 | −1.25338 | −0.626689 | − | 0.779269i | \(-0.715591\pi\) | ||||
−0.626689 | + | 0.779269i | \(0.715591\pi\) | |||||||
\(762\) | 0.472953 | 0.0171333 | ||||||||
\(763\) | 79.9582 | 2.89468 | ||||||||
\(764\) | 19.3541 | 0.700209 | ||||||||
\(765\) | 0.472123 | 0.0170696 | ||||||||
\(766\) | 14.4162 | 0.520878 | ||||||||
\(767\) | −2.90936 | −0.105051 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −48.7406 | −1.75763 | −0.878816 | − | 0.477161i | \(-0.841666\pi\) | ||||
−0.878816 | + | 0.477161i | \(0.841666\pi\) | |||||||
\(770\) | 20.9272 | 0.754164 | ||||||||
\(771\) | 21.6529 | 0.779808 | ||||||||
\(772\) | −3.45493 | −0.124346 | ||||||||
\(773\) | −24.0093 | −0.863556 | −0.431778 | − | 0.901980i | \(-0.642114\pi\) | ||||
−0.431778 | + | 0.901980i | \(0.642114\pi\) | |||||||
\(774\) | −8.24715 | −0.296438 | ||||||||
\(775\) | 35.8484 | 1.28771 | ||||||||
\(776\) | 15.5491 | 0.558180 | ||||||||
\(777\) | −32.5752 | −1.16863 | ||||||||
\(778\) | 15.2367 | 0.546262 | ||||||||
\(779\) | 10.7969 | 0.386840 | ||||||||
\(780\) | −1.02849 | −0.0368258 | ||||||||
\(781\) | 52.3222 | 1.87223 | ||||||||
\(782\) | −3.65963 | −0.130868 | ||||||||
\(783\) | −3.58639 | −0.128167 | ||||||||
\(784\) | 17.6884 | 0.631728 | ||||||||
\(785\) | −17.1991 | −0.613863 | ||||||||
\(786\) | 5.27085 | 0.188005 | ||||||||
\(787\) | 42.5645 | 1.51726 | 0.758630 | − | 0.651522i | \(-0.225869\pi\) | ||||
0.758630 | + | 0.651522i | \(0.225869\pi\) | |||||||
\(788\) | −8.07696 | −0.287730 | ||||||||
\(789\) | −16.9718 | −0.604214 | ||||||||
\(790\) | −11.0549 | −0.393317 | ||||||||
\(791\) | 73.7652 | 2.62279 | ||||||||
\(792\) | −4.09511 | −0.145513 | ||||||||
\(793\) | −9.24844 | −0.328422 | ||||||||
\(794\) | 31.4044 | 1.11450 | ||||||||
\(795\) | −5.64758 | −0.200299 | ||||||||
\(796\) | 10.6009 | 0.375739 | ||||||||
\(797\) | −31.2353 | −1.10641 | −0.553205 | − | 0.833045i | \(-0.686595\pi\) | ||||
−0.553205 | + | 0.833045i | \(0.686595\pi\) | |||||||
\(798\) | −10.2326 | −0.362231 | ||||||||
\(799\) | 0.731605 | 0.0258823 | ||||||||
\(800\) | 3.94221 | 0.139378 | ||||||||
\(801\) | 15.5497 | 0.549422 | ||||||||
\(802\) | 8.39107 | 0.296299 | ||||||||
\(803\) | −4.83880 | −0.170757 | ||||||||
\(804\) | 1.92754 | 0.0679792 | ||||||||
\(805\) | −40.7406 | −1.43592 | ||||||||
\(806\) | 9.09347 | 0.320304 | ||||||||
\(807\) | −5.09786 | −0.179453 | ||||||||
\(808\) | 11.6401 | 0.409498 | ||||||||
\(809\) | −21.3621 | −0.751050 | −0.375525 | − | 0.926812i | \(-0.622538\pi\) | ||||
−0.375525 | + | 0.926812i | \(0.622538\pi\) | |||||||
\(810\) | −1.02849 | −0.0361374 | ||||||||
\(811\) | 37.5767 | 1.31949 | 0.659747 | − | 0.751487i | \(-0.270663\pi\) | ||||
0.659747 | + | 0.751487i | \(0.270663\pi\) | |||||||
\(812\) | −17.8198 | −0.625353 | ||||||||
\(813\) | 25.2640 | 0.886046 | ||||||||
\(814\) | 26.8477 | 0.941010 | ||||||||
\(815\) | 10.6472 | 0.372954 | ||||||||
\(816\) | −0.459045 | −0.0160698 | ||||||||
\(817\) | 16.9842 | 0.594202 | ||||||||
\(818\) | 14.6020 | 0.510546 | ||||||||
\(819\) | −4.96874 | −0.173622 | ||||||||
\(820\) | 5.39210 | 0.188300 | ||||||||
\(821\) | 16.8858 | 0.589320 | 0.294660 | − | 0.955602i | \(-0.404794\pi\) | ||||
0.294660 | + | 0.955602i | \(0.404794\pi\) | |||||||
\(822\) | −3.17885 | −0.110875 | ||||||||
\(823\) | 21.1535 | 0.737363 | 0.368682 | − | 0.929556i | \(-0.379809\pi\) | ||||
0.368682 | + | 0.929556i | \(0.379809\pi\) | |||||||
\(824\) | 1.00000 | 0.0348367 | ||||||||
\(825\) | 16.1438 | 0.562055 | ||||||||
\(826\) | −14.4559 | −0.502984 | ||||||||
\(827\) | 28.1599 | 0.979215 | 0.489607 | − | 0.871943i | \(-0.337140\pi\) | ||||
0.489607 | + | 0.871943i | \(0.337140\pi\) | |||||||
\(828\) | 7.97226 | 0.277055 | ||||||||
\(829\) | 37.7971 | 1.31275 | 0.656374 | − | 0.754436i | \(-0.272090\pi\) | ||||
0.656374 | + | 0.754436i | \(0.272090\pi\) | |||||||
\(830\) | 16.5216 | 0.573475 | ||||||||
\(831\) | −30.4540 | −1.05644 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 8.11977 | 0.281334 | ||||||||
\(834\) | −0.950817 | −0.0329241 | ||||||||
\(835\) | −12.1984 | −0.422144 | ||||||||
\(836\) | 8.43348 | 0.291678 | ||||||||
\(837\) | 9.09347 | 0.314316 | ||||||||
\(838\) | 34.2605 | 1.18351 | ||||||||
\(839\) | −26.5497 | −0.916597 | −0.458298 | − | 0.888798i | \(-0.651541\pi\) | ||||
−0.458298 | + | 0.888798i | \(0.651541\pi\) | |||||||
\(840\) | −5.11029 | −0.176322 | ||||||||
\(841\) | −16.1378 | −0.556477 | ||||||||
\(842\) | −35.7527 | −1.23212 | ||||||||
\(843\) | 21.9475 | 0.755911 | ||||||||
\(844\) | −6.54374 | −0.225245 | ||||||||
\(845\) | 1.02849 | 0.0353811 | ||||||||
\(846\) | −1.59375 | −0.0547944 | ||||||||
\(847\) | −28.6694 | −0.985091 | ||||||||
\(848\) | 5.49115 | 0.188567 | ||||||||
\(849\) | 14.0193 | 0.481141 | ||||||||
\(850\) | 1.80965 | 0.0620706 | ||||||||
\(851\) | −52.2663 | −1.79167 | ||||||||
\(852\) | −12.7767 | −0.437724 | ||||||||
\(853\) | 15.7644 | 0.539764 | 0.269882 | − | 0.962893i | \(-0.413015\pi\) | ||||
0.269882 | + | 0.962893i | \(0.413015\pi\) | |||||||
\(854\) | −45.9531 | −1.57248 | ||||||||
\(855\) | 2.11807 | 0.0724364 | ||||||||
\(856\) | −10.8455 | −0.370693 | ||||||||
\(857\) | 15.3382 | 0.523944 | 0.261972 | − | 0.965075i | \(-0.415627\pi\) | ||||
0.261972 | + | 0.965075i | \(0.415627\pi\) | |||||||
\(858\) | 4.09511 | 0.139805 | ||||||||
\(859\) | 38.6477 | 1.31864 | 0.659322 | − | 0.751861i | \(-0.270843\pi\) | ||||
0.659322 | + | 0.751861i | \(0.270843\pi\) | |||||||
\(860\) | 8.48210 | 0.289237 | ||||||||
\(861\) | 26.0498 | 0.887776 | ||||||||
\(862\) | 7.35529 | 0.250522 | ||||||||
\(863\) | −2.61626 | −0.0890585 | −0.0445293 | − | 0.999008i | \(-0.514179\pi\) | ||||
−0.0445293 | + | 0.999008i | \(0.514179\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 25.5830 | 0.869847 | ||||||||
\(866\) | 15.3502 | 0.521621 | ||||||||
\(867\) | 16.7893 | 0.570194 | ||||||||
\(868\) | 45.1831 | 1.53361 | ||||||||
\(869\) | 44.0173 | 1.49318 | ||||||||
\(870\) | 3.68855 | 0.125054 | ||||||||
\(871\) | −1.92754 | −0.0653123 | ||||||||
\(872\) | 16.0922 | 0.544952 | ||||||||
\(873\) | −15.5491 | −0.526257 | ||||||||
\(874\) | −16.4181 | −0.555350 | ||||||||
\(875\) | 45.6973 | 1.54485 | ||||||||
\(876\) | 1.18160 | 0.0399226 | ||||||||
\(877\) | 53.7139 | 1.81379 | 0.906895 | − | 0.421356i | \(-0.138446\pi\) | ||||
0.906895 | + | 0.421356i | \(0.138446\pi\) | |||||||
\(878\) | −28.9661 | −0.977558 | ||||||||
\(879\) | −32.0087 | −1.07963 | ||||||||
\(880\) | 4.21177 | 0.141979 | ||||||||
\(881\) | 20.3295 | 0.684917 | 0.342459 | − | 0.939533i | \(-0.388740\pi\) | ||||
0.342459 | + | 0.939533i | \(0.388740\pi\) | |||||||
\(882\) | −17.6884 | −0.595599 | ||||||||
\(883\) | 2.47317 | 0.0832289 | 0.0416145 | − | 0.999134i | \(-0.486750\pi\) | ||||
0.0416145 | + | 0.999134i | \(0.486750\pi\) | |||||||
\(884\) | 0.459045 | 0.0154394 | ||||||||
\(885\) | 2.99224 | 0.100583 | ||||||||
\(886\) | −19.1078 | −0.641938 | ||||||||
\(887\) | 47.5265 | 1.59578 | 0.797892 | − | 0.602800i | \(-0.205948\pi\) | ||||
0.797892 | + | 0.602800i | \(0.205948\pi\) | |||||||
\(888\) | −6.55603 | −0.220006 | ||||||||
\(889\) | −2.34998 | −0.0788158 | ||||||||
\(890\) | −15.9927 | −0.536076 | ||||||||
\(891\) | 4.09511 | 0.137191 | ||||||||
\(892\) | −5.38319 | −0.180243 | ||||||||
\(893\) | 3.28218 | 0.109834 | ||||||||
\(894\) | 6.42360 | 0.214837 | ||||||||
\(895\) | 7.97221 | 0.266482 | ||||||||
\(896\) | 4.96874 | 0.165994 | ||||||||
\(897\) | −7.97226 | −0.266186 | ||||||||
\(898\) | −13.3828 | −0.446591 | ||||||||
\(899\) | −32.6127 | −1.08769 | ||||||||
\(900\) | −3.94221 | −0.131407 | ||||||||
\(901\) | 2.52068 | 0.0839762 | ||||||||
\(902\) | −21.4696 | −0.714861 | ||||||||
\(903\) | 40.9780 | 1.36366 | ||||||||
\(904\) | 14.8459 | 0.493766 | ||||||||
\(905\) | 18.2253 | 0.605830 | ||||||||
\(906\) | 12.5514 | 0.416993 | ||||||||
\(907\) | −42.7178 | −1.41842 | −0.709211 | − | 0.704996i | \(-0.750949\pi\) | ||||
−0.709211 | + | 0.704996i | \(0.750949\pi\) | |||||||
\(908\) | −5.14503 | −0.170744 | ||||||||
\(909\) | −11.6401 | −0.386078 | ||||||||
\(910\) | 5.11029 | 0.169404 | ||||||||
\(911\) | −14.2876 | −0.473368 | −0.236684 | − | 0.971587i | \(-0.576061\pi\) | ||||
−0.236684 | + | 0.971587i | \(0.576061\pi\) | |||||||
\(912\) | −2.05940 | −0.0681936 | ||||||||
\(913\) | −65.7839 | −2.17713 | ||||||||
\(914\) | −28.3863 | −0.938936 | ||||||||
\(915\) | 9.51191 | 0.314454 | ||||||||
\(916\) | 14.1375 | 0.467116 | ||||||||
\(917\) | −26.1895 | −0.864854 | ||||||||
\(918\) | 0.459045 | 0.0151508 | ||||||||
\(919\) | −17.1869 | −0.566944 | −0.283472 | − | 0.958980i | \(-0.591486\pi\) | ||||
−0.283472 | + | 0.958980i | \(0.591486\pi\) | |||||||
\(920\) | −8.19937 | −0.270325 | ||||||||
\(921\) | −8.88019 | −0.292612 | ||||||||
\(922\) | −21.3334 | −0.702577 | ||||||||
\(923\) | 12.7767 | 0.420551 | ||||||||
\(924\) | 20.3476 | 0.669385 | ||||||||
\(925\) | 25.8453 | 0.849787 | ||||||||
\(926\) | −17.6985 | −0.581609 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | −3.58639 | −0.117729 | ||||||||
\(929\) | 18.2463 | 0.598642 | 0.299321 | − | 0.954152i | \(-0.403240\pi\) | ||||
0.299321 | + | 0.954152i | \(0.403240\pi\) | |||||||
\(930\) | −9.35253 | −0.306681 | ||||||||
\(931\) | 36.4275 | 1.19386 | ||||||||
\(932\) | −8.36084 | −0.273869 | ||||||||
\(933\) | −3.26270 | −0.106816 | ||||||||
\(934\) | −2.08932 | −0.0683646 | ||||||||
\(935\) | 1.93339 | 0.0632288 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | 21.6826 | 0.708339 | 0.354169 | − | 0.935181i | \(-0.384764\pi\) | ||||
0.354169 | + | 0.935181i | \(0.384764\pi\) | |||||||
\(938\) | −9.57747 | −0.312715 | ||||||||
\(939\) | −15.9412 | −0.520221 | ||||||||
\(940\) | 1.63916 | 0.0534634 | ||||||||
\(941\) | 54.5765 | 1.77914 | 0.889571 | − | 0.456796i | \(-0.151003\pi\) | ||||
0.889571 | + | 0.456796i | \(0.151003\pi\) | |||||||
\(942\) | −16.7227 | −0.544856 | ||||||||
\(943\) | 41.7965 | 1.36108 | ||||||||
\(944\) | −2.90936 | −0.0946917 | ||||||||
\(945\) | 5.11029 | 0.166238 | ||||||||
\(946\) | −33.7730 | −1.09806 | ||||||||
\(947\) | −32.0403 | −1.04117 | −0.520585 | − | 0.853810i | \(-0.674286\pi\) | ||||
−0.520585 | + | 0.853810i | \(0.674286\pi\) | |||||||
\(948\) | −10.7487 | −0.349102 | ||||||||
\(949\) | −1.18160 | −0.0383564 | ||||||||
\(950\) | 8.11860 | 0.263402 | ||||||||
\(951\) | −31.6414 | −1.02604 | ||||||||
\(952\) | 2.28088 | 0.0739237 | ||||||||
\(953\) | 52.5012 | 1.70068 | 0.850341 | − | 0.526232i | \(-0.176396\pi\) | ||||
0.850341 | + | 0.526232i | \(0.176396\pi\) | |||||||
\(954\) | −5.49115 | −0.177782 | ||||||||
\(955\) | 19.9055 | 0.644127 | ||||||||
\(956\) | 17.7749 | 0.574882 | ||||||||
\(957\) | −14.6867 | −0.474752 | ||||||||
\(958\) | −42.6843 | −1.37907 | ||||||||
\(959\) | 15.7949 | 0.510043 | ||||||||
\(960\) | −1.02849 | −0.0331943 | ||||||||
\(961\) | 51.6913 | 1.66746 | ||||||||
\(962\) | 6.55603 | 0.211375 | ||||||||
\(963\) | 10.8455 | 0.349492 | ||||||||
\(964\) | −1.63447 | −0.0526426 | ||||||||
\(965\) | −3.55335 | −0.114386 | ||||||||
\(966\) | −39.6121 | −1.27450 | ||||||||
\(967\) | −2.86221 | −0.0920424 | −0.0460212 | − | 0.998940i | \(-0.514654\pi\) | ||||
−0.0460212 | + | 0.998940i | \(0.514654\pi\) | |||||||
\(968\) | −5.76995 | −0.185453 | ||||||||
\(969\) | −0.945359 | −0.0303693 | ||||||||
\(970\) | 15.9921 | 0.513474 | ||||||||
\(971\) | −0.791041 | −0.0253857 | −0.0126928 | − | 0.999919i | \(-0.504040\pi\) | ||||
−0.0126928 | + | 0.999919i | \(0.504040\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 4.72437 | 0.151456 | ||||||||
\(974\) | 10.8026 | 0.346137 | ||||||||
\(975\) | 3.94221 | 0.126252 | ||||||||
\(976\) | −9.24844 | −0.296035 | ||||||||
\(977\) | −1.03227 | −0.0330252 | −0.0165126 | − | 0.999864i | \(-0.505256\pi\) | ||||
−0.0165126 | + | 0.999864i | \(0.505256\pi\) | |||||||
\(978\) | 10.3522 | 0.331028 | ||||||||
\(979\) | 63.6778 | 2.03515 | ||||||||
\(980\) | 18.1923 | 0.581132 | ||||||||
\(981\) | −16.0922 | −0.513786 | ||||||||
\(982\) | 3.24078 | 0.103417 | ||||||||
\(983\) | 37.2289 | 1.18742 | 0.593709 | − | 0.804679i | \(-0.297663\pi\) | ||||
0.593709 | + | 0.804679i | \(0.297663\pi\) | |||||||
\(984\) | 5.24275 | 0.167133 | ||||||||
\(985\) | −8.30705 | −0.264685 | ||||||||
\(986\) | −1.64631 | −0.0524293 | ||||||||
\(987\) | 7.91895 | 0.252063 | ||||||||
\(988\) | 2.05940 | 0.0655183 | ||||||||
\(989\) | 65.7484 | 2.09068 | ||||||||
\(990\) | −4.21177 | −0.133859 | ||||||||
\(991\) | 27.2031 | 0.864134 | 0.432067 | − | 0.901842i | \(-0.357784\pi\) | ||||
0.432067 | + | 0.901842i | \(0.357784\pi\) | |||||||
\(992\) | 9.09347 | 0.288718 | ||||||||
\(993\) | −23.7022 | −0.752168 | ||||||||
\(994\) | 63.4843 | 2.01360 | ||||||||
\(995\) | 10.9029 | 0.345645 | ||||||||
\(996\) | 16.0640 | 0.509008 | ||||||||
\(997\) | 18.8700 | 0.597620 | 0.298810 | − | 0.954313i | \(-0.403410\pi\) | ||||
0.298810 | + | 0.954313i | \(0.403410\pi\) | |||||||
\(998\) | −42.1087 | −1.33293 | ||||||||
\(999\) | 6.55603 | 0.207423 |
(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 | 8034.2.a.z.1.9 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.z.1.9 | ✓ | 14 | 1.1 | even | 1 | trivial |