Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6017,2,Mod(1,6017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6017, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6017 = 11 \cdot 547 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6017.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: | \(48.0459868962\) |
Analytic rank: | \(0\) |
Dimension: | \(121\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 6017.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.37440 | −1.67895 | −0.839475 | − | 0.543398i | \(-0.817138\pi\) | ||||
−0.839475 | + | 0.543398i | \(0.817138\pi\) | |||||||
\(3\) | −0.379878 | −0.219323 | −0.109661 | − | 0.993969i | \(-0.534977\pi\) | ||||
−0.109661 | + | 0.993969i | \(0.534977\pi\) | |||||||
\(4\) | 3.63775 | 1.81888 | ||||||||
\(5\) | −1.52566 | −0.682294 | −0.341147 | − | 0.940010i | \(-0.610815\pi\) | ||||
−0.341147 | + | 0.940010i | \(0.610815\pi\) | |||||||
\(6\) | 0.901981 | 0.368232 | ||||||||
\(7\) | 2.31296 | 0.874217 | 0.437109 | − | 0.899409i | \(-0.356003\pi\) | ||||
0.437109 | + | 0.899409i | \(0.356003\pi\) | |||||||
\(8\) | −3.88867 | −1.37485 | ||||||||
\(9\) | −2.85569 | −0.951897 | ||||||||
\(10\) | 3.62251 | 1.14554 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −1.38190 | −0.398921 | ||||||||
\(13\) | 1.64625 | 0.456586 | 0.228293 | − | 0.973592i | \(-0.426686\pi\) | ||||
0.228293 | + | 0.973592i | \(0.426686\pi\) | |||||||
\(14\) | −5.49189 | −1.46777 | ||||||||
\(15\) | 0.579563 | 0.149643 | ||||||||
\(16\) | 1.95774 | 0.489434 | ||||||||
\(17\) | −7.33107 | −1.77805 | −0.889023 | − | 0.457863i | \(-0.848615\pi\) | ||||
−0.889023 | + | 0.457863i | \(0.848615\pi\) | |||||||
\(18\) | 6.78054 | 1.59819 | ||||||||
\(19\) | 0.596356 | 0.136813 | 0.0684067 | − | 0.997658i | \(-0.478208\pi\) | ||||
0.0684067 | + | 0.997658i | \(0.478208\pi\) | |||||||
\(20\) | −5.54996 | −1.24101 | ||||||||
\(21\) | −0.878644 | −0.191736 | ||||||||
\(22\) | 2.37440 | 0.506223 | ||||||||
\(23\) | −4.14341 | −0.863960 | −0.431980 | − | 0.901883i | \(-0.642185\pi\) | ||||
−0.431980 | + | 0.901883i | \(0.642185\pi\) | |||||||
\(24\) | 1.47722 | 0.301537 | ||||||||
\(25\) | −2.67238 | −0.534475 | ||||||||
\(26\) | −3.90884 | −0.766586 | ||||||||
\(27\) | 2.22445 | 0.428096 | ||||||||
\(28\) | 8.41398 | 1.59009 | ||||||||
\(29\) | −1.76317 | −0.327412 | −0.163706 | − | 0.986509i | \(-0.552345\pi\) | ||||
−0.163706 | + | 0.986509i | \(0.552345\pi\) | |||||||
\(30\) | −1.37611 | −0.251243 | ||||||||
\(31\) | −1.69038 | −0.303602 | −0.151801 | − | 0.988411i | \(-0.548507\pi\) | ||||
−0.151801 | + | 0.988411i | \(0.548507\pi\) | |||||||
\(32\) | 3.12890 | 0.553117 | ||||||||
\(33\) | 0.379878 | 0.0661283 | ||||||||
\(34\) | 17.4069 | 2.98525 | ||||||||
\(35\) | −3.52878 | −0.596473 | ||||||||
\(36\) | −10.3883 | −1.73138 | ||||||||
\(37\) | 3.15531 | 0.518730 | 0.259365 | − | 0.965779i | \(-0.416487\pi\) | ||||
0.259365 | + | 0.965779i | \(0.416487\pi\) | |||||||
\(38\) | −1.41598 | −0.229703 | ||||||||
\(39\) | −0.625373 | −0.100140 | ||||||||
\(40\) | 5.93277 | 0.938054 | ||||||||
\(41\) | −11.5466 | −1.80328 | −0.901639 | − | 0.432490i | \(-0.857635\pi\) | ||||
−0.901639 | + | 0.432490i | \(0.857635\pi\) | |||||||
\(42\) | 2.08625 | 0.321915 | ||||||||
\(43\) | −0.926674 | −0.141316 | −0.0706582 | − | 0.997501i | \(-0.522510\pi\) | ||||
−0.0706582 | + | 0.997501i | \(0.522510\pi\) | |||||||
\(44\) | −3.63775 | −0.548412 | ||||||||
\(45\) | 4.35680 | 0.649474 | ||||||||
\(46\) | 9.83809 | 1.45055 | ||||||||
\(47\) | −7.87778 | −1.14909 | −0.574546 | − | 0.818472i | \(-0.694822\pi\) | ||||
−0.574546 | + | 0.818472i | \(0.694822\pi\) | |||||||
\(48\) | −0.743702 | −0.107344 | ||||||||
\(49\) | −1.65021 | −0.235744 | ||||||||
\(50\) | 6.34528 | 0.897358 | ||||||||
\(51\) | 2.78491 | 0.389966 | ||||||||
\(52\) | 5.98863 | 0.830474 | ||||||||
\(53\) | −2.09800 | −0.288183 | −0.144091 | − | 0.989564i | \(-0.546026\pi\) | ||||
−0.144091 | + | 0.989564i | \(0.546026\pi\) | |||||||
\(54\) | −5.28172 | −0.718752 | ||||||||
\(55\) | 1.52566 | 0.205719 | ||||||||
\(56\) | −8.99435 | −1.20192 | ||||||||
\(57\) | −0.226543 | −0.0300063 | ||||||||
\(58\) | 4.18645 | 0.549708 | ||||||||
\(59\) | −6.92361 | −0.901377 | −0.450689 | − | 0.892681i | \(-0.648821\pi\) | ||||
−0.450689 | + | 0.892681i | \(0.648821\pi\) | |||||||
\(60\) | 2.10831 | 0.272181 | ||||||||
\(61\) | 7.40456 | 0.948057 | 0.474028 | − | 0.880510i | \(-0.342799\pi\) | ||||
0.474028 | + | 0.880510i | \(0.342799\pi\) | |||||||
\(62\) | 4.01364 | 0.509732 | ||||||||
\(63\) | −6.60511 | −0.832165 | ||||||||
\(64\) | −11.3447 | −1.41809 | ||||||||
\(65\) | −2.51160 | −0.311526 | ||||||||
\(66\) | −0.901981 | −0.111026 | ||||||||
\(67\) | −5.55057 | −0.678110 | −0.339055 | − | 0.940767i | \(-0.610107\pi\) | ||||
−0.339055 | + | 0.940767i | \(0.610107\pi\) | |||||||
\(68\) | −26.6686 | −3.23404 | ||||||||
\(69\) | 1.57399 | 0.189486 | ||||||||
\(70\) | 8.37872 | 1.00145 | ||||||||
\(71\) | 14.5635 | 1.72837 | 0.864183 | − | 0.503177i | \(-0.167836\pi\) | ||||
0.864183 | + | 0.503177i | \(0.167836\pi\) | |||||||
\(72\) | 11.1048 | 1.30872 | ||||||||
\(73\) | 2.39854 | 0.280727 | 0.140364 | − | 0.990100i | \(-0.455173\pi\) | ||||
0.140364 | + | 0.990100i | \(0.455173\pi\) | |||||||
\(74\) | −7.49195 | −0.870922 | ||||||||
\(75\) | 1.01518 | 0.117223 | ||||||||
\(76\) | 2.16939 | 0.248847 | ||||||||
\(77\) | −2.31296 | −0.263586 | ||||||||
\(78\) | 1.48488 | 0.168130 | ||||||||
\(79\) | 3.21438 | 0.361646 | 0.180823 | − | 0.983516i | \(-0.442124\pi\) | ||||
0.180823 | + | 0.983516i | \(0.442124\pi\) | |||||||
\(80\) | −2.98683 | −0.333938 | ||||||||
\(81\) | 7.72206 | 0.858006 | ||||||||
\(82\) | 27.4162 | 3.02761 | ||||||||
\(83\) | 6.04068 | 0.663051 | 0.331525 | − | 0.943446i | \(-0.392437\pi\) | ||||
0.331525 | + | 0.943446i | \(0.392437\pi\) | |||||||
\(84\) | −3.19629 | −0.348744 | ||||||||
\(85\) | 11.1847 | 1.21315 | ||||||||
\(86\) | 2.20029 | 0.237263 | ||||||||
\(87\) | 0.669789 | 0.0718089 | ||||||||
\(88\) | 3.88867 | 0.414534 | ||||||||
\(89\) | 11.7278 | 1.24314 | 0.621572 | − | 0.783357i | \(-0.286494\pi\) | ||||
0.621572 | + | 0.783357i | \(0.286494\pi\) | |||||||
\(90\) | −10.3448 | −1.09043 | ||||||||
\(91\) | 3.80770 | 0.399156 | ||||||||
\(92\) | −15.0727 | −1.57144 | ||||||||
\(93\) | 0.642140 | 0.0665868 | ||||||||
\(94\) | 18.7050 | 1.92927 | ||||||||
\(95\) | −0.909833 | −0.0933469 | ||||||||
\(96\) | −1.18860 | −0.121311 | ||||||||
\(97\) | 0.507957 | 0.0515753 | 0.0257876 | − | 0.999667i | \(-0.491791\pi\) | ||||
0.0257876 | + | 0.999667i | \(0.491791\pi\) | |||||||
\(98\) | 3.91825 | 0.395803 | ||||||||
\(99\) | 2.85569 | 0.287008 | ||||||||
\(100\) | −9.72144 | −0.972144 | ||||||||
\(101\) | 1.80900 | 0.180002 | 0.0900011 | − | 0.995942i | \(-0.471313\pi\) | ||||
0.0900011 | + | 0.995942i | \(0.471313\pi\) | |||||||
\(102\) | −6.61249 | −0.654734 | ||||||||
\(103\) | −16.4299 | −1.61889 | −0.809444 | − | 0.587196i | \(-0.800232\pi\) | ||||
−0.809444 | + | 0.587196i | \(0.800232\pi\) | |||||||
\(104\) | −6.40171 | −0.627739 | ||||||||
\(105\) | 1.34051 | 0.130820 | ||||||||
\(106\) | 4.98149 | 0.483845 | ||||||||
\(107\) | 0.129922 | 0.0125600 | 0.00628000 | − | 0.999980i | \(-0.498001\pi\) | ||||
0.00628000 | + | 0.999980i | \(0.498001\pi\) | |||||||
\(108\) | 8.09200 | 0.778653 | ||||||||
\(109\) | −7.00572 | −0.671027 | −0.335513 | − | 0.942035i | \(-0.608910\pi\) | ||||
−0.335513 | + | 0.942035i | \(0.608910\pi\) | |||||||
\(110\) | −3.62251 | −0.345393 | ||||||||
\(111\) | −1.19863 | −0.113769 | ||||||||
\(112\) | 4.52817 | 0.427872 | ||||||||
\(113\) | −11.3320 | −1.06603 | −0.533014 | − | 0.846107i | \(-0.678941\pi\) | ||||
−0.533014 | + | 0.846107i | \(0.678941\pi\) | |||||||
\(114\) | 0.537902 | 0.0503791 | ||||||||
\(115\) | 6.32141 | 0.589475 | ||||||||
\(116\) | −6.41396 | −0.595521 | ||||||||
\(117\) | −4.70117 | −0.434623 | ||||||||
\(118\) | 16.4394 | 1.51337 | ||||||||
\(119\) | −16.9565 | −1.55440 | ||||||||
\(120\) | −2.25373 | −0.205737 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −17.5814 | −1.59174 | ||||||||
\(123\) | 4.38631 | 0.395500 | ||||||||
\(124\) | −6.14919 | −0.552214 | ||||||||
\(125\) | 11.7054 | 1.04696 | ||||||||
\(126\) | 15.6831 | 1.39716 | ||||||||
\(127\) | 14.8251 | 1.31551 | 0.657756 | − | 0.753231i | \(-0.271506\pi\) | ||||
0.657756 | + | 0.753231i | \(0.271506\pi\) | |||||||
\(128\) | 20.6790 | 1.82779 | ||||||||
\(129\) | 0.352023 | 0.0309939 | ||||||||
\(130\) | 5.96354 | 0.523037 | ||||||||
\(131\) | 3.08854 | 0.269847 | 0.134923 | − | 0.990856i | \(-0.456921\pi\) | ||||
0.134923 | + | 0.990856i | \(0.456921\pi\) | |||||||
\(132\) | 1.38190 | 0.120279 | ||||||||
\(133\) | 1.37935 | 0.119605 | ||||||||
\(134\) | 13.1792 | 1.13851 | ||||||||
\(135\) | −3.39374 | −0.292087 | ||||||||
\(136\) | 28.5081 | 2.44455 | ||||||||
\(137\) | −20.1994 | −1.72575 | −0.862876 | − | 0.505416i | \(-0.831339\pi\) | ||||
−0.862876 | + | 0.505416i | \(0.831339\pi\) | |||||||
\(138\) | −3.73728 | −0.318138 | ||||||||
\(139\) | 11.8822 | 1.00784 | 0.503918 | − | 0.863751i | \(-0.331891\pi\) | ||||
0.503918 | + | 0.863751i | \(0.331891\pi\) | |||||||
\(140\) | −12.8368 | −1.08491 | ||||||||
\(141\) | 2.99260 | 0.252022 | ||||||||
\(142\) | −34.5794 | −2.90184 | ||||||||
\(143\) | −1.64625 | −0.137666 | ||||||||
\(144\) | −5.59070 | −0.465891 | ||||||||
\(145\) | 2.68998 | 0.223391 | ||||||||
\(146\) | −5.69507 | −0.471327 | ||||||||
\(147\) | 0.626878 | 0.0517041 | ||||||||
\(148\) | 11.4782 | 0.943505 | ||||||||
\(149\) | 2.83933 | 0.232607 | 0.116304 | − | 0.993214i | \(-0.462895\pi\) | ||||
0.116304 | + | 0.993214i | \(0.462895\pi\) | |||||||
\(150\) | −2.41043 | −0.196811 | ||||||||
\(151\) | −17.8172 | −1.44994 | −0.724970 | − | 0.688780i | \(-0.758146\pi\) | ||||
−0.724970 | + | 0.688780i | \(0.758146\pi\) | |||||||
\(152\) | −2.31903 | −0.188098 | ||||||||
\(153\) | 20.9353 | 1.69252 | ||||||||
\(154\) | 5.49189 | 0.442549 | ||||||||
\(155\) | 2.57894 | 0.207146 | ||||||||
\(156\) | −2.27495 | −0.182142 | ||||||||
\(157\) | 11.7988 | 0.941643 | 0.470821 | − | 0.882229i | \(-0.343958\pi\) | ||||
0.470821 | + | 0.882229i | \(0.343958\pi\) | |||||||
\(158\) | −7.63222 | −0.607187 | ||||||||
\(159\) | 0.796986 | 0.0632051 | ||||||||
\(160\) | −4.77362 | −0.377388 | ||||||||
\(161\) | −9.58354 | −0.755289 | ||||||||
\(162\) | −18.3352 | −1.44055 | ||||||||
\(163\) | 3.20119 | 0.250737 | 0.125368 | − | 0.992110i | \(-0.459989\pi\) | ||||
0.125368 | + | 0.992110i | \(0.459989\pi\) | |||||||
\(164\) | −42.0037 | −3.27994 | ||||||||
\(165\) | −0.579563 | −0.0451189 | ||||||||
\(166\) | −14.3430 | −1.11323 | ||||||||
\(167\) | −9.12246 | −0.705917 | −0.352959 | − | 0.935639i | \(-0.614824\pi\) | ||||
−0.352959 | + | 0.935639i | \(0.614824\pi\) | |||||||
\(168\) | 3.41676 | 0.263609 | ||||||||
\(169\) | −10.2899 | −0.791529 | ||||||||
\(170\) | −26.5569 | −2.03682 | ||||||||
\(171\) | −1.70301 | −0.130232 | ||||||||
\(172\) | −3.37101 | −0.257037 | ||||||||
\(173\) | 21.7426 | 1.65306 | 0.826530 | − | 0.562893i | \(-0.190312\pi\) | ||||
0.826530 | + | 0.562893i | \(0.190312\pi\) | |||||||
\(174\) | −1.59034 | −0.120564 | ||||||||
\(175\) | −6.18110 | −0.467247 | ||||||||
\(176\) | −1.95774 | −0.147570 | ||||||||
\(177\) | 2.63013 | 0.197693 | ||||||||
\(178\) | −27.8464 | −2.08718 | ||||||||
\(179\) | 17.8020 | 1.33058 | 0.665291 | − | 0.746584i | \(-0.268307\pi\) | ||||
0.665291 | + | 0.746584i | \(0.268307\pi\) | |||||||
\(180\) | 15.8490 | 1.18131 | ||||||||
\(181\) | −7.42484 | −0.551884 | −0.275942 | − | 0.961174i | \(-0.588990\pi\) | ||||
−0.275942 | + | 0.961174i | \(0.588990\pi\) | |||||||
\(182\) | −9.04099 | −0.670163 | ||||||||
\(183\) | −2.81283 | −0.207931 | ||||||||
\(184\) | 16.1123 | 1.18782 | ||||||||
\(185\) | −4.81392 | −0.353926 | ||||||||
\(186\) | −1.52469 | −0.111796 | ||||||||
\(187\) | 7.33107 | 0.536101 | ||||||||
\(188\) | −28.6574 | −2.09006 | ||||||||
\(189\) | 5.14507 | 0.374249 | ||||||||
\(190\) | 2.16030 | 0.156725 | ||||||||
\(191\) | −2.49913 | −0.180831 | −0.0904153 | − | 0.995904i | \(-0.528819\pi\) | ||||
−0.0904153 | + | 0.995904i | \(0.528819\pi\) | |||||||
\(192\) | 4.30961 | 0.311020 | ||||||||
\(193\) | 0.317512 | 0.0228550 | 0.0114275 | − | 0.999935i | \(-0.496362\pi\) | ||||
0.0114275 | + | 0.999935i | \(0.496362\pi\) | |||||||
\(194\) | −1.20609 | −0.0865923 | ||||||||
\(195\) | 0.954103 | 0.0683248 | ||||||||
\(196\) | −6.00305 | −0.428789 | ||||||||
\(197\) | 26.4283 | 1.88294 | 0.941470 | − | 0.337096i | \(-0.109445\pi\) | ||||
0.941470 | + | 0.337096i | \(0.109445\pi\) | |||||||
\(198\) | −6.78054 | −0.481872 | ||||||||
\(199\) | −9.18108 | −0.650829 | −0.325415 | − | 0.945571i | \(-0.605504\pi\) | ||||
−0.325415 | + | 0.945571i | \(0.605504\pi\) | |||||||
\(200\) | 10.3920 | 0.734825 | ||||||||
\(201\) | 2.10854 | 0.148725 | ||||||||
\(202\) | −4.29528 | −0.302215 | ||||||||
\(203\) | −4.07814 | −0.286229 | ||||||||
\(204\) | 10.1308 | 0.709300 | ||||||||
\(205\) | 17.6161 | 1.23036 | ||||||||
\(206\) | 39.0111 | 2.71804 | ||||||||
\(207\) | 11.8323 | 0.822401 | ||||||||
\(208\) | 3.22292 | 0.223469 | ||||||||
\(209\) | −0.596356 | −0.0412508 | ||||||||
\(210\) | −3.18290 | −0.219641 | ||||||||
\(211\) | 10.2506 | 0.705677 | 0.352839 | − | 0.935684i | \(-0.385216\pi\) | ||||
0.352839 | + | 0.935684i | \(0.385216\pi\) | |||||||
\(212\) | −7.63202 | −0.524169 | ||||||||
\(213\) | −5.53235 | −0.379070 | ||||||||
\(214\) | −0.308485 | −0.0210876 | ||||||||
\(215\) | 1.41378 | 0.0964193 | ||||||||
\(216\) | −8.65016 | −0.588569 | ||||||||
\(217\) | −3.90979 | −0.265414 | ||||||||
\(218\) | 16.6344 | 1.12662 | ||||||||
\(219\) | −0.911152 | −0.0615699 | ||||||||
\(220\) | 5.54996 | 0.374178 | ||||||||
\(221\) | −12.0687 | −0.811831 | ||||||||
\(222\) | 2.84603 | 0.191013 | ||||||||
\(223\) | −1.50988 | −0.101109 | −0.0505545 | − | 0.998721i | \(-0.516099\pi\) | ||||
−0.0505545 | + | 0.998721i | \(0.516099\pi\) | |||||||
\(224\) | 7.23702 | 0.483544 | ||||||||
\(225\) | 7.63148 | 0.508766 | ||||||||
\(226\) | 26.9067 | 1.78981 | ||||||||
\(227\) | 14.5784 | 0.967600 | 0.483800 | − | 0.875178i | \(-0.339256\pi\) | ||||
0.483800 | + | 0.875178i | \(0.339256\pi\) | |||||||
\(228\) | −0.824106 | −0.0545777 | ||||||||
\(229\) | −6.95382 | −0.459521 | −0.229761 | − | 0.973247i | \(-0.573794\pi\) | ||||
−0.229761 | + | 0.973247i | \(0.573794\pi\) | |||||||
\(230\) | −15.0095 | −0.989699 | ||||||||
\(231\) | 0.878644 | 0.0578105 | ||||||||
\(232\) | 6.85637 | 0.450143 | ||||||||
\(233\) | −11.6686 | −0.764437 | −0.382219 | − | 0.924072i | \(-0.624840\pi\) | ||||
−0.382219 | + | 0.924072i | \(0.624840\pi\) | |||||||
\(234\) | 11.1624 | 0.729711 | ||||||||
\(235\) | 12.0188 | 0.784019 | ||||||||
\(236\) | −25.1864 | −1.63949 | ||||||||
\(237\) | −1.22107 | −0.0793173 | ||||||||
\(238\) | 40.2614 | 2.60976 | ||||||||
\(239\) | −0.604201 | −0.0390825 | −0.0195413 | − | 0.999809i | \(-0.506221\pi\) | ||||
−0.0195413 | + | 0.999809i | \(0.506221\pi\) | |||||||
\(240\) | 1.13463 | 0.0732403 | ||||||||
\(241\) | −1.52378 | −0.0981555 | −0.0490777 | − | 0.998795i | \(-0.515628\pi\) | ||||
−0.0490777 | + | 0.998795i | \(0.515628\pi\) | |||||||
\(242\) | −2.37440 | −0.152632 | ||||||||
\(243\) | −9.60679 | −0.616276 | ||||||||
\(244\) | 26.9360 | 1.72440 | ||||||||
\(245\) | 2.51765 | 0.160847 | ||||||||
\(246\) | −10.4148 | −0.664025 | ||||||||
\(247\) | 0.981748 | 0.0624671 | ||||||||
\(248\) | 6.57334 | 0.417408 | ||||||||
\(249\) | −2.29472 | −0.145422 | ||||||||
\(250\) | −27.7932 | −1.75780 | ||||||||
\(251\) | −13.3257 | −0.841112 | −0.420556 | − | 0.907267i | \(-0.638165\pi\) | ||||
−0.420556 | + | 0.907267i | \(0.638165\pi\) | |||||||
\(252\) | −24.0277 | −1.51361 | ||||||||
\(253\) | 4.14341 | 0.260494 | ||||||||
\(254\) | −35.2006 | −2.20868 | ||||||||
\(255\) | −4.24882 | −0.266071 | ||||||||
\(256\) | −26.4108 | −1.65067 | ||||||||
\(257\) | 30.6765 | 1.91355 | 0.956775 | − | 0.290831i | \(-0.0939316\pi\) | ||||
0.956775 | + | 0.290831i | \(0.0939316\pi\) | |||||||
\(258\) | −0.835842 | −0.0520373 | ||||||||
\(259\) | 7.29811 | 0.453483 | ||||||||
\(260\) | −9.13659 | −0.566627 | ||||||||
\(261\) | 5.03506 | 0.311662 | ||||||||
\(262\) | −7.33341 | −0.453059 | ||||||||
\(263\) | −32.1757 | −1.98404 | −0.992019 | − | 0.126090i | \(-0.959757\pi\) | ||||
−0.992019 | + | 0.126090i | \(0.959757\pi\) | |||||||
\(264\) | −1.47722 | −0.0909167 | ||||||||
\(265\) | 3.20083 | 0.196625 | ||||||||
\(266\) | −3.27512 | −0.200810 | ||||||||
\(267\) | −4.45514 | −0.272650 | ||||||||
\(268\) | −20.1916 | −1.23340 | ||||||||
\(269\) | 4.26628 | 0.260120 | 0.130060 | − | 0.991506i | \(-0.458483\pi\) | ||||
0.130060 | + | 0.991506i | \(0.458483\pi\) | |||||||
\(270\) | 8.05809 | 0.490400 | ||||||||
\(271\) | −7.00480 | −0.425511 | −0.212756 | − | 0.977105i | \(-0.568244\pi\) | ||||
−0.212756 | + | 0.977105i | \(0.568244\pi\) | |||||||
\(272\) | −14.3523 | −0.870237 | ||||||||
\(273\) | −1.44646 | −0.0875440 | ||||||||
\(274\) | 47.9614 | 2.89745 | ||||||||
\(275\) | 2.67238 | 0.161150 | ||||||||
\(276\) | 5.72579 | 0.344652 | ||||||||
\(277\) | −32.0766 | −1.92729 | −0.963647 | − | 0.267179i | \(-0.913908\pi\) | ||||
−0.963647 | + | 0.267179i | \(0.913908\pi\) | |||||||
\(278\) | −28.2131 | −1.69211 | ||||||||
\(279\) | 4.82721 | 0.288998 | ||||||||
\(280\) | 13.7223 | 0.820063 | ||||||||
\(281\) | −12.4777 | −0.744358 | −0.372179 | − | 0.928161i | \(-0.621389\pi\) | ||||
−0.372179 | + | 0.928161i | \(0.621389\pi\) | |||||||
\(282\) | −7.10561 | −0.423133 | ||||||||
\(283\) | −17.9083 | −1.06454 | −0.532270 | − | 0.846575i | \(-0.678661\pi\) | ||||
−0.532270 | + | 0.846575i | \(0.678661\pi\) | |||||||
\(284\) | 52.9783 | 3.14368 | ||||||||
\(285\) | 0.345626 | 0.0204731 | ||||||||
\(286\) | 3.90884 | 0.231134 | ||||||||
\(287\) | −26.7069 | −1.57646 | ||||||||
\(288\) | −8.93517 | −0.526510 | ||||||||
\(289\) | 36.7446 | 2.16145 | ||||||||
\(290\) | −6.38708 | −0.375062 | ||||||||
\(291\) | −0.192962 | −0.0113116 | ||||||||
\(292\) | 8.72528 | 0.510608 | ||||||||
\(293\) | −16.2794 | −0.951056 | −0.475528 | − | 0.879701i | \(-0.657743\pi\) | ||||
−0.475528 | + | 0.879701i | \(0.657743\pi\) | |||||||
\(294\) | −1.48846 | −0.0868086 | ||||||||
\(295\) | 10.5630 | 0.615004 | ||||||||
\(296\) | −12.2700 | −0.713177 | ||||||||
\(297\) | −2.22445 | −0.129076 | ||||||||
\(298\) | −6.74170 | −0.390536 | ||||||||
\(299\) | −6.82106 | −0.394472 | ||||||||
\(300\) | 3.69296 | 0.213213 | ||||||||
\(301\) | −2.14336 | −0.123541 | ||||||||
\(302\) | 42.3050 | 2.43438 | ||||||||
\(303\) | −0.687200 | −0.0394786 | ||||||||
\(304\) | 1.16751 | 0.0669612 | ||||||||
\(305\) | −11.2968 | −0.646853 | ||||||||
\(306\) | −49.7086 | −2.84165 | ||||||||
\(307\) | −19.3620 | −1.10505 | −0.552524 | − | 0.833497i | \(-0.686335\pi\) | ||||
−0.552524 | + | 0.833497i | \(0.686335\pi\) | |||||||
\(308\) | −8.41398 | −0.479431 | ||||||||
\(309\) | 6.24137 | 0.355059 | ||||||||
\(310\) | −6.12343 | −0.347787 | ||||||||
\(311\) | −32.2489 | −1.82867 | −0.914335 | − | 0.404959i | \(-0.867286\pi\) | ||||
−0.914335 | + | 0.404959i | \(0.867286\pi\) | |||||||
\(312\) | 2.43187 | 0.137678 | ||||||||
\(313\) | 27.9487 | 1.57975 | 0.789877 | − | 0.613266i | \(-0.210144\pi\) | ||||
0.789877 | + | 0.613266i | \(0.210144\pi\) | |||||||
\(314\) | −28.0149 | −1.58097 | ||||||||
\(315\) | 10.0771 | 0.567781 | ||||||||
\(316\) | 11.6931 | 0.657790 | ||||||||
\(317\) | 15.0173 | 0.843458 | 0.421729 | − | 0.906722i | \(-0.361423\pi\) | ||||
0.421729 | + | 0.906722i | \(0.361423\pi\) | |||||||
\(318\) | −1.89236 | −0.106118 | ||||||||
\(319\) | 1.76317 | 0.0987183 | ||||||||
\(320\) | 17.3081 | 0.967554 | ||||||||
\(321\) | −0.0493544 | −0.00275469 | ||||||||
\(322\) | 22.7551 | 1.26809 | ||||||||
\(323\) | −4.37193 | −0.243260 | ||||||||
\(324\) | 28.0909 | 1.56061 | ||||||||
\(325\) | −4.39939 | −0.244034 | ||||||||
\(326\) | −7.60089 | −0.420975 | ||||||||
\(327\) | 2.66132 | 0.147171 | ||||||||
\(328\) | 44.9010 | 2.47924 | ||||||||
\(329\) | −18.2210 | −1.00456 | ||||||||
\(330\) | 1.37611 | 0.0757525 | ||||||||
\(331\) | 18.8230 | 1.03461 | 0.517303 | − | 0.855802i | \(-0.326936\pi\) | ||||
0.517303 | + | 0.855802i | \(0.326936\pi\) | |||||||
\(332\) | 21.9745 | 1.20601 | ||||||||
\(333\) | −9.01060 | −0.493778 | ||||||||
\(334\) | 21.6603 | 1.18520 | ||||||||
\(335\) | 8.46825 | 0.462670 | ||||||||
\(336\) | −1.72015 | −0.0938421 | ||||||||
\(337\) | 24.9740 | 1.36042 | 0.680211 | − | 0.733017i | \(-0.261888\pi\) | ||||
0.680211 | + | 0.733017i | \(0.261888\pi\) | |||||||
\(338\) | 24.4322 | 1.32894 | ||||||||
\(339\) | 4.30479 | 0.233804 | ||||||||
\(340\) | 40.6871 | 2.20657 | ||||||||
\(341\) | 1.69038 | 0.0915394 | ||||||||
\(342\) | 4.04362 | 0.218654 | ||||||||
\(343\) | −20.0076 | −1.08031 | ||||||||
\(344\) | 3.60353 | 0.194289 | ||||||||
\(345\) | −2.40137 | −0.129285 | ||||||||
\(346\) | −51.6255 | −2.77541 | ||||||||
\(347\) | 1.78528 | 0.0958390 | 0.0479195 | − | 0.998851i | \(-0.484741\pi\) | ||||
0.0479195 | + | 0.998851i | \(0.484741\pi\) | |||||||
\(348\) | 2.43652 | 0.130611 | ||||||||
\(349\) | −28.2923 | −1.51445 | −0.757226 | − | 0.653153i | \(-0.773446\pi\) | ||||
−0.757226 | + | 0.653153i | \(0.773446\pi\) | |||||||
\(350\) | 14.6764 | 0.784486 | ||||||||
\(351\) | 3.66199 | 0.195463 | ||||||||
\(352\) | −3.12890 | −0.166771 | ||||||||
\(353\) | 0.673531 | 0.0358484 | 0.0179242 | − | 0.999839i | \(-0.494294\pi\) | ||||
0.0179242 | + | 0.999839i | \(0.494294\pi\) | |||||||
\(354\) | −6.24496 | −0.331916 | ||||||||
\(355\) | −22.2188 | −1.17925 | ||||||||
\(356\) | 42.6629 | 2.26113 | ||||||||
\(357\) | 6.44140 | 0.340915 | ||||||||
\(358\) | −42.2689 | −2.23398 | ||||||||
\(359\) | −21.2194 | −1.11992 | −0.559958 | − | 0.828521i | \(-0.689183\pi\) | ||||
−0.559958 | + | 0.828521i | \(0.689183\pi\) | |||||||
\(360\) | −16.9422 | −0.892931 | ||||||||
\(361\) | −18.6444 | −0.981282 | ||||||||
\(362\) | 17.6295 | 0.926586 | ||||||||
\(363\) | −0.379878 | −0.0199384 | ||||||||
\(364\) | 13.8515 | 0.726015 | ||||||||
\(365\) | −3.65934 | −0.191539 | ||||||||
\(366\) | 6.67877 | 0.349105 | ||||||||
\(367\) | 11.7727 | 0.614528 | 0.307264 | − | 0.951624i | \(-0.400587\pi\) | ||||
0.307264 | + | 0.951624i | \(0.400587\pi\) | |||||||
\(368\) | −8.11170 | −0.422852 | ||||||||
\(369\) | 32.9736 | 1.71654 | ||||||||
\(370\) | 11.4301 | 0.594225 | ||||||||
\(371\) | −4.85260 | −0.251934 | ||||||||
\(372\) | 2.33595 | 0.121113 | ||||||||
\(373\) | 34.7053 | 1.79697 | 0.898485 | − | 0.439003i | \(-0.144668\pi\) | ||||
0.898485 | + | 0.439003i | \(0.144668\pi\) | |||||||
\(374\) | −17.4069 | −0.900087 | ||||||||
\(375\) | −4.44663 | −0.229623 | ||||||||
\(376\) | 30.6341 | 1.57983 | ||||||||
\(377\) | −2.90260 | −0.149492 | ||||||||
\(378\) | −12.2164 | −0.628345 | ||||||||
\(379\) | 11.8470 | 0.608542 | 0.304271 | − | 0.952586i | \(-0.401587\pi\) | ||||
0.304271 | + | 0.952586i | \(0.401587\pi\) | |||||||
\(380\) | −3.30975 | −0.169787 | ||||||||
\(381\) | −5.63172 | −0.288522 | ||||||||
\(382\) | 5.93392 | 0.303606 | ||||||||
\(383\) | 2.81172 | 0.143672 | 0.0718360 | − | 0.997416i | \(-0.477114\pi\) | ||||
0.0718360 | + | 0.997416i | \(0.477114\pi\) | |||||||
\(384\) | −7.85552 | −0.400875 | ||||||||
\(385\) | 3.52878 | 0.179843 | ||||||||
\(386\) | −0.753900 | −0.0383725 | ||||||||
\(387\) | 2.64630 | 0.134519 | ||||||||
\(388\) | 1.84782 | 0.0938090 | ||||||||
\(389\) | 29.2873 | 1.48493 | 0.742464 | − | 0.669886i | \(-0.233657\pi\) | ||||
0.742464 | + | 0.669886i | \(0.233657\pi\) | |||||||
\(390\) | −2.26542 | −0.114714 | ||||||||
\(391\) | 30.3756 | 1.53616 | ||||||||
\(392\) | 6.41712 | 0.324113 | ||||||||
\(393\) | −1.17327 | −0.0591835 | ||||||||
\(394\) | −62.7513 | −3.16136 | ||||||||
\(395\) | −4.90404 | −0.246749 | ||||||||
\(396\) | 10.3883 | 0.522032 | ||||||||
\(397\) | 12.9833 | 0.651613 | 0.325806 | − | 0.945437i | \(-0.394364\pi\) | ||||
0.325806 | + | 0.945437i | \(0.394364\pi\) | |||||||
\(398\) | 21.7995 | 1.09271 | ||||||||
\(399\) | −0.523984 | −0.0262320 | ||||||||
\(400\) | −5.23181 | −0.261591 | ||||||||
\(401\) | 19.2524 | 0.961419 | 0.480709 | − | 0.876880i | \(-0.340379\pi\) | ||||
0.480709 | + | 0.876880i | \(0.340379\pi\) | |||||||
\(402\) | −5.00651 | −0.249702 | ||||||||
\(403\) | −2.78279 | −0.138620 | ||||||||
\(404\) | 6.58069 | 0.327402 | ||||||||
\(405\) | −11.7812 | −0.585412 | ||||||||
\(406\) | 9.68311 | 0.480564 | ||||||||
\(407\) | −3.15531 | −0.156403 | ||||||||
\(408\) | −10.8296 | −0.536146 | ||||||||
\(409\) | −34.0648 | −1.68440 | −0.842199 | − | 0.539167i | \(-0.818739\pi\) | ||||
−0.842199 | + | 0.539167i | \(0.818739\pi\) | |||||||
\(410\) | −41.8277 | −2.06572 | ||||||||
\(411\) | 7.67331 | 0.378497 | ||||||||
\(412\) | −59.7680 | −2.94456 | ||||||||
\(413\) | −16.0140 | −0.787999 | ||||||||
\(414\) | −28.0945 | −1.38077 | ||||||||
\(415\) | −9.21600 | −0.452396 | ||||||||
\(416\) | 5.15094 | 0.252545 | ||||||||
\(417\) | −4.51380 | −0.221042 | ||||||||
\(418\) | 1.41598 | 0.0692581 | ||||||||
\(419\) | −26.3897 | −1.28922 | −0.644610 | − | 0.764512i | \(-0.722980\pi\) | ||||
−0.644610 | + | 0.764512i | \(0.722980\pi\) | |||||||
\(420\) | 4.87644 | 0.237946 | ||||||||
\(421\) | −4.56363 | −0.222418 | −0.111209 | − | 0.993797i | \(-0.535472\pi\) | ||||
−0.111209 | + | 0.993797i | \(0.535472\pi\) | |||||||
\(422\) | −24.3389 | −1.18480 | ||||||||
\(423\) | 22.4965 | 1.09382 | ||||||||
\(424\) | 8.15844 | 0.396209 | ||||||||
\(425\) | 19.5914 | 0.950321 | ||||||||
\(426\) | 13.1360 | 0.636440 | ||||||||
\(427\) | 17.1265 | 0.828808 | ||||||||
\(428\) | 0.472623 | 0.0228451 | ||||||||
\(429\) | 0.625373 | 0.0301933 | ||||||||
\(430\) | −3.35688 | −0.161883 | ||||||||
\(431\) | −4.27167 | −0.205759 | −0.102880 | − | 0.994694i | \(-0.532806\pi\) | ||||
−0.102880 | + | 0.994694i | \(0.532806\pi\) | |||||||
\(432\) | 4.35489 | 0.209525 | ||||||||
\(433\) | 31.0919 | 1.49418 | 0.747090 | − | 0.664723i | \(-0.231450\pi\) | ||||
0.747090 | + | 0.664723i | \(0.231450\pi\) | |||||||
\(434\) | 9.28339 | 0.445617 | ||||||||
\(435\) | −1.02187 | −0.0489947 | ||||||||
\(436\) | −25.4851 | −1.22051 | ||||||||
\(437\) | −2.47094 | −0.118201 | ||||||||
\(438\) | 2.16343 | 0.103373 | ||||||||
\(439\) | 32.6791 | 1.55969 | 0.779844 | − | 0.625974i | \(-0.215298\pi\) | ||||
0.779844 | + | 0.625974i | \(0.215298\pi\) | |||||||
\(440\) | −5.93277 | −0.282834 | ||||||||
\(441\) | 4.71249 | 0.224404 | ||||||||
\(442\) | 28.6560 | 1.36302 | ||||||||
\(443\) | 18.8986 | 0.897897 | 0.448949 | − | 0.893558i | \(-0.351799\pi\) | ||||
0.448949 | + | 0.893558i | \(0.351799\pi\) | |||||||
\(444\) | −4.36033 | −0.206932 | ||||||||
\(445\) | −17.8926 | −0.848190 | ||||||||
\(446\) | 3.58505 | 0.169757 | ||||||||
\(447\) | −1.07860 | −0.0510161 | ||||||||
\(448\) | −26.2399 | −1.23972 | ||||||||
\(449\) | −7.56865 | −0.357187 | −0.178593 | − | 0.983923i | \(-0.557155\pi\) | ||||
−0.178593 | + | 0.983923i | \(0.557155\pi\) | |||||||
\(450\) | −18.1202 | −0.854192 | ||||||||
\(451\) | 11.5466 | 0.543709 | ||||||||
\(452\) | −41.2231 | −1.93897 | ||||||||
\(453\) | 6.76835 | 0.318005 | ||||||||
\(454\) | −34.6148 | −1.62455 | ||||||||
\(455\) | −5.80924 | −0.272341 | ||||||||
\(456\) | 0.880950 | 0.0412543 | ||||||||
\(457\) | 11.6773 | 0.546242 | 0.273121 | − | 0.961980i | \(-0.411944\pi\) | ||||
0.273121 | + | 0.961980i | \(0.411944\pi\) | |||||||
\(458\) | 16.5111 | 0.771514 | ||||||||
\(459\) | −16.3076 | −0.761174 | ||||||||
\(460\) | 22.9957 | 1.07218 | ||||||||
\(461\) | −4.24332 | −0.197631 | −0.0988157 | − | 0.995106i | \(-0.531505\pi\) | ||||
−0.0988157 | + | 0.995106i | \(0.531505\pi\) | |||||||
\(462\) | −2.08625 | −0.0970610 | ||||||||
\(463\) | 14.9966 | 0.696949 | 0.348474 | − | 0.937318i | \(-0.386700\pi\) | ||||
0.348474 | + | 0.937318i | \(0.386700\pi\) | |||||||
\(464\) | −3.45182 | −0.160247 | ||||||||
\(465\) | −0.979684 | −0.0454318 | ||||||||
\(466\) | 27.7059 | 1.28345 | ||||||||
\(467\) | 34.3602 | 1.59000 | 0.795001 | − | 0.606608i | \(-0.207470\pi\) | ||||
0.795001 | + | 0.606608i | \(0.207470\pi\) | |||||||
\(468\) | −17.1017 | −0.790526 | ||||||||
\(469\) | −12.8383 | −0.592815 | ||||||||
\(470\) | −28.5373 | −1.31633 | ||||||||
\(471\) | −4.48209 | −0.206524 | ||||||||
\(472\) | 26.9236 | 1.23926 | ||||||||
\(473\) | 0.926674 | 0.0426085 | ||||||||
\(474\) | 2.89931 | 0.133170 | ||||||||
\(475\) | −1.59369 | −0.0731234 | ||||||||
\(476\) | −61.6835 | −2.82726 | ||||||||
\(477\) | 5.99125 | 0.274321 | ||||||||
\(478\) | 1.43461 | 0.0656176 | ||||||||
\(479\) | 24.6064 | 1.12429 | 0.562147 | − | 0.827037i | \(-0.309975\pi\) | ||||
0.562147 | + | 0.827037i | \(0.309975\pi\) | |||||||
\(480\) | 1.81340 | 0.0827698 | ||||||||
\(481\) | 5.19441 | 0.236845 | ||||||||
\(482\) | 3.61806 | 0.164798 | ||||||||
\(483\) | 3.64058 | 0.165652 | ||||||||
\(484\) | 3.63775 | 0.165352 | ||||||||
\(485\) | −0.774968 | −0.0351895 | ||||||||
\(486\) | 22.8103 | 1.03470 | ||||||||
\(487\) | 0.127499 | 0.00577752 | 0.00288876 | − | 0.999996i | \(-0.499080\pi\) | ||||
0.00288876 | + | 0.999996i | \(0.499080\pi\) | |||||||
\(488\) | −28.7939 | −1.30344 | ||||||||
\(489\) | −1.21606 | −0.0549923 | ||||||||
\(490\) | −5.97789 | −0.270054 | ||||||||
\(491\) | −36.3290 | −1.63951 | −0.819753 | − | 0.572717i | \(-0.805889\pi\) | ||||
−0.819753 | + | 0.572717i | \(0.805889\pi\) | |||||||
\(492\) | 15.9563 | 0.719365 | ||||||||
\(493\) | 12.9259 | 0.582153 | ||||||||
\(494\) | −2.33106 | −0.104879 | ||||||||
\(495\) | −4.35680 | −0.195824 | ||||||||
\(496\) | −3.30933 | −0.148593 | ||||||||
\(497\) | 33.6848 | 1.51097 | ||||||||
\(498\) | 5.44858 | 0.244157 | ||||||||
\(499\) | −16.1578 | −0.723324 | −0.361662 | − | 0.932309i | \(-0.617791\pi\) | ||||
−0.361662 | + | 0.932309i | \(0.617791\pi\) | |||||||
\(500\) | 42.5814 | 1.90430 | ||||||||
\(501\) | 3.46542 | 0.154824 | ||||||||
\(502\) | 31.6405 | 1.41219 | ||||||||
\(503\) | −23.5017 | −1.04789 | −0.523943 | − | 0.851753i | \(-0.675540\pi\) | ||||
−0.523943 | + | 0.851753i | \(0.675540\pi\) | |||||||
\(504\) | 25.6851 | 1.14410 | ||||||||
\(505\) | −2.75991 | −0.122814 | ||||||||
\(506\) | −9.83809 | −0.437356 | ||||||||
\(507\) | 3.90890 | 0.173600 | ||||||||
\(508\) | 53.9299 | 2.39275 | ||||||||
\(509\) | 39.0973 | 1.73296 | 0.866478 | − | 0.499216i | \(-0.166378\pi\) | ||||
0.866478 | + | 0.499216i | \(0.166378\pi\) | |||||||
\(510\) | 10.0884 | 0.446721 | ||||||||
\(511\) | 5.54772 | 0.245417 | ||||||||
\(512\) | 21.3516 | 0.943615 | ||||||||
\(513\) | 1.32656 | 0.0585692 | ||||||||
\(514\) | −72.8382 | −3.21276 | ||||||||
\(515\) | 25.0664 | 1.10456 | ||||||||
\(516\) | 1.28057 | 0.0563741 | ||||||||
\(517\) | 7.87778 | 0.346465 | ||||||||
\(518\) | −17.3286 | −0.761375 | ||||||||
\(519\) | −8.25954 | −0.362554 | ||||||||
\(520\) | 9.76680 | 0.428302 | ||||||||
\(521\) | 28.1116 | 1.23159 | 0.615796 | − | 0.787906i | \(-0.288835\pi\) | ||||
0.615796 | + | 0.787906i | \(0.288835\pi\) | |||||||
\(522\) | −11.9552 | −0.523266 | ||||||||
\(523\) | −32.9979 | −1.44290 | −0.721448 | − | 0.692468i | \(-0.756523\pi\) | ||||
−0.721448 | + | 0.692468i | \(0.756523\pi\) | |||||||
\(524\) | 11.2353 | 0.490818 | ||||||||
\(525\) | 2.34807 | 0.102478 | ||||||||
\(526\) | 76.3978 | 3.33110 | ||||||||
\(527\) | 12.3923 | 0.539818 | ||||||||
\(528\) | 0.743702 | 0.0323655 | ||||||||
\(529\) | −5.83218 | −0.253573 | ||||||||
\(530\) | −7.60003 | −0.330124 | ||||||||
\(531\) | 19.7717 | 0.858019 | ||||||||
\(532\) | 5.01773 | 0.217546 | ||||||||
\(533\) | −19.0085 | −0.823352 | ||||||||
\(534\) | 10.5783 | 0.457766 | ||||||||
\(535\) | −0.198216 | −0.00856961 | ||||||||
\(536\) | 21.5843 | 0.932301 | ||||||||
\(537\) | −6.76259 | −0.291827 | ||||||||
\(538\) | −10.1298 | −0.436728 | ||||||||
\(539\) | 1.65021 | 0.0710795 | ||||||||
\(540\) | −12.3456 | −0.531270 | ||||||||
\(541\) | −5.22353 | −0.224577 | −0.112289 | − | 0.993676i | \(-0.535818\pi\) | ||||
−0.112289 | + | 0.993676i | \(0.535818\pi\) | |||||||
\(542\) | 16.6322 | 0.714413 | ||||||||
\(543\) | 2.82053 | 0.121041 | ||||||||
\(544\) | −22.9382 | −0.983466 | ||||||||
\(545\) | 10.6883 | 0.457837 | ||||||||
\(546\) | 3.43448 | 0.146982 | ||||||||
\(547\) | 1.00000 | 0.0427569 | ||||||||
\(548\) | −73.4804 | −3.13893 | ||||||||
\(549\) | −21.1451 | −0.902453 | ||||||||
\(550\) | −6.34528 | −0.270563 | ||||||||
\(551\) | −1.05147 | −0.0447943 | ||||||||
\(552\) | −6.12073 | −0.260516 | ||||||||
\(553\) | 7.43475 | 0.316158 | ||||||||
\(554\) | 76.1624 | 3.23583 | ||||||||
\(555\) | 1.82870 | 0.0776241 | ||||||||
\(556\) | 43.2246 | 1.83313 | ||||||||
\(557\) | −28.2444 | −1.19675 | −0.598377 | − | 0.801215i | \(-0.704187\pi\) | ||||
−0.598377 | + | 0.801215i | \(0.704187\pi\) | |||||||
\(558\) | −11.4617 | −0.485213 | ||||||||
\(559\) | −1.52553 | −0.0645231 | ||||||||
\(560\) | −6.90843 | −0.291934 | ||||||||
\(561\) | −2.78491 | −0.117579 | ||||||||
\(562\) | 29.6270 | 1.24974 | ||||||||
\(563\) | 32.5021 | 1.36980 | 0.684900 | − | 0.728637i | \(-0.259846\pi\) | ||||
0.684900 | + | 0.728637i | \(0.259846\pi\) | |||||||
\(564\) | 10.8863 | 0.458397 | ||||||||
\(565\) | 17.2888 | 0.727344 | ||||||||
\(566\) | 42.5214 | 1.78731 | ||||||||
\(567\) | 17.8608 | 0.750084 | ||||||||
\(568\) | −56.6326 | −2.37625 | ||||||||
\(569\) | −4.88569 | −0.204819 | −0.102409 | − | 0.994742i | \(-0.532655\pi\) | ||||
−0.102409 | + | 0.994742i | \(0.532655\pi\) | |||||||
\(570\) | −0.820653 | −0.0343734 | ||||||||
\(571\) | 10.1483 | 0.424692 | 0.212346 | − | 0.977195i | \(-0.431890\pi\) | ||||
0.212346 | + | 0.977195i | \(0.431890\pi\) | |||||||
\(572\) | −5.98863 | −0.250397 | ||||||||
\(573\) | 0.949364 | 0.0396603 | ||||||||
\(574\) | 63.4126 | 2.64679 | ||||||||
\(575\) | 11.0727 | 0.461765 | ||||||||
\(576\) | 32.3970 | 1.34988 | ||||||||
\(577\) | 18.4933 | 0.769888 | 0.384944 | − | 0.922940i | \(-0.374221\pi\) | ||||
0.384944 | + | 0.922940i | \(0.374221\pi\) | |||||||
\(578\) | −87.2461 | −3.62896 | ||||||||
\(579\) | −0.120616 | −0.00501263 | ||||||||
\(580\) | 9.78549 | 0.406321 | ||||||||
\(581\) | 13.9719 | 0.579651 | ||||||||
\(582\) | 0.458168 | 0.0189917 | ||||||||
\(583\) | 2.09800 | 0.0868904 | ||||||||
\(584\) | −9.32712 | −0.385959 | ||||||||
\(585\) | 7.17237 | 0.296541 | ||||||||
\(586\) | 38.6538 | 1.59678 | ||||||||
\(587\) | −33.4541 | −1.38080 | −0.690400 | − | 0.723428i | \(-0.742565\pi\) | ||||
−0.690400 | + | 0.723428i | \(0.742565\pi\) | |||||||
\(588\) | 2.28043 | 0.0940433 | ||||||||
\(589\) | −1.00807 | −0.0415368 | ||||||||
\(590\) | −25.0808 | −1.03256 | ||||||||
\(591\) | −10.0395 | −0.412972 | ||||||||
\(592\) | 6.17727 | 0.253884 | ||||||||
\(593\) | 20.0698 | 0.824168 | 0.412084 | − | 0.911146i | \(-0.364801\pi\) | ||||
0.412084 | + | 0.911146i | \(0.364801\pi\) | |||||||
\(594\) | 5.28172 | 0.216712 | ||||||||
\(595\) | 25.8697 | 1.06056 | ||||||||
\(596\) | 10.3288 | 0.423084 | ||||||||
\(597\) | 3.48769 | 0.142742 | ||||||||
\(598\) | 16.1959 | 0.662300 | ||||||||
\(599\) | −2.26682 | −0.0926197 | −0.0463098 | − | 0.998927i | \(-0.514746\pi\) | ||||
−0.0463098 | + | 0.998927i | \(0.514746\pi\) | |||||||
\(600\) | −3.94769 | −0.161164 | ||||||||
\(601\) | 21.4662 | 0.875626 | 0.437813 | − | 0.899066i | \(-0.355753\pi\) | ||||
0.437813 | + | 0.899066i | \(0.355753\pi\) | |||||||
\(602\) | 5.08919 | 0.207420 | ||||||||
\(603\) | 15.8507 | 0.645491 | ||||||||
\(604\) | −64.8144 | −2.63726 | ||||||||
\(605\) | −1.52566 | −0.0620267 | ||||||||
\(606\) | 1.63168 | 0.0662826 | ||||||||
\(607\) | −10.0336 | −0.407252 | −0.203626 | − | 0.979049i | \(-0.565273\pi\) | ||||
−0.203626 | + | 0.979049i | \(0.565273\pi\) | |||||||
\(608\) | 1.86594 | 0.0756738 | ||||||||
\(609\) | 1.54920 | 0.0627766 | ||||||||
\(610\) | 26.8231 | 1.08604 | ||||||||
\(611\) | −12.9688 | −0.524660 | ||||||||
\(612\) | 76.1574 | 3.07848 | ||||||||
\(613\) | −5.97121 | −0.241175 | −0.120587 | − | 0.992703i | \(-0.538478\pi\) | ||||
−0.120587 | + | 0.992703i | \(0.538478\pi\) | |||||||
\(614\) | 45.9730 | 1.85532 | ||||||||
\(615\) | −6.69199 | −0.269847 | ||||||||
\(616\) | 8.99435 | 0.362393 | ||||||||
\(617\) | −11.7149 | −0.471622 | −0.235811 | − | 0.971799i | \(-0.575775\pi\) | ||||
−0.235811 | + | 0.971799i | \(0.575775\pi\) | |||||||
\(618\) | −14.8195 | −0.596127 | ||||||||
\(619\) | 33.8837 | 1.36190 | 0.680950 | − | 0.732330i | \(-0.261567\pi\) | ||||
0.680950 | + | 0.732330i | \(0.261567\pi\) | |||||||
\(620\) | 9.38155 | 0.376772 | ||||||||
\(621\) | −9.21680 | −0.369858 | ||||||||
\(622\) | 76.5717 | 3.07025 | ||||||||
\(623\) | 27.1260 | 1.08678 | ||||||||
\(624\) | −1.22432 | −0.0490119 | ||||||||
\(625\) | −4.49653 | −0.179861 | ||||||||
\(626\) | −66.3612 | −2.65233 | ||||||||
\(627\) | 0.226543 | 0.00904724 | ||||||||
\(628\) | 42.9209 | 1.71273 | ||||||||
\(629\) | −23.1318 | −0.922325 | ||||||||
\(630\) | −23.9271 | −0.953277 | ||||||||
\(631\) | 35.4607 | 1.41167 | 0.705835 | − | 0.708376i | \(-0.250572\pi\) | ||||
0.705835 | + | 0.708376i | \(0.250572\pi\) | |||||||
\(632\) | −12.4997 | −0.497211 | ||||||||
\(633\) | −3.89396 | −0.154771 | ||||||||
\(634\) | −35.6571 | −1.41612 | ||||||||
\(635\) | −22.6179 | −0.897566 | ||||||||
\(636\) | 2.89924 | 0.114962 | ||||||||
\(637\) | −2.71665 | −0.107637 | ||||||||
\(638\) | −4.18645 | −0.165743 | ||||||||
\(639\) | −41.5888 | −1.64523 | ||||||||
\(640\) | −31.5491 | −1.24709 | ||||||||
\(641\) | 5.77380 | 0.228051 | 0.114026 | − | 0.993478i | \(-0.463625\pi\) | ||||
0.114026 | + | 0.993478i | \(0.463625\pi\) | |||||||
\(642\) | 0.117187 | 0.00462500 | ||||||||
\(643\) | 20.6036 | 0.812528 | 0.406264 | − | 0.913756i | \(-0.366831\pi\) | ||||
0.406264 | + | 0.913756i | \(0.366831\pi\) | |||||||
\(644\) | −34.8626 | −1.37378 | ||||||||
\(645\) | −0.537066 | −0.0211470 | ||||||||
\(646\) | 10.3807 | 0.408422 | ||||||||
\(647\) | −3.12303 | −0.122779 | −0.0613895 | − | 0.998114i | \(-0.519553\pi\) | ||||
−0.0613895 | + | 0.998114i | \(0.519553\pi\) | |||||||
\(648\) | −30.0285 | −1.17963 | ||||||||
\(649\) | 6.92361 | 0.271775 | ||||||||
\(650\) | 10.4459 | 0.409721 | ||||||||
\(651\) | 1.48524 | 0.0582113 | ||||||||
\(652\) | 11.6451 | 0.456059 | ||||||||
\(653\) | 23.5311 | 0.920845 | 0.460422 | − | 0.887700i | \(-0.347698\pi\) | ||||
0.460422 | + | 0.887700i | \(0.347698\pi\) | |||||||
\(654\) | −6.31903 | −0.247094 | ||||||||
\(655\) | −4.71204 | −0.184115 | ||||||||
\(656\) | −22.6052 | −0.882586 | ||||||||
\(657\) | −6.84948 | −0.267224 | ||||||||
\(658\) | 43.2639 | 1.68660 | ||||||||
\(659\) | 44.6544 | 1.73949 | 0.869744 | − | 0.493503i | \(-0.164284\pi\) | ||||
0.869744 | + | 0.493503i | \(0.164284\pi\) | |||||||
\(660\) | −2.10831 | −0.0820658 | ||||||||
\(661\) | −13.6967 | −0.532741 | −0.266371 | − | 0.963871i | \(-0.585825\pi\) | ||||
−0.266371 | + | 0.963871i | \(0.585825\pi\) | |||||||
\(662\) | −44.6933 | −1.73705 | ||||||||
\(663\) | 4.58465 | 0.178053 | ||||||||
\(664\) | −23.4902 | −0.911598 | ||||||||
\(665\) | −2.10441 | −0.0816055 | ||||||||
\(666\) | 21.3947 | 0.829028 | ||||||||
\(667\) | 7.30551 | 0.282871 | ||||||||
\(668\) | −33.1853 | −1.28398 | ||||||||
\(669\) | 0.573570 | 0.0221755 | ||||||||
\(670\) | −20.1070 | −0.776800 | ||||||||
\(671\) | −7.40456 | −0.285850 | ||||||||
\(672\) | −2.74919 | −0.106052 | ||||||||
\(673\) | 28.3961 | 1.09459 | 0.547294 | − | 0.836940i | \(-0.315658\pi\) | ||||
0.547294 | + | 0.836940i | \(0.315658\pi\) | |||||||
\(674\) | −59.2982 | −2.28408 | ||||||||
\(675\) | −5.94457 | −0.228807 | ||||||||
\(676\) | −37.4320 | −1.43969 | ||||||||
\(677\) | 21.7804 | 0.837088 | 0.418544 | − | 0.908197i | \(-0.362541\pi\) | ||||
0.418544 | + | 0.908197i | \(0.362541\pi\) | |||||||
\(678\) | −10.2213 | −0.392546 | ||||||||
\(679\) | 1.17489 | 0.0450880 | ||||||||
\(680\) | −43.4936 | −1.66790 | ||||||||
\(681\) | −5.53801 | −0.212217 | ||||||||
\(682\) | −4.01364 | −0.153690 | ||||||||
\(683\) | 47.0415 | 1.79999 | 0.899997 | − | 0.435896i | \(-0.143568\pi\) | ||||
0.899997 | + | 0.435896i | \(0.143568\pi\) | |||||||
\(684\) | −6.19512 | −0.236876 | ||||||||
\(685\) | 30.8173 | 1.17747 | ||||||||
\(686\) | 47.5059 | 1.81379 | ||||||||
\(687\) | 2.64160 | 0.100783 | ||||||||
\(688\) | −1.81418 | −0.0691651 | ||||||||
\(689\) | −3.45383 | −0.131580 | ||||||||
\(690\) | 5.70179 | 0.217064 | ||||||||
\(691\) | −45.6569 | −1.73687 | −0.868435 | − | 0.495804i | \(-0.834874\pi\) | ||||
−0.868435 | + | 0.495804i | \(0.834874\pi\) | |||||||
\(692\) | 79.0942 | 3.00671 | ||||||||
\(693\) | 6.60511 | 0.250907 | ||||||||
\(694\) | −4.23897 | −0.160909 | ||||||||
\(695\) | −18.1282 | −0.687641 | ||||||||
\(696\) | −2.60459 | −0.0987266 | ||||||||
\(697\) | 84.6490 | 3.20631 | ||||||||
\(698\) | 67.1771 | 2.54269 | ||||||||
\(699\) | 4.43266 | 0.167659 | ||||||||
\(700\) | −22.4853 | −0.849865 | ||||||||
\(701\) | 1.01791 | 0.0384460 | 0.0192230 | − | 0.999815i | \(-0.493881\pi\) | ||||
0.0192230 | + | 0.999815i | \(0.493881\pi\) | |||||||
\(702\) | −8.69501 | −0.328172 | ||||||||
\(703\) | 1.88169 | 0.0709692 | ||||||||
\(704\) | 11.3447 | 0.427570 | ||||||||
\(705\) | −4.56567 | −0.171953 | ||||||||
\(706\) | −1.59923 | −0.0601878 | ||||||||
\(707\) | 4.18415 | 0.157361 | ||||||||
\(708\) | 9.56776 | 0.359578 | ||||||||
\(709\) | 37.3897 | 1.40420 | 0.702099 | − | 0.712079i | \(-0.252246\pi\) | ||||
0.702099 | + | 0.712079i | \(0.252246\pi\) | |||||||
\(710\) | 52.7563 | 1.97991 | ||||||||
\(711\) | −9.17929 | −0.344250 | ||||||||
\(712\) | −45.6056 | −1.70914 | ||||||||
\(713\) | 7.00394 | 0.262300 | ||||||||
\(714\) | −15.2944 | −0.572380 | ||||||||
\(715\) | 2.51160 | 0.0939286 | ||||||||
\(716\) | 64.7592 | 2.42016 | ||||||||
\(717\) | 0.229523 | 0.00857169 | ||||||||
\(718\) | 50.3832 | 1.88028 | ||||||||
\(719\) | −38.6234 | −1.44041 | −0.720205 | − | 0.693761i | \(-0.755952\pi\) | ||||
−0.720205 | + | 0.693761i | \(0.755952\pi\) | |||||||
\(720\) | 8.52948 | 0.317875 | ||||||||
\(721\) | −38.0018 | −1.41526 | ||||||||
\(722\) | 44.2691 | 1.64752 | ||||||||
\(723\) | 0.578852 | 0.0215277 | ||||||||
\(724\) | −27.0097 | −1.00381 | ||||||||
\(725\) | 4.71184 | 0.174993 | ||||||||
\(726\) | 0.901981 | 0.0334757 | ||||||||
\(727\) | 20.6368 | 0.765378 | 0.382689 | − | 0.923877i | \(-0.374998\pi\) | ||||
0.382689 | + | 0.923877i | \(0.374998\pi\) | |||||||
\(728\) | −14.8069 | −0.548780 | ||||||||
\(729\) | −19.5168 | −0.722843 | ||||||||
\(730\) | 8.68872 | 0.321584 | ||||||||
\(731\) | 6.79351 | 0.251267 | ||||||||
\(732\) | −10.2324 | −0.378200 | ||||||||
\(733\) | −29.8075 | −1.10097 | −0.550483 | − | 0.834846i | \(-0.685556\pi\) | ||||
−0.550483 | + | 0.834846i | \(0.685556\pi\) | |||||||
\(734\) | −27.9529 | −1.03176 | ||||||||
\(735\) | −0.956400 | −0.0352774 | ||||||||
\(736\) | −12.9643 | −0.477871 | ||||||||
\(737\) | 5.55057 | 0.204458 | ||||||||
\(738\) | −78.2923 | −2.88198 | ||||||||
\(739\) | −4.96854 | −0.182771 | −0.0913853 | − | 0.995816i | \(-0.529129\pi\) | ||||
−0.0913853 | + | 0.995816i | \(0.529129\pi\) | |||||||
\(740\) | −17.5118 | −0.643748 | ||||||||
\(741\) | −0.372945 | −0.0137005 | ||||||||
\(742\) | 11.5220 | 0.422986 | ||||||||
\(743\) | 8.27933 | 0.303739 | 0.151870 | − | 0.988401i | \(-0.451471\pi\) | ||||
0.151870 | + | 0.988401i | \(0.451471\pi\) | |||||||
\(744\) | −2.49707 | −0.0915471 | ||||||||
\(745\) | −4.33184 | −0.158706 | ||||||||
\(746\) | −82.4040 | −3.01703 | ||||||||
\(747\) | −17.2503 | −0.631157 | ||||||||
\(748\) | 26.6686 | 0.975101 | ||||||||
\(749\) | 0.300504 | 0.0109802 | ||||||||
\(750\) | 10.5581 | 0.385526 | ||||||||
\(751\) | 46.2989 | 1.68947 | 0.844735 | − | 0.535185i | \(-0.179758\pi\) | ||||
0.844735 | + | 0.535185i | \(0.179758\pi\) | |||||||
\(752\) | −15.4226 | −0.562406 | ||||||||
\(753\) | 5.06215 | 0.184475 | ||||||||
\(754\) | 6.89193 | 0.250989 | ||||||||
\(755\) | 27.1828 | 0.989285 | ||||||||
\(756\) | 18.7165 | 0.680712 | ||||||||
\(757\) | −18.3597 | −0.667295 | −0.333647 | − | 0.942698i | \(-0.608279\pi\) | ||||
−0.333647 | + | 0.942698i | \(0.608279\pi\) | |||||||
\(758\) | −28.1296 | −1.02171 | ||||||||
\(759\) | −1.57399 | −0.0571322 | ||||||||
\(760\) | 3.53804 | 0.128338 | ||||||||
\(761\) | 48.2636 | 1.74955 | 0.874777 | − | 0.484526i | \(-0.161008\pi\) | ||||
0.874777 | + | 0.484526i | \(0.161008\pi\) | |||||||
\(762\) | 13.3719 | 0.484414 | ||||||||
\(763\) | −16.2040 | −0.586623 | ||||||||
\(764\) | −9.09121 | −0.328908 | ||||||||
\(765\) | −31.9400 | −1.15479 | ||||||||
\(766\) | −6.67613 | −0.241218 | ||||||||
\(767\) | −11.3980 | −0.411556 | ||||||||
\(768\) | 10.0329 | 0.362031 | ||||||||
\(769\) | −21.0854 | −0.760358 | −0.380179 | − | 0.924913i | \(-0.624138\pi\) | ||||
−0.380179 | + | 0.924913i | \(0.624138\pi\) | |||||||
\(770\) | −8.37872 | −0.301948 | ||||||||
\(771\) | −11.6533 | −0.419685 | ||||||||
\(772\) | 1.15503 | 0.0415705 | ||||||||
\(773\) | 35.3472 | 1.27135 | 0.635674 | − | 0.771957i | \(-0.280722\pi\) | ||||
0.635674 | + | 0.771957i | \(0.280722\pi\) | |||||||
\(774\) | −6.28335 | −0.225850 | ||||||||
\(775\) | 4.51734 | 0.162268 | ||||||||
\(776\) | −1.97528 | −0.0709084 | ||||||||
\(777\) | −2.77239 | −0.0994591 | ||||||||
\(778\) | −69.5397 | −2.49312 | ||||||||
\(779\) | −6.88589 | −0.246712 | ||||||||
\(780\) | 3.47079 | 0.124274 | ||||||||
\(781\) | −14.5635 | −0.521122 | ||||||||
\(782\) | −72.1237 | −2.57914 | ||||||||
\(783\) | −3.92208 | −0.140164 | ||||||||
\(784\) | −3.23068 | −0.115381 | ||||||||
\(785\) | −18.0008 | −0.642477 | ||||||||
\(786\) | 2.78580 | 0.0993663 | ||||||||
\(787\) | 31.7552 | 1.13195 | 0.565976 | − | 0.824422i | \(-0.308500\pi\) | ||||
0.565976 | + | 0.824422i | \(0.308500\pi\) | |||||||
\(788\) | 96.1397 | 3.42484 | ||||||||
\(789\) | 12.2228 | 0.435145 | ||||||||
\(790\) | 11.6441 | 0.414280 | ||||||||
\(791\) | −26.2105 | −0.931940 | ||||||||
\(792\) | −11.1048 | −0.394594 | ||||||||
\(793\) | 12.1897 | 0.432870 | ||||||||
\(794\) | −30.8275 | −1.09403 | ||||||||
\(795\) | −1.21593 | −0.0431244 | ||||||||
\(796\) | −33.3985 | −1.18378 | ||||||||
\(797\) | −18.6362 | −0.660129 | −0.330064 | − | 0.943958i | \(-0.607070\pi\) | ||||
−0.330064 | + | 0.943958i | \(0.607070\pi\) | |||||||
\(798\) | 1.24415 | 0.0440423 | ||||||||
\(799\) | 57.7526 | 2.04314 | ||||||||
\(800\) | −8.36160 | −0.295627 | ||||||||
\(801\) | −33.4910 | −1.18335 | ||||||||
\(802\) | −45.7128 | −1.61417 | ||||||||
\(803\) | −2.39854 | −0.0846425 | ||||||||
\(804\) | 7.67035 | 0.270512 | ||||||||
\(805\) | 14.6212 | 0.515329 | ||||||||
\(806\) | 6.60743 | 0.232737 | ||||||||
\(807\) | −1.62067 | −0.0570502 | ||||||||
\(808\) | −7.03461 | −0.247477 | ||||||||
\(809\) | 18.7206 | 0.658182 | 0.329091 | − | 0.944298i | \(-0.393258\pi\) | ||||
0.329091 | + | 0.944298i | \(0.393258\pi\) | |||||||
\(810\) | 27.9732 | 0.982879 | ||||||||
\(811\) | 33.9505 | 1.19216 | 0.596082 | − | 0.802923i | \(-0.296723\pi\) | ||||
0.596082 | + | 0.802923i | \(0.296723\pi\) | |||||||
\(812\) | −14.8352 | −0.520615 | ||||||||
\(813\) | 2.66097 | 0.0933244 | ||||||||
\(814\) | 7.49195 | 0.262593 | ||||||||
\(815\) | −4.88391 | −0.171076 | ||||||||
\(816\) | 5.45213 | 0.190863 | ||||||||
\(817\) | −0.552627 | −0.0193340 | ||||||||
\(818\) | 80.8834 | 2.82802 | ||||||||
\(819\) | −10.8736 | −0.379955 | ||||||||
\(820\) | 64.0832 | 2.23788 | ||||||||
\(821\) | 0.942862 | 0.0329061 | 0.0164530 | − | 0.999865i | \(-0.494763\pi\) | ||||
0.0164530 | + | 0.999865i | \(0.494763\pi\) | |||||||
\(822\) | −18.2195 | −0.635477 | ||||||||
\(823\) | 19.9823 | 0.696540 | 0.348270 | − | 0.937394i | \(-0.386769\pi\) | ||||
0.348270 | + | 0.937394i | \(0.386769\pi\) | |||||||
\(824\) | 63.8906 | 2.22573 | ||||||||
\(825\) | −1.01518 | −0.0353439 | ||||||||
\(826\) | 38.0237 | 1.32301 | ||||||||
\(827\) | 49.3839 | 1.71725 | 0.858624 | − | 0.512606i | \(-0.171320\pi\) | ||||
0.858624 | + | 0.512606i | \(0.171320\pi\) | |||||||
\(828\) | 43.0430 | 1.49585 | ||||||||
\(829\) | 31.0129 | 1.07712 | 0.538561 | − | 0.842587i | \(-0.318968\pi\) | ||||
0.538561 | + | 0.842587i | \(0.318968\pi\) | |||||||
\(830\) | 21.8824 | 0.759550 | ||||||||
\(831\) | 12.1852 | 0.422700 | ||||||||
\(832\) | −18.6762 | −0.647480 | ||||||||
\(833\) | 12.0978 | 0.419164 | ||||||||
\(834\) | 10.7175 | 0.371118 | ||||||||
\(835\) | 13.9177 | 0.481643 | ||||||||
\(836\) | −2.16939 | −0.0750301 | ||||||||
\(837\) | −3.76017 | −0.129971 | ||||||||
\(838\) | 62.6595 | 2.16454 | ||||||||
\(839\) | 44.5836 | 1.53920 | 0.769598 | − | 0.638529i | \(-0.220457\pi\) | ||||
0.769598 | + | 0.638529i | \(0.220457\pi\) | |||||||
\(840\) | −5.21279 | −0.179858 | ||||||||
\(841\) | −25.8912 | −0.892802 | ||||||||
\(842\) | 10.8359 | 0.373428 | ||||||||
\(843\) | 4.74001 | 0.163255 | ||||||||
\(844\) | 37.2890 | 1.28354 | ||||||||
\(845\) | 15.6988 | 0.540055 | ||||||||
\(846\) | −53.4156 | −1.83647 | ||||||||
\(847\) | 2.31296 | 0.0794743 | ||||||||
\(848\) | −4.10734 | −0.141047 | ||||||||
\(849\) | 6.80298 | 0.233478 | ||||||||
\(850\) | −46.5177 | −1.59554 | ||||||||
\(851\) | −13.0737 | −0.448162 | ||||||||
\(852\) | −20.1253 | −0.689482 | ||||||||
\(853\) | 19.1985 | 0.657345 | 0.328672 | − | 0.944444i | \(-0.393399\pi\) | ||||
0.328672 | + | 0.944444i | \(0.393399\pi\) | |||||||
\(854\) | −40.6650 | −1.39153 | ||||||||
\(855\) | 2.59820 | 0.0888567 | ||||||||
\(856\) | −0.505223 | −0.0172682 | ||||||||
\(857\) | −27.0414 | −0.923716 | −0.461858 | − | 0.886954i | \(-0.652817\pi\) | ||||
−0.461858 | + | 0.886954i | \(0.652817\pi\) | |||||||
\(858\) | −1.48488 | −0.0506930 | ||||||||
\(859\) | −28.9901 | −0.989130 | −0.494565 | − | 0.869141i | \(-0.664673\pi\) | ||||
−0.494565 | + | 0.869141i | \(0.664673\pi\) | |||||||
\(860\) | 5.14300 | 0.175375 | ||||||||
\(861\) | 10.1454 | 0.345753 | ||||||||
\(862\) | 10.1426 | 0.345460 | ||||||||
\(863\) | −52.5172 | −1.78771 | −0.893853 | − | 0.448361i | \(-0.852008\pi\) | ||||
−0.893853 | + | 0.448361i | \(0.852008\pi\) | |||||||
\(864\) | 6.96008 | 0.236787 | ||||||||
\(865\) | −33.1717 | −1.12787 | ||||||||
\(866\) | −73.8244 | −2.50865 | ||||||||
\(867\) | −13.9585 | −0.474054 | ||||||||
\(868\) | −14.2229 | −0.482755 | ||||||||
\(869\) | −3.21438 | −0.109041 | ||||||||
\(870\) | 2.42631 | 0.0822598 | ||||||||
\(871\) | −9.13760 | −0.309616 | ||||||||
\(872\) | 27.2430 | 0.922563 | ||||||||
\(873\) | −1.45057 | −0.0490944 | ||||||||
\(874\) | 5.86700 | 0.198454 | ||||||||
\(875\) | 27.0741 | 0.915273 | ||||||||
\(876\) | −3.31454 | −0.111988 | ||||||||
\(877\) | −17.3204 | −0.584867 | −0.292434 | − | 0.956286i | \(-0.594465\pi\) | ||||
−0.292434 | + | 0.956286i | \(0.594465\pi\) | |||||||
\(878\) | −77.5931 | −2.61864 | ||||||||
\(879\) | 6.18421 | 0.208588 | ||||||||
\(880\) | 2.98683 | 0.100686 | ||||||||
\(881\) | −17.9414 | −0.604462 | −0.302231 | − | 0.953235i | \(-0.597731\pi\) | ||||
−0.302231 | + | 0.953235i | \(0.597731\pi\) | |||||||
\(882\) | −11.1893 | −0.376764 | ||||||||
\(883\) | −7.93763 | −0.267123 | −0.133561 | − | 0.991041i | \(-0.542641\pi\) | ||||
−0.133561 | + | 0.991041i | \(0.542641\pi\) | |||||||
\(884\) | −43.9031 | −1.47662 | ||||||||
\(885\) | −4.01267 | −0.134884 | ||||||||
\(886\) | −44.8726 | −1.50753 | ||||||||
\(887\) | 45.4386 | 1.52568 | 0.762840 | − | 0.646587i | \(-0.223804\pi\) | ||||
0.762840 | + | 0.646587i | \(0.223804\pi\) | |||||||
\(888\) | 4.66109 | 0.156416 | ||||||||
\(889\) | 34.2898 | 1.15004 | ||||||||
\(890\) | 42.4841 | 1.42407 | ||||||||
\(891\) | −7.72206 | −0.258699 | ||||||||
\(892\) | −5.49257 | −0.183905 | ||||||||
\(893\) | −4.69796 | −0.157211 | ||||||||
\(894\) | 2.56102 | 0.0856535 | ||||||||
\(895\) | −27.1597 | −0.907848 | ||||||||
\(896\) | 47.8298 | 1.59788 | ||||||||
\(897\) | 2.59117 | 0.0865168 | ||||||||
\(898\) | 17.9710 | 0.599699 | ||||||||
\(899\) | 2.98043 | 0.0994028 | ||||||||
\(900\) | 27.7614 | 0.925382 | ||||||||
\(901\) | 15.3806 | 0.512402 | ||||||||
\(902\) | −27.4162 | −0.912860 | ||||||||
\(903\) | 0.814216 | 0.0270954 | ||||||||
\(904\) | 44.0665 | 1.46563 | ||||||||
\(905\) | 11.3277 | 0.376547 | ||||||||
\(906\) | −16.0707 | −0.533915 | ||||||||
\(907\) | 31.2975 | 1.03922 | 0.519609 | − | 0.854404i | \(-0.326078\pi\) | ||||
0.519609 | + | 0.854404i | \(0.326078\pi\) | |||||||
\(908\) | 53.0325 | 1.75995 | ||||||||
\(909\) | −5.16595 | −0.171344 | ||||||||
\(910\) | 13.7934 | 0.457248 | ||||||||
\(911\) | −51.8452 | −1.71771 | −0.858855 | − | 0.512219i | \(-0.828824\pi\) | ||||
−0.858855 | + | 0.512219i | \(0.828824\pi\) | |||||||
\(912\) | −0.443511 | −0.0146861 | ||||||||
\(913\) | −6.04068 | −0.199917 | ||||||||
\(914\) | −27.7266 | −0.917114 | ||||||||
\(915\) | 4.29141 | 0.141870 | ||||||||
\(916\) | −25.2963 | −0.835812 | ||||||||
\(917\) | 7.14367 | 0.235905 | ||||||||
\(918\) | 38.7207 | 1.27797 | ||||||||
\(919\) | −22.2196 | −0.732958 | −0.366479 | − | 0.930426i | \(-0.619437\pi\) | ||||
−0.366479 | + | 0.930426i | \(0.619437\pi\) | |||||||
\(920\) | −24.5819 | −0.810441 | ||||||||
\(921\) | 7.35520 | 0.242362 | ||||||||
\(922\) | 10.0753 | 0.331813 | ||||||||
\(923\) | 23.9750 | 0.789148 | ||||||||
\(924\) | 3.19629 | 0.105150 | ||||||||
\(925\) | −8.43217 | −0.277248 | ||||||||
\(926\) | −35.6077 | −1.17014 | ||||||||
\(927\) | 46.9188 | 1.54102 | ||||||||
\(928\) | −5.51677 | −0.181097 | ||||||||
\(929\) | −13.1563 | −0.431643 | −0.215822 | − | 0.976433i | \(-0.569243\pi\) | ||||
−0.215822 | + | 0.976433i | \(0.569243\pi\) | |||||||
\(930\) | 2.32616 | 0.0762777 | ||||||||
\(931\) | −0.984111 | −0.0322529 | ||||||||
\(932\) | −42.4476 | −1.39042 | ||||||||
\(933\) | 12.2507 | 0.401069 | ||||||||
\(934\) | −81.5847 | −2.66953 | ||||||||
\(935\) | −11.1847 | −0.365778 | ||||||||
\(936\) | 18.2813 | 0.597543 | ||||||||
\(937\) | 34.2681 | 1.11949 | 0.559744 | − | 0.828665i | \(-0.310899\pi\) | ||||
0.559744 | + | 0.828665i | \(0.310899\pi\) | |||||||
\(938\) | 30.4831 | 0.995308 | ||||||||
\(939\) | −10.6171 | −0.346476 | ||||||||
\(940\) | 43.7214 | 1.42603 | ||||||||
\(941\) | −34.9287 | −1.13864 | −0.569321 | − | 0.822115i | \(-0.692794\pi\) | ||||
−0.569321 | + | 0.822115i | \(0.692794\pi\) | |||||||
\(942\) | 10.6423 | 0.346743 | ||||||||
\(943\) | 47.8423 | 1.55796 | ||||||||
\(944\) | −13.5546 | −0.441165 | ||||||||
\(945\) | −7.84960 | −0.255348 | ||||||||
\(946\) | −2.20029 | −0.0715376 | ||||||||
\(947\) | 18.7070 | 0.607894 | 0.303947 | − | 0.952689i | \(-0.401695\pi\) | ||||
0.303947 | + | 0.952689i | \(0.401695\pi\) | |||||||
\(948\) | −4.44197 | −0.144268 | ||||||||
\(949\) | 3.94858 | 0.128176 | ||||||||
\(950\) | 3.78404 | 0.122771 | ||||||||
\(951\) | −5.70476 | −0.184989 | ||||||||
\(952\) | 65.9382 | 2.13707 | ||||||||
\(953\) | 1.52844 | 0.0495109 | 0.0247555 | − | 0.999694i | \(-0.492119\pi\) | ||||
0.0247555 | + | 0.999694i | \(0.492119\pi\) | |||||||
\(954\) | −14.2256 | −0.460571 | ||||||||
\(955\) | 3.81281 | 0.123380 | ||||||||
\(956\) | −2.19793 | −0.0710863 | ||||||||
\(957\) | −0.669789 | −0.0216512 | ||||||||
\(958\) | −58.4253 | −1.88764 | ||||||||
\(959\) | −46.7204 | −1.50868 | ||||||||
\(960\) | −6.57498 | −0.212207 | ||||||||
\(961\) | −28.1426 | −0.907826 | ||||||||
\(962\) | −12.3336 | −0.397651 | ||||||||
\(963\) | −0.371016 | −0.0119558 | ||||||||
\(964\) | −5.54315 | −0.178533 | ||||||||
\(965\) | −0.484414 | −0.0155939 | ||||||||
\(966\) | −8.64417 | −0.278122 | ||||||||
\(967\) | 39.8422 | 1.28124 | 0.640619 | − | 0.767859i | \(-0.278678\pi\) | ||||
0.640619 | + | 0.767859i | \(0.278678\pi\) | |||||||
\(968\) | −3.88867 | −0.124987 | ||||||||
\(969\) | 1.66080 | 0.0533526 | ||||||||
\(970\) | 1.84008 | 0.0590814 | ||||||||
\(971\) | 7.42297 | 0.238214 | 0.119107 | − | 0.992881i | \(-0.461997\pi\) | ||||
0.119107 | + | 0.992881i | \(0.461997\pi\) | |||||||
\(972\) | −34.9471 | −1.12093 | ||||||||
\(973\) | 27.4831 | 0.881068 | ||||||||
\(974\) | −0.302732 | −0.00970017 | ||||||||
\(975\) | 1.67123 | 0.0535222 | ||||||||
\(976\) | 14.4962 | 0.464012 | ||||||||
\(977\) | 11.9392 | 0.381970 | 0.190985 | − | 0.981593i | \(-0.438832\pi\) | ||||
0.190985 | + | 0.981593i | \(0.438832\pi\) | |||||||
\(978\) | 2.88741 | 0.0923293 | ||||||||
\(979\) | −11.7278 | −0.374822 | ||||||||
\(980\) | 9.15858 | 0.292560 | ||||||||
\(981\) | 20.0062 | 0.638749 | ||||||||
\(982\) | 86.2595 | 2.75265 | ||||||||
\(983\) | −18.7762 | −0.598869 | −0.299434 | − | 0.954117i | \(-0.596798\pi\) | ||||
−0.299434 | + | 0.954117i | \(0.596798\pi\) | |||||||
\(984\) | −17.0569 | −0.543754 | ||||||||
\(985\) | −40.3205 | −1.28472 | ||||||||
\(986\) | −30.6912 | −0.977406 | ||||||||
\(987\) | 6.92177 | 0.220322 | ||||||||
\(988\) | 3.57136 | 0.113620 | ||||||||
\(989\) | 3.83959 | 0.122092 | ||||||||
\(990\) | 10.3448 | 0.328778 | ||||||||
\(991\) | 44.9718 | 1.42858 | 0.714289 | − | 0.699851i | \(-0.246750\pi\) | ||||
0.714289 | + | 0.699851i | \(0.246750\pi\) | |||||||
\(992\) | −5.28904 | −0.167927 | ||||||||
\(993\) | −7.15046 | −0.226913 | ||||||||
\(994\) | −79.9809 | −2.53684 | ||||||||
\(995\) | 14.0072 | 0.444057 | ||||||||
\(996\) | −8.34764 | −0.264505 | ||||||||
\(997\) | 0.591835 | 0.0187436 | 0.00937181 | − | 0.999956i | \(-0.497017\pi\) | ||||
0.00937181 | + | 0.999956i | \(0.497017\pi\) | |||||||
\(998\) | 38.3651 | 1.21443 | ||||||||
\(999\) | 7.01883 | 0.222066 |
(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 | 6017.2.a.f.1.12 | ✓ | 121 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6017.2.a.f.1.12 | ✓ | 121 | 1.1 | even | 1 | trivial |