Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7098,2,Mod(1,7098)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7098, 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("7098.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7098.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: | \(56.6778153547\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.48406561.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} - 17x^{4} + 39x^{3} + 111x^{2} - 131x - 281 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(3.41496\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7098.1 |
$q$-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 | ||||||||
\(5\) | 3.41496 | 1.52722 | 0.763608 | − | 0.645680i | \(-0.223426\pi\) | ||||
0.763608 | + | 0.645680i | \(0.223426\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.41496 | 1.07990 | ||||||||
\(11\) | 3.24698 | 0.979001 | 0.489501 | − | 0.872003i | \(-0.337179\pi\) | ||||
0.489501 | + | 0.872003i | \(0.337179\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 3.41496 | 0.881738 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.80194 | 0.437034 | 0.218517 | − | 0.975833i | \(-0.429878\pi\) | ||||
0.218517 | + | 0.975833i | \(0.429878\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 1.93665 | 0.444297 | 0.222149 | − | 0.975013i | \(-0.428693\pi\) | ||||
0.222149 | + | 0.975013i | \(0.428693\pi\) | |||||||
\(20\) | 3.41496 | 0.763608 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 3.24698 | 0.692258 | ||||||||
\(23\) | 3.28422 | 0.684808 | 0.342404 | − | 0.939553i | \(-0.388759\pi\) | ||||
0.342404 | + | 0.939553i | \(0.388759\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 6.66194 | 1.33239 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −3.64112 | −0.676139 | −0.338069 | − | 0.941121i | \(-0.609774\pi\) | ||||
−0.338069 | + | 0.941121i | \(0.609774\pi\) | |||||||
\(30\) | 3.41496 | 0.623483 | ||||||||
\(31\) | −3.10698 | −0.558030 | −0.279015 | − | 0.960287i | \(-0.590008\pi\) | ||||
−0.279015 | + | 0.960287i | \(0.590008\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 3.24698 | 0.565227 | ||||||||
\(34\) | 1.80194 | 0.309030 | ||||||||
\(35\) | 3.41496 | 0.577233 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −4.80172 | −0.789398 | −0.394699 | − | 0.918810i | \(-0.629151\pi\) | ||||
−0.394699 | + | 0.918810i | \(0.629151\pi\) | |||||||
\(38\) | 1.93665 | 0.314165 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.41496 | 0.539952 | ||||||||
\(41\) | −4.58189 | −0.715571 | −0.357785 | − | 0.933804i | \(-0.616468\pi\) | ||||
−0.357785 | + | 0.933804i | \(0.616468\pi\) | |||||||
\(42\) | 1.00000 | 0.154303 | ||||||||
\(43\) | 5.11205 | 0.779581 | 0.389790 | − | 0.920904i | \(-0.372547\pi\) | ||||
0.389790 | + | 0.920904i | \(0.372547\pi\) | |||||||
\(44\) | 3.24698 | 0.489501 | ||||||||
\(45\) | 3.41496 | 0.509072 | ||||||||
\(46\) | 3.28422 | 0.484232 | ||||||||
\(47\) | −10.5966 | −1.54567 | −0.772836 | − | 0.634605i | \(-0.781163\pi\) | ||||
−0.772836 | + | 0.634605i | \(0.781163\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 6.66194 | 0.942140 | ||||||||
\(51\) | 1.80194 | 0.252322 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.46409 | −0.338469 | −0.169235 | − | 0.985576i | \(-0.554130\pi\) | ||||
−0.169235 | + | 0.985576i | \(0.554130\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 11.0883 | 1.49515 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 1.93665 | 0.256515 | ||||||||
\(58\) | −3.64112 | −0.478102 | ||||||||
\(59\) | 13.2749 | 1.72824 | 0.864120 | − | 0.503286i | \(-0.167876\pi\) | ||||
0.864120 | + | 0.503286i | \(0.167876\pi\) | |||||||
\(60\) | 3.41496 | 0.440869 | ||||||||
\(61\) | −1.76668 | −0.226200 | −0.113100 | − | 0.993584i | \(-0.536078\pi\) | ||||
−0.113100 | + | 0.993584i | \(0.536078\pi\) | |||||||
\(62\) | −3.10698 | −0.394587 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.24698 | 0.399676 | ||||||||
\(67\) | −12.4092 | −1.51603 | −0.758013 | − | 0.652240i | \(-0.773830\pi\) | ||||
−0.758013 | + | 0.652240i | \(0.773830\pi\) | |||||||
\(68\) | 1.80194 | 0.218517 | ||||||||
\(69\) | 3.28422 | 0.395374 | ||||||||
\(70\) | 3.41496 | 0.408166 | ||||||||
\(71\) | −2.66429 | −0.316193 | −0.158097 | − | 0.987424i | \(-0.550536\pi\) | ||||
−0.158097 | + | 0.987424i | \(0.550536\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 0.368396 | 0.0431175 | 0.0215587 | − | 0.999768i | \(-0.493137\pi\) | ||||
0.0215587 | + | 0.999768i | \(0.493137\pi\) | |||||||
\(74\) | −4.80172 | −0.558189 | ||||||||
\(75\) | 6.66194 | 0.769254 | ||||||||
\(76\) | 1.93665 | 0.222149 | ||||||||
\(77\) | 3.24698 | 0.370028 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.0033 | −1.68801 | −0.844004 | − | 0.536336i | \(-0.819808\pi\) | ||||
−0.844004 | + | 0.536336i | \(0.819808\pi\) | |||||||
\(80\) | 3.41496 | 0.381804 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.58189 | −0.505985 | ||||||||
\(83\) | −1.43401 | −0.157403 | −0.0787014 | − | 0.996898i | \(-0.525077\pi\) | ||||
−0.0787014 | + | 0.996898i | \(0.525077\pi\) | |||||||
\(84\) | 1.00000 | 0.109109 | ||||||||
\(85\) | 6.15354 | 0.667445 | ||||||||
\(86\) | 5.11205 | 0.551247 | ||||||||
\(87\) | −3.64112 | −0.390369 | ||||||||
\(88\) | 3.24698 | 0.346129 | ||||||||
\(89\) | 5.10615 | 0.541251 | 0.270625 | − | 0.962685i | \(-0.412770\pi\) | ||||
0.270625 | + | 0.962685i | \(0.412770\pi\) | |||||||
\(90\) | 3.41496 | 0.359968 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.28422 | 0.342404 | ||||||||
\(93\) | −3.10698 | −0.322179 | ||||||||
\(94\) | −10.5966 | −1.09296 | ||||||||
\(95\) | 6.61356 | 0.678537 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −11.9553 | −1.21387 | −0.606936 | − | 0.794750i | \(-0.707602\pi\) | ||||
−0.606936 | + | 0.794750i | \(0.707602\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 3.24698 | 0.326334 | ||||||||
\(100\) | 6.66194 | 0.666194 | ||||||||
\(101\) | −18.5354 | −1.84434 | −0.922170 | − | 0.386785i | \(-0.873585\pi\) | ||||
−0.922170 | + | 0.386785i | \(0.873585\pi\) | |||||||
\(102\) | 1.80194 | 0.178418 | ||||||||
\(103\) | 18.2577 | 1.79899 | 0.899493 | − | 0.436936i | \(-0.143936\pi\) | ||||
0.899493 | + | 0.436936i | \(0.143936\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.41496 | 0.333266 | ||||||||
\(106\) | −2.46409 | −0.239334 | ||||||||
\(107\) | −15.0210 | −1.45213 | −0.726066 | − | 0.687625i | \(-0.758653\pi\) | ||||
−0.726066 | + | 0.687625i | \(0.758653\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 11.7533 | 1.12577 | 0.562883 | − | 0.826536i | \(-0.309692\pi\) | ||||
0.562883 | + | 0.826536i | \(0.309692\pi\) | |||||||
\(110\) | 11.0883 | 1.05723 | ||||||||
\(111\) | −4.80172 | −0.455759 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 3.69957 | 0.348026 | 0.174013 | − | 0.984743i | \(-0.444326\pi\) | ||||
0.174013 | + | 0.984743i | \(0.444326\pi\) | |||||||
\(114\) | 1.93665 | 0.181384 | ||||||||
\(115\) | 11.2155 | 1.04585 | ||||||||
\(116\) | −3.64112 | −0.338069 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 13.2749 | 1.22205 | ||||||||
\(119\) | 1.80194 | 0.165183 | ||||||||
\(120\) | 3.41496 | 0.311742 | ||||||||
\(121\) | −0.457123 | −0.0415567 | ||||||||
\(122\) | −1.76668 | −0.159948 | ||||||||
\(123\) | −4.58189 | −0.413135 | ||||||||
\(124\) | −3.10698 | −0.279015 | ||||||||
\(125\) | 5.67545 | 0.507627 | ||||||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | 3.89724 | 0.345824 | 0.172912 | − | 0.984937i | \(-0.444682\pi\) | ||||
0.172912 | + | 0.984937i | \(0.444682\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 5.11205 | 0.450091 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.6740 | −1.54418 | −0.772091 | − | 0.635511i | \(-0.780789\pi\) | ||||
−0.772091 | + | 0.635511i | \(0.780789\pi\) | |||||||
\(132\) | 3.24698 | 0.282613 | ||||||||
\(133\) | 1.93665 | 0.167928 | ||||||||
\(134\) | −12.4092 | −1.07199 | ||||||||
\(135\) | 3.41496 | 0.293913 | ||||||||
\(136\) | 1.80194 | 0.154515 | ||||||||
\(137\) | −14.9195 | −1.27466 | −0.637331 | − | 0.770590i | \(-0.719962\pi\) | ||||
−0.637331 | + | 0.770590i | \(0.719962\pi\) | |||||||
\(138\) | 3.28422 | 0.279572 | ||||||||
\(139\) | −3.27513 | −0.277793 | −0.138897 | − | 0.990307i | \(-0.544356\pi\) | ||||
−0.138897 | + | 0.990307i | \(0.544356\pi\) | |||||||
\(140\) | 3.41496 | 0.288617 | ||||||||
\(141\) | −10.5966 | −0.892395 | ||||||||
\(142\) | −2.66429 | −0.223582 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −12.4343 | −1.03261 | ||||||||
\(146\) | 0.368396 | 0.0304887 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −4.80172 | −0.394699 | ||||||||
\(149\) | 8.92475 | 0.731144 | 0.365572 | − | 0.930783i | \(-0.380873\pi\) | ||||
0.365572 | + | 0.930783i | \(0.380873\pi\) | |||||||
\(150\) | 6.66194 | 0.543945 | ||||||||
\(151\) | −0.712364 | −0.0579714 | −0.0289857 | − | 0.999580i | \(-0.509228\pi\) | ||||
−0.0289857 | + | 0.999580i | \(0.509228\pi\) | |||||||
\(152\) | 1.93665 | 0.157083 | ||||||||
\(153\) | 1.80194 | 0.145678 | ||||||||
\(154\) | 3.24698 | 0.261649 | ||||||||
\(155\) | −10.6102 | −0.852232 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.1436 | −1.12879 | −0.564393 | − | 0.825506i | \(-0.690890\pi\) | ||||
−0.564393 | + | 0.825506i | \(0.690890\pi\) | |||||||
\(158\) | −15.0033 | −1.19360 | ||||||||
\(159\) | −2.46409 | −0.195415 | ||||||||
\(160\) | 3.41496 | 0.269976 | ||||||||
\(161\) | 3.28422 | 0.258833 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 15.6565 | 1.22632 | 0.613158 | − | 0.789960i | \(-0.289899\pi\) | ||||
0.613158 | + | 0.789960i | \(0.289899\pi\) | |||||||
\(164\) | −4.58189 | −0.357785 | ||||||||
\(165\) | 11.0883 | 0.863223 | ||||||||
\(166\) | −1.43401 | −0.111301 | ||||||||
\(167\) | 19.6904 | 1.52369 | 0.761845 | − | 0.647759i | \(-0.224294\pi\) | ||||
0.761845 | + | 0.647759i | \(0.224294\pi\) | |||||||
\(168\) | 1.00000 | 0.0771517 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 6.15354 | 0.471955 | ||||||||
\(171\) | 1.93665 | 0.148099 | ||||||||
\(172\) | 5.11205 | 0.389790 | ||||||||
\(173\) | 16.3915 | 1.24622 | 0.623112 | − | 0.782132i | \(-0.285868\pi\) | ||||
0.623112 | + | 0.782132i | \(0.285868\pi\) | |||||||
\(174\) | −3.64112 | −0.276033 | ||||||||
\(175\) | 6.66194 | 0.503595 | ||||||||
\(176\) | 3.24698 | 0.244750 | ||||||||
\(177\) | 13.2749 | 0.997800 | ||||||||
\(178\) | 5.10615 | 0.382722 | ||||||||
\(179\) | −17.0906 | −1.27741 | −0.638704 | − | 0.769452i | \(-0.720529\pi\) | ||||
−0.638704 | + | 0.769452i | \(0.720529\pi\) | |||||||
\(180\) | 3.41496 | 0.254536 | ||||||||
\(181\) | 21.3647 | 1.58803 | 0.794015 | − | 0.607899i | \(-0.207987\pi\) | ||||
0.794015 | + | 0.607899i | \(0.207987\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.76668 | −0.130597 | ||||||||
\(184\) | 3.28422 | 0.242116 | ||||||||
\(185\) | −16.3977 | −1.20558 | ||||||||
\(186\) | −3.10698 | −0.227815 | ||||||||
\(187\) | 5.85086 | 0.427857 | ||||||||
\(188\) | −10.5966 | −0.772836 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 6.61356 | 0.479798 | ||||||||
\(191\) | 16.2973 | 1.17923 | 0.589614 | − | 0.807685i | \(-0.299280\pi\) | ||||
0.589614 | + | 0.807685i | \(0.299280\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 18.7221 | 1.34765 | 0.673824 | − | 0.738892i | \(-0.264651\pi\) | ||||
0.673824 | + | 0.738892i | \(0.264651\pi\) | |||||||
\(194\) | −11.9553 | −0.858338 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 6.35011 | 0.452426 | 0.226213 | − | 0.974078i | \(-0.427365\pi\) | ||||
0.226213 | + | 0.974078i | \(0.427365\pi\) | |||||||
\(198\) | 3.24698 | 0.230753 | ||||||||
\(199\) | 11.9820 | 0.849380 | 0.424690 | − | 0.905339i | \(-0.360383\pi\) | ||||
0.424690 | + | 0.905339i | \(0.360383\pi\) | |||||||
\(200\) | 6.66194 | 0.471070 | ||||||||
\(201\) | −12.4092 | −0.875278 | ||||||||
\(202\) | −18.5354 | −1.30414 | ||||||||
\(203\) | −3.64112 | −0.255556 | ||||||||
\(204\) | 1.80194 | 0.126161 | ||||||||
\(205\) | −15.6470 | −1.09283 | ||||||||
\(206\) | 18.2577 | 1.27207 | ||||||||
\(207\) | 3.28422 | 0.228269 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.28825 | 0.434967 | ||||||||
\(210\) | 3.41496 | 0.235654 | ||||||||
\(211\) | 9.42870 | 0.649099 | 0.324549 | − | 0.945869i | \(-0.394787\pi\) | ||||
0.324549 | + | 0.945869i | \(0.394787\pi\) | |||||||
\(212\) | −2.46409 | −0.169235 | ||||||||
\(213\) | −2.66429 | −0.182554 | ||||||||
\(214\) | −15.0210 | −1.02681 | ||||||||
\(215\) | 17.4575 | 1.19059 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −3.10698 | −0.210916 | ||||||||
\(218\) | 11.7533 | 0.796037 | ||||||||
\(219\) | 0.368396 | 0.0248939 | ||||||||
\(220\) | 11.0883 | 0.747573 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −4.80172 | −0.322270 | ||||||||
\(223\) | −15.9921 | −1.07091 | −0.535456 | − | 0.844563i | \(-0.679860\pi\) | ||||
−0.535456 | + | 0.844563i | \(0.679860\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 6.66194 | 0.444129 | ||||||||
\(226\) | 3.69957 | 0.246092 | ||||||||
\(227\) | 4.11815 | 0.273331 | 0.136665 | − | 0.990617i | \(-0.456361\pi\) | ||||
0.136665 | + | 0.990617i | \(0.456361\pi\) | |||||||
\(228\) | 1.93665 | 0.128258 | ||||||||
\(229\) | 0.403067 | 0.0266354 | 0.0133177 | − | 0.999911i | \(-0.495761\pi\) | ||||
0.0133177 | + | 0.999911i | \(0.495761\pi\) | |||||||
\(230\) | 11.2155 | 0.739527 | ||||||||
\(231\) | 3.24698 | 0.213636 | ||||||||
\(232\) | −3.64112 | −0.239051 | ||||||||
\(233\) | −18.7561 | −1.22875 | −0.614376 | − | 0.789014i | \(-0.710592\pi\) | ||||
−0.614376 | + | 0.789014i | \(0.710592\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −36.1869 | −2.36058 | ||||||||
\(236\) | 13.2749 | 0.864120 | ||||||||
\(237\) | −15.0033 | −0.974572 | ||||||||
\(238\) | 1.80194 | 0.116802 | ||||||||
\(239\) | −10.3497 | −0.669466 | −0.334733 | − | 0.942313i | \(-0.608646\pi\) | ||||
−0.334733 | + | 0.942313i | \(0.608646\pi\) | |||||||
\(240\) | 3.41496 | 0.220435 | ||||||||
\(241\) | −9.33396 | −0.601253 | −0.300627 | − | 0.953742i | \(-0.597196\pi\) | ||||
−0.300627 | + | 0.953742i | \(0.597196\pi\) | |||||||
\(242\) | −0.457123 | −0.0293850 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −1.76668 | −0.113100 | ||||||||
\(245\) | 3.41496 | 0.218174 | ||||||||
\(246\) | −4.58189 | −0.292131 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −3.10698 | −0.197293 | ||||||||
\(249\) | −1.43401 | −0.0908766 | ||||||||
\(250\) | 5.67545 | 0.358947 | ||||||||
\(251\) | −30.9745 | −1.95509 | −0.977547 | − | 0.210718i | \(-0.932420\pi\) | ||||
−0.977547 | + | 0.210718i | \(0.932420\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | 10.6638 | 0.670428 | ||||||||
\(254\) | 3.89724 | 0.244535 | ||||||||
\(255\) | 6.15354 | 0.385350 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −2.27305 | −0.141789 | −0.0708944 | − | 0.997484i | \(-0.522585\pi\) | ||||
−0.0708944 | + | 0.997484i | \(0.522585\pi\) | |||||||
\(258\) | 5.11205 | 0.318263 | ||||||||
\(259\) | −4.80172 | −0.298364 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.64112 | −0.225380 | ||||||||
\(262\) | −17.6740 | −1.09190 | ||||||||
\(263\) | −18.5834 | −1.14590 | −0.572950 | − | 0.819590i | \(-0.694201\pi\) | ||||
−0.572950 | + | 0.819590i | \(0.694201\pi\) | |||||||
\(264\) | 3.24698 | 0.199838 | ||||||||
\(265\) | −8.41477 | −0.516915 | ||||||||
\(266\) | 1.93665 | 0.118743 | ||||||||
\(267\) | 5.10615 | 0.312491 | ||||||||
\(268\) | −12.4092 | −0.758013 | ||||||||
\(269\) | 26.7522 | 1.63111 | 0.815555 | − | 0.578679i | \(-0.196432\pi\) | ||||
0.815555 | + | 0.578679i | \(0.196432\pi\) | |||||||
\(270\) | 3.41496 | 0.207828 | ||||||||
\(271\) | 5.33182 | 0.323885 | 0.161943 | − | 0.986800i | \(-0.448224\pi\) | ||||
0.161943 | + | 0.986800i | \(0.448224\pi\) | |||||||
\(272\) | 1.80194 | 0.109259 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.9195 | −0.901323 | ||||||||
\(275\) | 21.6312 | 1.30441 | ||||||||
\(276\) | 3.28422 | 0.197687 | ||||||||
\(277\) | 25.0045 | 1.50238 | 0.751188 | − | 0.660088i | \(-0.229481\pi\) | ||||
0.751188 | + | 0.660088i | \(0.229481\pi\) | |||||||
\(278\) | −3.27513 | −0.196429 | ||||||||
\(279\) | −3.10698 | −0.186010 | ||||||||
\(280\) | 3.41496 | 0.204083 | ||||||||
\(281\) | 13.8066 | 0.823633 | 0.411817 | − | 0.911267i | \(-0.364894\pi\) | ||||
0.411817 | + | 0.911267i | \(0.364894\pi\) | |||||||
\(282\) | −10.5966 | −0.631018 | ||||||||
\(283\) | −22.0224 | −1.30910 | −0.654548 | − | 0.756021i | \(-0.727141\pi\) | ||||
−0.654548 | + | 0.756021i | \(0.727141\pi\) | |||||||
\(284\) | −2.66429 | −0.158097 | ||||||||
\(285\) | 6.61356 | 0.391754 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.58189 | −0.270460 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −13.7530 | −0.809001 | ||||||||
\(290\) | −12.4343 | −0.730165 | ||||||||
\(291\) | −11.9553 | −0.700830 | ||||||||
\(292\) | 0.368396 | 0.0215587 | ||||||||
\(293\) | −2.17514 | −0.127073 | −0.0635364 | − | 0.997980i | \(-0.520238\pi\) | ||||
−0.0635364 | + | 0.997980i | \(0.520238\pi\) | |||||||
\(294\) | 1.00000 | 0.0583212 | ||||||||
\(295\) | 45.3331 | 2.63939 | ||||||||
\(296\) | −4.80172 | −0.279094 | ||||||||
\(297\) | 3.24698 | 0.188409 | ||||||||
\(298\) | 8.92475 | 0.516997 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 6.66194 | 0.384627 | ||||||||
\(301\) | 5.11205 | 0.294654 | ||||||||
\(302\) | −0.712364 | −0.0409920 | ||||||||
\(303\) | −18.5354 | −1.06483 | ||||||||
\(304\) | 1.93665 | 0.111074 | ||||||||
\(305\) | −6.03315 | −0.345457 | ||||||||
\(306\) | 1.80194 | 0.103010 | ||||||||
\(307\) | 21.5338 | 1.22900 | 0.614500 | − | 0.788917i | \(-0.289358\pi\) | ||||
0.614500 | + | 0.788917i | \(0.289358\pi\) | |||||||
\(308\) | 3.24698 | 0.185014 | ||||||||
\(309\) | 18.2577 | 1.03864 | ||||||||
\(310\) | −10.6102 | −0.602619 | ||||||||
\(311\) | −10.5043 | −0.595644 | −0.297822 | − | 0.954621i | \(-0.596260\pi\) | ||||
−0.297822 | + | 0.954621i | \(0.596260\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.0754 | −0.908635 | −0.454317 | − | 0.890840i | \(-0.650117\pi\) | ||||
−0.454317 | + | 0.890840i | \(0.650117\pi\) | |||||||
\(314\) | −14.1436 | −0.798172 | ||||||||
\(315\) | 3.41496 | 0.192411 | ||||||||
\(316\) | −15.0033 | −0.844004 | ||||||||
\(317\) | 15.3743 | 0.863508 | 0.431754 | − | 0.901991i | \(-0.357895\pi\) | ||||
0.431754 | + | 0.901991i | \(0.357895\pi\) | |||||||
\(318\) | −2.46409 | −0.138179 | ||||||||
\(319\) | −11.8226 | −0.661941 | ||||||||
\(320\) | 3.41496 | 0.190902 | ||||||||
\(321\) | −15.0210 | −0.838389 | ||||||||
\(322\) | 3.28422 | 0.183023 | ||||||||
\(323\) | 3.48972 | 0.194173 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 15.6565 | 0.867136 | ||||||||
\(327\) | 11.7533 | 0.649962 | ||||||||
\(328\) | −4.58189 | −0.252992 | ||||||||
\(329\) | −10.5966 | −0.584209 | ||||||||
\(330\) | 11.0883 | 0.610391 | ||||||||
\(331\) | −8.21249 | −0.451399 | −0.225700 | − | 0.974197i | \(-0.572467\pi\) | ||||
−0.225700 | + | 0.974197i | \(0.572467\pi\) | |||||||
\(332\) | −1.43401 | −0.0787014 | ||||||||
\(333\) | −4.80172 | −0.263133 | ||||||||
\(334\) | 19.6904 | 1.07741 | ||||||||
\(335\) | −42.3769 | −2.31530 | ||||||||
\(336\) | 1.00000 | 0.0545545 | ||||||||
\(337\) | −18.4567 | −1.00540 | −0.502701 | − | 0.864460i | \(-0.667660\pi\) | ||||
−0.502701 | + | 0.864460i | \(0.667660\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.69957 | 0.200933 | ||||||||
\(340\) | 6.15354 | 0.333723 | ||||||||
\(341\) | −10.0883 | −0.546312 | ||||||||
\(342\) | 1.93665 | 0.104722 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 5.11205 | 0.275623 | ||||||||
\(345\) | 11.2155 | 0.603821 | ||||||||
\(346\) | 16.3915 | 0.881214 | ||||||||
\(347\) | 31.3648 | 1.68375 | 0.841876 | − | 0.539671i | \(-0.181451\pi\) | ||||
0.841876 | + | 0.539671i | \(0.181451\pi\) | |||||||
\(348\) | −3.64112 | −0.195184 | ||||||||
\(349\) | −6.96959 | −0.373073 | −0.186537 | − | 0.982448i | \(-0.559726\pi\) | ||||
−0.186537 | + | 0.982448i | \(0.559726\pi\) | |||||||
\(350\) | 6.66194 | 0.356096 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.24698 | 0.173065 | ||||||||
\(353\) | 13.0978 | 0.697127 | 0.348563 | − | 0.937285i | \(-0.386670\pi\) | ||||
0.348563 | + | 0.937285i | \(0.386670\pi\) | |||||||
\(354\) | 13.2749 | 0.705551 | ||||||||
\(355\) | −9.09845 | −0.482895 | ||||||||
\(356\) | 5.10615 | 0.270625 | ||||||||
\(357\) | 1.80194 | 0.0953687 | ||||||||
\(358\) | −17.0906 | −0.903264 | ||||||||
\(359\) | −8.01400 | −0.422963 | −0.211481 | − | 0.977382i | \(-0.567829\pi\) | ||||
−0.211481 | + | 0.977382i | \(0.567829\pi\) | |||||||
\(360\) | 3.41496 | 0.179984 | ||||||||
\(361\) | −15.2494 | −0.802600 | ||||||||
\(362\) | 21.3647 | 1.12291 | ||||||||
\(363\) | −0.457123 | −0.0239928 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.25806 | 0.0658497 | ||||||||
\(366\) | −1.76668 | −0.0923460 | ||||||||
\(367\) | −25.7361 | −1.34342 | −0.671708 | − | 0.740816i | \(-0.734439\pi\) | ||||
−0.671708 | + | 0.740816i | \(0.734439\pi\) | |||||||
\(368\) | 3.28422 | 0.171202 | ||||||||
\(369\) | −4.58189 | −0.238524 | ||||||||
\(370\) | −16.3977 | −0.852474 | ||||||||
\(371\) | −2.46409 | −0.127929 | ||||||||
\(372\) | −3.10698 | −0.161089 | ||||||||
\(373\) | −0.973483 | −0.0504050 | −0.0252025 | − | 0.999682i | \(-0.508023\pi\) | ||||
−0.0252025 | + | 0.999682i | \(0.508023\pi\) | |||||||
\(374\) | 5.85086 | 0.302541 | ||||||||
\(375\) | 5.67545 | 0.293079 | ||||||||
\(376\) | −10.5966 | −0.546478 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.00000 | 0.0514344 | ||||||||
\(379\) | −5.27383 | −0.270899 | −0.135449 | − | 0.990784i | \(-0.543248\pi\) | ||||
−0.135449 | + | 0.990784i | \(0.543248\pi\) | |||||||
\(380\) | 6.61356 | 0.339269 | ||||||||
\(381\) | 3.89724 | 0.199662 | ||||||||
\(382\) | 16.2973 | 0.833840 | ||||||||
\(383\) | 11.1179 | 0.568100 | 0.284050 | − | 0.958810i | \(-0.408322\pi\) | ||||
0.284050 | + | 0.958810i | \(0.408322\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 11.0883 | 0.565112 | ||||||||
\(386\) | 18.7221 | 0.952931 | ||||||||
\(387\) | 5.11205 | 0.259860 | ||||||||
\(388\) | −11.9553 | −0.606936 | ||||||||
\(389\) | −13.6798 | −0.693595 | −0.346797 | − | 0.937940i | \(-0.612731\pi\) | ||||
−0.346797 | + | 0.937940i | \(0.612731\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.91797 | 0.299284 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −17.6740 | −0.891534 | ||||||||
\(394\) | 6.35011 | 0.319914 | ||||||||
\(395\) | −51.2358 | −2.57795 | ||||||||
\(396\) | 3.24698 | 0.163167 | ||||||||
\(397\) | 16.3683 | 0.821500 | 0.410750 | − | 0.911748i | \(-0.365267\pi\) | ||||
0.410750 | + | 0.911748i | \(0.365267\pi\) | |||||||
\(398\) | 11.9820 | 0.600603 | ||||||||
\(399\) | 1.93665 | 0.0969536 | ||||||||
\(400\) | 6.66194 | 0.333097 | ||||||||
\(401\) | −35.9089 | −1.79320 | −0.896602 | − | 0.442837i | \(-0.853972\pi\) | ||||
−0.896602 | + | 0.442837i | \(0.853972\pi\) | |||||||
\(402\) | −12.4092 | −0.618915 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −18.5354 | −0.922170 | ||||||||
\(405\) | 3.41496 | 0.169691 | ||||||||
\(406\) | −3.64112 | −0.180706 | ||||||||
\(407\) | −15.5911 | −0.772822 | ||||||||
\(408\) | 1.80194 | 0.0892092 | ||||||||
\(409\) | 12.4416 | 0.615197 | 0.307599 | − | 0.951516i | \(-0.400475\pi\) | ||||
0.307599 | + | 0.951516i | \(0.400475\pi\) | |||||||
\(410\) | −15.6470 | −0.772748 | ||||||||
\(411\) | −14.9195 | −0.735927 | ||||||||
\(412\) | 18.2577 | 0.899493 | ||||||||
\(413\) | 13.2749 | 0.653213 | ||||||||
\(414\) | 3.28422 | 0.161411 | ||||||||
\(415\) | −4.89708 | −0.240388 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.27513 | −0.160384 | ||||||||
\(418\) | 6.28825 | 0.307568 | ||||||||
\(419\) | 9.73591 | 0.475630 | 0.237815 | − | 0.971310i | \(-0.423569\pi\) | ||||
0.237815 | + | 0.971310i | \(0.423569\pi\) | |||||||
\(420\) | 3.41496 | 0.166633 | ||||||||
\(421\) | 24.4352 | 1.19090 | 0.595449 | − | 0.803393i | \(-0.296974\pi\) | ||||
0.595449 | + | 0.803393i | \(0.296974\pi\) | |||||||
\(422\) | 9.42870 | 0.458982 | ||||||||
\(423\) | −10.5966 | −0.515224 | ||||||||
\(424\) | −2.46409 | −0.119667 | ||||||||
\(425\) | 12.0044 | 0.582299 | ||||||||
\(426\) | −2.66429 | −0.129085 | ||||||||
\(427\) | −1.76668 | −0.0854957 | ||||||||
\(428\) | −15.0210 | −0.726066 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 17.4575 | 0.841873 | ||||||||
\(431\) | 38.2356 | 1.84174 | 0.920872 | − | 0.389864i | \(-0.127478\pi\) | ||||
0.920872 | + | 0.389864i | \(0.127478\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 31.9423 | 1.53505 | 0.767524 | − | 0.641021i | \(-0.221489\pi\) | ||||
0.767524 | + | 0.641021i | \(0.221489\pi\) | |||||||
\(434\) | −3.10698 | −0.149140 | ||||||||
\(435\) | −12.4343 | −0.596177 | ||||||||
\(436\) | 11.7533 | 0.562883 | ||||||||
\(437\) | 6.36038 | 0.304258 | ||||||||
\(438\) | 0.368396 | 0.0176026 | ||||||||
\(439\) | 20.6203 | 0.984152 | 0.492076 | − | 0.870552i | \(-0.336238\pi\) | ||||
0.492076 | + | 0.870552i | \(0.336238\pi\) | |||||||
\(440\) | 11.0883 | 0.528614 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.760370 | −0.0361263 | −0.0180631 | − | 0.999837i | \(-0.505750\pi\) | ||||
−0.0180631 | + | 0.999837i | \(0.505750\pi\) | |||||||
\(444\) | −4.80172 | −0.227880 | ||||||||
\(445\) | 17.4373 | 0.826606 | ||||||||
\(446\) | −15.9921 | −0.757250 | ||||||||
\(447\) | 8.92475 | 0.422126 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 19.8729 | 0.937859 | 0.468929 | − | 0.883236i | \(-0.344640\pi\) | ||||
0.468929 | + | 0.883236i | \(0.344640\pi\) | |||||||
\(450\) | 6.66194 | 0.314047 | ||||||||
\(451\) | −14.8773 | −0.700545 | ||||||||
\(452\) | 3.69957 | 0.174013 | ||||||||
\(453\) | −0.712364 | −0.0334698 | ||||||||
\(454\) | 4.11815 | 0.193274 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.93665 | 0.0906918 | ||||||||
\(457\) | 39.0448 | 1.82644 | 0.913220 | − | 0.407466i | \(-0.133587\pi\) | ||||
0.913220 | + | 0.407466i | \(0.133587\pi\) | |||||||
\(458\) | 0.403067 | 0.0188341 | ||||||||
\(459\) | 1.80194 | 0.0841073 | ||||||||
\(460\) | 11.2155 | 0.522925 | ||||||||
\(461\) | −25.0785 | −1.16802 | −0.584011 | − | 0.811746i | \(-0.698517\pi\) | ||||
−0.584011 | + | 0.811746i | \(0.698517\pi\) | |||||||
\(462\) | 3.24698 | 0.151063 | ||||||||
\(463\) | 11.3140 | 0.525807 | 0.262904 | − | 0.964822i | \(-0.415320\pi\) | ||||
0.262904 | + | 0.964822i | \(0.415320\pi\) | |||||||
\(464\) | −3.64112 | −0.169035 | ||||||||
\(465\) | −10.6102 | −0.492036 | ||||||||
\(466\) | −18.7561 | −0.868858 | ||||||||
\(467\) | 12.6861 | 0.587043 | 0.293521 | − | 0.955952i | \(-0.405173\pi\) | ||||
0.293521 | + | 0.955952i | \(0.405173\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.4092 | −0.573004 | ||||||||
\(470\) | −36.1869 | −1.66918 | ||||||||
\(471\) | −14.1436 | −0.651705 | ||||||||
\(472\) | 13.2749 | 0.611025 | ||||||||
\(473\) | 16.5987 | 0.763211 | ||||||||
\(474\) | −15.0033 | −0.689127 | ||||||||
\(475\) | 12.9018 | 0.591976 | ||||||||
\(476\) | 1.80194 | 0.0825917 | ||||||||
\(477\) | −2.46409 | −0.112823 | ||||||||
\(478\) | −10.3497 | −0.473384 | ||||||||
\(479\) | 5.31845 | 0.243006 | 0.121503 | − | 0.992591i | \(-0.461229\pi\) | ||||
0.121503 | + | 0.992591i | \(0.461229\pi\) | |||||||
\(480\) | 3.41496 | 0.155871 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −9.33396 | −0.425150 | ||||||||
\(483\) | 3.28422 | 0.149437 | ||||||||
\(484\) | −0.457123 | −0.0207783 | ||||||||
\(485\) | −40.8267 | −1.85385 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −31.2192 | −1.41468 | −0.707338 | − | 0.706875i | \(-0.750104\pi\) | ||||
−0.707338 | + | 0.706875i | \(0.750104\pi\) | |||||||
\(488\) | −1.76668 | −0.0799739 | ||||||||
\(489\) | 15.6565 | 0.708014 | ||||||||
\(490\) | 3.41496 | 0.154272 | ||||||||
\(491\) | 24.9801 | 1.12734 | 0.563668 | − | 0.826001i | \(-0.309390\pi\) | ||||
0.563668 | + | 0.826001i | \(0.309390\pi\) | |||||||
\(492\) | −4.58189 | −0.206567 | ||||||||
\(493\) | −6.56107 | −0.295496 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11.0883 | 0.498382 | ||||||||
\(496\) | −3.10698 | −0.139507 | ||||||||
\(497\) | −2.66429 | −0.119510 | ||||||||
\(498\) | −1.43401 | −0.0642595 | ||||||||
\(499\) | 8.22457 | 0.368182 | 0.184091 | − | 0.982909i | \(-0.441066\pi\) | ||||
0.184091 | + | 0.982909i | \(0.441066\pi\) | |||||||
\(500\) | 5.67545 | 0.253814 | ||||||||
\(501\) | 19.6904 | 0.879703 | ||||||||
\(502\) | −30.9745 | −1.38246 | ||||||||
\(503\) | −28.4248 | −1.26740 | −0.633700 | − | 0.773579i | \(-0.718465\pi\) | ||||
−0.633700 | + | 0.773579i | \(0.718465\pi\) | |||||||
\(504\) | 1.00000 | 0.0445435 | ||||||||
\(505\) | −63.2975 | −2.81670 | ||||||||
\(506\) | 10.6638 | 0.474064 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.89724 | 0.172912 | ||||||||
\(509\) | 8.58953 | 0.380724 | 0.190362 | − | 0.981714i | \(-0.439034\pi\) | ||||
0.190362 | + | 0.981714i | \(0.439034\pi\) | |||||||
\(510\) | 6.15354 | 0.272483 | ||||||||
\(511\) | 0.368396 | 0.0162969 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.93665 | 0.0855050 | ||||||||
\(514\) | −2.27305 | −0.100260 | ||||||||
\(515\) | 62.3493 | 2.74744 | ||||||||
\(516\) | 5.11205 | 0.225046 | ||||||||
\(517\) | −34.4069 | −1.51322 | ||||||||
\(518\) | −4.80172 | −0.210975 | ||||||||
\(519\) | 16.3915 | 0.719508 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.0161 | 1.05216 | 0.526082 | − | 0.850434i | \(-0.323660\pi\) | ||||
0.526082 | + | 0.850434i | \(0.323660\pi\) | |||||||
\(522\) | −3.64112 | −0.159367 | ||||||||
\(523\) | −28.7110 | −1.25544 | −0.627721 | − | 0.778438i | \(-0.716012\pi\) | ||||
−0.627721 | + | 0.778438i | \(0.716012\pi\) | |||||||
\(524\) | −17.6740 | −0.772091 | ||||||||
\(525\) | 6.66194 | 0.290751 | ||||||||
\(526\) | −18.5834 | −0.810274 | ||||||||
\(527\) | −5.59858 | −0.243878 | ||||||||
\(528\) | 3.24698 | 0.141307 | ||||||||
\(529\) | −12.2139 | −0.531038 | ||||||||
\(530\) | −8.41477 | −0.365514 | ||||||||
\(531\) | 13.2749 | 0.576080 | ||||||||
\(532\) | 1.93665 | 0.0839642 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 5.10615 | 0.220965 | ||||||||
\(535\) | −51.2960 | −2.21772 | ||||||||
\(536\) | −12.4092 | −0.535996 | ||||||||
\(537\) | −17.0906 | −0.737512 | ||||||||
\(538\) | 26.7522 | 1.15337 | ||||||||
\(539\) | 3.24698 | 0.139857 | ||||||||
\(540\) | 3.41496 | 0.146956 | ||||||||
\(541\) | −13.3317 | −0.573173 | −0.286587 | − | 0.958054i | \(-0.592521\pi\) | ||||
−0.286587 | + | 0.958054i | \(0.592521\pi\) | |||||||
\(542\) | 5.33182 | 0.229021 | ||||||||
\(543\) | 21.3647 | 0.916849 | ||||||||
\(544\) | 1.80194 | 0.0772574 | ||||||||
\(545\) | 40.1372 | 1.71929 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.82136 | 0.419931 | 0.209965 | − | 0.977709i | \(-0.432665\pi\) | ||||
0.209965 | + | 0.977709i | \(0.432665\pi\) | |||||||
\(548\) | −14.9195 | −0.637331 | ||||||||
\(549\) | −1.76668 | −0.0754002 | ||||||||
\(550\) | 21.6312 | 0.922356 | ||||||||
\(551\) | −7.05156 | −0.300406 | ||||||||
\(552\) | 3.28422 | 0.139786 | ||||||||
\(553\) | −15.0033 | −0.638007 | ||||||||
\(554\) | 25.0045 | 1.06234 | ||||||||
\(555\) | −16.3977 | −0.696042 | ||||||||
\(556\) | −3.27513 | −0.138897 | ||||||||
\(557\) | 25.6623 | 1.08735 | 0.543674 | − | 0.839297i | \(-0.317033\pi\) | ||||
0.543674 | + | 0.839297i | \(0.317033\pi\) | |||||||
\(558\) | −3.10698 | −0.131529 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 3.41496 | 0.144308 | ||||||||
\(561\) | 5.85086 | 0.247023 | ||||||||
\(562\) | 13.8066 | 0.582396 | ||||||||
\(563\) | −39.5263 | −1.66584 | −0.832918 | − | 0.553396i | \(-0.813331\pi\) | ||||
−0.832918 | + | 0.553396i | \(0.813331\pi\) | |||||||
\(564\) | −10.5966 | −0.446197 | ||||||||
\(565\) | 12.6339 | 0.531511 | ||||||||
\(566\) | −22.0224 | −0.925670 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −2.66429 | −0.111791 | ||||||||
\(569\) | 4.74188 | 0.198790 | 0.0993949 | − | 0.995048i | \(-0.468309\pi\) | ||||
0.0993949 | + | 0.995048i | \(0.468309\pi\) | |||||||
\(570\) | 6.61356 | 0.277012 | ||||||||
\(571\) | −7.02759 | −0.294095 | −0.147048 | − | 0.989129i | \(-0.546977\pi\) | ||||
−0.147048 | + | 0.989129i | \(0.546977\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.2973 | 0.680828 | ||||||||
\(574\) | −4.58189 | −0.191244 | ||||||||
\(575\) | 21.8793 | 0.912429 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 10.9656 | 0.456503 | 0.228251 | − | 0.973602i | \(-0.426699\pi\) | ||||
0.228251 | + | 0.973602i | \(0.426699\pi\) | |||||||
\(578\) | −13.7530 | −0.572050 | ||||||||
\(579\) | 18.7221 | 0.778065 | ||||||||
\(580\) | −12.4343 | −0.516305 | ||||||||
\(581\) | −1.43401 | −0.0594927 | ||||||||
\(582\) | −11.9553 | −0.495562 | ||||||||
\(583\) | −8.00086 | −0.331362 | ||||||||
\(584\) | 0.368396 | 0.0152443 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.17514 | −0.0898541 | ||||||||
\(587\) | −28.8685 | −1.19153 | −0.595766 | − | 0.803158i | \(-0.703151\pi\) | ||||
−0.595766 | + | 0.803158i | \(0.703151\pi\) | |||||||
\(588\) | 1.00000 | 0.0412393 | ||||||||
\(589\) | −6.01712 | −0.247931 | ||||||||
\(590\) | 45.3331 | 1.86633 | ||||||||
\(591\) | 6.35011 | 0.261208 | ||||||||
\(592\) | −4.80172 | −0.197350 | ||||||||
\(593\) | 17.5637 | 0.721255 | 0.360628 | − | 0.932710i | \(-0.382563\pi\) | ||||
0.360628 | + | 0.932710i | \(0.382563\pi\) | |||||||
\(594\) | 3.24698 | 0.133225 | ||||||||
\(595\) | 6.15354 | 0.252271 | ||||||||
\(596\) | 8.92475 | 0.365572 | ||||||||
\(597\) | 11.9820 | 0.490390 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.82575 | 0.401469 | 0.200735 | − | 0.979646i | \(-0.435667\pi\) | ||||
0.200735 | + | 0.979646i | \(0.435667\pi\) | |||||||
\(600\) | 6.66194 | 0.271972 | ||||||||
\(601\) | 22.3197 | 0.910438 | 0.455219 | − | 0.890380i | \(-0.349561\pi\) | ||||
0.455219 | + | 0.890380i | \(0.349561\pi\) | |||||||
\(602\) | 5.11205 | 0.208352 | ||||||||
\(603\) | −12.4092 | −0.505342 | ||||||||
\(604\) | −0.712364 | −0.0289857 | ||||||||
\(605\) | −1.56106 | −0.0634660 | ||||||||
\(606\) | −18.5354 | −0.752948 | ||||||||
\(607\) | 29.0228 | 1.17800 | 0.588999 | − | 0.808134i | \(-0.299522\pi\) | ||||
0.588999 | + | 0.808134i | \(0.299522\pi\) | |||||||
\(608\) | 1.93665 | 0.0785414 | ||||||||
\(609\) | −3.64112 | −0.147546 | ||||||||
\(610\) | −6.03315 | −0.244275 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 1.80194 | 0.0728390 | ||||||||
\(613\) | −36.4576 | −1.47251 | −0.736255 | − | 0.676704i | \(-0.763408\pi\) | ||||
−0.736255 | + | 0.676704i | \(0.763408\pi\) | |||||||
\(614\) | 21.5338 | 0.869035 | ||||||||
\(615\) | −15.6470 | −0.630946 | ||||||||
\(616\) | 3.24698 | 0.130825 | ||||||||
\(617\) | −33.4147 | −1.34522 | −0.672612 | − | 0.739995i | \(-0.734828\pi\) | ||||
−0.672612 | + | 0.739995i | \(0.734828\pi\) | |||||||
\(618\) | 18.2577 | 0.734433 | ||||||||
\(619\) | −12.8283 | −0.515614 | −0.257807 | − | 0.966196i | \(-0.583000\pi\) | ||||
−0.257807 | + | 0.966196i | \(0.583000\pi\) | |||||||
\(620\) | −10.6102 | −0.426116 | ||||||||
\(621\) | 3.28422 | 0.131791 | ||||||||
\(622\) | −10.5043 | −0.421184 | ||||||||
\(623\) | 5.10615 | 0.204574 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.9283 | −0.557131 | ||||||||
\(626\) | −16.0754 | −0.642502 | ||||||||
\(627\) | 6.28825 | 0.251129 | ||||||||
\(628\) | −14.1436 | −0.564393 | ||||||||
\(629\) | −8.65240 | −0.344994 | ||||||||
\(630\) | 3.41496 | 0.136055 | ||||||||
\(631\) | 28.1757 | 1.12166 | 0.560828 | − | 0.827933i | \(-0.310483\pi\) | ||||
0.560828 | + | 0.827933i | \(0.310483\pi\) | |||||||
\(632\) | −15.0033 | −0.596801 | ||||||||
\(633\) | 9.42870 | 0.374757 | ||||||||
\(634\) | 15.3743 | 0.610592 | ||||||||
\(635\) | 13.3089 | 0.528148 | ||||||||
\(636\) | −2.46409 | −0.0977076 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −11.8226 | −0.468063 | ||||||||
\(639\) | −2.66429 | −0.105398 | ||||||||
\(640\) | 3.41496 | 0.134988 | ||||||||
\(641\) | 48.0176 | 1.89658 | 0.948291 | − | 0.317404i | \(-0.102811\pi\) | ||||
0.948291 | + | 0.317404i | \(0.102811\pi\) | |||||||
\(642\) | −15.0210 | −0.592830 | ||||||||
\(643\) | 8.71604 | 0.343727 | 0.171864 | − | 0.985121i | \(-0.445021\pi\) | ||||
0.171864 | + | 0.985121i | \(0.445021\pi\) | |||||||
\(644\) | 3.28422 | 0.129417 | ||||||||
\(645\) | 17.4575 | 0.687386 | ||||||||
\(646\) | 3.48972 | 0.137301 | ||||||||
\(647\) | 27.8665 | 1.09555 | 0.547773 | − | 0.836627i | \(-0.315476\pi\) | ||||
0.547773 | + | 0.836627i | \(0.315476\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 43.1032 | 1.69195 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.10698 | −0.121772 | ||||||||
\(652\) | 15.6565 | 0.613158 | ||||||||
\(653\) | −12.1077 | −0.473810 | −0.236905 | − | 0.971533i | \(-0.576133\pi\) | ||||
−0.236905 | + | 0.971533i | \(0.576133\pi\) | |||||||
\(654\) | 11.7533 | 0.459592 | ||||||||
\(655\) | −60.3559 | −2.35830 | ||||||||
\(656\) | −4.58189 | −0.178893 | ||||||||
\(657\) | 0.368396 | 0.0143725 | ||||||||
\(658\) | −10.5966 | −0.413098 | ||||||||
\(659\) | −23.4234 | −0.912448 | −0.456224 | − | 0.889865i | \(-0.650798\pi\) | ||||
−0.456224 | + | 0.889865i | \(0.650798\pi\) | |||||||
\(660\) | 11.0883 | 0.431611 | ||||||||
\(661\) | 5.85897 | 0.227888 | 0.113944 | − | 0.993487i | \(-0.463652\pi\) | ||||
0.113944 | + | 0.993487i | \(0.463652\pi\) | |||||||
\(662\) | −8.21249 | −0.319187 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.43401 | −0.0556503 | ||||||||
\(665\) | 6.61356 | 0.256463 | ||||||||
\(666\) | −4.80172 | −0.186063 | ||||||||
\(667\) | −11.9582 | −0.463025 | ||||||||
\(668\) | 19.6904 | 0.761845 | ||||||||
\(669\) | −15.9921 | −0.618292 | ||||||||
\(670\) | −42.3769 | −1.63716 | ||||||||
\(671\) | −5.73638 | −0.221451 | ||||||||
\(672\) | 1.00000 | 0.0385758 | ||||||||
\(673\) | −12.6299 | −0.486845 | −0.243423 | − | 0.969920i | \(-0.578270\pi\) | ||||
−0.243423 | + | 0.969920i | \(0.578270\pi\) | |||||||
\(674\) | −18.4567 | −0.710927 | ||||||||
\(675\) | 6.66194 | 0.256418 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.8183 | 0.569515 | 0.284757 | − | 0.958600i | \(-0.408087\pi\) | ||||
0.284757 | + | 0.958600i | \(0.408087\pi\) | |||||||
\(678\) | 3.69957 | 0.142081 | ||||||||
\(679\) | −11.9553 | −0.458801 | ||||||||
\(680\) | 6.15354 | 0.235978 | ||||||||
\(681\) | 4.11815 | 0.157808 | ||||||||
\(682\) | −10.0883 | −0.386301 | ||||||||
\(683\) | −26.9967 | −1.03300 | −0.516499 | − | 0.856288i | \(-0.672765\pi\) | ||||
−0.516499 | + | 0.856288i | \(0.672765\pi\) | |||||||
\(684\) | 1.93665 | 0.0740495 | ||||||||
\(685\) | −50.9496 | −1.94668 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 0.403067 | 0.0153780 | ||||||||
\(688\) | 5.11205 | 0.194895 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 11.2155 | 0.426966 | ||||||||
\(691\) | −14.4624 | −0.550174 | −0.275087 | − | 0.961419i | \(-0.588707\pi\) | ||||
−0.275087 | + | 0.961419i | \(0.588707\pi\) | |||||||
\(692\) | 16.3915 | 0.623112 | ||||||||
\(693\) | 3.24698 | 0.123343 | ||||||||
\(694\) | 31.3648 | 1.19059 | ||||||||
\(695\) | −11.1844 | −0.424250 | ||||||||
\(696\) | −3.64112 | −0.138016 | ||||||||
\(697\) | −8.25628 | −0.312729 | ||||||||
\(698\) | −6.96959 | −0.263803 | ||||||||
\(699\) | −18.7561 | −0.709420 | ||||||||
\(700\) | 6.66194 | 0.251798 | ||||||||
\(701\) | 31.2297 | 1.17953 | 0.589764 | − | 0.807575i | \(-0.299221\pi\) | ||||
0.589764 | + | 0.807575i | \(0.299221\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.29923 | −0.350727 | ||||||||
\(704\) | 3.24698 | 0.122375 | ||||||||
\(705\) | −36.1869 | −1.36288 | ||||||||
\(706\) | 13.0978 | 0.492943 | ||||||||
\(707\) | −18.5354 | −0.697095 | ||||||||
\(708\) | 13.2749 | 0.498900 | ||||||||
\(709\) | 23.8268 | 0.894834 | 0.447417 | − | 0.894325i | \(-0.352344\pi\) | ||||
0.447417 | + | 0.894325i | \(0.352344\pi\) | |||||||
\(710\) | −9.09845 | −0.341459 | ||||||||
\(711\) | −15.0033 | −0.562670 | ||||||||
\(712\) | 5.10615 | 0.191361 | ||||||||
\(713\) | −10.2040 | −0.382143 | ||||||||
\(714\) | 1.80194 | 0.0674358 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −17.0906 | −0.638704 | ||||||||
\(717\) | −10.3497 | −0.386516 | ||||||||
\(718\) | −8.01400 | −0.299080 | ||||||||
\(719\) | 37.7147 | 1.40652 | 0.703261 | − | 0.710931i | \(-0.251726\pi\) | ||||
0.703261 | + | 0.710931i | \(0.251726\pi\) | |||||||
\(720\) | 3.41496 | 0.127268 | ||||||||
\(721\) | 18.2577 | 0.679952 | ||||||||
\(722\) | −15.2494 | −0.567524 | ||||||||
\(723\) | −9.33396 | −0.347134 | ||||||||
\(724\) | 21.3647 | 0.794015 | ||||||||
\(725\) | −24.2569 | −0.900879 | ||||||||
\(726\) | −0.457123 | −0.0169654 | ||||||||
\(727\) | 40.5041 | 1.50222 | 0.751108 | − | 0.660180i | \(-0.229520\pi\) | ||||
0.751108 | + | 0.660180i | \(0.229520\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.25806 | 0.0465627 | ||||||||
\(731\) | 9.21160 | 0.340703 | ||||||||
\(732\) | −1.76668 | −0.0652985 | ||||||||
\(733\) | 46.1126 | 1.70321 | 0.851604 | − | 0.524185i | \(-0.175630\pi\) | ||||
0.851604 | + | 0.524185i | \(0.175630\pi\) | |||||||
\(734\) | −25.7361 | −0.949938 | ||||||||
\(735\) | 3.41496 | 0.125963 | ||||||||
\(736\) | 3.28422 | 0.121058 | ||||||||
\(737\) | −40.2924 | −1.48419 | ||||||||
\(738\) | −4.58189 | −0.168662 | ||||||||
\(739\) | −12.9995 | −0.478195 | −0.239097 | − | 0.970996i | \(-0.576852\pi\) | ||||
−0.239097 | + | 0.970996i | \(0.576852\pi\) | |||||||
\(740\) | −16.3977 | −0.602790 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.46409 | −0.0904597 | ||||||||
\(743\) | 31.1171 | 1.14158 | 0.570788 | − | 0.821098i | \(-0.306638\pi\) | ||||
0.570788 | + | 0.821098i | \(0.306638\pi\) | |||||||
\(744\) | −3.10698 | −0.113907 | ||||||||
\(745\) | 30.4777 | 1.11662 | ||||||||
\(746\) | −0.973483 | −0.0356417 | ||||||||
\(747\) | −1.43401 | −0.0524676 | ||||||||
\(748\) | 5.85086 | 0.213928 | ||||||||
\(749\) | −15.0210 | −0.548854 | ||||||||
\(750\) | 5.67545 | 0.207238 | ||||||||
\(751\) | −49.5868 | −1.80945 | −0.904725 | − | 0.425997i | \(-0.859924\pi\) | ||||
−0.904725 | + | 0.425997i | \(0.859924\pi\) | |||||||
\(752\) | −10.5966 | −0.386418 | ||||||||
\(753\) | −30.9745 | −1.12877 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.43269 | −0.0885348 | ||||||||
\(756\) | 1.00000 | 0.0363696 | ||||||||
\(757\) | −24.1697 | −0.878462 | −0.439231 | − | 0.898374i | \(-0.644749\pi\) | ||||
−0.439231 | + | 0.898374i | \(0.644749\pi\) | |||||||
\(758\) | −5.27383 | −0.191554 | ||||||||
\(759\) | 10.6638 | 0.387072 | ||||||||
\(760\) | 6.61356 | 0.239899 | ||||||||
\(761\) | 52.4508 | 1.90134 | 0.950670 | − | 0.310204i | \(-0.100397\pi\) | ||||
0.950670 | + | 0.310204i | \(0.100397\pi\) | |||||||
\(762\) | 3.89724 | 0.141182 | ||||||||
\(763\) | 11.7533 | 0.425500 | ||||||||
\(764\) | 16.2973 | 0.589614 | ||||||||
\(765\) | 6.15354 | 0.222482 | ||||||||
\(766\) | 11.1179 | 0.401707 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 21.4549 | 0.773685 | 0.386842 | − | 0.922146i | \(-0.373566\pi\) | ||||
0.386842 | + | 0.922146i | \(0.373566\pi\) | |||||||
\(770\) | 11.0883 | 0.399595 | ||||||||
\(771\) | −2.27305 | −0.0818618 | ||||||||
\(772\) | 18.7221 | 0.673824 | ||||||||
\(773\) | −19.1744 | −0.689654 | −0.344827 | − | 0.938666i | \(-0.612062\pi\) | ||||
−0.344827 | + | 0.938666i | \(0.612062\pi\) | |||||||
\(774\) | 5.11205 | 0.183749 | ||||||||
\(775\) | −20.6985 | −0.743512 | ||||||||
\(776\) | −11.9553 | −0.429169 | ||||||||
\(777\) | −4.80172 | −0.172261 | ||||||||
\(778\) | −13.6798 | −0.490446 | ||||||||
\(779\) | −8.87349 | −0.317926 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.65090 | −0.309554 | ||||||||
\(782\) | 5.91797 | 0.211626 | ||||||||
\(783\) | −3.64112 | −0.130123 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −48.2999 | −1.72390 | ||||||||
\(786\) | −17.6740 | −0.630410 | ||||||||
\(787\) | 0.0274054 | 0.000976897 0 | 0.000488449 | − | 1.00000i | \(-0.499845\pi\) | ||||
0.000488449 | 1.00000i | \(0.499845\pi\) | ||||||||
\(788\) | 6.35011 | 0.226213 | ||||||||
\(789\) | −18.5834 | −0.661586 | ||||||||
\(790\) | −51.2358 | −1.82289 | ||||||||
\(791\) | 3.69957 | 0.131542 | ||||||||
\(792\) | 3.24698 | 0.115376 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 16.3683 | 0.580888 | ||||||||
\(795\) | −8.41477 | −0.298441 | ||||||||
\(796\) | 11.9820 | 0.424690 | ||||||||
\(797\) | 6.95916 | 0.246506 | 0.123253 | − | 0.992375i | \(-0.460667\pi\) | ||||
0.123253 | + | 0.992375i | \(0.460667\pi\) | |||||||
\(798\) | 1.93665 | 0.0685565 | ||||||||
\(799\) | −19.0944 | −0.675512 | ||||||||
\(800\) | 6.66194 | 0.235535 | ||||||||
\(801\) | 5.10615 | 0.180417 | ||||||||
\(802\) | −35.9089 | −1.26799 | ||||||||
\(803\) | 1.19617 | 0.0422120 | ||||||||
\(804\) | −12.4092 | −0.437639 | ||||||||
\(805\) | 11.2155 | 0.395294 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 26.7522 | 0.941722 | ||||||||
\(808\) | −18.5354 | −0.652072 | ||||||||
\(809\) | −35.2083 | −1.23786 | −0.618930 | − | 0.785446i | \(-0.712433\pi\) | ||||
−0.618930 | + | 0.785446i | \(0.712433\pi\) | |||||||
\(810\) | 3.41496 | 0.119989 | ||||||||
\(811\) | 25.6464 | 0.900567 | 0.450284 | − | 0.892886i | \(-0.351323\pi\) | ||||
0.450284 | + | 0.892886i | \(0.351323\pi\) | |||||||
\(812\) | −3.64112 | −0.127778 | ||||||||
\(813\) | 5.33182 | 0.186995 | ||||||||
\(814\) | −15.5911 | −0.546467 | ||||||||
\(815\) | 53.4665 | 1.87285 | ||||||||
\(816\) | 1.80194 | 0.0630804 | ||||||||
\(817\) | 9.90024 | 0.346366 | ||||||||
\(818\) | 12.4416 | 0.435010 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −15.6470 | −0.546415 | ||||||||
\(821\) | 31.8661 | 1.11214 | 0.556068 | − | 0.831137i | \(-0.312309\pi\) | ||||
0.556068 | + | 0.831137i | \(0.312309\pi\) | |||||||
\(822\) | −14.9195 | −0.520379 | ||||||||
\(823\) | −48.6456 | −1.69568 | −0.847839 | − | 0.530254i | \(-0.822097\pi\) | ||||
−0.847839 | + | 0.530254i | \(0.822097\pi\) | |||||||
\(824\) | 18.2577 | 0.636037 | ||||||||
\(825\) | 21.6312 | 0.753101 | ||||||||
\(826\) | 13.2749 | 0.461891 | ||||||||
\(827\) | −3.18286 | −0.110679 | −0.0553394 | − | 0.998468i | \(-0.517624\pi\) | ||||
−0.0553394 | + | 0.998468i | \(0.517624\pi\) | |||||||
\(828\) | 3.28422 | 0.114135 | ||||||||
\(829\) | −0.573876 | −0.0199315 | −0.00996576 | − | 0.999950i | \(-0.503172\pi\) | ||||
−0.00996576 | + | 0.999950i | \(0.503172\pi\) | |||||||
\(830\) | −4.89708 | −0.169980 | ||||||||
\(831\) | 25.0045 | 0.867398 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.80194 | 0.0624334 | ||||||||
\(834\) | −3.27513 | −0.113409 | ||||||||
\(835\) | 67.2419 | 2.32700 | ||||||||
\(836\) | 6.28825 | 0.217484 | ||||||||
\(837\) | −3.10698 | −0.107393 | ||||||||
\(838\) | 9.73591 | 0.336321 | ||||||||
\(839\) | −30.7253 | −1.06076 | −0.530378 | − | 0.847762i | \(-0.677950\pi\) | ||||
−0.530378 | + | 0.847762i | \(0.677950\pi\) | |||||||
\(840\) | 3.41496 | 0.117827 | ||||||||
\(841\) | −15.7423 | −0.542836 | ||||||||
\(842\) | 24.4352 | 0.842092 | ||||||||
\(843\) | 13.8066 | 0.475525 | ||||||||
\(844\) | 9.42870 | 0.324549 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −10.5966 | −0.364319 | ||||||||
\(847\) | −0.457123 | −0.0157069 | ||||||||
\(848\) | −2.46409 | −0.0846173 | ||||||||
\(849\) | −22.0224 | −0.755806 | ||||||||
\(850\) | 12.0044 | 0.411747 | ||||||||
\(851\) | −15.7699 | −0.540586 | ||||||||
\(852\) | −2.66429 | −0.0912772 | ||||||||
\(853\) | −23.5695 | −0.807005 | −0.403502 | − | 0.914979i | \(-0.632207\pi\) | ||||
−0.403502 | + | 0.914979i | \(0.632207\pi\) | |||||||
\(854\) | −1.76668 | −0.0604546 | ||||||||
\(855\) | 6.61356 | 0.226179 | ||||||||
\(856\) | −15.0210 | −0.513406 | ||||||||
\(857\) | −18.7309 | −0.639834 | −0.319917 | − | 0.947446i | \(-0.603655\pi\) | ||||
−0.319917 | + | 0.947446i | \(0.603655\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35.0464 | −1.19577 | −0.597884 | − | 0.801582i | \(-0.703992\pi\) | ||||
−0.597884 | + | 0.801582i | \(0.703992\pi\) | |||||||
\(860\) | 17.4575 | 0.595294 | ||||||||
\(861\) | −4.58189 | −0.156150 | ||||||||
\(862\) | 38.2356 | 1.30231 | ||||||||
\(863\) | 35.2615 | 1.20032 | 0.600158 | − | 0.799881i | \(-0.295104\pi\) | ||||
0.600158 | + | 0.799881i | \(0.295104\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 55.9764 | 1.90325 | ||||||||
\(866\) | 31.9423 | 1.08544 | ||||||||
\(867\) | −13.7530 | −0.467077 | ||||||||
\(868\) | −3.10698 | −0.105458 | ||||||||
\(869\) | −48.7156 | −1.65256 | ||||||||
\(870\) | −12.4343 | −0.421561 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 11.7533 | 0.398019 | ||||||||
\(873\) | −11.9553 | −0.404624 | ||||||||
\(874\) | 6.36038 | 0.215143 | ||||||||
\(875\) | 5.67545 | 0.191865 | ||||||||
\(876\) | 0.368396 | 0.0124469 | ||||||||
\(877\) | 31.7171 | 1.07101 | 0.535506 | − | 0.844532i | \(-0.320121\pi\) | ||||
0.535506 | + | 0.844532i | \(0.320121\pi\) | |||||||
\(878\) | 20.6203 | 0.695900 | ||||||||
\(879\) | −2.17514 | −0.0733656 | ||||||||
\(880\) | 11.0883 | 0.373786 | ||||||||
\(881\) | −16.3131 | −0.549602 | −0.274801 | − | 0.961501i | \(-0.588612\pi\) | ||||
−0.274801 | + | 0.961501i | \(0.588612\pi\) | |||||||
\(882\) | 1.00000 | 0.0336718 | ||||||||
\(883\) | −20.4148 | −0.687014 | −0.343507 | − | 0.939150i | \(-0.611615\pi\) | ||||
−0.343507 | + | 0.939150i | \(0.611615\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 45.3331 | 1.52386 | ||||||||
\(886\) | −0.760370 | −0.0255451 | ||||||||
\(887\) | −8.78093 | −0.294835 | −0.147417 | − | 0.989074i | \(-0.547096\pi\) | ||||
−0.147417 | + | 0.989074i | \(0.547096\pi\) | |||||||
\(888\) | −4.80172 | −0.161135 | ||||||||
\(889\) | 3.89724 | 0.130709 | ||||||||
\(890\) | 17.4373 | 0.584499 | ||||||||
\(891\) | 3.24698 | 0.108778 | ||||||||
\(892\) | −15.9921 | −0.535456 | ||||||||
\(893\) | −20.5219 | −0.686738 | ||||||||
\(894\) | 8.92475 | 0.298488 | ||||||||
\(895\) | −58.3635 | −1.95088 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 19.8729 | 0.663166 | ||||||||
\(899\) | 11.3129 | 0.377306 | ||||||||
\(900\) | 6.66194 | 0.222065 | ||||||||
\(901\) | −4.44014 | −0.147923 | ||||||||
\(902\) | −14.8773 | −0.495360 | ||||||||
\(903\) | 5.11205 | 0.170119 | ||||||||
\(904\) | 3.69957 | 0.123046 | ||||||||
\(905\) | 72.9597 | 2.42526 | ||||||||
\(906\) | −0.712364 | −0.0236667 | ||||||||
\(907\) | 12.4859 | 0.414588 | 0.207294 | − | 0.978279i | \(-0.433534\pi\) | ||||
0.207294 | + | 0.978279i | \(0.433534\pi\) | |||||||
\(908\) | 4.11815 | 0.136665 | ||||||||
\(909\) | −18.5354 | −0.614780 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.1753 | −0.502780 | −0.251390 | − | 0.967886i | \(-0.580888\pi\) | ||||
−0.251390 | + | 0.967886i | \(0.580888\pi\) | |||||||
\(912\) | 1.93665 | 0.0641288 | ||||||||
\(913\) | −4.65620 | −0.154098 | ||||||||
\(914\) | 39.0448 | 1.29149 | ||||||||
\(915\) | −6.03315 | −0.199450 | ||||||||
\(916\) | 0.403067 | 0.0133177 | ||||||||
\(917\) | −17.6740 | −0.583646 | ||||||||
\(918\) | 1.80194 | 0.0594728 | ||||||||
\(919\) | −0.144447 | −0.00476487 | −0.00238243 | − | 0.999997i | \(-0.500758\pi\) | ||||
−0.00238243 | + | 0.999997i | \(0.500758\pi\) | |||||||
\(920\) | 11.2155 | 0.369764 | ||||||||
\(921\) | 21.5338 | 0.709564 | ||||||||
\(922\) | −25.0785 | −0.825916 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 3.24698 | 0.106818 | ||||||||
\(925\) | −31.9888 | −1.05178 | ||||||||
\(926\) | 11.3140 | 0.371802 | ||||||||
\(927\) | 18.2577 | 0.599662 | ||||||||
\(928\) | −3.64112 | −0.119526 | ||||||||
\(929\) | 40.2284 | 1.31985 | 0.659926 | − | 0.751331i | \(-0.270588\pi\) | ||||
0.659926 | + | 0.751331i | \(0.270588\pi\) | |||||||
\(930\) | −10.6102 | −0.347922 | ||||||||
\(931\) | 1.93665 | 0.0634710 | ||||||||
\(932\) | −18.7561 | −0.614376 | ||||||||
\(933\) | −10.5043 | −0.343895 | ||||||||
\(934\) | 12.6861 | 0.415102 | ||||||||
\(935\) | 19.9804 | 0.653430 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.4246 | 0.961261 | 0.480630 | − | 0.876923i | \(-0.340408\pi\) | ||||
0.480630 | + | 0.876923i | \(0.340408\pi\) | |||||||
\(938\) | −12.4092 | −0.405175 | ||||||||
\(939\) | −16.0754 | −0.524600 | ||||||||
\(940\) | −36.1869 | −1.18029 | ||||||||
\(941\) | −23.6938 | −0.772395 | −0.386197 | − | 0.922416i | \(-0.626212\pi\) | ||||
−0.386197 | + | 0.922416i | \(0.626212\pi\) | |||||||
\(942\) | −14.1436 | −0.460825 | ||||||||
\(943\) | −15.0479 | −0.490028 | ||||||||
\(944\) | 13.2749 | 0.432060 | ||||||||
\(945\) | 3.41496 | 0.111089 | ||||||||
\(946\) | 16.5987 | 0.539671 | ||||||||
\(947\) | 16.5847 | 0.538932 | 0.269466 | − | 0.963010i | \(-0.413153\pi\) | ||||
0.269466 | + | 0.963010i | \(0.413153\pi\) | |||||||
\(948\) | −15.0033 | −0.487286 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 12.9018 | 0.418590 | ||||||||
\(951\) | 15.3743 | 0.498546 | ||||||||
\(952\) | 1.80194 | 0.0584011 | ||||||||
\(953\) | 17.5290 | 0.567820 | 0.283910 | − | 0.958851i | \(-0.408368\pi\) | ||||
0.283910 | + | 0.958851i | \(0.408368\pi\) | |||||||
\(954\) | −2.46409 | −0.0797779 | ||||||||
\(955\) | 55.6545 | 1.80094 | ||||||||
\(956\) | −10.3497 | −0.334733 | ||||||||
\(957\) | −11.8226 | −0.382172 | ||||||||
\(958\) | 5.31845 | 0.171831 | ||||||||
\(959\) | −14.9195 | −0.481777 | ||||||||
\(960\) | 3.41496 | 0.110217 | ||||||||
\(961\) | −21.3467 | −0.688603 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.0210 | −0.484044 | ||||||||
\(964\) | −9.33396 | −0.300627 | ||||||||
\(965\) | 63.9353 | 2.05815 | ||||||||
\(966\) | 3.28422 | 0.105668 | ||||||||
\(967\) | −44.7198 | −1.43809 | −0.719045 | − | 0.694963i | \(-0.755421\pi\) | ||||
−0.719045 | + | 0.694963i | \(0.755421\pi\) | |||||||
\(968\) | −0.457123 | −0.0146925 | ||||||||
\(969\) | 3.48972 | 0.112106 | ||||||||
\(970\) | −40.8267 | −1.31087 | ||||||||
\(971\) | −31.6941 | −1.01711 | −0.508555 | − | 0.861029i | \(-0.669820\pi\) | ||||
−0.508555 | + | 0.861029i | \(0.669820\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −3.27513 | −0.104996 | ||||||||
\(974\) | −31.2192 | −1.00033 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.76668 | −0.0565501 | ||||||||
\(977\) | 43.1638 | 1.38093 | 0.690467 | − | 0.723364i | \(-0.257405\pi\) | ||||
0.690467 | + | 0.723364i | \(0.257405\pi\) | |||||||
\(978\) | 15.6565 | 0.500641 | ||||||||
\(979\) | 16.5796 | 0.529885 | ||||||||
\(980\) | 3.41496 | 0.109087 | ||||||||
\(981\) | 11.7533 | 0.375255 | ||||||||
\(982\) | 24.9801 | 0.797147 | ||||||||
\(983\) | −58.3576 | −1.86132 | −0.930659 | − | 0.365887i | \(-0.880766\pi\) | ||||
−0.930659 | + | 0.365887i | \(0.880766\pi\) | |||||||
\(984\) | −4.58189 | −0.146065 | ||||||||
\(985\) | 21.6853 | 0.690953 | ||||||||
\(986\) | −6.56107 | −0.208947 | ||||||||
\(987\) | −10.5966 | −0.337293 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.7891 | 0.533863 | ||||||||
\(990\) | 11.0883 | 0.352409 | ||||||||
\(991\) | −38.6339 | −1.22725 | −0.613623 | − | 0.789599i | \(-0.710288\pi\) | ||||
−0.613623 | + | 0.789599i | \(0.710288\pi\) | |||||||
\(992\) | −3.10698 | −0.0986467 | ||||||||
\(993\) | −8.21249 | −0.260615 | ||||||||
\(994\) | −2.66429 | −0.0845062 | ||||||||
\(995\) | 40.9180 | 1.29719 | ||||||||
\(996\) | −1.43401 | −0.0454383 | ||||||||
\(997\) | 13.4648 | 0.426433 | 0.213217 | − | 0.977005i | \(-0.431606\pi\) | ||||
0.213217 | + | 0.977005i | \(0.431606\pi\) | |||||||
\(998\) | 8.22457 | 0.260344 | ||||||||
\(999\) | −4.80172 | −0.151920 |
(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 | 7098.2.a.ct.1.6 | yes | 6 | |
13.12 | even | 2 | 7098.2.a.cr.1.1 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7098.2.a.cr.1.1 | ✓ | 6 | 13.12 | even | 2 | ||
7098.2.a.ct.1.6 | yes | 6 | 1.1 | even | 1 | trivial |