Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6762,2,Mod(1,6762)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6762, 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("6762.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6762.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: | \(53.9948418468\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.10304.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 7x^{2} + 8x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(3.16053\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6762.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.74632 | 0.780977 | 0.390489 | − | 0.920608i | \(-0.372306\pi\) | ||||
0.390489 | + | 0.920608i | \(0.372306\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.74632 | 0.552234 | ||||||||
\(11\) | −1.85140 | −0.558217 | −0.279109 | − | 0.960260i | \(-0.590039\pi\) | ||||
−0.279109 | + | 0.960260i | \(0.590039\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 4.13756 | 1.14755 | 0.573777 | − | 0.819012i | \(-0.305478\pi\) | ||||
0.573777 | + | 0.819012i | \(0.305478\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.74632 | −0.450897 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.82843 | −1.65614 | −0.828068 | − | 0.560627i | \(-0.810560\pi\) | ||||
−0.828068 | + | 0.560627i | \(0.810560\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −1.20406 | −0.276229 | −0.138115 | − | 0.990416i | \(-0.544104\pi\) | ||||
−0.138115 | + | 0.990416i | \(0.544104\pi\) | |||||||
\(20\) | 1.74632 | 0.390489 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.85140 | −0.394719 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −1.95037 | −0.390075 | ||||||||
\(26\) | 4.13756 | 0.811443 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.51929 | −0.653516 | −0.326758 | − | 0.945108i | \(-0.605956\pi\) | ||||
−0.326758 | + | 0.945108i | \(0.605956\pi\) | |||||||
\(30\) | −1.74632 | −0.318833 | ||||||||
\(31\) | −8.90685 | −1.59972 | −0.799859 | − | 0.600188i | \(-0.795092\pi\) | ||||
−0.799859 | + | 0.600188i | \(0.795092\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.85140 | 0.322287 | ||||||||
\(34\) | −6.82843 | −1.17107 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −7.42004 | −1.21985 | −0.609924 | − | 0.792460i | \(-0.708800\pi\) | ||||
−0.609924 | + | 0.792460i | \(0.708800\pi\) | |||||||
\(38\) | −1.20406 | −0.195324 | ||||||||
\(39\) | −4.13756 | −0.662540 | ||||||||
\(40\) | 1.74632 | 0.276117 | ||||||||
\(41\) | −1.57386 | −0.245795 | −0.122898 | − | 0.992419i | \(-0.539219\pi\) | ||||
−0.122898 | + | 0.992419i | \(0.539219\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.69175 | 1.17298 | 0.586491 | − | 0.809956i | \(-0.300509\pi\) | ||||
0.586491 | + | 0.809956i | \(0.300509\pi\) | |||||||
\(44\) | −1.85140 | −0.279109 | ||||||||
\(45\) | 1.74632 | 0.260326 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −10.6857 | −1.55866 | −0.779331 | − | 0.626612i | \(-0.784441\pi\) | ||||
−0.779331 | + | 0.626612i | \(0.784441\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.95037 | −0.275825 | ||||||||
\(51\) | 6.82843 | 0.956171 | ||||||||
\(52\) | 4.13756 | 0.573777 | ||||||||
\(53\) | −8.17246 | −1.12257 | −0.561287 | − | 0.827621i | \(-0.689694\pi\) | ||||
−0.561287 | + | 0.827621i | \(0.689694\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −3.23313 | −0.435955 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.20406 | 0.159481 | ||||||||
\(58\) | −3.51929 | −0.462106 | ||||||||
\(59\) | −1.18719 | −0.154559 | −0.0772794 | − | 0.997009i | \(-0.524623\pi\) | ||||
−0.0772794 | + | 0.997009i | \(0.524623\pi\) | |||||||
\(60\) | −1.74632 | −0.225449 | ||||||||
\(61\) | −12.6746 | −1.62282 | −0.811409 | − | 0.584479i | \(-0.801299\pi\) | ||||
−0.811409 | + | 0.584479i | \(0.801299\pi\) | |||||||
\(62\) | −8.90685 | −1.13117 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 7.22550 | 0.896213 | ||||||||
\(66\) | 1.85140 | 0.227891 | ||||||||
\(67\) | 6.64213 | 0.811465 | 0.405732 | − | 0.913992i | \(-0.367016\pi\) | ||||
0.405732 | + | 0.913992i | \(0.367016\pi\) | |||||||
\(68\) | −6.82843 | −0.828068 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.46967 | 0.767808 | 0.383904 | − | 0.923373i | \(-0.374579\pi\) | ||||
0.383904 | + | 0.923373i | \(0.374579\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 0.750005 | 0.0877815 | 0.0438907 | − | 0.999036i | \(-0.486025\pi\) | ||||
0.0438907 | + | 0.999036i | \(0.486025\pi\) | |||||||
\(74\) | −7.42004 | −0.862562 | ||||||||
\(75\) | 1.95037 | 0.225210 | ||||||||
\(76\) | −1.20406 | −0.138115 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.13756 | −0.468487 | ||||||||
\(79\) | 8.76687 | 0.986350 | 0.493175 | − | 0.869930i | \(-0.335836\pi\) | ||||
0.493175 | + | 0.869930i | \(0.335836\pi\) | |||||||
\(80\) | 1.74632 | 0.195244 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.57386 | −0.173804 | ||||||||
\(83\) | −4.43718 | −0.487044 | −0.243522 | − | 0.969895i | \(-0.578303\pi\) | ||||
−0.243522 | + | 0.969895i | \(0.578303\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.9246 | −1.29340 | ||||||||
\(86\) | 7.69175 | 0.829423 | ||||||||
\(87\) | 3.51929 | 0.377308 | ||||||||
\(88\) | −1.85140 | −0.197360 | ||||||||
\(89\) | 0.766874 | 0.0812884 | 0.0406442 | − | 0.999174i | \(-0.487059\pi\) | ||||
0.0406442 | + | 0.999174i | \(0.487059\pi\) | |||||||
\(90\) | 1.74632 | 0.184078 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | 8.90685 | 0.923597 | ||||||||
\(94\) | −10.6857 | −1.10214 | ||||||||
\(95\) | −2.10267 | −0.215729 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 18.9062 | 1.91963 | 0.959817 | − | 0.280626i | \(-0.0905419\pi\) | ||||
0.959817 | + | 0.280626i | \(0.0905419\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.85140 | −0.186072 | ||||||||
\(100\) | −1.95037 | −0.195037 | ||||||||
\(101\) | −9.10014 | −0.905498 | −0.452749 | − | 0.891638i | \(-0.649557\pi\) | ||||
−0.452749 | + | 0.891638i | \(0.649557\pi\) | |||||||
\(102\) | 6.82843 | 0.676115 | ||||||||
\(103\) | −13.0119 | −1.28210 | −0.641052 | − | 0.767498i | \(-0.721502\pi\) | ||||
−0.641052 | + | 0.767498i | \(0.721502\pi\) | |||||||
\(104\) | 4.13756 | 0.405721 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.17246 | −0.793779 | ||||||||
\(107\) | −4.00000 | −0.386695 | −0.193347 | − | 0.981130i | \(-0.561934\pi\) | ||||
−0.193347 | + | 0.981130i | \(0.561934\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −0.603815 | −0.0578350 | −0.0289175 | − | 0.999582i | \(-0.509206\pi\) | ||||
−0.0289175 | + | 0.999582i | \(0.509206\pi\) | |||||||
\(110\) | −3.23313 | −0.308267 | ||||||||
\(111\) | 7.42004 | 0.704279 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.431356 | 0.0405786 | 0.0202893 | − | 0.999794i | \(-0.493541\pi\) | ||||
0.0202893 | + | 0.999794i | \(0.493541\pi\) | |||||||
\(114\) | 1.20406 | 0.112770 | ||||||||
\(115\) | 1.74632 | 0.162845 | ||||||||
\(116\) | −3.51929 | −0.326758 | ||||||||
\(117\) | 4.13756 | 0.382518 | ||||||||
\(118\) | −1.18719 | −0.109290 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.74632 | −0.159416 | ||||||||
\(121\) | −7.57233 | −0.688394 | ||||||||
\(122\) | −12.6746 | −1.14751 | ||||||||
\(123\) | 1.57386 | 0.141910 | ||||||||
\(124\) | −8.90685 | −0.799859 | ||||||||
\(125\) | −12.1376 | −1.08562 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.3594 | 1.62913 | 0.814565 | − | 0.580072i | \(-0.196975\pi\) | ||||
0.814565 | + | 0.580072i | \(0.196975\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −7.69175 | −0.677221 | ||||||||
\(130\) | 7.22550 | 0.633718 | ||||||||
\(131\) | 5.40900 | 0.472586 | 0.236293 | − | 0.971682i | \(-0.424067\pi\) | ||||
0.236293 | + | 0.971682i | \(0.424067\pi\) | |||||||
\(132\) | 1.85140 | 0.161143 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 6.64213 | 0.573792 | ||||||||
\(135\) | −1.74632 | −0.150299 | ||||||||
\(136\) | −6.82843 | −0.585533 | ||||||||
\(137\) | −10.3100 | −0.880845 | −0.440422 | − | 0.897791i | \(-0.645171\pi\) | ||||
−0.440422 | + | 0.897791i | \(0.645171\pi\) | |||||||
\(138\) | −1.00000 | −0.0851257 | ||||||||
\(139\) | 6.61943 | 0.561453 | 0.280726 | − | 0.959788i | \(-0.409425\pi\) | ||||
0.280726 | + | 0.959788i | \(0.409425\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.6857 | 0.899894 | ||||||||
\(142\) | 6.46967 | 0.542922 | ||||||||
\(143\) | −7.66027 | −0.640584 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −6.14580 | −0.510381 | ||||||||
\(146\) | 0.750005 | 0.0620709 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.42004 | −0.609924 | ||||||||
\(149\) | 19.8072 | 1.62267 | 0.811336 | − | 0.584580i | \(-0.198741\pi\) | ||||
0.811336 | + | 0.584580i | \(0.198741\pi\) | |||||||
\(150\) | 1.95037 | 0.159247 | ||||||||
\(151\) | −14.8330 | −1.20709 | −0.603546 | − | 0.797328i | \(-0.706246\pi\) | ||||
−0.603546 | + | 0.797328i | \(0.706246\pi\) | |||||||
\(152\) | −1.20406 | −0.0976619 | ||||||||
\(153\) | −6.82843 | −0.552046 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.5542 | −1.24934 | ||||||||
\(156\) | −4.13756 | −0.331270 | ||||||||
\(157\) | 0.242641 | 0.0193648 | 0.00968242 | − | 0.999953i | \(-0.496918\pi\) | ||||
0.00968242 | + | 0.999953i | \(0.496918\pi\) | |||||||
\(158\) | 8.76687 | 0.697455 | ||||||||
\(159\) | 8.17246 | 0.648118 | ||||||||
\(160\) | 1.74632 | 0.138059 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 18.0018 | 1.41001 | 0.705004 | − | 0.709204i | \(-0.250945\pi\) | ||||
0.705004 | + | 0.709204i | \(0.250945\pi\) | |||||||
\(164\) | −1.57386 | −0.122898 | ||||||||
\(165\) | 3.23313 | 0.251699 | ||||||||
\(166\) | −4.43718 | −0.344392 | ||||||||
\(167\) | −5.88388 | −0.455308 | −0.227654 | − | 0.973742i | \(-0.573106\pi\) | ||||
−0.227654 | + | 0.973742i | \(0.573106\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.11942 | 0.316878 | ||||||||
\(170\) | −11.9246 | −0.914575 | ||||||||
\(171\) | −1.20406 | −0.0920765 | ||||||||
\(172\) | 7.69175 | 0.586491 | ||||||||
\(173\) | −9.74390 | −0.740815 | −0.370408 | − | 0.928869i | \(-0.620782\pi\) | ||||
−0.370408 | + | 0.928869i | \(0.620782\pi\) | |||||||
\(174\) | 3.51929 | 0.266797 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.85140 | −0.139554 | ||||||||
\(177\) | 1.18719 | 0.0892345 | ||||||||
\(178\) | 0.766874 | 0.0574796 | ||||||||
\(179\) | 1.98896 | 0.148662 | 0.0743309 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743309 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(180\) | 1.74632 | 0.130163 | ||||||||
\(181\) | −25.2674 | −1.87811 | −0.939055 | − | 0.343767i | \(-0.888297\pi\) | ||||
−0.939055 | + | 0.343767i | \(0.888297\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.6746 | 0.936934 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | −12.9577 | −0.952673 | ||||||||
\(186\) | 8.90685 | 0.653082 | ||||||||
\(187\) | 12.6421 | 0.924484 | ||||||||
\(188\) | −10.6857 | −0.779331 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.10267 | −0.152543 | ||||||||
\(191\) | −3.97792 | −0.287832 | −0.143916 | − | 0.989590i | \(-0.545970\pi\) | ||||
−0.143916 | + | 0.989590i | \(0.545970\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 12.5539 | 0.903651 | 0.451825 | − | 0.892106i | \(-0.350773\pi\) | ||||
0.451825 | + | 0.892106i | \(0.350773\pi\) | |||||||
\(194\) | 18.9062 | 1.35739 | ||||||||
\(195\) | −7.22550 | −0.517429 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.8018 | −1.05458 | −0.527291 | − | 0.849685i | \(-0.676792\pi\) | ||||
−0.527291 | + | 0.849685i | \(0.676792\pi\) | |||||||
\(198\) | −1.85140 | −0.131573 | ||||||||
\(199\) | 13.9513 | 0.988979 | 0.494489 | − | 0.869184i | \(-0.335355\pi\) | ||||
0.494489 | + | 0.869184i | \(0.335355\pi\) | |||||||
\(200\) | −1.95037 | −0.137912 | ||||||||
\(201\) | −6.64213 | −0.468499 | ||||||||
\(202\) | −9.10014 | −0.640283 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 6.82843 | 0.478086 | ||||||||
\(205\) | −2.74846 | −0.191961 | ||||||||
\(206\) | −13.0119 | −0.906584 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 4.13756 | 0.286888 | ||||||||
\(209\) | 2.22919 | 0.154196 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.71356 | 0.599866 | 0.299933 | − | 0.953960i | \(-0.403036\pi\) | ||||
0.299933 | + | 0.953960i | \(0.403036\pi\) | |||||||
\(212\) | −8.17246 | −0.561287 | ||||||||
\(213\) | −6.46967 | −0.443294 | ||||||||
\(214\) | −4.00000 | −0.273434 | ||||||||
\(215\) | 13.4322 | 0.916071 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.603815 | −0.0408955 | ||||||||
\(219\) | −0.750005 | −0.0506806 | ||||||||
\(220\) | −3.23313 | −0.217977 | ||||||||
\(221\) | −28.2530 | −1.90051 | ||||||||
\(222\) | 7.42004 | 0.498001 | ||||||||
\(223\) | −24.0481 | −1.61038 | −0.805190 | − | 0.593017i | \(-0.797937\pi\) | ||||
−0.805190 | + | 0.593017i | \(0.797937\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.95037 | −0.130025 | ||||||||
\(226\) | 0.431356 | 0.0286934 | ||||||||
\(227\) | 2.51319 | 0.166806 | 0.0834032 | − | 0.996516i | \(-0.473421\pi\) | ||||
0.0834032 | + | 0.996516i | \(0.473421\pi\) | |||||||
\(228\) | 1.20406 | 0.0797406 | ||||||||
\(229\) | 14.4029 | 0.951770 | 0.475885 | − | 0.879507i | \(-0.342128\pi\) | ||||
0.475885 | + | 0.879507i | \(0.342128\pi\) | |||||||
\(230\) | 1.74632 | 0.115149 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.51929 | −0.231053 | ||||||||
\(233\) | 22.0273 | 1.44305 | 0.721527 | − | 0.692386i | \(-0.243440\pi\) | ||||
0.721527 | + | 0.692386i | \(0.243440\pi\) | |||||||
\(234\) | 4.13756 | 0.270481 | ||||||||
\(235\) | −18.6605 | −1.21728 | ||||||||
\(236\) | −1.18719 | −0.0772794 | ||||||||
\(237\) | −8.76687 | −0.569470 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.55760 | −0.618230 | −0.309115 | − | 0.951025i | \(-0.600033\pi\) | ||||
−0.309115 | + | 0.951025i | \(0.600033\pi\) | |||||||
\(240\) | −1.74632 | −0.112724 | ||||||||
\(241\) | −5.08336 | −0.327448 | −0.163724 | − | 0.986506i | \(-0.552351\pi\) | ||||
−0.163724 | + | 0.986506i | \(0.552351\pi\) | |||||||
\(242\) | −7.57233 | −0.486768 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −12.6746 | −0.811409 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.57386 | 0.100346 | ||||||||
\(247\) | −4.98186 | −0.316988 | ||||||||
\(248\) | −8.90685 | −0.565585 | ||||||||
\(249\) | 4.43718 | 0.281195 | ||||||||
\(250\) | −12.1376 | −0.767647 | ||||||||
\(251\) | 27.0683 | 1.70853 | 0.854267 | − | 0.519835i | \(-0.174006\pi\) | ||||
0.854267 | + | 0.519835i | \(0.174006\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.85140 | −0.116396 | ||||||||
\(254\) | 18.3594 | 1.15197 | ||||||||
\(255\) | 11.9246 | 0.746748 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −11.2773 | −0.703456 | −0.351728 | − | 0.936102i | \(-0.614406\pi\) | ||||
−0.351728 | + | 0.936102i | \(0.614406\pi\) | |||||||
\(258\) | −7.69175 | −0.478868 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 7.22550 | 0.448106 | ||||||||
\(261\) | −3.51929 | −0.217839 | ||||||||
\(262\) | 5.40900 | 0.334169 | ||||||||
\(263\) | 31.3980 | 1.93608 | 0.968040 | − | 0.250794i | \(-0.0806917\pi\) | ||||
0.968040 | + | 0.250794i | \(0.0806917\pi\) | |||||||
\(264\) | 1.85140 | 0.113946 | ||||||||
\(265\) | −14.2717 | −0.876704 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.766874 | −0.0469319 | ||||||||
\(268\) | 6.64213 | 0.405732 | ||||||||
\(269\) | −5.32195 | −0.324485 | −0.162242 | − | 0.986751i | \(-0.551873\pi\) | ||||
−0.162242 | + | 0.986751i | \(0.551873\pi\) | |||||||
\(270\) | −1.74632 | −0.106278 | ||||||||
\(271\) | −26.5416 | −1.61229 | −0.806144 | − | 0.591719i | \(-0.798450\pi\) | ||||
−0.806144 | + | 0.591719i | \(0.798450\pi\) | |||||||
\(272\) | −6.82843 | −0.414034 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.3100 | −0.622851 | ||||||||
\(275\) | 3.61092 | 0.217746 | ||||||||
\(276\) | −1.00000 | −0.0601929 | ||||||||
\(277\) | −14.4476 | −0.868071 | −0.434036 | − | 0.900896i | \(-0.642911\pi\) | ||||
−0.434036 | + | 0.900896i | \(0.642911\pi\) | |||||||
\(278\) | 6.61943 | 0.397007 | ||||||||
\(279\) | −8.90685 | −0.533239 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.2016 | −1.14547 | −0.572737 | − | 0.819739i | \(-0.694118\pi\) | ||||
−0.572737 | + | 0.819739i | \(0.694118\pi\) | |||||||
\(282\) | 10.6857 | 0.636321 | ||||||||
\(283\) | 18.7739 | 1.11599 | 0.557995 | − | 0.829844i | \(-0.311571\pi\) | ||||
0.557995 | + | 0.829844i | \(0.311571\pi\) | |||||||
\(284\) | 6.46967 | 0.383904 | ||||||||
\(285\) | 2.10267 | 0.124551 | ||||||||
\(286\) | −7.66027 | −0.452961 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 29.6274 | 1.74279 | ||||||||
\(290\) | −6.14580 | −0.360894 | ||||||||
\(291\) | −18.9062 | −1.10830 | ||||||||
\(292\) | 0.750005 | 0.0438907 | ||||||||
\(293\) | 13.6296 | 0.796247 | 0.398124 | − | 0.917332i | \(-0.369662\pi\) | ||||
0.398124 | + | 0.917332i | \(0.369662\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.07321 | −0.120707 | ||||||||
\(296\) | −7.42004 | −0.431281 | ||||||||
\(297\) | 1.85140 | 0.107429 | ||||||||
\(298\) | 19.8072 | 1.14740 | ||||||||
\(299\) | 4.13756 | 0.239281 | ||||||||
\(300\) | 1.95037 | 0.112605 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −14.8330 | −0.853543 | ||||||||
\(303\) | 9.10014 | 0.522789 | ||||||||
\(304\) | −1.20406 | −0.0690574 | ||||||||
\(305\) | −22.1339 | −1.26738 | ||||||||
\(306\) | −6.82843 | −0.390355 | ||||||||
\(307\) | −22.9933 | −1.31229 | −0.656147 | − | 0.754633i | \(-0.727815\pi\) | ||||
−0.656147 | + | 0.754633i | \(0.727815\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.0119 | 0.740223 | ||||||||
\(310\) | −15.5542 | −0.883419 | ||||||||
\(311\) | 29.5983 | 1.67837 | 0.839184 | − | 0.543848i | \(-0.183033\pi\) | ||||
0.839184 | + | 0.543848i | \(0.183033\pi\) | |||||||
\(312\) | −4.13756 | −0.234243 | ||||||||
\(313\) | 17.7604 | 1.00388 | 0.501938 | − | 0.864904i | \(-0.332620\pi\) | ||||
0.501938 | + | 0.864904i | \(0.332620\pi\) | |||||||
\(314\) | 0.242641 | 0.0136930 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.76687 | 0.493175 | ||||||||
\(317\) | −21.6952 | −1.21852 | −0.609261 | − | 0.792970i | \(-0.708534\pi\) | ||||
−0.609261 | + | 0.792970i | \(0.708534\pi\) | |||||||
\(318\) | 8.17246 | 0.458289 | ||||||||
\(319\) | 6.51560 | 0.364804 | ||||||||
\(320\) | 1.74632 | 0.0976221 | ||||||||
\(321\) | 4.00000 | 0.223258 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.22181 | 0.457474 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −8.06979 | −0.447632 | ||||||||
\(326\) | 18.0018 | 0.997026 | ||||||||
\(327\) | 0.603815 | 0.0333911 | ||||||||
\(328\) | −1.57386 | −0.0869018 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 3.23313 | 0.177978 | ||||||||
\(331\) | 10.0018 | 0.549747 | 0.274874 | − | 0.961480i | \(-0.411364\pi\) | ||||
0.274874 | + | 0.961480i | \(0.411364\pi\) | |||||||
\(332\) | −4.43718 | −0.243522 | ||||||||
\(333\) | −7.42004 | −0.406616 | ||||||||
\(334\) | −5.88388 | −0.321952 | ||||||||
\(335\) | 11.5993 | 0.633735 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.79810 | −0.370316 | −0.185158 | − | 0.982709i | \(-0.559280\pi\) | ||||
−0.185158 | + | 0.982709i | \(0.559280\pi\) | |||||||
\(338\) | 4.11942 | 0.224067 | ||||||||
\(339\) | −0.431356 | −0.0234280 | ||||||||
\(340\) | −11.9246 | −0.646702 | ||||||||
\(341\) | 16.4901 | 0.892989 | ||||||||
\(342\) | −1.20406 | −0.0651079 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 7.69175 | 0.414711 | ||||||||
\(345\) | −1.74632 | −0.0940186 | ||||||||
\(346\) | −9.74390 | −0.523836 | ||||||||
\(347\) | −22.0202 | −1.18211 | −0.591053 | − | 0.806633i | \(-0.701288\pi\) | ||||
−0.591053 | + | 0.806633i | \(0.701288\pi\) | |||||||
\(348\) | 3.51929 | 0.188654 | ||||||||
\(349\) | −31.6005 | −1.69154 | −0.845768 | − | 0.533551i | \(-0.820857\pi\) | ||||
−0.845768 | + | 0.533551i | \(0.820857\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.13756 | −0.220847 | ||||||||
\(352\) | −1.85140 | −0.0986798 | ||||||||
\(353\) | 11.7325 | 0.624457 | 0.312228 | − | 0.950007i | \(-0.398925\pi\) | ||||
0.312228 | + | 0.950007i | \(0.398925\pi\) | |||||||
\(354\) | 1.18719 | 0.0630983 | ||||||||
\(355\) | 11.2981 | 0.599641 | ||||||||
\(356\) | 0.766874 | 0.0406442 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.98896 | 0.105120 | ||||||||
\(359\) | 5.13021 | 0.270762 | 0.135381 | − | 0.990794i | \(-0.456774\pi\) | ||||
0.135381 | + | 0.990794i | \(0.456774\pi\) | |||||||
\(360\) | 1.74632 | 0.0920390 | ||||||||
\(361\) | −17.5502 | −0.923697 | ||||||||
\(362\) | −25.2674 | −1.32802 | ||||||||
\(363\) | 7.57233 | 0.397444 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.30975 | 0.0685553 | ||||||||
\(366\) | 12.6746 | 0.662512 | ||||||||
\(367\) | −3.30176 | −0.172350 | −0.0861752 | − | 0.996280i | \(-0.527464\pi\) | ||||
−0.0861752 | + | 0.996280i | \(0.527464\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | −1.57386 | −0.0819318 | ||||||||
\(370\) | −12.9577 | −0.673641 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 8.90685 | 0.461799 | ||||||||
\(373\) | −13.4056 | −0.694115 | −0.347057 | − | 0.937844i | \(-0.612819\pi\) | ||||
−0.347057 | + | 0.937844i | \(0.612819\pi\) | |||||||
\(374\) | 12.6421 | 0.653709 | ||||||||
\(375\) | 12.1376 | 0.626781 | ||||||||
\(376\) | −10.6857 | −0.551070 | ||||||||
\(377\) | −14.5613 | −0.749945 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.8290 | −1.48085 | −0.740424 | − | 0.672140i | \(-0.765375\pi\) | ||||
−0.740424 | + | 0.672140i | \(0.765375\pi\) | |||||||
\(380\) | −2.10267 | −0.107864 | ||||||||
\(381\) | −18.3594 | −0.940579 | ||||||||
\(382\) | −3.97792 | −0.203528 | ||||||||
\(383\) | 3.33183 | 0.170249 | 0.0851243 | − | 0.996370i | \(-0.472871\pi\) | ||||
0.0851243 | + | 0.996370i | \(0.472871\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.5539 | 0.638977 | ||||||||
\(387\) | 7.69175 | 0.390994 | ||||||||
\(388\) | 18.9062 | 0.959817 | ||||||||
\(389\) | −8.67158 | −0.439667 | −0.219833 | − | 0.975537i | \(-0.570551\pi\) | ||||
−0.219833 | + | 0.975537i | \(0.570551\pi\) | |||||||
\(390\) | −7.22550 | −0.365877 | ||||||||
\(391\) | −6.82843 | −0.345328 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.40900 | −0.272848 | ||||||||
\(394\) | −14.8018 | −0.745702 | ||||||||
\(395\) | 15.3097 | 0.770317 | ||||||||
\(396\) | −1.85140 | −0.0930362 | ||||||||
\(397\) | −26.2677 | −1.31834 | −0.659170 | − | 0.751994i | \(-0.729092\pi\) | ||||
−0.659170 | + | 0.751994i | \(0.729092\pi\) | |||||||
\(398\) | 13.9513 | 0.699313 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.95037 | −0.0975187 | ||||||||
\(401\) | 8.35229 | 0.417094 | 0.208547 | − | 0.978012i | \(-0.433127\pi\) | ||||
0.208547 | + | 0.978012i | \(0.433127\pi\) | |||||||
\(402\) | −6.64213 | −0.331279 | ||||||||
\(403\) | −36.8526 | −1.83576 | ||||||||
\(404\) | −9.10014 | −0.452749 | ||||||||
\(405\) | 1.74632 | 0.0867752 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.7374 | 0.680939 | ||||||||
\(408\) | 6.82843 | 0.338058 | ||||||||
\(409\) | 27.6434 | 1.36688 | 0.683439 | − | 0.730008i | \(-0.260483\pi\) | ||||
0.683439 | + | 0.730008i | \(0.260483\pi\) | |||||||
\(410\) | −2.74846 | −0.135737 | ||||||||
\(411\) | 10.3100 | 0.508556 | ||||||||
\(412\) | −13.0119 | −0.641052 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.00000 | 0.0491473 | ||||||||
\(415\) | −7.74873 | −0.380370 | ||||||||
\(416\) | 4.13756 | 0.202861 | ||||||||
\(417\) | −6.61943 | −0.324155 | ||||||||
\(418\) | 2.22919 | 0.109033 | ||||||||
\(419\) | 23.7509 | 1.16031 | 0.580153 | − | 0.814507i | \(-0.302993\pi\) | ||||
0.580153 | + | 0.814507i | \(0.302993\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.4365 | 1.28844 | 0.644219 | − | 0.764841i | \(-0.277182\pi\) | ||||
0.644219 | + | 0.764841i | \(0.277182\pi\) | |||||||
\(422\) | 8.71356 | 0.424169 | ||||||||
\(423\) | −10.6857 | −0.519554 | ||||||||
\(424\) | −8.17246 | −0.396890 | ||||||||
\(425\) | 13.3180 | 0.646017 | ||||||||
\(426\) | −6.46967 | −0.313456 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −4.00000 | −0.193347 | ||||||||
\(429\) | 7.66027 | 0.369841 | ||||||||
\(430\) | 13.4322 | 0.647760 | ||||||||
\(431\) | −24.7099 | −1.19023 | −0.595117 | − | 0.803639i | \(-0.702894\pi\) | ||||
−0.595117 | + | 0.803639i | \(0.702894\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −18.9816 | −0.912198 | −0.456099 | − | 0.889929i | \(-0.650754\pi\) | ||||
−0.456099 | + | 0.889929i | \(0.650754\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.14580 | 0.294669 | ||||||||
\(436\) | −0.603815 | −0.0289175 | ||||||||
\(437\) | −1.20406 | −0.0575978 | ||||||||
\(438\) | −0.750005 | −0.0358366 | ||||||||
\(439\) | −33.4883 | −1.59831 | −0.799155 | − | 0.601125i | \(-0.794720\pi\) | ||||
−0.799155 | + | 0.601125i | \(0.794720\pi\) | |||||||
\(440\) | −3.23313 | −0.154133 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −28.2530 | −1.34386 | ||||||||
\(443\) | −26.0656 | −1.23841 | −0.619207 | − | 0.785228i | \(-0.712546\pi\) | ||||
−0.619207 | + | 0.785228i | \(0.712546\pi\) | |||||||
\(444\) | 7.42004 | 0.352140 | ||||||||
\(445\) | 1.33920 | 0.0634844 | ||||||||
\(446\) | −24.0481 | −1.13871 | ||||||||
\(447\) | −19.8072 | −0.936850 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.9172 | −0.987146 | −0.493573 | − | 0.869704i | \(-0.664309\pi\) | ||||
−0.493573 | + | 0.869704i | \(0.664309\pi\) | |||||||
\(450\) | −1.95037 | −0.0919415 | ||||||||
\(451\) | 2.91384 | 0.137207 | ||||||||
\(452\) | 0.431356 | 0.0202893 | ||||||||
\(453\) | 14.8330 | 0.696915 | ||||||||
\(454\) | 2.51319 | 0.117950 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.20406 | 0.0563851 | ||||||||
\(457\) | 3.63477 | 0.170027 | 0.0850137 | − | 0.996380i | \(-0.472907\pi\) | ||||
0.0850137 | + | 0.996380i | \(0.472907\pi\) | |||||||
\(458\) | 14.4029 | 0.673003 | ||||||||
\(459\) | 6.82843 | 0.318724 | ||||||||
\(460\) | 1.74632 | 0.0814225 | ||||||||
\(461\) | −10.6027 | −0.493815 | −0.246907 | − | 0.969039i | \(-0.579414\pi\) | ||||
−0.246907 | + | 0.969039i | \(0.579414\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.3355 | 1.03802 | 0.519010 | − | 0.854768i | \(-0.326301\pi\) | ||||
0.519010 | + | 0.854768i | \(0.326301\pi\) | |||||||
\(464\) | −3.51929 | −0.163379 | ||||||||
\(465\) | 15.5542 | 0.721308 | ||||||||
\(466\) | 22.0273 | 1.02039 | ||||||||
\(467\) | 29.5469 | 1.36727 | 0.683635 | − | 0.729824i | \(-0.260398\pi\) | ||||
0.683635 | + | 0.729824i | \(0.260398\pi\) | |||||||
\(468\) | 4.13756 | 0.191259 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −18.6605 | −0.860747 | ||||||||
\(471\) | −0.242641 | −0.0111803 | ||||||||
\(472\) | −1.18719 | −0.0546448 | ||||||||
\(473\) | −14.2405 | −0.654778 | ||||||||
\(474\) | −8.76687 | −0.402676 | ||||||||
\(475\) | 2.34836 | 0.107750 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.17246 | −0.374191 | ||||||||
\(478\) | −9.55760 | −0.437155 | ||||||||
\(479\) | −25.4944 | −1.16487 | −0.582435 | − | 0.812878i | \(-0.697900\pi\) | ||||
−0.582435 | + | 0.812878i | \(0.697900\pi\) | |||||||
\(480\) | −1.74632 | −0.0797081 | ||||||||
\(481\) | −30.7009 | −1.39984 | ||||||||
\(482\) | −5.08336 | −0.231541 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.57233 | −0.344197 | ||||||||
\(485\) | 33.0162 | 1.49919 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 19.6419 | 0.890057 | 0.445029 | − | 0.895516i | \(-0.353193\pi\) | ||||
0.445029 | + | 0.895516i | \(0.353193\pi\) | |||||||
\(488\) | −12.6746 | −0.573753 | ||||||||
\(489\) | −18.0018 | −0.814068 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −32.7187 | −1.47658 | −0.738288 | − | 0.674485i | \(-0.764366\pi\) | ||||
−0.738288 | + | 0.674485i | \(0.764366\pi\) | |||||||
\(492\) | 1.57386 | 0.0709550 | ||||||||
\(493\) | 24.0312 | 1.08231 | ||||||||
\(494\) | −4.98186 | −0.224144 | ||||||||
\(495\) | −3.23313 | −0.145318 | ||||||||
\(496\) | −8.90685 | −0.399929 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 4.43718 | 0.198835 | ||||||||
\(499\) | 11.8860 | 0.532092 | 0.266046 | − | 0.963960i | \(-0.414283\pi\) | ||||
0.266046 | + | 0.963960i | \(0.414283\pi\) | |||||||
\(500\) | −12.1376 | −0.542808 | ||||||||
\(501\) | 5.88388 | 0.262872 | ||||||||
\(502\) | 27.0683 | 1.20812 | ||||||||
\(503\) | −11.2620 | −0.502149 | −0.251075 | − | 0.967968i | \(-0.580784\pi\) | ||||
−0.251075 | + | 0.967968i | \(0.580784\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.8917 | −0.707173 | ||||||||
\(506\) | −1.85140 | −0.0823046 | ||||||||
\(507\) | −4.11942 | −0.182950 | ||||||||
\(508\) | 18.3594 | 0.814565 | ||||||||
\(509\) | −22.0174 | −0.975904 | −0.487952 | − | 0.872871i | \(-0.662256\pi\) | ||||
−0.487952 | + | 0.872871i | \(0.662256\pi\) | |||||||
\(510\) | 11.9246 | 0.528030 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.20406 | 0.0531604 | ||||||||
\(514\) | −11.2773 | −0.497419 | ||||||||
\(515\) | −22.7230 | −1.00129 | ||||||||
\(516\) | −7.69175 | −0.338610 | ||||||||
\(517\) | 19.7834 | 0.870072 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.74390 | 0.427710 | ||||||||
\(520\) | 7.22550 | 0.316859 | ||||||||
\(521\) | 22.0239 | 0.964883 | 0.482441 | − | 0.875928i | \(-0.339750\pi\) | ||||
0.482441 | + | 0.875928i | \(0.339750\pi\) | |||||||
\(522\) | −3.51929 | −0.154035 | ||||||||
\(523\) | 6.85572 | 0.299780 | 0.149890 | − | 0.988703i | \(-0.452108\pi\) | ||||
0.149890 | + | 0.988703i | \(0.452108\pi\) | |||||||
\(524\) | 5.40900 | 0.236293 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 31.3980 | 1.36902 | ||||||||
\(527\) | 60.8198 | 2.64935 | ||||||||
\(528\) | 1.85140 | 0.0805717 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −14.2717 | −0.619924 | ||||||||
\(531\) | −1.18719 | −0.0515196 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.51194 | −0.282063 | ||||||||
\(534\) | −0.766874 | −0.0331859 | ||||||||
\(535\) | −6.98527 | −0.302000 | ||||||||
\(536\) | 6.64213 | 0.286896 | ||||||||
\(537\) | −1.98896 | −0.0858299 | ||||||||
\(538\) | −5.32195 | −0.229446 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.74632 | −0.0751496 | ||||||||
\(541\) | 15.1322 | 0.650586 | 0.325293 | − | 0.945613i | \(-0.394537\pi\) | ||||
0.325293 | + | 0.945613i | \(0.394537\pi\) | |||||||
\(542\) | −26.5416 | −1.14006 | ||||||||
\(543\) | 25.2674 | 1.08433 | ||||||||
\(544\) | −6.82843 | −0.292766 | ||||||||
\(545\) | −1.05445 | −0.0451678 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.1617 | −0.648267 | −0.324134 | − | 0.946011i | \(-0.605073\pi\) | ||||
−0.324134 | + | 0.946011i | \(0.605073\pi\) | |||||||
\(548\) | −10.3100 | −0.440422 | ||||||||
\(549\) | −12.6746 | −0.540939 | ||||||||
\(550\) | 3.61092 | 0.153970 | ||||||||
\(551\) | 4.23743 | 0.180520 | ||||||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −14.4476 | −0.613819 | ||||||||
\(555\) | 12.9577 | 0.550026 | ||||||||
\(556\) | 6.61943 | 0.280726 | ||||||||
\(557\) | −32.6972 | −1.38543 | −0.692713 | − | 0.721214i | \(-0.743585\pi\) | ||||
−0.692713 | + | 0.721214i | \(0.743585\pi\) | |||||||
\(558\) | −8.90685 | −0.377057 | ||||||||
\(559\) | 31.8251 | 1.34606 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.6421 | −0.533751 | ||||||||
\(562\) | −19.2016 | −0.809972 | ||||||||
\(563\) | −8.20128 | −0.345643 | −0.172821 | − | 0.984953i | \(-0.555288\pi\) | ||||
−0.172821 | + | 0.984953i | \(0.555288\pi\) | |||||||
\(564\) | 10.6857 | 0.449947 | ||||||||
\(565\) | 0.753285 | 0.0316909 | ||||||||
\(566\) | 18.7739 | 0.789124 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.46967 | 0.271461 | ||||||||
\(569\) | 32.6935 | 1.37058 | 0.685292 | − | 0.728268i | \(-0.259674\pi\) | ||||
0.685292 | + | 0.728268i | \(0.259674\pi\) | |||||||
\(570\) | 2.10267 | 0.0880709 | ||||||||
\(571\) | 23.4130 | 0.979802 | 0.489901 | − | 0.871778i | \(-0.337033\pi\) | ||||
0.489901 | + | 0.871778i | \(0.337033\pi\) | |||||||
\(572\) | −7.66027 | −0.320292 | ||||||||
\(573\) | 3.97792 | 0.166180 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.95037 | −0.0813362 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 27.2387 | 1.13396 | 0.566981 | − | 0.823731i | \(-0.308111\pi\) | ||||
0.566981 | + | 0.823731i | \(0.308111\pi\) | |||||||
\(578\) | 29.6274 | 1.23234 | ||||||||
\(579\) | −12.5539 | −0.521723 | ||||||||
\(580\) | −6.14580 | −0.255191 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −18.9062 | −0.783688 | ||||||||
\(583\) | 15.1305 | 0.626640 | ||||||||
\(584\) | 0.750005 | 0.0310354 | ||||||||
\(585\) | 7.22550 | 0.298738 | ||||||||
\(586\) | 13.6296 | 0.563032 | ||||||||
\(587\) | 11.8704 | 0.489945 | 0.244972 | − | 0.969530i | \(-0.421221\pi\) | ||||
0.244972 | + | 0.969530i | \(0.421221\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.7243 | 0.441889 | ||||||||
\(590\) | −2.07321 | −0.0853526 | ||||||||
\(591\) | 14.8018 | 0.608863 | ||||||||
\(592\) | −7.42004 | −0.304962 | ||||||||
\(593\) | −41.6284 | −1.70947 | −0.854737 | − | 0.519062i | \(-0.826281\pi\) | ||||
−0.854737 | + | 0.519062i | \(0.826281\pi\) | |||||||
\(594\) | 1.85140 | 0.0759637 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 19.8072 | 0.811336 | ||||||||
\(597\) | −13.9513 | −0.570987 | ||||||||
\(598\) | 4.13756 | 0.169197 | ||||||||
\(599\) | 25.8839 | 1.05759 | 0.528793 | − | 0.848751i | \(-0.322645\pi\) | ||||
0.528793 | + | 0.848751i | \(0.322645\pi\) | |||||||
\(600\) | 1.95037 | 0.0796237 | ||||||||
\(601\) | 24.3397 | 0.992837 | 0.496419 | − | 0.868083i | \(-0.334648\pi\) | ||||
0.496419 | + | 0.868083i | \(0.334648\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.64213 | 0.270488 | ||||||||
\(604\) | −14.8330 | −0.603546 | ||||||||
\(605\) | −13.2237 | −0.537620 | ||||||||
\(606\) | 9.10014 | 0.369668 | ||||||||
\(607\) | 42.5516 | 1.72712 | 0.863559 | − | 0.504248i | \(-0.168230\pi\) | ||||
0.863559 | + | 0.504248i | \(0.168230\pi\) | |||||||
\(608\) | −1.20406 | −0.0488309 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −22.1339 | −0.896175 | ||||||||
\(611\) | −44.2125 | −1.78865 | ||||||||
\(612\) | −6.82843 | −0.276023 | ||||||||
\(613\) | −9.17615 | −0.370621 | −0.185311 | − | 0.982680i | \(-0.559329\pi\) | ||||
−0.185311 | + | 0.982680i | \(0.559329\pi\) | |||||||
\(614\) | −22.9933 | −0.927932 | ||||||||
\(615\) | 2.74846 | 0.110828 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.6421 | 0.911538 | 0.455769 | − | 0.890098i | \(-0.349364\pi\) | ||||
0.455769 | + | 0.890098i | \(0.349364\pi\) | |||||||
\(618\) | 13.0119 | 0.523416 | ||||||||
\(619\) | −10.9142 | −0.438680 | −0.219340 | − | 0.975649i | \(-0.570390\pi\) | ||||
−0.219340 | + | 0.975649i | \(0.570390\pi\) | |||||||
\(620\) | −15.5542 | −0.624671 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 29.5983 | 1.18678 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −4.13756 | −0.165635 | ||||||||
\(625\) | −11.4442 | −0.457767 | ||||||||
\(626\) | 17.7604 | 0.709848 | ||||||||
\(627\) | −2.22919 | −0.0890251 | ||||||||
\(628\) | 0.242641 | 0.00968242 | ||||||||
\(629\) | 50.6672 | 2.02023 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.3875 | 1.09028 | 0.545139 | − | 0.838346i | \(-0.316477\pi\) | ||||
0.545139 | + | 0.838346i | \(0.316477\pi\) | |||||||
\(632\) | 8.76687 | 0.348728 | ||||||||
\(633\) | −8.71356 | −0.346333 | ||||||||
\(634\) | −21.6952 | −0.861625 | ||||||||
\(635\) | 32.0613 | 1.27231 | ||||||||
\(636\) | 8.17246 | 0.324059 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 6.51560 | 0.257955 | ||||||||
\(639\) | 6.46967 | 0.255936 | ||||||||
\(640\) | 1.74632 | 0.0690293 | ||||||||
\(641\) | −30.7372 | −1.21404 | −0.607022 | − | 0.794685i | \(-0.707636\pi\) | ||||
−0.607022 | + | 0.794685i | \(0.707636\pi\) | |||||||
\(642\) | 4.00000 | 0.157867 | ||||||||
\(643\) | −4.56712 | −0.180110 | −0.0900548 | − | 0.995937i | \(-0.528704\pi\) | ||||
−0.0900548 | + | 0.995937i | \(0.528704\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −13.4322 | −0.528894 | ||||||||
\(646\) | 8.22181 | 0.323483 | ||||||||
\(647\) | −37.2453 | −1.46426 | −0.732132 | − | 0.681163i | \(-0.761475\pi\) | ||||
−0.732132 | + | 0.681163i | \(0.761475\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 2.19796 | 0.0862773 | ||||||||
\(650\) | −8.06979 | −0.316523 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 18.0018 | 0.705004 | ||||||||
\(653\) | −15.0990 | −0.590869 | −0.295434 | − | 0.955363i | \(-0.595464\pi\) | ||||
−0.295434 | + | 0.955363i | \(0.595464\pi\) | |||||||
\(654\) | 0.603815 | 0.0236110 | ||||||||
\(655\) | 9.44583 | 0.369079 | ||||||||
\(656\) | −1.57386 | −0.0614489 | ||||||||
\(657\) | 0.750005 | 0.0292605 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.1725 | −0.668945 | −0.334472 | − | 0.942406i | \(-0.608558\pi\) | ||||
−0.334472 | + | 0.942406i | \(0.608558\pi\) | |||||||
\(660\) | 3.23313 | 0.125849 | ||||||||
\(661\) | 8.11307 | 0.315562 | 0.157781 | − | 0.987474i | \(-0.449566\pi\) | ||||
0.157781 | + | 0.987474i | \(0.449566\pi\) | |||||||
\(662\) | 10.0018 | 0.388730 | ||||||||
\(663\) | 28.2530 | 1.09726 | ||||||||
\(664\) | −4.43718 | −0.172196 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.42004 | −0.287521 | ||||||||
\(667\) | −3.51929 | −0.136268 | ||||||||
\(668\) | −5.88388 | −0.227654 | ||||||||
\(669\) | 24.0481 | 0.929753 | ||||||||
\(670\) | 11.5993 | 0.448119 | ||||||||
\(671\) | 23.4657 | 0.905884 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.7592 | 0.568927 | 0.284464 | − | 0.958687i | \(-0.408185\pi\) | ||||
0.284464 | + | 0.958687i | \(0.408185\pi\) | |||||||
\(674\) | −6.79810 | −0.261853 | ||||||||
\(675\) | 1.95037 | 0.0750699 | ||||||||
\(676\) | 4.11942 | 0.158439 | ||||||||
\(677\) | −26.3133 | −1.01130 | −0.505652 | − | 0.862738i | \(-0.668748\pi\) | ||||
−0.505652 | + | 0.862738i | \(0.668748\pi\) | |||||||
\(678\) | −0.431356 | −0.0165661 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −11.9246 | −0.457288 | ||||||||
\(681\) | −2.51319 | −0.0963057 | ||||||||
\(682\) | 16.4901 | 0.631439 | ||||||||
\(683\) | 18.1980 | 0.696325 | 0.348163 | − | 0.937434i | \(-0.386806\pi\) | ||||
0.348163 | + | 0.937434i | \(0.386806\pi\) | |||||||
\(684\) | −1.20406 | −0.0460382 | ||||||||
\(685\) | −18.0046 | −0.687919 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.4029 | −0.549505 | ||||||||
\(688\) | 7.69175 | 0.293245 | ||||||||
\(689\) | −33.8141 | −1.28821 | ||||||||
\(690\) | −1.74632 | −0.0664812 | ||||||||
\(691\) | −7.83389 | −0.298015 | −0.149008 | − | 0.988836i | \(-0.547608\pi\) | ||||
−0.149008 | + | 0.988836i | \(0.547608\pi\) | |||||||
\(692\) | −9.74390 | −0.370408 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −22.0202 | −0.835875 | ||||||||
\(695\) | 11.5596 | 0.438482 | ||||||||
\(696\) | 3.51929 | 0.133398 | ||||||||
\(697\) | 10.7470 | 0.407071 | ||||||||
\(698\) | −31.6005 | −1.19610 | ||||||||
\(699\) | −22.0273 | −0.833148 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −42.4454 | −1.60314 | −0.801570 | − | 0.597901i | \(-0.796002\pi\) | ||||
−0.801570 | + | 0.597901i | \(0.796002\pi\) | |||||||
\(702\) | −4.13756 | −0.156162 | ||||||||
\(703\) | 8.93415 | 0.336958 | ||||||||
\(704\) | −1.85140 | −0.0697771 | ||||||||
\(705\) | 18.6605 | 0.702797 | ||||||||
\(706\) | 11.7325 | 0.441558 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.18719 | 0.0446173 | ||||||||
\(709\) | 18.6183 | 0.699224 | 0.349612 | − | 0.936895i | \(-0.386313\pi\) | ||||
0.349612 | + | 0.936895i | \(0.386313\pi\) | |||||||
\(710\) | 11.2981 | 0.424010 | ||||||||
\(711\) | 8.76687 | 0.328783 | ||||||||
\(712\) | 0.766874 | 0.0287398 | ||||||||
\(713\) | −8.90685 | −0.333564 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.3773 | −0.500281 | ||||||||
\(716\) | 1.98896 | 0.0743309 | ||||||||
\(717\) | 9.55760 | 0.356935 | ||||||||
\(718\) | 5.13021 | 0.191458 | ||||||||
\(719\) | 20.2844 | 0.756479 | 0.378240 | − | 0.925708i | \(-0.376530\pi\) | ||||
0.378240 | + | 0.925708i | \(0.376530\pi\) | |||||||
\(720\) | 1.74632 | 0.0650814 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −17.5502 | −0.653153 | ||||||||
\(723\) | 5.08336 | 0.189052 | ||||||||
\(724\) | −25.2674 | −0.939055 | ||||||||
\(725\) | 6.86394 | 0.254920 | ||||||||
\(726\) | 7.57233 | 0.281036 | ||||||||
\(727\) | −13.8228 | −0.512661 | −0.256330 | − | 0.966589i | \(-0.582514\pi\) | ||||
−0.256330 | + | 0.966589i | \(0.582514\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.30975 | 0.0484759 | ||||||||
\(731\) | −52.5226 | −1.94262 | ||||||||
\(732\) | 12.6746 | 0.468467 | ||||||||
\(733\) | 31.7132 | 1.17135 | 0.585677 | − | 0.810545i | \(-0.300829\pi\) | ||||
0.585677 | + | 0.810545i | \(0.300829\pi\) | |||||||
\(734\) | −3.30176 | −0.121870 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −12.2972 | −0.452973 | ||||||||
\(738\) | −1.57386 | −0.0579345 | ||||||||
\(739\) | 12.6682 | 0.466006 | 0.233003 | − | 0.972476i | \(-0.425145\pi\) | ||||
0.233003 | + | 0.972476i | \(0.425145\pi\) | |||||||
\(740\) | −12.9577 | −0.476336 | ||||||||
\(741\) | 4.98186 | 0.183013 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.97056 | 0.182352 | 0.0911761 | − | 0.995835i | \(-0.470937\pi\) | ||||
0.0911761 | + | 0.995835i | \(0.470937\pi\) | |||||||
\(744\) | 8.90685 | 0.326541 | ||||||||
\(745\) | 34.5897 | 1.26727 | ||||||||
\(746\) | −13.4056 | −0.490813 | ||||||||
\(747\) | −4.43718 | −0.162348 | ||||||||
\(748\) | 12.6421 | 0.462242 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 12.1376 | 0.443201 | ||||||||
\(751\) | −22.6014 | −0.824736 | −0.412368 | − | 0.911017i | \(-0.635298\pi\) | ||||
−0.412368 | + | 0.911017i | \(0.635298\pi\) | |||||||
\(752\) | −10.6857 | −0.389666 | ||||||||
\(753\) | −27.0683 | −0.986422 | ||||||||
\(754\) | −14.5613 | −0.530291 | ||||||||
\(755\) | −25.9031 | −0.942712 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −44.3081 | −1.61041 | −0.805203 | − | 0.592999i | \(-0.797944\pi\) | ||||
−0.805203 | + | 0.592999i | \(0.797944\pi\) | |||||||
\(758\) | −28.8290 | −1.04712 | ||||||||
\(759\) | 1.85140 | 0.0672014 | ||||||||
\(760\) | −2.10267 | −0.0762717 | ||||||||
\(761\) | −0.760018 | −0.0275506 | −0.0137753 | − | 0.999905i | \(-0.504385\pi\) | ||||
−0.0137753 | + | 0.999905i | \(0.504385\pi\) | |||||||
\(762\) | −18.3594 | −0.665090 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −3.97792 | −0.143916 | ||||||||
\(765\) | −11.9246 | −0.431135 | ||||||||
\(766\) | 3.33183 | 0.120384 | ||||||||
\(767\) | −4.91206 | −0.177364 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 29.2831 | 1.05598 | 0.527988 | − | 0.849252i | \(-0.322947\pi\) | ||||
0.527988 | + | 0.849252i | \(0.322947\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.2773 | 0.406141 | ||||||||
\(772\) | 12.5539 | 0.451825 | ||||||||
\(773\) | 30.7679 | 1.10664 | 0.553322 | − | 0.832968i | \(-0.313360\pi\) | ||||
0.553322 | + | 0.832968i | \(0.313360\pi\) | |||||||
\(774\) | 7.69175 | 0.276474 | ||||||||
\(775\) | 17.3717 | 0.624009 | ||||||||
\(776\) | 18.9062 | 0.678693 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.67158 | −0.310891 | ||||||||
\(779\) | 1.89501 | 0.0678959 | ||||||||
\(780\) | −7.22550 | −0.258714 | ||||||||
\(781\) | −11.9779 | −0.428604 | ||||||||
\(782\) | −6.82843 | −0.244184 | ||||||||
\(783\) | 3.51929 | 0.125769 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.423728 | 0.0151235 | ||||||||
\(786\) | −5.40900 | −0.192933 | ||||||||
\(787\) | 20.1079 | 0.716768 | 0.358384 | − | 0.933574i | \(-0.383328\pi\) | ||||
0.358384 | + | 0.933574i | \(0.383328\pi\) | |||||||
\(788\) | −14.8018 | −0.527291 | ||||||||
\(789\) | −31.3980 | −1.11780 | ||||||||
\(790\) | 15.3097 | 0.544696 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.85140 | −0.0657865 | ||||||||
\(793\) | −52.4420 | −1.86227 | ||||||||
\(794\) | −26.2677 | −0.932208 | ||||||||
\(795\) | 14.2717 | 0.506165 | ||||||||
\(796\) | 13.9513 | 0.494489 | ||||||||
\(797\) | 28.1801 | 0.998189 | 0.499094 | − | 0.866548i | \(-0.333666\pi\) | ||||
0.499094 | + | 0.866548i | \(0.333666\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 72.9662 | 2.58136 | ||||||||
\(800\) | −1.95037 | −0.0689561 | ||||||||
\(801\) | 0.766874 | 0.0270961 | ||||||||
\(802\) | 8.35229 | 0.294930 | ||||||||
\(803\) | −1.38856 | −0.0490011 | ||||||||
\(804\) | −6.64213 | −0.234250 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −36.8526 | −1.29808 | ||||||||
\(807\) | 5.32195 | 0.187341 | ||||||||
\(808\) | −9.10014 | −0.320142 | ||||||||
\(809\) | −7.96481 | −0.280028 | −0.140014 | − | 0.990150i | \(-0.544715\pi\) | ||||
−0.140014 | + | 0.990150i | \(0.544715\pi\) | |||||||
\(810\) | 1.74632 | 0.0613594 | ||||||||
\(811\) | −15.1280 | −0.531217 | −0.265608 | − | 0.964081i | \(-0.585573\pi\) | ||||
−0.265608 | + | 0.964081i | \(0.585573\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 26.5416 | 0.930855 | ||||||||
\(814\) | 13.7374 | 0.481497 | ||||||||
\(815\) | 31.4368 | 1.10118 | ||||||||
\(816\) | 6.82843 | 0.239043 | ||||||||
\(817\) | −9.26130 | −0.324012 | ||||||||
\(818\) | 27.6434 | 0.966529 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.74846 | −0.0959803 | ||||||||
\(821\) | −25.9502 | −0.905669 | −0.452835 | − | 0.891595i | \(-0.649587\pi\) | ||||
−0.452835 | + | 0.891595i | \(0.649587\pi\) | |||||||
\(822\) | 10.3100 | 0.359603 | ||||||||
\(823\) | −31.3208 | −1.09177 | −0.545887 | − | 0.837859i | \(-0.683807\pi\) | ||||
−0.545887 | + | 0.837859i | \(0.683807\pi\) | |||||||
\(824\) | −13.0119 | −0.453292 | ||||||||
\(825\) | −3.61092 | −0.125716 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.90075 | −0.344283 | −0.172141 | − | 0.985072i | \(-0.555069\pi\) | ||||
−0.172141 | + | 0.985072i | \(0.555069\pi\) | |||||||
\(828\) | 1.00000 | 0.0347524 | ||||||||
\(829\) | 41.6218 | 1.44559 | 0.722793 | − | 0.691065i | \(-0.242858\pi\) | ||||
0.722793 | + | 0.691065i | \(0.242858\pi\) | |||||||
\(830\) | −7.74873 | −0.268962 | ||||||||
\(831\) | 14.4476 | 0.501181 | ||||||||
\(832\) | 4.13756 | 0.143444 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −6.61943 | −0.229212 | ||||||||
\(835\) | −10.2751 | −0.355585 | ||||||||
\(836\) | 2.22919 | 0.0770980 | ||||||||
\(837\) | 8.90685 | 0.307866 | ||||||||
\(838\) | 23.7509 | 0.820461 | ||||||||
\(839\) | 34.8697 | 1.20383 | 0.601917 | − | 0.798558i | \(-0.294404\pi\) | ||||
0.601917 | + | 0.798558i | \(0.294404\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.6146 | −0.572917 | ||||||||
\(842\) | 26.4365 | 0.911063 | ||||||||
\(843\) | 19.2016 | 0.661340 | ||||||||
\(844\) | 8.71356 | 0.299933 | ||||||||
\(845\) | 7.19382 | 0.247475 | ||||||||
\(846\) | −10.6857 | −0.367380 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −8.17246 | −0.280643 | ||||||||
\(849\) | −18.7739 | −0.644317 | ||||||||
\(850\) | 13.3180 | 0.456803 | ||||||||
\(851\) | −7.42004 | −0.254356 | ||||||||
\(852\) | −6.46967 | −0.221647 | ||||||||
\(853\) | −20.7632 | −0.710919 | −0.355459 | − | 0.934692i | \(-0.615676\pi\) | ||||
−0.355459 | + | 0.934692i | \(0.615676\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.10267 | −0.0719096 | ||||||||
\(856\) | −4.00000 | −0.136717 | ||||||||
\(857\) | 16.4837 | 0.563074 | 0.281537 | − | 0.959550i | \(-0.409156\pi\) | ||||
0.281537 | + | 0.959550i | \(0.409156\pi\) | |||||||
\(858\) | 7.66027 | 0.261517 | ||||||||
\(859\) | −26.7948 | −0.914225 | −0.457113 | − | 0.889409i | \(-0.651116\pi\) | ||||
−0.457113 | + | 0.889409i | \(0.651116\pi\) | |||||||
\(860\) | 13.4322 | 0.458036 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −24.7099 | −0.841622 | ||||||||
\(863\) | 0.321063 | 0.0109291 | 0.00546455 | − | 0.999985i | \(-0.498261\pi\) | ||||
0.00546455 | + | 0.999985i | \(0.498261\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −17.0160 | −0.578560 | ||||||||
\(866\) | −18.9816 | −0.645021 | ||||||||
\(867\) | −29.6274 | −1.00620 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.2310 | −0.550598 | ||||||||
\(870\) | 6.14580 | 0.208362 | ||||||||
\(871\) | 27.4822 | 0.931199 | ||||||||
\(872\) | −0.603815 | −0.0204478 | ||||||||
\(873\) | 18.9062 | 0.639878 | ||||||||
\(874\) | −1.20406 | −0.0407278 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.750005 | −0.0253403 | ||||||||
\(877\) | 48.0274 | 1.62177 | 0.810885 | − | 0.585205i | \(-0.198986\pi\) | ||||
0.810885 | + | 0.585205i | \(0.198986\pi\) | |||||||
\(878\) | −33.4883 | −1.13018 | ||||||||
\(879\) | −13.6296 | −0.459714 | ||||||||
\(880\) | −3.23313 | −0.108989 | ||||||||
\(881\) | −11.9607 | −0.402965 | −0.201482 | − | 0.979492i | \(-0.564576\pi\) | ||||
−0.201482 | + | 0.979492i | \(0.564576\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.6093 | −0.659905 | −0.329952 | − | 0.943998i | \(-0.607033\pi\) | ||||
−0.329952 | + | 0.943998i | \(0.607033\pi\) | |||||||
\(884\) | −28.2530 | −0.950253 | ||||||||
\(885\) | 2.07321 | 0.0696901 | ||||||||
\(886\) | −26.0656 | −0.875690 | ||||||||
\(887\) | 54.2833 | 1.82266 | 0.911328 | − | 0.411681i | \(-0.135058\pi\) | ||||
0.911328 | + | 0.411681i | \(0.135058\pi\) | |||||||
\(888\) | 7.42004 | 0.249000 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.33920 | 0.0448902 | ||||||||
\(891\) | −1.85140 | −0.0620241 | ||||||||
\(892\) | −24.0481 | −0.805190 | ||||||||
\(893\) | 12.8661 | 0.430548 | ||||||||
\(894\) | −19.8072 | −0.662453 | ||||||||
\(895\) | 3.47335 | 0.116101 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.13756 | −0.138149 | ||||||||
\(898\) | −20.9172 | −0.698018 | ||||||||
\(899\) | 31.3458 | 1.04544 | ||||||||
\(900\) | −1.95037 | −0.0650125 | ||||||||
\(901\) | 55.8050 | 1.85914 | ||||||||
\(902\) | 2.91384 | 0.0970201 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.431356 | 0.0143467 | ||||||||
\(905\) | −44.1249 | −1.46676 | ||||||||
\(906\) | 14.8330 | 0.492793 | ||||||||
\(907\) | 11.2255 | 0.372737 | 0.186368 | − | 0.982480i | \(-0.440328\pi\) | ||||
0.186368 | + | 0.982480i | \(0.440328\pi\) | |||||||
\(908\) | 2.51319 | 0.0834032 | ||||||||
\(909\) | −9.10014 | −0.301833 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.02183 | 0.0669862 | 0.0334931 | − | 0.999439i | \(-0.489337\pi\) | ||||
0.0334931 | + | 0.999439i | \(0.489337\pi\) | |||||||
\(912\) | 1.20406 | 0.0398703 | ||||||||
\(913\) | 8.21498 | 0.271876 | ||||||||
\(914\) | 3.63477 | 0.120228 | ||||||||
\(915\) | 22.1339 | 0.731724 | ||||||||
\(916\) | 14.4029 | 0.475885 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 6.82843 | 0.225372 | ||||||||
\(919\) | 0.0606470 | 0.00200056 | 0.00100028 | − | 0.999999i | \(-0.499682\pi\) | ||||
0.00100028 | + | 0.999999i | \(0.499682\pi\) | |||||||
\(920\) | 1.74632 | 0.0575744 | ||||||||
\(921\) | 22.9933 | 0.757654 | ||||||||
\(922\) | −10.6027 | −0.349180 | ||||||||
\(923\) | 26.7686 | 0.881101 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.4719 | 0.475832 | ||||||||
\(926\) | 22.3355 | 0.733991 | ||||||||
\(927\) | −13.0119 | −0.427368 | ||||||||
\(928\) | −3.51929 | −0.115526 | ||||||||
\(929\) | −13.5959 | −0.446068 | −0.223034 | − | 0.974811i | \(-0.571596\pi\) | ||||
−0.223034 | + | 0.974811i | \(0.571596\pi\) | |||||||
\(930\) | 15.5542 | 0.510042 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 22.0273 | 0.721527 | ||||||||
\(933\) | −29.5983 | −0.969006 | ||||||||
\(934\) | 29.5469 | 0.966806 | ||||||||
\(935\) | 22.0772 | 0.722001 | ||||||||
\(936\) | 4.13756 | 0.135240 | ||||||||
\(937\) | −5.18999 | −0.169550 | −0.0847748 | − | 0.996400i | \(-0.527017\pi\) | ||||
−0.0847748 | + | 0.996400i | \(0.527017\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.7604 | −0.579588 | ||||||||
\(940\) | −18.6605 | −0.608640 | ||||||||
\(941\) | 4.13112 | 0.134671 | 0.0673354 | − | 0.997730i | \(-0.478550\pi\) | ||||
0.0673354 | + | 0.997730i | \(0.478550\pi\) | |||||||
\(942\) | −0.242641 | −0.00790566 | ||||||||
\(943\) | −1.57386 | −0.0512519 | ||||||||
\(944\) | −1.18719 | −0.0386397 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −14.2405 | −0.462998 | ||||||||
\(947\) | 19.5613 | 0.635656 | 0.317828 | − | 0.948148i | \(-0.397047\pi\) | ||||
0.317828 | + | 0.948148i | \(0.397047\pi\) | |||||||
\(948\) | −8.76687 | −0.284735 | ||||||||
\(949\) | 3.10319 | 0.100734 | ||||||||
\(950\) | 2.34836 | 0.0761909 | ||||||||
\(951\) | 21.6952 | 0.703514 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.0698 | −0.844483 | −0.422242 | − | 0.906483i | \(-0.638757\pi\) | ||||
−0.422242 | + | 0.906483i | \(0.638757\pi\) | |||||||
\(954\) | −8.17246 | −0.264593 | ||||||||
\(955\) | −6.94671 | −0.224790 | ||||||||
\(956\) | −9.55760 | −0.309115 | ||||||||
\(957\) | −6.51560 | −0.210620 | ||||||||
\(958\) | −25.4944 | −0.823687 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.74632 | −0.0563622 | ||||||||
\(961\) | 48.3320 | 1.55910 | ||||||||
\(962\) | −30.7009 | −0.989836 | ||||||||
\(963\) | −4.00000 | −0.128898 | ||||||||
\(964\) | −5.08336 | −0.163724 | ||||||||
\(965\) | 21.9231 | 0.705730 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.7358 | 0.827607 | 0.413804 | − | 0.910366i | \(-0.364200\pi\) | ||||
0.413804 | + | 0.910366i | \(0.364200\pi\) | |||||||
\(968\) | −7.57233 | −0.243384 | ||||||||
\(969\) | −8.22181 | −0.264123 | ||||||||
\(970\) | 33.0162 | 1.06009 | ||||||||
\(971\) | 2.02907 | 0.0651160 | 0.0325580 | − | 0.999470i | \(-0.489635\pi\) | ||||
0.0325580 | + | 0.999470i | \(0.489635\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 19.6419 | 0.629366 | ||||||||
\(975\) | 8.06979 | 0.258440 | ||||||||
\(976\) | −12.6746 | −0.405704 | ||||||||
\(977\) | −57.3775 | −1.83567 | −0.917835 | − | 0.396963i | \(-0.870064\pi\) | ||||
−0.917835 | + | 0.396963i | \(0.870064\pi\) | |||||||
\(978\) | −18.0018 | −0.575633 | ||||||||
\(979\) | −1.41979 | −0.0453766 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.603815 | −0.0192783 | ||||||||
\(982\) | −32.7187 | −1.04410 | ||||||||
\(983\) | −20.0273 | −0.638771 | −0.319385 | − | 0.947625i | \(-0.603476\pi\) | ||||
−0.319385 | + | 0.947625i | \(0.603476\pi\) | |||||||
\(984\) | 1.57386 | 0.0501728 | ||||||||
\(985\) | −25.8486 | −0.823605 | ||||||||
\(986\) | 24.0312 | 0.765310 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.98186 | −0.158494 | ||||||||
\(989\) | 7.69175 | 0.244583 | ||||||||
\(990\) | −3.23313 | −0.102756 | ||||||||
\(991\) | 19.1832 | 0.609375 | 0.304688 | − | 0.952452i | \(-0.401448\pi\) | ||||
0.304688 | + | 0.952452i | \(0.401448\pi\) | |||||||
\(992\) | −8.90685 | −0.282793 | ||||||||
\(993\) | −10.0018 | −0.317397 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.3633 | 0.772370 | ||||||||
\(996\) | 4.43718 | 0.140598 | ||||||||
\(997\) | 40.7909 | 1.29186 | 0.645930 | − | 0.763397i | \(-0.276470\pi\) | ||||
0.645930 | + | 0.763397i | \(0.276470\pi\) | |||||||
\(998\) | 11.8860 | 0.376246 | ||||||||
\(999\) | 7.42004 | 0.234760 |
(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 | 6762.2.a.ck.1.3 | ✓ | 4 | |
7.6 | odd | 2 | 6762.2.a.cq.1.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6762.2.a.ck.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial | |
6762.2.a.cq.1.2 | yes | 4 | 7.6 | odd | 2 |