Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1258372982\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.785.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x + 5 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 861) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.812716\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.812716 | 0.574677 | 0.287339 | − | 0.957829i | \(-0.407230\pi\) | ||||
0.287339 | + | 0.957829i | \(0.407230\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.33949 | −0.669746 | ||||||||
\(5\) | −1.00000 | −0.447214 | −0.223607 | − | 0.974679i | \(-0.571783\pi\) | ||||
−0.223607 | + | 0.974679i | \(0.571783\pi\) | |||||||
\(6\) | −0.812716 | −0.331790 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.71406 | −0.959565 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.812716 | −0.257003 | ||||||||
\(11\) | −5.15221 | −1.55345 | −0.776725 | − | 0.629840i | \(-0.783120\pi\) | ||||
−0.776725 | + | 0.629840i | \(0.783120\pi\) | |||||||
\(12\) | 1.33949 | 0.386678 | ||||||||
\(13\) | −2.18728 | −0.606643 | −0.303322 | − | 0.952888i | \(-0.598096\pi\) | ||||
−0.303322 | + | 0.952888i | \(0.598096\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0.473224 | 0.118306 | ||||||||
\(17\) | 5.86627 | 1.42278 | 0.711390 | − | 0.702798i | \(-0.248066\pi\) | ||||
0.711390 | + | 0.702798i | \(0.248066\pi\) | |||||||
\(18\) | 0.812716 | 0.191559 | ||||||||
\(19\) | 5.33949 | 1.22496 | 0.612482 | − | 0.790485i | \(-0.290171\pi\) | ||||
0.612482 | + | 0.790485i | \(0.290171\pi\) | |||||||
\(20\) | 1.33949 | 0.299520 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.18728 | −0.892732 | ||||||||
\(23\) | 7.49170 | 1.56213 | 0.781064 | − | 0.624451i | \(-0.214677\pi\) | ||||
0.781064 | + | 0.624451i | \(0.214677\pi\) | |||||||
\(24\) | 2.71406 | 0.554005 | ||||||||
\(25\) | −4.00000 | −0.800000 | ||||||||
\(26\) | −1.77764 | −0.348624 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.96492 | −0.736268 | −0.368134 | − | 0.929773i | \(-0.620003\pi\) | ||||
−0.368134 | + | 0.929773i | \(0.620003\pi\) | |||||||
\(30\) | 0.812716 | 0.148381 | ||||||||
\(31\) | −4.77764 | −0.858090 | −0.429045 | − | 0.903283i | \(-0.641150\pi\) | ||||
−0.429045 | + | 0.903283i | \(0.641150\pi\) | |||||||
\(32\) | 5.81272 | 1.02755 | ||||||||
\(33\) | 5.15221 | 0.896884 | ||||||||
\(34\) | 4.76761 | 0.817639 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.33949 | −0.223249 | ||||||||
\(37\) | 9.96492 | 1.63822 | 0.819112 | − | 0.573634i | \(-0.194467\pi\) | ||||
0.819112 | + | 0.573634i | \(0.194467\pi\) | |||||||
\(38\) | 4.33949 | 0.703959 | ||||||||
\(39\) | 2.18728 | 0.350246 | ||||||||
\(40\) | 2.71406 | 0.429131 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.05355 | 1.38065 | 0.690327 | − | 0.723498i | \(-0.257467\pi\) | ||||
0.690327 | + | 0.723498i | \(0.257467\pi\) | |||||||
\(44\) | 6.90134 | 1.04042 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 6.08863 | 0.897719 | ||||||||
\(47\) | −8.49170 | −1.23864 | −0.619321 | − | 0.785138i | \(-0.712592\pi\) | ||||
−0.619321 | + | 0.785138i | \(0.712592\pi\) | |||||||
\(48\) | −0.473224 | −0.0683040 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −3.25087 | −0.459742 | ||||||||
\(51\) | −5.86627 | −0.821442 | ||||||||
\(52\) | 2.92985 | 0.406297 | ||||||||
\(53\) | 7.52678 | 1.03388 | 0.516941 | − | 0.856021i | \(-0.327071\pi\) | ||||
0.516941 | + | 0.856021i | \(0.327071\pi\) | |||||||
\(54\) | −0.812716 | −0.110597 | ||||||||
\(55\) | 5.15221 | 0.694724 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.33949 | −0.707233 | ||||||||
\(58\) | −3.22236 | −0.423116 | ||||||||
\(59\) | 0.964925 | 0.125623 | 0.0628113 | − | 0.998025i | \(-0.479993\pi\) | ||||
0.0628113 | + | 0.998025i | \(0.479993\pi\) | |||||||
\(60\) | −1.33949 | −0.172928 | ||||||||
\(61\) | −4.90134 | −0.627553 | −0.313776 | − | 0.949497i | \(-0.601594\pi\) | ||||
−0.313776 | + | 0.949497i | \(0.601594\pi\) | |||||||
\(62\) | −3.88287 | −0.493125 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.77764 | 0.472205 | ||||||||
\(65\) | 2.18728 | 0.271299 | ||||||||
\(66\) | 4.18728 | 0.515419 | ||||||||
\(67\) | −2.47322 | −0.302152 | −0.151076 | − | 0.988522i | \(-0.548274\pi\) | ||||
−0.151076 | + | 0.988522i | \(0.548274\pi\) | |||||||
\(68\) | −7.85782 | −0.952901 | ||||||||
\(69\) | −7.49170 | −0.901895 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.0536 | 1.90521 | 0.952603 | − | 0.304216i | \(-0.0983945\pi\) | ||||
0.952603 | + | 0.304216i | \(0.0983945\pi\) | |||||||
\(72\) | −2.71406 | −0.319855 | ||||||||
\(73\) | −3.66051 | −0.428430 | −0.214215 | − | 0.976787i | \(-0.568719\pi\) | ||||
−0.214215 | + | 0.976787i | \(0.568719\pi\) | |||||||
\(74\) | 8.09866 | 0.941450 | ||||||||
\(75\) | 4.00000 | 0.461880 | ||||||||
\(76\) | −7.15221 | −0.820415 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.77764 | 0.201278 | ||||||||
\(79\) | −12.1522 | −1.36723 | −0.683615 | − | 0.729843i | \(-0.739593\pi\) | ||||
−0.683615 | + | 0.729843i | \(0.739593\pi\) | |||||||
\(80\) | −0.473224 | −0.0529081 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.812716 | −0.0897495 | ||||||||
\(83\) | −15.2944 | −1.67878 | −0.839389 | − | 0.543532i | \(-0.817087\pi\) | ||||
−0.839389 | + | 0.543532i | \(0.817087\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.86627 | −0.636286 | ||||||||
\(86\) | 7.35797 | 0.793430 | ||||||||
\(87\) | 3.96492 | 0.425085 | ||||||||
\(88\) | 13.9834 | 1.49064 | ||||||||
\(89\) | −3.77764 | −0.400429 | −0.200215 | − | 0.979752i | \(-0.564164\pi\) | ||||
−0.200215 | + | 0.979752i | \(0.564164\pi\) | |||||||
\(90\) | −0.812716 | −0.0856678 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −10.0351 | −1.04623 | ||||||||
\(93\) | 4.77764 | 0.495418 | ||||||||
\(94\) | −6.90134 | −0.711819 | ||||||||
\(95\) | −5.33949 | −0.547820 | ||||||||
\(96\) | −5.81272 | −0.593258 | ||||||||
\(97\) | −7.87630 | −0.799717 | −0.399858 | − | 0.916577i | \(-0.630941\pi\) | ||||
−0.399858 | + | 0.916577i | \(0.630941\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.15221 | −0.517816 | ||||||||
\(100\) | 5.35797 | 0.535797 | ||||||||
\(101\) | −3.96492 | −0.394525 | −0.197262 | − | 0.980351i | \(-0.563205\pi\) | ||||
−0.197262 | + | 0.980351i | \(0.563205\pi\) | |||||||
\(102\) | −4.76761 | −0.472064 | ||||||||
\(103\) | 9.45663 | 0.931789 | 0.465895 | − | 0.884840i | \(-0.345733\pi\) | ||||
0.465895 | + | 0.884840i | \(0.345733\pi\) | |||||||
\(104\) | 5.93642 | 0.582114 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.11713 | 0.594149 | ||||||||
\(107\) | 4.81272 | 0.465263 | 0.232631 | − | 0.972565i | \(-0.425266\pi\) | ||||
0.232631 | + | 0.972565i | \(0.425266\pi\) | |||||||
\(108\) | 1.33949 | 0.128893 | ||||||||
\(109\) | −13.1707 | −1.26152 | −0.630761 | − | 0.775977i | \(-0.717257\pi\) | ||||
−0.630761 | + | 0.775977i | \(0.717257\pi\) | |||||||
\(110\) | 4.18728 | 0.399242 | ||||||||
\(111\) | −9.96492 | −0.945829 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.81272 | 0.452742 | 0.226371 | − | 0.974041i | \(-0.427314\pi\) | ||||
0.226371 | + | 0.974041i | \(0.427314\pi\) | |||||||
\(114\) | −4.33949 | −0.406431 | ||||||||
\(115\) | −7.49170 | −0.698605 | ||||||||
\(116\) | 5.31099 | 0.493113 | ||||||||
\(117\) | −2.18728 | −0.202214 | ||||||||
\(118\) | 0.784210 | 0.0721924 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.71406 | −0.247759 | ||||||||
\(121\) | 15.5453 | 1.41320 | ||||||||
\(122\) | −3.98340 | −0.360640 | ||||||||
\(123\) | 1.00000 | 0.0901670 | ||||||||
\(124\) | 6.39961 | 0.574702 | ||||||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.76761 | −0.600528 | −0.300264 | − | 0.953856i | \(-0.597075\pi\) | ||||
−0.300264 | + | 0.953856i | \(0.597075\pi\) | |||||||
\(128\) | −8.55528 | −0.756187 | ||||||||
\(129\) | −9.05355 | −0.797121 | ||||||||
\(130\) | 1.77764 | 0.155909 | ||||||||
\(131\) | −13.4281 | −1.17322 | −0.586610 | − | 0.809869i | \(-0.699538\pi\) | ||||
−0.586610 | + | 0.809869i | \(0.699538\pi\) | |||||||
\(132\) | −6.90134 | −0.600685 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.01003 | −0.173640 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | −15.9214 | −1.36525 | ||||||||
\(137\) | −1.87630 | −0.160303 | −0.0801515 | − | 0.996783i | \(-0.525540\pi\) | ||||
−0.0801515 | + | 0.996783i | \(0.525540\pi\) | |||||||
\(138\) | −6.08863 | −0.518298 | ||||||||
\(139\) | 4.46319 | 0.378563 | 0.189282 | − | 0.981923i | \(-0.439384\pi\) | ||||
0.189282 | + | 0.981923i | \(0.439384\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.49170 | 0.715130 | ||||||||
\(142\) | 13.0470 | 1.09488 | ||||||||
\(143\) | 11.2693 | 0.942390 | ||||||||
\(144\) | 0.473224 | 0.0394353 | ||||||||
\(145\) | 3.96492 | 0.329269 | ||||||||
\(146\) | −2.97495 | −0.246209 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −13.3479 | −1.09719 | ||||||||
\(149\) | −12.8497 | −1.05269 | −0.526343 | − | 0.850272i | \(-0.676437\pi\) | ||||
−0.526343 | + | 0.850272i | \(0.676437\pi\) | |||||||
\(150\) | 3.25087 | 0.265432 | ||||||||
\(151\) | 5.98340 | 0.486922 | 0.243461 | − | 0.969911i | \(-0.421717\pi\) | ||||
0.243461 | + | 0.969911i | \(0.421717\pi\) | |||||||
\(152\) | −14.4917 | −1.17543 | ||||||||
\(153\) | 5.86627 | 0.474260 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.77764 | 0.383749 | ||||||||
\(156\) | −2.92985 | −0.234576 | ||||||||
\(157\) | −3.65048 | −0.291340 | −0.145670 | − | 0.989333i | \(-0.546534\pi\) | ||||
−0.145670 | + | 0.989333i | \(0.546534\pi\) | |||||||
\(158\) | −9.87630 | −0.785716 | ||||||||
\(159\) | −7.52678 | −0.596912 | ||||||||
\(160\) | −5.81272 | −0.459536 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.812716 | 0.0638530 | ||||||||
\(163\) | −9.18728 | −0.719604 | −0.359802 | − | 0.933029i | \(-0.617156\pi\) | ||||
−0.359802 | + | 0.933029i | \(0.617156\pi\) | |||||||
\(164\) | 1.33949 | 0.104597 | ||||||||
\(165\) | −5.15221 | −0.401099 | ||||||||
\(166\) | −12.4300 | −0.964755 | ||||||||
\(167\) | 7.72409 | 0.597708 | 0.298854 | − | 0.954299i | \(-0.403396\pi\) | ||||
0.298854 | + | 0.954299i | \(0.403396\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.21579 | −0.631984 | ||||||||
\(170\) | −4.76761 | −0.365659 | ||||||||
\(171\) | 5.33949 | 0.408321 | ||||||||
\(172\) | −12.1272 | −0.924687 | ||||||||
\(173\) | 5.03508 | 0.382810 | 0.191405 | − | 0.981511i | \(-0.438696\pi\) | ||||
0.191405 | + | 0.981511i | \(0.438696\pi\) | |||||||
\(174\) | 3.22236 | 0.244286 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.43815 | −0.183782 | ||||||||
\(177\) | −0.964925 | −0.0725282 | ||||||||
\(178\) | −3.07015 | −0.230118 | ||||||||
\(179\) | 3.52678 | 0.263604 | 0.131802 | − | 0.991276i | \(-0.457924\pi\) | ||||
0.131802 | + | 0.991276i | \(0.457924\pi\) | |||||||
\(180\) | 1.33949 | 0.0998399 | ||||||||
\(181\) | 15.9834 | 1.18804 | 0.594018 | − | 0.804451i | \(-0.297541\pi\) | ||||
0.594018 | + | 0.804451i | \(0.297541\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.90134 | 0.362318 | ||||||||
\(184\) | −20.3329 | −1.49896 | ||||||||
\(185\) | −9.96492 | −0.732636 | ||||||||
\(186\) | 3.88287 | 0.284706 | ||||||||
\(187\) | −30.2242 | −2.21022 | ||||||||
\(188\) | 11.3746 | 0.829576 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.33949 | −0.314820 | ||||||||
\(191\) | 17.7961 | 1.28768 | 0.643841 | − | 0.765159i | \(-0.277340\pi\) | ||||
0.643841 | + | 0.765159i | \(0.277340\pi\) | |||||||
\(192\) | −3.77764 | −0.272628 | ||||||||
\(193\) | −20.5202 | −1.47708 | −0.738538 | − | 0.674211i | \(-0.764484\pi\) | ||||
−0.738538 | + | 0.674211i | \(0.764484\pi\) | |||||||
\(194\) | −6.40120 | −0.459579 | ||||||||
\(195\) | −2.18728 | −0.156635 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.0185 | 0.785034 | 0.392517 | − | 0.919745i | \(-0.371604\pi\) | ||||
0.392517 | + | 0.919745i | \(0.371604\pi\) | |||||||
\(198\) | −4.18728 | −0.297577 | ||||||||
\(199\) | −20.4115 | −1.44693 | −0.723467 | − | 0.690359i | \(-0.757453\pi\) | ||||
−0.723467 | + | 0.690359i | \(0.757453\pi\) | |||||||
\(200\) | 10.8562 | 0.767652 | ||||||||
\(201\) | 2.47322 | 0.174448 | ||||||||
\(202\) | −3.22236 | −0.226724 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 7.85782 | 0.550158 | ||||||||
\(205\) | 1.00000 | 0.0698430 | ||||||||
\(206\) | 7.68555 | 0.535478 | ||||||||
\(207\) | 7.49170 | 0.520709 | ||||||||
\(208\) | −1.03508 | −0.0717696 | ||||||||
\(209\) | −27.5102 | −1.90292 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.3930 | −0.990858 | −0.495429 | − | 0.868648i | \(-0.664989\pi\) | ||||
−0.495429 | + | 0.868648i | \(0.664989\pi\) | |||||||
\(212\) | −10.0821 | −0.692439 | ||||||||
\(213\) | −16.0536 | −1.09997 | ||||||||
\(214\) | 3.91137 | 0.267376 | ||||||||
\(215\) | −9.05355 | −0.617447 | ||||||||
\(216\) | 2.71406 | 0.184668 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −10.7040 | −0.724968 | ||||||||
\(219\) | 3.66051 | 0.247354 | ||||||||
\(220\) | −6.90134 | −0.465288 | ||||||||
\(221\) | −12.8312 | −0.863119 | ||||||||
\(222\) | −8.09866 | −0.543546 | ||||||||
\(223\) | 15.2593 | 1.02184 | 0.510920 | − | 0.859629i | \(-0.329305\pi\) | ||||
0.510920 | + | 0.859629i | \(0.329305\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.00000 | −0.266667 | ||||||||
\(226\) | 3.91137 | 0.260181 | ||||||||
\(227\) | −13.4031 | −0.889593 | −0.444797 | − | 0.895632i | \(-0.646724\pi\) | ||||
−0.444797 | + | 0.895632i | \(0.646724\pi\) | |||||||
\(228\) | 7.15221 | 0.473667 | ||||||||
\(229\) | −23.9834 | −1.58487 | −0.792434 | − | 0.609958i | \(-0.791186\pi\) | ||||
−0.792434 | + | 0.609958i | \(0.791186\pi\) | |||||||
\(230\) | −6.08863 | −0.401472 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.7610 | 0.706497 | ||||||||
\(233\) | 20.4281 | 1.33829 | 0.669145 | − | 0.743132i | \(-0.266660\pi\) | ||||
0.669145 | + | 0.743132i | \(0.266660\pi\) | |||||||
\(234\) | −1.77764 | −0.116208 | ||||||||
\(235\) | 8.49170 | 0.553937 | ||||||||
\(236\) | −1.29251 | −0.0841352 | ||||||||
\(237\) | 12.1522 | 0.789371 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.6439 | −0.882551 | −0.441276 | − | 0.897372i | \(-0.645474\pi\) | ||||
−0.441276 | + | 0.897372i | \(0.645474\pi\) | |||||||
\(240\) | 0.473224 | 0.0305465 | ||||||||
\(241\) | −29.5988 | −1.90663 | −0.953313 | − | 0.301983i | \(-0.902351\pi\) | ||||
−0.953313 | + | 0.301983i | \(0.902351\pi\) | |||||||
\(242\) | 12.6339 | 0.812137 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 6.56531 | 0.420301 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.812716 | 0.0518169 | ||||||||
\(247\) | −11.6790 | −0.743116 | ||||||||
\(248\) | 12.9668 | 0.823393 | ||||||||
\(249\) | 15.2944 | 0.969242 | ||||||||
\(250\) | 7.31445 | 0.462606 | ||||||||
\(251\) | −8.96492 | −0.565861 | −0.282931 | − | 0.959140i | \(-0.591307\pi\) | ||||
−0.282931 | + | 0.959140i | \(0.591307\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −38.5988 | −2.42669 | ||||||||
\(254\) | −5.50015 | −0.345110 | ||||||||
\(255\) | 5.86627 | 0.367360 | ||||||||
\(256\) | −14.5083 | −0.906769 | ||||||||
\(257\) | 19.7510 | 1.23203 | 0.616017 | − | 0.787733i | \(-0.288745\pi\) | ||||
0.616017 | + | 0.787733i | \(0.288745\pi\) | |||||||
\(258\) | −7.35797 | −0.458087 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2.92985 | −0.181702 | ||||||||
\(261\) | −3.96492 | −0.245423 | ||||||||
\(262\) | −10.9133 | −0.674223 | ||||||||
\(263\) | −13.8763 | −0.855649 | −0.427825 | − | 0.903862i | \(-0.640720\pi\) | ||||
−0.427825 | + | 0.903862i | \(0.640720\pi\) | |||||||
\(264\) | −13.9834 | −0.860619 | ||||||||
\(265\) | −7.52678 | −0.462366 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.77764 | 0.231188 | ||||||||
\(268\) | 3.31286 | 0.202365 | ||||||||
\(269\) | −7.18728 | −0.438216 | −0.219108 | − | 0.975701i | \(-0.570315\pi\) | ||||
−0.219108 | + | 0.975701i | \(0.570315\pi\) | |||||||
\(270\) | 0.812716 | 0.0494603 | ||||||||
\(271\) | −6.09866 | −0.370467 | −0.185234 | − | 0.982695i | \(-0.559304\pi\) | ||||
−0.185234 | + | 0.982695i | \(0.559304\pi\) | |||||||
\(272\) | 2.77606 | 0.168323 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.52490 | −0.0921224 | ||||||||
\(275\) | 20.6088 | 1.24276 | ||||||||
\(276\) | 10.0351 | 0.604041 | ||||||||
\(277\) | 27.7426 | 1.66689 | 0.833445 | − | 0.552603i | \(-0.186365\pi\) | ||||
0.833445 | + | 0.552603i | \(0.186365\pi\) | |||||||
\(278\) | 3.62731 | 0.217552 | ||||||||
\(279\) | −4.77764 | −0.286030 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.25087 | −0.372895 | −0.186448 | − | 0.982465i | \(-0.559697\pi\) | ||||
−0.186448 | + | 0.982465i | \(0.559697\pi\) | |||||||
\(282\) | 6.90134 | 0.410969 | ||||||||
\(283\) | 16.4817 | 0.979734 | 0.489867 | − | 0.871797i | \(-0.337045\pi\) | ||||
0.489867 | + | 0.871797i | \(0.337045\pi\) | |||||||
\(284\) | −21.5036 | −1.27600 | ||||||||
\(285\) | 5.33949 | 0.316284 | ||||||||
\(286\) | 9.15878 | 0.541570 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 5.81272 | 0.342518 | ||||||||
\(289\) | 17.4131 | 1.02430 | ||||||||
\(290\) | 3.22236 | 0.189223 | ||||||||
\(291\) | 7.87630 | 0.461717 | ||||||||
\(292\) | 4.90322 | 0.286939 | ||||||||
\(293\) | 9.40307 | 0.549333 | 0.274667 | − | 0.961539i | \(-0.411432\pi\) | ||||
0.274667 | + | 0.961539i | \(0.411432\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.964925 | −0.0561801 | ||||||||
\(296\) | −27.0454 | −1.57198 | ||||||||
\(297\) | 5.15221 | 0.298961 | ||||||||
\(298\) | −10.4431 | −0.604955 | ||||||||
\(299\) | −16.3865 | −0.947654 | ||||||||
\(300\) | −5.35797 | −0.309342 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 4.86281 | 0.279823 | ||||||||
\(303\) | 3.96492 | 0.227779 | ||||||||
\(304\) | 2.52678 | 0.144921 | ||||||||
\(305\) | 4.90134 | 0.280650 | ||||||||
\(306\) | 4.76761 | 0.272546 | ||||||||
\(307\) | 9.03508 | 0.515659 | 0.257829 | − | 0.966190i | \(-0.416993\pi\) | ||||
0.257829 | + | 0.966190i | \(0.416993\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.45663 | −0.537969 | ||||||||
\(310\) | 3.88287 | 0.220532 | ||||||||
\(311\) | 2.26746 | 0.128576 | 0.0642880 | − | 0.997931i | \(-0.479522\pi\) | ||||
0.0642880 | + | 0.997931i | \(0.479522\pi\) | |||||||
\(312\) | −5.93642 | −0.336084 | ||||||||
\(313\) | 14.9649 | 0.845868 | 0.422934 | − | 0.906161i | \(-0.361000\pi\) | ||||
0.422934 | + | 0.906161i | \(0.361000\pi\) | |||||||
\(314\) | −2.96680 | −0.167426 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 16.2778 | 0.915697 | ||||||||
\(317\) | −14.3846 | −0.807919 | −0.403960 | − | 0.914777i | \(-0.632366\pi\) | ||||
−0.403960 | + | 0.914777i | \(0.632366\pi\) | |||||||
\(318\) | −6.11713 | −0.343032 | ||||||||
\(319\) | 20.4281 | 1.14376 | ||||||||
\(320\) | −3.77764 | −0.211177 | ||||||||
\(321\) | −4.81272 | −0.268620 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 31.3229 | 1.74285 | ||||||||
\(324\) | −1.33949 | −0.0744162 | ||||||||
\(325\) | 8.74913 | 0.485315 | ||||||||
\(326\) | −7.46666 | −0.413540 | ||||||||
\(327\) | 13.1707 | 0.728341 | ||||||||
\(328\) | 2.71406 | 0.149859 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −4.18728 | −0.230502 | ||||||||
\(331\) | 16.3830 | 0.900492 | 0.450246 | − | 0.892905i | \(-0.351336\pi\) | ||||
0.450246 | + | 0.892905i | \(0.351336\pi\) | |||||||
\(332\) | 20.4867 | 1.12435 | ||||||||
\(333\) | 9.96492 | 0.546075 | ||||||||
\(334\) | 6.27749 | 0.343489 | ||||||||
\(335\) | 2.47322 | 0.135127 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.2076 | 1.48209 | 0.741047 | − | 0.671453i | \(-0.234329\pi\) | ||||
0.741047 | + | 0.671453i | \(0.234329\pi\) | |||||||
\(338\) | −6.67711 | −0.363187 | ||||||||
\(339\) | −4.81272 | −0.261391 | ||||||||
\(340\) | 7.85782 | 0.426150 | ||||||||
\(341\) | 24.6154 | 1.33300 | ||||||||
\(342\) | 4.33949 | 0.234653 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −24.5719 | −1.32483 | ||||||||
\(345\) | 7.49170 | 0.403340 | ||||||||
\(346\) | 4.09209 | 0.219992 | ||||||||
\(347\) | −21.5703 | −1.15795 | −0.578977 | − | 0.815344i | \(-0.696548\pi\) | ||||
−0.578977 | + | 0.815344i | \(0.696548\pi\) | |||||||
\(348\) | −5.31099 | −0.284699 | ||||||||
\(349\) | −36.9734 | −1.97914 | −0.989570 | − | 0.144055i | \(-0.953986\pi\) | ||||
−0.989570 | + | 0.144055i | \(0.953986\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.18728 | 0.116749 | ||||||||
\(352\) | −29.9483 | −1.59625 | ||||||||
\(353\) | −5.98997 | −0.318814 | −0.159407 | − | 0.987213i | \(-0.550958\pi\) | ||||
−0.159407 | + | 0.987213i | \(0.550958\pi\) | |||||||
\(354\) | −0.784210 | −0.0416803 | ||||||||
\(355\) | −16.0536 | −0.852034 | ||||||||
\(356\) | 5.06012 | 0.268186 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.86627 | 0.151487 | ||||||||
\(359\) | 1.35609 | 0.0715717 | 0.0357859 | − | 0.999359i | \(-0.488607\pi\) | ||||
0.0357859 | + | 0.999359i | \(0.488607\pi\) | |||||||
\(360\) | 2.71406 | 0.143044 | ||||||||
\(361\) | 9.51018 | 0.500536 | ||||||||
\(362\) | 12.9900 | 0.682738 | ||||||||
\(363\) | −15.5453 | −0.815914 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.66051 | 0.191600 | ||||||||
\(366\) | 3.98340 | 0.208216 | ||||||||
\(367\) | 6.82275 | 0.356144 | 0.178072 | − | 0.984017i | \(-0.443014\pi\) | ||||
0.178072 | + | 0.984017i | \(0.443014\pi\) | |||||||
\(368\) | 3.54525 | 0.184809 | ||||||||
\(369\) | −1.00000 | −0.0520579 | ||||||||
\(370\) | −8.09866 | −0.421029 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −6.39961 | −0.331804 | ||||||||
\(373\) | 5.59036 | 0.289458 | 0.144729 | − | 0.989471i | \(-0.453769\pi\) | ||||
0.144729 | + | 0.989471i | \(0.453769\pi\) | |||||||
\(374\) | −24.5637 | −1.27016 | ||||||||
\(375\) | −9.00000 | −0.464758 | ||||||||
\(376\) | 23.0470 | 1.18856 | ||||||||
\(377\) | 8.67242 | 0.446652 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.10710 | 0.262334 | 0.131167 | − | 0.991360i | \(-0.458128\pi\) | ||||
0.131167 | + | 0.991360i | \(0.458128\pi\) | |||||||
\(380\) | 7.15221 | 0.366901 | ||||||||
\(381\) | 6.76761 | 0.346715 | ||||||||
\(382\) | 14.4632 | 0.740001 | ||||||||
\(383\) | −24.9483 | −1.27480 | −0.637400 | − | 0.770533i | \(-0.719990\pi\) | ||||
−0.637400 | + | 0.770533i | \(0.719990\pi\) | |||||||
\(384\) | 8.55528 | 0.436585 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −16.6771 | −0.848842 | ||||||||
\(387\) | 9.05355 | 0.460218 | ||||||||
\(388\) | 10.5502 | 0.535607 | ||||||||
\(389\) | −7.48167 | −0.379336 | −0.189668 | − | 0.981848i | \(-0.560741\pi\) | ||||
−0.189668 | + | 0.981848i | \(0.560741\pi\) | |||||||
\(390\) | −1.77764 | −0.0900144 | ||||||||
\(391\) | 43.9483 | 2.22256 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.4281 | 0.677359 | ||||||||
\(394\) | 8.95490 | 0.451141 | ||||||||
\(395\) | 12.1522 | 0.611444 | ||||||||
\(396\) | 6.90134 | 0.346806 | ||||||||
\(397\) | −26.2443 | −1.31716 | −0.658582 | − | 0.752509i | \(-0.728843\pi\) | ||||
−0.658582 | + | 0.752509i | \(0.728843\pi\) | |||||||
\(398\) | −16.5888 | −0.831520 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.89290 | −0.0946448 | ||||||||
\(401\) | 5.56531 | 0.277918 | 0.138959 | − | 0.990298i | \(-0.455624\pi\) | ||||
0.138959 | + | 0.990298i | \(0.455624\pi\) | |||||||
\(402\) | 2.01003 | 0.100251 | ||||||||
\(403\) | 10.4501 | 0.520554 | ||||||||
\(404\) | 5.31099 | 0.264231 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −51.3414 | −2.54490 | ||||||||
\(408\) | 15.9214 | 0.788227 | ||||||||
\(409\) | −33.9032 | −1.67641 | −0.838203 | − | 0.545358i | \(-0.816394\pi\) | ||||
−0.838203 | + | 0.545358i | \(0.816394\pi\) | |||||||
\(410\) | 0.812716 | 0.0401372 | ||||||||
\(411\) | 1.87630 | 0.0925509 | ||||||||
\(412\) | −12.6671 | −0.624062 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 6.08863 | 0.299240 | ||||||||
\(415\) | 15.2944 | 0.750772 | ||||||||
\(416\) | −12.7141 | −0.623358 | ||||||||
\(417\) | −4.46319 | −0.218564 | ||||||||
\(418\) | −22.3580 | −1.09356 | ||||||||
\(419\) | −18.1422 | −0.886303 | −0.443152 | − | 0.896447i | \(-0.646140\pi\) | ||||
−0.443152 | + | 0.896447i | \(0.646140\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.9483 | −1.45959 | −0.729796 | − | 0.683665i | \(-0.760385\pi\) | ||||
−0.729796 | + | 0.683665i | \(0.760385\pi\) | |||||||
\(422\) | −11.6975 | −0.569424 | ||||||||
\(423\) | −8.49170 | −0.412881 | ||||||||
\(424\) | −20.4281 | −0.992077 | ||||||||
\(425\) | −23.4651 | −1.13822 | ||||||||
\(426\) | −13.0470 | −0.632128 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −6.44660 | −0.311608 | ||||||||
\(429\) | −11.2693 | −0.544089 | ||||||||
\(430\) | −7.35797 | −0.354833 | ||||||||
\(431\) | 9.94833 | 0.479194 | 0.239597 | − | 0.970872i | \(-0.422985\pi\) | ||||
0.239597 | + | 0.970872i | \(0.422985\pi\) | |||||||
\(432\) | −0.473224 | −0.0227680 | ||||||||
\(433\) | −15.2593 | −0.733316 | −0.366658 | − | 0.930356i | \(-0.619498\pi\) | ||||
−0.366658 | + | 0.930356i | \(0.619498\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.96492 | −0.190104 | ||||||||
\(436\) | 17.6420 | 0.844900 | ||||||||
\(437\) | 40.0019 | 1.91355 | ||||||||
\(438\) | 2.97495 | 0.142149 | ||||||||
\(439\) | 6.37457 | 0.304242 | 0.152121 | − | 0.988362i | \(-0.451390\pi\) | ||||
0.152121 | + | 0.988362i | \(0.451390\pi\) | |||||||
\(440\) | −13.9834 | −0.666633 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −10.4281 | −0.496015 | ||||||||
\(443\) | −11.0720 | −0.526048 | −0.263024 | − | 0.964789i | \(-0.584720\pi\) | ||||
−0.263024 | + | 0.964789i | \(0.584720\pi\) | |||||||
\(444\) | 13.3479 | 0.633465 | ||||||||
\(445\) | 3.77764 | 0.179077 | ||||||||
\(446\) | 12.4015 | 0.587228 | ||||||||
\(447\) | 12.8497 | 0.607769 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −36.6173 | −1.72808 | −0.864038 | − | 0.503426i | \(-0.832073\pi\) | ||||
−0.864038 | + | 0.503426i | \(0.832073\pi\) | |||||||
\(450\) | −3.25087 | −0.153247 | ||||||||
\(451\) | 5.15221 | 0.242608 | ||||||||
\(452\) | −6.44660 | −0.303222 | ||||||||
\(453\) | −5.98340 | −0.281125 | ||||||||
\(454\) | −10.8929 | −0.511229 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 14.4917 | 0.678636 | ||||||||
\(457\) | 6.91794 | 0.323608 | 0.161804 | − | 0.986823i | \(-0.448269\pi\) | ||||
0.161804 | + | 0.986823i | \(0.448269\pi\) | |||||||
\(458\) | −19.4917 | −0.910787 | ||||||||
\(459\) | −5.86627 | −0.273814 | ||||||||
\(460\) | 10.0351 | 0.467888 | ||||||||
\(461\) | −18.7676 | −0.874095 | −0.437047 | − | 0.899438i | \(-0.643976\pi\) | ||||
−0.437047 | + | 0.899438i | \(0.643976\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.53334 | 0.164208 | 0.0821042 | − | 0.996624i | \(-0.473836\pi\) | ||||
0.0821042 | + | 0.996624i | \(0.473836\pi\) | |||||||
\(464\) | −1.87630 | −0.0871049 | ||||||||
\(465\) | −4.77764 | −0.221558 | ||||||||
\(466\) | 16.6023 | 0.769085 | ||||||||
\(467\) | −9.06358 | −0.419413 | −0.209706 | − | 0.977764i | \(-0.567251\pi\) | ||||
−0.209706 | + | 0.977764i | \(0.567251\pi\) | |||||||
\(468\) | 2.92985 | 0.135432 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 6.90134 | 0.318335 | ||||||||
\(471\) | 3.65048 | 0.168205 | ||||||||
\(472\) | −2.61886 | −0.120543 | ||||||||
\(473\) | −46.6458 | −2.14478 | ||||||||
\(474\) | 9.87630 | 0.453633 | ||||||||
\(475\) | −21.3580 | −0.979971 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.52678 | 0.344627 | ||||||||
\(478\) | −11.0886 | −0.507182 | ||||||||
\(479\) | 37.3063 | 1.70457 | 0.852284 | − | 0.523079i | \(-0.175217\pi\) | ||||
0.852284 | + | 0.523079i | \(0.175217\pi\) | |||||||
\(480\) | 5.81272 | 0.265313 | ||||||||
\(481\) | −21.7961 | −0.993817 | ||||||||
\(482\) | −24.0554 | −1.09569 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −20.8227 | −0.946488 | ||||||||
\(485\) | 7.87630 | 0.357644 | ||||||||
\(486\) | −0.812716 | −0.0368656 | ||||||||
\(487\) | 1.84779 | 0.0837314 | 0.0418657 | − | 0.999123i | \(-0.486670\pi\) | ||||
0.0418657 | + | 0.999123i | \(0.486670\pi\) | |||||||
\(488\) | 13.3025 | 0.602178 | ||||||||
\(489\) | 9.18728 | 0.415463 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.7610 | 0.711286 | 0.355643 | − | 0.934622i | \(-0.384262\pi\) | ||||
0.355643 | + | 0.934622i | \(0.384262\pi\) | |||||||
\(492\) | −1.33949 | −0.0603890 | ||||||||
\(493\) | −23.2593 | −1.04755 | ||||||||
\(494\) | −9.49170 | −0.427052 | ||||||||
\(495\) | 5.15221 | 0.231575 | ||||||||
\(496\) | −2.26089 | −0.101517 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 12.4300 | 0.557002 | ||||||||
\(499\) | −32.1071 | −1.43731 | −0.718656 | − | 0.695366i | \(-0.755242\pi\) | ||||
−0.718656 | + | 0.695366i | \(0.755242\pi\) | |||||||
\(500\) | −12.0554 | −0.539135 | ||||||||
\(501\) | −7.72409 | −0.345087 | ||||||||
\(502\) | −7.28594 | −0.325187 | ||||||||
\(503\) | 20.3680 | 0.908164 | 0.454082 | − | 0.890960i | \(-0.349967\pi\) | ||||
0.454082 | + | 0.890960i | \(0.349967\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.96492 | 0.176437 | ||||||||
\(506\) | −31.3699 | −1.39456 | ||||||||
\(507\) | 8.21579 | 0.364876 | ||||||||
\(508\) | 9.06516 | 0.402202 | ||||||||
\(509\) | −36.6339 | −1.62377 | −0.811884 | − | 0.583819i | \(-0.801558\pi\) | ||||
−0.811884 | + | 0.583819i | \(0.801558\pi\) | |||||||
\(510\) | 4.76761 | 0.211113 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 5.31943 | 0.235088 | ||||||||
\(513\) | −5.33949 | −0.235744 | ||||||||
\(514\) | 16.0520 | 0.708022 | ||||||||
\(515\) | −9.45663 | −0.416709 | ||||||||
\(516\) | 12.1272 | 0.533869 | ||||||||
\(517\) | 43.7510 | 1.92417 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.03508 | −0.221015 | ||||||||
\(520\) | −5.93642 | −0.260329 | ||||||||
\(521\) | −37.0536 | −1.62335 | −0.811673 | − | 0.584112i | \(-0.801443\pi\) | ||||
−0.811673 | + | 0.584112i | \(0.801443\pi\) | |||||||
\(522\) | −3.22236 | −0.141039 | ||||||||
\(523\) | 40.1090 | 1.75384 | 0.876922 | − | 0.480633i | \(-0.159593\pi\) | ||||
0.876922 | + | 0.480633i | \(0.159593\pi\) | |||||||
\(524\) | 17.9869 | 0.785760 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.2775 | −0.491722 | ||||||||
\(527\) | −28.0269 | −1.22087 | ||||||||
\(528\) | 2.43815 | 0.106107 | ||||||||
\(529\) | 33.1256 | 1.44024 | ||||||||
\(530\) | −6.11713 | −0.265711 | ||||||||
\(531\) | 0.964925 | 0.0418742 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.18728 | 0.0947418 | ||||||||
\(534\) | 3.07015 | 0.132858 | ||||||||
\(535\) | −4.81272 | −0.208072 | ||||||||
\(536\) | 6.71248 | 0.289935 | ||||||||
\(537\) | −3.52678 | −0.152192 | ||||||||
\(538\) | −5.84122 | −0.251833 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.33949 | −0.0576426 | ||||||||
\(541\) | −40.1506 | −1.72621 | −0.863105 | − | 0.505024i | \(-0.831484\pi\) | ||||
−0.863105 | + | 0.505024i | \(0.831484\pi\) | |||||||
\(542\) | −4.95648 | −0.212899 | ||||||||
\(543\) | −15.9834 | −0.685913 | ||||||||
\(544\) | 34.0990 | 1.46198 | ||||||||
\(545\) | 13.1707 | 0.564170 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.7260 | −0.800665 | −0.400332 | − | 0.916370i | \(-0.631105\pi\) | ||||
−0.400332 | + | 0.916370i | \(0.631105\pi\) | |||||||
\(548\) | 2.51329 | 0.107362 | ||||||||
\(549\) | −4.90134 | −0.209184 | ||||||||
\(550\) | 16.7491 | 0.714186 | ||||||||
\(551\) | −21.1707 | −0.901902 | ||||||||
\(552\) | 20.3329 | 0.865427 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 22.5468 | 0.957923 | ||||||||
\(555\) | 9.96492 | 0.422988 | ||||||||
\(556\) | −5.97841 | −0.253541 | ||||||||
\(557\) | 36.6993 | 1.55500 | 0.777500 | − | 0.628882i | \(-0.216487\pi\) | ||||
0.777500 | + | 0.628882i | \(0.216487\pi\) | |||||||
\(558\) | −3.88287 | −0.164375 | ||||||||
\(559\) | −19.8027 | −0.837564 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 30.2242 | 1.27607 | ||||||||
\(562\) | −5.08018 | −0.214294 | ||||||||
\(563\) | −1.11367 | −0.0469357 | −0.0234679 | − | 0.999725i | \(-0.507471\pi\) | ||||
−0.0234679 | + | 0.999725i | \(0.507471\pi\) | |||||||
\(564\) | −11.3746 | −0.478956 | ||||||||
\(565\) | −4.81272 | −0.202472 | ||||||||
\(566\) | 13.3949 | 0.563031 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −43.5703 | −1.82817 | ||||||||
\(569\) | 33.9568 | 1.42354 | 0.711771 | − | 0.702412i | \(-0.247893\pi\) | ||||
0.711771 | + | 0.702412i | \(0.247893\pi\) | |||||||
\(570\) | 4.33949 | 0.181761 | ||||||||
\(571\) | 3.14875 | 0.131771 | 0.0658855 | − | 0.997827i | \(-0.479013\pi\) | ||||
0.0658855 | + | 0.997827i | \(0.479013\pi\) | |||||||
\(572\) | −15.0952 | −0.631162 | ||||||||
\(573\) | −17.7961 | −0.743443 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −29.9668 | −1.24970 | ||||||||
\(576\) | 3.77764 | 0.157402 | ||||||||
\(577\) | 15.6724 | 0.652451 | 0.326226 | − | 0.945292i | \(-0.394223\pi\) | ||||
0.326226 | + | 0.945292i | \(0.394223\pi\) | |||||||
\(578\) | 14.1519 | 0.588642 | ||||||||
\(579\) | 20.5202 | 0.852791 | ||||||||
\(580\) | −5.31099 | −0.220527 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 6.40120 | 0.265338 | ||||||||
\(583\) | −38.7795 | −1.60608 | ||||||||
\(584\) | 9.93484 | 0.411106 | ||||||||
\(585\) | 2.18728 | 0.0904331 | ||||||||
\(586\) | 7.64203 | 0.315689 | ||||||||
\(587\) | 8.27937 | 0.341726 | 0.170863 | − | 0.985295i | \(-0.445344\pi\) | ||||
0.170863 | + | 0.985295i | \(0.445344\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −25.5102 | −1.05113 | ||||||||
\(590\) | −0.784210 | −0.0322854 | ||||||||
\(591\) | −11.0185 | −0.453240 | ||||||||
\(592\) | 4.71564 | 0.193812 | ||||||||
\(593\) | −1.74069 | −0.0714815 | −0.0357407 | − | 0.999361i | \(-0.511379\pi\) | ||||
−0.0357407 | + | 0.999361i | \(0.511379\pi\) | |||||||
\(594\) | 4.18728 | 0.171806 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 17.2120 | 0.705032 | ||||||||
\(597\) | 20.4115 | 0.835388 | ||||||||
\(598\) | −13.3176 | −0.544595 | ||||||||
\(599\) | 22.0185 | 0.899651 | 0.449825 | − | 0.893117i | \(-0.351486\pi\) | ||||
0.449825 | + | 0.893117i | \(0.351486\pi\) | |||||||
\(600\) | −10.8562 | −0.443204 | ||||||||
\(601\) | −47.2963 | −1.92925 | −0.964627 | − | 0.263617i | \(-0.915085\pi\) | ||||
−0.964627 | + | 0.263617i | \(0.915085\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.47322 | −0.100717 | ||||||||
\(604\) | −8.01472 | −0.326114 | ||||||||
\(605\) | −15.5453 | −0.632004 | ||||||||
\(606\) | 3.22236 | 0.130899 | ||||||||
\(607\) | 6.67242 | 0.270825 | 0.135412 | − | 0.990789i | \(-0.456764\pi\) | ||||
0.135412 | + | 0.990789i | \(0.456764\pi\) | |||||||
\(608\) | 31.0370 | 1.25871 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.98340 | 0.161283 | ||||||||
\(611\) | 18.5738 | 0.751414 | ||||||||
\(612\) | −7.85782 | −0.317634 | ||||||||
\(613\) | −25.1873 | −1.01730 | −0.508652 | − | 0.860972i | \(-0.669856\pi\) | ||||
−0.508652 | + | 0.860972i | \(0.669856\pi\) | |||||||
\(614\) | 7.34295 | 0.296337 | ||||||||
\(615\) | −1.00000 | −0.0403239 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.51176 | 0.101120 | 0.0505598 | − | 0.998721i | \(-0.483899\pi\) | ||||
0.0505598 | + | 0.998721i | \(0.483899\pi\) | |||||||
\(618\) | −7.68555 | −0.309158 | ||||||||
\(619\) | −0.287819 | −0.0115684 | −0.00578420 | − | 0.999983i | \(-0.501841\pi\) | ||||
−0.00578420 | + | 0.999983i | \(0.501841\pi\) | |||||||
\(620\) | −6.39961 | −0.257015 | ||||||||
\(621\) | −7.49170 | −0.300632 | ||||||||
\(622\) | 1.84280 | 0.0738897 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.03508 | 0.0414362 | ||||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | 12.1622 | 0.486101 | ||||||||
\(627\) | 27.5102 | 1.09865 | ||||||||
\(628\) | 4.88979 | 0.195124 | ||||||||
\(629\) | 58.4569 | 2.33083 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.6358 | −1.33902 | −0.669509 | − | 0.742804i | \(-0.733496\pi\) | ||||
−0.669509 | + | 0.742804i | \(0.733496\pi\) | |||||||
\(632\) | 32.9818 | 1.31195 | ||||||||
\(633\) | 14.3930 | 0.572072 | ||||||||
\(634\) | −11.6906 | −0.464293 | ||||||||
\(635\) | 6.76761 | 0.268564 | ||||||||
\(636\) | 10.0821 | 0.399780 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 16.6023 | 0.657290 | ||||||||
\(639\) | 16.0536 | 0.635069 | ||||||||
\(640\) | 8.55528 | 0.338177 | ||||||||
\(641\) | 43.9934 | 1.73764 | 0.868818 | − | 0.495132i | \(-0.164880\pi\) | ||||
0.868818 | + | 0.495132i | \(0.164880\pi\) | |||||||
\(642\) | −3.91137 | −0.154370 | ||||||||
\(643\) | −8.74257 | −0.344773 | −0.172387 | − | 0.985029i | \(-0.555148\pi\) | ||||
−0.172387 | + | 0.985029i | \(0.555148\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.05355 | 0.356483 | ||||||||
\(646\) | 25.4566 | 1.00158 | ||||||||
\(647\) | −21.0720 | −0.828427 | −0.414213 | − | 0.910180i | \(-0.635943\pi\) | ||||
−0.414213 | + | 0.910180i | \(0.635943\pi\) | |||||||
\(648\) | −2.71406 | −0.106618 | ||||||||
\(649\) | −4.97149 | −0.195148 | ||||||||
\(650\) | 7.11056 | 0.278899 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.3063 | 0.481952 | ||||||||
\(653\) | 29.1237 | 1.13970 | 0.569849 | − | 0.821749i | \(-0.307002\pi\) | ||||
0.569849 | + | 0.821749i | \(0.307002\pi\) | |||||||
\(654\) | 10.7040 | 0.418561 | ||||||||
\(655\) | 13.4281 | 0.524680 | ||||||||
\(656\) | −0.473224 | −0.0184763 | ||||||||
\(657\) | −3.66051 | −0.142810 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 31.8681 | 1.24141 | 0.620703 | − | 0.784045i | \(-0.286847\pi\) | ||||
0.620703 | + | 0.784045i | \(0.286847\pi\) | |||||||
\(660\) | 6.90134 | 0.268634 | ||||||||
\(661\) | 7.91137 | 0.307717 | 0.153858 | − | 0.988093i | \(-0.450830\pi\) | ||||
0.153858 | + | 0.988093i | \(0.450830\pi\) | |||||||
\(662\) | 13.3147 | 0.517492 | ||||||||
\(663\) | 12.8312 | 0.498322 | ||||||||
\(664\) | 41.5099 | 1.61090 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.09866 | 0.313817 | ||||||||
\(667\) | −29.7040 | −1.15014 | ||||||||
\(668\) | −10.3464 | −0.400313 | ||||||||
\(669\) | −15.2593 | −0.589959 | ||||||||
\(670\) | 2.01003 | 0.0776542 | ||||||||
\(671\) | 25.2527 | 0.974871 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.4150 | 1.24951 | 0.624753 | − | 0.780823i | \(-0.285200\pi\) | ||||
0.624753 | + | 0.780823i | \(0.285200\pi\) | |||||||
\(674\) | 22.1121 | 0.851726 | ||||||||
\(675\) | 4.00000 | 0.153960 | ||||||||
\(676\) | 11.0050 | 0.423269 | ||||||||
\(677\) | −26.5368 | −1.01989 | −0.509946 | − | 0.860206i | \(-0.670335\pi\) | ||||
−0.509946 | + | 0.860206i | \(0.670335\pi\) | |||||||
\(678\) | −3.91137 | −0.150215 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 15.9214 | 0.610558 | ||||||||
\(681\) | 13.4031 | 0.513607 | ||||||||
\(682\) | 20.0053 | 0.766044 | ||||||||
\(683\) | −39.6624 | −1.51764 | −0.758820 | − | 0.651301i | \(-0.774224\pi\) | ||||
−0.758820 | + | 0.651301i | \(0.774224\pi\) | |||||||
\(684\) | −7.15221 | −0.273472 | ||||||||
\(685\) | 1.87630 | 0.0716896 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 23.9834 | 0.915024 | ||||||||
\(688\) | 4.28436 | 0.163340 | ||||||||
\(689\) | −16.4632 | −0.627198 | ||||||||
\(690\) | 6.08863 | 0.231790 | ||||||||
\(691\) | −34.3930 | −1.30837 | −0.654187 | − | 0.756333i | \(-0.726989\pi\) | ||||
−0.654187 | + | 0.756333i | \(0.726989\pi\) | |||||||
\(692\) | −6.74444 | −0.256385 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −17.5305 | −0.665450 | ||||||||
\(695\) | −4.46319 | −0.169299 | ||||||||
\(696\) | −10.7610 | −0.407896 | ||||||||
\(697\) | −5.86627 | −0.222201 | ||||||||
\(698\) | −30.0489 | −1.13737 | ||||||||
\(699\) | −20.4281 | −0.772662 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.3949 | −0.694767 | −0.347383 | − | 0.937723i | \(-0.612930\pi\) | ||||
−0.347383 | + | 0.937723i | \(0.612930\pi\) | |||||||
\(702\) | 1.77764 | 0.0670927 | ||||||||
\(703\) | 53.2076 | 2.00676 | ||||||||
\(704\) | −19.4632 | −0.733547 | ||||||||
\(705\) | −8.49170 | −0.319816 | ||||||||
\(706\) | −4.86815 | −0.183215 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.29251 | 0.0485755 | ||||||||
\(709\) | −8.34606 | −0.313443 | −0.156721 | − | 0.987643i | \(-0.550092\pi\) | ||||
−0.156721 | + | 0.987643i | \(0.550092\pi\) | |||||||
\(710\) | −13.0470 | −0.489645 | ||||||||
\(711\) | −12.1522 | −0.455743 | ||||||||
\(712\) | 10.2527 | 0.384238 | ||||||||
\(713\) | −35.7927 | −1.34045 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.2693 | −0.421449 | ||||||||
\(716\) | −4.72409 | −0.176547 | ||||||||
\(717\) | 13.6439 | 0.509541 | ||||||||
\(718\) | 1.10212 | 0.0411306 | ||||||||
\(719\) | −29.1541 | −1.08726 | −0.543632 | − | 0.839324i | \(-0.682951\pi\) | ||||
−0.543632 | + | 0.839324i | \(0.682951\pi\) | |||||||
\(720\) | −0.473224 | −0.0176360 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 7.72908 | 0.287646 | ||||||||
\(723\) | 29.5988 | 1.10079 | ||||||||
\(724\) | −21.4096 | −0.795683 | ||||||||
\(725\) | 15.8597 | 0.589014 | ||||||||
\(726\) | −12.6339 | −0.468887 | ||||||||
\(727\) | 23.9298 | 0.887509 | 0.443754 | − | 0.896148i | \(-0.353646\pi\) | ||||
0.443754 | + | 0.896148i | \(0.353646\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.97495 | 0.110108 | ||||||||
\(731\) | 53.1106 | 1.96437 | ||||||||
\(732\) | −6.56531 | −0.242661 | ||||||||
\(733\) | −10.1672 | −0.375535 | −0.187768 | − | 0.982214i | \(-0.560125\pi\) | ||||
−0.187768 | + | 0.982214i | \(0.560125\pi\) | |||||||
\(734\) | 5.54496 | 0.204668 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 43.5471 | 1.60517 | ||||||||
\(737\) | 12.7426 | 0.469378 | ||||||||
\(738\) | −0.812716 | −0.0299165 | ||||||||
\(739\) | −23.3664 | −0.859548 | −0.429774 | − | 0.902937i | \(-0.641407\pi\) | ||||
−0.429774 | + | 0.902937i | \(0.641407\pi\) | |||||||
\(740\) | 13.3479 | 0.490680 | ||||||||
\(741\) | 11.6790 | 0.429038 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.7861 | 0.872627 | 0.436313 | − | 0.899795i | \(-0.356284\pi\) | ||||
0.436313 | + | 0.899795i | \(0.356284\pi\) | |||||||
\(744\) | −12.9668 | −0.475386 | ||||||||
\(745\) | 12.8497 | 0.470775 | ||||||||
\(746\) | 4.54337 | 0.166345 | ||||||||
\(747\) | −15.2944 | −0.559592 | ||||||||
\(748\) | 40.4851 | 1.48028 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −7.31445 | −0.267086 | ||||||||
\(751\) | 22.9233 | 0.836482 | 0.418241 | − | 0.908336i | \(-0.362647\pi\) | ||||
0.418241 | + | 0.908336i | \(0.362647\pi\) | |||||||
\(752\) | −4.01848 | −0.146539 | ||||||||
\(753\) | 8.96492 | 0.326700 | ||||||||
\(754\) | 7.04821 | 0.256681 | ||||||||
\(755\) | −5.98340 | −0.217758 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.4632 | −0.743747 | −0.371874 | − | 0.928283i | \(-0.621285\pi\) | ||||
−0.371874 | + | 0.928283i | \(0.621285\pi\) | |||||||
\(758\) | 4.15063 | 0.150758 | ||||||||
\(759\) | 38.5988 | 1.40105 | ||||||||
\(760\) | 14.4917 | 0.525669 | ||||||||
\(761\) | 42.6154 | 1.54481 | 0.772404 | − | 0.635132i | \(-0.219054\pi\) | ||||
0.772404 | + | 0.635132i | \(0.219054\pi\) | |||||||
\(762\) | 5.50015 | 0.199249 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −23.8378 | −0.862420 | ||||||||
\(765\) | −5.86627 | −0.212095 | ||||||||
\(766\) | −20.2759 | −0.732598 | ||||||||
\(767\) | −2.11056 | −0.0762081 | ||||||||
\(768\) | 14.5083 | 0.523523 | ||||||||
\(769\) | 47.4735 | 1.71194 | 0.855969 | − | 0.517026i | \(-0.172961\pi\) | ||||
0.855969 | + | 0.517026i | \(0.172961\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.7510 | −0.711315 | ||||||||
\(772\) | 27.4867 | 0.989266 | ||||||||
\(773\) | −36.0119 | −1.29526 | −0.647629 | − | 0.761956i | \(-0.724239\pi\) | ||||
−0.647629 | + | 0.761956i | \(0.724239\pi\) | |||||||
\(774\) | 7.35797 | 0.264477 | ||||||||
\(775\) | 19.1106 | 0.686472 | ||||||||
\(776\) | 21.3767 | 0.767380 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.08048 | −0.217996 | ||||||||
\(779\) | −5.33949 | −0.191307 | ||||||||
\(780\) | 2.92985 | 0.104905 | ||||||||
\(781\) | −82.7112 | −2.95964 | ||||||||
\(782\) | 35.7175 | 1.27726 | ||||||||
\(783\) | 3.96492 | 0.141695 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.65048 | 0.130291 | ||||||||
\(786\) | 10.9133 | 0.389263 | ||||||||
\(787\) | 7.66896 | 0.273369 | 0.136684 | − | 0.990615i | \(-0.456355\pi\) | ||||
0.136684 | + | 0.990615i | \(0.456355\pi\) | |||||||
\(788\) | −14.7592 | −0.525773 | ||||||||
\(789\) | 13.8763 | 0.494009 | ||||||||
\(790\) | 9.87630 | 0.351383 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 13.9834 | 0.496879 | ||||||||
\(793\) | 10.7206 | 0.380701 | ||||||||
\(794\) | −21.3292 | −0.756944 | ||||||||
\(795\) | 7.52678 | 0.266947 | ||||||||
\(796\) | 27.3411 | 0.969079 | ||||||||
\(797\) | −17.0035 | −0.602293 | −0.301147 | − | 0.953578i | \(-0.597369\pi\) | ||||
−0.301147 | + | 0.953578i | \(0.597369\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −49.8146 | −1.76231 | ||||||||
\(800\) | −23.2509 | −0.822042 | ||||||||
\(801\) | −3.77764 | −0.133476 | ||||||||
\(802\) | 4.52302 | 0.159713 | ||||||||
\(803\) | 18.8597 | 0.665544 | ||||||||
\(804\) | −3.31286 | −0.116836 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 8.49293 | 0.299151 | ||||||||
\(807\) | 7.18728 | 0.253004 | ||||||||
\(808\) | 10.7610 | 0.378572 | ||||||||
\(809\) | −8.73066 | −0.306954 | −0.153477 | − | 0.988152i | \(-0.549047\pi\) | ||||
−0.153477 | + | 0.988152i | \(0.549047\pi\) | |||||||
\(810\) | −0.812716 | −0.0285559 | ||||||||
\(811\) | 20.6339 | 0.724554 | 0.362277 | − | 0.932071i | \(-0.382000\pi\) | ||||
0.362277 | + | 0.932071i | \(0.382000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.09866 | 0.213889 | ||||||||
\(814\) | −41.7260 | −1.46249 | ||||||||
\(815\) | 9.18728 | 0.321817 | ||||||||
\(816\) | −2.77606 | −0.0971815 | ||||||||
\(817\) | 48.3414 | 1.69125 | ||||||||
\(818\) | −27.5537 | −0.963393 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.33949 | −0.0467771 | ||||||||
\(821\) | 26.7360 | 0.933093 | 0.466546 | − | 0.884497i | \(-0.345498\pi\) | ||||
0.466546 | + | 0.884497i | \(0.345498\pi\) | |||||||
\(822\) | 1.52490 | 0.0531869 | ||||||||
\(823\) | −48.7595 | −1.69965 | −0.849824 | − | 0.527067i | \(-0.823292\pi\) | ||||
−0.849824 | + | 0.527067i | \(0.823292\pi\) | |||||||
\(824\) | −25.6658 | −0.894112 | ||||||||
\(825\) | −20.6088 | −0.717508 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.2427 | 0.460494 | 0.230247 | − | 0.973132i | \(-0.426047\pi\) | ||||
0.230247 | + | 0.973132i | \(0.426047\pi\) | |||||||
\(828\) | −10.0351 | −0.348743 | ||||||||
\(829\) | −11.5619 | −0.401560 | −0.200780 | − | 0.979636i | \(-0.564348\pi\) | ||||
−0.200780 | + | 0.979636i | \(0.564348\pi\) | |||||||
\(830\) | 12.4300 | 0.431452 | ||||||||
\(831\) | −27.7426 | −0.962379 | ||||||||
\(832\) | −8.26277 | −0.286460 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −3.62731 | −0.125604 | ||||||||
\(835\) | −7.72409 | −0.267303 | ||||||||
\(836\) | 36.8497 | 1.27447 | ||||||||
\(837\) | 4.77764 | 0.165139 | ||||||||
\(838\) | −14.7444 | −0.509338 | ||||||||
\(839\) | 36.1375 | 1.24760 | 0.623802 | − | 0.781582i | \(-0.285587\pi\) | ||||
0.623802 | + | 0.781582i | \(0.285587\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.2794 | −0.457909 | ||||||||
\(842\) | −24.3395 | −0.838794 | ||||||||
\(843\) | 6.25087 | 0.215291 | ||||||||
\(844\) | 19.2794 | 0.663623 | ||||||||
\(845\) | 8.21579 | 0.282632 | ||||||||
\(846\) | −6.90134 | −0.237273 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3.56185 | 0.122314 | ||||||||
\(849\) | −16.4817 | −0.565649 | ||||||||
\(850\) | −19.0704 | −0.654111 | ||||||||
\(851\) | 74.6542 | 2.55911 | ||||||||
\(852\) | 21.5036 | 0.736701 | ||||||||
\(853\) | −38.2593 | −1.30997 | −0.654987 | − | 0.755640i | \(-0.727326\pi\) | ||||
−0.654987 | + | 0.755640i | \(0.727326\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.33949 | −0.182607 | ||||||||
\(856\) | −13.0620 | −0.446450 | ||||||||
\(857\) | 30.8431 | 1.05358 | 0.526790 | − | 0.849995i | \(-0.323395\pi\) | ||||
0.526790 | + | 0.849995i | \(0.323395\pi\) | |||||||
\(858\) | −9.15878 | −0.312676 | ||||||||
\(859\) | −13.7942 | −0.470653 | −0.235327 | − | 0.971916i | \(-0.575616\pi\) | ||||
−0.235327 | + | 0.971916i | \(0.575616\pi\) | |||||||
\(860\) | 12.1272 | 0.413533 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8.08517 | 0.275382 | ||||||||
\(863\) | −18.3295 | −0.623942 | −0.311971 | − | 0.950092i | \(-0.600989\pi\) | ||||
−0.311971 | + | 0.950092i | \(0.600989\pi\) | |||||||
\(864\) | −5.81272 | −0.197753 | ||||||||
\(865\) | −5.03508 | −0.171198 | ||||||||
\(866\) | −12.4015 | −0.421420 | ||||||||
\(867\) | −17.4131 | −0.591380 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 62.6107 | 2.12392 | ||||||||
\(870\) | −3.22236 | −0.109248 | ||||||||
\(871\) | 5.40964 | 0.183299 | ||||||||
\(872\) | 35.7460 | 1.21051 | ||||||||
\(873\) | −7.87630 | −0.266572 | ||||||||
\(874\) | 32.5102 | 1.09967 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.90322 | −0.165665 | ||||||||
\(877\) | −20.6373 | −0.696873 | −0.348437 | − | 0.937332i | \(-0.613287\pi\) | ||||
−0.348437 | + | 0.937332i | \(0.613287\pi\) | |||||||
\(878\) | 5.18071 | 0.174841 | ||||||||
\(879\) | −9.40307 | −0.317158 | ||||||||
\(880\) | 2.43815 | 0.0821900 | ||||||||
\(881\) | −40.6007 | −1.36787 | −0.683936 | − | 0.729542i | \(-0.739733\pi\) | ||||
−0.683936 | + | 0.729542i | \(0.739733\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 54.8431 | 1.84562 | 0.922809 | − | 0.385259i | \(-0.125888\pi\) | ||||
0.922809 | + | 0.385259i | \(0.125888\pi\) | |||||||
\(884\) | 17.1873 | 0.578071 | ||||||||
\(885\) | 0.964925 | 0.0324356 | ||||||||
\(886\) | −8.99842 | −0.302308 | ||||||||
\(887\) | 56.1910 | 1.88671 | 0.943355 | − | 0.331784i | \(-0.107651\pi\) | ||||
0.943355 | + | 0.331784i | \(0.107651\pi\) | |||||||
\(888\) | 27.0454 | 0.907584 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 3.07015 | 0.102912 | ||||||||
\(891\) | −5.15221 | −0.172605 | ||||||||
\(892\) | −20.4397 | −0.684373 | ||||||||
\(893\) | −45.3414 | −1.51729 | ||||||||
\(894\) | 10.4431 | 0.349271 | ||||||||
\(895\) | −3.52678 | −0.117887 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16.3865 | 0.547128 | ||||||||
\(898\) | −29.7595 | −0.993086 | ||||||||
\(899\) | 18.9430 | 0.631784 | ||||||||
\(900\) | 5.35797 | 0.178599 | ||||||||
\(901\) | 44.1541 | 1.47099 | ||||||||
\(902\) | 4.18728 | 0.139421 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13.0620 | −0.434436 | ||||||||
\(905\) | −15.9834 | −0.531306 | ||||||||
\(906\) | −4.86281 | −0.161556 | ||||||||
\(907\) | 18.0620 | 0.599739 | 0.299869 | − | 0.953980i | \(-0.403057\pi\) | ||||
0.299869 | + | 0.953980i | \(0.403057\pi\) | |||||||
\(908\) | 17.9533 | 0.595802 | ||||||||
\(909\) | −3.96492 | −0.131508 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.1337 | 0.402008 | 0.201004 | − | 0.979590i | \(-0.435579\pi\) | ||||
0.201004 | + | 0.979590i | \(0.435579\pi\) | |||||||
\(912\) | −2.52678 | −0.0836699 | ||||||||
\(913\) | 78.7999 | 2.60790 | ||||||||
\(914\) | 5.62232 | 0.185970 | ||||||||
\(915\) | −4.90134 | −0.162033 | ||||||||
\(916\) | 32.1256 | 1.06146 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −4.76761 | −0.157355 | ||||||||
\(919\) | −55.1475 | −1.81915 | −0.909574 | − | 0.415541i | \(-0.863592\pi\) | ||||
−0.909574 | + | 0.415541i | \(0.863592\pi\) | |||||||
\(920\) | 20.3329 | 0.670357 | ||||||||
\(921\) | −9.03508 | −0.297716 | ||||||||
\(922\) | −15.2527 | −0.502322 | ||||||||
\(923\) | −35.1137 | −1.15578 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −39.8597 | −1.31058 | ||||||||
\(926\) | 2.87161 | 0.0943669 | ||||||||
\(927\) | 9.45663 | 0.310596 | ||||||||
\(928\) | −23.0470 | −0.756554 | ||||||||
\(929\) | −14.3545 | −0.470956 | −0.235478 | − | 0.971880i | \(-0.575666\pi\) | ||||
−0.235478 | + | 0.971880i | \(0.575666\pi\) | |||||||
\(930\) | −3.88287 | −0.127324 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −27.3633 | −0.896315 | ||||||||
\(933\) | −2.26746 | −0.0742334 | ||||||||
\(934\) | −7.36612 | −0.241027 | ||||||||
\(935\) | 30.2242 | 0.988438 | ||||||||
\(936\) | 5.93642 | 0.194038 | ||||||||
\(937\) | −55.8331 | −1.82399 | −0.911993 | − | 0.410205i | \(-0.865457\pi\) | ||||
−0.911993 | + | 0.410205i | \(0.865457\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14.9649 | −0.488362 | ||||||||
\(940\) | −11.3746 | −0.370997 | ||||||||
\(941\) | −32.8697 | −1.07152 | −0.535761 | − | 0.844370i | \(-0.679975\pi\) | ||||
−0.535761 | + | 0.844370i | \(0.679975\pi\) | |||||||
\(942\) | 2.96680 | 0.0966637 | ||||||||
\(943\) | −7.49170 | −0.243963 | ||||||||
\(944\) | 0.456626 | 0.0148619 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −37.9098 | −1.23255 | ||||||||
\(947\) | 12.6355 | 0.410597 | 0.205299 | − | 0.978699i | \(-0.434183\pi\) | ||||
0.205299 | + | 0.978699i | \(0.434183\pi\) | |||||||
\(948\) | −16.2778 | −0.528678 | ||||||||
\(949\) | 8.00657 | 0.259904 | ||||||||
\(950\) | −17.3580 | −0.563167 | ||||||||
\(951\) | 14.3846 | 0.466453 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42.7125 | 1.38359 | 0.691796 | − | 0.722093i | \(-0.256820\pi\) | ||||
0.691796 | + | 0.722093i | \(0.256820\pi\) | |||||||
\(954\) | 6.11713 | 0.198050 | ||||||||
\(955\) | −17.7961 | −0.575869 | ||||||||
\(956\) | 18.2759 | 0.591085 | ||||||||
\(957\) | −20.4281 | −0.660347 | ||||||||
\(958\) | 30.3194 | 0.979576 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 3.77764 | 0.121923 | ||||||||
\(961\) | −8.17415 | −0.263682 | ||||||||
\(962\) | −17.7141 | −0.571124 | ||||||||
\(963\) | 4.81272 | 0.155088 | ||||||||
\(964\) | 39.6474 | 1.27696 | ||||||||
\(965\) | 20.5202 | 0.660569 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.3764 | 1.55568 | 0.777841 | − | 0.628461i | \(-0.216315\pi\) | ||||
0.777841 | + | 0.628461i | \(0.216315\pi\) | |||||||
\(968\) | −42.1907 | −1.35606 | ||||||||
\(969\) | −31.3229 | −1.00624 | ||||||||
\(970\) | 6.40120 | 0.205530 | ||||||||
\(971\) | 18.8681 | 0.605508 | 0.302754 | − | 0.953069i | \(-0.402094\pi\) | ||||
0.302754 | + | 0.953069i | \(0.402094\pi\) | |||||||
\(972\) | 1.33949 | 0.0429642 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1.50173 | 0.0481185 | ||||||||
\(975\) | −8.74913 | −0.280197 | ||||||||
\(976\) | −2.31943 | −0.0742433 | ||||||||
\(977\) | −15.8513 | −0.507126 | −0.253563 | − | 0.967319i | \(-0.581603\pi\) | ||||
−0.253563 | + | 0.967319i | \(0.581603\pi\) | |||||||
\(978\) | 7.46666 | 0.238757 | ||||||||
\(979\) | 19.4632 | 0.622046 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.1707 | −0.420508 | ||||||||
\(982\) | 12.8093 | 0.408760 | ||||||||
\(983\) | 7.71406 | 0.246040 | 0.123020 | − | 0.992404i | \(-0.460742\pi\) | ||||
0.123020 | + | 0.992404i | \(0.460742\pi\) | |||||||
\(984\) | −2.71406 | −0.0865211 | ||||||||
\(985\) | −11.0185 | −0.351078 | ||||||||
\(986\) | −18.9032 | −0.602001 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 15.6439 | 0.497699 | ||||||||
\(989\) | 67.8265 | 2.15676 | ||||||||
\(990\) | 4.18728 | 0.133081 | ||||||||
\(991\) | −0.611943 | −0.0194390 | −0.00971950 | − | 0.999953i | \(-0.503094\pi\) | ||||
−0.00971950 | + | 0.999953i | \(0.503094\pi\) | |||||||
\(992\) | −27.7711 | −0.881732 | ||||||||
\(993\) | −16.3830 | −0.519899 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.4115 | 0.647089 | ||||||||
\(996\) | −20.4867 | −0.649146 | ||||||||
\(997\) | 25.8866 | 0.819838 | 0.409919 | − | 0.912122i | \(-0.365557\pi\) | ||||
0.409919 | + | 0.912122i | \(0.365557\pi\) | |||||||
\(998\) | −26.0940 | −0.825990 | ||||||||
\(999\) | −9.96492 | −0.315276 |
(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 | 6027.2.a.r.1.2 | 3 | ||
7.2 | even | 3 | 861.2.i.b.739.2 | yes | 6 | ||
7.4 | even | 3 | 861.2.i.b.247.2 | ✓ | 6 | ||
7.6 | odd | 2 | 6027.2.a.t.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
861.2.i.b.247.2 | ✓ | 6 | 7.4 | even | 3 | ||
861.2.i.b.739.2 | yes | 6 | 7.2 | even | 3 | ||
6027.2.a.r.1.2 | 3 | 1.1 | even | 1 | trivial | ||
6027.2.a.t.1.2 | 3 | 7.6 | odd | 2 |