Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1968,2,Mod(1,1968)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1968, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1968.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1968 = 2^{4} \cdot 3 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1968.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: | \(15.7145591178\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.316.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 123) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.81361\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1968.1 |
$q$-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 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.10278 | −0.493176 | −0.246588 | − | 0.969120i | \(-0.579309\pi\) | ||||
−0.246588 | + | 0.969120i | \(0.579309\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.52444 | −0.954148 | −0.477074 | − | 0.878863i | \(-0.658303\pi\) | ||||
−0.477074 | + | 0.878863i | \(0.658303\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.813607 | −0.245312 | −0.122656 | − | 0.992449i | \(-0.539141\pi\) | ||||
−0.122656 | + | 0.992449i | \(0.539141\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.10278 | 1.41526 | 0.707628 | − | 0.706586i | \(-0.249765\pi\) | ||||
0.707628 | + | 0.706586i | \(0.249765\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.10278 | −0.284735 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.39194 | 0.822667 | 0.411334 | − | 0.911485i | \(-0.365063\pi\) | ||||
0.411334 | + | 0.911485i | \(0.365063\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.10278 | −0.711825 | −0.355913 | − | 0.934519i | \(-0.615830\pi\) | ||||
−0.355913 | + | 0.934519i | \(0.615830\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.52444 | −0.550878 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.897225 | 0.187084 | 0.0935422 | − | 0.995615i | \(-0.470181\pi\) | ||||
0.0935422 | + | 0.995615i | \(0.470181\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.78389 | −0.756777 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.44082 | 0.824639 | 0.412320 | − | 0.911039i | \(-0.364719\pi\) | ||||
0.412320 | + | 0.911039i | \(0.364719\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.96526 | 1.61021 | 0.805104 | − | 0.593134i | \(-0.202110\pi\) | ||||
0.805104 | + | 0.593134i | \(0.202110\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.813607 | −0.141631 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.78389 | 0.470563 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.08362 | 0.342545 | 0.171272 | − | 0.985224i | \(-0.445212\pi\) | ||||
0.171272 | + | 0.985224i | \(0.445212\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.10278 | 0.817098 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.07306 | −1.38363 | −0.691814 | − | 0.722076i | \(-0.743188\pi\) | ||||
−0.691814 | + | 0.722076i | \(0.743188\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.10278 | −0.164392 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.235269 | 0.0343176 | 0.0171588 | − | 0.999853i | \(-0.494538\pi\) | ||||
0.0171588 | + | 0.999853i | \(0.494538\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.627213 | −0.0896019 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.39194 | 0.474967 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.8328 | 1.90008 | 0.950038 | − | 0.312134i | \(-0.101044\pi\) | ||||
0.950038 | + | 0.312134i | \(0.101044\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.897225 | 0.120982 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.10278 | −0.410973 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.04888 | −0.136552 | −0.0682760 | − | 0.997666i | \(-0.521750\pi\) | ||||
−0.0682760 | + | 0.997666i | \(0.521750\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.91638 | 0.245368 | 0.122684 | − | 0.992446i | \(-0.460850\pi\) | ||||
0.122684 | + | 0.992446i | \(0.460850\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.52444 | −0.318049 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.62721 | −0.697970 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.0383 | 1.22638 | 0.613188 | − | 0.789937i | \(-0.289887\pi\) | ||||
0.613188 | + | 0.789937i | \(0.289887\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.897225 | 0.108013 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.8136 | 1.52070 | 0.760348 | − | 0.649516i | \(-0.225029\pi\) | ||||
0.760348 | + | 0.649516i | \(0.225029\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.75971 | 0.557082 | 0.278541 | − | 0.960424i | \(-0.410149\pi\) | ||||
0.278541 | + | 0.960424i | \(0.410149\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.78389 | −0.436926 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.05390 | 0.234064 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.8328 | 1.78133 | 0.890663 | − | 0.454665i | \(-0.150241\pi\) | ||||
0.890663 | + | 0.454665i | \(0.150241\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.68111 | 0.843112 | 0.421556 | − | 0.906802i | \(-0.361484\pi\) | ||||
0.421556 | + | 0.906802i | \(0.361484\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.74055 | −0.405720 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.44082 | 0.476106 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.2544 | 1.40497 | 0.702483 | − | 0.711700i | \(-0.252075\pi\) | ||||
0.702483 | + | 0.711700i | \(0.252075\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.8816 | −1.35036 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.96526 | 0.929654 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.42166 | 0.351055 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.72999 | 0.277188 | 0.138594 | − | 0.990349i | \(-0.455742\pi\) | ||||
0.138594 | + | 0.990349i | \(0.455742\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.813607 | −0.0817705 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.8625 | −1.18036 | −0.590181 | − | 0.807271i | \(-0.700943\pi\) | ||||
−0.590181 | + | 0.807271i | \(0.700943\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.494719 | 0.0487461 | 0.0243730 | − | 0.999703i | \(-0.492241\pi\) | ||||
0.0243730 | + | 0.999703i | \(0.492241\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.78389 | 0.271680 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.0872 | 1.45853 | 0.729267 | − | 0.684229i | \(-0.239861\pi\) | ||||
0.729267 | + | 0.684229i | \(0.239861\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.10278 | 0.488757 | 0.244379 | − | 0.969680i | \(-0.421416\pi\) | ||||
0.244379 | + | 0.969680i | \(0.421416\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.08362 | 0.197768 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.5139 | −1.64757 | −0.823783 | − | 0.566905i | \(-0.808141\pi\) | ||||
−0.823783 | + | 0.566905i | \(0.808141\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.989437 | −0.0922655 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.10278 | 0.471752 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.56275 | −0.784946 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3380 | −0.939822 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.00000 | 0.0901670 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.68665 | 0.866400 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.8816 | −1.14306 | −0.571530 | − | 0.820581i | \(-0.693650\pi\) | ||||
−0.571530 | + | 0.820581i | \(0.693650\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.07306 | −0.798838 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.35720 | 0.555431 | 0.277716 | − | 0.960663i | \(-0.410423\pi\) | ||||
0.277716 | + | 0.960663i | \(0.410423\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.83276 | 0.679187 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.10278 | −0.0949118 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −17.4897 | −1.49425 | −0.747123 | − | 0.664686i | \(-0.768565\pi\) | ||||
−0.747123 | + | 0.664686i | \(0.768565\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.7250 | −1.33377 | −0.666887 | − | 0.745159i | \(-0.732374\pi\) | ||||
−0.666887 | + | 0.745159i | \(0.732374\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.235269 | 0.0198133 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.15165 | −0.347178 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.89722 | −0.406692 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.627213 | −0.0517317 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.5678 | 0.947669 | 0.473835 | − | 0.880614i | \(-0.342869\pi\) | ||||
0.473835 | + | 0.880614i | \(0.342869\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.2544 | −1.56690 | −0.783451 | − | 0.621453i | \(-0.786543\pi\) | ||||
−0.783451 | + | 0.621453i | \(0.786543\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.39194 | 0.274222 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.88666 | −0.794116 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.9200 | −1.66959 | −0.834797 | − | 0.550558i | \(-0.814415\pi\) | ||||
−0.834797 | + | 0.550558i | \(0.814415\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.8328 | 1.09701 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.26499 | −0.178506 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.7980 | 1.00242 | 0.501209 | − | 0.865326i | \(-0.332889\pi\) | ||||
0.501209 | + | 0.865326i | \(0.332889\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.897225 | 0.0698489 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.62721 | −0.744976 | −0.372488 | − | 0.928037i | \(-0.621495\pi\) | ||||
−0.372488 | + | 0.928037i | \(0.621495\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0383 | 1.00295 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.10278 | −0.237275 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.9461 | 0.908245 | 0.454123 | − | 0.890939i | \(-0.349953\pi\) | ||||
0.454123 | + | 0.890939i | \(0.349953\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.55219 | 0.722078 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.04888 | −0.0788383 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.13752 | 0.159766 | 0.0798828 | − | 0.996804i | \(-0.474545\pi\) | ||||
0.0798828 | + | 0.996804i | \(0.474545\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.83276 | −0.136228 | −0.0681141 | − | 0.997678i | \(-0.521698\pi\) | ||||
−0.0681141 | + | 0.997678i | \(0.521698\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.91638 | 0.141663 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.29776 | −0.168935 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.75971 | −0.201810 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.52444 | −0.183626 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.6167 | 1.34705 | 0.673527 | − | 0.739163i | \(-0.264779\pi\) | ||||
0.673527 | + | 0.739163i | \(0.264779\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.6116 | 1.12375 | 0.561875 | − | 0.827222i | \(-0.310080\pi\) | ||||
0.561875 | + | 0.827222i | \(0.310080\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.62721 | −0.402973 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.21057 | −0.371238 | −0.185619 | − | 0.982622i | \(-0.559429\pi\) | ||||
−0.185619 | + | 0.982622i | \(0.559429\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.05390 | −0.145597 | −0.0727985 | − | 0.997347i | \(-0.523193\pi\) | ||||
−0.0727985 | + | 0.997347i | \(0.523193\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.0383 | 0.708048 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −11.2106 | −0.786828 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.10278 | −0.0770212 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.897225 | 0.0623614 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.52444 | 0.174619 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.04888 | 0.622950 | 0.311475 | − | 0.950254i | \(-0.399177\pi\) | ||||
0.311475 | + | 0.950254i | \(0.399177\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.8136 | 0.877974 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.0055 | 0.682372 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −22.6322 | −1.53638 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.75971 | 0.321631 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.3083 | 1.16428 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.8222 | −1.66222 | −0.831109 | − | 0.556110i | \(-0.812293\pi\) | ||||
−0.831109 | + | 0.556110i | \(0.812293\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.78389 | −0.252259 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.6464 | −1.10486 | −0.552429 | − | 0.833560i | \(-0.686299\pi\) | ||||
−0.552429 | + | 0.833560i | \(0.686299\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.7789 | −1.04270 | −0.521348 | − | 0.853344i | \(-0.674571\pi\) | ||||
−0.521348 | + | 0.853344i | \(0.674571\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.05390 | 0.135137 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −24.9200 | −1.63256 | −0.816280 | − | 0.577656i | \(-0.803967\pi\) | ||||
−0.816280 | + | 0.577656i | \(0.803967\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.259449 | −0.0169246 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.8328 | 1.02845 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.95112 | 0.190892 | 0.0954462 | − | 0.995435i | \(-0.469572\pi\) | ||||
0.0954462 | + | 0.995435i | \(0.469572\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.5925 | −1.06881 | −0.534407 | − | 0.845227i | \(-0.679465\pi\) | ||||
−0.534407 | + | 0.845227i | \(0.679465\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.691675 | 0.0441895 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.8328 | −1.00741 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.68111 | 0.486771 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.1361 | 1.27098 | 0.635489 | − | 0.772110i | \(-0.280799\pi\) | ||||
0.635489 | + | 0.772110i | \(0.280799\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.729988 | −0.0458940 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.74055 | −0.234242 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 25.9008 | 1.61565 | 0.807824 | − | 0.589424i | \(-0.200645\pi\) | ||||
0.807824 | + | 0.589424i | \(0.200645\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.25997 | −0.326838 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.44082 | 0.274880 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.4408 | 1.38376 | 0.691880 | − | 0.722012i | \(-0.256783\pi\) | ||||
0.691880 | + | 0.722012i | \(0.256783\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −15.2544 | −0.937072 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.2544 | 0.811158 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.62721 | 0.465039 | 0.232520 | − | 0.972592i | \(-0.425303\pi\) | ||||
0.232520 | + | 0.972592i | \(0.425303\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.9164 | −1.20983 | −0.604917 | − | 0.796289i | \(-0.706794\pi\) | ||||
−0.604917 | + | 0.796289i | \(0.706794\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −12.8816 | −0.779632 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.07860 | 0.185646 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.6413 | −1.05997 | −0.529983 | − | 0.848008i | \(-0.677802\pi\) | ||||
−0.529983 | + | 0.848008i | \(0.677802\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.96526 | 0.536736 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.0297193 | −0.00177291 | −0.000886453 | − | 1.00000i | \(-0.500282\pi\) | ||||
−0.000886453 | 1.00000i | \(0.500282\pi\) | ||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.1814 | 0.605220 | 0.302610 | − | 0.953115i | \(-0.402142\pi\) | ||||
0.302610 | + | 0.953115i | \(0.402142\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.42166 | 0.202682 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.52444 | −0.149013 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.49472 | −0.323219 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.72999 | 0.160035 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.14808 | 0.183913 | 0.0919564 | − | 0.995763i | \(-0.470688\pi\) | ||||
0.0919564 | + | 0.995763i | \(0.470688\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.15667 | 0.0673442 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.813607 | −0.0472102 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.57834 | 0.264772 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 22.9044 | 1.32019 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −11.8625 | −0.681482 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.11334 | −0.121009 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.7980 | 0.730422 | 0.365211 | − | 0.930925i | \(-0.380997\pi\) | ||||
0.365211 | + | 0.930925i | \(0.380997\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.494719 | 0.0281436 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.6167 | −1.50929 | −0.754646 | − | 0.656132i | \(-0.772191\pi\) | ||||
−0.754646 | + | 0.656132i | \(0.772191\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.00502 | −0.169854 | −0.0849270 | − | 0.996387i | \(-0.527066\pi\) | ||||
−0.0849270 | + | 0.996387i | \(0.527066\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.78389 | 0.156854 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.33302 | −0.243367 | −0.121683 | − | 0.992569i | \(-0.538829\pi\) | ||||
−0.121683 | + | 0.992569i | \(0.538829\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.61308 | −0.202294 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.0872 | 0.842085 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.5244 | −0.585595 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −19.3083 | −1.07103 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.10278 | 0.282184 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.593923 | −0.0327440 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.53500 | −0.304231 | −0.152116 | − | 0.988363i | \(-0.548609\pi\) | ||||
−0.152116 | + | 0.988363i | \(0.548609\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.08362 | 0.114182 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.0700 | −0.604819 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.71083 | −0.202142 | −0.101071 | − | 0.994879i | \(-0.532227\pi\) | ||||
−0.101071 | + | 0.994879i | \(0.532227\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −17.5139 | −0.951223 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.29419 | −0.395003 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.2544 | 1.03964 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.989437 | −0.0532695 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.07860 | −0.165268 | −0.0826338 | − | 0.996580i | \(-0.526333\pi\) | ||||
−0.0826338 | + | 0.996580i | \(0.526333\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.7980 | 0.792120 | 0.396060 | − | 0.918225i | \(-0.370377\pi\) | ||||
0.396060 | + | 0.918225i | \(0.370377\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.10278 | 0.272366 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 26.8222 | 1.42760 | 0.713801 | − | 0.700349i | \(-0.246972\pi\) | ||||
0.713801 | + | 0.700349i | \(0.246972\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.1305 | −0.749970 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.56275 | −0.453189 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.35720 | −0.124408 | −0.0622042 | − | 0.998063i | \(-0.519813\pi\) | ||||
−0.0622042 | + | 0.998063i | \(0.519813\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.37279 | −0.493305 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.3380 | −0.542607 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.24889 | −0.274739 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.1708 | −1.20951 | −0.604753 | − | 0.796413i | \(-0.706728\pi\) | ||||
−0.604753 | + | 0.796413i | \(0.706728\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −34.9200 | −1.81295 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 35.2091 | 1.82306 | 0.911530 | − | 0.411235i | \(-0.134902\pi\) | ||||
0.911530 | + | 0.411235i | \(0.134902\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.68665 | 0.500217 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 22.6605 | 1.16708 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.0383 | 1.33750 | 0.668749 | − | 0.743488i | \(-0.266830\pi\) | ||||
0.668749 | + | 0.743488i | \(0.266830\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.8816 | −0.659946 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.3819 | −0.785978 | −0.392989 | − | 0.919543i | \(-0.628559\pi\) | ||||
−0.392989 | + | 0.919543i | \(0.628559\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.26499 | −0.115435 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.07306 | −0.461209 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.46500 | 0.226384 | 0.113192 | − | 0.993573i | \(-0.463892\pi\) | ||||
0.113192 | + | 0.993573i | \(0.463892\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.04334 | 0.153908 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.35720 | 0.320678 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −17.4600 | −0.878507 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.5628 | −0.530129 | −0.265065 | − | 0.964231i | \(-0.585393\pi\) | ||||
−0.265065 | + | 0.964231i | \(0.585393\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.83276 | 0.392129 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.0872 | 0.653543 | 0.326772 | − | 0.945103i | \(-0.394039\pi\) | ||||
0.326772 | + | 0.945103i | \(0.394039\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 45.7477 | 2.27885 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.10278 | −0.0547973 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.69525 | −0.0840302 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.5542 | −0.917444 | −0.458722 | − | 0.888580i | \(-0.651693\pi\) | ||||
−0.458722 | + | 0.888580i | \(0.651693\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −17.4897 | −0.862703 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.64782 | 0.130291 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.47054 | −0.415802 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −15.7250 | −0.770055 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.6116 | 1.25121 | 0.625605 | − | 0.780140i | \(-0.284852\pi\) | ||||
0.625605 | + | 0.780140i | \(0.284852\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.67609 | −0.422847 | −0.211423 | − | 0.977395i | \(-0.567810\pi\) | ||||
−0.211423 | + | 0.977395i | \(0.567810\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.235269 | 0.0114392 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −12.8347 | −0.622576 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.83779 | −0.234117 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.15165 | −0.200444 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.10278 | −0.342129 | −0.171064 | − | 0.985260i | \(-0.554721\pi\) | ||||
−0.171064 | + | 0.985260i | \(0.554721\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.0247 | −0.529813 | −0.264907 | − | 0.964274i | \(-0.585341\pi\) | ||||
−0.264907 | + | 0.964274i | \(0.585341\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.89722 | −0.234804 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.78389 | −0.133171 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.32391 | 0.0631868 | 0.0315934 | − | 0.999501i | \(-0.489942\pi\) | ||||
0.0315934 | + | 0.999501i | \(0.489942\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.627213 | −0.0298673 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.5889 | −0.740651 | −0.370325 | − | 0.928902i | \(-0.620754\pi\) | ||||
−0.370325 | + | 0.928902i | \(0.620754\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.6167 | −0.692896 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.5678 | 0.547137 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −32.7839 | −1.54717 | −0.773584 | − | 0.633694i | \(-0.781538\pi\) | ||||
−0.773584 | + | 0.633694i | \(0.781538\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.813607 | −0.0383112 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −19.2544 | −0.904652 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 14.2056 | 0.665966 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.1672 | −0.662715 | −0.331358 | − | 0.943505i | \(-0.607507\pi\) | ||||
−0.331358 | + | 0.943505i | \(0.607507\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.39194 | 0.158322 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.0766 | −1.40081 | −0.700404 | − | 0.713747i | \(-0.746997\pi\) | ||||
−0.700404 | + | 0.713747i | \(0.746997\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.8766 | 1.10964 | 0.554820 | − | 0.831970i | \(-0.312787\pi\) | ||||
0.554820 | + | 0.831970i | \(0.312787\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.88666 | −0.458483 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.73501 | 0.450483 | 0.225241 | − | 0.974303i | \(-0.427683\pi\) | ||||
0.225241 | + | 0.974303i | \(0.427683\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −25.3411 | −1.17014 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.9200 | −0.963941 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.38190 | 0.339420 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.7406 | 0.538693 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.8328 | 0.633359 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.17635 | 0.0537487 | 0.0268743 | − | 0.999639i | \(-0.491445\pi\) | ||||
0.0268743 | + | 0.999639i | \(0.491445\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.6322 | 0.484788 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.26499 | −0.103061 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.01056 | −0.136703 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.6025 | −0.933589 | −0.466795 | − | 0.884366i | \(-0.654591\pi\) | ||||
−0.466795 | + | 0.884366i | \(0.654591\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.7980 | 0.578746 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.1900 | −0.640384 | −0.320192 | − | 0.947353i | \(-0.603747\pi\) | ||||
−0.320192 | + | 0.947353i | \(0.603747\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.0630 | 0.678404 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.897225 | 0.0403273 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −32.3472 | −1.45097 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.4600 | 0.960680 | 0.480340 | − | 0.877082i | \(-0.340513\pi\) | ||||
0.480340 | + | 0.877082i | \(0.340513\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.62721 | −0.430112 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.5491 | 0.693302 | 0.346651 | − | 0.937994i | \(-0.387319\pi\) | ||||
0.346651 | + | 0.937994i | \(0.387319\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.0816 | 0.582126 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.0383 | 0.579052 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.7542 | 1.00856 | 0.504280 | − | 0.863540i | \(-0.331758\pi\) | ||||
0.504280 | + | 0.863540i | \(0.331758\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.0156 | −0.531538 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.10278 | −0.136991 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.545563 | −0.0240404 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.191417 | −0.00841850 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.9461 | 0.524376 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −38.7230 | −1.69649 | −0.848243 | − | 0.529608i | \(-0.822339\pi\) | ||||
−0.848243 | + | 0.529608i | \(0.822339\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.56829 | −0.287211 | −0.143606 | − | 0.989635i | \(-0.545870\pi\) | ||||
−0.143606 | + | 0.989635i | \(0.545870\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.55219 | 0.416892 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 30.4096 | 1.32467 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.1950 | −0.964999 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.04888 | −0.0455173 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.10278 | 0.221026 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.6378 | −0.719314 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.13752 | 0.0922407 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.510305 | 0.0219804 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 42.0766 | 1.80902 | 0.904508 | − | 0.426457i | \(-0.140239\pi\) | ||||
0.904508 | + | 0.426457i | \(0.140239\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.83276 | −0.0786514 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.62721 | −0.241043 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.9688 | −0.853805 | −0.426903 | − | 0.904298i | \(-0.640395\pi\) | ||||
−0.426903 | + | 0.904298i | \(0.640395\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.91638 | 0.0817892 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.7789 | −0.586999 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −39.9688 | −1.69965 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.29776 | −0.0975346 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.5491 | 0.574095 | 0.287048 | − | 0.957916i | \(-0.407326\pi\) | ||||
0.287048 | + | 0.957916i | \(0.407326\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −46.2978 | −1.95819 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.75971 | −0.116515 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.75468 | −0.411111 | −0.205555 | − | 0.978645i | \(-0.565900\pi\) | ||||
−0.205555 | + | 0.978645i | \(0.565900\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.3139 | 0.812540 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.52444 | −0.106016 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.4544 | −0.899417 | −0.449708 | − | 0.893175i | \(-0.648472\pi\) | ||||
−0.449708 | + | 0.893175i | \(0.648472\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.9411 | −0.876357 | −0.438178 | − | 0.898888i | \(-0.644376\pi\) | ||||
−0.438178 | + | 0.898888i | \(0.644376\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.6167 | 0.777722 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.39500 | −0.141581 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.4705 | 0.768939 | 0.384469 | − | 0.923138i | \(-0.374384\pi\) | ||||
0.384469 | + | 0.923138i | \(0.374384\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15.6116 | 0.648797 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −19.3905 | −0.804453 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.2544 | −0.466111 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.62721 | −0.232657 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.127471 | 0.00526130 | 0.00263065 | − | 0.999997i | \(-0.499163\pi\) | ||||
0.00263065 | + | 0.999997i | \(0.499163\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27.8172 | −1.14619 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.21057 | −0.214334 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −27.2841 | −1.12043 | −0.560213 | − | 0.828349i | \(-0.689281\pi\) | ||||
−0.560213 | + | 0.828349i | \(0.689281\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.44279 | 0.387117 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.05390 | −0.0840605 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 42.3260 | 1.72939 | 0.864697 | − | 0.502293i | \(-0.167510\pi\) | ||||
0.864697 | + | 0.502293i | \(0.167510\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.6756 | −0.639420 | −0.319710 | − | 0.947515i | \(-0.603585\pi\) | ||||
−0.319710 | + | 0.947515i | \(0.603585\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.0383 | 0.408792 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.4005 | 0.463498 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.93051 | 0.0783572 | 0.0391786 | − | 0.999232i | \(-0.487526\pi\) | ||||
0.0391786 | + | 0.999232i | \(0.487526\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −11.2106 | −0.454275 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.20053 | 0.0485681 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.372787 | −0.0150567 | −0.00752836 | − | 0.999972i | \(-0.502396\pi\) | ||||
−0.00752836 | + | 0.999972i | \(0.502396\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.10278 | −0.0444682 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.3083 | 1.26043 | 0.630213 | − | 0.776422i | \(-0.282968\pi\) | ||||
0.630213 | + | 0.776422i | \(0.282968\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −34.3658 | −1.38128 | −0.690639 | − | 0.723200i | \(-0.742671\pi\) | ||||
−0.690639 | + | 0.723200i | \(0.742671\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.897225 | 0.0360044 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −33.4600 | −1.34055 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.23724 | 0.329490 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.52444 | 0.100816 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.06752 | 0.281800 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.33804 | −0.292123 | −0.146061 | − | 0.989276i | \(-0.546660\pi\) | ||||
−0.146061 | + | 0.989276i | \(0.546660\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.04888 | 0.359661 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.2056 | 0.563730 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.20053 | −0.126809 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.8136 | 0.506898 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31.5764 | −1.24719 | −0.623596 | − | 0.781747i | \(-0.714329\pi\) | ||||
−0.623596 | + | 0.781747i | \(0.714329\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.51890 | 0.178208 | 0.0891040 | − | 0.996022i | \(-0.471600\pi\) | ||||
0.0891040 | + | 0.996022i | \(0.471600\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.0055 | 0.393968 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.6705 | 0.812643 | 0.406322 | − | 0.913730i | \(-0.366811\pi\) | ||||
0.406322 | + | 0.913730i | \(0.366811\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.853372 | 0.0334978 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −22.6322 | −0.887027 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.381381 | 0.0149246 | 0.00746229 | − | 0.999972i | \(-0.497625\pi\) | ||||
0.00746229 | + | 0.999972i | \(0.497625\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.01056 | −0.273925 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.75971 | 0.185694 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.4600 | −0.524326 | −0.262163 | − | 0.965024i | \(-0.584436\pi\) | ||||
−0.262163 | + | 0.965024i | \(0.584436\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.7738 | 1.19696 | 0.598482 | − | 0.801136i | \(-0.295771\pi\) | ||||
0.598482 | + | 0.801136i | \(0.295771\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 17.3083 | 0.672200 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.63778 | −0.334959 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.98441 | 0.154277 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −24.8222 | −0.959682 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.55918 | −0.0601915 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.48110 | 0.0570923 | 0.0285461 | − | 0.999592i | \(-0.490912\pi\) | ||||
0.0285461 | + | 0.999592i | \(0.490912\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.78389 | −0.145642 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 45.3749 | 1.74390 | 0.871950 | − | 0.489596i | \(-0.162856\pi\) | ||||
0.871950 | + | 0.489596i | \(0.162856\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.89169 | −0.264479 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16.6464 | −0.637890 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.0594386 | 0.00227436 | 0.00113718 | − | 0.999999i | \(-0.499638\pi\) | ||||
0.00113718 | + | 0.999999i | \(0.499638\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.2872 | 0.736926 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.7789 | −0.602001 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 70.5855 | 2.68909 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.9355 | 0.720342 | 0.360171 | − | 0.932886i | \(-0.382718\pi\) | ||||
0.360171 | + | 0.932886i | \(0.382718\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.05390 | 0.0780212 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17.3411 | 0.657785 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.39194 | 0.128479 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −24.9200 | −0.942559 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.540024 | −0.0203964 | −0.0101982 | − | 0.999948i | \(-0.503246\pi\) | ||||
−0.0101982 | + | 0.999948i | \(0.503246\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.46500 | −0.243832 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.259449 | −0.00977142 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 29.9461 | 1.12624 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.0867 | 1.05482 | 0.527409 | − | 0.849612i | \(-0.323164\pi\) | ||||
0.527409 | + | 0.849612i | \(0.323164\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.8328 | 0.593775 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.04385 | 0.301245 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.57834 | 0.171220 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.95112 | 0.110212 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.86248 | −0.367809 | −0.183904 | − | 0.982944i | \(-0.558874\pi\) | ||||
−0.183904 | + | 0.982944i | \(0.558874\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.24889 | −0.0465110 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −16.5925 | −0.617081 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −16.8036 | −0.624069 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.4650 | 1.12988 | 0.564942 | − | 0.825131i | \(-0.308898\pi\) | ||||
0.564942 | + | 0.825131i | \(0.308898\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −30.7753 | −1.13827 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.5436 | 1.01735 | 0.508673 | − | 0.860960i | \(-0.330136\pi\) | ||||
0.508673 | + | 0.860960i | \(0.330136\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.691675 | 0.0255128 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.16724 | −0.300844 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.1013 | −0.481940 | −0.240970 | − | 0.970533i | \(-0.577466\pi\) | ||||
−0.240970 | + | 0.970533i | \(0.577466\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −15.8328 | −0.581631 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.7527 | −1.27495 | −0.637477 | − | 0.770470i | \(-0.720022\pi\) | ||||
−0.637477 | + | 0.770470i | \(0.720022\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.7567 | −0.467368 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.68111 | 0.281037 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −38.0867 | −1.39166 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32.7738 | −1.19593 | −0.597967 | − | 0.801521i | \(-0.704025\pi\) | ||||
−0.597967 | + | 0.801521i | \(0.704025\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 20.1361 | 0.733799 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.2333 | 0.772759 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.2978 | −1.17388 | −0.586941 | − | 0.809630i | \(-0.699668\pi\) | ||||
−0.586941 | + | 0.809630i | \(0.699668\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.729988 | −0.0264969 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 44.4494 | 1.61129 | 0.805645 | − | 0.592399i | \(-0.201819\pi\) | ||||
0.805645 | + | 0.592399i | \(0.201819\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.8816 | −0.466347 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.74055 | −0.135240 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.35218 | −0.193256 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.7108 | −0.710791 | −0.355395 | − | 0.934716i | \(-0.615654\pi\) | ||||
−0.355395 | + | 0.934716i | \(0.615654\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 25.9008 | 0.932794 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 43.2530 | 1.55570 | 0.777851 | − | 0.628449i | \(-0.216310\pi\) | ||||
0.777851 | + | 0.628449i | \(0.216310\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −33.9235 | −1.21857 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.25997 | −0.188700 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.10278 | −0.111168 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.4252 | −0.373044 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.44082 | 0.158702 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 23.0700 | 0.823404 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.4358 | 0.764104 | 0.382052 | − | 0.924141i | \(-0.375218\pi\) | ||||
0.382052 | + | 0.924141i | \(0.375218\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 22.4408 | 0.798914 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 44.2127 | 1.57202 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.77886 | 0.347258 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −15.2544 | −0.541019 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.40105 | −0.155893 | −0.0779467 | − | 0.996958i | \(-0.524836\pi\) | ||||
−0.0779467 | + | 0.996958i | \(0.524836\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.798021 | 0.0282319 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.2544 | 0.468322 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.87253 | −0.136659 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.49777 | 0.0880349 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.62721 | 0.268491 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −26.3799 | −0.927469 | −0.463734 | − | 0.885974i | \(-0.653491\pi\) | ||||
−0.463734 | + | 0.885974i | \(0.653491\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.96526 | −0.174354 | −0.0871769 | − | 0.996193i | \(-0.527785\pi\) | ||||
−0.0871769 | + | 0.996193i | \(0.527785\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.9164 | −0.698498 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.1133 | −0.494369 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 28.1517 | 0.984902 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −12.8816 | −0.450121 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.7789 | −0.550686 | −0.275343 | − | 0.961346i | \(-0.588791\pi\) | ||||
−0.275343 | + | 0.961346i | \(0.588791\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.35166 | 0.291121 | 0.145560 | − | 0.989349i | \(-0.453502\pi\) | ||||
0.145560 | + | 0.989349i | \(0.453502\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.07860 | 0.107183 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.3925 | 0.639568 | 0.319784 | − | 0.947490i | \(-0.396390\pi\) | ||||
0.319784 | + | 0.947490i | \(0.396390\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29.4147 | −1.02161 | −0.510807 | − | 0.859695i | \(-0.670653\pi\) | ||||
−0.510807 | + | 0.859695i | \(0.670653\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.6413 | −0.611972 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.12747 | −0.0737125 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.6167 | 0.367404 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.96526 | 0.309885 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 33.4600 | 1.15517 | 0.577583 | − | 0.816332i | \(-0.303996\pi\) | ||||
0.577583 | + | 0.816332i | \(0.303996\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.27912 | −0.319970 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.0297193 | −0.00102359 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −14.3783 | −0.494629 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26.0978 | 0.896729 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.1814 | 0.349424 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.86947 | 0.0640848 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40.4494 | 1.38496 | 0.692481 | − | 0.721436i | \(-0.256518\pi\) | ||||
0.692481 | + | 0.721436i | \(0.256518\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.42166 | 0.117018 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.4494 | 0.425264 | 0.212632 | − | 0.977132i | \(-0.431796\pi\) | ||||
0.212632 | + | 0.977132i | \(0.431796\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.6514 | 0.738736 | 0.369368 | − | 0.929283i | \(-0.379574\pi\) | ||||
0.369368 | + | 0.929283i | \(0.379574\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.52444 | −0.0860326 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.3778 | −0.659628 | −0.329814 | − | 0.944046i | \(-0.606986\pi\) | ||||
−0.329814 | + | 0.944046i | \(0.606986\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.1739 | −0.447925 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.49472 | −0.186610 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.8816 | −0.436980 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 51.2233 | 1.73563 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.72999 | 0.0923961 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −24.4534 | −0.826674 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.08413 | −0.104144 | −0.0520719 | − | 0.998643i | \(-0.516583\pi\) | ||||
−0.0520719 | + | 0.998643i | \(0.516583\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.14808 | 0.106182 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.5783 | −1.16497 | −0.582487 | − | 0.812840i | \(-0.697920\pi\) | ||||
−0.582487 | + | 0.812840i | \(0.697920\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.64280 | 0.324506 | 0.162253 | − | 0.986749i | \(-0.448124\pi\) | ||||
0.162253 | + | 0.986749i | \(0.448124\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.15667 | 0.0388812 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −32.2041 | −1.08131 | −0.540654 | − | 0.841245i | \(-0.681823\pi\) | ||||
−0.540654 | + | 0.841245i | \(0.681823\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 32.5189 | 1.09065 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.813607 | −0.0272568 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.729988 | −0.0244281 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.35720 | −0.0787925 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.57834 | 0.152866 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 39.8131 | 1.32784 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 46.9200 | 1.56313 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 22.9044 | 0.762210 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.02113 | 0.0671845 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.8227 | 0.591794 | 0.295897 | − | 0.955220i | \(-0.404382\pi\) | ||||
0.295897 | + | 0.955220i | \(0.404382\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.8625 | −0.393454 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.7894 | 0.688784 | 0.344392 | − | 0.938826i | \(-0.388085\pi\) | ||||
0.344392 | + | 0.938826i | \(0.388085\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.24940 | −0.206825 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.11334 | −0.0698648 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16.0484 | −0.529964 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −33.8555 | −1.11679 | −0.558395 | − | 0.829575i | \(-0.688583\pi\) | ||||
−0.558395 | + | 0.829575i | \(0.688583\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.7980 | 0.421709 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 65.3850 | 2.15217 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.88418 | −0.259230 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.494719 | 0.0162487 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.10635 | −0.134725 | −0.0673624 | − | 0.997729i | \(-0.521458\pi\) | ||||
−0.0673624 | + | 0.997729i | \(0.521458\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.94610 | 0.0637809 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −26.6167 | −0.871390 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.04334 | 0.0995277 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13.3028 | 0.434583 | 0.217292 | − | 0.976107i | \(-0.430278\pi\) | ||||
0.217292 | + | 0.976107i | \(0.430278\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.00502 | −0.0980652 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.7633 | −0.383472 | −0.191736 | − | 0.981447i | \(-0.561412\pi\) | ||||
−0.191736 | + | 0.981447i | \(0.561412\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.897225 | 0.0292177 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.78389 | 0.0905599 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.40054 | −0.0455114 | −0.0227557 | − | 0.999741i | \(-0.507244\pi\) | ||||
−0.0227557 | + | 0.999741i | \(0.507244\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.2877 | 0.788413 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.33302 | −0.140508 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.7577 | 1.09352 | 0.546760 | − | 0.837289i | \(-0.315861\pi\) | ||||
0.546760 | + | 0.837289i | \(0.315861\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20.5300 | −0.664334 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.61308 | −0.116794 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 44.1517 | 1.42573 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 49.3758 | 1.59277 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15.0872 | 0.486178 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17.2161 | −0.554206 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.4806 | 0.337033 | 0.168516 | − | 0.985699i | \(-0.446102\pi\) | ||||
0.168516 | + | 0.985699i | \(0.446102\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10.5244 | −0.338094 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −57.6358 | −1.84962 | −0.924811 | − | 0.380428i | \(-0.875777\pi\) | ||||
−0.924811 | + | 0.380428i | \(0.875777\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 39.6967 | 1.27262 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −19.3083 | −0.618361 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 41.9008 | 1.34053 | 0.670263 | − | 0.742124i | \(-0.266181\pi\) | ||||
0.670263 | + | 0.742124i | \(0.266181\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.7839 | −0.344655 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.10278 | 0.162919 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.4056 | 0.587046 | 0.293523 | − | 0.955952i | \(-0.405172\pi\) | ||||
0.293523 | + | 0.955952i | \(0.405172\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.74609 | 0.183086 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.593923 | −0.0189048 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.14057 | −0.258855 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.0666 | −0.828032 | −0.414016 | − | 0.910270i | \(-0.635874\pi\) | ||||
−0.414016 | + | 0.910270i | \(0.635874\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.53500 | −0.175648 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.26499 | 0.0718050 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.8483 | −0.945307 | −0.472653 | − | 0.881248i | \(-0.656704\pi\) | ||||
−0.472653 | + | 0.881248i | \(0.656704\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.08362 | 0.0659228 |
(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 | 1968.2.a.w.1.1 | 3 | ||
3.2 | odd | 2 | 5904.2.a.bd.1.3 | 3 | |||
4.3 | odd | 2 | 123.2.a.d.1.1 | ✓ | 3 | ||
8.3 | odd | 2 | 7872.2.a.bx.1.3 | 3 | |||
8.5 | even | 2 | 7872.2.a.bs.1.3 | 3 | |||
12.11 | even | 2 | 369.2.a.e.1.3 | 3 | |||
20.19 | odd | 2 | 3075.2.a.t.1.3 | 3 | |||
28.27 | even | 2 | 6027.2.a.s.1.1 | 3 | |||
60.59 | even | 2 | 9225.2.a.bx.1.1 | 3 | |||
164.163 | odd | 2 | 5043.2.a.n.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
123.2.a.d.1.1 | ✓ | 3 | 4.3 | odd | 2 | ||
369.2.a.e.1.3 | 3 | 12.11 | even | 2 | |||
1968.2.a.w.1.1 | 3 | 1.1 | even | 1 | trivial | ||
3075.2.a.t.1.3 | 3 | 20.19 | odd | 2 | |||
5043.2.a.n.1.1 | 3 | 164.163 | odd | 2 | |||
5904.2.a.bd.1.3 | 3 | 3.2 | odd | 2 | |||
6027.2.a.s.1.1 | 3 | 28.27 | even | 2 | |||
7872.2.a.bs.1.3 | 3 | 8.5 | even | 2 | |||
7872.2.a.bx.1.3 | 3 | 8.3 | odd | 2 | |||
9225.2.a.bx.1.1 | 3 | 60.59 | even | 2 |