Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [123,2,Mod(1,123)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(123, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("123.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 123 = 3 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 123.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: | \(0.982159944862\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.81361\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 123.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.81361 | −1.28241 | −0.641207 | − | 0.767368i | \(-0.721566\pi\) | ||||
−0.641207 | + | 0.767368i | \(0.721566\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.28917 | 0.644584 | ||||||||
\(5\) | −1.10278 | −0.493176 | −0.246588 | − | 0.969120i | \(-0.579309\pi\) | ||||
−0.246588 | + | 0.969120i | \(0.579309\pi\) | |||||||
\(6\) | 1.81361 | 0.740402 | ||||||||
\(7\) | 2.52444 | 0.954148 | 0.477074 | − | 0.878863i | \(-0.341697\pi\) | ||||
0.477074 | + | 0.878863i | \(0.341697\pi\) | |||||||
\(8\) | 1.28917 | 0.455790 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.00000 | 0.632456 | ||||||||
\(11\) | 0.813607 | 0.245312 | 0.122656 | − | 0.992449i | \(-0.460859\pi\) | ||||
0.122656 | + | 0.992449i | \(0.460859\pi\) | |||||||
\(12\) | −1.28917 | −0.372151 | ||||||||
\(13\) | 5.10278 | 1.41526 | 0.707628 | − | 0.706586i | \(-0.249765\pi\) | ||||
0.707628 | + | 0.706586i | \(0.249765\pi\) | |||||||
\(14\) | −4.57834 | −1.22361 | ||||||||
\(15\) | 1.10278 | 0.284735 | ||||||||
\(16\) | −4.91638 | −1.22910 | ||||||||
\(17\) | 3.39194 | 0.822667 | 0.411334 | − | 0.911485i | \(-0.365063\pi\) | ||||
0.411334 | + | 0.911485i | \(0.365063\pi\) | |||||||
\(18\) | −1.81361 | −0.427471 | ||||||||
\(19\) | 3.10278 | 0.711825 | 0.355913 | − | 0.934519i | \(-0.384170\pi\) | ||||
0.355913 | + | 0.934519i | \(0.384170\pi\) | |||||||
\(20\) | −1.42166 | −0.317893 | ||||||||
\(21\) | −2.52444 | −0.550878 | ||||||||
\(22\) | −1.47556 | −0.314591 | ||||||||
\(23\) | −0.897225 | −0.187084 | −0.0935422 | − | 0.995615i | \(-0.529819\pi\) | ||||
−0.0935422 | + | 0.995615i | \(0.529819\pi\) | |||||||
\(24\) | −1.28917 | −0.263150 | ||||||||
\(25\) | −3.78389 | −0.756777 | ||||||||
\(26\) | −9.25443 | −1.81494 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 3.25443 | 0.615029 | ||||||||
\(29\) | 4.44082 | 0.824639 | 0.412320 | − | 0.911039i | \(-0.364719\pi\) | ||||
0.412320 | + | 0.911039i | \(0.364719\pi\) | |||||||
\(30\) | −2.00000 | −0.365148 | ||||||||
\(31\) | −8.96526 | −1.61021 | −0.805104 | − | 0.593134i | \(-0.797890\pi\) | ||||
−0.805104 | + | 0.593134i | \(0.797890\pi\) | |||||||
\(32\) | 6.33804 | 1.12042 | ||||||||
\(33\) | −0.813607 | −0.141631 | ||||||||
\(34\) | −6.15165 | −1.05500 | ||||||||
\(35\) | −2.78389 | −0.470563 | ||||||||
\(36\) | 1.28917 | 0.214861 | ||||||||
\(37\) | 2.08362 | 0.342545 | 0.171272 | − | 0.985224i | \(-0.445212\pi\) | ||||
0.171272 | + | 0.985224i | \(0.445212\pi\) | |||||||
\(38\) | −5.62721 | −0.912854 | ||||||||
\(39\) | −5.10278 | −0.817098 | ||||||||
\(40\) | −1.42166 | −0.224785 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 4.57834 | 0.706453 | ||||||||
\(43\) | 9.07306 | 1.38363 | 0.691814 | − | 0.722076i | \(-0.256812\pi\) | ||||
0.691814 | + | 0.722076i | \(0.256812\pi\) | |||||||
\(44\) | 1.04888 | 0.158124 | ||||||||
\(45\) | −1.10278 | −0.164392 | ||||||||
\(46\) | 1.62721 | 0.239919 | ||||||||
\(47\) | −0.235269 | −0.0343176 | −0.0171588 | − | 0.999853i | \(-0.505462\pi\) | ||||
−0.0171588 | + | 0.999853i | \(0.505462\pi\) | |||||||
\(48\) | 4.91638 | 0.709619 | ||||||||
\(49\) | −0.627213 | −0.0896019 | ||||||||
\(50\) | 6.86248 | 0.970502 | ||||||||
\(51\) | −3.39194 | −0.474967 | ||||||||
\(52\) | 6.57834 | 0.912251 | ||||||||
\(53\) | 13.8328 | 1.90008 | 0.950038 | − | 0.312134i | \(-0.101044\pi\) | ||||
0.950038 | + | 0.312134i | \(0.101044\pi\) | |||||||
\(54\) | 1.81361 | 0.246801 | ||||||||
\(55\) | −0.897225 | −0.120982 | ||||||||
\(56\) | 3.25443 | 0.434891 | ||||||||
\(57\) | −3.10278 | −0.410973 | ||||||||
\(58\) | −8.05390 | −1.05753 | ||||||||
\(59\) | 1.04888 | 0.136552 | 0.0682760 | − | 0.997666i | \(-0.478250\pi\) | ||||
0.0682760 | + | 0.997666i | \(0.478250\pi\) | |||||||
\(60\) | 1.42166 | 0.183536 | ||||||||
\(61\) | 1.91638 | 0.245368 | 0.122684 | − | 0.992446i | \(-0.460850\pi\) | ||||
0.122684 | + | 0.992446i | \(0.460850\pi\) | |||||||
\(62\) | 16.2594 | 2.06495 | ||||||||
\(63\) | 2.52444 | 0.318049 | ||||||||
\(64\) | −1.66196 | −0.207744 | ||||||||
\(65\) | −5.62721 | −0.697970 | ||||||||
\(66\) | 1.47556 | 0.181629 | ||||||||
\(67\) | −10.0383 | −1.22638 | −0.613188 | − | 0.789937i | \(-0.710113\pi\) | ||||
−0.613188 | + | 0.789937i | \(0.710113\pi\) | |||||||
\(68\) | 4.37279 | 0.530278 | ||||||||
\(69\) | 0.897225 | 0.108013 | ||||||||
\(70\) | 5.04888 | 0.603456 | ||||||||
\(71\) | −12.8136 | −1.52070 | −0.760348 | − | 0.649516i | \(-0.774971\pi\) | ||||
−0.760348 | + | 0.649516i | \(0.774971\pi\) | |||||||
\(72\) | 1.28917 | 0.151930 | ||||||||
\(73\) | 4.75971 | 0.557082 | 0.278541 | − | 0.960424i | \(-0.410149\pi\) | ||||
0.278541 | + | 0.960424i | \(0.410149\pi\) | |||||||
\(74\) | −3.77886 | −0.439284 | ||||||||
\(75\) | 3.78389 | 0.436926 | ||||||||
\(76\) | 4.00000 | 0.458831 | ||||||||
\(77\) | 2.05390 | 0.234064 | ||||||||
\(78\) | 9.25443 | 1.04786 | ||||||||
\(79\) | −15.8328 | −1.78133 | −0.890663 | − | 0.454665i | \(-0.849759\pi\) | ||||
−0.890663 | + | 0.454665i | \(0.849759\pi\) | |||||||
\(80\) | 5.42166 | 0.606160 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.81361 | −0.200279 | ||||||||
\(83\) | −7.68111 | −0.843112 | −0.421556 | − | 0.906802i | \(-0.638516\pi\) | ||||
−0.421556 | + | 0.906802i | \(0.638516\pi\) | |||||||
\(84\) | −3.25443 | −0.355087 | ||||||||
\(85\) | −3.74055 | −0.405720 | ||||||||
\(86\) | −16.4550 | −1.77438 | ||||||||
\(87\) | −4.44082 | −0.476106 | ||||||||
\(88\) | 1.04888 | 0.111811 | ||||||||
\(89\) | 13.2544 | 1.40497 | 0.702483 | − | 0.711700i | \(-0.252075\pi\) | ||||
0.702483 | + | 0.711700i | \(0.252075\pi\) | |||||||
\(90\) | 2.00000 | 0.210819 | ||||||||
\(91\) | 12.8816 | 1.35036 | ||||||||
\(92\) | −1.15667 | −0.120592 | ||||||||
\(93\) | 8.96526 | 0.929654 | ||||||||
\(94\) | 0.426686 | 0.0440093 | ||||||||
\(95\) | −3.42166 | −0.351055 | ||||||||
\(96\) | −6.33804 | −0.646874 | ||||||||
\(97\) | 2.72999 | 0.277188 | 0.138594 | − | 0.990349i | \(-0.455742\pi\) | ||||
0.138594 | + | 0.990349i | \(0.455742\pi\) | |||||||
\(98\) | 1.13752 | 0.114907 | ||||||||
\(99\) | 0.813607 | 0.0817705 | ||||||||
\(100\) | −4.87807 | −0.487807 | ||||||||
\(101\) | −11.8625 | −1.18036 | −0.590181 | − | 0.807271i | \(-0.700943\pi\) | ||||
−0.590181 | + | 0.807271i | \(0.700943\pi\) | |||||||
\(102\) | 6.15165 | 0.609104 | ||||||||
\(103\) | −0.494719 | −0.0487461 | −0.0243730 | − | 0.999703i | \(-0.507759\pi\) | ||||
−0.0243730 | + | 0.999703i | \(0.507759\pi\) | |||||||
\(104\) | 6.57834 | 0.645059 | ||||||||
\(105\) | 2.78389 | 0.271680 | ||||||||
\(106\) | −25.0872 | −2.43668 | ||||||||
\(107\) | −15.0872 | −1.45853 | −0.729267 | − | 0.684229i | \(-0.760139\pi\) | ||||
−0.729267 | + | 0.684229i | \(0.760139\pi\) | |||||||
\(108\) | −1.28917 | −0.124050 | ||||||||
\(109\) | 5.10278 | 0.488757 | 0.244379 | − | 0.969680i | \(-0.421416\pi\) | ||||
0.244379 | + | 0.969680i | \(0.421416\pi\) | |||||||
\(110\) | 1.62721 | 0.155149 | ||||||||
\(111\) | −2.08362 | −0.197768 | ||||||||
\(112\) | −12.4111 | −1.17274 | ||||||||
\(113\) | −17.5139 | −1.64757 | −0.823783 | − | 0.566905i | \(-0.808141\pi\) | ||||
−0.823783 | + | 0.566905i | \(0.808141\pi\) | |||||||
\(114\) | 5.62721 | 0.527037 | ||||||||
\(115\) | 0.989437 | 0.0922655 | ||||||||
\(116\) | 5.72496 | 0.531550 | ||||||||
\(117\) | 5.10278 | 0.471752 | ||||||||
\(118\) | −1.90225 | −0.175116 | ||||||||
\(119\) | 8.56275 | 0.784946 | ||||||||
\(120\) | 1.42166 | 0.129779 | ||||||||
\(121\) | −10.3380 | −0.939822 | ||||||||
\(122\) | −3.47556 | −0.314663 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | −11.5577 | −1.03791 | ||||||||
\(125\) | 9.68665 | 0.866400 | ||||||||
\(126\) | −4.57834 | −0.407871 | ||||||||
\(127\) | 12.8816 | 1.14306 | 0.571530 | − | 0.820581i | \(-0.306350\pi\) | ||||
0.571530 | + | 0.820581i | \(0.306350\pi\) | |||||||
\(128\) | −9.66196 | −0.854004 | ||||||||
\(129\) | −9.07306 | −0.798838 | ||||||||
\(130\) | 10.2056 | 0.895086 | ||||||||
\(131\) | −6.35720 | −0.555431 | −0.277716 | − | 0.960663i | \(-0.589577\pi\) | ||||
−0.277716 | + | 0.960663i | \(0.589577\pi\) | |||||||
\(132\) | −1.04888 | −0.0912929 | ||||||||
\(133\) | 7.83276 | 0.679187 | ||||||||
\(134\) | 18.2056 | 1.57272 | ||||||||
\(135\) | 1.10278 | 0.0949118 | ||||||||
\(136\) | 4.37279 | 0.374963 | ||||||||
\(137\) | −17.4897 | −1.49425 | −0.747123 | − | 0.664686i | \(-0.768565\pi\) | ||||
−0.747123 | + | 0.664686i | \(0.768565\pi\) | |||||||
\(138\) | −1.62721 | −0.138518 | ||||||||
\(139\) | 15.7250 | 1.33377 | 0.666887 | − | 0.745159i | \(-0.267626\pi\) | ||||
0.666887 | + | 0.745159i | \(0.267626\pi\) | |||||||
\(140\) | −3.58890 | −0.303317 | ||||||||
\(141\) | 0.235269 | 0.0198133 | ||||||||
\(142\) | 23.2388 | 1.95016 | ||||||||
\(143\) | 4.15165 | 0.347178 | ||||||||
\(144\) | −4.91638 | −0.409698 | ||||||||
\(145\) | −4.89722 | −0.406692 | ||||||||
\(146\) | −8.63224 | −0.714409 | ||||||||
\(147\) | 0.627213 | 0.0517317 | ||||||||
\(148\) | 2.68614 | 0.220799 | ||||||||
\(149\) | 11.5678 | 0.947669 | 0.473835 | − | 0.880614i | \(-0.342869\pi\) | ||||
0.473835 | + | 0.880614i | \(0.342869\pi\) | |||||||
\(150\) | −6.86248 | −0.560319 | ||||||||
\(151\) | 19.2544 | 1.56690 | 0.783451 | − | 0.621453i | \(-0.213457\pi\) | ||||
0.783451 | + | 0.621453i | \(0.213457\pi\) | |||||||
\(152\) | 4.00000 | 0.324443 | ||||||||
\(153\) | 3.39194 | 0.274222 | ||||||||
\(154\) | −3.72496 | −0.300166 | ||||||||
\(155\) | 9.88666 | 0.794116 | ||||||||
\(156\) | −6.57834 | −0.526688 | ||||||||
\(157\) | −20.9200 | −1.66959 | −0.834797 | − | 0.550558i | \(-0.814415\pi\) | ||||
−0.834797 | + | 0.550558i | \(0.814415\pi\) | |||||||
\(158\) | 28.7144 | 2.28440 | ||||||||
\(159\) | −13.8328 | −1.09701 | ||||||||
\(160\) | −6.98944 | −0.552564 | ||||||||
\(161\) | −2.26499 | −0.178506 | ||||||||
\(162\) | −1.81361 | −0.142490 | ||||||||
\(163\) | −12.7980 | −1.00242 | −0.501209 | − | 0.865326i | \(-0.667111\pi\) | ||||
−0.501209 | + | 0.865326i | \(0.667111\pi\) | |||||||
\(164\) | 1.28917 | 0.100667 | ||||||||
\(165\) | 0.897225 | 0.0698489 | ||||||||
\(166\) | 13.9305 | 1.08122 | ||||||||
\(167\) | 9.62721 | 0.744976 | 0.372488 | − | 0.928037i | \(-0.378505\pi\) | ||||
0.372488 | + | 0.928037i | \(0.378505\pi\) | |||||||
\(168\) | −3.25443 | −0.251084 | ||||||||
\(169\) | 13.0383 | 1.00295 | ||||||||
\(170\) | 6.78389 | 0.520300 | ||||||||
\(171\) | 3.10278 | 0.237275 | ||||||||
\(172\) | 11.6967 | 0.891865 | ||||||||
\(173\) | 11.9461 | 0.908245 | 0.454123 | − | 0.890939i | \(-0.349953\pi\) | ||||
0.454123 | + | 0.890939i | \(0.349953\pi\) | |||||||
\(174\) | 8.05390 | 0.610565 | ||||||||
\(175\) | −9.55219 | −0.722078 | ||||||||
\(176\) | −4.00000 | −0.301511 | ||||||||
\(177\) | −1.04888 | −0.0788383 | ||||||||
\(178\) | −24.0383 | −1.80175 | ||||||||
\(179\) | −2.13752 | −0.159766 | −0.0798828 | − | 0.996804i | \(-0.525455\pi\) | ||||
−0.0798828 | + | 0.996804i | \(0.525455\pi\) | |||||||
\(180\) | −1.42166 | −0.105964 | ||||||||
\(181\) | −1.83276 | −0.136228 | −0.0681141 | − | 0.997678i | \(-0.521698\pi\) | ||||
−0.0681141 | + | 0.997678i | \(0.521698\pi\) | |||||||
\(182\) | −23.3622 | −1.73172 | ||||||||
\(183\) | −1.91638 | −0.141663 | ||||||||
\(184\) | −1.15667 | −0.0852712 | ||||||||
\(185\) | −2.29776 | −0.168935 | ||||||||
\(186\) | −16.2594 | −1.19220 | ||||||||
\(187\) | 2.75971 | 0.201810 | ||||||||
\(188\) | −0.303302 | −0.0221206 | ||||||||
\(189\) | −2.52444 | −0.183626 | ||||||||
\(190\) | 6.20555 | 0.450198 | ||||||||
\(191\) | −18.6167 | −1.34705 | −0.673527 | − | 0.739163i | \(-0.735221\pi\) | ||||
−0.673527 | + | 0.739163i | \(0.735221\pi\) | |||||||
\(192\) | 1.66196 | 0.119941 | ||||||||
\(193\) | 15.6116 | 1.12375 | 0.561875 | − | 0.827222i | \(-0.310080\pi\) | ||||
0.561875 | + | 0.827222i | \(0.310080\pi\) | |||||||
\(194\) | −4.95112 | −0.355470 | ||||||||
\(195\) | 5.62721 | 0.402973 | ||||||||
\(196\) | −0.808583 | −0.0577559 | ||||||||
\(197\) | −5.21057 | −0.371238 | −0.185619 | − | 0.982622i | \(-0.559429\pi\) | ||||
−0.185619 | + | 0.982622i | \(0.559429\pi\) | |||||||
\(198\) | −1.47556 | −0.104864 | ||||||||
\(199\) | 2.05390 | 0.145597 | 0.0727985 | − | 0.997347i | \(-0.476807\pi\) | ||||
0.0727985 | + | 0.997347i | \(0.476807\pi\) | |||||||
\(200\) | −4.87807 | −0.344932 | ||||||||
\(201\) | 10.0383 | 0.708048 | ||||||||
\(202\) | 21.5139 | 1.51371 | ||||||||
\(203\) | 11.2106 | 0.786828 | ||||||||
\(204\) | −4.37279 | −0.306156 | ||||||||
\(205\) | −1.10278 | −0.0770212 | ||||||||
\(206\) | 0.897225 | 0.0625126 | ||||||||
\(207\) | −0.897225 | −0.0623614 | ||||||||
\(208\) | −25.0872 | −1.73948 | ||||||||
\(209\) | 2.52444 | 0.174619 | ||||||||
\(210\) | −5.04888 | −0.348406 | ||||||||
\(211\) | −9.04888 | −0.622950 | −0.311475 | − | 0.950254i | \(-0.600823\pi\) | ||||
−0.311475 | + | 0.950254i | \(0.600823\pi\) | |||||||
\(212\) | 17.8328 | 1.22476 | ||||||||
\(213\) | 12.8136 | 0.877974 | ||||||||
\(214\) | 27.3622 | 1.87044 | ||||||||
\(215\) | −10.0055 | −0.682372 | ||||||||
\(216\) | −1.28917 | −0.0877168 | ||||||||
\(217\) | −22.6322 | −1.53638 | ||||||||
\(218\) | −9.25443 | −0.626789 | ||||||||
\(219\) | −4.75971 | −0.321631 | ||||||||
\(220\) | −1.15667 | −0.0779830 | ||||||||
\(221\) | 17.3083 | 1.16428 | ||||||||
\(222\) | 3.77886 | 0.253621 | ||||||||
\(223\) | 24.8222 | 1.66222 | 0.831109 | − | 0.556110i | \(-0.187707\pi\) | ||||
0.831109 | + | 0.556110i | \(0.187707\pi\) | |||||||
\(224\) | 16.0000 | 1.06904 | ||||||||
\(225\) | −3.78389 | −0.252259 | ||||||||
\(226\) | 31.7633 | 2.11286 | ||||||||
\(227\) | 16.6464 | 1.10486 | 0.552429 | − | 0.833560i | \(-0.313701\pi\) | ||||
0.552429 | + | 0.833560i | \(0.313701\pi\) | |||||||
\(228\) | −4.00000 | −0.264906 | ||||||||
\(229\) | −15.7789 | −1.04270 | −0.521348 | − | 0.853344i | \(-0.674571\pi\) | ||||
−0.521348 | + | 0.853344i | \(0.674571\pi\) | |||||||
\(230\) | −1.79445 | −0.118323 | ||||||||
\(231\) | −2.05390 | −0.135137 | ||||||||
\(232\) | 5.72496 | 0.375862 | ||||||||
\(233\) | −24.9200 | −1.63256 | −0.816280 | − | 0.577656i | \(-0.803967\pi\) | ||||
−0.816280 | + | 0.577656i | \(0.803967\pi\) | |||||||
\(234\) | −9.25443 | −0.604981 | ||||||||
\(235\) | 0.259449 | 0.0169246 | ||||||||
\(236\) | 1.35218 | 0.0880193 | ||||||||
\(237\) | 15.8328 | 1.02845 | ||||||||
\(238\) | −15.5295 | −1.00663 | ||||||||
\(239\) | −2.95112 | −0.190892 | −0.0954462 | − | 0.995435i | \(-0.530428\pi\) | ||||
−0.0954462 | + | 0.995435i | \(0.530428\pi\) | |||||||
\(240\) | −5.42166 | −0.349967 | ||||||||
\(241\) | −16.5925 | −1.06881 | −0.534407 | − | 0.845227i | \(-0.679465\pi\) | ||||
−0.534407 | + | 0.845227i | \(0.679465\pi\) | |||||||
\(242\) | 18.7491 | 1.20524 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 2.47054 | 0.158160 | ||||||||
\(245\) | 0.691675 | 0.0441895 | ||||||||
\(246\) | 1.81361 | 0.115631 | ||||||||
\(247\) | 15.8328 | 1.00741 | ||||||||
\(248\) | −11.5577 | −0.733916 | ||||||||
\(249\) | 7.68111 | 0.486771 | ||||||||
\(250\) | −17.5678 | −1.11108 | ||||||||
\(251\) | −20.1361 | −1.27098 | −0.635489 | − | 0.772110i | \(-0.719201\pi\) | ||||
−0.635489 | + | 0.772110i | \(0.719201\pi\) | |||||||
\(252\) | 3.25443 | 0.205010 | ||||||||
\(253\) | −0.729988 | −0.0458940 | ||||||||
\(254\) | −23.3622 | −1.46588 | ||||||||
\(255\) | 3.74055 | 0.234242 | ||||||||
\(256\) | 20.8469 | 1.30293 | ||||||||
\(257\) | 25.9008 | 1.61565 | 0.807824 | − | 0.589424i | \(-0.200645\pi\) | ||||
0.807824 | + | 0.589424i | \(0.200645\pi\) | |||||||
\(258\) | 16.4550 | 1.02444 | ||||||||
\(259\) | 5.25997 | 0.326838 | ||||||||
\(260\) | −7.25443 | −0.449900 | ||||||||
\(261\) | 4.44082 | 0.274880 | ||||||||
\(262\) | 11.5295 | 0.712292 | ||||||||
\(263\) | −22.4408 | −1.38376 | −0.691880 | − | 0.722012i | \(-0.743217\pi\) | ||||
−0.691880 | + | 0.722012i | \(0.743217\pi\) | |||||||
\(264\) | −1.04888 | −0.0645538 | ||||||||
\(265\) | −15.2544 | −0.937072 | ||||||||
\(266\) | −14.2056 | −0.870998 | ||||||||
\(267\) | −13.2544 | −0.811158 | ||||||||
\(268\) | −12.9411 | −0.790502 | ||||||||
\(269\) | 7.62721 | 0.465039 | 0.232520 | − | 0.972592i | \(-0.425303\pi\) | ||||
0.232520 | + | 0.972592i | \(0.425303\pi\) | |||||||
\(270\) | −2.00000 | −0.121716 | ||||||||
\(271\) | 19.9164 | 1.20983 | 0.604917 | − | 0.796289i | \(-0.293206\pi\) | ||||
0.604917 | + | 0.796289i | \(0.293206\pi\) | |||||||
\(272\) | −16.6761 | −1.01114 | ||||||||
\(273\) | −12.8816 | −0.779632 | ||||||||
\(274\) | 31.7194 | 1.91624 | ||||||||
\(275\) | −3.07860 | −0.185646 | ||||||||
\(276\) | 1.15667 | 0.0696236 | ||||||||
\(277\) | −17.6413 | −1.05997 | −0.529983 | − | 0.848008i | \(-0.677802\pi\) | ||||
−0.529983 | + | 0.848008i | \(0.677802\pi\) | |||||||
\(278\) | −28.5189 | −1.71045 | ||||||||
\(279\) | −8.96526 | −0.536736 | ||||||||
\(280\) | −3.58890 | −0.214478 | ||||||||
\(281\) | −0.0297193 | −0.00177291 | −0.000886453 | − | 1.00000i | \(-0.500282\pi\) | ||||
−0.000886453 | 1.00000i | \(0.500282\pi\) | ||||||||
\(282\) | −0.426686 | −0.0254088 | ||||||||
\(283\) | −10.1814 | −0.605220 | −0.302610 | − | 0.953115i | \(-0.597858\pi\) | ||||
−0.302610 | + | 0.953115i | \(0.597858\pi\) | |||||||
\(284\) | −16.5189 | −0.980216 | ||||||||
\(285\) | 3.42166 | 0.202682 | ||||||||
\(286\) | −7.52946 | −0.445226 | ||||||||
\(287\) | 2.52444 | 0.149013 | ||||||||
\(288\) | 6.33804 | 0.373473 | ||||||||
\(289\) | −5.49472 | −0.323219 | ||||||||
\(290\) | 8.88164 | 0.521548 | ||||||||
\(291\) | −2.72999 | −0.160035 | ||||||||
\(292\) | 6.13607 | 0.359086 | ||||||||
\(293\) | 3.14808 | 0.183913 | 0.0919564 | − | 0.995763i | \(-0.470688\pi\) | ||||
0.0919564 | + | 0.995763i | \(0.470688\pi\) | |||||||
\(294\) | −1.13752 | −0.0663414 | ||||||||
\(295\) | −1.15667 | −0.0673442 | ||||||||
\(296\) | 2.68614 | 0.156128 | ||||||||
\(297\) | −0.813607 | −0.0472102 | ||||||||
\(298\) | −20.9794 | −1.21530 | ||||||||
\(299\) | −4.57834 | −0.264772 | ||||||||
\(300\) | 4.87807 | 0.281635 | ||||||||
\(301\) | 22.9044 | 1.32019 | ||||||||
\(302\) | −34.9200 | −2.00942 | ||||||||
\(303\) | 11.8625 | 0.681482 | ||||||||
\(304\) | −15.2544 | −0.874901 | ||||||||
\(305\) | −2.11334 | −0.121009 | ||||||||
\(306\) | −6.15165 | −0.351666 | ||||||||
\(307\) | −12.7980 | −0.730422 | −0.365211 | − | 0.930925i | \(-0.619003\pi\) | ||||
−0.365211 | + | 0.930925i | \(0.619003\pi\) | |||||||
\(308\) | 2.64782 | 0.150874 | ||||||||
\(309\) | 0.494719 | 0.0281436 | ||||||||
\(310\) | −17.9305 | −1.01838 | ||||||||
\(311\) | 26.6167 | 1.50929 | 0.754646 | − | 0.656132i | \(-0.227809\pi\) | ||||
0.754646 | + | 0.656132i | \(0.227809\pi\) | |||||||
\(312\) | −6.57834 | −0.372425 | ||||||||
\(313\) | −3.00502 | −0.169854 | −0.0849270 | − | 0.996387i | \(-0.527066\pi\) | ||||
−0.0849270 | + | 0.996387i | \(0.527066\pi\) | |||||||
\(314\) | 37.9406 | 2.14111 | ||||||||
\(315\) | −2.78389 | −0.156854 | ||||||||
\(316\) | −20.4111 | −1.14821 | ||||||||
\(317\) | −4.33302 | −0.243367 | −0.121683 | − | 0.992569i | \(-0.538829\pi\) | ||||
−0.121683 | + | 0.992569i | \(0.538829\pi\) | |||||||
\(318\) | 25.0872 | 1.40682 | ||||||||
\(319\) | 3.61308 | 0.202294 | ||||||||
\(320\) | 1.83276 | 0.102455 | ||||||||
\(321\) | 15.0872 | 0.842085 | ||||||||
\(322\) | 4.10780 | 0.228919 | ||||||||
\(323\) | 10.5244 | 0.585595 | ||||||||
\(324\) | 1.28917 | 0.0716205 | ||||||||
\(325\) | −19.3083 | −1.07103 | ||||||||
\(326\) | 23.2106 | 1.28551 | ||||||||
\(327\) | −5.10278 | −0.282184 | ||||||||
\(328\) | 1.28917 | 0.0711824 | ||||||||
\(329\) | −0.593923 | −0.0327440 | ||||||||
\(330\) | −1.62721 | −0.0895751 | ||||||||
\(331\) | 5.53500 | 0.304231 | 0.152116 | − | 0.988363i | \(-0.451391\pi\) | ||||
0.152116 | + | 0.988363i | \(0.451391\pi\) | |||||||
\(332\) | −9.90225 | −0.543456 | ||||||||
\(333\) | 2.08362 | 0.114182 | ||||||||
\(334\) | −17.4600 | −0.955367 | ||||||||
\(335\) | 11.0700 | 0.604819 | ||||||||
\(336\) | 12.4111 | 0.677081 | ||||||||
\(337\) | −3.71083 | −0.202142 | −0.101071 | − | 0.994879i | \(-0.532227\pi\) | ||||
−0.101071 | + | 0.994879i | \(0.532227\pi\) | |||||||
\(338\) | −23.6464 | −1.28619 | ||||||||
\(339\) | 17.5139 | 0.951223 | ||||||||
\(340\) | −4.82220 | −0.261521 | ||||||||
\(341\) | −7.29419 | −0.395003 | ||||||||
\(342\) | −5.62721 | −0.304285 | ||||||||
\(343\) | −19.2544 | −1.03964 | ||||||||
\(344\) | 11.6967 | 0.630644 | ||||||||
\(345\) | −0.989437 | −0.0532695 | ||||||||
\(346\) | −21.6655 | −1.16475 | ||||||||
\(347\) | 3.07860 | 0.165268 | 0.0826338 | − | 0.996580i | \(-0.473667\pi\) | ||||
0.0826338 | + | 0.996580i | \(0.473667\pi\) | |||||||
\(348\) | −5.72496 | −0.306890 | ||||||||
\(349\) | 14.7980 | 0.792120 | 0.396060 | − | 0.918225i | \(-0.370377\pi\) | ||||
0.396060 | + | 0.918225i | \(0.370377\pi\) | |||||||
\(350\) | 17.3239 | 0.926002 | ||||||||
\(351\) | −5.10278 | −0.272366 | ||||||||
\(352\) | 5.15667 | 0.274852 | ||||||||
\(353\) | 26.8222 | 1.42760 | 0.713801 | − | 0.700349i | \(-0.246972\pi\) | ||||
0.713801 | + | 0.700349i | \(0.246972\pi\) | |||||||
\(354\) | 1.90225 | 0.101103 | ||||||||
\(355\) | 14.1305 | 0.749970 | ||||||||
\(356\) | 17.0872 | 0.905619 | ||||||||
\(357\) | −8.56275 | −0.453189 | ||||||||
\(358\) | 3.87662 | 0.204886 | ||||||||
\(359\) | 2.35720 | 0.124408 | 0.0622042 | − | 0.998063i | \(-0.480187\pi\) | ||||
0.0622042 | + | 0.998063i | \(0.480187\pi\) | |||||||
\(360\) | −1.42166 | −0.0749282 | ||||||||
\(361\) | −9.37279 | −0.493305 | ||||||||
\(362\) | 3.32391 | 0.174701 | ||||||||
\(363\) | 10.3380 | 0.542607 | ||||||||
\(364\) | 16.6066 | 0.870423 | ||||||||
\(365\) | −5.24889 | −0.274739 | ||||||||
\(366\) | 3.47556 | 0.181671 | ||||||||
\(367\) | 23.1708 | 1.20951 | 0.604753 | − | 0.796413i | \(-0.293272\pi\) | ||||
0.604753 | + | 0.796413i | \(0.293272\pi\) | |||||||
\(368\) | 4.41110 | 0.229944 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | 4.16724 | 0.216644 | ||||||||
\(371\) | 34.9200 | 1.81295 | ||||||||
\(372\) | 11.5577 | 0.599240 | ||||||||
\(373\) | 35.2091 | 1.82306 | 0.911530 | − | 0.411235i | \(-0.134902\pi\) | ||||
0.911530 | + | 0.411235i | \(0.134902\pi\) | |||||||
\(374\) | −5.00502 | −0.258804 | ||||||||
\(375\) | −9.68665 | −0.500217 | ||||||||
\(376\) | −0.303302 | −0.0156416 | ||||||||
\(377\) | 22.6605 | 1.16708 | ||||||||
\(378\) | 4.57834 | 0.235484 | ||||||||
\(379\) | −26.0383 | −1.33750 | −0.668749 | − | 0.743488i | \(-0.733170\pi\) | ||||
−0.668749 | + | 0.743488i | \(0.733170\pi\) | |||||||
\(380\) | −4.41110 | −0.226285 | ||||||||
\(381\) | −12.8816 | −0.659946 | ||||||||
\(382\) | 33.7633 | 1.72748 | ||||||||
\(383\) | 15.3819 | 0.785978 | 0.392989 | − | 0.919543i | \(-0.371441\pi\) | ||||
0.392989 | + | 0.919543i | \(0.371441\pi\) | |||||||
\(384\) | 9.66196 | 0.493060 | ||||||||
\(385\) | −2.26499 | −0.115435 | ||||||||
\(386\) | −28.3133 | −1.44111 | ||||||||
\(387\) | 9.07306 | 0.461209 | ||||||||
\(388\) | 3.51941 | 0.178671 | ||||||||
\(389\) | 4.46500 | 0.226384 | 0.113192 | − | 0.993573i | \(-0.463892\pi\) | ||||
0.113192 | + | 0.993573i | \(0.463892\pi\) | |||||||
\(390\) | −10.2056 | −0.516778 | ||||||||
\(391\) | −3.04334 | −0.153908 | ||||||||
\(392\) | −0.808583 | −0.0408396 | ||||||||
\(393\) | 6.35720 | 0.320678 | ||||||||
\(394\) | 9.44993 | 0.476081 | ||||||||
\(395\) | 17.4600 | 0.878507 | ||||||||
\(396\) | 1.04888 | 0.0527080 | ||||||||
\(397\) | −10.5628 | −0.530129 | −0.265065 | − | 0.964231i | \(-0.585393\pi\) | ||||
−0.265065 | + | 0.964231i | \(0.585393\pi\) | |||||||
\(398\) | −3.72496 | −0.186716 | ||||||||
\(399\) | −7.83276 | −0.392129 | ||||||||
\(400\) | 18.6030 | 0.930152 | ||||||||
\(401\) | 13.0872 | 0.653543 | 0.326772 | − | 0.945103i | \(-0.394039\pi\) | ||||
0.326772 | + | 0.945103i | \(0.394039\pi\) | |||||||
\(402\) | −18.2056 | −0.908010 | ||||||||
\(403\) | −45.7477 | −2.27885 | ||||||||
\(404\) | −15.2927 | −0.760842 | ||||||||
\(405\) | −1.10278 | −0.0547973 | ||||||||
\(406\) | −20.3316 | −1.00904 | ||||||||
\(407\) | 1.69525 | 0.0840302 | ||||||||
\(408\) | −4.37279 | −0.216485 | ||||||||
\(409\) | −18.5542 | −0.917444 | −0.458722 | − | 0.888580i | \(-0.651693\pi\) | ||||
−0.458722 | + | 0.888580i | \(0.651693\pi\) | |||||||
\(410\) | 2.00000 | 0.0987730 | ||||||||
\(411\) | 17.4897 | 0.862703 | ||||||||
\(412\) | −0.637776 | −0.0314210 | ||||||||
\(413\) | 2.64782 | 0.130291 | ||||||||
\(414\) | 1.62721 | 0.0799732 | ||||||||
\(415\) | 8.47054 | 0.415802 | ||||||||
\(416\) | 32.3416 | 1.58568 | ||||||||
\(417\) | −15.7250 | −0.770055 | ||||||||
\(418\) | −4.57834 | −0.223934 | ||||||||
\(419\) | −25.6116 | −1.25121 | −0.625605 | − | 0.780140i | \(-0.715148\pi\) | ||||
−0.625605 | + | 0.780140i | \(0.715148\pi\) | |||||||
\(420\) | 3.58890 | 0.175120 | ||||||||
\(421\) | −8.67609 | −0.422847 | −0.211423 | − | 0.977395i | \(-0.567810\pi\) | ||||
−0.211423 | + | 0.977395i | \(0.567810\pi\) | |||||||
\(422\) | 16.4111 | 0.798880 | ||||||||
\(423\) | −0.235269 | −0.0114392 | ||||||||
\(424\) | 17.8328 | 0.866036 | ||||||||
\(425\) | −12.8347 | −0.622576 | ||||||||
\(426\) | −23.2388 | −1.12593 | ||||||||
\(427\) | 4.83779 | 0.234117 | ||||||||
\(428\) | −19.4499 | −0.940148 | ||||||||
\(429\) | −4.15165 | −0.200444 | ||||||||
\(430\) | 18.1461 | 0.875083 | ||||||||
\(431\) | 7.10278 | 0.342129 | 0.171064 | − | 0.985260i | \(-0.445279\pi\) | ||||
0.171064 | + | 0.985260i | \(0.445279\pi\) | |||||||
\(432\) | 4.91638 | 0.236540 | ||||||||
\(433\) | −11.0247 | −0.529813 | −0.264907 | − | 0.964274i | \(-0.585341\pi\) | ||||
−0.264907 | + | 0.964274i | \(0.585341\pi\) | |||||||
\(434\) | 41.0460 | 1.97027 | ||||||||
\(435\) | 4.89722 | 0.234804 | ||||||||
\(436\) | 6.57834 | 0.315045 | ||||||||
\(437\) | −2.78389 | −0.133171 | ||||||||
\(438\) | 8.63224 | 0.412464 | ||||||||
\(439\) | −1.32391 | −0.0631868 | −0.0315934 | − | 0.999501i | \(-0.510058\pi\) | ||||
−0.0315934 | + | 0.999501i | \(0.510058\pi\) | |||||||
\(440\) | −1.15667 | −0.0551423 | ||||||||
\(441\) | −0.627213 | −0.0298673 | ||||||||
\(442\) | −31.3905 | −1.49309 | ||||||||
\(443\) | 15.5889 | 0.740651 | 0.370325 | − | 0.928902i | \(-0.379246\pi\) | ||||
0.370325 | + | 0.928902i | \(0.379246\pi\) | |||||||
\(444\) | −2.68614 | −0.127478 | ||||||||
\(445\) | −14.6167 | −0.692896 | ||||||||
\(446\) | −45.0177 | −2.13165 | ||||||||
\(447\) | −11.5678 | −0.547137 | ||||||||
\(448\) | −4.19550 | −0.198219 | ||||||||
\(449\) | −32.7839 | −1.54717 | −0.773584 | − | 0.633694i | \(-0.781538\pi\) | ||||
−0.773584 | + | 0.633694i | \(0.781538\pi\) | |||||||
\(450\) | 6.86248 | 0.323501 | ||||||||
\(451\) | 0.813607 | 0.0383112 | ||||||||
\(452\) | −22.5783 | −1.06200 | ||||||||
\(453\) | −19.2544 | −0.904652 | ||||||||
\(454\) | −30.1900 | −1.41689 | ||||||||
\(455\) | −14.2056 | −0.665966 | ||||||||
\(456\) | −4.00000 | −0.187317 | ||||||||
\(457\) | −14.1672 | −0.662715 | −0.331358 | − | 0.943505i | \(-0.607507\pi\) | ||||
−0.331358 | + | 0.943505i | \(0.607507\pi\) | |||||||
\(458\) | 28.6167 | 1.33717 | ||||||||
\(459\) | −3.39194 | −0.158322 | ||||||||
\(460\) | 1.27555 | 0.0594729 | ||||||||
\(461\) | −30.0766 | −1.40081 | −0.700404 | − | 0.713747i | \(-0.746997\pi\) | ||||
−0.700404 | + | 0.713747i | \(0.746997\pi\) | |||||||
\(462\) | 3.72496 | 0.173301 | ||||||||
\(463\) | −23.8766 | −1.10964 | −0.554820 | − | 0.831970i | \(-0.687213\pi\) | ||||
−0.554820 | + | 0.831970i | \(0.687213\pi\) | |||||||
\(464\) | −21.8328 | −1.01356 | ||||||||
\(465\) | −9.88666 | −0.458483 | ||||||||
\(466\) | 45.1950 | 2.09362 | ||||||||
\(467\) | −9.73501 | −0.450483 | −0.225241 | − | 0.974303i | \(-0.572317\pi\) | ||||
−0.225241 | + | 0.974303i | \(0.572317\pi\) | |||||||
\(468\) | 6.57834 | 0.304084 | ||||||||
\(469\) | −25.3411 | −1.17014 | ||||||||
\(470\) | −0.470539 | −0.0217043 | ||||||||
\(471\) | 20.9200 | 0.963941 | ||||||||
\(472\) | 1.35218 | 0.0622390 | ||||||||
\(473\) | 7.38190 | 0.339420 | ||||||||
\(474\) | −28.7144 | −1.31890 | ||||||||
\(475\) | −11.7406 | −0.538693 | ||||||||
\(476\) | 11.0388 | 0.505964 | ||||||||
\(477\) | 13.8328 | 0.633359 | ||||||||
\(478\) | 5.35218 | 0.244803 | ||||||||
\(479\) | −1.17635 | −0.0537487 | −0.0268743 | − | 0.999639i | \(-0.508555\pi\) | ||||
−0.0268743 | + | 0.999639i | \(0.508555\pi\) | |||||||
\(480\) | 6.98944 | 0.319023 | ||||||||
\(481\) | 10.6322 | 0.484788 | ||||||||
\(482\) | 30.0922 | 1.37066 | ||||||||
\(483\) | 2.26499 | 0.103061 | ||||||||
\(484\) | −13.3275 | −0.605795 | ||||||||
\(485\) | −3.01056 | −0.136703 | ||||||||
\(486\) | 1.81361 | 0.0822669 | ||||||||
\(487\) | 20.6025 | 0.933589 | 0.466795 | − | 0.884366i | \(-0.345409\pi\) | ||||
0.466795 | + | 0.884366i | \(0.345409\pi\) | |||||||
\(488\) | 2.47054 | 0.111836 | ||||||||
\(489\) | 12.7980 | 0.578746 | ||||||||
\(490\) | −1.25443 | −0.0566692 | ||||||||
\(491\) | 14.1900 | 0.640384 | 0.320192 | − | 0.947353i | \(-0.396253\pi\) | ||||
0.320192 | + | 0.947353i | \(0.396253\pi\) | |||||||
\(492\) | −1.28917 | −0.0581202 | ||||||||
\(493\) | 15.0630 | 0.678404 | ||||||||
\(494\) | −28.7144 | −1.29192 | ||||||||
\(495\) | −0.897225 | −0.0403273 | ||||||||
\(496\) | 44.0766 | 1.97910 | ||||||||
\(497\) | −32.3472 | −1.45097 | ||||||||
\(498\) | −13.9305 | −0.624241 | ||||||||
\(499\) | −21.4600 | −0.960680 | −0.480340 | − | 0.877082i | \(-0.659487\pi\) | ||||
−0.480340 | + | 0.877082i | \(0.659487\pi\) | |||||||
\(500\) | 12.4877 | 0.558468 | ||||||||
\(501\) | −9.62721 | −0.430112 | ||||||||
\(502\) | 36.5189 | 1.62992 | ||||||||
\(503\) | −15.5491 | −0.693302 | −0.346651 | − | 0.937994i | \(-0.612681\pi\) | ||||
−0.346651 | + | 0.937994i | \(0.612681\pi\) | |||||||
\(504\) | 3.25443 | 0.144964 | ||||||||
\(505\) | 13.0816 | 0.582126 | ||||||||
\(506\) | 1.32391 | 0.0588550 | ||||||||
\(507\) | −13.0383 | −0.579052 | ||||||||
\(508\) | 16.6066 | 0.736799 | ||||||||
\(509\) | 22.7542 | 1.00856 | 0.504280 | − | 0.863540i | \(-0.331758\pi\) | ||||
0.504280 | + | 0.863540i | \(0.331758\pi\) | |||||||
\(510\) | −6.78389 | −0.300396 | ||||||||
\(511\) | 12.0156 | 0.531538 | ||||||||
\(512\) | −18.4842 | −0.816892 | ||||||||
\(513\) | −3.10278 | −0.136991 | ||||||||
\(514\) | −46.9739 | −2.07193 | ||||||||
\(515\) | 0.545563 | 0.0240404 | ||||||||
\(516\) | −11.6967 | −0.514918 | ||||||||
\(517\) | −0.191417 | −0.00841850 | ||||||||
\(518\) | −9.53951 | −0.419142 | ||||||||
\(519\) | −11.9461 | −0.524376 | ||||||||
\(520\) | −7.25443 | −0.318128 | ||||||||
\(521\) | −38.7230 | −1.69649 | −0.848243 | − | 0.529608i | \(-0.822339\pi\) | ||||
−0.848243 | + | 0.529608i | \(0.822339\pi\) | |||||||
\(522\) | −8.05390 | −0.352510 | ||||||||
\(523\) | 6.56829 | 0.287211 | 0.143606 | − | 0.989635i | \(-0.454130\pi\) | ||||
0.143606 | + | 0.989635i | \(0.454130\pi\) | |||||||
\(524\) | −8.19550 | −0.358022 | ||||||||
\(525\) | 9.55219 | 0.416892 | ||||||||
\(526\) | 40.6988 | 1.77455 | ||||||||
\(527\) | −30.4096 | −1.32467 | ||||||||
\(528\) | 4.00000 | 0.174078 | ||||||||
\(529\) | −22.1950 | −0.964999 | ||||||||
\(530\) | 27.6655 | 1.20171 | ||||||||
\(531\) | 1.04888 | 0.0455173 | ||||||||
\(532\) | 10.0978 | 0.437793 | ||||||||
\(533\) | 5.10278 | 0.221026 | ||||||||
\(534\) | 24.0383 | 1.04024 | ||||||||
\(535\) | 16.6378 | 0.719314 | ||||||||
\(536\) | −12.9411 | −0.558969 | ||||||||
\(537\) | 2.13752 | 0.0922407 | ||||||||
\(538\) | −13.8328 | −0.596373 | ||||||||
\(539\) | −0.510305 | −0.0219804 | ||||||||
\(540\) | 1.42166 | 0.0611786 | ||||||||
\(541\) | 42.0766 | 1.80902 | 0.904508 | − | 0.426457i | \(-0.140239\pi\) | ||||
0.904508 | + | 0.426457i | \(0.140239\pi\) | |||||||
\(542\) | −36.1205 | −1.55151 | ||||||||
\(543\) | 1.83276 | 0.0786514 | ||||||||
\(544\) | 21.4983 | 0.921732 | ||||||||
\(545\) | −5.62721 | −0.241043 | ||||||||
\(546\) | 23.3622 | 0.999811 | ||||||||
\(547\) | 19.9688 | 0.853805 | 0.426903 | − | 0.904298i | \(-0.359605\pi\) | ||||
0.426903 | + | 0.904298i | \(0.359605\pi\) | |||||||
\(548\) | −22.5472 | −0.963167 | ||||||||
\(549\) | 1.91638 | 0.0817892 | ||||||||
\(550\) | 5.58336 | 0.238075 | ||||||||
\(551\) | 13.7789 | 0.586999 | ||||||||
\(552\) | 1.15667 | 0.0492313 | ||||||||
\(553\) | −39.9688 | −1.69965 | ||||||||
\(554\) | 31.9945 | 1.35931 | ||||||||
\(555\) | 2.29776 | 0.0975346 | ||||||||
\(556\) | 20.2721 | 0.859730 | ||||||||
\(557\) | 13.5491 | 0.574095 | 0.287048 | − | 0.957916i | \(-0.407326\pi\) | ||||
0.287048 | + | 0.957916i | \(0.407326\pi\) | |||||||
\(558\) | 16.2594 | 0.688317 | ||||||||
\(559\) | 46.2978 | 1.95819 | ||||||||
\(560\) | 13.6867 | 0.578367 | ||||||||
\(561\) | −2.75971 | −0.116515 | ||||||||
\(562\) | 0.0538991 | 0.00227360 | ||||||||
\(563\) | 9.75468 | 0.411111 | 0.205555 | − | 0.978645i | \(-0.434100\pi\) | ||||
0.205555 | + | 0.978645i | \(0.434100\pi\) | |||||||
\(564\) | 0.303302 | 0.0127713 | ||||||||
\(565\) | 19.3139 | 0.812540 | ||||||||
\(566\) | 18.4650 | 0.776142 | ||||||||
\(567\) | 2.52444 | 0.106016 | ||||||||
\(568\) | −16.5189 | −0.693118 | ||||||||
\(569\) | −21.4544 | −0.899417 | −0.449708 | − | 0.893175i | \(-0.648472\pi\) | ||||
−0.449708 | + | 0.893175i | \(0.648472\pi\) | |||||||
\(570\) | −6.20555 | −0.259922 | ||||||||
\(571\) | 20.9411 | 0.876357 | 0.438178 | − | 0.898888i | \(-0.355624\pi\) | ||||
0.438178 | + | 0.898888i | \(0.355624\pi\) | |||||||
\(572\) | 5.35218 | 0.223786 | ||||||||
\(573\) | 18.6167 | 0.777722 | ||||||||
\(574\) | −4.57834 | −0.191096 | ||||||||
\(575\) | 3.39500 | 0.141581 | ||||||||
\(576\) | −1.66196 | −0.0692481 | ||||||||
\(577\) | 18.4705 | 0.768939 | 0.384469 | − | 0.923138i | \(-0.374384\pi\) | ||||
0.384469 | + | 0.923138i | \(0.374384\pi\) | |||||||
\(578\) | 9.96526 | 0.414500 | ||||||||
\(579\) | −15.6116 | −0.648797 | ||||||||
\(580\) | −6.31335 | −0.262148 | ||||||||
\(581\) | −19.3905 | −0.804453 | ||||||||
\(582\) | 4.95112 | 0.205231 | ||||||||
\(583\) | 11.2544 | 0.466111 | ||||||||
\(584\) | 6.13607 | 0.253912 | ||||||||
\(585\) | −5.62721 | −0.232657 | ||||||||
\(586\) | −5.70938 | −0.235852 | ||||||||
\(587\) | −0.127471 | −0.00526130 | −0.00263065 | − | 0.999997i | \(-0.500837\pi\) | ||||
−0.00263065 | + | 0.999997i | \(0.500837\pi\) | |||||||
\(588\) | 0.808583 | 0.0333454 | ||||||||
\(589\) | −27.8172 | −1.14619 | ||||||||
\(590\) | 2.09775 | 0.0863631 | ||||||||
\(591\) | 5.21057 | 0.214334 | ||||||||
\(592\) | −10.2439 | −0.421020 | ||||||||
\(593\) | −27.2841 | −1.12043 | −0.560213 | − | 0.828349i | \(-0.689281\pi\) | ||||
−0.560213 | + | 0.828349i | \(0.689281\pi\) | |||||||
\(594\) | 1.47556 | 0.0605430 | ||||||||
\(595\) | −9.44279 | −0.387117 | ||||||||
\(596\) | 14.9128 | 0.610853 | ||||||||
\(597\) | −2.05390 | −0.0840605 | ||||||||
\(598\) | 8.30330 | 0.339547 | ||||||||
\(599\) | −42.3260 | −1.72939 | −0.864697 | − | 0.502293i | \(-0.832490\pi\) | ||||
−0.864697 | + | 0.502293i | \(0.832490\pi\) | |||||||
\(600\) | 4.87807 | 0.199146 | ||||||||
\(601\) | −15.6756 | −0.639420 | −0.319710 | − | 0.947515i | \(-0.603585\pi\) | ||||
−0.319710 | + | 0.947515i | \(0.603585\pi\) | |||||||
\(602\) | −41.5395 | −1.69302 | ||||||||
\(603\) | −10.0383 | −0.408792 | ||||||||
\(604\) | 24.8222 | 1.01000 | ||||||||
\(605\) | 11.4005 | 0.463498 | ||||||||
\(606\) | −21.5139 | −0.873941 | ||||||||
\(607\) | −1.93051 | −0.0783572 | −0.0391786 | − | 0.999232i | \(-0.512474\pi\) | ||||
−0.0391786 | + | 0.999232i | \(0.512474\pi\) | |||||||
\(608\) | 19.6655 | 0.797542 | ||||||||
\(609\) | −11.2106 | −0.454275 | ||||||||
\(610\) | 3.83276 | 0.155184 | ||||||||
\(611\) | −1.20053 | −0.0485681 | ||||||||
\(612\) | 4.37279 | 0.176759 | ||||||||
\(613\) | −0.372787 | −0.0150567 | −0.00752836 | − | 0.999972i | \(-0.502396\pi\) | ||||
−0.00752836 | + | 0.999972i | \(0.502396\pi\) | |||||||
\(614\) | 23.2106 | 0.936703 | ||||||||
\(615\) | 1.10278 | 0.0444682 | ||||||||
\(616\) | 2.64782 | 0.106684 | ||||||||
\(617\) | 31.3083 | 1.26043 | 0.630213 | − | 0.776422i | \(-0.282968\pi\) | ||||
0.630213 | + | 0.776422i | \(0.282968\pi\) | |||||||
\(618\) | −0.897225 | −0.0360917 | ||||||||
\(619\) | 34.3658 | 1.38128 | 0.690639 | − | 0.723200i | \(-0.257329\pi\) | ||||
0.690639 | + | 0.723200i | \(0.257329\pi\) | |||||||
\(620\) | 12.7456 | 0.511875 | ||||||||
\(621\) | 0.897225 | 0.0360044 | ||||||||
\(622\) | −48.2721 | −1.93554 | ||||||||
\(623\) | 33.4600 | 1.34055 | ||||||||
\(624\) | 25.0872 | 1.00429 | ||||||||
\(625\) | 8.23724 | 0.329490 | ||||||||
\(626\) | 5.44993 | 0.217823 | ||||||||
\(627\) | −2.52444 | −0.100816 | ||||||||
\(628\) | −26.9693 | −1.07619 | ||||||||
\(629\) | 7.06752 | 0.281800 | ||||||||
\(630\) | 5.04888 | 0.201152 | ||||||||
\(631\) | 7.33804 | 0.292123 | 0.146061 | − | 0.989276i | \(-0.453340\pi\) | ||||
0.146061 | + | 0.989276i | \(0.453340\pi\) | |||||||
\(632\) | −20.4111 | −0.811910 | ||||||||
\(633\) | 9.04888 | 0.359661 | ||||||||
\(634\) | 7.85840 | 0.312097 | ||||||||
\(635\) | −14.2056 | −0.563730 | ||||||||
\(636\) | −17.8328 | −0.707115 | ||||||||
\(637\) | −3.20053 | −0.126809 | ||||||||
\(638\) | −6.55270 | −0.259424 | ||||||||
\(639\) | −12.8136 | −0.506898 | ||||||||
\(640\) | 10.6550 | 0.421174 | ||||||||
\(641\) | −31.5764 | −1.24719 | −0.623596 | − | 0.781747i | \(-0.714329\pi\) | ||||
−0.623596 | + | 0.781747i | \(0.714329\pi\) | |||||||
\(642\) | −27.3622 | −1.07990 | ||||||||
\(643\) | −4.51890 | −0.178208 | −0.0891040 | − | 0.996022i | \(-0.528400\pi\) | ||||
−0.0891040 | + | 0.996022i | \(0.528400\pi\) | |||||||
\(644\) | −2.91995 | −0.115062 | ||||||||
\(645\) | 10.0055 | 0.393968 | ||||||||
\(646\) | −19.0872 | −0.750975 | ||||||||
\(647\) | −20.6705 | −0.812643 | −0.406322 | − | 0.913730i | \(-0.633189\pi\) | ||||
−0.406322 | + | 0.913730i | \(0.633189\pi\) | |||||||
\(648\) | 1.28917 | 0.0506433 | ||||||||
\(649\) | 0.853372 | 0.0334978 | ||||||||
\(650\) | 35.0177 | 1.37351 | ||||||||
\(651\) | 22.6322 | 0.887027 | ||||||||
\(652\) | −16.4988 | −0.646143 | ||||||||
\(653\) | 0.381381 | 0.0149246 | 0.00746229 | − | 0.999972i | \(-0.497625\pi\) | ||||
0.00746229 | + | 0.999972i | \(0.497625\pi\) | |||||||
\(654\) | 9.25443 | 0.361877 | ||||||||
\(655\) | 7.01056 | 0.273925 | ||||||||
\(656\) | −4.91638 | −0.191952 | ||||||||
\(657\) | 4.75971 | 0.185694 | ||||||||
\(658\) | 1.07714 | 0.0419914 | ||||||||
\(659\) | 13.4600 | 0.524326 | 0.262163 | − | 0.965024i | \(-0.415564\pi\) | ||||
0.262163 | + | 0.965024i | \(0.415564\pi\) | |||||||
\(660\) | 1.15667 | 0.0450235 | ||||||||
\(661\) | 30.7738 | 1.19696 | 0.598482 | − | 0.801136i | \(-0.295771\pi\) | ||||
0.598482 | + | 0.801136i | \(0.295771\pi\) | |||||||
\(662\) | −10.0383 | −0.390150 | ||||||||
\(663\) | −17.3083 | −0.672200 | ||||||||
\(664\) | −9.90225 | −0.384282 | ||||||||
\(665\) | −8.63778 | −0.334959 | ||||||||
\(666\) | −3.77886 | −0.146428 | ||||||||
\(667\) | −3.98441 | −0.154277 | ||||||||
\(668\) | 12.4111 | 0.480200 | ||||||||
\(669\) | −24.8222 | −0.959682 | ||||||||
\(670\) | −20.0766 | −0.775628 | ||||||||
\(671\) | 1.55918 | 0.0601915 | ||||||||
\(672\) | −16.0000 | −0.617213 | ||||||||
\(673\) | 1.48110 | 0.0570923 | 0.0285461 | − | 0.999592i | \(-0.490912\pi\) | ||||
0.0285461 | + | 0.999592i | \(0.490912\pi\) | |||||||
\(674\) | 6.72999 | 0.259229 | ||||||||
\(675\) | 3.78389 | 0.145642 | ||||||||
\(676\) | 16.8086 | 0.646484 | ||||||||
\(677\) | 45.3749 | 1.74390 | 0.871950 | − | 0.489596i | \(-0.162856\pi\) | ||||
0.871950 | + | 0.489596i | \(0.162856\pi\) | |||||||
\(678\) | −31.7633 | −1.21986 | ||||||||
\(679\) | 6.89169 | 0.264479 | ||||||||
\(680\) | −4.82220 | −0.184923 | ||||||||
\(681\) | −16.6464 | −0.637890 | ||||||||
\(682\) | 13.2288 | 0.506557 | ||||||||
\(683\) | −0.0594386 | −0.00227436 | −0.00113718 | − | 0.999999i | \(-0.500362\pi\) | ||||
−0.00113718 | + | 0.999999i | \(0.500362\pi\) | |||||||
\(684\) | 4.00000 | 0.152944 | ||||||||
\(685\) | 19.2872 | 0.736926 | ||||||||
\(686\) | 34.9200 | 1.33325 | ||||||||
\(687\) | 15.7789 | 0.602001 | ||||||||
\(688\) | −44.6066 | −1.70061 | ||||||||
\(689\) | 70.5855 | 2.68909 | ||||||||
\(690\) | 1.79445 | 0.0683135 | ||||||||
\(691\) | −18.9355 | −0.720342 | −0.360171 | − | 0.932886i | \(-0.617282\pi\) | ||||
−0.360171 | + | 0.932886i | \(0.617282\pi\) | |||||||
\(692\) | 15.4005 | 0.585441 | ||||||||
\(693\) | 2.05390 | 0.0780212 | ||||||||
\(694\) | −5.58336 | −0.211941 | ||||||||
\(695\) | −17.3411 | −0.657785 | ||||||||
\(696\) | −5.72496 | −0.217004 | ||||||||
\(697\) | 3.39194 | 0.128479 | ||||||||
\(698\) | −26.8378 | −1.01583 | ||||||||
\(699\) | 24.9200 | 0.942559 | ||||||||
\(700\) | −12.3144 | −0.465440 | ||||||||
\(701\) | −0.540024 | −0.0203964 | −0.0101982 | − | 0.999948i | \(-0.503246\pi\) | ||||
−0.0101982 | + | 0.999948i | \(0.503246\pi\) | |||||||
\(702\) | 9.25443 | 0.349286 | ||||||||
\(703\) | 6.46500 | 0.243832 | ||||||||
\(704\) | −1.35218 | −0.0509621 | ||||||||
\(705\) | −0.259449 | −0.00977142 | ||||||||
\(706\) | −48.6449 | −1.83078 | ||||||||
\(707\) | −29.9461 | −1.12624 | ||||||||
\(708\) | −1.35218 | −0.0508180 | ||||||||
\(709\) | 28.0867 | 1.05482 | 0.527409 | − | 0.849612i | \(-0.323164\pi\) | ||||
0.527409 | + | 0.849612i | \(0.323164\pi\) | |||||||
\(710\) | −25.6272 | −0.961772 | ||||||||
\(711\) | −15.8328 | −0.593775 | ||||||||
\(712\) | 17.0872 | 0.640369 | ||||||||
\(713\) | 8.04385 | 0.301245 | ||||||||
\(714\) | 15.5295 | 0.581175 | ||||||||
\(715\) | −4.57834 | −0.171220 | ||||||||
\(716\) | −2.75562 | −0.102982 | ||||||||
\(717\) | 2.95112 | 0.110212 | ||||||||
\(718\) | −4.27504 | −0.159543 | ||||||||
\(719\) | 9.86248 | 0.367809 | 0.183904 | − | 0.982944i | \(-0.441126\pi\) | ||||
0.183904 | + | 0.982944i | \(0.441126\pi\) | |||||||
\(720\) | 5.42166 | 0.202053 | ||||||||
\(721\) | −1.24889 | −0.0465110 | ||||||||
\(722\) | 16.9985 | 0.632620 | ||||||||
\(723\) | 16.5925 | 0.617081 | ||||||||
\(724\) | −2.36274 | −0.0878106 | ||||||||
\(725\) | −16.8036 | −0.624069 | ||||||||
\(726\) | −18.7491 | −0.695846 | ||||||||
\(727\) | −30.4650 | −1.12988 | −0.564942 | − | 0.825131i | \(-0.691102\pi\) | ||||
−0.564942 | + | 0.825131i | \(0.691102\pi\) | |||||||
\(728\) | 16.6066 | 0.615482 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 9.51941 | 0.352329 | ||||||||
\(731\) | 30.7753 | 1.13827 | ||||||||
\(732\) | −2.47054 | −0.0913137 | ||||||||
\(733\) | 27.5436 | 1.01735 | 0.508673 | − | 0.860960i | \(-0.330136\pi\) | ||||
0.508673 | + | 0.860960i | \(0.330136\pi\) | |||||||
\(734\) | −42.0227 | −1.55109 | ||||||||
\(735\) | −0.691675 | −0.0255128 | ||||||||
\(736\) | −5.68665 | −0.209613 | ||||||||
\(737\) | −8.16724 | −0.300844 | ||||||||
\(738\) | −1.81361 | −0.0667598 | ||||||||
\(739\) | 13.1013 | 0.481940 | 0.240970 | − | 0.970533i | \(-0.422534\pi\) | ||||
0.240970 | + | 0.970533i | \(0.422534\pi\) | |||||||
\(740\) | −2.96220 | −0.108893 | ||||||||
\(741\) | −15.8328 | −0.581631 | ||||||||
\(742\) | −63.3311 | −2.32496 | ||||||||
\(743\) | 34.7527 | 1.27495 | 0.637477 | − | 0.770470i | \(-0.279978\pi\) | ||||
0.637477 | + | 0.770470i | \(0.279978\pi\) | |||||||
\(744\) | 11.5577 | 0.423727 | ||||||||
\(745\) | −12.7567 | −0.467368 | ||||||||
\(746\) | −63.8555 | −2.33792 | ||||||||
\(747\) | −7.68111 | −0.281037 | ||||||||
\(748\) | 3.55773 | 0.130083 | ||||||||
\(749\) | −38.0867 | −1.39166 | ||||||||
\(750\) | 17.5678 | 0.641484 | ||||||||
\(751\) | 32.7738 | 1.19593 | 0.597967 | − | 0.801521i | \(-0.295975\pi\) | ||||
0.597967 | + | 0.801521i | \(0.295975\pi\) | |||||||
\(752\) | 1.15667 | 0.0421796 | ||||||||
\(753\) | 20.1361 | 0.733799 | ||||||||
\(754\) | −41.0972 | −1.49667 | ||||||||
\(755\) | −21.2333 | −0.772759 | ||||||||
\(756\) | −3.25443 | −0.118362 | ||||||||
\(757\) | −32.2978 | −1.17388 | −0.586941 | − | 0.809630i | \(-0.699668\pi\) | ||||
−0.586941 | + | 0.809630i | \(0.699668\pi\) | |||||||
\(758\) | 47.2233 | 1.71523 | ||||||||
\(759\) | 0.729988 | 0.0264969 | ||||||||
\(760\) | −4.41110 | −0.160007 | ||||||||
\(761\) | 44.4494 | 1.61129 | 0.805645 | − | 0.592399i | \(-0.201819\pi\) | ||||
0.805645 | + | 0.592399i | \(0.201819\pi\) | |||||||
\(762\) | 23.3622 | 0.846324 | ||||||||
\(763\) | 12.8816 | 0.466347 | ||||||||
\(764\) | −24.0000 | −0.868290 | ||||||||
\(765\) | −3.74055 | −0.135240 | ||||||||
\(766\) | −27.8967 | −1.00795 | ||||||||
\(767\) | 5.35218 | 0.193256 | ||||||||
\(768\) | −20.8469 | −0.752248 | ||||||||
\(769\) | −19.7108 | −0.710791 | −0.355395 | − | 0.934716i | \(-0.615654\pi\) | ||||
−0.355395 | + | 0.934716i | \(0.615654\pi\) | |||||||
\(770\) | 4.10780 | 0.148035 | ||||||||
\(771\) | −25.9008 | −0.932794 | ||||||||
\(772\) | 20.1260 | 0.724351 | ||||||||
\(773\) | 43.2530 | 1.55570 | 0.777851 | − | 0.628449i | \(-0.216310\pi\) | ||||
0.777851 | + | 0.628449i | \(0.216310\pi\) | |||||||
\(774\) | −16.4550 | −0.591461 | ||||||||
\(775\) | 33.9235 | 1.21857 | ||||||||
\(776\) | 3.51941 | 0.126340 | ||||||||
\(777\) | −5.25997 | −0.188700 | ||||||||
\(778\) | −8.09775 | −0.290318 | ||||||||
\(779\) | 3.10278 | 0.111168 | ||||||||
\(780\) | 7.25443 | 0.259750 | ||||||||
\(781\) | −10.4252 | −0.373044 | ||||||||
\(782\) | 5.51941 | 0.197374 | ||||||||
\(783\) | −4.44082 | −0.158702 | ||||||||
\(784\) | 3.08362 | 0.110129 | ||||||||
\(785\) | 23.0700 | 0.823404 | ||||||||
\(786\) | −11.5295 | −0.411242 | ||||||||
\(787\) | −21.4358 | −0.764104 | −0.382052 | − | 0.924141i | \(-0.624782\pi\) | ||||
−0.382052 | + | 0.924141i | \(0.624782\pi\) | |||||||
\(788\) | −6.71731 | −0.239294 | ||||||||
\(789\) | 22.4408 | 0.798914 | ||||||||
\(790\) | −31.6655 | −1.12661 | ||||||||
\(791\) | −44.2127 | −1.57202 | ||||||||
\(792\) | 1.04888 | 0.0372702 | ||||||||
\(793\) | 9.77886 | 0.347258 | ||||||||
\(794\) | 19.1567 | 0.679845 | ||||||||
\(795\) | 15.2544 | 0.541019 | ||||||||
\(796\) | 2.64782 | 0.0938496 | ||||||||
\(797\) | −4.40105 | −0.155893 | −0.0779467 | − | 0.996958i | \(-0.524836\pi\) | ||||
−0.0779467 | + | 0.996958i | \(0.524836\pi\) | |||||||
\(798\) | 14.2056 | 0.502871 | ||||||||
\(799\) | −0.798021 | −0.0282319 | ||||||||
\(800\) | −23.9824 | −0.847907 | ||||||||
\(801\) | 13.2544 | 0.468322 | ||||||||
\(802\) | −23.7350 | −0.838112 | ||||||||
\(803\) | 3.87253 | 0.136659 | ||||||||
\(804\) | 12.9411 | 0.456397 | ||||||||
\(805\) | 2.49777 | 0.0880349 | ||||||||
\(806\) | 82.9683 | 2.92243 | ||||||||
\(807\) | −7.62721 | −0.268491 | ||||||||
\(808\) | −15.2927 | −0.537997 | ||||||||
\(809\) | −26.3799 | −0.927469 | −0.463734 | − | 0.885974i | \(-0.653491\pi\) | ||||
−0.463734 | + | 0.885974i | \(0.653491\pi\) | |||||||
\(810\) | 2.00000 | 0.0702728 | ||||||||
\(811\) | 4.96526 | 0.174354 | 0.0871769 | − | 0.996193i | \(-0.472215\pi\) | ||||
0.0871769 | + | 0.996193i | \(0.472215\pi\) | |||||||
\(812\) | 14.4523 | 0.507177 | ||||||||
\(813\) | −19.9164 | −0.698498 | ||||||||
\(814\) | −3.07451 | −0.107761 | ||||||||
\(815\) | 14.1133 | 0.494369 | ||||||||
\(816\) | 16.6761 | 0.583780 | ||||||||
\(817\) | 28.1517 | 0.984902 | ||||||||
\(818\) | 33.6499 | 1.17654 | ||||||||
\(819\) | 12.8816 | 0.450121 | ||||||||
\(820\) | −1.42166 | −0.0496466 | ||||||||
\(821\) | −15.7789 | −0.550686 | −0.275343 | − | 0.961346i | \(-0.588791\pi\) | ||||
−0.275343 | + | 0.961346i | \(0.588791\pi\) | |||||||
\(822\) | −31.7194 | −1.10634 | ||||||||
\(823\) | −8.35166 | −0.291121 | −0.145560 | − | 0.989349i | \(-0.546498\pi\) | ||||
−0.145560 | + | 0.989349i | \(0.546498\pi\) | |||||||
\(824\) | −0.637776 | −0.0222180 | ||||||||
\(825\) | 3.07860 | 0.107183 | ||||||||
\(826\) | −4.80211 | −0.167087 | ||||||||
\(827\) | −18.3925 | −0.639568 | −0.319784 | − | 0.947490i | \(-0.603610\pi\) | ||||
−0.319784 | + | 0.947490i | \(0.603610\pi\) | |||||||
\(828\) | −1.15667 | −0.0401972 | ||||||||
\(829\) | −29.4147 | −1.02161 | −0.510807 | − | 0.859695i | \(-0.670653\pi\) | ||||
−0.510807 | + | 0.859695i | \(0.670653\pi\) | |||||||
\(830\) | −15.3622 | −0.533231 | ||||||||
\(831\) | 17.6413 | 0.611972 | ||||||||
\(832\) | −8.48059 | −0.294011 | ||||||||
\(833\) | −2.12747 | −0.0737125 | ||||||||
\(834\) | 28.5189 | 0.987529 | ||||||||
\(835\) | −10.6167 | −0.367404 | ||||||||
\(836\) | 3.25443 | 0.112557 | ||||||||
\(837\) | 8.96526 | 0.309885 | ||||||||
\(838\) | 46.4494 | 1.60457 | ||||||||
\(839\) | −33.4600 | −1.15517 | −0.577583 | − | 0.816332i | \(-0.696004\pi\) | ||||
−0.577583 | + | 0.816332i | \(0.696004\pi\) | |||||||
\(840\) | 3.58890 | 0.123829 | ||||||||
\(841\) | −9.27912 | −0.319970 | ||||||||
\(842\) | 15.7350 | 0.542264 | ||||||||
\(843\) | 0.0297193 | 0.00102359 | ||||||||
\(844\) | −11.6655 | −0.401544 | ||||||||
\(845\) | −14.3783 | −0.494629 | ||||||||
\(846\) | 0.426686 | 0.0146698 | ||||||||
\(847\) | −26.0978 | −0.896729 | ||||||||
\(848\) | −68.0071 | −2.33537 | ||||||||
\(849\) | 10.1814 | 0.349424 | ||||||||
\(850\) | 23.2772 | 0.798400 | ||||||||
\(851\) | −1.86947 | −0.0640848 | ||||||||
\(852\) | 16.5189 | 0.565928 | ||||||||
\(853\) | 40.4494 | 1.38496 | 0.692481 | − | 0.721436i | \(-0.256518\pi\) | ||||
0.692481 | + | 0.721436i | \(0.256518\pi\) | |||||||
\(854\) | −8.77384 | −0.300235 | ||||||||
\(855\) | −3.42166 | −0.117018 | ||||||||
\(856\) | −19.4499 | −0.664785 | ||||||||
\(857\) | 12.4494 | 0.425264 | 0.212632 | − | 0.977132i | \(-0.431796\pi\) | ||||
0.212632 | + | 0.977132i | \(0.431796\pi\) | |||||||
\(858\) | 7.52946 | 0.257052 | ||||||||
\(859\) | −21.6514 | −0.738736 | −0.369368 | − | 0.929283i | \(-0.620426\pi\) | ||||
−0.369368 | + | 0.929283i | \(0.620426\pi\) | |||||||
\(860\) | −12.8988 | −0.439846 | ||||||||
\(861\) | −2.52444 | −0.0860326 | ||||||||
\(862\) | −12.8816 | −0.438750 | ||||||||
\(863\) | 19.3778 | 0.659628 | 0.329814 | − | 0.944046i | \(-0.393014\pi\) | ||||
0.329814 | + | 0.944046i | \(0.393014\pi\) | |||||||
\(864\) | −6.33804 | −0.215625 | ||||||||
\(865\) | −13.1739 | −0.447925 | ||||||||
\(866\) | 19.9945 | 0.679439 | ||||||||
\(867\) | 5.49472 | 0.186610 | ||||||||
\(868\) | −29.1768 | −0.990324 | ||||||||
\(869\) | −12.8816 | −0.436980 | ||||||||
\(870\) | −8.88164 | −0.301116 | ||||||||
\(871\) | −51.2233 | −1.73563 | ||||||||
\(872\) | 6.57834 | 0.222771 | ||||||||
\(873\) | 2.72999 | 0.0923961 | ||||||||
\(874\) | 5.04888 | 0.170781 | ||||||||
\(875\) | 24.4534 | 0.826674 | ||||||||
\(876\) | −6.13607 | −0.207318 | ||||||||
\(877\) | −3.08413 | −0.104144 | −0.0520719 | − | 0.998643i | \(-0.516583\pi\) | ||||
−0.0520719 | + | 0.998643i | \(0.516583\pi\) | |||||||
\(878\) | 2.40105 | 0.0810316 | ||||||||
\(879\) | −3.14808 | −0.106182 | ||||||||
\(880\) | 4.41110 | 0.148698 | ||||||||
\(881\) | −34.5783 | −1.16497 | −0.582487 | − | 0.812840i | \(-0.697920\pi\) | ||||
−0.582487 | + | 0.812840i | \(0.697920\pi\) | |||||||
\(882\) | 1.13752 | 0.0383022 | ||||||||
\(883\) | −9.64280 | −0.324506 | −0.162253 | − | 0.986749i | \(-0.551876\pi\) | ||||
−0.162253 | + | 0.986749i | \(0.551876\pi\) | |||||||
\(884\) | 22.3133 | 0.750479 | ||||||||
\(885\) | 1.15667 | 0.0388812 | ||||||||
\(886\) | −28.2721 | −0.949821 | ||||||||
\(887\) | 32.2041 | 1.08131 | 0.540654 | − | 0.841245i | \(-0.318177\pi\) | ||||
0.540654 | + | 0.841245i | \(0.318177\pi\) | |||||||
\(888\) | −2.68614 | −0.0901408 | ||||||||
\(889\) | 32.5189 | 1.09065 | ||||||||
\(890\) | 26.5089 | 0.888579 | ||||||||
\(891\) | 0.813607 | 0.0272568 | ||||||||
\(892\) | 32.0000 | 1.07144 | ||||||||
\(893\) | −0.729988 | −0.0244281 | ||||||||
\(894\) | 20.9794 | 0.701656 | ||||||||
\(895\) | 2.35720 | 0.0787925 | ||||||||
\(896\) | −24.3910 | −0.814846 | ||||||||
\(897\) | 4.57834 | 0.152866 | ||||||||
\(898\) | 59.4571 | 1.98411 | ||||||||
\(899\) | −39.8131 | −1.32784 | ||||||||
\(900\) | −4.87807 | −0.162602 | ||||||||
\(901\) | 46.9200 | 1.56313 | ||||||||
\(902\) | −1.47556 | −0.0491308 | ||||||||
\(903\) | −22.9044 | −0.762210 | ||||||||
\(904\) | −22.5783 | −0.750944 | ||||||||
\(905\) | 2.02113 | 0.0671845 | ||||||||
\(906\) | 34.9200 | 1.16014 | ||||||||
\(907\) | −17.8227 | −0.591794 | −0.295897 | − | 0.955220i | \(-0.595618\pi\) | ||||
−0.295897 | + | 0.955220i | \(0.595618\pi\) | |||||||
\(908\) | 21.4600 | 0.712174 | ||||||||
\(909\) | −11.8625 | −0.393454 | ||||||||
\(910\) | 25.7633 | 0.854044 | ||||||||
\(911\) | −20.7894 | −0.688784 | −0.344392 | − | 0.938826i | \(-0.611915\pi\) | ||||
−0.344392 | + | 0.938826i | \(0.611915\pi\) | |||||||
\(912\) | 15.2544 | 0.505125 | ||||||||
\(913\) | −6.24940 | −0.206825 | ||||||||
\(914\) | 25.6938 | 0.849875 | ||||||||
\(915\) | 2.11334 | 0.0698648 | ||||||||
\(916\) | −20.3416 | −0.672106 | ||||||||
\(917\) | −16.0484 | −0.529964 | ||||||||
\(918\) | 6.15165 | 0.203035 | ||||||||
\(919\) | 33.8555 | 1.11679 | 0.558395 | − | 0.829575i | \(-0.311417\pi\) | ||||
0.558395 | + | 0.829575i | \(0.311417\pi\) | |||||||
\(920\) | 1.27555 | 0.0420537 | ||||||||
\(921\) | 12.7980 | 0.421709 | ||||||||
\(922\) | 54.5472 | 1.79642 | ||||||||
\(923\) | −65.3850 | −2.15217 | ||||||||
\(924\) | −2.64782 | −0.0871070 | ||||||||
\(925\) | −7.88418 | −0.259230 | ||||||||
\(926\) | 43.3028 | 1.42302 | ||||||||
\(927\) | −0.494719 | −0.0162487 | ||||||||
\(928\) | 28.1461 | 0.923941 | ||||||||
\(929\) | −4.10635 | −0.134725 | −0.0673624 | − | 0.997729i | \(-0.521458\pi\) | ||||
−0.0673624 | + | 0.997729i | \(0.521458\pi\) | |||||||
\(930\) | 17.9305 | 0.587965 | ||||||||
\(931\) | −1.94610 | −0.0637809 | ||||||||
\(932\) | −32.1260 | −1.05232 | ||||||||
\(933\) | −26.6167 | −0.871390 | ||||||||
\(934\) | 17.6555 | 0.577705 | ||||||||
\(935\) | −3.04334 | −0.0995277 | ||||||||
\(936\) | 6.57834 | 0.215020 | ||||||||
\(937\) | 13.3028 | 0.434583 | 0.217292 | − | 0.976107i | \(-0.430278\pi\) | ||||
0.217292 | + | 0.976107i | \(0.430278\pi\) | |||||||
\(938\) | 45.9588 | 1.50061 | ||||||||
\(939\) | 3.00502 | 0.0980652 | ||||||||
\(940\) | 0.334474 | 0.0109093 | ||||||||
\(941\) | −11.7633 | −0.383472 | −0.191736 | − | 0.981447i | \(-0.561412\pi\) | ||||
−0.191736 | + | 0.981447i | \(0.561412\pi\) | |||||||
\(942\) | −37.9406 | −1.23617 | ||||||||
\(943\) | −0.897225 | −0.0292177 | ||||||||
\(944\) | −5.15667 | −0.167835 | ||||||||
\(945\) | 2.78389 | 0.0905599 | ||||||||
\(946\) | −13.3879 | −0.435277 | ||||||||
\(947\) | 1.40054 | 0.0455114 | 0.0227557 | − | 0.999741i | \(-0.492756\pi\) | ||||
0.0227557 | + | 0.999741i | \(0.492756\pi\) | |||||||
\(948\) | 20.4111 | 0.662922 | ||||||||
\(949\) | 24.2877 | 0.788413 | ||||||||
\(950\) | 21.2927 | 0.690828 | ||||||||
\(951\) | 4.33302 | 0.140508 | ||||||||
\(952\) | 11.0388 | 0.357771 | ||||||||
\(953\) | 33.7577 | 1.09352 | 0.546760 | − | 0.837289i | \(-0.315861\pi\) | ||||
0.546760 | + | 0.837289i | \(0.315861\pi\) | |||||||
\(954\) | −25.0872 | −0.812228 | ||||||||
\(955\) | 20.5300 | 0.664334 | ||||||||
\(956\) | −3.80450 | −0.123046 | ||||||||
\(957\) | −3.61308 | −0.116794 | ||||||||
\(958\) | 2.13343 | 0.0689280 | ||||||||
\(959\) | −44.1517 | −1.42573 | ||||||||
\(960\) | −1.83276 | −0.0591522 | ||||||||
\(961\) | 49.3758 | 1.59277 | ||||||||
\(962\) | −19.2827 | −0.621699 | ||||||||
\(963\) | −15.0872 | −0.486178 | ||||||||
\(964\) | −21.3905 | −0.688941 | ||||||||
\(965\) | −17.2161 | −0.554206 | ||||||||
\(966\) | −4.10780 | −0.132166 | ||||||||
\(967\) | −10.4806 | −0.337033 | −0.168516 | − | 0.985699i | \(-0.553898\pi\) | ||||
−0.168516 | + | 0.985699i | \(0.553898\pi\) | |||||||
\(968\) | −13.3275 | −0.428361 | ||||||||
\(969\) | −10.5244 | −0.338094 | ||||||||
\(970\) | 5.45998 | 0.175309 | ||||||||
\(971\) | 57.6358 | 1.84962 | 0.924811 | − | 0.380428i | \(-0.124223\pi\) | ||||
0.924811 | + | 0.380428i | \(0.124223\pi\) | |||||||
\(972\) | −1.28917 | −0.0413501 | ||||||||
\(973\) | 39.6967 | 1.27262 | ||||||||
\(974\) | −37.3649 | −1.19725 | ||||||||
\(975\) | 19.3083 | 0.618361 | ||||||||
\(976\) | −9.42166 | −0.301580 | ||||||||
\(977\) | 41.9008 | 1.34053 | 0.670263 | − | 0.742124i | \(-0.266181\pi\) | ||||
0.670263 | + | 0.742124i | \(0.266181\pi\) | |||||||
\(978\) | −23.2106 | −0.742192 | ||||||||
\(979\) | 10.7839 | 0.344655 | ||||||||
\(980\) | 0.891685 | 0.0284838 | ||||||||
\(981\) | 5.10278 | 0.162919 | ||||||||
\(982\) | −25.7350 | −0.821237 | ||||||||
\(983\) | −18.4056 | −0.587046 | −0.293523 | − | 0.955952i | \(-0.594828\pi\) | ||||
−0.293523 | + | 0.955952i | \(0.594828\pi\) | |||||||
\(984\) | −1.28917 | −0.0410972 | ||||||||
\(985\) | 5.74609 | 0.183086 | ||||||||
\(986\) | −27.3184 | −0.869994 | ||||||||
\(987\) | 0.593923 | 0.0189048 | ||||||||
\(988\) | 20.4111 | 0.649364 | ||||||||
\(989\) | −8.14057 | −0.258855 | ||||||||
\(990\) | 1.62721 | 0.0517162 | ||||||||
\(991\) | 26.0666 | 0.828032 | 0.414016 | − | 0.910270i | \(-0.364126\pi\) | ||||
0.414016 | + | 0.910270i | \(0.364126\pi\) | |||||||
\(992\) | −56.8222 | −1.80411 | ||||||||
\(993\) | −5.53500 | −0.175648 | ||||||||
\(994\) | 58.6650 | 1.86074 | ||||||||
\(995\) | −2.26499 | −0.0718050 | ||||||||
\(996\) | 9.90225 | 0.313765 | ||||||||
\(997\) | −29.8483 | −0.945307 | −0.472653 | − | 0.881248i | \(-0.656704\pi\) | ||||
−0.472653 | + | 0.881248i | \(0.656704\pi\) | |||||||
\(998\) | 38.9200 | 1.23199 | ||||||||
\(999\) | −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 | 123.2.a.d.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 369.2.a.e.1.3 | 3 | |||
4.3 | odd | 2 | 1968.2.a.w.1.1 | 3 | |||
5.4 | even | 2 | 3075.2.a.t.1.3 | 3 | |||
7.6 | odd | 2 | 6027.2.a.s.1.1 | 3 | |||
8.3 | odd | 2 | 7872.2.a.bs.1.3 | 3 | |||
8.5 | even | 2 | 7872.2.a.bx.1.3 | 3 | |||
12.11 | even | 2 | 5904.2.a.bd.1.3 | 3 | |||
15.14 | odd | 2 | 9225.2.a.bx.1.1 | 3 | |||
41.40 | even | 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 | 1.1 | even | 1 | trivial | |
369.2.a.e.1.3 | 3 | 3.2 | odd | 2 | |||
1968.2.a.w.1.1 | 3 | 4.3 | odd | 2 | |||
3075.2.a.t.1.3 | 3 | 5.4 | even | 2 | |||
5043.2.a.n.1.1 | 3 | 41.40 | even | 2 | |||
5904.2.a.bd.1.3 | 3 | 12.11 | even | 2 | |||
6027.2.a.s.1.1 | 3 | 7.6 | odd | 2 | |||
7872.2.a.bs.1.3 | 3 | 8.3 | odd | 2 | |||
7872.2.a.bx.1.3 | 3 | 8.5 | even | 2 | |||
9225.2.a.bx.1.1 | 3 | 15.14 | odd | 2 |