Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(0\) |
Dimension: | \(63\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.11232 | −1.49364 | −0.746819 | − | 0.665028i | \(-0.768420\pi\) | ||||
−0.746819 | + | 0.665028i | \(0.768420\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 2.46191 | 1.23095 | ||||||||
\(5\) | −3.85779 | −1.72526 | −0.862628 | − | 0.505838i | \(-0.831183\pi\) | ||||
−0.862628 | + | 0.505838i | \(0.831183\pi\) | |||||||
\(6\) | −2.11232 | −0.862352 | ||||||||
\(7\) | 0.0837724 | 0.0316630 | 0.0158315 | − | 0.999875i | \(-0.494960\pi\) | ||||
0.0158315 | + | 0.999875i | \(0.494960\pi\) | |||||||
\(8\) | −0.975695 | −0.344960 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 8.14890 | 2.57691 | ||||||||
\(11\) | 3.28960 | 0.991852 | 0.495926 | − | 0.868365i | \(-0.334829\pi\) | ||||
0.495926 | + | 0.868365i | \(0.334829\pi\) | |||||||
\(12\) | 2.46191 | 0.710691 | ||||||||
\(13\) | −3.49121 | −0.968288 | −0.484144 | − | 0.874988i | \(-0.660869\pi\) | ||||
−0.484144 | + | 0.874988i | \(0.660869\pi\) | |||||||
\(14\) | −0.176954 | −0.0472930 | ||||||||
\(15\) | −3.85779 | −0.996077 | ||||||||
\(16\) | −2.86283 | −0.715707 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −2.11232 | −0.497879 | ||||||||
\(19\) | 4.74031 | 1.08750 | 0.543751 | − | 0.839247i | \(-0.317004\pi\) | ||||
0.543751 | + | 0.839247i | \(0.317004\pi\) | |||||||
\(20\) | −9.49752 | −2.12371 | ||||||||
\(21\) | 0.0837724 | 0.0182806 | ||||||||
\(22\) | −6.94869 | −1.48147 | ||||||||
\(23\) | 0.819634 | 0.170906 | 0.0854528 | − | 0.996342i | \(-0.472766\pi\) | ||||
0.0854528 | + | 0.996342i | \(0.472766\pi\) | |||||||
\(24\) | −0.975695 | −0.199163 | ||||||||
\(25\) | 9.88256 | 1.97651 | ||||||||
\(26\) | 7.37456 | 1.44627 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.206240 | 0.0389756 | ||||||||
\(29\) | 8.30917 | 1.54297 | 0.771487 | − | 0.636245i | \(-0.219513\pi\) | ||||
0.771487 | + | 0.636245i | \(0.219513\pi\) | |||||||
\(30\) | 8.14890 | 1.48778 | ||||||||
\(31\) | 1.21037 | 0.217388 | 0.108694 | − | 0.994075i | \(-0.465333\pi\) | ||||
0.108694 | + | 0.994075i | \(0.465333\pi\) | |||||||
\(32\) | 7.99861 | 1.41397 | ||||||||
\(33\) | 3.28960 | 0.572646 | ||||||||
\(34\) | −2.11232 | −0.362260 | ||||||||
\(35\) | −0.323176 | −0.0546268 | ||||||||
\(36\) | 2.46191 | 0.410318 | ||||||||
\(37\) | −0.312542 | −0.0513816 | −0.0256908 | − | 0.999670i | \(-0.508179\pi\) | ||||
−0.0256908 | + | 0.999670i | \(0.508179\pi\) | |||||||
\(38\) | −10.0131 | −1.62433 | ||||||||
\(39\) | −3.49121 | −0.559041 | ||||||||
\(40\) | 3.76403 | 0.595145 | ||||||||
\(41\) | 7.40198 | 1.15600 | 0.577998 | − | 0.816038i | \(-0.303834\pi\) | ||||
0.577998 | + | 0.816038i | \(0.303834\pi\) | |||||||
\(42\) | −0.176954 | −0.0273046 | ||||||||
\(43\) | 7.91175 | 1.20653 | 0.603266 | − | 0.797540i | \(-0.293866\pi\) | ||||
0.603266 | + | 0.797540i | \(0.293866\pi\) | |||||||
\(44\) | 8.09869 | 1.22092 | ||||||||
\(45\) | −3.85779 | −0.575086 | ||||||||
\(46\) | −1.73133 | −0.255271 | ||||||||
\(47\) | 9.53497 | 1.39082 | 0.695409 | − | 0.718614i | \(-0.255223\pi\) | ||||
0.695409 | + | 0.718614i | \(0.255223\pi\) | |||||||
\(48\) | −2.86283 | −0.413214 | ||||||||
\(49\) | −6.99298 | −0.998997 | ||||||||
\(50\) | −20.8751 | −2.95219 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −8.59503 | −1.19192 | ||||||||
\(53\) | −1.20268 | −0.165200 | −0.0826001 | − | 0.996583i | \(-0.526322\pi\) | ||||
−0.0826001 | + | 0.996583i | \(0.526322\pi\) | |||||||
\(54\) | −2.11232 | −0.287451 | ||||||||
\(55\) | −12.6906 | −1.71120 | ||||||||
\(56\) | −0.0817363 | −0.0109225 | ||||||||
\(57\) | 4.74031 | 0.627869 | ||||||||
\(58\) | −17.5517 | −2.30464 | ||||||||
\(59\) | 1.03027 | 0.134129 | 0.0670646 | − | 0.997749i | \(-0.478637\pi\) | ||||
0.0670646 | + | 0.997749i | \(0.478637\pi\) | |||||||
\(60\) | −9.49752 | −1.22612 | ||||||||
\(61\) | −13.1488 | −1.68353 | −0.841766 | − | 0.539842i | \(-0.818484\pi\) | ||||
−0.841766 | + | 0.539842i | \(0.818484\pi\) | |||||||
\(62\) | −2.55669 | −0.324700 | ||||||||
\(63\) | 0.0837724 | 0.0105543 | ||||||||
\(64\) | −11.1700 | −1.39625 | ||||||||
\(65\) | 13.4684 | 1.67054 | ||||||||
\(66\) | −6.94869 | −0.855325 | ||||||||
\(67\) | −13.9564 | −1.70504 | −0.852521 | − | 0.522693i | \(-0.824927\pi\) | ||||
−0.852521 | + | 0.522693i | \(0.824927\pi\) | |||||||
\(68\) | 2.46191 | 0.298550 | ||||||||
\(69\) | 0.819634 | 0.0986724 | ||||||||
\(70\) | 0.682653 | 0.0815926 | ||||||||
\(71\) | −6.92804 | −0.822208 | −0.411104 | − | 0.911589i | \(-0.634857\pi\) | ||||
−0.411104 | + | 0.911589i | \(0.634857\pi\) | |||||||
\(72\) | −0.975695 | −0.114987 | ||||||||
\(73\) | −9.27996 | −1.08614 | −0.543069 | − | 0.839688i | \(-0.682738\pi\) | ||||
−0.543069 | + | 0.839688i | \(0.682738\pi\) | |||||||
\(74\) | 0.660190 | 0.0767455 | ||||||||
\(75\) | 9.88256 | 1.14114 | ||||||||
\(76\) | 11.6702 | 1.33866 | ||||||||
\(77\) | 0.275578 | 0.0314050 | ||||||||
\(78\) | 7.37456 | 0.835005 | ||||||||
\(79\) | −8.39490 | −0.944500 | −0.472250 | − | 0.881465i | \(-0.656558\pi\) | ||||
−0.472250 | + | 0.881465i | \(0.656558\pi\) | |||||||
\(80\) | 11.0442 | 1.23478 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −15.6354 | −1.72664 | ||||||||
\(83\) | 15.5618 | 1.70813 | 0.854064 | − | 0.520168i | \(-0.174131\pi\) | ||||
0.854064 | + | 0.520168i | \(0.174131\pi\) | |||||||
\(84\) | 0.206240 | 0.0225026 | ||||||||
\(85\) | −3.85779 | −0.418436 | ||||||||
\(86\) | −16.7122 | −1.80212 | ||||||||
\(87\) | 8.30917 | 0.890837 | ||||||||
\(88\) | −3.20965 | −0.342149 | ||||||||
\(89\) | −11.1482 | −1.18171 | −0.590854 | − | 0.806778i | \(-0.701209\pi\) | ||||
−0.590854 | + | 0.806778i | \(0.701209\pi\) | |||||||
\(90\) | 8.14890 | 0.858969 | ||||||||
\(91\) | −0.292467 | −0.0306589 | ||||||||
\(92\) | 2.01786 | 0.210377 | ||||||||
\(93\) | 1.21037 | 0.125509 | ||||||||
\(94\) | −20.1409 | −2.07738 | ||||||||
\(95\) | −18.2871 | −1.87622 | ||||||||
\(96\) | 7.99861 | 0.816355 | ||||||||
\(97\) | 6.83225 | 0.693710 | 0.346855 | − | 0.937919i | \(-0.387250\pi\) | ||||
0.346855 | + | 0.937919i | \(0.387250\pi\) | |||||||
\(98\) | 14.7714 | 1.49214 | ||||||||
\(99\) | 3.28960 | 0.330617 | ||||||||
\(100\) | 24.3299 | 2.43299 | ||||||||
\(101\) | 10.2117 | 1.01610 | 0.508050 | − | 0.861328i | \(-0.330367\pi\) | ||||
0.508050 | + | 0.861328i | \(0.330367\pi\) | |||||||
\(102\) | −2.11232 | −0.209151 | ||||||||
\(103\) | 3.79265 | 0.373701 | 0.186850 | − | 0.982388i | \(-0.440172\pi\) | ||||
0.186850 | + | 0.982388i | \(0.440172\pi\) | |||||||
\(104\) | 3.40636 | 0.334021 | ||||||||
\(105\) | −0.323176 | −0.0315388 | ||||||||
\(106\) | 2.54044 | 0.246749 | ||||||||
\(107\) | −7.53774 | −0.728701 | −0.364351 | − | 0.931262i | \(-0.618709\pi\) | ||||
−0.364351 | + | 0.931262i | \(0.618709\pi\) | |||||||
\(108\) | 2.46191 | 0.236897 | ||||||||
\(109\) | 13.4909 | 1.29220 | 0.646098 | − | 0.763255i | \(-0.276400\pi\) | ||||
0.646098 | + | 0.763255i | \(0.276400\pi\) | |||||||
\(110\) | 26.8066 | 2.55591 | ||||||||
\(111\) | −0.312542 | −0.0296652 | ||||||||
\(112\) | −0.239826 | −0.0226614 | ||||||||
\(113\) | −1.78842 | −0.168241 | −0.0841204 | − | 0.996456i | \(-0.526808\pi\) | ||||
−0.0841204 | + | 0.996456i | \(0.526808\pi\) | |||||||
\(114\) | −10.0131 | −0.937809 | ||||||||
\(115\) | −3.16198 | −0.294856 | ||||||||
\(116\) | 20.4564 | 1.89933 | ||||||||
\(117\) | −3.49121 | −0.322763 | ||||||||
\(118\) | −2.17626 | −0.200341 | ||||||||
\(119\) | 0.0837724 | 0.00767940 | ||||||||
\(120\) | 3.76403 | 0.343607 | ||||||||
\(121\) | −0.178535 | −0.0162305 | ||||||||
\(122\) | 27.7745 | 2.51459 | ||||||||
\(123\) | 7.40198 | 0.667414 | ||||||||
\(124\) | 2.97981 | 0.267595 | ||||||||
\(125\) | −18.8359 | −1.68473 | ||||||||
\(126\) | −0.176954 | −0.0157643 | ||||||||
\(127\) | 14.2397 | 1.26357 | 0.631784 | − | 0.775144i | \(-0.282323\pi\) | ||||
0.631784 | + | 0.775144i | \(0.282323\pi\) | |||||||
\(128\) | 7.59739 | 0.671521 | ||||||||
\(129\) | 7.91175 | 0.696591 | ||||||||
\(130\) | −28.4495 | −2.49519 | ||||||||
\(131\) | 0.0964608 | 0.00842782 | 0.00421391 | − | 0.999991i | \(-0.498659\pi\) | ||||
0.00421391 | + | 0.999991i | \(0.498659\pi\) | |||||||
\(132\) | 8.09869 | 0.704900 | ||||||||
\(133\) | 0.397107 | 0.0344336 | ||||||||
\(134\) | 29.4803 | 2.54671 | ||||||||
\(135\) | −3.85779 | −0.332026 | ||||||||
\(136\) | −0.975695 | −0.0836652 | ||||||||
\(137\) | 1.54857 | 0.132303 | 0.0661516 | − | 0.997810i | \(-0.478928\pi\) | ||||
0.0661516 | + | 0.997810i | \(0.478928\pi\) | |||||||
\(138\) | −1.73133 | −0.147381 | ||||||||
\(139\) | 12.0571 | 1.02267 | 0.511335 | − | 0.859381i | \(-0.329151\pi\) | ||||
0.511335 | + | 0.859381i | \(0.329151\pi\) | |||||||
\(140\) | −0.795630 | −0.0672430 | ||||||||
\(141\) | 9.53497 | 0.802989 | ||||||||
\(142\) | 14.6343 | 1.22808 | ||||||||
\(143\) | −11.4847 | −0.960398 | ||||||||
\(144\) | −2.86283 | −0.238569 | ||||||||
\(145\) | −32.0551 | −2.66203 | ||||||||
\(146\) | 19.6023 | 1.62230 | ||||||||
\(147\) | −6.99298 | −0.576771 | ||||||||
\(148\) | −0.769449 | −0.0632483 | ||||||||
\(149\) | 7.97528 | 0.653360 | 0.326680 | − | 0.945135i | \(-0.394070\pi\) | ||||
0.326680 | + | 0.945135i | \(0.394070\pi\) | |||||||
\(150\) | −20.8751 | −1.70445 | ||||||||
\(151\) | −1.43329 | −0.116640 | −0.0583198 | − | 0.998298i | \(-0.518574\pi\) | ||||
−0.0583198 | + | 0.998298i | \(0.518574\pi\) | |||||||
\(152\) | −4.62510 | −0.375145 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | −0.582109 | −0.0469077 | ||||||||
\(155\) | −4.66935 | −0.375051 | ||||||||
\(156\) | −8.59503 | −0.688153 | ||||||||
\(157\) | 1.00000 | 0.0798087 | ||||||||
\(158\) | 17.7327 | 1.41074 | ||||||||
\(159\) | −1.20268 | −0.0953784 | ||||||||
\(160\) | −30.8570 | −2.43946 | ||||||||
\(161\) | 0.0686627 | 0.00541138 | ||||||||
\(162\) | −2.11232 | −0.165960 | ||||||||
\(163\) | 9.76673 | 0.764990 | 0.382495 | − | 0.923958i | \(-0.375065\pi\) | ||||
0.382495 | + | 0.923958i | \(0.375065\pi\) | |||||||
\(164\) | 18.2230 | 1.42298 | ||||||||
\(165\) | −12.6906 | −0.987961 | ||||||||
\(166\) | −32.8715 | −2.55132 | ||||||||
\(167\) | 3.52868 | 0.273058 | 0.136529 | − | 0.990636i | \(-0.456405\pi\) | ||||
0.136529 | + | 0.990636i | \(0.456405\pi\) | |||||||
\(168\) | −0.0817363 | −0.00630609 | ||||||||
\(169\) | −0.811446 | −0.0624189 | ||||||||
\(170\) | 8.14890 | 0.624992 | ||||||||
\(171\) | 4.74031 | 0.362501 | ||||||||
\(172\) | 19.4780 | 1.48518 | ||||||||
\(173\) | 5.11778 | 0.389097 | 0.194549 | − | 0.980893i | \(-0.437676\pi\) | ||||
0.194549 | + | 0.980893i | \(0.437676\pi\) | |||||||
\(174\) | −17.5517 | −1.33059 | ||||||||
\(175\) | 0.827885 | 0.0625822 | ||||||||
\(176\) | −9.41756 | −0.709876 | ||||||||
\(177\) | 1.03027 | 0.0774396 | ||||||||
\(178\) | 23.5486 | 1.76504 | ||||||||
\(179\) | −9.15852 | −0.684540 | −0.342270 | − | 0.939602i | \(-0.611196\pi\) | ||||
−0.342270 | + | 0.939602i | \(0.611196\pi\) | |||||||
\(180\) | −9.49752 | −0.707903 | ||||||||
\(181\) | −21.4494 | −1.59432 | −0.797161 | − | 0.603767i | \(-0.793666\pi\) | ||||
−0.797161 | + | 0.603767i | \(0.793666\pi\) | |||||||
\(182\) | 0.617785 | 0.0457932 | ||||||||
\(183\) | −13.1488 | −0.971988 | ||||||||
\(184\) | −0.799713 | −0.0589556 | ||||||||
\(185\) | 1.20572 | 0.0886465 | ||||||||
\(186\) | −2.55669 | −0.187465 | ||||||||
\(187\) | 3.28960 | 0.240559 | ||||||||
\(188\) | 23.4742 | 1.71203 | ||||||||
\(189\) | 0.0837724 | 0.00609354 | ||||||||
\(190\) | 38.6283 | 2.80239 | ||||||||
\(191\) | −1.23719 | −0.0895197 | −0.0447598 | − | 0.998998i | \(-0.514252\pi\) | ||||
−0.0447598 | + | 0.998998i | \(0.514252\pi\) | |||||||
\(192\) | −11.1700 | −0.806124 | ||||||||
\(193\) | 1.58559 | 0.114133 | 0.0570665 | − | 0.998370i | \(-0.481825\pi\) | ||||
0.0570665 | + | 0.998370i | \(0.481825\pi\) | |||||||
\(194\) | −14.4319 | −1.03615 | ||||||||
\(195\) | 13.4684 | 0.964490 | ||||||||
\(196\) | −17.2161 | −1.22972 | ||||||||
\(197\) | −14.2162 | −1.01286 | −0.506432 | − | 0.862280i | \(-0.669036\pi\) | ||||
−0.506432 | + | 0.862280i | \(0.669036\pi\) | |||||||
\(198\) | −6.94869 | −0.493822 | ||||||||
\(199\) | −16.6082 | −1.17732 | −0.588662 | − | 0.808379i | \(-0.700345\pi\) | ||||
−0.588662 | + | 0.808379i | \(0.700345\pi\) | |||||||
\(200\) | −9.64236 | −0.681818 | ||||||||
\(201\) | −13.9564 | −0.984406 | ||||||||
\(202\) | −21.5704 | −1.51768 | ||||||||
\(203\) | 0.696079 | 0.0488552 | ||||||||
\(204\) | 2.46191 | 0.172368 | ||||||||
\(205\) | −28.5553 | −1.99439 | ||||||||
\(206\) | −8.01129 | −0.558173 | ||||||||
\(207\) | 0.819634 | 0.0569685 | ||||||||
\(208\) | 9.99474 | 0.693011 | ||||||||
\(209\) | 15.5937 | 1.07864 | ||||||||
\(210\) | 0.682653 | 0.0471075 | ||||||||
\(211\) | 18.2578 | 1.25692 | 0.628458 | − | 0.777843i | \(-0.283686\pi\) | ||||
0.628458 | + | 0.777843i | \(0.283686\pi\) | |||||||
\(212\) | −2.96087 | −0.203354 | ||||||||
\(213\) | −6.92804 | −0.474702 | ||||||||
\(214\) | 15.9221 | 1.08842 | ||||||||
\(215\) | −30.5219 | −2.08158 | ||||||||
\(216\) | −0.975695 | −0.0663877 | ||||||||
\(217\) | 0.101395 | 0.00688317 | ||||||||
\(218\) | −28.4972 | −1.93007 | ||||||||
\(219\) | −9.27996 | −0.627082 | ||||||||
\(220\) | −31.2430 | −2.10641 | ||||||||
\(221\) | −3.49121 | −0.234844 | ||||||||
\(222\) | 0.660190 | 0.0443090 | ||||||||
\(223\) | 7.91171 | 0.529807 | 0.264904 | − | 0.964275i | \(-0.414660\pi\) | ||||
0.264904 | + | 0.964275i | \(0.414660\pi\) | |||||||
\(224\) | 0.670063 | 0.0447704 | ||||||||
\(225\) | 9.88256 | 0.658837 | ||||||||
\(226\) | 3.77773 | 0.251291 | ||||||||
\(227\) | −7.91386 | −0.525261 | −0.262631 | − | 0.964896i | \(-0.584590\pi\) | ||||
−0.262631 | + | 0.964896i | \(0.584590\pi\) | |||||||
\(228\) | 11.6702 | 0.772878 | ||||||||
\(229\) | 19.5929 | 1.29474 | 0.647369 | − | 0.762177i | \(-0.275869\pi\) | ||||
0.647369 | + | 0.762177i | \(0.275869\pi\) | |||||||
\(230\) | 6.67912 | 0.440408 | ||||||||
\(231\) | 0.275578 | 0.0181317 | ||||||||
\(232\) | −8.10722 | −0.532265 | ||||||||
\(233\) | 24.0682 | 1.57676 | 0.788379 | − | 0.615190i | \(-0.210921\pi\) | ||||
0.788379 | + | 0.615190i | \(0.210921\pi\) | |||||||
\(234\) | 7.37456 | 0.482090 | ||||||||
\(235\) | −36.7839 | −2.39952 | ||||||||
\(236\) | 2.53642 | 0.165107 | ||||||||
\(237\) | −8.39490 | −0.545308 | ||||||||
\(238\) | −0.176954 | −0.0114702 | ||||||||
\(239\) | −29.0671 | −1.88019 | −0.940096 | − | 0.340909i | \(-0.889265\pi\) | ||||
−0.940096 | + | 0.340909i | \(0.889265\pi\) | |||||||
\(240\) | 11.0442 | 0.712900 | ||||||||
\(241\) | −12.7214 | −0.819460 | −0.409730 | − | 0.912207i | \(-0.634377\pi\) | ||||
−0.409730 | + | 0.912207i | \(0.634377\pi\) | |||||||
\(242\) | 0.377124 | 0.0242425 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −32.3711 | −2.07235 | ||||||||
\(245\) | 26.9775 | 1.72353 | ||||||||
\(246\) | −15.6354 | −0.996875 | ||||||||
\(247\) | −16.5494 | −1.05301 | ||||||||
\(248\) | −1.18095 | −0.0749904 | ||||||||
\(249\) | 15.5618 | 0.986188 | ||||||||
\(250\) | 39.7875 | 2.51638 | ||||||||
\(251\) | 18.9280 | 1.19472 | 0.597361 | − | 0.801972i | \(-0.296216\pi\) | ||||
0.597361 | + | 0.801972i | \(0.296216\pi\) | |||||||
\(252\) | 0.206240 | 0.0129919 | ||||||||
\(253\) | 2.69627 | 0.169513 | ||||||||
\(254\) | −30.0788 | −1.88731 | ||||||||
\(255\) | −3.85779 | −0.241584 | ||||||||
\(256\) | 6.29183 | 0.393240 | ||||||||
\(257\) | −16.0993 | −1.00425 | −0.502123 | − | 0.864796i | \(-0.667448\pi\) | ||||
−0.502123 | + | 0.864796i | \(0.667448\pi\) | |||||||
\(258\) | −16.7122 | −1.04045 | ||||||||
\(259\) | −0.0261824 | −0.00162689 | ||||||||
\(260\) | 33.1579 | 2.05636 | ||||||||
\(261\) | 8.30917 | 0.514325 | ||||||||
\(262\) | −0.203756 | −0.0125881 | ||||||||
\(263\) | −3.74690 | −0.231044 | −0.115522 | − | 0.993305i | \(-0.536854\pi\) | ||||
−0.115522 | + | 0.993305i | \(0.536854\pi\) | |||||||
\(264\) | −3.20965 | −0.197540 | ||||||||
\(265\) | 4.63967 | 0.285013 | ||||||||
\(266\) | −0.838818 | −0.0514312 | ||||||||
\(267\) | −11.1482 | −0.682260 | ||||||||
\(268\) | −34.3593 | −2.09883 | ||||||||
\(269\) | −19.3314 | −1.17866 | −0.589329 | − | 0.807893i | \(-0.700608\pi\) | ||||
−0.589329 | + | 0.807893i | \(0.700608\pi\) | |||||||
\(270\) | 8.14890 | 0.495926 | ||||||||
\(271\) | −4.22295 | −0.256526 | −0.128263 | − | 0.991740i | \(-0.540940\pi\) | ||||
−0.128263 | + | 0.991740i | \(0.540940\pi\) | |||||||
\(272\) | −2.86283 | −0.173585 | ||||||||
\(273\) | −0.292467 | −0.0177009 | ||||||||
\(274\) | −3.27108 | −0.197613 | ||||||||
\(275\) | 32.5096 | 1.96041 | ||||||||
\(276\) | 2.01786 | 0.121461 | ||||||||
\(277\) | 18.2497 | 1.09652 | 0.548260 | − | 0.836308i | \(-0.315290\pi\) | ||||
0.548260 | + | 0.836308i | \(0.315290\pi\) | |||||||
\(278\) | −25.4685 | −1.52750 | ||||||||
\(279\) | 1.21037 | 0.0724628 | ||||||||
\(280\) | 0.315322 | 0.0188441 | ||||||||
\(281\) | −24.6776 | −1.47214 | −0.736072 | − | 0.676903i | \(-0.763322\pi\) | ||||
−0.736072 | + | 0.676903i | \(0.763322\pi\) | |||||||
\(282\) | −20.1409 | −1.19937 | ||||||||
\(283\) | 7.23941 | 0.430339 | 0.215169 | − | 0.976577i | \(-0.430970\pi\) | ||||
0.215169 | + | 0.976577i | \(0.430970\pi\) | |||||||
\(284\) | −17.0562 | −1.01210 | ||||||||
\(285\) | −18.2871 | −1.08324 | ||||||||
\(286\) | 24.2594 | 1.43449 | ||||||||
\(287\) | 0.620082 | 0.0366023 | ||||||||
\(288\) | 7.99861 | 0.471323 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 67.7106 | 3.97610 | ||||||||
\(291\) | 6.83225 | 0.400514 | ||||||||
\(292\) | −22.8464 | −1.33698 | ||||||||
\(293\) | 22.0683 | 1.28924 | 0.644621 | − | 0.764502i | \(-0.277015\pi\) | ||||
0.644621 | + | 0.764502i | \(0.277015\pi\) | |||||||
\(294\) | 14.7714 | 0.861488 | ||||||||
\(295\) | −3.97455 | −0.231407 | ||||||||
\(296\) | 0.304946 | 0.0177246 | ||||||||
\(297\) | 3.28960 | 0.190882 | ||||||||
\(298\) | −16.8464 | −0.975883 | ||||||||
\(299\) | −2.86152 | −0.165486 | ||||||||
\(300\) | 24.3299 | 1.40469 | ||||||||
\(301\) | 0.662786 | 0.0382024 | ||||||||
\(302\) | 3.02757 | 0.174217 | ||||||||
\(303\) | 10.2117 | 0.586645 | ||||||||
\(304\) | −13.5707 | −0.778333 | ||||||||
\(305\) | 50.7254 | 2.90453 | ||||||||
\(306\) | −2.11232 | −0.120753 | ||||||||
\(307\) | −9.48581 | −0.541384 | −0.270692 | − | 0.962666i | \(-0.587252\pi\) | ||||
−0.270692 | + | 0.962666i | \(0.587252\pi\) | |||||||
\(308\) | 0.678446 | 0.0386581 | ||||||||
\(309\) | 3.79265 | 0.215756 | ||||||||
\(310\) | 9.86317 | 0.560190 | ||||||||
\(311\) | 6.78881 | 0.384958 | 0.192479 | − | 0.981301i | \(-0.438347\pi\) | ||||
0.192479 | + | 0.981301i | \(0.438347\pi\) | |||||||
\(312\) | 3.40636 | 0.192847 | ||||||||
\(313\) | 9.41729 | 0.532296 | 0.266148 | − | 0.963932i | \(-0.414249\pi\) | ||||
0.266148 | + | 0.963932i | \(0.414249\pi\) | |||||||
\(314\) | −2.11232 | −0.119205 | ||||||||
\(315\) | −0.323176 | −0.0182089 | ||||||||
\(316\) | −20.6675 | −1.16264 | ||||||||
\(317\) | −8.95658 | −0.503052 | −0.251526 | − | 0.967851i | \(-0.580932\pi\) | ||||
−0.251526 | + | 0.967851i | \(0.580932\pi\) | |||||||
\(318\) | 2.54044 | 0.142461 | ||||||||
\(319\) | 27.3339 | 1.53040 | ||||||||
\(320\) | 43.0915 | 2.40889 | ||||||||
\(321\) | −7.53774 | −0.420716 | ||||||||
\(322\) | −0.145038 | −0.00808264 | ||||||||
\(323\) | 4.74031 | 0.263758 | ||||||||
\(324\) | 2.46191 | 0.136773 | ||||||||
\(325\) | −34.5021 | −1.91383 | ||||||||
\(326\) | −20.6305 | −1.14262 | ||||||||
\(327\) | 13.4909 | 0.746050 | ||||||||
\(328\) | −7.22208 | −0.398773 | ||||||||
\(329\) | 0.798767 | 0.0440374 | ||||||||
\(330\) | 26.8066 | 1.47566 | ||||||||
\(331\) | 0.761518 | 0.0418568 | 0.0209284 | − | 0.999781i | \(-0.493338\pi\) | ||||
0.0209284 | + | 0.999781i | \(0.493338\pi\) | |||||||
\(332\) | 38.3117 | 2.10263 | ||||||||
\(333\) | −0.312542 | −0.0171272 | ||||||||
\(334\) | −7.45372 | −0.407849 | ||||||||
\(335\) | 53.8407 | 2.94163 | ||||||||
\(336\) | −0.239826 | −0.0130836 | ||||||||
\(337\) | 35.2617 | 1.92083 | 0.960413 | − | 0.278581i | \(-0.0898640\pi\) | ||||
0.960413 | + | 0.278581i | \(0.0898640\pi\) | |||||||
\(338\) | 1.71404 | 0.0932313 | ||||||||
\(339\) | −1.78842 | −0.0971339 | ||||||||
\(340\) | −9.49752 | −0.515075 | ||||||||
\(341\) | 3.98163 | 0.215617 | ||||||||
\(342\) | −10.0131 | −0.541445 | ||||||||
\(343\) | −1.17223 | −0.0632942 | ||||||||
\(344\) | −7.71946 | −0.416205 | ||||||||
\(345\) | −3.16198 | −0.170235 | ||||||||
\(346\) | −10.8104 | −0.581171 | ||||||||
\(347\) | 30.0431 | 1.61280 | 0.806398 | − | 0.591373i | \(-0.201414\pi\) | ||||
0.806398 | + | 0.591373i | \(0.201414\pi\) | |||||||
\(348\) | 20.4564 | 1.09658 | ||||||||
\(349\) | −18.8364 | −1.00829 | −0.504144 | − | 0.863620i | \(-0.668192\pi\) | ||||
−0.504144 | + | 0.863620i | \(0.668192\pi\) | |||||||
\(350\) | −1.74876 | −0.0934752 | ||||||||
\(351\) | −3.49121 | −0.186347 | ||||||||
\(352\) | 26.3122 | 1.40245 | ||||||||
\(353\) | 21.5124 | 1.14499 | 0.572495 | − | 0.819908i | \(-0.305976\pi\) | ||||
0.572495 | + | 0.819908i | \(0.305976\pi\) | |||||||
\(354\) | −2.17626 | −0.115667 | ||||||||
\(355\) | 26.7269 | 1.41852 | ||||||||
\(356\) | −27.4459 | −1.45463 | ||||||||
\(357\) | 0.0837724 | 0.00443370 | ||||||||
\(358\) | 19.3457 | 1.02245 | ||||||||
\(359\) | 7.54776 | 0.398355 | 0.199178 | − | 0.979963i | \(-0.436173\pi\) | ||||
0.199178 | + | 0.979963i | \(0.436173\pi\) | |||||||
\(360\) | 3.76403 | 0.198382 | ||||||||
\(361\) | 3.47054 | 0.182660 | ||||||||
\(362\) | 45.3081 | 2.38134 | ||||||||
\(363\) | −0.178535 | −0.00937068 | ||||||||
\(364\) | −0.720026 | −0.0377396 | ||||||||
\(365\) | 35.8002 | 1.87387 | ||||||||
\(366\) | 27.7745 | 1.45180 | ||||||||
\(367\) | −16.9178 | −0.883103 | −0.441551 | − | 0.897236i | \(-0.645572\pi\) | ||||
−0.441551 | + | 0.897236i | \(0.645572\pi\) | |||||||
\(368\) | −2.34647 | −0.122318 | ||||||||
\(369\) | 7.40198 | 0.385332 | ||||||||
\(370\) | −2.54687 | −0.132406 | ||||||||
\(371\) | −0.100751 | −0.00523073 | ||||||||
\(372\) | 2.97981 | 0.154496 | ||||||||
\(373\) | −12.5433 | −0.649467 | −0.324734 | − | 0.945806i | \(-0.605275\pi\) | ||||
−0.324734 | + | 0.945806i | \(0.605275\pi\) | |||||||
\(374\) | −6.94869 | −0.359308 | ||||||||
\(375\) | −18.8359 | −0.972681 | ||||||||
\(376\) | −9.30322 | −0.479777 | ||||||||
\(377\) | −29.0091 | −1.49404 | ||||||||
\(378\) | −0.176954 | −0.00910155 | ||||||||
\(379\) | −32.6144 | −1.67529 | −0.837646 | − | 0.546214i | \(-0.816069\pi\) | ||||
−0.837646 | + | 0.546214i | \(0.816069\pi\) | |||||||
\(380\) | −45.0212 | −2.30954 | ||||||||
\(381\) | 14.2397 | 0.729521 | ||||||||
\(382\) | 2.61334 | 0.133710 | ||||||||
\(383\) | 32.2739 | 1.64912 | 0.824559 | − | 0.565776i | \(-0.191423\pi\) | ||||
0.824559 | + | 0.565776i | \(0.191423\pi\) | |||||||
\(384\) | 7.59739 | 0.387703 | ||||||||
\(385\) | −1.06312 | −0.0541817 | ||||||||
\(386\) | −3.34927 | −0.170473 | ||||||||
\(387\) | 7.91175 | 0.402177 | ||||||||
\(388\) | 16.8204 | 0.853925 | ||||||||
\(389\) | 7.31594 | 0.370933 | 0.185467 | − | 0.982651i | \(-0.440620\pi\) | ||||
0.185467 | + | 0.982651i | \(0.440620\pi\) | |||||||
\(390\) | −28.4495 | −1.44060 | ||||||||
\(391\) | 0.819634 | 0.0414507 | ||||||||
\(392\) | 6.82302 | 0.344615 | ||||||||
\(393\) | 0.0964608 | 0.00486580 | ||||||||
\(394\) | 30.0292 | 1.51285 | ||||||||
\(395\) | 32.3858 | 1.62951 | ||||||||
\(396\) | 8.09869 | 0.406974 | ||||||||
\(397\) | −22.9548 | −1.15207 | −0.576035 | − | 0.817425i | \(-0.695401\pi\) | ||||
−0.576035 | + | 0.817425i | \(0.695401\pi\) | |||||||
\(398\) | 35.0819 | 1.75850 | ||||||||
\(399\) | 0.397107 | 0.0198802 | ||||||||
\(400\) | −28.2921 | −1.41460 | ||||||||
\(401\) | −26.6492 | −1.33080 | −0.665399 | − | 0.746487i | \(-0.731739\pi\) | ||||
−0.665399 | + | 0.746487i | \(0.731739\pi\) | |||||||
\(402\) | 29.4803 | 1.47035 | ||||||||
\(403\) | −4.22565 | −0.210495 | ||||||||
\(404\) | 25.1402 | 1.25077 | ||||||||
\(405\) | −3.85779 | −0.191695 | ||||||||
\(406\) | −1.47034 | −0.0729719 | ||||||||
\(407\) | −1.02814 | −0.0509629 | ||||||||
\(408\) | −0.975695 | −0.0483041 | ||||||||
\(409\) | 25.2943 | 1.25072 | 0.625361 | − | 0.780335i | \(-0.284952\pi\) | ||||
0.625361 | + | 0.780335i | \(0.284952\pi\) | |||||||
\(410\) | 60.3180 | 2.97889 | ||||||||
\(411\) | 1.54857 | 0.0763853 | ||||||||
\(412\) | 9.33714 | 0.460008 | ||||||||
\(413\) | 0.0863079 | 0.00424693 | ||||||||
\(414\) | −1.73133 | −0.0850903 | ||||||||
\(415\) | −60.0341 | −2.94696 | ||||||||
\(416\) | −27.9248 | −1.36913 | ||||||||
\(417\) | 12.0571 | 0.590439 | ||||||||
\(418\) | −32.9390 | −1.61110 | ||||||||
\(419\) | −12.2950 | −0.600651 | −0.300325 | − | 0.953837i | \(-0.597095\pi\) | ||||
−0.300325 | + | 0.953837i | \(0.597095\pi\) | |||||||
\(420\) | −0.795630 | −0.0388228 | ||||||||
\(421\) | −21.7221 | −1.05867 | −0.529335 | − | 0.848413i | \(-0.677559\pi\) | ||||
−0.529335 | + | 0.848413i | \(0.677559\pi\) | |||||||
\(422\) | −38.5663 | −1.87738 | ||||||||
\(423\) | 9.53497 | 0.463606 | ||||||||
\(424\) | 1.17344 | 0.0569875 | ||||||||
\(425\) | 9.88256 | 0.479374 | ||||||||
\(426\) | 14.6343 | 0.709032 | ||||||||
\(427\) | −1.10151 | −0.0533057 | ||||||||
\(428\) | −18.5572 | −0.896997 | ||||||||
\(429\) | −11.4847 | −0.554486 | ||||||||
\(430\) | 64.4721 | 3.10912 | ||||||||
\(431\) | 21.4619 | 1.03378 | 0.516891 | − | 0.856051i | \(-0.327089\pi\) | ||||
0.516891 | + | 0.856051i | \(0.327089\pi\) | |||||||
\(432\) | −2.86283 | −0.137738 | ||||||||
\(433\) | −28.4746 | −1.36840 | −0.684202 | − | 0.729293i | \(-0.739849\pi\) | ||||
−0.684202 | + | 0.729293i | \(0.739849\pi\) | |||||||
\(434\) | −0.214180 | −0.0102810 | ||||||||
\(435\) | −32.0551 | −1.53692 | ||||||||
\(436\) | 33.2134 | 1.59063 | ||||||||
\(437\) | 3.88532 | 0.185860 | ||||||||
\(438\) | 19.6023 | 0.936633 | ||||||||
\(439\) | 3.93877 | 0.187987 | 0.0939937 | − | 0.995573i | \(-0.470037\pi\) | ||||
0.0939937 | + | 0.995573i | \(0.470037\pi\) | |||||||
\(440\) | 12.3821 | 0.590296 | ||||||||
\(441\) | −6.99298 | −0.332999 | ||||||||
\(442\) | 7.37456 | 0.350772 | ||||||||
\(443\) | 20.9465 | 0.995198 | 0.497599 | − | 0.867407i | \(-0.334215\pi\) | ||||
0.497599 | + | 0.867407i | \(0.334215\pi\) | |||||||
\(444\) | −0.769449 | −0.0365165 | ||||||||
\(445\) | 43.0075 | 2.03875 | ||||||||
\(446\) | −16.7121 | −0.791340 | ||||||||
\(447\) | 7.97528 | 0.377218 | ||||||||
\(448\) | −0.935736 | −0.0442094 | ||||||||
\(449\) | 0.922103 | 0.0435167 | 0.0217584 | − | 0.999763i | \(-0.493074\pi\) | ||||
0.0217584 | + | 0.999763i | \(0.493074\pi\) | |||||||
\(450\) | −20.8751 | −0.984064 | ||||||||
\(451\) | 24.3496 | 1.14658 | ||||||||
\(452\) | −4.40293 | −0.207097 | ||||||||
\(453\) | −1.43329 | −0.0673419 | ||||||||
\(454\) | 16.7166 | 0.784550 | ||||||||
\(455\) | 1.12828 | 0.0528944 | ||||||||
\(456\) | −4.62510 | −0.216590 | ||||||||
\(457\) | 28.1637 | 1.31744 | 0.658722 | − | 0.752386i | \(-0.271097\pi\) | ||||
0.658722 | + | 0.752386i | \(0.271097\pi\) | |||||||
\(458\) | −41.3866 | −1.93387 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −7.78449 | −0.362954 | ||||||||
\(461\) | −7.31400 | −0.340647 | −0.170323 | − | 0.985388i | \(-0.554481\pi\) | ||||
−0.170323 | + | 0.985388i | \(0.554481\pi\) | |||||||
\(462\) | −0.582109 | −0.0270821 | ||||||||
\(463\) | −15.5195 | −0.721253 | −0.360626 | − | 0.932710i | \(-0.617437\pi\) | ||||
−0.360626 | + | 0.932710i | \(0.617437\pi\) | |||||||
\(464\) | −23.7877 | −1.10432 | ||||||||
\(465\) | −4.66935 | −0.216536 | ||||||||
\(466\) | −50.8397 | −2.35510 | ||||||||
\(467\) | 35.8519 | 1.65903 | 0.829514 | − | 0.558486i | \(-0.188618\pi\) | ||||
0.829514 | + | 0.558486i | \(0.188618\pi\) | |||||||
\(468\) | −8.59503 | −0.397306 | ||||||||
\(469\) | −1.16916 | −0.0539867 | ||||||||
\(470\) | 77.6995 | 3.58401 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | −1.00523 | −0.0462693 | ||||||||
\(473\) | 26.0265 | 1.19670 | ||||||||
\(474\) | 17.7327 | 0.814492 | ||||||||
\(475\) | 46.8464 | 2.14946 | ||||||||
\(476\) | 0.206240 | 0.00945298 | ||||||||
\(477\) | −1.20268 | −0.0550667 | ||||||||
\(478\) | 61.3990 | 2.80833 | ||||||||
\(479\) | 12.2746 | 0.560841 | 0.280421 | − | 0.959877i | \(-0.409526\pi\) | ||||
0.280421 | + | 0.959877i | \(0.409526\pi\) | |||||||
\(480\) | −30.8570 | −1.40842 | ||||||||
\(481\) | 1.09115 | 0.0497522 | ||||||||
\(482\) | 26.8718 | 1.22398 | ||||||||
\(483\) | 0.0686627 | 0.00312426 | ||||||||
\(484\) | −0.439538 | −0.0199790 | ||||||||
\(485\) | −26.3574 | −1.19683 | ||||||||
\(486\) | −2.11232 | −0.0958169 | ||||||||
\(487\) | 25.5448 | 1.15755 | 0.578773 | − | 0.815489i | \(-0.303532\pi\) | ||||
0.578773 | + | 0.815489i | \(0.303532\pi\) | |||||||
\(488\) | 12.8292 | 0.580752 | ||||||||
\(489\) | 9.76673 | 0.441667 | ||||||||
\(490\) | −56.9851 | −2.57432 | ||||||||
\(491\) | 18.7433 | 0.845872 | 0.422936 | − | 0.906160i | \(-0.361000\pi\) | ||||
0.422936 | + | 0.906160i | \(0.361000\pi\) | |||||||
\(492\) | 18.2230 | 0.821556 | ||||||||
\(493\) | 8.30917 | 0.374226 | ||||||||
\(494\) | 34.9577 | 1.57282 | ||||||||
\(495\) | −12.6906 | −0.570400 | ||||||||
\(496\) | −3.46508 | −0.155587 | ||||||||
\(497\) | −0.580379 | −0.0260335 | ||||||||
\(498\) | −32.8715 | −1.47301 | ||||||||
\(499\) | 12.4105 | 0.555570 | 0.277785 | − | 0.960643i | \(-0.410400\pi\) | ||||
0.277785 | + | 0.960643i | \(0.410400\pi\) | |||||||
\(500\) | −46.3722 | −2.07383 | ||||||||
\(501\) | 3.52868 | 0.157650 | ||||||||
\(502\) | −39.9820 | −1.78448 | ||||||||
\(503\) | 27.6254 | 1.23175 | 0.615877 | − | 0.787842i | \(-0.288802\pi\) | ||||
0.615877 | + | 0.787842i | \(0.288802\pi\) | |||||||
\(504\) | −0.0817363 | −0.00364082 | ||||||||
\(505\) | −39.3945 | −1.75303 | ||||||||
\(506\) | −5.69539 | −0.253191 | ||||||||
\(507\) | −0.811446 | −0.0360376 | ||||||||
\(508\) | 35.0568 | 1.55539 | ||||||||
\(509\) | −22.0597 | −0.977779 | −0.488889 | − | 0.872346i | \(-0.662598\pi\) | ||||
−0.488889 | + | 0.872346i | \(0.662598\pi\) | |||||||
\(510\) | 8.14890 | 0.360839 | ||||||||
\(511\) | −0.777405 | −0.0343904 | ||||||||
\(512\) | −28.4852 | −1.25888 | ||||||||
\(513\) | 4.74031 | 0.209290 | ||||||||
\(514\) | 34.0069 | 1.49998 | ||||||||
\(515\) | −14.6312 | −0.644729 | ||||||||
\(516\) | 19.4780 | 0.857471 | ||||||||
\(517\) | 31.3662 | 1.37948 | ||||||||
\(518\) | 0.0553057 | 0.00242999 | ||||||||
\(519\) | 5.11778 | 0.224646 | ||||||||
\(520\) | −13.1410 | −0.576272 | ||||||||
\(521\) | 3.00735 | 0.131755 | 0.0658773 | − | 0.997828i | \(-0.479015\pi\) | ||||
0.0658773 | + | 0.997828i | \(0.479015\pi\) | |||||||
\(522\) | −17.5517 | −0.768215 | ||||||||
\(523\) | 25.3845 | 1.10999 | 0.554993 | − | 0.831855i | \(-0.312721\pi\) | ||||
0.554993 | + | 0.831855i | \(0.312721\pi\) | |||||||
\(524\) | 0.237477 | 0.0103743 | ||||||||
\(525\) | 0.827885 | 0.0361319 | ||||||||
\(526\) | 7.91465 | 0.345095 | ||||||||
\(527\) | 1.21037 | 0.0527245 | ||||||||
\(528\) | −9.41756 | −0.409847 | ||||||||
\(529\) | −22.3282 | −0.970791 | ||||||||
\(530\) | −9.80048 | −0.425706 | ||||||||
\(531\) | 1.03027 | 0.0447098 | ||||||||
\(532\) | 0.977640 | 0.0423861 | ||||||||
\(533\) | −25.8419 | −1.11934 | ||||||||
\(534\) | 23.5486 | 1.01905 | ||||||||
\(535\) | 29.0790 | 1.25720 | ||||||||
\(536\) | 13.6172 | 0.588172 | ||||||||
\(537\) | −9.15852 | −0.395219 | ||||||||
\(538\) | 40.8342 | 1.76049 | ||||||||
\(539\) | −23.0041 | −0.990857 | ||||||||
\(540\) | −9.49752 | −0.408708 | ||||||||
\(541\) | −9.81458 | −0.421962 | −0.210981 | − | 0.977490i | \(-0.567666\pi\) | ||||
−0.210981 | + | 0.977490i | \(0.567666\pi\) | |||||||
\(542\) | 8.92023 | 0.383157 | ||||||||
\(543\) | −21.4494 | −0.920482 | ||||||||
\(544\) | 7.99861 | 0.342938 | ||||||||
\(545\) | −52.0452 | −2.22937 | ||||||||
\(546\) | 0.617785 | 0.0264387 | ||||||||
\(547\) | −13.4096 | −0.573352 | −0.286676 | − | 0.958028i | \(-0.592550\pi\) | ||||
−0.286676 | + | 0.958028i | \(0.592550\pi\) | |||||||
\(548\) | 3.81243 | 0.162859 | ||||||||
\(549\) | −13.1488 | −0.561178 | ||||||||
\(550\) | −68.6709 | −2.92814 | ||||||||
\(551\) | 39.3881 | 1.67799 | ||||||||
\(552\) | −0.799713 | −0.0340381 | ||||||||
\(553\) | −0.703261 | −0.0299057 | ||||||||
\(554\) | −38.5493 | −1.63780 | ||||||||
\(555\) | 1.20572 | 0.0511801 | ||||||||
\(556\) | 29.6835 | 1.25886 | ||||||||
\(557\) | 26.4273 | 1.11976 | 0.559881 | − | 0.828573i | \(-0.310847\pi\) | ||||
0.559881 | + | 0.828573i | \(0.310847\pi\) | |||||||
\(558\) | −2.55669 | −0.108233 | ||||||||
\(559\) | −27.6216 | −1.16827 | ||||||||
\(560\) | 0.925199 | 0.0390968 | ||||||||
\(561\) | 3.28960 | 0.138887 | ||||||||
\(562\) | 52.1271 | 2.19885 | ||||||||
\(563\) | 26.4686 | 1.11552 | 0.557758 | − | 0.830003i | \(-0.311662\pi\) | ||||
0.557758 | + | 0.830003i | \(0.311662\pi\) | |||||||
\(564\) | 23.4742 | 0.988442 | ||||||||
\(565\) | 6.89937 | 0.290259 | ||||||||
\(566\) | −15.2920 | −0.642770 | ||||||||
\(567\) | 0.0837724 | 0.00351811 | ||||||||
\(568\) | 6.75966 | 0.283629 | ||||||||
\(569\) | 9.36662 | 0.392669 | 0.196335 | − | 0.980537i | \(-0.437096\pi\) | ||||
0.196335 | + | 0.980537i | \(0.437096\pi\) | |||||||
\(570\) | 38.6283 | 1.61796 | ||||||||
\(571\) | 22.7683 | 0.952825 | 0.476413 | − | 0.879222i | \(-0.341937\pi\) | ||||
0.476413 | + | 0.879222i | \(0.341937\pi\) | |||||||
\(572\) | −28.2742 | −1.18220 | ||||||||
\(573\) | −1.23719 | −0.0516842 | ||||||||
\(574\) | −1.30981 | −0.0546705 | ||||||||
\(575\) | 8.10008 | 0.337797 | ||||||||
\(576\) | −11.1700 | −0.465416 | ||||||||
\(577\) | 33.7123 | 1.40346 | 0.701731 | − | 0.712442i | \(-0.252411\pi\) | ||||
0.701731 | + | 0.712442i | \(0.252411\pi\) | |||||||
\(578\) | −2.11232 | −0.0878610 | ||||||||
\(579\) | 1.58559 | 0.0658947 | ||||||||
\(580\) | −78.9165 | −3.27683 | ||||||||
\(581\) | 1.30365 | 0.0540844 | ||||||||
\(582\) | −14.4319 | −0.598222 | ||||||||
\(583\) | −3.95632 | −0.163854 | ||||||||
\(584\) | 9.05441 | 0.374674 | ||||||||
\(585\) | 13.4684 | 0.556848 | ||||||||
\(586\) | −46.6153 | −1.92566 | ||||||||
\(587\) | 7.90311 | 0.326196 | 0.163098 | − | 0.986610i | \(-0.447851\pi\) | ||||
0.163098 | + | 0.986610i | \(0.447851\pi\) | |||||||
\(588\) | −17.2161 | −0.709979 | ||||||||
\(589\) | 5.73752 | 0.236410 | ||||||||
\(590\) | 8.39554 | 0.345639 | ||||||||
\(591\) | −14.2162 | −0.584777 | ||||||||
\(592\) | 0.894755 | 0.0367742 | ||||||||
\(593\) | −41.3715 | −1.69892 | −0.849462 | − | 0.527650i | \(-0.823073\pi\) | ||||
−0.849462 | + | 0.527650i | \(0.823073\pi\) | |||||||
\(594\) | −6.94869 | −0.285108 | ||||||||
\(595\) | −0.323176 | −0.0132489 | ||||||||
\(596\) | 19.6344 | 0.804256 | ||||||||
\(597\) | −16.6082 | −0.679728 | ||||||||
\(598\) | 6.04444 | 0.247176 | ||||||||
\(599\) | 12.7615 | 0.521420 | 0.260710 | − | 0.965417i | \(-0.416043\pi\) | ||||
0.260710 | + | 0.965417i | \(0.416043\pi\) | |||||||
\(600\) | −9.64236 | −0.393648 | ||||||||
\(601\) | 7.56493 | 0.308580 | 0.154290 | − | 0.988026i | \(-0.450691\pi\) | ||||
0.154290 | + | 0.988026i | \(0.450691\pi\) | |||||||
\(602\) | −1.40002 | −0.0570605 | ||||||||
\(603\) | −13.9564 | −0.568347 | ||||||||
\(604\) | −3.52863 | −0.143578 | ||||||||
\(605\) | 0.688753 | 0.0280018 | ||||||||
\(606\) | −21.5704 | −0.876236 | ||||||||
\(607\) | 6.53133 | 0.265099 | 0.132549 | − | 0.991176i | \(-0.457684\pi\) | ||||
0.132549 | + | 0.991176i | \(0.457684\pi\) | |||||||
\(608\) | 37.9159 | 1.53769 | ||||||||
\(609\) | 0.696079 | 0.0282066 | ||||||||
\(610\) | −107.148 | −4.33831 | ||||||||
\(611\) | −33.2886 | −1.34671 | ||||||||
\(612\) | 2.46191 | 0.0995167 | ||||||||
\(613\) | 17.0046 | 0.686810 | 0.343405 | − | 0.939187i | \(-0.388420\pi\) | ||||
0.343405 | + | 0.939187i | \(0.388420\pi\) | |||||||
\(614\) | 20.0371 | 0.808631 | ||||||||
\(615\) | −28.5553 | −1.15146 | ||||||||
\(616\) | −0.268880 | −0.0108335 | ||||||||
\(617\) | 31.1825 | 1.25536 | 0.627681 | − | 0.778471i | \(-0.284004\pi\) | ||||
0.627681 | + | 0.778471i | \(0.284004\pi\) | |||||||
\(618\) | −8.01129 | −0.322261 | ||||||||
\(619\) | 36.1570 | 1.45327 | 0.726637 | − | 0.687022i | \(-0.241082\pi\) | ||||
0.726637 | + | 0.687022i | \(0.241082\pi\) | |||||||
\(620\) | −11.4955 | −0.461670 | ||||||||
\(621\) | 0.819634 | 0.0328908 | ||||||||
\(622\) | −14.3402 | −0.574988 | ||||||||
\(623\) | −0.933913 | −0.0374164 | ||||||||
\(624\) | 9.99474 | 0.400110 | ||||||||
\(625\) | 23.2521 | 0.930085 | ||||||||
\(626\) | −19.8923 | −0.795058 | ||||||||
\(627\) | 15.5937 | 0.622753 | ||||||||
\(628\) | 2.46191 | 0.0982408 | ||||||||
\(629\) | −0.312542 | −0.0124619 | ||||||||
\(630\) | 0.682653 | 0.0271975 | ||||||||
\(631\) | −11.8536 | −0.471886 | −0.235943 | − | 0.971767i | \(-0.575818\pi\) | ||||
−0.235943 | + | 0.971767i | \(0.575818\pi\) | |||||||
\(632\) | 8.19087 | 0.325815 | ||||||||
\(633\) | 18.2578 | 0.725681 | ||||||||
\(634\) | 18.9192 | 0.751377 | ||||||||
\(635\) | −54.9337 | −2.17998 | ||||||||
\(636\) | −2.96087 | −0.117406 | ||||||||
\(637\) | 24.4140 | 0.967317 | ||||||||
\(638\) | −57.7379 | −2.28587 | ||||||||
\(639\) | −6.92804 | −0.274069 | ||||||||
\(640\) | −29.3091 | −1.15855 | ||||||||
\(641\) | 23.5467 | 0.930039 | 0.465020 | − | 0.885300i | \(-0.346047\pi\) | ||||
0.465020 | + | 0.885300i | \(0.346047\pi\) | |||||||
\(642\) | 15.9221 | 0.628397 | ||||||||
\(643\) | −47.6515 | −1.87919 | −0.939596 | − | 0.342284i | \(-0.888799\pi\) | ||||
−0.939596 | + | 0.342284i | \(0.888799\pi\) | |||||||
\(644\) | 0.169041 | 0.00666115 | ||||||||
\(645\) | −30.5219 | −1.20180 | ||||||||
\(646\) | −10.0131 | −0.393959 | ||||||||
\(647\) | −4.36478 | −0.171597 | −0.0857987 | − | 0.996312i | \(-0.527344\pi\) | ||||
−0.0857987 | + | 0.996312i | \(0.527344\pi\) | |||||||
\(648\) | −0.975695 | −0.0383289 | ||||||||
\(649\) | 3.38916 | 0.133036 | ||||||||
\(650\) | 72.8795 | 2.85857 | ||||||||
\(651\) | 0.101395 | 0.00397400 | ||||||||
\(652\) | 24.0448 | 0.941666 | ||||||||
\(653\) | −36.8843 | −1.44339 | −0.721697 | − | 0.692209i | \(-0.756638\pi\) | ||||
−0.721697 | + | 0.692209i | \(0.756638\pi\) | |||||||
\(654\) | −28.4972 | −1.11433 | ||||||||
\(655\) | −0.372126 | −0.0145402 | ||||||||
\(656\) | −21.1906 | −0.827355 | ||||||||
\(657\) | −9.27996 | −0.362046 | ||||||||
\(658\) | −1.68725 | −0.0657760 | ||||||||
\(659\) | 14.1194 | 0.550012 | 0.275006 | − | 0.961442i | \(-0.411320\pi\) | ||||
0.275006 | + | 0.961442i | \(0.411320\pi\) | |||||||
\(660\) | −31.2430 | −1.21613 | ||||||||
\(661\) | −24.8128 | −0.965108 | −0.482554 | − | 0.875866i | \(-0.660291\pi\) | ||||
−0.482554 | + | 0.875866i | \(0.660291\pi\) | |||||||
\(662\) | −1.60857 | −0.0625189 | ||||||||
\(663\) | −3.49121 | −0.135587 | ||||||||
\(664\) | −15.1836 | −0.589236 | ||||||||
\(665\) | −1.53196 | −0.0594067 | ||||||||
\(666\) | 0.660190 | 0.0255818 | ||||||||
\(667\) | 6.81048 | 0.263703 | ||||||||
\(668\) | 8.68729 | 0.336121 | ||||||||
\(669\) | 7.91171 | 0.305884 | ||||||||
\(670\) | −113.729 | −4.39374 | ||||||||
\(671\) | −43.2543 | −1.66981 | ||||||||
\(672\) | 0.670063 | 0.0258482 | ||||||||
\(673\) | 7.18553 | 0.276982 | 0.138491 | − | 0.990364i | \(-0.455775\pi\) | ||||
0.138491 | + | 0.990364i | \(0.455775\pi\) | |||||||
\(674\) | −74.4840 | −2.86902 | ||||||||
\(675\) | 9.88256 | 0.380380 | ||||||||
\(676\) | −1.99770 | −0.0768348 | ||||||||
\(677\) | −40.9665 | −1.57447 | −0.787235 | − | 0.616653i | \(-0.788488\pi\) | ||||
−0.787235 | + | 0.616653i | \(0.788488\pi\) | |||||||
\(678\) | 3.77773 | 0.145083 | ||||||||
\(679\) | 0.572354 | 0.0219649 | ||||||||
\(680\) | 3.76403 | 0.144344 | ||||||||
\(681\) | −7.91386 | −0.303260 | ||||||||
\(682\) | −8.41048 | −0.322054 | ||||||||
\(683\) | 45.2067 | 1.72979 | 0.864894 | − | 0.501955i | \(-0.167386\pi\) | ||||
0.864894 | + | 0.501955i | \(0.167386\pi\) | |||||||
\(684\) | 11.6702 | 0.446221 | ||||||||
\(685\) | −5.97406 | −0.228257 | ||||||||
\(686\) | 2.47612 | 0.0945386 | ||||||||
\(687\) | 19.5929 | 0.747517 | ||||||||
\(688\) | −22.6500 | −0.863523 | ||||||||
\(689\) | 4.19879 | 0.159961 | ||||||||
\(690\) | 6.67912 | 0.254270 | ||||||||
\(691\) | −16.9414 | −0.644482 | −0.322241 | − | 0.946658i | \(-0.604436\pi\) | ||||
−0.322241 | + | 0.946658i | \(0.604436\pi\) | |||||||
\(692\) | 12.5995 | 0.478961 | ||||||||
\(693\) | 0.275578 | 0.0104683 | ||||||||
\(694\) | −63.4607 | −2.40893 | ||||||||
\(695\) | −46.5138 | −1.76437 | ||||||||
\(696\) | −8.10722 | −0.307303 | ||||||||
\(697\) | 7.40198 | 0.280370 | ||||||||
\(698\) | 39.7885 | 1.50602 | ||||||||
\(699\) | 24.0682 | 0.910341 | ||||||||
\(700\) | 2.03818 | 0.0770358 | ||||||||
\(701\) | −11.8484 | −0.447507 | −0.223754 | − | 0.974646i | \(-0.571831\pi\) | ||||
−0.223754 | + | 0.974646i | \(0.571831\pi\) | |||||||
\(702\) | 7.37456 | 0.278335 | ||||||||
\(703\) | −1.48155 | −0.0558776 | ||||||||
\(704\) | −36.7448 | −1.38487 | ||||||||
\(705\) | −36.7839 | −1.38536 | ||||||||
\(706\) | −45.4411 | −1.71020 | ||||||||
\(707\) | 0.855456 | 0.0321727 | ||||||||
\(708\) | 2.53642 | 0.0953245 | ||||||||
\(709\) | 10.0177 | 0.376223 | 0.188111 | − | 0.982148i | \(-0.439763\pi\) | ||||
0.188111 | + | 0.982148i | \(0.439763\pi\) | |||||||
\(710\) | −56.4559 | −2.11875 | ||||||||
\(711\) | −8.39490 | −0.314833 | ||||||||
\(712\) | 10.8773 | 0.407643 | ||||||||
\(713\) | 0.992059 | 0.0371529 | ||||||||
\(714\) | −0.176954 | −0.00662235 | ||||||||
\(715\) | 44.3055 | 1.65693 | ||||||||
\(716\) | −22.5474 | −0.842636 | ||||||||
\(717\) | −29.0671 | −1.08553 | ||||||||
\(718\) | −15.9433 | −0.594999 | ||||||||
\(719\) | −5.05620 | −0.188564 | −0.0942822 | − | 0.995546i | \(-0.530056\pi\) | ||||
−0.0942822 | + | 0.995546i | \(0.530056\pi\) | |||||||
\(720\) | 11.0442 | 0.411593 | ||||||||
\(721\) | 0.317719 | 0.0118325 | ||||||||
\(722\) | −7.33091 | −0.272828 | ||||||||
\(723\) | −12.7214 | −0.473115 | ||||||||
\(724\) | −52.8064 | −1.96254 | ||||||||
\(725\) | 82.1159 | 3.04971 | ||||||||
\(726\) | 0.377124 | 0.0139964 | ||||||||
\(727\) | 9.64578 | 0.357742 | 0.178871 | − | 0.983873i | \(-0.442755\pi\) | ||||
0.178871 | + | 0.983873i | \(0.442755\pi\) | |||||||
\(728\) | 0.285359 | 0.0105761 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −75.6215 | −2.79888 | ||||||||
\(731\) | 7.91175 | 0.292627 | ||||||||
\(732\) | −32.3711 | −1.19647 | ||||||||
\(733\) | −3.85024 | −0.142212 | −0.0711059 | − | 0.997469i | \(-0.522653\pi\) | ||||
−0.0711059 | + | 0.997469i | \(0.522653\pi\) | |||||||
\(734\) | 35.7359 | 1.31904 | ||||||||
\(735\) | 26.9775 | 0.995079 | ||||||||
\(736\) | 6.55593 | 0.241655 | ||||||||
\(737\) | −45.9109 | −1.69115 | ||||||||
\(738\) | −15.6354 | −0.575546 | ||||||||
\(739\) | 35.6039 | 1.30971 | 0.654855 | − | 0.755755i | \(-0.272730\pi\) | ||||
0.654855 | + | 0.755755i | \(0.272730\pi\) | |||||||
\(740\) | 2.96838 | 0.109120 | ||||||||
\(741\) | −16.5494 | −0.607958 | ||||||||
\(742\) | 0.212819 | 0.00781281 | ||||||||
\(743\) | −15.1966 | −0.557510 | −0.278755 | − | 0.960362i | \(-0.589922\pi\) | ||||
−0.278755 | + | 0.960362i | \(0.589922\pi\) | |||||||
\(744\) | −1.18095 | −0.0432957 | ||||||||
\(745\) | −30.7670 | −1.12721 | ||||||||
\(746\) | 26.4955 | 0.970068 | ||||||||
\(747\) | 15.5618 | 0.569376 | ||||||||
\(748\) | 8.09869 | 0.296117 | ||||||||
\(749\) | −0.631455 | −0.0230729 | ||||||||
\(750\) | 39.7875 | 1.45283 | ||||||||
\(751\) | 48.7581 | 1.77921 | 0.889604 | − | 0.456733i | \(-0.150980\pi\) | ||||
0.889604 | + | 0.456733i | \(0.150980\pi\) | |||||||
\(752\) | −27.2970 | −0.995419 | ||||||||
\(753\) | 18.9280 | 0.689774 | ||||||||
\(754\) | 61.2765 | 2.23156 | ||||||||
\(755\) | 5.52934 | 0.201233 | ||||||||
\(756\) | 0.206240 | 0.00750087 | ||||||||
\(757\) | 46.4489 | 1.68821 | 0.844106 | − | 0.536176i | \(-0.180132\pi\) | ||||
0.844106 | + | 0.536176i | \(0.180132\pi\) | |||||||
\(758\) | 68.8922 | 2.50228 | ||||||||
\(759\) | 2.69627 | 0.0978683 | ||||||||
\(760\) | 17.8427 | 0.647221 | ||||||||
\(761\) | 28.1943 | 1.02204 | 0.511022 | − | 0.859568i | \(-0.329267\pi\) | ||||
0.511022 | + | 0.859568i | \(0.329267\pi\) | |||||||
\(762\) | −30.0788 | −1.08964 | ||||||||
\(763\) | 1.13017 | 0.0409148 | ||||||||
\(764\) | −3.04584 | −0.110195 | ||||||||
\(765\) | −3.85779 | −0.139479 | ||||||||
\(766\) | −68.1728 | −2.46318 | ||||||||
\(767\) | −3.59688 | −0.129876 | ||||||||
\(768\) | 6.29183 | 0.227037 | ||||||||
\(769\) | 48.1225 | 1.73534 | 0.867672 | − | 0.497138i | \(-0.165616\pi\) | ||||
0.867672 | + | 0.497138i | \(0.165616\pi\) | |||||||
\(770\) | 2.24565 | 0.0809278 | ||||||||
\(771\) | −16.0993 | −0.579802 | ||||||||
\(772\) | 3.90357 | 0.140492 | ||||||||
\(773\) | −15.7830 | −0.567675 | −0.283838 | − | 0.958872i | \(-0.591608\pi\) | ||||
−0.283838 | + | 0.958872i | \(0.591608\pi\) | |||||||
\(774\) | −16.7122 | −0.600707 | ||||||||
\(775\) | 11.9615 | 0.429671 | ||||||||
\(776\) | −6.66620 | −0.239303 | ||||||||
\(777\) | −0.0261824 | −0.000939288 0 | ||||||||
\(778\) | −15.4536 | −0.554040 | ||||||||
\(779\) | 35.0877 | 1.25715 | ||||||||
\(780\) | 33.1579 | 1.18724 | ||||||||
\(781\) | −22.7905 | −0.815508 | ||||||||
\(782\) | −1.73133 | −0.0619123 | ||||||||
\(783\) | 8.30917 | 0.296946 | ||||||||
\(784\) | 20.0197 | 0.714990 | ||||||||
\(785\) | −3.85779 | −0.137690 | ||||||||
\(786\) | −0.203756 | −0.00726775 | ||||||||
\(787\) | −1.51220 | −0.0539042 | −0.0269521 | − | 0.999637i | \(-0.508580\pi\) | ||||
−0.0269521 | + | 0.999637i | \(0.508580\pi\) | |||||||
\(788\) | −34.9990 | −1.24679 | ||||||||
\(789\) | −3.74690 | −0.133393 | ||||||||
\(790\) | −68.4092 | −2.43389 | ||||||||
\(791\) | −0.149821 | −0.00532701 | ||||||||
\(792\) | −3.20965 | −0.114050 | ||||||||
\(793\) | 45.9053 | 1.63014 | ||||||||
\(794\) | 48.4880 | 1.72078 | ||||||||
\(795\) | 4.63967 | 0.164552 | ||||||||
\(796\) | −40.8878 | −1.44923 | ||||||||
\(797\) | −7.59320 | −0.268965 | −0.134482 | − | 0.990916i | \(-0.542937\pi\) | ||||
−0.134482 | + | 0.990916i | \(0.542937\pi\) | |||||||
\(798\) | −0.838818 | −0.0296938 | ||||||||
\(799\) | 9.53497 | 0.337323 | ||||||||
\(800\) | 79.0467 | 2.79472 | ||||||||
\(801\) | −11.1482 | −0.393903 | ||||||||
\(802\) | 56.2918 | 1.98773 | ||||||||
\(803\) | −30.5274 | −1.07729 | ||||||||
\(804\) | −34.3593 | −1.21176 | ||||||||
\(805\) | −0.264886 | −0.00933602 | ||||||||
\(806\) | 8.92593 | 0.314403 | ||||||||
\(807\) | −19.3314 | −0.680498 | ||||||||
\(808\) | −9.96348 | −0.350514 | ||||||||
\(809\) | 33.2929 | 1.17052 | 0.585258 | − | 0.810847i | \(-0.300993\pi\) | ||||
0.585258 | + | 0.810847i | \(0.300993\pi\) | |||||||
\(810\) | 8.14890 | 0.286323 | ||||||||
\(811\) | 34.8871 | 1.22505 | 0.612526 | − | 0.790450i | \(-0.290153\pi\) | ||||
0.612526 | + | 0.790450i | \(0.290153\pi\) | |||||||
\(812\) | 1.71368 | 0.0601384 | ||||||||
\(813\) | −4.22295 | −0.148105 | ||||||||
\(814\) | 2.17176 | 0.0761201 | ||||||||
\(815\) | −37.6780 | −1.31980 | ||||||||
\(816\) | −2.86283 | −0.100219 | ||||||||
\(817\) | 37.5042 | 1.31210 | ||||||||
\(818\) | −53.4297 | −1.86813 | ||||||||
\(819\) | −0.292467 | −0.0102196 | ||||||||
\(820\) | −70.3005 | −2.45500 | ||||||||
\(821\) | −24.5704 | −0.857514 | −0.428757 | − | 0.903420i | \(-0.641048\pi\) | ||||
−0.428757 | + | 0.903420i | \(0.641048\pi\) | |||||||
\(822\) | −3.27108 | −0.114092 | ||||||||
\(823\) | 43.1170 | 1.50296 | 0.751482 | − | 0.659753i | \(-0.229339\pi\) | ||||
0.751482 | + | 0.659753i | \(0.229339\pi\) | |||||||
\(824\) | −3.70047 | −0.128912 | ||||||||
\(825\) | 32.5096 | 1.13184 | ||||||||
\(826\) | −0.182310 | −0.00634338 | ||||||||
\(827\) | −22.3819 | −0.778295 | −0.389147 | − | 0.921176i | \(-0.627230\pi\) | ||||
−0.389147 | + | 0.921176i | \(0.627230\pi\) | |||||||
\(828\) | 2.01786 | 0.0701256 | ||||||||
\(829\) | −18.1372 | −0.629933 | −0.314966 | − | 0.949103i | \(-0.601993\pi\) | ||||
−0.314966 | + | 0.949103i | \(0.601993\pi\) | |||||||
\(830\) | 126.811 | 4.40169 | ||||||||
\(831\) | 18.2497 | 0.633077 | ||||||||
\(832\) | 38.9968 | 1.35197 | ||||||||
\(833\) | −6.99298 | −0.242292 | ||||||||
\(834\) | −25.4685 | −0.881902 | ||||||||
\(835\) | −13.6129 | −0.471095 | ||||||||
\(836\) | 38.3903 | 1.32776 | ||||||||
\(837\) | 1.21037 | 0.0418364 | ||||||||
\(838\) | 25.9710 | 0.897154 | ||||||||
\(839\) | 55.1696 | 1.90467 | 0.952333 | − | 0.305060i | \(-0.0986765\pi\) | ||||
0.952333 | + | 0.305060i | \(0.0986765\pi\) | |||||||
\(840\) | 0.315322 | 0.0108796 | ||||||||
\(841\) | 40.0424 | 1.38077 | ||||||||
\(842\) | 45.8841 | 1.58127 | ||||||||
\(843\) | −24.6776 | −0.849943 | ||||||||
\(844\) | 44.9489 | 1.54720 | ||||||||
\(845\) | 3.13039 | 0.107689 | ||||||||
\(846\) | −20.1409 | −0.692459 | ||||||||
\(847\) | −0.0149563 | −0.000513906 0 | ||||||||
\(848\) | 3.44305 | 0.118235 | ||||||||
\(849\) | 7.23941 | 0.248456 | ||||||||
\(850\) | −20.8751 | −0.716012 | ||||||||
\(851\) | −0.256170 | −0.00878140 | ||||||||
\(852\) | −17.0562 | −0.584336 | ||||||||
\(853\) | −50.7648 | −1.73816 | −0.869078 | − | 0.494676i | \(-0.835287\pi\) | ||||
−0.869078 | + | 0.494676i | \(0.835287\pi\) | |||||||
\(854\) | 2.32674 | 0.0796193 | ||||||||
\(855\) | −18.2871 | −0.625407 | ||||||||
\(856\) | 7.35454 | 0.251373 | ||||||||
\(857\) | 28.9427 | 0.988664 | 0.494332 | − | 0.869273i | \(-0.335413\pi\) | ||||
0.494332 | + | 0.869273i | \(0.335413\pi\) | |||||||
\(858\) | 24.2594 | 0.828201 | ||||||||
\(859\) | 13.5767 | 0.463232 | 0.231616 | − | 0.972807i | \(-0.425599\pi\) | ||||
0.231616 | + | 0.972807i | \(0.425599\pi\) | |||||||
\(860\) | −75.1420 | −2.56232 | ||||||||
\(861\) | 0.620082 | 0.0211323 | ||||||||
\(862\) | −45.3344 | −1.54410 | ||||||||
\(863\) | 25.2055 | 0.858004 | 0.429002 | − | 0.903304i | \(-0.358865\pi\) | ||||
0.429002 | + | 0.903304i | \(0.358865\pi\) | |||||||
\(864\) | 7.99861 | 0.272118 | ||||||||
\(865\) | −19.7433 | −0.671293 | ||||||||
\(866\) | 60.1476 | 2.04390 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 0.249626 | 0.00847286 | ||||||||
\(869\) | −27.6159 | −0.936804 | ||||||||
\(870\) | 67.7106 | 2.29560 | ||||||||
\(871\) | 48.7246 | 1.65097 | ||||||||
\(872\) | −13.1630 | −0.445756 | ||||||||
\(873\) | 6.83225 | 0.231237 | ||||||||
\(874\) | −8.20705 | −0.277608 | ||||||||
\(875\) | −1.57793 | −0.0533436 | ||||||||
\(876\) | −22.8464 | −0.771908 | ||||||||
\(877\) | −42.3697 | −1.43072 | −0.715362 | − | 0.698754i | \(-0.753738\pi\) | ||||
−0.715362 | + | 0.698754i | \(0.753738\pi\) | |||||||
\(878\) | −8.31996 | −0.280785 | ||||||||
\(879\) | 22.0683 | 0.744344 | ||||||||
\(880\) | 36.3310 | 1.22472 | ||||||||
\(881\) | 14.0307 | 0.472707 | 0.236354 | − | 0.971667i | \(-0.424048\pi\) | ||||
0.236354 | + | 0.971667i | \(0.424048\pi\) | |||||||
\(882\) | 14.7714 | 0.497380 | ||||||||
\(883\) | −34.1366 | −1.14879 | −0.574395 | − | 0.818579i | \(-0.694762\pi\) | ||||
−0.574395 | + | 0.818579i | \(0.694762\pi\) | |||||||
\(884\) | −8.59503 | −0.289082 | ||||||||
\(885\) | −3.97455 | −0.133603 | ||||||||
\(886\) | −44.2458 | −1.48647 | ||||||||
\(887\) | −6.24853 | −0.209805 | −0.104903 | − | 0.994483i | \(-0.533453\pi\) | ||||
−0.104903 | + | 0.994483i | \(0.533453\pi\) | |||||||
\(888\) | 0.304946 | 0.0102333 | ||||||||
\(889\) | 1.19289 | 0.0400083 | ||||||||
\(890\) | −90.8457 | −3.04515 | ||||||||
\(891\) | 3.28960 | 0.110206 | ||||||||
\(892\) | 19.4779 | 0.652168 | ||||||||
\(893\) | 45.1987 | 1.51252 | ||||||||
\(894\) | −16.8464 | −0.563427 | ||||||||
\(895\) | 35.3316 | 1.18101 | ||||||||
\(896\) | 0.636451 | 0.0212623 | ||||||||
\(897\) | −2.86152 | −0.0955432 | ||||||||
\(898\) | −1.94778 | −0.0649982 | ||||||||
\(899\) | 10.0572 | 0.335425 | ||||||||
\(900\) | 24.3299 | 0.810998 | ||||||||
\(901\) | −1.20268 | −0.0400669 | ||||||||
\(902\) | −51.4341 | −1.71257 | ||||||||
\(903\) | 0.662786 | 0.0220562 | ||||||||
\(904\) | 1.74496 | 0.0580364 | ||||||||
\(905\) | 82.7473 | 2.75061 | ||||||||
\(906\) | 3.02757 | 0.100584 | ||||||||
\(907\) | −26.5967 | −0.883127 | −0.441564 | − | 0.897230i | \(-0.645576\pi\) | ||||
−0.441564 | + | 0.897230i | \(0.645576\pi\) | |||||||
\(908\) | −19.4832 | −0.646572 | ||||||||
\(909\) | 10.2117 | 0.338700 | ||||||||
\(910\) | −2.38328 | −0.0790051 | ||||||||
\(911\) | 40.9867 | 1.35795 | 0.678975 | − | 0.734161i | \(-0.262424\pi\) | ||||
0.678975 | + | 0.734161i | \(0.262424\pi\) | |||||||
\(912\) | −13.5707 | −0.449371 | ||||||||
\(913\) | 51.1920 | 1.69421 | ||||||||
\(914\) | −59.4909 | −1.96778 | ||||||||
\(915\) | 50.7254 | 1.67693 | ||||||||
\(916\) | 48.2360 | 1.59376 | ||||||||
\(917\) | 0.00808075 | 0.000266850 0 | ||||||||
\(918\) | −2.11232 | −0.0697170 | ||||||||
\(919\) | 35.2733 | 1.16356 | 0.581780 | − | 0.813346i | \(-0.302357\pi\) | ||||
0.581780 | + | 0.813346i | \(0.302357\pi\) | |||||||
\(920\) | 3.08513 | 0.101714 | ||||||||
\(921\) | −9.48581 | −0.312568 | ||||||||
\(922\) | 15.4495 | 0.508803 | ||||||||
\(923\) | 24.1873 | 0.796133 | ||||||||
\(924\) | 0.678446 | 0.0223192 | ||||||||
\(925\) | −3.08871 | −0.101556 | ||||||||
\(926\) | 32.7822 | 1.07729 | ||||||||
\(927\) | 3.79265 | 0.124567 | ||||||||
\(928\) | 66.4618 | 2.18172 | ||||||||
\(929\) | −5.27974 | −0.173223 | −0.0866114 | − | 0.996242i | \(-0.527604\pi\) | ||||
−0.0866114 | + | 0.996242i | \(0.527604\pi\) | |||||||
\(930\) | 9.86317 | 0.323426 | ||||||||
\(931\) | −33.1489 | −1.08641 | ||||||||
\(932\) | 59.2535 | 1.94091 | ||||||||
\(933\) | 6.78881 | 0.222256 | ||||||||
\(934\) | −75.7307 | −2.47799 | ||||||||
\(935\) | −12.6906 | −0.415027 | ||||||||
\(936\) | 3.40636 | 0.111340 | ||||||||
\(937\) | 9.85356 | 0.321902 | 0.160951 | − | 0.986962i | \(-0.448544\pi\) | ||||
0.160951 | + | 0.986962i | \(0.448544\pi\) | |||||||
\(938\) | 2.46964 | 0.0806366 | ||||||||
\(939\) | 9.41729 | 0.307321 | ||||||||
\(940\) | −90.5585 | −2.95369 | ||||||||
\(941\) | 3.03598 | 0.0989701 | 0.0494851 | − | 0.998775i | \(-0.484242\pi\) | ||||
0.0494851 | + | 0.998775i | \(0.484242\pi\) | |||||||
\(942\) | −2.11232 | −0.0688232 | ||||||||
\(943\) | 6.06692 | 0.197566 | ||||||||
\(944\) | −2.94948 | −0.0959973 | ||||||||
\(945\) | −0.323176 | −0.0105129 | ||||||||
\(946\) | −54.9764 | −1.78744 | ||||||||
\(947\) | −2.51612 | −0.0817630 | −0.0408815 | − | 0.999164i | \(-0.513017\pi\) | ||||
−0.0408815 | + | 0.999164i | \(0.513017\pi\) | |||||||
\(948\) | −20.6675 | −0.671248 | ||||||||
\(949\) | 32.3983 | 1.05169 | ||||||||
\(950\) | −98.9547 | −3.21051 | ||||||||
\(951\) | −8.95658 | −0.290437 | ||||||||
\(952\) | −0.0817363 | −0.00264909 | ||||||||
\(953\) | −20.7319 | −0.671571 | −0.335785 | − | 0.941939i | \(-0.609002\pi\) | ||||
−0.335785 | + | 0.941939i | \(0.609002\pi\) | |||||||
\(954\) | 2.54044 | 0.0822497 | ||||||||
\(955\) | 4.77281 | 0.154444 | ||||||||
\(956\) | −71.5604 | −2.31443 | ||||||||
\(957\) | 27.3339 | 0.883578 | ||||||||
\(958\) | −25.9279 | −0.837693 | ||||||||
\(959\) | 0.129727 | 0.00418912 | ||||||||
\(960\) | 43.0915 | 1.39077 | ||||||||
\(961\) | −29.5350 | −0.952742 | ||||||||
\(962\) | −2.30486 | −0.0743117 | ||||||||
\(963\) | −7.53774 | −0.242900 | ||||||||
\(964\) | −31.3190 | −1.00872 | ||||||||
\(965\) | −6.11686 | −0.196909 | ||||||||
\(966\) | −0.145038 | −0.00466651 | ||||||||
\(967\) | 6.62227 | 0.212958 | 0.106479 | − | 0.994315i | \(-0.466042\pi\) | ||||
0.106479 | + | 0.994315i | \(0.466042\pi\) | |||||||
\(968\) | 0.174196 | 0.00559888 | ||||||||
\(969\) | 4.74031 | 0.152281 | ||||||||
\(970\) | 55.6753 | 1.78763 | ||||||||
\(971\) | 16.2706 | 0.522148 | 0.261074 | − | 0.965319i | \(-0.415923\pi\) | ||||
0.261074 | + | 0.965319i | \(0.415923\pi\) | |||||||
\(972\) | 2.46191 | 0.0789657 | ||||||||
\(973\) | 1.01005 | 0.0323808 | ||||||||
\(974\) | −53.9589 | −1.72895 | ||||||||
\(975\) | −34.5021 | −1.10495 | ||||||||
\(976\) | 37.6428 | 1.20492 | ||||||||
\(977\) | −13.0246 | −0.416694 | −0.208347 | − | 0.978055i | \(-0.566808\pi\) | ||||
−0.208347 | + | 0.978055i | \(0.566808\pi\) | |||||||
\(978\) | −20.6305 | −0.659690 | ||||||||
\(979\) | −36.6732 | −1.17208 | ||||||||
\(980\) | 66.4160 | 2.12158 | ||||||||
\(981\) | 13.4909 | 0.430732 | ||||||||
\(982\) | −39.5918 | −1.26343 | ||||||||
\(983\) | 30.6327 | 0.977030 | 0.488515 | − | 0.872555i | \(-0.337539\pi\) | ||||
0.488515 | + | 0.872555i | \(0.337539\pi\) | |||||||
\(984\) | −7.22208 | −0.230231 | ||||||||
\(985\) | 54.8432 | 1.74745 | ||||||||
\(986\) | −17.5517 | −0.558959 | ||||||||
\(987\) | 0.798767 | 0.0254250 | ||||||||
\(988\) | −40.7431 | −1.29621 | ||||||||
\(989\) | 6.48474 | 0.206203 | ||||||||
\(990\) | 26.8066 | 0.851970 | ||||||||
\(991\) | 23.0228 | 0.731344 | 0.365672 | − | 0.930744i | \(-0.380839\pi\) | ||||
0.365672 | + | 0.930744i | \(0.380839\pi\) | |||||||
\(992\) | 9.68126 | 0.307380 | ||||||||
\(993\) | 0.761518 | 0.0241660 | ||||||||
\(994\) | 1.22595 | 0.0388847 | ||||||||
\(995\) | 64.0710 | 2.03119 | ||||||||
\(996\) | 38.3117 | 1.21395 | ||||||||
\(997\) | 40.2870 | 1.27590 | 0.637951 | − | 0.770077i | \(-0.279782\pi\) | ||||
0.637951 | + | 0.770077i | \(0.279782\pi\) | |||||||
\(998\) | −26.2150 | −0.829820 | ||||||||
\(999\) | −0.312542 | −0.00988839 |
(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 | 8007.2.a.i.1.10 | ✓ | 63 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.i.1.10 | ✓ | 63 | 1.1 | even | 1 | trivial |