Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8027,2,Mod(1,8027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8027, 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("8027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8027 = 23 \cdot 349 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8027.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: | \(64.0959177025\) |
Analytic rank: | \(1\) |
Dimension: | \(143\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 8027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.30190 | −1.62769 | −0.813844 | − | 0.581083i | \(-0.802629\pi\) | ||||
−0.813844 | + | 0.581083i | \(0.802629\pi\) | |||||||
\(3\) | 0.450462 | 0.260074 | 0.130037 | − | 0.991509i | \(-0.458490\pi\) | ||||
0.130037 | + | 0.991509i | \(0.458490\pi\) | |||||||
\(4\) | 3.29874 | 1.64937 | ||||||||
\(5\) | −0.676454 | −0.302520 | −0.151260 | − | 0.988494i | \(-0.548333\pi\) | ||||
−0.151260 | + | 0.988494i | \(0.548333\pi\) | |||||||
\(6\) | −1.03692 | −0.423320 | ||||||||
\(7\) | 2.59801 | 0.981954 | 0.490977 | − | 0.871172i | \(-0.336640\pi\) | ||||
0.490977 | + | 0.871172i | \(0.336640\pi\) | |||||||
\(8\) | −2.98957 | −1.05697 | ||||||||
\(9\) | −2.79708 | −0.932361 | ||||||||
\(10\) | 1.55713 | 0.492408 | ||||||||
\(11\) | −0.532065 | −0.160424 | −0.0802118 | − | 0.996778i | \(-0.525560\pi\) | ||||
−0.0802118 | + | 0.996778i | \(0.525560\pi\) | |||||||
\(12\) | 1.48596 | 0.428959 | ||||||||
\(13\) | 0.729873 | 0.202430 | 0.101215 | − | 0.994865i | \(-0.467727\pi\) | ||||
0.101215 | + | 0.994865i | \(0.467727\pi\) | |||||||
\(14\) | −5.98035 | −1.59832 | ||||||||
\(15\) | −0.304717 | −0.0786776 | ||||||||
\(16\) | 0.284200 | 0.0710501 | ||||||||
\(17\) | 5.25909 | 1.27552 | 0.637759 | − | 0.770236i | \(-0.279862\pi\) | ||||
0.637759 | + | 0.770236i | \(0.279862\pi\) | |||||||
\(18\) | 6.43860 | 1.51759 | ||||||||
\(19\) | 7.16390 | 1.64351 | 0.821756 | − | 0.569839i | \(-0.192995\pi\) | ||||
0.821756 | + | 0.569839i | \(0.192995\pi\) | |||||||
\(20\) | −2.23145 | −0.498967 | ||||||||
\(21\) | 1.17030 | 0.255381 | ||||||||
\(22\) | 1.22476 | 0.261119 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −1.34669 | −0.274891 | ||||||||
\(25\) | −4.54241 | −0.908482 | ||||||||
\(26\) | −1.68009 | −0.329493 | ||||||||
\(27\) | −2.61137 | −0.502558 | ||||||||
\(28\) | 8.57015 | 1.61961 | ||||||||
\(29\) | −2.03287 | −0.377495 | −0.188748 | − | 0.982026i | \(-0.560443\pi\) | ||||
−0.188748 | + | 0.982026i | \(0.560443\pi\) | |||||||
\(30\) | 0.701428 | 0.128063 | ||||||||
\(31\) | −5.72890 | −1.02894 | −0.514471 | − | 0.857508i | \(-0.672012\pi\) | ||||
−0.514471 | + | 0.857508i | \(0.672012\pi\) | |||||||
\(32\) | 5.32493 | 0.941324 | ||||||||
\(33\) | −0.239675 | −0.0417220 | ||||||||
\(34\) | −12.1059 | −2.07614 | ||||||||
\(35\) | −1.75743 | −0.297060 | ||||||||
\(36\) | −9.22685 | −1.53781 | ||||||||
\(37\) | −2.86077 | −0.470307 | −0.235154 | − | 0.971958i | \(-0.575559\pi\) | ||||
−0.235154 | + | 0.971958i | \(0.575559\pi\) | |||||||
\(38\) | −16.4906 | −2.67513 | ||||||||
\(39\) | 0.328780 | 0.0526469 | ||||||||
\(40\) | 2.02230 | 0.319754 | ||||||||
\(41\) | 9.47383 | 1.47956 | 0.739782 | − | 0.672847i | \(-0.234929\pi\) | ||||
0.739782 | + | 0.672847i | \(0.234929\pi\) | |||||||
\(42\) | −2.69392 | −0.415681 | ||||||||
\(43\) | −2.30599 | −0.351660 | −0.175830 | − | 0.984421i | \(-0.556261\pi\) | ||||
−0.175830 | + | 0.984421i | \(0.556261\pi\) | |||||||
\(44\) | −1.75514 | −0.264598 | ||||||||
\(45\) | 1.89210 | 0.282058 | ||||||||
\(46\) | −2.30190 | −0.339396 | ||||||||
\(47\) | −9.97423 | −1.45489 | −0.727446 | − | 0.686165i | \(-0.759293\pi\) | ||||
−0.727446 | + | 0.686165i | \(0.759293\pi\) | |||||||
\(48\) | 0.128021 | 0.0184783 | ||||||||
\(49\) | −0.250360 | −0.0357657 | ||||||||
\(50\) | 10.4562 | 1.47873 | ||||||||
\(51\) | 2.36902 | 0.331729 | ||||||||
\(52\) | 2.40766 | 0.333882 | ||||||||
\(53\) | −0.217009 | −0.0298085 | −0.0149043 | − | 0.999889i | \(-0.504744\pi\) | ||||
−0.0149043 | + | 0.999889i | \(0.504744\pi\) | |||||||
\(54\) | 6.01110 | 0.818007 | ||||||||
\(55\) | 0.359917 | 0.0485313 | ||||||||
\(56\) | −7.76691 | −1.03790 | ||||||||
\(57\) | 3.22707 | 0.427435 | ||||||||
\(58\) | 4.67947 | 0.614445 | ||||||||
\(59\) | −9.30020 | −1.21078 | −0.605391 | − | 0.795928i | \(-0.706983\pi\) | ||||
−0.605391 | + | 0.795928i | \(0.706983\pi\) | |||||||
\(60\) | −1.00518 | −0.129768 | ||||||||
\(61\) | −12.0722 | −1.54568 | −0.772841 | − | 0.634600i | \(-0.781165\pi\) | ||||
−0.772841 | + | 0.634600i | \(0.781165\pi\) | |||||||
\(62\) | 13.1874 | 1.67480 | ||||||||
\(63\) | −7.26684 | −0.915536 | ||||||||
\(64\) | −12.8259 | −1.60323 | ||||||||
\(65\) | −0.493726 | −0.0612391 | ||||||||
\(66\) | 0.551707 | 0.0679105 | ||||||||
\(67\) | −11.4418 | −1.39783 | −0.698917 | − | 0.715203i | \(-0.746334\pi\) | ||||
−0.698917 | + | 0.715203i | \(0.746334\pi\) | |||||||
\(68\) | 17.3484 | 2.10380 | ||||||||
\(69\) | 0.450462 | 0.0542293 | ||||||||
\(70\) | 4.04543 | 0.483522 | ||||||||
\(71\) | 8.16300 | 0.968769 | 0.484385 | − | 0.874855i | \(-0.339044\pi\) | ||||
0.484385 | + | 0.874855i | \(0.339044\pi\) | |||||||
\(72\) | 8.36207 | 0.985479 | ||||||||
\(73\) | −8.03668 | −0.940622 | −0.470311 | − | 0.882501i | \(-0.655858\pi\) | ||||
−0.470311 | + | 0.882501i | \(0.655858\pi\) | |||||||
\(74\) | 6.58520 | 0.765514 | ||||||||
\(75\) | −2.04618 | −0.236273 | ||||||||
\(76\) | 23.6318 | 2.71076 | ||||||||
\(77\) | −1.38231 | −0.157529 | ||||||||
\(78\) | −0.756818 | −0.0856928 | ||||||||
\(79\) | 6.16246 | 0.693330 | 0.346665 | − | 0.937989i | \(-0.387314\pi\) | ||||
0.346665 | + | 0.937989i | \(0.387314\pi\) | |||||||
\(80\) | −0.192249 | −0.0214941 | ||||||||
\(81\) | 7.21493 | 0.801659 | ||||||||
\(82\) | −21.8078 | −2.40827 | ||||||||
\(83\) | −1.85525 | −0.203640 | −0.101820 | − | 0.994803i | \(-0.532467\pi\) | ||||
−0.101820 | + | 0.994803i | \(0.532467\pi\) | |||||||
\(84\) | 3.86053 | 0.421218 | ||||||||
\(85\) | −3.55754 | −0.385869 | ||||||||
\(86\) | 5.30816 | 0.572393 | ||||||||
\(87\) | −0.915733 | −0.0981768 | ||||||||
\(88\) | 1.59064 | 0.169563 | ||||||||
\(89\) | 12.2675 | 1.30036 | 0.650179 | − | 0.759781i | \(-0.274694\pi\) | ||||
0.650179 | + | 0.759781i | \(0.274694\pi\) | |||||||
\(90\) | −4.35542 | −0.459102 | ||||||||
\(91\) | 1.89621 | 0.198777 | ||||||||
\(92\) | 3.29874 | 0.343917 | ||||||||
\(93\) | −2.58065 | −0.267601 | ||||||||
\(94\) | 22.9597 | 2.36811 | ||||||||
\(95\) | −4.84605 | −0.497195 | ||||||||
\(96\) | 2.39868 | 0.244814 | ||||||||
\(97\) | 6.62865 | 0.673038 | 0.336519 | − | 0.941677i | \(-0.390750\pi\) | ||||
0.336519 | + | 0.941677i | \(0.390750\pi\) | |||||||
\(98\) | 0.576303 | 0.0582154 | ||||||||
\(99\) | 1.48823 | 0.149573 | ||||||||
\(100\) | −14.9842 | −1.49842 | ||||||||
\(101\) | −10.9290 | −1.08748 | −0.543738 | − | 0.839255i | \(-0.682992\pi\) | ||||
−0.543738 | + | 0.839255i | \(0.682992\pi\) | |||||||
\(102\) | −5.45325 | −0.539952 | ||||||||
\(103\) | 16.5985 | 1.63550 | 0.817750 | − | 0.575574i | \(-0.195221\pi\) | ||||
0.817750 | + | 0.575574i | \(0.195221\pi\) | |||||||
\(104\) | −2.18200 | −0.213963 | ||||||||
\(105\) | −0.791657 | −0.0772578 | ||||||||
\(106\) | 0.499533 | 0.0485190 | ||||||||
\(107\) | 10.4331 | 1.00860 | 0.504302 | − | 0.863528i | \(-0.331750\pi\) | ||||
0.504302 | + | 0.863528i | \(0.331750\pi\) | |||||||
\(108\) | −8.61422 | −0.828903 | ||||||||
\(109\) | −18.4203 | −1.76435 | −0.882174 | − | 0.470923i | \(-0.843921\pi\) | ||||
−0.882174 | + | 0.470923i | \(0.843921\pi\) | |||||||
\(110\) | −0.828494 | −0.0789938 | ||||||||
\(111\) | −1.28867 | −0.122315 | ||||||||
\(112\) | 0.738355 | 0.0697680 | ||||||||
\(113\) | −8.54331 | −0.803687 | −0.401843 | − | 0.915708i | \(-0.631630\pi\) | ||||
−0.401843 | + | 0.915708i | \(0.631630\pi\) | |||||||
\(114\) | −7.42838 | −0.695732 | ||||||||
\(115\) | −0.676454 | −0.0630797 | ||||||||
\(116\) | −6.70592 | −0.622629 | ||||||||
\(117\) | −2.04152 | −0.188738 | ||||||||
\(118\) | 21.4081 | 1.97078 | ||||||||
\(119\) | 13.6632 | 1.25250 | ||||||||
\(120\) | 0.910972 | 0.0831599 | ||||||||
\(121\) | −10.7169 | −0.974264 | ||||||||
\(122\) | 27.7889 | 2.51589 | ||||||||
\(123\) | 4.26760 | 0.384797 | ||||||||
\(124\) | −18.8982 | −1.69710 | ||||||||
\(125\) | 6.45500 | 0.577353 | ||||||||
\(126\) | 16.7275 | 1.49021 | ||||||||
\(127\) | −1.87428 | −0.166315 | −0.0831575 | − | 0.996536i | \(-0.526500\pi\) | ||||
−0.0831575 | + | 0.996536i | \(0.526500\pi\) | |||||||
\(128\) | 18.8740 | 1.66824 | ||||||||
\(129\) | −1.03876 | −0.0914578 | ||||||||
\(130\) | 1.13651 | 0.0996782 | ||||||||
\(131\) | −3.19986 | −0.279573 | −0.139787 | − | 0.990182i | \(-0.544642\pi\) | ||||
−0.139787 | + | 0.990182i | \(0.544642\pi\) | |||||||
\(132\) | −0.790625 | −0.0688151 | ||||||||
\(133\) | 18.6119 | 1.61385 | ||||||||
\(134\) | 26.3378 | 2.27524 | ||||||||
\(135\) | 1.76647 | 0.152034 | ||||||||
\(136\) | −15.7224 | −1.34818 | ||||||||
\(137\) | 17.2803 | 1.47636 | 0.738179 | − | 0.674605i | \(-0.235686\pi\) | ||||
0.738179 | + | 0.674605i | \(0.235686\pi\) | |||||||
\(138\) | −1.03692 | −0.0882683 | ||||||||
\(139\) | −13.2952 | −1.12769 | −0.563843 | − | 0.825882i | \(-0.690678\pi\) | ||||
−0.563843 | + | 0.825882i | \(0.690678\pi\) | |||||||
\(140\) | −5.79731 | −0.489962 | ||||||||
\(141\) | −4.49301 | −0.378380 | ||||||||
\(142\) | −18.7904 | −1.57685 | ||||||||
\(143\) | −0.388339 | −0.0324746 | ||||||||
\(144\) | −0.794932 | −0.0662444 | ||||||||
\(145\) | 1.37515 | 0.114200 | ||||||||
\(146\) | 18.4996 | 1.53104 | ||||||||
\(147\) | −0.112778 | −0.00930174 | ||||||||
\(148\) | −9.43693 | −0.775711 | ||||||||
\(149\) | −10.9380 | −0.896076 | −0.448038 | − | 0.894015i | \(-0.647877\pi\) | ||||
−0.448038 | + | 0.894015i | \(0.647877\pi\) | |||||||
\(150\) | 4.71011 | 0.384579 | ||||||||
\(151\) | 7.20621 | 0.586433 | 0.293216 | − | 0.956046i | \(-0.405274\pi\) | ||||
0.293216 | + | 0.956046i | \(0.405274\pi\) | |||||||
\(152\) | −21.4170 | −1.73715 | ||||||||
\(153\) | −14.7101 | −1.18924 | ||||||||
\(154\) | 3.18193 | 0.256407 | ||||||||
\(155\) | 3.87534 | 0.311275 | ||||||||
\(156\) | 1.08456 | 0.0868342 | ||||||||
\(157\) | −12.0129 | −0.958733 | −0.479367 | − | 0.877615i | \(-0.659134\pi\) | ||||
−0.479367 | + | 0.877615i | \(0.659134\pi\) | |||||||
\(158\) | −14.1854 | −1.12853 | ||||||||
\(159\) | −0.0977544 | −0.00775243 | ||||||||
\(160\) | −3.60207 | −0.284769 | ||||||||
\(161\) | 2.59801 | 0.204752 | ||||||||
\(162\) | −16.6080 | −1.30485 | ||||||||
\(163\) | 2.76599 | 0.216649 | 0.108325 | − | 0.994116i | \(-0.465451\pi\) | ||||
0.108325 | + | 0.994116i | \(0.465451\pi\) | |||||||
\(164\) | 31.2517 | 2.44035 | ||||||||
\(165\) | 0.162129 | 0.0126217 | ||||||||
\(166\) | 4.27059 | 0.331462 | ||||||||
\(167\) | 1.56285 | 0.120937 | 0.0604685 | − | 0.998170i | \(-0.480741\pi\) | ||||
0.0604685 | + | 0.998170i | \(0.480741\pi\) | |||||||
\(168\) | −3.49870 | −0.269930 | ||||||||
\(169\) | −12.4673 | −0.959022 | ||||||||
\(170\) | 8.18909 | 0.628075 | ||||||||
\(171\) | −20.0380 | −1.53235 | ||||||||
\(172\) | −7.60686 | −0.580018 | ||||||||
\(173\) | 12.9134 | 0.981785 | 0.490892 | − | 0.871220i | \(-0.336671\pi\) | ||||
0.490892 | + | 0.871220i | \(0.336671\pi\) | |||||||
\(174\) | 2.10792 | 0.159801 | ||||||||
\(175\) | −11.8012 | −0.892088 | ||||||||
\(176\) | −0.151213 | −0.0113981 | ||||||||
\(177\) | −4.18938 | −0.314893 | ||||||||
\(178\) | −28.2387 | −2.11658 | ||||||||
\(179\) | 3.84425 | 0.287333 | 0.143666 | − | 0.989626i | \(-0.454111\pi\) | ||||
0.143666 | + | 0.989626i | \(0.454111\pi\) | |||||||
\(180\) | 6.24154 | 0.465217 | ||||||||
\(181\) | −20.0182 | −1.48794 | −0.743971 | − | 0.668212i | \(-0.767060\pi\) | ||||
−0.743971 | + | 0.668212i | \(0.767060\pi\) | |||||||
\(182\) | −4.36489 | −0.323547 | ||||||||
\(183\) | −5.43805 | −0.401992 | ||||||||
\(184\) | −2.98957 | −0.220394 | ||||||||
\(185\) | 1.93518 | 0.142277 | ||||||||
\(186\) | 5.94040 | 0.435571 | ||||||||
\(187\) | −2.79818 | −0.204623 | ||||||||
\(188\) | −32.9024 | −2.39965 | ||||||||
\(189\) | −6.78435 | −0.493489 | ||||||||
\(190\) | 11.1551 | 0.809278 | ||||||||
\(191\) | −25.6972 | −1.85938 | −0.929692 | − | 0.368337i | \(-0.879927\pi\) | ||||
−0.929692 | + | 0.368337i | \(0.879927\pi\) | |||||||
\(192\) | −5.77756 | −0.416959 | ||||||||
\(193\) | 11.6595 | 0.839270 | 0.419635 | − | 0.907693i | \(-0.362158\pi\) | ||||
0.419635 | + | 0.907693i | \(0.362158\pi\) | |||||||
\(194\) | −15.2585 | −1.09550 | ||||||||
\(195\) | −0.222405 | −0.0159267 | ||||||||
\(196\) | −0.825871 | −0.0589908 | ||||||||
\(197\) | 5.06007 | 0.360515 | 0.180257 | − | 0.983619i | \(-0.442307\pi\) | ||||
0.180257 | + | 0.983619i | \(0.442307\pi\) | |||||||
\(198\) | −3.42575 | −0.243458 | ||||||||
\(199\) | 3.06102 | 0.216990 | 0.108495 | − | 0.994097i | \(-0.465397\pi\) | ||||
0.108495 | + | 0.994097i | \(0.465397\pi\) | |||||||
\(200\) | 13.5798 | 0.960239 | ||||||||
\(201\) | −5.15408 | −0.363541 | ||||||||
\(202\) | 25.1575 | 1.77007 | ||||||||
\(203\) | −5.28142 | −0.370683 | ||||||||
\(204\) | 7.81478 | 0.547144 | ||||||||
\(205\) | −6.40862 | −0.447597 | ||||||||
\(206\) | −38.2081 | −2.66208 | ||||||||
\(207\) | −2.79708 | −0.194411 | ||||||||
\(208\) | 0.207430 | 0.0143827 | ||||||||
\(209\) | −3.81166 | −0.263658 | ||||||||
\(210\) | 1.82231 | 0.125752 | ||||||||
\(211\) | −12.6479 | −0.870716 | −0.435358 | − | 0.900257i | \(-0.643378\pi\) | ||||
−0.435358 | + | 0.900257i | \(0.643378\pi\) | |||||||
\(212\) | −0.715857 | −0.0491652 | ||||||||
\(213\) | 3.67712 | 0.251952 | ||||||||
\(214\) | −24.0159 | −1.64169 | ||||||||
\(215\) | 1.55990 | 0.106384 | ||||||||
\(216\) | 7.80685 | 0.531189 | ||||||||
\(217\) | −14.8837 | −1.01037 | ||||||||
\(218\) | 42.4018 | 2.87181 | ||||||||
\(219\) | −3.62022 | −0.244632 | ||||||||
\(220\) | 1.18727 | 0.0800460 | ||||||||
\(221\) | 3.83847 | 0.258203 | ||||||||
\(222\) | 2.96638 | 0.199091 | ||||||||
\(223\) | 7.22817 | 0.484034 | 0.242017 | − | 0.970272i | \(-0.422191\pi\) | ||||
0.242017 | + | 0.970272i | \(0.422191\pi\) | |||||||
\(224\) | 13.8342 | 0.924337 | ||||||||
\(225\) | 12.7055 | 0.847033 | ||||||||
\(226\) | 19.6658 | 1.30815 | ||||||||
\(227\) | 20.3368 | 1.34980 | 0.674899 | − | 0.737910i | \(-0.264187\pi\) | ||||
0.674899 | + | 0.737910i | \(0.264187\pi\) | |||||||
\(228\) | 10.6453 | 0.704999 | ||||||||
\(229\) | −2.09707 | −0.138578 | −0.0692891 | − | 0.997597i | \(-0.522073\pi\) | ||||
−0.0692891 | + | 0.997597i | \(0.522073\pi\) | |||||||
\(230\) | 1.55713 | 0.102674 | ||||||||
\(231\) | −0.622677 | −0.0409691 | ||||||||
\(232\) | 6.07741 | 0.399002 | ||||||||
\(233\) | −18.0222 | −1.18067 | −0.590337 | − | 0.807157i | \(-0.701005\pi\) | ||||
−0.590337 | + | 0.807157i | \(0.701005\pi\) | |||||||
\(234\) | 4.69936 | 0.307207 | ||||||||
\(235\) | 6.74711 | 0.440133 | ||||||||
\(236\) | −30.6789 | −1.99703 | ||||||||
\(237\) | 2.77595 | 0.180317 | ||||||||
\(238\) | −31.4512 | −2.03868 | ||||||||
\(239\) | −1.23873 | −0.0801269 | −0.0400635 | − | 0.999197i | \(-0.512756\pi\) | ||||
−0.0400635 | + | 0.999197i | \(0.512756\pi\) | |||||||
\(240\) | −0.0866007 | −0.00559005 | ||||||||
\(241\) | 18.7225 | 1.20602 | 0.603011 | − | 0.797733i | \(-0.293967\pi\) | ||||
0.603011 | + | 0.797733i | \(0.293967\pi\) | |||||||
\(242\) | 24.6692 | 1.58580 | ||||||||
\(243\) | 11.0842 | 0.711049 | ||||||||
\(244\) | −39.8229 | −2.54940 | ||||||||
\(245\) | 0.169357 | 0.0108198 | ||||||||
\(246\) | −9.82359 | −0.626329 | ||||||||
\(247\) | 5.22874 | 0.332697 | ||||||||
\(248\) | 17.1269 | 1.08756 | ||||||||
\(249\) | −0.835718 | −0.0529615 | ||||||||
\(250\) | −14.8588 | −0.939751 | ||||||||
\(251\) | 16.1000 | 1.01622 | 0.508111 | − | 0.861291i | \(-0.330344\pi\) | ||||
0.508111 | + | 0.861291i | \(0.330344\pi\) | |||||||
\(252\) | −23.9714 | −1.51006 | ||||||||
\(253\) | −0.532065 | −0.0334506 | ||||||||
\(254\) | 4.31439 | 0.270709 | ||||||||
\(255\) | −1.60254 | −0.100355 | ||||||||
\(256\) | −17.7942 | −1.11214 | ||||||||
\(257\) | 15.0426 | 0.938334 | 0.469167 | − | 0.883109i | \(-0.344554\pi\) | ||||
0.469167 | + | 0.883109i | \(0.344554\pi\) | |||||||
\(258\) | 2.39112 | 0.148865 | ||||||||
\(259\) | −7.43229 | −0.461820 | ||||||||
\(260\) | −1.62867 | −0.101006 | ||||||||
\(261\) | 5.68612 | 0.351962 | ||||||||
\(262\) | 7.36576 | 0.455058 | ||||||||
\(263\) | −17.1549 | −1.05782 | −0.528910 | − | 0.848678i | \(-0.677399\pi\) | ||||
−0.528910 | + | 0.848678i | \(0.677399\pi\) | |||||||
\(264\) | 0.716524 | 0.0440990 | ||||||||
\(265\) | 0.146797 | 0.00901766 | ||||||||
\(266\) | −42.8427 | −2.62685 | ||||||||
\(267\) | 5.52607 | 0.338190 | ||||||||
\(268\) | −37.7434 | −2.30555 | ||||||||
\(269\) | 8.67351 | 0.528834 | 0.264417 | − | 0.964409i | \(-0.414821\pi\) | ||||
0.264417 | + | 0.964409i | \(0.414821\pi\) | |||||||
\(270\) | −4.06624 | −0.247463 | ||||||||
\(271\) | 4.90192 | 0.297771 | 0.148885 | − | 0.988854i | \(-0.452431\pi\) | ||||
0.148885 | + | 0.988854i | \(0.452431\pi\) | |||||||
\(272\) | 1.49464 | 0.0906256 | ||||||||
\(273\) | 0.854173 | 0.0516969 | ||||||||
\(274\) | −39.7776 | −2.40305 | ||||||||
\(275\) | 2.41686 | 0.145742 | ||||||||
\(276\) | 1.48596 | 0.0894441 | ||||||||
\(277\) | 9.46268 | 0.568557 | 0.284279 | − | 0.958742i | \(-0.408246\pi\) | ||||
0.284279 | + | 0.958742i | \(0.408246\pi\) | |||||||
\(278\) | 30.6042 | 1.83552 | ||||||||
\(279\) | 16.0242 | 0.959345 | ||||||||
\(280\) | 5.25396 | 0.313984 | ||||||||
\(281\) | −26.3523 | −1.57204 | −0.786022 | − | 0.618198i | \(-0.787863\pi\) | ||||
−0.786022 | + | 0.618198i | \(0.787863\pi\) | |||||||
\(282\) | 10.3425 | 0.615885 | ||||||||
\(283\) | −15.5302 | −0.923172 | −0.461586 | − | 0.887096i | \(-0.652719\pi\) | ||||
−0.461586 | + | 0.887096i | \(0.652719\pi\) | |||||||
\(284\) | 26.9276 | 1.59786 | ||||||||
\(285\) | −2.18296 | −0.129308 | ||||||||
\(286\) | 0.893918 | 0.0528585 | ||||||||
\(287\) | 24.6131 | 1.45286 | ||||||||
\(288\) | −14.8943 | −0.877654 | ||||||||
\(289\) | 10.6581 | 0.626945 | ||||||||
\(290\) | −3.16545 | −0.185882 | ||||||||
\(291\) | 2.98596 | 0.175040 | ||||||||
\(292\) | −26.5109 | −1.55143 | ||||||||
\(293\) | −26.5973 | −1.55383 | −0.776915 | − | 0.629605i | \(-0.783217\pi\) | ||||
−0.776915 | + | 0.629605i | \(0.783217\pi\) | |||||||
\(294\) | 0.259603 | 0.0151403 | ||||||||
\(295\) | 6.29116 | 0.366285 | ||||||||
\(296\) | 8.55245 | 0.497101 | ||||||||
\(297\) | 1.38942 | 0.0806221 | ||||||||
\(298\) | 25.1782 | 1.45853 | ||||||||
\(299\) | 0.729873 | 0.0422096 | ||||||||
\(300\) | −6.74982 | −0.389701 | ||||||||
\(301\) | −5.99098 | −0.345314 | ||||||||
\(302\) | −16.5880 | −0.954530 | ||||||||
\(303\) | −4.92310 | −0.282825 | ||||||||
\(304\) | 2.03598 | 0.116772 | ||||||||
\(305\) | 8.16627 | 0.467599 | ||||||||
\(306\) | 33.8612 | 1.93572 | ||||||||
\(307\) | −17.2748 | −0.985923 | −0.492962 | − | 0.870051i | \(-0.664086\pi\) | ||||
−0.492962 | + | 0.870051i | \(0.664086\pi\) | |||||||
\(308\) | −4.55987 | −0.259823 | ||||||||
\(309\) | 7.47700 | 0.425352 | ||||||||
\(310\) | −8.92064 | −0.506658 | ||||||||
\(311\) | −3.83308 | −0.217354 | −0.108677 | − | 0.994077i | \(-0.534661\pi\) | ||||
−0.108677 | + | 0.994077i | \(0.534661\pi\) | |||||||
\(312\) | −0.982909 | −0.0556463 | ||||||||
\(313\) | 3.35058 | 0.189386 | 0.0946930 | − | 0.995507i | \(-0.469813\pi\) | ||||
0.0946930 | + | 0.995507i | \(0.469813\pi\) | |||||||
\(314\) | 27.6525 | 1.56052 | ||||||||
\(315\) | 4.91569 | 0.276968 | ||||||||
\(316\) | 20.3283 | 1.14356 | ||||||||
\(317\) | 1.11245 | 0.0624817 | 0.0312408 | − | 0.999512i | \(-0.490054\pi\) | ||||
0.0312408 | + | 0.999512i | \(0.490054\pi\) | |||||||
\(318\) | 0.225021 | 0.0126185 | ||||||||
\(319\) | 1.08162 | 0.0605591 | ||||||||
\(320\) | 8.67610 | 0.485009 | ||||||||
\(321\) | 4.69970 | 0.262312 | ||||||||
\(322\) | −5.98035 | −0.333272 | ||||||||
\(323\) | 37.6756 | 2.09633 | ||||||||
\(324\) | 23.8002 | 1.32223 | ||||||||
\(325\) | −3.31538 | −0.183904 | ||||||||
\(326\) | −6.36703 | −0.352637 | ||||||||
\(327\) | −8.29766 | −0.458862 | ||||||||
\(328\) | −28.3226 | −1.56386 | ||||||||
\(329\) | −25.9131 | −1.42864 | ||||||||
\(330\) | −0.373205 | −0.0205443 | ||||||||
\(331\) | 2.25969 | 0.124204 | 0.0621018 | − | 0.998070i | \(-0.480220\pi\) | ||||
0.0621018 | + | 0.998070i | \(0.480220\pi\) | |||||||
\(332\) | −6.11998 | −0.335877 | ||||||||
\(333\) | 8.00181 | 0.438496 | ||||||||
\(334\) | −3.59753 | −0.196848 | ||||||||
\(335\) | 7.73983 | 0.422872 | ||||||||
\(336\) | 0.332601 | 0.0181449 | ||||||||
\(337\) | 18.1162 | 0.986850 | 0.493425 | − | 0.869788i | \(-0.335745\pi\) | ||||
0.493425 | + | 0.869788i | \(0.335745\pi\) | |||||||
\(338\) | 28.6984 | 1.56099 | ||||||||
\(339\) | −3.84844 | −0.209018 | ||||||||
\(340\) | −11.7354 | −0.636441 | ||||||||
\(341\) | 3.04815 | 0.165066 | ||||||||
\(342\) | 46.1255 | 2.49418 | ||||||||
\(343\) | −18.8365 | −1.01707 | ||||||||
\(344\) | 6.89391 | 0.371695 | ||||||||
\(345\) | −0.304717 | −0.0164054 | ||||||||
\(346\) | −29.7253 | −1.59804 | ||||||||
\(347\) | −23.5290 | −1.26310 | −0.631552 | − | 0.775334i | \(-0.717582\pi\) | ||||
−0.631552 | + | 0.775334i | \(0.717582\pi\) | |||||||
\(348\) | −3.02076 | −0.161930 | ||||||||
\(349\) | 1.00000 | 0.0535288 | ||||||||
\(350\) | 27.1652 | 1.45204 | ||||||||
\(351\) | −1.90596 | −0.101733 | ||||||||
\(352\) | −2.83321 | −0.151010 | ||||||||
\(353\) | 14.6673 | 0.780662 | 0.390331 | − | 0.920675i | \(-0.372361\pi\) | ||||
0.390331 | + | 0.920675i | \(0.372361\pi\) | |||||||
\(354\) | 9.64354 | 0.512548 | ||||||||
\(355\) | −5.52189 | −0.293072 | ||||||||
\(356\) | 40.4674 | 2.14477 | ||||||||
\(357\) | 6.15473 | 0.325743 | ||||||||
\(358\) | −8.84908 | −0.467688 | ||||||||
\(359\) | −7.09296 | −0.374352 | −0.187176 | − | 0.982326i | \(-0.559933\pi\) | ||||
−0.187176 | + | 0.982326i | \(0.559933\pi\) | |||||||
\(360\) | −5.65656 | −0.298127 | ||||||||
\(361\) | 32.3215 | 1.70113 | ||||||||
\(362\) | 46.0799 | 2.42191 | ||||||||
\(363\) | −4.82756 | −0.253381 | ||||||||
\(364\) | 6.25512 | 0.327857 | ||||||||
\(365\) | 5.43645 | 0.284557 | ||||||||
\(366\) | 12.5178 | 0.654318 | ||||||||
\(367\) | −34.1665 | −1.78348 | −0.891739 | − | 0.452550i | \(-0.850514\pi\) | ||||
−0.891739 | + | 0.452550i | \(0.850514\pi\) | |||||||
\(368\) | 0.284200 | 0.0148150 | ||||||||
\(369\) | −26.4991 | −1.37949 | ||||||||
\(370\) | −4.45459 | −0.231583 | ||||||||
\(371\) | −0.563791 | −0.0292706 | ||||||||
\(372\) | −8.51290 | −0.441373 | ||||||||
\(373\) | 19.4167 | 1.00536 | 0.502679 | − | 0.864473i | \(-0.332348\pi\) | ||||
0.502679 | + | 0.864473i | \(0.332348\pi\) | |||||||
\(374\) | 6.44112 | 0.333062 | ||||||||
\(375\) | 2.90773 | 0.150155 | ||||||||
\(376\) | 29.8186 | 1.53778 | ||||||||
\(377\) | −1.48374 | −0.0764165 | ||||||||
\(378\) | 15.6169 | 0.803246 | ||||||||
\(379\) | 5.78176 | 0.296989 | 0.148495 | − | 0.988913i | \(-0.452557\pi\) | ||||
0.148495 | + | 0.988913i | \(0.452557\pi\) | |||||||
\(380\) | −15.9859 | −0.820058 | ||||||||
\(381\) | −0.844290 | −0.0432543 | ||||||||
\(382\) | 59.1524 | 3.02650 | ||||||||
\(383\) | −7.60060 | −0.388372 | −0.194186 | − | 0.980965i | \(-0.562207\pi\) | ||||
−0.194186 | + | 0.980965i | \(0.562207\pi\) | |||||||
\(384\) | 8.50200 | 0.433866 | ||||||||
\(385\) | 0.935068 | 0.0476555 | ||||||||
\(386\) | −26.8390 | −1.36607 | ||||||||
\(387\) | 6.45005 | 0.327875 | ||||||||
\(388\) | 21.8662 | 1.11009 | ||||||||
\(389\) | −18.8645 | −0.956467 | −0.478233 | − | 0.878233i | \(-0.658723\pi\) | ||||
−0.478233 | + | 0.878233i | \(0.658723\pi\) | |||||||
\(390\) | 0.511953 | 0.0259237 | ||||||||
\(391\) | 5.25909 | 0.265964 | ||||||||
\(392\) | 0.748467 | 0.0378033 | ||||||||
\(393\) | −1.44142 | −0.0727098 | ||||||||
\(394\) | −11.6478 | −0.586806 | ||||||||
\(395\) | −4.16862 | −0.209746 | ||||||||
\(396\) | 4.90928 | 0.246701 | ||||||||
\(397\) | −1.67839 | −0.0842359 | −0.0421180 | − | 0.999113i | \(-0.513411\pi\) | ||||
−0.0421180 | + | 0.999113i | \(0.513411\pi\) | |||||||
\(398\) | −7.04616 | −0.353192 | ||||||||
\(399\) | 8.38394 | 0.419722 | ||||||||
\(400\) | −1.29095 | −0.0645477 | ||||||||
\(401\) | 7.75110 | 0.387071 | 0.193536 | − | 0.981093i | \(-0.438004\pi\) | ||||
0.193536 | + | 0.981093i | \(0.438004\pi\) | |||||||
\(402\) | 11.8642 | 0.591731 | ||||||||
\(403\) | −4.18137 | −0.208289 | ||||||||
\(404\) | −36.0519 | −1.79365 | ||||||||
\(405\) | −4.88057 | −0.242518 | ||||||||
\(406\) | 12.1573 | 0.603357 | ||||||||
\(407\) | 1.52211 | 0.0754484 | ||||||||
\(408\) | −7.08235 | −0.350628 | ||||||||
\(409\) | 21.1155 | 1.04409 | 0.522047 | − | 0.852917i | \(-0.325169\pi\) | ||||
0.522047 | + | 0.852917i | \(0.325169\pi\) | |||||||
\(410\) | 14.7520 | 0.728549 | ||||||||
\(411\) | 7.78413 | 0.383963 | ||||||||
\(412\) | 54.7542 | 2.69754 | ||||||||
\(413\) | −24.1620 | −1.18893 | ||||||||
\(414\) | 6.43860 | 0.316440 | ||||||||
\(415\) | 1.25499 | 0.0616050 | ||||||||
\(416\) | 3.88652 | 0.190552 | ||||||||
\(417\) | −5.98899 | −0.293282 | ||||||||
\(418\) | 8.77406 | 0.429153 | ||||||||
\(419\) | −7.75518 | −0.378866 | −0.189433 | − | 0.981894i | \(-0.560665\pi\) | ||||
−0.189433 | + | 0.981894i | \(0.560665\pi\) | |||||||
\(420\) | −2.61147 | −0.127427 | ||||||||
\(421\) | −2.97097 | −0.144796 | −0.0723982 | − | 0.997376i | \(-0.523065\pi\) | ||||
−0.0723982 | + | 0.997376i | \(0.523065\pi\) | |||||||
\(422\) | 29.1142 | 1.41725 | ||||||||
\(423\) | 27.8988 | 1.35648 | ||||||||
\(424\) | 0.648763 | 0.0315067 | ||||||||
\(425\) | −23.8890 | −1.15878 | ||||||||
\(426\) | −8.46436 | −0.410099 | ||||||||
\(427\) | −31.3636 | −1.51779 | ||||||||
\(428\) | 34.4160 | 1.66356 | ||||||||
\(429\) | −0.174932 | −0.00844580 | ||||||||
\(430\) | −3.59073 | −0.173160 | ||||||||
\(431\) | 37.5503 | 1.80873 | 0.904367 | − | 0.426755i | \(-0.140343\pi\) | ||||
0.904367 | + | 0.426755i | \(0.140343\pi\) | |||||||
\(432\) | −0.742151 | −0.0357068 | ||||||||
\(433\) | 22.5975 | 1.08597 | 0.542984 | − | 0.839743i | \(-0.317294\pi\) | ||||
0.542984 | + | 0.839743i | \(0.317294\pi\) | |||||||
\(434\) | 34.2608 | 1.64457 | ||||||||
\(435\) | 0.619451 | 0.0297004 | ||||||||
\(436\) | −60.7639 | −2.91006 | ||||||||
\(437\) | 7.16390 | 0.342696 | ||||||||
\(438\) | 8.33338 | 0.398184 | ||||||||
\(439\) | 3.47082 | 0.165653 | 0.0828265 | − | 0.996564i | \(-0.473605\pi\) | ||||
0.0828265 | + | 0.996564i | \(0.473605\pi\) | |||||||
\(440\) | −1.07600 | −0.0512961 | ||||||||
\(441\) | 0.700277 | 0.0333465 | ||||||||
\(442\) | −8.83577 | −0.420275 | ||||||||
\(443\) | 28.8446 | 1.37045 | 0.685223 | − | 0.728333i | \(-0.259705\pi\) | ||||
0.685223 | + | 0.728333i | \(0.259705\pi\) | |||||||
\(444\) | −4.25098 | −0.201742 | ||||||||
\(445\) | −8.29844 | −0.393384 | ||||||||
\(446\) | −16.6385 | −0.787856 | ||||||||
\(447\) | −4.92715 | −0.233046 | ||||||||
\(448\) | −33.3217 | −1.57430 | ||||||||
\(449\) | 35.5161 | 1.67611 | 0.838053 | − | 0.545588i | \(-0.183694\pi\) | ||||
0.838053 | + | 0.545588i | \(0.183694\pi\) | |||||||
\(450\) | −29.2468 | −1.37871 | ||||||||
\(451\) | −5.04069 | −0.237357 | ||||||||
\(452\) | −28.1821 | −1.32558 | ||||||||
\(453\) | 3.24612 | 0.152516 | ||||||||
\(454\) | −46.8132 | −2.19705 | ||||||||
\(455\) | −1.28270 | −0.0601340 | ||||||||
\(456\) | −9.64753 | −0.451787 | ||||||||
\(457\) | 2.67908 | 0.125322 | 0.0626610 | − | 0.998035i | \(-0.480041\pi\) | ||||
0.0626610 | + | 0.998035i | \(0.480041\pi\) | |||||||
\(458\) | 4.82724 | 0.225562 | ||||||||
\(459\) | −13.7334 | −0.641021 | ||||||||
\(460\) | −2.23145 | −0.104042 | ||||||||
\(461\) | −6.34928 | −0.295715 | −0.147858 | − | 0.989009i | \(-0.547238\pi\) | ||||
−0.147858 | + | 0.989009i | \(0.547238\pi\) | |||||||
\(462\) | 1.43334 | 0.0666850 | ||||||||
\(463\) | −39.6465 | −1.84253 | −0.921264 | − | 0.388938i | \(-0.872842\pi\) | ||||
−0.921264 | + | 0.388938i | \(0.872842\pi\) | |||||||
\(464\) | −0.577744 | −0.0268211 | ||||||||
\(465\) | 1.74569 | 0.0809546 | ||||||||
\(466\) | 41.4853 | 1.92177 | ||||||||
\(467\) | 37.2245 | 1.72254 | 0.861272 | − | 0.508145i | \(-0.169669\pi\) | ||||
0.861272 | + | 0.508145i | \(0.169669\pi\) | |||||||
\(468\) | −6.73443 | −0.311299 | ||||||||
\(469\) | −29.7258 | −1.37261 | ||||||||
\(470\) | −15.5312 | −0.716400 | ||||||||
\(471\) | −5.41135 | −0.249342 | ||||||||
\(472\) | 27.8035 | 1.27976 | ||||||||
\(473\) | 1.22694 | 0.0564146 | ||||||||
\(474\) | −6.38996 | −0.293501 | ||||||||
\(475\) | −32.5414 | −1.49310 | ||||||||
\(476\) | 45.0712 | 2.06583 | ||||||||
\(477\) | 0.606993 | 0.0277923 | ||||||||
\(478\) | 2.85144 | 0.130422 | ||||||||
\(479\) | −3.93541 | −0.179814 | −0.0899068 | − | 0.995950i | \(-0.528657\pi\) | ||||
−0.0899068 | + | 0.995950i | \(0.528657\pi\) | |||||||
\(480\) | −1.62260 | −0.0740611 | ||||||||
\(481\) | −2.08800 | −0.0952044 | ||||||||
\(482\) | −43.0973 | −1.96303 | ||||||||
\(483\) | 1.17030 | 0.0532507 | ||||||||
\(484\) | −35.3523 | −1.60692 | ||||||||
\(485\) | −4.48398 | −0.203607 | ||||||||
\(486\) | −25.5146 | −1.15737 | ||||||||
\(487\) | −36.3550 | −1.64740 | −0.823701 | − | 0.567024i | \(-0.808095\pi\) | ||||
−0.823701 | + | 0.567024i | \(0.808095\pi\) | |||||||
\(488\) | 36.0905 | 1.63374 | ||||||||
\(489\) | 1.24597 | 0.0563449 | ||||||||
\(490\) | −0.389843 | −0.0176113 | ||||||||
\(491\) | −43.1950 | −1.94936 | −0.974681 | − | 0.223601i | \(-0.928219\pi\) | ||||
−0.974681 | + | 0.223601i | \(0.928219\pi\) | |||||||
\(492\) | 14.0777 | 0.634672 | ||||||||
\(493\) | −10.6911 | −0.481502 | ||||||||
\(494\) | −12.0360 | −0.541526 | ||||||||
\(495\) | −1.00672 | −0.0452487 | ||||||||
\(496\) | −1.62816 | −0.0731064 | ||||||||
\(497\) | 21.2075 | 0.951287 | ||||||||
\(498\) | 1.92374 | 0.0862048 | ||||||||
\(499\) | −22.0846 | −0.988641 | −0.494320 | − | 0.869280i | \(-0.664583\pi\) | ||||
−0.494320 | + | 0.869280i | \(0.664583\pi\) | |||||||
\(500\) | 21.2934 | 0.952269 | ||||||||
\(501\) | 0.704005 | 0.0314526 | ||||||||
\(502\) | −37.0606 | −1.65409 | ||||||||
\(503\) | 36.5671 | 1.63045 | 0.815223 | − | 0.579147i | \(-0.196614\pi\) | ||||
0.815223 | + | 0.579147i | \(0.196614\pi\) | |||||||
\(504\) | 21.7247 | 0.967695 | ||||||||
\(505\) | 7.39297 | 0.328983 | ||||||||
\(506\) | 1.22476 | 0.0544472 | ||||||||
\(507\) | −5.61604 | −0.249417 | ||||||||
\(508\) | −6.18274 | −0.274315 | ||||||||
\(509\) | −9.53790 | −0.422760 | −0.211380 | − | 0.977404i | \(-0.567796\pi\) | ||||
−0.211380 | + | 0.977404i | \(0.567796\pi\) | |||||||
\(510\) | 3.68887 | 0.163346 | ||||||||
\(511\) | −20.8793 | −0.923648 | ||||||||
\(512\) | 3.21262 | 0.141979 | ||||||||
\(513\) | −18.7076 | −0.825960 | ||||||||
\(514\) | −34.6266 | −1.52732 | ||||||||
\(515\) | −11.2281 | −0.494771 | ||||||||
\(516\) | −3.42660 | −0.150848 | ||||||||
\(517\) | 5.30694 | 0.233399 | ||||||||
\(518\) | 17.1084 | 0.751700 | ||||||||
\(519\) | 5.81698 | 0.255337 | ||||||||
\(520\) | 1.47603 | 0.0647280 | ||||||||
\(521\) | −38.1601 | −1.67183 | −0.835913 | − | 0.548862i | \(-0.815061\pi\) | ||||
−0.835913 | + | 0.548862i | \(0.815061\pi\) | |||||||
\(522\) | −13.0889 | −0.572884 | ||||||||
\(523\) | −24.7989 | −1.08438 | −0.542190 | − | 0.840256i | \(-0.682405\pi\) | ||||
−0.542190 | + | 0.840256i | \(0.682405\pi\) | |||||||
\(524\) | −10.5555 | −0.461119 | ||||||||
\(525\) | −5.31600 | −0.232009 | ||||||||
\(526\) | 39.4890 | 1.72180 | ||||||||
\(527\) | −30.1288 | −1.31243 | ||||||||
\(528\) | −0.0681157 | −0.00296436 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −0.337911 | −0.0146779 | ||||||||
\(531\) | 26.0134 | 1.12889 | ||||||||
\(532\) | 61.3957 | 2.66184 | ||||||||
\(533\) | 6.91469 | 0.299509 | ||||||||
\(534\) | −12.7204 | −0.550467 | ||||||||
\(535\) | −7.05750 | −0.305122 | ||||||||
\(536\) | 34.2059 | 1.47747 | ||||||||
\(537\) | 1.73169 | 0.0747279 | ||||||||
\(538\) | −19.9656 | −0.860776 | ||||||||
\(539\) | 0.133208 | 0.00573766 | ||||||||
\(540\) | 5.82712 | 0.250759 | ||||||||
\(541\) | −25.0101 | −1.07527 | −0.537633 | − | 0.843179i | \(-0.680681\pi\) | ||||
−0.537633 | + | 0.843179i | \(0.680681\pi\) | |||||||
\(542\) | −11.2837 | −0.484678 | ||||||||
\(543\) | −9.01745 | −0.386976 | ||||||||
\(544\) | 28.0043 | 1.20067 | ||||||||
\(545\) | 12.4605 | 0.533750 | ||||||||
\(546\) | −1.96622 | −0.0841464 | ||||||||
\(547\) | −21.0696 | −0.900873 | −0.450437 | − | 0.892808i | \(-0.648732\pi\) | ||||
−0.450437 | + | 0.892808i | \(0.648732\pi\) | |||||||
\(548\) | 57.0033 | 2.43506 | ||||||||
\(549\) | 33.7668 | 1.44113 | ||||||||
\(550\) | −5.56336 | −0.237222 | ||||||||
\(551\) | −14.5633 | −0.620418 | ||||||||
\(552\) | −1.34669 | −0.0573188 | ||||||||
\(553\) | 16.0101 | 0.680819 | ||||||||
\(554\) | −21.7821 | −0.925434 | ||||||||
\(555\) | 0.871725 | 0.0370027 | ||||||||
\(556\) | −43.8574 | −1.85997 | ||||||||
\(557\) | 35.8969 | 1.52100 | 0.760501 | − | 0.649337i | \(-0.224954\pi\) | ||||
0.760501 | + | 0.649337i | \(0.224954\pi\) | |||||||
\(558\) | −36.8861 | −1.56151 | ||||||||
\(559\) | −1.68308 | −0.0711867 | ||||||||
\(560\) | −0.499463 | −0.0211062 | ||||||||
\(561\) | −1.26047 | −0.0532172 | ||||||||
\(562\) | 60.6602 | 2.55880 | ||||||||
\(563\) | −20.6084 | −0.868540 | −0.434270 | − | 0.900783i | \(-0.642994\pi\) | ||||
−0.434270 | + | 0.900783i | \(0.642994\pi\) | |||||||
\(564\) | −14.8213 | −0.624088 | ||||||||
\(565\) | 5.77916 | 0.243131 | ||||||||
\(566\) | 35.7488 | 1.50264 | ||||||||
\(567\) | 18.7444 | 0.787192 | ||||||||
\(568\) | −24.4038 | −1.02396 | ||||||||
\(569\) | 47.6202 | 1.99634 | 0.998172 | − | 0.0604411i | \(-0.0192507\pi\) | ||||
0.998172 | + | 0.0604411i | \(0.0192507\pi\) | |||||||
\(570\) | 5.02496 | 0.210472 | ||||||||
\(571\) | −4.18551 | −0.175158 | −0.0875791 | − | 0.996158i | \(-0.527913\pi\) | ||||
−0.0875791 | + | 0.996158i | \(0.527913\pi\) | |||||||
\(572\) | −1.28103 | −0.0535626 | ||||||||
\(573\) | −11.5756 | −0.483578 | ||||||||
\(574\) | −56.6568 | −2.36481 | ||||||||
\(575\) | −4.54241 | −0.189432 | ||||||||
\(576\) | 35.8750 | 1.49479 | ||||||||
\(577\) | 45.4693 | 1.89291 | 0.946457 | − | 0.322831i | \(-0.104635\pi\) | ||||
0.946457 | + | 0.322831i | \(0.104635\pi\) | |||||||
\(578\) | −24.5338 | −1.02047 | ||||||||
\(579\) | 5.25217 | 0.218273 | ||||||||
\(580\) | 4.53625 | 0.188358 | ||||||||
\(581\) | −4.81994 | −0.199965 | ||||||||
\(582\) | −6.87337 | −0.284910 | ||||||||
\(583\) | 0.115463 | 0.00478198 | ||||||||
\(584\) | 24.0262 | 0.994210 | ||||||||
\(585\) | 1.38099 | 0.0570970 | ||||||||
\(586\) | 61.2243 | 2.52915 | ||||||||
\(587\) | −40.6615 | −1.67828 | −0.839140 | − | 0.543915i | \(-0.816941\pi\) | ||||
−0.839140 | + | 0.543915i | \(0.816941\pi\) | |||||||
\(588\) | −0.372024 | −0.0153420 | ||||||||
\(589\) | −41.0413 | −1.69108 | ||||||||
\(590\) | −14.4816 | −0.596198 | ||||||||
\(591\) | 2.27937 | 0.0937607 | ||||||||
\(592\) | −0.813031 | −0.0334154 | ||||||||
\(593\) | 9.23175 | 0.379103 | 0.189551 | − | 0.981871i | \(-0.439297\pi\) | ||||
0.189551 | + | 0.981871i | \(0.439297\pi\) | |||||||
\(594\) | −3.19829 | −0.131228 | ||||||||
\(595\) | −9.24250 | −0.378906 | ||||||||
\(596\) | −36.0816 | −1.47796 | ||||||||
\(597\) | 1.37887 | 0.0564336 | ||||||||
\(598\) | −1.68009 | −0.0687041 | ||||||||
\(599\) | −12.1800 | −0.497661 | −0.248830 | − | 0.968547i | \(-0.580046\pi\) | ||||
−0.248830 | + | 0.968547i | \(0.580046\pi\) | |||||||
\(600\) | 6.11720 | 0.249734 | ||||||||
\(601\) | −1.82296 | −0.0743600 | −0.0371800 | − | 0.999309i | \(-0.511837\pi\) | ||||
−0.0371800 | + | 0.999309i | \(0.511837\pi\) | |||||||
\(602\) | 13.7906 | 0.562064 | ||||||||
\(603\) | 32.0036 | 1.30329 | ||||||||
\(604\) | 23.7714 | 0.967244 | ||||||||
\(605\) | 7.24950 | 0.294734 | ||||||||
\(606\) | 11.3325 | 0.460351 | ||||||||
\(607\) | −18.2677 | −0.741464 | −0.370732 | − | 0.928740i | \(-0.620893\pi\) | ||||
−0.370732 | + | 0.928740i | \(0.620893\pi\) | |||||||
\(608\) | 38.1473 | 1.54708 | ||||||||
\(609\) | −2.37908 | −0.0964052 | ||||||||
\(610\) | −18.7979 | −0.761106 | ||||||||
\(611\) | −7.27992 | −0.294514 | ||||||||
\(612\) | −48.5249 | −1.96150 | ||||||||
\(613\) | −11.0989 | −0.448280 | −0.224140 | − | 0.974557i | \(-0.571957\pi\) | ||||
−0.224140 | + | 0.974557i | \(0.571957\pi\) | |||||||
\(614\) | 39.7648 | 1.60478 | ||||||||
\(615\) | −2.88684 | −0.116409 | ||||||||
\(616\) | 4.13250 | 0.166503 | ||||||||
\(617\) | −43.5771 | −1.75435 | −0.877173 | − | 0.480174i | \(-0.840573\pi\) | ||||
−0.877173 | + | 0.480174i | \(0.840573\pi\) | |||||||
\(618\) | −17.2113 | −0.692340 | ||||||||
\(619\) | −15.1405 | −0.608547 | −0.304274 | − | 0.952585i | \(-0.598414\pi\) | ||||
−0.304274 | + | 0.952585i | \(0.598414\pi\) | |||||||
\(620\) | 12.7837 | 0.513407 | ||||||||
\(621\) | −2.61137 | −0.104791 | ||||||||
\(622\) | 8.82336 | 0.353784 | ||||||||
\(623\) | 31.8712 | 1.27689 | ||||||||
\(624\) | 0.0934394 | 0.00374057 | ||||||||
\(625\) | 18.3455 | 0.733821 | ||||||||
\(626\) | −7.71270 | −0.308261 | ||||||||
\(627\) | −1.71701 | −0.0685707 | ||||||||
\(628\) | −39.6274 | −1.58131 | ||||||||
\(629\) | −15.0450 | −0.599885 | ||||||||
\(630\) | −11.3154 | −0.450817 | ||||||||
\(631\) | 7.89231 | 0.314188 | 0.157094 | − | 0.987584i | \(-0.449787\pi\) | ||||
0.157094 | + | 0.987584i | \(0.449787\pi\) | |||||||
\(632\) | −18.4231 | −0.732830 | ||||||||
\(633\) | −5.69739 | −0.226451 | ||||||||
\(634\) | −2.56076 | −0.101701 | ||||||||
\(635\) | 1.26786 | 0.0503136 | ||||||||
\(636\) | −0.322466 | −0.0127866 | ||||||||
\(637\) | −0.182731 | −0.00724005 | ||||||||
\(638\) | −2.48978 | −0.0985714 | ||||||||
\(639\) | −22.8326 | −0.903243 | ||||||||
\(640\) | −12.7674 | −0.504675 | ||||||||
\(641\) | −34.6711 | −1.36943 | −0.684714 | − | 0.728812i | \(-0.740073\pi\) | ||||
−0.684714 | + | 0.728812i | \(0.740073\pi\) | |||||||
\(642\) | −10.8182 | −0.426962 | ||||||||
\(643\) | −36.8908 | −1.45483 | −0.727416 | − | 0.686197i | \(-0.759279\pi\) | ||||
−0.727416 | + | 0.686197i | \(0.759279\pi\) | |||||||
\(644\) | 8.57015 | 0.337711 | ||||||||
\(645\) | 0.702675 | 0.0276678 | ||||||||
\(646\) | −86.7255 | −3.41217 | ||||||||
\(647\) | 19.4703 | 0.765455 | 0.382727 | − | 0.923861i | \(-0.374985\pi\) | ||||
0.382727 | + | 0.923861i | \(0.374985\pi\) | |||||||
\(648\) | −21.5695 | −0.847330 | ||||||||
\(649\) | 4.94831 | 0.194238 | ||||||||
\(650\) | 7.63167 | 0.299339 | ||||||||
\(651\) | −6.70455 | −0.262772 | ||||||||
\(652\) | 9.12428 | 0.357334 | ||||||||
\(653\) | 2.57892 | 0.100921 | 0.0504606 | − | 0.998726i | \(-0.483931\pi\) | ||||
0.0504606 | + | 0.998726i | \(0.483931\pi\) | |||||||
\(654\) | 19.1004 | 0.746884 | ||||||||
\(655\) | 2.16456 | 0.0845764 | ||||||||
\(656\) | 2.69247 | 0.105123 | ||||||||
\(657\) | 22.4793 | 0.876999 | ||||||||
\(658\) | 59.6494 | 2.32538 | ||||||||
\(659\) | 4.90585 | 0.191105 | 0.0955524 | − | 0.995424i | \(-0.469538\pi\) | ||||
0.0955524 | + | 0.995424i | \(0.469538\pi\) | |||||||
\(660\) | 0.534822 | 0.0208179 | ||||||||
\(661\) | 33.3328 | 1.29650 | 0.648248 | − | 0.761429i | \(-0.275502\pi\) | ||||
0.648248 | + | 0.761429i | \(0.275502\pi\) | |||||||
\(662\) | −5.20157 | −0.202165 | ||||||||
\(663\) | 1.72908 | 0.0671521 | ||||||||
\(664\) | 5.54638 | 0.215241 | ||||||||
\(665\) | −12.5901 | −0.488223 | ||||||||
\(666\) | −18.4194 | −0.713735 | ||||||||
\(667\) | −2.03287 | −0.0787132 | ||||||||
\(668\) | 5.15544 | 0.199470 | ||||||||
\(669\) | 3.25602 | 0.125885 | ||||||||
\(670\) | −17.8163 | −0.688304 | ||||||||
\(671\) | 6.42317 | 0.247964 | ||||||||
\(672\) | 6.23178 | 0.240396 | ||||||||
\(673\) | 8.76446 | 0.337845 | 0.168923 | − | 0.985629i | \(-0.445971\pi\) | ||||
0.168923 | + | 0.985629i | \(0.445971\pi\) | |||||||
\(674\) | −41.7016 | −1.60628 | ||||||||
\(675\) | 11.8619 | 0.456565 | ||||||||
\(676\) | −41.1263 | −1.58178 | ||||||||
\(677\) | −16.0614 | −0.617291 | −0.308645 | − | 0.951177i | \(-0.599876\pi\) | ||||
−0.308645 | + | 0.951177i | \(0.599876\pi\) | |||||||
\(678\) | 8.85871 | 0.340217 | ||||||||
\(679\) | 17.2213 | 0.660892 | ||||||||
\(680\) | 10.6355 | 0.407852 | ||||||||
\(681\) | 9.16094 | 0.351048 | ||||||||
\(682\) | −7.01652 | −0.268677 | ||||||||
\(683\) | 27.3422 | 1.04622 | 0.523109 | − | 0.852266i | \(-0.324772\pi\) | ||||
0.523109 | + | 0.852266i | \(0.324772\pi\) | |||||||
\(684\) | −66.1003 | −2.52741 | ||||||||
\(685\) | −11.6893 | −0.446627 | ||||||||
\(686\) | 43.3597 | 1.65548 | ||||||||
\(687\) | −0.944650 | −0.0360407 | ||||||||
\(688\) | −0.655364 | −0.0249855 | ||||||||
\(689\) | −0.158389 | −0.00603414 | ||||||||
\(690\) | 0.701428 | 0.0267029 | ||||||||
\(691\) | −19.3882 | −0.737562 | −0.368781 | − | 0.929516i | \(-0.620225\pi\) | ||||
−0.368781 | + | 0.929516i | \(0.620225\pi\) | |||||||
\(692\) | 42.5978 | 1.61933 | ||||||||
\(693\) | 3.86643 | 0.146874 | ||||||||
\(694\) | 54.1614 | 2.05594 | ||||||||
\(695\) | 8.99361 | 0.341147 | ||||||||
\(696\) | 2.73764 | 0.103770 | ||||||||
\(697\) | 49.8238 | 1.88721 | ||||||||
\(698\) | −2.30190 | −0.0871282 | ||||||||
\(699\) | −8.11832 | −0.307063 | ||||||||
\(700\) | −38.9291 | −1.47138 | ||||||||
\(701\) | −47.5515 | −1.79599 | −0.897997 | − | 0.440001i | \(-0.854978\pi\) | ||||
−0.897997 | + | 0.440001i | \(0.854978\pi\) | |||||||
\(702\) | 4.38734 | 0.165589 | ||||||||
\(703\) | −20.4943 | −0.772956 | ||||||||
\(704\) | 6.82418 | 0.257196 | ||||||||
\(705\) | 3.03932 | 0.114467 | ||||||||
\(706\) | −33.7627 | −1.27067 | ||||||||
\(707\) | −28.3936 | −1.06785 | ||||||||
\(708\) | −13.8197 | −0.519376 | ||||||||
\(709\) | 40.2461 | 1.51147 | 0.755737 | − | 0.654875i | \(-0.227279\pi\) | ||||
0.755737 | + | 0.654875i | \(0.227279\pi\) | |||||||
\(710\) | 12.7108 | 0.477029 | ||||||||
\(711\) | −17.2369 | −0.646435 | ||||||||
\(712\) | −36.6746 | −1.37444 | ||||||||
\(713\) | −5.72890 | −0.214549 | ||||||||
\(714\) | −14.1676 | −0.530208 | ||||||||
\(715\) | 0.262694 | 0.00982420 | ||||||||
\(716\) | 12.6812 | 0.473918 | ||||||||
\(717\) | −0.558002 | −0.0208390 | ||||||||
\(718\) | 16.3273 | 0.609328 | ||||||||
\(719\) | −6.19770 | −0.231135 | −0.115568 | − | 0.993300i | \(-0.536869\pi\) | ||||
−0.115568 | + | 0.993300i | \(0.536869\pi\) | |||||||
\(720\) | 0.537736 | 0.0200402 | ||||||||
\(721\) | 43.1231 | 1.60599 | ||||||||
\(722\) | −74.4009 | −2.76891 | ||||||||
\(723\) | 8.43378 | 0.313656 | ||||||||
\(724\) | −66.0349 | −2.45417 | ||||||||
\(725\) | 9.23415 | 0.342948 | ||||||||
\(726\) | 11.1126 | 0.412426 | ||||||||
\(727\) | −20.4663 | −0.759053 | −0.379527 | − | 0.925181i | \(-0.623913\pi\) | ||||
−0.379527 | + | 0.925181i | \(0.623913\pi\) | |||||||
\(728\) | −5.66886 | −0.210102 | ||||||||
\(729\) | −16.6518 | −0.616733 | ||||||||
\(730\) | −12.5141 | −0.463169 | ||||||||
\(731\) | −12.1274 | −0.448549 | ||||||||
\(732\) | −17.9387 | −0.663034 | ||||||||
\(733\) | 26.2574 | 0.969837 | 0.484919 | − | 0.874559i | \(-0.338849\pi\) | ||||
0.484919 | + | 0.874559i | \(0.338849\pi\) | |||||||
\(734\) | 78.6479 | 2.90295 | ||||||||
\(735\) | 0.0762889 | 0.00281396 | ||||||||
\(736\) | 5.32493 | 0.196280 | ||||||||
\(737\) | 6.08776 | 0.224245 | ||||||||
\(738\) | 60.9983 | 2.24538 | ||||||||
\(739\) | 39.3874 | 1.44889 | 0.724445 | − | 0.689333i | \(-0.242096\pi\) | ||||
0.724445 | + | 0.689333i | \(0.242096\pi\) | |||||||
\(740\) | 6.38365 | 0.234668 | ||||||||
\(741\) | 2.35535 | 0.0865259 | ||||||||
\(742\) | 1.29779 | 0.0476434 | ||||||||
\(743\) | −44.1735 | −1.62057 | −0.810284 | − | 0.586037i | \(-0.800687\pi\) | ||||
−0.810284 | + | 0.586037i | \(0.800687\pi\) | |||||||
\(744\) | 7.71503 | 0.282847 | ||||||||
\(745\) | 7.39906 | 0.271080 | ||||||||
\(746\) | −44.6952 | −1.63641 | ||||||||
\(747\) | 5.18928 | 0.189866 | ||||||||
\(748\) | −9.23046 | −0.337499 | ||||||||
\(749\) | 27.1052 | 0.990402 | ||||||||
\(750\) | −6.69331 | −0.244405 | ||||||||
\(751\) | 41.6869 | 1.52118 | 0.760588 | − | 0.649235i | \(-0.224911\pi\) | ||||
0.760588 | + | 0.649235i | \(0.224911\pi\) | |||||||
\(752\) | −2.83468 | −0.103370 | ||||||||
\(753\) | 7.25244 | 0.264294 | ||||||||
\(754\) | 3.41542 | 0.124382 | ||||||||
\(755\) | −4.87467 | −0.177407 | ||||||||
\(756\) | −22.3798 | −0.813945 | ||||||||
\(757\) | 9.54400 | 0.346883 | 0.173441 | − | 0.984844i | \(-0.444511\pi\) | ||||
0.173441 | + | 0.984844i | \(0.444511\pi\) | |||||||
\(758\) | −13.3090 | −0.483406 | ||||||||
\(759\) | −0.239675 | −0.00869965 | ||||||||
\(760\) | 14.4876 | 0.525520 | ||||||||
\(761\) | 11.6267 | 0.421466 | 0.210733 | − | 0.977544i | \(-0.432415\pi\) | ||||
0.210733 | + | 0.977544i | \(0.432415\pi\) | |||||||
\(762\) | 1.94347 | 0.0704045 | ||||||||
\(763\) | −47.8562 | −1.73251 | ||||||||
\(764\) | −84.7684 | −3.06681 | ||||||||
\(765\) | 9.95073 | 0.359769 | ||||||||
\(766\) | 17.4958 | 0.632149 | ||||||||
\(767\) | −6.78796 | −0.245099 | ||||||||
\(768\) | −8.01563 | −0.289239 | ||||||||
\(769\) | −47.2710 | −1.70464 | −0.852318 | − | 0.523023i | \(-0.824804\pi\) | ||||
−0.852318 | + | 0.523023i | \(0.824804\pi\) | |||||||
\(770\) | −2.15243 | −0.0775683 | ||||||||
\(771\) | 6.77614 | 0.244037 | ||||||||
\(772\) | 38.4617 | 1.38427 | ||||||||
\(773\) | −25.4283 | −0.914593 | −0.457297 | − | 0.889314i | \(-0.651182\pi\) | ||||
−0.457297 | + | 0.889314i | \(0.651182\pi\) | |||||||
\(774\) | −14.8474 | −0.533678 | ||||||||
\(775\) | 26.0230 | 0.934774 | ||||||||
\(776\) | −19.8168 | −0.711381 | ||||||||
\(777\) | −3.34797 | −0.120108 | ||||||||
\(778\) | 43.4241 | 1.55683 | ||||||||
\(779\) | 67.8696 | 2.43168 | ||||||||
\(780\) | −0.733655 | −0.0262691 | ||||||||
\(781\) | −4.34324 | −0.155413 | ||||||||
\(782\) | −12.1059 | −0.432906 | ||||||||
\(783\) | 5.30858 | 0.189713 | ||||||||
\(784\) | −0.0711523 | −0.00254116 | ||||||||
\(785\) | 8.12618 | 0.290036 | ||||||||
\(786\) | 3.31799 | 0.118349 | ||||||||
\(787\) | −12.1955 | −0.434722 | −0.217361 | − | 0.976091i | \(-0.569745\pi\) | ||||
−0.217361 | + | 0.976091i | \(0.569745\pi\) | |||||||
\(788\) | 16.6918 | 0.594622 | ||||||||
\(789\) | −7.72765 | −0.275112 | ||||||||
\(790\) | 9.59574 | 0.341401 | ||||||||
\(791\) | −22.1956 | −0.789184 | ||||||||
\(792\) | −4.44916 | −0.158094 | ||||||||
\(793\) | −8.81114 | −0.312893 | ||||||||
\(794\) | 3.86348 | 0.137110 | ||||||||
\(795\) | 0.0661264 | 0.00234526 | ||||||||
\(796\) | 10.0975 | 0.357897 | ||||||||
\(797\) | −26.2616 | −0.930232 | −0.465116 | − | 0.885250i | \(-0.653987\pi\) | ||||
−0.465116 | + | 0.885250i | \(0.653987\pi\) | |||||||
\(798\) | −19.2990 | −0.683177 | ||||||||
\(799\) | −52.4554 | −1.85574 | ||||||||
\(800\) | −24.1880 | −0.855175 | ||||||||
\(801\) | −34.3134 | −1.21240 | ||||||||
\(802\) | −17.8422 | −0.630031 | ||||||||
\(803\) | 4.27603 | 0.150898 | ||||||||
\(804\) | −17.0020 | −0.599613 | ||||||||
\(805\) | −1.75743 | −0.0619414 | ||||||||
\(806\) | 9.62509 | 0.339029 | ||||||||
\(807\) | 3.90709 | 0.137536 | ||||||||
\(808\) | 32.6730 | 1.14943 | ||||||||
\(809\) | −23.3633 | −0.821408 | −0.410704 | − | 0.911769i | \(-0.634717\pi\) | ||||
−0.410704 | + | 0.911769i | \(0.634717\pi\) | |||||||
\(810\) | 11.2346 | 0.394743 | ||||||||
\(811\) | 31.0247 | 1.08942 | 0.544712 | − | 0.838623i | \(-0.316639\pi\) | ||||
0.544712 | + | 0.838623i | \(0.316639\pi\) | |||||||
\(812\) | −17.4220 | −0.611393 | ||||||||
\(813\) | 2.20813 | 0.0774425 | ||||||||
\(814\) | −3.50375 | −0.122806 | ||||||||
\(815\) | −1.87107 | −0.0655406 | ||||||||
\(816\) | 0.673277 | 0.0235694 | ||||||||
\(817\) | −16.5199 | −0.577958 | ||||||||
\(818\) | −48.6057 | −1.69946 | ||||||||
\(819\) | −5.30387 | −0.185332 | ||||||||
\(820\) | −21.1403 | −0.738253 | ||||||||
\(821\) | 30.2399 | 1.05538 | 0.527689 | − | 0.849437i | \(-0.323059\pi\) | ||||
0.527689 | + | 0.849437i | \(0.323059\pi\) | |||||||
\(822\) | −17.9183 | −0.624972 | ||||||||
\(823\) | −29.6483 | −1.03347 | −0.516737 | − | 0.856144i | \(-0.672853\pi\) | ||||
−0.516737 | + | 0.856144i | \(0.672853\pi\) | |||||||
\(824\) | −49.6223 | −1.72868 | ||||||||
\(825\) | 1.08870 | 0.0379037 | ||||||||
\(826\) | 55.6184 | 1.93521 | ||||||||
\(827\) | 0.638474 | 0.0222019 | 0.0111010 | − | 0.999938i | \(-0.496466\pi\) | ||||
0.0111010 | + | 0.999938i | \(0.496466\pi\) | |||||||
\(828\) | −9.22685 | −0.320655 | ||||||||
\(829\) | 29.4268 | 1.02204 | 0.511018 | − | 0.859570i | \(-0.329268\pi\) | ||||
0.511018 | + | 0.859570i | \(0.329268\pi\) | |||||||
\(830\) | −2.88886 | −0.100274 | ||||||||
\(831\) | 4.26258 | 0.147867 | ||||||||
\(832\) | −9.36124 | −0.324543 | ||||||||
\(833\) | −1.31667 | −0.0456197 | ||||||||
\(834\) | 13.7860 | 0.477372 | ||||||||
\(835\) | −1.05720 | −0.0365858 | ||||||||
\(836\) | −12.5737 | −0.434870 | ||||||||
\(837\) | 14.9603 | 0.517102 | ||||||||
\(838\) | 17.8516 | 0.616675 | ||||||||
\(839\) | −52.5348 | −1.81370 | −0.906851 | − | 0.421452i | \(-0.861521\pi\) | ||||
−0.906851 | + | 0.421452i | \(0.861521\pi\) | |||||||
\(840\) | 2.36671 | 0.0816593 | ||||||||
\(841\) | −24.8674 | −0.857497 | ||||||||
\(842\) | 6.83888 | 0.235683 | ||||||||
\(843\) | −11.8707 | −0.408848 | ||||||||
\(844\) | −41.7221 | −1.43613 | ||||||||
\(845\) | 8.43355 | 0.290123 | ||||||||
\(846\) | −64.2201 | −2.20793 | ||||||||
\(847\) | −27.8426 | −0.956683 | ||||||||
\(848\) | −0.0616741 | −0.00211790 | ||||||||
\(849\) | −6.99574 | −0.240093 | ||||||||
\(850\) | 54.9900 | 1.88614 | ||||||||
\(851\) | −2.86077 | −0.0980659 | ||||||||
\(852\) | 12.1299 | 0.415562 | ||||||||
\(853\) | −2.68199 | −0.0918294 | −0.0459147 | − | 0.998945i | \(-0.514620\pi\) | ||||
−0.0459147 | + | 0.998945i | \(0.514620\pi\) | |||||||
\(854\) | 72.1957 | 2.47049 | ||||||||
\(855\) | 13.5548 | 0.463565 | ||||||||
\(856\) | −31.1904 | −1.06606 | ||||||||
\(857\) | −11.6838 | −0.399111 | −0.199556 | − | 0.979887i | \(-0.563950\pi\) | ||||
−0.199556 | + | 0.979887i | \(0.563950\pi\) | |||||||
\(858\) | 0.402676 | 0.0137471 | ||||||||
\(859\) | 4.29914 | 0.146685 | 0.0733424 | − | 0.997307i | \(-0.476633\pi\) | ||||
0.0733424 | + | 0.997307i | \(0.476633\pi\) | |||||||
\(860\) | 5.14570 | 0.175467 | ||||||||
\(861\) | 11.0873 | 0.377853 | ||||||||
\(862\) | −86.4370 | −2.94406 | ||||||||
\(863\) | −40.9437 | −1.39374 | −0.696870 | − | 0.717197i | \(-0.745425\pi\) | ||||
−0.696870 | + | 0.717197i | \(0.745425\pi\) | |||||||
\(864\) | −13.9053 | −0.473069 | ||||||||
\(865\) | −8.73530 | −0.297009 | ||||||||
\(866\) | −52.0172 | −1.76762 | ||||||||
\(867\) | 4.80105 | 0.163052 | ||||||||
\(868\) | −49.0975 | −1.66648 | ||||||||
\(869\) | −3.27882 | −0.111227 | ||||||||
\(870\) | −1.42591 | −0.0483430 | ||||||||
\(871\) | −8.35103 | −0.282964 | ||||||||
\(872\) | 55.0688 | 1.86487 | ||||||||
\(873\) | −18.5409 | −0.627514 | ||||||||
\(874\) | −16.4906 | −0.557802 | ||||||||
\(875\) | 16.7701 | 0.566934 | ||||||||
\(876\) | −11.9422 | −0.403488 | ||||||||
\(877\) | 15.8310 | 0.534576 | 0.267288 | − | 0.963617i | \(-0.413872\pi\) | ||||
0.267288 | + | 0.963617i | \(0.413872\pi\) | |||||||
\(878\) | −7.98947 | −0.269632 | ||||||||
\(879\) | −11.9811 | −0.404112 | ||||||||
\(880\) | 0.102289 | 0.00344815 | ||||||||
\(881\) | 16.2842 | 0.548629 | 0.274315 | − | 0.961640i | \(-0.411549\pi\) | ||||
0.274315 | + | 0.961640i | \(0.411549\pi\) | |||||||
\(882\) | −1.61197 | −0.0542778 | ||||||||
\(883\) | 36.9930 | 1.24491 | 0.622457 | − | 0.782654i | \(-0.286135\pi\) | ||||
0.622457 | + | 0.782654i | \(0.286135\pi\) | |||||||
\(884\) | 12.6621 | 0.425873 | ||||||||
\(885\) | 2.83393 | 0.0952614 | ||||||||
\(886\) | −66.3973 | −2.23066 | ||||||||
\(887\) | −24.7479 | −0.830955 | −0.415477 | − | 0.909604i | \(-0.636385\pi\) | ||||
−0.415477 | + | 0.909604i | \(0.636385\pi\) | |||||||
\(888\) | 3.85256 | 0.129283 | ||||||||
\(889\) | −4.86938 | −0.163314 | ||||||||
\(890\) | 19.1022 | 0.640306 | ||||||||
\(891\) | −3.83881 | −0.128605 | ||||||||
\(892\) | 23.8438 | 0.798351 | ||||||||
\(893\) | −71.4544 | −2.39113 | ||||||||
\(894\) | 11.3418 | 0.379327 | ||||||||
\(895\) | −2.60046 | −0.0869238 | ||||||||
\(896\) | 49.0347 | 1.63813 | ||||||||
\(897\) | 0.328780 | 0.0109776 | ||||||||
\(898\) | −81.7544 | −2.72818 | ||||||||
\(899\) | 11.6461 | 0.388420 | ||||||||
\(900\) | 41.9121 | 1.39707 | ||||||||
\(901\) | −1.14127 | −0.0380213 | ||||||||
\(902\) | 11.6032 | 0.386343 | ||||||||
\(903\) | −2.69871 | −0.0898074 | ||||||||
\(904\) | 25.5408 | 0.849474 | ||||||||
\(905\) | 13.5414 | 0.450132 | ||||||||
\(906\) | −7.47225 | −0.248249 | ||||||||
\(907\) | −23.6237 | −0.784412 | −0.392206 | − | 0.919877i | \(-0.628288\pi\) | ||||
−0.392206 | + | 0.919877i | \(0.628288\pi\) | |||||||
\(908\) | 67.0857 | 2.22632 | ||||||||
\(909\) | 30.5694 | 1.01392 | ||||||||
\(910\) | 2.95265 | 0.0978794 | ||||||||
\(911\) | −44.0244 | −1.45859 | −0.729297 | − | 0.684197i | \(-0.760153\pi\) | ||||
−0.729297 | + | 0.684197i | \(0.760153\pi\) | |||||||
\(912\) | 0.917134 | 0.0303693 | ||||||||
\(913\) | 0.987111 | 0.0326686 | ||||||||
\(914\) | −6.16697 | −0.203985 | ||||||||
\(915\) | 3.67859 | 0.121611 | ||||||||
\(916\) | −6.91769 | −0.228567 | ||||||||
\(917\) | −8.31326 | −0.274528 | ||||||||
\(918\) | 31.6129 | 1.04338 | ||||||||
\(919\) | −5.00612 | −0.165137 | −0.0825683 | − | 0.996585i | \(-0.526312\pi\) | ||||
−0.0825683 | + | 0.996585i | \(0.526312\pi\) | |||||||
\(920\) | 2.02230 | 0.0666734 | ||||||||
\(921\) | −7.78163 | −0.256413 | ||||||||
\(922\) | 14.6154 | 0.481333 | ||||||||
\(923\) | 5.95795 | 0.196108 | ||||||||
\(924\) | −2.05405 | −0.0675733 | ||||||||
\(925\) | 12.9948 | 0.427266 | ||||||||
\(926\) | 91.2622 | 2.99906 | ||||||||
\(927\) | −46.4274 | −1.52488 | ||||||||
\(928\) | −10.8249 | −0.355345 | ||||||||
\(929\) | 23.4320 | 0.768778 | 0.384389 | − | 0.923171i | \(-0.374412\pi\) | ||||
0.384389 | + | 0.923171i | \(0.374412\pi\) | |||||||
\(930\) | −4.01841 | −0.131769 | ||||||||
\(931\) | −1.79355 | −0.0587813 | ||||||||
\(932\) | −59.4505 | −1.94737 | ||||||||
\(933\) | −1.72666 | −0.0565282 | ||||||||
\(934\) | −85.6870 | −2.80376 | ||||||||
\(935\) | 1.89284 | 0.0619025 | ||||||||
\(936\) | 6.10324 | 0.199491 | ||||||||
\(937\) | −49.4856 | −1.61662 | −0.808312 | − | 0.588755i | \(-0.799618\pi\) | ||||
−0.808312 | + | 0.588755i | \(0.799618\pi\) | |||||||
\(938\) | 68.4258 | 2.23418 | ||||||||
\(939\) | 1.50931 | 0.0492544 | ||||||||
\(940\) | 22.2570 | 0.725942 | ||||||||
\(941\) | −3.88524 | −0.126655 | −0.0633277 | − | 0.997993i | \(-0.520171\pi\) | ||||
−0.0633277 | + | 0.997993i | \(0.520171\pi\) | |||||||
\(942\) | 12.4564 | 0.405851 | ||||||||
\(943\) | 9.47383 | 0.308510 | ||||||||
\(944\) | −2.64312 | −0.0860262 | ||||||||
\(945\) | 4.58930 | 0.149290 | ||||||||
\(946\) | −2.82428 | −0.0918254 | ||||||||
\(947\) | 44.5798 | 1.44865 | 0.724325 | − | 0.689459i | \(-0.242152\pi\) | ||||
0.724325 | + | 0.689459i | \(0.242152\pi\) | |||||||
\(948\) | 9.15714 | 0.297410 | ||||||||
\(949\) | −5.86575 | −0.190410 | ||||||||
\(950\) | 74.9070 | 2.43030 | ||||||||
\(951\) | 0.501119 | 0.0162499 | ||||||||
\(952\) | −40.8469 | −1.32386 | ||||||||
\(953\) | −42.7096 | −1.38350 | −0.691750 | − | 0.722137i | \(-0.743160\pi\) | ||||
−0.691750 | + | 0.722137i | \(0.743160\pi\) | |||||||
\(954\) | −1.39724 | −0.0452372 | ||||||||
\(955\) | 17.3830 | 0.562500 | ||||||||
\(956\) | −4.08625 | −0.132159 | ||||||||
\(957\) | 0.487229 | 0.0157499 | ||||||||
\(958\) | 9.05892 | 0.292681 | ||||||||
\(959\) | 44.8944 | 1.44972 | ||||||||
\(960\) | 3.90826 | 0.126138 | ||||||||
\(961\) | 1.82032 | 0.0587199 | ||||||||
\(962\) | 4.80636 | 0.154963 | ||||||||
\(963\) | −29.1822 | −0.940383 | ||||||||
\(964\) | 61.7607 | 1.98918 | ||||||||
\(965\) | −7.88713 | −0.253896 | ||||||||
\(966\) | −2.69392 | −0.0866755 | ||||||||
\(967\) | −53.1748 | −1.70999 | −0.854993 | − | 0.518639i | \(-0.826439\pi\) | ||||
−0.854993 | + | 0.518639i | \(0.826439\pi\) | |||||||
\(968\) | 32.0389 | 1.02977 | ||||||||
\(969\) | 16.9714 | 0.545201 | ||||||||
\(970\) | 10.3217 | 0.331409 | ||||||||
\(971\) | 30.7375 | 0.986415 | 0.493207 | − | 0.869912i | \(-0.335824\pi\) | ||||
0.493207 | + | 0.869912i | \(0.335824\pi\) | |||||||
\(972\) | 36.5637 | 1.17278 | ||||||||
\(973\) | −34.5411 | −1.10734 | ||||||||
\(974\) | 83.6855 | 2.68146 | ||||||||
\(975\) | −1.49345 | −0.0478288 | ||||||||
\(976\) | −3.43091 | −0.109821 | ||||||||
\(977\) | −38.4939 | −1.23153 | −0.615764 | − | 0.787930i | \(-0.711153\pi\) | ||||
−0.615764 | + | 0.787930i | \(0.711153\pi\) | |||||||
\(978\) | −2.86811 | −0.0917119 | ||||||||
\(979\) | −6.52713 | −0.208608 | ||||||||
\(980\) | 0.558664 | 0.0178459 | ||||||||
\(981\) | 51.5232 | 1.64501 | ||||||||
\(982\) | 99.4304 | 3.17295 | ||||||||
\(983\) | −17.0256 | −0.543034 | −0.271517 | − | 0.962434i | \(-0.587525\pi\) | ||||
−0.271517 | + | 0.962434i | \(0.587525\pi\) | |||||||
\(984\) | −12.7583 | −0.406719 | ||||||||
\(985\) | −3.42291 | −0.109063 | ||||||||
\(986\) | 24.6098 | 0.783735 | ||||||||
\(987\) | −11.6729 | −0.371552 | ||||||||
\(988\) | 17.2482 | 0.548740 | ||||||||
\(989\) | −2.30599 | −0.0733263 | ||||||||
\(990\) | 2.31737 | 0.0736507 | ||||||||
\(991\) | −0.579966 | −0.0184232 | −0.00921161 | − | 0.999958i | \(-0.502932\pi\) | ||||
−0.00921161 | + | 0.999958i | \(0.502932\pi\) | |||||||
\(992\) | −30.5060 | −0.968567 | ||||||||
\(993\) | 1.01790 | 0.0323022 | ||||||||
\(994\) | −48.8176 | −1.54840 | ||||||||
\(995\) | −2.07064 | −0.0656438 | ||||||||
\(996\) | −2.75682 | −0.0873531 | ||||||||
\(997\) | −16.9796 | −0.537749 | −0.268875 | − | 0.963175i | \(-0.586652\pi\) | ||||
−0.268875 | + | 0.963175i | \(0.586652\pi\) | |||||||
\(998\) | 50.8364 | 1.60920 | ||||||||
\(999\) | 7.47051 | 0.236357 |
(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 | 8027.2.a.c.1.20 | ✓ | 143 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8027.2.a.c.1.20 | ✓ | 143 | 1.1 | even | 1 | trivial |