Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4730,2,Mod(1,4730)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4730, 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("4730.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4730.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: | \(37.7692401561\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 32 x^{11} - 5 x^{10} + 376 x^{9} + 100 x^{8} - 1985 x^{7} - 576 x^{6} + 4708 x^{5} + 889 x^{4} + \cdots - 128 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(-2.24942\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4730.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 2.24942 | 1.29870 | 0.649352 | − | 0.760488i | \(-0.275040\pi\) | ||||
0.649352 | + | 0.760488i | \(0.275040\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 2.24942 | 0.918322 | ||||||||
\(7\) | −1.43432 | −0.542123 | −0.271061 | − | 0.962562i | \(-0.587375\pi\) | ||||
−0.271061 | + | 0.962562i | \(0.587375\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.05989 | 0.686631 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 2.24942 | 0.649352 | ||||||||
\(13\) | 4.69328 | 1.30168 | 0.650840 | − | 0.759215i | \(-0.274417\pi\) | ||||
0.650840 | + | 0.759215i | \(0.274417\pi\) | |||||||
\(14\) | −1.43432 | −0.383339 | ||||||||
\(15\) | −2.24942 | −0.580798 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.69172 | 0.652837 | 0.326418 | − | 0.945225i | \(-0.394158\pi\) | ||||
0.326418 | + | 0.945225i | \(0.394158\pi\) | |||||||
\(18\) | 2.05989 | 0.485522 | ||||||||
\(19\) | 5.09763 | 1.16948 | 0.584738 | − | 0.811222i | \(-0.301197\pi\) | ||||
0.584738 | + | 0.811222i | \(0.301197\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −3.22639 | −0.704057 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 2.31042 | 0.481755 | 0.240877 | − | 0.970556i | \(-0.422565\pi\) | ||||
0.240877 | + | 0.970556i | \(0.422565\pi\) | |||||||
\(24\) | 2.24942 | 0.459161 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 4.69328 | 0.920427 | ||||||||
\(27\) | −2.11469 | −0.406973 | ||||||||
\(28\) | −1.43432 | −0.271061 | ||||||||
\(29\) | −5.94499 | −1.10396 | −0.551979 | − | 0.833858i | \(-0.686127\pi\) | ||||
−0.551979 | + | 0.833858i | \(0.686127\pi\) | |||||||
\(30\) | −2.24942 | −0.410686 | ||||||||
\(31\) | −6.78435 | −1.21851 | −0.609253 | − | 0.792976i | \(-0.708531\pi\) | ||||
−0.609253 | + | 0.792976i | \(0.708531\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 2.24942 | 0.391574 | ||||||||
\(34\) | 2.69172 | 0.461625 | ||||||||
\(35\) | 1.43432 | 0.242445 | ||||||||
\(36\) | 2.05989 | 0.343316 | ||||||||
\(37\) | 3.88177 | 0.638159 | 0.319080 | − | 0.947728i | \(-0.396626\pi\) | ||||
0.319080 | + | 0.947728i | \(0.396626\pi\) | |||||||
\(38\) | 5.09763 | 0.826944 | ||||||||
\(39\) | 10.5572 | 1.69050 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 7.01704 | 1.09588 | 0.547939 | − | 0.836518i | \(-0.315413\pi\) | ||||
0.547939 | + | 0.836518i | \(0.315413\pi\) | |||||||
\(42\) | −3.22639 | −0.497843 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | −2.05989 | −0.307071 | ||||||||
\(46\) | 2.31042 | 0.340652 | ||||||||
\(47\) | 0.722561 | 0.105396 | 0.0526982 | − | 0.998610i | \(-0.483218\pi\) | ||||
0.0526982 | + | 0.998610i | \(0.483218\pi\) | |||||||
\(48\) | 2.24942 | 0.324676 | ||||||||
\(49\) | −4.94272 | −0.706103 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 6.05480 | 0.847842 | ||||||||
\(52\) | 4.69328 | 0.650840 | ||||||||
\(53\) | 9.28737 | 1.27572 | 0.637859 | − | 0.770153i | \(-0.279820\pi\) | ||||
0.637859 | + | 0.770153i | \(0.279820\pi\) | |||||||
\(54\) | −2.11469 | −0.287773 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | −1.43432 | −0.191669 | ||||||||
\(57\) | 11.4667 | 1.51880 | ||||||||
\(58\) | −5.94499 | −0.780616 | ||||||||
\(59\) | −14.7355 | −1.91840 | −0.959200 | − | 0.282728i | \(-0.908760\pi\) | ||||
−0.959200 | + | 0.282728i | \(0.908760\pi\) | |||||||
\(60\) | −2.24942 | −0.290399 | ||||||||
\(61\) | 11.9068 | 1.52451 | 0.762255 | − | 0.647277i | \(-0.224092\pi\) | ||||
0.762255 | + | 0.647277i | \(0.224092\pi\) | |||||||
\(62\) | −6.78435 | −0.861614 | ||||||||
\(63\) | −2.95455 | −0.372238 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.69328 | −0.582129 | ||||||||
\(66\) | 2.24942 | 0.276885 | ||||||||
\(67\) | 9.71230 | 1.18655 | 0.593273 | − | 0.805001i | \(-0.297835\pi\) | ||||
0.593273 | + | 0.805001i | \(0.297835\pi\) | |||||||
\(68\) | 2.69172 | 0.326418 | ||||||||
\(69\) | 5.19710 | 0.625657 | ||||||||
\(70\) | 1.43432 | 0.171434 | ||||||||
\(71\) | 12.2764 | 1.45695 | 0.728473 | − | 0.685075i | \(-0.240231\pi\) | ||||
0.728473 | + | 0.685075i | \(0.240231\pi\) | |||||||
\(72\) | 2.05989 | 0.242761 | ||||||||
\(73\) | −6.20325 | −0.726035 | −0.363018 | − | 0.931782i | \(-0.618254\pi\) | ||||
−0.363018 | + | 0.931782i | \(0.618254\pi\) | |||||||
\(74\) | 3.88177 | 0.451247 | ||||||||
\(75\) | 2.24942 | 0.259741 | ||||||||
\(76\) | 5.09763 | 0.584738 | ||||||||
\(77\) | −1.43432 | −0.163456 | ||||||||
\(78\) | 10.5572 | 1.19536 | ||||||||
\(79\) | −10.4505 | −1.17577 | −0.587885 | − | 0.808944i | \(-0.700039\pi\) | ||||
−0.587885 | + | 0.808944i | \(0.700039\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −10.9365 | −1.21517 | ||||||||
\(82\) | 7.01704 | 0.774903 | ||||||||
\(83\) | 4.45987 | 0.489534 | 0.244767 | − | 0.969582i | \(-0.421288\pi\) | ||||
0.244767 | + | 0.969582i | \(0.421288\pi\) | |||||||
\(84\) | −3.22639 | −0.352028 | ||||||||
\(85\) | −2.69172 | −0.291958 | ||||||||
\(86\) | 1.00000 | 0.107833 | ||||||||
\(87\) | −13.3728 | −1.43371 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | −6.38594 | −0.676908 | −0.338454 | − | 0.940983i | \(-0.609904\pi\) | ||||
−0.338454 | + | 0.940983i | \(0.609904\pi\) | |||||||
\(90\) | −2.05989 | −0.217132 | ||||||||
\(91\) | −6.73167 | −0.705671 | ||||||||
\(92\) | 2.31042 | 0.240877 | ||||||||
\(93\) | −15.2609 | −1.58248 | ||||||||
\(94\) | 0.722561 | 0.0745265 | ||||||||
\(95\) | −5.09763 | −0.523006 | ||||||||
\(96\) | 2.24942 | 0.229581 | ||||||||
\(97\) | 0.328464 | 0.0333505 | 0.0166753 | − | 0.999861i | \(-0.494692\pi\) | ||||
0.0166753 | + | 0.999861i | \(0.494692\pi\) | |||||||
\(98\) | −4.94272 | −0.499290 | ||||||||
\(99\) | 2.05989 | 0.207027 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 13.3472 | 1.32809 | 0.664047 | − | 0.747691i | \(-0.268837\pi\) | ||||
0.664047 | + | 0.747691i | \(0.268837\pi\) | |||||||
\(102\) | 6.05480 | 0.599515 | ||||||||
\(103\) | 15.0788 | 1.48576 | 0.742879 | − | 0.669426i | \(-0.233460\pi\) | ||||
0.742879 | + | 0.669426i | \(0.233460\pi\) | |||||||
\(104\) | 4.69328 | 0.460214 | ||||||||
\(105\) | 3.22639 | 0.314864 | ||||||||
\(106\) | 9.28737 | 0.902069 | ||||||||
\(107\) | −1.72911 | −0.167160 | −0.0835798 | − | 0.996501i | \(-0.526635\pi\) | ||||
−0.0835798 | + | 0.996501i | \(0.526635\pi\) | |||||||
\(108\) | −2.11469 | −0.203487 | ||||||||
\(109\) | 9.13341 | 0.874822 | 0.437411 | − | 0.899262i | \(-0.355895\pi\) | ||||
0.437411 | + | 0.899262i | \(0.355895\pi\) | |||||||
\(110\) | −1.00000 | −0.0953463 | ||||||||
\(111\) | 8.73174 | 0.828780 | ||||||||
\(112\) | −1.43432 | −0.135531 | ||||||||
\(113\) | 4.62839 | 0.435403 | 0.217701 | − | 0.976015i | \(-0.430144\pi\) | ||||
0.217701 | + | 0.976015i | \(0.430144\pi\) | |||||||
\(114\) | 11.4667 | 1.07396 | ||||||||
\(115\) | −2.31042 | −0.215447 | ||||||||
\(116\) | −5.94499 | −0.551979 | ||||||||
\(117\) | 9.66765 | 0.893775 | ||||||||
\(118\) | −14.7355 | −1.35651 | ||||||||
\(119\) | −3.86079 | −0.353918 | ||||||||
\(120\) | −2.24942 | −0.205343 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 11.9068 | 1.07799 | ||||||||
\(123\) | 15.7843 | 1.42322 | ||||||||
\(124\) | −6.78435 | −0.609253 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −2.95455 | −0.263212 | ||||||||
\(127\) | −7.81461 | −0.693435 | −0.346717 | − | 0.937970i | \(-0.612704\pi\) | ||||
−0.346717 | + | 0.937970i | \(0.612704\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 2.24942 | 0.198050 | ||||||||
\(130\) | −4.69328 | −0.411628 | ||||||||
\(131\) | −6.71338 | −0.586551 | −0.293275 | − | 0.956028i | \(-0.594745\pi\) | ||||
−0.293275 | + | 0.956028i | \(0.594745\pi\) | |||||||
\(132\) | 2.24942 | 0.195787 | ||||||||
\(133\) | −7.31164 | −0.633999 | ||||||||
\(134\) | 9.71230 | 0.839015 | ||||||||
\(135\) | 2.11469 | 0.182004 | ||||||||
\(136\) | 2.69172 | 0.230813 | ||||||||
\(137\) | −14.4584 | −1.23526 | −0.617632 | − | 0.786467i | \(-0.711908\pi\) | ||||
−0.617632 | + | 0.786467i | \(0.711908\pi\) | |||||||
\(138\) | 5.19710 | 0.442406 | ||||||||
\(139\) | 1.30594 | 0.110768 | 0.0553840 | − | 0.998465i | \(-0.482362\pi\) | ||||
0.0553840 | + | 0.998465i | \(0.482362\pi\) | |||||||
\(140\) | 1.43432 | 0.121222 | ||||||||
\(141\) | 1.62534 | 0.136879 | ||||||||
\(142\) | 12.2764 | 1.03022 | ||||||||
\(143\) | 4.69328 | 0.392472 | ||||||||
\(144\) | 2.05989 | 0.171658 | ||||||||
\(145\) | 5.94499 | 0.493705 | ||||||||
\(146\) | −6.20325 | −0.513385 | ||||||||
\(147\) | −11.1183 | −0.917019 | ||||||||
\(148\) | 3.88177 | 0.319080 | ||||||||
\(149\) | 9.28161 | 0.760379 | 0.380190 | − | 0.924909i | \(-0.375859\pi\) | ||||
0.380190 | + | 0.924909i | \(0.375859\pi\) | |||||||
\(150\) | 2.24942 | 0.183664 | ||||||||
\(151\) | −5.35962 | −0.436160 | −0.218080 | − | 0.975931i | \(-0.569979\pi\) | ||||
−0.218080 | + | 0.975931i | \(0.569979\pi\) | |||||||
\(152\) | 5.09763 | 0.413472 | ||||||||
\(153\) | 5.54465 | 0.448258 | ||||||||
\(154\) | −1.43432 | −0.115581 | ||||||||
\(155\) | 6.78435 | 0.544932 | ||||||||
\(156\) | 10.5572 | 0.845249 | ||||||||
\(157\) | 18.6665 | 1.48975 | 0.744876 | − | 0.667203i | \(-0.232509\pi\) | ||||
0.744876 | + | 0.667203i | \(0.232509\pi\) | |||||||
\(158\) | −10.4505 | −0.831395 | ||||||||
\(159\) | 20.8912 | 1.65678 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −3.31388 | −0.261170 | ||||||||
\(162\) | −10.9365 | −0.859254 | ||||||||
\(163\) | 23.7568 | 1.86078 | 0.930388 | − | 0.366577i | \(-0.119470\pi\) | ||||
0.930388 | + | 0.366577i | \(0.119470\pi\) | |||||||
\(164\) | 7.01704 | 0.547939 | ||||||||
\(165\) | −2.24942 | −0.175117 | ||||||||
\(166\) | 4.45987 | 0.346153 | ||||||||
\(167\) | −4.94648 | −0.382770 | −0.191385 | − | 0.981515i | \(-0.561298\pi\) | ||||
−0.191385 | + | 0.981515i | \(0.561298\pi\) | |||||||
\(168\) | −3.22639 | −0.248922 | ||||||||
\(169\) | 9.02685 | 0.694373 | ||||||||
\(170\) | −2.69172 | −0.206445 | ||||||||
\(171\) | 10.5006 | 0.802999 | ||||||||
\(172\) | 1.00000 | 0.0762493 | ||||||||
\(173\) | 24.4374 | 1.85794 | 0.928971 | − | 0.370154i | \(-0.120695\pi\) | ||||
0.928971 | + | 0.370154i | \(0.120695\pi\) | |||||||
\(174\) | −13.3728 | −1.01379 | ||||||||
\(175\) | −1.43432 | −0.108425 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −33.1464 | −2.49143 | ||||||||
\(178\) | −6.38594 | −0.478646 | ||||||||
\(179\) | −16.6363 | −1.24346 | −0.621729 | − | 0.783233i | \(-0.713569\pi\) | ||||
−0.621729 | + | 0.783233i | \(0.713569\pi\) | |||||||
\(180\) | −2.05989 | −0.153535 | ||||||||
\(181\) | −14.4304 | −1.07260 | −0.536302 | − | 0.844026i | \(-0.680179\pi\) | ||||
−0.536302 | + | 0.844026i | \(0.680179\pi\) | |||||||
\(182\) | −6.73167 | −0.498985 | ||||||||
\(183\) | 26.7834 | 1.97989 | ||||||||
\(184\) | 2.31042 | 0.170326 | ||||||||
\(185\) | −3.88177 | −0.285394 | ||||||||
\(186\) | −15.2609 | −1.11898 | ||||||||
\(187\) | 2.69172 | 0.196838 | ||||||||
\(188\) | 0.722561 | 0.0526982 | ||||||||
\(189\) | 3.03315 | 0.220629 | ||||||||
\(190\) | −5.09763 | −0.369821 | ||||||||
\(191\) | 6.94965 | 0.502859 | 0.251430 | − | 0.967876i | \(-0.419099\pi\) | ||||
0.251430 | + | 0.967876i | \(0.419099\pi\) | |||||||
\(192\) | 2.24942 | 0.162338 | ||||||||
\(193\) | 3.04767 | 0.219376 | 0.109688 | − | 0.993966i | \(-0.465015\pi\) | ||||
0.109688 | + | 0.993966i | \(0.465015\pi\) | |||||||
\(194\) | 0.328464 | 0.0235824 | ||||||||
\(195\) | −10.5572 | −0.756014 | ||||||||
\(196\) | −4.94272 | −0.353051 | ||||||||
\(197\) | −12.9605 | −0.923398 | −0.461699 | − | 0.887037i | \(-0.652760\pi\) | ||||
−0.461699 | + | 0.887037i | \(0.652760\pi\) | |||||||
\(198\) | 2.05989 | 0.146390 | ||||||||
\(199\) | 5.53937 | 0.392675 | 0.196338 | − | 0.980536i | \(-0.437095\pi\) | ||||
0.196338 | + | 0.980536i | \(0.437095\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 21.8471 | 1.54097 | ||||||||
\(202\) | 13.3472 | 0.939104 | ||||||||
\(203\) | 8.52703 | 0.598480 | ||||||||
\(204\) | 6.05480 | 0.423921 | ||||||||
\(205\) | −7.01704 | −0.490092 | ||||||||
\(206\) | 15.0788 | 1.05059 | ||||||||
\(207\) | 4.75921 | 0.330788 | ||||||||
\(208\) | 4.69328 | 0.325420 | ||||||||
\(209\) | 5.09763 | 0.352610 | ||||||||
\(210\) | 3.22639 | 0.222642 | ||||||||
\(211\) | 1.49551 | 0.102955 | 0.0514775 | − | 0.998674i | \(-0.483607\pi\) | ||||
0.0514775 | + | 0.998674i | \(0.483607\pi\) | |||||||
\(212\) | 9.28737 | 0.637859 | ||||||||
\(213\) | 27.6149 | 1.89214 | ||||||||
\(214\) | −1.72911 | −0.118200 | ||||||||
\(215\) | −1.00000 | −0.0681994 | ||||||||
\(216\) | −2.11469 | −0.143887 | ||||||||
\(217\) | 9.73095 | 0.660580 | ||||||||
\(218\) | 9.13341 | 0.618593 | ||||||||
\(219\) | −13.9537 | −0.942905 | ||||||||
\(220\) | −1.00000 | −0.0674200 | ||||||||
\(221\) | 12.6330 | 0.849785 | ||||||||
\(222\) | 8.73174 | 0.586036 | ||||||||
\(223\) | −20.6795 | −1.38480 | −0.692400 | − | 0.721514i | \(-0.743447\pi\) | ||||
−0.692400 | + | 0.721514i | \(0.743447\pi\) | |||||||
\(224\) | −1.43432 | −0.0958347 | ||||||||
\(225\) | 2.05989 | 0.137326 | ||||||||
\(226\) | 4.62839 | 0.307876 | ||||||||
\(227\) | −21.9344 | −1.45583 | −0.727917 | − | 0.685665i | \(-0.759512\pi\) | ||||
−0.727917 | + | 0.685665i | \(0.759512\pi\) | |||||||
\(228\) | 11.4667 | 0.759401 | ||||||||
\(229\) | −21.3370 | −1.40999 | −0.704995 | − | 0.709212i | \(-0.749051\pi\) | ||||
−0.704995 | + | 0.709212i | \(0.749051\pi\) | |||||||
\(230\) | −2.31042 | −0.152344 | ||||||||
\(231\) | −3.22639 | −0.212281 | ||||||||
\(232\) | −5.94499 | −0.390308 | ||||||||
\(233\) | −18.4304 | −1.20741 | −0.603706 | − | 0.797207i | \(-0.706310\pi\) | ||||
−0.603706 | + | 0.797207i | \(0.706310\pi\) | |||||||
\(234\) | 9.66765 | 0.631994 | ||||||||
\(235\) | −0.722561 | −0.0471347 | ||||||||
\(236\) | −14.7355 | −0.959200 | ||||||||
\(237\) | −23.5075 | −1.52698 | ||||||||
\(238\) | −3.86079 | −0.250258 | ||||||||
\(239\) | 4.81697 | 0.311584 | 0.155792 | − | 0.987790i | \(-0.450207\pi\) | ||||
0.155792 | + | 0.987790i | \(0.450207\pi\) | |||||||
\(240\) | −2.24942 | −0.145199 | ||||||||
\(241\) | 5.77599 | 0.372064 | 0.186032 | − | 0.982544i | \(-0.440437\pi\) | ||||
0.186032 | + | 0.982544i | \(0.440437\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | −18.2568 | −1.17117 | ||||||||
\(244\) | 11.9068 | 0.762255 | ||||||||
\(245\) | 4.94272 | 0.315779 | ||||||||
\(246\) | 15.7843 | 1.00637 | ||||||||
\(247\) | 23.9246 | 1.52228 | ||||||||
\(248\) | −6.78435 | −0.430807 | ||||||||
\(249\) | 10.0321 | 0.635760 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −27.9375 | −1.76340 | −0.881701 | − | 0.471809i | \(-0.843601\pi\) | ||||
−0.881701 | + | 0.471809i | \(0.843601\pi\) | |||||||
\(252\) | −2.95455 | −0.186119 | ||||||||
\(253\) | 2.31042 | 0.145255 | ||||||||
\(254\) | −7.81461 | −0.490332 | ||||||||
\(255\) | −6.05480 | −0.379166 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.69635 | −0.604841 | −0.302421 | − | 0.953175i | \(-0.597795\pi\) | ||||
−0.302421 | + | 0.953175i | \(0.597795\pi\) | |||||||
\(258\) | 2.24942 | 0.140043 | ||||||||
\(259\) | −5.56771 | −0.345961 | ||||||||
\(260\) | −4.69328 | −0.291065 | ||||||||
\(261\) | −12.2461 | −0.758012 | ||||||||
\(262\) | −6.71338 | −0.414754 | ||||||||
\(263\) | −20.4163 | −1.25892 | −0.629461 | − | 0.777032i | \(-0.716724\pi\) | ||||
−0.629461 | + | 0.777032i | \(0.716724\pi\) | |||||||
\(264\) | 2.24942 | 0.138442 | ||||||||
\(265\) | −9.28737 | −0.570518 | ||||||||
\(266\) | −7.31164 | −0.448305 | ||||||||
\(267\) | −14.3647 | −0.879103 | ||||||||
\(268\) | 9.71230 | 0.593273 | ||||||||
\(269\) | 13.9619 | 0.851273 | 0.425637 | − | 0.904894i | \(-0.360050\pi\) | ||||
0.425637 | + | 0.904894i | \(0.360050\pi\) | |||||||
\(270\) | 2.11469 | 0.128696 | ||||||||
\(271\) | −18.0976 | −1.09935 | −0.549675 | − | 0.835379i | \(-0.685248\pi\) | ||||
−0.549675 | + | 0.835379i | \(0.685248\pi\) | |||||||
\(272\) | 2.69172 | 0.163209 | ||||||||
\(273\) | −15.1424 | −0.916457 | ||||||||
\(274\) | −14.4584 | −0.873463 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 5.19710 | 0.312828 | ||||||||
\(277\) | −8.13107 | −0.488549 | −0.244274 | − | 0.969706i | \(-0.578550\pi\) | ||||
−0.244274 | + | 0.969706i | \(0.578550\pi\) | |||||||
\(278\) | 1.30594 | 0.0783248 | ||||||||
\(279\) | −13.9751 | −0.836664 | ||||||||
\(280\) | 1.43432 | 0.0857171 | ||||||||
\(281\) | −5.99636 | −0.357713 | −0.178856 | − | 0.983875i | \(-0.557240\pi\) | ||||
−0.178856 | + | 0.983875i | \(0.557240\pi\) | |||||||
\(282\) | 1.62534 | 0.0967878 | ||||||||
\(283\) | −21.0031 | −1.24850 | −0.624252 | − | 0.781223i | \(-0.714596\pi\) | ||||
−0.624252 | + | 0.781223i | \(0.714596\pi\) | |||||||
\(284\) | 12.2764 | 0.728473 | ||||||||
\(285\) | −11.4667 | −0.679229 | ||||||||
\(286\) | 4.69328 | 0.277519 | ||||||||
\(287\) | −10.0647 | −0.594100 | ||||||||
\(288\) | 2.05989 | 0.121380 | ||||||||
\(289\) | −9.75467 | −0.573804 | ||||||||
\(290\) | 5.94499 | 0.349102 | ||||||||
\(291\) | 0.738855 | 0.0433124 | ||||||||
\(292\) | −6.20325 | −0.363018 | ||||||||
\(293\) | −29.8493 | −1.74382 | −0.871908 | − | 0.489671i | \(-0.837117\pi\) | ||||
−0.871908 | + | 0.489671i | \(0.837117\pi\) | |||||||
\(294\) | −11.1183 | −0.648430 | ||||||||
\(295\) | 14.7355 | 0.857935 | ||||||||
\(296\) | 3.88177 | 0.225623 | ||||||||
\(297\) | −2.11469 | −0.122707 | ||||||||
\(298\) | 9.28161 | 0.537669 | ||||||||
\(299\) | 10.8434 | 0.627091 | ||||||||
\(300\) | 2.24942 | 0.129870 | ||||||||
\(301\) | −1.43432 | −0.0826729 | ||||||||
\(302\) | −5.35962 | −0.308412 | ||||||||
\(303\) | 30.0234 | 1.72480 | ||||||||
\(304\) | 5.09763 | 0.292369 | ||||||||
\(305\) | −11.9068 | −0.681782 | ||||||||
\(306\) | 5.54465 | 0.316966 | ||||||||
\(307\) | 3.81085 | 0.217497 | 0.108748 | − | 0.994069i | \(-0.465316\pi\) | ||||
0.108748 | + | 0.994069i | \(0.465316\pi\) | |||||||
\(308\) | −1.43432 | −0.0817281 | ||||||||
\(309\) | 33.9185 | 1.92956 | ||||||||
\(310\) | 6.78435 | 0.385325 | ||||||||
\(311\) | 17.9922 | 1.02025 | 0.510123 | − | 0.860101i | \(-0.329600\pi\) | ||||
0.510123 | + | 0.860101i | \(0.329600\pi\) | |||||||
\(312\) | 10.5572 | 0.597681 | ||||||||
\(313\) | 4.23321 | 0.239275 | 0.119638 | − | 0.992818i | \(-0.461827\pi\) | ||||
0.119638 | + | 0.992818i | \(0.461827\pi\) | |||||||
\(314\) | 18.6665 | 1.05341 | ||||||||
\(315\) | 2.95455 | 0.166470 | ||||||||
\(316\) | −10.4505 | −0.587885 | ||||||||
\(317\) | 22.6847 | 1.27410 | 0.637050 | − | 0.770822i | \(-0.280154\pi\) | ||||
0.637050 | + | 0.770822i | \(0.280154\pi\) | |||||||
\(318\) | 20.8912 | 1.17152 | ||||||||
\(319\) | −5.94499 | −0.332856 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −3.88950 | −0.217091 | ||||||||
\(322\) | −3.31388 | −0.184675 | ||||||||
\(323\) | 13.7214 | 0.763477 | ||||||||
\(324\) | −10.9365 | −0.607584 | ||||||||
\(325\) | 4.69328 | 0.260336 | ||||||||
\(326\) | 23.7568 | 1.31577 | ||||||||
\(327\) | 20.5449 | 1.13613 | ||||||||
\(328\) | 7.01704 | 0.387451 | ||||||||
\(329\) | −1.03639 | −0.0571378 | ||||||||
\(330\) | −2.24942 | −0.123827 | ||||||||
\(331\) | 20.9408 | 1.15101 | 0.575505 | − | 0.817798i | \(-0.304805\pi\) | ||||
0.575505 | + | 0.817798i | \(0.304805\pi\) | |||||||
\(332\) | 4.45987 | 0.244767 | ||||||||
\(333\) | 7.99604 | 0.438180 | ||||||||
\(334\) | −4.94648 | −0.270660 | ||||||||
\(335\) | −9.71230 | −0.530640 | ||||||||
\(336\) | −3.22639 | −0.176014 | ||||||||
\(337\) | 12.2906 | 0.669512 | 0.334756 | − | 0.942305i | \(-0.391346\pi\) | ||||
0.334756 | + | 0.942305i | \(0.391346\pi\) | |||||||
\(338\) | 9.02685 | 0.490996 | ||||||||
\(339\) | 10.4112 | 0.565459 | ||||||||
\(340\) | −2.69172 | −0.145979 | ||||||||
\(341\) | −6.78435 | −0.367393 | ||||||||
\(342\) | 10.5006 | 0.567806 | ||||||||
\(343\) | 17.1297 | 0.924917 | ||||||||
\(344\) | 1.00000 | 0.0539164 | ||||||||
\(345\) | −5.19710 | −0.279802 | ||||||||
\(346\) | 24.4374 | 1.31376 | ||||||||
\(347\) | −31.6551 | −1.69933 | −0.849667 | − | 0.527319i | \(-0.823197\pi\) | ||||
−0.849667 | + | 0.527319i | \(0.823197\pi\) | |||||||
\(348\) | −13.3728 | −0.716857 | ||||||||
\(349\) | 21.3475 | 1.14270 | 0.571352 | − | 0.820705i | \(-0.306419\pi\) | ||||
0.571352 | + | 0.820705i | \(0.306419\pi\) | |||||||
\(350\) | −1.43432 | −0.0766677 | ||||||||
\(351\) | −9.92484 | −0.529749 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −16.1131 | −0.857611 | −0.428806 | − | 0.903397i | \(-0.641065\pi\) | ||||
−0.428806 | + | 0.903397i | \(0.641065\pi\) | |||||||
\(354\) | −33.1464 | −1.76171 | ||||||||
\(355\) | −12.2764 | −0.651566 | ||||||||
\(356\) | −6.38594 | −0.338454 | ||||||||
\(357\) | −8.68453 | −0.459634 | ||||||||
\(358\) | −16.6363 | −0.879257 | ||||||||
\(359\) | −21.6717 | −1.14379 | −0.571894 | − | 0.820328i | \(-0.693791\pi\) | ||||
−0.571894 | + | 0.820328i | \(0.693791\pi\) | |||||||
\(360\) | −2.05989 | −0.108566 | ||||||||
\(361\) | 6.98581 | 0.367674 | ||||||||
\(362\) | −14.4304 | −0.758446 | ||||||||
\(363\) | 2.24942 | 0.118064 | ||||||||
\(364\) | −6.73167 | −0.352835 | ||||||||
\(365\) | 6.20325 | 0.324693 | ||||||||
\(366\) | 26.7834 | 1.39999 | ||||||||
\(367\) | −15.0819 | −0.787269 | −0.393635 | − | 0.919267i | \(-0.628782\pi\) | ||||
−0.393635 | + | 0.919267i | \(0.628782\pi\) | |||||||
\(368\) | 2.31042 | 0.120439 | ||||||||
\(369\) | 14.4544 | 0.752464 | ||||||||
\(370\) | −3.88177 | −0.201804 | ||||||||
\(371\) | −13.3211 | −0.691596 | ||||||||
\(372\) | −15.2609 | −0.791239 | ||||||||
\(373\) | −23.7371 | −1.22906 | −0.614529 | − | 0.788894i | \(-0.710654\pi\) | ||||
−0.614529 | + | 0.788894i | \(0.710654\pi\) | |||||||
\(374\) | 2.69172 | 0.139185 | ||||||||
\(375\) | −2.24942 | −0.116160 | ||||||||
\(376\) | 0.722561 | 0.0372632 | ||||||||
\(377\) | −27.9015 | −1.43700 | ||||||||
\(378\) | 3.03315 | 0.156008 | ||||||||
\(379\) | 11.5566 | 0.593622 | 0.296811 | − | 0.954936i | \(-0.404077\pi\) | ||||
0.296811 | + | 0.954936i | \(0.404077\pi\) | |||||||
\(380\) | −5.09763 | −0.261503 | ||||||||
\(381\) | −17.5784 | −0.900566 | ||||||||
\(382\) | 6.94965 | 0.355575 | ||||||||
\(383\) | 24.9628 | 1.27554 | 0.637769 | − | 0.770228i | \(-0.279857\pi\) | ||||
0.637769 | + | 0.770228i | \(0.279857\pi\) | |||||||
\(384\) | 2.24942 | 0.114790 | ||||||||
\(385\) | 1.43432 | 0.0730998 | ||||||||
\(386\) | 3.04767 | 0.155122 | ||||||||
\(387\) | 2.05989 | 0.104710 | ||||||||
\(388\) | 0.328464 | 0.0166753 | ||||||||
\(389\) | −26.8036 | −1.35899 | −0.679497 | − | 0.733678i | \(-0.737802\pi\) | ||||
−0.679497 | + | 0.733678i | \(0.737802\pi\) | |||||||
\(390\) | −10.5572 | −0.534582 | ||||||||
\(391\) | 6.21898 | 0.314507 | ||||||||
\(392\) | −4.94272 | −0.249645 | ||||||||
\(393\) | −15.1012 | −0.761756 | ||||||||
\(394\) | −12.9605 | −0.652941 | ||||||||
\(395\) | 10.4505 | 0.525820 | ||||||||
\(396\) | 2.05989 | 0.103514 | ||||||||
\(397\) | −6.69149 | −0.335836 | −0.167918 | − | 0.985801i | \(-0.553704\pi\) | ||||
−0.167918 | + | 0.985801i | \(0.553704\pi\) | |||||||
\(398\) | 5.53937 | 0.277663 | ||||||||
\(399\) | −16.4470 | −0.823377 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −7.04199 | −0.351660 | −0.175830 | − | 0.984421i | \(-0.556261\pi\) | ||||
−0.175830 | + | 0.984421i | \(0.556261\pi\) | |||||||
\(402\) | 21.8471 | 1.08963 | ||||||||
\(403\) | −31.8409 | −1.58611 | ||||||||
\(404\) | 13.3472 | 0.664047 | ||||||||
\(405\) | 10.9365 | 0.543440 | ||||||||
\(406\) | 8.52703 | 0.423190 | ||||||||
\(407\) | 3.88177 | 0.192412 | ||||||||
\(408\) | 6.05480 | 0.299757 | ||||||||
\(409\) | 0.530901 | 0.0262514 | 0.0131257 | − | 0.999914i | \(-0.495822\pi\) | ||||
0.0131257 | + | 0.999914i | \(0.495822\pi\) | |||||||
\(410\) | −7.01704 | −0.346547 | ||||||||
\(411\) | −32.5230 | −1.60424 | ||||||||
\(412\) | 15.0788 | 0.742879 | ||||||||
\(413\) | 21.1355 | 1.04001 | ||||||||
\(414\) | 4.75921 | 0.233902 | ||||||||
\(415\) | −4.45987 | −0.218926 | ||||||||
\(416\) | 4.69328 | 0.230107 | ||||||||
\(417\) | 2.93760 | 0.143855 | ||||||||
\(418\) | 5.09763 | 0.249333 | ||||||||
\(419\) | −21.8429 | −1.06710 | −0.533548 | − | 0.845770i | \(-0.679142\pi\) | ||||
−0.533548 | + | 0.845770i | \(0.679142\pi\) | |||||||
\(420\) | 3.22639 | 0.157432 | ||||||||
\(421\) | −29.9008 | −1.45727 | −0.728637 | − | 0.684900i | \(-0.759846\pi\) | ||||
−0.728637 | + | 0.684900i | \(0.759846\pi\) | |||||||
\(422\) | 1.49551 | 0.0728002 | ||||||||
\(423\) | 1.48840 | 0.0723684 | ||||||||
\(424\) | 9.28737 | 0.451034 | ||||||||
\(425\) | 2.69172 | 0.130567 | ||||||||
\(426\) | 27.6149 | 1.33795 | ||||||||
\(427\) | −17.0782 | −0.826472 | ||||||||
\(428\) | −1.72911 | −0.0835798 | ||||||||
\(429\) | 10.5572 | 0.509704 | ||||||||
\(430\) | −1.00000 | −0.0482243 | ||||||||
\(431\) | −3.74480 | −0.180381 | −0.0901903 | − | 0.995925i | \(-0.528748\pi\) | ||||
−0.0901903 | + | 0.995925i | \(0.528748\pi\) | |||||||
\(432\) | −2.11469 | −0.101743 | ||||||||
\(433\) | 15.2090 | 0.730898 | 0.365449 | − | 0.930831i | \(-0.380915\pi\) | ||||
0.365449 | + | 0.930831i | \(0.380915\pi\) | |||||||
\(434\) | 9.73095 | 0.467100 | ||||||||
\(435\) | 13.3728 | 0.641176 | ||||||||
\(436\) | 9.13341 | 0.437411 | ||||||||
\(437\) | 11.7776 | 0.563401 | ||||||||
\(438\) | −13.9537 | −0.666734 | ||||||||
\(439\) | −35.0097 | −1.67092 | −0.835462 | − | 0.549548i | \(-0.814800\pi\) | ||||
−0.835462 | + | 0.549548i | \(0.814800\pi\) | |||||||
\(440\) | −1.00000 | −0.0476731 | ||||||||
\(441\) | −10.1815 | −0.484832 | ||||||||
\(442\) | 12.6330 | 0.600889 | ||||||||
\(443\) | −31.3131 | −1.48773 | −0.743864 | − | 0.668330i | \(-0.767009\pi\) | ||||
−0.743864 | + | 0.668330i | \(0.767009\pi\) | |||||||
\(444\) | 8.73174 | 0.414390 | ||||||||
\(445\) | 6.38594 | 0.302723 | ||||||||
\(446\) | −20.6795 | −0.979201 | ||||||||
\(447\) | 20.8782 | 0.987507 | ||||||||
\(448\) | −1.43432 | −0.0677653 | ||||||||
\(449\) | 1.28870 | 0.0608177 | 0.0304088 | − | 0.999538i | \(-0.490319\pi\) | ||||
0.0304088 | + | 0.999538i | \(0.490319\pi\) | |||||||
\(450\) | 2.05989 | 0.0971043 | ||||||||
\(451\) | 7.01704 | 0.330420 | ||||||||
\(452\) | 4.62839 | 0.217701 | ||||||||
\(453\) | −12.0560 | −0.566443 | ||||||||
\(454\) | −21.9344 | −1.02943 | ||||||||
\(455\) | 6.73167 | 0.315586 | ||||||||
\(456\) | 11.4667 | 0.536978 | ||||||||
\(457\) | −35.6533 | −1.66779 | −0.833895 | − | 0.551922i | \(-0.813894\pi\) | ||||
−0.833895 | + | 0.551922i | \(0.813894\pi\) | |||||||
\(458\) | −21.3370 | −0.997014 | ||||||||
\(459\) | −5.69215 | −0.265687 | ||||||||
\(460\) | −2.31042 | −0.107724 | ||||||||
\(461\) | −10.0290 | −0.467096 | −0.233548 | − | 0.972345i | \(-0.575034\pi\) | ||||
−0.233548 | + | 0.972345i | \(0.575034\pi\) | |||||||
\(462\) | −3.22639 | −0.150105 | ||||||||
\(463\) | −26.9399 | −1.25200 | −0.626001 | − | 0.779822i | \(-0.715309\pi\) | ||||
−0.626001 | + | 0.779822i | \(0.715309\pi\) | |||||||
\(464\) | −5.94499 | −0.275989 | ||||||||
\(465\) | 15.2609 | 0.707706 | ||||||||
\(466\) | −18.4304 | −0.853770 | ||||||||
\(467\) | −17.3201 | −0.801479 | −0.400740 | − | 0.916192i | \(-0.631247\pi\) | ||||
−0.400740 | + | 0.916192i | \(0.631247\pi\) | |||||||
\(468\) | 9.66765 | 0.446887 | ||||||||
\(469\) | −13.9306 | −0.643254 | ||||||||
\(470\) | −0.722561 | −0.0333293 | ||||||||
\(471\) | 41.9889 | 1.93475 | ||||||||
\(472\) | −14.7355 | −0.678257 | ||||||||
\(473\) | 1.00000 | 0.0459800 | ||||||||
\(474\) | −23.5075 | −1.07974 | ||||||||
\(475\) | 5.09763 | 0.233895 | ||||||||
\(476\) | −3.86079 | −0.176959 | ||||||||
\(477\) | 19.1310 | 0.875948 | ||||||||
\(478\) | 4.81697 | 0.220323 | ||||||||
\(479\) | −29.6771 | −1.35598 | −0.677990 | − | 0.735071i | \(-0.737149\pi\) | ||||
−0.677990 | + | 0.735071i | \(0.737149\pi\) | |||||||
\(480\) | −2.24942 | −0.102672 | ||||||||
\(481\) | 18.2182 | 0.830680 | ||||||||
\(482\) | 5.77599 | 0.263089 | ||||||||
\(483\) | −7.45431 | −0.339183 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −0.328464 | −0.0149148 | ||||||||
\(486\) | −18.2568 | −0.828143 | ||||||||
\(487\) | 20.7138 | 0.938631 | 0.469316 | − | 0.883030i | \(-0.344501\pi\) | ||||
0.469316 | + | 0.883030i | \(0.344501\pi\) | |||||||
\(488\) | 11.9068 | 0.538996 | ||||||||
\(489\) | 53.4390 | 2.41660 | ||||||||
\(490\) | 4.94272 | 0.223289 | ||||||||
\(491\) | 0.702895 | 0.0317212 | 0.0158606 | − | 0.999874i | \(-0.494951\pi\) | ||||
0.0158606 | + | 0.999874i | \(0.494951\pi\) | |||||||
\(492\) | 15.7843 | 0.711611 | ||||||||
\(493\) | −16.0022 | −0.720704 | ||||||||
\(494\) | 23.9246 | 1.07642 | ||||||||
\(495\) | −2.05989 | −0.0925854 | ||||||||
\(496\) | −6.78435 | −0.304627 | ||||||||
\(497\) | −17.6084 | −0.789843 | ||||||||
\(498\) | 10.0321 | 0.449550 | ||||||||
\(499\) | 7.52040 | 0.336659 | 0.168330 | − | 0.985731i | \(-0.446163\pi\) | ||||
0.168330 | + | 0.985731i | \(0.446163\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −11.1267 | −0.497105 | ||||||||
\(502\) | −27.9375 | −1.24691 | ||||||||
\(503\) | 20.6329 | 0.919975 | 0.459988 | − | 0.887925i | \(-0.347854\pi\) | ||||
0.459988 | + | 0.887925i | \(0.347854\pi\) | |||||||
\(504\) | −2.95455 | −0.131606 | ||||||||
\(505\) | −13.3472 | −0.593942 | ||||||||
\(506\) | 2.31042 | 0.102710 | ||||||||
\(507\) | 20.3052 | 0.901785 | ||||||||
\(508\) | −7.81461 | −0.346717 | ||||||||
\(509\) | 41.8117 | 1.85327 | 0.926636 | − | 0.375959i | \(-0.122687\pi\) | ||||
0.926636 | + | 0.375959i | \(0.122687\pi\) | |||||||
\(510\) | −6.05480 | −0.268111 | ||||||||
\(511\) | 8.89746 | 0.393600 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −10.7799 | −0.475945 | ||||||||
\(514\) | −9.69635 | −0.427687 | ||||||||
\(515\) | −15.0788 | −0.664451 | ||||||||
\(516\) | 2.24942 | 0.0990252 | ||||||||
\(517\) | 0.722561 | 0.0317782 | ||||||||
\(518\) | −5.56771 | −0.244631 | ||||||||
\(519\) | 54.9700 | 2.41292 | ||||||||
\(520\) | −4.69328 | −0.205814 | ||||||||
\(521\) | −23.7301 | −1.03964 | −0.519818 | − | 0.854277i | \(-0.674000\pi\) | ||||
−0.519818 | + | 0.854277i | \(0.674000\pi\) | |||||||
\(522\) | −12.2461 | −0.535995 | ||||||||
\(523\) | 24.1764 | 1.05716 | 0.528581 | − | 0.848883i | \(-0.322724\pi\) | ||||
0.528581 | + | 0.848883i | \(0.322724\pi\) | |||||||
\(524\) | −6.71338 | −0.293275 | ||||||||
\(525\) | −3.22639 | −0.140811 | ||||||||
\(526\) | −20.4163 | −0.890193 | ||||||||
\(527\) | −18.2616 | −0.795486 | ||||||||
\(528\) | 2.24942 | 0.0978935 | ||||||||
\(529\) | −17.6620 | −0.767912 | ||||||||
\(530\) | −9.28737 | −0.403417 | ||||||||
\(531\) | −30.3536 | −1.31723 | ||||||||
\(532\) | −7.31164 | −0.317000 | ||||||||
\(533\) | 32.9329 | 1.42648 | ||||||||
\(534\) | −14.3647 | −0.621620 | ||||||||
\(535\) | 1.72911 | 0.0747561 | ||||||||
\(536\) | 9.71230 | 0.419508 | ||||||||
\(537\) | −37.4221 | −1.61488 | ||||||||
\(538\) | 13.9619 | 0.601941 | ||||||||
\(539\) | −4.94272 | −0.212898 | ||||||||
\(540\) | 2.11469 | 0.0910019 | ||||||||
\(541\) | −10.3446 | −0.444750 | −0.222375 | − | 0.974961i | \(-0.571381\pi\) | ||||
−0.222375 | + | 0.974961i | \(0.571381\pi\) | |||||||
\(542\) | −18.0976 | −0.777357 | ||||||||
\(543\) | −32.4601 | −1.39300 | ||||||||
\(544\) | 2.69172 | 0.115406 | ||||||||
\(545\) | −9.13341 | −0.391232 | ||||||||
\(546\) | −15.1424 | −0.648033 | ||||||||
\(547\) | 11.4357 | 0.488955 | 0.244477 | − | 0.969655i | \(-0.421384\pi\) | ||||
0.244477 | + | 0.969655i | \(0.421384\pi\) | |||||||
\(548\) | −14.4584 | −0.617632 | ||||||||
\(549\) | 24.5268 | 1.04678 | ||||||||
\(550\) | 1.00000 | 0.0426401 | ||||||||
\(551\) | −30.3054 | −1.29105 | ||||||||
\(552\) | 5.19710 | 0.221203 | ||||||||
\(553\) | 14.9893 | 0.637412 | ||||||||
\(554\) | −8.13107 | −0.345456 | ||||||||
\(555\) | −8.73174 | −0.370642 | ||||||||
\(556\) | 1.30594 | 0.0553840 | ||||||||
\(557\) | 42.4216 | 1.79746 | 0.898731 | − | 0.438500i | \(-0.144490\pi\) | ||||
0.898731 | + | 0.438500i | \(0.144490\pi\) | |||||||
\(558\) | −13.9751 | −0.591611 | ||||||||
\(559\) | 4.69328 | 0.198504 | ||||||||
\(560\) | 1.43432 | 0.0606112 | ||||||||
\(561\) | 6.05480 | 0.255634 | ||||||||
\(562\) | −5.99636 | −0.252941 | ||||||||
\(563\) | 27.0026 | 1.13802 | 0.569012 | − | 0.822330i | \(-0.307326\pi\) | ||||
0.569012 | + | 0.822330i | \(0.307326\pi\) | |||||||
\(564\) | 1.62534 | 0.0684393 | ||||||||
\(565\) | −4.62839 | −0.194718 | ||||||||
\(566\) | −21.0031 | −0.882826 | ||||||||
\(567\) | 15.6865 | 0.658771 | ||||||||
\(568\) | 12.2764 | 0.515108 | ||||||||
\(569\) | −35.6919 | −1.49628 | −0.748141 | − | 0.663540i | \(-0.769053\pi\) | ||||
−0.748141 | + | 0.663540i | \(0.769053\pi\) | |||||||
\(570\) | −11.4667 | −0.480288 | ||||||||
\(571\) | −4.76591 | −0.199447 | −0.0997235 | − | 0.995015i | \(-0.531796\pi\) | ||||
−0.0997235 | + | 0.995015i | \(0.531796\pi\) | |||||||
\(572\) | 4.69328 | 0.196236 | ||||||||
\(573\) | 15.6327 | 0.653065 | ||||||||
\(574\) | −10.0647 | −0.420092 | ||||||||
\(575\) | 2.31042 | 0.0963510 | ||||||||
\(576\) | 2.05989 | 0.0858289 | ||||||||
\(577\) | −17.3230 | −0.721167 | −0.360583 | − | 0.932727i | \(-0.617422\pi\) | ||||
−0.360583 | + | 0.932727i | \(0.617422\pi\) | |||||||
\(578\) | −9.75467 | −0.405741 | ||||||||
\(579\) | 6.85550 | 0.284905 | ||||||||
\(580\) | 5.94499 | 0.246852 | ||||||||
\(581\) | −6.39689 | −0.265388 | ||||||||
\(582\) | 0.738855 | 0.0306265 | ||||||||
\(583\) | 9.28737 | 0.384643 | ||||||||
\(584\) | −6.20325 | −0.256692 | ||||||||
\(585\) | −9.66765 | −0.399708 | ||||||||
\(586\) | −29.8493 | −1.23306 | ||||||||
\(587\) | 34.5220 | 1.42488 | 0.712438 | − | 0.701735i | \(-0.247591\pi\) | ||||
0.712438 | + | 0.701735i | \(0.247591\pi\) | |||||||
\(588\) | −11.1183 | −0.458509 | ||||||||
\(589\) | −34.5841 | −1.42501 | ||||||||
\(590\) | 14.7355 | 0.606651 | ||||||||
\(591\) | −29.1536 | −1.19922 | ||||||||
\(592\) | 3.88177 | 0.159540 | ||||||||
\(593\) | 6.36844 | 0.261521 | 0.130760 | − | 0.991414i | \(-0.458258\pi\) | ||||
0.130760 | + | 0.991414i | \(0.458258\pi\) | |||||||
\(594\) | −2.11469 | −0.0867669 | ||||||||
\(595\) | 3.86079 | 0.158277 | ||||||||
\(596\) | 9.28161 | 0.380190 | ||||||||
\(597\) | 12.4604 | 0.509969 | ||||||||
\(598\) | 10.8434 | 0.443420 | ||||||||
\(599\) | 41.4623 | 1.69410 | 0.847051 | − | 0.531511i | \(-0.178376\pi\) | ||||
0.847051 | + | 0.531511i | \(0.178376\pi\) | |||||||
\(600\) | 2.24942 | 0.0918322 | ||||||||
\(601\) | −20.1939 | −0.823725 | −0.411863 | − | 0.911246i | \(-0.635122\pi\) | ||||
−0.411863 | + | 0.911246i | \(0.635122\pi\) | |||||||
\(602\) | −1.43432 | −0.0584586 | ||||||||
\(603\) | 20.0063 | 0.814720 | ||||||||
\(604\) | −5.35962 | −0.218080 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | 30.0234 | 1.21962 | ||||||||
\(607\) | 20.7568 | 0.842491 | 0.421246 | − | 0.906947i | \(-0.361593\pi\) | ||||
0.421246 | + | 0.906947i | \(0.361593\pi\) | |||||||
\(608\) | 5.09763 | 0.206736 | ||||||||
\(609\) | 19.1809 | 0.777249 | ||||||||
\(610\) | −11.9068 | −0.482093 | ||||||||
\(611\) | 3.39118 | 0.137192 | ||||||||
\(612\) | 5.54465 | 0.224129 | ||||||||
\(613\) | −18.5042 | −0.747376 | −0.373688 | − | 0.927554i | \(-0.621907\pi\) | ||||
−0.373688 | + | 0.927554i | \(0.621907\pi\) | |||||||
\(614\) | 3.81085 | 0.153793 | ||||||||
\(615\) | −15.7843 | −0.636484 | ||||||||
\(616\) | −1.43432 | −0.0577905 | ||||||||
\(617\) | −9.52812 | −0.383587 | −0.191794 | − | 0.981435i | \(-0.561430\pi\) | ||||
−0.191794 | + | 0.981435i | \(0.561430\pi\) | |||||||
\(618\) | 33.9185 | 1.36440 | ||||||||
\(619\) | −8.29009 | −0.333207 | −0.166604 | − | 0.986024i | \(-0.553280\pi\) | ||||
−0.166604 | + | 0.986024i | \(0.553280\pi\) | |||||||
\(620\) | 6.78435 | 0.272466 | ||||||||
\(621\) | −4.88582 | −0.196061 | ||||||||
\(622\) | 17.9922 | 0.721423 | ||||||||
\(623\) | 9.15949 | 0.366967 | ||||||||
\(624\) | 10.5572 | 0.422624 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 4.23321 | 0.169193 | ||||||||
\(627\) | 11.4667 | 0.457936 | ||||||||
\(628\) | 18.6665 | 0.744876 | ||||||||
\(629\) | 10.4486 | 0.416614 | ||||||||
\(630\) | 2.95455 | 0.117712 | ||||||||
\(631\) | 39.4944 | 1.57225 | 0.786123 | − | 0.618070i | \(-0.212085\pi\) | ||||
0.786123 | + | 0.618070i | \(0.212085\pi\) | |||||||
\(632\) | −10.4505 | −0.415698 | ||||||||
\(633\) | 3.36403 | 0.133708 | ||||||||
\(634\) | 22.6847 | 0.900925 | ||||||||
\(635\) | 7.81461 | 0.310113 | ||||||||
\(636\) | 20.8912 | 0.828390 | ||||||||
\(637\) | −23.1976 | −0.919121 | ||||||||
\(638\) | −5.94499 | −0.235365 | ||||||||
\(639\) | 25.2882 | 1.00038 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 15.3879 | 0.607787 | 0.303893 | − | 0.952706i | \(-0.401713\pi\) | ||||
0.303893 | + | 0.952706i | \(0.401713\pi\) | |||||||
\(642\) | −3.88950 | −0.153506 | ||||||||
\(643\) | 6.81634 | 0.268810 | 0.134405 | − | 0.990926i | \(-0.457088\pi\) | ||||
0.134405 | + | 0.990926i | \(0.457088\pi\) | |||||||
\(644\) | −3.31388 | −0.130585 | ||||||||
\(645\) | −2.24942 | −0.0885709 | ||||||||
\(646\) | 13.7214 | 0.539860 | ||||||||
\(647\) | −28.1040 | −1.10488 | −0.552442 | − | 0.833551i | \(-0.686304\pi\) | ||||
−0.552442 | + | 0.833551i | \(0.686304\pi\) | |||||||
\(648\) | −10.9365 | −0.429627 | ||||||||
\(649\) | −14.7355 | −0.578419 | ||||||||
\(650\) | 4.69328 | 0.184085 | ||||||||
\(651\) | 21.8890 | 0.857897 | ||||||||
\(652\) | 23.7568 | 0.930388 | ||||||||
\(653\) | −13.1673 | −0.515277 | −0.257639 | − | 0.966241i | \(-0.582944\pi\) | ||||
−0.257639 | + | 0.966241i | \(0.582944\pi\) | |||||||
\(654\) | 20.5449 | 0.803369 | ||||||||
\(655\) | 6.71338 | 0.262313 | ||||||||
\(656\) | 7.01704 | 0.273970 | ||||||||
\(657\) | −12.7780 | −0.498519 | ||||||||
\(658\) | −1.03639 | −0.0404025 | ||||||||
\(659\) | 34.7212 | 1.35254 | 0.676272 | − | 0.736652i | \(-0.263594\pi\) | ||||
0.676272 | + | 0.736652i | \(0.263594\pi\) | |||||||
\(660\) | −2.24942 | −0.0875586 | ||||||||
\(661\) | 30.9514 | 1.20387 | 0.601935 | − | 0.798545i | \(-0.294396\pi\) | ||||
0.601935 | + | 0.798545i | \(0.294396\pi\) | |||||||
\(662\) | 20.9408 | 0.813887 | ||||||||
\(663\) | 28.4169 | 1.10362 | ||||||||
\(664\) | 4.45987 | 0.173077 | ||||||||
\(665\) | 7.31164 | 0.283533 | ||||||||
\(666\) | 7.99604 | 0.309840 | ||||||||
\(667\) | −13.7354 | −0.531837 | ||||||||
\(668\) | −4.94648 | −0.191385 | ||||||||
\(669\) | −46.5168 | −1.79844 | ||||||||
\(670\) | −9.71230 | −0.375219 | ||||||||
\(671\) | 11.9068 | 0.459657 | ||||||||
\(672\) | −3.22639 | −0.124461 | ||||||||
\(673\) | −26.2301 | −1.01110 | −0.505549 | − | 0.862798i | \(-0.668710\pi\) | ||||
−0.505549 | + | 0.862798i | \(0.668710\pi\) | |||||||
\(674\) | 12.2906 | 0.473416 | ||||||||
\(675\) | −2.11469 | −0.0813946 | ||||||||
\(676\) | 9.02685 | 0.347187 | ||||||||
\(677\) | −9.28209 | −0.356740 | −0.178370 | − | 0.983963i | \(-0.557082\pi\) | ||||
−0.178370 | + | 0.983963i | \(0.557082\pi\) | |||||||
\(678\) | 10.4112 | 0.399840 | ||||||||
\(679\) | −0.471124 | −0.0180801 | ||||||||
\(680\) | −2.69172 | −0.103223 | ||||||||
\(681\) | −49.3396 | −1.89070 | ||||||||
\(682\) | −6.78435 | −0.259786 | ||||||||
\(683\) | 19.0813 | 0.730124 | 0.365062 | − | 0.930983i | \(-0.381048\pi\) | ||||
0.365062 | + | 0.930983i | \(0.381048\pi\) | |||||||
\(684\) | 10.5006 | 0.401499 | ||||||||
\(685\) | 14.4584 | 0.552427 | ||||||||
\(686\) | 17.1297 | 0.654015 | ||||||||
\(687\) | −47.9960 | −1.83116 | ||||||||
\(688\) | 1.00000 | 0.0381246 | ||||||||
\(689\) | 43.5882 | 1.66058 | ||||||||
\(690\) | −5.19710 | −0.197850 | ||||||||
\(691\) | −22.5886 | −0.859311 | −0.429656 | − | 0.902993i | \(-0.641365\pi\) | ||||
−0.429656 | + | 0.902993i | \(0.641365\pi\) | |||||||
\(692\) | 24.4374 | 0.928971 | ||||||||
\(693\) | −2.95455 | −0.112234 | ||||||||
\(694\) | −31.6551 | −1.20161 | ||||||||
\(695\) | −1.30594 | −0.0495370 | ||||||||
\(696\) | −13.3728 | −0.506894 | ||||||||
\(697\) | 18.8879 | 0.715430 | ||||||||
\(698\) | 21.3475 | 0.808014 | ||||||||
\(699\) | −41.4576 | −1.56807 | ||||||||
\(700\) | −1.43432 | −0.0542123 | ||||||||
\(701\) | −40.5973 | −1.53334 | −0.766669 | − | 0.642042i | \(-0.778087\pi\) | ||||
−0.766669 | + | 0.642042i | \(0.778087\pi\) | |||||||
\(702\) | −9.92484 | −0.374589 | ||||||||
\(703\) | 19.7878 | 0.746312 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | −1.62534 | −0.0612140 | ||||||||
\(706\) | −16.1131 | −0.606423 | ||||||||
\(707\) | −19.1442 | −0.719990 | ||||||||
\(708\) | −33.1464 | −1.24572 | ||||||||
\(709\) | 39.4834 | 1.48283 | 0.741414 | − | 0.671048i | \(-0.234155\pi\) | ||||
0.741414 | + | 0.671048i | \(0.234155\pi\) | |||||||
\(710\) | −12.2764 | −0.460727 | ||||||||
\(711\) | −21.5269 | −0.807321 | ||||||||
\(712\) | −6.38594 | −0.239323 | ||||||||
\(713\) | −15.6747 | −0.587021 | ||||||||
\(714\) | −8.68453 | −0.325010 | ||||||||
\(715\) | −4.69328 | −0.175519 | ||||||||
\(716\) | −16.6363 | −0.621729 | ||||||||
\(717\) | 10.8354 | 0.404655 | ||||||||
\(718\) | −21.6717 | −0.808780 | ||||||||
\(719\) | 17.8020 | 0.663902 | 0.331951 | − | 0.943297i | \(-0.392293\pi\) | ||||
0.331951 | + | 0.943297i | \(0.392293\pi\) | |||||||
\(720\) | −2.05989 | −0.0767677 | ||||||||
\(721\) | −21.6278 | −0.805463 | ||||||||
\(722\) | 6.98581 | 0.259985 | ||||||||
\(723\) | 12.9926 | 0.483201 | ||||||||
\(724\) | −14.4304 | −0.536302 | ||||||||
\(725\) | −5.94499 | −0.220791 | ||||||||
\(726\) | 2.24942 | 0.0834838 | ||||||||
\(727\) | 39.2561 | 1.45593 | 0.727964 | − | 0.685615i | \(-0.240467\pi\) | ||||
0.727964 | + | 0.685615i | \(0.240467\pi\) | |||||||
\(728\) | −6.73167 | −0.249492 | ||||||||
\(729\) | −8.25756 | −0.305836 | ||||||||
\(730\) | 6.20325 | 0.229593 | ||||||||
\(731\) | 2.69172 | 0.0995567 | ||||||||
\(732\) | 26.7834 | 0.989944 | ||||||||
\(733\) | 38.5716 | 1.42467 | 0.712337 | − | 0.701838i | \(-0.247637\pi\) | ||||
0.712337 | + | 0.701838i | \(0.247637\pi\) | |||||||
\(734\) | −15.0819 | −0.556683 | ||||||||
\(735\) | 11.1183 | 0.410103 | ||||||||
\(736\) | 2.31042 | 0.0851630 | ||||||||
\(737\) | 9.71230 | 0.357757 | ||||||||
\(738\) | 14.4544 | 0.532073 | ||||||||
\(739\) | 23.2463 | 0.855128 | 0.427564 | − | 0.903985i | \(-0.359372\pi\) | ||||
0.427564 | + | 0.903985i | \(0.359372\pi\) | |||||||
\(740\) | −3.88177 | −0.142697 | ||||||||
\(741\) | 53.8164 | 1.97700 | ||||||||
\(742\) | −13.3211 | −0.489032 | ||||||||
\(743\) | 18.0655 | 0.662760 | 0.331380 | − | 0.943497i | \(-0.392486\pi\) | ||||
0.331380 | + | 0.943497i | \(0.392486\pi\) | |||||||
\(744\) | −15.2609 | −0.559491 | ||||||||
\(745\) | −9.28161 | −0.340052 | ||||||||
\(746\) | −23.7371 | −0.869076 | ||||||||
\(747\) | 9.18686 | 0.336130 | ||||||||
\(748\) | 2.69172 | 0.0984189 | ||||||||
\(749\) | 2.48011 | 0.0906211 | ||||||||
\(750\) | −2.24942 | −0.0821372 | ||||||||
\(751\) | −37.8733 | −1.38202 | −0.691008 | − | 0.722847i | \(-0.742833\pi\) | ||||
−0.691008 | + | 0.722847i | \(0.742833\pi\) | |||||||
\(752\) | 0.722561 | 0.0263491 | ||||||||
\(753\) | −62.8433 | −2.29014 | ||||||||
\(754\) | −27.9015 | −1.01611 | ||||||||
\(755\) | 5.35962 | 0.195057 | ||||||||
\(756\) | 3.03315 | 0.110315 | ||||||||
\(757\) | −0.0136388 | −0.000495711 0 | −0.000247856 | − | 1.00000i | \(-0.500079\pi\) | ||||
−0.000247856 | 1.00000i | \(0.500079\pi\) | ||||||||
\(758\) | 11.5566 | 0.419754 | ||||||||
\(759\) | 5.19710 | 0.188643 | ||||||||
\(760\) | −5.09763 | −0.184910 | ||||||||
\(761\) | 11.8236 | 0.428606 | 0.214303 | − | 0.976767i | \(-0.431252\pi\) | ||||
0.214303 | + | 0.976767i | \(0.431252\pi\) | |||||||
\(762\) | −17.5784 | −0.636796 | ||||||||
\(763\) | −13.1003 | −0.474261 | ||||||||
\(764\) | 6.94965 | 0.251430 | ||||||||
\(765\) | −5.54465 | −0.200467 | ||||||||
\(766\) | 24.9628 | 0.901942 | ||||||||
\(767\) | −69.1578 | −2.49714 | ||||||||
\(768\) | 2.24942 | 0.0811690 | ||||||||
\(769\) | −35.4685 | −1.27903 | −0.639514 | − | 0.768779i | \(-0.720864\pi\) | ||||
−0.639514 | + | 0.768779i | \(0.720864\pi\) | |||||||
\(770\) | 1.43432 | 0.0516894 | ||||||||
\(771\) | −21.8112 | −0.785510 | ||||||||
\(772\) | 3.04767 | 0.109688 | ||||||||
\(773\) | 2.29853 | 0.0826723 | 0.0413361 | − | 0.999145i | \(-0.486839\pi\) | ||||
0.0413361 | + | 0.999145i | \(0.486839\pi\) | |||||||
\(774\) | 2.05989 | 0.0740414 | ||||||||
\(775\) | −6.78435 | −0.243701 | ||||||||
\(776\) | 0.328464 | 0.0117912 | ||||||||
\(777\) | −12.5241 | −0.449300 | ||||||||
\(778\) | −26.8036 | −0.960954 | ||||||||
\(779\) | 35.7703 | 1.28160 | ||||||||
\(780\) | −10.5572 | −0.378007 | ||||||||
\(781\) | 12.2764 | 0.439286 | ||||||||
\(782\) | 6.21898 | 0.222390 | ||||||||
\(783\) | 12.5718 | 0.449281 | ||||||||
\(784\) | −4.94272 | −0.176526 | ||||||||
\(785\) | −18.6665 | −0.666237 | ||||||||
\(786\) | −15.1012 | −0.538643 | ||||||||
\(787\) | −6.00131 | −0.213924 | −0.106962 | − | 0.994263i | \(-0.534112\pi\) | ||||
−0.106962 | + | 0.994263i | \(0.534112\pi\) | |||||||
\(788\) | −12.9605 | −0.461699 | ||||||||
\(789\) | −45.9248 | −1.63497 | ||||||||
\(790\) | 10.4505 | 0.371811 | ||||||||
\(791\) | −6.63861 | −0.236042 | ||||||||
\(792\) | 2.05989 | 0.0731951 | ||||||||
\(793\) | 55.8819 | 1.98443 | ||||||||
\(794\) | −6.69149 | −0.237472 | ||||||||
\(795\) | −20.8912 | −0.740934 | ||||||||
\(796\) | 5.53937 | 0.196338 | ||||||||
\(797\) | 48.1581 | 1.70585 | 0.852924 | − | 0.522036i | \(-0.174827\pi\) | ||||
0.852924 | + | 0.522036i | \(0.174827\pi\) | |||||||
\(798\) | −16.4470 | −0.582216 | ||||||||
\(799\) | 1.94493 | 0.0688066 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −13.1544 | −0.464786 | ||||||||
\(802\) | −7.04199 | −0.248661 | ||||||||
\(803\) | −6.20325 | −0.218908 | ||||||||
\(804\) | 21.8471 | 0.770486 | ||||||||
\(805\) | 3.31388 | 0.116799 | ||||||||
\(806\) | −31.8409 | −1.12155 | ||||||||
\(807\) | 31.4062 | 1.10555 | ||||||||
\(808\) | 13.3472 | 0.469552 | ||||||||
\(809\) | −30.9838 | −1.08933 | −0.544666 | − | 0.838653i | \(-0.683343\pi\) | ||||
−0.544666 | + | 0.838653i | \(0.683343\pi\) | |||||||
\(810\) | 10.9365 | 0.384270 | ||||||||
\(811\) | −4.33544 | −0.152238 | −0.0761190 | − | 0.997099i | \(-0.524253\pi\) | ||||
−0.0761190 | + | 0.997099i | \(0.524253\pi\) | |||||||
\(812\) | 8.52703 | 0.299240 | ||||||||
\(813\) | −40.7091 | −1.42773 | ||||||||
\(814\) | 3.88177 | 0.136056 | ||||||||
\(815\) | −23.7568 | −0.832164 | ||||||||
\(816\) | 6.05480 | 0.211960 | ||||||||
\(817\) | 5.09763 | 0.178343 | ||||||||
\(818\) | 0.530901 | 0.0185625 | ||||||||
\(819\) | −13.8665 | −0.484536 | ||||||||
\(820\) | −7.01704 | −0.245046 | ||||||||
\(821\) | 12.9425 | 0.451695 | 0.225847 | − | 0.974163i | \(-0.427485\pi\) | ||||
0.225847 | + | 0.974163i | \(0.427485\pi\) | |||||||
\(822\) | −32.5230 | −1.13437 | ||||||||
\(823\) | 26.9475 | 0.939331 | 0.469665 | − | 0.882844i | \(-0.344375\pi\) | ||||
0.469665 | + | 0.882844i | \(0.344375\pi\) | |||||||
\(824\) | 15.0788 | 0.525295 | ||||||||
\(825\) | 2.24942 | 0.0783148 | ||||||||
\(826\) | 21.1355 | 0.735397 | ||||||||
\(827\) | −12.4487 | −0.432884 | −0.216442 | − | 0.976295i | \(-0.569445\pi\) | ||||
−0.216442 | + | 0.976295i | \(0.569445\pi\) | |||||||
\(828\) | 4.75921 | 0.165394 | ||||||||
\(829\) | −1.36229 | −0.0473144 | −0.0236572 | − | 0.999720i | \(-0.507531\pi\) | ||||
−0.0236572 | + | 0.999720i | \(0.507531\pi\) | |||||||
\(830\) | −4.45987 | −0.154804 | ||||||||
\(831\) | −18.2902 | −0.634480 | ||||||||
\(832\) | 4.69328 | 0.162710 | ||||||||
\(833\) | −13.3044 | −0.460970 | ||||||||
\(834\) | 2.93760 | 0.101721 | ||||||||
\(835\) | 4.94648 | 0.171180 | ||||||||
\(836\) | 5.09763 | 0.176305 | ||||||||
\(837\) | 14.3468 | 0.495899 | ||||||||
\(838\) | −21.8429 | −0.754551 | ||||||||
\(839\) | 26.2011 | 0.904564 | 0.452282 | − | 0.891875i | \(-0.350610\pi\) | ||||
0.452282 | + | 0.891875i | \(0.350610\pi\) | |||||||
\(840\) | 3.22639 | 0.111321 | ||||||||
\(841\) | 6.34294 | 0.218722 | ||||||||
\(842\) | −29.9008 | −1.03045 | ||||||||
\(843\) | −13.4883 | −0.464563 | ||||||||
\(844\) | 1.49551 | 0.0514775 | ||||||||
\(845\) | −9.02685 | −0.310533 | ||||||||
\(846\) | 1.48840 | 0.0511722 | ||||||||
\(847\) | −1.43432 | −0.0492839 | ||||||||
\(848\) | 9.28737 | 0.318929 | ||||||||
\(849\) | −47.2448 | −1.62144 | ||||||||
\(850\) | 2.69172 | 0.0923251 | ||||||||
\(851\) | 8.96851 | 0.307436 | ||||||||
\(852\) | 27.6149 | 0.946070 | ||||||||
\(853\) | 25.9974 | 0.890135 | 0.445068 | − | 0.895497i | \(-0.353180\pi\) | ||||
0.445068 | + | 0.895497i | \(0.353180\pi\) | |||||||
\(854\) | −17.0782 | −0.584404 | ||||||||
\(855\) | −10.5006 | −0.359112 | ||||||||
\(856\) | −1.72911 | −0.0590999 | ||||||||
\(857\) | 4.12590 | 0.140938 | 0.0704690 | − | 0.997514i | \(-0.477550\pi\) | ||||
0.0704690 | + | 0.997514i | \(0.477550\pi\) | |||||||
\(858\) | 10.5572 | 0.360415 | ||||||||
\(859\) | 49.0374 | 1.67313 | 0.836567 | − | 0.547864i | \(-0.184559\pi\) | ||||
0.836567 | + | 0.547864i | \(0.184559\pi\) | |||||||
\(860\) | −1.00000 | −0.0340997 | ||||||||
\(861\) | −22.6397 | −0.771560 | ||||||||
\(862\) | −3.74480 | −0.127548 | ||||||||
\(863\) | −12.7928 | −0.435472 | −0.217736 | − | 0.976008i | \(-0.569867\pi\) | ||||
−0.217736 | + | 0.976008i | \(0.569867\pi\) | |||||||
\(864\) | −2.11469 | −0.0719433 | ||||||||
\(865\) | −24.4374 | −0.830897 | ||||||||
\(866\) | 15.2090 | 0.516823 | ||||||||
\(867\) | −21.9424 | −0.745201 | ||||||||
\(868\) | 9.73095 | 0.330290 | ||||||||
\(869\) | −10.4505 | −0.354508 | ||||||||
\(870\) | 13.3728 | 0.453380 | ||||||||
\(871\) | 45.5825 | 1.54451 | ||||||||
\(872\) | 9.13341 | 0.309296 | ||||||||
\(873\) | 0.676602 | 0.0228995 | ||||||||
\(874\) | 11.7776 | 0.398385 | ||||||||
\(875\) | 1.43432 | 0.0484889 | ||||||||
\(876\) | −13.9537 | −0.471452 | ||||||||
\(877\) | 36.9386 | 1.24733 | 0.623664 | − | 0.781693i | \(-0.285643\pi\) | ||||
0.623664 | + | 0.781693i | \(0.285643\pi\) | |||||||
\(878\) | −35.0097 | −1.18152 | ||||||||
\(879\) | −67.1437 | −2.26470 | ||||||||
\(880\) | −1.00000 | −0.0337100 | ||||||||
\(881\) | 50.0472 | 1.68613 | 0.843066 | − | 0.537811i | \(-0.180748\pi\) | ||||
0.843066 | + | 0.537811i | \(0.180748\pi\) | |||||||
\(882\) | −10.1815 | −0.342828 | ||||||||
\(883\) | 44.2846 | 1.49030 | 0.745148 | − | 0.666899i | \(-0.232379\pi\) | ||||
0.745148 | + | 0.666899i | \(0.232379\pi\) | |||||||
\(884\) | 12.6330 | 0.424893 | ||||||||
\(885\) | 33.1464 | 1.11420 | ||||||||
\(886\) | −31.3131 | −1.05198 | ||||||||
\(887\) | −37.3745 | −1.25491 | −0.627456 | − | 0.778652i | \(-0.715904\pi\) | ||||
−0.627456 | + | 0.778652i | \(0.715904\pi\) | |||||||
\(888\) | 8.73174 | 0.293018 | ||||||||
\(889\) | 11.2087 | 0.375927 | ||||||||
\(890\) | 6.38594 | 0.214057 | ||||||||
\(891\) | −10.9365 | −0.366387 | ||||||||
\(892\) | −20.6795 | −0.692400 | ||||||||
\(893\) | 3.68335 | 0.123259 | ||||||||
\(894\) | 20.8782 | 0.698273 | ||||||||
\(895\) | 16.6363 | 0.556091 | ||||||||
\(896\) | −1.43432 | −0.0479173 | ||||||||
\(897\) | 24.3914 | 0.814406 | ||||||||
\(898\) | 1.28870 | 0.0430046 | ||||||||
\(899\) | 40.3329 | 1.34518 | ||||||||
\(900\) | 2.05989 | 0.0686631 | ||||||||
\(901\) | 24.9989 | 0.832836 | ||||||||
\(902\) | 7.01704 | 0.233642 | ||||||||
\(903\) | −3.22639 | −0.107368 | ||||||||
\(904\) | 4.62839 | 0.153938 | ||||||||
\(905\) | 14.4304 | 0.479683 | ||||||||
\(906\) | −12.0560 | −0.400535 | ||||||||
\(907\) | −13.2860 | −0.441154 | −0.220577 | − | 0.975370i | \(-0.570794\pi\) | ||||
−0.220577 | + | 0.975370i | \(0.570794\pi\) | |||||||
\(908\) | −21.9344 | −0.727917 | ||||||||
\(909\) | 27.4938 | 0.911911 | ||||||||
\(910\) | 6.73167 | 0.223153 | ||||||||
\(911\) | −37.1564 | −1.23105 | −0.615523 | − | 0.788119i | \(-0.711055\pi\) | ||||
−0.615523 | + | 0.788119i | \(0.711055\pi\) | |||||||
\(912\) | 11.4667 | 0.379701 | ||||||||
\(913\) | 4.45987 | 0.147600 | ||||||||
\(914\) | −35.6533 | −1.17931 | ||||||||
\(915\) | −26.7834 | −0.885433 | ||||||||
\(916\) | −21.3370 | −0.704995 | ||||||||
\(917\) | 9.62915 | 0.317982 | ||||||||
\(918\) | −5.69215 | −0.187869 | ||||||||
\(919\) | 12.2813 | 0.405122 | 0.202561 | − | 0.979270i | \(-0.435074\pi\) | ||||
0.202561 | + | 0.979270i | \(0.435074\pi\) | |||||||
\(920\) | −2.31042 | −0.0761721 | ||||||||
\(921\) | 8.57221 | 0.282464 | ||||||||
\(922\) | −10.0290 | −0.330286 | ||||||||
\(923\) | 57.6167 | 1.89648 | ||||||||
\(924\) | −3.22639 | −0.106141 | ||||||||
\(925\) | 3.88177 | 0.127632 | ||||||||
\(926\) | −26.9399 | −0.885299 | ||||||||
\(927\) | 31.0607 | 1.02017 | ||||||||
\(928\) | −5.94499 | −0.195154 | ||||||||
\(929\) | −16.4206 | −0.538741 | −0.269371 | − | 0.963037i | \(-0.586816\pi\) | ||||
−0.269371 | + | 0.963037i | \(0.586816\pi\) | |||||||
\(930\) | 15.2609 | 0.500424 | ||||||||
\(931\) | −25.1962 | −0.825770 | ||||||||
\(932\) | −18.4304 | −0.603706 | ||||||||
\(933\) | 40.4721 | 1.32500 | ||||||||
\(934\) | −17.3201 | −0.566731 | ||||||||
\(935\) | −2.69172 | −0.0880285 | ||||||||
\(936\) | 9.66765 | 0.315997 | ||||||||
\(937\) | 37.7828 | 1.23431 | 0.617156 | − | 0.786841i | \(-0.288285\pi\) | ||||
0.617156 | + | 0.786841i | \(0.288285\pi\) | |||||||
\(938\) | −13.9306 | −0.454849 | ||||||||
\(939\) | 9.52228 | 0.310748 | ||||||||
\(940\) | −0.722561 | −0.0235673 | ||||||||
\(941\) | −17.0274 | −0.555077 | −0.277539 | − | 0.960715i | \(-0.589519\pi\) | ||||
−0.277539 | + | 0.960715i | \(0.589519\pi\) | |||||||
\(942\) | 41.9889 | 1.36807 | ||||||||
\(943\) | 16.2123 | 0.527945 | ||||||||
\(944\) | −14.7355 | −0.479600 | ||||||||
\(945\) | −3.03315 | −0.0986684 | ||||||||
\(946\) | 1.00000 | 0.0325128 | ||||||||
\(947\) | −2.03265 | −0.0660521 | −0.0330260 | − | 0.999454i | \(-0.510514\pi\) | ||||
−0.0330260 | + | 0.999454i | \(0.510514\pi\) | |||||||
\(948\) | −23.5075 | −0.763489 | ||||||||
\(949\) | −29.1136 | −0.945066 | ||||||||
\(950\) | 5.09763 | 0.165389 | ||||||||
\(951\) | 51.0274 | 1.65468 | ||||||||
\(952\) | −3.86079 | −0.125129 | ||||||||
\(953\) | 1.53425 | 0.0496994 | 0.0248497 | − | 0.999691i | \(-0.492089\pi\) | ||||
0.0248497 | + | 0.999691i | \(0.492089\pi\) | |||||||
\(954\) | 19.1310 | 0.619389 | ||||||||
\(955\) | −6.94965 | −0.224885 | ||||||||
\(956\) | 4.81697 | 0.155792 | ||||||||
\(957\) | −13.3728 | −0.432281 | ||||||||
\(958\) | −29.6771 | −0.958823 | ||||||||
\(959\) | 20.7380 | 0.669664 | ||||||||
\(960\) | −2.24942 | −0.0725997 | ||||||||
\(961\) | 15.0275 | 0.484757 | ||||||||
\(962\) | 18.2182 | 0.587379 | ||||||||
\(963\) | −3.56179 | −0.114777 | ||||||||
\(964\) | 5.77599 | 0.186032 | ||||||||
\(965\) | −3.04767 | −0.0981081 | ||||||||
\(966\) | −7.45431 | −0.239838 | ||||||||
\(967\) | −12.6438 | −0.406597 | −0.203298 | − | 0.979117i | \(-0.565166\pi\) | ||||
−0.203298 | + | 0.979117i | \(0.565166\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 30.8651 | 0.991531 | ||||||||
\(970\) | −0.328464 | −0.0105464 | ||||||||
\(971\) | 22.1070 | 0.709446 | 0.354723 | − | 0.934971i | \(-0.384575\pi\) | ||||
0.354723 | + | 0.934971i | \(0.384575\pi\) | |||||||
\(972\) | −18.2568 | −0.585586 | ||||||||
\(973\) | −1.87313 | −0.0600499 | ||||||||
\(974\) | 20.7138 | 0.663713 | ||||||||
\(975\) | 10.5572 | 0.338100 | ||||||||
\(976\) | 11.9068 | 0.381128 | ||||||||
\(977\) | 6.61636 | 0.211676 | 0.105838 | − | 0.994383i | \(-0.466248\pi\) | ||||
0.105838 | + | 0.994383i | \(0.466248\pi\) | |||||||
\(978\) | 53.4390 | 1.70879 | ||||||||
\(979\) | −6.38594 | −0.204096 | ||||||||
\(980\) | 4.94272 | 0.157889 | ||||||||
\(981\) | 18.8139 | 0.600680 | ||||||||
\(982\) | 0.702895 | 0.0224303 | ||||||||
\(983\) | −45.9786 | −1.46649 | −0.733245 | − | 0.679964i | \(-0.761995\pi\) | ||||
−0.733245 | + | 0.679964i | \(0.761995\pi\) | |||||||
\(984\) | 15.7843 | 0.503185 | ||||||||
\(985\) | 12.9605 | 0.412956 | ||||||||
\(986\) | −16.0022 | −0.509615 | ||||||||
\(987\) | −2.33127 | −0.0742050 | ||||||||
\(988\) | 23.9246 | 0.761142 | ||||||||
\(989\) | 2.31042 | 0.0734669 | ||||||||
\(990\) | −2.05989 | −0.0654677 | ||||||||
\(991\) | 17.3138 | 0.549991 | 0.274995 | − | 0.961446i | \(-0.411324\pi\) | ||||
0.274995 | + | 0.961446i | \(0.411324\pi\) | |||||||
\(992\) | −6.78435 | −0.215403 | ||||||||
\(993\) | 47.1047 | 1.49482 | ||||||||
\(994\) | −17.6084 | −0.558503 | ||||||||
\(995\) | −5.53937 | −0.175610 | ||||||||
\(996\) | 10.0321 | 0.317880 | ||||||||
\(997\) | −42.1164 | −1.33384 | −0.666921 | − | 0.745129i | \(-0.732388\pi\) | ||||
−0.666921 | + | 0.745129i | \(0.732388\pi\) | |||||||
\(998\) | 7.52040 | 0.238054 | ||||||||
\(999\) | −8.20876 | −0.259714 |
(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 | 4730.2.a.bf.1.11 | ✓ | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4730.2.a.bf.1.11 | ✓ | 13 | 1.1 | even | 1 | trivial |