Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4031,2,Mod(1,4031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4031, 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("4031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4031 = 29 \cdot 139 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4031.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: | \(32.1876970548\) |
Analytic rank: | \(1\) |
Dimension: | \(59\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 4031.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.49699 | −1.76564 | −0.882819 | − | 0.469712i | \(-0.844358\pi\) | ||||
−0.882819 | + | 0.469712i | \(0.844358\pi\) | |||||||
\(3\) | −1.64487 | −0.949665 | −0.474833 | − | 0.880076i | \(-0.657491\pi\) | ||||
−0.474833 | + | 0.880076i | \(0.657491\pi\) | |||||||
\(4\) | 4.23496 | 2.11748 | ||||||||
\(5\) | 3.35969 | 1.50250 | 0.751249 | − | 0.660019i | \(-0.229452\pi\) | ||||
0.751249 | + | 0.660019i | \(0.229452\pi\) | |||||||
\(6\) | 4.10722 | 1.67677 | ||||||||
\(7\) | 2.65574 | 1.00378 | 0.501888 | − | 0.864932i | \(-0.332639\pi\) | ||||
0.501888 | + | 0.864932i | \(0.332639\pi\) | |||||||
\(8\) | −5.58068 | −1.97307 | ||||||||
\(9\) | −0.294408 | −0.0981359 | ||||||||
\(10\) | −8.38911 | −2.65287 | ||||||||
\(11\) | −1.44302 | −0.435085 | −0.217543 | − | 0.976051i | \(-0.569804\pi\) | ||||
−0.217543 | + | 0.976051i | \(0.569804\pi\) | |||||||
\(12\) | −6.96596 | −2.01090 | ||||||||
\(13\) | −1.58926 | −0.440783 | −0.220391 | − | 0.975412i | \(-0.570733\pi\) | ||||
−0.220391 | + | 0.975412i | \(0.570733\pi\) | |||||||
\(14\) | −6.63137 | −1.77231 | ||||||||
\(15\) | −5.52624 | −1.42687 | ||||||||
\(16\) | 5.46498 | 1.36624 | ||||||||
\(17\) | −2.75463 | −0.668096 | −0.334048 | − | 0.942556i | \(-0.608415\pi\) | ||||
−0.334048 | + | 0.942556i | \(0.608415\pi\) | |||||||
\(18\) | 0.735133 | 0.173273 | ||||||||
\(19\) | −1.18144 | −0.271042 | −0.135521 | − | 0.990774i | \(-0.543271\pi\) | ||||
−0.135521 | + | 0.990774i | \(0.543271\pi\) | |||||||
\(20\) | 14.2281 | 3.18151 | ||||||||
\(21\) | −4.36835 | −0.953252 | ||||||||
\(22\) | 3.60320 | 0.768204 | ||||||||
\(23\) | 1.11583 | 0.232666 | 0.116333 | − | 0.993210i | \(-0.462886\pi\) | ||||
0.116333 | + | 0.993210i | \(0.462886\pi\) | |||||||
\(24\) | 9.17948 | 1.87375 | ||||||||
\(25\) | 6.28750 | 1.25750 | ||||||||
\(26\) | 3.96838 | 0.778263 | ||||||||
\(27\) | 5.41887 | 1.04286 | ||||||||
\(28\) | 11.2470 | 2.12548 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 13.7990 | 2.51934 | ||||||||
\(31\) | −3.87621 | −0.696187 | −0.348094 | − | 0.937460i | \(-0.613171\pi\) | ||||
−0.348094 | + | 0.937460i | \(0.613171\pi\) | |||||||
\(32\) | −2.48464 | −0.439227 | ||||||||
\(33\) | 2.37357 | 0.413186 | ||||||||
\(34\) | 6.87829 | 1.17962 | ||||||||
\(35\) | 8.92247 | 1.50817 | ||||||||
\(36\) | −1.24681 | −0.207801 | ||||||||
\(37\) | −10.3550 | −1.70234 | −0.851172 | − | 0.524887i | \(-0.824108\pi\) | ||||
−0.851172 | + | 0.524887i | \(0.824108\pi\) | |||||||
\(38\) | 2.95005 | 0.478562 | ||||||||
\(39\) | 2.61413 | 0.418596 | ||||||||
\(40\) | −18.7493 | −2.96453 | ||||||||
\(41\) | 7.07077 | 1.10427 | 0.552134 | − | 0.833755i | \(-0.313814\pi\) | ||||
0.552134 | + | 0.833755i | \(0.313814\pi\) | |||||||
\(42\) | 10.9077 | 1.68310 | ||||||||
\(43\) | 11.3569 | 1.73191 | 0.865955 | − | 0.500122i | \(-0.166711\pi\) | ||||
0.865955 | + | 0.500122i | \(0.166711\pi\) | |||||||
\(44\) | −6.11111 | −0.921285 | ||||||||
\(45\) | −0.989118 | −0.147449 | ||||||||
\(46\) | −2.78621 | −0.410804 | ||||||||
\(47\) | −12.8863 | −1.87965 | −0.939827 | − | 0.341649i | \(-0.889014\pi\) | ||||
−0.939827 | + | 0.341649i | \(0.889014\pi\) | |||||||
\(48\) | −8.98917 | −1.29747 | ||||||||
\(49\) | 0.0529764 | 0.00756806 | ||||||||
\(50\) | −15.6998 | −2.22029 | ||||||||
\(51\) | 4.53101 | 0.634468 | ||||||||
\(52\) | −6.73047 | −0.933349 | ||||||||
\(53\) | 10.5507 | 1.44925 | 0.724623 | − | 0.689145i | \(-0.242014\pi\) | ||||
0.724623 | + | 0.689145i | \(0.242014\pi\) | |||||||
\(54\) | −13.5309 | −1.84132 | ||||||||
\(55\) | −4.84808 | −0.653715 | ||||||||
\(56\) | −14.8209 | −1.98052 | ||||||||
\(57\) | 1.94332 | 0.257399 | ||||||||
\(58\) | −2.49699 | −0.327871 | ||||||||
\(59\) | −1.08776 | −0.141614 | −0.0708069 | − | 0.997490i | \(-0.522557\pi\) | ||||
−0.0708069 | + | 0.997490i | \(0.522557\pi\) | |||||||
\(60\) | −23.4034 | −3.02137 | ||||||||
\(61\) | −6.20476 | −0.794438 | −0.397219 | − | 0.917724i | \(-0.630025\pi\) | ||||
−0.397219 | + | 0.917724i | \(0.630025\pi\) | |||||||
\(62\) | 9.67885 | 1.22922 | ||||||||
\(63\) | −0.781872 | −0.0985066 | ||||||||
\(64\) | −4.72583 | −0.590729 | ||||||||
\(65\) | −5.33943 | −0.662275 | ||||||||
\(66\) | −5.92678 | −0.729536 | ||||||||
\(67\) | 0.654700 | 0.0799844 | 0.0399922 | − | 0.999200i | \(-0.487267\pi\) | ||||
0.0399922 | + | 0.999200i | \(0.487267\pi\) | |||||||
\(68\) | −11.6658 | −1.41468 | ||||||||
\(69\) | −1.83539 | −0.220955 | ||||||||
\(70\) | −22.2793 | −2.66289 | ||||||||
\(71\) | 1.51803 | 0.180157 | 0.0900784 | − | 0.995935i | \(-0.471288\pi\) | ||||
0.0900784 | + | 0.995935i | \(0.471288\pi\) | |||||||
\(72\) | 1.64299 | 0.193629 | ||||||||
\(73\) | −15.9517 | −1.86700 | −0.933501 | − | 0.358575i | \(-0.883263\pi\) | ||||
−0.933501 | + | 0.358575i | \(0.883263\pi\) | |||||||
\(74\) | 25.8562 | 3.00573 | ||||||||
\(75\) | −10.3421 | −1.19420 | ||||||||
\(76\) | −5.00337 | −0.573926 | ||||||||
\(77\) | −3.83228 | −0.436729 | ||||||||
\(78\) | −6.52746 | −0.739089 | ||||||||
\(79\) | −4.67693 | −0.526195 | −0.263098 | − | 0.964769i | \(-0.584744\pi\) | ||||
−0.263098 | + | 0.964769i | \(0.584744\pi\) | |||||||
\(80\) | 18.3606 | 2.05278 | ||||||||
\(81\) | −8.03010 | −0.892233 | ||||||||
\(82\) | −17.6556 | −1.94974 | ||||||||
\(83\) | −8.32610 | −0.913908 | −0.456954 | − | 0.889490i | \(-0.651060\pi\) | ||||
−0.456954 | + | 0.889490i | \(0.651060\pi\) | |||||||
\(84\) | −18.4998 | −2.01849 | ||||||||
\(85\) | −9.25470 | −1.00381 | ||||||||
\(86\) | −28.3581 | −3.05793 | ||||||||
\(87\) | −1.64487 | −0.176348 | ||||||||
\(88\) | 8.05300 | 0.858453 | ||||||||
\(89\) | 6.66528 | 0.706518 | 0.353259 | − | 0.935526i | \(-0.385073\pi\) | ||||
0.353259 | + | 0.935526i | \(0.385073\pi\) | |||||||
\(90\) | 2.46982 | 0.260342 | ||||||||
\(91\) | −4.22068 | −0.442447 | ||||||||
\(92\) | 4.72548 | 0.492665 | ||||||||
\(93\) | 6.37585 | 0.661145 | ||||||||
\(94\) | 32.1769 | 3.31879 | ||||||||
\(95\) | −3.96928 | −0.407240 | ||||||||
\(96\) | 4.08691 | 0.417118 | ||||||||
\(97\) | 10.6505 | 1.08139 | 0.540696 | − | 0.841218i | \(-0.318161\pi\) | ||||
0.540696 | + | 0.841218i | \(0.318161\pi\) | |||||||
\(98\) | −0.132282 | −0.0133625 | ||||||||
\(99\) | 0.424835 | 0.0426975 | ||||||||
\(100\) | 26.6273 | 2.66273 | ||||||||
\(101\) | −8.52962 | −0.848729 | −0.424365 | − | 0.905491i | \(-0.639503\pi\) | ||||
−0.424365 | + | 0.905491i | \(0.639503\pi\) | |||||||
\(102\) | −11.3139 | −1.12024 | ||||||||
\(103\) | 5.68028 | 0.559694 | 0.279847 | − | 0.960045i | \(-0.409716\pi\) | ||||
0.279847 | + | 0.960045i | \(0.409716\pi\) | |||||||
\(104\) | 8.86917 | 0.869694 | ||||||||
\(105\) | −14.6763 | −1.43226 | ||||||||
\(106\) | −26.3449 | −2.55885 | ||||||||
\(107\) | −17.1341 | −1.65642 | −0.828208 | − | 0.560421i | \(-0.810639\pi\) | ||||
−0.828208 | + | 0.560421i | \(0.810639\pi\) | |||||||
\(108\) | 22.9487 | 2.20824 | ||||||||
\(109\) | −6.77580 | −0.649004 | −0.324502 | − | 0.945885i | \(-0.605197\pi\) | ||||
−0.324502 | + | 0.945885i | \(0.605197\pi\) | |||||||
\(110\) | 12.1056 | 1.15422 | ||||||||
\(111\) | 17.0325 | 1.61666 | ||||||||
\(112\) | 14.5136 | 1.37140 | ||||||||
\(113\) | 8.89649 | 0.836911 | 0.418456 | − | 0.908237i | \(-0.362572\pi\) | ||||
0.418456 | + | 0.908237i | \(0.362572\pi\) | |||||||
\(114\) | −4.85245 | −0.454474 | ||||||||
\(115\) | 3.74883 | 0.349580 | ||||||||
\(116\) | 4.23496 | 0.393206 | ||||||||
\(117\) | 0.467892 | 0.0432566 | ||||||||
\(118\) | 2.71612 | 0.250039 | ||||||||
\(119\) | −7.31560 | −0.670620 | ||||||||
\(120\) | 30.8402 | 2.81531 | ||||||||
\(121\) | −8.91771 | −0.810701 | ||||||||
\(122\) | 15.4932 | 1.40269 | ||||||||
\(123\) | −11.6305 | −1.04868 | ||||||||
\(124\) | −16.4156 | −1.47416 | ||||||||
\(125\) | 4.32561 | 0.386894 | ||||||||
\(126\) | 1.95233 | 0.173927 | ||||||||
\(127\) | −12.2028 | −1.08283 | −0.541413 | − | 0.840757i | \(-0.682111\pi\) | ||||
−0.541413 | + | 0.840757i | \(0.682111\pi\) | |||||||
\(128\) | 16.7696 | 1.48224 | ||||||||
\(129\) | −18.6806 | −1.64473 | ||||||||
\(130\) | 13.3325 | 1.16934 | ||||||||
\(131\) | 1.65229 | 0.144361 | 0.0721804 | − | 0.997392i | \(-0.477004\pi\) | ||||
0.0721804 | + | 0.997392i | \(0.477004\pi\) | |||||||
\(132\) | 10.0520 | 0.874912 | ||||||||
\(133\) | −3.13761 | −0.272065 | ||||||||
\(134\) | −1.63478 | −0.141224 | ||||||||
\(135\) | 18.2057 | 1.56690 | ||||||||
\(136\) | 15.3727 | 1.31820 | ||||||||
\(137\) | 10.0485 | 0.858503 | 0.429251 | − | 0.903185i | \(-0.358777\pi\) | ||||
0.429251 | + | 0.903185i | \(0.358777\pi\) | |||||||
\(138\) | 4.58294 | 0.390126 | ||||||||
\(139\) | 1.00000 | 0.0848189 | ||||||||
\(140\) | 37.7863 | 3.19353 | ||||||||
\(141\) | 21.1962 | 1.78504 | ||||||||
\(142\) | −3.79050 | −0.318092 | ||||||||
\(143\) | 2.29333 | 0.191778 | ||||||||
\(144\) | −1.60893 | −0.134078 | ||||||||
\(145\) | 3.35969 | 0.279007 | ||||||||
\(146\) | 39.8312 | 3.29645 | ||||||||
\(147\) | −0.0871393 | −0.00718712 | ||||||||
\(148\) | −43.8528 | −3.60468 | ||||||||
\(149\) | 6.18242 | 0.506483 | 0.253242 | − | 0.967403i | \(-0.418503\pi\) | ||||
0.253242 | + | 0.967403i | \(0.418503\pi\) | |||||||
\(150\) | 25.8242 | 2.10853 | ||||||||
\(151\) | −4.03288 | −0.328191 | −0.164096 | − | 0.986444i | \(-0.552471\pi\) | ||||
−0.164096 | + | 0.986444i | \(0.552471\pi\) | |||||||
\(152\) | 6.59326 | 0.534784 | ||||||||
\(153\) | 0.810985 | 0.0655642 | ||||||||
\(154\) | 9.56916 | 0.771105 | ||||||||
\(155\) | −13.0228 | −1.04602 | ||||||||
\(156\) | 11.0707 | 0.886369 | ||||||||
\(157\) | 9.95214 | 0.794268 | 0.397134 | − | 0.917761i | \(-0.370005\pi\) | ||||
0.397134 | + | 0.917761i | \(0.370005\pi\) | |||||||
\(158\) | 11.6782 | 0.929071 | ||||||||
\(159\) | −17.3545 | −1.37630 | ||||||||
\(160\) | −8.34762 | −0.659937 | ||||||||
\(161\) | 2.96335 | 0.233545 | ||||||||
\(162\) | 20.0511 | 1.57536 | ||||||||
\(163\) | −14.2973 | −1.11985 | −0.559924 | − | 0.828544i | \(-0.689170\pi\) | ||||
−0.559924 | + | 0.828544i | \(0.689170\pi\) | |||||||
\(164\) | 29.9444 | 2.33827 | ||||||||
\(165\) | 7.97445 | 0.620810 | ||||||||
\(166\) | 20.7902 | 1.61363 | ||||||||
\(167\) | 16.9733 | 1.31343 | 0.656716 | − | 0.754138i | \(-0.271945\pi\) | ||||
0.656716 | + | 0.754138i | \(0.271945\pi\) | |||||||
\(168\) | 24.3784 | 1.88083 | ||||||||
\(169\) | −10.4742 | −0.805711 | ||||||||
\(170\) | 23.1089 | 1.77237 | ||||||||
\(171\) | 0.347826 | 0.0265989 | ||||||||
\(172\) | 48.0960 | 3.66729 | ||||||||
\(173\) | −7.31591 | −0.556218 | −0.278109 | − | 0.960549i | \(-0.589708\pi\) | ||||
−0.278109 | + | 0.960549i | \(0.589708\pi\) | |||||||
\(174\) | 4.10722 | 0.311368 | ||||||||
\(175\) | 16.6980 | 1.26225 | ||||||||
\(176\) | −7.88605 | −0.594433 | ||||||||
\(177\) | 1.78922 | 0.134486 | ||||||||
\(178\) | −16.6431 | −1.24746 | ||||||||
\(179\) | 20.9837 | 1.56840 | 0.784199 | − | 0.620509i | \(-0.213074\pi\) | ||||
0.784199 | + | 0.620509i | \(0.213074\pi\) | |||||||
\(180\) | −4.18888 | −0.312220 | ||||||||
\(181\) | −11.4341 | −0.849890 | −0.424945 | − | 0.905219i | \(-0.639707\pi\) | ||||
−0.424945 | + | 0.905219i | \(0.639707\pi\) | |||||||
\(182\) | 10.5390 | 0.781202 | ||||||||
\(183\) | 10.2060 | 0.754450 | ||||||||
\(184\) | −6.22706 | −0.459065 | ||||||||
\(185\) | −34.7894 | −2.55777 | ||||||||
\(186\) | −15.9204 | −1.16734 | ||||||||
\(187\) | 3.97498 | 0.290679 | ||||||||
\(188\) | −54.5728 | −3.98013 | ||||||||
\(189\) | 14.3911 | 1.04680 | ||||||||
\(190\) | 9.91126 | 0.719038 | ||||||||
\(191\) | −27.3743 | −1.98073 | −0.990366 | − | 0.138472i | \(-0.955781\pi\) | ||||
−0.990366 | + | 0.138472i | \(0.955781\pi\) | |||||||
\(192\) | 7.77337 | 0.560995 | ||||||||
\(193\) | 20.9509 | 1.50808 | 0.754038 | − | 0.656830i | \(-0.228103\pi\) | ||||
0.754038 | + | 0.656830i | \(0.228103\pi\) | |||||||
\(194\) | −26.5941 | −1.90935 | ||||||||
\(195\) | 8.78266 | 0.628939 | ||||||||
\(196\) | 0.224353 | 0.0160252 | ||||||||
\(197\) | −12.9317 | −0.921342 | −0.460671 | − | 0.887571i | \(-0.652391\pi\) | ||||
−0.460671 | + | 0.887571i | \(0.652391\pi\) | |||||||
\(198\) | −1.06081 | −0.0753884 | ||||||||
\(199\) | 7.24092 | 0.513295 | 0.256647 | − | 0.966505i | \(-0.417382\pi\) | ||||
0.256647 | + | 0.966505i | \(0.417382\pi\) | |||||||
\(200\) | −35.0885 | −2.48113 | ||||||||
\(201\) | −1.07690 | −0.0759584 | ||||||||
\(202\) | 21.2984 | 1.49855 | ||||||||
\(203\) | 2.65574 | 0.186397 | ||||||||
\(204\) | 19.1886 | 1.34347 | ||||||||
\(205\) | 23.7556 | 1.65916 | ||||||||
\(206\) | −14.1836 | −0.988218 | ||||||||
\(207\) | −0.328508 | −0.0228329 | ||||||||
\(208\) | −8.68529 | −0.602217 | ||||||||
\(209\) | 1.70484 | 0.117926 | ||||||||
\(210\) | 36.6466 | 2.52885 | ||||||||
\(211\) | −20.9654 | −1.44331 | −0.721657 | − | 0.692251i | \(-0.756619\pi\) | ||||
−0.721657 | + | 0.692251i | \(0.756619\pi\) | |||||||
\(212\) | 44.6817 | 3.06875 | ||||||||
\(213\) | −2.49696 | −0.171089 | ||||||||
\(214\) | 42.7837 | 2.92463 | ||||||||
\(215\) | 38.1556 | 2.60219 | ||||||||
\(216\) | −30.2410 | −2.05764 | ||||||||
\(217\) | −10.2942 | −0.698817 | ||||||||
\(218\) | 16.9191 | 1.14591 | ||||||||
\(219\) | 26.2384 | 1.77303 | ||||||||
\(220\) | −20.5314 | −1.38423 | ||||||||
\(221\) | 4.37784 | 0.294485 | ||||||||
\(222\) | −42.5301 | −2.85443 | ||||||||
\(223\) | 2.39949 | 0.160682 | 0.0803408 | − | 0.996767i | \(-0.474399\pi\) | ||||
0.0803408 | + | 0.996767i | \(0.474399\pi\) | |||||||
\(224\) | −6.59857 | −0.440886 | ||||||||
\(225\) | −1.85109 | −0.123406 | ||||||||
\(226\) | −22.2145 | −1.47768 | ||||||||
\(227\) | 18.2496 | 1.21127 | 0.605633 | − | 0.795744i | \(-0.292920\pi\) | ||||
0.605633 | + | 0.795744i | \(0.292920\pi\) | |||||||
\(228\) | 8.22988 | 0.545037 | ||||||||
\(229\) | −25.3716 | −1.67661 | −0.838303 | − | 0.545205i | \(-0.816452\pi\) | ||||
−0.838303 | + | 0.545205i | \(0.816452\pi\) | |||||||
\(230\) | −9.36078 | −0.617232 | ||||||||
\(231\) | 6.30359 | 0.414746 | ||||||||
\(232\) | −5.58068 | −0.366389 | ||||||||
\(233\) | −18.4927 | −1.21150 | −0.605749 | − | 0.795655i | \(-0.707127\pi\) | ||||
−0.605749 | + | 0.795655i | \(0.707127\pi\) | |||||||
\(234\) | −1.16832 | −0.0763755 | ||||||||
\(235\) | −43.2938 | −2.82418 | ||||||||
\(236\) | −4.60661 | −0.299865 | ||||||||
\(237\) | 7.69293 | 0.499710 | ||||||||
\(238\) | 18.2670 | 1.18407 | ||||||||
\(239\) | 15.4825 | 1.00148 | 0.500741 | − | 0.865597i | \(-0.333061\pi\) | ||||
0.500741 | + | 0.865597i | \(0.333061\pi\) | |||||||
\(240\) | −30.2008 | −1.94945 | ||||||||
\(241\) | −21.3856 | −1.37757 | −0.688785 | − | 0.724965i | \(-0.741856\pi\) | ||||
−0.688785 | + | 0.724965i | \(0.741856\pi\) | |||||||
\(242\) | 22.2674 | 1.43140 | ||||||||
\(243\) | −3.04814 | −0.195538 | ||||||||
\(244\) | −26.2769 | −1.68221 | ||||||||
\(245\) | 0.177984 | 0.0113710 | ||||||||
\(246\) | 29.0412 | 1.85160 | ||||||||
\(247\) | 1.87763 | 0.119470 | ||||||||
\(248\) | 21.6319 | 1.37362 | ||||||||
\(249\) | 13.6953 | 0.867907 | ||||||||
\(250\) | −10.8010 | −0.683115 | ||||||||
\(251\) | −9.77403 | −0.616931 | −0.308466 | − | 0.951235i | \(-0.599816\pi\) | ||||
−0.308466 | + | 0.951235i | \(0.599816\pi\) | |||||||
\(252\) | −3.31120 | −0.208586 | ||||||||
\(253\) | −1.61015 | −0.101229 | ||||||||
\(254\) | 30.4704 | 1.91188 | ||||||||
\(255\) | 15.2228 | 0.953287 | ||||||||
\(256\) | −32.4220 | −2.02637 | ||||||||
\(257\) | −10.6832 | −0.666402 | −0.333201 | − | 0.942856i | \(-0.608129\pi\) | ||||
−0.333201 | + | 0.942856i | \(0.608129\pi\) | |||||||
\(258\) | 46.6453 | 2.90401 | ||||||||
\(259\) | −27.5001 | −1.70877 | ||||||||
\(260\) | −22.6123 | −1.40235 | ||||||||
\(261\) | −0.294408 | −0.0182234 | ||||||||
\(262\) | −4.12574 | −0.254889 | ||||||||
\(263\) | 25.2549 | 1.55728 | 0.778642 | − | 0.627469i | \(-0.215909\pi\) | ||||
0.778642 | + | 0.627469i | \(0.215909\pi\) | |||||||
\(264\) | −13.2461 | −0.815243 | ||||||||
\(265\) | 35.4470 | 2.17749 | ||||||||
\(266\) | 7.83459 | 0.480369 | ||||||||
\(267\) | −10.9635 | −0.670956 | ||||||||
\(268\) | 2.77263 | 0.169365 | ||||||||
\(269\) | −24.5680 | −1.49794 | −0.748969 | − | 0.662605i | \(-0.769451\pi\) | ||||
−0.748969 | + | 0.662605i | \(0.769451\pi\) | |||||||
\(270\) | −45.4595 | −2.76658 | ||||||||
\(271\) | 7.38985 | 0.448902 | 0.224451 | − | 0.974485i | \(-0.427941\pi\) | ||||
0.224451 | + | 0.974485i | \(0.427941\pi\) | |||||||
\(272\) | −15.0540 | −0.912783 | ||||||||
\(273\) | 6.94246 | 0.420177 | ||||||||
\(274\) | −25.0911 | −1.51581 | ||||||||
\(275\) | −9.07296 | −0.547120 | ||||||||
\(276\) | −7.77279 | −0.467867 | ||||||||
\(277\) | −2.42883 | −0.145934 | −0.0729671 | − | 0.997334i | \(-0.523247\pi\) | ||||
−0.0729671 | + | 0.997334i | \(0.523247\pi\) | |||||||
\(278\) | −2.49699 | −0.149760 | ||||||||
\(279\) | 1.14119 | 0.0683210 | ||||||||
\(280\) | −49.7934 | −2.97573 | ||||||||
\(281\) | −18.8033 | −1.12171 | −0.560856 | − | 0.827913i | \(-0.689528\pi\) | ||||
−0.560856 | + | 0.827913i | \(0.689528\pi\) | |||||||
\(282\) | −52.9267 | −3.15174 | ||||||||
\(283\) | 24.9836 | 1.48512 | 0.742559 | − | 0.669780i | \(-0.233612\pi\) | ||||
0.742559 | + | 0.669780i | \(0.233612\pi\) | |||||||
\(284\) | 6.42879 | 0.381479 | ||||||||
\(285\) | 6.52895 | 0.386741 | ||||||||
\(286\) | −5.72643 | −0.338611 | ||||||||
\(287\) | 18.7781 | 1.10844 | ||||||||
\(288\) | 0.731498 | 0.0431039 | ||||||||
\(289\) | −9.41201 | −0.553647 | ||||||||
\(290\) | −8.38911 | −0.492625 | ||||||||
\(291\) | −17.5186 | −1.02696 | ||||||||
\(292\) | −67.5547 | −3.95334 | ||||||||
\(293\) | −6.76619 | −0.395285 | −0.197643 | − | 0.980274i | \(-0.563329\pi\) | ||||
−0.197643 | + | 0.980274i | \(0.563329\pi\) | |||||||
\(294\) | 0.217586 | 0.0126899 | ||||||||
\(295\) | −3.65452 | −0.212775 | ||||||||
\(296\) | 57.7877 | 3.35884 | ||||||||
\(297\) | −7.81951 | −0.453734 | ||||||||
\(298\) | −15.4374 | −0.894267 | ||||||||
\(299\) | −1.77334 | −0.102555 | ||||||||
\(300\) | −43.7985 | −2.52871 | ||||||||
\(301\) | 30.1610 | 1.73845 | ||||||||
\(302\) | 10.0701 | 0.579467 | ||||||||
\(303\) | 14.0301 | 0.806009 | ||||||||
\(304\) | −6.45656 | −0.370309 | ||||||||
\(305\) | −20.8461 | −1.19364 | ||||||||
\(306\) | −2.02502 | −0.115763 | ||||||||
\(307\) | −5.40587 | −0.308529 | −0.154265 | − | 0.988030i | \(-0.549301\pi\) | ||||
−0.154265 | + | 0.988030i | \(0.549301\pi\) | |||||||
\(308\) | −16.2296 | −0.924765 | ||||||||
\(309\) | −9.34331 | −0.531522 | ||||||||
\(310\) | 32.5179 | 1.84689 | ||||||||
\(311\) | 16.1425 | 0.915359 | 0.457680 | − | 0.889117i | \(-0.348681\pi\) | ||||
0.457680 | + | 0.889117i | \(0.348681\pi\) | |||||||
\(312\) | −14.5886 | −0.825918 | ||||||||
\(313\) | −6.76520 | −0.382392 | −0.191196 | − | 0.981552i | \(-0.561237\pi\) | ||||
−0.191196 | + | 0.981552i | \(0.561237\pi\) | |||||||
\(314\) | −24.8504 | −1.40239 | ||||||||
\(315\) | −2.62684 | −0.148006 | ||||||||
\(316\) | −19.8066 | −1.11421 | ||||||||
\(317\) | 22.2330 | 1.24873 | 0.624365 | − | 0.781133i | \(-0.285358\pi\) | ||||
0.624365 | + | 0.781133i | \(0.285358\pi\) | |||||||
\(318\) | 43.3340 | 2.43005 | ||||||||
\(319\) | −1.44302 | −0.0807933 | ||||||||
\(320\) | −15.8773 | −0.887569 | ||||||||
\(321\) | 28.1833 | 1.57304 | ||||||||
\(322\) | −7.39945 | −0.412355 | ||||||||
\(323\) | 3.25444 | 0.181082 | ||||||||
\(324\) | −34.0072 | −1.88929 | ||||||||
\(325\) | −9.99250 | −0.554284 | ||||||||
\(326\) | 35.7001 | 1.97725 | ||||||||
\(327\) | 11.1453 | 0.616337 | ||||||||
\(328\) | −39.4597 | −2.17880 | ||||||||
\(329\) | −34.2226 | −1.88675 | ||||||||
\(330\) | −19.9121 | −1.09613 | ||||||||
\(331\) | 12.6863 | 0.697299 | 0.348650 | − | 0.937253i | \(-0.386640\pi\) | ||||
0.348650 | + | 0.937253i | \(0.386640\pi\) | |||||||
\(332\) | −35.2607 | −1.93518 | ||||||||
\(333\) | 3.04858 | 0.167061 | ||||||||
\(334\) | −42.3821 | −2.31905 | ||||||||
\(335\) | 2.19959 | 0.120176 | ||||||||
\(336\) | −23.8729 | −1.30238 | ||||||||
\(337\) | 22.3956 | 1.21997 | 0.609984 | − | 0.792414i | \(-0.291176\pi\) | ||||
0.609984 | + | 0.792414i | \(0.291176\pi\) | |||||||
\(338\) | 26.1541 | 1.42259 | ||||||||
\(339\) | −14.6336 | −0.794786 | ||||||||
\(340\) | −39.1933 | −2.12556 | ||||||||
\(341\) | 5.59342 | 0.302901 | ||||||||
\(342\) | −0.868519 | −0.0469641 | ||||||||
\(343\) | −18.4495 | −0.996180 | ||||||||
\(344\) | −63.3792 | −3.41718 | ||||||||
\(345\) | −6.16633 | −0.331984 | ||||||||
\(346\) | 18.2678 | 0.982080 | ||||||||
\(347\) | −14.0204 | −0.752654 | −0.376327 | − | 0.926487i | \(-0.622813\pi\) | ||||
−0.376327 | + | 0.926487i | \(0.622813\pi\) | |||||||
\(348\) | −6.96596 | −0.373414 | ||||||||
\(349\) | −0.480731 | −0.0257329 | −0.0128665 | − | 0.999917i | \(-0.504096\pi\) | ||||
−0.0128665 | + | 0.999917i | \(0.504096\pi\) | |||||||
\(350\) | −41.6947 | −2.22868 | ||||||||
\(351\) | −8.61201 | −0.459675 | ||||||||
\(352\) | 3.58537 | 0.191101 | ||||||||
\(353\) | 23.1003 | 1.22951 | 0.614753 | − | 0.788720i | \(-0.289256\pi\) | ||||
0.614753 | + | 0.788720i | \(0.289256\pi\) | |||||||
\(354\) | −4.46766 | −0.237453 | ||||||||
\(355\) | 5.10010 | 0.270685 | ||||||||
\(356\) | 28.2272 | 1.49604 | ||||||||
\(357\) | 12.0332 | 0.636864 | ||||||||
\(358\) | −52.3962 | −2.76922 | ||||||||
\(359\) | 8.93834 | 0.471748 | 0.235874 | − | 0.971784i | \(-0.424205\pi\) | ||||
0.235874 | + | 0.971784i | \(0.424205\pi\) | |||||||
\(360\) | 5.51995 | 0.290927 | ||||||||
\(361\) | −17.6042 | −0.926536 | ||||||||
\(362\) | 28.5508 | 1.50060 | ||||||||
\(363\) | 14.6685 | 0.769894 | ||||||||
\(364\) | −17.8744 | −0.936874 | ||||||||
\(365\) | −53.5926 | −2.80517 | ||||||||
\(366\) | −25.4843 | −1.33209 | ||||||||
\(367\) | −0.224077 | −0.0116967 | −0.00584836 | − | 0.999983i | \(-0.501862\pi\) | ||||
−0.00584836 | + | 0.999983i | \(0.501862\pi\) | |||||||
\(368\) | 6.09796 | 0.317878 | ||||||||
\(369\) | −2.08169 | −0.108368 | ||||||||
\(370\) | 86.8688 | 4.51610 | ||||||||
\(371\) | 28.0199 | 1.45472 | ||||||||
\(372\) | 27.0015 | 1.39996 | ||||||||
\(373\) | −3.45908 | −0.179105 | −0.0895523 | − | 0.995982i | \(-0.528544\pi\) | ||||
−0.0895523 | + | 0.995982i | \(0.528544\pi\) | |||||||
\(374\) | −9.92548 | −0.513234 | ||||||||
\(375\) | −7.11505 | −0.367420 | ||||||||
\(376\) | 71.9141 | 3.70869 | ||||||||
\(377\) | −1.58926 | −0.0818513 | ||||||||
\(378\) | −35.9345 | −1.84827 | ||||||||
\(379\) | −14.0565 | −0.722035 | −0.361018 | − | 0.932559i | \(-0.617571\pi\) | ||||
−0.361018 | + | 0.932559i | \(0.617571\pi\) | |||||||
\(380\) | −16.8098 | −0.862322 | ||||||||
\(381\) | 20.0721 | 1.02832 | ||||||||
\(382\) | 68.3533 | 3.49726 | ||||||||
\(383\) | 15.2901 | 0.781285 | 0.390643 | − | 0.920542i | \(-0.372253\pi\) | ||||
0.390643 | + | 0.920542i | \(0.372253\pi\) | |||||||
\(384\) | −27.5838 | −1.40763 | ||||||||
\(385\) | −12.8753 | −0.656184 | ||||||||
\(386\) | −52.3141 | −2.66272 | ||||||||
\(387\) | −3.34356 | −0.169963 | ||||||||
\(388\) | 45.1043 | 2.28983 | ||||||||
\(389\) | −26.2883 | −1.33287 | −0.666436 | − | 0.745563i | \(-0.732181\pi\) | ||||
−0.666436 | + | 0.745563i | \(0.732181\pi\) | |||||||
\(390\) | −21.9302 | −1.11048 | ||||||||
\(391\) | −3.07369 | −0.155443 | ||||||||
\(392\) | −0.295644 | −0.0149323 | ||||||||
\(393\) | −2.71779 | −0.137094 | ||||||||
\(394\) | 32.2902 | 1.62676 | ||||||||
\(395\) | −15.7130 | −0.790608 | ||||||||
\(396\) | 1.79916 | 0.0904112 | ||||||||
\(397\) | 5.62692 | 0.282407 | 0.141203 | − | 0.989981i | \(-0.454903\pi\) | ||||
0.141203 | + | 0.989981i | \(0.454903\pi\) | |||||||
\(398\) | −18.0805 | −0.906293 | ||||||||
\(399\) | 5.16096 | 0.258371 | ||||||||
\(400\) | 34.3611 | 1.71805 | ||||||||
\(401\) | −27.8936 | −1.39294 | −0.696470 | − | 0.717586i | \(-0.745247\pi\) | ||||
−0.696470 | + | 0.717586i | \(0.745247\pi\) | |||||||
\(402\) | 2.68900 | 0.134115 | ||||||||
\(403\) | 6.16031 | 0.306867 | ||||||||
\(404\) | −36.1226 | −1.79717 | ||||||||
\(405\) | −26.9786 | −1.34058 | ||||||||
\(406\) | −6.63137 | −0.329109 | ||||||||
\(407\) | 14.9424 | 0.740665 | ||||||||
\(408\) | −25.2861 | −1.25185 | ||||||||
\(409\) | 4.43537 | 0.219315 | 0.109657 | − | 0.993969i | \(-0.465025\pi\) | ||||
0.109657 | + | 0.993969i | \(0.465025\pi\) | |||||||
\(410\) | −59.3174 | −2.92948 | ||||||||
\(411\) | −16.5285 | −0.815290 | ||||||||
\(412\) | 24.0558 | 1.18514 | ||||||||
\(413\) | −2.88880 | −0.142149 | ||||||||
\(414\) | 0.820281 | 0.0403146 | ||||||||
\(415\) | −27.9731 | −1.37315 | ||||||||
\(416\) | 3.94875 | 0.193603 | ||||||||
\(417\) | −1.64487 | −0.0805496 | ||||||||
\(418\) | −4.25697 | −0.208215 | ||||||||
\(419\) | −12.8489 | −0.627712 | −0.313856 | − | 0.949471i | \(-0.601621\pi\) | ||||
−0.313856 | + | 0.949471i | \(0.601621\pi\) | |||||||
\(420\) | −62.1535 | −3.03278 | ||||||||
\(421\) | −6.89588 | −0.336085 | −0.168042 | − | 0.985780i | \(-0.553745\pi\) | ||||
−0.168042 | + | 0.985780i | \(0.553745\pi\) | |||||||
\(422\) | 52.3503 | 2.54837 | ||||||||
\(423\) | 3.79382 | 0.184462 | ||||||||
\(424\) | −58.8799 | −2.85946 | ||||||||
\(425\) | −17.3198 | −0.840131 | ||||||||
\(426\) | 6.23488 | 0.302081 | ||||||||
\(427\) | −16.4783 | −0.797439 | ||||||||
\(428\) | −72.5622 | −3.50743 | ||||||||
\(429\) | −3.77223 | −0.182125 | ||||||||
\(430\) | −95.2742 | −4.59453 | ||||||||
\(431\) | −21.3752 | −1.02961 | −0.514803 | − | 0.857308i | \(-0.672135\pi\) | ||||
−0.514803 | + | 0.857308i | \(0.672135\pi\) | |||||||
\(432\) | 29.6140 | 1.42480 | ||||||||
\(433\) | −31.3707 | −1.50758 | −0.753791 | − | 0.657115i | \(-0.771777\pi\) | ||||
−0.753791 | + | 0.657115i | \(0.771777\pi\) | |||||||
\(434\) | 25.7045 | 1.23386 | ||||||||
\(435\) | −5.52624 | −0.264963 | ||||||||
\(436\) | −28.6953 | −1.37425 | ||||||||
\(437\) | −1.31829 | −0.0630621 | ||||||||
\(438\) | −65.5170 | −3.13053 | ||||||||
\(439\) | 18.8567 | 0.899982 | 0.449991 | − | 0.893033i | \(-0.351427\pi\) | ||||
0.449991 | + | 0.893033i | \(0.351427\pi\) | |||||||
\(440\) | 27.0556 | 1.28982 | ||||||||
\(441\) | −0.0155967 | −0.000742699 0 | ||||||||
\(442\) | −10.9314 | −0.519954 | ||||||||
\(443\) | 10.9523 | 0.520362 | 0.260181 | − | 0.965560i | \(-0.416218\pi\) | ||||
0.260181 | + | 0.965560i | \(0.416218\pi\) | |||||||
\(444\) | 72.1322 | 3.42324 | ||||||||
\(445\) | 22.3933 | 1.06154 | ||||||||
\(446\) | −5.99150 | −0.283706 | ||||||||
\(447\) | −10.1693 | −0.480990 | ||||||||
\(448\) | −12.5506 | −0.592960 | ||||||||
\(449\) | −20.3161 | −0.958778 | −0.479389 | − | 0.877603i | \(-0.659142\pi\) | ||||
−0.479389 | + | 0.877603i | \(0.659142\pi\) | |||||||
\(450\) | 4.62215 | 0.217890 | ||||||||
\(451\) | −10.2032 | −0.480451 | ||||||||
\(452\) | 37.6763 | 1.77214 | ||||||||
\(453\) | 6.63356 | 0.311672 | ||||||||
\(454\) | −45.5690 | −2.13866 | ||||||||
\(455\) | −14.1802 | −0.664776 | ||||||||
\(456\) | −10.8450 | −0.507866 | ||||||||
\(457\) | −26.6303 | −1.24571 | −0.622857 | − | 0.782336i | \(-0.714028\pi\) | ||||
−0.622857 | + | 0.782336i | \(0.714028\pi\) | |||||||
\(458\) | 63.3527 | 2.96028 | ||||||||
\(459\) | −14.9270 | −0.696732 | ||||||||
\(460\) | 15.8761 | 0.740229 | ||||||||
\(461\) | 22.3445 | 1.04069 | 0.520343 | − | 0.853958i | \(-0.325804\pi\) | ||||
0.520343 | + | 0.853958i | \(0.325804\pi\) | |||||||
\(462\) | −15.7400 | −0.732292 | ||||||||
\(463\) | −6.37362 | −0.296207 | −0.148104 | − | 0.988972i | \(-0.547317\pi\) | ||||
−0.148104 | + | 0.988972i | \(0.547317\pi\) | |||||||
\(464\) | 5.46498 | 0.253705 | ||||||||
\(465\) | 21.4209 | 0.993369 | ||||||||
\(466\) | 46.1762 | 2.13907 | ||||||||
\(467\) | 22.7290 | 1.05177 | 0.525885 | − | 0.850556i | \(-0.323734\pi\) | ||||
0.525885 | + | 0.850556i | \(0.323734\pi\) | |||||||
\(468\) | 1.98150 | 0.0915950 | ||||||||
\(469\) | 1.73872 | 0.0802865 | ||||||||
\(470\) | 108.104 | 4.98648 | ||||||||
\(471\) | −16.3700 | −0.754288 | ||||||||
\(472\) | 6.07042 | 0.279414 | ||||||||
\(473\) | −16.3882 | −0.753529 | ||||||||
\(474\) | −19.2092 | −0.882307 | ||||||||
\(475\) | −7.42833 | −0.340835 | ||||||||
\(476\) | −30.9813 | −1.42002 | ||||||||
\(477\) | −3.10620 | −0.142223 | ||||||||
\(478\) | −38.6597 | −1.76825 | ||||||||
\(479\) | −3.31497 | −0.151465 | −0.0757323 | − | 0.997128i | \(-0.524129\pi\) | ||||
−0.0757323 | + | 0.997128i | \(0.524129\pi\) | |||||||
\(480\) | 13.7307 | 0.626719 | ||||||||
\(481\) | 16.4568 | 0.750364 | ||||||||
\(482\) | 53.3998 | 2.43229 | ||||||||
\(483\) | −4.87432 | −0.221789 | ||||||||
\(484\) | −37.7661 | −1.71664 | ||||||||
\(485\) | 35.7822 | 1.62479 | ||||||||
\(486\) | 7.61118 | 0.345250 | ||||||||
\(487\) | 32.1780 | 1.45812 | 0.729062 | − | 0.684448i | \(-0.239957\pi\) | ||||
0.729062 | + | 0.684448i | \(0.239957\pi\) | |||||||
\(488\) | 34.6268 | 1.56748 | ||||||||
\(489\) | 23.5171 | 1.06348 | ||||||||
\(490\) | −0.444425 | −0.0200771 | ||||||||
\(491\) | 1.71274 | 0.0772949 | 0.0386474 | − | 0.999253i | \(-0.487695\pi\) | ||||
0.0386474 | + | 0.999253i | \(0.487695\pi\) | |||||||
\(492\) | −49.2546 | −2.22057 | ||||||||
\(493\) | −2.75463 | −0.124062 | ||||||||
\(494\) | −4.68841 | −0.210942 | ||||||||
\(495\) | 1.42731 | 0.0641529 | ||||||||
\(496\) | −21.1834 | −0.951162 | ||||||||
\(497\) | 4.03150 | 0.180837 | ||||||||
\(498\) | −34.1971 | −1.53241 | ||||||||
\(499\) | 1.56043 | 0.0698546 | 0.0349273 | − | 0.999390i | \(-0.488880\pi\) | ||||
0.0349273 | + | 0.999390i | \(0.488880\pi\) | |||||||
\(500\) | 18.3188 | 0.819240 | ||||||||
\(501\) | −27.9188 | −1.24732 | ||||||||
\(502\) | 24.4057 | 1.08928 | ||||||||
\(503\) | −4.72499 | −0.210677 | −0.105338 | − | 0.994436i | \(-0.533593\pi\) | ||||
−0.105338 | + | 0.994436i | \(0.533593\pi\) | |||||||
\(504\) | 4.36337 | 0.194360 | ||||||||
\(505\) | −28.6569 | −1.27521 | ||||||||
\(506\) | 4.02054 | 0.178735 | ||||||||
\(507\) | 17.2287 | 0.765156 | ||||||||
\(508\) | −51.6785 | −2.29286 | ||||||||
\(509\) | −5.24997 | −0.232701 | −0.116350 | − | 0.993208i | \(-0.537120\pi\) | ||||
−0.116350 | + | 0.993208i | \(0.537120\pi\) | |||||||
\(510\) | −38.0111 | −1.68316 | ||||||||
\(511\) | −42.3636 | −1.87405 | ||||||||
\(512\) | 47.4181 | 2.09560 | ||||||||
\(513\) | −6.40209 | −0.282659 | ||||||||
\(514\) | 26.6759 | 1.17662 | ||||||||
\(515\) | 19.0840 | 0.840940 | ||||||||
\(516\) | −79.1116 | −3.48269 | ||||||||
\(517\) | 18.5951 | 0.817810 | ||||||||
\(518\) | 68.6675 | 3.01708 | ||||||||
\(519\) | 12.0337 | 0.528221 | ||||||||
\(520\) | 29.7976 | 1.30671 | ||||||||
\(521\) | 9.72129 | 0.425898 | 0.212949 | − | 0.977063i | \(-0.431693\pi\) | ||||
0.212949 | + | 0.977063i | \(0.431693\pi\) | |||||||
\(522\) | 0.735133 | 0.0321759 | ||||||||
\(523\) | 12.5361 | 0.548167 | 0.274083 | − | 0.961706i | \(-0.411626\pi\) | ||||
0.274083 | + | 0.961706i | \(0.411626\pi\) | |||||||
\(524\) | 6.99737 | 0.305681 | ||||||||
\(525\) | −27.4660 | −1.19871 | ||||||||
\(526\) | −63.0612 | −2.74960 | ||||||||
\(527\) | 10.6775 | 0.465120 | ||||||||
\(528\) | 12.9715 | 0.564512 | ||||||||
\(529\) | −21.7549 | −0.945867 | ||||||||
\(530\) | −88.5108 | −3.84466 | ||||||||
\(531\) | 0.320244 | 0.0138974 | ||||||||
\(532\) | −13.2877 | −0.576093 | ||||||||
\(533\) | −11.2373 | −0.486742 | ||||||||
\(534\) | 27.3758 | 1.18467 | ||||||||
\(535\) | −57.5652 | −2.48876 | ||||||||
\(536\) | −3.65367 | −0.157815 | ||||||||
\(537\) | −34.5155 | −1.48945 | ||||||||
\(538\) | 61.3461 | 2.64482 | ||||||||
\(539\) | −0.0764458 | −0.00329275 | ||||||||
\(540\) | 77.1005 | 3.31788 | ||||||||
\(541\) | 12.9027 | 0.554730 | 0.277365 | − | 0.960765i | \(-0.410539\pi\) | ||||
0.277365 | + | 0.960765i | \(0.410539\pi\) | |||||||
\(542\) | −18.4524 | −0.792598 | ||||||||
\(543\) | 18.8076 | 0.807111 | ||||||||
\(544\) | 6.84427 | 0.293446 | ||||||||
\(545\) | −22.7646 | −0.975127 | ||||||||
\(546\) | −17.3353 | −0.741881 | ||||||||
\(547\) | −18.9601 | −0.810676 | −0.405338 | − | 0.914167i | \(-0.632846\pi\) | ||||
−0.405338 | + | 0.914167i | \(0.632846\pi\) | |||||||
\(548\) | 42.5551 | 1.81786 | ||||||||
\(549\) | 1.82673 | 0.0779629 | ||||||||
\(550\) | 22.6551 | 0.966017 | ||||||||
\(551\) | −1.18144 | −0.0503312 | ||||||||
\(552\) | 10.2427 | 0.435958 | ||||||||
\(553\) | −12.4207 | −0.528183 | ||||||||
\(554\) | 6.06476 | 0.257667 | ||||||||
\(555\) | 57.2240 | 2.42902 | ||||||||
\(556\) | 4.23496 | 0.179602 | ||||||||
\(557\) | −7.97679 | −0.337987 | −0.168994 | − | 0.985617i | \(-0.554052\pi\) | ||||
−0.168994 | + | 0.985617i | \(0.554052\pi\) | |||||||
\(558\) | −2.84953 | −0.120630 | ||||||||
\(559\) | −18.0491 | −0.763396 | ||||||||
\(560\) | 48.7611 | 2.06053 | ||||||||
\(561\) | −6.53831 | −0.276048 | ||||||||
\(562\) | 46.9517 | 1.98054 | ||||||||
\(563\) | 24.3492 | 1.02620 | 0.513098 | − | 0.858330i | \(-0.328498\pi\) | ||||
0.513098 | + | 0.858330i | \(0.328498\pi\) | |||||||
\(564\) | 89.7651 | 3.77979 | ||||||||
\(565\) | 29.8894 | 1.25746 | ||||||||
\(566\) | −62.3837 | −2.62218 | ||||||||
\(567\) | −21.3259 | −0.895603 | ||||||||
\(568\) | −8.47163 | −0.355462 | ||||||||
\(569\) | 9.25964 | 0.388184 | 0.194092 | − | 0.980983i | \(-0.437824\pi\) | ||||
0.194092 | + | 0.980983i | \(0.437824\pi\) | |||||||
\(570\) | −16.3027 | −0.682846 | ||||||||
\(571\) | 22.7673 | 0.952781 | 0.476391 | − | 0.879234i | \(-0.341945\pi\) | ||||
0.476391 | + | 0.879234i | \(0.341945\pi\) | |||||||
\(572\) | 9.71217 | 0.406086 | ||||||||
\(573\) | 45.0271 | 1.88103 | ||||||||
\(574\) | −46.8888 | −1.95710 | ||||||||
\(575\) | 7.01576 | 0.292577 | ||||||||
\(576\) | 1.39132 | 0.0579717 | ||||||||
\(577\) | −18.1896 | −0.757243 | −0.378622 | − | 0.925552i | \(-0.623602\pi\) | ||||
−0.378622 | + | 0.925552i | \(0.623602\pi\) | |||||||
\(578\) | 23.5017 | 0.977541 | ||||||||
\(579\) | −34.4614 | −1.43217 | ||||||||
\(580\) | 14.2281 | 0.590792 | ||||||||
\(581\) | −22.1120 | −0.917360 | ||||||||
\(582\) | 43.7438 | 1.81324 | ||||||||
\(583\) | −15.2248 | −0.630546 | ||||||||
\(584\) | 89.0212 | 3.68372 | ||||||||
\(585\) | 1.57197 | 0.0649929 | ||||||||
\(586\) | 16.8951 | 0.697931 | ||||||||
\(587\) | 30.8811 | 1.27460 | 0.637300 | − | 0.770616i | \(-0.280051\pi\) | ||||
0.637300 | + | 0.770616i | \(0.280051\pi\) | |||||||
\(588\) | −0.369031 | −0.0152186 | ||||||||
\(589\) | 4.57952 | 0.188696 | ||||||||
\(590\) | 9.12531 | 0.375683 | ||||||||
\(591\) | 21.2709 | 0.874967 | ||||||||
\(592\) | −56.5896 | −2.32582 | ||||||||
\(593\) | −16.5289 | −0.678762 | −0.339381 | − | 0.940649i | \(-0.610218\pi\) | ||||
−0.339381 | + | 0.940649i | \(0.610218\pi\) | |||||||
\(594\) | 19.5252 | 0.801130 | ||||||||
\(595\) | −24.5781 | −1.00760 | ||||||||
\(596\) | 26.1823 | 1.07247 | ||||||||
\(597\) | −11.9104 | −0.487458 | ||||||||
\(598\) | 4.42802 | 0.181075 | ||||||||
\(599\) | 2.42945 | 0.0992647 | 0.0496324 | − | 0.998768i | \(-0.484195\pi\) | ||||
0.0496324 | + | 0.998768i | \(0.484195\pi\) | |||||||
\(600\) | 57.7160 | 2.35625 | ||||||||
\(601\) | −11.4692 | −0.467836 | −0.233918 | − | 0.972256i | \(-0.575155\pi\) | ||||
−0.233918 | + | 0.972256i | \(0.575155\pi\) | |||||||
\(602\) | −75.3117 | −3.06948 | ||||||||
\(603\) | −0.192749 | −0.00784934 | ||||||||
\(604\) | −17.0791 | −0.694938 | ||||||||
\(605\) | −29.9607 | −1.21808 | ||||||||
\(606\) | −35.0330 | −1.42312 | ||||||||
\(607\) | 39.2906 | 1.59476 | 0.797378 | − | 0.603480i | \(-0.206220\pi\) | ||||
0.797378 | + | 0.603480i | \(0.206220\pi\) | |||||||
\(608\) | 2.93546 | 0.119049 | ||||||||
\(609\) | −4.36835 | −0.177014 | ||||||||
\(610\) | 52.0524 | 2.10754 | ||||||||
\(611\) | 20.4797 | 0.828519 | ||||||||
\(612\) | 3.43449 | 0.138831 | ||||||||
\(613\) | −39.0765 | −1.57828 | −0.789142 | − | 0.614211i | \(-0.789474\pi\) | ||||
−0.789142 | + | 0.614211i | \(0.789474\pi\) | |||||||
\(614\) | 13.4984 | 0.544751 | ||||||||
\(615\) | −39.0748 | −1.57565 | ||||||||
\(616\) | 21.3867 | 0.861695 | ||||||||
\(617\) | 27.6791 | 1.11432 | 0.557158 | − | 0.830406i | \(-0.311892\pi\) | ||||
0.557158 | + | 0.830406i | \(0.311892\pi\) | |||||||
\(618\) | 23.3302 | 0.938477 | ||||||||
\(619\) | −39.4805 | −1.58686 | −0.793428 | − | 0.608664i | \(-0.791706\pi\) | ||||
−0.793428 | + | 0.608664i | \(0.791706\pi\) | |||||||
\(620\) | −55.1512 | −2.21493 | ||||||||
\(621\) | 6.04651 | 0.242638 | ||||||||
\(622\) | −40.3078 | −1.61619 | ||||||||
\(623\) | 17.7013 | 0.709187 | ||||||||
\(624\) | 14.2862 | 0.571904 | ||||||||
\(625\) | −16.9048 | −0.676193 | ||||||||
\(626\) | 16.8926 | 0.675165 | ||||||||
\(627\) | −2.80424 | −0.111991 | ||||||||
\(628\) | 42.1469 | 1.68185 | ||||||||
\(629\) | 28.5241 | 1.13733 | ||||||||
\(630\) | 6.55921 | 0.261325 | ||||||||
\(631\) | 33.0853 | 1.31710 | 0.658552 | − | 0.752535i | \(-0.271169\pi\) | ||||
0.658552 | + | 0.752535i | \(0.271169\pi\) | |||||||
\(632\) | 26.1004 | 1.03822 | ||||||||
\(633\) | 34.4852 | 1.37067 | ||||||||
\(634\) | −55.5156 | −2.20481 | ||||||||
\(635\) | −40.9977 | −1.62694 | ||||||||
\(636\) | −73.4955 | −2.91429 | ||||||||
\(637\) | −0.0841935 | −0.00333587 | ||||||||
\(638\) | 3.60320 | 0.142652 | ||||||||
\(639\) | −0.446919 | −0.0176799 | ||||||||
\(640\) | 56.3407 | 2.22706 | ||||||||
\(641\) | 8.24486 | 0.325652 | 0.162826 | − | 0.986655i | \(-0.447939\pi\) | ||||
0.162826 | + | 0.986655i | \(0.447939\pi\) | |||||||
\(642\) | −70.3735 | −2.77742 | ||||||||
\(643\) | −30.5515 | −1.20483 | −0.602416 | − | 0.798182i | \(-0.705795\pi\) | ||||
−0.602416 | + | 0.798182i | \(0.705795\pi\) | |||||||
\(644\) | 12.5497 | 0.494526 | ||||||||
\(645\) | −62.7610 | −2.47121 | ||||||||
\(646\) | −8.12631 | −0.319725 | ||||||||
\(647\) | 35.3839 | 1.39108 | 0.695541 | − | 0.718486i | \(-0.255165\pi\) | ||||
0.695541 | + | 0.718486i | \(0.255165\pi\) | |||||||
\(648\) | 44.8134 | 1.76044 | ||||||||
\(649\) | 1.56965 | 0.0616141 | ||||||||
\(650\) | 24.9512 | 0.978666 | ||||||||
\(651\) | 16.9326 | 0.663642 | ||||||||
\(652\) | −60.5484 | −2.37126 | ||||||||
\(653\) | −23.8978 | −0.935192 | −0.467596 | − | 0.883942i | \(-0.654880\pi\) | ||||
−0.467596 | + | 0.883942i | \(0.654880\pi\) | |||||||
\(654\) | −27.8297 | −1.08823 | ||||||||
\(655\) | 5.55116 | 0.216902 | ||||||||
\(656\) | 38.6416 | 1.50870 | ||||||||
\(657\) | 4.69630 | 0.183220 | ||||||||
\(658\) | 85.4536 | 3.33133 | ||||||||
\(659\) | 22.7142 | 0.884819 | 0.442409 | − | 0.896813i | \(-0.354124\pi\) | ||||
0.442409 | + | 0.896813i | \(0.354124\pi\) | |||||||
\(660\) | 33.7715 | 1.31455 | ||||||||
\(661\) | 17.2869 | 0.672382 | 0.336191 | − | 0.941794i | \(-0.390861\pi\) | ||||
0.336191 | + | 0.941794i | \(0.390861\pi\) | |||||||
\(662\) | −31.6775 | −1.23118 | ||||||||
\(663\) | −7.20097 | −0.279662 | ||||||||
\(664\) | 46.4653 | 1.80320 | ||||||||
\(665\) | −10.5414 | −0.408778 | ||||||||
\(666\) | −7.61227 | −0.294970 | ||||||||
\(667\) | 1.11583 | 0.0432049 | ||||||||
\(668\) | 71.8812 | 2.78117 | ||||||||
\(669\) | −3.94684 | −0.152594 | ||||||||
\(670\) | −5.49235 | −0.212188 | ||||||||
\(671\) | 8.95356 | 0.345649 | ||||||||
\(672\) | 10.8538 | 0.418694 | ||||||||
\(673\) | −46.8739 | −1.80686 | −0.903428 | − | 0.428741i | \(-0.858957\pi\) | ||||
−0.903428 | + | 0.428741i | \(0.858957\pi\) | |||||||
\(674\) | −55.9217 | −2.15402 | ||||||||
\(675\) | 34.0711 | 1.31140 | ||||||||
\(676\) | −44.3580 | −1.70608 | ||||||||
\(677\) | −34.2492 | −1.31631 | −0.658153 | − | 0.752885i | \(-0.728662\pi\) | ||||
−0.658153 | + | 0.752885i | \(0.728662\pi\) | |||||||
\(678\) | 36.5399 | 1.40330 | ||||||||
\(679\) | 28.2849 | 1.08548 | ||||||||
\(680\) | 51.6475 | 1.98059 | ||||||||
\(681\) | −30.0181 | −1.15030 | ||||||||
\(682\) | −13.9667 | −0.534814 | ||||||||
\(683\) | 22.4911 | 0.860596 | 0.430298 | − | 0.902687i | \(-0.358408\pi\) | ||||
0.430298 | + | 0.902687i | \(0.358408\pi\) | |||||||
\(684\) | 1.47303 | 0.0563227 | ||||||||
\(685\) | 33.7599 | 1.28990 | ||||||||
\(686\) | 46.0683 | 1.75889 | ||||||||
\(687\) | 41.7330 | 1.59221 | ||||||||
\(688\) | 62.0652 | 2.36621 | ||||||||
\(689\) | −16.7678 | −0.638803 | ||||||||
\(690\) | 15.3973 | 0.586164 | ||||||||
\(691\) | 19.8073 | 0.753505 | 0.376753 | − | 0.926314i | \(-0.377041\pi\) | ||||
0.376753 | + | 0.926314i | \(0.377041\pi\) | |||||||
\(692\) | −30.9826 | −1.17778 | ||||||||
\(693\) | 1.12825 | 0.0428588 | ||||||||
\(694\) | 35.0088 | 1.32892 | ||||||||
\(695\) | 3.35969 | 0.127440 | ||||||||
\(696\) | 9.17948 | 0.347947 | ||||||||
\(697\) | −19.4774 | −0.737757 | ||||||||
\(698\) | 1.20038 | 0.0454350 | ||||||||
\(699\) | 30.4181 | 1.15052 | ||||||||
\(700\) | 70.7154 | 2.67279 | ||||||||
\(701\) | −15.2918 | −0.577564 | −0.288782 | − | 0.957395i | \(-0.593250\pi\) | ||||
−0.288782 | + | 0.957395i | \(0.593250\pi\) | |||||||
\(702\) | 21.5041 | 0.811620 | ||||||||
\(703\) | 12.2338 | 0.461406 | ||||||||
\(704\) | 6.81945 | 0.257018 | ||||||||
\(705\) | 71.2127 | 2.68202 | ||||||||
\(706\) | −57.6813 | −2.17086 | ||||||||
\(707\) | −22.6525 | −0.851935 | ||||||||
\(708\) | 7.57727 | 0.284771 | ||||||||
\(709\) | 10.4939 | 0.394107 | 0.197054 | − | 0.980393i | \(-0.436863\pi\) | ||||
0.197054 | + | 0.980393i | \(0.436863\pi\) | |||||||
\(710\) | −12.7349 | −0.477933 | ||||||||
\(711\) | 1.37692 | 0.0516387 | ||||||||
\(712\) | −37.1968 | −1.39401 | ||||||||
\(713\) | −4.32517 | −0.161979 | ||||||||
\(714\) | −30.0468 | −1.12447 | ||||||||
\(715\) | 7.70488 | 0.288146 | ||||||||
\(716\) | 88.8653 | 3.32105 | ||||||||
\(717\) | −25.4667 | −0.951072 | ||||||||
\(718\) | −22.3190 | −0.832936 | ||||||||
\(719\) | −35.0305 | −1.30642 | −0.653208 | − | 0.757179i | \(-0.726577\pi\) | ||||
−0.653208 | + | 0.757179i | \(0.726577\pi\) | |||||||
\(720\) | −5.40551 | −0.201451 | ||||||||
\(721\) | 15.0854 | 0.561808 | ||||||||
\(722\) | 43.9575 | 1.63593 | ||||||||
\(723\) | 35.1766 | 1.30823 | ||||||||
\(724\) | −48.4230 | −1.79963 | ||||||||
\(725\) | 6.28750 | 0.233512 | ||||||||
\(726\) | −36.6270 | −1.35936 | ||||||||
\(727\) | −16.6871 | −0.618890 | −0.309445 | − | 0.950917i | \(-0.600143\pi\) | ||||
−0.309445 | + | 0.950917i | \(0.600143\pi\) | |||||||
\(728\) | 23.5542 | 0.872979 | ||||||||
\(729\) | 29.1041 | 1.07793 | ||||||||
\(730\) | 133.820 | 4.95291 | ||||||||
\(731\) | −31.2841 | −1.15708 | ||||||||
\(732\) | 43.2221 | 1.59753 | ||||||||
\(733\) | 26.9810 | 0.996566 | 0.498283 | − | 0.867014i | \(-0.333964\pi\) | ||||
0.498283 | + | 0.867014i | \(0.333964\pi\) | |||||||
\(734\) | 0.559518 | 0.0206522 | ||||||||
\(735\) | −0.292761 | −0.0107986 | ||||||||
\(736\) | −2.77243 | −0.102193 | ||||||||
\(737\) | −0.944742 | −0.0348000 | ||||||||
\(738\) | 5.19796 | 0.191339 | ||||||||
\(739\) | −13.6493 | −0.502099 | −0.251049 | − | 0.967974i | \(-0.580776\pi\) | ||||
−0.251049 | + | 0.967974i | \(0.580776\pi\) | |||||||
\(740\) | −147.332 | −5.41603 | ||||||||
\(741\) | −3.08845 | −0.113457 | ||||||||
\(742\) | −69.9654 | −2.56851 | ||||||||
\(743\) | −29.8524 | −1.09518 | −0.547589 | − | 0.836747i | \(-0.684454\pi\) | ||||
−0.547589 | + | 0.836747i | \(0.684454\pi\) | |||||||
\(744\) | −35.5816 | −1.30448 | ||||||||
\(745\) | 20.7710 | 0.760990 | ||||||||
\(746\) | 8.63730 | 0.316234 | ||||||||
\(747\) | 2.45127 | 0.0896872 | ||||||||
\(748\) | 16.8339 | 0.615507 | ||||||||
\(749\) | −45.5038 | −1.66267 | ||||||||
\(750\) | 17.7662 | 0.648731 | ||||||||
\(751\) | 19.3906 | 0.707574 | 0.353787 | − | 0.935326i | \(-0.384894\pi\) | ||||
0.353787 | + | 0.935326i | \(0.384894\pi\) | |||||||
\(752\) | −70.4232 | −2.56807 | ||||||||
\(753\) | 16.0770 | 0.585878 | ||||||||
\(754\) | 3.96838 | 0.144520 | ||||||||
\(755\) | −13.5492 | −0.493106 | ||||||||
\(756\) | 60.9459 | 2.21658 | ||||||||
\(757\) | −46.5885 | −1.69329 | −0.846644 | − | 0.532159i | \(-0.821381\pi\) | ||||
−0.846644 | + | 0.532159i | \(0.821381\pi\) | |||||||
\(758\) | 35.0990 | 1.27485 | ||||||||
\(759\) | 2.64849 | 0.0961341 | ||||||||
\(760\) | 22.1513 | 0.803512 | ||||||||
\(761\) | −12.3401 | −0.447330 | −0.223665 | − | 0.974666i | \(-0.571802\pi\) | ||||
−0.223665 | + | 0.974666i | \(0.571802\pi\) | |||||||
\(762\) | −50.1197 | −1.81565 | ||||||||
\(763\) | −17.9948 | −0.651455 | ||||||||
\(764\) | −115.929 | −4.19416 | ||||||||
\(765\) | 2.72466 | 0.0985101 | ||||||||
\(766\) | −38.1791 | −1.37947 | ||||||||
\(767\) | 1.72873 | 0.0624209 | ||||||||
\(768\) | 53.3299 | 1.92438 | ||||||||
\(769\) | −46.5874 | −1.67999 | −0.839993 | − | 0.542598i | \(-0.817441\pi\) | ||||
−0.839993 | + | 0.542598i | \(0.817441\pi\) | |||||||
\(770\) | 32.1494 | 1.15858 | ||||||||
\(771\) | 17.5725 | 0.632859 | ||||||||
\(772\) | 88.7261 | 3.19332 | ||||||||
\(773\) | −19.2581 | −0.692665 | −0.346333 | − | 0.938112i | \(-0.612573\pi\) | ||||
−0.346333 | + | 0.938112i | \(0.612573\pi\) | |||||||
\(774\) | 8.34883 | 0.300093 | ||||||||
\(775\) | −24.3717 | −0.875456 | ||||||||
\(776\) | −59.4368 | −2.13366 | ||||||||
\(777\) | 45.2341 | 1.62276 | ||||||||
\(778\) | 65.6417 | 2.35337 | ||||||||
\(779\) | −8.35371 | −0.299303 | ||||||||
\(780\) | 37.1942 | 1.33177 | ||||||||
\(781\) | −2.19054 | −0.0783836 | ||||||||
\(782\) | 7.67497 | 0.274456 | ||||||||
\(783\) | 5.41887 | 0.193655 | ||||||||
\(784\) | 0.289515 | 0.0103398 | ||||||||
\(785\) | 33.4361 | 1.19339 | ||||||||
\(786\) | 6.78630 | 0.242059 | ||||||||
\(787\) | −34.5240 | −1.23065 | −0.615324 | − | 0.788274i | \(-0.710975\pi\) | ||||
−0.615324 | + | 0.788274i | \(0.710975\pi\) | |||||||
\(788\) | −54.7651 | −1.95092 | ||||||||
\(789\) | −41.5410 | −1.47890 | ||||||||
\(790\) | 39.2353 | 1.39593 | ||||||||
\(791\) | 23.6268 | 0.840072 | ||||||||
\(792\) | −2.37087 | −0.0842451 | ||||||||
\(793\) | 9.86100 | 0.350174 | ||||||||
\(794\) | −14.0504 | −0.498629 | ||||||||
\(795\) | −58.3056 | −2.06789 | ||||||||
\(796\) | 30.6650 | 1.08689 | ||||||||
\(797\) | 20.9223 | 0.741107 | 0.370554 | − | 0.928811i | \(-0.379168\pi\) | ||||
0.370554 | + | 0.928811i | \(0.379168\pi\) | |||||||
\(798\) | −12.8869 | −0.456190 | ||||||||
\(799\) | 35.4969 | 1.25579 | ||||||||
\(800\) | −15.6222 | −0.552328 | ||||||||
\(801\) | −1.96231 | −0.0693348 | ||||||||
\(802\) | 69.6500 | 2.45943 | ||||||||
\(803\) | 23.0185 | 0.812305 | ||||||||
\(804\) | −4.56061 | −0.160840 | ||||||||
\(805\) | 9.95592 | 0.350900 | ||||||||
\(806\) | −15.3822 | −0.541817 | ||||||||
\(807\) | 40.4112 | 1.42254 | ||||||||
\(808\) | 47.6011 | 1.67460 | ||||||||
\(809\) | 33.3318 | 1.17188 | 0.585942 | − | 0.810353i | \(-0.300724\pi\) | ||||
0.585942 | + | 0.810353i | \(0.300724\pi\) | |||||||
\(810\) | 67.3654 | 2.36698 | ||||||||
\(811\) | −14.7125 | −0.516627 | −0.258314 | − | 0.966061i | \(-0.583167\pi\) | ||||
−0.258314 | + | 0.966061i | \(0.583167\pi\) | |||||||
\(812\) | 11.2470 | 0.394691 | ||||||||
\(813\) | −12.1553 | −0.426306 | ||||||||
\(814\) | −37.3109 | −1.30775 | ||||||||
\(815\) | −48.0343 | −1.68257 | ||||||||
\(816\) | 24.7618 | 0.866838 | ||||||||
\(817\) | −13.4175 | −0.469420 | ||||||||
\(818\) | −11.0751 | −0.387231 | ||||||||
\(819\) | 1.24260 | 0.0434200 | ||||||||
\(820\) | 100.604 | 3.51324 | ||||||||
\(821\) | −7.56726 | −0.264099 | −0.132050 | − | 0.991243i | \(-0.542156\pi\) | ||||
−0.132050 | + | 0.991243i | \(0.542156\pi\) | |||||||
\(822\) | 41.2715 | 1.43951 | ||||||||
\(823\) | −32.0914 | −1.11864 | −0.559318 | − | 0.828953i | \(-0.688937\pi\) | ||||
−0.559318 | + | 0.828953i | \(0.688937\pi\) | |||||||
\(824\) | −31.6998 | −1.10432 | ||||||||
\(825\) | 14.9238 | 0.519581 | ||||||||
\(826\) | 7.21332 | 0.250983 | ||||||||
\(827\) | −31.6708 | −1.10130 | −0.550650 | − | 0.834736i | \(-0.685620\pi\) | ||||
−0.550650 | + | 0.834736i | \(0.685620\pi\) | |||||||
\(828\) | −1.39122 | −0.0483482 | ||||||||
\(829\) | 36.7716 | 1.27713 | 0.638566 | − | 0.769567i | \(-0.279528\pi\) | ||||
0.638566 | + | 0.769567i | \(0.279528\pi\) | |||||||
\(830\) | 69.8486 | 2.42448 | ||||||||
\(831\) | 3.99511 | 0.138589 | ||||||||
\(832\) | 7.51059 | 0.260383 | ||||||||
\(833\) | −0.145931 | −0.00505619 | ||||||||
\(834\) | 4.10722 | 0.142221 | ||||||||
\(835\) | 57.0249 | 1.97343 | ||||||||
\(836\) | 7.21994 | 0.249707 | ||||||||
\(837\) | −21.0046 | −0.726027 | ||||||||
\(838\) | 32.0837 | 1.10831 | ||||||||
\(839\) | −32.8907 | −1.13551 | −0.567757 | − | 0.823196i | \(-0.692189\pi\) | ||||
−0.567757 | + | 0.823196i | \(0.692189\pi\) | |||||||
\(840\) | 81.9037 | 2.82594 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 17.2189 | 0.593404 | ||||||||
\(843\) | 30.9290 | 1.06525 | ||||||||
\(844\) | −88.7875 | −3.05619 | ||||||||
\(845\) | −35.1902 | −1.21058 | ||||||||
\(846\) | −9.47312 | −0.325693 | ||||||||
\(847\) | −23.6831 | −0.813763 | ||||||||
\(848\) | 57.6592 | 1.98003 | ||||||||
\(849\) | −41.0947 | −1.41037 | ||||||||
\(850\) | 43.2473 | 1.48337 | ||||||||
\(851\) | −11.5543 | −0.396077 | ||||||||
\(852\) | −10.5745 | −0.362277 | ||||||||
\(853\) | 19.8295 | 0.678950 | 0.339475 | − | 0.940615i | \(-0.389751\pi\) | ||||
0.339475 | + | 0.940615i | \(0.389751\pi\) | |||||||
\(854\) | 41.1461 | 1.40799 | ||||||||
\(855\) | 1.16859 | 0.0399648 | ||||||||
\(856\) | 95.6199 | 3.26822 | ||||||||
\(857\) | 35.2039 | 1.20254 | 0.601271 | − | 0.799045i | \(-0.294661\pi\) | ||||
0.601271 | + | 0.799045i | \(0.294661\pi\) | |||||||
\(858\) | 9.41922 | 0.321567 | ||||||||
\(859\) | −45.2210 | −1.54292 | −0.771460 | − | 0.636278i | \(-0.780473\pi\) | ||||
−0.771460 | + | 0.636278i | \(0.780473\pi\) | |||||||
\(860\) | 161.588 | 5.51009 | ||||||||
\(861\) | −30.8876 | −1.05265 | ||||||||
\(862\) | 53.3737 | 1.81791 | ||||||||
\(863\) | 19.7302 | 0.671625 | 0.335812 | − | 0.941929i | \(-0.390989\pi\) | ||||
0.335812 | + | 0.941929i | \(0.390989\pi\) | |||||||
\(864\) | −13.4639 | −0.458053 | ||||||||
\(865\) | −24.5792 | −0.835717 | ||||||||
\(866\) | 78.3324 | 2.66184 | ||||||||
\(867\) | 15.4815 | 0.525780 | ||||||||
\(868\) | −43.5956 | −1.47973 | ||||||||
\(869\) | 6.74888 | 0.228940 | ||||||||
\(870\) | 13.7990 | 0.467829 | ||||||||
\(871\) | −1.04049 | −0.0352557 | ||||||||
\(872\) | 37.8136 | 1.28053 | ||||||||
\(873\) | −3.13558 | −0.106123 | ||||||||
\(874\) | 3.29175 | 0.111345 | ||||||||
\(875\) | 11.4877 | 0.388355 | ||||||||
\(876\) | 111.119 | 3.75435 | ||||||||
\(877\) | 11.1899 | 0.377856 | 0.188928 | − | 0.981991i | \(-0.439499\pi\) | ||||
0.188928 | + | 0.981991i | \(0.439499\pi\) | |||||||
\(878\) | −47.0850 | −1.58904 | ||||||||
\(879\) | 11.1295 | 0.375388 | ||||||||
\(880\) | −26.4947 | −0.893135 | ||||||||
\(881\) | 10.5144 | 0.354238 | 0.177119 | − | 0.984189i | \(-0.443322\pi\) | ||||
0.177119 | + | 0.984189i | \(0.443322\pi\) | |||||||
\(882\) | 0.0389447 | 0.00131134 | ||||||||
\(883\) | −42.7272 | −1.43789 | −0.718943 | − | 0.695069i | \(-0.755374\pi\) | ||||
−0.718943 | + | 0.695069i | \(0.755374\pi\) | |||||||
\(884\) | 18.5400 | 0.623567 | ||||||||
\(885\) | 6.01121 | 0.202065 | ||||||||
\(886\) | −27.3479 | −0.918771 | ||||||||
\(887\) | 21.7025 | 0.728700 | 0.364350 | − | 0.931262i | \(-0.381291\pi\) | ||||
0.364350 | + | 0.931262i | \(0.381291\pi\) | |||||||
\(888\) | −95.0531 | −3.18977 | ||||||||
\(889\) | −32.4076 | −1.08692 | ||||||||
\(890\) | −55.9157 | −1.87430 | ||||||||
\(891\) | 11.5876 | 0.388198 | ||||||||
\(892\) | 10.1617 | 0.340240 | ||||||||
\(893\) | 15.2244 | 0.509465 | ||||||||
\(894\) | 25.3926 | 0.849254 | ||||||||
\(895\) | 70.4988 | 2.35652 | ||||||||
\(896\) | 44.5359 | 1.48784 | ||||||||
\(897\) | 2.91691 | 0.0973929 | ||||||||
\(898\) | 50.7292 | 1.69286 | ||||||||
\(899\) | −3.87621 | −0.129279 | ||||||||
\(900\) | −7.83929 | −0.261310 | ||||||||
\(901\) | −29.0632 | −0.968236 | ||||||||
\(902\) | 25.4773 | 0.848303 | ||||||||
\(903\) | −49.6109 | −1.65095 | ||||||||
\(904\) | −49.6485 | −1.65128 | ||||||||
\(905\) | −38.4150 | −1.27696 | ||||||||
\(906\) | −16.5639 | −0.550300 | ||||||||
\(907\) | 49.2469 | 1.63522 | 0.817609 | − | 0.575774i | \(-0.195299\pi\) | ||||
0.817609 | + | 0.575774i | \(0.195299\pi\) | |||||||
\(908\) | 77.2862 | 2.56483 | ||||||||
\(909\) | 2.51119 | 0.0832908 | ||||||||
\(910\) | 35.4077 | 1.17375 | ||||||||
\(911\) | 2.33396 | 0.0773274 | 0.0386637 | − | 0.999252i | \(-0.487690\pi\) | ||||
0.0386637 | + | 0.999252i | \(0.487690\pi\) | |||||||
\(912\) | 10.6202 | 0.351670 | ||||||||
\(913\) | 12.0147 | 0.397628 | ||||||||
\(914\) | 66.4956 | 2.19948 | ||||||||
\(915\) | 34.2890 | 1.13356 | ||||||||
\(916\) | −107.448 | −3.55018 | ||||||||
\(917\) | 4.38805 | 0.144906 | ||||||||
\(918\) | 37.2725 | 1.23018 | ||||||||
\(919\) | −42.1536 | −1.39052 | −0.695259 | − | 0.718759i | \(-0.744710\pi\) | ||||
−0.695259 | + | 0.718759i | \(0.744710\pi\) | |||||||
\(920\) | −20.9210 | −0.689745 | ||||||||
\(921\) | 8.89194 | 0.293000 | ||||||||
\(922\) | −55.7939 | −1.83747 | ||||||||
\(923\) | −2.41255 | −0.0794100 | ||||||||
\(924\) | 26.6955 | 0.878217 | ||||||||
\(925\) | −65.1068 | −2.14070 | ||||||||
\(926\) | 15.9149 | 0.522995 | ||||||||
\(927\) | −1.67232 | −0.0549261 | ||||||||
\(928\) | −2.48464 | −0.0815623 | ||||||||
\(929\) | 10.1722 | 0.333739 | 0.166870 | − | 0.985979i | \(-0.446634\pi\) | ||||
0.166870 | + | 0.985979i | \(0.446634\pi\) | |||||||
\(930\) | −53.4877 | −1.75393 | ||||||||
\(931\) | −0.0625887 | −0.00205126 | ||||||||
\(932\) | −78.3160 | −2.56533 | ||||||||
\(933\) | −26.5523 | −0.869285 | ||||||||
\(934\) | −56.7540 | −1.85705 | ||||||||
\(935\) | 13.3547 | 0.436745 | ||||||||
\(936\) | −2.61115 | −0.0853482 | ||||||||
\(937\) | −18.9928 | −0.620468 | −0.310234 | − | 0.950660i | \(-0.600407\pi\) | ||||
−0.310234 | + | 0.950660i | \(0.600407\pi\) | |||||||
\(938\) | −4.34156 | −0.141757 | ||||||||
\(939\) | 11.1279 | 0.363144 | ||||||||
\(940\) | −183.348 | −5.98014 | ||||||||
\(941\) | −59.9551 | −1.95448 | −0.977241 | − | 0.212132i | \(-0.931959\pi\) | ||||
−0.977241 | + | 0.212132i | \(0.931959\pi\) | |||||||
\(942\) | 40.8757 | 1.33180 | ||||||||
\(943\) | 7.88974 | 0.256925 | ||||||||
\(944\) | −5.94457 | −0.193479 | ||||||||
\(945\) | 48.3497 | 1.57282 | ||||||||
\(946\) | 40.9211 | 1.33046 | ||||||||
\(947\) | 42.8168 | 1.39136 | 0.695679 | − | 0.718353i | \(-0.255104\pi\) | ||||
0.695679 | + | 0.718353i | \(0.255104\pi\) | |||||||
\(948\) | 32.5793 | 1.05813 | ||||||||
\(949\) | 25.3514 | 0.822942 | ||||||||
\(950\) | 18.5485 | 0.601792 | ||||||||
\(951\) | −36.5704 | −1.18588 | ||||||||
\(952\) | 40.8260 | 1.32318 | ||||||||
\(953\) | −28.0572 | −0.908861 | −0.454430 | − | 0.890782i | \(-0.650157\pi\) | ||||
−0.454430 | + | 0.890782i | \(0.650157\pi\) | |||||||
\(954\) | 7.75615 | 0.251115 | ||||||||
\(955\) | −91.9690 | −2.97605 | ||||||||
\(956\) | 65.5679 | 2.12062 | ||||||||
\(957\) | 2.37357 | 0.0767266 | ||||||||
\(958\) | 8.27744 | 0.267432 | ||||||||
\(959\) | 26.6863 | 0.861745 | ||||||||
\(960\) | 26.1161 | 0.842893 | ||||||||
\(961\) | −15.9750 | −0.515323 | ||||||||
\(962\) | −41.0924 | −1.32487 | ||||||||
\(963\) | 5.04441 | 0.162554 | ||||||||
\(964\) | −90.5674 | −2.91698 | ||||||||
\(965\) | 70.3884 | 2.26588 | ||||||||
\(966\) | 12.1711 | 0.391599 | ||||||||
\(967\) | −46.6731 | −1.50091 | −0.750453 | − | 0.660924i | \(-0.770165\pi\) | ||||
−0.750453 | + | 0.660924i | \(0.770165\pi\) | |||||||
\(968\) | 49.7669 | 1.59957 | ||||||||
\(969\) | −5.35313 | −0.171967 | ||||||||
\(970\) | −89.3479 | −2.86879 | ||||||||
\(971\) | 5.43855 | 0.174531 | 0.0872657 | − | 0.996185i | \(-0.472187\pi\) | ||||
0.0872657 | + | 0.996185i | \(0.472187\pi\) | |||||||
\(972\) | −12.9088 | −0.414049 | ||||||||
\(973\) | 2.65574 | 0.0851392 | ||||||||
\(974\) | −80.3481 | −2.57452 | ||||||||
\(975\) | 16.4363 | 0.526384 | ||||||||
\(976\) | −33.9089 | −1.08540 | ||||||||
\(977\) | 50.3371 | 1.61043 | 0.805213 | − | 0.592986i | \(-0.202051\pi\) | ||||
0.805213 | + | 0.592986i | \(0.202051\pi\) | |||||||
\(978\) | −58.7220 | −1.87772 | ||||||||
\(979\) | −9.61810 | −0.307396 | ||||||||
\(980\) | 0.753757 | 0.0240779 | ||||||||
\(981\) | 1.99485 | 0.0636906 | ||||||||
\(982\) | −4.27669 | −0.136475 | ||||||||
\(983\) | −48.8725 | −1.55879 | −0.779395 | − | 0.626533i | \(-0.784473\pi\) | ||||
−0.779395 | + | 0.626533i | \(0.784473\pi\) | |||||||
\(984\) | 64.9060 | 2.06913 | ||||||||
\(985\) | −43.4463 | −1.38431 | ||||||||
\(986\) | 6.87829 | 0.219049 | ||||||||
\(987\) | 56.2917 | 1.79178 | ||||||||
\(988\) | 7.95167 | 0.252976 | ||||||||
\(989\) | 12.6723 | 0.402956 | ||||||||
\(990\) | −3.56399 | −0.113271 | ||||||||
\(991\) | −23.1052 | −0.733961 | −0.366980 | − | 0.930229i | \(-0.619608\pi\) | ||||
−0.366980 | + | 0.930229i | \(0.619608\pi\) | |||||||
\(992\) | 9.63098 | 0.305784 | ||||||||
\(993\) | −20.8672 | −0.662201 | ||||||||
\(994\) | −10.0666 | −0.319293 | ||||||||
\(995\) | 24.3272 | 0.771225 | ||||||||
\(996\) | 57.9992 | 1.83778 | ||||||||
\(997\) | 25.9052 | 0.820425 | 0.410213 | − | 0.911990i | \(-0.365455\pi\) | ||||
0.410213 | + | 0.911990i | \(0.365455\pi\) | |||||||
\(998\) | −3.89639 | −0.123338 | ||||||||
\(999\) | −56.1121 | −1.77531 |
(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 | 4031.2.a.b.1.3 | ✓ | 59 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4031.2.a.b.1.3 | ✓ | 59 | 1.1 | even | 1 | trivial |