Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6001,2,Mod(1,6001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6001, 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("6001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6001 = 17 \cdot 353 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6001.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: | \(47.9182262530\) |
Analytic rank: | \(1\) |
Dimension: | \(114\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 6001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.39289 | −1.69203 | −0.846016 | − | 0.533158i | \(-0.821005\pi\) | ||||
−0.846016 | + | 0.533158i | \(0.821005\pi\) | |||||||
\(3\) | −2.96659 | −1.71276 | −0.856380 | − | 0.516346i | \(-0.827292\pi\) | ||||
−0.856380 | + | 0.516346i | \(0.827292\pi\) | |||||||
\(4\) | 3.72594 | 1.86297 | ||||||||
\(5\) | 3.31044 | 1.48047 | 0.740236 | − | 0.672347i | \(-0.234714\pi\) | ||||
0.740236 | + | 0.672347i | \(0.234714\pi\) | |||||||
\(6\) | 7.09873 | 2.89804 | ||||||||
\(7\) | 0.664206 | 0.251046 | 0.125523 | − | 0.992091i | \(-0.459939\pi\) | ||||
0.125523 | + | 0.992091i | \(0.459939\pi\) | |||||||
\(8\) | −4.12999 | −1.46017 | ||||||||
\(9\) | 5.80065 | 1.93355 | ||||||||
\(10\) | −7.92153 | −2.50501 | ||||||||
\(11\) | 1.52127 | 0.458681 | 0.229341 | − | 0.973346i | \(-0.426343\pi\) | ||||
0.229341 | + | 0.973346i | \(0.426343\pi\) | |||||||
\(12\) | −11.0533 | −3.19082 | ||||||||
\(13\) | −4.57960 | −1.27015 | −0.635077 | − | 0.772449i | \(-0.719031\pi\) | ||||
−0.635077 | + | 0.772449i | \(0.719031\pi\) | |||||||
\(14\) | −1.58938 | −0.424778 | ||||||||
\(15\) | −9.82071 | −2.53570 | ||||||||
\(16\) | 2.43075 | 0.607688 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −13.8803 | −3.27163 | ||||||||
\(19\) | −7.18664 | −1.64873 | −0.824364 | − | 0.566060i | \(-0.808467\pi\) | ||||
−0.824364 | + | 0.566060i | \(0.808467\pi\) | |||||||
\(20\) | 12.3345 | 2.75808 | ||||||||
\(21\) | −1.97043 | −0.429982 | ||||||||
\(22\) | −3.64025 | −0.776103 | ||||||||
\(23\) | 7.41494 | 1.54612 | 0.773061 | − | 0.634332i | \(-0.218725\pi\) | ||||
0.773061 | + | 0.634332i | \(0.218725\pi\) | |||||||
\(24\) | 12.2520 | 2.50093 | ||||||||
\(25\) | 5.95900 | 1.19180 | ||||||||
\(26\) | 10.9585 | 2.14914 | ||||||||
\(27\) | −8.30836 | −1.59895 | ||||||||
\(28\) | 2.47479 | 0.467692 | ||||||||
\(29\) | 0.513282 | 0.0953141 | 0.0476571 | − | 0.998864i | \(-0.484825\pi\) | ||||
0.0476571 | + | 0.998864i | \(0.484825\pi\) | |||||||
\(30\) | 23.4999 | 4.29048 | ||||||||
\(31\) | −6.03318 | −1.08359 | −0.541795 | − | 0.840511i | \(-0.682255\pi\) | ||||
−0.541795 | + | 0.840511i | \(0.682255\pi\) | |||||||
\(32\) | 2.44345 | 0.431945 | ||||||||
\(33\) | −4.51299 | −0.785611 | ||||||||
\(34\) | −2.39289 | −0.410378 | ||||||||
\(35\) | 2.19881 | 0.371667 | ||||||||
\(36\) | 21.6129 | 3.60214 | ||||||||
\(37\) | 0.496483 | 0.0816214 | 0.0408107 | − | 0.999167i | \(-0.487006\pi\) | ||||
0.0408107 | + | 0.999167i | \(0.487006\pi\) | |||||||
\(38\) | 17.1969 | 2.78970 | ||||||||
\(39\) | 13.5858 | 2.17547 | ||||||||
\(40\) | −13.6721 | −2.16175 | ||||||||
\(41\) | −1.38303 | −0.215993 | −0.107996 | − | 0.994151i | \(-0.534443\pi\) | ||||
−0.107996 | + | 0.994151i | \(0.534443\pi\) | |||||||
\(42\) | 4.71502 | 0.727544 | ||||||||
\(43\) | 10.6191 | 1.61939 | 0.809695 | − | 0.586851i | \(-0.199633\pi\) | ||||
0.809695 | + | 0.586851i | \(0.199633\pi\) | |||||||
\(44\) | 5.66818 | 0.854510 | ||||||||
\(45\) | 19.2027 | 2.86257 | ||||||||
\(46\) | −17.7432 | −2.61609 | ||||||||
\(47\) | 3.44692 | 0.502786 | 0.251393 | − | 0.967885i | \(-0.419111\pi\) | ||||
0.251393 | + | 0.967885i | \(0.419111\pi\) | |||||||
\(48\) | −7.21104 | −1.04082 | ||||||||
\(49\) | −6.55883 | −0.936976 | ||||||||
\(50\) | −14.2593 | −2.01656 | ||||||||
\(51\) | −2.96659 | −0.415405 | ||||||||
\(52\) | −17.0633 | −2.36626 | ||||||||
\(53\) | 7.55815 | 1.03819 | 0.519096 | − | 0.854716i | \(-0.326269\pi\) | ||||
0.519096 | + | 0.854716i | \(0.326269\pi\) | |||||||
\(54\) | 19.8810 | 2.70547 | ||||||||
\(55\) | 5.03608 | 0.679065 | ||||||||
\(56\) | −2.74317 | −0.366571 | ||||||||
\(57\) | 21.3198 | 2.82388 | ||||||||
\(58\) | −1.22823 | −0.161274 | ||||||||
\(59\) | −10.6847 | −1.39102 | −0.695512 | − | 0.718514i | \(-0.744822\pi\) | ||||
−0.695512 | + | 0.718514i | \(0.744822\pi\) | |||||||
\(60\) | −36.5914 | −4.72393 | ||||||||
\(61\) | 5.41605 | 0.693455 | 0.346727 | − | 0.937966i | \(-0.387293\pi\) | ||||
0.346727 | + | 0.937966i | \(0.387293\pi\) | |||||||
\(62\) | 14.4367 | 1.83347 | ||||||||
\(63\) | 3.85283 | 0.485411 | ||||||||
\(64\) | −10.7084 | −1.33855 | ||||||||
\(65\) | −15.1605 | −1.88043 | ||||||||
\(66\) | 10.7991 | 1.32928 | ||||||||
\(67\) | −12.4063 | −1.51567 | −0.757834 | − | 0.652447i | \(-0.773742\pi\) | ||||
−0.757834 | + | 0.652447i | \(0.773742\pi\) | |||||||
\(68\) | 3.72594 | 0.451837 | ||||||||
\(69\) | −21.9971 | −2.64814 | ||||||||
\(70\) | −5.26153 | −0.628873 | ||||||||
\(71\) | 3.25374 | 0.386148 | 0.193074 | − | 0.981184i | \(-0.438154\pi\) | ||||
0.193074 | + | 0.981184i | \(0.438154\pi\) | |||||||
\(72\) | −23.9566 | −2.82332 | ||||||||
\(73\) | −2.96888 | −0.347482 | −0.173741 | − | 0.984791i | \(-0.555585\pi\) | ||||
−0.173741 | + | 0.984791i | \(0.555585\pi\) | |||||||
\(74\) | −1.18803 | −0.138106 | ||||||||
\(75\) | −17.6779 | −2.04127 | ||||||||
\(76\) | −26.7770 | −3.07153 | ||||||||
\(77\) | 1.01044 | 0.115150 | ||||||||
\(78\) | −32.5094 | −3.68096 | ||||||||
\(79\) | −9.14033 | −1.02837 | −0.514184 | − | 0.857680i | \(-0.671905\pi\) | ||||
−0.514184 | + | 0.857680i | \(0.671905\pi\) | |||||||
\(80\) | 8.04686 | 0.899666 | ||||||||
\(81\) | 7.24556 | 0.805062 | ||||||||
\(82\) | 3.30944 | 0.365466 | ||||||||
\(83\) | −6.20141 | −0.680694 | −0.340347 | − | 0.940300i | \(-0.610544\pi\) | ||||
−0.340347 | + | 0.940300i | \(0.610544\pi\) | |||||||
\(84\) | −7.34170 | −0.801045 | ||||||||
\(85\) | 3.31044 | 0.359067 | ||||||||
\(86\) | −25.4103 | −2.74006 | ||||||||
\(87\) | −1.52270 | −0.163250 | ||||||||
\(88\) | −6.28285 | −0.669754 | ||||||||
\(89\) | 8.10180 | 0.858789 | 0.429394 | − | 0.903117i | \(-0.358727\pi\) | ||||
0.429394 | + | 0.903117i | \(0.358727\pi\) | |||||||
\(90\) | −45.9500 | −4.84355 | ||||||||
\(91\) | −3.04180 | −0.318867 | ||||||||
\(92\) | 27.6276 | 2.88038 | ||||||||
\(93\) | 17.8979 | 1.85593 | ||||||||
\(94\) | −8.24812 | −0.850729 | ||||||||
\(95\) | −23.7909 | −2.44090 | ||||||||
\(96\) | −7.24872 | −0.739819 | ||||||||
\(97\) | 7.46187 | 0.757638 | 0.378819 | − | 0.925471i | \(-0.376330\pi\) | ||||
0.378819 | + | 0.925471i | \(0.376330\pi\) | |||||||
\(98\) | 15.6946 | 1.58539 | ||||||||
\(99\) | 8.82437 | 0.886883 | ||||||||
\(100\) | 22.2029 | 2.22029 | ||||||||
\(101\) | −8.55186 | −0.850942 | −0.425471 | − | 0.904972i | \(-0.639891\pi\) | ||||
−0.425471 | + | 0.904972i | \(0.639891\pi\) | |||||||
\(102\) | 7.09873 | 0.702879 | ||||||||
\(103\) | −12.4538 | −1.22711 | −0.613553 | − | 0.789654i | \(-0.710260\pi\) | ||||
−0.613553 | + | 0.789654i | \(0.710260\pi\) | |||||||
\(104\) | 18.9137 | 1.85464 | ||||||||
\(105\) | −6.52298 | −0.636577 | ||||||||
\(106\) | −18.0859 | −1.75665 | ||||||||
\(107\) | 14.0075 | 1.35415 | 0.677077 | − | 0.735912i | \(-0.263246\pi\) | ||||
0.677077 | + | 0.735912i | \(0.263246\pi\) | |||||||
\(108\) | −30.9565 | −2.97879 | ||||||||
\(109\) | 19.0845 | 1.82797 | 0.913983 | − | 0.405752i | \(-0.132990\pi\) | ||||
0.913983 | + | 0.405752i | \(0.132990\pi\) | |||||||
\(110\) | −12.0508 | −1.14900 | ||||||||
\(111\) | −1.47286 | −0.139798 | ||||||||
\(112\) | 1.61452 | 0.152558 | ||||||||
\(113\) | −6.46803 | −0.608461 | −0.304231 | − | 0.952598i | \(-0.598399\pi\) | ||||
−0.304231 | + | 0.952598i | \(0.598399\pi\) | |||||||
\(114\) | −51.0160 | −4.77809 | ||||||||
\(115\) | 24.5467 | 2.28899 | ||||||||
\(116\) | 1.91246 | 0.177567 | ||||||||
\(117\) | −26.5647 | −2.45590 | ||||||||
\(118\) | 25.5673 | 2.35366 | ||||||||
\(119\) | 0.664206 | 0.0608877 | ||||||||
\(120\) | 40.5594 | 3.70255 | ||||||||
\(121\) | −8.68573 | −0.789612 | ||||||||
\(122\) | −12.9600 | −1.17335 | ||||||||
\(123\) | 4.10287 | 0.369944 | ||||||||
\(124\) | −22.4793 | −2.01870 | ||||||||
\(125\) | 3.17471 | 0.283955 | ||||||||
\(126\) | −9.21941 | −0.821330 | ||||||||
\(127\) | −14.8891 | −1.32119 | −0.660597 | − | 0.750741i | \(-0.729697\pi\) | ||||
−0.660597 | + | 0.750741i | \(0.729697\pi\) | |||||||
\(128\) | 20.7372 | 1.83293 | ||||||||
\(129\) | −31.5024 | −2.77363 | ||||||||
\(130\) | 36.2774 | 3.18174 | ||||||||
\(131\) | −7.57558 | −0.661881 | −0.330941 | − | 0.943652i | \(-0.607366\pi\) | ||||
−0.330941 | + | 0.943652i | \(0.607366\pi\) | |||||||
\(132\) | −16.8151 | −1.46357 | ||||||||
\(133\) | −4.77341 | −0.413907 | ||||||||
\(134\) | 29.6869 | 2.56456 | ||||||||
\(135\) | −27.5043 | −2.36720 | ||||||||
\(136\) | −4.12999 | −0.354144 | ||||||||
\(137\) | 3.84937 | 0.328874 | 0.164437 | − | 0.986388i | \(-0.447419\pi\) | ||||
0.164437 | + | 0.986388i | \(0.447419\pi\) | |||||||
\(138\) | 52.6366 | 4.48073 | ||||||||
\(139\) | 7.24027 | 0.614111 | 0.307056 | − | 0.951692i | \(-0.400656\pi\) | ||||
0.307056 | + | 0.951692i | \(0.400656\pi\) | |||||||
\(140\) | 8.19265 | 0.692405 | ||||||||
\(141\) | −10.2256 | −0.861151 | ||||||||
\(142\) | −7.78585 | −0.653374 | ||||||||
\(143\) | −6.96683 | −0.582595 | ||||||||
\(144\) | 14.0999 | 1.17499 | ||||||||
\(145\) | 1.69919 | 0.141110 | ||||||||
\(146\) | 7.10422 | 0.587950 | ||||||||
\(147\) | 19.4573 | 1.60482 | ||||||||
\(148\) | 1.84987 | 0.152058 | ||||||||
\(149\) | 1.30583 | 0.106978 | 0.0534889 | − | 0.998568i | \(-0.482966\pi\) | ||||
0.0534889 | + | 0.998568i | \(0.482966\pi\) | |||||||
\(150\) | 42.3013 | 3.45389 | ||||||||
\(151\) | 12.9743 | 1.05584 | 0.527918 | − | 0.849295i | \(-0.322973\pi\) | ||||
0.527918 | + | 0.849295i | \(0.322973\pi\) | |||||||
\(152\) | 29.6808 | 2.40743 | ||||||||
\(153\) | 5.80065 | 0.468954 | ||||||||
\(154\) | −2.41788 | −0.194838 | ||||||||
\(155\) | −19.9725 | −1.60423 | ||||||||
\(156\) | 50.6199 | 4.05283 | ||||||||
\(157\) | −10.5795 | −0.844336 | −0.422168 | − | 0.906518i | \(-0.638731\pi\) | ||||
−0.422168 | + | 0.906518i | \(0.638731\pi\) | |||||||
\(158\) | 21.8718 | 1.74003 | ||||||||
\(159\) | −22.4219 | −1.77817 | ||||||||
\(160\) | 8.08890 | 0.639483 | ||||||||
\(161\) | 4.92505 | 0.388148 | ||||||||
\(162\) | −17.3379 | −1.36219 | ||||||||
\(163\) | −12.2255 | −0.957574 | −0.478787 | − | 0.877931i | \(-0.658923\pi\) | ||||
−0.478787 | + | 0.877931i | \(0.658923\pi\) | |||||||
\(164\) | −5.15308 | −0.402388 | ||||||||
\(165\) | −14.9400 | −1.16308 | ||||||||
\(166\) | 14.8393 | 1.15176 | ||||||||
\(167\) | −13.6663 | −1.05753 | −0.528765 | − | 0.848768i | \(-0.677345\pi\) | ||||
−0.528765 | + | 0.848768i | \(0.677345\pi\) | |||||||
\(168\) | 8.13785 | 0.627849 | ||||||||
\(169\) | 7.97275 | 0.613289 | ||||||||
\(170\) | −7.92153 | −0.607553 | ||||||||
\(171\) | −41.6872 | −3.18790 | ||||||||
\(172\) | 39.5660 | 3.01688 | ||||||||
\(173\) | −2.07228 | −0.157553 | −0.0787764 | − | 0.996892i | \(-0.525101\pi\) | ||||
−0.0787764 | + | 0.996892i | \(0.525101\pi\) | |||||||
\(174\) | 3.64365 | 0.276225 | ||||||||
\(175\) | 3.95801 | 0.299197 | ||||||||
\(176\) | 3.69784 | 0.278735 | ||||||||
\(177\) | 31.6970 | 2.38249 | ||||||||
\(178\) | −19.3867 | −1.45310 | ||||||||
\(179\) | −11.3940 | −0.851627 | −0.425813 | − | 0.904811i | \(-0.640012\pi\) | ||||
−0.425813 | + | 0.904811i | \(0.640012\pi\) | |||||||
\(180\) | 71.5480 | 5.33288 | ||||||||
\(181\) | 14.6896 | 1.09187 | 0.545934 | − | 0.837828i | \(-0.316175\pi\) | ||||
0.545934 | + | 0.837828i | \(0.316175\pi\) | |||||||
\(182\) | 7.27871 | 0.539534 | ||||||||
\(183\) | −16.0672 | −1.18772 | ||||||||
\(184\) | −30.6236 | −2.25760 | ||||||||
\(185\) | 1.64358 | 0.120838 | ||||||||
\(186\) | −42.8279 | −3.14029 | ||||||||
\(187\) | 1.52127 | 0.111247 | ||||||||
\(188\) | 12.8430 | 0.936675 | ||||||||
\(189\) | −5.51847 | −0.401410 | ||||||||
\(190\) | 56.9292 | 4.13008 | ||||||||
\(191\) | −23.3121 | −1.68681 | −0.843404 | − | 0.537280i | \(-0.819452\pi\) | ||||
−0.843404 | + | 0.537280i | \(0.819452\pi\) | |||||||
\(192\) | 31.7675 | 2.29262 | ||||||||
\(193\) | 0.0943234 | 0.00678955 | 0.00339477 | − | 0.999994i | \(-0.498919\pi\) | ||||
0.00339477 | + | 0.999994i | \(0.498919\pi\) | |||||||
\(194\) | −17.8555 | −1.28195 | ||||||||
\(195\) | 44.9749 | 3.22072 | ||||||||
\(196\) | −24.4378 | −1.74556 | ||||||||
\(197\) | 11.9398 | 0.850676 | 0.425338 | − | 0.905035i | \(-0.360155\pi\) | ||||
0.425338 | + | 0.905035i | \(0.360155\pi\) | |||||||
\(198\) | −21.1158 | −1.50063 | ||||||||
\(199\) | −3.25428 | −0.230689 | −0.115345 | − | 0.993326i | \(-0.536797\pi\) | ||||
−0.115345 | + | 0.993326i | \(0.536797\pi\) | |||||||
\(200\) | −24.6106 | −1.74023 | ||||||||
\(201\) | 36.8043 | 2.59598 | ||||||||
\(202\) | 20.4637 | 1.43982 | ||||||||
\(203\) | 0.340925 | 0.0239283 | ||||||||
\(204\) | −11.0533 | −0.773888 | ||||||||
\(205\) | −4.57843 | −0.319771 | ||||||||
\(206\) | 29.8005 | 2.07630 | ||||||||
\(207\) | 43.0114 | 2.98950 | ||||||||
\(208\) | −11.1319 | −0.771857 | ||||||||
\(209\) | −10.9328 | −0.756241 | ||||||||
\(210\) | 15.6088 | 1.07711 | ||||||||
\(211\) | −15.9941 | −1.10108 | −0.550539 | − | 0.834810i | \(-0.685578\pi\) | ||||
−0.550539 | + | 0.834810i | \(0.685578\pi\) | |||||||
\(212\) | 28.1612 | 1.93412 | ||||||||
\(213\) | −9.65250 | −0.661378 | ||||||||
\(214\) | −33.5184 | −2.29127 | ||||||||
\(215\) | 35.1537 | 2.39746 | ||||||||
\(216\) | 34.3135 | 2.33474 | ||||||||
\(217\) | −4.00727 | −0.272032 | ||||||||
\(218\) | −45.6673 | −3.09298 | ||||||||
\(219\) | 8.80746 | 0.595153 | ||||||||
\(220\) | 18.7641 | 1.26508 | ||||||||
\(221\) | −4.57960 | −0.308057 | ||||||||
\(222\) | 3.52440 | 0.236542 | ||||||||
\(223\) | 23.2597 | 1.55759 | 0.778793 | − | 0.627281i | \(-0.215832\pi\) | ||||
0.778793 | + | 0.627281i | \(0.215832\pi\) | |||||||
\(224\) | 1.62296 | 0.108438 | ||||||||
\(225\) | 34.5661 | 2.30440 | ||||||||
\(226\) | 15.4773 | 1.02954 | ||||||||
\(227\) | 12.5582 | 0.833517 | 0.416759 | − | 0.909017i | \(-0.363166\pi\) | ||||
0.416759 | + | 0.909017i | \(0.363166\pi\) | |||||||
\(228\) | 79.4363 | 5.26080 | ||||||||
\(229\) | −5.46352 | −0.361039 | −0.180520 | − | 0.983571i | \(-0.557778\pi\) | ||||
−0.180520 | + | 0.983571i | \(0.557778\pi\) | |||||||
\(230\) | −58.7376 | −3.87304 | ||||||||
\(231\) | −2.99756 | −0.197225 | ||||||||
\(232\) | −2.11985 | −0.139175 | ||||||||
\(233\) | 16.0949 | 1.05441 | 0.527207 | − | 0.849737i | \(-0.323239\pi\) | ||||
0.527207 | + | 0.849737i | \(0.323239\pi\) | |||||||
\(234\) | 63.5664 | 4.15546 | ||||||||
\(235\) | 11.4108 | 0.744360 | ||||||||
\(236\) | −39.8104 | −2.59144 | ||||||||
\(237\) | 27.1156 | 1.76135 | ||||||||
\(238\) | −1.58938 | −0.103024 | ||||||||
\(239\) | 11.4399 | 0.739982 | 0.369991 | − | 0.929035i | \(-0.379361\pi\) | ||||
0.369991 | + | 0.929035i | \(0.379361\pi\) | |||||||
\(240\) | −23.8717 | −1.54091 | ||||||||
\(241\) | −1.91523 | −0.123371 | −0.0616853 | − | 0.998096i | \(-0.519648\pi\) | ||||
−0.0616853 | + | 0.998096i | \(0.519648\pi\) | |||||||
\(242\) | 20.7840 | 1.33605 | ||||||||
\(243\) | 3.43050 | 0.220067 | ||||||||
\(244\) | 20.1799 | 1.29189 | ||||||||
\(245\) | −21.7126 | −1.38717 | ||||||||
\(246\) | −9.81774 | −0.625956 | ||||||||
\(247\) | 32.9120 | 2.09414 | ||||||||
\(248\) | 24.9170 | 1.58223 | ||||||||
\(249\) | 18.3970 | 1.16587 | ||||||||
\(250\) | −7.59674 | −0.480460 | ||||||||
\(251\) | −29.0417 | −1.83310 | −0.916548 | − | 0.399924i | \(-0.869037\pi\) | ||||
−0.916548 | + | 0.399924i | \(0.869037\pi\) | |||||||
\(252\) | 14.3554 | 0.904306 | ||||||||
\(253\) | 11.2801 | 0.709177 | ||||||||
\(254\) | 35.6280 | 2.23550 | ||||||||
\(255\) | −9.82071 | −0.614997 | ||||||||
\(256\) | −28.2051 | −1.76282 | ||||||||
\(257\) | −25.4618 | −1.58826 | −0.794132 | − | 0.607746i | \(-0.792074\pi\) | ||||
−0.794132 | + | 0.607746i | \(0.792074\pi\) | |||||||
\(258\) | 75.3818 | 4.69306 | ||||||||
\(259\) | 0.329768 | 0.0204908 | ||||||||
\(260\) | −56.4871 | −3.50318 | ||||||||
\(261\) | 2.97737 | 0.184295 | ||||||||
\(262\) | 18.1275 | 1.11992 | ||||||||
\(263\) | 10.3690 | 0.639382 | 0.319691 | − | 0.947522i | \(-0.396421\pi\) | ||||
0.319691 | + | 0.947522i | \(0.396421\pi\) | |||||||
\(264\) | 18.6386 | 1.14713 | ||||||||
\(265\) | 25.0208 | 1.53702 | ||||||||
\(266\) | 11.4223 | 0.700344 | ||||||||
\(267\) | −24.0347 | −1.47090 | ||||||||
\(268\) | −46.2251 | −2.82364 | ||||||||
\(269\) | 26.9442 | 1.64282 | 0.821409 | − | 0.570339i | \(-0.193188\pi\) | ||||
0.821409 | + | 0.570339i | \(0.193188\pi\) | |||||||
\(270\) | 65.8149 | 4.00537 | ||||||||
\(271\) | −14.9819 | −0.910085 | −0.455043 | − | 0.890470i | \(-0.650376\pi\) | ||||
−0.455043 | + | 0.890470i | \(0.650376\pi\) | |||||||
\(272\) | 2.43075 | 0.147386 | ||||||||
\(273\) | 9.02377 | 0.546144 | ||||||||
\(274\) | −9.21114 | −0.556466 | ||||||||
\(275\) | 9.06527 | 0.546656 | ||||||||
\(276\) | −81.9598 | −4.93340 | ||||||||
\(277\) | 28.3994 | 1.70635 | 0.853176 | − | 0.521623i | \(-0.174673\pi\) | ||||
0.853176 | + | 0.521623i | \(0.174673\pi\) | |||||||
\(278\) | −17.3252 | −1.03910 | ||||||||
\(279\) | −34.9963 | −2.09517 | ||||||||
\(280\) | −9.08109 | −0.542699 | ||||||||
\(281\) | −31.3888 | −1.87250 | −0.936250 | − | 0.351334i | \(-0.885728\pi\) | ||||
−0.936250 | + | 0.351334i | \(0.885728\pi\) | |||||||
\(282\) | 24.4688 | 1.45710 | ||||||||
\(283\) | 14.5001 | 0.861944 | 0.430972 | − | 0.902365i | \(-0.358171\pi\) | ||||
0.430972 | + | 0.902365i | \(0.358171\pi\) | |||||||
\(284\) | 12.1232 | 0.719381 | ||||||||
\(285\) | 70.5779 | 4.18067 | ||||||||
\(286\) | 16.6709 | 0.985770 | ||||||||
\(287\) | −0.918616 | −0.0542242 | ||||||||
\(288\) | 14.1736 | 0.835188 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −4.06598 | −0.238763 | ||||||||
\(291\) | −22.1363 | −1.29765 | ||||||||
\(292\) | −11.0619 | −0.647348 | ||||||||
\(293\) | −4.82214 | −0.281712 | −0.140856 | − | 0.990030i | \(-0.544986\pi\) | ||||
−0.140856 | + | 0.990030i | \(0.544986\pi\) | |||||||
\(294\) | −46.5594 | −2.71540 | ||||||||
\(295\) | −35.3709 | −2.05937 | ||||||||
\(296\) | −2.05047 | −0.119181 | ||||||||
\(297\) | −12.6393 | −0.733406 | ||||||||
\(298\) | −3.12471 | −0.181010 | ||||||||
\(299\) | −33.9575 | −1.96381 | ||||||||
\(300\) | −65.8668 | −3.80282 | ||||||||
\(301\) | 7.05324 | 0.406542 | ||||||||
\(302\) | −31.0462 | −1.78651 | ||||||||
\(303\) | 25.3698 | 1.45746 | ||||||||
\(304\) | −17.4689 | −1.00191 | ||||||||
\(305\) | 17.9295 | 1.02664 | ||||||||
\(306\) | −13.8803 | −0.793486 | ||||||||
\(307\) | −19.6934 | −1.12396 | −0.561980 | − | 0.827151i | \(-0.689960\pi\) | ||||
−0.561980 | + | 0.827151i | \(0.689960\pi\) | |||||||
\(308\) | 3.76484 | 0.214522 | ||||||||
\(309\) | 36.9452 | 2.10174 | ||||||||
\(310\) | 47.7920 | 2.71440 | ||||||||
\(311\) | −2.09304 | −0.118685 | −0.0593427 | − | 0.998238i | \(-0.518900\pi\) | ||||
−0.0593427 | + | 0.998238i | \(0.518900\pi\) | |||||||
\(312\) | −56.1092 | −3.17656 | ||||||||
\(313\) | −32.5181 | −1.83803 | −0.919017 | − | 0.394219i | \(-0.871015\pi\) | ||||
−0.919017 | + | 0.394219i | \(0.871015\pi\) | |||||||
\(314\) | 25.3156 | 1.42864 | ||||||||
\(315\) | 12.7545 | 0.718637 | ||||||||
\(316\) | −34.0563 | −1.91582 | ||||||||
\(317\) | 18.0121 | 1.01166 | 0.505831 | − | 0.862632i | \(-0.331186\pi\) | ||||
0.505831 | + | 0.862632i | \(0.331186\pi\) | |||||||
\(318\) | 53.6533 | 3.00873 | ||||||||
\(319\) | 0.780843 | 0.0437188 | ||||||||
\(320\) | −35.4496 | −1.98169 | ||||||||
\(321\) | −41.5544 | −2.31934 | ||||||||
\(322\) | −11.7851 | −0.656759 | ||||||||
\(323\) | −7.18664 | −0.399875 | ||||||||
\(324\) | 26.9965 | 1.49981 | ||||||||
\(325\) | −27.2898 | −1.51377 | ||||||||
\(326\) | 29.2543 | 1.62025 | ||||||||
\(327\) | −56.6159 | −3.13087 | ||||||||
\(328\) | 5.71189 | 0.315387 | ||||||||
\(329\) | 2.28947 | 0.126223 | ||||||||
\(330\) | 35.7498 | 1.96796 | ||||||||
\(331\) | 0.686909 | 0.0377560 | 0.0188780 | − | 0.999822i | \(-0.493991\pi\) | ||||
0.0188780 | + | 0.999822i | \(0.493991\pi\) | |||||||
\(332\) | −23.1061 | −1.26811 | ||||||||
\(333\) | 2.87993 | 0.157819 | ||||||||
\(334\) | 32.7020 | 1.78937 | ||||||||
\(335\) | −41.0702 | −2.24391 | ||||||||
\(336\) | −4.78962 | −0.261295 | ||||||||
\(337\) | −22.2664 | −1.21293 | −0.606465 | − | 0.795110i | \(-0.707413\pi\) | ||||
−0.606465 | + | 0.795110i | \(0.707413\pi\) | |||||||
\(338\) | −19.0780 | −1.03770 | ||||||||
\(339\) | 19.1880 | 1.04215 | ||||||||
\(340\) | 12.3345 | 0.668932 | ||||||||
\(341\) | −9.17811 | −0.497023 | ||||||||
\(342\) | 99.7530 | 5.39402 | ||||||||
\(343\) | −9.00586 | −0.486271 | ||||||||
\(344\) | −43.8566 | −2.36459 | ||||||||
\(345\) | −72.8199 | −3.92049 | ||||||||
\(346\) | 4.95875 | 0.266584 | ||||||||
\(347\) | 32.1424 | 1.72549 | 0.862747 | − | 0.505635i | \(-0.168742\pi\) | ||||
0.862747 | + | 0.505635i | \(0.168742\pi\) | |||||||
\(348\) | −5.67348 | −0.304130 | ||||||||
\(349\) | 34.4468 | 1.84389 | 0.921947 | − | 0.387317i | \(-0.126598\pi\) | ||||
0.921947 | + | 0.387317i | \(0.126598\pi\) | |||||||
\(350\) | −9.47109 | −0.506251 | ||||||||
\(351\) | 38.0490 | 2.03091 | ||||||||
\(352\) | 3.71716 | 0.198125 | ||||||||
\(353\) | 1.00000 | 0.0532246 | ||||||||
\(354\) | −75.8475 | −4.03125 | ||||||||
\(355\) | 10.7713 | 0.571681 | ||||||||
\(356\) | 30.1868 | 1.59990 | ||||||||
\(357\) | −1.97043 | −0.104286 | ||||||||
\(358\) | 27.2646 | 1.44098 | ||||||||
\(359\) | −24.2077 | −1.27763 | −0.638816 | − | 0.769359i | \(-0.720576\pi\) | ||||
−0.638816 | + | 0.769359i | \(0.720576\pi\) | |||||||
\(360\) | −79.3069 | −4.17984 | ||||||||
\(361\) | 32.6478 | 1.71831 | ||||||||
\(362\) | −35.1506 | −1.84747 | ||||||||
\(363\) | 25.7670 | 1.35242 | ||||||||
\(364\) | −11.3336 | −0.594041 | ||||||||
\(365\) | −9.82831 | −0.514437 | ||||||||
\(366\) | 38.4471 | 2.00966 | ||||||||
\(367\) | 7.67252 | 0.400502 | 0.200251 | − | 0.979745i | \(-0.435824\pi\) | ||||
0.200251 | + | 0.979745i | \(0.435824\pi\) | |||||||
\(368\) | 18.0239 | 0.939560 | ||||||||
\(369\) | −8.02245 | −0.417632 | ||||||||
\(370\) | −3.93291 | −0.204462 | ||||||||
\(371\) | 5.02017 | 0.260634 | ||||||||
\(372\) | 66.6867 | 3.45754 | ||||||||
\(373\) | −4.16614 | −0.215715 | −0.107857 | − | 0.994166i | \(-0.534399\pi\) | ||||
−0.107857 | + | 0.994166i | \(0.534399\pi\) | |||||||
\(374\) | −3.64025 | −0.188233 | ||||||||
\(375\) | −9.41806 | −0.486346 | ||||||||
\(376\) | −14.2358 | −0.734154 | ||||||||
\(377\) | −2.35063 | −0.121064 | ||||||||
\(378\) | 13.2051 | 0.679198 | ||||||||
\(379\) | −9.94519 | −0.510850 | −0.255425 | − | 0.966829i | \(-0.582215\pi\) | ||||
−0.255425 | + | 0.966829i | \(0.582215\pi\) | |||||||
\(380\) | −88.6436 | −4.54732 | ||||||||
\(381\) | 44.1698 | 2.26289 | ||||||||
\(382\) | 55.7835 | 2.85413 | ||||||||
\(383\) | 29.7105 | 1.51814 | 0.759068 | − | 0.651012i | \(-0.225655\pi\) | ||||
0.759068 | + | 0.651012i | \(0.225655\pi\) | |||||||
\(384\) | −61.5188 | −3.13937 | ||||||||
\(385\) | 3.34500 | 0.170477 | ||||||||
\(386\) | −0.225706 | −0.0114881 | ||||||||
\(387\) | 61.5974 | 3.13117 | ||||||||
\(388\) | 27.8025 | 1.41146 | ||||||||
\(389\) | −28.5712 | −1.44862 | −0.724309 | − | 0.689476i | \(-0.757841\pi\) | ||||
−0.724309 | + | 0.689476i | \(0.757841\pi\) | |||||||
\(390\) | −107.620 | −5.44956 | ||||||||
\(391\) | 7.41494 | 0.374990 | ||||||||
\(392\) | 27.0879 | 1.36815 | ||||||||
\(393\) | 22.4736 | 1.13364 | ||||||||
\(394\) | −28.5707 | −1.43937 | ||||||||
\(395\) | −30.2585 | −1.52247 | ||||||||
\(396\) | 32.8791 | 1.65224 | ||||||||
\(397\) | −35.7002 | −1.79174 | −0.895870 | − | 0.444317i | \(-0.853446\pi\) | ||||
−0.895870 | + | 0.444317i | \(0.853446\pi\) | |||||||
\(398\) | 7.78713 | 0.390334 | ||||||||
\(399\) | 14.1608 | 0.708924 | ||||||||
\(400\) | 14.4849 | 0.724243 | ||||||||
\(401\) | −28.2692 | −1.41170 | −0.705848 | − | 0.708363i | \(-0.749434\pi\) | ||||
−0.705848 | + | 0.708363i | \(0.749434\pi\) | |||||||
\(402\) | −88.0688 | −4.39247 | ||||||||
\(403\) | 27.6295 | 1.37633 | ||||||||
\(404\) | −31.8637 | −1.58528 | ||||||||
\(405\) | 23.9860 | 1.19187 | ||||||||
\(406\) | −0.815798 | −0.0404874 | ||||||||
\(407\) | 0.755287 | 0.0374382 | ||||||||
\(408\) | 12.2520 | 0.606564 | ||||||||
\(409\) | −2.06218 | −0.101968 | −0.0509841 | − | 0.998699i | \(-0.516236\pi\) | ||||
−0.0509841 | + | 0.998699i | \(0.516236\pi\) | |||||||
\(410\) | 10.9557 | 0.541063 | ||||||||
\(411\) | −11.4195 | −0.563283 | ||||||||
\(412\) | −46.4020 | −2.28606 | ||||||||
\(413\) | −7.09682 | −0.349212 | ||||||||
\(414\) | −102.922 | −5.05833 | ||||||||
\(415\) | −20.5294 | −1.00775 | ||||||||
\(416\) | −11.1900 | −0.548637 | ||||||||
\(417\) | −21.4789 | −1.05183 | ||||||||
\(418\) | 26.1611 | 1.27958 | ||||||||
\(419\) | −2.11486 | −0.103318 | −0.0516588 | − | 0.998665i | \(-0.516451\pi\) | ||||
−0.0516588 | + | 0.998665i | \(0.516451\pi\) | |||||||
\(420\) | −24.3042 | −1.18592 | ||||||||
\(421\) | 23.6134 | 1.15085 | 0.575424 | − | 0.817855i | \(-0.304837\pi\) | ||||
0.575424 | + | 0.817855i | \(0.304837\pi\) | |||||||
\(422\) | 38.2721 | 1.86306 | ||||||||
\(423\) | 19.9944 | 0.972161 | ||||||||
\(424\) | −31.2151 | −1.51594 | ||||||||
\(425\) | 5.95900 | 0.289054 | ||||||||
\(426\) | 23.0974 | 1.11907 | ||||||||
\(427\) | 3.59738 | 0.174089 | ||||||||
\(428\) | 52.1910 | 2.52275 | ||||||||
\(429\) | 20.6677 | 0.997846 | ||||||||
\(430\) | −84.1191 | −4.05658 | ||||||||
\(431\) | −10.0667 | −0.484894 | −0.242447 | − | 0.970165i | \(-0.577950\pi\) | ||||
−0.242447 | + | 0.970165i | \(0.577950\pi\) | |||||||
\(432\) | −20.1956 | −0.971660 | ||||||||
\(433\) | −20.2518 | −0.973238 | −0.486619 | − | 0.873614i | \(-0.661770\pi\) | ||||
−0.486619 | + | 0.873614i | \(0.661770\pi\) | |||||||
\(434\) | 9.58898 | 0.460286 | ||||||||
\(435\) | −5.04079 | −0.241688 | ||||||||
\(436\) | 71.1078 | 3.40545 | ||||||||
\(437\) | −53.2885 | −2.54913 | ||||||||
\(438\) | −21.0753 | −1.00702 | ||||||||
\(439\) | 1.13571 | 0.0542044 | 0.0271022 | − | 0.999633i | \(-0.491372\pi\) | ||||
0.0271022 | + | 0.999633i | \(0.491372\pi\) | |||||||
\(440\) | −20.7990 | −0.991553 | ||||||||
\(441\) | −38.0455 | −1.81169 | ||||||||
\(442\) | 10.9585 | 0.521243 | ||||||||
\(443\) | 11.4368 | 0.543381 | 0.271690 | − | 0.962385i | \(-0.412417\pi\) | ||||
0.271690 | + | 0.962385i | \(0.412417\pi\) | |||||||
\(444\) | −5.48780 | −0.260439 | ||||||||
\(445\) | 26.8205 | 1.27141 | ||||||||
\(446\) | −55.6580 | −2.63548 | ||||||||
\(447\) | −3.87386 | −0.183227 | ||||||||
\(448\) | −7.11261 | −0.336039 | ||||||||
\(449\) | −0.799392 | −0.0377257 | −0.0188628 | − | 0.999822i | \(-0.506005\pi\) | ||||
−0.0188628 | + | 0.999822i | \(0.506005\pi\) | |||||||
\(450\) | −82.7129 | −3.89912 | ||||||||
\(451\) | −2.10396 | −0.0990718 | ||||||||
\(452\) | −24.0995 | −1.13355 | ||||||||
\(453\) | −38.4895 | −1.80839 | ||||||||
\(454\) | −30.0505 | −1.41034 | ||||||||
\(455\) | −10.0697 | −0.472075 | ||||||||
\(456\) | −88.0506 | −4.12335 | ||||||||
\(457\) | 13.0399 | 0.609983 | 0.304992 | − | 0.952355i | \(-0.401346\pi\) | ||||
0.304992 | + | 0.952355i | \(0.401346\pi\) | |||||||
\(458\) | 13.0736 | 0.610890 | ||||||||
\(459\) | −8.30836 | −0.387801 | ||||||||
\(460\) | 91.4595 | 4.26432 | ||||||||
\(461\) | 36.6927 | 1.70895 | 0.854475 | − | 0.519492i | \(-0.173879\pi\) | ||||
0.854475 | + | 0.519492i | \(0.173879\pi\) | |||||||
\(462\) | 7.17284 | 0.333711 | ||||||||
\(463\) | −32.4335 | −1.50731 | −0.753656 | − | 0.657270i | \(-0.771711\pi\) | ||||
−0.753656 | + | 0.657270i | \(0.771711\pi\) | |||||||
\(464\) | 1.24766 | 0.0579213 | ||||||||
\(465\) | 59.2500 | 2.74766 | ||||||||
\(466\) | −38.5134 | −1.78410 | ||||||||
\(467\) | −12.6535 | −0.585532 | −0.292766 | − | 0.956184i | \(-0.594576\pi\) | ||||
−0.292766 | + | 0.956184i | \(0.594576\pi\) | |||||||
\(468\) | −98.9783 | −4.57527 | ||||||||
\(469\) | −8.24033 | −0.380503 | ||||||||
\(470\) | −27.3049 | −1.25948 | ||||||||
\(471\) | 31.3850 | 1.44615 | ||||||||
\(472\) | 44.1276 | 2.03114 | ||||||||
\(473\) | 16.1545 | 0.742784 | ||||||||
\(474\) | −64.8847 | −2.98025 | ||||||||
\(475\) | −42.8252 | −1.96495 | ||||||||
\(476\) | 2.47479 | 0.113432 | ||||||||
\(477\) | 43.8422 | 2.00740 | ||||||||
\(478\) | −27.3743 | −1.25207 | ||||||||
\(479\) | −17.3201 | −0.791375 | −0.395687 | − | 0.918385i | \(-0.629494\pi\) | ||||
−0.395687 | + | 0.918385i | \(0.629494\pi\) | |||||||
\(480\) | −23.9964 | −1.09528 | ||||||||
\(481\) | −2.27370 | −0.103672 | ||||||||
\(482\) | 4.58293 | 0.208747 | ||||||||
\(483\) | −14.6106 | −0.664805 | ||||||||
\(484\) | −32.3625 | −1.47102 | ||||||||
\(485\) | 24.7021 | 1.12166 | ||||||||
\(486\) | −8.20883 | −0.372360 | ||||||||
\(487\) | 11.0941 | 0.502723 | 0.251361 | − | 0.967893i | \(-0.419122\pi\) | ||||
0.251361 | + | 0.967893i | \(0.419122\pi\) | |||||||
\(488\) | −22.3683 | −1.01256 | ||||||||
\(489\) | 36.2680 | 1.64010 | ||||||||
\(490\) | 51.9559 | 2.34713 | ||||||||
\(491\) | 23.2433 | 1.04895 | 0.524477 | − | 0.851425i | \(-0.324261\pi\) | ||||
0.524477 | + | 0.851425i | \(0.324261\pi\) | |||||||
\(492\) | 15.2871 | 0.689194 | ||||||||
\(493\) | 0.513282 | 0.0231171 | ||||||||
\(494\) | −78.7548 | −3.54335 | ||||||||
\(495\) | 29.2125 | 1.31301 | ||||||||
\(496\) | −14.6652 | −0.658485 | ||||||||
\(497\) | 2.16115 | 0.0969410 | ||||||||
\(498\) | −44.0222 | −1.97268 | ||||||||
\(499\) | −40.4438 | −1.81051 | −0.905256 | − | 0.424867i | \(-0.860321\pi\) | ||||
−0.905256 | + | 0.424867i | \(0.860321\pi\) | |||||||
\(500\) | 11.8288 | 0.528999 | ||||||||
\(501\) | 40.5423 | 1.81130 | ||||||||
\(502\) | 69.4937 | 3.10166 | ||||||||
\(503\) | −6.49672 | −0.289674 | −0.144837 | − | 0.989456i | \(-0.546266\pi\) | ||||
−0.144837 | + | 0.989456i | \(0.546266\pi\) | |||||||
\(504\) | −15.9121 | −0.708783 | ||||||||
\(505\) | −28.3104 | −1.25980 | ||||||||
\(506\) | −26.9922 | −1.19995 | ||||||||
\(507\) | −23.6519 | −1.05042 | ||||||||
\(508\) | −55.4759 | −2.46135 | ||||||||
\(509\) | −7.85252 | −0.348057 | −0.174028 | − | 0.984741i | \(-0.555678\pi\) | ||||
−0.174028 | + | 0.984741i | \(0.555678\pi\) | |||||||
\(510\) | 23.4999 | 1.04059 | ||||||||
\(511\) | −1.97195 | −0.0872340 | ||||||||
\(512\) | 26.0174 | 1.14982 | ||||||||
\(513\) | 59.7092 | 2.63623 | ||||||||
\(514\) | 60.9274 | 2.68739 | ||||||||
\(515\) | −41.2274 | −1.81670 | ||||||||
\(516\) | −117.376 | −5.16719 | ||||||||
\(517\) | 5.24372 | 0.230618 | ||||||||
\(518\) | −0.789099 | −0.0346710 | ||||||||
\(519\) | 6.14761 | 0.269850 | ||||||||
\(520\) | 62.6127 | 2.74575 | ||||||||
\(521\) | 24.5419 | 1.07520 | 0.537600 | − | 0.843200i | \(-0.319331\pi\) | ||||
0.537600 | + | 0.843200i | \(0.319331\pi\) | |||||||
\(522\) | −7.12453 | −0.311832 | ||||||||
\(523\) | −5.67476 | −0.248140 | −0.124070 | − | 0.992273i | \(-0.539595\pi\) | ||||
−0.124070 | + | 0.992273i | \(0.539595\pi\) | |||||||
\(524\) | −28.2261 | −1.23306 | ||||||||
\(525\) | −11.7418 | −0.512453 | ||||||||
\(526\) | −24.8120 | −1.08185 | ||||||||
\(527\) | −6.03318 | −0.262809 | ||||||||
\(528\) | −10.9700 | −0.477407 | ||||||||
\(529\) | 31.9813 | 1.39049 | ||||||||
\(530\) | −59.8721 | −2.60068 | ||||||||
\(531\) | −61.9779 | −2.68961 | ||||||||
\(532\) | −17.7855 | −0.771097 | ||||||||
\(533\) | 6.33371 | 0.274344 | ||||||||
\(534\) | 57.5125 | 2.48881 | ||||||||
\(535\) | 46.3709 | 2.00479 | ||||||||
\(536\) | 51.2378 | 2.21314 | ||||||||
\(537\) | 33.8013 | 1.45863 | ||||||||
\(538\) | −64.4747 | −2.77970 | ||||||||
\(539\) | −9.97777 | −0.429773 | ||||||||
\(540\) | −102.479 | −4.41002 | ||||||||
\(541\) | 9.12384 | 0.392265 | 0.196132 | − | 0.980577i | \(-0.437162\pi\) | ||||
0.196132 | + | 0.980577i | \(0.437162\pi\) | |||||||
\(542\) | 35.8501 | 1.53989 | ||||||||
\(543\) | −43.5779 | −1.87011 | ||||||||
\(544\) | 2.44345 | 0.104762 | ||||||||
\(545\) | 63.1782 | 2.70625 | ||||||||
\(546\) | −21.5929 | −0.924092 | ||||||||
\(547\) | 45.4620 | 1.94381 | 0.971907 | − | 0.235365i | \(-0.0756285\pi\) | ||||
0.971907 | + | 0.235365i | \(0.0756285\pi\) | |||||||
\(548\) | 14.3425 | 0.612683 | ||||||||
\(549\) | 31.4166 | 1.34083 | ||||||||
\(550\) | −21.6922 | −0.924960 | ||||||||
\(551\) | −3.68878 | −0.157147 | ||||||||
\(552\) | 90.8477 | 3.86674 | ||||||||
\(553\) | −6.07107 | −0.258168 | ||||||||
\(554\) | −67.9566 | −2.88720 | ||||||||
\(555\) | −4.87582 | −0.206967 | ||||||||
\(556\) | 26.9768 | 1.14407 | ||||||||
\(557\) | −8.19119 | −0.347072 | −0.173536 | − | 0.984828i | \(-0.555519\pi\) | ||||
−0.173536 | + | 0.984828i | \(0.555519\pi\) | |||||||
\(558\) | 83.7425 | 3.54510 | ||||||||
\(559\) | −48.6310 | −2.05687 | ||||||||
\(560\) | 5.34477 | 0.225858 | ||||||||
\(561\) | −4.51299 | −0.190539 | ||||||||
\(562\) | 75.1101 | 3.16833 | ||||||||
\(563\) | −25.0413 | −1.05536 | −0.527682 | − | 0.849442i | \(-0.676939\pi\) | ||||
−0.527682 | + | 0.849442i | \(0.676939\pi\) | |||||||
\(564\) | −38.1000 | −1.60430 | ||||||||
\(565\) | −21.4120 | −0.900811 | ||||||||
\(566\) | −34.6973 | −1.45844 | ||||||||
\(567\) | 4.81255 | 0.202108 | ||||||||
\(568\) | −13.4379 | −0.563842 | ||||||||
\(569\) | 2.12544 | 0.0891032 | 0.0445516 | − | 0.999007i | \(-0.485814\pi\) | ||||
0.0445516 | + | 0.999007i | \(0.485814\pi\) | |||||||
\(570\) | −168.885 | −7.07383 | ||||||||
\(571\) | −12.3339 | −0.516157 | −0.258078 | − | 0.966124i | \(-0.583089\pi\) | ||||
−0.258078 | + | 0.966124i | \(0.583089\pi\) | |||||||
\(572\) | −25.9580 | −1.08536 | ||||||||
\(573\) | 69.1575 | 2.88910 | ||||||||
\(574\) | 2.19815 | 0.0917490 | ||||||||
\(575\) | 44.1856 | 1.84267 | ||||||||
\(576\) | −62.1158 | −2.58816 | ||||||||
\(577\) | −40.0784 | −1.66849 | −0.834243 | − | 0.551397i | \(-0.814095\pi\) | ||||
−0.834243 | + | 0.551397i | \(0.814095\pi\) | |||||||
\(578\) | −2.39289 | −0.0995313 | ||||||||
\(579\) | −0.279819 | −0.0116289 | ||||||||
\(580\) | 6.33108 | 0.262884 | ||||||||
\(581\) | −4.11902 | −0.170886 | ||||||||
\(582\) | 52.9698 | 2.19567 | ||||||||
\(583\) | 11.4980 | 0.476199 | ||||||||
\(584\) | 12.2615 | 0.507383 | ||||||||
\(585\) | −87.9406 | −3.63590 | ||||||||
\(586\) | 11.5389 | 0.476666 | ||||||||
\(587\) | 4.83871 | 0.199715 | 0.0998575 | − | 0.995002i | \(-0.468161\pi\) | ||||
0.0998575 | + | 0.995002i | \(0.468161\pi\) | |||||||
\(588\) | 72.4969 | 2.98972 | ||||||||
\(589\) | 43.3583 | 1.78655 | ||||||||
\(590\) | 84.6388 | 3.48453 | ||||||||
\(591\) | −35.4205 | −1.45700 | ||||||||
\(592\) | 1.20683 | 0.0496004 | ||||||||
\(593\) | −16.1196 | −0.661953 | −0.330976 | − | 0.943639i | \(-0.607378\pi\) | ||||
−0.330976 | + | 0.943639i | \(0.607378\pi\) | |||||||
\(594\) | 30.2445 | 1.24095 | ||||||||
\(595\) | 2.19881 | 0.0901426 | ||||||||
\(596\) | 4.86544 | 0.199296 | ||||||||
\(597\) | 9.65409 | 0.395116 | ||||||||
\(598\) | 81.2566 | 3.32283 | ||||||||
\(599\) | −39.1231 | −1.59853 | −0.799264 | − | 0.600980i | \(-0.794777\pi\) | ||||
−0.799264 | + | 0.600980i | \(0.794777\pi\) | |||||||
\(600\) | 73.0096 | 2.98060 | ||||||||
\(601\) | −4.43535 | −0.180922 | −0.0904608 | − | 0.995900i | \(-0.528834\pi\) | ||||
−0.0904608 | + | 0.995900i | \(0.528834\pi\) | |||||||
\(602\) | −16.8777 | −0.687882 | ||||||||
\(603\) | −71.9644 | −2.93062 | ||||||||
\(604\) | 48.3416 | 1.96699 | ||||||||
\(605\) | −28.7536 | −1.16900 | ||||||||
\(606\) | −60.7073 | −2.46607 | ||||||||
\(607\) | 12.5813 | 0.510660 | 0.255330 | − | 0.966854i | \(-0.417816\pi\) | ||||
0.255330 | + | 0.966854i | \(0.417816\pi\) | |||||||
\(608\) | −17.5602 | −0.712161 | ||||||||
\(609\) | −1.01139 | −0.0409834 | ||||||||
\(610\) | −42.9034 | −1.73711 | ||||||||
\(611\) | −15.7855 | −0.638615 | ||||||||
\(612\) | 21.6129 | 0.873648 | ||||||||
\(613\) | −16.6562 | −0.672736 | −0.336368 | − | 0.941731i | \(-0.609199\pi\) | ||||
−0.336368 | + | 0.941731i | \(0.609199\pi\) | |||||||
\(614\) | 47.1242 | 1.90178 | ||||||||
\(615\) | 13.5823 | 0.547691 | ||||||||
\(616\) | −4.17311 | −0.168139 | ||||||||
\(617\) | 38.4925 | 1.54965 | 0.774824 | − | 0.632177i | \(-0.217838\pi\) | ||||
0.774824 | + | 0.632177i | \(0.217838\pi\) | |||||||
\(618\) | −88.4059 | −3.55621 | ||||||||
\(619\) | −11.9418 | −0.479980 | −0.239990 | − | 0.970775i | \(-0.577144\pi\) | ||||
−0.239990 | + | 0.970775i | \(0.577144\pi\) | |||||||
\(620\) | −74.4162 | −2.98863 | ||||||||
\(621\) | −61.6060 | −2.47216 | ||||||||
\(622\) | 5.00842 | 0.200819 | ||||||||
\(623\) | 5.38127 | 0.215596 | ||||||||
\(624\) | 33.0237 | 1.32201 | ||||||||
\(625\) | −19.2853 | −0.771413 | ||||||||
\(626\) | 77.8124 | 3.11001 | ||||||||
\(627\) | 32.4333 | 1.29526 | ||||||||
\(628\) | −39.4186 | −1.57297 | ||||||||
\(629\) | 0.496483 | 0.0197961 | ||||||||
\(630\) | −30.5203 | −1.21596 | ||||||||
\(631\) | 2.20919 | 0.0879466 | 0.0439733 | − | 0.999033i | \(-0.485998\pi\) | ||||
0.0439733 | + | 0.999033i | \(0.485998\pi\) | |||||||
\(632\) | 37.7495 | 1.50159 | ||||||||
\(633\) | 47.4478 | 1.88588 | ||||||||
\(634\) | −43.1011 | −1.71177 | ||||||||
\(635\) | −49.2894 | −1.95599 | ||||||||
\(636\) | −83.5428 | −3.31269 | ||||||||
\(637\) | 30.0368 | 1.19010 | ||||||||
\(638\) | −1.86847 | −0.0739736 | ||||||||
\(639\) | 18.8738 | 0.746635 | ||||||||
\(640\) | 68.6493 | 2.71360 | ||||||||
\(641\) | 26.7565 | 1.05682 | 0.528410 | − | 0.848989i | \(-0.322788\pi\) | ||||
0.528410 | + | 0.848989i | \(0.322788\pi\) | |||||||
\(642\) | 99.4353 | 3.92440 | ||||||||
\(643\) | 5.95750 | 0.234941 | 0.117470 | − | 0.993076i | \(-0.462521\pi\) | ||||
0.117470 | + | 0.993076i | \(0.462521\pi\) | |||||||
\(644\) | 18.3504 | 0.723109 | ||||||||
\(645\) | −104.287 | −4.10628 | ||||||||
\(646\) | 17.1969 | 0.676602 | ||||||||
\(647\) | −18.0701 | −0.710408 | −0.355204 | − | 0.934789i | \(-0.615589\pi\) | ||||
−0.355204 | + | 0.934789i | \(0.615589\pi\) | |||||||
\(648\) | −29.9241 | −1.17553 | ||||||||
\(649\) | −16.2543 | −0.638037 | ||||||||
\(650\) | 65.3017 | 2.56134 | ||||||||
\(651\) | 11.8879 | 0.465925 | ||||||||
\(652\) | −45.5514 | −1.78393 | ||||||||
\(653\) | 32.9171 | 1.28815 | 0.644073 | − | 0.764964i | \(-0.277243\pi\) | ||||
0.644073 | + | 0.764964i | \(0.277243\pi\) | |||||||
\(654\) | 135.476 | 5.29753 | ||||||||
\(655\) | −25.0785 | −0.979897 | ||||||||
\(656\) | −3.36180 | −0.131256 | ||||||||
\(657\) | −17.2214 | −0.671873 | ||||||||
\(658\) | −5.47846 | −0.213573 | ||||||||
\(659\) | −44.0159 | −1.71462 | −0.857309 | − | 0.514802i | \(-0.827865\pi\) | ||||
−0.857309 | + | 0.514802i | \(0.827865\pi\) | |||||||
\(660\) | −55.6655 | −2.16678 | ||||||||
\(661\) | 38.3417 | 1.49132 | 0.745660 | − | 0.666326i | \(-0.232134\pi\) | ||||
0.745660 | + | 0.666326i | \(0.232134\pi\) | |||||||
\(662\) | −1.64370 | −0.0638843 | ||||||||
\(663\) | 13.5858 | 0.527628 | ||||||||
\(664\) | 25.6118 | 0.993931 | ||||||||
\(665\) | −15.8021 | −0.612779 | ||||||||
\(666\) | −6.89135 | −0.267035 | ||||||||
\(667\) | 3.80596 | 0.147367 | ||||||||
\(668\) | −50.9198 | −1.97015 | ||||||||
\(669\) | −69.0020 | −2.66777 | ||||||||
\(670\) | 98.2767 | 3.79676 | ||||||||
\(671\) | 8.23930 | 0.318075 | ||||||||
\(672\) | −4.81464 | −0.185729 | ||||||||
\(673\) | 0.394697 | 0.0152145 | 0.00760723 | − | 0.999971i | \(-0.497579\pi\) | ||||
0.00760723 | + | 0.999971i | \(0.497579\pi\) | |||||||
\(674\) | 53.2812 | 2.05232 | ||||||||
\(675\) | −49.5095 | −1.90562 | ||||||||
\(676\) | 29.7060 | 1.14254 | ||||||||
\(677\) | 27.3401 | 1.05077 | 0.525383 | − | 0.850866i | \(-0.323922\pi\) | ||||
0.525383 | + | 0.850866i | \(0.323922\pi\) | |||||||
\(678\) | −45.9148 | −1.76335 | ||||||||
\(679\) | 4.95622 | 0.190202 | ||||||||
\(680\) | −13.6721 | −0.524301 | ||||||||
\(681\) | −37.2550 | −1.42762 | ||||||||
\(682\) | 21.9622 | 0.840978 | ||||||||
\(683\) | −24.9374 | −0.954203 | −0.477101 | − | 0.878848i | \(-0.658313\pi\) | ||||
−0.477101 | + | 0.878848i | \(0.658313\pi\) | |||||||
\(684\) | −155.324 | −5.93896 | ||||||||
\(685\) | 12.7431 | 0.486889 | ||||||||
\(686\) | 21.5501 | 0.822786 | ||||||||
\(687\) | 16.2080 | 0.618374 | ||||||||
\(688\) | 25.8123 | 0.984084 | ||||||||
\(689\) | −34.6133 | −1.31866 | ||||||||
\(690\) | 174.250 | 6.63360 | ||||||||
\(691\) | 12.2531 | 0.466131 | 0.233066 | − | 0.972461i | \(-0.425124\pi\) | ||||
0.233066 | + | 0.972461i | \(0.425124\pi\) | |||||||
\(692\) | −7.72121 | −0.293516 | ||||||||
\(693\) | 5.86120 | 0.222649 | ||||||||
\(694\) | −76.9134 | −2.91959 | ||||||||
\(695\) | 23.9685 | 0.909175 | ||||||||
\(696\) | 6.28873 | 0.238374 | ||||||||
\(697\) | −1.38303 | −0.0523859 | ||||||||
\(698\) | −82.4275 | −3.11993 | ||||||||
\(699\) | −47.7470 | −1.80596 | ||||||||
\(700\) | 14.7473 | 0.557395 | ||||||||
\(701\) | 25.8486 | 0.976289 | 0.488144 | − | 0.872763i | \(-0.337674\pi\) | ||||
0.488144 | + | 0.872763i | \(0.337674\pi\) | |||||||
\(702\) | −91.0472 | −3.43636 | ||||||||
\(703\) | −3.56805 | −0.134571 | ||||||||
\(704\) | −16.2904 | −0.613969 | ||||||||
\(705\) | −33.8512 | −1.27491 | ||||||||
\(706\) | −2.39289 | −0.0900577 | ||||||||
\(707\) | −5.68020 | −0.213626 | ||||||||
\(708\) | 118.101 | 4.43851 | ||||||||
\(709\) | −2.08673 | −0.0783688 | −0.0391844 | − | 0.999232i | \(-0.512476\pi\) | ||||
−0.0391844 | + | 0.999232i | \(0.512476\pi\) | |||||||
\(710\) | −25.7746 | −0.967302 | ||||||||
\(711\) | −53.0198 | −1.98840 | ||||||||
\(712\) | −33.4604 | −1.25398 | ||||||||
\(713\) | −44.7356 | −1.67536 | ||||||||
\(714\) | 4.71502 | 0.176455 | ||||||||
\(715\) | −23.0633 | −0.862517 | ||||||||
\(716\) | −42.4533 | −1.58656 | ||||||||
\(717\) | −33.9373 | −1.26741 | ||||||||
\(718\) | 57.9264 | 2.16179 | ||||||||
\(719\) | −10.2721 | −0.383086 | −0.191543 | − | 0.981484i | \(-0.561349\pi\) | ||||
−0.191543 | + | 0.981484i | \(0.561349\pi\) | |||||||
\(720\) | 46.6770 | 1.73955 | ||||||||
\(721\) | −8.27187 | −0.308060 | ||||||||
\(722\) | −78.1227 | −2.90743 | ||||||||
\(723\) | 5.68169 | 0.211304 | ||||||||
\(724\) | 54.7325 | 2.03412 | ||||||||
\(725\) | 3.05865 | 0.113595 | ||||||||
\(726\) | −61.6576 | −2.28833 | ||||||||
\(727\) | −10.3579 | −0.384152 | −0.192076 | − | 0.981380i | \(-0.561522\pi\) | ||||
−0.192076 | + | 0.981380i | \(0.561522\pi\) | |||||||
\(728\) | 12.5626 | 0.465602 | ||||||||
\(729\) | −31.9136 | −1.18198 | ||||||||
\(730\) | 23.5181 | 0.870444 | ||||||||
\(731\) | 10.6191 | 0.392760 | ||||||||
\(732\) | −59.8654 | −2.21269 | ||||||||
\(733\) | −6.60155 | −0.243834 | −0.121917 | − | 0.992540i | \(-0.538904\pi\) | ||||
−0.121917 | + | 0.992540i | \(0.538904\pi\) | |||||||
\(734\) | −18.3595 | −0.677662 | ||||||||
\(735\) | 64.4123 | 2.37589 | ||||||||
\(736\) | 18.1180 | 0.667840 | ||||||||
\(737\) | −18.8733 | −0.695209 | ||||||||
\(738\) | 19.1969 | 0.706647 | ||||||||
\(739\) | −23.1340 | −0.850996 | −0.425498 | − | 0.904959i | \(-0.639901\pi\) | ||||
−0.425498 | + | 0.904959i | \(0.639901\pi\) | |||||||
\(740\) | 6.12387 | 0.225118 | ||||||||
\(741\) | −97.6362 | −3.58676 | ||||||||
\(742\) | −12.0127 | −0.441002 | ||||||||
\(743\) | −14.5616 | −0.534212 | −0.267106 | − | 0.963667i | \(-0.586067\pi\) | ||||
−0.267106 | + | 0.963667i | \(0.586067\pi\) | |||||||
\(744\) | −73.9184 | −2.70998 | ||||||||
\(745\) | 4.32287 | 0.158378 | ||||||||
\(746\) | 9.96913 | 0.364996 | ||||||||
\(747\) | −35.9722 | −1.31615 | ||||||||
\(748\) | 5.66818 | 0.207249 | ||||||||
\(749\) | 9.30385 | 0.339955 | ||||||||
\(750\) | 22.5364 | 0.822913 | ||||||||
\(751\) | −14.0225 | −0.511689 | −0.255844 | − | 0.966718i | \(-0.582353\pi\) | ||||
−0.255844 | + | 0.966718i | \(0.582353\pi\) | |||||||
\(752\) | 8.37862 | 0.305537 | ||||||||
\(753\) | 86.1548 | 3.13966 | ||||||||
\(754\) | 5.62480 | 0.204843 | ||||||||
\(755\) | 42.9507 | 1.56314 | ||||||||
\(756\) | −20.5615 | −0.747814 | ||||||||
\(757\) | 19.2348 | 0.699102 | 0.349551 | − | 0.936917i | \(-0.386334\pi\) | ||||
0.349551 | + | 0.936917i | \(0.386334\pi\) | |||||||
\(758\) | 23.7978 | 0.864374 | ||||||||
\(759\) | −33.4636 | −1.21465 | ||||||||
\(760\) | 98.2564 | 3.56413 | ||||||||
\(761\) | −50.9408 | −1.84660 | −0.923301 | − | 0.384078i | \(-0.874519\pi\) | ||||
−0.923301 | + | 0.384078i | \(0.874519\pi\) | |||||||
\(762\) | −105.694 | −3.82888 | ||||||||
\(763\) | 12.6761 | 0.458904 | ||||||||
\(764\) | −86.8597 | −3.14247 | ||||||||
\(765\) | 19.2027 | 0.694274 | ||||||||
\(766\) | −71.0941 | −2.56873 | ||||||||
\(767\) | 48.9315 | 1.76681 | ||||||||
\(768\) | 83.6730 | 3.01929 | ||||||||
\(769\) | 8.70472 | 0.313900 | 0.156950 | − | 0.987607i | \(-0.449834\pi\) | ||||
0.156950 | + | 0.987607i | \(0.449834\pi\) | |||||||
\(770\) | −8.00423 | −0.288452 | ||||||||
\(771\) | 75.5347 | 2.72031 | ||||||||
\(772\) | 0.351443 | 0.0126487 | ||||||||
\(773\) | −12.6343 | −0.454424 | −0.227212 | − | 0.973845i | \(-0.572961\pi\) | ||||
−0.227212 | + | 0.973845i | \(0.572961\pi\) | |||||||
\(774\) | −147.396 | −5.29804 | ||||||||
\(775\) | −35.9517 | −1.29142 | ||||||||
\(776\) | −30.8175 | −1.10628 | ||||||||
\(777\) | −0.978285 | −0.0350958 | ||||||||
\(778\) | 68.3678 | 2.45111 | ||||||||
\(779\) | 9.93932 | 0.356113 | ||||||||
\(780\) | 167.574 | 6.00011 | ||||||||
\(781\) | 4.94982 | 0.177119 | ||||||||
\(782\) | −17.7432 | −0.634494 | ||||||||
\(783\) | −4.26454 | −0.152402 | ||||||||
\(784\) | −15.9429 | −0.569389 | ||||||||
\(785\) | −35.0228 | −1.25002 | ||||||||
\(786\) | −53.7770 | −1.91816 | ||||||||
\(787\) | 3.44042 | 0.122638 | 0.0613188 | − | 0.998118i | \(-0.480469\pi\) | ||||
0.0613188 | + | 0.998118i | \(0.480469\pi\) | |||||||
\(788\) | 44.4870 | 1.58478 | ||||||||
\(789\) | −30.7606 | −1.09511 | ||||||||
\(790\) | 72.4053 | 2.57607 | ||||||||
\(791\) | −4.29611 | −0.152752 | ||||||||
\(792\) | −36.4446 | −1.29500 | ||||||||
\(793\) | −24.8034 | −0.880793 | ||||||||
\(794\) | 85.4267 | 3.03168 | ||||||||
\(795\) | −74.2264 | −2.63254 | ||||||||
\(796\) | −12.1252 | −0.429768 | ||||||||
\(797\) | 41.1756 | 1.45851 | 0.729256 | − | 0.684240i | \(-0.239866\pi\) | ||||
0.729256 | + | 0.684240i | \(0.239866\pi\) | |||||||
\(798\) | −33.8852 | −1.19952 | ||||||||
\(799\) | 3.44692 | 0.121943 | ||||||||
\(800\) | 14.5605 | 0.514793 | ||||||||
\(801\) | 46.9957 | 1.66051 | ||||||||
\(802\) | 67.6452 | 2.38863 | ||||||||
\(803\) | −4.51649 | −0.159383 | ||||||||
\(804\) | 137.131 | 4.83623 | ||||||||
\(805\) | 16.3041 | 0.574643 | ||||||||
\(806\) | −66.1146 | −2.32879 | ||||||||
\(807\) | −79.9324 | −2.81375 | ||||||||
\(808\) | 35.3191 | 1.24252 | ||||||||
\(809\) | 6.91375 | 0.243075 | 0.121537 | − | 0.992587i | \(-0.461218\pi\) | ||||
0.121537 | + | 0.992587i | \(0.461218\pi\) | |||||||
\(810\) | −57.3959 | −2.01669 | ||||||||
\(811\) | 2.15880 | 0.0758056 | 0.0379028 | − | 0.999281i | \(-0.487932\pi\) | ||||
0.0379028 | + | 0.999281i | \(0.487932\pi\) | |||||||
\(812\) | 1.27027 | 0.0445777 | ||||||||
\(813\) | 44.4451 | 1.55876 | ||||||||
\(814\) | −1.80732 | −0.0633466 | ||||||||
\(815\) | −40.4717 | −1.41766 | ||||||||
\(816\) | −7.21104 | −0.252437 | ||||||||
\(817\) | −76.3153 | −2.66993 | ||||||||
\(818\) | 4.93457 | 0.172533 | ||||||||
\(819\) | −17.6444 | −0.616546 | ||||||||
\(820\) | −17.0589 | −0.595724 | ||||||||
\(821\) | 6.86394 | 0.239553 | 0.119777 | − | 0.992801i | \(-0.461782\pi\) | ||||
0.119777 | + | 0.992801i | \(0.461782\pi\) | |||||||
\(822\) | 27.3257 | 0.953092 | ||||||||
\(823\) | 3.42194 | 0.119281 | 0.0596406 | − | 0.998220i | \(-0.481005\pi\) | ||||
0.0596406 | + | 0.998220i | \(0.481005\pi\) | |||||||
\(824\) | 51.4339 | 1.79179 | ||||||||
\(825\) | −26.8929 | −0.936291 | ||||||||
\(826\) | 16.9819 | 0.590877 | ||||||||
\(827\) | 5.66646 | 0.197042 | 0.0985210 | − | 0.995135i | \(-0.468589\pi\) | ||||
0.0985210 | + | 0.995135i | \(0.468589\pi\) | |||||||
\(828\) | 160.258 | 5.56935 | ||||||||
\(829\) | 45.1402 | 1.56778 | 0.783892 | − | 0.620897i | \(-0.213231\pi\) | ||||
0.783892 | + | 0.620897i | \(0.213231\pi\) | |||||||
\(830\) | 49.1247 | 1.70514 | ||||||||
\(831\) | −84.2492 | −2.92257 | ||||||||
\(832\) | 49.0403 | 1.70017 | ||||||||
\(833\) | −6.55883 | −0.227250 | ||||||||
\(834\) | 51.3967 | 1.77972 | ||||||||
\(835\) | −45.2414 | −1.56564 | ||||||||
\(836\) | −40.7351 | −1.40885 | ||||||||
\(837\) | 50.1258 | 1.73260 | ||||||||
\(838\) | 5.06063 | 0.174817 | ||||||||
\(839\) | −25.5119 | −0.880768 | −0.440384 | − | 0.897809i | \(-0.645158\pi\) | ||||
−0.440384 | + | 0.897809i | \(0.645158\pi\) | |||||||
\(840\) | 26.9398 | 0.929513 | ||||||||
\(841\) | −28.7365 | −0.990915 | ||||||||
\(842\) | −56.5045 | −1.94727 | ||||||||
\(843\) | 93.1177 | 3.20715 | ||||||||
\(844\) | −59.5930 | −2.05127 | ||||||||
\(845\) | 26.3933 | 0.907957 | ||||||||
\(846\) | −47.8445 | −1.64493 | ||||||||
\(847\) | −5.76912 | −0.198229 | ||||||||
\(848\) | 18.3720 | 0.630897 | ||||||||
\(849\) | −43.0160 | −1.47630 | ||||||||
\(850\) | −14.2593 | −0.489088 | ||||||||
\(851\) | 3.68139 | 0.126197 | ||||||||
\(852\) | −35.9646 | −1.23213 | ||||||||
\(853\) | −42.9552 | −1.47076 | −0.735378 | − | 0.677657i | \(-0.762995\pi\) | ||||
−0.735378 | + | 0.677657i | \(0.762995\pi\) | |||||||
\(854\) | −8.60814 | −0.294565 | ||||||||
\(855\) | −138.003 | −4.71960 | ||||||||
\(856\) | −57.8508 | −1.97730 | ||||||||
\(857\) | −38.7699 | −1.32435 | −0.662177 | − | 0.749347i | \(-0.730367\pi\) | ||||
−0.662177 | + | 0.749347i | \(0.730367\pi\) | |||||||
\(858\) | −49.4556 | −1.68839 | ||||||||
\(859\) | 9.42261 | 0.321495 | 0.160748 | − | 0.986996i | \(-0.448609\pi\) | ||||
0.160748 | + | 0.986996i | \(0.448609\pi\) | |||||||
\(860\) | 130.981 | 4.46640 | ||||||||
\(861\) | 2.72515 | 0.0928730 | ||||||||
\(862\) | 24.0885 | 0.820457 | ||||||||
\(863\) | −10.0989 | −0.343771 | −0.171885 | − | 0.985117i | \(-0.554986\pi\) | ||||
−0.171885 | + | 0.985117i | \(0.554986\pi\) | |||||||
\(864\) | −20.3011 | −0.690657 | ||||||||
\(865\) | −6.86017 | −0.233253 | ||||||||
\(866\) | 48.4603 | 1.64675 | ||||||||
\(867\) | −2.96659 | −0.100751 | ||||||||
\(868\) | −14.9309 | −0.506787 | ||||||||
\(869\) | −13.9049 | −0.471693 | ||||||||
\(870\) | 12.0621 | 0.408943 | ||||||||
\(871\) | 56.8158 | 1.92513 | ||||||||
\(872\) | −78.8190 | −2.66915 | ||||||||
\(873\) | 43.2837 | 1.46493 | ||||||||
\(874\) | 127.514 | 4.31322 | ||||||||
\(875\) | 2.10866 | 0.0712858 | ||||||||
\(876\) | 32.8161 | 1.10875 | ||||||||
\(877\) | 10.0707 | 0.340064 | 0.170032 | − | 0.985438i | \(-0.445613\pi\) | ||||
0.170032 | + | 0.985438i | \(0.445613\pi\) | |||||||
\(878\) | −2.71763 | −0.0917156 | ||||||||
\(879\) | 14.3053 | 0.482506 | ||||||||
\(880\) | 12.2415 | 0.412660 | ||||||||
\(881\) | 17.7225 | 0.597086 | 0.298543 | − | 0.954396i | \(-0.403499\pi\) | ||||
0.298543 | + | 0.954396i | \(0.403499\pi\) | |||||||
\(882\) | 91.0387 | 3.06543 | ||||||||
\(883\) | −12.4113 | −0.417672 | −0.208836 | − | 0.977951i | \(-0.566967\pi\) | ||||
−0.208836 | + | 0.977951i | \(0.566967\pi\) | |||||||
\(884\) | −17.0633 | −0.573902 | ||||||||
\(885\) | 104.931 | 3.52721 | ||||||||
\(886\) | −27.3671 | −0.919417 | ||||||||
\(887\) | −19.6307 | −0.659134 | −0.329567 | − | 0.944132i | \(-0.606903\pi\) | ||||
−0.329567 | + | 0.944132i | \(0.606903\pi\) | |||||||
\(888\) | 6.08291 | 0.204129 | ||||||||
\(889\) | −9.88944 | −0.331681 | ||||||||
\(890\) | −64.1786 | −2.15127 | ||||||||
\(891\) | 11.0225 | 0.369267 | ||||||||
\(892\) | 86.6643 | 2.90174 | ||||||||
\(893\) | −24.7718 | −0.828957 | ||||||||
\(894\) | 9.26973 | 0.310026 | ||||||||
\(895\) | −37.7191 | −1.26081 | ||||||||
\(896\) | 13.7738 | 0.460150 | ||||||||
\(897\) | 100.738 | 3.36354 | ||||||||
\(898\) | 1.91286 | 0.0638330 | ||||||||
\(899\) | −3.09672 | −0.103281 | ||||||||
\(900\) | 128.791 | 4.29304 | ||||||||
\(901\) | 7.55815 | 0.251799 | ||||||||
\(902\) | 5.03456 | 0.167633 | ||||||||
\(903\) | −20.9241 | −0.696309 | ||||||||
\(904\) | 26.7129 | 0.888459 | ||||||||
\(905\) | 48.6289 | 1.61648 | ||||||||
\(906\) | 92.1013 | 3.05986 | ||||||||
\(907\) | −52.0106 | −1.72698 | −0.863492 | − | 0.504363i | \(-0.831727\pi\) | ||||
−0.863492 | + | 0.504363i | \(0.831727\pi\) | |||||||
\(908\) | 46.7911 | 1.55282 | ||||||||
\(909\) | −49.6063 | −1.64534 | ||||||||
\(910\) | 24.0957 | 0.798765 | ||||||||
\(911\) | 0.973267 | 0.0322458 | 0.0161229 | − | 0.999870i | \(-0.494868\pi\) | ||||
0.0161229 | + | 0.999870i | \(0.494868\pi\) | |||||||
\(912\) | 51.8232 | 1.71604 | ||||||||
\(913\) | −9.43405 | −0.312221 | ||||||||
\(914\) | −31.2032 | −1.03211 | ||||||||
\(915\) | −53.1895 | −1.75839 | ||||||||
\(916\) | −20.3567 | −0.672605 | ||||||||
\(917\) | −5.03175 | −0.166163 | ||||||||
\(918\) | 19.8810 | 0.656172 | ||||||||
\(919\) | −3.05292 | −0.100707 | −0.0503533 | − | 0.998731i | \(-0.516035\pi\) | ||||
−0.0503533 | + | 0.998731i | \(0.516035\pi\) | |||||||
\(920\) | −101.378 | −3.34232 | ||||||||
\(921\) | 58.4222 | 1.92508 | ||||||||
\(922\) | −87.8018 | −2.89160 | ||||||||
\(923\) | −14.9008 | −0.490466 | ||||||||
\(924\) | −11.1687 | −0.367424 | ||||||||
\(925\) | 2.95854 | 0.0972764 | ||||||||
\(926\) | 77.6098 | 2.55042 | ||||||||
\(927\) | −72.2398 | −2.37267 | ||||||||
\(928\) | 1.25418 | 0.0411705 | ||||||||
\(929\) | 5.72496 | 0.187830 | 0.0939150 | − | 0.995580i | \(-0.470062\pi\) | ||||
0.0939150 | + | 0.995580i | \(0.470062\pi\) | |||||||
\(930\) | −141.779 | −4.64912 | ||||||||
\(931\) | 47.1360 | 1.54482 | ||||||||
\(932\) | 59.9687 | 1.96434 | ||||||||
\(933\) | 6.20918 | 0.203280 | ||||||||
\(934\) | 30.2784 | 0.990739 | ||||||||
\(935\) | 5.03608 | 0.164697 | ||||||||
\(936\) | 109.712 | 3.58604 | ||||||||
\(937\) | −5.60332 | −0.183053 | −0.0915263 | − | 0.995803i | \(-0.529175\pi\) | ||||
−0.0915263 | + | 0.995803i | \(0.529175\pi\) | |||||||
\(938\) | 19.7182 | 0.643823 | ||||||||
\(939\) | 96.4679 | 3.14811 | ||||||||
\(940\) | 42.5161 | 1.38672 | ||||||||
\(941\) | 29.0085 | 0.945649 | 0.472824 | − | 0.881157i | \(-0.343234\pi\) | ||||
0.472824 | + | 0.881157i | \(0.343234\pi\) | |||||||
\(942\) | −75.1010 | −2.44692 | ||||||||
\(943\) | −10.2551 | −0.333951 | ||||||||
\(944\) | −25.9718 | −0.845309 | ||||||||
\(945\) | −18.2686 | −0.594276 | ||||||||
\(946\) | −38.6560 | −1.25681 | ||||||||
\(947\) | 53.1651 | 1.72763 | 0.863817 | − | 0.503806i | \(-0.168067\pi\) | ||||
0.863817 | + | 0.503806i | \(0.168067\pi\) | |||||||
\(948\) | 101.031 | 3.28134 | ||||||||
\(949\) | 13.5963 | 0.441355 | ||||||||
\(950\) | 102.476 | 3.32476 | ||||||||
\(951\) | −53.4346 | −1.73274 | ||||||||
\(952\) | −2.74317 | −0.0889066 | ||||||||
\(953\) | −56.1998 | −1.82049 | −0.910245 | − | 0.414070i | \(-0.864107\pi\) | ||||
−0.910245 | + | 0.414070i | \(0.864107\pi\) | |||||||
\(954\) | −104.910 | −3.39658 | ||||||||
\(955\) | −77.1734 | −2.49727 | ||||||||
\(956\) | 42.6242 | 1.37857 | ||||||||
\(957\) | −2.31644 | −0.0748798 | ||||||||
\(958\) | 41.4451 | 1.33903 | ||||||||
\(959\) | 2.55678 | 0.0825627 | ||||||||
\(960\) | 105.164 | 3.39416 | ||||||||
\(961\) | 5.39921 | 0.174168 | ||||||||
\(962\) | 5.44071 | 0.175416 | ||||||||
\(963\) | 81.2524 | 2.61832 | ||||||||
\(964\) | −7.13602 | −0.229836 | ||||||||
\(965\) | 0.312252 | 0.0100517 | ||||||||
\(966\) | 34.9616 | 1.12487 | ||||||||
\(967\) | 28.2464 | 0.908342 | 0.454171 | − | 0.890915i | \(-0.349936\pi\) | ||||
0.454171 | + | 0.890915i | \(0.349936\pi\) | |||||||
\(968\) | 35.8720 | 1.15297 | ||||||||
\(969\) | 21.3198 | 0.684891 | ||||||||
\(970\) | −59.1094 | −1.89789 | ||||||||
\(971\) | 9.23425 | 0.296341 | 0.148171 | − | 0.988962i | \(-0.452662\pi\) | ||||
0.148171 | + | 0.988962i | \(0.452662\pi\) | |||||||
\(972\) | 12.7818 | 0.409978 | ||||||||
\(973\) | 4.80903 | 0.154170 | ||||||||
\(974\) | −26.5471 | −0.850623 | ||||||||
\(975\) | 80.9577 | 2.59272 | ||||||||
\(976\) | 13.1651 | 0.421404 | ||||||||
\(977\) | 7.32781 | 0.234438 | 0.117219 | − | 0.993106i | \(-0.462602\pi\) | ||||
0.117219 | + | 0.993106i | \(0.462602\pi\) | |||||||
\(978\) | −86.7855 | −2.77509 | ||||||||
\(979\) | 12.3251 | 0.393910 | ||||||||
\(980\) | −80.8999 | −2.58425 | ||||||||
\(981\) | 110.703 | 3.53446 | ||||||||
\(982\) | −55.6186 | −1.77486 | ||||||||
\(983\) | −13.1255 | −0.418638 | −0.209319 | − | 0.977847i | \(-0.567125\pi\) | ||||
−0.209319 | + | 0.977847i | \(0.567125\pi\) | |||||||
\(984\) | −16.9448 | −0.540182 | ||||||||
\(985\) | 39.5260 | 1.25940 | ||||||||
\(986\) | −1.22823 | −0.0391148 | ||||||||
\(987\) | −6.79191 | −0.216189 | ||||||||
\(988\) | 122.628 | 3.90132 | ||||||||
\(989\) | 78.7396 | 2.50377 | ||||||||
\(990\) | −69.9025 | −2.22165 | ||||||||
\(991\) | 46.8070 | 1.48687 | 0.743437 | − | 0.668806i | \(-0.233194\pi\) | ||||
0.743437 | + | 0.668806i | \(0.233194\pi\) | |||||||
\(992\) | −14.7418 | −0.468052 | ||||||||
\(993\) | −2.03778 | −0.0646669 | ||||||||
\(994\) | −5.17141 | −0.164027 | ||||||||
\(995\) | −10.7731 | −0.341529 | ||||||||
\(996\) | 68.5463 | 2.17197 | ||||||||
\(997\) | 15.9560 | 0.505333 | 0.252666 | − | 0.967553i | \(-0.418693\pi\) | ||||
0.252666 | + | 0.967553i | \(0.418693\pi\) | |||||||
\(998\) | 96.7777 | 3.06344 | ||||||||
\(999\) | −4.12497 | −0.130508 |
(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 | 6001.2.a.b.1.10 | ✓ | 114 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6001.2.a.b.1.10 | ✓ | 114 | 1.1 | even | 1 | trivial |