Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6026,2,Mod(1,6026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6026, 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("6026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6026 = 2 \cdot 23 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6026.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: | \(48.1178522580\) |
Analytic rank: | \(1\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 6026.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0.825726 | 0.476733 | 0.238366 | − | 0.971175i | \(-0.423388\pi\) | ||||
0.238366 | + | 0.971175i | \(0.423388\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.91252 | −1.30252 | −0.651259 | − | 0.758855i | \(-0.725759\pi\) | ||||
−0.651259 | + | 0.758855i | \(0.725759\pi\) | |||||||
\(6\) | 0.825726 | 0.337101 | ||||||||
\(7\) | −1.72528 | −0.652093 | −0.326047 | − | 0.945354i | \(-0.605717\pi\) | ||||
−0.326047 | + | 0.945354i | \(0.605717\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.31818 | −0.772726 | ||||||||
\(10\) | −2.91252 | −0.921020 | ||||||||
\(11\) | 3.70152 | 1.11605 | 0.558025 | − | 0.829824i | \(-0.311559\pi\) | ||||
0.558025 | + | 0.829824i | \(0.311559\pi\) | |||||||
\(12\) | 0.825726 | 0.238366 | ||||||||
\(13\) | −4.64552 | −1.28844 | −0.644218 | − | 0.764842i | \(-0.722817\pi\) | ||||
−0.644218 | + | 0.764842i | \(0.722817\pi\) | |||||||
\(14\) | −1.72528 | −0.461100 | ||||||||
\(15\) | −2.40494 | −0.620954 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.45979 | 1.08166 | 0.540829 | − | 0.841133i | \(-0.318111\pi\) | ||||
0.540829 | + | 0.841133i | \(0.318111\pi\) | |||||||
\(18\) | −2.31818 | −0.546400 | ||||||||
\(19\) | 8.38053 | 1.92263 | 0.961313 | − | 0.275458i | \(-0.0888295\pi\) | ||||
0.961313 | + | 0.275458i | \(0.0888295\pi\) | |||||||
\(20\) | −2.91252 | −0.651259 | ||||||||
\(21\) | −1.42461 | −0.310874 | ||||||||
\(22\) | 3.70152 | 0.789167 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0.825726 | 0.168551 | ||||||||
\(25\) | 3.48278 | 0.696555 | ||||||||
\(26\) | −4.64552 | −0.911062 | ||||||||
\(27\) | −4.39136 | −0.845117 | ||||||||
\(28\) | −1.72528 | −0.326047 | ||||||||
\(29\) | 0.958192 | 0.177932 | 0.0889659 | − | 0.996035i | \(-0.471644\pi\) | ||||
0.0889659 | + | 0.996035i | \(0.471644\pi\) | |||||||
\(30\) | −2.40494 | −0.439081 | ||||||||
\(31\) | 0.0262738 | 0.00471892 | 0.00235946 | − | 0.999997i | \(-0.499249\pi\) | ||||
0.00235946 | + | 0.999997i | \(0.499249\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 3.05644 | 0.532058 | ||||||||
\(34\) | 4.45979 | 0.764847 | ||||||||
\(35\) | 5.02490 | 0.849364 | ||||||||
\(36\) | −2.31818 | −0.386363 | ||||||||
\(37\) | 0.0277632 | 0.00456425 | 0.00228212 | − | 0.999997i | \(-0.499274\pi\) | ||||
0.00228212 | + | 0.999997i | \(0.499274\pi\) | |||||||
\(38\) | 8.38053 | 1.35950 | ||||||||
\(39\) | −3.83593 | −0.614240 | ||||||||
\(40\) | −2.91252 | −0.460510 | ||||||||
\(41\) | −2.57987 | −0.402909 | −0.201454 | − | 0.979498i | \(-0.564567\pi\) | ||||
−0.201454 | + | 0.979498i | \(0.564567\pi\) | |||||||
\(42\) | −1.42461 | −0.219821 | ||||||||
\(43\) | 4.39952 | 0.670921 | 0.335460 | − | 0.942054i | \(-0.391108\pi\) | ||||
0.335460 | + | 0.942054i | \(0.391108\pi\) | |||||||
\(44\) | 3.70152 | 0.558025 | ||||||||
\(45\) | 6.75174 | 1.00649 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −2.76732 | −0.403655 | −0.201828 | − | 0.979421i | \(-0.564688\pi\) | ||||
−0.201828 | + | 0.979421i | \(0.564688\pi\) | |||||||
\(48\) | 0.825726 | 0.119183 | ||||||||
\(49\) | −4.02342 | −0.574774 | ||||||||
\(50\) | 3.48278 | 0.492539 | ||||||||
\(51\) | 3.68256 | 0.515662 | ||||||||
\(52\) | −4.64552 | −0.644218 | ||||||||
\(53\) | −6.42047 | −0.881919 | −0.440960 | − | 0.897527i | \(-0.645362\pi\) | ||||
−0.440960 | + | 0.897527i | \(0.645362\pi\) | |||||||
\(54\) | −4.39136 | −0.597588 | ||||||||
\(55\) | −10.7808 | −1.45368 | ||||||||
\(56\) | −1.72528 | −0.230550 | ||||||||
\(57\) | 6.92002 | 0.916579 | ||||||||
\(58\) | 0.958192 | 0.125817 | ||||||||
\(59\) | −10.5683 | −1.37588 | −0.687940 | − | 0.725768i | \(-0.741485\pi\) | ||||
−0.687940 | + | 0.725768i | \(0.741485\pi\) | |||||||
\(60\) | −2.40494 | −0.310477 | ||||||||
\(61\) | −9.59785 | −1.22888 | −0.614439 | − | 0.788964i | \(-0.710618\pi\) | ||||
−0.614439 | + | 0.788964i | \(0.710618\pi\) | |||||||
\(62\) | 0.0262738 | 0.00333678 | ||||||||
\(63\) | 3.99950 | 0.503889 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 13.5302 | 1.67821 | ||||||||
\(66\) | 3.05644 | 0.376222 | ||||||||
\(67\) | −6.74945 | −0.824576 | −0.412288 | − | 0.911053i | \(-0.635270\pi\) | ||||
−0.412288 | + | 0.911053i | \(0.635270\pi\) | |||||||
\(68\) | 4.45979 | 0.540829 | ||||||||
\(69\) | −0.825726 | −0.0994057 | ||||||||
\(70\) | 5.02490 | 0.600591 | ||||||||
\(71\) | −3.62262 | −0.429926 | −0.214963 | − | 0.976622i | \(-0.568963\pi\) | ||||
−0.214963 | + | 0.976622i | \(0.568963\pi\) | |||||||
\(72\) | −2.31818 | −0.273200 | ||||||||
\(73\) | −0.166419 | −0.0194779 | −0.00973893 | − | 0.999953i | \(-0.503100\pi\) | ||||
−0.00973893 | + | 0.999953i | \(0.503100\pi\) | |||||||
\(74\) | 0.0277632 | 0.00322741 | ||||||||
\(75\) | 2.87582 | 0.332071 | ||||||||
\(76\) | 8.38053 | 0.961313 | ||||||||
\(77\) | −6.38615 | −0.727769 | ||||||||
\(78\) | −3.83593 | −0.434333 | ||||||||
\(79\) | −8.12246 | −0.913848 | −0.456924 | − | 0.889506i | \(-0.651049\pi\) | ||||
−0.456924 | + | 0.889506i | \(0.651049\pi\) | |||||||
\(80\) | −2.91252 | −0.325630 | ||||||||
\(81\) | 3.32848 | 0.369831 | ||||||||
\(82\) | −2.57987 | −0.284899 | ||||||||
\(83\) | −4.83091 | −0.530262 | −0.265131 | − | 0.964212i | \(-0.585415\pi\) | ||||
−0.265131 | + | 0.964212i | \(0.585415\pi\) | |||||||
\(84\) | −1.42461 | −0.155437 | ||||||||
\(85\) | −12.9892 | −1.40888 | ||||||||
\(86\) | 4.39952 | 0.474413 | ||||||||
\(87\) | 0.791204 | 0.0848260 | ||||||||
\(88\) | 3.70152 | 0.394583 | ||||||||
\(89\) | 0.889547 | 0.0942918 | 0.0471459 | − | 0.998888i | \(-0.484987\pi\) | ||||
0.0471459 | + | 0.998888i | \(0.484987\pi\) | |||||||
\(90\) | 6.75174 | 0.711696 | ||||||||
\(91\) | 8.01481 | 0.840181 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 0.0216950 | 0.00224966 | ||||||||
\(94\) | −2.76732 | −0.285427 | ||||||||
\(95\) | −24.4085 | −2.50426 | ||||||||
\(96\) | 0.825726 | 0.0842753 | ||||||||
\(97\) | 3.83775 | 0.389664 | 0.194832 | − | 0.980837i | \(-0.437584\pi\) | ||||
0.194832 | + | 0.980837i | \(0.437584\pi\) | |||||||
\(98\) | −4.02342 | −0.406427 | ||||||||
\(99\) | −8.58078 | −0.862401 | ||||||||
\(100\) | 3.48278 | 0.348278 | ||||||||
\(101\) | −12.9059 | −1.28418 | −0.642092 | − | 0.766628i | \(-0.721933\pi\) | ||||
−0.642092 | + | 0.766628i | \(0.721933\pi\) | |||||||
\(102\) | 3.68256 | 0.364628 | ||||||||
\(103\) | 4.12459 | 0.406408 | 0.203204 | − | 0.979136i | \(-0.434865\pi\) | ||||
0.203204 | + | 0.979136i | \(0.434865\pi\) | |||||||
\(104\) | −4.64552 | −0.455531 | ||||||||
\(105\) | 4.14919 | 0.404920 | ||||||||
\(106\) | −6.42047 | −0.623611 | ||||||||
\(107\) | −3.70214 | −0.357899 | −0.178950 | − | 0.983858i | \(-0.557270\pi\) | ||||
−0.178950 | + | 0.983858i | \(0.557270\pi\) | |||||||
\(108\) | −4.39136 | −0.422558 | ||||||||
\(109\) | −10.7316 | −1.02790 | −0.513949 | − | 0.857821i | \(-0.671818\pi\) | ||||
−0.513949 | + | 0.857821i | \(0.671818\pi\) | |||||||
\(110\) | −10.7808 | −1.02790 | ||||||||
\(111\) | 0.0229248 | 0.00217593 | ||||||||
\(112\) | −1.72528 | −0.163023 | ||||||||
\(113\) | −9.91209 | −0.932451 | −0.466225 | − | 0.884666i | \(-0.654386\pi\) | ||||
−0.466225 | + | 0.884666i | \(0.654386\pi\) | |||||||
\(114\) | 6.92002 | 0.648119 | ||||||||
\(115\) | 2.91252 | 0.271594 | ||||||||
\(116\) | 0.958192 | 0.0889659 | ||||||||
\(117\) | 10.7691 | 0.995608 | ||||||||
\(118\) | −10.5683 | −0.972894 | ||||||||
\(119\) | −7.69437 | −0.705342 | ||||||||
\(120\) | −2.40494 | −0.219540 | ||||||||
\(121\) | 2.70126 | 0.245569 | ||||||||
\(122\) | −9.59785 | −0.868949 | ||||||||
\(123\) | −2.13027 | −0.192080 | ||||||||
\(124\) | 0.0262738 | 0.00235946 | ||||||||
\(125\) | 4.41895 | 0.395243 | ||||||||
\(126\) | 3.99950 | 0.356304 | ||||||||
\(127\) | −0.314178 | −0.0278788 | −0.0139394 | − | 0.999903i | \(-0.504437\pi\) | ||||
−0.0139394 | + | 0.999903i | \(0.504437\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 3.63280 | 0.319850 | ||||||||
\(130\) | 13.5302 | 1.18668 | ||||||||
\(131\) | 1.00000 | 0.0873704 | ||||||||
\(132\) | 3.05644 | 0.266029 | ||||||||
\(133\) | −14.4587 | −1.25373 | ||||||||
\(134\) | −6.74945 | −0.583064 | ||||||||
\(135\) | 12.7899 | 1.10078 | ||||||||
\(136\) | 4.45979 | 0.382424 | ||||||||
\(137\) | −14.7354 | −1.25893 | −0.629466 | − | 0.777028i | \(-0.716726\pi\) | ||||
−0.629466 | + | 0.777028i | \(0.716726\pi\) | |||||||
\(138\) | −0.825726 | −0.0702904 | ||||||||
\(139\) | −6.44780 | −0.546895 | −0.273448 | − | 0.961887i | \(-0.588164\pi\) | ||||
−0.273448 | + | 0.961887i | \(0.588164\pi\) | |||||||
\(140\) | 5.02490 | 0.424682 | ||||||||
\(141\) | −2.28505 | −0.192436 | ||||||||
\(142\) | −3.62262 | −0.304004 | ||||||||
\(143\) | −17.1955 | −1.43796 | ||||||||
\(144\) | −2.31818 | −0.193181 | ||||||||
\(145\) | −2.79075 | −0.231760 | ||||||||
\(146\) | −0.166419 | −0.0137729 | ||||||||
\(147\) | −3.32224 | −0.274014 | ||||||||
\(148\) | 0.0277632 | 0.00228212 | ||||||||
\(149\) | 16.1454 | 1.32268 | 0.661340 | − | 0.750087i | \(-0.269988\pi\) | ||||
0.661340 | + | 0.750087i | \(0.269988\pi\) | |||||||
\(150\) | 2.87582 | 0.234810 | ||||||||
\(151\) | 1.92980 | 0.157045 | 0.0785224 | − | 0.996912i | \(-0.474980\pi\) | ||||
0.0785224 | + | 0.996912i | \(0.474980\pi\) | |||||||
\(152\) | 8.38053 | 0.679751 | ||||||||
\(153\) | −10.3386 | −0.835824 | ||||||||
\(154\) | −6.38615 | −0.514611 | ||||||||
\(155\) | −0.0765231 | −0.00614648 | ||||||||
\(156\) | −3.83593 | −0.307120 | ||||||||
\(157\) | −16.6026 | −1.32503 | −0.662514 | − | 0.749049i | \(-0.730511\pi\) | ||||
−0.662514 | + | 0.749049i | \(0.730511\pi\) | |||||||
\(158\) | −8.12246 | −0.646188 | ||||||||
\(159\) | −5.30155 | −0.420440 | ||||||||
\(160\) | −2.91252 | −0.230255 | ||||||||
\(161\) | 1.72528 | 0.135971 | ||||||||
\(162\) | 3.32848 | 0.261510 | ||||||||
\(163\) | −1.82033 | −0.142579 | −0.0712895 | − | 0.997456i | \(-0.522711\pi\) | ||||
−0.0712895 | + | 0.997456i | \(0.522711\pi\) | |||||||
\(164\) | −2.57987 | −0.201454 | ||||||||
\(165\) | −8.90195 | −0.693016 | ||||||||
\(166\) | −4.83091 | −0.374952 | ||||||||
\(167\) | −2.76385 | −0.213873 | −0.106937 | − | 0.994266i | \(-0.534104\pi\) | ||||
−0.106937 | + | 0.994266i | \(0.534104\pi\) | |||||||
\(168\) | −1.42461 | −0.109911 | ||||||||
\(169\) | 8.58089 | 0.660068 | ||||||||
\(170\) | −12.9892 | −0.996228 | ||||||||
\(171\) | −19.4276 | −1.48566 | ||||||||
\(172\) | 4.39952 | 0.335460 | ||||||||
\(173\) | 22.8026 | 1.73365 | 0.866825 | − | 0.498612i | \(-0.166157\pi\) | ||||
0.866825 | + | 0.498612i | \(0.166157\pi\) | |||||||
\(174\) | 0.791204 | 0.0599810 | ||||||||
\(175\) | −6.00875 | −0.454219 | ||||||||
\(176\) | 3.70152 | 0.279013 | ||||||||
\(177\) | −8.72654 | −0.655927 | ||||||||
\(178\) | 0.889547 | 0.0666743 | ||||||||
\(179\) | 6.71468 | 0.501879 | 0.250939 | − | 0.968003i | \(-0.419261\pi\) | ||||
0.250939 | + | 0.968003i | \(0.419261\pi\) | |||||||
\(180\) | 6.75174 | 0.503245 | ||||||||
\(181\) | 11.4355 | 0.849996 | 0.424998 | − | 0.905194i | \(-0.360275\pi\) | ||||
0.424998 | + | 0.905194i | \(0.360275\pi\) | |||||||
\(182\) | 8.01481 | 0.594098 | ||||||||
\(183\) | −7.92519 | −0.585847 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | −0.0808610 | −0.00594502 | ||||||||
\(186\) | 0.0216950 | 0.00159075 | ||||||||
\(187\) | 16.5080 | 1.20718 | ||||||||
\(188\) | −2.76732 | −0.201828 | ||||||||
\(189\) | 7.57630 | 0.551095 | ||||||||
\(190\) | −24.4085 | −1.77078 | ||||||||
\(191\) | −18.0493 | −1.30600 | −0.653001 | − | 0.757357i | \(-0.726490\pi\) | ||||
−0.653001 | + | 0.757357i | \(0.726490\pi\) | |||||||
\(192\) | 0.825726 | 0.0595916 | ||||||||
\(193\) | 15.4934 | 1.11524 | 0.557619 | − | 0.830097i | \(-0.311715\pi\) | ||||
0.557619 | + | 0.830097i | \(0.311715\pi\) | |||||||
\(194\) | 3.83775 | 0.275534 | ||||||||
\(195\) | 11.1722 | 0.800059 | ||||||||
\(196\) | −4.02342 | −0.287387 | ||||||||
\(197\) | 15.8107 | 1.12646 | 0.563232 | − | 0.826299i | \(-0.309558\pi\) | ||||
0.563232 | + | 0.826299i | \(0.309558\pi\) | |||||||
\(198\) | −8.58078 | −0.609810 | ||||||||
\(199\) | 0.796066 | 0.0564316 | 0.0282158 | − | 0.999602i | \(-0.491017\pi\) | ||||
0.0282158 | + | 0.999602i | \(0.491017\pi\) | |||||||
\(200\) | 3.48278 | 0.246269 | ||||||||
\(201\) | −5.57319 | −0.393103 | ||||||||
\(202\) | −12.9059 | −0.908055 | ||||||||
\(203\) | −1.65315 | −0.116028 | ||||||||
\(204\) | 3.68256 | 0.257831 | ||||||||
\(205\) | 7.51393 | 0.524796 | ||||||||
\(206\) | 4.12459 | 0.287374 | ||||||||
\(207\) | 2.31818 | 0.161124 | ||||||||
\(208\) | −4.64552 | −0.322109 | ||||||||
\(209\) | 31.0207 | 2.14575 | ||||||||
\(210\) | 4.14919 | 0.286322 | ||||||||
\(211\) | −26.4759 | −1.82268 | −0.911338 | − | 0.411659i | \(-0.864950\pi\) | ||||
−0.911338 | + | 0.411659i | \(0.864950\pi\) | |||||||
\(212\) | −6.42047 | −0.440960 | ||||||||
\(213\) | −2.99129 | −0.204960 | ||||||||
\(214\) | −3.70214 | −0.253073 | ||||||||
\(215\) | −12.8137 | −0.873887 | ||||||||
\(216\) | −4.39136 | −0.298794 | ||||||||
\(217\) | −0.0453296 | −0.00307718 | ||||||||
\(218\) | −10.7316 | −0.726833 | ||||||||
\(219\) | −0.137416 | −0.00928574 | ||||||||
\(220\) | −10.7808 | −0.726838 | ||||||||
\(221\) | −20.7180 | −1.39365 | ||||||||
\(222\) | 0.0229248 | 0.00153861 | ||||||||
\(223\) | −20.0246 | −1.34095 | −0.670473 | − | 0.741934i | \(-0.733909\pi\) | ||||
−0.670473 | + | 0.741934i | \(0.733909\pi\) | |||||||
\(224\) | −1.72528 | −0.115275 | ||||||||
\(225\) | −8.07369 | −0.538246 | ||||||||
\(226\) | −9.91209 | −0.659342 | ||||||||
\(227\) | −10.7338 | −0.712428 | −0.356214 | − | 0.934404i | \(-0.615933\pi\) | ||||
−0.356214 | + | 0.934404i | \(0.615933\pi\) | |||||||
\(228\) | 6.92002 | 0.458290 | ||||||||
\(229\) | −11.0900 | −0.732848 | −0.366424 | − | 0.930448i | \(-0.619418\pi\) | ||||
−0.366424 | + | 0.930448i | \(0.619418\pi\) | |||||||
\(230\) | 2.91252 | 0.192046 | ||||||||
\(231\) | −5.27321 | −0.346952 | ||||||||
\(232\) | 0.958192 | 0.0629084 | ||||||||
\(233\) | −16.4885 | −1.08020 | −0.540099 | − | 0.841601i | \(-0.681613\pi\) | ||||
−0.540099 | + | 0.841601i | \(0.681613\pi\) | |||||||
\(234\) | 10.7691 | 0.704001 | ||||||||
\(235\) | 8.05988 | 0.525768 | ||||||||
\(236\) | −10.5683 | −0.687940 | ||||||||
\(237\) | −6.70693 | −0.435662 | ||||||||
\(238\) | −7.69437 | −0.498752 | ||||||||
\(239\) | −20.8880 | −1.35113 | −0.675565 | − | 0.737300i | \(-0.736100\pi\) | ||||
−0.675565 | + | 0.737300i | \(0.736100\pi\) | |||||||
\(240\) | −2.40494 | −0.155238 | ||||||||
\(241\) | −0.268081 | −0.0172686 | −0.00863431 | − | 0.999963i | \(-0.502748\pi\) | ||||
−0.00863431 | + | 0.999963i | \(0.502748\pi\) | |||||||
\(242\) | 2.70126 | 0.173643 | ||||||||
\(243\) | 15.9225 | 1.02143 | ||||||||
\(244\) | −9.59785 | −0.614439 | ||||||||
\(245\) | 11.7183 | 0.748654 | ||||||||
\(246\) | −2.13027 | −0.135821 | ||||||||
\(247\) | −38.9320 | −2.47718 | ||||||||
\(248\) | 0.0262738 | 0.00166839 | ||||||||
\(249\) | −3.98901 | −0.252793 | ||||||||
\(250\) | 4.41895 | 0.279479 | ||||||||
\(251\) | 14.2857 | 0.901704 | 0.450852 | − | 0.892599i | \(-0.351120\pi\) | ||||
0.450852 | + | 0.892599i | \(0.351120\pi\) | |||||||
\(252\) | 3.99950 | 0.251945 | ||||||||
\(253\) | −3.70152 | −0.232713 | ||||||||
\(254\) | −0.314178 | −0.0197133 | ||||||||
\(255\) | −10.7255 | −0.671659 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 28.4449 | 1.77434 | 0.887172 | − | 0.461439i | \(-0.152667\pi\) | ||||
0.887172 | + | 0.461439i | \(0.152667\pi\) | |||||||
\(258\) | 3.63280 | 0.226168 | ||||||||
\(259\) | −0.0478993 | −0.00297632 | ||||||||
\(260\) | 13.5302 | 0.839106 | ||||||||
\(261\) | −2.22126 | −0.137492 | ||||||||
\(262\) | 1.00000 | 0.0617802 | ||||||||
\(263\) | −17.2177 | −1.06169 | −0.530844 | − | 0.847470i | \(-0.678125\pi\) | ||||
−0.530844 | + | 0.847470i | \(0.678125\pi\) | |||||||
\(264\) | 3.05644 | 0.188111 | ||||||||
\(265\) | 18.6997 | 1.14872 | ||||||||
\(266\) | −14.4587 | −0.886522 | ||||||||
\(267\) | 0.734522 | 0.0449520 | ||||||||
\(268\) | −6.74945 | −0.412288 | ||||||||
\(269\) | 2.89267 | 0.176369 | 0.0881847 | − | 0.996104i | \(-0.471893\pi\) | ||||
0.0881847 | + | 0.996104i | \(0.471893\pi\) | |||||||
\(270\) | 12.7899 | 0.778369 | ||||||||
\(271\) | 22.1434 | 1.34512 | 0.672558 | − | 0.740044i | \(-0.265196\pi\) | ||||
0.672558 | + | 0.740044i | \(0.265196\pi\) | |||||||
\(272\) | 4.45979 | 0.270414 | ||||||||
\(273\) | 6.61804 | 0.400542 | ||||||||
\(274\) | −14.7354 | −0.890199 | ||||||||
\(275\) | 12.8916 | 0.777391 | ||||||||
\(276\) | −0.825726 | −0.0497028 | ||||||||
\(277\) | 16.3344 | 0.981438 | 0.490719 | − | 0.871318i | \(-0.336734\pi\) | ||||
0.490719 | + | 0.871318i | \(0.336734\pi\) | |||||||
\(278\) | −6.44780 | −0.386713 | ||||||||
\(279\) | −0.0609074 | −0.00364643 | ||||||||
\(280\) | 5.02490 | 0.300295 | ||||||||
\(281\) | 17.2067 | 1.02647 | 0.513234 | − | 0.858249i | \(-0.328447\pi\) | ||||
0.513234 | + | 0.858249i | \(0.328447\pi\) | |||||||
\(282\) | −2.28505 | −0.136073 | ||||||||
\(283\) | 5.88667 | 0.349926 | 0.174963 | − | 0.984575i | \(-0.444019\pi\) | ||||
0.174963 | + | 0.984575i | \(0.444019\pi\) | |||||||
\(284\) | −3.62262 | −0.214963 | ||||||||
\(285\) | −20.1547 | −1.19386 | ||||||||
\(286\) | −17.1955 | −1.01679 | ||||||||
\(287\) | 4.45100 | 0.262734 | ||||||||
\(288\) | −2.31818 | −0.136600 | ||||||||
\(289\) | 2.88971 | 0.169983 | ||||||||
\(290\) | −2.79075 | −0.163879 | ||||||||
\(291\) | 3.16893 | 0.185766 | ||||||||
\(292\) | −0.166419 | −0.00973893 | ||||||||
\(293\) | 18.0716 | 1.05575 | 0.527876 | − | 0.849321i | \(-0.322989\pi\) | ||||
0.527876 | + | 0.849321i | \(0.322989\pi\) | |||||||
\(294\) | −3.32224 | −0.193757 | ||||||||
\(295\) | 30.7805 | 1.79211 | ||||||||
\(296\) | 0.0277632 | 0.00161371 | ||||||||
\(297\) | −16.2547 | −0.943193 | ||||||||
\(298\) | 16.1454 | 0.935276 | ||||||||
\(299\) | 4.64552 | 0.268658 | ||||||||
\(300\) | 2.87582 | 0.166035 | ||||||||
\(301\) | −7.59040 | −0.437503 | ||||||||
\(302\) | 1.92980 | 0.111047 | ||||||||
\(303\) | −10.6567 | −0.612212 | ||||||||
\(304\) | 8.38053 | 0.480657 | ||||||||
\(305\) | 27.9539 | 1.60064 | ||||||||
\(306\) | −10.3386 | −0.591017 | ||||||||
\(307\) | 16.7644 | 0.956797 | 0.478398 | − | 0.878143i | \(-0.341218\pi\) | ||||
0.478398 | + | 0.878143i | \(0.341218\pi\) | |||||||
\(308\) | −6.38615 | −0.363885 | ||||||||
\(309\) | 3.40578 | 0.193748 | ||||||||
\(310\) | −0.0765231 | −0.00434622 | ||||||||
\(311\) | 9.48145 | 0.537644 | 0.268822 | − | 0.963190i | \(-0.413366\pi\) | ||||
0.268822 | + | 0.963190i | \(0.413366\pi\) | |||||||
\(312\) | −3.83593 | −0.217167 | ||||||||
\(313\) | 19.1669 | 1.08338 | 0.541689 | − | 0.840579i | \(-0.317785\pi\) | ||||
0.541689 | + | 0.840579i | \(0.317785\pi\) | |||||||
\(314\) | −16.6026 | −0.936937 | ||||||||
\(315\) | −11.6486 | −0.656325 | ||||||||
\(316\) | −8.12246 | −0.456924 | ||||||||
\(317\) | −25.4875 | −1.43152 | −0.715761 | − | 0.698345i | \(-0.753920\pi\) | ||||
−0.715761 | + | 0.698345i | \(0.753920\pi\) | |||||||
\(318\) | −5.30155 | −0.297296 | ||||||||
\(319\) | 3.54677 | 0.198581 | ||||||||
\(320\) | −2.91252 | −0.162815 | ||||||||
\(321\) | −3.05695 | −0.170622 | ||||||||
\(322\) | 1.72528 | 0.0961459 | ||||||||
\(323\) | 37.3754 | 2.07962 | ||||||||
\(324\) | 3.32848 | 0.184915 | ||||||||
\(325\) | −16.1793 | −0.897467 | ||||||||
\(326\) | −1.82033 | −0.100819 | ||||||||
\(327\) | −8.86133 | −0.490033 | ||||||||
\(328\) | −2.57987 | −0.142450 | ||||||||
\(329\) | 4.77439 | 0.263221 | ||||||||
\(330\) | −8.90195 | −0.490036 | ||||||||
\(331\) | 18.1211 | 0.996025 | 0.498012 | − | 0.867170i | \(-0.334063\pi\) | ||||
0.498012 | + | 0.867170i | \(0.334063\pi\) | |||||||
\(332\) | −4.83091 | −0.265131 | ||||||||
\(333\) | −0.0643601 | −0.00352691 | ||||||||
\(334\) | −2.76385 | −0.151231 | ||||||||
\(335\) | 19.6579 | 1.07403 | ||||||||
\(336\) | −1.42461 | −0.0777186 | ||||||||
\(337\) | −29.3256 | −1.59747 | −0.798733 | − | 0.601686i | \(-0.794496\pi\) | ||||
−0.798733 | + | 0.601686i | \(0.794496\pi\) | |||||||
\(338\) | 8.58089 | 0.466739 | ||||||||
\(339\) | −8.18466 | −0.444530 | ||||||||
\(340\) | −12.9892 | −0.704440 | ||||||||
\(341\) | 0.0972531 | 0.00526655 | ||||||||
\(342\) | −19.4276 | −1.05052 | ||||||||
\(343\) | 19.0185 | 1.02690 | ||||||||
\(344\) | 4.39952 | 0.237206 | ||||||||
\(345\) | 2.40494 | 0.129478 | ||||||||
\(346\) | 22.8026 | 1.22588 | ||||||||
\(347\) | 7.46569 | 0.400779 | 0.200390 | − | 0.979716i | \(-0.435779\pi\) | ||||
0.200390 | + | 0.979716i | \(0.435779\pi\) | |||||||
\(348\) | 0.791204 | 0.0424130 | ||||||||
\(349\) | −11.4966 | −0.615400 | −0.307700 | − | 0.951483i | \(-0.599559\pi\) | ||||
−0.307700 | + | 0.951483i | \(0.599559\pi\) | |||||||
\(350\) | −6.00875 | −0.321181 | ||||||||
\(351\) | 20.4001 | 1.08888 | ||||||||
\(352\) | 3.70152 | 0.197292 | ||||||||
\(353\) | −6.34943 | −0.337946 | −0.168973 | − | 0.985621i | \(-0.554045\pi\) | ||||
−0.168973 | + | 0.985621i | \(0.554045\pi\) | |||||||
\(354\) | −8.72654 | −0.463810 | ||||||||
\(355\) | 10.5510 | 0.559987 | ||||||||
\(356\) | 0.889547 | 0.0471459 | ||||||||
\(357\) | −6.35344 | −0.336260 | ||||||||
\(358\) | 6.71468 | 0.354882 | ||||||||
\(359\) | −4.27204 | −0.225470 | −0.112735 | − | 0.993625i | \(-0.535961\pi\) | ||||
−0.112735 | + | 0.993625i | \(0.535961\pi\) | |||||||
\(360\) | 6.75174 | 0.355848 | ||||||||
\(361\) | 51.2333 | 2.69649 | ||||||||
\(362\) | 11.4355 | 0.601038 | ||||||||
\(363\) | 2.23050 | 0.117071 | ||||||||
\(364\) | 8.01481 | 0.420090 | ||||||||
\(365\) | 0.484699 | 0.0253703 | ||||||||
\(366\) | −7.92519 | −0.414256 | ||||||||
\(367\) | −27.5219 | −1.43663 | −0.718315 | − | 0.695718i | \(-0.755086\pi\) | ||||
−0.718315 | + | 0.695718i | \(0.755086\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | 5.98060 | 0.311338 | ||||||||
\(370\) | −0.0808610 | −0.00420376 | ||||||||
\(371\) | 11.0771 | 0.575094 | ||||||||
\(372\) | 0.0216950 | 0.00112483 | ||||||||
\(373\) | 17.6082 | 0.911720 | 0.455860 | − | 0.890052i | \(-0.349332\pi\) | ||||
0.455860 | + | 0.890052i | \(0.349332\pi\) | |||||||
\(374\) | 16.5080 | 0.853608 | ||||||||
\(375\) | 3.64884 | 0.188425 | ||||||||
\(376\) | −2.76732 | −0.142714 | ||||||||
\(377\) | −4.45130 | −0.229254 | ||||||||
\(378\) | 7.57630 | 0.389683 | ||||||||
\(379\) | −34.4193 | −1.76800 | −0.884000 | − | 0.467486i | \(-0.845160\pi\) | ||||
−0.884000 | + | 0.467486i | \(0.845160\pi\) | |||||||
\(380\) | −24.4085 | −1.25213 | ||||||||
\(381\) | −0.259425 | −0.0132907 | ||||||||
\(382\) | −18.0493 | −0.923483 | ||||||||
\(383\) | −14.4656 | −0.739158 | −0.369579 | − | 0.929199i | \(-0.620498\pi\) | ||||
−0.369579 | + | 0.929199i | \(0.620498\pi\) | |||||||
\(384\) | 0.825726 | 0.0421376 | ||||||||
\(385\) | 18.5998 | 0.947933 | ||||||||
\(386\) | 15.4934 | 0.788592 | ||||||||
\(387\) | −10.1989 | −0.518438 | ||||||||
\(388\) | 3.83775 | 0.194832 | ||||||||
\(389\) | −14.7539 | −0.748052 | −0.374026 | − | 0.927418i | \(-0.622023\pi\) | ||||
−0.374026 | + | 0.927418i | \(0.622023\pi\) | |||||||
\(390\) | 11.1722 | 0.565727 | ||||||||
\(391\) | −4.45979 | −0.225541 | ||||||||
\(392\) | −4.02342 | −0.203213 | ||||||||
\(393\) | 0.825726 | 0.0416524 | ||||||||
\(394\) | 15.8107 | 0.796531 | ||||||||
\(395\) | 23.6568 | 1.19030 | ||||||||
\(396\) | −8.58078 | −0.431200 | ||||||||
\(397\) | −1.90888 | −0.0958041 | −0.0479020 | − | 0.998852i | \(-0.515254\pi\) | ||||
−0.0479020 | + | 0.998852i | \(0.515254\pi\) | |||||||
\(398\) | 0.796066 | 0.0399032 | ||||||||
\(399\) | −11.9390 | −0.597695 | ||||||||
\(400\) | 3.48278 | 0.174139 | ||||||||
\(401\) | −11.0337 | −0.550999 | −0.275499 | − | 0.961301i | \(-0.588843\pi\) | ||||
−0.275499 | + | 0.961301i | \(0.588843\pi\) | |||||||
\(402\) | −5.57319 | −0.277966 | ||||||||
\(403\) | −0.122056 | −0.00608003 | ||||||||
\(404\) | −12.9059 | −0.642092 | ||||||||
\(405\) | −9.69425 | −0.481711 | ||||||||
\(406\) | −1.65315 | −0.0820443 | ||||||||
\(407\) | 0.102766 | 0.00509393 | ||||||||
\(408\) | 3.68256 | 0.182314 | ||||||||
\(409\) | −7.05569 | −0.348881 | −0.174441 | − | 0.984668i | \(-0.555812\pi\) | ||||
−0.174441 | + | 0.984668i | \(0.555812\pi\) | |||||||
\(410\) | 7.51393 | 0.371087 | ||||||||
\(411\) | −12.1674 | −0.600174 | ||||||||
\(412\) | 4.12459 | 0.203204 | ||||||||
\(413\) | 18.2333 | 0.897202 | ||||||||
\(414\) | 2.31818 | 0.113932 | ||||||||
\(415\) | 14.0701 | 0.690676 | ||||||||
\(416\) | −4.64552 | −0.227766 | ||||||||
\(417\) | −5.32412 | −0.260723 | ||||||||
\(418\) | 31.0207 | 1.51727 | ||||||||
\(419\) | −6.44623 | −0.314919 | −0.157460 | − | 0.987525i | \(-0.550330\pi\) | ||||
−0.157460 | + | 0.987525i | \(0.550330\pi\) | |||||||
\(420\) | 4.14919 | 0.202460 | ||||||||
\(421\) | −30.3425 | −1.47880 | −0.739401 | − | 0.673265i | \(-0.764891\pi\) | ||||
−0.739401 | + | 0.673265i | \(0.764891\pi\) | |||||||
\(422\) | −26.4759 | −1.28883 | ||||||||
\(423\) | 6.41514 | 0.311915 | ||||||||
\(424\) | −6.42047 | −0.311806 | ||||||||
\(425\) | 15.5324 | 0.753434 | ||||||||
\(426\) | −2.99129 | −0.144928 | ||||||||
\(427\) | 16.5590 | 0.801344 | ||||||||
\(428\) | −3.70214 | −0.178950 | ||||||||
\(429\) | −14.1988 | −0.685523 | ||||||||
\(430\) | −12.8137 | −0.617932 | ||||||||
\(431\) | −8.21996 | −0.395942 | −0.197971 | − | 0.980208i | \(-0.563435\pi\) | ||||
−0.197971 | + | 0.980208i | \(0.563435\pi\) | |||||||
\(432\) | −4.39136 | −0.211279 | ||||||||
\(433\) | 38.4408 | 1.84735 | 0.923673 | − | 0.383183i | \(-0.125172\pi\) | ||||
0.923673 | + | 0.383183i | \(0.125172\pi\) | |||||||
\(434\) | −0.0453296 | −0.00217589 | ||||||||
\(435\) | −2.30440 | −0.110487 | ||||||||
\(436\) | −10.7316 | −0.513949 | ||||||||
\(437\) | −8.38053 | −0.400895 | ||||||||
\(438\) | −0.137416 | −0.00656601 | ||||||||
\(439\) | 11.8125 | 0.563779 | 0.281890 | − | 0.959447i | \(-0.409039\pi\) | ||||
0.281890 | + | 0.959447i | \(0.409039\pi\) | |||||||
\(440\) | −10.7808 | −0.513952 | ||||||||
\(441\) | 9.32700 | 0.444143 | ||||||||
\(442\) | −20.7180 | −0.985457 | ||||||||
\(443\) | −13.4654 | −0.639763 | −0.319881 | − | 0.947458i | \(-0.603643\pi\) | ||||
−0.319881 | + | 0.947458i | \(0.603643\pi\) | |||||||
\(444\) | 0.0229248 | 0.00108796 | ||||||||
\(445\) | −2.59082 | −0.122817 | ||||||||
\(446\) | −20.0246 | −0.948192 | ||||||||
\(447\) | 13.3316 | 0.630565 | ||||||||
\(448\) | −1.72528 | −0.0815117 | ||||||||
\(449\) | −2.87075 | −0.135479 | −0.0677395 | − | 0.997703i | \(-0.521579\pi\) | ||||
−0.0677395 | + | 0.997703i | \(0.521579\pi\) | |||||||
\(450\) | −8.07369 | −0.380597 | ||||||||
\(451\) | −9.54946 | −0.449666 | ||||||||
\(452\) | −9.91209 | −0.466225 | ||||||||
\(453\) | 1.59348 | 0.0748684 | ||||||||
\(454\) | −10.7338 | −0.503763 | ||||||||
\(455\) | −23.3433 | −1.09435 | ||||||||
\(456\) | 6.92002 | 0.324060 | ||||||||
\(457\) | 22.9351 | 1.07286 | 0.536430 | − | 0.843945i | \(-0.319773\pi\) | ||||
0.536430 | + | 0.843945i | \(0.319773\pi\) | |||||||
\(458\) | −11.0900 | −0.518202 | ||||||||
\(459\) | −19.5845 | −0.914127 | ||||||||
\(460\) | 2.91252 | 0.135797 | ||||||||
\(461\) | −7.78624 | −0.362641 | −0.181321 | − | 0.983424i | \(-0.558037\pi\) | ||||
−0.181321 | + | 0.983424i | \(0.558037\pi\) | |||||||
\(462\) | −5.27321 | −0.245332 | ||||||||
\(463\) | 23.9570 | 1.11337 | 0.556687 | − | 0.830722i | \(-0.312072\pi\) | ||||
0.556687 | + | 0.830722i | \(0.312072\pi\) | |||||||
\(464\) | 0.958192 | 0.0444829 | ||||||||
\(465\) | −0.0631871 | −0.00293023 | ||||||||
\(466\) | −16.4885 | −0.763816 | ||||||||
\(467\) | −34.5877 | −1.60053 | −0.800263 | − | 0.599649i | \(-0.795307\pi\) | ||||
−0.800263 | + | 0.599649i | \(0.795307\pi\) | |||||||
\(468\) | 10.7691 | 0.497804 | ||||||||
\(469\) | 11.6447 | 0.537701 | ||||||||
\(470\) | 8.05988 | 0.371774 | ||||||||
\(471\) | −13.7092 | −0.631685 | ||||||||
\(472\) | −10.5683 | −0.486447 | ||||||||
\(473\) | 16.2849 | 0.748782 | ||||||||
\(474\) | −6.70693 | −0.308059 | ||||||||
\(475\) | 29.1875 | 1.33922 | ||||||||
\(476\) | −7.69437 | −0.352671 | ||||||||
\(477\) | 14.8838 | 0.681482 | ||||||||
\(478\) | −20.8880 | −0.955393 | ||||||||
\(479\) | −18.1571 | −0.829618 | −0.414809 | − | 0.909909i | \(-0.636152\pi\) | ||||
−0.414809 | + | 0.909909i | \(0.636152\pi\) | |||||||
\(480\) | −2.40494 | −0.109770 | ||||||||
\(481\) | −0.128975 | −0.00588074 | ||||||||
\(482\) | −0.268081 | −0.0122108 | ||||||||
\(483\) | 1.42461 | 0.0648218 | ||||||||
\(484\) | 2.70126 | 0.122784 | ||||||||
\(485\) | −11.1775 | −0.507545 | ||||||||
\(486\) | 15.9225 | 0.722258 | ||||||||
\(487\) | 26.3758 | 1.19520 | 0.597600 | − | 0.801794i | \(-0.296121\pi\) | ||||
0.597600 | + | 0.801794i | \(0.296121\pi\) | |||||||
\(488\) | −9.59785 | −0.434474 | ||||||||
\(489\) | −1.50309 | −0.0679721 | ||||||||
\(490\) | 11.7183 | 0.529378 | ||||||||
\(491\) | 35.7810 | 1.61477 | 0.807387 | − | 0.590022i | \(-0.200881\pi\) | ||||
0.807387 | + | 0.590022i | \(0.200881\pi\) | |||||||
\(492\) | −2.13027 | −0.0960399 | ||||||||
\(493\) | 4.27333 | 0.192461 | ||||||||
\(494\) | −38.9320 | −1.75163 | ||||||||
\(495\) | 24.9917 | 1.12329 | ||||||||
\(496\) | 0.0262738 | 0.00117973 | ||||||||
\(497\) | 6.25002 | 0.280352 | ||||||||
\(498\) | −3.98901 | −0.178752 | ||||||||
\(499\) | −21.7609 | −0.974154 | −0.487077 | − | 0.873359i | \(-0.661937\pi\) | ||||
−0.487077 | + | 0.873359i | \(0.661937\pi\) | |||||||
\(500\) | 4.41895 | 0.197621 | ||||||||
\(501\) | −2.28218 | −0.101960 | ||||||||
\(502\) | 14.2857 | 0.637601 | ||||||||
\(503\) | 13.9850 | 0.623560 | 0.311780 | − | 0.950154i | \(-0.399075\pi\) | ||||
0.311780 | + | 0.950154i | \(0.399075\pi\) | |||||||
\(504\) | 3.99950 | 0.178152 | ||||||||
\(505\) | 37.5886 | 1.67267 | ||||||||
\(506\) | −3.70152 | −0.164553 | ||||||||
\(507\) | 7.08546 | 0.314676 | ||||||||
\(508\) | −0.314178 | −0.0139394 | ||||||||
\(509\) | −36.5256 | −1.61897 | −0.809484 | − | 0.587142i | \(-0.800253\pi\) | ||||
−0.809484 | + | 0.587142i | \(0.800253\pi\) | |||||||
\(510\) | −10.7255 | −0.474935 | ||||||||
\(511\) | 0.287119 | 0.0127014 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −36.8019 | −1.62484 | ||||||||
\(514\) | 28.4449 | 1.25465 | ||||||||
\(515\) | −12.0129 | −0.529354 | ||||||||
\(516\) | 3.63280 | 0.159925 | ||||||||
\(517\) | −10.2433 | −0.450500 | ||||||||
\(518\) | −0.0478993 | −0.00210457 | ||||||||
\(519\) | 18.8287 | 0.826488 | ||||||||
\(520\) | 13.5302 | 0.593338 | ||||||||
\(521\) | −4.41620 | −0.193477 | −0.0967386 | − | 0.995310i | \(-0.530841\pi\) | ||||
−0.0967386 | + | 0.995310i | \(0.530841\pi\) | |||||||
\(522\) | −2.22126 | −0.0972219 | ||||||||
\(523\) | −32.0404 | −1.40103 | −0.700515 | − | 0.713637i | \(-0.747046\pi\) | ||||
−0.700515 | + | 0.713637i | \(0.747046\pi\) | |||||||
\(524\) | 1.00000 | 0.0436852 | ||||||||
\(525\) | −4.96158 | −0.216541 | ||||||||
\(526\) | −17.2177 | −0.750727 | ||||||||
\(527\) | 0.117176 | 0.00510425 | ||||||||
\(528\) | 3.05644 | 0.133015 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 18.6997 | 0.812265 | ||||||||
\(531\) | 24.4993 | 1.06318 | ||||||||
\(532\) | −14.4587 | −0.626866 | ||||||||
\(533\) | 11.9849 | 0.519122 | ||||||||
\(534\) | 0.734522 | 0.0317859 | ||||||||
\(535\) | 10.7826 | 0.466170 | ||||||||
\(536\) | −6.74945 | −0.291532 | ||||||||
\(537\) | 5.54448 | 0.239262 | ||||||||
\(538\) | 2.89267 | 0.124712 | ||||||||
\(539\) | −14.8928 | −0.641477 | ||||||||
\(540\) | 12.7899 | 0.550390 | ||||||||
\(541\) | −19.7636 | −0.849702 | −0.424851 | − | 0.905263i | \(-0.639674\pi\) | ||||
−0.424851 | + | 0.905263i | \(0.639674\pi\) | |||||||
\(542\) | 22.1434 | 0.951141 | ||||||||
\(543\) | 9.44260 | 0.405221 | ||||||||
\(544\) | 4.45979 | 0.191212 | ||||||||
\(545\) | 31.2559 | 1.33886 | ||||||||
\(546\) | 6.61804 | 0.283226 | ||||||||
\(547\) | −28.0042 | −1.19737 | −0.598686 | − | 0.800984i | \(-0.704310\pi\) | ||||
−0.598686 | + | 0.800984i | \(0.704310\pi\) | |||||||
\(548\) | −14.7354 | −0.629466 | ||||||||
\(549\) | 22.2495 | 0.949586 | ||||||||
\(550\) | 12.8916 | 0.549698 | ||||||||
\(551\) | 8.03016 | 0.342096 | ||||||||
\(552\) | −0.825726 | −0.0351452 | ||||||||
\(553\) | 14.0135 | 0.595915 | ||||||||
\(554\) | 16.3344 | 0.693981 | ||||||||
\(555\) | −0.0667690 | −0.00283419 | ||||||||
\(556\) | −6.44780 | −0.273448 | ||||||||
\(557\) | 31.7381 | 1.34479 | 0.672394 | − | 0.740194i | \(-0.265266\pi\) | ||||
0.672394 | + | 0.740194i | \(0.265266\pi\) | |||||||
\(558\) | −0.0609074 | −0.00257841 | ||||||||
\(559\) | −20.4381 | −0.864439 | ||||||||
\(560\) | 5.02490 | 0.212341 | ||||||||
\(561\) | 13.6311 | 0.575505 | ||||||||
\(562\) | 17.2067 | 0.725823 | ||||||||
\(563\) | 2.36905 | 0.0998437 | 0.0499218 | − | 0.998753i | \(-0.484103\pi\) | ||||
0.0499218 | + | 0.998753i | \(0.484103\pi\) | |||||||
\(564\) | −2.28505 | −0.0962179 | ||||||||
\(565\) | 28.8692 | 1.21453 | ||||||||
\(566\) | 5.88667 | 0.247435 | ||||||||
\(567\) | −5.74254 | −0.241164 | ||||||||
\(568\) | −3.62262 | −0.152002 | ||||||||
\(569\) | −24.9149 | −1.04449 | −0.522243 | − | 0.852797i | \(-0.674905\pi\) | ||||
−0.522243 | + | 0.852797i | \(0.674905\pi\) | |||||||
\(570\) | −20.1547 | −0.844188 | ||||||||
\(571\) | −28.5277 | −1.19385 | −0.596924 | − | 0.802298i | \(-0.703611\pi\) | ||||
−0.596924 | + | 0.802298i | \(0.703611\pi\) | |||||||
\(572\) | −17.1955 | −0.718980 | ||||||||
\(573\) | −14.9038 | −0.622614 | ||||||||
\(574\) | 4.45100 | 0.185781 | ||||||||
\(575\) | −3.48278 | −0.145242 | ||||||||
\(576\) | −2.31818 | −0.0965907 | ||||||||
\(577\) | 30.9672 | 1.28918 | 0.644590 | − | 0.764528i | \(-0.277028\pi\) | ||||
0.644590 | + | 0.764528i | \(0.277028\pi\) | |||||||
\(578\) | 2.88971 | 0.120196 | ||||||||
\(579\) | 12.7933 | 0.531671 | ||||||||
\(580\) | −2.79075 | −0.115880 | ||||||||
\(581\) | 8.33466 | 0.345780 | ||||||||
\(582\) | 3.16893 | 0.131356 | ||||||||
\(583\) | −23.7655 | −0.984266 | ||||||||
\(584\) | −0.166419 | −0.00688647 | ||||||||
\(585\) | −31.3654 | −1.29680 | ||||||||
\(586\) | 18.0716 | 0.746530 | ||||||||
\(587\) | 22.4958 | 0.928501 | 0.464251 | − | 0.885704i | \(-0.346324\pi\) | ||||
0.464251 | + | 0.885704i | \(0.346324\pi\) | |||||||
\(588\) | −3.32224 | −0.137007 | ||||||||
\(589\) | 0.220189 | 0.00907272 | ||||||||
\(590\) | 30.7805 | 1.26721 | ||||||||
\(591\) | 13.0553 | 0.537023 | ||||||||
\(592\) | 0.0277632 | 0.00114106 | ||||||||
\(593\) | 6.62297 | 0.271973 | 0.135986 | − | 0.990711i | \(-0.456580\pi\) | ||||
0.135986 | + | 0.990711i | \(0.456580\pi\) | |||||||
\(594\) | −16.2547 | −0.666938 | ||||||||
\(595\) | 22.4100 | 0.918721 | ||||||||
\(596\) | 16.1454 | 0.661340 | ||||||||
\(597\) | 0.657332 | 0.0269028 | ||||||||
\(598\) | 4.64552 | 0.189970 | ||||||||
\(599\) | 24.8385 | 1.01487 | 0.507436 | − | 0.861689i | \(-0.330593\pi\) | ||||
0.507436 | + | 0.861689i | \(0.330593\pi\) | |||||||
\(600\) | 2.87582 | 0.117405 | ||||||||
\(601\) | 8.30968 | 0.338959 | 0.169480 | − | 0.985534i | \(-0.445791\pi\) | ||||
0.169480 | + | 0.985534i | \(0.445791\pi\) | |||||||
\(602\) | −7.59040 | −0.309361 | ||||||||
\(603\) | 15.6464 | 0.637171 | ||||||||
\(604\) | 1.92980 | 0.0785224 | ||||||||
\(605\) | −7.86746 | −0.319858 | ||||||||
\(606\) | −10.6567 | −0.432900 | ||||||||
\(607\) | 35.0562 | 1.42289 | 0.711444 | − | 0.702743i | \(-0.248042\pi\) | ||||
0.711444 | + | 0.702743i | \(0.248042\pi\) | |||||||
\(608\) | 8.38053 | 0.339876 | ||||||||
\(609\) | −1.36505 | −0.0553144 | ||||||||
\(610\) | 27.9539 | 1.13182 | ||||||||
\(611\) | 12.8557 | 0.520084 | ||||||||
\(612\) | −10.3386 | −0.417912 | ||||||||
\(613\) | 10.8224 | 0.437111 | 0.218555 | − | 0.975825i | \(-0.429866\pi\) | ||||
0.218555 | + | 0.975825i | \(0.429866\pi\) | |||||||
\(614\) | 16.7644 | 0.676557 | ||||||||
\(615\) | 6.20445 | 0.250188 | ||||||||
\(616\) | −6.38615 | −0.257305 | ||||||||
\(617\) | 6.24292 | 0.251330 | 0.125665 | − | 0.992073i | \(-0.459893\pi\) | ||||
0.125665 | + | 0.992073i | \(0.459893\pi\) | |||||||
\(618\) | 3.40578 | 0.137000 | ||||||||
\(619\) | 5.19792 | 0.208922 | 0.104461 | − | 0.994529i | \(-0.466688\pi\) | ||||
0.104461 | + | 0.994529i | \(0.466688\pi\) | |||||||
\(620\) | −0.0765231 | −0.00307324 | ||||||||
\(621\) | 4.39136 | 0.176219 | ||||||||
\(622\) | 9.48145 | 0.380171 | ||||||||
\(623\) | −1.53471 | −0.0614870 | ||||||||
\(624\) | −3.83593 | −0.153560 | ||||||||
\(625\) | −30.2842 | −1.21137 | ||||||||
\(626\) | 19.1669 | 0.766064 | ||||||||
\(627\) | 25.6146 | 1.02295 | ||||||||
\(628\) | −16.6026 | −0.662514 | ||||||||
\(629\) | 0.123818 | 0.00493695 | ||||||||
\(630\) | −11.6486 | −0.464092 | ||||||||
\(631\) | −9.74097 | −0.387782 | −0.193891 | − | 0.981023i | \(-0.562111\pi\) | ||||
−0.193891 | + | 0.981023i | \(0.562111\pi\) | |||||||
\(632\) | −8.12246 | −0.323094 | ||||||||
\(633\) | −21.8618 | −0.868930 | ||||||||
\(634\) | −25.4875 | −1.01224 | ||||||||
\(635\) | 0.915050 | 0.0363126 | ||||||||
\(636\) | −5.30155 | −0.210220 | ||||||||
\(637\) | 18.6909 | 0.740560 | ||||||||
\(638\) | 3.54677 | 0.140418 | ||||||||
\(639\) | 8.39787 | 0.332215 | ||||||||
\(640\) | −2.91252 | −0.115127 | ||||||||
\(641\) | −25.2230 | −0.996250 | −0.498125 | − | 0.867105i | \(-0.665978\pi\) | ||||
−0.498125 | + | 0.867105i | \(0.665978\pi\) | |||||||
\(642\) | −3.05695 | −0.120648 | ||||||||
\(643\) | 10.9839 | 0.433162 | 0.216581 | − | 0.976265i | \(-0.430509\pi\) | ||||
0.216581 | + | 0.976265i | \(0.430509\pi\) | |||||||
\(644\) | 1.72528 | 0.0679854 | ||||||||
\(645\) | −10.5806 | −0.416611 | ||||||||
\(646\) | 37.3754 | 1.47052 | ||||||||
\(647\) | 13.1182 | 0.515728 | 0.257864 | − | 0.966181i | \(-0.416981\pi\) | ||||
0.257864 | + | 0.966181i | \(0.416981\pi\) | |||||||
\(648\) | 3.32848 | 0.130755 | ||||||||
\(649\) | −39.1189 | −1.53555 | ||||||||
\(650\) | −16.1793 | −0.634605 | ||||||||
\(651\) | −0.0374298 | −0.00146699 | ||||||||
\(652\) | −1.82033 | −0.0712895 | ||||||||
\(653\) | −42.8881 | −1.67834 | −0.839170 | − | 0.543870i | \(-0.816959\pi\) | ||||
−0.839170 | + | 0.543870i | \(0.816959\pi\) | |||||||
\(654\) | −8.86133 | −0.346505 | ||||||||
\(655\) | −2.91252 | −0.113802 | ||||||||
\(656\) | −2.57987 | −0.100727 | ||||||||
\(657\) | 0.385789 | 0.0150510 | ||||||||
\(658\) | 4.77439 | 0.186125 | ||||||||
\(659\) | 10.3626 | 0.403671 | 0.201836 | − | 0.979419i | \(-0.435309\pi\) | ||||
0.201836 | + | 0.979419i | \(0.435309\pi\) | |||||||
\(660\) | −8.90195 | −0.346508 | ||||||||
\(661\) | 5.10877 | 0.198708 | 0.0993541 | − | 0.995052i | \(-0.468322\pi\) | ||||
0.0993541 | + | 0.995052i | \(0.468322\pi\) | |||||||
\(662\) | 18.1211 | 0.704296 | ||||||||
\(663\) | −17.1074 | −0.664397 | ||||||||
\(664\) | −4.83091 | −0.187476 | ||||||||
\(665\) | 42.1114 | 1.63301 | ||||||||
\(666\) | −0.0643601 | −0.00249390 | ||||||||
\(667\) | −0.958192 | −0.0371013 | ||||||||
\(668\) | −2.76385 | −0.106937 | ||||||||
\(669\) | −16.5348 | −0.639273 | ||||||||
\(670\) | 19.6579 | 0.759451 | ||||||||
\(671\) | −35.5266 | −1.37149 | ||||||||
\(672\) | −1.42461 | −0.0549554 | ||||||||
\(673\) | −1.25257 | −0.0482830 | −0.0241415 | − | 0.999709i | \(-0.507685\pi\) | ||||
−0.0241415 | + | 0.999709i | \(0.507685\pi\) | |||||||
\(674\) | −29.3256 | −1.12958 | ||||||||
\(675\) | −15.2941 | −0.588671 | ||||||||
\(676\) | 8.58089 | 0.330034 | ||||||||
\(677\) | 17.0467 | 0.655158 | 0.327579 | − | 0.944824i | \(-0.393767\pi\) | ||||
0.327579 | + | 0.944824i | \(0.393767\pi\) | |||||||
\(678\) | −8.18466 | −0.314330 | ||||||||
\(679\) | −6.62118 | −0.254098 | ||||||||
\(680\) | −12.9892 | −0.498114 | ||||||||
\(681\) | −8.86318 | −0.339638 | ||||||||
\(682\) | 0.0972531 | 0.00372401 | ||||||||
\(683\) | 7.12925 | 0.272793 | 0.136397 | − | 0.990654i | \(-0.456448\pi\) | ||||
0.136397 | + | 0.990654i | \(0.456448\pi\) | |||||||
\(684\) | −19.4276 | −0.742831 | ||||||||
\(685\) | 42.9172 | 1.63978 | ||||||||
\(686\) | 19.0185 | 0.726128 | ||||||||
\(687\) | −9.15731 | −0.349373 | ||||||||
\(688\) | 4.39952 | 0.167730 | ||||||||
\(689\) | 29.8264 | 1.13630 | ||||||||
\(690\) | 2.40494 | 0.0915546 | ||||||||
\(691\) | −4.74540 | −0.180524 | −0.0902618 | − | 0.995918i | \(-0.528770\pi\) | ||||
−0.0902618 | + | 0.995918i | \(0.528770\pi\) | |||||||
\(692\) | 22.8026 | 0.866825 | ||||||||
\(693\) | 14.8042 | 0.562366 | ||||||||
\(694\) | 7.46569 | 0.283394 | ||||||||
\(695\) | 18.7794 | 0.712342 | ||||||||
\(696\) | 0.791204 | 0.0299905 | ||||||||
\(697\) | −11.5057 | −0.435809 | ||||||||
\(698\) | −11.4966 | −0.435153 | ||||||||
\(699\) | −13.6150 | −0.514966 | ||||||||
\(700\) | −6.00875 | −0.227110 | ||||||||
\(701\) | 19.8587 | 0.750053 | 0.375027 | − | 0.927014i | \(-0.377634\pi\) | ||||
0.375027 | + | 0.927014i | \(0.377634\pi\) | |||||||
\(702\) | 20.4001 | 0.769954 | ||||||||
\(703\) | 0.232671 | 0.00877534 | ||||||||
\(704\) | 3.70152 | 0.139506 | ||||||||
\(705\) | 6.65525 | 0.250651 | ||||||||
\(706\) | −6.34943 | −0.238964 | ||||||||
\(707\) | 22.2662 | 0.837407 | ||||||||
\(708\) | −8.72654 | −0.327964 | ||||||||
\(709\) | 13.9649 | 0.524463 | 0.262232 | − | 0.965005i | \(-0.415542\pi\) | ||||
0.262232 | + | 0.965005i | \(0.415542\pi\) | |||||||
\(710\) | 10.5510 | 0.395970 | ||||||||
\(711\) | 18.8293 | 0.706154 | ||||||||
\(712\) | 0.889547 | 0.0333372 | ||||||||
\(713\) | −0.0262738 | −0.000983963 0 | ||||||||
\(714\) | −6.35344 | −0.237771 | ||||||||
\(715\) | 50.0823 | 1.87297 | ||||||||
\(716\) | 6.71468 | 0.250939 | ||||||||
\(717\) | −17.2477 | −0.644128 | ||||||||
\(718\) | −4.27204 | −0.159431 | ||||||||
\(719\) | −42.3501 | −1.57939 | −0.789697 | − | 0.613497i | \(-0.789762\pi\) | ||||
−0.789697 | + | 0.613497i | \(0.789762\pi\) | |||||||
\(720\) | 6.75174 | 0.251622 | ||||||||
\(721\) | −7.11605 | −0.265016 | ||||||||
\(722\) | 51.2333 | 1.90671 | ||||||||
\(723\) | −0.221361 | −0.00823252 | ||||||||
\(724\) | 11.4355 | 0.424998 | ||||||||
\(725\) | 3.33717 | 0.123939 | ||||||||
\(726\) | 2.23050 | 0.0827815 | ||||||||
\(727\) | −6.18336 | −0.229328 | −0.114664 | − | 0.993404i | \(-0.536579\pi\) | ||||
−0.114664 | + | 0.993404i | \(0.536579\pi\) | |||||||
\(728\) | 8.01481 | 0.297049 | ||||||||
\(729\) | 3.16217 | 0.117117 | ||||||||
\(730\) | 0.484699 | 0.0179395 | ||||||||
\(731\) | 19.6209 | 0.725707 | ||||||||
\(732\) | −7.92519 | −0.292924 | ||||||||
\(733\) | −1.34665 | −0.0497398 | −0.0248699 | − | 0.999691i | \(-0.507917\pi\) | ||||
−0.0248699 | + | 0.999691i | \(0.507917\pi\) | |||||||
\(734\) | −27.5219 | −1.01585 | ||||||||
\(735\) | 9.67610 | 0.356908 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −24.9832 | −0.920269 | ||||||||
\(738\) | 5.98060 | 0.220149 | ||||||||
\(739\) | −38.8738 | −1.43000 | −0.714999 | − | 0.699126i | \(-0.753573\pi\) | ||||
−0.714999 | + | 0.699126i | \(0.753573\pi\) | |||||||
\(740\) | −0.0808610 | −0.00297251 | ||||||||
\(741\) | −32.1471 | −1.18095 | ||||||||
\(742\) | 11.0771 | 0.406653 | ||||||||
\(743\) | 9.35104 | 0.343056 | 0.171528 | − | 0.985179i | \(-0.445130\pi\) | ||||
0.171528 | + | 0.985179i | \(0.445130\pi\) | |||||||
\(744\) | 0.0216950 | 0.000795376 0 | ||||||||
\(745\) | −47.0237 | −1.72281 | ||||||||
\(746\) | 17.6082 | 0.644683 | ||||||||
\(747\) | 11.1989 | 0.409747 | ||||||||
\(748\) | 16.5080 | 0.603592 | ||||||||
\(749\) | 6.38721 | 0.233384 | ||||||||
\(750\) | 3.64884 | 0.133237 | ||||||||
\(751\) | −11.8407 | −0.432073 | −0.216036 | − | 0.976385i | \(-0.569313\pi\) | ||||
−0.216036 | + | 0.976385i | \(0.569313\pi\) | |||||||
\(752\) | −2.76732 | −0.100914 | ||||||||
\(753\) | 11.7961 | 0.429872 | ||||||||
\(754\) | −4.45130 | −0.162107 | ||||||||
\(755\) | −5.62058 | −0.204554 | ||||||||
\(756\) | 7.57630 | 0.275548 | ||||||||
\(757\) | 10.9057 | 0.396376 | 0.198188 | − | 0.980164i | \(-0.436494\pi\) | ||||
0.198188 | + | 0.980164i | \(0.436494\pi\) | |||||||
\(758\) | −34.4193 | −1.25017 | ||||||||
\(759\) | −3.05644 | −0.110942 | ||||||||
\(760\) | −24.4085 | −0.885388 | ||||||||
\(761\) | −9.22732 | −0.334490 | −0.167245 | − | 0.985915i | \(-0.553487\pi\) | ||||
−0.167245 | + | 0.985915i | \(0.553487\pi\) | |||||||
\(762\) | −0.259425 | −0.00939797 | ||||||||
\(763\) | 18.5149 | 0.670285 | ||||||||
\(764\) | −18.0493 | −0.653001 | ||||||||
\(765\) | 30.1113 | 1.08868 | ||||||||
\(766\) | −14.4656 | −0.522664 | ||||||||
\(767\) | 49.0954 | 1.77273 | ||||||||
\(768\) | 0.825726 | 0.0297958 | ||||||||
\(769\) | 17.6746 | 0.637364 | 0.318682 | − | 0.947862i | \(-0.396760\pi\) | ||||
0.318682 | + | 0.947862i | \(0.396760\pi\) | |||||||
\(770\) | 18.5998 | 0.670290 | ||||||||
\(771\) | 23.4877 | 0.845888 | ||||||||
\(772\) | 15.4934 | 0.557619 | ||||||||
\(773\) | 26.6069 | 0.956984 | 0.478492 | − | 0.878092i | \(-0.341184\pi\) | ||||
0.478492 | + | 0.878092i | \(0.341184\pi\) | |||||||
\(774\) | −10.1989 | −0.366591 | ||||||||
\(775\) | 0.0915059 | 0.00328699 | ||||||||
\(776\) | 3.83775 | 0.137767 | ||||||||
\(777\) | −0.0395517 | −0.00141891 | ||||||||
\(778\) | −14.7539 | −0.528952 | ||||||||
\(779\) | −21.6207 | −0.774643 | ||||||||
\(780\) | 11.1722 | 0.400030 | ||||||||
\(781\) | −13.4092 | −0.479819 | ||||||||
\(782\) | −4.45979 | −0.159482 | ||||||||
\(783\) | −4.20776 | −0.150373 | ||||||||
\(784\) | −4.02342 | −0.143694 | ||||||||
\(785\) | 48.3553 | 1.72587 | ||||||||
\(786\) | 0.825726 | 0.0294527 | ||||||||
\(787\) | 14.0817 | 0.501958 | 0.250979 | − | 0.967993i | \(-0.419248\pi\) | ||||
0.250979 | + | 0.967993i | \(0.419248\pi\) | |||||||
\(788\) | 15.8107 | 0.563232 | ||||||||
\(789\) | −14.2171 | −0.506142 | ||||||||
\(790\) | 23.6568 | 0.841673 | ||||||||
\(791\) | 17.1011 | 0.608045 | ||||||||
\(792\) | −8.58078 | −0.304905 | ||||||||
\(793\) | 44.5870 | 1.58333 | ||||||||
\(794\) | −1.90888 | −0.0677437 | ||||||||
\(795\) | 15.4409 | 0.547631 | ||||||||
\(796\) | 0.796066 | 0.0282158 | ||||||||
\(797\) | −31.6007 | −1.11936 | −0.559678 | − | 0.828710i | \(-0.689075\pi\) | ||||
−0.559678 | + | 0.828710i | \(0.689075\pi\) | |||||||
\(798\) | −11.9390 | −0.422634 | ||||||||
\(799\) | −12.3417 | −0.436617 | ||||||||
\(800\) | 3.48278 | 0.123135 | ||||||||
\(801\) | −2.06213 | −0.0728617 | ||||||||
\(802\) | −11.0337 | −0.389615 | ||||||||
\(803\) | −0.616003 | −0.0217383 | ||||||||
\(804\) | −5.57319 | −0.196551 | ||||||||
\(805\) | −5.02490 | −0.177105 | ||||||||
\(806\) | −0.122056 | −0.00429923 | ||||||||
\(807\) | 2.38855 | 0.0840811 | ||||||||
\(808\) | −12.9059 | −0.454027 | ||||||||
\(809\) | 36.5813 | 1.28613 | 0.643066 | − | 0.765811i | \(-0.277662\pi\) | ||||
0.643066 | + | 0.765811i | \(0.277662\pi\) | |||||||
\(810\) | −9.69425 | −0.340621 | ||||||||
\(811\) | −8.05806 | −0.282957 | −0.141478 | − | 0.989941i | \(-0.545186\pi\) | ||||
−0.141478 | + | 0.989941i | \(0.545186\pi\) | |||||||
\(812\) | −1.65315 | −0.0580141 | ||||||||
\(813\) | 18.2844 | 0.641261 | ||||||||
\(814\) | 0.102766 | 0.00360195 | ||||||||
\(815\) | 5.30174 | 0.185712 | ||||||||
\(816\) | 3.68256 | 0.128915 | ||||||||
\(817\) | 36.8704 | 1.28993 | ||||||||
\(818\) | −7.05569 | −0.246696 | ||||||||
\(819\) | −18.5798 | −0.649229 | ||||||||
\(820\) | 7.51393 | 0.262398 | ||||||||
\(821\) | −15.9326 | −0.556053 | −0.278026 | − | 0.960573i | \(-0.589680\pi\) | ||||
−0.278026 | + | 0.960573i | \(0.589680\pi\) | |||||||
\(822\) | −12.1674 | −0.424387 | ||||||||
\(823\) | −53.5115 | −1.86529 | −0.932647 | − | 0.360791i | \(-0.882507\pi\) | ||||
−0.932647 | + | 0.360791i | \(0.882507\pi\) | |||||||
\(824\) | 4.12459 | 0.143687 | ||||||||
\(825\) | 10.6449 | 0.370608 | ||||||||
\(826\) | 18.2333 | 0.634417 | ||||||||
\(827\) | 46.6305 | 1.62150 | 0.810751 | − | 0.585391i | \(-0.199059\pi\) | ||||
0.810751 | + | 0.585391i | \(0.199059\pi\) | |||||||
\(828\) | 2.31818 | 0.0805622 | ||||||||
\(829\) | −42.0387 | −1.46006 | −0.730032 | − | 0.683413i | \(-0.760495\pi\) | ||||
−0.730032 | + | 0.683413i | \(0.760495\pi\) | |||||||
\(830\) | 14.0701 | 0.488382 | ||||||||
\(831\) | 13.4877 | 0.467884 | ||||||||
\(832\) | −4.64552 | −0.161055 | ||||||||
\(833\) | −17.9436 | −0.621709 | ||||||||
\(834\) | −5.32412 | −0.184359 | ||||||||
\(835\) | 8.04978 | 0.278574 | ||||||||
\(836\) | 31.0207 | 1.07287 | ||||||||
\(837\) | −0.115378 | −0.00398804 | ||||||||
\(838\) | −6.44623 | −0.222681 | ||||||||
\(839\) | 7.73543 | 0.267057 | 0.133528 | − | 0.991045i | \(-0.457369\pi\) | ||||
0.133528 | + | 0.991045i | \(0.457369\pi\) | |||||||
\(840\) | 4.14919 | 0.143161 | ||||||||
\(841\) | −28.0819 | −0.968340 | ||||||||
\(842\) | −30.3425 | −1.04567 | ||||||||
\(843\) | 14.2080 | 0.489351 | ||||||||
\(844\) | −26.4759 | −0.911338 | ||||||||
\(845\) | −24.9920 | −0.859751 | ||||||||
\(846\) | 6.41514 | 0.220557 | ||||||||
\(847\) | −4.66042 | −0.160134 | ||||||||
\(848\) | −6.42047 | −0.220480 | ||||||||
\(849\) | 4.86077 | 0.166821 | ||||||||
\(850\) | 15.5324 | 0.532758 | ||||||||
\(851\) | −0.0277632 | −0.000951712 0 | ||||||||
\(852\) | −2.99129 | −0.102480 | ||||||||
\(853\) | −34.9691 | −1.19732 | −0.598660 | − | 0.801003i | \(-0.704300\pi\) | ||||
−0.598660 | + | 0.801003i | \(0.704300\pi\) | |||||||
\(854\) | 16.5590 | 0.566636 | ||||||||
\(855\) | 56.5832 | 1.93510 | ||||||||
\(856\) | −3.70214 | −0.126536 | ||||||||
\(857\) | 42.6996 | 1.45859 | 0.729295 | − | 0.684200i | \(-0.239848\pi\) | ||||
0.729295 | + | 0.684200i | \(0.239848\pi\) | |||||||
\(858\) | −14.1988 | −0.484738 | ||||||||
\(859\) | −52.0855 | −1.77714 | −0.888568 | − | 0.458745i | \(-0.848299\pi\) | ||||
−0.888568 | + | 0.458745i | \(0.848299\pi\) | |||||||
\(860\) | −12.8137 | −0.436944 | ||||||||
\(861\) | 3.67530 | 0.125254 | ||||||||
\(862\) | −8.21996 | −0.279973 | ||||||||
\(863\) | 0.726688 | 0.0247367 | 0.0123684 | − | 0.999924i | \(-0.496063\pi\) | ||||
0.0123684 | + | 0.999924i | \(0.496063\pi\) | |||||||
\(864\) | −4.39136 | −0.149397 | ||||||||
\(865\) | −66.4131 | −2.25811 | ||||||||
\(866\) | 38.4408 | 1.30627 | ||||||||
\(867\) | 2.38610 | 0.0810363 | ||||||||
\(868\) | −0.0453296 | −0.00153859 | ||||||||
\(869\) | −30.0655 | −1.01990 | ||||||||
\(870\) | −2.30440 | −0.0781264 | ||||||||
\(871\) | 31.3547 | 1.06241 | ||||||||
\(872\) | −10.7316 | −0.363417 | ||||||||
\(873\) | −8.89658 | −0.301104 | ||||||||
\(874\) | −8.38053 | −0.283476 | ||||||||
\(875\) | −7.62391 | −0.257735 | ||||||||
\(876\) | −0.137416 | −0.00464287 | ||||||||
\(877\) | −38.4960 | −1.29992 | −0.649959 | − | 0.759969i | \(-0.725214\pi\) | ||||
−0.649959 | + | 0.759969i | \(0.725214\pi\) | |||||||
\(878\) | 11.8125 | 0.398652 | ||||||||
\(879\) | 14.9222 | 0.503312 | ||||||||
\(880\) | −10.7808 | −0.363419 | ||||||||
\(881\) | 23.8585 | 0.803814 | 0.401907 | − | 0.915681i | \(-0.368348\pi\) | ||||
0.401907 | + | 0.915681i | \(0.368348\pi\) | |||||||
\(882\) | 9.32700 | 0.314056 | ||||||||
\(883\) | −17.9819 | −0.605141 | −0.302570 | − | 0.953127i | \(-0.597845\pi\) | ||||
−0.302570 | + | 0.953127i | \(0.597845\pi\) | |||||||
\(884\) | −20.7180 | −0.696823 | ||||||||
\(885\) | 25.4162 | 0.854357 | ||||||||
\(886\) | −13.4654 | −0.452380 | ||||||||
\(887\) | −10.0919 | −0.338853 | −0.169426 | − | 0.985543i | \(-0.554192\pi\) | ||||
−0.169426 | + | 0.985543i | \(0.554192\pi\) | |||||||
\(888\) | 0.0229248 | 0.000769307 0 | ||||||||
\(889\) | 0.542044 | 0.0181796 | ||||||||
\(890\) | −2.59082 | −0.0868446 | ||||||||
\(891\) | 12.3204 | 0.412750 | ||||||||
\(892\) | −20.0246 | −0.670473 | ||||||||
\(893\) | −23.1916 | −0.776078 | ||||||||
\(894\) | 13.3316 | 0.445877 | ||||||||
\(895\) | −19.5566 | −0.653706 | ||||||||
\(896\) | −1.72528 | −0.0576375 | ||||||||
\(897\) | 3.83593 | 0.128078 | ||||||||
\(898\) | −2.87075 | −0.0957981 | ||||||||
\(899\) | 0.0251754 | 0.000839646 0 | ||||||||
\(900\) | −8.07369 | −0.269123 | ||||||||
\(901\) | −28.6339 | −0.953934 | ||||||||
\(902\) | −9.54946 | −0.317962 | ||||||||
\(903\) | −6.26759 | −0.208572 | ||||||||
\(904\) | −9.91209 | −0.329671 | ||||||||
\(905\) | −33.3062 | −1.10714 | ||||||||
\(906\) | 1.59348 | 0.0529400 | ||||||||
\(907\) | 18.6354 | 0.618777 | 0.309388 | − | 0.950936i | \(-0.399876\pi\) | ||||
0.309388 | + | 0.950936i | \(0.399876\pi\) | |||||||
\(908\) | −10.7338 | −0.356214 | ||||||||
\(909\) | 29.9181 | 0.992321 | ||||||||
\(910\) | −23.3433 | −0.773823 | ||||||||
\(911\) | 8.01001 | 0.265384 | 0.132692 | − | 0.991157i | \(-0.457638\pi\) | ||||
0.132692 | + | 0.991157i | \(0.457638\pi\) | |||||||
\(912\) | 6.92002 | 0.229145 | ||||||||
\(913\) | −17.8817 | −0.591799 | ||||||||
\(914\) | 22.9351 | 0.758626 | ||||||||
\(915\) | 23.0823 | 0.763077 | ||||||||
\(916\) | −11.0900 | −0.366424 | ||||||||
\(917\) | −1.72528 | −0.0569737 | ||||||||
\(918\) | −19.5845 | −0.646385 | ||||||||
\(919\) | 12.4560 | 0.410886 | 0.205443 | − | 0.978669i | \(-0.434137\pi\) | ||||
0.205443 | + | 0.978669i | \(0.434137\pi\) | |||||||
\(920\) | 2.91252 | 0.0960230 | ||||||||
\(921\) | 13.8428 | 0.456137 | ||||||||
\(922\) | −7.78624 | −0.256426 | ||||||||
\(923\) | 16.8290 | 0.553932 | ||||||||
\(924\) | −5.27321 | −0.173476 | ||||||||
\(925\) | 0.0966931 | 0.00317925 | ||||||||
\(926\) | 23.9570 | 0.787275 | ||||||||
\(927\) | −9.56152 | −0.314042 | ||||||||
\(928\) | 0.958192 | 0.0314542 | ||||||||
\(929\) | −47.9843 | −1.57431 | −0.787157 | − | 0.616753i | \(-0.788448\pi\) | ||||
−0.787157 | + | 0.616753i | \(0.788448\pi\) | |||||||
\(930\) | −0.0631871 | −0.00207199 | ||||||||
\(931\) | −33.7184 | −1.10508 | ||||||||
\(932\) | −16.4885 | −0.540099 | ||||||||
\(933\) | 7.82907 | 0.256312 | ||||||||
\(934\) | −34.5877 | −1.13174 | ||||||||
\(935\) | −48.0799 | −1.57238 | ||||||||
\(936\) | 10.7691 | 0.352001 | ||||||||
\(937\) | −39.2493 | −1.28222 | −0.641109 | − | 0.767450i | \(-0.721525\pi\) | ||||
−0.641109 | + | 0.767450i | \(0.721525\pi\) | |||||||
\(938\) | 11.6447 | 0.380212 | ||||||||
\(939\) | 15.8266 | 0.516482 | ||||||||
\(940\) | 8.05988 | 0.262884 | ||||||||
\(941\) | −33.8853 | −1.10463 | −0.552314 | − | 0.833636i | \(-0.686255\pi\) | ||||
−0.552314 | + | 0.833636i | \(0.686255\pi\) | |||||||
\(942\) | −13.7092 | −0.446669 | ||||||||
\(943\) | 2.57987 | 0.0840122 | ||||||||
\(944\) | −10.5683 | −0.343970 | ||||||||
\(945\) | −22.0661 | −0.717812 | ||||||||
\(946\) | 16.2849 | 0.529469 | ||||||||
\(947\) | 5.75179 | 0.186908 | 0.0934541 | − | 0.995624i | \(-0.470209\pi\) | ||||
0.0934541 | + | 0.995624i | \(0.470209\pi\) | |||||||
\(948\) | −6.70693 | −0.217831 | ||||||||
\(949\) | 0.773103 | 0.0250960 | ||||||||
\(950\) | 29.1875 | 0.946968 | ||||||||
\(951\) | −21.0457 | −0.682454 | ||||||||
\(952\) | −7.69437 | −0.249376 | ||||||||
\(953\) | −1.12943 | −0.0365860 | −0.0182930 | − | 0.999833i | \(-0.505823\pi\) | ||||
−0.0182930 | + | 0.999833i | \(0.505823\pi\) | |||||||
\(954\) | 14.8838 | 0.481880 | ||||||||
\(955\) | 52.5690 | 1.70109 | ||||||||
\(956\) | −20.8880 | −0.675565 | ||||||||
\(957\) | 2.92866 | 0.0946700 | ||||||||
\(958\) | −18.1571 | −0.586628 | ||||||||
\(959\) | 25.4227 | 0.820941 | ||||||||
\(960\) | −2.40494 | −0.0776192 | ||||||||
\(961\) | −30.9993 | −0.999978 | ||||||||
\(962\) | −0.128975 | −0.00415831 | ||||||||
\(963\) | 8.58221 | 0.276558 | ||||||||
\(964\) | −0.268081 | −0.00863431 | ||||||||
\(965\) | −45.1248 | −1.45262 | ||||||||
\(966\) | 1.42461 | 0.0458359 | ||||||||
\(967\) | 10.9368 | 0.351703 | 0.175851 | − | 0.984417i | \(-0.443732\pi\) | ||||
0.175851 | + | 0.984417i | \(0.443732\pi\) | |||||||
\(968\) | 2.70126 | 0.0868217 | ||||||||
\(969\) | 30.8618 | 0.991425 | ||||||||
\(970\) | −11.1775 | −0.358889 | ||||||||
\(971\) | 15.7024 | 0.503915 | 0.251957 | − | 0.967738i | \(-0.418926\pi\) | ||||
0.251957 | + | 0.967738i | \(0.418926\pi\) | |||||||
\(972\) | 15.9225 | 0.510714 | ||||||||
\(973\) | 11.1242 | 0.356627 | ||||||||
\(974\) | 26.3758 | 0.845135 | ||||||||
\(975\) | −13.3597 | −0.427852 | ||||||||
\(976\) | −9.59785 | −0.307220 | ||||||||
\(977\) | −8.72265 | −0.279062 | −0.139531 | − | 0.990218i | \(-0.544560\pi\) | ||||
−0.139531 | + | 0.990218i | \(0.544560\pi\) | |||||||
\(978\) | −1.50309 | −0.0480635 | ||||||||
\(979\) | 3.29268 | 0.105234 | ||||||||
\(980\) | 11.7183 | 0.374327 | ||||||||
\(981\) | 24.8777 | 0.794283 | ||||||||
\(982\) | 35.7810 | 1.14182 | ||||||||
\(983\) | −61.2127 | −1.95238 | −0.976190 | − | 0.216916i | \(-0.930400\pi\) | ||||
−0.976190 | + | 0.216916i | \(0.930400\pi\) | |||||||
\(984\) | −2.13027 | −0.0679105 | ||||||||
\(985\) | −46.0489 | −1.46724 | ||||||||
\(986\) | 4.27333 | 0.136091 | ||||||||
\(987\) | 3.94234 | 0.125486 | ||||||||
\(988\) | −38.9320 | −1.23859 | ||||||||
\(989\) | −4.39952 | −0.139897 | ||||||||
\(990\) | 24.9917 | 0.794288 | ||||||||
\(991\) | −2.13953 | −0.0679643 | −0.0339821 | − | 0.999422i | \(-0.510819\pi\) | ||||
−0.0339821 | + | 0.999422i | \(0.510819\pi\) | |||||||
\(992\) | 0.0262738 | 0.000834195 0 | ||||||||
\(993\) | 14.9630 | 0.474838 | ||||||||
\(994\) | 6.25002 | 0.198239 | ||||||||
\(995\) | −2.31856 | −0.0735033 | ||||||||
\(996\) | −3.98901 | −0.126397 | ||||||||
\(997\) | 27.2390 | 0.862669 | 0.431334 | − | 0.902192i | \(-0.358043\pi\) | ||||
0.431334 | + | 0.902192i | \(0.358043\pi\) | |||||||
\(998\) | −21.7609 | −0.688831 | ||||||||
\(999\) | −0.121918 | −0.00385732 |
(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 | 6026.2.a.g.1.14 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6026.2.a.g.1.14 | ✓ | 21 | 1.1 | even | 1 | trivial |