Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1518129839\) |
Analytic rank: | \(1\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 4x^{10} - 18x^{9} + 64x^{8} + 85x^{7} - 249x^{6} - 109x^{5} + 230x^{4} + 97x^{3} - 53x^{2} - 32x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-3.29880\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.113923 | 0.0509479 | 0.0254739 | − | 0.999675i | \(-0.491891\pi\) | ||||
0.0254739 | + | 0.999675i | \(0.491891\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 2.65133 | 1.00211 | 0.501054 | − | 0.865416i | \(-0.332946\pi\) | ||||
0.501054 | + | 0.865416i | \(0.332946\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.113923 | 0.0360256 | ||||||||
\(11\) | −3.17383 | −0.956947 | −0.478473 | − | 0.878102i | \(-0.658810\pi\) | ||||
−0.478473 | + | 0.878102i | \(0.658810\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 2.65133 | 0.708597 | ||||||||
\(15\) | −0.113923 | −0.0294148 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.51081 | 0.851495 | 0.425748 | − | 0.904842i | \(-0.360011\pi\) | ||||
0.425748 | + | 0.904842i | \(0.360011\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −2.25761 | −0.517930 | −0.258965 | − | 0.965887i | \(-0.583382\pi\) | ||||
−0.258965 | + | 0.965887i | \(0.583382\pi\) | |||||||
\(20\) | 0.113923 | 0.0254739 | ||||||||
\(21\) | −2.65133 | −0.578567 | ||||||||
\(22\) | −3.17383 | −0.676663 | ||||||||
\(23\) | −4.90813 | −1.02342 | −0.511708 | − | 0.859159i | \(-0.670987\pi\) | ||||
−0.511708 | + | 0.859159i | \(0.670987\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −4.98702 | −0.997404 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.65133 | 0.501054 | ||||||||
\(29\) | 0.991065 | 0.184036 | 0.0920181 | − | 0.995757i | \(-0.470668\pi\) | ||||
0.0920181 | + | 0.995757i | \(0.470668\pi\) | |||||||
\(30\) | −0.113923 | −0.0207994 | ||||||||
\(31\) | 5.57567 | 1.00142 | 0.500710 | − | 0.865615i | \(-0.333072\pi\) | ||||
0.500710 | + | 0.865615i | \(0.333072\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 3.17383 | 0.552493 | ||||||||
\(34\) | 3.51081 | 0.602098 | ||||||||
\(35\) | 0.302047 | 0.0510552 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −7.31136 | −1.20198 | −0.600990 | − | 0.799256i | \(-0.705227\pi\) | ||||
−0.600990 | + | 0.799256i | \(0.705227\pi\) | |||||||
\(38\) | −2.25761 | −0.366232 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0.113923 | 0.0180128 | ||||||||
\(41\) | −8.22718 | −1.28487 | −0.642434 | − | 0.766341i | \(-0.722076\pi\) | ||||
−0.642434 | + | 0.766341i | \(0.722076\pi\) | |||||||
\(42\) | −2.65133 | −0.409109 | ||||||||
\(43\) | −6.12885 | −0.934641 | −0.467320 | − | 0.884088i | \(-0.654781\pi\) | ||||
−0.467320 | + | 0.884088i | \(0.654781\pi\) | |||||||
\(44\) | −3.17383 | −0.478473 | ||||||||
\(45\) | 0.113923 | 0.0169826 | ||||||||
\(46\) | −4.90813 | −0.723665 | ||||||||
\(47\) | −0.711399 | −0.103768 | −0.0518841 | − | 0.998653i | \(-0.516523\pi\) | ||||
−0.0518841 | + | 0.998653i | \(0.516523\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0.0295321 | 0.00421887 | ||||||||
\(50\) | −4.98702 | −0.705271 | ||||||||
\(51\) | −3.51081 | −0.491611 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | 7.20535 | 0.989730 | 0.494865 | − | 0.868970i | \(-0.335217\pi\) | ||||
0.494865 | + | 0.868970i | \(0.335217\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −0.361572 | −0.0487544 | ||||||||
\(56\) | 2.65133 | 0.354298 | ||||||||
\(57\) | 2.25761 | 0.299027 | ||||||||
\(58\) | 0.991065 | 0.130133 | ||||||||
\(59\) | −8.39566 | −1.09302 | −0.546511 | − | 0.837452i | \(-0.684044\pi\) | ||||
−0.546511 | + | 0.837452i | \(0.684044\pi\) | |||||||
\(60\) | −0.113923 | −0.0147074 | ||||||||
\(61\) | −1.34766 | −0.172550 | −0.0862751 | − | 0.996271i | \(-0.527496\pi\) | ||||
−0.0862751 | + | 0.996271i | \(0.527496\pi\) | |||||||
\(62\) | 5.57567 | 0.708111 | ||||||||
\(63\) | 2.65133 | 0.334036 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.113923 | −0.0141304 | ||||||||
\(66\) | 3.17383 | 0.390672 | ||||||||
\(67\) | −10.6030 | −1.29536 | −0.647679 | − | 0.761913i | \(-0.724260\pi\) | ||||
−0.647679 | + | 0.761913i | \(0.724260\pi\) | |||||||
\(68\) | 3.51081 | 0.425748 | ||||||||
\(69\) | 4.90813 | 0.590870 | ||||||||
\(70\) | 0.302047 | 0.0361015 | ||||||||
\(71\) | 13.6456 | 1.61943 | 0.809716 | − | 0.586822i | \(-0.199621\pi\) | ||||
0.809716 | + | 0.586822i | \(0.199621\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −1.59020 | −0.186119 | −0.0930593 | − | 0.995661i | \(-0.529665\pi\) | ||||
−0.0930593 | + | 0.995661i | \(0.529665\pi\) | |||||||
\(74\) | −7.31136 | −0.849928 | ||||||||
\(75\) | 4.98702 | 0.575852 | ||||||||
\(76\) | −2.25761 | −0.258965 | ||||||||
\(77\) | −8.41487 | −0.958963 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | 5.88236 | 0.661818 | 0.330909 | − | 0.943663i | \(-0.392645\pi\) | ||||
0.330909 | + | 0.943663i | \(0.392645\pi\) | |||||||
\(80\) | 0.113923 | 0.0127370 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −8.22718 | −0.908540 | ||||||||
\(83\) | −12.1432 | −1.33289 | −0.666444 | − | 0.745555i | \(-0.732185\pi\) | ||||
−0.666444 | + | 0.745555i | \(0.732185\pi\) | |||||||
\(84\) | −2.65133 | −0.289283 | ||||||||
\(85\) | 0.399961 | 0.0433819 | ||||||||
\(86\) | −6.12885 | −0.660891 | ||||||||
\(87\) | −0.991065 | −0.106253 | ||||||||
\(88\) | −3.17383 | −0.338332 | ||||||||
\(89\) | −8.95858 | −0.949607 | −0.474804 | − | 0.880092i | \(-0.657481\pi\) | ||||
−0.474804 | + | 0.880092i | \(0.657481\pi\) | |||||||
\(90\) | 0.113923 | 0.0120085 | ||||||||
\(91\) | −2.65133 | −0.277935 | ||||||||
\(92\) | −4.90813 | −0.511708 | ||||||||
\(93\) | −5.57567 | −0.578170 | ||||||||
\(94\) | −0.711399 | −0.0733752 | ||||||||
\(95\) | −0.257193 | −0.0263874 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 10.4001 | 1.05597 | 0.527986 | − | 0.849253i | \(-0.322947\pi\) | ||||
0.527986 | + | 0.849253i | \(0.322947\pi\) | |||||||
\(98\) | 0.0295321 | 0.00298319 | ||||||||
\(99\) | −3.17383 | −0.318982 | ||||||||
\(100\) | −4.98702 | −0.498702 | ||||||||
\(101\) | −15.9846 | −1.59053 | −0.795264 | − | 0.606263i | \(-0.792668\pi\) | ||||
−0.795264 | + | 0.606263i | \(0.792668\pi\) | |||||||
\(102\) | −3.51081 | −0.347622 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | −0.302047 | −0.0294767 | ||||||||
\(106\) | 7.20535 | 0.699845 | ||||||||
\(107\) | 14.4797 | 1.39980 | 0.699901 | − | 0.714240i | \(-0.253227\pi\) | ||||
0.699901 | + | 0.714240i | \(0.253227\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −17.6514 | −1.69070 | −0.845351 | − | 0.534211i | \(-0.820609\pi\) | ||||
−0.845351 | + | 0.534211i | \(0.820609\pi\) | |||||||
\(110\) | −0.361572 | −0.0344745 | ||||||||
\(111\) | 7.31136 | 0.693964 | ||||||||
\(112\) | 2.65133 | 0.250527 | ||||||||
\(113\) | 17.4659 | 1.64305 | 0.821525 | − | 0.570173i | \(-0.193124\pi\) | ||||
0.821525 | + | 0.570173i | \(0.193124\pi\) | |||||||
\(114\) | 2.25761 | 0.211444 | ||||||||
\(115\) | −0.559148 | −0.0521409 | ||||||||
\(116\) | 0.991065 | 0.0920181 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | −8.39566 | −0.772883 | ||||||||
\(119\) | 9.30829 | 0.853290 | ||||||||
\(120\) | −0.113923 | −0.0103997 | ||||||||
\(121\) | −0.926787 | −0.0842533 | ||||||||
\(122\) | −1.34766 | −0.122011 | ||||||||
\(123\) | 8.22718 | 0.741819 | ||||||||
\(124\) | 5.57567 | 0.500710 | ||||||||
\(125\) | −1.13775 | −0.101763 | ||||||||
\(126\) | 2.65133 | 0.236199 | ||||||||
\(127\) | −16.0196 | −1.42151 | −0.710757 | − | 0.703438i | \(-0.751647\pi\) | ||||
−0.710757 | + | 0.703438i | \(0.751647\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 6.12885 | 0.539615 | ||||||||
\(130\) | −0.113923 | −0.00999170 | ||||||||
\(131\) | 8.02984 | 0.701570 | 0.350785 | − | 0.936456i | \(-0.385915\pi\) | ||||
0.350785 | + | 0.936456i | \(0.385915\pi\) | |||||||
\(132\) | 3.17383 | 0.276247 | ||||||||
\(133\) | −5.98565 | −0.519022 | ||||||||
\(134\) | −10.6030 | −0.915957 | ||||||||
\(135\) | −0.113923 | −0.00980492 | ||||||||
\(136\) | 3.51081 | 0.301049 | ||||||||
\(137\) | −0.471978 | −0.0403238 | −0.0201619 | − | 0.999797i | \(-0.506418\pi\) | ||||
−0.0201619 | + | 0.999797i | \(0.506418\pi\) | |||||||
\(138\) | 4.90813 | 0.417808 | ||||||||
\(139\) | 2.51841 | 0.213609 | 0.106805 | − | 0.994280i | \(-0.465938\pi\) | ||||
0.106805 | + | 0.994280i | \(0.465938\pi\) | |||||||
\(140\) | 0.302047 | 0.0255276 | ||||||||
\(141\) | 0.711399 | 0.0599106 | ||||||||
\(142\) | 13.6456 | 1.14511 | ||||||||
\(143\) | 3.17383 | 0.265409 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0.112905 | 0.00937624 | ||||||||
\(146\) | −1.59020 | −0.131606 | ||||||||
\(147\) | −0.0295321 | −0.00243576 | ||||||||
\(148\) | −7.31136 | −0.600990 | ||||||||
\(149\) | −12.0279 | −0.985367 | −0.492684 | − | 0.870208i | \(-0.663984\pi\) | ||||
−0.492684 | + | 0.870208i | \(0.663984\pi\) | |||||||
\(150\) | 4.98702 | 0.407189 | ||||||||
\(151\) | 19.7757 | 1.60932 | 0.804662 | − | 0.593733i | \(-0.202347\pi\) | ||||
0.804662 | + | 0.593733i | \(0.202347\pi\) | |||||||
\(152\) | −2.25761 | −0.183116 | ||||||||
\(153\) | 3.51081 | 0.283832 | ||||||||
\(154\) | −8.41487 | −0.678089 | ||||||||
\(155\) | 0.635196 | 0.0510202 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | −3.75589 | −0.299752 | −0.149876 | − | 0.988705i | \(-0.547887\pi\) | ||||
−0.149876 | + | 0.988705i | \(0.547887\pi\) | |||||||
\(158\) | 5.88236 | 0.467976 | ||||||||
\(159\) | −7.20535 | −0.571421 | ||||||||
\(160\) | 0.113923 | 0.00900639 | ||||||||
\(161\) | −13.0131 | −1.02557 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −11.0445 | −0.865076 | −0.432538 | − | 0.901616i | \(-0.642382\pi\) | ||||
−0.432538 | + | 0.901616i | \(0.642382\pi\) | |||||||
\(164\) | −8.22718 | −0.642434 | ||||||||
\(165\) | 0.361572 | 0.0281483 | ||||||||
\(166\) | −12.1432 | −0.942495 | ||||||||
\(167\) | 1.02005 | 0.0789340 | 0.0394670 | − | 0.999221i | \(-0.487434\pi\) | ||||
0.0394670 | + | 0.999221i | \(0.487434\pi\) | |||||||
\(168\) | −2.65133 | −0.204554 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0.399961 | 0.0306756 | ||||||||
\(171\) | −2.25761 | −0.172643 | ||||||||
\(172\) | −6.12885 | −0.467320 | ||||||||
\(173\) | −2.77538 | −0.211008 | −0.105504 | − | 0.994419i | \(-0.533646\pi\) | ||||
−0.105504 | + | 0.994419i | \(0.533646\pi\) | |||||||
\(174\) | −0.991065 | −0.0751324 | ||||||||
\(175\) | −13.2222 | −0.999506 | ||||||||
\(176\) | −3.17383 | −0.239237 | ||||||||
\(177\) | 8.39566 | 0.631056 | ||||||||
\(178\) | −8.95858 | −0.671474 | ||||||||
\(179\) | 11.4232 | 0.853811 | 0.426906 | − | 0.904296i | \(-0.359604\pi\) | ||||
0.426906 | + | 0.904296i | \(0.359604\pi\) | |||||||
\(180\) | 0.113923 | 0.00849131 | ||||||||
\(181\) | −14.5444 | −1.08108 | −0.540540 | − | 0.841318i | \(-0.681780\pi\) | ||||
−0.540540 | + | 0.841318i | \(0.681780\pi\) | |||||||
\(182\) | −2.65133 | −0.196529 | ||||||||
\(183\) | 1.34766 | 0.0996218 | ||||||||
\(184\) | −4.90813 | −0.361832 | ||||||||
\(185\) | −0.832931 | −0.0612383 | ||||||||
\(186\) | −5.57567 | −0.408828 | ||||||||
\(187\) | −11.1427 | −0.814836 | ||||||||
\(188\) | −0.711399 | −0.0518841 | ||||||||
\(189\) | −2.65133 | −0.192856 | ||||||||
\(190\) | −0.257193 | −0.0186587 | ||||||||
\(191\) | −11.4688 | −0.829851 | −0.414925 | − | 0.909855i | \(-0.636192\pi\) | ||||
−0.414925 | + | 0.909855i | \(0.636192\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −7.05090 | −0.507535 | −0.253767 | − | 0.967265i | \(-0.581670\pi\) | ||||
−0.253767 | + | 0.967265i | \(0.581670\pi\) | |||||||
\(194\) | 10.4001 | 0.746684 | ||||||||
\(195\) | 0.113923 | 0.00815819 | ||||||||
\(196\) | 0.0295321 | 0.00210943 | ||||||||
\(197\) | 3.41934 | 0.243618 | 0.121809 | − | 0.992554i | \(-0.461130\pi\) | ||||
0.121809 | + | 0.992554i | \(0.461130\pi\) | |||||||
\(198\) | −3.17383 | −0.225554 | ||||||||
\(199\) | 12.7201 | 0.901702 | 0.450851 | − | 0.892599i | \(-0.351121\pi\) | ||||
0.450851 | + | 0.892599i | \(0.351121\pi\) | |||||||
\(200\) | −4.98702 | −0.352636 | ||||||||
\(201\) | 10.6030 | 0.747876 | ||||||||
\(202\) | −15.9846 | −1.12467 | ||||||||
\(203\) | 2.62764 | 0.184424 | ||||||||
\(204\) | −3.51081 | −0.245806 | ||||||||
\(205\) | −0.937263 | −0.0654613 | ||||||||
\(206\) | 1.00000 | 0.0696733 | ||||||||
\(207\) | −4.90813 | −0.341139 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | 7.16527 | 0.495632 | ||||||||
\(210\) | −0.302047 | −0.0208432 | ||||||||
\(211\) | −8.15531 | −0.561435 | −0.280717 | − | 0.959790i | \(-0.590572\pi\) | ||||
−0.280717 | + | 0.959790i | \(0.590572\pi\) | |||||||
\(212\) | 7.20535 | 0.494865 | ||||||||
\(213\) | −13.6456 | −0.934980 | ||||||||
\(214\) | 14.4797 | 0.989810 | ||||||||
\(215\) | −0.698216 | −0.0476179 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 14.7829 | 1.00353 | ||||||||
\(218\) | −17.6514 | −1.19551 | ||||||||
\(219\) | 1.59020 | 0.107456 | ||||||||
\(220\) | −0.361572 | −0.0243772 | ||||||||
\(221\) | −3.51081 | −0.236162 | ||||||||
\(222\) | 7.31136 | 0.490706 | ||||||||
\(223\) | 1.92053 | 0.128608 | 0.0643041 | − | 0.997930i | \(-0.479517\pi\) | ||||
0.0643041 | + | 0.997930i | \(0.479517\pi\) | |||||||
\(224\) | 2.65133 | 0.177149 | ||||||||
\(225\) | −4.98702 | −0.332468 | ||||||||
\(226\) | 17.4659 | 1.16181 | ||||||||
\(227\) | 7.73629 | 0.513475 | 0.256738 | − | 0.966481i | \(-0.417352\pi\) | ||||
0.256738 | + | 0.966481i | \(0.417352\pi\) | |||||||
\(228\) | 2.25761 | 0.149514 | ||||||||
\(229\) | 3.09858 | 0.204760 | 0.102380 | − | 0.994745i | \(-0.467354\pi\) | ||||
0.102380 | + | 0.994745i | \(0.467354\pi\) | |||||||
\(230\) | −0.559148 | −0.0368692 | ||||||||
\(231\) | 8.41487 | 0.553658 | ||||||||
\(232\) | 0.991065 | 0.0650666 | ||||||||
\(233\) | 3.97487 | 0.260402 | 0.130201 | − | 0.991488i | \(-0.458438\pi\) | ||||
0.130201 | + | 0.991488i | \(0.458438\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | −0.0810446 | −0.00528677 | ||||||||
\(236\) | −8.39566 | −0.546511 | ||||||||
\(237\) | −5.88236 | −0.382101 | ||||||||
\(238\) | 9.30829 | 0.603367 | ||||||||
\(239\) | −17.6397 | −1.14102 | −0.570509 | − | 0.821291i | \(-0.693254\pi\) | ||||
−0.570509 | + | 0.821291i | \(0.693254\pi\) | |||||||
\(240\) | −0.113923 | −0.00735369 | ||||||||
\(241\) | 24.3235 | 1.56682 | 0.783408 | − | 0.621508i | \(-0.213480\pi\) | ||||
0.783408 | + | 0.621508i | \(0.213480\pi\) | |||||||
\(242\) | −0.926787 | −0.0595761 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −1.34766 | −0.0862751 | ||||||||
\(245\) | 0.00336438 | 0.000214942 0 | ||||||||
\(246\) | 8.22718 | 0.524546 | ||||||||
\(247\) | 2.25761 | 0.143648 | ||||||||
\(248\) | 5.57567 | 0.354055 | ||||||||
\(249\) | 12.1432 | 0.769544 | ||||||||
\(250\) | −1.13775 | −0.0719576 | ||||||||
\(251\) | 16.8621 | 1.06433 | 0.532163 | − | 0.846642i | \(-0.321379\pi\) | ||||
0.532163 | + | 0.846642i | \(0.321379\pi\) | |||||||
\(252\) | 2.65133 | 0.167018 | ||||||||
\(253\) | 15.5776 | 0.979355 | ||||||||
\(254\) | −16.0196 | −1.00516 | ||||||||
\(255\) | −0.399961 | −0.0250465 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −19.0078 | −1.18567 | −0.592837 | − | 0.805322i | \(-0.701992\pi\) | ||||
−0.592837 | + | 0.805322i | \(0.701992\pi\) | |||||||
\(258\) | 6.12885 | 0.381565 | ||||||||
\(259\) | −19.3848 | −1.20451 | ||||||||
\(260\) | −0.113923 | −0.00706520 | ||||||||
\(261\) | 0.991065 | 0.0613454 | ||||||||
\(262\) | 8.02984 | 0.496085 | ||||||||
\(263\) | 16.5275 | 1.01913 | 0.509566 | − | 0.860432i | \(-0.329806\pi\) | ||||
0.509566 | + | 0.860432i | \(0.329806\pi\) | |||||||
\(264\) | 3.17383 | 0.195336 | ||||||||
\(265\) | 0.820854 | 0.0504246 | ||||||||
\(266\) | −5.98565 | −0.367004 | ||||||||
\(267\) | 8.95858 | 0.548256 | ||||||||
\(268\) | −10.6030 | −0.647679 | ||||||||
\(269\) | 1.06645 | 0.0650228 | 0.0325114 | − | 0.999471i | \(-0.489649\pi\) | ||||
0.0325114 | + | 0.999471i | \(0.489649\pi\) | |||||||
\(270\) | −0.113923 | −0.00693312 | ||||||||
\(271\) | −28.1094 | −1.70752 | −0.853761 | − | 0.520664i | \(-0.825684\pi\) | ||||
−0.853761 | + | 0.520664i | \(0.825684\pi\) | |||||||
\(272\) | 3.51081 | 0.212874 | ||||||||
\(273\) | 2.65133 | 0.160466 | ||||||||
\(274\) | −0.471978 | −0.0285133 | ||||||||
\(275\) | 15.8280 | 0.954463 | ||||||||
\(276\) | 4.90813 | 0.295435 | ||||||||
\(277\) | −8.95306 | −0.537937 | −0.268969 | − | 0.963149i | \(-0.586683\pi\) | ||||
−0.268969 | + | 0.963149i | \(0.586683\pi\) | |||||||
\(278\) | 2.51841 | 0.151044 | ||||||||
\(279\) | 5.57567 | 0.333807 | ||||||||
\(280\) | 0.302047 | 0.0180507 | ||||||||
\(281\) | 23.4140 | 1.39676 | 0.698381 | − | 0.715726i | \(-0.253904\pi\) | ||||
0.698381 | + | 0.715726i | \(0.253904\pi\) | |||||||
\(282\) | 0.711399 | 0.0423632 | ||||||||
\(283\) | −9.20239 | −0.547025 | −0.273513 | − | 0.961868i | \(-0.588186\pi\) | ||||
−0.273513 | + | 0.961868i | \(0.588186\pi\) | |||||||
\(284\) | 13.6456 | 0.809716 | ||||||||
\(285\) | 0.257193 | 0.0152348 | ||||||||
\(286\) | 3.17383 | 0.187673 | ||||||||
\(287\) | −21.8129 | −1.28758 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −4.67425 | −0.274956 | ||||||||
\(290\) | 0.112905 | 0.00663001 | ||||||||
\(291\) | −10.4001 | −0.609665 | ||||||||
\(292\) | −1.59020 | −0.0930593 | ||||||||
\(293\) | −12.8741 | −0.752111 | −0.376055 | − | 0.926597i | \(-0.622720\pi\) | ||||
−0.376055 | + | 0.926597i | \(0.622720\pi\) | |||||||
\(294\) | −0.0295321 | −0.00172234 | ||||||||
\(295\) | −0.956458 | −0.0556871 | ||||||||
\(296\) | −7.31136 | −0.424964 | ||||||||
\(297\) | 3.17383 | 0.184164 | ||||||||
\(298\) | −12.0279 | −0.696760 | ||||||||
\(299\) | 4.90813 | 0.283845 | ||||||||
\(300\) | 4.98702 | 0.287926 | ||||||||
\(301\) | −16.2496 | −0.936610 | ||||||||
\(302\) | 19.7757 | 1.13796 | ||||||||
\(303\) | 15.9846 | 0.918292 | ||||||||
\(304\) | −2.25761 | −0.129483 | ||||||||
\(305\) | −0.153529 | −0.00879106 | ||||||||
\(306\) | 3.51081 | 0.200699 | ||||||||
\(307\) | −7.06703 | −0.403337 | −0.201668 | − | 0.979454i | \(-0.564636\pi\) | ||||
−0.201668 | + | 0.979454i | \(0.564636\pi\) | |||||||
\(308\) | −8.41487 | −0.479482 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | 0.635196 | 0.0360767 | ||||||||
\(311\) | 8.92110 | 0.505869 | 0.252935 | − | 0.967483i | \(-0.418604\pi\) | ||||
0.252935 | + | 0.967483i | \(0.418604\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | −13.7395 | −0.776604 | −0.388302 | − | 0.921532i | \(-0.626938\pi\) | ||||
−0.388302 | + | 0.921532i | \(0.626938\pi\) | |||||||
\(314\) | −3.75589 | −0.211957 | ||||||||
\(315\) | 0.302047 | 0.0170184 | ||||||||
\(316\) | 5.88236 | 0.330909 | ||||||||
\(317\) | 21.1401 | 1.18734 | 0.593672 | − | 0.804707i | \(-0.297678\pi\) | ||||
0.593672 | + | 0.804707i | \(0.297678\pi\) | |||||||
\(318\) | −7.20535 | −0.404056 | ||||||||
\(319\) | −3.14547 | −0.176113 | ||||||||
\(320\) | 0.113923 | 0.00636848 | ||||||||
\(321\) | −14.4797 | −0.808176 | ||||||||
\(322\) | −13.0131 | −0.725189 | ||||||||
\(323\) | −7.92602 | −0.441015 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 4.98702 | 0.276630 | ||||||||
\(326\) | −11.0445 | −0.611701 | ||||||||
\(327\) | 17.6514 | 0.976127 | ||||||||
\(328\) | −8.22718 | −0.454270 | ||||||||
\(329\) | −1.88615 | −0.103987 | ||||||||
\(330\) | 0.361572 | 0.0199039 | ||||||||
\(331\) | −19.2913 | −1.06034 | −0.530172 | − | 0.847890i | \(-0.677873\pi\) | ||||
−0.530172 | + | 0.847890i | \(0.677873\pi\) | |||||||
\(332\) | −12.1432 | −0.666444 | ||||||||
\(333\) | −7.31136 | −0.400660 | ||||||||
\(334\) | 1.02005 | 0.0558148 | ||||||||
\(335\) | −1.20792 | −0.0659957 | ||||||||
\(336\) | −2.65133 | −0.144642 | ||||||||
\(337\) | 14.3407 | 0.781189 | 0.390594 | − | 0.920563i | \(-0.372270\pi\) | ||||
0.390594 | + | 0.920563i | \(0.372270\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | −17.4659 | −0.948615 | ||||||||
\(340\) | 0.399961 | 0.0216909 | ||||||||
\(341\) | −17.6962 | −0.958305 | ||||||||
\(342\) | −2.25761 | −0.122077 | ||||||||
\(343\) | −18.4810 | −0.997879 | ||||||||
\(344\) | −6.12885 | −0.330445 | ||||||||
\(345\) | 0.559148 | 0.0301035 | ||||||||
\(346\) | −2.77538 | −0.149205 | ||||||||
\(347\) | 16.7458 | 0.898963 | 0.449482 | − | 0.893290i | \(-0.351609\pi\) | ||||
0.449482 | + | 0.893290i | \(0.351609\pi\) | |||||||
\(348\) | −0.991065 | −0.0531266 | ||||||||
\(349\) | −13.2076 | −0.706986 | −0.353493 | − | 0.935437i | \(-0.615006\pi\) | ||||
−0.353493 | + | 0.935437i | \(0.615006\pi\) | |||||||
\(350\) | −13.2222 | −0.706758 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | −3.17383 | −0.169166 | ||||||||
\(353\) | −2.26811 | −0.120719 | −0.0603596 | − | 0.998177i | \(-0.519225\pi\) | ||||
−0.0603596 | + | 0.998177i | \(0.519225\pi\) | |||||||
\(354\) | 8.39566 | 0.446224 | ||||||||
\(355\) | 1.55454 | 0.0825066 | ||||||||
\(356\) | −8.95858 | −0.474804 | ||||||||
\(357\) | −9.30829 | −0.492647 | ||||||||
\(358\) | 11.4232 | 0.603736 | ||||||||
\(359\) | −2.18365 | −0.115249 | −0.0576243 | − | 0.998338i | \(-0.518353\pi\) | ||||
−0.0576243 | + | 0.998338i | \(0.518353\pi\) | |||||||
\(360\) | 0.113923 | 0.00600426 | ||||||||
\(361\) | −13.9032 | −0.731748 | ||||||||
\(362\) | −14.5444 | −0.764439 | ||||||||
\(363\) | 0.926787 | 0.0486437 | ||||||||
\(364\) | −2.65133 | −0.138967 | ||||||||
\(365\) | −0.181160 | −0.00948234 | ||||||||
\(366\) | 1.34766 | 0.0704433 | ||||||||
\(367\) | −18.7772 | −0.980162 | −0.490081 | − | 0.871677i | \(-0.663033\pi\) | ||||
−0.490081 | + | 0.871677i | \(0.663033\pi\) | |||||||
\(368\) | −4.90813 | −0.255854 | ||||||||
\(369\) | −8.22718 | −0.428290 | ||||||||
\(370\) | −0.832931 | −0.0433020 | ||||||||
\(371\) | 19.1037 | 0.991816 | ||||||||
\(372\) | −5.57567 | −0.289085 | ||||||||
\(373\) | −16.7478 | −0.867168 | −0.433584 | − | 0.901113i | \(-0.642751\pi\) | ||||
−0.433584 | + | 0.901113i | \(0.642751\pi\) | |||||||
\(374\) | −11.1427 | −0.576176 | ||||||||
\(375\) | 1.13775 | 0.0587532 | ||||||||
\(376\) | −0.711399 | −0.0366876 | ||||||||
\(377\) | −0.991065 | −0.0510424 | ||||||||
\(378\) | −2.65133 | −0.136370 | ||||||||
\(379\) | 13.4554 | 0.691160 | 0.345580 | − | 0.938389i | \(-0.387682\pi\) | ||||
0.345580 | + | 0.938389i | \(0.387682\pi\) | |||||||
\(380\) | −0.257193 | −0.0131937 | ||||||||
\(381\) | 16.0196 | 0.820711 | ||||||||
\(382\) | −11.4688 | −0.586793 | ||||||||
\(383\) | −18.2146 | −0.930723 | −0.465362 | − | 0.885121i | \(-0.654076\pi\) | ||||
−0.465362 | + | 0.885121i | \(0.654076\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −0.958646 | −0.0488571 | ||||||||
\(386\) | −7.05090 | −0.358881 | ||||||||
\(387\) | −6.12885 | −0.311547 | ||||||||
\(388\) | 10.4001 | 0.527986 | ||||||||
\(389\) | −16.0164 | −0.812064 | −0.406032 | − | 0.913859i | \(-0.633088\pi\) | ||||
−0.406032 | + | 0.913859i | \(0.633088\pi\) | |||||||
\(390\) | 0.113923 | 0.00576871 | ||||||||
\(391\) | −17.2315 | −0.871434 | ||||||||
\(392\) | 0.0295321 | 0.00149159 | ||||||||
\(393\) | −8.02984 | −0.405052 | ||||||||
\(394\) | 3.41934 | 0.172264 | ||||||||
\(395\) | 0.670136 | 0.0337182 | ||||||||
\(396\) | −3.17383 | −0.159491 | ||||||||
\(397\) | −7.31848 | −0.367304 | −0.183652 | − | 0.982991i | \(-0.558792\pi\) | ||||
−0.183652 | + | 0.982991i | \(0.558792\pi\) | |||||||
\(398\) | 12.7201 | 0.637599 | ||||||||
\(399\) | 5.98565 | 0.299657 | ||||||||
\(400\) | −4.98702 | −0.249351 | ||||||||
\(401\) | 0.477356 | 0.0238380 | 0.0119190 | − | 0.999929i | \(-0.496206\pi\) | ||||
0.0119190 | + | 0.999929i | \(0.496206\pi\) | |||||||
\(402\) | 10.6030 | 0.528828 | ||||||||
\(403\) | −5.57567 | −0.277744 | ||||||||
\(404\) | −15.9846 | −0.795264 | ||||||||
\(405\) | 0.113923 | 0.00566087 | ||||||||
\(406\) | 2.62764 | 0.130407 | ||||||||
\(407\) | 23.2050 | 1.15023 | ||||||||
\(408\) | −3.51081 | −0.173811 | ||||||||
\(409\) | −14.8337 | −0.733480 | −0.366740 | − | 0.930324i | \(-0.619526\pi\) | ||||
−0.366740 | + | 0.930324i | \(0.619526\pi\) | |||||||
\(410\) | −0.937263 | −0.0462881 | ||||||||
\(411\) | 0.471978 | 0.0232810 | ||||||||
\(412\) | 1.00000 | 0.0492665 | ||||||||
\(413\) | −22.2596 | −1.09533 | ||||||||
\(414\) | −4.90813 | −0.241222 | ||||||||
\(415\) | −1.38339 | −0.0679078 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −2.51841 | −0.123327 | ||||||||
\(418\) | 7.16527 | 0.350465 | ||||||||
\(419\) | 6.72517 | 0.328546 | 0.164273 | − | 0.986415i | \(-0.447472\pi\) | ||||
0.164273 | + | 0.986415i | \(0.447472\pi\) | |||||||
\(420\) | −0.302047 | −0.0147384 | ||||||||
\(421\) | 23.3325 | 1.13716 | 0.568579 | − | 0.822629i | \(-0.307493\pi\) | ||||
0.568579 | + | 0.822629i | \(0.307493\pi\) | |||||||
\(422\) | −8.15531 | −0.396994 | ||||||||
\(423\) | −0.711399 | −0.0345894 | ||||||||
\(424\) | 7.20535 | 0.349923 | ||||||||
\(425\) | −17.5085 | −0.849285 | ||||||||
\(426\) | −13.6456 | −0.661131 | ||||||||
\(427\) | −3.57309 | −0.172914 | ||||||||
\(428\) | 14.4797 | 0.699901 | ||||||||
\(429\) | −3.17383 | −0.153234 | ||||||||
\(430\) | −0.698216 | −0.0336710 | ||||||||
\(431\) | 7.72227 | 0.371968 | 0.185984 | − | 0.982553i | \(-0.440453\pi\) | ||||
0.185984 | + | 0.982553i | \(0.440453\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 2.83059 | 0.136030 | 0.0680148 | − | 0.997684i | \(-0.478333\pi\) | ||||
0.0680148 | + | 0.997684i | \(0.478333\pi\) | |||||||
\(434\) | 14.7829 | 0.709603 | ||||||||
\(435\) | −0.112905 | −0.00541338 | ||||||||
\(436\) | −17.6514 | −0.845351 | ||||||||
\(437\) | 11.0806 | 0.530058 | ||||||||
\(438\) | 1.59020 | 0.0759826 | ||||||||
\(439\) | 12.0883 | 0.576943 | 0.288471 | − | 0.957489i | \(-0.406853\pi\) | ||||
0.288471 | + | 0.957489i | \(0.406853\pi\) | |||||||
\(440\) | −0.361572 | −0.0172373 | ||||||||
\(441\) | 0.0295321 | 0.00140629 | ||||||||
\(442\) | −3.51081 | −0.166992 | ||||||||
\(443\) | 10.8630 | 0.516115 | 0.258057 | − | 0.966130i | \(-0.416918\pi\) | ||||
0.258057 | + | 0.966130i | \(0.416918\pi\) | |||||||
\(444\) | 7.31136 | 0.346982 | ||||||||
\(445\) | −1.02059 | −0.0483805 | ||||||||
\(446\) | 1.92053 | 0.0909397 | ||||||||
\(447\) | 12.0279 | 0.568902 | ||||||||
\(448\) | 2.65133 | 0.125263 | ||||||||
\(449\) | −18.7203 | −0.883467 | −0.441733 | − | 0.897146i | \(-0.645636\pi\) | ||||
−0.441733 | + | 0.897146i | \(0.645636\pi\) | |||||||
\(450\) | −4.98702 | −0.235090 | ||||||||
\(451\) | 26.1117 | 1.22955 | ||||||||
\(452\) | 17.4659 | 0.821525 | ||||||||
\(453\) | −19.7757 | −0.929144 | ||||||||
\(454\) | 7.73629 | 0.363082 | ||||||||
\(455\) | −0.302047 | −0.0141602 | ||||||||
\(456\) | 2.25761 | 0.105722 | ||||||||
\(457\) | −1.82995 | −0.0856014 | −0.0428007 | − | 0.999084i | \(-0.513628\pi\) | ||||
−0.0428007 | + | 0.999084i | \(0.513628\pi\) | |||||||
\(458\) | 3.09858 | 0.144787 | ||||||||
\(459\) | −3.51081 | −0.163870 | ||||||||
\(460\) | −0.559148 | −0.0260704 | ||||||||
\(461\) | 5.02597 | 0.234083 | 0.117041 | − | 0.993127i | \(-0.462659\pi\) | ||||
0.117041 | + | 0.993127i | \(0.462659\pi\) | |||||||
\(462\) | 8.41487 | 0.391495 | ||||||||
\(463\) | −22.5592 | −1.04842 | −0.524208 | − | 0.851590i | \(-0.675638\pi\) | ||||
−0.524208 | + | 0.851590i | \(0.675638\pi\) | |||||||
\(464\) | 0.991065 | 0.0460090 | ||||||||
\(465\) | −0.635196 | −0.0294565 | ||||||||
\(466\) | 3.97487 | 0.184132 | ||||||||
\(467\) | 31.3275 | 1.44966 | 0.724832 | − | 0.688926i | \(-0.241917\pi\) | ||||
0.724832 | + | 0.688926i | \(0.241917\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | −28.1119 | −1.29809 | ||||||||
\(470\) | −0.0810446 | −0.00373831 | ||||||||
\(471\) | 3.75589 | 0.173062 | ||||||||
\(472\) | −8.39566 | −0.386442 | ||||||||
\(473\) | 19.4519 | 0.894401 | ||||||||
\(474\) | −5.88236 | −0.270186 | ||||||||
\(475\) | 11.2587 | 0.516586 | ||||||||
\(476\) | 9.30829 | 0.426645 | ||||||||
\(477\) | 7.20535 | 0.329910 | ||||||||
\(478\) | −17.6397 | −0.806822 | ||||||||
\(479\) | −9.71552 | −0.443913 | −0.221957 | − | 0.975057i | \(-0.571244\pi\) | ||||
−0.221957 | + | 0.975057i | \(0.571244\pi\) | |||||||
\(480\) | −0.113923 | −0.00519984 | ||||||||
\(481\) | 7.31136 | 0.333369 | ||||||||
\(482\) | 24.3235 | 1.10791 | ||||||||
\(483\) | 13.0131 | 0.592115 | ||||||||
\(484\) | −0.926787 | −0.0421267 | ||||||||
\(485\) | 1.18481 | 0.0537995 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −22.4933 | −1.01927 | −0.509634 | − | 0.860391i | \(-0.670219\pi\) | ||||
−0.509634 | + | 0.860391i | \(0.670219\pi\) | |||||||
\(488\) | −1.34766 | −0.0610057 | ||||||||
\(489\) | 11.0445 | 0.499452 | ||||||||
\(490\) | 0.00336438 | 0.000151987 0 | ||||||||
\(491\) | −13.9549 | −0.629778 | −0.314889 | − | 0.949129i | \(-0.601967\pi\) | ||||
−0.314889 | + | 0.949129i | \(0.601967\pi\) | |||||||
\(492\) | 8.22718 | 0.370910 | ||||||||
\(493\) | 3.47944 | 0.156706 | ||||||||
\(494\) | 2.25761 | 0.101575 | ||||||||
\(495\) | −0.361572 | −0.0162515 | ||||||||
\(496\) | 5.57567 | 0.250355 | ||||||||
\(497\) | 36.1789 | 1.62285 | ||||||||
\(498\) | 12.1432 | 0.544150 | ||||||||
\(499\) | 22.1708 | 0.992502 | 0.496251 | − | 0.868179i | \(-0.334710\pi\) | ||||
0.496251 | + | 0.868179i | \(0.334710\pi\) | |||||||
\(500\) | −1.13775 | −0.0508817 | ||||||||
\(501\) | −1.02005 | −0.0455726 | ||||||||
\(502\) | 16.8621 | 0.752592 | ||||||||
\(503\) | −23.8656 | −1.06411 | −0.532057 | − | 0.846709i | \(-0.678581\pi\) | ||||
−0.532057 | + | 0.846709i | \(0.678581\pi\) | |||||||
\(504\) | 2.65133 | 0.118099 | ||||||||
\(505\) | −1.82101 | −0.0810340 | ||||||||
\(506\) | 15.5776 | 0.692508 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −16.0196 | −0.710757 | ||||||||
\(509\) | 6.89132 | 0.305452 | 0.152726 | − | 0.988269i | \(-0.451195\pi\) | ||||
0.152726 | + | 0.988269i | \(0.451195\pi\) | |||||||
\(510\) | −0.399961 | −0.0177106 | ||||||||
\(511\) | −4.21613 | −0.186511 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 2.25761 | 0.0996758 | ||||||||
\(514\) | −19.0078 | −0.838399 | ||||||||
\(515\) | 0.113923 | 0.00502004 | ||||||||
\(516\) | 6.12885 | 0.269808 | ||||||||
\(517\) | 2.25786 | 0.0993007 | ||||||||
\(518\) | −19.3848 | −0.851719 | ||||||||
\(519\) | 2.77538 | 0.121825 | ||||||||
\(520\) | −0.113923 | −0.00499585 | ||||||||
\(521\) | −14.4424 | −0.632734 | −0.316367 | − | 0.948637i | \(-0.602463\pi\) | ||||
−0.316367 | + | 0.948637i | \(0.602463\pi\) | |||||||
\(522\) | 0.991065 | 0.0433777 | ||||||||
\(523\) | −21.0139 | −0.918874 | −0.459437 | − | 0.888210i | \(-0.651949\pi\) | ||||
−0.459437 | + | 0.888210i | \(0.651949\pi\) | |||||||
\(524\) | 8.02984 | 0.350785 | ||||||||
\(525\) | 13.2222 | 0.577065 | ||||||||
\(526\) | 16.5275 | 0.720635 | ||||||||
\(527\) | 19.5751 | 0.852704 | ||||||||
\(528\) | 3.17383 | 0.138123 | ||||||||
\(529\) | 1.08976 | 0.0473808 | ||||||||
\(530\) | 0.820854 | 0.0356556 | ||||||||
\(531\) | −8.39566 | −0.364341 | ||||||||
\(532\) | −5.98565 | −0.259511 | ||||||||
\(533\) | 8.22718 | 0.356359 | ||||||||
\(534\) | 8.95858 | 0.387676 | ||||||||
\(535\) | 1.64956 | 0.0713169 | ||||||||
\(536\) | −10.6030 | −0.457979 | ||||||||
\(537\) | −11.4232 | −0.492948 | ||||||||
\(538\) | 1.06645 | 0.0459781 | ||||||||
\(539\) | −0.0937298 | −0.00403723 | ||||||||
\(540\) | −0.113923 | −0.00490246 | ||||||||
\(541\) | 10.5619 | 0.454093 | 0.227046 | − | 0.973884i | \(-0.427093\pi\) | ||||
0.227046 | + | 0.973884i | \(0.427093\pi\) | |||||||
\(542\) | −28.1094 | −1.20740 | ||||||||
\(543\) | 14.5444 | 0.624162 | ||||||||
\(544\) | 3.51081 | 0.150525 | ||||||||
\(545\) | −2.01090 | −0.0861376 | ||||||||
\(546\) | 2.65133 | 0.113466 | ||||||||
\(547\) | 25.2712 | 1.08052 | 0.540259 | − | 0.841499i | \(-0.318326\pi\) | ||||
0.540259 | + | 0.841499i | \(0.318326\pi\) | |||||||
\(548\) | −0.471978 | −0.0201619 | ||||||||
\(549\) | −1.34766 | −0.0575167 | ||||||||
\(550\) | 15.8280 | 0.674907 | ||||||||
\(551\) | −2.23743 | −0.0953179 | ||||||||
\(552\) | 4.90813 | 0.208904 | ||||||||
\(553\) | 15.5961 | 0.663212 | ||||||||
\(554\) | −8.95306 | −0.380379 | ||||||||
\(555\) | 0.832931 | 0.0353560 | ||||||||
\(556\) | 2.51841 | 0.106805 | ||||||||
\(557\) | −34.1539 | −1.44715 | −0.723574 | − | 0.690247i | \(-0.757502\pi\) | ||||
−0.723574 | + | 0.690247i | \(0.757502\pi\) | |||||||
\(558\) | 5.57567 | 0.236037 | ||||||||
\(559\) | 6.12885 | 0.259223 | ||||||||
\(560\) | 0.302047 | 0.0127638 | ||||||||
\(561\) | 11.1427 | 0.470446 | ||||||||
\(562\) | 23.4140 | 0.987660 | ||||||||
\(563\) | −13.9801 | −0.589191 | −0.294596 | − | 0.955622i | \(-0.595185\pi\) | ||||
−0.294596 | + | 0.955622i | \(0.595185\pi\) | |||||||
\(564\) | 0.711399 | 0.0299553 | ||||||||
\(565\) | 1.98976 | 0.0837098 | ||||||||
\(566\) | −9.20239 | −0.386805 | ||||||||
\(567\) | 2.65133 | 0.111345 | ||||||||
\(568\) | 13.6456 | 0.572556 | ||||||||
\(569\) | −31.7065 | −1.32920 | −0.664602 | − | 0.747197i | \(-0.731399\pi\) | ||||
−0.664602 | + | 0.747197i | \(0.731399\pi\) | |||||||
\(570\) | 0.257193 | 0.0107726 | ||||||||
\(571\) | −40.9651 | −1.71433 | −0.857167 | − | 0.515038i | \(-0.827778\pi\) | ||||
−0.857167 | + | 0.515038i | \(0.827778\pi\) | |||||||
\(572\) | 3.17383 | 0.132705 | ||||||||
\(573\) | 11.4688 | 0.479114 | ||||||||
\(574\) | −21.8129 | −0.910454 | ||||||||
\(575\) | 24.4770 | 1.02076 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 19.1531 | 0.797353 | 0.398677 | − | 0.917092i | \(-0.369470\pi\) | ||||
0.398677 | + | 0.917092i | \(0.369470\pi\) | |||||||
\(578\) | −4.67425 | −0.194423 | ||||||||
\(579\) | 7.05090 | 0.293025 | ||||||||
\(580\) | 0.112905 | 0.00468812 | ||||||||
\(581\) | −32.1956 | −1.33570 | ||||||||
\(582\) | −10.4001 | −0.431098 | ||||||||
\(583\) | −22.8686 | −0.947119 | ||||||||
\(584\) | −1.59020 | −0.0658029 | ||||||||
\(585\) | −0.113923 | −0.00471013 | ||||||||
\(586\) | −12.8741 | −0.531823 | ||||||||
\(587\) | 9.44305 | 0.389757 | 0.194878 | − | 0.980827i | \(-0.437569\pi\) | ||||
0.194878 | + | 0.980827i | \(0.437569\pi\) | |||||||
\(588\) | −0.0295321 | −0.00121788 | ||||||||
\(589\) | −12.5877 | −0.518666 | ||||||||
\(590\) | −0.956458 | −0.0393767 | ||||||||
\(591\) | −3.41934 | −0.140653 | ||||||||
\(592\) | −7.31136 | −0.300495 | ||||||||
\(593\) | 3.05451 | 0.125434 | 0.0627169 | − | 0.998031i | \(-0.480023\pi\) | ||||
0.0627169 | + | 0.998031i | \(0.480023\pi\) | |||||||
\(594\) | 3.17383 | 0.130224 | ||||||||
\(595\) | 1.06043 | 0.0434733 | ||||||||
\(596\) | −12.0279 | −0.492684 | ||||||||
\(597\) | −12.7201 | −0.520598 | ||||||||
\(598\) | 4.90813 | 0.200708 | ||||||||
\(599\) | 20.8674 | 0.852621 | 0.426310 | − | 0.904577i | \(-0.359813\pi\) | ||||
0.426310 | + | 0.904577i | \(0.359813\pi\) | |||||||
\(600\) | 4.98702 | 0.203594 | ||||||||
\(601\) | 11.1295 | 0.453981 | 0.226991 | − | 0.973897i | \(-0.427111\pi\) | ||||
0.226991 | + | 0.973897i | \(0.427111\pi\) | |||||||
\(602\) | −16.2496 | −0.662283 | ||||||||
\(603\) | −10.6030 | −0.431786 | ||||||||
\(604\) | 19.7757 | 0.804662 | ||||||||
\(605\) | −0.105582 | −0.00429253 | ||||||||
\(606\) | 15.9846 | 0.649330 | ||||||||
\(607\) | 48.9659 | 1.98747 | 0.993733 | − | 0.111783i | \(-0.0356563\pi\) | ||||
0.993733 | + | 0.111783i | \(0.0356563\pi\) | |||||||
\(608\) | −2.25761 | −0.0915580 | ||||||||
\(609\) | −2.62764 | −0.106477 | ||||||||
\(610\) | −0.153529 | −0.00621622 | ||||||||
\(611\) | 0.711399 | 0.0287801 | ||||||||
\(612\) | 3.51081 | 0.141916 | ||||||||
\(613\) | −29.6137 | −1.19609 | −0.598043 | − | 0.801464i | \(-0.704055\pi\) | ||||
−0.598043 | + | 0.801464i | \(0.704055\pi\) | |||||||
\(614\) | −7.06703 | −0.285202 | ||||||||
\(615\) | 0.937263 | 0.0377941 | ||||||||
\(616\) | −8.41487 | −0.339045 | ||||||||
\(617\) | −31.9205 | −1.28507 | −0.642536 | − | 0.766255i | \(-0.722118\pi\) | ||||
−0.642536 | + | 0.766255i | \(0.722118\pi\) | |||||||
\(618\) | −1.00000 | −0.0402259 | ||||||||
\(619\) | 34.9784 | 1.40590 | 0.702950 | − | 0.711240i | \(-0.251866\pi\) | ||||
0.702950 | + | 0.711240i | \(0.251866\pi\) | |||||||
\(620\) | 0.635196 | 0.0255101 | ||||||||
\(621\) | 4.90813 | 0.196957 | ||||||||
\(622\) | 8.92110 | 0.357704 | ||||||||
\(623\) | −23.7521 | −0.951608 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | 24.8055 | 0.992220 | ||||||||
\(626\) | −13.7395 | −0.549142 | ||||||||
\(627\) | −7.16527 | −0.286153 | ||||||||
\(628\) | −3.75589 | −0.149876 | ||||||||
\(629\) | −25.6688 | −1.02348 | ||||||||
\(630\) | 0.302047 | 0.0120338 | ||||||||
\(631\) | −1.28189 | −0.0510311 | −0.0255156 | − | 0.999674i | \(-0.508123\pi\) | ||||
−0.0255156 | + | 0.999674i | \(0.508123\pi\) | |||||||
\(632\) | 5.88236 | 0.233988 | ||||||||
\(633\) | 8.15531 | 0.324144 | ||||||||
\(634\) | 21.1401 | 0.839579 | ||||||||
\(635\) | −1.82500 | −0.0724230 | ||||||||
\(636\) | −7.20535 | −0.285711 | ||||||||
\(637\) | −0.0295321 | −0.00117010 | ||||||||
\(638\) | −3.14547 | −0.124530 | ||||||||
\(639\) | 13.6456 | 0.539811 | ||||||||
\(640\) | 0.113923 | 0.00450320 | ||||||||
\(641\) | −16.0646 | −0.634514 | −0.317257 | − | 0.948340i | \(-0.602762\pi\) | ||||
−0.317257 | + | 0.948340i | \(0.602762\pi\) | |||||||
\(642\) | −14.4797 | −0.571467 | ||||||||
\(643\) | 12.2700 | 0.483881 | 0.241940 | − | 0.970291i | \(-0.422216\pi\) | ||||
0.241940 | + | 0.970291i | \(0.422216\pi\) | |||||||
\(644\) | −13.0131 | −0.512786 | ||||||||
\(645\) | 0.698216 | 0.0274922 | ||||||||
\(646\) | −7.92602 | −0.311845 | ||||||||
\(647\) | 36.5059 | 1.43519 | 0.717597 | − | 0.696459i | \(-0.245242\pi\) | ||||
0.717597 | + | 0.696459i | \(0.245242\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 26.6464 | 1.04596 | ||||||||
\(650\) | 4.98702 | 0.195607 | ||||||||
\(651\) | −14.7829 | −0.579388 | ||||||||
\(652\) | −11.0445 | −0.432538 | ||||||||
\(653\) | −40.3637 | −1.57955 | −0.789777 | − | 0.613394i | \(-0.789804\pi\) | ||||
−0.789777 | + | 0.613394i | \(0.789804\pi\) | |||||||
\(654\) | 17.6514 | 0.690226 | ||||||||
\(655\) | 0.914782 | 0.0357435 | ||||||||
\(656\) | −8.22718 | −0.321217 | ||||||||
\(657\) | −1.59020 | −0.0620395 | ||||||||
\(658\) | −1.88615 | −0.0735299 | ||||||||
\(659\) | −1.13751 | −0.0443112 | −0.0221556 | − | 0.999755i | \(-0.507053\pi\) | ||||
−0.0221556 | + | 0.999755i | \(0.507053\pi\) | |||||||
\(660\) | 0.361572 | 0.0140742 | ||||||||
\(661\) | 22.7149 | 0.883506 | 0.441753 | − | 0.897137i | \(-0.354357\pi\) | ||||
0.441753 | + | 0.897137i | \(0.354357\pi\) | |||||||
\(662\) | −19.2913 | −0.749776 | ||||||||
\(663\) | 3.51081 | 0.136348 | ||||||||
\(664\) | −12.1432 | −0.471247 | ||||||||
\(665\) | −0.681903 | −0.0264430 | ||||||||
\(666\) | −7.31136 | −0.283309 | ||||||||
\(667\) | −4.86428 | −0.188346 | ||||||||
\(668\) | 1.02005 | 0.0394670 | ||||||||
\(669\) | −1.92053 | −0.0742520 | ||||||||
\(670\) | −1.20792 | −0.0466660 | ||||||||
\(671\) | 4.27725 | 0.165121 | ||||||||
\(672\) | −2.65133 | −0.102277 | ||||||||
\(673\) | 5.46060 | 0.210491 | 0.105245 | − | 0.994446i | \(-0.466437\pi\) | ||||
0.105245 | + | 0.994446i | \(0.466437\pi\) | |||||||
\(674\) | 14.3407 | 0.552384 | ||||||||
\(675\) | 4.98702 | 0.191951 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −12.4615 | −0.478936 | −0.239468 | − | 0.970904i | \(-0.576973\pi\) | ||||
−0.239468 | + | 0.970904i | \(0.576973\pi\) | |||||||
\(678\) | −17.4659 | −0.670772 | ||||||||
\(679\) | 27.5741 | 1.05820 | ||||||||
\(680\) | 0.399961 | 0.0153378 | ||||||||
\(681\) | −7.73629 | −0.296455 | ||||||||
\(682\) | −17.6962 | −0.677624 | ||||||||
\(683\) | −3.23234 | −0.123682 | −0.0618410 | − | 0.998086i | \(-0.519697\pi\) | ||||
−0.0618410 | + | 0.998086i | \(0.519697\pi\) | |||||||
\(684\) | −2.25761 | −0.0863217 | ||||||||
\(685\) | −0.0537691 | −0.00205441 | ||||||||
\(686\) | −18.4810 | −0.705607 | ||||||||
\(687\) | −3.09858 | −0.118218 | ||||||||
\(688\) | −6.12885 | −0.233660 | ||||||||
\(689\) | −7.20535 | −0.274502 | ||||||||
\(690\) | 0.559148 | 0.0212864 | ||||||||
\(691\) | −19.9201 | −0.757798 | −0.378899 | − | 0.925438i | \(-0.623697\pi\) | ||||
−0.378899 | + | 0.925438i | \(0.623697\pi\) | |||||||
\(692\) | −2.77538 | −0.105504 | ||||||||
\(693\) | −8.41487 | −0.319654 | ||||||||
\(694\) | 16.7458 | 0.635663 | ||||||||
\(695\) | 0.286905 | 0.0108829 | ||||||||
\(696\) | −0.991065 | −0.0375662 | ||||||||
\(697\) | −28.8840 | −1.09406 | ||||||||
\(698\) | −13.2076 | −0.499914 | ||||||||
\(699\) | −3.97487 | −0.150343 | ||||||||
\(700\) | −13.2222 | −0.499753 | ||||||||
\(701\) | 42.0697 | 1.58895 | 0.794476 | − | 0.607295i | \(-0.207746\pi\) | ||||
0.794476 | + | 0.607295i | \(0.207746\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | 16.5062 | 0.622542 | ||||||||
\(704\) | −3.17383 | −0.119618 | ||||||||
\(705\) | 0.0810446 | 0.00305232 | ||||||||
\(706\) | −2.26811 | −0.0853613 | ||||||||
\(707\) | −42.3804 | −1.59388 | ||||||||
\(708\) | 8.39566 | 0.315528 | ||||||||
\(709\) | −13.6687 | −0.513340 | −0.256670 | − | 0.966499i | \(-0.582625\pi\) | ||||
−0.256670 | + | 0.966499i | \(0.582625\pi\) | |||||||
\(710\) | 1.55454 | 0.0583410 | ||||||||
\(711\) | 5.88236 | 0.220606 | ||||||||
\(712\) | −8.95858 | −0.335737 | ||||||||
\(713\) | −27.3661 | −1.02487 | ||||||||
\(714\) | −9.30829 | −0.348354 | ||||||||
\(715\) | 0.361572 | 0.0135220 | ||||||||
\(716\) | 11.4232 | 0.426906 | ||||||||
\(717\) | 17.6397 | 0.658768 | ||||||||
\(718\) | −2.18365 | −0.0814931 | ||||||||
\(719\) | 31.2150 | 1.16412 | 0.582061 | − | 0.813145i | \(-0.302247\pi\) | ||||
0.582061 | + | 0.813145i | \(0.302247\pi\) | |||||||
\(720\) | 0.113923 | 0.00424565 | ||||||||
\(721\) | 2.65133 | 0.0987406 | ||||||||
\(722\) | −13.9032 | −0.517424 | ||||||||
\(723\) | −24.3235 | −0.904601 | ||||||||
\(724\) | −14.5444 | −0.540540 | ||||||||
\(725\) | −4.94246 | −0.183558 | ||||||||
\(726\) | 0.926787 | 0.0343963 | ||||||||
\(727\) | −44.5784 | −1.65332 | −0.826661 | − | 0.562700i | \(-0.809762\pi\) | ||||
−0.826661 | + | 0.562700i | \(0.809762\pi\) | |||||||
\(728\) | −2.65133 | −0.0982647 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.181160 | −0.00670503 | ||||||||
\(731\) | −21.5172 | −0.795842 | ||||||||
\(732\) | 1.34766 | 0.0498109 | ||||||||
\(733\) | 21.7393 | 0.802961 | 0.401480 | − | 0.915868i | \(-0.368496\pi\) | ||||
0.401480 | + | 0.915868i | \(0.368496\pi\) | |||||||
\(734\) | −18.7772 | −0.693079 | ||||||||
\(735\) | −0.00336438 | −0.000124097 0 | ||||||||
\(736\) | −4.90813 | −0.180916 | ||||||||
\(737\) | 33.6520 | 1.23959 | ||||||||
\(738\) | −8.22718 | −0.302847 | ||||||||
\(739\) | −4.53334 | −0.166762 | −0.0833808 | − | 0.996518i | \(-0.526572\pi\) | ||||
−0.0833808 | + | 0.996518i | \(0.526572\pi\) | |||||||
\(740\) | −0.832931 | −0.0306192 | ||||||||
\(741\) | −2.25761 | −0.0829353 | ||||||||
\(742\) | 19.1037 | 0.701320 | ||||||||
\(743\) | −39.9930 | −1.46720 | −0.733601 | − | 0.679581i | \(-0.762162\pi\) | ||||
−0.733601 | + | 0.679581i | \(0.762162\pi\) | |||||||
\(744\) | −5.57567 | −0.204414 | ||||||||
\(745\) | −1.37026 | −0.0502024 | ||||||||
\(746\) | −16.7478 | −0.613180 | ||||||||
\(747\) | −12.1432 | −0.444296 | ||||||||
\(748\) | −11.1427 | −0.407418 | ||||||||
\(749\) | 38.3903 | 1.40275 | ||||||||
\(750\) | 1.13775 | 0.0415448 | ||||||||
\(751\) | −3.51993 | −0.128444 | −0.0642221 | − | 0.997936i | \(-0.520457\pi\) | ||||
−0.0642221 | + | 0.997936i | \(0.520457\pi\) | |||||||
\(752\) | −0.711399 | −0.0259421 | ||||||||
\(753\) | −16.8621 | −0.614489 | ||||||||
\(754\) | −0.991065 | −0.0360924 | ||||||||
\(755\) | 2.25290 | 0.0819916 | ||||||||
\(756\) | −2.65133 | −0.0964278 | ||||||||
\(757\) | −21.0596 | −0.765425 | −0.382712 | − | 0.923868i | \(-0.625010\pi\) | ||||
−0.382712 | + | 0.923868i | \(0.625010\pi\) | |||||||
\(758\) | 13.4554 | 0.488724 | ||||||||
\(759\) | −15.5776 | −0.565431 | ||||||||
\(760\) | −0.257193 | −0.00932937 | ||||||||
\(761\) | −32.5443 | −1.17973 | −0.589865 | − | 0.807502i | \(-0.700819\pi\) | ||||
−0.589865 | + | 0.807502i | \(0.700819\pi\) | |||||||
\(762\) | 16.0196 | 0.580330 | ||||||||
\(763\) | −46.7998 | −1.69426 | ||||||||
\(764\) | −11.4688 | −0.414925 | ||||||||
\(765\) | 0.399961 | 0.0144606 | ||||||||
\(766\) | −18.2146 | −0.658121 | ||||||||
\(767\) | 8.39566 | 0.303150 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −32.0823 | −1.15692 | −0.578460 | − | 0.815711i | \(-0.696346\pi\) | ||||
−0.578460 | + | 0.815711i | \(0.696346\pi\) | |||||||
\(770\) | −0.958646 | −0.0345472 | ||||||||
\(771\) | 19.0078 | 0.684550 | ||||||||
\(772\) | −7.05090 | −0.253767 | ||||||||
\(773\) | 46.5934 | 1.67585 | 0.837923 | − | 0.545788i | \(-0.183770\pi\) | ||||
0.837923 | + | 0.545788i | \(0.183770\pi\) | |||||||
\(774\) | −6.12885 | −0.220297 | ||||||||
\(775\) | −27.8060 | −0.998820 | ||||||||
\(776\) | 10.4001 | 0.373342 | ||||||||
\(777\) | 19.3848 | 0.695426 | ||||||||
\(778\) | −16.0164 | −0.574216 | ||||||||
\(779\) | 18.5737 | 0.665473 | ||||||||
\(780\) | 0.113923 | 0.00407909 | ||||||||
\(781\) | −43.3088 | −1.54971 | ||||||||
\(782\) | −17.2315 | −0.616197 | ||||||||
\(783\) | −0.991065 | −0.0354178 | ||||||||
\(784\) | 0.0295321 | 0.00105472 | ||||||||
\(785\) | −0.427881 | −0.0152717 | ||||||||
\(786\) | −8.02984 | −0.286415 | ||||||||
\(787\) | −41.6570 | −1.48491 | −0.742456 | − | 0.669895i | \(-0.766339\pi\) | ||||
−0.742456 | + | 0.669895i | \(0.766339\pi\) | |||||||
\(788\) | 3.41934 | 0.121809 | ||||||||
\(789\) | −16.5275 | −0.588396 | ||||||||
\(790\) | 0.670136 | 0.0238424 | ||||||||
\(791\) | 46.3077 | 1.64651 | ||||||||
\(792\) | −3.17383 | −0.112777 | ||||||||
\(793\) | 1.34766 | 0.0478568 | ||||||||
\(794\) | −7.31848 | −0.259723 | ||||||||
\(795\) | −0.820854 | −0.0291127 | ||||||||
\(796\) | 12.7201 | 0.450851 | ||||||||
\(797\) | 47.6889 | 1.68923 | 0.844614 | − | 0.535376i | \(-0.179830\pi\) | ||||
0.844614 | + | 0.535376i | \(0.179830\pi\) | |||||||
\(798\) | 5.98565 | 0.211890 | ||||||||
\(799\) | −2.49758 | −0.0883582 | ||||||||
\(800\) | −4.98702 | −0.176318 | ||||||||
\(801\) | −8.95858 | −0.316536 | ||||||||
\(802\) | 0.477356 | 0.0168560 | ||||||||
\(803\) | 5.04702 | 0.178106 | ||||||||
\(804\) | 10.6030 | 0.373938 | ||||||||
\(805\) | −1.48249 | −0.0522507 | ||||||||
\(806\) | −5.57567 | −0.196395 | ||||||||
\(807\) | −1.06645 | −0.0375409 | ||||||||
\(808\) | −15.9846 | −0.562336 | ||||||||
\(809\) | −12.8475 | −0.451692 | −0.225846 | − | 0.974163i | \(-0.572515\pi\) | ||||
−0.225846 | + | 0.974163i | \(0.572515\pi\) | |||||||
\(810\) | 0.113923 | 0.00400284 | ||||||||
\(811\) | −2.80173 | −0.0983821 | −0.0491911 | − | 0.998789i | \(-0.515664\pi\) | ||||
−0.0491911 | + | 0.998789i | \(0.515664\pi\) | |||||||
\(812\) | 2.62764 | 0.0922120 | ||||||||
\(813\) | 28.1094 | 0.985839 | ||||||||
\(814\) | 23.2050 | 0.813336 | ||||||||
\(815\) | −1.25823 | −0.0440737 | ||||||||
\(816\) | −3.51081 | −0.122903 | ||||||||
\(817\) | 13.8365 | 0.484079 | ||||||||
\(818\) | −14.8337 | −0.518649 | ||||||||
\(819\) | −2.65133 | −0.0926448 | ||||||||
\(820\) | −0.937263 | −0.0327307 | ||||||||
\(821\) | 6.26417 | 0.218621 | 0.109310 | − | 0.994008i | \(-0.465136\pi\) | ||||
0.109310 | + | 0.994008i | \(0.465136\pi\) | |||||||
\(822\) | 0.471978 | 0.0164621 | ||||||||
\(823\) | 4.76304 | 0.166029 | 0.0830145 | − | 0.996548i | \(-0.473545\pi\) | ||||
0.0830145 | + | 0.996548i | \(0.473545\pi\) | |||||||
\(824\) | 1.00000 | 0.0348367 | ||||||||
\(825\) | −15.8280 | −0.551059 | ||||||||
\(826\) | −22.2596 | −0.774512 | ||||||||
\(827\) | −1.23342 | −0.0428901 | −0.0214451 | − | 0.999770i | \(-0.506827\pi\) | ||||
−0.0214451 | + | 0.999770i | \(0.506827\pi\) | |||||||
\(828\) | −4.90813 | −0.170569 | ||||||||
\(829\) | 17.6034 | 0.611391 | 0.305696 | − | 0.952129i | \(-0.401111\pi\) | ||||
0.305696 | + | 0.952129i | \(0.401111\pi\) | |||||||
\(830\) | −1.38339 | −0.0480181 | ||||||||
\(831\) | 8.95306 | 0.310578 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 0.103681 | 0.00359234 | ||||||||
\(834\) | −2.51841 | −0.0872055 | ||||||||
\(835\) | 0.116207 | 0.00402152 | ||||||||
\(836\) | 7.16527 | 0.247816 | ||||||||
\(837\) | −5.57567 | −0.192723 | ||||||||
\(838\) | 6.72517 | 0.232317 | ||||||||
\(839\) | −22.2105 | −0.766792 | −0.383396 | − | 0.923584i | \(-0.625246\pi\) | ||||
−0.383396 | + | 0.923584i | \(0.625246\pi\) | |||||||
\(840\) | −0.302047 | −0.0104216 | ||||||||
\(841\) | −28.0178 | −0.966131 | ||||||||
\(842\) | 23.3325 | 0.804092 | ||||||||
\(843\) | −23.4140 | −0.806421 | ||||||||
\(844\) | −8.15531 | −0.280717 | ||||||||
\(845\) | 0.113923 | 0.00391907 | ||||||||
\(846\) | −0.711399 | −0.0244584 | ||||||||
\(847\) | −2.45721 | −0.0844309 | ||||||||
\(848\) | 7.20535 | 0.247433 | ||||||||
\(849\) | 9.20239 | 0.315825 | ||||||||
\(850\) | −17.5085 | −0.600535 | ||||||||
\(851\) | 35.8851 | 1.23013 | ||||||||
\(852\) | −13.6456 | −0.467490 | ||||||||
\(853\) | 10.9095 | 0.373536 | 0.186768 | − | 0.982404i | \(-0.440199\pi\) | ||||
0.186768 | + | 0.982404i | \(0.440199\pi\) | |||||||
\(854\) | −3.57309 | −0.122268 | ||||||||
\(855\) | −0.257193 | −0.00879582 | ||||||||
\(856\) | 14.4797 | 0.494905 | ||||||||
\(857\) | 13.6307 | 0.465616 | 0.232808 | − | 0.972523i | \(-0.425209\pi\) | ||||
0.232808 | + | 0.972523i | \(0.425209\pi\) | |||||||
\(858\) | −3.17383 | −0.108353 | ||||||||
\(859\) | 30.4612 | 1.03932 | 0.519662 | − | 0.854372i | \(-0.326058\pi\) | ||||
0.519662 | + | 0.854372i | \(0.326058\pi\) | |||||||
\(860\) | −0.698216 | −0.0238090 | ||||||||
\(861\) | 21.8129 | 0.743383 | ||||||||
\(862\) | 7.72227 | 0.263021 | ||||||||
\(863\) | −4.66223 | −0.158704 | −0.0793520 | − | 0.996847i | \(-0.525285\pi\) | ||||
−0.0793520 | + | 0.996847i | \(0.525285\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −0.316179 | −0.0107504 | ||||||||
\(866\) | 2.83059 | 0.0961875 | ||||||||
\(867\) | 4.67425 | 0.158746 | ||||||||
\(868\) | 14.7829 | 0.501765 | ||||||||
\(869\) | −18.6696 | −0.633324 | ||||||||
\(870\) | −0.112905 | −0.00382784 | ||||||||
\(871\) | 10.6030 | 0.359268 | ||||||||
\(872\) | −17.6514 | −0.597753 | ||||||||
\(873\) | 10.4001 | 0.351990 | ||||||||
\(874\) | 11.0806 | 0.374808 | ||||||||
\(875\) | −3.01655 | −0.101978 | ||||||||
\(876\) | 1.59020 | 0.0537278 | ||||||||
\(877\) | 23.9947 | 0.810245 | 0.405122 | − | 0.914262i | \(-0.367229\pi\) | ||||
0.405122 | + | 0.914262i | \(0.367229\pi\) | |||||||
\(878\) | 12.0883 | 0.407960 | ||||||||
\(879\) | 12.8741 | 0.434231 | ||||||||
\(880\) | −0.361572 | −0.0121886 | ||||||||
\(881\) | −17.6645 | −0.595133 | −0.297567 | − | 0.954701i | \(-0.596175\pi\) | ||||
−0.297567 | + | 0.954701i | \(0.596175\pi\) | |||||||
\(882\) | 0.0295321 | 0.000994396 0 | ||||||||
\(883\) | 29.8929 | 1.00598 | 0.502988 | − | 0.864294i | \(-0.332234\pi\) | ||||
0.502988 | + | 0.864294i | \(0.332234\pi\) | |||||||
\(884\) | −3.51081 | −0.118081 | ||||||||
\(885\) | 0.956458 | 0.0321510 | ||||||||
\(886\) | 10.8630 | 0.364948 | ||||||||
\(887\) | 13.8077 | 0.463616 | 0.231808 | − | 0.972762i | \(-0.425536\pi\) | ||||
0.231808 | + | 0.972762i | \(0.425536\pi\) | |||||||
\(888\) | 7.31136 | 0.245353 | ||||||||
\(889\) | −42.4733 | −1.42451 | ||||||||
\(890\) | −1.02059 | −0.0342101 | ||||||||
\(891\) | −3.17383 | −0.106327 | ||||||||
\(892\) | 1.92053 | 0.0643041 | ||||||||
\(893\) | 1.60606 | 0.0537447 | ||||||||
\(894\) | 12.0279 | 0.402275 | ||||||||
\(895\) | 1.30137 | 0.0434999 | ||||||||
\(896\) | 2.65133 | 0.0885746 | ||||||||
\(897\) | −4.90813 | −0.163878 | ||||||||
\(898\) | −18.7203 | −0.624705 | ||||||||
\(899\) | 5.52585 | 0.184297 | ||||||||
\(900\) | −4.98702 | −0.166234 | ||||||||
\(901\) | 25.2966 | 0.842751 | ||||||||
\(902\) | 26.1117 | 0.869424 | ||||||||
\(903\) | 16.2496 | 0.540752 | ||||||||
\(904\) | 17.4659 | 0.580906 | ||||||||
\(905\) | −1.65695 | −0.0550787 | ||||||||
\(906\) | −19.7757 | −0.657004 | ||||||||
\(907\) | 35.2314 | 1.16984 | 0.584920 | − | 0.811091i | \(-0.301126\pi\) | ||||
0.584920 | + | 0.811091i | \(0.301126\pi\) | |||||||
\(908\) | 7.73629 | 0.256738 | ||||||||
\(909\) | −15.9846 | −0.530176 | ||||||||
\(910\) | −0.302047 | −0.0100128 | ||||||||
\(911\) | 45.9998 | 1.52404 | 0.762021 | − | 0.647552i | \(-0.224207\pi\) | ||||
0.762021 | + | 0.647552i | \(0.224207\pi\) | |||||||
\(912\) | 2.25761 | 0.0747568 | ||||||||
\(913\) | 38.5405 | 1.27550 | ||||||||
\(914\) | −1.82995 | −0.0605293 | ||||||||
\(915\) | 0.153529 | 0.00507552 | ||||||||
\(916\) | 3.09858 | 0.102380 | ||||||||
\(917\) | 21.2897 | 0.703049 | ||||||||
\(918\) | −3.51081 | −0.115874 | ||||||||
\(919\) | −4.21035 | −0.138887 | −0.0694434 | − | 0.997586i | \(-0.522122\pi\) | ||||
−0.0694434 | + | 0.997586i | \(0.522122\pi\) | |||||||
\(920\) | −0.559148 | −0.0184346 | ||||||||
\(921\) | 7.06703 | 0.232867 | ||||||||
\(922\) | 5.02597 | 0.165522 | ||||||||
\(923\) | −13.6456 | −0.449150 | ||||||||
\(924\) | 8.41487 | 0.276829 | ||||||||
\(925\) | 36.4619 | 1.19886 | ||||||||
\(926\) | −22.5592 | −0.741342 | ||||||||
\(927\) | 1.00000 | 0.0328443 | ||||||||
\(928\) | 0.991065 | 0.0325333 | ||||||||
\(929\) | 32.5571 | 1.06816 | 0.534082 | − | 0.845433i | \(-0.320657\pi\) | ||||
0.534082 | + | 0.845433i | \(0.320657\pi\) | |||||||
\(930\) | −0.635196 | −0.0208289 | ||||||||
\(931\) | −0.0666718 | −0.00218508 | ||||||||
\(932\) | 3.97487 | 0.130201 | ||||||||
\(933\) | −8.92110 | −0.292064 | ||||||||
\(934\) | 31.3275 | 1.02507 | ||||||||
\(935\) | −1.26941 | −0.0415141 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | −30.1835 | −0.986053 | −0.493027 | − | 0.870014i | \(-0.664109\pi\) | ||||
−0.493027 | + | 0.870014i | \(0.664109\pi\) | |||||||
\(938\) | −28.1119 | −0.917887 | ||||||||
\(939\) | 13.7395 | 0.448373 | ||||||||
\(940\) | −0.0810446 | −0.00264338 | ||||||||
\(941\) | −22.3403 | −0.728273 | −0.364136 | − | 0.931346i | \(-0.618636\pi\) | ||||
−0.364136 | + | 0.931346i | \(0.618636\pi\) | |||||||
\(942\) | 3.75589 | 0.122373 | ||||||||
\(943\) | 40.3801 | 1.31496 | ||||||||
\(944\) | −8.39566 | −0.273255 | ||||||||
\(945\) | −0.302047 | −0.00982558 | ||||||||
\(946\) | 19.4519 | 0.632437 | ||||||||
\(947\) | 52.4983 | 1.70596 | 0.852982 | − | 0.521940i | \(-0.174792\pi\) | ||||
0.852982 | + | 0.521940i | \(0.174792\pi\) | |||||||
\(948\) | −5.88236 | −0.191050 | ||||||||
\(949\) | 1.59020 | 0.0516200 | ||||||||
\(950\) | 11.2587 | 0.365282 | ||||||||
\(951\) | −21.1401 | −0.685513 | ||||||||
\(952\) | 9.30829 | 0.301683 | ||||||||
\(953\) | 31.1909 | 1.01037 | 0.505186 | − | 0.863010i | \(-0.331424\pi\) | ||||
0.505186 | + | 0.863010i | \(0.331424\pi\) | |||||||
\(954\) | 7.20535 | 0.233282 | ||||||||
\(955\) | −1.30655 | −0.0422791 | ||||||||
\(956\) | −17.6397 | −0.570509 | ||||||||
\(957\) | 3.14547 | 0.101679 | ||||||||
\(958\) | −9.71552 | −0.313894 | ||||||||
\(959\) | −1.25137 | −0.0404088 | ||||||||
\(960\) | −0.113923 | −0.00367684 | ||||||||
\(961\) | 0.0880923 | 0.00284169 | ||||||||
\(962\) | 7.31136 | 0.235728 | ||||||||
\(963\) | 14.4797 | 0.466601 | ||||||||
\(964\) | 24.3235 | 0.783408 | ||||||||
\(965\) | −0.803258 | −0.0258578 | ||||||||
\(966\) | 13.0131 | 0.418688 | ||||||||
\(967\) | 13.8566 | 0.445599 | 0.222800 | − | 0.974864i | \(-0.428480\pi\) | ||||
0.222800 | + | 0.974864i | \(0.428480\pi\) | |||||||
\(968\) | −0.926787 | −0.0297880 | ||||||||
\(969\) | 7.92602 | 0.254620 | ||||||||
\(970\) | 1.18481 | 0.0380420 | ||||||||
\(971\) | 18.3937 | 0.590282 | 0.295141 | − | 0.955454i | \(-0.404633\pi\) | ||||
0.295141 | + | 0.955454i | \(0.404633\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 6.67714 | 0.214059 | ||||||||
\(974\) | −22.4933 | −0.720731 | ||||||||
\(975\) | −4.98702 | −0.159713 | ||||||||
\(976\) | −1.34766 | −0.0431375 | ||||||||
\(977\) | 19.2772 | 0.616732 | 0.308366 | − | 0.951268i | \(-0.400218\pi\) | ||||
0.308366 | + | 0.951268i | \(0.400218\pi\) | |||||||
\(978\) | 11.0445 | 0.353166 | ||||||||
\(979\) | 28.4330 | 0.908723 | ||||||||
\(980\) | 0.00336438 | 0.000107471 0 | ||||||||
\(981\) | −17.6514 | −0.563567 | ||||||||
\(982\) | −13.9549 | −0.445320 | ||||||||
\(983\) | −56.7511 | −1.81008 | −0.905039 | − | 0.425329i | \(-0.860158\pi\) | ||||
−0.905039 | + | 0.425329i | \(0.860158\pi\) | |||||||
\(984\) | 8.22718 | 0.262273 | ||||||||
\(985\) | 0.389541 | 0.0124118 | ||||||||
\(986\) | 3.47944 | 0.110808 | ||||||||
\(987\) | 1.88615 | 0.0600369 | ||||||||
\(988\) | 2.25761 | 0.0718240 | ||||||||
\(989\) | 30.0812 | 0.956526 | ||||||||
\(990\) | −0.361572 | −0.0114915 | ||||||||
\(991\) | 4.71272 | 0.149705 | 0.0748523 | − | 0.997195i | \(-0.476151\pi\) | ||||
0.0748523 | + | 0.997195i | \(0.476151\pi\) | |||||||
\(992\) | 5.57567 | 0.177028 | ||||||||
\(993\) | 19.2913 | 0.612190 | ||||||||
\(994\) | 36.1789 | 1.14752 | ||||||||
\(995\) | 1.44911 | 0.0459398 | ||||||||
\(996\) | 12.1432 | 0.384772 | ||||||||
\(997\) | 9.06102 | 0.286965 | 0.143483 | − | 0.989653i | \(-0.454170\pi\) | ||||
0.143483 | + | 0.989653i | \(0.454170\pi\) | |||||||
\(998\) | 22.1708 | 0.701805 | ||||||||
\(999\) | 7.31136 | 0.231321 |
(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 | 8034.2.a.u.1.6 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.u.1.6 | ✓ | 11 | 1.1 | even | 1 | trivial |