Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2013,2,Mod(1,2013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2013, 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("2013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2013 = 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2013.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: | \(16.0738859269\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - x^{13} - 21 x^{12} + 20 x^{11} + 167 x^{10} - 148 x^{9} - 627 x^{8} + 497 x^{7} + 1123 x^{6} + \cdots - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(-1.76637\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.76637 | 1.24901 | 0.624505 | − | 0.781020i | \(-0.285301\pi\) | ||||
0.624505 | + | 0.781020i | \(0.285301\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.12006 | 0.560028 | ||||||||
\(5\) | −2.50284 | −1.11930 | −0.559652 | − | 0.828727i | \(-0.689065\pi\) | ||||
−0.559652 | + | 0.828727i | \(0.689065\pi\) | |||||||
\(6\) | −1.76637 | −0.721117 | ||||||||
\(7\) | −4.08919 | −1.54557 | −0.772784 | − | 0.634670i | \(-0.781136\pi\) | ||||
−0.772784 | + | 0.634670i | \(0.781136\pi\) | |||||||
\(8\) | −1.55430 | −0.549530 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −4.42094 | −1.39802 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −1.12006 | −0.323332 | ||||||||
\(13\) | 4.58176 | 1.27075 | 0.635376 | − | 0.772203i | \(-0.280845\pi\) | ||||
0.635376 | + | 0.772203i | \(0.280845\pi\) | |||||||
\(14\) | −7.22301 | −1.93043 | ||||||||
\(15\) | 2.50284 | 0.646231 | ||||||||
\(16\) | −4.98559 | −1.24640 | ||||||||
\(17\) | −1.68948 | −0.409759 | −0.204879 | − | 0.978787i | \(-0.565680\pi\) | ||||
−0.204879 | + | 0.978787i | \(0.565680\pi\) | |||||||
\(18\) | 1.76637 | 0.416337 | ||||||||
\(19\) | 2.54310 | 0.583426 | 0.291713 | − | 0.956506i | \(-0.405775\pi\) | ||||
0.291713 | + | 0.956506i | \(0.405775\pi\) | |||||||
\(20\) | −2.80332 | −0.626842 | ||||||||
\(21\) | 4.08919 | 0.892334 | ||||||||
\(22\) | −1.76637 | −0.376591 | ||||||||
\(23\) | 6.64905 | 1.38642 | 0.693212 | − | 0.720734i | \(-0.256195\pi\) | ||||
0.693212 | + | 0.720734i | \(0.256195\pi\) | |||||||
\(24\) | 1.55430 | 0.317271 | ||||||||
\(25\) | 1.26422 | 0.252844 | ||||||||
\(26\) | 8.09307 | 1.58718 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −4.58012 | −0.865561 | ||||||||
\(29\) | 2.87310 | 0.533521 | 0.266760 | − | 0.963763i | \(-0.414047\pi\) | ||||
0.266760 | + | 0.963763i | \(0.414047\pi\) | |||||||
\(30\) | 4.42094 | 0.807150 | ||||||||
\(31\) | 5.77320 | 1.03690 | 0.518449 | − | 0.855109i | \(-0.326510\pi\) | ||||
0.518449 | + | 0.855109i | \(0.326510\pi\) | |||||||
\(32\) | −5.69777 | −1.00723 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | −2.98424 | −0.511793 | ||||||||
\(35\) | 10.2346 | 1.72996 | ||||||||
\(36\) | 1.12006 | 0.186676 | ||||||||
\(37\) | 10.5546 | 1.73516 | 0.867582 | − | 0.497293i | \(-0.165673\pi\) | ||||
0.867582 | + | 0.497293i | \(0.165673\pi\) | |||||||
\(38\) | 4.49204 | 0.728706 | ||||||||
\(39\) | −4.58176 | −0.733669 | ||||||||
\(40\) | 3.89018 | 0.615091 | ||||||||
\(41\) | −7.50568 | −1.17219 | −0.586095 | − | 0.810242i | \(-0.699336\pi\) | ||||
−0.586095 | + | 0.810242i | \(0.699336\pi\) | |||||||
\(42\) | 7.22301 | 1.11453 | ||||||||
\(43\) | −5.62451 | −0.857729 | −0.428865 | − | 0.903369i | \(-0.641086\pi\) | ||||
−0.428865 | + | 0.903369i | \(0.641086\pi\) | |||||||
\(44\) | −1.12006 | −0.168855 | ||||||||
\(45\) | −2.50284 | −0.373102 | ||||||||
\(46\) | 11.7447 | 1.73166 | ||||||||
\(47\) | 8.24063 | 1.20202 | 0.601010 | − | 0.799242i | \(-0.294765\pi\) | ||||
0.601010 | + | 0.799242i | \(0.294765\pi\) | |||||||
\(48\) | 4.98559 | 0.719607 | ||||||||
\(49\) | 9.72144 | 1.38878 | ||||||||
\(50\) | 2.23307 | 0.315804 | ||||||||
\(51\) | 1.68948 | 0.236574 | ||||||||
\(52\) | 5.13183 | 0.711657 | ||||||||
\(53\) | −6.73746 | −0.925461 | −0.462730 | − | 0.886499i | \(-0.653130\pi\) | ||||
−0.462730 | + | 0.886499i | \(0.653130\pi\) | |||||||
\(54\) | −1.76637 | −0.240372 | ||||||||
\(55\) | 2.50284 | 0.337483 | ||||||||
\(56\) | 6.35584 | 0.849335 | ||||||||
\(57\) | −2.54310 | −0.336841 | ||||||||
\(58\) | 5.07495 | 0.666373 | ||||||||
\(59\) | 1.44956 | 0.188717 | 0.0943584 | − | 0.995538i | \(-0.469920\pi\) | ||||
0.0943584 | + | 0.995538i | \(0.469920\pi\) | |||||||
\(60\) | 2.80332 | 0.361908 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | 10.1976 | 1.29510 | ||||||||
\(63\) | −4.08919 | −0.515189 | ||||||||
\(64\) | −0.0931904 | −0.0116488 | ||||||||
\(65\) | −11.4674 | −1.42236 | ||||||||
\(66\) | 1.76637 | 0.217425 | ||||||||
\(67\) | −2.89684 | −0.353905 | −0.176953 | − | 0.984219i | \(-0.556624\pi\) | ||||
−0.176953 | + | 0.984219i | \(0.556624\pi\) | |||||||
\(68\) | −1.89231 | −0.229477 | ||||||||
\(69\) | −6.64905 | −0.800452 | ||||||||
\(70\) | 18.0780 | 2.16074 | ||||||||
\(71\) | −3.64666 | −0.432779 | −0.216389 | − | 0.976307i | \(-0.569428\pi\) | ||||
−0.216389 | + | 0.976307i | \(0.569428\pi\) | |||||||
\(72\) | −1.55430 | −0.183177 | ||||||||
\(73\) | −1.53009 | −0.179084 | −0.0895419 | − | 0.995983i | \(-0.528540\pi\) | ||||
−0.0895419 | + | 0.995983i | \(0.528540\pi\) | |||||||
\(74\) | 18.6433 | 2.16724 | ||||||||
\(75\) | −1.26422 | −0.145979 | ||||||||
\(76\) | 2.84841 | 0.326735 | ||||||||
\(77\) | 4.08919 | 0.466006 | ||||||||
\(78\) | −8.09307 | −0.916360 | ||||||||
\(79\) | 6.59373 | 0.741853 | 0.370926 | − | 0.928662i | \(-0.379040\pi\) | ||||
0.370926 | + | 0.928662i | \(0.379040\pi\) | |||||||
\(80\) | 12.4781 | 1.39510 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −13.2578 | −1.46408 | ||||||||
\(83\) | 4.68950 | 0.514739 | 0.257370 | − | 0.966313i | \(-0.417144\pi\) | ||||
0.257370 | + | 0.966313i | \(0.417144\pi\) | |||||||
\(84\) | 4.58012 | 0.499732 | ||||||||
\(85\) | 4.22850 | 0.458645 | ||||||||
\(86\) | −9.93495 | −1.07131 | ||||||||
\(87\) | −2.87310 | −0.308028 | ||||||||
\(88\) | 1.55430 | 0.165689 | ||||||||
\(89\) | 8.01389 | 0.849471 | 0.424735 | − | 0.905318i | \(-0.360367\pi\) | ||||
0.424735 | + | 0.905318i | \(0.360367\pi\) | |||||||
\(90\) | −4.42094 | −0.466008 | ||||||||
\(91\) | −18.7357 | −1.96403 | ||||||||
\(92\) | 7.44732 | 0.776436 | ||||||||
\(93\) | −5.77320 | −0.598653 | ||||||||
\(94\) | 14.5560 | 1.50134 | ||||||||
\(95\) | −6.36497 | −0.653032 | ||||||||
\(96\) | 5.69777 | 0.581526 | ||||||||
\(97\) | −8.48718 | −0.861743 | −0.430871 | − | 0.902413i | \(-0.641794\pi\) | ||||
−0.430871 | + | 0.902413i | \(0.641794\pi\) | |||||||
\(98\) | 17.1716 | 1.73460 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 1.41600 | 0.141600 | ||||||||
\(101\) | −18.2735 | −1.81828 | −0.909138 | − | 0.416495i | \(-0.863258\pi\) | ||||
−0.909138 | + | 0.416495i | \(0.863258\pi\) | |||||||
\(102\) | 2.98424 | 0.295484 | ||||||||
\(103\) | 13.5101 | 1.33119 | 0.665594 | − | 0.746314i | \(-0.268178\pi\) | ||||
0.665594 | + | 0.746314i | \(0.268178\pi\) | |||||||
\(104\) | −7.12145 | −0.698315 | ||||||||
\(105\) | −10.2346 | −0.998793 | ||||||||
\(106\) | −11.9008 | −1.15591 | ||||||||
\(107\) | 6.25580 | 0.604771 | 0.302385 | − | 0.953186i | \(-0.402217\pi\) | ||||
0.302385 | + | 0.953186i | \(0.402217\pi\) | |||||||
\(108\) | −1.12006 | −0.107777 | ||||||||
\(109\) | 9.80803 | 0.939439 | 0.469720 | − | 0.882816i | \(-0.344355\pi\) | ||||
0.469720 | + | 0.882816i | \(0.344355\pi\) | |||||||
\(110\) | 4.42094 | 0.421520 | ||||||||
\(111\) | −10.5546 | −1.00180 | ||||||||
\(112\) | 20.3870 | 1.92639 | ||||||||
\(113\) | 4.30188 | 0.404687 | 0.202343 | − | 0.979315i | \(-0.435144\pi\) | ||||
0.202343 | + | 0.979315i | \(0.435144\pi\) | |||||||
\(114\) | −4.49204 | −0.420718 | ||||||||
\(115\) | −16.6415 | −1.55183 | ||||||||
\(116\) | 3.21803 | 0.298787 | ||||||||
\(117\) | 4.58176 | 0.423584 | ||||||||
\(118\) | 2.56046 | 0.235709 | ||||||||
\(119\) | 6.90859 | 0.633310 | ||||||||
\(120\) | −3.89018 | −0.355123 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 1.76637 | 0.159919 | ||||||||
\(123\) | 7.50568 | 0.676764 | ||||||||
\(124\) | 6.46631 | 0.580692 | ||||||||
\(125\) | 9.35007 | 0.836296 | ||||||||
\(126\) | −7.22301 | −0.643477 | ||||||||
\(127\) | 8.95668 | 0.794776 | 0.397388 | − | 0.917651i | \(-0.369917\pi\) | ||||
0.397388 | + | 0.917651i | \(0.369917\pi\) | |||||||
\(128\) | 11.2309 | 0.992684 | ||||||||
\(129\) | 5.62451 | 0.495210 | ||||||||
\(130\) | −20.2557 | −1.77654 | ||||||||
\(131\) | 16.6930 | 1.45848 | 0.729239 | − | 0.684259i | \(-0.239874\pi\) | ||||
0.729239 | + | 0.684259i | \(0.239874\pi\) | |||||||
\(132\) | 1.12006 | 0.0974884 | ||||||||
\(133\) | −10.3992 | −0.901724 | ||||||||
\(134\) | −5.11689 | −0.442032 | ||||||||
\(135\) | 2.50284 | 0.215410 | ||||||||
\(136\) | 2.62596 | 0.225175 | ||||||||
\(137\) | 1.84979 | 0.158038 | 0.0790192 | − | 0.996873i | \(-0.474821\pi\) | ||||
0.0790192 | + | 0.996873i | \(0.474821\pi\) | |||||||
\(138\) | −11.7447 | −0.999773 | ||||||||
\(139\) | −2.09830 | −0.177975 | −0.0889877 | − | 0.996033i | \(-0.528363\pi\) | ||||
−0.0889877 | + | 0.996033i | \(0.528363\pi\) | |||||||
\(140\) | 11.4633 | 0.968827 | ||||||||
\(141\) | −8.24063 | −0.693986 | ||||||||
\(142\) | −6.44134 | −0.540545 | ||||||||
\(143\) | −4.58176 | −0.383146 | ||||||||
\(144\) | −4.98559 | −0.415466 | ||||||||
\(145\) | −7.19091 | −0.597172 | ||||||||
\(146\) | −2.70271 | −0.223678 | ||||||||
\(147\) | −9.72144 | −0.801811 | ||||||||
\(148\) | 11.8217 | 0.971741 | ||||||||
\(149\) | −10.6609 | −0.873374 | −0.436687 | − | 0.899614i | \(-0.643848\pi\) | ||||
−0.436687 | + | 0.899614i | \(0.643848\pi\) | |||||||
\(150\) | −2.23307 | −0.182330 | ||||||||
\(151\) | −15.9563 | −1.29850 | −0.649252 | − | 0.760573i | \(-0.724918\pi\) | ||||
−0.649252 | + | 0.760573i | \(0.724918\pi\) | |||||||
\(152\) | −3.95274 | −0.320610 | ||||||||
\(153\) | −1.68948 | −0.136586 | ||||||||
\(154\) | 7.22301 | 0.582047 | ||||||||
\(155\) | −14.4494 | −1.16060 | ||||||||
\(156\) | −5.13183 | −0.410875 | ||||||||
\(157\) | −12.6000 | −1.00559 | −0.502795 | − | 0.864406i | \(-0.667695\pi\) | ||||
−0.502795 | + | 0.864406i | \(0.667695\pi\) | |||||||
\(158\) | 11.6470 | 0.926582 | ||||||||
\(159\) | 6.73746 | 0.534315 | ||||||||
\(160\) | 14.2606 | 1.12740 | ||||||||
\(161\) | −27.1892 | −2.14281 | ||||||||
\(162\) | 1.76637 | 0.138779 | ||||||||
\(163\) | 19.5726 | 1.53305 | 0.766523 | − | 0.642217i | \(-0.221985\pi\) | ||||
0.766523 | + | 0.642217i | \(0.221985\pi\) | |||||||
\(164\) | −8.40679 | −0.656460 | ||||||||
\(165\) | −2.50284 | −0.194846 | ||||||||
\(166\) | 8.28338 | 0.642915 | ||||||||
\(167\) | −1.21481 | −0.0940045 | −0.0470023 | − | 0.998895i | \(-0.514967\pi\) | ||||
−0.0470023 | + | 0.998895i | \(0.514967\pi\) | |||||||
\(168\) | −6.35584 | −0.490364 | ||||||||
\(169\) | 7.99251 | 0.614809 | ||||||||
\(170\) | 7.46909 | 0.572853 | ||||||||
\(171\) | 2.54310 | 0.194475 | ||||||||
\(172\) | −6.29977 | −0.480353 | ||||||||
\(173\) | −16.2092 | −1.23236 | −0.616180 | − | 0.787605i | \(-0.711321\pi\) | ||||
−0.616180 | + | 0.787605i | \(0.711321\pi\) | |||||||
\(174\) | −5.07495 | −0.384731 | ||||||||
\(175\) | −5.16962 | −0.390787 | ||||||||
\(176\) | 4.98559 | 0.375803 | ||||||||
\(177\) | −1.44956 | −0.108956 | ||||||||
\(178\) | 14.1555 | 1.06100 | ||||||||
\(179\) | −0.460529 | −0.0344216 | −0.0172108 | − | 0.999852i | \(-0.505479\pi\) | ||||
−0.0172108 | + | 0.999852i | \(0.505479\pi\) | |||||||
\(180\) | −2.80332 | −0.208947 | ||||||||
\(181\) | 21.1108 | 1.56916 | 0.784578 | − | 0.620030i | \(-0.212879\pi\) | ||||
0.784578 | + | 0.620030i | \(0.212879\pi\) | |||||||
\(182\) | −33.0941 | −2.45310 | ||||||||
\(183\) | −1.00000 | −0.0739221 | ||||||||
\(184\) | −10.3347 | −0.761881 | ||||||||
\(185\) | −26.4165 | −1.94218 | ||||||||
\(186\) | −10.1976 | −0.747724 | ||||||||
\(187\) | 1.68948 | 0.123547 | ||||||||
\(188\) | 9.22997 | 0.673165 | ||||||||
\(189\) | 4.08919 | 0.297445 | ||||||||
\(190\) | −11.2429 | −0.815644 | ||||||||
\(191\) | 20.7120 | 1.49867 | 0.749333 | − | 0.662193i | \(-0.230374\pi\) | ||||
0.749333 | + | 0.662193i | \(0.230374\pi\) | |||||||
\(192\) | 0.0931904 | 0.00672544 | ||||||||
\(193\) | 4.36796 | 0.314413 | 0.157206 | − | 0.987566i | \(-0.449751\pi\) | ||||
0.157206 | + | 0.987566i | \(0.449751\pi\) | |||||||
\(194\) | −14.9915 | −1.07633 | ||||||||
\(195\) | 11.4674 | 0.821199 | ||||||||
\(196\) | 10.8886 | 0.777755 | ||||||||
\(197\) | −14.9041 | −1.06187 | −0.530935 | − | 0.847413i | \(-0.678159\pi\) | ||||
−0.530935 | + | 0.847413i | \(0.678159\pi\) | |||||||
\(198\) | −1.76637 | −0.125530 | ||||||||
\(199\) | 12.3150 | 0.872990 | 0.436495 | − | 0.899707i | \(-0.356220\pi\) | ||||
0.436495 | + | 0.899707i | \(0.356220\pi\) | |||||||
\(200\) | −1.96498 | −0.138945 | ||||||||
\(201\) | 2.89684 | 0.204327 | ||||||||
\(202\) | −32.2776 | −2.27105 | ||||||||
\(203\) | −11.7486 | −0.824592 | ||||||||
\(204\) | 1.89231 | 0.132488 | ||||||||
\(205\) | 18.7855 | 1.31204 | ||||||||
\(206\) | 23.8638 | 1.66267 | ||||||||
\(207\) | 6.64905 | 0.462141 | ||||||||
\(208\) | −22.8428 | −1.58386 | ||||||||
\(209\) | −2.54310 | −0.175910 | ||||||||
\(210\) | −18.0780 | −1.24750 | ||||||||
\(211\) | −0.624271 | −0.0429766 | −0.0214883 | − | 0.999769i | \(-0.506840\pi\) | ||||
−0.0214883 | + | 0.999769i | \(0.506840\pi\) | |||||||
\(212\) | −7.54633 | −0.518284 | ||||||||
\(213\) | 3.64666 | 0.249865 | ||||||||
\(214\) | 11.0500 | 0.755365 | ||||||||
\(215\) | 14.0773 | 0.960061 | ||||||||
\(216\) | 1.55430 | 0.105757 | ||||||||
\(217\) | −23.6077 | −1.60259 | ||||||||
\(218\) | 17.3246 | 1.17337 | ||||||||
\(219\) | 1.53009 | 0.103394 | ||||||||
\(220\) | 2.80332 | 0.189000 | ||||||||
\(221\) | −7.74079 | −0.520702 | ||||||||
\(222\) | −18.6433 | −1.25126 | ||||||||
\(223\) | 1.10168 | 0.0737740 | 0.0368870 | − | 0.999319i | \(-0.488256\pi\) | ||||
0.0368870 | + | 0.999319i | \(0.488256\pi\) | |||||||
\(224\) | 23.2993 | 1.55675 | ||||||||
\(225\) | 1.26422 | 0.0842812 | ||||||||
\(226\) | 7.59871 | 0.505458 | ||||||||
\(227\) | 24.3655 | 1.61720 | 0.808599 | − | 0.588360i | \(-0.200226\pi\) | ||||
0.808599 | + | 0.588360i | \(0.200226\pi\) | |||||||
\(228\) | −2.84841 | −0.188641 | ||||||||
\(229\) | −10.0662 | −0.665193 | −0.332597 | − | 0.943069i | \(-0.607925\pi\) | ||||
−0.332597 | + | 0.943069i | \(0.607925\pi\) | |||||||
\(230\) | −29.3951 | −1.93825 | ||||||||
\(231\) | −4.08919 | −0.269049 | ||||||||
\(232\) | −4.46567 | −0.293185 | ||||||||
\(233\) | −2.64216 | −0.173094 | −0.0865470 | − | 0.996248i | \(-0.527583\pi\) | ||||
−0.0865470 | + | 0.996248i | \(0.527583\pi\) | |||||||
\(234\) | 8.09307 | 0.529061 | ||||||||
\(235\) | −20.6250 | −1.34543 | ||||||||
\(236\) | 1.62359 | 0.105687 | ||||||||
\(237\) | −6.59373 | −0.428309 | ||||||||
\(238\) | 12.2031 | 0.791011 | ||||||||
\(239\) | −24.0202 | −1.55374 | −0.776870 | − | 0.629662i | \(-0.783194\pi\) | ||||
−0.776870 | + | 0.629662i | \(0.783194\pi\) | |||||||
\(240\) | −12.4781 | −0.805460 | ||||||||
\(241\) | 20.2998 | 1.30763 | 0.653813 | − | 0.756656i | \(-0.273168\pi\) | ||||
0.653813 | + | 0.756656i | \(0.273168\pi\) | |||||||
\(242\) | 1.76637 | 0.113546 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 1.12006 | 0.0717043 | ||||||||
\(245\) | −24.3312 | −1.55447 | ||||||||
\(246\) | 13.2578 | 0.845286 | ||||||||
\(247\) | 11.6518 | 0.741389 | ||||||||
\(248\) | −8.97331 | −0.569806 | ||||||||
\(249\) | −4.68950 | −0.297185 | ||||||||
\(250\) | 16.5157 | 1.04454 | ||||||||
\(251\) | −7.85638 | −0.495890 | −0.247945 | − | 0.968774i | \(-0.579755\pi\) | ||||
−0.247945 | + | 0.968774i | \(0.579755\pi\) | |||||||
\(252\) | −4.58012 | −0.288520 | ||||||||
\(253\) | −6.64905 | −0.418022 | ||||||||
\(254\) | 15.8208 | 0.992684 | ||||||||
\(255\) | −4.22850 | −0.264799 | ||||||||
\(256\) | 20.0243 | 1.25152 | ||||||||
\(257\) | 8.43220 | 0.525986 | 0.262993 | − | 0.964798i | \(-0.415290\pi\) | ||||
0.262993 | + | 0.964798i | \(0.415290\pi\) | |||||||
\(258\) | 9.93495 | 0.618523 | ||||||||
\(259\) | −43.1597 | −2.68181 | ||||||||
\(260\) | −12.8442 | −0.796561 | ||||||||
\(261\) | 2.87310 | 0.177840 | ||||||||
\(262\) | 29.4861 | 1.82165 | ||||||||
\(263\) | −15.8210 | −0.975563 | −0.487781 | − | 0.872966i | \(-0.662194\pi\) | ||||
−0.487781 | + | 0.872966i | \(0.662194\pi\) | |||||||
\(264\) | −1.55430 | −0.0956608 | ||||||||
\(265\) | 16.8628 | 1.03587 | ||||||||
\(266\) | −18.3688 | −1.12626 | ||||||||
\(267\) | −8.01389 | −0.490442 | ||||||||
\(268\) | −3.24462 | −0.198197 | ||||||||
\(269\) | 29.6760 | 1.80938 | 0.904690 | − | 0.426070i | \(-0.140102\pi\) | ||||
0.904690 | + | 0.426070i | \(0.140102\pi\) | |||||||
\(270\) | 4.42094 | 0.269050 | ||||||||
\(271\) | 13.8327 | 0.840277 | 0.420139 | − | 0.907460i | \(-0.361981\pi\) | ||||
0.420139 | + | 0.907460i | \(0.361981\pi\) | |||||||
\(272\) | 8.42304 | 0.510722 | ||||||||
\(273\) | 18.7357 | 1.13393 | ||||||||
\(274\) | 3.26742 | 0.197392 | ||||||||
\(275\) | −1.26422 | −0.0762352 | ||||||||
\(276\) | −7.44732 | −0.448276 | ||||||||
\(277\) | 10.7545 | 0.646174 | 0.323087 | − | 0.946369i | \(-0.395279\pi\) | ||||
0.323087 | + | 0.946369i | \(0.395279\pi\) | |||||||
\(278\) | −3.70637 | −0.222293 | ||||||||
\(279\) | 5.77320 | 0.345632 | ||||||||
\(280\) | −15.9077 | −0.950665 | ||||||||
\(281\) | 18.7346 | 1.11761 | 0.558807 | − | 0.829298i | \(-0.311259\pi\) | ||||
0.558807 | + | 0.829298i | \(0.311259\pi\) | |||||||
\(282\) | −14.5560 | −0.866796 | ||||||||
\(283\) | 24.5140 | 1.45721 | 0.728603 | − | 0.684936i | \(-0.240170\pi\) | ||||
0.728603 | + | 0.684936i | \(0.240170\pi\) | |||||||
\(284\) | −4.08446 | −0.242368 | ||||||||
\(285\) | 6.36497 | 0.377028 | ||||||||
\(286\) | −8.09307 | −0.478553 | ||||||||
\(287\) | 30.6921 | 1.81170 | ||||||||
\(288\) | −5.69777 | −0.335744 | ||||||||
\(289\) | −14.1457 | −0.832098 | ||||||||
\(290\) | −12.7018 | −0.745875 | ||||||||
\(291\) | 8.48718 | 0.497527 | ||||||||
\(292\) | −1.71379 | −0.100292 | ||||||||
\(293\) | 22.3094 | 1.30333 | 0.651665 | − | 0.758507i | \(-0.274071\pi\) | ||||
0.651665 | + | 0.758507i | \(0.274071\pi\) | |||||||
\(294\) | −17.1716 | −1.00147 | ||||||||
\(295\) | −3.62802 | −0.211232 | ||||||||
\(296\) | −16.4051 | −0.953524 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | −18.8310 | −1.09085 | ||||||||
\(299\) | 30.4644 | 1.76180 | ||||||||
\(300\) | −1.41600 | −0.0817525 | ||||||||
\(301\) | 22.9997 | 1.32568 | ||||||||
\(302\) | −28.1847 | −1.62185 | ||||||||
\(303\) | 18.2735 | 1.04978 | ||||||||
\(304\) | −12.6788 | −0.727180 | ||||||||
\(305\) | −2.50284 | −0.143312 | ||||||||
\(306\) | −2.98424 | −0.170598 | ||||||||
\(307\) | 9.79575 | 0.559073 | 0.279536 | − | 0.960135i | \(-0.409819\pi\) | ||||
0.279536 | + | 0.960135i | \(0.409819\pi\) | |||||||
\(308\) | 4.58012 | 0.260977 | ||||||||
\(309\) | −13.5101 | −0.768562 | ||||||||
\(310\) | −25.5230 | −1.44961 | ||||||||
\(311\) | 21.0159 | 1.19170 | 0.595852 | − | 0.803094i | \(-0.296814\pi\) | ||||
0.595852 | + | 0.803094i | \(0.296814\pi\) | |||||||
\(312\) | 7.12145 | 0.403173 | ||||||||
\(313\) | −11.8868 | −0.671880 | −0.335940 | − | 0.941883i | \(-0.609054\pi\) | ||||
−0.335940 | + | 0.941883i | \(0.609054\pi\) | |||||||
\(314\) | −22.2563 | −1.25599 | ||||||||
\(315\) | 10.2346 | 0.576654 | ||||||||
\(316\) | 7.38535 | 0.415458 | ||||||||
\(317\) | −20.3584 | −1.14344 | −0.571720 | − | 0.820449i | \(-0.693723\pi\) | ||||
−0.571720 | + | 0.820449i | \(0.693723\pi\) | |||||||
\(318\) | 11.9008 | 0.667365 | ||||||||
\(319\) | −2.87310 | −0.160863 | ||||||||
\(320\) | 0.233241 | 0.0130386 | ||||||||
\(321\) | −6.25580 | −0.349164 | ||||||||
\(322\) | −48.0262 | −2.67639 | ||||||||
\(323\) | −4.29651 | −0.239064 | ||||||||
\(324\) | 1.12006 | 0.0622254 | ||||||||
\(325\) | 5.79234 | 0.321301 | ||||||||
\(326\) | 34.5725 | 1.91479 | ||||||||
\(327\) | −9.80803 | −0.542385 | ||||||||
\(328\) | 11.6661 | 0.644153 | ||||||||
\(329\) | −33.6975 | −1.85780 | ||||||||
\(330\) | −4.42094 | −0.243365 | ||||||||
\(331\) | −18.5600 | −1.02015 | −0.510074 | − | 0.860130i | \(-0.670382\pi\) | ||||
−0.510074 | + | 0.860130i | \(0.670382\pi\) | |||||||
\(332\) | 5.25250 | 0.288268 | ||||||||
\(333\) | 10.5546 | 0.578388 | ||||||||
\(334\) | −2.14579 | −0.117413 | ||||||||
\(335\) | 7.25033 | 0.396128 | ||||||||
\(336\) | −20.3870 | −1.11220 | ||||||||
\(337\) | 10.9967 | 0.599029 | 0.299515 | − | 0.954092i | \(-0.403175\pi\) | ||||
0.299515 | + | 0.954092i | \(0.403175\pi\) | |||||||
\(338\) | 14.1177 | 0.767903 | ||||||||
\(339\) | −4.30188 | −0.233646 | ||||||||
\(340\) | 4.73616 | 0.256854 | ||||||||
\(341\) | −5.77320 | −0.312636 | ||||||||
\(342\) | 4.49204 | 0.242902 | ||||||||
\(343\) | −11.1285 | −0.600882 | ||||||||
\(344\) | 8.74220 | 0.471348 | ||||||||
\(345\) | 16.6415 | 0.895950 | ||||||||
\(346\) | −28.6314 | −1.53923 | ||||||||
\(347\) | −6.33081 | −0.339856 | −0.169928 | − | 0.985457i | \(-0.554353\pi\) | ||||
−0.169928 | + | 0.985457i | \(0.554353\pi\) | |||||||
\(348\) | −3.21803 | −0.172505 | ||||||||
\(349\) | −14.8101 | −0.792766 | −0.396383 | − | 0.918085i | \(-0.629735\pi\) | ||||
−0.396383 | + | 0.918085i | \(0.629735\pi\) | |||||||
\(350\) | −9.13146 | −0.488097 | ||||||||
\(351\) | −4.58176 | −0.244556 | ||||||||
\(352\) | 5.69777 | 0.303692 | ||||||||
\(353\) | 18.2039 | 0.968897 | 0.484448 | − | 0.874820i | \(-0.339020\pi\) | ||||
0.484448 | + | 0.874820i | \(0.339020\pi\) | |||||||
\(354\) | −2.56046 | −0.136087 | ||||||||
\(355\) | 9.12701 | 0.484411 | ||||||||
\(356\) | 8.97601 | 0.475728 | ||||||||
\(357\) | −6.90859 | −0.365642 | ||||||||
\(358\) | −0.813464 | −0.0429929 | ||||||||
\(359\) | −31.9112 | −1.68421 | −0.842105 | − | 0.539313i | \(-0.818684\pi\) | ||||
−0.842105 | + | 0.539313i | \(0.818684\pi\) | |||||||
\(360\) | 3.89018 | 0.205030 | ||||||||
\(361\) | −12.5327 | −0.659614 | ||||||||
\(362\) | 37.2895 | 1.95989 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | −20.9850 | −1.09991 | ||||||||
\(365\) | 3.82958 | 0.200449 | ||||||||
\(366\) | −1.76637 | −0.0923295 | ||||||||
\(367\) | 27.3610 | 1.42823 | 0.714117 | − | 0.700026i | \(-0.246828\pi\) | ||||
0.714117 | + | 0.700026i | \(0.246828\pi\) | |||||||
\(368\) | −33.1494 | −1.72803 | ||||||||
\(369\) | −7.50568 | −0.390730 | ||||||||
\(370\) | −46.6612 | −2.42580 | ||||||||
\(371\) | 27.5507 | 1.43036 | ||||||||
\(372\) | −6.46631 | −0.335263 | ||||||||
\(373\) | −10.8401 | −0.561279 | −0.280639 | − | 0.959813i | \(-0.590546\pi\) | ||||
−0.280639 | + | 0.959813i | \(0.590546\pi\) | |||||||
\(374\) | 2.98424 | 0.154311 | ||||||||
\(375\) | −9.35007 | −0.482836 | ||||||||
\(376\) | −12.8084 | −0.660545 | ||||||||
\(377\) | 13.1638 | 0.677972 | ||||||||
\(378\) | 7.22301 | 0.371511 | ||||||||
\(379\) | 28.1412 | 1.44552 | 0.722758 | − | 0.691101i | \(-0.242874\pi\) | ||||
0.722758 | + | 0.691101i | \(0.242874\pi\) | |||||||
\(380\) | −7.12912 | −0.365716 | ||||||||
\(381\) | −8.95668 | −0.458864 | ||||||||
\(382\) | 36.5850 | 1.87185 | ||||||||
\(383\) | 12.3294 | 0.630003 | 0.315002 | − | 0.949091i | \(-0.397995\pi\) | ||||
0.315002 | + | 0.949091i | \(0.397995\pi\) | |||||||
\(384\) | −11.2309 | −0.573126 | ||||||||
\(385\) | −10.2346 | −0.521603 | ||||||||
\(386\) | 7.71543 | 0.392705 | ||||||||
\(387\) | −5.62451 | −0.285910 | ||||||||
\(388\) | −9.50612 | −0.482600 | ||||||||
\(389\) | 2.35013 | 0.119156 | 0.0595782 | − | 0.998224i | \(-0.481024\pi\) | ||||
0.0595782 | + | 0.998224i | \(0.481024\pi\) | |||||||
\(390\) | 20.2557 | 1.02569 | ||||||||
\(391\) | −11.2334 | −0.568099 | ||||||||
\(392\) | −15.1101 | −0.763174 | ||||||||
\(393\) | −16.6930 | −0.842052 | ||||||||
\(394\) | −26.3261 | −1.32629 | ||||||||
\(395\) | −16.5031 | −0.830359 | ||||||||
\(396\) | −1.12006 | −0.0562850 | ||||||||
\(397\) | 7.28324 | 0.365535 | 0.182768 | − | 0.983156i | \(-0.441494\pi\) | ||||
0.182768 | + | 0.983156i | \(0.441494\pi\) | |||||||
\(398\) | 21.7529 | 1.09037 | ||||||||
\(399\) | 10.3992 | 0.520611 | ||||||||
\(400\) | −6.30287 | −0.315143 | ||||||||
\(401\) | −5.92148 | −0.295704 | −0.147852 | − | 0.989009i | \(-0.547236\pi\) | ||||
−0.147852 | + | 0.989009i | \(0.547236\pi\) | |||||||
\(402\) | 5.11689 | 0.255207 | ||||||||
\(403\) | 26.4514 | 1.31764 | ||||||||
\(404\) | −20.4673 | −1.01829 | ||||||||
\(405\) | −2.50284 | −0.124367 | ||||||||
\(406\) | −20.7524 | −1.02992 | ||||||||
\(407\) | −10.5546 | −0.523172 | ||||||||
\(408\) | −2.62596 | −0.130005 | ||||||||
\(409\) | 37.5868 | 1.85855 | 0.929273 | − | 0.369395i | \(-0.120435\pi\) | ||||
0.929273 | + | 0.369395i | \(0.120435\pi\) | |||||||
\(410\) | 33.1822 | 1.63875 | ||||||||
\(411\) | −1.84979 | −0.0912436 | ||||||||
\(412\) | 15.1321 | 0.745503 | ||||||||
\(413\) | −5.92753 | −0.291675 | ||||||||
\(414\) | 11.7447 | 0.577219 | ||||||||
\(415\) | −11.7371 | −0.576150 | ||||||||
\(416\) | −26.1058 | −1.27994 | ||||||||
\(417\) | 2.09830 | 0.102754 | ||||||||
\(418\) | −4.49204 | −0.219713 | ||||||||
\(419\) | 2.49710 | 0.121991 | 0.0609957 | − | 0.998138i | \(-0.480572\pi\) | ||||
0.0609957 | + | 0.998138i | \(0.480572\pi\) | |||||||
\(420\) | −11.4633 | −0.559352 | ||||||||
\(421\) | −4.42273 | −0.215551 | −0.107775 | − | 0.994175i | \(-0.534373\pi\) | ||||
−0.107775 | + | 0.994175i | \(0.534373\pi\) | |||||||
\(422\) | −1.10269 | −0.0536783 | ||||||||
\(423\) | 8.24063 | 0.400673 | ||||||||
\(424\) | 10.4721 | 0.508568 | ||||||||
\(425\) | −2.13587 | −0.103605 | ||||||||
\(426\) | 6.44134 | 0.312084 | ||||||||
\(427\) | −4.08919 | −0.197890 | ||||||||
\(428\) | 7.00684 | 0.338689 | ||||||||
\(429\) | 4.58176 | 0.221209 | ||||||||
\(430\) | 24.8656 | 1.19913 | ||||||||
\(431\) | −9.88068 | −0.475936 | −0.237968 | − | 0.971273i | \(-0.576481\pi\) | ||||
−0.237968 | + | 0.971273i | \(0.576481\pi\) | |||||||
\(432\) | 4.98559 | 0.239869 | ||||||||
\(433\) | −39.0060 | −1.87451 | −0.937254 | − | 0.348648i | \(-0.886641\pi\) | ||||
−0.937254 | + | 0.348648i | \(0.886641\pi\) | |||||||
\(434\) | −41.6999 | −2.00166 | ||||||||
\(435\) | 7.19091 | 0.344778 | ||||||||
\(436\) | 10.9855 | 0.526112 | ||||||||
\(437\) | 16.9092 | 0.808876 | ||||||||
\(438\) | 2.70271 | 0.129140 | ||||||||
\(439\) | 20.6364 | 0.984924 | 0.492462 | − | 0.870334i | \(-0.336097\pi\) | ||||
0.492462 | + | 0.870334i | \(0.336097\pi\) | |||||||
\(440\) | −3.89018 | −0.185457 | ||||||||
\(441\) | 9.72144 | 0.462926 | ||||||||
\(442\) | −13.6731 | −0.650362 | ||||||||
\(443\) | −32.1706 | −1.52847 | −0.764235 | − | 0.644938i | \(-0.776883\pi\) | ||||
−0.764235 | + | 0.644938i | \(0.776883\pi\) | |||||||
\(444\) | −11.8217 | −0.561035 | ||||||||
\(445\) | −20.0575 | −0.950817 | ||||||||
\(446\) | 1.94597 | 0.0921445 | ||||||||
\(447\) | 10.6609 | 0.504242 | ||||||||
\(448\) | 0.381073 | 0.0180040 | ||||||||
\(449\) | −5.85730 | −0.276423 | −0.138212 | − | 0.990403i | \(-0.544135\pi\) | ||||
−0.138212 | + | 0.990403i | \(0.544135\pi\) | |||||||
\(450\) | 2.23307 | 0.105268 | ||||||||
\(451\) | 7.50568 | 0.353429 | ||||||||
\(452\) | 4.81835 | 0.226636 | ||||||||
\(453\) | 15.9563 | 0.749692 | ||||||||
\(454\) | 43.0385 | 2.01990 | ||||||||
\(455\) | 46.8924 | 2.19835 | ||||||||
\(456\) | 3.95274 | 0.185104 | ||||||||
\(457\) | −1.68219 | −0.0786896 | −0.0393448 | − | 0.999226i | \(-0.512527\pi\) | ||||
−0.0393448 | + | 0.999226i | \(0.512527\pi\) | |||||||
\(458\) | −17.7806 | −0.830833 | ||||||||
\(459\) | 1.68948 | 0.0788581 | ||||||||
\(460\) | −18.6395 | −0.869069 | ||||||||
\(461\) | −6.22874 | −0.290101 | −0.145051 | − | 0.989424i | \(-0.546335\pi\) | ||||
−0.145051 | + | 0.989424i | \(0.546335\pi\) | |||||||
\(462\) | −7.22301 | −0.336045 | ||||||||
\(463\) | 20.0233 | 0.930560 | 0.465280 | − | 0.885163i | \(-0.345954\pi\) | ||||
0.465280 | + | 0.885163i | \(0.345954\pi\) | |||||||
\(464\) | −14.3241 | −0.664978 | ||||||||
\(465\) | 14.4494 | 0.670075 | ||||||||
\(466\) | −4.66704 | −0.216196 | ||||||||
\(467\) | 11.2040 | 0.518457 | 0.259229 | − | 0.965816i | \(-0.416532\pi\) | ||||
0.259229 | + | 0.965816i | \(0.416532\pi\) | |||||||
\(468\) | 5.13183 | 0.237219 | ||||||||
\(469\) | 11.8457 | 0.546985 | ||||||||
\(470\) | −36.4313 | −1.68045 | ||||||||
\(471\) | 12.6000 | 0.580578 | ||||||||
\(472\) | −2.25306 | −0.103705 | ||||||||
\(473\) | 5.62451 | 0.258615 | ||||||||
\(474\) | −11.6470 | −0.534962 | ||||||||
\(475\) | 3.21503 | 0.147516 | ||||||||
\(476\) | 7.73802 | 0.354671 | ||||||||
\(477\) | −6.73746 | −0.308487 | ||||||||
\(478\) | −42.4286 | −1.94064 | ||||||||
\(479\) | −36.8757 | −1.68490 | −0.842448 | − | 0.538778i | \(-0.818886\pi\) | ||||
−0.842448 | + | 0.538778i | \(0.818886\pi\) | |||||||
\(480\) | −14.2606 | −0.650905 | ||||||||
\(481\) | 48.3586 | 2.20496 | ||||||||
\(482\) | 35.8569 | 1.63324 | ||||||||
\(483\) | 27.1892 | 1.23715 | ||||||||
\(484\) | 1.12006 | 0.0509117 | ||||||||
\(485\) | 21.2421 | 0.964553 | ||||||||
\(486\) | −1.76637 | −0.0801241 | ||||||||
\(487\) | −27.2350 | −1.23414 | −0.617069 | − | 0.786909i | \(-0.711680\pi\) | ||||
−0.617069 | + | 0.786909i | \(0.711680\pi\) | |||||||
\(488\) | −1.55430 | −0.0703601 | ||||||||
\(489\) | −19.5726 | −0.885104 | ||||||||
\(490\) | −42.9779 | −1.94154 | ||||||||
\(491\) | −9.95507 | −0.449266 | −0.224633 | − | 0.974443i | \(-0.572118\pi\) | ||||
−0.224633 | + | 0.974443i | \(0.572118\pi\) | |||||||
\(492\) | 8.40679 | 0.379007 | ||||||||
\(493\) | −4.85404 | −0.218615 | ||||||||
\(494\) | 20.5815 | 0.926003 | ||||||||
\(495\) | 2.50284 | 0.112494 | ||||||||
\(496\) | −28.7828 | −1.29239 | ||||||||
\(497\) | 14.9119 | 0.668888 | ||||||||
\(498\) | −8.28338 | −0.371187 | ||||||||
\(499\) | −24.8590 | −1.11284 | −0.556421 | − | 0.830901i | \(-0.687826\pi\) | ||||
−0.556421 | + | 0.830901i | \(0.687826\pi\) | |||||||
\(500\) | 10.4726 | 0.468349 | ||||||||
\(501\) | 1.21481 | 0.0542735 | ||||||||
\(502\) | −13.8773 | −0.619372 | ||||||||
\(503\) | −7.90956 | −0.352670 | −0.176335 | − | 0.984330i | \(-0.556424\pi\) | ||||
−0.176335 | + | 0.984330i | \(0.556424\pi\) | |||||||
\(504\) | 6.35584 | 0.283112 | ||||||||
\(505\) | 45.7356 | 2.03521 | ||||||||
\(506\) | −11.7447 | −0.522115 | ||||||||
\(507\) | −7.99251 | −0.354960 | ||||||||
\(508\) | 10.0320 | 0.445097 | ||||||||
\(509\) | −26.7176 | −1.18423 | −0.592117 | − | 0.805852i | \(-0.701708\pi\) | ||||
−0.592117 | + | 0.805852i | \(0.701708\pi\) | |||||||
\(510\) | −7.46909 | −0.330737 | ||||||||
\(511\) | 6.25683 | 0.276786 | ||||||||
\(512\) | 12.9085 | 0.570480 | ||||||||
\(513\) | −2.54310 | −0.112280 | ||||||||
\(514\) | 14.8944 | 0.656963 | ||||||||
\(515\) | −33.8136 | −1.49001 | ||||||||
\(516\) | 6.29977 | 0.277332 | ||||||||
\(517\) | −8.24063 | −0.362422 | ||||||||
\(518\) | −76.2359 | −3.34961 | ||||||||
\(519\) | 16.2092 | 0.711503 | ||||||||
\(520\) | 17.8239 | 0.781628 | ||||||||
\(521\) | −44.3858 | −1.94458 | −0.972288 | − | 0.233788i | \(-0.924888\pi\) | ||||
−0.972288 | + | 0.233788i | \(0.924888\pi\) | |||||||
\(522\) | 5.07495 | 0.222124 | ||||||||
\(523\) | −9.29556 | −0.406466 | −0.203233 | − | 0.979130i | \(-0.565145\pi\) | ||||
−0.203233 | + | 0.979130i | \(0.565145\pi\) | |||||||
\(524\) | 18.6971 | 0.816789 | ||||||||
\(525\) | 5.16962 | 0.225621 | ||||||||
\(526\) | −27.9457 | −1.21849 | ||||||||
\(527\) | −9.75370 | −0.424878 | ||||||||
\(528\) | −4.98559 | −0.216970 | ||||||||
\(529\) | 21.2099 | 0.922171 | ||||||||
\(530\) | 29.7859 | 1.29382 | ||||||||
\(531\) | 1.44956 | 0.0629056 | ||||||||
\(532\) | −11.6477 | −0.504991 | ||||||||
\(533\) | −34.3892 | −1.48956 | ||||||||
\(534\) | −14.1555 | −0.612568 | ||||||||
\(535\) | −15.6573 | −0.676923 | ||||||||
\(536\) | 4.50257 | 0.194481 | ||||||||
\(537\) | 0.460529 | 0.0198733 | ||||||||
\(538\) | 52.4188 | 2.25994 | ||||||||
\(539\) | −9.72144 | −0.418732 | ||||||||
\(540\) | 2.80332 | 0.120636 | ||||||||
\(541\) | −12.2230 | −0.525508 | −0.262754 | − | 0.964863i | \(-0.584631\pi\) | ||||
−0.262754 | + | 0.964863i | \(0.584631\pi\) | |||||||
\(542\) | 24.4337 | 1.04952 | ||||||||
\(543\) | −21.1108 | −0.905953 | ||||||||
\(544\) | 9.62627 | 0.412723 | ||||||||
\(545\) | −24.5480 | −1.05152 | ||||||||
\(546\) | 33.0941 | 1.41630 | ||||||||
\(547\) | 41.0194 | 1.75386 | 0.876932 | − | 0.480615i | \(-0.159587\pi\) | ||||
0.876932 | + | 0.480615i | \(0.159587\pi\) | |||||||
\(548\) | 2.07187 | 0.0885060 | ||||||||
\(549\) | 1.00000 | 0.0426790 | ||||||||
\(550\) | −2.23307 | −0.0952186 | ||||||||
\(551\) | 7.30656 | 0.311270 | ||||||||
\(552\) | 10.3347 | 0.439872 | ||||||||
\(553\) | −26.9630 | −1.14658 | ||||||||
\(554\) | 18.9964 | 0.807079 | ||||||||
\(555\) | 26.4165 | 1.12132 | ||||||||
\(556\) | −2.35021 | −0.0996713 | ||||||||
\(557\) | 37.2860 | 1.57986 | 0.789930 | − | 0.613197i | \(-0.210117\pi\) | ||||
0.789930 | + | 0.613197i | \(0.210117\pi\) | |||||||
\(558\) | 10.1976 | 0.431699 | ||||||||
\(559\) | −25.7701 | −1.08996 | ||||||||
\(560\) | −51.0254 | −2.15622 | ||||||||
\(561\) | −1.68948 | −0.0713299 | ||||||||
\(562\) | 33.0922 | 1.39591 | ||||||||
\(563\) | −21.0358 | −0.886553 | −0.443276 | − | 0.896385i | \(-0.646184\pi\) | ||||
−0.443276 | + | 0.896385i | \(0.646184\pi\) | |||||||
\(564\) | −9.22997 | −0.388652 | ||||||||
\(565\) | −10.7669 | −0.452968 | ||||||||
\(566\) | 43.3007 | 1.82007 | ||||||||
\(567\) | −4.08919 | −0.171730 | ||||||||
\(568\) | 5.66802 | 0.237825 | ||||||||
\(569\) | −14.9610 | −0.627198 | −0.313599 | − | 0.949556i | \(-0.601535\pi\) | ||||
−0.313599 | + | 0.949556i | \(0.601535\pi\) | |||||||
\(570\) | 11.2429 | 0.470912 | ||||||||
\(571\) | 22.6822 | 0.949220 | 0.474610 | − | 0.880196i | \(-0.342589\pi\) | ||||
0.474610 | + | 0.880196i | \(0.342589\pi\) | |||||||
\(572\) | −5.13183 | −0.214573 | ||||||||
\(573\) | −20.7120 | −0.865256 | ||||||||
\(574\) | 54.2136 | 2.26283 | ||||||||
\(575\) | 8.40585 | 0.350548 | ||||||||
\(576\) | −0.0931904 | −0.00388293 | ||||||||
\(577\) | 16.8414 | 0.701115 | 0.350558 | − | 0.936541i | \(-0.385992\pi\) | ||||
0.350558 | + | 0.936541i | \(0.385992\pi\) | |||||||
\(578\) | −24.9864 | −1.03930 | ||||||||
\(579\) | −4.36796 | −0.181526 | ||||||||
\(580\) | −8.05422 | −0.334433 | ||||||||
\(581\) | −19.1762 | −0.795564 | ||||||||
\(582\) | 14.9915 | 0.621417 | ||||||||
\(583\) | 6.73746 | 0.279037 | ||||||||
\(584\) | 2.37823 | 0.0984118 | ||||||||
\(585\) | −11.4674 | −0.474119 | ||||||||
\(586\) | 39.4067 | 1.62787 | ||||||||
\(587\) | 24.6219 | 1.01625 | 0.508127 | − | 0.861282i | \(-0.330338\pi\) | ||||
0.508127 | + | 0.861282i | \(0.330338\pi\) | |||||||
\(588\) | −10.8886 | −0.449037 | ||||||||
\(589\) | 14.6818 | 0.604953 | ||||||||
\(590\) | −6.40843 | −0.263831 | ||||||||
\(591\) | 14.9041 | 0.613071 | ||||||||
\(592\) | −52.6208 | −2.16270 | ||||||||
\(593\) | −29.1431 | −1.19676 | −0.598381 | − | 0.801212i | \(-0.704189\pi\) | ||||
−0.598381 | + | 0.801212i | \(0.704189\pi\) | |||||||
\(594\) | 1.76637 | 0.0724750 | ||||||||
\(595\) | −17.2911 | −0.708867 | ||||||||
\(596\) | −11.9408 | −0.489114 | ||||||||
\(597\) | −12.3150 | −0.504021 | ||||||||
\(598\) | 53.8113 | 2.20051 | ||||||||
\(599\) | −13.0824 | −0.534533 | −0.267266 | − | 0.963623i | \(-0.586120\pi\) | ||||
−0.267266 | + | 0.963623i | \(0.586120\pi\) | |||||||
\(600\) | 1.96498 | 0.0802200 | ||||||||
\(601\) | 23.1391 | 0.943864 | 0.471932 | − | 0.881635i | \(-0.343557\pi\) | ||||
0.471932 | + | 0.881635i | \(0.343557\pi\) | |||||||
\(602\) | 40.6259 | 1.65579 | ||||||||
\(603\) | −2.89684 | −0.117968 | ||||||||
\(604\) | −17.8719 | −0.727199 | ||||||||
\(605\) | −2.50284 | −0.101755 | ||||||||
\(606\) | 32.2776 | 1.31119 | ||||||||
\(607\) | 8.61728 | 0.349765 | 0.174882 | − | 0.984589i | \(-0.444046\pi\) | ||||
0.174882 | + | 0.984589i | \(0.444046\pi\) | |||||||
\(608\) | −14.4900 | −0.587646 | ||||||||
\(609\) | 11.7486 | 0.476078 | ||||||||
\(610\) | −4.42094 | −0.178999 | ||||||||
\(611\) | 37.7566 | 1.52747 | ||||||||
\(612\) | −1.89231 | −0.0764922 | ||||||||
\(613\) | 41.9165 | 1.69299 | 0.846496 | − | 0.532396i | \(-0.178708\pi\) | ||||
0.846496 | + | 0.532396i | \(0.178708\pi\) | |||||||
\(614\) | 17.3029 | 0.698288 | ||||||||
\(615\) | −18.7855 | −0.757506 | ||||||||
\(616\) | −6.35584 | −0.256084 | ||||||||
\(617\) | 40.7094 | 1.63890 | 0.819449 | − | 0.573152i | \(-0.194279\pi\) | ||||
0.819449 | + | 0.573152i | \(0.194279\pi\) | |||||||
\(618\) | −23.8638 | −0.959942 | ||||||||
\(619\) | 38.7050 | 1.55569 | 0.777843 | − | 0.628459i | \(-0.216314\pi\) | ||||
0.777843 | + | 0.628459i | \(0.216314\pi\) | |||||||
\(620\) | −16.1842 | −0.649971 | ||||||||
\(621\) | −6.64905 | −0.266817 | ||||||||
\(622\) | 37.1219 | 1.48845 | ||||||||
\(623\) | −32.7703 | −1.31291 | ||||||||
\(624\) | 22.8428 | 0.914442 | ||||||||
\(625\) | −29.7228 | −1.18891 | ||||||||
\(626\) | −20.9964 | −0.839186 | ||||||||
\(627\) | 2.54310 | 0.101561 | ||||||||
\(628\) | −14.1127 | −0.563159 | ||||||||
\(629\) | −17.8318 | −0.710999 | ||||||||
\(630\) | 18.0780 | 0.720247 | ||||||||
\(631\) | 2.44555 | 0.0973560 | 0.0486780 | − | 0.998815i | \(-0.484499\pi\) | ||||
0.0486780 | + | 0.998815i | \(0.484499\pi\) | |||||||
\(632\) | −10.2487 | −0.407670 | ||||||||
\(633\) | 0.624271 | 0.0248126 | ||||||||
\(634\) | −35.9604 | −1.42817 | ||||||||
\(635\) | −22.4171 | −0.889597 | ||||||||
\(636\) | 7.54633 | 0.299231 | ||||||||
\(637\) | 44.5413 | 1.76479 | ||||||||
\(638\) | −5.07495 | −0.200919 | ||||||||
\(639\) | −3.64666 | −0.144260 | ||||||||
\(640\) | −28.1093 | −1.11112 | ||||||||
\(641\) | −3.52047 | −0.139050 | −0.0695250 | − | 0.997580i | \(-0.522148\pi\) | ||||
−0.0695250 | + | 0.997580i | \(0.522148\pi\) | |||||||
\(642\) | −11.0500 | −0.436110 | ||||||||
\(643\) | 12.7865 | 0.504250 | 0.252125 | − | 0.967695i | \(-0.418871\pi\) | ||||
0.252125 | + | 0.967695i | \(0.418871\pi\) | |||||||
\(644\) | −30.4535 | −1.20003 | ||||||||
\(645\) | −14.0773 | −0.554291 | ||||||||
\(646\) | −7.58921 | −0.298594 | ||||||||
\(647\) | 7.00044 | 0.275216 | 0.137608 | − | 0.990487i | \(-0.456059\pi\) | ||||
0.137608 | + | 0.990487i | \(0.456059\pi\) | |||||||
\(648\) | −1.55430 | −0.0610588 | ||||||||
\(649\) | −1.44956 | −0.0569003 | ||||||||
\(650\) | 10.2314 | 0.401309 | ||||||||
\(651\) | 23.6077 | 0.925258 | ||||||||
\(652\) | 21.9224 | 0.858549 | ||||||||
\(653\) | −13.6757 | −0.535171 | −0.267586 | − | 0.963534i | \(-0.586226\pi\) | ||||
−0.267586 | + | 0.963534i | \(0.586226\pi\) | |||||||
\(654\) | −17.3246 | −0.677445 | ||||||||
\(655\) | −41.7800 | −1.63248 | ||||||||
\(656\) | 37.4202 | 1.46101 | ||||||||
\(657\) | −1.53009 | −0.0596946 | ||||||||
\(658\) | −59.5221 | −2.32041 | ||||||||
\(659\) | −44.0565 | −1.71620 | −0.858099 | − | 0.513484i | \(-0.828355\pi\) | ||||
−0.858099 | + | 0.513484i | \(0.828355\pi\) | |||||||
\(660\) | −2.80332 | −0.109119 | ||||||||
\(661\) | −1.47619 | −0.0574170 | −0.0287085 | − | 0.999588i | \(-0.509139\pi\) | ||||
−0.0287085 | + | 0.999588i | \(0.509139\pi\) | |||||||
\(662\) | −32.7837 | −1.27418 | ||||||||
\(663\) | 7.74079 | 0.300627 | ||||||||
\(664\) | −7.28891 | −0.282864 | ||||||||
\(665\) | 26.0275 | 1.00930 | ||||||||
\(666\) | 18.6433 | 0.722413 | ||||||||
\(667\) | 19.1034 | 0.739686 | ||||||||
\(668\) | −1.36065 | −0.0526452 | ||||||||
\(669\) | −1.10168 | −0.0425934 | ||||||||
\(670\) | 12.8068 | 0.494768 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | −23.2993 | −0.898788 | ||||||||
\(673\) | 24.3555 | 0.938836 | 0.469418 | − | 0.882976i | \(-0.344464\pi\) | ||||
0.469418 | + | 0.882976i | \(0.344464\pi\) | |||||||
\(674\) | 19.4243 | 0.748194 | ||||||||
\(675\) | −1.26422 | −0.0486598 | ||||||||
\(676\) | 8.95207 | 0.344310 | ||||||||
\(677\) | −23.0375 | −0.885403 | −0.442701 | − | 0.896669i | \(-0.645980\pi\) | ||||
−0.442701 | + | 0.896669i | \(0.645980\pi\) | |||||||
\(678\) | −7.59871 | −0.291827 | ||||||||
\(679\) | 34.7057 | 1.33188 | ||||||||
\(680\) | −6.57238 | −0.252039 | ||||||||
\(681\) | −24.3655 | −0.933690 | ||||||||
\(682\) | −10.1976 | −0.390486 | ||||||||
\(683\) | −48.5599 | −1.85809 | −0.929047 | − | 0.369962i | \(-0.879371\pi\) | ||||
−0.929047 | + | 0.369962i | \(0.879371\pi\) | |||||||
\(684\) | 2.84841 | 0.108912 | ||||||||
\(685\) | −4.62974 | −0.176893 | ||||||||
\(686\) | −19.6570 | −0.750508 | ||||||||
\(687\) | 10.0662 | 0.384049 | ||||||||
\(688\) | 28.0415 | 1.06907 | ||||||||
\(689\) | −30.8694 | −1.17603 | ||||||||
\(690\) | 29.3951 | 1.11905 | ||||||||
\(691\) | 21.8077 | 0.829606 | 0.414803 | − | 0.909911i | \(-0.363851\pi\) | ||||
0.414803 | + | 0.909911i | \(0.363851\pi\) | |||||||
\(692\) | −18.1552 | −0.690156 | ||||||||
\(693\) | 4.08919 | 0.155335 | ||||||||
\(694\) | −11.1825 | −0.424483 | ||||||||
\(695\) | 5.25171 | 0.199209 | ||||||||
\(696\) | 4.46567 | 0.169271 | ||||||||
\(697\) | 12.6807 | 0.480315 | ||||||||
\(698\) | −26.1601 | −0.990173 | ||||||||
\(699\) | 2.64216 | 0.0999359 | ||||||||
\(700\) | −5.79027 | −0.218852 | ||||||||
\(701\) | 12.3112 | 0.464988 | 0.232494 | − | 0.972598i | \(-0.425311\pi\) | ||||
0.232494 | + | 0.972598i | \(0.425311\pi\) | |||||||
\(702\) | −8.09307 | −0.305453 | ||||||||
\(703\) | 26.8413 | 1.01234 | ||||||||
\(704\) | 0.0931904 | 0.00351224 | ||||||||
\(705\) | 20.6250 | 0.776782 | ||||||||
\(706\) | 32.1548 | 1.21016 | ||||||||
\(707\) | 74.7235 | 2.81027 | ||||||||
\(708\) | −1.62359 | −0.0610183 | ||||||||
\(709\) | 7.64608 | 0.287155 | 0.143577 | − | 0.989639i | \(-0.454139\pi\) | ||||
0.143577 | + | 0.989639i | \(0.454139\pi\) | |||||||
\(710\) | 16.1217 | 0.605035 | ||||||||
\(711\) | 6.59373 | 0.247284 | ||||||||
\(712\) | −12.4560 | −0.466809 | ||||||||
\(713\) | 38.3863 | 1.43758 | ||||||||
\(714\) | −12.2031 | −0.456690 | ||||||||
\(715\) | 11.4674 | 0.428857 | ||||||||
\(716\) | −0.515819 | −0.0192771 | ||||||||
\(717\) | 24.0202 | 0.897052 | ||||||||
\(718\) | −56.3670 | −2.10360 | ||||||||
\(719\) | −19.7235 | −0.735564 | −0.367782 | − | 0.929912i | \(-0.619883\pi\) | ||||
−0.367782 | + | 0.929912i | \(0.619883\pi\) | |||||||
\(720\) | 12.4781 | 0.465033 | ||||||||
\(721\) | −55.2452 | −2.05744 | ||||||||
\(722\) | −22.1373 | −0.823865 | ||||||||
\(723\) | −20.2998 | −0.754958 | ||||||||
\(724\) | 23.6453 | 0.878772 | ||||||||
\(725\) | 3.63222 | 0.134897 | ||||||||
\(726\) | −1.76637 | −0.0655561 | ||||||||
\(727\) | −12.7551 | −0.473061 | −0.236531 | − | 0.971624i | \(-0.576010\pi\) | ||||
−0.236531 | + | 0.971624i | \(0.576010\pi\) | |||||||
\(728\) | 29.1209 | 1.07929 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 6.76445 | 0.250363 | ||||||||
\(731\) | 9.50249 | 0.351462 | ||||||||
\(732\) | −1.12006 | −0.0413985 | ||||||||
\(733\) | 40.2693 | 1.48738 | 0.743690 | − | 0.668524i | \(-0.233074\pi\) | ||||
0.743690 | + | 0.668524i | \(0.233074\pi\) | |||||||
\(734\) | 48.3297 | 1.78388 | ||||||||
\(735\) | 24.3312 | 0.897471 | ||||||||
\(736\) | −37.8848 | −1.39645 | ||||||||
\(737\) | 2.89684 | 0.106706 | ||||||||
\(738\) | −13.2578 | −0.488026 | ||||||||
\(739\) | 13.7457 | 0.505644 | 0.252822 | − | 0.967513i | \(-0.418641\pi\) | ||||
0.252822 | + | 0.967513i | \(0.418641\pi\) | |||||||
\(740\) | −29.5880 | −1.08767 | ||||||||
\(741\) | −11.6518 | −0.428041 | ||||||||
\(742\) | 48.6647 | 1.78654 | ||||||||
\(743\) | 44.8666 | 1.64599 | 0.822997 | − | 0.568045i | \(-0.192300\pi\) | ||||
0.822997 | + | 0.568045i | \(0.192300\pi\) | |||||||
\(744\) | 8.97331 | 0.328978 | ||||||||
\(745\) | 26.6825 | 0.977571 | ||||||||
\(746\) | −19.1476 | −0.701043 | ||||||||
\(747\) | 4.68950 | 0.171580 | ||||||||
\(748\) | 1.89231 | 0.0691898 | ||||||||
\(749\) | −25.5811 | −0.934713 | ||||||||
\(750\) | −16.5157 | −0.603067 | ||||||||
\(751\) | −23.6834 | −0.864219 | −0.432109 | − | 0.901821i | \(-0.642231\pi\) | ||||
−0.432109 | + | 0.901821i | \(0.642231\pi\) | |||||||
\(752\) | −41.0844 | −1.49819 | ||||||||
\(753\) | 7.85638 | 0.286302 | ||||||||
\(754\) | 23.2522 | 0.846794 | ||||||||
\(755\) | 39.9361 | 1.45342 | ||||||||
\(756\) | 4.58012 | 0.166577 | ||||||||
\(757\) | 23.5395 | 0.855557 | 0.427778 | − | 0.903884i | \(-0.359296\pi\) | ||||
0.427778 | + | 0.903884i | \(0.359296\pi\) | |||||||
\(758\) | 49.7077 | 1.80546 | ||||||||
\(759\) | 6.64905 | 0.241345 | ||||||||
\(760\) | 9.89309 | 0.358860 | ||||||||
\(761\) | 14.0136 | 0.507992 | 0.253996 | − | 0.967205i | \(-0.418255\pi\) | ||||
0.253996 | + | 0.967205i | \(0.418255\pi\) | |||||||
\(762\) | −15.8208 | −0.573127 | ||||||||
\(763\) | −40.1069 | −1.45197 | ||||||||
\(764\) | 23.1986 | 0.839296 | ||||||||
\(765\) | 4.22850 | 0.152882 | ||||||||
\(766\) | 21.7783 | 0.786881 | ||||||||
\(767\) | 6.64154 | 0.239812 | ||||||||
\(768\) | −20.0243 | −0.722566 | ||||||||
\(769\) | 44.6655 | 1.61068 | 0.805339 | − | 0.592814i | \(-0.201983\pi\) | ||||
0.805339 | + | 0.592814i | \(0.201983\pi\) | |||||||
\(770\) | −18.0780 | −0.651488 | ||||||||
\(771\) | −8.43220 | −0.303678 | ||||||||
\(772\) | 4.89237 | 0.176080 | ||||||||
\(773\) | 36.4789 | 1.31205 | 0.656027 | − | 0.754737i | \(-0.272236\pi\) | ||||
0.656027 | + | 0.754737i | \(0.272236\pi\) | |||||||
\(774\) | −9.93495 | −0.357104 | ||||||||
\(775\) | 7.29858 | 0.262173 | ||||||||
\(776\) | 13.1917 | 0.473553 | ||||||||
\(777\) | 43.1597 | 1.54835 | ||||||||
\(778\) | 4.15120 | 0.148828 | ||||||||
\(779\) | −19.0877 | −0.683886 | ||||||||
\(780\) | 12.8442 | 0.459895 | ||||||||
\(781\) | 3.64666 | 0.130488 | ||||||||
\(782\) | −19.8424 | −0.709562 | ||||||||
\(783\) | −2.87310 | −0.102676 | ||||||||
\(784\) | −48.4671 | −1.73097 | ||||||||
\(785\) | 31.5358 | 1.12556 | ||||||||
\(786\) | −29.4861 | −1.05173 | ||||||||
\(787\) | 41.9161 | 1.49415 | 0.747075 | − | 0.664740i | \(-0.231458\pi\) | ||||
0.747075 | + | 0.664740i | \(0.231458\pi\) | |||||||
\(788\) | −16.6934 | −0.594677 | ||||||||
\(789\) | 15.8210 | 0.563242 | ||||||||
\(790\) | −29.1505 | −1.03713 | ||||||||
\(791\) | −17.5912 | −0.625471 | ||||||||
\(792\) | 1.55430 | 0.0552298 | ||||||||
\(793\) | 4.58176 | 0.162703 | ||||||||
\(794\) | 12.8649 | 0.456558 | ||||||||
\(795\) | −16.8628 | −0.598061 | ||||||||
\(796\) | 13.7935 | 0.488899 | ||||||||
\(797\) | 7.04587 | 0.249577 | 0.124789 | − | 0.992183i | \(-0.460175\pi\) | ||||
0.124789 | + | 0.992183i | \(0.460175\pi\) | |||||||
\(798\) | 18.3688 | 0.650248 | ||||||||
\(799\) | −13.9224 | −0.492538 | ||||||||
\(800\) | −7.20323 | −0.254673 | ||||||||
\(801\) | 8.01389 | 0.283157 | ||||||||
\(802\) | −10.4595 | −0.369338 | ||||||||
\(803\) | 1.53009 | 0.0539958 | ||||||||
\(804\) | 3.24462 | 0.114429 | ||||||||
\(805\) | 68.0503 | 2.39846 | ||||||||
\(806\) | 46.7229 | 1.64575 | ||||||||
\(807\) | −29.6760 | −1.04465 | ||||||||
\(808\) | 28.4025 | 0.999197 | ||||||||
\(809\) | −37.9979 | −1.33594 | −0.667968 | − | 0.744190i | \(-0.732836\pi\) | ||||
−0.667968 | + | 0.744190i | \(0.732836\pi\) | |||||||
\(810\) | −4.42094 | −0.155336 | ||||||||
\(811\) | −54.3212 | −1.90748 | −0.953738 | − | 0.300641i | \(-0.902800\pi\) | ||||
−0.953738 | + | 0.300641i | \(0.902800\pi\) | |||||||
\(812\) | −13.1591 | −0.461795 | ||||||||
\(813\) | −13.8327 | −0.485134 | ||||||||
\(814\) | −18.6433 | −0.653447 | ||||||||
\(815\) | −48.9872 | −1.71595 | ||||||||
\(816\) | −8.42304 | −0.294866 | ||||||||
\(817\) | −14.3037 | −0.500422 | ||||||||
\(818\) | 66.3920 | 2.32134 | ||||||||
\(819\) | −18.7357 | −0.654677 | ||||||||
\(820\) | 21.0409 | 0.734779 | ||||||||
\(821\) | 0.336067 | 0.0117288 | 0.00586440 | − | 0.999983i | \(-0.498133\pi\) | ||||
0.00586440 | + | 0.999983i | \(0.498133\pi\) | |||||||
\(822\) | −3.26742 | −0.113964 | ||||||||
\(823\) | −26.5549 | −0.925646 | −0.462823 | − | 0.886451i | \(-0.653163\pi\) | ||||
−0.462823 | + | 0.886451i | \(0.653163\pi\) | |||||||
\(824\) | −20.9988 | −0.731527 | ||||||||
\(825\) | 1.26422 | 0.0440144 | ||||||||
\(826\) | −10.4702 | −0.364305 | ||||||||
\(827\) | 28.7699 | 1.00043 | 0.500214 | − | 0.865902i | \(-0.333255\pi\) | ||||
0.500214 | + | 0.865902i | \(0.333255\pi\) | |||||||
\(828\) | 7.44732 | 0.258812 | ||||||||
\(829\) | 36.5733 | 1.27024 | 0.635122 | − | 0.772412i | \(-0.280950\pi\) | ||||
0.635122 | + | 0.772412i | \(0.280950\pi\) | |||||||
\(830\) | −20.7320 | −0.719618 | ||||||||
\(831\) | −10.7545 | −0.373069 | ||||||||
\(832\) | −0.426976 | −0.0148027 | ||||||||
\(833\) | −16.4242 | −0.569064 | ||||||||
\(834\) | 3.70637 | 0.128341 | ||||||||
\(835\) | 3.04047 | 0.105220 | ||||||||
\(836\) | −2.84841 | −0.0985143 | ||||||||
\(837\) | −5.77320 | −0.199551 | ||||||||
\(838\) | 4.41080 | 0.152369 | ||||||||
\(839\) | −36.5200 | −1.26081 | −0.630405 | − | 0.776267i | \(-0.717111\pi\) | ||||
−0.630405 | + | 0.776267i | \(0.717111\pi\) | |||||||
\(840\) | 15.9077 | 0.548867 | ||||||||
\(841\) | −20.7453 | −0.715356 | ||||||||
\(842\) | −7.81217 | −0.269225 | ||||||||
\(843\) | −18.7346 | −0.645255 | ||||||||
\(844\) | −0.699219 | −0.0240681 | ||||||||
\(845\) | −20.0040 | −0.688159 | ||||||||
\(846\) | 14.5560 | 0.500445 | ||||||||
\(847\) | −4.08919 | −0.140506 | ||||||||
\(848\) | 33.5902 | 1.15349 | ||||||||
\(849\) | −24.5140 | −0.841318 | ||||||||
\(850\) | −3.77273 | −0.129404 | ||||||||
\(851\) | 70.1781 | 2.40567 | ||||||||
\(852\) | 4.08446 | 0.139931 | ||||||||
\(853\) | −30.1362 | −1.03184 | −0.515922 | − | 0.856635i | \(-0.672551\pi\) | ||||
−0.515922 | + | 0.856635i | \(0.672551\pi\) | |||||||
\(854\) | −7.22301 | −0.247166 | ||||||||
\(855\) | −6.36497 | −0.217677 | ||||||||
\(856\) | −9.72341 | −0.332339 | ||||||||
\(857\) | −31.6160 | −1.07998 | −0.539991 | − | 0.841671i | \(-0.681572\pi\) | ||||
−0.539991 | + | 0.841671i | \(0.681572\pi\) | |||||||
\(858\) | 8.09307 | 0.276293 | ||||||||
\(859\) | 44.5621 | 1.52044 | 0.760219 | − | 0.649667i | \(-0.225092\pi\) | ||||
0.760219 | + | 0.649667i | \(0.225092\pi\) | |||||||
\(860\) | 15.7673 | 0.537661 | ||||||||
\(861\) | −30.6921 | −1.04598 | ||||||||
\(862\) | −17.4529 | −0.594449 | ||||||||
\(863\) | 15.9335 | 0.542382 | 0.271191 | − | 0.962526i | \(-0.412583\pi\) | ||||
0.271191 | + | 0.962526i | \(0.412583\pi\) | |||||||
\(864\) | 5.69777 | 0.193842 | ||||||||
\(865\) | 40.5690 | 1.37939 | ||||||||
\(866\) | −68.8989 | −2.34128 | ||||||||
\(867\) | 14.1457 | 0.480412 | ||||||||
\(868\) | −26.4419 | −0.897498 | ||||||||
\(869\) | −6.59373 | −0.223677 | ||||||||
\(870\) | 12.7018 | 0.430631 | ||||||||
\(871\) | −13.2726 | −0.449726 | ||||||||
\(872\) | −15.2447 | −0.516250 | ||||||||
\(873\) | −8.48718 | −0.287248 | ||||||||
\(874\) | 29.8678 | 1.01029 | ||||||||
\(875\) | −38.2342 | −1.29255 | ||||||||
\(876\) | 1.71379 | 0.0579036 | ||||||||
\(877\) | −19.4169 | −0.655662 | −0.327831 | − | 0.944736i | \(-0.606318\pi\) | ||||
−0.327831 | + | 0.944736i | \(0.606318\pi\) | |||||||
\(878\) | 36.4516 | 1.23018 | ||||||||
\(879\) | −22.3094 | −0.752478 | ||||||||
\(880\) | −12.4781 | −0.420638 | ||||||||
\(881\) | −37.0820 | −1.24932 | −0.624661 | − | 0.780896i | \(-0.714763\pi\) | ||||
−0.624661 | + | 0.780896i | \(0.714763\pi\) | |||||||
\(882\) | 17.1716 | 0.578200 | ||||||||
\(883\) | 9.54777 | 0.321308 | 0.160654 | − | 0.987011i | \(-0.448640\pi\) | ||||
0.160654 | + | 0.987011i | \(0.448640\pi\) | |||||||
\(884\) | −8.67012 | −0.291608 | ||||||||
\(885\) | 3.62802 | 0.121955 | ||||||||
\(886\) | −56.8251 | −1.90908 | ||||||||
\(887\) | 34.6540 | 1.16357 | 0.581783 | − | 0.813344i | \(-0.302355\pi\) | ||||
0.581783 | + | 0.813344i | \(0.302355\pi\) | |||||||
\(888\) | 16.4051 | 0.550518 | ||||||||
\(889\) | −36.6255 | −1.22838 | ||||||||
\(890\) | −35.4289 | −1.18758 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 1.23394 | 0.0413155 | ||||||||
\(893\) | 20.9567 | 0.701289 | ||||||||
\(894\) | 18.8310 | 0.629804 | ||||||||
\(895\) | 1.15263 | 0.0385282 | ||||||||
\(896\) | −45.9254 | −1.53426 | ||||||||
\(897\) | −30.4644 | −1.01718 | ||||||||
\(898\) | −10.3462 | −0.345256 | ||||||||
\(899\) | 16.5870 | 0.553206 | ||||||||
\(900\) | 1.41600 | 0.0471998 | ||||||||
\(901\) | 11.3828 | 0.379216 | ||||||||
\(902\) | 13.2578 | 0.441436 | ||||||||
\(903\) | −22.9997 | −0.765381 | ||||||||
\(904\) | −6.68643 | −0.222387 | ||||||||
\(905\) | −52.8371 | −1.75636 | ||||||||
\(906\) | 28.1847 | 0.936374 | ||||||||
\(907\) | 39.5498 | 1.31323 | 0.656614 | − | 0.754227i | \(-0.271988\pi\) | ||||
0.656614 | + | 0.754227i | \(0.271988\pi\) | |||||||
\(908\) | 27.2908 | 0.905677 | ||||||||
\(909\) | −18.2735 | −0.606092 | ||||||||
\(910\) | 82.8293 | 2.74576 | ||||||||
\(911\) | 57.7089 | 1.91198 | 0.955991 | − | 0.293395i | \(-0.0947851\pi\) | ||||
0.955991 | + | 0.293395i | \(0.0947851\pi\) | |||||||
\(912\) | 12.6788 | 0.419838 | ||||||||
\(913\) | −4.68950 | −0.155200 | ||||||||
\(914\) | −2.97137 | −0.0982842 | ||||||||
\(915\) | 2.50284 | 0.0827414 | ||||||||
\(916\) | −11.2747 | −0.372527 | ||||||||
\(917\) | −68.2610 | −2.25418 | ||||||||
\(918\) | 2.98424 | 0.0984947 | ||||||||
\(919\) | −36.0033 | −1.18764 | −0.593820 | − | 0.804598i | \(-0.702381\pi\) | ||||
−0.593820 | + | 0.804598i | \(0.702381\pi\) | |||||||
\(920\) | 25.8660 | 0.852777 | ||||||||
\(921\) | −9.79575 | −0.322781 | ||||||||
\(922\) | −11.0022 | −0.362340 | ||||||||
\(923\) | −16.7081 | −0.549954 | ||||||||
\(924\) | −4.58012 | −0.150675 | ||||||||
\(925\) | 13.3433 | 0.438725 | ||||||||
\(926\) | 35.3685 | 1.16228 | ||||||||
\(927\) | 13.5101 | 0.443729 | ||||||||
\(928\) | −16.3702 | −0.537380 | ||||||||
\(929\) | −5.93686 | −0.194782 | −0.0973910 | − | 0.995246i | \(-0.531050\pi\) | ||||
−0.0973910 | + | 0.995246i | \(0.531050\pi\) | |||||||
\(930\) | 25.5230 | 0.836931 | ||||||||
\(931\) | 24.7226 | 0.810249 | ||||||||
\(932\) | −2.95937 | −0.0969375 | ||||||||
\(933\) | −21.0159 | −0.688031 | ||||||||
\(934\) | 19.7903 | 0.647559 | ||||||||
\(935\) | −4.22850 | −0.138287 | ||||||||
\(936\) | −7.12145 | −0.232772 | ||||||||
\(937\) | 31.8437 | 1.04029 | 0.520145 | − | 0.854078i | \(-0.325878\pi\) | ||||
0.520145 | + | 0.854078i | \(0.325878\pi\) | |||||||
\(938\) | 20.9239 | 0.683190 | ||||||||
\(939\) | 11.8868 | 0.387910 | ||||||||
\(940\) | −23.1012 | −0.753477 | ||||||||
\(941\) | 39.0802 | 1.27398 | 0.636989 | − | 0.770873i | \(-0.280180\pi\) | ||||
0.636989 | + | 0.770873i | \(0.280180\pi\) | |||||||
\(942\) | 22.2563 | 0.725148 | ||||||||
\(943\) | −49.9057 | −1.62515 | ||||||||
\(944\) | −7.22691 | −0.235216 | ||||||||
\(945\) | −10.2346 | −0.332931 | ||||||||
\(946\) | 9.93495 | 0.323013 | ||||||||
\(947\) | 24.9953 | 0.812237 | 0.406119 | − | 0.913820i | \(-0.366882\pi\) | ||||
0.406119 | + | 0.913820i | \(0.366882\pi\) | |||||||
\(948\) | −7.38535 | −0.239865 | ||||||||
\(949\) | −7.01051 | −0.227571 | ||||||||
\(950\) | 5.67892 | 0.184249 | ||||||||
\(951\) | 20.3584 | 0.660165 | ||||||||
\(952\) | −10.7381 | −0.348023 | ||||||||
\(953\) | 20.1451 | 0.652564 | 0.326282 | − | 0.945273i | \(-0.394204\pi\) | ||||
0.326282 | + | 0.945273i | \(0.394204\pi\) | |||||||
\(954\) | −11.9008 | −0.385304 | ||||||||
\(955\) | −51.8388 | −1.67747 | ||||||||
\(956\) | −26.9040 | −0.870138 | ||||||||
\(957\) | 2.87310 | 0.0928740 | ||||||||
\(958\) | −65.1361 | −2.10445 | ||||||||
\(959\) | −7.56415 | −0.244259 | ||||||||
\(960\) | −0.233241 | −0.00752781 | ||||||||
\(961\) | 2.32984 | 0.0751562 | ||||||||
\(962\) | 85.4191 | 2.75402 | ||||||||
\(963\) | 6.25580 | 0.201590 | ||||||||
\(964\) | 22.7369 | 0.732307 | ||||||||
\(965\) | −10.9323 | −0.351924 | ||||||||
\(966\) | 48.0262 | 1.54522 | ||||||||
\(967\) | −19.5208 | −0.627746 | −0.313873 | − | 0.949465i | \(-0.601627\pi\) | ||||
−0.313873 | + | 0.949465i | \(0.601627\pi\) | |||||||
\(968\) | −1.55430 | −0.0499572 | ||||||||
\(969\) | 4.29651 | 0.138024 | ||||||||
\(970\) | 37.5213 | 1.20474 | ||||||||
\(971\) | −23.1778 | −0.743811 | −0.371905 | − | 0.928271i | \(-0.621295\pi\) | ||||
−0.371905 | + | 0.928271i | \(0.621295\pi\) | |||||||
\(972\) | −1.12006 | −0.0359258 | ||||||||
\(973\) | 8.58034 | 0.275073 | ||||||||
\(974\) | −48.1071 | −1.54145 | ||||||||
\(975\) | −5.79234 | −0.185503 | ||||||||
\(976\) | −4.98559 | −0.159585 | ||||||||
\(977\) | 25.0807 | 0.802401 | 0.401201 | − | 0.915990i | \(-0.368593\pi\) | ||||
0.401201 | + | 0.915990i | \(0.368593\pi\) | |||||||
\(978\) | −34.5725 | −1.10551 | ||||||||
\(979\) | −8.01389 | −0.256125 | ||||||||
\(980\) | −27.2524 | −0.870545 | ||||||||
\(981\) | 9.80803 | 0.313146 | ||||||||
\(982\) | −17.5843 | −0.561138 | ||||||||
\(983\) | 23.1549 | 0.738527 | 0.369263 | − | 0.929325i | \(-0.379610\pi\) | ||||
0.369263 | + | 0.929325i | \(0.379610\pi\) | |||||||
\(984\) | −11.6661 | −0.371902 | ||||||||
\(985\) | 37.3025 | 1.18856 | ||||||||
\(986\) | −8.57402 | −0.273052 | ||||||||
\(987\) | 33.6975 | 1.07260 | ||||||||
\(988\) | 13.0507 | 0.415199 | ||||||||
\(989\) | −37.3977 | −1.18918 | ||||||||
\(990\) | 4.42094 | 0.140507 | ||||||||
\(991\) | −20.3916 | −0.647762 | −0.323881 | − | 0.946098i | \(-0.604988\pi\) | ||||
−0.323881 | + | 0.946098i | \(0.604988\pi\) | |||||||
\(992\) | −32.8944 | −1.04440 | ||||||||
\(993\) | 18.5600 | 0.588983 | ||||||||
\(994\) | 26.3398 | 0.835449 | ||||||||
\(995\) | −30.8226 | −0.977142 | ||||||||
\(996\) | −5.25250 | −0.166432 | ||||||||
\(997\) | −37.9430 | −1.20167 | −0.600834 | − | 0.799374i | \(-0.705165\pi\) | ||||
−0.600834 | + | 0.799374i | \(0.705165\pi\) | |||||||
\(998\) | −43.9101 | −1.38995 | ||||||||
\(999\) | −10.5546 | −0.333933 |
(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 | 2013.2.a.h.1.12 | ✓ | 14 | |
3.2 | odd | 2 | 6039.2.a.j.1.3 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.2.a.h.1.12 | ✓ | 14 | 1.1 | even | 1 | trivial | |
6039.2.a.j.1.3 | 14 | 3.2 | odd | 2 |