Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, 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("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.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: | \(64.0000972201\) |
Analytic rank: | \(1\) |
Dimension: | \(49\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.80610 | −1.27711 | −0.638554 | − | 0.769577i | \(-0.720467\pi\) | ||||
−0.638554 | + | 0.769577i | \(0.720467\pi\) | |||||||
\(3\) | 2.35882 | 1.36186 | 0.680932 | − | 0.732346i | \(-0.261575\pi\) | ||||
0.680932 | + | 0.732346i | \(0.261575\pi\) | |||||||
\(4\) | 1.26200 | 0.631002 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −4.26027 | −1.73925 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.33289 | 0.471249 | ||||||||
\(9\) | 2.56402 | 0.854675 | ||||||||
\(10\) | 1.80610 | 0.571140 | ||||||||
\(11\) | −2.69801 | −0.813481 | −0.406741 | − | 0.913544i | \(-0.633335\pi\) | ||||
−0.406741 | + | 0.913544i | \(0.633335\pi\) | |||||||
\(12\) | 2.97684 | 0.859340 | ||||||||
\(13\) | 3.47935 | 0.964997 | 0.482498 | − | 0.875897i | \(-0.339729\pi\) | ||||
0.482498 | + | 0.875897i | \(0.339729\pi\) | |||||||
\(14\) | 1.80610 | 0.482701 | ||||||||
\(15\) | −2.35882 | −0.609044 | ||||||||
\(16\) | −4.93135 | −1.23284 | ||||||||
\(17\) | 0.778691 | 0.188860 | 0.0944302 | − | 0.995531i | \(-0.469897\pi\) | ||||
0.0944302 | + | 0.995531i | \(0.469897\pi\) | |||||||
\(18\) | −4.63089 | −1.09151 | ||||||||
\(19\) | −3.47577 | −0.797397 | −0.398698 | − | 0.917082i | \(-0.630538\pi\) | ||||
−0.398698 | + | 0.917082i | \(0.630538\pi\) | |||||||
\(20\) | −1.26200 | −0.282193 | ||||||||
\(21\) | −2.35882 | −0.514736 | ||||||||
\(22\) | 4.87288 | 1.03890 | ||||||||
\(23\) | −3.41103 | −0.711248 | −0.355624 | − | 0.934629i | \(-0.615732\pi\) | ||||
−0.355624 | + | 0.934629i | \(0.615732\pi\) | |||||||
\(24\) | 3.14406 | 0.641778 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −6.28405 | −1.23240 | ||||||||
\(27\) | −1.02839 | −0.197913 | ||||||||
\(28\) | −1.26200 | −0.238496 | ||||||||
\(29\) | 1.67574 | 0.311176 | 0.155588 | − | 0.987822i | \(-0.450273\pi\) | ||||
0.155588 | + | 0.987822i | \(0.450273\pi\) | |||||||
\(30\) | 4.26027 | 0.777815 | ||||||||
\(31\) | 2.44606 | 0.439326 | 0.219663 | − | 0.975576i | \(-0.429504\pi\) | ||||
0.219663 | + | 0.975576i | \(0.429504\pi\) | |||||||
\(32\) | 6.24074 | 1.10322 | ||||||||
\(33\) | −6.36412 | −1.10785 | ||||||||
\(34\) | −1.40640 | −0.241195 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 3.23581 | 0.539302 | ||||||||
\(37\) | −6.83263 | −1.12328 | −0.561639 | − | 0.827383i | \(-0.689829\pi\) | ||||
−0.561639 | + | 0.827383i | \(0.689829\pi\) | |||||||
\(38\) | 6.27760 | 1.01836 | ||||||||
\(39\) | 8.20714 | 1.31419 | ||||||||
\(40\) | −1.33289 | −0.210749 | ||||||||
\(41\) | 2.85499 | 0.445875 | 0.222937 | − | 0.974833i | \(-0.428435\pi\) | ||||
0.222937 | + | 0.974833i | \(0.428435\pi\) | |||||||
\(42\) | 4.26027 | 0.657373 | ||||||||
\(43\) | 8.30335 | 1.26625 | 0.633125 | − | 0.774050i | \(-0.281772\pi\) | ||||
0.633125 | + | 0.774050i | \(0.281772\pi\) | |||||||
\(44\) | −3.40490 | −0.513309 | ||||||||
\(45\) | −2.56402 | −0.382222 | ||||||||
\(46\) | 6.16066 | 0.908340 | ||||||||
\(47\) | 8.26335 | 1.20533 | 0.602667 | − | 0.797993i | \(-0.294105\pi\) | ||||
0.602667 | + | 0.797993i | \(0.294105\pi\) | |||||||
\(48\) | −11.6322 | −1.67896 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.80610 | −0.255421 | ||||||||
\(51\) | 1.83679 | 0.257202 | ||||||||
\(52\) | 4.39095 | 0.608915 | ||||||||
\(53\) | 8.82198 | 1.21179 | 0.605896 | − | 0.795544i | \(-0.292815\pi\) | ||||
0.605896 | + | 0.795544i | \(0.292815\pi\) | |||||||
\(54\) | 1.85737 | 0.252756 | ||||||||
\(55\) | 2.69801 | 0.363800 | ||||||||
\(56\) | −1.33289 | −0.178116 | ||||||||
\(57\) | −8.19872 | −1.08595 | ||||||||
\(58\) | −3.02655 | −0.397406 | ||||||||
\(59\) | 4.26791 | 0.555635 | 0.277817 | − | 0.960634i | \(-0.410389\pi\) | ||||
0.277817 | + | 0.960634i | \(0.410389\pi\) | |||||||
\(60\) | −2.97684 | −0.384308 | ||||||||
\(61\) | 0.270428 | 0.0346247 | 0.0173124 | − | 0.999850i | \(-0.494489\pi\) | ||||
0.0173124 | + | 0.999850i | \(0.494489\pi\) | |||||||
\(62\) | −4.41784 | −0.561066 | ||||||||
\(63\) | −2.56402 | −0.323037 | ||||||||
\(64\) | −1.40870 | −0.176088 | ||||||||
\(65\) | −3.47935 | −0.431560 | ||||||||
\(66\) | 11.4943 | 1.41484 | ||||||||
\(67\) | −8.19429 | −1.00109 | −0.500546 | − | 0.865710i | \(-0.666867\pi\) | ||||
−0.500546 | + | 0.865710i | \(0.666867\pi\) | |||||||
\(68\) | 0.982712 | 0.119171 | ||||||||
\(69\) | −8.04599 | −0.968623 | ||||||||
\(70\) | −1.80610 | −0.215870 | ||||||||
\(71\) | −13.5386 | −1.60673 | −0.803366 | − | 0.595485i | \(-0.796960\pi\) | ||||
−0.803366 | + | 0.595485i | \(0.796960\pi\) | |||||||
\(72\) | 3.41757 | 0.402765 | ||||||||
\(73\) | 7.03308 | 0.823159 | 0.411580 | − | 0.911374i | \(-0.364977\pi\) | ||||
0.411580 | + | 0.911374i | \(0.364977\pi\) | |||||||
\(74\) | 12.3404 | 1.43455 | ||||||||
\(75\) | 2.35882 | 0.272373 | ||||||||
\(76\) | −4.38644 | −0.503159 | ||||||||
\(77\) | 2.69801 | 0.307467 | ||||||||
\(78\) | −14.8229 | −1.67837 | ||||||||
\(79\) | −0.794791 | −0.0894210 | −0.0447105 | − | 0.999000i | \(-0.514237\pi\) | ||||
−0.0447105 | + | 0.999000i | \(0.514237\pi\) | |||||||
\(80\) | 4.93135 | 0.551342 | ||||||||
\(81\) | −10.1179 | −1.12421 | ||||||||
\(82\) | −5.15640 | −0.569429 | ||||||||
\(83\) | −11.2610 | −1.23605 | −0.618026 | − | 0.786158i | \(-0.712067\pi\) | ||||
−0.618026 | + | 0.786158i | \(0.712067\pi\) | |||||||
\(84\) | −2.97684 | −0.324800 | ||||||||
\(85\) | −0.778691 | −0.0844609 | ||||||||
\(86\) | −14.9967 | −1.61714 | ||||||||
\(87\) | 3.95276 | 0.423780 | ||||||||
\(88\) | −3.59617 | −0.383353 | ||||||||
\(89\) | 3.24583 | 0.344058 | 0.172029 | − | 0.985092i | \(-0.444968\pi\) | ||||
0.172029 | + | 0.985092i | \(0.444968\pi\) | |||||||
\(90\) | 4.63089 | 0.488139 | ||||||||
\(91\) | −3.47935 | −0.364734 | ||||||||
\(92\) | −4.30473 | −0.448799 | ||||||||
\(93\) | 5.76982 | 0.598302 | ||||||||
\(94\) | −14.9245 | −1.53934 | ||||||||
\(95\) | 3.47577 | 0.356607 | ||||||||
\(96\) | 14.7208 | 1.50243 | ||||||||
\(97\) | −9.06141 | −0.920047 | −0.460023 | − | 0.887907i | \(-0.652159\pi\) | ||||
−0.460023 | + | 0.887907i | \(0.652159\pi\) | |||||||
\(98\) | −1.80610 | −0.182444 | ||||||||
\(99\) | −6.91777 | −0.695262 | ||||||||
\(100\) | 1.26200 | 0.126200 | ||||||||
\(101\) | −17.5198 | −1.74328 | −0.871642 | − | 0.490144i | \(-0.836944\pi\) | ||||
−0.871642 | + | 0.490144i | \(0.836944\pi\) | |||||||
\(102\) | −3.31743 | −0.328475 | ||||||||
\(103\) | 12.4744 | 1.22914 | 0.614570 | − | 0.788862i | \(-0.289330\pi\) | ||||
0.614570 | + | 0.788862i | \(0.289330\pi\) | |||||||
\(104\) | 4.63760 | 0.454754 | ||||||||
\(105\) | 2.35882 | 0.230197 | ||||||||
\(106\) | −15.9334 | −1.54759 | ||||||||
\(107\) | 6.21181 | 0.600518 | 0.300259 | − | 0.953858i | \(-0.402927\pi\) | ||||
0.300259 | + | 0.953858i | \(0.402927\pi\) | |||||||
\(108\) | −1.29783 | −0.124884 | ||||||||
\(109\) | −9.79103 | −0.937810 | −0.468905 | − | 0.883249i | \(-0.655351\pi\) | ||||
−0.468905 | + | 0.883249i | \(0.655351\pi\) | |||||||
\(110\) | −4.87288 | −0.464611 | ||||||||
\(111\) | −16.1169 | −1.52975 | ||||||||
\(112\) | 4.93135 | 0.465969 | ||||||||
\(113\) | 5.38244 | 0.506337 | 0.253169 | − | 0.967422i | \(-0.418527\pi\) | ||||
0.253169 | + | 0.967422i | \(0.418527\pi\) | |||||||
\(114\) | 14.8077 | 1.38687 | ||||||||
\(115\) | 3.41103 | 0.318080 | ||||||||
\(116\) | 2.11479 | 0.196353 | ||||||||
\(117\) | 8.92113 | 0.824758 | ||||||||
\(118\) | −7.70829 | −0.709605 | ||||||||
\(119\) | −0.778691 | −0.0713825 | ||||||||
\(120\) | −3.14406 | −0.287012 | ||||||||
\(121\) | −3.72073 | −0.338248 | ||||||||
\(122\) | −0.488420 | −0.0442195 | ||||||||
\(123\) | 6.73440 | 0.607221 | ||||||||
\(124\) | 3.08694 | 0.277216 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 4.63089 | 0.412552 | ||||||||
\(127\) | −0.808924 | −0.0717804 | −0.0358902 | − | 0.999356i | \(-0.511427\pi\) | ||||
−0.0358902 | + | 0.999356i | \(0.511427\pi\) | |||||||
\(128\) | −9.93721 | −0.878334 | ||||||||
\(129\) | 19.5861 | 1.72446 | ||||||||
\(130\) | 6.28405 | 0.551148 | ||||||||
\(131\) | −14.3625 | −1.25486 | −0.627428 | − | 0.778674i | \(-0.715892\pi\) | ||||
−0.627428 | + | 0.778674i | \(0.715892\pi\) | |||||||
\(132\) | −8.03155 | −0.699057 | ||||||||
\(133\) | 3.47577 | 0.301388 | ||||||||
\(134\) | 14.7997 | 1.27850 | ||||||||
\(135\) | 1.02839 | 0.0885095 | ||||||||
\(136\) | 1.03791 | 0.0890003 | ||||||||
\(137\) | 4.04262 | 0.345384 | 0.172692 | − | 0.984976i | \(-0.444753\pi\) | ||||
0.172692 | + | 0.984976i | \(0.444753\pi\) | |||||||
\(138\) | 14.5319 | 1.23704 | ||||||||
\(139\) | −21.5514 | −1.82797 | −0.913984 | − | 0.405750i | \(-0.867010\pi\) | ||||
−0.913984 | + | 0.405750i | \(0.867010\pi\) | |||||||
\(140\) | 1.26200 | 0.106659 | ||||||||
\(141\) | 19.4918 | 1.64150 | ||||||||
\(142\) | 24.4520 | 2.05197 | ||||||||
\(143\) | −9.38731 | −0.785007 | ||||||||
\(144\) | −12.6441 | −1.05368 | ||||||||
\(145\) | −1.67574 | −0.139162 | ||||||||
\(146\) | −12.7025 | −1.05126 | ||||||||
\(147\) | 2.35882 | 0.194552 | ||||||||
\(148\) | −8.62281 | −0.708791 | ||||||||
\(149\) | −8.47320 | −0.694152 | −0.347076 | − | 0.937837i | \(-0.612825\pi\) | ||||
−0.347076 | + | 0.937837i | \(0.612825\pi\) | |||||||
\(150\) | −4.26027 | −0.347849 | ||||||||
\(151\) | −16.5614 | −1.34774 | −0.673872 | − | 0.738848i | \(-0.735370\pi\) | ||||
−0.673872 | + | 0.738848i | \(0.735370\pi\) | |||||||
\(152\) | −4.63284 | −0.375773 | ||||||||
\(153\) | 1.99658 | 0.161414 | ||||||||
\(154\) | −4.87288 | −0.392668 | ||||||||
\(155\) | −2.44606 | −0.196472 | ||||||||
\(156\) | 10.3575 | 0.829260 | ||||||||
\(157\) | −3.08498 | −0.246208 | −0.123104 | − | 0.992394i | \(-0.539285\pi\) | ||||
−0.123104 | + | 0.992394i | \(0.539285\pi\) | |||||||
\(158\) | 1.43547 | 0.114200 | ||||||||
\(159\) | 20.8095 | 1.65030 | ||||||||
\(160\) | −6.24074 | −0.493374 | ||||||||
\(161\) | 3.41103 | 0.268826 | ||||||||
\(162\) | 18.2739 | 1.43573 | ||||||||
\(163\) | −1.59303 | −0.124775 | −0.0623877 | − | 0.998052i | \(-0.519872\pi\) | ||||
−0.0623877 | + | 0.998052i | \(0.519872\pi\) | |||||||
\(164\) | 3.60301 | 0.281348 | ||||||||
\(165\) | 6.36412 | 0.495446 | ||||||||
\(166\) | 20.3385 | 1.57857 | ||||||||
\(167\) | 9.79861 | 0.758239 | 0.379120 | − | 0.925348i | \(-0.376227\pi\) | ||||
0.379120 | + | 0.925348i | \(0.376227\pi\) | |||||||
\(168\) | −3.14406 | −0.242569 | ||||||||
\(169\) | −0.894157 | −0.0687813 | ||||||||
\(170\) | 1.40640 | 0.107866 | ||||||||
\(171\) | −8.91197 | −0.681515 | ||||||||
\(172\) | 10.4789 | 0.799006 | ||||||||
\(173\) | −3.00346 | −0.228349 | −0.114175 | − | 0.993461i | \(-0.536422\pi\) | ||||
−0.114175 | + | 0.993461i | \(0.536422\pi\) | |||||||
\(174\) | −7.13908 | −0.541213 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 13.3048 | 1.00289 | ||||||||
\(177\) | 10.0672 | 0.756700 | ||||||||
\(178\) | −5.86231 | −0.439399 | ||||||||
\(179\) | 16.2014 | 1.21095 | 0.605473 | − | 0.795866i | \(-0.292984\pi\) | ||||
0.605473 | + | 0.795866i | \(0.292984\pi\) | |||||||
\(180\) | −3.23581 | −0.241183 | ||||||||
\(181\) | −7.32365 | −0.544362 | −0.272181 | − | 0.962246i | \(-0.587745\pi\) | ||||
−0.272181 | + | 0.962246i | \(0.587745\pi\) | |||||||
\(182\) | 6.28405 | 0.465805 | ||||||||
\(183\) | 0.637890 | 0.0471542 | ||||||||
\(184\) | −4.54654 | −0.335175 | ||||||||
\(185\) | 6.83263 | 0.502345 | ||||||||
\(186\) | −10.4209 | −0.764096 | ||||||||
\(187\) | −2.10092 | −0.153634 | ||||||||
\(188\) | 10.4284 | 0.760569 | ||||||||
\(189\) | 1.02839 | 0.0748041 | ||||||||
\(190\) | −6.27760 | −0.455425 | ||||||||
\(191\) | −20.0713 | −1.45231 | −0.726155 | − | 0.687531i | \(-0.758694\pi\) | ||||
−0.726155 | + | 0.687531i | \(0.758694\pi\) | |||||||
\(192\) | −3.32288 | −0.239808 | ||||||||
\(193\) | −0.770165 | −0.0554377 | −0.0277188 | − | 0.999616i | \(-0.508824\pi\) | ||||
−0.0277188 | + | 0.999616i | \(0.508824\pi\) | |||||||
\(194\) | 16.3658 | 1.17500 | ||||||||
\(195\) | −8.20714 | −0.587726 | ||||||||
\(196\) | 1.26200 | 0.0901432 | ||||||||
\(197\) | 7.98403 | 0.568838 | 0.284419 | − | 0.958700i | \(-0.408199\pi\) | ||||
0.284419 | + | 0.958700i | \(0.408199\pi\) | |||||||
\(198\) | 12.4942 | 0.887924 | ||||||||
\(199\) | 1.63400 | 0.115831 | 0.0579157 | − | 0.998321i | \(-0.481555\pi\) | ||||
0.0579157 | + | 0.998321i | \(0.481555\pi\) | |||||||
\(200\) | 1.33289 | 0.0942499 | ||||||||
\(201\) | −19.3289 | −1.36335 | ||||||||
\(202\) | 31.6425 | 2.22636 | ||||||||
\(203\) | −1.67574 | −0.117614 | ||||||||
\(204\) | 2.31804 | 0.162295 | ||||||||
\(205\) | −2.85499 | −0.199401 | ||||||||
\(206\) | −22.5301 | −1.56974 | ||||||||
\(207\) | −8.74595 | −0.607886 | ||||||||
\(208\) | −17.1579 | −1.18969 | ||||||||
\(209\) | 9.37767 | 0.648667 | ||||||||
\(210\) | −4.26027 | −0.293986 | ||||||||
\(211\) | 10.6926 | 0.736109 | 0.368055 | − | 0.929804i | \(-0.380024\pi\) | ||||
0.368055 | + | 0.929804i | \(0.380024\pi\) | |||||||
\(212\) | 11.1334 | 0.764644 | ||||||||
\(213\) | −31.9350 | −2.18815 | ||||||||
\(214\) | −11.2192 | −0.766926 | ||||||||
\(215\) | −8.30335 | −0.566284 | ||||||||
\(216\) | −1.37073 | −0.0932665 | ||||||||
\(217\) | −2.44606 | −0.166050 | ||||||||
\(218\) | 17.6836 | 1.19768 | ||||||||
\(219\) | 16.5897 | 1.12103 | ||||||||
\(220\) | 3.40490 | 0.229559 | ||||||||
\(221\) | 2.70933 | 0.182250 | ||||||||
\(222\) | 29.1088 | 1.95366 | ||||||||
\(223\) | −9.65827 | −0.646766 | −0.323383 | − | 0.946268i | \(-0.604820\pi\) | ||||
−0.323383 | + | 0.946268i | \(0.604820\pi\) | |||||||
\(224\) | −6.24074 | −0.416977 | ||||||||
\(225\) | 2.56402 | 0.170935 | ||||||||
\(226\) | −9.72123 | −0.646647 | ||||||||
\(227\) | 13.7845 | 0.914912 | 0.457456 | − | 0.889232i | \(-0.348761\pi\) | ||||
0.457456 | + | 0.889232i | \(0.348761\pi\) | |||||||
\(228\) | −10.3468 | −0.685235 | ||||||||
\(229\) | −1.00000 | −0.0660819 | ||||||||
\(230\) | −6.16066 | −0.406222 | ||||||||
\(231\) | 6.36412 | 0.418728 | ||||||||
\(232\) | 2.23358 | 0.146642 | ||||||||
\(233\) | −23.3690 | −1.53095 | −0.765476 | − | 0.643465i | \(-0.777496\pi\) | ||||
−0.765476 | + | 0.643465i | \(0.777496\pi\) | |||||||
\(234\) | −16.1125 | −1.05330 | ||||||||
\(235\) | −8.26335 | −0.539042 | ||||||||
\(236\) | 5.38613 | 0.350607 | ||||||||
\(237\) | −1.87477 | −0.121779 | ||||||||
\(238\) | 1.40640 | 0.0911631 | ||||||||
\(239\) | −7.31814 | −0.473371 | −0.236686 | − | 0.971586i | \(-0.576061\pi\) | ||||
−0.236686 | + | 0.971586i | \(0.576061\pi\) | |||||||
\(240\) | 11.6322 | 0.750853 | ||||||||
\(241\) | 27.2092 | 1.75270 | 0.876351 | − | 0.481673i | \(-0.159971\pi\) | ||||
0.876351 | + | 0.481673i | \(0.159971\pi\) | |||||||
\(242\) | 6.72002 | 0.431979 | ||||||||
\(243\) | −20.7810 | −1.33310 | ||||||||
\(244\) | 0.341281 | 0.0218483 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −12.1630 | −0.775486 | ||||||||
\(247\) | −12.0934 | −0.769485 | ||||||||
\(248\) | 3.26034 | 0.207032 | ||||||||
\(249\) | −26.5626 | −1.68333 | ||||||||
\(250\) | 1.80610 | 0.114228 | ||||||||
\(251\) | 30.1833 | 1.90515 | 0.952575 | − | 0.304303i | \(-0.0984234\pi\) | ||||
0.952575 | + | 0.304303i | \(0.0984234\pi\) | |||||||
\(252\) | −3.23581 | −0.203837 | ||||||||
\(253\) | 9.20299 | 0.578587 | ||||||||
\(254\) | 1.46100 | 0.0916713 | ||||||||
\(255\) | −1.83679 | −0.115024 | ||||||||
\(256\) | 20.7650 | 1.29781 | ||||||||
\(257\) | 11.1732 | 0.696963 | 0.348482 | − | 0.937316i | \(-0.386697\pi\) | ||||
0.348482 | + | 0.937316i | \(0.386697\pi\) | |||||||
\(258\) | −35.3745 | −2.20232 | ||||||||
\(259\) | 6.83263 | 0.424559 | ||||||||
\(260\) | −4.39095 | −0.272315 | ||||||||
\(261\) | 4.29663 | 0.265955 | ||||||||
\(262\) | 25.9401 | 1.60259 | ||||||||
\(263\) | 21.0183 | 1.29604 | 0.648020 | − | 0.761623i | \(-0.275597\pi\) | ||||
0.648020 | + | 0.761623i | \(0.275597\pi\) | |||||||
\(264\) | −8.48270 | −0.522074 | ||||||||
\(265\) | −8.82198 | −0.541930 | ||||||||
\(266\) | −6.27760 | −0.384904 | ||||||||
\(267\) | 7.65633 | 0.468560 | ||||||||
\(268\) | −10.3412 | −0.631692 | ||||||||
\(269\) | 19.1959 | 1.17040 | 0.585198 | − | 0.810891i | \(-0.301017\pi\) | ||||
0.585198 | + | 0.810891i | \(0.301017\pi\) | |||||||
\(270\) | −1.85737 | −0.113036 | ||||||||
\(271\) | −19.0389 | −1.15653 | −0.578264 | − | 0.815850i | \(-0.696270\pi\) | ||||
−0.578264 | + | 0.815850i | \(0.696270\pi\) | |||||||
\(272\) | −3.84000 | −0.232834 | ||||||||
\(273\) | −8.20714 | −0.496719 | ||||||||
\(274\) | −7.30138 | −0.441092 | ||||||||
\(275\) | −2.69801 | −0.162696 | ||||||||
\(276\) | −10.1541 | −0.611204 | ||||||||
\(277\) | −17.6164 | −1.05846 | −0.529232 | − | 0.848477i | \(-0.677520\pi\) | ||||
−0.529232 | + | 0.848477i | \(0.677520\pi\) | |||||||
\(278\) | 38.9241 | 2.33451 | ||||||||
\(279\) | 6.27176 | 0.375481 | ||||||||
\(280\) | 1.33289 | 0.0796557 | ||||||||
\(281\) | −31.8274 | −1.89867 | −0.949333 | − | 0.314273i | \(-0.898239\pi\) | ||||
−0.949333 | + | 0.314273i | \(0.898239\pi\) | |||||||
\(282\) | −35.2041 | −2.09637 | ||||||||
\(283\) | 13.6244 | 0.809885 | 0.404942 | − | 0.914342i | \(-0.367292\pi\) | ||||
0.404942 | + | 0.914342i | \(0.367292\pi\) | |||||||
\(284\) | −17.0857 | −1.01385 | ||||||||
\(285\) | 8.19872 | 0.485650 | ||||||||
\(286\) | 16.9544 | 1.00254 | ||||||||
\(287\) | −2.85499 | −0.168525 | ||||||||
\(288\) | 16.0014 | 0.942892 | ||||||||
\(289\) | −16.3936 | −0.964332 | ||||||||
\(290\) | 3.02655 | 0.177725 | ||||||||
\(291\) | −21.3742 | −1.25298 | ||||||||
\(292\) | 8.87577 | 0.519415 | ||||||||
\(293\) | −16.1345 | −0.942586 | −0.471293 | − | 0.881977i | \(-0.656212\pi\) | ||||
−0.471293 | + | 0.881977i | \(0.656212\pi\) | |||||||
\(294\) | −4.26027 | −0.248464 | ||||||||
\(295\) | −4.26791 | −0.248488 | ||||||||
\(296\) | −9.10718 | −0.529344 | ||||||||
\(297\) | 2.77460 | 0.160999 | ||||||||
\(298\) | 15.3035 | 0.886506 | ||||||||
\(299\) | −11.8681 | −0.686352 | ||||||||
\(300\) | 2.97684 | 0.171868 | ||||||||
\(301\) | −8.30335 | −0.478597 | ||||||||
\(302\) | 29.9115 | 1.72121 | ||||||||
\(303\) | −41.3260 | −2.37412 | ||||||||
\(304\) | 17.1403 | 0.983061 | ||||||||
\(305\) | −0.270428 | −0.0154847 | ||||||||
\(306\) | −3.60603 | −0.206143 | ||||||||
\(307\) | −23.4666 | −1.33931 | −0.669654 | − | 0.742674i | \(-0.733557\pi\) | ||||
−0.669654 | + | 0.742674i | \(0.733557\pi\) | |||||||
\(308\) | 3.40490 | 0.194012 | ||||||||
\(309\) | 29.4249 | 1.67392 | ||||||||
\(310\) | 4.41784 | 0.250916 | ||||||||
\(311\) | 28.4374 | 1.61254 | 0.806269 | − | 0.591550i | \(-0.201484\pi\) | ||||
0.806269 | + | 0.591550i | \(0.201484\pi\) | |||||||
\(312\) | 10.9393 | 0.619314 | ||||||||
\(313\) | −14.2227 | −0.803917 | −0.401958 | − | 0.915658i | \(-0.631670\pi\) | ||||
−0.401958 | + | 0.915658i | \(0.631670\pi\) | |||||||
\(314\) | 5.57178 | 0.314434 | ||||||||
\(315\) | 2.56402 | 0.144466 | ||||||||
\(316\) | −1.00303 | −0.0564249 | ||||||||
\(317\) | −1.76366 | −0.0990572 | −0.0495286 | − | 0.998773i | \(-0.515772\pi\) | ||||
−0.0495286 | + | 0.998773i | \(0.515772\pi\) | |||||||
\(318\) | −37.5840 | −2.10761 | ||||||||
\(319\) | −4.52116 | −0.253136 | ||||||||
\(320\) | 1.40870 | 0.0787489 | ||||||||
\(321\) | 14.6525 | 0.817824 | ||||||||
\(322\) | −6.16066 | −0.343320 | ||||||||
\(323\) | −2.70655 | −0.150597 | ||||||||
\(324\) | −12.7688 | −0.709376 | ||||||||
\(325\) | 3.47935 | 0.192999 | ||||||||
\(326\) | 2.87717 | 0.159352 | ||||||||
\(327\) | −23.0953 | −1.27717 | ||||||||
\(328\) | 3.80540 | 0.210118 | ||||||||
\(329\) | −8.26335 | −0.455573 | ||||||||
\(330\) | −11.4943 | −0.632738 | ||||||||
\(331\) | −13.6892 | −0.752427 | −0.376214 | − | 0.926533i | \(-0.622774\pi\) | ||||
−0.376214 | + | 0.926533i | \(0.622774\pi\) | |||||||
\(332\) | −14.2114 | −0.779951 | ||||||||
\(333\) | −17.5190 | −0.960037 | ||||||||
\(334\) | −17.6973 | −0.968352 | ||||||||
\(335\) | 8.19429 | 0.447702 | ||||||||
\(336\) | 11.6322 | 0.634587 | ||||||||
\(337\) | −26.8521 | −1.46273 | −0.731364 | − | 0.681988i | \(-0.761116\pi\) | ||||
−0.731364 | + | 0.681988i | \(0.761116\pi\) | |||||||
\(338\) | 1.61494 | 0.0878411 | ||||||||
\(339\) | 12.6962 | 0.689562 | ||||||||
\(340\) | −0.982712 | −0.0532950 | ||||||||
\(341\) | −6.59950 | −0.357383 | ||||||||
\(342\) | 16.0959 | 0.870368 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 11.0675 | 0.596719 | ||||||||
\(345\) | 8.04599 | 0.433181 | ||||||||
\(346\) | 5.42456 | 0.291626 | ||||||||
\(347\) | −9.72411 | −0.522018 | −0.261009 | − | 0.965336i | \(-0.584055\pi\) | ||||
−0.261009 | + | 0.965336i | \(0.584055\pi\) | |||||||
\(348\) | 4.98840 | 0.267406 | ||||||||
\(349\) | 3.37643 | 0.180736 | 0.0903681 | − | 0.995908i | \(-0.471196\pi\) | ||||
0.0903681 | + | 0.995908i | \(0.471196\pi\) | |||||||
\(350\) | 1.80610 | 0.0965402 | ||||||||
\(351\) | −3.57811 | −0.190986 | ||||||||
\(352\) | −16.8376 | −0.897446 | ||||||||
\(353\) | −35.2945 | −1.87853 | −0.939267 | − | 0.343186i | \(-0.888494\pi\) | ||||
−0.939267 | + | 0.343186i | \(0.888494\pi\) | |||||||
\(354\) | −18.1824 | −0.966386 | ||||||||
\(355\) | 13.5386 | 0.718553 | ||||||||
\(356\) | 4.09626 | 0.217101 | ||||||||
\(357\) | −1.83679 | −0.0972133 | ||||||||
\(358\) | −29.2613 | −1.54651 | ||||||||
\(359\) | −1.87438 | −0.0989257 | −0.0494629 | − | 0.998776i | \(-0.515751\pi\) | ||||
−0.0494629 | + | 0.998776i | \(0.515751\pi\) | |||||||
\(360\) | −3.41757 | −0.180122 | ||||||||
\(361\) | −6.91901 | −0.364158 | ||||||||
\(362\) | 13.2273 | 0.695209 | ||||||||
\(363\) | −8.77653 | −0.460649 | ||||||||
\(364\) | −4.39095 | −0.230148 | ||||||||
\(365\) | −7.03308 | −0.368128 | ||||||||
\(366\) | −1.15209 | −0.0602210 | ||||||||
\(367\) | −5.01404 | −0.261731 | −0.130865 | − | 0.991400i | \(-0.541776\pi\) | ||||
−0.130865 | + | 0.991400i | \(0.541776\pi\) | |||||||
\(368\) | 16.8210 | 0.876854 | ||||||||
\(369\) | 7.32026 | 0.381078 | ||||||||
\(370\) | −12.3404 | −0.641548 | ||||||||
\(371\) | −8.82198 | −0.458014 | ||||||||
\(372\) | 7.28154 | 0.377530 | ||||||||
\(373\) | −7.12713 | −0.369029 | −0.184514 | − | 0.982830i | \(-0.559071\pi\) | ||||
−0.184514 | + | 0.982830i | \(0.559071\pi\) | |||||||
\(374\) | 3.79447 | 0.196207 | ||||||||
\(375\) | −2.35882 | −0.121809 | ||||||||
\(376\) | 11.0142 | 0.568013 | ||||||||
\(377\) | 5.83047 | 0.300284 | ||||||||
\(378\) | −1.85737 | −0.0955329 | ||||||||
\(379\) | −1.47600 | −0.0758173 | −0.0379086 | − | 0.999281i | \(-0.512070\pi\) | ||||
−0.0379086 | + | 0.999281i | \(0.512070\pi\) | |||||||
\(380\) | 4.38644 | 0.225020 | ||||||||
\(381\) | −1.90810 | −0.0977552 | ||||||||
\(382\) | 36.2508 | 1.85475 | ||||||||
\(383\) | −10.8848 | −0.556187 | −0.278093 | − | 0.960554i | \(-0.589702\pi\) | ||||
−0.278093 | + | 0.960554i | \(0.589702\pi\) | |||||||
\(384\) | −23.4401 | −1.19617 | ||||||||
\(385\) | −2.69801 | −0.137503 | ||||||||
\(386\) | 1.39100 | 0.0707999 | ||||||||
\(387\) | 21.2900 | 1.08223 | ||||||||
\(388\) | −11.4355 | −0.580552 | ||||||||
\(389\) | −10.7866 | −0.546904 | −0.273452 | − | 0.961886i | \(-0.588166\pi\) | ||||
−0.273452 | + | 0.961886i | \(0.588166\pi\) | |||||||
\(390\) | 14.8229 | 0.750589 | ||||||||
\(391\) | −2.65613 | −0.134326 | ||||||||
\(392\) | 1.33289 | 0.0673214 | ||||||||
\(393\) | −33.8785 | −1.70894 | ||||||||
\(394\) | −14.4200 | −0.726467 | ||||||||
\(395\) | 0.794791 | 0.0399903 | ||||||||
\(396\) | −8.73026 | −0.438712 | ||||||||
\(397\) | 12.9324 | 0.649059 | 0.324529 | − | 0.945876i | \(-0.394794\pi\) | ||||
0.324529 | + | 0.945876i | \(0.394794\pi\) | |||||||
\(398\) | −2.95118 | −0.147929 | ||||||||
\(399\) | 8.19872 | 0.410449 | ||||||||
\(400\) | −4.93135 | −0.246568 | ||||||||
\(401\) | 19.7263 | 0.985086 | 0.492543 | − | 0.870288i | \(-0.336068\pi\) | ||||
0.492543 | + | 0.870288i | \(0.336068\pi\) | |||||||
\(402\) | 34.9099 | 1.74115 | ||||||||
\(403\) | 8.51070 | 0.423948 | ||||||||
\(404\) | −22.1100 | −1.10002 | ||||||||
\(405\) | 10.1179 | 0.502760 | ||||||||
\(406\) | 3.02655 | 0.150205 | ||||||||
\(407\) | 18.4345 | 0.913765 | ||||||||
\(408\) | 2.44825 | 0.121206 | ||||||||
\(409\) | −18.0336 | −0.891703 | −0.445852 | − | 0.895107i | \(-0.647099\pi\) | ||||
−0.445852 | + | 0.895107i | \(0.647099\pi\) | |||||||
\(410\) | 5.15640 | 0.254657 | ||||||||
\(411\) | 9.53580 | 0.470366 | ||||||||
\(412\) | 15.7428 | 0.775590 | ||||||||
\(413\) | −4.26791 | −0.210010 | ||||||||
\(414\) | 15.7961 | 0.776335 | ||||||||
\(415\) | 11.2610 | 0.552779 | ||||||||
\(416\) | 21.7137 | 1.06460 | ||||||||
\(417\) | −50.8359 | −2.48944 | ||||||||
\(418\) | −16.9370 | −0.828418 | ||||||||
\(419\) | 1.30530 | 0.0637681 | 0.0318841 | − | 0.999492i | \(-0.489849\pi\) | ||||
0.0318841 | + | 0.999492i | \(0.489849\pi\) | |||||||
\(420\) | 2.97684 | 0.145255 | ||||||||
\(421\) | −7.25636 | −0.353654 | −0.176827 | − | 0.984242i | \(-0.556583\pi\) | ||||
−0.176827 | + | 0.984242i | \(0.556583\pi\) | |||||||
\(422\) | −19.3119 | −0.940090 | ||||||||
\(423\) | 21.1874 | 1.03017 | ||||||||
\(424\) | 11.7588 | 0.571057 | ||||||||
\(425\) | 0.778691 | 0.0377721 | ||||||||
\(426\) | 57.6779 | 2.79450 | ||||||||
\(427\) | −0.270428 | −0.0130869 | ||||||||
\(428\) | 7.83933 | 0.378928 | ||||||||
\(429\) | −22.1430 | −1.06907 | ||||||||
\(430\) | 14.9967 | 0.723205 | ||||||||
\(431\) | 23.2032 | 1.11766 | 0.558830 | − | 0.829283i | \(-0.311251\pi\) | ||||
0.558830 | + | 0.829283i | \(0.311251\pi\) | |||||||
\(432\) | 5.07134 | 0.243995 | ||||||||
\(433\) | −25.4114 | −1.22119 | −0.610596 | − | 0.791942i | \(-0.709070\pi\) | ||||
−0.610596 | + | 0.791942i | \(0.709070\pi\) | |||||||
\(434\) | 4.41784 | 0.212063 | ||||||||
\(435\) | −3.95276 | −0.189520 | ||||||||
\(436\) | −12.3563 | −0.591761 | ||||||||
\(437\) | 11.8559 | 0.567147 | ||||||||
\(438\) | −29.9628 | −1.43168 | ||||||||
\(439\) | −18.0990 | −0.863817 | −0.431909 | − | 0.901917i | \(-0.642160\pi\) | ||||
−0.431909 | + | 0.901917i | \(0.642160\pi\) | |||||||
\(440\) | 3.59617 | 0.171440 | ||||||||
\(441\) | 2.56402 | 0.122096 | ||||||||
\(442\) | −4.89334 | −0.232752 | ||||||||
\(443\) | −28.7398 | −1.36547 | −0.682735 | − | 0.730666i | \(-0.739210\pi\) | ||||
−0.682735 | + | 0.730666i | \(0.739210\pi\) | |||||||
\(444\) | −20.3396 | −0.965277 | ||||||||
\(445\) | −3.24583 | −0.153867 | ||||||||
\(446\) | 17.4438 | 0.825989 | ||||||||
\(447\) | −19.9867 | −0.945340 | ||||||||
\(448\) | 1.40870 | 0.0665550 | ||||||||
\(449\) | −23.8604 | −1.12604 | −0.563021 | − | 0.826443i | \(-0.690361\pi\) | ||||
−0.563021 | + | 0.826443i | \(0.690361\pi\) | |||||||
\(450\) | −4.63089 | −0.218302 | ||||||||
\(451\) | −7.70280 | −0.362711 | ||||||||
\(452\) | 6.79266 | 0.319500 | ||||||||
\(453\) | −39.0652 | −1.83545 | ||||||||
\(454\) | −24.8963 | −1.16844 | ||||||||
\(455\) | 3.47935 | 0.163114 | ||||||||
\(456\) | −10.9280 | −0.511752 | ||||||||
\(457\) | −11.9053 | −0.556906 | −0.278453 | − | 0.960450i | \(-0.589822\pi\) | ||||
−0.278453 | + | 0.960450i | \(0.589822\pi\) | |||||||
\(458\) | 1.80610 | 0.0843936 | ||||||||
\(459\) | −0.800796 | −0.0373779 | ||||||||
\(460\) | 4.30473 | 0.200709 | ||||||||
\(461\) | 24.0076 | 1.11814 | 0.559072 | − | 0.829119i | \(-0.311157\pi\) | ||||
0.559072 | + | 0.829119i | \(0.311157\pi\) | |||||||
\(462\) | −11.4943 | −0.534761 | ||||||||
\(463\) | −13.3775 | −0.621704 | −0.310852 | − | 0.950458i | \(-0.600614\pi\) | ||||
−0.310852 | + | 0.950458i | \(0.600614\pi\) | |||||||
\(464\) | −8.26365 | −0.383630 | ||||||||
\(465\) | −5.76982 | −0.267569 | ||||||||
\(466\) | 42.2067 | 1.95519 | ||||||||
\(467\) | −16.8470 | −0.779586 | −0.389793 | − | 0.920902i | \(-0.627453\pi\) | ||||
−0.389793 | + | 0.920902i | \(0.627453\pi\) | |||||||
\(468\) | 11.2585 | 0.520425 | ||||||||
\(469\) | 8.19429 | 0.378377 | ||||||||
\(470\) | 14.9245 | 0.688414 | ||||||||
\(471\) | −7.27690 | −0.335302 | ||||||||
\(472\) | 5.68868 | 0.261843 | ||||||||
\(473\) | −22.4025 | −1.03007 | ||||||||
\(474\) | 3.38602 | 0.155525 | ||||||||
\(475\) | −3.47577 | −0.159479 | ||||||||
\(476\) | −0.982712 | −0.0450425 | ||||||||
\(477\) | 22.6198 | 1.03569 | ||||||||
\(478\) | 13.2173 | 0.604546 | ||||||||
\(479\) | 9.77482 | 0.446623 | 0.223312 | − | 0.974747i | \(-0.428313\pi\) | ||||
0.223312 | + | 0.974747i | \(0.428313\pi\) | |||||||
\(480\) | −14.7208 | −0.671908 | ||||||||
\(481\) | −23.7731 | −1.08396 | ||||||||
\(482\) | −49.1427 | −2.23839 | ||||||||
\(483\) | 8.04599 | 0.366105 | ||||||||
\(484\) | −4.69558 | −0.213436 | ||||||||
\(485\) | 9.06141 | 0.411457 | ||||||||
\(486\) | 37.5326 | 1.70251 | ||||||||
\(487\) | 3.93867 | 0.178478 | 0.0892390 | − | 0.996010i | \(-0.471557\pi\) | ||||
0.0892390 | + | 0.996010i | \(0.471557\pi\) | |||||||
\(488\) | 0.360452 | 0.0163169 | ||||||||
\(489\) | −3.75766 | −0.169927 | ||||||||
\(490\) | 1.80610 | 0.0815914 | ||||||||
\(491\) | 13.5362 | 0.610879 | 0.305439 | − | 0.952212i | \(-0.401197\pi\) | ||||
0.305439 | + | 0.952212i | \(0.401197\pi\) | |||||||
\(492\) | 8.49885 | 0.383158 | ||||||||
\(493\) | 1.30488 | 0.0587689 | ||||||||
\(494\) | 21.8419 | 0.982715 | ||||||||
\(495\) | 6.91777 | 0.310931 | ||||||||
\(496\) | −12.0624 | −0.541618 | ||||||||
\(497\) | 13.5386 | 0.607288 | ||||||||
\(498\) | 47.9747 | 2.14980 | ||||||||
\(499\) | 40.2323 | 1.80104 | 0.900522 | − | 0.434810i | \(-0.143184\pi\) | ||||
0.900522 | + | 0.434810i | \(0.143184\pi\) | |||||||
\(500\) | −1.26200 | −0.0564386 | ||||||||
\(501\) | 23.1131 | 1.03262 | ||||||||
\(502\) | −54.5141 | −2.43308 | ||||||||
\(503\) | 24.1807 | 1.07816 | 0.539082 | − | 0.842253i | \(-0.318771\pi\) | ||||
0.539082 | + | 0.842253i | \(0.318771\pi\) | |||||||
\(504\) | −3.41757 | −0.152231 | ||||||||
\(505\) | 17.5198 | 0.779620 | ||||||||
\(506\) | −16.6215 | −0.738917 | ||||||||
\(507\) | −2.10915 | −0.0936708 | ||||||||
\(508\) | −1.02087 | −0.0452936 | ||||||||
\(509\) | −28.1881 | −1.24941 | −0.624707 | − | 0.780859i | \(-0.714781\pi\) | ||||
−0.624707 | + | 0.780859i | \(0.714781\pi\) | |||||||
\(510\) | 3.31743 | 0.146898 | ||||||||
\(511\) | −7.03308 | −0.311125 | ||||||||
\(512\) | −17.6293 | −0.779114 | ||||||||
\(513\) | 3.57444 | 0.157815 | ||||||||
\(514\) | −20.1799 | −0.890097 | ||||||||
\(515\) | −12.4744 | −0.549688 | ||||||||
\(516\) | 24.7178 | 1.08814 | ||||||||
\(517\) | −22.2946 | −0.980516 | ||||||||
\(518\) | −12.3404 | −0.542207 | ||||||||
\(519\) | −7.08462 | −0.310980 | ||||||||
\(520\) | −4.63760 | −0.203372 | ||||||||
\(521\) | −14.7648 | −0.646856 | −0.323428 | − | 0.946253i | \(-0.604835\pi\) | ||||
−0.323428 | + | 0.946253i | \(0.604835\pi\) | |||||||
\(522\) | −7.76015 | −0.339653 | ||||||||
\(523\) | 13.1768 | 0.576182 | 0.288091 | − | 0.957603i | \(-0.406979\pi\) | ||||
0.288091 | + | 0.957603i | \(0.406979\pi\) | |||||||
\(524\) | −18.1255 | −0.791817 | ||||||||
\(525\) | −2.35882 | −0.102947 | ||||||||
\(526\) | −37.9611 | −1.65518 | ||||||||
\(527\) | 1.90473 | 0.0829712 | ||||||||
\(528\) | 31.3837 | 1.36580 | ||||||||
\(529\) | −11.3649 | −0.494126 | ||||||||
\(530\) | 15.9334 | 0.692103 | ||||||||
\(531\) | 10.9430 | 0.474887 | ||||||||
\(532\) | 4.38644 | 0.190176 | ||||||||
\(533\) | 9.93350 | 0.430267 | ||||||||
\(534\) | −13.8281 | −0.598401 | ||||||||
\(535\) | −6.21181 | −0.268560 | ||||||||
\(536\) | −10.9221 | −0.471764 | ||||||||
\(537\) | 38.2161 | 1.64915 | ||||||||
\(538\) | −34.6698 | −1.49472 | ||||||||
\(539\) | −2.69801 | −0.116212 | ||||||||
\(540\) | 1.29783 | 0.0558497 | ||||||||
\(541\) | −8.13954 | −0.349946 | −0.174973 | − | 0.984573i | \(-0.555984\pi\) | ||||
−0.174973 | + | 0.984573i | \(0.555984\pi\) | |||||||
\(542\) | 34.3861 | 1.47701 | ||||||||
\(543\) | −17.2752 | −0.741348 | ||||||||
\(544\) | 4.85961 | 0.208354 | ||||||||
\(545\) | 9.79103 | 0.419402 | ||||||||
\(546\) | 14.8229 | 0.634363 | ||||||||
\(547\) | 36.1200 | 1.54438 | 0.772190 | − | 0.635392i | \(-0.219161\pi\) | ||||
0.772190 | + | 0.635392i | \(0.219161\pi\) | |||||||
\(548\) | 5.10180 | 0.217938 | ||||||||
\(549\) | 0.693384 | 0.0295929 | ||||||||
\(550\) | 4.87288 | 0.207780 | ||||||||
\(551\) | −5.82448 | −0.248131 | ||||||||
\(552\) | −10.7245 | −0.456463 | ||||||||
\(553\) | 0.794791 | 0.0337980 | ||||||||
\(554\) | 31.8169 | 1.35177 | ||||||||
\(555\) | 16.1169 | 0.684126 | ||||||||
\(556\) | −27.1980 | −1.15345 | ||||||||
\(557\) | −43.1603 | −1.82876 | −0.914380 | − | 0.404856i | \(-0.867322\pi\) | ||||
−0.914380 | + | 0.404856i | \(0.867322\pi\) | |||||||
\(558\) | −11.3274 | −0.479529 | ||||||||
\(559\) | 28.8902 | 1.22193 | ||||||||
\(560\) | −4.93135 | −0.208388 | ||||||||
\(561\) | −4.95568 | −0.209229 | ||||||||
\(562\) | 57.4836 | 2.42480 | ||||||||
\(563\) | 29.7682 | 1.25458 | 0.627291 | − | 0.778785i | \(-0.284164\pi\) | ||||
0.627291 | + | 0.778785i | \(0.284164\pi\) | |||||||
\(564\) | 24.5987 | 1.03579 | ||||||||
\(565\) | −5.38244 | −0.226441 | ||||||||
\(566\) | −24.6070 | −1.03431 | ||||||||
\(567\) | 10.1179 | 0.424910 | ||||||||
\(568\) | −18.0455 | −0.757172 | ||||||||
\(569\) | 15.1312 | 0.634333 | 0.317167 | − | 0.948370i | \(-0.397269\pi\) | ||||
0.317167 | + | 0.948370i | \(0.397269\pi\) | |||||||
\(570\) | −14.8077 | −0.620227 | ||||||||
\(571\) | −8.76823 | −0.366939 | −0.183470 | − | 0.983025i | \(-0.558733\pi\) | ||||
−0.183470 | + | 0.983025i | \(0.558733\pi\) | |||||||
\(572\) | −11.8468 | −0.495341 | ||||||||
\(573\) | −47.3446 | −1.97785 | ||||||||
\(574\) | 5.15640 | 0.215224 | ||||||||
\(575\) | −3.41103 | −0.142250 | ||||||||
\(576\) | −3.61195 | −0.150498 | ||||||||
\(577\) | 46.7565 | 1.94650 | 0.973248 | − | 0.229755i | \(-0.0737925\pi\) | ||||
0.973248 | + | 0.229755i | \(0.0737925\pi\) | |||||||
\(578\) | 29.6086 | 1.23155 | ||||||||
\(579\) | −1.81668 | −0.0754986 | ||||||||
\(580\) | −2.11479 | −0.0878118 | ||||||||
\(581\) | 11.2610 | 0.467184 | ||||||||
\(582\) | 38.6040 | 1.60019 | ||||||||
\(583\) | −23.8018 | −0.985770 | ||||||||
\(584\) | 9.37435 | 0.387913 | ||||||||
\(585\) | −8.92113 | −0.368843 | ||||||||
\(586\) | 29.1405 | 1.20378 | ||||||||
\(587\) | −14.2095 | −0.586491 | −0.293245 | − | 0.956037i | \(-0.594735\pi\) | ||||
−0.293245 | + | 0.956037i | \(0.594735\pi\) | |||||||
\(588\) | 2.97684 | 0.122763 | ||||||||
\(589\) | −8.50196 | −0.350317 | ||||||||
\(590\) | 7.70829 | 0.317345 | ||||||||
\(591\) | 18.8329 | 0.774681 | ||||||||
\(592\) | 33.6941 | 1.38482 | ||||||||
\(593\) | −7.50225 | −0.308081 | −0.154040 | − | 0.988065i | \(-0.549229\pi\) | ||||
−0.154040 | + | 0.988065i | \(0.549229\pi\) | |||||||
\(594\) | −5.01121 | −0.205612 | ||||||||
\(595\) | 0.778691 | 0.0319232 | ||||||||
\(596\) | −10.6932 | −0.438011 | ||||||||
\(597\) | 3.85432 | 0.157747 | ||||||||
\(598\) | 21.4351 | 0.876545 | ||||||||
\(599\) | 1.90564 | 0.0778622 | 0.0389311 | − | 0.999242i | \(-0.487605\pi\) | ||||
0.0389311 | + | 0.999242i | \(0.487605\pi\) | |||||||
\(600\) | 3.14406 | 0.128356 | ||||||||
\(601\) | −21.3548 | −0.871079 | −0.435539 | − | 0.900170i | \(-0.643442\pi\) | ||||
−0.435539 | + | 0.900170i | \(0.643442\pi\) | |||||||
\(602\) | 14.9967 | 0.611220 | ||||||||
\(603\) | −21.0104 | −0.855609 | ||||||||
\(604\) | −20.9005 | −0.850430 | ||||||||
\(605\) | 3.72073 | 0.151269 | ||||||||
\(606\) | 74.6389 | 3.03200 | ||||||||
\(607\) | 3.74074 | 0.151832 | 0.0759159 | − | 0.997114i | \(-0.475812\pi\) | ||||
0.0759159 | + | 0.997114i | \(0.475812\pi\) | |||||||
\(608\) | −21.6914 | −0.879702 | ||||||||
\(609\) | −3.95276 | −0.160174 | ||||||||
\(610\) | 0.488420 | 0.0197756 | ||||||||
\(611\) | 28.7511 | 1.16314 | ||||||||
\(612\) | 2.51970 | 0.101853 | ||||||||
\(613\) | 7.27475 | 0.293824 | 0.146912 | − | 0.989150i | \(-0.453067\pi\) | ||||
0.146912 | + | 0.989150i | \(0.453067\pi\) | |||||||
\(614\) | 42.3830 | 1.71044 | ||||||||
\(615\) | −6.73440 | −0.271557 | ||||||||
\(616\) | 3.59617 | 0.144894 | ||||||||
\(617\) | −10.0873 | −0.406100 | −0.203050 | − | 0.979168i | \(-0.565085\pi\) | ||||
−0.203050 | + | 0.979168i | \(0.565085\pi\) | |||||||
\(618\) | −53.1443 | −2.13778 | ||||||||
\(619\) | 21.0990 | 0.848039 | 0.424019 | − | 0.905653i | \(-0.360619\pi\) | ||||
0.424019 | + | 0.905653i | \(0.360619\pi\) | |||||||
\(620\) | −3.08694 | −0.123975 | ||||||||
\(621\) | 3.50785 | 0.140765 | ||||||||
\(622\) | −51.3609 | −2.05938 | ||||||||
\(623\) | −3.24583 | −0.130042 | ||||||||
\(624\) | −40.4723 | −1.62019 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 25.6877 | 1.02669 | ||||||||
\(627\) | 22.1202 | 0.883397 | ||||||||
\(628\) | −3.89325 | −0.155358 | ||||||||
\(629\) | −5.32051 | −0.212143 | ||||||||
\(630\) | −4.63089 | −0.184499 | ||||||||
\(631\) | 38.0104 | 1.51317 | 0.756586 | − | 0.653895i | \(-0.226866\pi\) | ||||
0.756586 | + | 0.653895i | \(0.226866\pi\) | |||||||
\(632\) | −1.05937 | −0.0421396 | ||||||||
\(633\) | 25.2219 | 1.00248 | ||||||||
\(634\) | 3.18536 | 0.126507 | ||||||||
\(635\) | 0.808924 | 0.0321012 | ||||||||
\(636\) | 26.2616 | 1.04134 | ||||||||
\(637\) | 3.47935 | 0.137857 | ||||||||
\(638\) | 8.16567 | 0.323282 | ||||||||
\(639\) | −34.7132 | −1.37323 | ||||||||
\(640\) | 9.93721 | 0.392803 | ||||||||
\(641\) | −15.1214 | −0.597258 | −0.298629 | − | 0.954369i | \(-0.596529\pi\) | ||||
−0.298629 | + | 0.954369i | \(0.596529\pi\) | |||||||
\(642\) | −26.4640 | −1.04445 | ||||||||
\(643\) | −19.9404 | −0.786372 | −0.393186 | − | 0.919459i | \(-0.628627\pi\) | ||||
−0.393186 | + | 0.919459i | \(0.628627\pi\) | |||||||
\(644\) | 4.30473 | 0.169630 | ||||||||
\(645\) | −19.5861 | −0.771202 | ||||||||
\(646\) | 4.88831 | 0.192328 | ||||||||
\(647\) | −6.11764 | −0.240509 | −0.120255 | − | 0.992743i | \(-0.538371\pi\) | ||||
−0.120255 | + | 0.992743i | \(0.538371\pi\) | |||||||
\(648\) | −13.4860 | −0.529781 | ||||||||
\(649\) | −11.5149 | −0.451999 | ||||||||
\(650\) | −6.28405 | −0.246481 | ||||||||
\(651\) | −5.76982 | −0.226137 | ||||||||
\(652\) | −2.01041 | −0.0787336 | ||||||||
\(653\) | −24.6273 | −0.963743 | −0.481871 | − | 0.876242i | \(-0.660043\pi\) | ||||
−0.481871 | + | 0.876242i | \(0.660043\pi\) | |||||||
\(654\) | 41.7124 | 1.63108 | ||||||||
\(655\) | 14.3625 | 0.561189 | ||||||||
\(656\) | −14.0790 | −0.549691 | ||||||||
\(657\) | 18.0330 | 0.703533 | ||||||||
\(658\) | 14.9245 | 0.581816 | ||||||||
\(659\) | 47.6673 | 1.85685 | 0.928427 | − | 0.371514i | \(-0.121161\pi\) | ||||
0.928427 | + | 0.371514i | \(0.121161\pi\) | |||||||
\(660\) | 8.03155 | 0.312628 | ||||||||
\(661\) | −38.2695 | −1.48851 | −0.744255 | − | 0.667895i | \(-0.767195\pi\) | ||||
−0.744255 | + | 0.667895i | \(0.767195\pi\) | |||||||
\(662\) | 24.7241 | 0.960930 | ||||||||
\(663\) | 6.39083 | 0.248199 | ||||||||
\(664\) | −15.0097 | −0.582489 | ||||||||
\(665\) | −3.47577 | −0.134785 | ||||||||
\(666\) | 31.6412 | 1.22607 | ||||||||
\(667\) | −5.71598 | −0.221324 | ||||||||
\(668\) | 12.3659 | 0.478451 | ||||||||
\(669\) | −22.7821 | −0.880807 | ||||||||
\(670\) | −14.7997 | −0.571764 | ||||||||
\(671\) | −0.729617 | −0.0281666 | ||||||||
\(672\) | −14.7208 | −0.567866 | ||||||||
\(673\) | 38.9282 | 1.50057 | 0.750286 | − | 0.661113i | \(-0.229916\pi\) | ||||
0.750286 | + | 0.661113i | \(0.229916\pi\) | |||||||
\(674\) | 48.4976 | 1.86806 | ||||||||
\(675\) | −1.02839 | −0.0395826 | ||||||||
\(676\) | −1.12843 | −0.0434012 | ||||||||
\(677\) | −9.47715 | −0.364236 | −0.182118 | − | 0.983277i | \(-0.558295\pi\) | ||||
−0.182118 | + | 0.983277i | \(0.558295\pi\) | |||||||
\(678\) | −22.9306 | −0.880645 | ||||||||
\(679\) | 9.06141 | 0.347745 | ||||||||
\(680\) | −1.03791 | −0.0398022 | ||||||||
\(681\) | 32.5152 | 1.24599 | ||||||||
\(682\) | 11.9194 | 0.456417 | ||||||||
\(683\) | 28.6025 | 1.09444 | 0.547222 | − | 0.836987i | \(-0.315685\pi\) | ||||
0.547222 | + | 0.836987i | \(0.315685\pi\) | |||||||
\(684\) | −11.2469 | −0.430038 | ||||||||
\(685\) | −4.04262 | −0.154460 | ||||||||
\(686\) | 1.80610 | 0.0689573 | ||||||||
\(687\) | −2.35882 | −0.0899945 | ||||||||
\(688\) | −40.9468 | −1.56108 | ||||||||
\(689\) | 30.6947 | 1.16938 | ||||||||
\(690\) | −14.5319 | −0.553219 | ||||||||
\(691\) | −24.4699 | −0.930879 | −0.465440 | − | 0.885080i | \(-0.654104\pi\) | ||||
−0.465440 | + | 0.885080i | \(0.654104\pi\) | |||||||
\(692\) | −3.79038 | −0.144089 | ||||||||
\(693\) | 6.91777 | 0.262784 | ||||||||
\(694\) | 17.5627 | 0.666672 | ||||||||
\(695\) | 21.5514 | 0.817492 | ||||||||
\(696\) | 5.26861 | 0.199706 | ||||||||
\(697\) | 2.22315 | 0.0842080 | ||||||||
\(698\) | −6.09818 | −0.230819 | ||||||||
\(699\) | −55.1231 | −2.08495 | ||||||||
\(700\) | −1.26200 | −0.0476993 | ||||||||
\(701\) | 0.880539 | 0.0332575 | 0.0166288 | − | 0.999862i | \(-0.494707\pi\) | ||||
0.0166288 | + | 0.999862i | \(0.494707\pi\) | |||||||
\(702\) | 6.46244 | 0.243909 | ||||||||
\(703\) | 23.7487 | 0.895698 | ||||||||
\(704\) | 3.80070 | 0.143244 | ||||||||
\(705\) | −19.4918 | −0.734102 | ||||||||
\(706\) | 63.7454 | 2.39909 | ||||||||
\(707\) | 17.5198 | 0.658899 | ||||||||
\(708\) | 12.7049 | 0.477479 | ||||||||
\(709\) | 6.81673 | 0.256008 | 0.128004 | − | 0.991774i | \(-0.459143\pi\) | ||||
0.128004 | + | 0.991774i | \(0.459143\pi\) | |||||||
\(710\) | −24.4520 | −0.917669 | ||||||||
\(711\) | −2.03786 | −0.0764259 | ||||||||
\(712\) | 4.32636 | 0.162137 | ||||||||
\(713\) | −8.34358 | −0.312470 | ||||||||
\(714\) | 3.31743 | 0.124152 | ||||||||
\(715\) | 9.38731 | 0.351066 | ||||||||
\(716\) | 20.4462 | 0.764110 | ||||||||
\(717\) | −17.2622 | −0.644667 | ||||||||
\(718\) | 3.38531 | 0.126339 | ||||||||
\(719\) | 17.9723 | 0.670254 | 0.335127 | − | 0.942173i | \(-0.391221\pi\) | ||||
0.335127 | + | 0.942173i | \(0.391221\pi\) | |||||||
\(720\) | 12.6441 | 0.471218 | ||||||||
\(721\) | −12.4744 | −0.464571 | ||||||||
\(722\) | 12.4964 | 0.465069 | ||||||||
\(723\) | 64.1817 | 2.38694 | ||||||||
\(724\) | −9.24248 | −0.343494 | ||||||||
\(725\) | 1.67574 | 0.0622353 | ||||||||
\(726\) | 15.8513 | 0.588297 | ||||||||
\(727\) | 6.94947 | 0.257742 | 0.128871 | − | 0.991661i | \(-0.458865\pi\) | ||||
0.128871 | + | 0.991661i | \(0.458865\pi\) | |||||||
\(728\) | −4.63760 | −0.171881 | ||||||||
\(729\) | −18.6651 | −0.691299 | ||||||||
\(730\) | 12.7025 | 0.470139 | ||||||||
\(731\) | 6.46575 | 0.239144 | ||||||||
\(732\) | 0.805020 | 0.0297544 | ||||||||
\(733\) | −30.7773 | −1.13678 | −0.568392 | − | 0.822758i | \(-0.692434\pi\) | ||||
−0.568392 | + | 0.822758i | \(0.692434\pi\) | |||||||
\(734\) | 9.05588 | 0.334258 | ||||||||
\(735\) | −2.35882 | −0.0870063 | ||||||||
\(736\) | −21.2873 | −0.784661 | ||||||||
\(737\) | 22.1083 | 0.814370 | ||||||||
\(738\) | −13.2211 | −0.486677 | ||||||||
\(739\) | −43.8253 | −1.61214 | −0.806070 | − | 0.591820i | \(-0.798409\pi\) | ||||
−0.806070 | + | 0.591820i | \(0.798409\pi\) | |||||||
\(740\) | 8.62281 | 0.316981 | ||||||||
\(741\) | −28.5262 | −1.04793 | ||||||||
\(742\) | 15.9334 | 0.584934 | ||||||||
\(743\) | −19.9002 | −0.730069 | −0.365034 | − | 0.930994i | \(-0.618943\pi\) | ||||
−0.365034 | + | 0.930994i | \(0.618943\pi\) | |||||||
\(744\) | 7.69056 | 0.281950 | ||||||||
\(745\) | 8.47320 | 0.310434 | ||||||||
\(746\) | 12.8723 | 0.471289 | ||||||||
\(747\) | −28.8734 | −1.05642 | ||||||||
\(748\) | −2.65137 | −0.0969436 | ||||||||
\(749\) | −6.21181 | −0.226974 | ||||||||
\(750\) | 4.26027 | 0.155563 | ||||||||
\(751\) | −34.5488 | −1.26071 | −0.630353 | − | 0.776309i | \(-0.717090\pi\) | ||||
−0.630353 | + | 0.776309i | \(0.717090\pi\) | |||||||
\(752\) | −40.7495 | −1.48598 | ||||||||
\(753\) | 71.1968 | 2.59456 | ||||||||
\(754\) | −10.5304 | −0.383495 | ||||||||
\(755\) | 16.5614 | 0.602730 | ||||||||
\(756\) | 1.29783 | 0.0472016 | ||||||||
\(757\) | −6.66275 | −0.242162 | −0.121081 | − | 0.992643i | \(-0.538636\pi\) | ||||
−0.121081 | + | 0.992643i | \(0.538636\pi\) | |||||||
\(758\) | 2.66582 | 0.0968268 | ||||||||
\(759\) | 21.7082 | 0.787957 | ||||||||
\(760\) | 4.63284 | 0.168051 | ||||||||
\(761\) | 13.7146 | 0.497153 | 0.248576 | − | 0.968612i | \(-0.420037\pi\) | ||||
0.248576 | + | 0.968612i | \(0.420037\pi\) | |||||||
\(762\) | 3.44623 | 0.124844 | ||||||||
\(763\) | 9.79103 | 0.354459 | ||||||||
\(764\) | −25.3301 | −0.916411 | ||||||||
\(765\) | −1.99658 | −0.0721866 | ||||||||
\(766\) | 19.6590 | 0.710310 | ||||||||
\(767\) | 14.8495 | 0.536186 | ||||||||
\(768\) | 48.9809 | 1.76745 | ||||||||
\(769\) | 39.1739 | 1.41265 | 0.706323 | − | 0.707889i | \(-0.250352\pi\) | ||||
0.706323 | + | 0.707889i | \(0.250352\pi\) | |||||||
\(770\) | 4.87288 | 0.175607 | ||||||||
\(771\) | 26.3555 | 0.949169 | ||||||||
\(772\) | −0.971952 | −0.0349813 | ||||||||
\(773\) | −0.100450 | −0.00361295 | −0.00180648 | − | 0.999998i | \(-0.500575\pi\) | ||||
−0.00180648 | + | 0.999998i | \(0.500575\pi\) | |||||||
\(774\) | −38.4519 | −1.38213 | ||||||||
\(775\) | 2.44606 | 0.0878652 | ||||||||
\(776\) | −12.0779 | −0.433571 | ||||||||
\(777\) | 16.1169 | 0.578192 | ||||||||
\(778\) | 19.4818 | 0.698455 | ||||||||
\(779\) | −9.92330 | −0.355539 | ||||||||
\(780\) | −10.3575 | −0.370856 | ||||||||
\(781\) | 36.5272 | 1.30705 | ||||||||
\(782\) | 4.79725 | 0.171549 | ||||||||
\(783\) | −1.72331 | −0.0615859 | ||||||||
\(784\) | −4.93135 | −0.176120 | ||||||||
\(785\) | 3.08498 | 0.110108 | ||||||||
\(786\) | 61.1880 | 2.18250 | ||||||||
\(787\) | −12.7518 | −0.454553 | −0.227277 | − | 0.973830i | \(-0.572982\pi\) | ||||
−0.227277 | + | 0.973830i | \(0.572982\pi\) | |||||||
\(788\) | 10.0759 | 0.358938 | ||||||||
\(789\) | 49.5782 | 1.76503 | ||||||||
\(790\) | −1.43547 | −0.0510719 | ||||||||
\(791\) | −5.38244 | −0.191377 | ||||||||
\(792\) | −9.22066 | −0.327642 | ||||||||
\(793\) | 0.940912 | 0.0334128 | ||||||||
\(794\) | −23.3572 | −0.828918 | ||||||||
\(795\) | −20.8095 | −0.738035 | ||||||||
\(796\) | 2.06212 | 0.0730899 | ||||||||
\(797\) | 1.82432 | 0.0646209 | 0.0323104 | − | 0.999478i | \(-0.489713\pi\) | ||||
0.0323104 | + | 0.999478i | \(0.489713\pi\) | |||||||
\(798\) | −14.8077 | −0.524188 | ||||||||
\(799\) | 6.43460 | 0.227640 | ||||||||
\(800\) | 6.24074 | 0.220643 | ||||||||
\(801\) | 8.32240 | 0.294057 | ||||||||
\(802\) | −35.6278 | −1.25806 | ||||||||
\(803\) | −18.9753 | −0.669625 | ||||||||
\(804\) | −24.3931 | −0.860278 | ||||||||
\(805\) | −3.41103 | −0.120223 | ||||||||
\(806\) | −15.3712 | −0.541427 | ||||||||
\(807\) | 45.2797 | 1.59392 | ||||||||
\(808\) | −23.3520 | −0.821521 | ||||||||
\(809\) | −46.3515 | −1.62963 | −0.814816 | − | 0.579719i | \(-0.803162\pi\) | ||||
−0.814816 | + | 0.579719i | \(0.803162\pi\) | |||||||
\(810\) | −18.2739 | −0.642078 | ||||||||
\(811\) | 7.34056 | 0.257762 | 0.128881 | − | 0.991660i | \(-0.458862\pi\) | ||||
0.128881 | + | 0.991660i | \(0.458862\pi\) | |||||||
\(812\) | −2.11479 | −0.0742145 | ||||||||
\(813\) | −44.9092 | −1.57503 | ||||||||
\(814\) | −33.2946 | −1.16698 | ||||||||
\(815\) | 1.59303 | 0.0558013 | ||||||||
\(816\) | −9.05786 | −0.317089 | ||||||||
\(817\) | −28.8606 | −1.00970 | ||||||||
\(818\) | 32.5705 | 1.13880 | ||||||||
\(819\) | −8.92113 | −0.311729 | ||||||||
\(820\) | −3.60301 | −0.125823 | ||||||||
\(821\) | 46.8176 | 1.63395 | 0.816973 | − | 0.576676i | \(-0.195650\pi\) | ||||
0.816973 | + | 0.576676i | \(0.195650\pi\) | |||||||
\(822\) | −17.2226 | −0.600708 | ||||||||
\(823\) | 54.0930 | 1.88556 | 0.942782 | − | 0.333410i | \(-0.108199\pi\) | ||||
0.942782 | + | 0.333410i | \(0.108199\pi\) | |||||||
\(824\) | 16.6271 | 0.579232 | ||||||||
\(825\) | −6.36412 | −0.221570 | ||||||||
\(826\) | 7.70829 | 0.268206 | ||||||||
\(827\) | 18.0070 | 0.626166 | 0.313083 | − | 0.949726i | \(-0.398638\pi\) | ||||
0.313083 | + | 0.949726i | \(0.398638\pi\) | |||||||
\(828\) | −11.0374 | −0.383577 | ||||||||
\(829\) | 7.38649 | 0.256544 | 0.128272 | − | 0.991739i | \(-0.459057\pi\) | ||||
0.128272 | + | 0.991739i | \(0.459057\pi\) | |||||||
\(830\) | −20.3385 | −0.705958 | ||||||||
\(831\) | −41.5538 | −1.44149 | ||||||||
\(832\) | −4.90137 | −0.169924 | ||||||||
\(833\) | 0.778691 | 0.0269800 | ||||||||
\(834\) | 91.8148 | 3.17929 | ||||||||
\(835\) | −9.79861 | −0.339095 | ||||||||
\(836\) | 11.8347 | 0.409311 | ||||||||
\(837\) | −2.51550 | −0.0869483 | ||||||||
\(838\) | −2.35751 | −0.0814387 | ||||||||
\(839\) | 2.41776 | 0.0834704 | 0.0417352 | − | 0.999129i | \(-0.486711\pi\) | ||||
0.0417352 | + | 0.999129i | \(0.486711\pi\) | |||||||
\(840\) | 3.14406 | 0.108480 | ||||||||
\(841\) | −26.1919 | −0.903169 | ||||||||
\(842\) | 13.1057 | 0.451653 | ||||||||
\(843\) | −75.0751 | −2.58572 | ||||||||
\(844\) | 13.4941 | 0.464487 | ||||||||
\(845\) | 0.894157 | 0.0307599 | ||||||||
\(846\) | −38.2667 | −1.31564 | ||||||||
\(847\) | 3.72073 | 0.127846 | ||||||||
\(848\) | −43.5043 | −1.49394 | ||||||||
\(849\) | 32.1374 | 1.10295 | ||||||||
\(850\) | −1.40640 | −0.0482390 | ||||||||
\(851\) | 23.3063 | 0.798929 | ||||||||
\(852\) | −40.3022 | −1.38073 | ||||||||
\(853\) | −42.1871 | −1.44446 | −0.722229 | − | 0.691654i | \(-0.756882\pi\) | ||||
−0.722229 | + | 0.691654i | \(0.756882\pi\) | |||||||
\(854\) | 0.488420 | 0.0167134 | ||||||||
\(855\) | 8.91197 | 0.304783 | ||||||||
\(856\) | 8.27968 | 0.282994 | ||||||||
\(857\) | −48.2645 | −1.64868 | −0.824342 | − | 0.566092i | \(-0.808455\pi\) | ||||
−0.824342 | + | 0.566092i | \(0.808455\pi\) | |||||||
\(858\) | 39.9925 | 1.36532 | ||||||||
\(859\) | −16.9361 | −0.577851 | −0.288926 | − | 0.957352i | \(-0.593298\pi\) | ||||
−0.288926 | + | 0.957352i | \(0.593298\pi\) | |||||||
\(860\) | −10.4789 | −0.357327 | ||||||||
\(861\) | −6.73440 | −0.229508 | ||||||||
\(862\) | −41.9074 | −1.42737 | ||||||||
\(863\) | −36.7487 | −1.25094 | −0.625470 | − | 0.780248i | \(-0.715093\pi\) | ||||
−0.625470 | + | 0.780248i | \(0.715093\pi\) | |||||||
\(864\) | −6.41789 | −0.218341 | ||||||||
\(865\) | 3.00346 | 0.102121 | ||||||||
\(866\) | 45.8955 | 1.55959 | ||||||||
\(867\) | −38.6696 | −1.31329 | ||||||||
\(868\) | −3.08694 | −0.104778 | ||||||||
\(869\) | 2.14436 | 0.0727423 | ||||||||
\(870\) | 7.13908 | 0.242038 | ||||||||
\(871\) | −28.5108 | −0.966051 | ||||||||
\(872\) | −13.0504 | −0.441943 | ||||||||
\(873\) | −23.2337 | −0.786341 | ||||||||
\(874\) | −21.4130 | −0.724307 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 20.9363 | 0.707373 | ||||||||
\(877\) | −42.2279 | −1.42593 | −0.712967 | − | 0.701197i | \(-0.752649\pi\) | ||||
−0.712967 | + | 0.701197i | \(0.752649\pi\) | |||||||
\(878\) | 32.6886 | 1.10319 | ||||||||
\(879\) | −38.0583 | −1.28367 | ||||||||
\(880\) | −13.3048 | −0.448506 | ||||||||
\(881\) | −21.2963 | −0.717489 | −0.358745 | − | 0.933436i | \(-0.616795\pi\) | ||||
−0.358745 | + | 0.933436i | \(0.616795\pi\) | |||||||
\(882\) | −4.63089 | −0.155930 | ||||||||
\(883\) | −49.0025 | −1.64907 | −0.824533 | − | 0.565814i | \(-0.808562\pi\) | ||||
−0.824533 | + | 0.565814i | \(0.808562\pi\) | |||||||
\(884\) | 3.41919 | 0.115000 | ||||||||
\(885\) | −10.0672 | −0.338406 | ||||||||
\(886\) | 51.9071 | 1.74385 | ||||||||
\(887\) | 11.9802 | 0.402257 | 0.201128 | − | 0.979565i | \(-0.435539\pi\) | ||||
0.201128 | + | 0.979565i | \(0.435539\pi\) | |||||||
\(888\) | −21.4822 | −0.720895 | ||||||||
\(889\) | 0.808924 | 0.0271304 | ||||||||
\(890\) | 5.86231 | 0.196505 | ||||||||
\(891\) | 27.2981 | 0.914520 | ||||||||
\(892\) | −12.1888 | −0.408111 | ||||||||
\(893\) | −28.7215 | −0.961130 | ||||||||
\(894\) | 36.0981 | 1.20730 | ||||||||
\(895\) | −16.2014 | −0.541552 | ||||||||
\(896\) | 9.93721 | 0.331979 | ||||||||
\(897\) | −27.9948 | −0.934718 | ||||||||
\(898\) | 43.0943 | 1.43808 | ||||||||
\(899\) | 4.09896 | 0.136708 | ||||||||
\(900\) | 3.23581 | 0.107860 | ||||||||
\(901\) | 6.86960 | 0.228859 | ||||||||
\(902\) | 13.9120 | 0.463220 | ||||||||
\(903\) | −19.5861 | −0.651785 | ||||||||
\(904\) | 7.17422 | 0.238611 | ||||||||
\(905\) | 7.32365 | 0.243446 | ||||||||
\(906\) | 70.5558 | 2.34406 | ||||||||
\(907\) | −33.1736 | −1.10151 | −0.550755 | − | 0.834667i | \(-0.685660\pi\) | ||||
−0.550755 | + | 0.834667i | \(0.685660\pi\) | |||||||
\(908\) | 17.3962 | 0.577312 | ||||||||
\(909\) | −44.9211 | −1.48994 | ||||||||
\(910\) | −6.28405 | −0.208314 | ||||||||
\(911\) | −22.2094 | −0.735830 | −0.367915 | − | 0.929859i | \(-0.619928\pi\) | ||||
−0.367915 | + | 0.929859i | \(0.619928\pi\) | |||||||
\(912\) | 40.4308 | 1.33880 | ||||||||
\(913\) | 30.3822 | 1.00550 | ||||||||
\(914\) | 21.5022 | 0.711228 | ||||||||
\(915\) | −0.637890 | −0.0210880 | ||||||||
\(916\) | −1.26200 | −0.0416978 | ||||||||
\(917\) | 14.3625 | 0.474291 | ||||||||
\(918\) | 1.44632 | 0.0477356 | ||||||||
\(919\) | 3.58678 | 0.118317 | 0.0591585 | − | 0.998249i | \(-0.481158\pi\) | ||||
0.0591585 | + | 0.998249i | \(0.481158\pi\) | |||||||
\(920\) | 4.54654 | 0.149895 | ||||||||
\(921\) | −55.3533 | −1.82395 | ||||||||
\(922\) | −43.3601 | −1.42799 | ||||||||
\(923\) | −47.1054 | −1.55049 | ||||||||
\(924\) | 8.03155 | 0.264219 | ||||||||
\(925\) | −6.83263 | −0.224656 | ||||||||
\(926\) | 24.1611 | 0.793983 | ||||||||
\(927\) | 31.9847 | 1.05052 | ||||||||
\(928\) | 10.4578 | 0.343295 | ||||||||
\(929\) | 9.67444 | 0.317408 | 0.158704 | − | 0.987326i | \(-0.449268\pi\) | ||||
0.158704 | + | 0.987326i | \(0.449268\pi\) | |||||||
\(930\) | 10.4209 | 0.341714 | ||||||||
\(931\) | −3.47577 | −0.113914 | ||||||||
\(932\) | −29.4917 | −0.966034 | ||||||||
\(933\) | 67.0787 | 2.19606 | ||||||||
\(934\) | 30.4274 | 0.995615 | ||||||||
\(935\) | 2.10092 | 0.0687073 | ||||||||
\(936\) | 11.8909 | 0.388667 | ||||||||
\(937\) | 22.9093 | 0.748413 | 0.374207 | − | 0.927345i | \(-0.377915\pi\) | ||||
0.374207 | + | 0.927345i | \(0.377915\pi\) | |||||||
\(938\) | −14.7997 | −0.483228 | ||||||||
\(939\) | −33.5488 | −1.09483 | ||||||||
\(940\) | −10.4284 | −0.340137 | ||||||||
\(941\) | 0.817156 | 0.0266385 | 0.0133193 | − | 0.999911i | \(-0.495760\pi\) | ||||
0.0133193 | + | 0.999911i | \(0.495760\pi\) | |||||||
\(942\) | 13.1428 | 0.428216 | ||||||||
\(943\) | −9.73844 | −0.317127 | ||||||||
\(944\) | −21.0466 | −0.685008 | ||||||||
\(945\) | −1.02839 | −0.0334534 | ||||||||
\(946\) | 40.4613 | 1.31551 | ||||||||
\(947\) | 45.3299 | 1.47302 | 0.736512 | − | 0.676425i | \(-0.236472\pi\) | ||||
0.736512 | + | 0.676425i | \(0.236472\pi\) | |||||||
\(948\) | −2.36597 | −0.0768430 | ||||||||
\(949\) | 24.4705 | 0.794346 | ||||||||
\(950\) | 6.27760 | 0.203672 | ||||||||
\(951\) | −4.16016 | −0.134903 | ||||||||
\(952\) | −1.03791 | −0.0336390 | ||||||||
\(953\) | 20.6996 | 0.670527 | 0.335264 | − | 0.942124i | \(-0.391175\pi\) | ||||
0.335264 | + | 0.942124i | \(0.391175\pi\) | |||||||
\(954\) | −40.8536 | −1.32269 | ||||||||
\(955\) | 20.0713 | 0.649493 | ||||||||
\(956\) | −9.23553 | −0.298698 | ||||||||
\(957\) | −10.6646 | −0.344737 | ||||||||
\(958\) | −17.6543 | −0.570386 | ||||||||
\(959\) | −4.04262 | −0.130543 | ||||||||
\(960\) | 3.32288 | 0.107245 | ||||||||
\(961\) | −25.0168 | −0.806993 | ||||||||
\(962\) | 42.9366 | 1.38433 | ||||||||
\(963\) | 15.9272 | 0.513248 | ||||||||
\(964\) | 34.3382 | 1.10596 | ||||||||
\(965\) | 0.770165 | 0.0247925 | ||||||||
\(966\) | −14.5319 | −0.467555 | ||||||||
\(967\) | −60.6689 | −1.95098 | −0.975491 | − | 0.220041i | \(-0.929381\pi\) | ||||
−0.975491 | + | 0.220041i | \(0.929381\pi\) | |||||||
\(968\) | −4.95935 | −0.159399 | ||||||||
\(969\) | −6.38427 | −0.205092 | ||||||||
\(970\) | −16.3658 | −0.525475 | ||||||||
\(971\) | 34.0480 | 1.09265 | 0.546325 | − | 0.837573i | \(-0.316026\pi\) | ||||
0.546325 | + | 0.837573i | \(0.316026\pi\) | |||||||
\(972\) | −26.2257 | −0.841191 | ||||||||
\(973\) | 21.5514 | 0.690907 | ||||||||
\(974\) | −7.11363 | −0.227936 | ||||||||
\(975\) | 8.20714 | 0.262839 | ||||||||
\(976\) | −1.33358 | −0.0426867 | ||||||||
\(977\) | 4.97338 | 0.159112 | 0.0795562 | − | 0.996830i | \(-0.474650\pi\) | ||||
0.0795562 | + | 0.996830i | \(0.474650\pi\) | |||||||
\(978\) | 6.78672 | 0.217015 | ||||||||
\(979\) | −8.75730 | −0.279884 | ||||||||
\(980\) | −1.26200 | −0.0403133 | ||||||||
\(981\) | −25.1044 | −0.801523 | ||||||||
\(982\) | −24.4477 | −0.780157 | ||||||||
\(983\) | −0.482965 | −0.0154042 | −0.00770210 | − | 0.999970i | \(-0.502452\pi\) | ||||
−0.00770210 | + | 0.999970i | \(0.502452\pi\) | |||||||
\(984\) | 8.97625 | 0.286152 | ||||||||
\(985\) | −7.98403 | −0.254392 | ||||||||
\(986\) | −2.35675 | −0.0750541 | ||||||||
\(987\) | −19.4918 | −0.620429 | ||||||||
\(988\) | −15.2619 | −0.485547 | ||||||||
\(989\) | −28.3229 | −0.900617 | ||||||||
\(990\) | −12.4942 | −0.397092 | ||||||||
\(991\) | 1.01037 | 0.0320956 | 0.0160478 | − | 0.999871i | \(-0.494892\pi\) | ||||
0.0160478 | + | 0.999871i | \(0.494892\pi\) | |||||||
\(992\) | 15.2652 | 0.484672 | ||||||||
\(993\) | −32.2904 | −1.02470 | ||||||||
\(994\) | −24.4520 | −0.775572 | ||||||||
\(995\) | −1.63400 | −0.0518014 | ||||||||
\(996\) | −33.5221 | −1.06219 | ||||||||
\(997\) | 18.8767 | 0.597832 | 0.298916 | − | 0.954279i | \(-0.403375\pi\) | ||||
0.298916 | + | 0.954279i | \(0.403375\pi\) | |||||||
\(998\) | −72.6636 | −2.30013 | ||||||||
\(999\) | 7.02659 | 0.222311 |
(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 | 8015.2.a.k.1.12 | ✓ | 49 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.k.1.12 | ✓ | 49 | 1.1 | even | 1 | trivial |