Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7098,2,Mod(1,7098)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7098, 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("7098.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7098.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: | \(56.6778153547\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.445042\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7098.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.55496 | 1.14261 | 0.571306 | − | 0.820737i | \(-0.306437\pi\) | ||||
0.571306 | + | 0.820737i | \(0.306437\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.55496 | −0.807949 | ||||||||
\(11\) | 3.24698 | 0.979001 | 0.489501 | − | 0.872003i | \(-0.337179\pi\) | ||||
0.489501 | + | 0.872003i | \(0.337179\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 2.55496 | 0.659687 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.40581 | 0.826031 | 0.413016 | − | 0.910724i | \(-0.364476\pi\) | ||||
0.413016 | + | 0.910724i | \(0.364476\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −2.85086 | −0.654031 | −0.327016 | − | 0.945019i | \(-0.606043\pi\) | ||||
−0.327016 | + | 0.945019i | \(0.606043\pi\) | |||||||
\(20\) | 2.55496 | 0.571306 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −3.24698 | −0.692258 | ||||||||
\(23\) | −8.54288 | −1.78131 | −0.890656 | − | 0.454677i | \(-0.849755\pi\) | ||||
−0.890656 | + | 0.454677i | \(0.849755\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 1.52781 | 0.305562 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −6.18598 | −1.14871 | −0.574354 | − | 0.818607i | \(-0.694747\pi\) | ||||
−0.574354 | + | 0.818607i | \(0.694747\pi\) | |||||||
\(30\) | −2.55496 | −0.466469 | ||||||||
\(31\) | −0.423272 | −0.0760218 | −0.0380109 | − | 0.999277i | \(-0.512102\pi\) | ||||
−0.0380109 | + | 0.999277i | \(0.512102\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 3.24698 | 0.565227 | ||||||||
\(34\) | −3.40581 | −0.584092 | ||||||||
\(35\) | −2.55496 | −0.431867 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 5.54288 | 0.911243 | 0.455622 | − | 0.890174i | \(-0.349417\pi\) | ||||
0.455622 | + | 0.890174i | \(0.349417\pi\) | |||||||
\(38\) | 2.85086 | 0.462470 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.55496 | −0.403974 | ||||||||
\(41\) | −3.14675 | −0.491440 | −0.245720 | − | 0.969341i | \(-0.579024\pi\) | ||||
−0.245720 | + | 0.969341i | \(0.579024\pi\) | |||||||
\(42\) | 1.00000 | 0.154303 | ||||||||
\(43\) | 4.93900 | 0.753191 | 0.376595 | − | 0.926378i | \(-0.377095\pi\) | ||||
0.376595 | + | 0.926378i | \(0.377095\pi\) | |||||||
\(44\) | 3.24698 | 0.489501 | ||||||||
\(45\) | 2.55496 | 0.380871 | ||||||||
\(46\) | 8.54288 | 1.25958 | ||||||||
\(47\) | 4.50604 | 0.657274 | 0.328637 | − | 0.944456i | \(-0.393411\pi\) | ||||
0.328637 | + | 0.944456i | \(0.393411\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.52781 | −0.216065 | ||||||||
\(51\) | 3.40581 | 0.476909 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.12498 | 0.566610 | 0.283305 | − | 0.959030i | \(-0.408569\pi\) | ||||
0.283305 | + | 0.959030i | \(0.408569\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 8.29590 | 1.11862 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −2.85086 | −0.377605 | ||||||||
\(58\) | 6.18598 | 0.812259 | ||||||||
\(59\) | 14.9269 | 1.94332 | 0.971660 | − | 0.236384i | \(-0.0759624\pi\) | ||||
0.971660 | + | 0.236384i | \(0.0759624\pi\) | |||||||
\(60\) | 2.55496 | 0.329844 | ||||||||
\(61\) | 3.17629 | 0.406683 | 0.203341 | − | 0.979108i | \(-0.434820\pi\) | ||||
0.203341 | + | 0.979108i | \(0.434820\pi\) | |||||||
\(62\) | 0.423272 | 0.0537555 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.24698 | −0.399676 | ||||||||
\(67\) | 5.47219 | 0.668534 | 0.334267 | − | 0.942478i | \(-0.391511\pi\) | ||||
0.334267 | + | 0.942478i | \(0.391511\pi\) | |||||||
\(68\) | 3.40581 | 0.413016 | ||||||||
\(69\) | −8.54288 | −1.02844 | ||||||||
\(70\) | 2.55496 | 0.305376 | ||||||||
\(71\) | −4.21983 | −0.500802 | −0.250401 | − | 0.968142i | \(-0.580562\pi\) | ||||
−0.250401 | + | 0.968142i | \(0.580562\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 12.2959 | 1.43913 | 0.719563 | − | 0.694427i | \(-0.244342\pi\) | ||||
0.719563 | + | 0.694427i | \(0.244342\pi\) | |||||||
\(74\) | −5.54288 | −0.644346 | ||||||||
\(75\) | 1.52781 | 0.176416 | ||||||||
\(76\) | −2.85086 | −0.327016 | ||||||||
\(77\) | −3.24698 | −0.370028 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.2567 | 1.15397 | 0.576983 | − | 0.816756i | \(-0.304230\pi\) | ||||
0.576983 | + | 0.816756i | \(0.304230\pi\) | |||||||
\(80\) | 2.55496 | 0.285653 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.14675 | 0.347501 | ||||||||
\(83\) | 16.8509 | 1.84962 | 0.924811 | − | 0.380427i | \(-0.124223\pi\) | ||||
0.924811 | + | 0.380427i | \(0.124223\pi\) | |||||||
\(84\) | −1.00000 | −0.109109 | ||||||||
\(85\) | 8.70171 | 0.943833 | ||||||||
\(86\) | −4.93900 | −0.532586 | ||||||||
\(87\) | −6.18598 | −0.663207 | ||||||||
\(88\) | −3.24698 | −0.346129 | ||||||||
\(89\) | 1.96615 | 0.208411 | 0.104206 | − | 0.994556i | \(-0.466770\pi\) | ||||
0.104206 | + | 0.994556i | \(0.466770\pi\) | |||||||
\(90\) | −2.55496 | −0.269316 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −8.54288 | −0.890656 | ||||||||
\(93\) | −0.423272 | −0.0438912 | ||||||||
\(94\) | −4.50604 | −0.464763 | ||||||||
\(95\) | −7.28382 | −0.747304 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 1.12737 | 0.114468 | 0.0572338 | − | 0.998361i | \(-0.481772\pi\) | ||||
0.0572338 | + | 0.998361i | \(0.481772\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 3.24698 | 0.326334 | ||||||||
\(100\) | 1.52781 | 0.152781 | ||||||||
\(101\) | −1.03385 | −0.102872 | −0.0514361 | − | 0.998676i | \(-0.516380\pi\) | ||||
−0.0514361 | + | 0.998676i | \(0.516380\pi\) | |||||||
\(102\) | −3.40581 | −0.337226 | ||||||||
\(103\) | 8.18060 | 0.806059 | 0.403029 | − | 0.915187i | \(-0.367957\pi\) | ||||
0.403029 | + | 0.915187i | \(0.367957\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.55496 | −0.249338 | ||||||||
\(106\) | −4.12498 | −0.400654 | ||||||||
\(107\) | −0.780167 | −0.0754216 | −0.0377108 | − | 0.999289i | \(-0.512007\pi\) | ||||
−0.0377108 | + | 0.999289i | \(0.512007\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 6.93900 | 0.664636 | 0.332318 | − | 0.943167i | \(-0.392169\pi\) | ||||
0.332318 | + | 0.943167i | \(0.392169\pi\) | |||||||
\(110\) | −8.29590 | −0.790983 | ||||||||
\(111\) | 5.54288 | 0.526107 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −5.20237 | −0.489398 | −0.244699 | − | 0.969599i | \(-0.578689\pi\) | ||||
−0.244699 | + | 0.969599i | \(0.578689\pi\) | |||||||
\(114\) | 2.85086 | 0.267007 | ||||||||
\(115\) | −21.8267 | −2.03535 | ||||||||
\(116\) | −6.18598 | −0.574354 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −14.9269 | −1.37413 | ||||||||
\(119\) | −3.40581 | −0.312210 | ||||||||
\(120\) | −2.55496 | −0.233235 | ||||||||
\(121\) | −0.457123 | −0.0415567 | ||||||||
\(122\) | −3.17629 | −0.287568 | ||||||||
\(123\) | −3.14675 | −0.283733 | ||||||||
\(124\) | −0.423272 | −0.0380109 | ||||||||
\(125\) | −8.87130 | −0.793473 | ||||||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | −14.6136 | −1.29674 | −0.648372 | − | 0.761324i | \(-0.724550\pi\) | ||||
−0.648372 | + | 0.761324i | \(0.724550\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 4.93900 | 0.434855 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.7778 | 1.72799 | 0.863996 | − | 0.503499i | \(-0.167954\pi\) | ||||
0.863996 | + | 0.503499i | \(0.167954\pi\) | |||||||
\(132\) | 3.24698 | 0.282613 | ||||||||
\(133\) | 2.85086 | 0.247200 | ||||||||
\(134\) | −5.47219 | −0.472725 | ||||||||
\(135\) | 2.55496 | 0.219896 | ||||||||
\(136\) | −3.40581 | −0.292046 | ||||||||
\(137\) | 16.7627 | 1.43213 | 0.716067 | − | 0.698031i | \(-0.245940\pi\) | ||||
0.716067 | + | 0.698031i | \(0.245940\pi\) | |||||||
\(138\) | 8.54288 | 0.727218 | ||||||||
\(139\) | 12.1685 | 1.03212 | 0.516060 | − | 0.856552i | \(-0.327398\pi\) | ||||
0.516060 | + | 0.856552i | \(0.327398\pi\) | |||||||
\(140\) | −2.55496 | −0.215933 | ||||||||
\(141\) | 4.50604 | 0.379477 | ||||||||
\(142\) | 4.21983 | 0.354120 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −15.8049 | −1.31253 | ||||||||
\(146\) | −12.2959 | −1.01762 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 5.54288 | 0.455622 | ||||||||
\(149\) | 0.753020 | 0.0616898 | 0.0308449 | − | 0.999524i | \(-0.490180\pi\) | ||||
0.0308449 | + | 0.999524i | \(0.490180\pi\) | |||||||
\(150\) | −1.52781 | −0.124745 | ||||||||
\(151\) | 15.1021 | 1.22900 | 0.614498 | − | 0.788919i | \(-0.289359\pi\) | ||||
0.614498 | + | 0.788919i | \(0.289359\pi\) | |||||||
\(152\) | 2.85086 | 0.231235 | ||||||||
\(153\) | 3.40581 | 0.275344 | ||||||||
\(154\) | 3.24698 | 0.261649 | ||||||||
\(155\) | −1.08144 | −0.0868634 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.5133 | −1.47753 | −0.738763 | − | 0.673966i | \(-0.764590\pi\) | ||||
−0.738763 | + | 0.673966i | \(0.764590\pi\) | |||||||
\(158\) | −10.2567 | −0.815977 | ||||||||
\(159\) | 4.12498 | 0.327132 | ||||||||
\(160\) | −2.55496 | −0.201987 | ||||||||
\(161\) | 8.54288 | 0.673273 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −20.1444 | −1.57783 | −0.788914 | − | 0.614504i | \(-0.789356\pi\) | ||||
−0.788914 | + | 0.614504i | \(0.789356\pi\) | |||||||
\(164\) | −3.14675 | −0.245720 | ||||||||
\(165\) | 8.29590 | 0.645835 | ||||||||
\(166\) | −16.8509 | −1.30788 | ||||||||
\(167\) | 18.5157 | 1.43279 | 0.716395 | − | 0.697695i | \(-0.245791\pi\) | ||||
0.716395 | + | 0.697695i | \(0.245791\pi\) | |||||||
\(168\) | 1.00000 | 0.0771517 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −8.70171 | −0.667391 | ||||||||
\(171\) | −2.85086 | −0.218010 | ||||||||
\(172\) | 4.93900 | 0.376595 | ||||||||
\(173\) | −22.5676 | −1.71579 | −0.857893 | − | 0.513829i | \(-0.828227\pi\) | ||||
−0.857893 | + | 0.513829i | \(0.828227\pi\) | |||||||
\(174\) | 6.18598 | 0.468958 | ||||||||
\(175\) | −1.52781 | −0.115492 | ||||||||
\(176\) | 3.24698 | 0.244750 | ||||||||
\(177\) | 14.9269 | 1.12198 | ||||||||
\(178\) | −1.96615 | −0.147369 | ||||||||
\(179\) | 11.8116 | 0.882842 | 0.441421 | − | 0.897300i | \(-0.354474\pi\) | ||||
0.441421 | + | 0.897300i | \(0.354474\pi\) | |||||||
\(180\) | 2.55496 | 0.190435 | ||||||||
\(181\) | −5.48858 | −0.407963 | −0.203982 | − | 0.978975i | \(-0.565388\pi\) | ||||
−0.203982 | + | 0.978975i | \(0.565388\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.17629 | 0.234798 | ||||||||
\(184\) | 8.54288 | 0.629789 | ||||||||
\(185\) | 14.1618 | 1.04120 | ||||||||
\(186\) | 0.423272 | 0.0310358 | ||||||||
\(187\) | 11.0586 | 0.808685 | ||||||||
\(188\) | 4.50604 | 0.328637 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 7.28382 | 0.528424 | ||||||||
\(191\) | −5.17523 | −0.374466 | −0.187233 | − | 0.982316i | \(-0.559952\pi\) | ||||
−0.187233 | + | 0.982316i | \(0.559952\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 1.67696 | 0.120710 | 0.0603550 | − | 0.998177i | \(-0.480777\pi\) | ||||
0.0603550 | + | 0.998177i | \(0.480777\pi\) | |||||||
\(194\) | −1.12737 | −0.0809408 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −20.4916 | −1.45996 | −0.729982 | − | 0.683467i | \(-0.760472\pi\) | ||||
−0.729982 | + | 0.683467i | \(0.760472\pi\) | |||||||
\(198\) | −3.24698 | −0.230753 | ||||||||
\(199\) | −5.36898 | −0.380597 | −0.190298 | − | 0.981726i | \(-0.560946\pi\) | ||||
−0.190298 | + | 0.981726i | \(0.560946\pi\) | |||||||
\(200\) | −1.52781 | −0.108033 | ||||||||
\(201\) | 5.47219 | 0.385978 | ||||||||
\(202\) | 1.03385 | 0.0727416 | ||||||||
\(203\) | 6.18598 | 0.434171 | ||||||||
\(204\) | 3.40581 | 0.238455 | ||||||||
\(205\) | −8.03982 | −0.561525 | ||||||||
\(206\) | −8.18060 | −0.569970 | ||||||||
\(207\) | −8.54288 | −0.593771 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.25667 | −0.640297 | ||||||||
\(210\) | 2.55496 | 0.176309 | ||||||||
\(211\) | 6.69202 | 0.460698 | 0.230349 | − | 0.973108i | \(-0.426013\pi\) | ||||
0.230349 | + | 0.973108i | \(0.426013\pi\) | |||||||
\(212\) | 4.12498 | 0.283305 | ||||||||
\(213\) | −4.21983 | −0.289138 | ||||||||
\(214\) | 0.780167 | 0.0533312 | ||||||||
\(215\) | 12.6189 | 0.860605 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0.423272 | 0.0287335 | ||||||||
\(218\) | −6.93900 | −0.469968 | ||||||||
\(219\) | 12.2959 | 0.830880 | ||||||||
\(220\) | 8.29590 | 0.559309 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −5.54288 | −0.372014 | ||||||||
\(223\) | 18.5864 | 1.24464 | 0.622319 | − | 0.782764i | \(-0.286191\pi\) | ||||
0.622319 | + | 0.782764i | \(0.286191\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 1.52781 | 0.101854 | ||||||||
\(226\) | 5.20237 | 0.346057 | ||||||||
\(227\) | 6.92394 | 0.459558 | 0.229779 | − | 0.973243i | \(-0.426200\pi\) | ||||
0.229779 | + | 0.973243i | \(0.426200\pi\) | |||||||
\(228\) | −2.85086 | −0.188802 | ||||||||
\(229\) | 5.73855 | 0.379214 | 0.189607 | − | 0.981860i | \(-0.439279\pi\) | ||||
0.189607 | + | 0.981860i | \(0.439279\pi\) | |||||||
\(230\) | 21.8267 | 1.43921 | ||||||||
\(231\) | −3.24698 | −0.213636 | ||||||||
\(232\) | 6.18598 | 0.406130 | ||||||||
\(233\) | 11.2892 | 0.739580 | 0.369790 | − | 0.929115i | \(-0.379430\pi\) | ||||
0.369790 | + | 0.929115i | \(0.379430\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.5127 | 0.751009 | ||||||||
\(236\) | 14.9269 | 0.971660 | ||||||||
\(237\) | 10.2567 | 0.666242 | ||||||||
\(238\) | 3.40581 | 0.220766 | ||||||||
\(239\) | 19.3491 | 1.25159 | 0.625795 | − | 0.779987i | \(-0.284774\pi\) | ||||
0.625795 | + | 0.779987i | \(0.284774\pi\) | |||||||
\(240\) | 2.55496 | 0.164922 | ||||||||
\(241\) | −5.95108 | −0.383343 | −0.191671 | − | 0.981459i | \(-0.561391\pi\) | ||||
−0.191671 | + | 0.981459i | \(0.561391\pi\) | |||||||
\(242\) | 0.457123 | 0.0293850 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 3.17629 | 0.203341 | ||||||||
\(245\) | 2.55496 | 0.163230 | ||||||||
\(246\) | 3.14675 | 0.200630 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0.423272 | 0.0268778 | ||||||||
\(249\) | 16.8509 | 1.06788 | ||||||||
\(250\) | 8.87130 | 0.561070 | ||||||||
\(251\) | −8.84415 | −0.558238 | −0.279119 | − | 0.960257i | \(-0.590042\pi\) | ||||
−0.279119 | + | 0.960257i | \(0.590042\pi\) | |||||||
\(252\) | −1.00000 | −0.0629941 | ||||||||
\(253\) | −27.7385 | −1.74391 | ||||||||
\(254\) | 14.6136 | 0.916937 | ||||||||
\(255\) | 8.70171 | 0.544922 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −5.50902 | −0.343644 | −0.171822 | − | 0.985128i | \(-0.554965\pi\) | ||||
−0.171822 | + | 0.985128i | \(0.554965\pi\) | |||||||
\(258\) | −4.93900 | −0.307489 | ||||||||
\(259\) | −5.54288 | −0.344418 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.18598 | −0.382903 | ||||||||
\(262\) | −19.7778 | −1.22187 | ||||||||
\(263\) | −2.84548 | −0.175460 | −0.0877299 | − | 0.996144i | \(-0.527961\pi\) | ||||
−0.0877299 | + | 0.996144i | \(0.527961\pi\) | |||||||
\(264\) | −3.24698 | −0.199838 | ||||||||
\(265\) | 10.5392 | 0.647415 | ||||||||
\(266\) | −2.85086 | −0.174797 | ||||||||
\(267\) | 1.96615 | 0.120326 | ||||||||
\(268\) | 5.47219 | 0.334267 | ||||||||
\(269\) | 26.0291 | 1.58702 | 0.793510 | − | 0.608557i | \(-0.208251\pi\) | ||||
0.793510 | + | 0.608557i | \(0.208251\pi\) | |||||||
\(270\) | −2.55496 | −0.155490 | ||||||||
\(271\) | 2.45042 | 0.148852 | 0.0744262 | − | 0.997227i | \(-0.476287\pi\) | ||||
0.0744262 | + | 0.997227i | \(0.476287\pi\) | |||||||
\(272\) | 3.40581 | 0.206508 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −16.7627 | −1.01267 | ||||||||
\(275\) | 4.96077 | 0.299146 | ||||||||
\(276\) | −8.54288 | −0.514221 | ||||||||
\(277\) | −11.9812 | −0.719881 | −0.359941 | − | 0.932975i | \(-0.617203\pi\) | ||||
−0.359941 | + | 0.932975i | \(0.617203\pi\) | |||||||
\(278\) | −12.1685 | −0.729819 | ||||||||
\(279\) | −0.423272 | −0.0253406 | ||||||||
\(280\) | 2.55496 | 0.152688 | ||||||||
\(281\) | 2.88231 | 0.171944 | 0.0859722 | − | 0.996298i | \(-0.472600\pi\) | ||||
0.0859722 | + | 0.996298i | \(0.472600\pi\) | |||||||
\(282\) | −4.50604 | −0.268331 | ||||||||
\(283\) | −3.71917 | −0.221082 | −0.110541 | − | 0.993872i | \(-0.535258\pi\) | ||||
−0.110541 | + | 0.993872i | \(0.535258\pi\) | |||||||
\(284\) | −4.21983 | −0.250401 | ||||||||
\(285\) | −7.28382 | −0.431456 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.14675 | 0.185747 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −5.40044 | −0.317673 | ||||||||
\(290\) | 15.8049 | 0.928097 | ||||||||
\(291\) | 1.12737 | 0.0660879 | ||||||||
\(292\) | 12.2959 | 0.719563 | ||||||||
\(293\) | 16.2862 | 0.951450 | 0.475725 | − | 0.879594i | \(-0.342186\pi\) | ||||
0.475725 | + | 0.879594i | \(0.342186\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | 38.1377 | 2.22046 | ||||||||
\(296\) | −5.54288 | −0.322173 | ||||||||
\(297\) | 3.24698 | 0.188409 | ||||||||
\(298\) | −0.753020 | −0.0436213 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.52781 | 0.0882082 | ||||||||
\(301\) | −4.93900 | −0.284679 | ||||||||
\(302\) | −15.1021 | −0.869031 | ||||||||
\(303\) | −1.03385 | −0.0593932 | ||||||||
\(304\) | −2.85086 | −0.163508 | ||||||||
\(305\) | 8.11529 | 0.464680 | ||||||||
\(306\) | −3.40581 | −0.194697 | ||||||||
\(307\) | −1.91723 | −0.109422 | −0.0547111 | − | 0.998502i | \(-0.517424\pi\) | ||||
−0.0547111 | + | 0.998502i | \(0.517424\pi\) | |||||||
\(308\) | −3.24698 | −0.185014 | ||||||||
\(309\) | 8.18060 | 0.465378 | ||||||||
\(310\) | 1.08144 | 0.0614217 | ||||||||
\(311\) | −16.2064 | −0.918982 | −0.459491 | − | 0.888182i | \(-0.651968\pi\) | ||||
−0.459491 | + | 0.888182i | \(0.651968\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.2543 | −1.37093 | −0.685466 | − | 0.728104i | \(-0.740402\pi\) | ||||
−0.685466 | + | 0.728104i | \(0.740402\pi\) | |||||||
\(314\) | 18.5133 | 1.04477 | ||||||||
\(315\) | −2.55496 | −0.143956 | ||||||||
\(316\) | 10.2567 | 0.576983 | ||||||||
\(317\) | −23.2911 | −1.30816 | −0.654080 | − | 0.756426i | \(-0.726944\pi\) | ||||
−0.654080 | + | 0.756426i | \(0.726944\pi\) | |||||||
\(318\) | −4.12498 | −0.231317 | ||||||||
\(319\) | −20.0858 | −1.12459 | ||||||||
\(320\) | 2.55496 | 0.142827 | ||||||||
\(321\) | −0.780167 | −0.0435447 | ||||||||
\(322\) | −8.54288 | −0.476076 | ||||||||
\(323\) | −9.70948 | −0.540250 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 20.1444 | 1.11569 | ||||||||
\(327\) | 6.93900 | 0.383728 | ||||||||
\(328\) | 3.14675 | 0.173750 | ||||||||
\(329\) | −4.50604 | −0.248426 | ||||||||
\(330\) | −8.29590 | −0.456674 | ||||||||
\(331\) | −34.3957 | −1.89056 | −0.945278 | − | 0.326266i | \(-0.894209\pi\) | ||||
−0.945278 | + | 0.326266i | \(0.894209\pi\) | |||||||
\(332\) | 16.8509 | 0.924811 | ||||||||
\(333\) | 5.54288 | 0.303748 | ||||||||
\(334\) | −18.5157 | −1.01314 | ||||||||
\(335\) | 13.9812 | 0.763875 | ||||||||
\(336\) | −1.00000 | −0.0545545 | ||||||||
\(337\) | −14.8049 | −0.806475 | −0.403238 | − | 0.915095i | \(-0.632115\pi\) | ||||
−0.403238 | + | 0.915095i | \(0.632115\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.20237 | −0.282554 | ||||||||
\(340\) | 8.70171 | 0.471916 | ||||||||
\(341\) | −1.37435 | −0.0744255 | ||||||||
\(342\) | 2.85086 | 0.154157 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −4.93900 | −0.266293 | ||||||||
\(345\) | −21.8267 | −1.17511 | ||||||||
\(346\) | 22.5676 | 1.21324 | ||||||||
\(347\) | 26.6122 | 1.42862 | 0.714310 | − | 0.699830i | \(-0.246741\pi\) | ||||
0.714310 | + | 0.699830i | \(0.246741\pi\) | |||||||
\(348\) | −6.18598 | −0.331603 | ||||||||
\(349\) | −13.2567 | −0.709613 | −0.354807 | − | 0.934940i | \(-0.615453\pi\) | ||||
−0.354807 | + | 0.934940i | \(0.615453\pi\) | |||||||
\(350\) | 1.52781 | 0.0816649 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.24698 | −0.173065 | ||||||||
\(353\) | 22.5483 | 1.20012 | 0.600061 | − | 0.799954i | \(-0.295143\pi\) | ||||
0.600061 | + | 0.799954i | \(0.295143\pi\) | |||||||
\(354\) | −14.9269 | −0.793357 | ||||||||
\(355\) | −10.7815 | −0.572222 | ||||||||
\(356\) | 1.96615 | 0.104206 | ||||||||
\(357\) | −3.40581 | −0.180255 | ||||||||
\(358\) | −11.8116 | −0.624264 | ||||||||
\(359\) | 31.8025 | 1.67847 | 0.839237 | − | 0.543766i | \(-0.183002\pi\) | ||||
0.839237 | + | 0.543766i | \(0.183002\pi\) | |||||||
\(360\) | −2.55496 | −0.134658 | ||||||||
\(361\) | −10.8726 | −0.572243 | ||||||||
\(362\) | 5.48858 | 0.288473 | ||||||||
\(363\) | −0.457123 | −0.0239928 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 31.4155 | 1.64436 | ||||||||
\(366\) | −3.17629 | −0.166027 | ||||||||
\(367\) | −3.31037 | −0.172800 | −0.0864000 | − | 0.996261i | \(-0.527536\pi\) | ||||
−0.0864000 | + | 0.996261i | \(0.527536\pi\) | |||||||
\(368\) | −8.54288 | −0.445328 | ||||||||
\(369\) | −3.14675 | −0.163813 | ||||||||
\(370\) | −14.1618 | −0.736238 | ||||||||
\(371\) | −4.12498 | −0.214158 | ||||||||
\(372\) | −0.423272 | −0.0219456 | ||||||||
\(373\) | 34.8950 | 1.80679 | 0.903397 | − | 0.428805i | \(-0.141065\pi\) | ||||
0.903397 | + | 0.428805i | \(0.141065\pi\) | |||||||
\(374\) | −11.0586 | −0.571827 | ||||||||
\(375\) | −8.87130 | −0.458112 | ||||||||
\(376\) | −4.50604 | −0.232381 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.00000 | 0.0514344 | ||||||||
\(379\) | −33.3545 | −1.71331 | −0.856653 | − | 0.515893i | \(-0.827460\pi\) | ||||
−0.856653 | + | 0.515893i | \(0.827460\pi\) | |||||||
\(380\) | −7.28382 | −0.373652 | ||||||||
\(381\) | −14.6136 | −0.748676 | ||||||||
\(382\) | 5.17523 | 0.264788 | ||||||||
\(383\) | −23.3980 | −1.19558 | −0.597792 | − | 0.801651i | \(-0.703955\pi\) | ||||
−0.597792 | + | 0.801651i | \(0.703955\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −8.29590 | −0.422798 | ||||||||
\(386\) | −1.67696 | −0.0853548 | ||||||||
\(387\) | 4.93900 | 0.251064 | ||||||||
\(388\) | 1.12737 | 0.0572338 | ||||||||
\(389\) | −9.38644 | −0.475911 | −0.237956 | − | 0.971276i | \(-0.576477\pi\) | ||||
−0.237956 | + | 0.971276i | \(0.576477\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −29.0954 | −1.47142 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 19.7778 | 0.997657 | ||||||||
\(394\) | 20.4916 | 1.03235 | ||||||||
\(395\) | 26.2054 | 1.31853 | ||||||||
\(396\) | 3.24698 | 0.163167 | ||||||||
\(397\) | 7.96376 | 0.399689 | 0.199845 | − | 0.979828i | \(-0.435956\pi\) | ||||
0.199845 | + | 0.979828i | \(0.435956\pi\) | |||||||
\(398\) | 5.36898 | 0.269123 | ||||||||
\(399\) | 2.85086 | 0.142721 | ||||||||
\(400\) | 1.52781 | 0.0763906 | ||||||||
\(401\) | 25.4359 | 1.27021 | 0.635105 | − | 0.772426i | \(-0.280957\pi\) | ||||
0.635105 | + | 0.772426i | \(0.280957\pi\) | |||||||
\(402\) | −5.47219 | −0.272928 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −1.03385 | −0.0514361 | ||||||||
\(405\) | 2.55496 | 0.126957 | ||||||||
\(406\) | −6.18598 | −0.307005 | ||||||||
\(407\) | 17.9976 | 0.892108 | ||||||||
\(408\) | −3.40581 | −0.168613 | ||||||||
\(409\) | −26.9801 | −1.33408 | −0.667041 | − | 0.745021i | \(-0.732440\pi\) | ||||
−0.667041 | + | 0.745021i | \(0.732440\pi\) | |||||||
\(410\) | 8.03982 | 0.397058 | ||||||||
\(411\) | 16.7627 | 0.826843 | ||||||||
\(412\) | 8.18060 | 0.403029 | ||||||||
\(413\) | −14.9269 | −0.734506 | ||||||||
\(414\) | 8.54288 | 0.419859 | ||||||||
\(415\) | 43.0532 | 2.11340 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.1685 | 0.595895 | ||||||||
\(418\) | 9.25667 | 0.452758 | ||||||||
\(419\) | −38.1594 | −1.86421 | −0.932105 | − | 0.362188i | \(-0.882030\pi\) | ||||
−0.932105 | + | 0.362188i | \(0.882030\pi\) | |||||||
\(420\) | −2.55496 | −0.124669 | ||||||||
\(421\) | −12.0828 | −0.588878 | −0.294439 | − | 0.955670i | \(-0.595133\pi\) | ||||
−0.294439 | + | 0.955670i | \(0.595133\pi\) | |||||||
\(422\) | −6.69202 | −0.325763 | ||||||||
\(423\) | 4.50604 | 0.219091 | ||||||||
\(424\) | −4.12498 | −0.200327 | ||||||||
\(425\) | 5.20344 | 0.252404 | ||||||||
\(426\) | 4.21983 | 0.204452 | ||||||||
\(427\) | −3.17629 | −0.153712 | ||||||||
\(428\) | −0.780167 | −0.0377108 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −12.6189 | −0.608539 | ||||||||
\(431\) | −28.7023 | −1.38254 | −0.691271 | − | 0.722596i | \(-0.742949\pi\) | ||||
−0.691271 | + | 0.722596i | \(0.742949\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 9.33406 | 0.448566 | 0.224283 | − | 0.974524i | \(-0.427996\pi\) | ||||
0.224283 | + | 0.974524i | \(0.427996\pi\) | |||||||
\(434\) | −0.423272 | −0.0203177 | ||||||||
\(435\) | −15.8049 | −0.757788 | ||||||||
\(436\) | 6.93900 | 0.332318 | ||||||||
\(437\) | 24.3545 | 1.16503 | ||||||||
\(438\) | −12.2959 | −0.587521 | ||||||||
\(439\) | −15.3123 | −0.730816 | −0.365408 | − | 0.930848i | \(-0.619070\pi\) | ||||
−0.365408 | + | 0.930848i | \(0.619070\pi\) | |||||||
\(440\) | −8.29590 | −0.395491 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.89679 | 0.470211 | 0.235105 | − | 0.971970i | \(-0.424456\pi\) | ||||
0.235105 | + | 0.971970i | \(0.424456\pi\) | |||||||
\(444\) | 5.54288 | 0.263053 | ||||||||
\(445\) | 5.02343 | 0.238133 | ||||||||
\(446\) | −18.5864 | −0.880092 | ||||||||
\(447\) | 0.753020 | 0.0356166 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −26.9288 | −1.27085 | −0.635425 | − | 0.772162i | \(-0.719175\pi\) | ||||
−0.635425 | + | 0.772162i | \(0.719175\pi\) | |||||||
\(450\) | −1.52781 | −0.0720217 | ||||||||
\(451\) | −10.2174 | −0.481120 | ||||||||
\(452\) | −5.20237 | −0.244699 | ||||||||
\(453\) | 15.1021 | 0.709561 | ||||||||
\(454\) | −6.92394 | −0.324956 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.85086 | 0.133504 | ||||||||
\(457\) | −21.3351 | −0.998015 | −0.499008 | − | 0.866598i | \(-0.666302\pi\) | ||||
−0.499008 | + | 0.866598i | \(0.666302\pi\) | |||||||
\(458\) | −5.73855 | −0.268145 | ||||||||
\(459\) | 3.40581 | 0.158970 | ||||||||
\(460\) | −21.8267 | −1.01767 | ||||||||
\(461\) | 24.3045 | 1.13197 | 0.565987 | − | 0.824414i | \(-0.308495\pi\) | ||||
0.565987 | + | 0.824414i | \(0.308495\pi\) | |||||||
\(462\) | 3.24698 | 0.151063 | ||||||||
\(463\) | −37.0465 | −1.72170 | −0.860849 | − | 0.508860i | \(-0.830067\pi\) | ||||
−0.860849 | + | 0.508860i | \(0.830067\pi\) | |||||||
\(464\) | −6.18598 | −0.287177 | ||||||||
\(465\) | −1.08144 | −0.0501506 | ||||||||
\(466\) | −11.2892 | −0.522962 | ||||||||
\(467\) | 32.8582 | 1.52049 | 0.760247 | − | 0.649634i | \(-0.225078\pi\) | ||||
0.760247 | + | 0.649634i | \(0.225078\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.47219 | −0.252682 | ||||||||
\(470\) | −11.5127 | −0.531043 | ||||||||
\(471\) | −18.5133 | −0.853050 | ||||||||
\(472\) | −14.9269 | −0.687067 | ||||||||
\(473\) | 16.0368 | 0.737374 | ||||||||
\(474\) | −10.2567 | −0.471104 | ||||||||
\(475\) | −4.35557 | −0.199847 | ||||||||
\(476\) | −3.40581 | −0.156105 | ||||||||
\(477\) | 4.12498 | 0.188870 | ||||||||
\(478\) | −19.3491 | −0.885008 | ||||||||
\(479\) | −20.8829 | −0.954164 | −0.477082 | − | 0.878859i | \(-0.658306\pi\) | ||||
−0.477082 | + | 0.878859i | \(0.658306\pi\) | |||||||
\(480\) | −2.55496 | −0.116617 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 5.95108 | 0.271064 | ||||||||
\(483\) | 8.54288 | 0.388714 | ||||||||
\(484\) | −0.457123 | −0.0207783 | ||||||||
\(485\) | 2.88040 | 0.130792 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 33.0224 | 1.49639 | 0.748193 | − | 0.663481i | \(-0.230922\pi\) | ||||
0.748193 | + | 0.663481i | \(0.230922\pi\) | |||||||
\(488\) | −3.17629 | −0.143784 | ||||||||
\(489\) | −20.1444 | −0.910959 | ||||||||
\(490\) | −2.55496 | −0.115421 | ||||||||
\(491\) | 1.14244 | 0.0515576 | 0.0257788 | − | 0.999668i | \(-0.491793\pi\) | ||||
0.0257788 | + | 0.999668i | \(0.491793\pi\) | |||||||
\(492\) | −3.14675 | −0.141867 | ||||||||
\(493\) | −21.0683 | −0.948868 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.29590 | 0.372873 | ||||||||
\(496\) | −0.423272 | −0.0190055 | ||||||||
\(497\) | 4.21983 | 0.189285 | ||||||||
\(498\) | −16.8509 | −0.755105 | ||||||||
\(499\) | 16.4239 | 0.735233 | 0.367617 | − | 0.929977i | \(-0.380174\pi\) | ||||
0.367617 | + | 0.929977i | \(0.380174\pi\) | |||||||
\(500\) | −8.87130 | −0.396736 | ||||||||
\(501\) | 18.5157 | 0.827222 | ||||||||
\(502\) | 8.84415 | 0.394734 | ||||||||
\(503\) | −27.7797 | −1.23864 | −0.619318 | − | 0.785141i | \(-0.712591\pi\) | ||||
−0.619318 | + | 0.785141i | \(0.712591\pi\) | |||||||
\(504\) | 1.00000 | 0.0445435 | ||||||||
\(505\) | −2.64145 | −0.117543 | ||||||||
\(506\) | 27.7385 | 1.23313 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −14.6136 | −0.648372 | ||||||||
\(509\) | −16.3827 | −0.726151 | −0.363076 | − | 0.931760i | \(-0.618273\pi\) | ||||
−0.363076 | + | 0.931760i | \(0.618273\pi\) | |||||||
\(510\) | −8.70171 | −0.385318 | ||||||||
\(511\) | −12.2959 | −0.543938 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −2.85086 | −0.125868 | ||||||||
\(514\) | 5.50902 | 0.242993 | ||||||||
\(515\) | 20.9011 | 0.921013 | ||||||||
\(516\) | 4.93900 | 0.217427 | ||||||||
\(517\) | 14.6310 | 0.643472 | ||||||||
\(518\) | 5.54288 | 0.243540 | ||||||||
\(519\) | −22.5676 | −0.990609 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.65519 | 0.160137 | 0.0800683 | − | 0.996789i | \(-0.474486\pi\) | ||||
0.0800683 | + | 0.996789i | \(0.474486\pi\) | |||||||
\(522\) | 6.18598 | 0.270753 | ||||||||
\(523\) | −4.77884 | −0.208964 | −0.104482 | − | 0.994527i | \(-0.533318\pi\) | ||||
−0.104482 | + | 0.994527i | \(0.533318\pi\) | |||||||
\(524\) | 19.7778 | 0.863996 | ||||||||
\(525\) | −1.52781 | −0.0666791 | ||||||||
\(526\) | 2.84548 | 0.124069 | ||||||||
\(527\) | −1.44158 | −0.0627964 | ||||||||
\(528\) | 3.24698 | 0.141307 | ||||||||
\(529\) | 49.9807 | 2.17308 | ||||||||
\(530\) | −10.5392 | −0.457792 | ||||||||
\(531\) | 14.9269 | 0.647773 | ||||||||
\(532\) | 2.85086 | 0.123600 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −1.96615 | −0.0850836 | ||||||||
\(535\) | −1.99330 | −0.0861777 | ||||||||
\(536\) | −5.47219 | −0.236363 | ||||||||
\(537\) | 11.8116 | 0.509709 | ||||||||
\(538\) | −26.0291 | −1.12219 | ||||||||
\(539\) | 3.24698 | 0.139857 | ||||||||
\(540\) | 2.55496 | 0.109948 | ||||||||
\(541\) | −26.4450 | −1.13696 | −0.568481 | − | 0.822697i | \(-0.692469\pi\) | ||||
−0.568481 | + | 0.822697i | \(0.692469\pi\) | |||||||
\(542\) | −2.45042 | −0.105254 | ||||||||
\(543\) | −5.48858 | −0.235538 | ||||||||
\(544\) | −3.40581 | −0.146023 | ||||||||
\(545\) | 17.7289 | 0.759421 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.0073 | 1.11199 | 0.555996 | − | 0.831185i | \(-0.312337\pi\) | ||||
0.555996 | + | 0.831185i | \(0.312337\pi\) | |||||||
\(548\) | 16.7627 | 0.716067 | ||||||||
\(549\) | 3.17629 | 0.135561 | ||||||||
\(550\) | −4.96077 | −0.211528 | ||||||||
\(551\) | 17.6353 | 0.751291 | ||||||||
\(552\) | 8.54288 | 0.363609 | ||||||||
\(553\) | −10.2567 | −0.436158 | ||||||||
\(554\) | 11.9812 | 0.509033 | ||||||||
\(555\) | 14.1618 | 0.601136 | ||||||||
\(556\) | 12.1685 | 0.516060 | ||||||||
\(557\) | 27.9135 | 1.18273 | 0.591367 | − | 0.806403i | \(-0.298589\pi\) | ||||
0.591367 | + | 0.806403i | \(0.298589\pi\) | |||||||
\(558\) | 0.423272 | 0.0179185 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2.55496 | −0.107967 | ||||||||
\(561\) | 11.0586 | 0.466895 | ||||||||
\(562\) | −2.88231 | −0.121583 | ||||||||
\(563\) | 35.9323 | 1.51437 | 0.757183 | − | 0.653203i | \(-0.226575\pi\) | ||||
0.757183 | + | 0.653203i | \(0.226575\pi\) | |||||||
\(564\) | 4.50604 | 0.189739 | ||||||||
\(565\) | −13.2918 | −0.559192 | ||||||||
\(566\) | 3.71917 | 0.156328 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 4.21983 | 0.177060 | ||||||||
\(569\) | 37.1226 | 1.55626 | 0.778130 | − | 0.628103i | \(-0.216168\pi\) | ||||
0.778130 | + | 0.628103i | \(0.216168\pi\) | |||||||
\(570\) | 7.28382 | 0.305085 | ||||||||
\(571\) | −14.8280 | −0.620533 | −0.310267 | − | 0.950650i | \(-0.600418\pi\) | ||||
−0.310267 | + | 0.950650i | \(0.600418\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.17523 | −0.216198 | ||||||||
\(574\) | −3.14675 | −0.131343 | ||||||||
\(575\) | −13.0519 | −0.544302 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 27.4161 | 1.14135 | 0.570673 | − | 0.821177i | \(-0.306682\pi\) | ||||
0.570673 | + | 0.821177i | \(0.306682\pi\) | |||||||
\(578\) | 5.40044 | 0.224629 | ||||||||
\(579\) | 1.67696 | 0.0696919 | ||||||||
\(580\) | −15.8049 | −0.656264 | ||||||||
\(581\) | −16.8509 | −0.699091 | ||||||||
\(582\) | −1.12737 | −0.0467312 | ||||||||
\(583\) | 13.3937 | 0.554712 | ||||||||
\(584\) | −12.2959 | −0.508808 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.2862 | −0.672777 | ||||||||
\(587\) | −1.54288 | −0.0636813 | −0.0318407 | − | 0.999493i | \(-0.510137\pi\) | ||||
−0.0318407 | + | 0.999493i | \(0.510137\pi\) | |||||||
\(588\) | 1.00000 | 0.0412393 | ||||||||
\(589\) | 1.20669 | 0.0497206 | ||||||||
\(590\) | −38.1377 | −1.57010 | ||||||||
\(591\) | −20.4916 | −0.842910 | ||||||||
\(592\) | 5.54288 | 0.227811 | ||||||||
\(593\) | −35.9124 | −1.47475 | −0.737374 | − | 0.675485i | \(-0.763934\pi\) | ||||
−0.737374 | + | 0.675485i | \(0.763934\pi\) | |||||||
\(594\) | −3.24698 | −0.133225 | ||||||||
\(595\) | −8.70171 | −0.356735 | ||||||||
\(596\) | 0.753020 | 0.0308449 | ||||||||
\(597\) | −5.36898 | −0.219738 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −25.6209 | −1.04684 | −0.523420 | − | 0.852075i | \(-0.675344\pi\) | ||||
−0.523420 | + | 0.852075i | \(0.675344\pi\) | |||||||
\(600\) | −1.52781 | −0.0623726 | ||||||||
\(601\) | 9.42519 | 0.384462 | 0.192231 | − | 0.981350i | \(-0.438428\pi\) | ||||
0.192231 | + | 0.981350i | \(0.438428\pi\) | |||||||
\(602\) | 4.93900 | 0.201299 | ||||||||
\(603\) | 5.47219 | 0.222845 | ||||||||
\(604\) | 15.1021 | 0.614498 | ||||||||
\(605\) | −1.16793 | −0.0474832 | ||||||||
\(606\) | 1.03385 | 0.0419974 | ||||||||
\(607\) | −29.0495 | −1.17908 | −0.589542 | − | 0.807738i | \(-0.700692\pi\) | ||||
−0.589542 | + | 0.807738i | \(0.700692\pi\) | |||||||
\(608\) | 2.85086 | 0.115617 | ||||||||
\(609\) | 6.18598 | 0.250669 | ||||||||
\(610\) | −8.11529 | −0.328579 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 3.40581 | 0.137672 | ||||||||
\(613\) | −16.3763 | −0.661431 | −0.330716 | − | 0.943730i | \(-0.607290\pi\) | ||||
−0.330716 | + | 0.943730i | \(0.607290\pi\) | |||||||
\(614\) | 1.91723 | 0.0773731 | ||||||||
\(615\) | −8.03982 | −0.324197 | ||||||||
\(616\) | 3.24698 | 0.130825 | ||||||||
\(617\) | −21.7313 | −0.874867 | −0.437434 | − | 0.899251i | \(-0.644112\pi\) | ||||
−0.437434 | + | 0.899251i | \(0.644112\pi\) | |||||||
\(618\) | −8.18060 | −0.329072 | ||||||||
\(619\) | −29.4437 | −1.18344 | −0.591721 | − | 0.806143i | \(-0.701551\pi\) | ||||
−0.591721 | + | 0.806143i | \(0.701551\pi\) | |||||||
\(620\) | −1.08144 | −0.0434317 | ||||||||
\(621\) | −8.54288 | −0.342814 | ||||||||
\(622\) | 16.2064 | 0.649818 | ||||||||
\(623\) | −1.96615 | −0.0787721 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.3048 | −1.21219 | ||||||||
\(626\) | 24.2543 | 0.969396 | ||||||||
\(627\) | −9.25667 | −0.369676 | ||||||||
\(628\) | −18.5133 | −0.738763 | ||||||||
\(629\) | 18.8780 | 0.752715 | ||||||||
\(630\) | 2.55496 | 0.101792 | ||||||||
\(631\) | 31.9855 | 1.27332 | 0.636662 | − | 0.771143i | \(-0.280315\pi\) | ||||
0.636662 | + | 0.771143i | \(0.280315\pi\) | |||||||
\(632\) | −10.2567 | −0.407988 | ||||||||
\(633\) | 6.69202 | 0.265984 | ||||||||
\(634\) | 23.2911 | 0.925008 | ||||||||
\(635\) | −37.3370 | −1.48168 | ||||||||
\(636\) | 4.12498 | 0.163566 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 20.0858 | 0.795203 | ||||||||
\(639\) | −4.21983 | −0.166934 | ||||||||
\(640\) | −2.55496 | −0.100994 | ||||||||
\(641\) | −38.9353 | −1.53785 | −0.768926 | − | 0.639338i | \(-0.779208\pi\) | ||||
−0.768926 | + | 0.639338i | \(0.779208\pi\) | |||||||
\(642\) | 0.780167 | 0.0307908 | ||||||||
\(643\) | 43.4010 | 1.71157 | 0.855785 | − | 0.517332i | \(-0.173075\pi\) | ||||
0.855785 | + | 0.517332i | \(0.173075\pi\) | |||||||
\(644\) | 8.54288 | 0.336636 | ||||||||
\(645\) | 12.6189 | 0.496870 | ||||||||
\(646\) | 9.70948 | 0.382014 | ||||||||
\(647\) | 29.4825 | 1.15908 | 0.579538 | − | 0.814945i | \(-0.303233\pi\) | ||||
0.579538 | + | 0.814945i | \(0.303233\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 48.4674 | 1.90251 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.423272 | 0.0165893 | ||||||||
\(652\) | −20.1444 | −0.788914 | ||||||||
\(653\) | −36.3715 | −1.42333 | −0.711663 | − | 0.702521i | \(-0.752058\pi\) | ||||
−0.711663 | + | 0.702521i | \(0.752058\pi\) | |||||||
\(654\) | −6.93900 | −0.271336 | ||||||||
\(655\) | 50.5314 | 1.97442 | ||||||||
\(656\) | −3.14675 | −0.122860 | ||||||||
\(657\) | 12.2959 | 0.479709 | ||||||||
\(658\) | 4.50604 | 0.175664 | ||||||||
\(659\) | 5.29483 | 0.206257 | 0.103129 | − | 0.994668i | \(-0.467115\pi\) | ||||
0.103129 | + | 0.994668i | \(0.467115\pi\) | |||||||
\(660\) | 8.29590 | 0.322917 | ||||||||
\(661\) | 4.78209 | 0.186002 | 0.0930008 | − | 0.995666i | \(-0.470354\pi\) | ||||
0.0930008 | + | 0.995666i | \(0.470354\pi\) | |||||||
\(662\) | 34.3957 | 1.33682 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −16.8509 | −0.653940 | ||||||||
\(665\) | 7.28382 | 0.282454 | ||||||||
\(666\) | −5.54288 | −0.214782 | ||||||||
\(667\) | 52.8461 | 2.04621 | ||||||||
\(668\) | 18.5157 | 0.716395 | ||||||||
\(669\) | 18.5864 | 0.718592 | ||||||||
\(670\) | −13.9812 | −0.540141 | ||||||||
\(671\) | 10.3134 | 0.398143 | ||||||||
\(672\) | 1.00000 | 0.0385758 | ||||||||
\(673\) | 27.5687 | 1.06270 | 0.531348 | − | 0.847154i | \(-0.321686\pi\) | ||||
0.531348 | + | 0.847154i | \(0.321686\pi\) | |||||||
\(674\) | 14.8049 | 0.570264 | ||||||||
\(675\) | 1.52781 | 0.0588055 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.08038 | 0.233688 | 0.116844 | − | 0.993150i | \(-0.462722\pi\) | ||||
0.116844 | + | 0.993150i | \(0.462722\pi\) | |||||||
\(678\) | 5.20237 | 0.199796 | ||||||||
\(679\) | −1.12737 | −0.0432647 | ||||||||
\(680\) | −8.70171 | −0.333695 | ||||||||
\(681\) | 6.92394 | 0.265326 | ||||||||
\(682\) | 1.37435 | 0.0526267 | ||||||||
\(683\) | 50.2941 | 1.92445 | 0.962225 | − | 0.272255i | \(-0.0877695\pi\) | ||||
0.962225 | + | 0.272255i | \(0.0877695\pi\) | |||||||
\(684\) | −2.85086 | −0.109005 | ||||||||
\(685\) | 42.8280 | 1.63637 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 5.73855 | 0.218939 | ||||||||
\(688\) | 4.93900 | 0.188298 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 21.8267 | 0.830928 | ||||||||
\(691\) | −1.83340 | −0.0697457 | −0.0348728 | − | 0.999392i | \(-0.511103\pi\) | ||||
−0.0348728 | + | 0.999392i | \(0.511103\pi\) | |||||||
\(692\) | −22.5676 | −0.857893 | ||||||||
\(693\) | −3.24698 | −0.123343 | ||||||||
\(694\) | −26.6122 | −1.01019 | ||||||||
\(695\) | 31.0901 | 1.17931 | ||||||||
\(696\) | 6.18598 | 0.234479 | ||||||||
\(697\) | −10.7172 | −0.405945 | ||||||||
\(698\) | 13.2567 | 0.501772 | ||||||||
\(699\) | 11.2892 | 0.426996 | ||||||||
\(700\) | −1.52781 | −0.0577458 | ||||||||
\(701\) | 2.42327 | 0.0915257 | 0.0457629 | − | 0.998952i | \(-0.485428\pi\) | ||||
0.0457629 | + | 0.998952i | \(0.485428\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.8019 | −0.595981 | ||||||||
\(704\) | 3.24698 | 0.122375 | ||||||||
\(705\) | 11.5127 | 0.433595 | ||||||||
\(706\) | −22.5483 | −0.848615 | ||||||||
\(707\) | 1.03385 | 0.0388820 | ||||||||
\(708\) | 14.9269 | 0.560988 | ||||||||
\(709\) | −21.0355 | −0.790005 | −0.395003 | − | 0.918680i | \(-0.629256\pi\) | ||||
−0.395003 | + | 0.918680i | \(0.629256\pi\) | |||||||
\(710\) | 10.7815 | 0.404622 | ||||||||
\(711\) | 10.2567 | 0.384655 | ||||||||
\(712\) | −1.96615 | −0.0736845 | ||||||||
\(713\) | 3.61596 | 0.135419 | ||||||||
\(714\) | 3.40581 | 0.127459 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11.8116 | 0.441421 | ||||||||
\(717\) | 19.3491 | 0.722606 | ||||||||
\(718\) | −31.8025 | −1.18686 | ||||||||
\(719\) | 10.7584 | 0.401221 | 0.200610 | − | 0.979671i | \(-0.435708\pi\) | ||||
0.200610 | + | 0.979671i | \(0.435708\pi\) | |||||||
\(720\) | 2.55496 | 0.0952177 | ||||||||
\(721\) | −8.18060 | −0.304662 | ||||||||
\(722\) | 10.8726 | 0.404637 | ||||||||
\(723\) | −5.95108 | −0.221323 | ||||||||
\(724\) | −5.48858 | −0.203982 | ||||||||
\(725\) | −9.45101 | −0.351002 | ||||||||
\(726\) | 0.457123 | 0.0169654 | ||||||||
\(727\) | −8.15777 | −0.302555 | −0.151277 | − | 0.988491i | \(-0.548339\pi\) | ||||
−0.151277 | + | 0.988491i | \(0.548339\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −31.4155 | −1.16274 | ||||||||
\(731\) | 16.8213 | 0.622159 | ||||||||
\(732\) | 3.17629 | 0.117399 | ||||||||
\(733\) | 19.3884 | 0.716125 | 0.358063 | − | 0.933698i | \(-0.383437\pi\) | ||||
0.358063 | + | 0.933698i | \(0.383437\pi\) | |||||||
\(734\) | 3.31037 | 0.122188 | ||||||||
\(735\) | 2.55496 | 0.0942411 | ||||||||
\(736\) | 8.54288 | 0.314895 | ||||||||
\(737\) | 17.7681 | 0.654496 | ||||||||
\(738\) | 3.14675 | 0.115834 | ||||||||
\(739\) | −35.7579 | −1.31538 | −0.657688 | − | 0.753290i | \(-0.728466\pi\) | ||||
−0.657688 | + | 0.753290i | \(0.728466\pi\) | |||||||
\(740\) | 14.1618 | 0.520599 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.12498 | 0.151433 | ||||||||
\(743\) | −27.8799 | −1.02282 | −0.511408 | − | 0.859338i | \(-0.670876\pi\) | ||||
−0.511408 | + | 0.859338i | \(0.670876\pi\) | |||||||
\(744\) | 0.423272 | 0.0155179 | ||||||||
\(745\) | 1.92394 | 0.0704875 | ||||||||
\(746\) | −34.8950 | −1.27760 | ||||||||
\(747\) | 16.8509 | 0.616541 | ||||||||
\(748\) | 11.0586 | 0.404343 | ||||||||
\(749\) | 0.780167 | 0.0285067 | ||||||||
\(750\) | 8.87130 | 0.323934 | ||||||||
\(751\) | 20.3526 | 0.742676 | 0.371338 | − | 0.928498i | \(-0.378899\pi\) | ||||
0.371338 | + | 0.928498i | \(0.378899\pi\) | |||||||
\(752\) | 4.50604 | 0.164318 | ||||||||
\(753\) | −8.84415 | −0.322299 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 38.5854 | 1.40426 | ||||||||
\(756\) | −1.00000 | −0.0363696 | ||||||||
\(757\) | −53.9023 | −1.95911 | −0.979556 | − | 0.201172i | \(-0.935525\pi\) | ||||
−0.979556 | + | 0.201172i | \(0.935525\pi\) | |||||||
\(758\) | 33.3545 | 1.21149 | ||||||||
\(759\) | −27.7385 | −1.00685 | ||||||||
\(760\) | 7.28382 | 0.264212 | ||||||||
\(761\) | −20.2446 | −0.733866 | −0.366933 | − | 0.930247i | \(-0.619592\pi\) | ||||
−0.366933 | + | 0.930247i | \(0.619592\pi\) | |||||||
\(762\) | 14.6136 | 0.529394 | ||||||||
\(763\) | −6.93900 | −0.251209 | ||||||||
\(764\) | −5.17523 | −0.187233 | ||||||||
\(765\) | 8.70171 | 0.314611 | ||||||||
\(766\) | 23.3980 | 0.845406 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 10.5351 | 0.379906 | 0.189953 | − | 0.981793i | \(-0.439166\pi\) | ||||
0.189953 | + | 0.981793i | \(0.439166\pi\) | |||||||
\(770\) | 8.29590 | 0.298963 | ||||||||
\(771\) | −5.50902 | −0.198403 | ||||||||
\(772\) | 1.67696 | 0.0603550 | ||||||||
\(773\) | −24.5526 | −0.883094 | −0.441547 | − | 0.897238i | \(-0.645570\pi\) | ||||
−0.441547 | + | 0.897238i | \(0.645570\pi\) | |||||||
\(774\) | −4.93900 | −0.177529 | ||||||||
\(775\) | −0.646679 | −0.0232294 | ||||||||
\(776\) | −1.12737 | −0.0404704 | ||||||||
\(777\) | −5.54288 | −0.198850 | ||||||||
\(778\) | 9.38644 | 0.336520 | ||||||||
\(779\) | 8.97093 | 0.321417 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.7017 | −0.490286 | ||||||||
\(782\) | 29.0954 | 1.04045 | ||||||||
\(783\) | −6.18598 | −0.221069 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −47.3008 | −1.68824 | ||||||||
\(786\) | −19.7778 | −0.705450 | ||||||||
\(787\) | −37.2301 | −1.32711 | −0.663555 | − | 0.748127i | \(-0.730953\pi\) | ||||
−0.663555 | + | 0.748127i | \(0.730953\pi\) | |||||||
\(788\) | −20.4916 | −0.729982 | ||||||||
\(789\) | −2.84548 | −0.101302 | ||||||||
\(790\) | −26.2054 | −0.932345 | ||||||||
\(791\) | 5.20237 | 0.184975 | ||||||||
\(792\) | −3.24698 | −0.115376 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −7.96376 | −0.282623 | ||||||||
\(795\) | 10.5392 | 0.373785 | ||||||||
\(796\) | −5.36898 | −0.190298 | ||||||||
\(797\) | 23.5163 | 0.832991 | 0.416495 | − | 0.909138i | \(-0.363258\pi\) | ||||
0.416495 | + | 0.909138i | \(0.363258\pi\) | |||||||
\(798\) | −2.85086 | −0.100919 | ||||||||
\(799\) | 15.3467 | 0.542928 | ||||||||
\(800\) | −1.52781 | −0.0540163 | ||||||||
\(801\) | 1.96615 | 0.0694704 | ||||||||
\(802\) | −25.4359 | −0.898174 | ||||||||
\(803\) | 39.9245 | 1.40891 | ||||||||
\(804\) | 5.47219 | 0.192989 | ||||||||
\(805\) | 21.8267 | 0.769290 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 26.0291 | 0.916267 | ||||||||
\(808\) | 1.03385 | 0.0363708 | ||||||||
\(809\) | 45.8437 | 1.61178 | 0.805889 | − | 0.592067i | \(-0.201688\pi\) | ||||
0.805889 | + | 0.592067i | \(0.201688\pi\) | |||||||
\(810\) | −2.55496 | −0.0897721 | ||||||||
\(811\) | 39.7192 | 1.39473 | 0.697364 | − | 0.716717i | \(-0.254356\pi\) | ||||
0.697364 | + | 0.716717i | \(0.254356\pi\) | |||||||
\(812\) | 6.18598 | 0.217085 | ||||||||
\(813\) | 2.45042 | 0.0859399 | ||||||||
\(814\) | −17.9976 | −0.630816 | ||||||||
\(815\) | −51.4680 | −1.80285 | ||||||||
\(816\) | 3.40581 | 0.119227 | ||||||||
\(817\) | −14.0804 | −0.492610 | ||||||||
\(818\) | 26.9801 | 0.943339 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.03982 | −0.280763 | ||||||||
\(821\) | −21.5319 | −0.751467 | −0.375734 | − | 0.926728i | \(-0.622609\pi\) | ||||
−0.375734 | + | 0.926728i | \(0.622609\pi\) | |||||||
\(822\) | −16.7627 | −0.584667 | ||||||||
\(823\) | 22.2107 | 0.774218 | 0.387109 | − | 0.922034i | \(-0.373474\pi\) | ||||
0.387109 | + | 0.922034i | \(0.373474\pi\) | |||||||
\(824\) | −8.18060 | −0.284985 | ||||||||
\(825\) | 4.96077 | 0.172712 | ||||||||
\(826\) | 14.9269 | 0.519374 | ||||||||
\(827\) | −15.8793 | −0.552178 | −0.276089 | − | 0.961132i | \(-0.589039\pi\) | ||||
−0.276089 | + | 0.961132i | \(0.589039\pi\) | |||||||
\(828\) | −8.54288 | −0.296885 | ||||||||
\(829\) | 11.5948 | 0.402703 | 0.201352 | − | 0.979519i | \(-0.435467\pi\) | ||||
0.201352 | + | 0.979519i | \(0.435467\pi\) | |||||||
\(830\) | −43.0532 | −1.49440 | ||||||||
\(831\) | −11.9812 | −0.415624 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.40581 | 0.118004 | ||||||||
\(834\) | −12.1685 | −0.421361 | ||||||||
\(835\) | 47.3069 | 1.63712 | ||||||||
\(836\) | −9.25667 | −0.320149 | ||||||||
\(837\) | −0.423272 | −0.0146304 | ||||||||
\(838\) | 38.1594 | 1.31820 | ||||||||
\(839\) | 16.7759 | 0.579167 | 0.289583 | − | 0.957153i | \(-0.406483\pi\) | ||||
0.289583 | + | 0.957153i | \(0.406483\pi\) | |||||||
\(840\) | 2.55496 | 0.0881544 | ||||||||
\(841\) | 9.26636 | 0.319530 | ||||||||
\(842\) | 12.0828 | 0.416400 | ||||||||
\(843\) | 2.88231 | 0.0992722 | ||||||||
\(844\) | 6.69202 | 0.230349 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.50604 | −0.154921 | ||||||||
\(847\) | 0.457123 | 0.0157069 | ||||||||
\(848\) | 4.12498 | 0.141652 | ||||||||
\(849\) | −3.71917 | −0.127642 | ||||||||
\(850\) | −5.20344 | −0.178476 | ||||||||
\(851\) | −47.3521 | −1.62321 | ||||||||
\(852\) | −4.21983 | −0.144569 | ||||||||
\(853\) | −25.7864 | −0.882909 | −0.441455 | − | 0.897284i | \(-0.645537\pi\) | ||||
−0.441455 | + | 0.897284i | \(0.645537\pi\) | |||||||
\(854\) | 3.17629 | 0.108690 | ||||||||
\(855\) | −7.28382 | −0.249101 | ||||||||
\(856\) | 0.780167 | 0.0266656 | ||||||||
\(857\) | −7.85517 | −0.268327 | −0.134164 | − | 0.990959i | \(-0.542835\pi\) | ||||
−0.134164 | + | 0.990959i | \(0.542835\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.97179 | 0.271994 | 0.135997 | − | 0.990709i | \(-0.456576\pi\) | ||||
0.135997 | + | 0.990709i | \(0.456576\pi\) | |||||||
\(860\) | 12.6189 | 0.430302 | ||||||||
\(861\) | 3.14675 | 0.107241 | ||||||||
\(862\) | 28.7023 | 0.977604 | ||||||||
\(863\) | 5.64310 | 0.192093 | 0.0960467 | − | 0.995377i | \(-0.469380\pi\) | ||||
0.0960467 | + | 0.995377i | \(0.469380\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −57.6594 | −1.96048 | ||||||||
\(866\) | −9.33406 | −0.317184 | ||||||||
\(867\) | −5.40044 | −0.183408 | ||||||||
\(868\) | 0.423272 | 0.0143668 | ||||||||
\(869\) | 33.3032 | 1.12973 | ||||||||
\(870\) | 15.8049 | 0.535837 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −6.93900 | −0.234984 | ||||||||
\(873\) | 1.12737 | 0.0381559 | ||||||||
\(874\) | −24.3545 | −0.823803 | ||||||||
\(875\) | 8.87130 | 0.299905 | ||||||||
\(876\) | 12.2959 | 0.415440 | ||||||||
\(877\) | 4.71273 | 0.159137 | 0.0795687 | − | 0.996829i | \(-0.474646\pi\) | ||||
0.0795687 | + | 0.996829i | \(0.474646\pi\) | |||||||
\(878\) | 15.3123 | 0.516765 | ||||||||
\(879\) | 16.2862 | 0.549320 | ||||||||
\(880\) | 8.29590 | 0.279655 | ||||||||
\(881\) | 24.1400 | 0.813299 | 0.406649 | − | 0.913584i | \(-0.366697\pi\) | ||||
0.406649 | + | 0.913584i | \(0.366697\pi\) | |||||||
\(882\) | −1.00000 | −0.0336718 | ||||||||
\(883\) | 9.48858 | 0.319316 | 0.159658 | − | 0.987172i | \(-0.448961\pi\) | ||||
0.159658 | + | 0.987172i | \(0.448961\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 38.1377 | 1.28198 | ||||||||
\(886\) | −9.89679 | −0.332489 | ||||||||
\(887\) | 37.4319 | 1.25684 | 0.628420 | − | 0.777874i | \(-0.283702\pi\) | ||||
0.628420 | + | 0.777874i | \(0.283702\pi\) | |||||||
\(888\) | −5.54288 | −0.186007 | ||||||||
\(889\) | 14.6136 | 0.490123 | ||||||||
\(890\) | −5.02343 | −0.168386 | ||||||||
\(891\) | 3.24698 | 0.108778 | ||||||||
\(892\) | 18.5864 | 0.622319 | ||||||||
\(893\) | −12.8461 | −0.429877 | ||||||||
\(894\) | −0.753020 | −0.0251848 | ||||||||
\(895\) | 30.1782 | 1.00875 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 26.9288 | 0.898627 | ||||||||
\(899\) | 2.61835 | 0.0873269 | ||||||||
\(900\) | 1.52781 | 0.0509270 | ||||||||
\(901\) | 14.0489 | 0.468037 | ||||||||
\(902\) | 10.2174 | 0.340204 | ||||||||
\(903\) | −4.93900 | −0.164360 | ||||||||
\(904\) | 5.20237 | 0.173028 | ||||||||
\(905\) | −14.0231 | −0.466144 | ||||||||
\(906\) | −15.1021 | −0.501735 | ||||||||
\(907\) | −53.1041 | −1.76329 | −0.881646 | − | 0.471912i | \(-0.843564\pi\) | ||||
−0.881646 | + | 0.471912i | \(0.843564\pi\) | |||||||
\(908\) | 6.92394 | 0.229779 | ||||||||
\(909\) | −1.03385 | −0.0342907 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.68127 | −0.155097 | −0.0775487 | − | 0.996989i | \(-0.524709\pi\) | ||||
−0.0775487 | + | 0.996989i | \(0.524709\pi\) | |||||||
\(912\) | −2.85086 | −0.0944012 | ||||||||
\(913\) | 54.7144 | 1.81078 | ||||||||
\(914\) | 21.3351 | 0.705703 | ||||||||
\(915\) | 8.11529 | 0.268283 | ||||||||
\(916\) | 5.73855 | 0.189607 | ||||||||
\(917\) | −19.7778 | −0.653120 | ||||||||
\(918\) | −3.40581 | −0.112409 | ||||||||
\(919\) | 17.1515 | 0.565777 | 0.282889 | − | 0.959153i | \(-0.408707\pi\) | ||||
0.282889 | + | 0.959153i | \(0.408707\pi\) | |||||||
\(920\) | 21.8267 | 0.719605 | ||||||||
\(921\) | −1.91723 | −0.0631749 | ||||||||
\(922\) | −24.3045 | −0.800427 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −3.24698 | −0.106818 | ||||||||
\(925\) | 8.46847 | 0.278442 | ||||||||
\(926\) | 37.0465 | 1.21742 | ||||||||
\(927\) | 8.18060 | 0.268686 | ||||||||
\(928\) | 6.18598 | 0.203065 | ||||||||
\(929\) | −27.7235 | −0.909578 | −0.454789 | − | 0.890599i | \(-0.650285\pi\) | ||||
−0.454789 | + | 0.890599i | \(0.650285\pi\) | |||||||
\(930\) | 1.08144 | 0.0354619 | ||||||||
\(931\) | −2.85086 | −0.0934330 | ||||||||
\(932\) | 11.2892 | 0.369790 | ||||||||
\(933\) | −16.2064 | −0.530574 | ||||||||
\(934\) | −32.8582 | −1.07515 | ||||||||
\(935\) | 28.2543 | 0.924014 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.49396 | −0.212148 | −0.106074 | − | 0.994358i | \(-0.533828\pi\) | ||||
−0.106074 | + | 0.994358i | \(0.533828\pi\) | |||||||
\(938\) | 5.47219 | 0.178673 | ||||||||
\(939\) | −24.2543 | −0.791508 | ||||||||
\(940\) | 11.5127 | 0.375504 | ||||||||
\(941\) | −7.95779 | −0.259416 | −0.129708 | − | 0.991552i | \(-0.541404\pi\) | ||||
−0.129708 | + | 0.991552i | \(0.541404\pi\) | |||||||
\(942\) | 18.5133 | 0.603197 | ||||||||
\(943\) | 26.8823 | 0.875409 | ||||||||
\(944\) | 14.9269 | 0.485830 | ||||||||
\(945\) | −2.55496 | −0.0831128 | ||||||||
\(946\) | −16.0368 | −0.521403 | ||||||||
\(947\) | 56.4717 | 1.83508 | 0.917542 | − | 0.397639i | \(-0.130170\pi\) | ||||
0.917542 | + | 0.397639i | \(0.130170\pi\) | |||||||
\(948\) | 10.2567 | 0.333121 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 4.35557 | 0.141313 | ||||||||
\(951\) | −23.2911 | −0.755266 | ||||||||
\(952\) | 3.40581 | 0.110383 | ||||||||
\(953\) | 37.2204 | 1.20569 | 0.602844 | − | 0.797859i | \(-0.294034\pi\) | ||||
0.602844 | + | 0.797859i | \(0.294034\pi\) | |||||||
\(954\) | −4.12498 | −0.133551 | ||||||||
\(955\) | −13.2225 | −0.427870 | ||||||||
\(956\) | 19.3491 | 0.625795 | ||||||||
\(957\) | −20.0858 | −0.649280 | ||||||||
\(958\) | 20.8829 | 0.674696 | ||||||||
\(959\) | −16.7627 | −0.541296 | ||||||||
\(960\) | 2.55496 | 0.0824609 | ||||||||
\(961\) | −30.8208 | −0.994221 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.780167 | −0.0251405 | ||||||||
\(964\) | −5.95108 | −0.191671 | ||||||||
\(965\) | 4.28455 | 0.137925 | ||||||||
\(966\) | −8.54288 | −0.274863 | ||||||||
\(967\) | −24.0790 | −0.774330 | −0.387165 | − | 0.922010i | \(-0.626546\pi\) | ||||
−0.387165 | + | 0.922010i | \(0.626546\pi\) | |||||||
\(968\) | 0.457123 | 0.0146925 | ||||||||
\(969\) | −9.70948 | −0.311913 | ||||||||
\(970\) | −2.88040 | −0.0924839 | ||||||||
\(971\) | −28.4204 | −0.912054 | −0.456027 | − | 0.889966i | \(-0.650728\pi\) | ||||
−0.456027 | + | 0.889966i | \(0.650728\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −12.1685 | −0.390105 | ||||||||
\(974\) | −33.0224 | −1.05810 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.17629 | 0.101671 | ||||||||
\(977\) | −20.6297 | −0.660002 | −0.330001 | − | 0.943981i | \(-0.607049\pi\) | ||||
−0.330001 | + | 0.943981i | \(0.607049\pi\) | |||||||
\(978\) | 20.1444 | 0.644146 | ||||||||
\(979\) | 6.38404 | 0.204035 | ||||||||
\(980\) | 2.55496 | 0.0816151 | ||||||||
\(981\) | 6.93900 | 0.221545 | ||||||||
\(982\) | −1.14244 | −0.0364567 | ||||||||
\(983\) | 48.3749 | 1.54292 | 0.771461 | − | 0.636277i | \(-0.219527\pi\) | ||||
0.771461 | + | 0.636277i | \(0.219527\pi\) | |||||||
\(984\) | 3.14675 | 0.100315 | ||||||||
\(985\) | −52.3551 | −1.66817 | ||||||||
\(986\) | 21.0683 | 0.670951 | ||||||||
\(987\) | −4.50604 | −0.143429 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −42.1933 | −1.34167 | ||||||||
\(990\) | −8.29590 | −0.263661 | ||||||||
\(991\) | 12.6276 | 0.401128 | 0.200564 | − | 0.979681i | \(-0.435723\pi\) | ||||
0.200564 | + | 0.979681i | \(0.435723\pi\) | |||||||
\(992\) | 0.423272 | 0.0134389 | ||||||||
\(993\) | −34.3957 | −1.09151 | ||||||||
\(994\) | −4.21983 | −0.133845 | ||||||||
\(995\) | −13.7175 | −0.434874 | ||||||||
\(996\) | 16.8509 | 0.533940 | ||||||||
\(997\) | −11.1733 | −0.353862 | −0.176931 | − | 0.984223i | \(-0.556617\pi\) | ||||
−0.176931 | + | 0.984223i | \(0.556617\pi\) | |||||||
\(998\) | −16.4239 | −0.519888 | ||||||||
\(999\) | 5.54288 | 0.175369 |
(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 | 7098.2.a.cg.1.2 | ✓ | 3 | |
13.12 | even | 2 | 7098.2.a.cl.1.2 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7098.2.a.cg.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
7098.2.a.cl.1.2 | yes | 3 | 13.12 | even | 2 |