Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6022,2,Mod(1,6022)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6022, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6022.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6022 = 2 \cdot 3011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6022.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.0859120972\) |
Analytic rank: | \(0\) |
Dimension: | \(68\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 6022.1 |
$q$-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 | ||||||||
\(3\) | −3.35476 | −1.93687 | −0.968435 | − | 0.249268i | \(-0.919810\pi\) | ||||
−0.968435 | + | 0.249268i | \(0.919810\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.57894 | −1.60055 | −0.800275 | − | 0.599634i | \(-0.795313\pi\) | ||||
−0.800275 | + | 0.599634i | \(0.795313\pi\) | |||||||
\(6\) | −3.35476 | −1.36957 | ||||||||
\(7\) | 1.79257 | 0.677530 | 0.338765 | − | 0.940871i | \(-0.389991\pi\) | ||||
0.338765 | + | 0.940871i | \(0.389991\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 8.25439 | 2.75146 | ||||||||
\(10\) | −3.57894 | −1.13176 | ||||||||
\(11\) | −1.09193 | −0.329231 | −0.164615 | − | 0.986358i | \(-0.552638\pi\) | ||||
−0.164615 | + | 0.986358i | \(0.552638\pi\) | |||||||
\(12\) | −3.35476 | −0.968435 | ||||||||
\(13\) | 3.65827 | 1.01462 | 0.507310 | − | 0.861764i | \(-0.330640\pi\) | ||||
0.507310 | + | 0.861764i | \(0.330640\pi\) | |||||||
\(14\) | 1.79257 | 0.479086 | ||||||||
\(15\) | 12.0065 | 3.10005 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 8.01652 | 1.94429 | 0.972146 | − | 0.234376i | \(-0.0753046\pi\) | ||||
0.972146 | + | 0.234376i | \(0.0753046\pi\) | |||||||
\(18\) | 8.25439 | 1.94558 | ||||||||
\(19\) | 6.30514 | 1.44650 | 0.723249 | − | 0.690588i | \(-0.242648\pi\) | ||||
0.723249 | + | 0.690588i | \(0.242648\pi\) | |||||||
\(20\) | −3.57894 | −0.800275 | ||||||||
\(21\) | −6.01365 | −1.31229 | ||||||||
\(22\) | −1.09193 | −0.232801 | ||||||||
\(23\) | 6.33291 | 1.32050 | 0.660251 | − | 0.751045i | \(-0.270450\pi\) | ||||
0.660251 | + | 0.751045i | \(0.270450\pi\) | |||||||
\(24\) | −3.35476 | −0.684787 | ||||||||
\(25\) | 7.80879 | 1.56176 | ||||||||
\(26\) | 3.65827 | 0.717445 | ||||||||
\(27\) | −17.6272 | −3.39235 | ||||||||
\(28\) | 1.79257 | 0.338765 | ||||||||
\(29\) | −4.69220 | −0.871319 | −0.435659 | − | 0.900112i | \(-0.643485\pi\) | ||||
−0.435659 | + | 0.900112i | \(0.643485\pi\) | |||||||
\(30\) | 12.0065 | 2.19207 | ||||||||
\(31\) | 3.58165 | 0.643284 | 0.321642 | − | 0.946861i | \(-0.395765\pi\) | ||||
0.321642 | + | 0.946861i | \(0.395765\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 3.66317 | 0.637677 | ||||||||
\(34\) | 8.01652 | 1.37482 | ||||||||
\(35\) | −6.41551 | −1.08442 | ||||||||
\(36\) | 8.25439 | 1.37573 | ||||||||
\(37\) | −7.64723 | −1.25720 | −0.628599 | − | 0.777730i | \(-0.716371\pi\) | ||||
−0.628599 | + | 0.777730i | \(0.716371\pi\) | |||||||
\(38\) | 6.30514 | 1.02283 | ||||||||
\(39\) | −12.2726 | −1.96519 | ||||||||
\(40\) | −3.57894 | −0.565880 | ||||||||
\(41\) | 4.32902 | 0.676079 | 0.338039 | − | 0.941132i | \(-0.390236\pi\) | ||||
0.338039 | + | 0.941132i | \(0.390236\pi\) | |||||||
\(42\) | −6.01365 | −0.927927 | ||||||||
\(43\) | −4.16493 | −0.635145 | −0.317573 | − | 0.948234i | \(-0.602868\pi\) | ||||
−0.317573 | + | 0.948234i | \(0.602868\pi\) | |||||||
\(44\) | −1.09193 | −0.164615 | ||||||||
\(45\) | −29.5419 | −4.40385 | ||||||||
\(46\) | 6.33291 | 0.933736 | ||||||||
\(47\) | −0.819644 | −0.119557 | −0.0597786 | − | 0.998212i | \(-0.519039\pi\) | ||||
−0.0597786 | + | 0.998212i | \(0.519039\pi\) | |||||||
\(48\) | −3.35476 | −0.484217 | ||||||||
\(49\) | −3.78668 | −0.540954 | ||||||||
\(50\) | 7.80879 | 1.10433 | ||||||||
\(51\) | −26.8935 | −3.76584 | ||||||||
\(52\) | 3.65827 | 0.507310 | ||||||||
\(53\) | 9.26718 | 1.27295 | 0.636473 | − | 0.771299i | \(-0.280393\pi\) | ||||
0.636473 | + | 0.771299i | \(0.280393\pi\) | |||||||
\(54\) | −17.6272 | −2.39876 | ||||||||
\(55\) | 3.90797 | 0.526950 | ||||||||
\(56\) | 1.79257 | 0.239543 | ||||||||
\(57\) | −21.1522 | −2.80168 | ||||||||
\(58\) | −4.69220 | −0.616115 | ||||||||
\(59\) | 7.26145 | 0.945361 | 0.472680 | − | 0.881234i | \(-0.343287\pi\) | ||||
0.472680 | + | 0.881234i | \(0.343287\pi\) | |||||||
\(60\) | 12.0065 | 1.55003 | ||||||||
\(61\) | −4.09228 | −0.523962 | −0.261981 | − | 0.965073i | \(-0.584376\pi\) | ||||
−0.261981 | + | 0.965073i | \(0.584376\pi\) | |||||||
\(62\) | 3.58165 | 0.454870 | ||||||||
\(63\) | 14.7966 | 1.86420 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −13.0927 | −1.62395 | ||||||||
\(66\) | 3.66317 | 0.450906 | ||||||||
\(67\) | 1.21956 | 0.148993 | 0.0744966 | − | 0.997221i | \(-0.476265\pi\) | ||||
0.0744966 | + | 0.997221i | \(0.476265\pi\) | |||||||
\(68\) | 8.01652 | 0.972146 | ||||||||
\(69\) | −21.2454 | −2.55764 | ||||||||
\(70\) | −6.41551 | −0.766800 | ||||||||
\(71\) | 7.85175 | 0.931832 | 0.465916 | − | 0.884829i | \(-0.345725\pi\) | ||||
0.465916 | + | 0.884829i | \(0.345725\pi\) | |||||||
\(72\) | 8.25439 | 0.972789 | ||||||||
\(73\) | −4.15959 | −0.486844 | −0.243422 | − | 0.969921i | \(-0.578270\pi\) | ||||
−0.243422 | + | 0.969921i | \(0.578270\pi\) | |||||||
\(74\) | −7.64723 | −0.888973 | ||||||||
\(75\) | −26.1966 | −3.02492 | ||||||||
\(76\) | 6.30514 | 0.723249 | ||||||||
\(77\) | −1.95737 | −0.223064 | ||||||||
\(78\) | −12.2726 | −1.38960 | ||||||||
\(79\) | −3.31384 | −0.372836 | −0.186418 | − | 0.982470i | \(-0.559688\pi\) | ||||
−0.186418 | + | 0.982470i | \(0.559688\pi\) | |||||||
\(80\) | −3.57894 | −0.400137 | ||||||||
\(81\) | 34.3718 | 3.81908 | ||||||||
\(82\) | 4.32902 | 0.478060 | ||||||||
\(83\) | 0.00149686 | 0.000164301 0 | 8.21506e−5 | − | 1.00000i | \(-0.499974\pi\) | ||||
8.21506e−5 | 1.00000i | \(0.499974\pi\) | ||||||||
\(84\) | −6.01365 | −0.656143 | ||||||||
\(85\) | −28.6906 | −3.11194 | ||||||||
\(86\) | −4.16493 | −0.449115 | ||||||||
\(87\) | 15.7412 | 1.68763 | ||||||||
\(88\) | −1.09193 | −0.116401 | ||||||||
\(89\) | 0.505484 | 0.0535812 | 0.0267906 | − | 0.999641i | \(-0.491471\pi\) | ||||
0.0267906 | + | 0.999641i | \(0.491471\pi\) | |||||||
\(90\) | −29.5419 | −3.11399 | ||||||||
\(91\) | 6.55771 | 0.687435 | ||||||||
\(92\) | 6.33291 | 0.660251 | ||||||||
\(93\) | −12.0156 | −1.24596 | ||||||||
\(94\) | −0.819644 | −0.0845398 | ||||||||
\(95\) | −22.5657 | −2.31519 | ||||||||
\(96\) | −3.35476 | −0.342393 | ||||||||
\(97\) | 13.1705 | 1.33726 | 0.668631 | − | 0.743595i | \(-0.266881\pi\) | ||||
0.668631 | + | 0.743595i | \(0.266881\pi\) | |||||||
\(98\) | −3.78668 | −0.382512 | ||||||||
\(99\) | −9.01325 | −0.905866 | ||||||||
\(100\) | 7.80879 | 0.780879 | ||||||||
\(101\) | 0.00889696 | 0.000885281 0 | 0.000442641 | − | 1.00000i | \(-0.499859\pi\) | ||||
0.000442641 | 1.00000i | \(0.499859\pi\) | ||||||||
\(102\) | −26.8935 | −2.66285 | ||||||||
\(103\) | −5.70849 | −0.562474 | −0.281237 | − | 0.959638i | \(-0.590745\pi\) | ||||
−0.281237 | + | 0.959638i | \(0.590745\pi\) | |||||||
\(104\) | 3.65827 | 0.358722 | ||||||||
\(105\) | 21.5225 | 2.10038 | ||||||||
\(106\) | 9.26718 | 0.900108 | ||||||||
\(107\) | 10.4291 | 1.00822 | 0.504108 | − | 0.863641i | \(-0.331821\pi\) | ||||
0.504108 | + | 0.863641i | \(0.331821\pi\) | |||||||
\(108\) | −17.6272 | −1.69618 | ||||||||
\(109\) | 11.1233 | 1.06542 | 0.532708 | − | 0.846299i | \(-0.321174\pi\) | ||||
0.532708 | + | 0.846299i | \(0.321174\pi\) | |||||||
\(110\) | 3.90797 | 0.372610 | ||||||||
\(111\) | 25.6546 | 2.43503 | ||||||||
\(112\) | 1.79257 | 0.169382 | ||||||||
\(113\) | −14.6343 | −1.37668 | −0.688338 | − | 0.725390i | \(-0.741659\pi\) | ||||
−0.688338 | + | 0.725390i | \(0.741659\pi\) | |||||||
\(114\) | −21.1522 | −1.98108 | ||||||||
\(115\) | −22.6651 | −2.11353 | ||||||||
\(116\) | −4.69220 | −0.435659 | ||||||||
\(117\) | 30.1967 | 2.79169 | ||||||||
\(118\) | 7.26145 | 0.668471 | ||||||||
\(119\) | 14.3702 | 1.31732 | ||||||||
\(120\) | 12.0065 | 1.09603 | ||||||||
\(121\) | −9.80768 | −0.891607 | ||||||||
\(122\) | −4.09228 | −0.370497 | ||||||||
\(123\) | −14.5228 | −1.30948 | ||||||||
\(124\) | 3.58165 | 0.321642 | ||||||||
\(125\) | −10.0525 | −0.899120 | ||||||||
\(126\) | 14.7966 | 1.31819 | ||||||||
\(127\) | −6.72888 | −0.597092 | −0.298546 | − | 0.954395i | \(-0.596502\pi\) | ||||
−0.298546 | + | 0.954395i | \(0.596502\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 13.9723 | 1.23019 | ||||||||
\(130\) | −13.0927 | −1.14831 | ||||||||
\(131\) | 13.8913 | 1.21369 | 0.606844 | − | 0.794821i | \(-0.292435\pi\) | ||||
0.606844 | + | 0.794821i | \(0.292435\pi\) | |||||||
\(132\) | 3.66317 | 0.318838 | ||||||||
\(133\) | 11.3024 | 0.980045 | ||||||||
\(134\) | 1.21956 | 0.105354 | ||||||||
\(135\) | 63.0866 | 5.42963 | ||||||||
\(136\) | 8.01652 | 0.687411 | ||||||||
\(137\) | 13.3834 | 1.14342 | 0.571711 | − | 0.820455i | \(-0.306280\pi\) | ||||
0.571711 | + | 0.820455i | \(0.306280\pi\) | |||||||
\(138\) | −21.2454 | −1.80853 | ||||||||
\(139\) | 2.97490 | 0.252328 | 0.126164 | − | 0.992009i | \(-0.459733\pi\) | ||||
0.126164 | + | 0.992009i | \(0.459733\pi\) | |||||||
\(140\) | −6.41551 | −0.542210 | ||||||||
\(141\) | 2.74970 | 0.231567 | ||||||||
\(142\) | 7.85175 | 0.658905 | ||||||||
\(143\) | −3.99459 | −0.334044 | ||||||||
\(144\) | 8.25439 | 0.687866 | ||||||||
\(145\) | 16.7931 | 1.39459 | ||||||||
\(146\) | −4.15959 | −0.344251 | ||||||||
\(147\) | 12.7034 | 1.04776 | ||||||||
\(148\) | −7.64723 | −0.628599 | ||||||||
\(149\) | −15.3432 | −1.25697 | −0.628483 | − | 0.777823i | \(-0.716324\pi\) | ||||
−0.628483 | + | 0.777823i | \(0.716324\pi\) | |||||||
\(150\) | −26.1966 | −2.13894 | ||||||||
\(151\) | 5.99985 | 0.488261 | 0.244130 | − | 0.969742i | \(-0.421497\pi\) | ||||
0.244130 | + | 0.969742i | \(0.421497\pi\) | |||||||
\(152\) | 6.30514 | 0.511414 | ||||||||
\(153\) | 66.1715 | 5.34965 | ||||||||
\(154\) | −1.95737 | −0.157730 | ||||||||
\(155\) | −12.8185 | −1.02961 | ||||||||
\(156\) | −12.2726 | −0.982593 | ||||||||
\(157\) | −14.8361 | −1.18405 | −0.592023 | − | 0.805921i | \(-0.701671\pi\) | ||||
−0.592023 | + | 0.805921i | \(0.701671\pi\) | |||||||
\(158\) | −3.31384 | −0.263635 | ||||||||
\(159\) | −31.0891 | −2.46553 | ||||||||
\(160\) | −3.57894 | −0.282940 | ||||||||
\(161\) | 11.3522 | 0.894680 | ||||||||
\(162\) | 34.3718 | 2.70050 | ||||||||
\(163\) | −11.8622 | −0.929119 | −0.464560 | − | 0.885542i | \(-0.653787\pi\) | ||||
−0.464560 | + | 0.885542i | \(0.653787\pi\) | |||||||
\(164\) | 4.32902 | 0.338039 | ||||||||
\(165\) | −13.1103 | −1.02063 | ||||||||
\(166\) | 0.00149686 | 0.000116179 0 | ||||||||
\(167\) | −2.37796 | −0.184012 | −0.0920060 | − | 0.995758i | \(-0.529328\pi\) | ||||
−0.0920060 | + | 0.995758i | \(0.529328\pi\) | |||||||
\(168\) | −6.01365 | −0.463963 | ||||||||
\(169\) | 0.382907 | 0.0294544 | ||||||||
\(170\) | −28.6906 | −2.20047 | ||||||||
\(171\) | 52.0450 | 3.97998 | ||||||||
\(172\) | −4.16493 | −0.317573 | ||||||||
\(173\) | 6.73048 | 0.511709 | 0.255854 | − | 0.966715i | \(-0.417643\pi\) | ||||
0.255854 | + | 0.966715i | \(0.417643\pi\) | |||||||
\(174\) | 15.7412 | 1.19333 | ||||||||
\(175\) | 13.9978 | 1.05814 | ||||||||
\(176\) | −1.09193 | −0.0823077 | ||||||||
\(177\) | −24.3604 | −1.83104 | ||||||||
\(178\) | 0.505484 | 0.0378877 | ||||||||
\(179\) | 7.86388 | 0.587774 | 0.293887 | − | 0.955840i | \(-0.405051\pi\) | ||||
0.293887 | + | 0.955840i | \(0.405051\pi\) | |||||||
\(180\) | −29.5419 | −2.20193 | ||||||||
\(181\) | −16.1105 | −1.19749 | −0.598743 | − | 0.800941i | \(-0.704333\pi\) | ||||
−0.598743 | + | 0.800941i | \(0.704333\pi\) | |||||||
\(182\) | 6.55771 | 0.486090 | ||||||||
\(183\) | 13.7286 | 1.01485 | ||||||||
\(184\) | 6.33291 | 0.466868 | ||||||||
\(185\) | 27.3690 | 2.01221 | ||||||||
\(186\) | −12.0156 | −0.881024 | ||||||||
\(187\) | −8.75352 | −0.640121 | ||||||||
\(188\) | −0.819644 | −0.0597786 | ||||||||
\(189\) | −31.5981 | −2.29842 | ||||||||
\(190\) | −22.5657 | −1.63709 | ||||||||
\(191\) | 25.2272 | 1.82537 | 0.912686 | − | 0.408661i | \(-0.134004\pi\) | ||||
0.912686 | + | 0.408661i | \(0.134004\pi\) | |||||||
\(192\) | −3.35476 | −0.242109 | ||||||||
\(193\) | −10.7465 | −0.773553 | −0.386776 | − | 0.922174i | \(-0.626411\pi\) | ||||
−0.386776 | + | 0.922174i | \(0.626411\pi\) | |||||||
\(194\) | 13.1705 | 0.945586 | ||||||||
\(195\) | 43.9228 | 3.14538 | ||||||||
\(196\) | −3.78668 | −0.270477 | ||||||||
\(197\) | −0.178585 | −0.0127236 | −0.00636182 | − | 0.999980i | \(-0.502025\pi\) | ||||
−0.00636182 | + | 0.999980i | \(0.502025\pi\) | |||||||
\(198\) | −9.01325 | −0.640544 | ||||||||
\(199\) | 7.22038 | 0.511839 | 0.255919 | − | 0.966698i | \(-0.417622\pi\) | ||||
0.255919 | + | 0.966698i | \(0.417622\pi\) | |||||||
\(200\) | 7.80879 | 0.552165 | ||||||||
\(201\) | −4.09133 | −0.288580 | ||||||||
\(202\) | 0.00889696 | 0.000625988 0 | ||||||||
\(203\) | −8.41111 | −0.590344 | ||||||||
\(204\) | −26.8935 | −1.88292 | ||||||||
\(205\) | −15.4933 | −1.08210 | ||||||||
\(206\) | −5.70849 | −0.397729 | ||||||||
\(207\) | 52.2743 | 3.63331 | ||||||||
\(208\) | 3.65827 | 0.253655 | ||||||||
\(209\) | −6.88480 | −0.476231 | ||||||||
\(210\) | 21.5225 | 1.48519 | ||||||||
\(211\) | −22.8969 | −1.57629 | −0.788145 | − | 0.615489i | \(-0.788958\pi\) | ||||
−0.788145 | + | 0.615489i | \(0.788958\pi\) | |||||||
\(212\) | 9.26718 | 0.636473 | ||||||||
\(213\) | −26.3407 | −1.80484 | ||||||||
\(214\) | 10.4291 | 0.712917 | ||||||||
\(215\) | 14.9060 | 1.01658 | ||||||||
\(216\) | −17.6272 | −1.19938 | ||||||||
\(217\) | 6.42038 | 0.435844 | ||||||||
\(218\) | 11.1233 | 0.753363 | ||||||||
\(219\) | 13.9544 | 0.942953 | ||||||||
\(220\) | 3.90797 | 0.263475 | ||||||||
\(221\) | 29.3266 | 1.97272 | ||||||||
\(222\) | 25.6546 | 1.72182 | ||||||||
\(223\) | 17.9641 | 1.20296 | 0.601481 | − | 0.798887i | \(-0.294577\pi\) | ||||
0.601481 | + | 0.798887i | \(0.294577\pi\) | |||||||
\(224\) | 1.79257 | 0.119771 | ||||||||
\(225\) | 64.4567 | 4.29712 | ||||||||
\(226\) | −14.6343 | −0.973456 | ||||||||
\(227\) | 27.6520 | 1.83533 | 0.917664 | − | 0.397358i | \(-0.130073\pi\) | ||||
0.917664 | + | 0.397358i | \(0.130073\pi\) | |||||||
\(228\) | −21.1522 | −1.40084 | ||||||||
\(229\) | 18.4296 | 1.21786 | 0.608930 | − | 0.793224i | \(-0.291599\pi\) | ||||
0.608930 | + | 0.793224i | \(0.291599\pi\) | |||||||
\(230\) | −22.6651 | −1.49449 | ||||||||
\(231\) | 6.56651 | 0.432045 | ||||||||
\(232\) | −4.69220 | −0.308058 | ||||||||
\(233\) | −17.2596 | −1.13071 | −0.565357 | − | 0.824847i | \(-0.691261\pi\) | ||||
−0.565357 | + | 0.824847i | \(0.691261\pi\) | |||||||
\(234\) | 30.1967 | 1.97402 | ||||||||
\(235\) | 2.93345 | 0.191357 | ||||||||
\(236\) | 7.26145 | 0.472680 | ||||||||
\(237\) | 11.1171 | 0.722135 | ||||||||
\(238\) | 14.3702 | 0.931483 | ||||||||
\(239\) | −23.7782 | −1.53808 | −0.769041 | − | 0.639200i | \(-0.779266\pi\) | ||||
−0.769041 | + | 0.639200i | \(0.779266\pi\) | |||||||
\(240\) | 12.0065 | 0.775014 | ||||||||
\(241\) | −29.4282 | −1.89564 | −0.947820 | − | 0.318807i | \(-0.896718\pi\) | ||||
−0.947820 | + | 0.318807i | \(0.896718\pi\) | |||||||
\(242\) | −9.80768 | −0.630461 | ||||||||
\(243\) | −62.4273 | −4.00471 | ||||||||
\(244\) | −4.09228 | −0.261981 | ||||||||
\(245\) | 13.5523 | 0.865823 | ||||||||
\(246\) | −14.5228 | −0.925939 | ||||||||
\(247\) | 23.0659 | 1.46765 | ||||||||
\(248\) | 3.58165 | 0.227435 | ||||||||
\(249\) | −0.00502158 | −0.000318230 0 | ||||||||
\(250\) | −10.0525 | −0.635774 | ||||||||
\(251\) | 29.9729 | 1.89187 | 0.945936 | − | 0.324355i | \(-0.105147\pi\) | ||||
0.945936 | + | 0.324355i | \(0.105147\pi\) | |||||||
\(252\) | 14.7966 | 0.932099 | ||||||||
\(253\) | −6.91512 | −0.434750 | ||||||||
\(254\) | −6.72888 | −0.422208 | ||||||||
\(255\) | 96.2500 | 6.02741 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.70097 | 0.542752 | 0.271376 | − | 0.962473i | \(-0.412521\pi\) | ||||
0.271376 | + | 0.962473i | \(0.412521\pi\) | |||||||
\(258\) | 13.9723 | 0.869878 | ||||||||
\(259\) | −13.7082 | −0.851788 | ||||||||
\(260\) | −13.0927 | −0.811975 | ||||||||
\(261\) | −38.7312 | −2.39740 | ||||||||
\(262\) | 13.8913 | 0.858208 | ||||||||
\(263\) | −19.5655 | −1.20646 | −0.603230 | − | 0.797567i | \(-0.706120\pi\) | ||||
−0.603230 | + | 0.797567i | \(0.706120\pi\) | |||||||
\(264\) | 3.66317 | 0.225453 | ||||||||
\(265\) | −33.1667 | −2.03741 | ||||||||
\(266\) | 11.3024 | 0.692996 | ||||||||
\(267\) | −1.69578 | −0.103780 | ||||||||
\(268\) | 1.21956 | 0.0744966 | ||||||||
\(269\) | 9.34653 | 0.569868 | 0.284934 | − | 0.958547i | \(-0.408028\pi\) | ||||
0.284934 | + | 0.958547i | \(0.408028\pi\) | |||||||
\(270\) | 63.0866 | 3.83933 | ||||||||
\(271\) | 13.2398 | 0.804259 | 0.402129 | − | 0.915583i | \(-0.368270\pi\) | ||||
0.402129 | + | 0.915583i | \(0.368270\pi\) | |||||||
\(272\) | 8.01652 | 0.486073 | ||||||||
\(273\) | −21.9995 | −1.33147 | ||||||||
\(274\) | 13.3834 | 0.808522 | ||||||||
\(275\) | −8.52668 | −0.514178 | ||||||||
\(276\) | −21.2454 | −1.27882 | ||||||||
\(277\) | 11.5887 | 0.696299 | 0.348150 | − | 0.937439i | \(-0.386810\pi\) | ||||
0.348150 | + | 0.937439i | \(0.386810\pi\) | |||||||
\(278\) | 2.97490 | 0.178423 | ||||||||
\(279\) | 29.5643 | 1.76997 | ||||||||
\(280\) | −6.41551 | −0.383400 | ||||||||
\(281\) | −10.0446 | −0.599209 | −0.299605 | − | 0.954063i | \(-0.596855\pi\) | ||||
−0.299605 | + | 0.954063i | \(0.596855\pi\) | |||||||
\(282\) | 2.74970 | 0.163742 | ||||||||
\(283\) | −25.5327 | −1.51776 | −0.758879 | − | 0.651231i | \(-0.774253\pi\) | ||||
−0.758879 | + | 0.651231i | \(0.774253\pi\) | |||||||
\(284\) | 7.85175 | 0.465916 | ||||||||
\(285\) | 75.7024 | 4.48422 | ||||||||
\(286\) | −3.99459 | −0.236205 | ||||||||
\(287\) | 7.76008 | 0.458063 | ||||||||
\(288\) | 8.25439 | 0.486394 | ||||||||
\(289\) | 47.2646 | 2.78027 | ||||||||
\(290\) | 16.7931 | 0.986123 | ||||||||
\(291\) | −44.1838 | −2.59010 | ||||||||
\(292\) | −4.15959 | −0.243422 | ||||||||
\(293\) | 20.2283 | 1.18175 | 0.590876 | − | 0.806763i | \(-0.298782\pi\) | ||||
0.590876 | + | 0.806763i | \(0.298782\pi\) | |||||||
\(294\) | 12.7034 | 0.740876 | ||||||||
\(295\) | −25.9883 | −1.51310 | ||||||||
\(296\) | −7.64723 | −0.444486 | ||||||||
\(297\) | 19.2477 | 1.11687 | ||||||||
\(298\) | −15.3432 | −0.888810 | ||||||||
\(299\) | 23.1675 | 1.33981 | ||||||||
\(300\) | −26.1966 | −1.51246 | ||||||||
\(301\) | −7.46594 | −0.430330 | ||||||||
\(302\) | 5.99985 | 0.345253 | ||||||||
\(303\) | −0.0298471 | −0.00171467 | ||||||||
\(304\) | 6.30514 | 0.361624 | ||||||||
\(305\) | 14.6460 | 0.838627 | ||||||||
\(306\) | 66.1715 | 3.78277 | ||||||||
\(307\) | 25.0653 | 1.43055 | 0.715275 | − | 0.698843i | \(-0.246301\pi\) | ||||
0.715275 | + | 0.698843i | \(0.246301\pi\) | |||||||
\(308\) | −1.95737 | −0.111532 | ||||||||
\(309\) | 19.1506 | 1.08944 | ||||||||
\(310\) | −12.8185 | −0.728042 | ||||||||
\(311\) | −23.4401 | −1.32917 | −0.664583 | − | 0.747215i | \(-0.731391\pi\) | ||||
−0.664583 | + | 0.747215i | \(0.731391\pi\) | |||||||
\(312\) | −12.2726 | −0.694799 | ||||||||
\(313\) | −6.05460 | −0.342226 | −0.171113 | − | 0.985251i | \(-0.554736\pi\) | ||||
−0.171113 | + | 0.985251i | \(0.554736\pi\) | |||||||
\(314\) | −14.8361 | −0.837247 | ||||||||
\(315\) | −52.9561 | −2.98374 | ||||||||
\(316\) | −3.31384 | −0.186418 | ||||||||
\(317\) | −15.0739 | −0.846637 | −0.423318 | − | 0.905981i | \(-0.639135\pi\) | ||||
−0.423318 | + | 0.905981i | \(0.639135\pi\) | |||||||
\(318\) | −31.0891 | −1.74339 | ||||||||
\(319\) | 5.12357 | 0.286865 | ||||||||
\(320\) | −3.57894 | −0.200069 | ||||||||
\(321\) | −34.9870 | −1.95278 | ||||||||
\(322\) | 11.3522 | 0.632634 | ||||||||
\(323\) | 50.5453 | 2.81241 | ||||||||
\(324\) | 34.3718 | 1.90954 | ||||||||
\(325\) | 28.5666 | 1.58459 | ||||||||
\(326\) | −11.8622 | −0.656987 | ||||||||
\(327\) | −37.3159 | −2.06357 | ||||||||
\(328\) | 4.32902 | 0.239030 | ||||||||
\(329\) | −1.46927 | −0.0810036 | ||||||||
\(330\) | −13.1103 | −0.721697 | ||||||||
\(331\) | −13.3559 | −0.734108 | −0.367054 | − | 0.930200i | \(-0.619634\pi\) | ||||
−0.367054 | + | 0.930200i | \(0.619634\pi\) | |||||||
\(332\) | 0.00149686 | 8.21506e−5 0 | ||||||||
\(333\) | −63.1232 | −3.45913 | ||||||||
\(334\) | −2.37796 | −0.130116 | ||||||||
\(335\) | −4.36473 | −0.238471 | ||||||||
\(336\) | −6.01365 | −0.328072 | ||||||||
\(337\) | 6.84980 | 0.373132 | 0.186566 | − | 0.982442i | \(-0.440264\pi\) | ||||
0.186566 | + | 0.982442i | \(0.440264\pi\) | |||||||
\(338\) | 0.382907 | 0.0208274 | ||||||||
\(339\) | 49.0944 | 2.66644 | ||||||||
\(340\) | −28.6906 | −1.55597 | ||||||||
\(341\) | −3.91093 | −0.211789 | ||||||||
\(342\) | 52.0450 | 2.81427 | ||||||||
\(343\) | −19.3359 | −1.04404 | ||||||||
\(344\) | −4.16493 | −0.224558 | ||||||||
\(345\) | 76.0358 | 4.09363 | ||||||||
\(346\) | 6.73048 | 0.361833 | ||||||||
\(347\) | −11.8184 | −0.634446 | −0.317223 | − | 0.948351i | \(-0.602750\pi\) | ||||
−0.317223 | + | 0.948351i | \(0.602750\pi\) | |||||||
\(348\) | 15.7412 | 0.843815 | ||||||||
\(349\) | −11.7736 | −0.630225 | −0.315113 | − | 0.949054i | \(-0.602042\pi\) | ||||
−0.315113 | + | 0.949054i | \(0.602042\pi\) | |||||||
\(350\) | 13.9978 | 0.748216 | ||||||||
\(351\) | −64.4849 | −3.44195 | ||||||||
\(352\) | −1.09193 | −0.0582003 | ||||||||
\(353\) | −15.9335 | −0.848053 | −0.424026 | − | 0.905650i | \(-0.639384\pi\) | ||||
−0.424026 | + | 0.905650i | \(0.639384\pi\) | |||||||
\(354\) | −24.3604 | −1.29474 | ||||||||
\(355\) | −28.1009 | −1.49144 | ||||||||
\(356\) | 0.505484 | 0.0267906 | ||||||||
\(357\) | −48.2086 | −2.55147 | ||||||||
\(358\) | 7.86388 | 0.415619 | ||||||||
\(359\) | −26.9345 | −1.42155 | −0.710775 | − | 0.703420i | \(-0.751655\pi\) | ||||
−0.710775 | + | 0.703420i | \(0.751655\pi\) | |||||||
\(360\) | −29.5419 | −1.55700 | ||||||||
\(361\) | 20.7548 | 1.09236 | ||||||||
\(362\) | −16.1105 | −0.846751 | ||||||||
\(363\) | 32.9024 | 1.72693 | ||||||||
\(364\) | 6.55771 | 0.343718 | ||||||||
\(365\) | 14.8869 | 0.779217 | ||||||||
\(366\) | 13.7286 | 0.717605 | ||||||||
\(367\) | −13.8265 | −0.721736 | −0.360868 | − | 0.932617i | \(-0.617520\pi\) | ||||
−0.360868 | + | 0.932617i | \(0.617520\pi\) | |||||||
\(368\) | 6.33291 | 0.330126 | ||||||||
\(369\) | 35.7334 | 1.86021 | ||||||||
\(370\) | 27.3690 | 1.42284 | ||||||||
\(371\) | 16.6121 | 0.862458 | ||||||||
\(372\) | −12.0156 | −0.622978 | ||||||||
\(373\) | −10.4072 | −0.538867 | −0.269433 | − | 0.963019i | \(-0.586836\pi\) | ||||
−0.269433 | + | 0.963019i | \(0.586836\pi\) | |||||||
\(374\) | −8.75352 | −0.452634 | ||||||||
\(375\) | 33.7236 | 1.74148 | ||||||||
\(376\) | −0.819644 | −0.0422699 | ||||||||
\(377\) | −17.1653 | −0.884058 | ||||||||
\(378\) | −31.5981 | −1.62523 | ||||||||
\(379\) | −7.07875 | −0.363611 | −0.181806 | − | 0.983335i | \(-0.558194\pi\) | ||||
−0.181806 | + | 0.983335i | \(0.558194\pi\) | |||||||
\(380\) | −22.5657 | −1.15760 | ||||||||
\(381\) | 22.5738 | 1.15649 | ||||||||
\(382\) | 25.2272 | 1.29073 | ||||||||
\(383\) | −8.21579 | −0.419807 | −0.209904 | − | 0.977722i | \(-0.567315\pi\) | ||||
−0.209904 | + | 0.977722i | \(0.567315\pi\) | |||||||
\(384\) | −3.35476 | −0.171197 | ||||||||
\(385\) | 7.00532 | 0.357024 | ||||||||
\(386\) | −10.7465 | −0.546984 | ||||||||
\(387\) | −34.3789 | −1.74758 | ||||||||
\(388\) | 13.1705 | 0.668631 | ||||||||
\(389\) | −6.36587 | −0.322762 | −0.161381 | − | 0.986892i | \(-0.551595\pi\) | ||||
−0.161381 | + | 0.986892i | \(0.551595\pi\) | |||||||
\(390\) | 43.9228 | 2.22412 | ||||||||
\(391\) | 50.7679 | 2.56744 | ||||||||
\(392\) | −3.78668 | −0.191256 | ||||||||
\(393\) | −46.6019 | −2.35076 | ||||||||
\(394\) | −0.178585 | −0.00899697 | ||||||||
\(395\) | 11.8600 | 0.596743 | ||||||||
\(396\) | −9.01325 | −0.452933 | ||||||||
\(397\) | −6.79701 | −0.341132 | −0.170566 | − | 0.985346i | \(-0.554560\pi\) | ||||
−0.170566 | + | 0.985346i | \(0.554560\pi\) | |||||||
\(398\) | 7.22038 | 0.361925 | ||||||||
\(399\) | −37.9169 | −1.89822 | ||||||||
\(400\) | 7.80879 | 0.390439 | ||||||||
\(401\) | 36.0616 | 1.80083 | 0.900415 | − | 0.435033i | \(-0.143263\pi\) | ||||
0.900415 | + | 0.435033i | \(0.143263\pi\) | |||||||
\(402\) | −4.09133 | −0.204057 | ||||||||
\(403\) | 13.1026 | 0.652689 | ||||||||
\(404\) | 0.00889696 | 0.000442641 0 | ||||||||
\(405\) | −123.014 | −6.11263 | ||||||||
\(406\) | −8.41111 | −0.417436 | ||||||||
\(407\) | 8.35028 | 0.413908 | ||||||||
\(408\) | −26.8935 | −1.33143 | ||||||||
\(409\) | −31.9276 | −1.57872 | −0.789358 | − | 0.613933i | \(-0.789586\pi\) | ||||
−0.789358 | + | 0.613933i | \(0.789586\pi\) | |||||||
\(410\) | −15.4933 | −0.765158 | ||||||||
\(411\) | −44.8981 | −2.21466 | ||||||||
\(412\) | −5.70849 | −0.281237 | ||||||||
\(413\) | 13.0167 | 0.640510 | ||||||||
\(414\) | 52.2743 | 2.56914 | ||||||||
\(415\) | −0.00535715 | −0.000262972 0 | ||||||||
\(416\) | 3.65827 | 0.179361 | ||||||||
\(417\) | −9.98008 | −0.488727 | ||||||||
\(418\) | −6.88480 | −0.336746 | ||||||||
\(419\) | 2.92692 | 0.142989 | 0.0714946 | − | 0.997441i | \(-0.477223\pi\) | ||||
0.0714946 | + | 0.997441i | \(0.477223\pi\) | |||||||
\(420\) | 21.5225 | 1.05019 | ||||||||
\(421\) | −2.31229 | −0.112694 | −0.0563470 | − | 0.998411i | \(-0.517945\pi\) | ||||
−0.0563470 | + | 0.998411i | \(0.517945\pi\) | |||||||
\(422\) | −22.8969 | −1.11461 | ||||||||
\(423\) | −6.76566 | −0.328957 | ||||||||
\(424\) | 9.26718 | 0.450054 | ||||||||
\(425\) | 62.5993 | 3.03651 | ||||||||
\(426\) | −26.3407 | −1.27621 | ||||||||
\(427\) | −7.33571 | −0.355000 | ||||||||
\(428\) | 10.4291 | 0.504108 | ||||||||
\(429\) | 13.4009 | 0.647000 | ||||||||
\(430\) | 14.9060 | 0.718831 | ||||||||
\(431\) | −27.3341 | −1.31664 | −0.658318 | − | 0.752740i | \(-0.728732\pi\) | ||||
−0.658318 | + | 0.752740i | \(0.728732\pi\) | |||||||
\(432\) | −17.6272 | −0.848089 | ||||||||
\(433\) | 38.7803 | 1.86366 | 0.931832 | − | 0.362891i | \(-0.118210\pi\) | ||||
0.931832 | + | 0.362891i | \(0.118210\pi\) | |||||||
\(434\) | 6.42038 | 0.308188 | ||||||||
\(435\) | −56.3366 | −2.70114 | ||||||||
\(436\) | 11.1233 | 0.532708 | ||||||||
\(437\) | 39.9299 | 1.91010 | ||||||||
\(438\) | 13.9544 | 0.666768 | ||||||||
\(439\) | 3.11143 | 0.148500 | 0.0742501 | − | 0.997240i | \(-0.476344\pi\) | ||||
0.0742501 | + | 0.997240i | \(0.476344\pi\) | |||||||
\(440\) | 3.90797 | 0.186305 | ||||||||
\(441\) | −31.2567 | −1.48841 | ||||||||
\(442\) | 29.3266 | 1.39492 | ||||||||
\(443\) | −8.04748 | −0.382347 | −0.191174 | − | 0.981556i | \(-0.561229\pi\) | ||||
−0.191174 | + | 0.981556i | \(0.561229\pi\) | |||||||
\(444\) | 25.6546 | 1.21751 | ||||||||
\(445\) | −1.80910 | −0.0857594 | ||||||||
\(446\) | 17.9641 | 0.850623 | ||||||||
\(447\) | 51.4728 | 2.43458 | ||||||||
\(448\) | 1.79257 | 0.0846912 | ||||||||
\(449\) | −18.1602 | −0.857031 | −0.428515 | − | 0.903535i | \(-0.640963\pi\) | ||||
−0.428515 | + | 0.903535i | \(0.640963\pi\) | |||||||
\(450\) | 64.4567 | 3.03852 | ||||||||
\(451\) | −4.72700 | −0.222586 | ||||||||
\(452\) | −14.6343 | −0.688338 | ||||||||
\(453\) | −20.1280 | −0.945698 | ||||||||
\(454\) | 27.6520 | 1.29777 | ||||||||
\(455\) | −23.4696 | −1.10027 | ||||||||
\(456\) | −21.1522 | −0.990542 | ||||||||
\(457\) | 15.1244 | 0.707491 | 0.353745 | − | 0.935342i | \(-0.384908\pi\) | ||||
0.353745 | + | 0.935342i | \(0.384908\pi\) | |||||||
\(458\) | 18.4296 | 0.861158 | ||||||||
\(459\) | −141.309 | −6.59573 | ||||||||
\(460\) | −22.6651 | −1.05676 | ||||||||
\(461\) | 17.6429 | 0.821711 | 0.410855 | − | 0.911701i | \(-0.365230\pi\) | ||||
0.410855 | + | 0.911701i | \(0.365230\pi\) | |||||||
\(462\) | 6.56651 | 0.305502 | ||||||||
\(463\) | 34.6719 | 1.61134 | 0.805670 | − | 0.592364i | \(-0.201805\pi\) | ||||
0.805670 | + | 0.592364i | \(0.201805\pi\) | |||||||
\(464\) | −4.69220 | −0.217830 | ||||||||
\(465\) | 43.0030 | 1.99421 | ||||||||
\(466\) | −17.2596 | −0.799535 | ||||||||
\(467\) | 18.1834 | 0.841426 | 0.420713 | − | 0.907194i | \(-0.361780\pi\) | ||||
0.420713 | + | 0.907194i | \(0.361780\pi\) | |||||||
\(468\) | 30.1967 | 1.39584 | ||||||||
\(469\) | 2.18616 | 0.100947 | ||||||||
\(470\) | 2.93345 | 0.135310 | ||||||||
\(471\) | 49.7714 | 2.29334 | ||||||||
\(472\) | 7.26145 | 0.334235 | ||||||||
\(473\) | 4.54783 | 0.209109 | ||||||||
\(474\) | 11.1171 | 0.510627 | ||||||||
\(475\) | 49.2355 | 2.25908 | ||||||||
\(476\) | 14.3702 | 0.658658 | ||||||||
\(477\) | 76.4949 | 3.50246 | ||||||||
\(478\) | −23.7782 | −1.08759 | ||||||||
\(479\) | 31.7302 | 1.44979 | 0.724894 | − | 0.688860i | \(-0.241889\pi\) | ||||
0.724894 | + | 0.688860i | \(0.241889\pi\) | |||||||
\(480\) | 12.0065 | 0.548017 | ||||||||
\(481\) | −27.9756 | −1.27558 | ||||||||
\(482\) | −29.4282 | −1.34042 | ||||||||
\(483\) | −38.0839 | −1.73288 | ||||||||
\(484\) | −9.80768 | −0.445804 | ||||||||
\(485\) | −47.1364 | −2.14035 | ||||||||
\(486\) | −62.4273 | −2.83176 | ||||||||
\(487\) | 29.8048 | 1.35058 | 0.675291 | − | 0.737551i | \(-0.264018\pi\) | ||||
0.675291 | + | 0.737551i | \(0.264018\pi\) | |||||||
\(488\) | −4.09228 | −0.185249 | ||||||||
\(489\) | 39.7948 | 1.79958 | ||||||||
\(490\) | 13.5523 | 0.612229 | ||||||||
\(491\) | 41.6480 | 1.87955 | 0.939774 | − | 0.341796i | \(-0.111035\pi\) | ||||
0.939774 | + | 0.341796i | \(0.111035\pi\) | |||||||
\(492\) | −14.5228 | −0.654738 | ||||||||
\(493\) | −37.6151 | −1.69410 | ||||||||
\(494\) | 23.0659 | 1.03778 | ||||||||
\(495\) | 32.2579 | 1.44988 | ||||||||
\(496\) | 3.58165 | 0.160821 | ||||||||
\(497\) | 14.0749 | 0.631344 | ||||||||
\(498\) | −0.00502158 | −0.000225023 0 | ||||||||
\(499\) | 33.2866 | 1.49011 | 0.745056 | − | 0.667002i | \(-0.232423\pi\) | ||||
0.745056 | + | 0.667002i | \(0.232423\pi\) | |||||||
\(500\) | −10.0525 | −0.449560 | ||||||||
\(501\) | 7.97748 | 0.356407 | ||||||||
\(502\) | 29.9729 | 1.33775 | ||||||||
\(503\) | 34.1045 | 1.52065 | 0.760323 | − | 0.649546i | \(-0.225041\pi\) | ||||
0.760323 | + | 0.649546i | \(0.225041\pi\) | |||||||
\(504\) | 14.7966 | 0.659093 | ||||||||
\(505\) | −0.0318417 | −0.00141694 | ||||||||
\(506\) | −6.91512 | −0.307415 | ||||||||
\(507\) | −1.28456 | −0.0570493 | ||||||||
\(508\) | −6.72888 | −0.298546 | ||||||||
\(509\) | −12.8444 | −0.569317 | −0.284658 | − | 0.958629i | \(-0.591880\pi\) | ||||
−0.284658 | + | 0.958629i | \(0.591880\pi\) | |||||||
\(510\) | 96.2500 | 4.26202 | ||||||||
\(511\) | −7.45639 | −0.329851 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −111.142 | −4.90703 | ||||||||
\(514\) | 8.70097 | 0.383783 | ||||||||
\(515\) | 20.4303 | 0.900267 | ||||||||
\(516\) | 13.9723 | 0.615097 | ||||||||
\(517\) | 0.894997 | 0.0393619 | ||||||||
\(518\) | −13.7082 | −0.602305 | ||||||||
\(519\) | −22.5791 | −0.991113 | ||||||||
\(520\) | −13.0927 | −0.574153 | ||||||||
\(521\) | −2.37323 | −0.103973 | −0.0519865 | − | 0.998648i | \(-0.516555\pi\) | ||||
−0.0519865 | + | 0.998648i | \(0.516555\pi\) | |||||||
\(522\) | −38.7312 | −1.69522 | ||||||||
\(523\) | 42.1621 | 1.84362 | 0.921810 | − | 0.387643i | \(-0.126711\pi\) | ||||
0.921810 | + | 0.387643i | \(0.126711\pi\) | |||||||
\(524\) | 13.8913 | 0.606844 | ||||||||
\(525\) | −46.9593 | −2.04947 | ||||||||
\(526\) | −19.5655 | −0.853096 | ||||||||
\(527\) | 28.7124 | 1.25073 | ||||||||
\(528\) | 3.66317 | 0.159419 | ||||||||
\(529\) | 17.1057 | 0.743728 | ||||||||
\(530\) | −33.1667 | −1.44067 | ||||||||
\(531\) | 59.9389 | 2.60112 | ||||||||
\(532\) | 11.3024 | 0.490022 | ||||||||
\(533\) | 15.8367 | 0.685963 | ||||||||
\(534\) | −1.69578 | −0.0733834 | ||||||||
\(535\) | −37.3250 | −1.61370 | ||||||||
\(536\) | 1.21956 | 0.0526771 | ||||||||
\(537\) | −26.3814 | −1.13844 | ||||||||
\(538\) | 9.34653 | 0.402957 | ||||||||
\(539\) | 4.13480 | 0.178099 | ||||||||
\(540\) | 63.0866 | 2.71481 | ||||||||
\(541\) | 20.6984 | 0.889894 | 0.444947 | − | 0.895557i | \(-0.353223\pi\) | ||||
0.444947 | + | 0.895557i | \(0.353223\pi\) | |||||||
\(542\) | 13.2398 | 0.568697 | ||||||||
\(543\) | 54.0469 | 2.31938 | ||||||||
\(544\) | 8.01652 | 0.343706 | ||||||||
\(545\) | −39.8095 | −1.70525 | ||||||||
\(546\) | −21.9995 | −0.941493 | ||||||||
\(547\) | −15.2034 | −0.650050 | −0.325025 | − | 0.945705i | \(-0.605373\pi\) | ||||
−0.325025 | + | 0.945705i | \(0.605373\pi\) | |||||||
\(548\) | 13.3834 | 0.571711 | ||||||||
\(549\) | −33.7792 | −1.44166 | ||||||||
\(550\) | −8.52668 | −0.363579 | ||||||||
\(551\) | −29.5849 | −1.26036 | ||||||||
\(552\) | −21.2454 | −0.904263 | ||||||||
\(553\) | −5.94031 | −0.252608 | ||||||||
\(554\) | 11.5887 | 0.492358 | ||||||||
\(555\) | −91.8162 | −3.89738 | ||||||||
\(556\) | 2.97490 | 0.126164 | ||||||||
\(557\) | −3.49715 | −0.148179 | −0.0740895 | − | 0.997252i | \(-0.523605\pi\) | ||||
−0.0740895 | + | 0.997252i | \(0.523605\pi\) | |||||||
\(558\) | 29.5643 | 1.25156 | ||||||||
\(559\) | −15.2364 | −0.644431 | ||||||||
\(560\) | −6.41551 | −0.271105 | ||||||||
\(561\) | 29.3659 | 1.23983 | ||||||||
\(562\) | −10.0446 | −0.423705 | ||||||||
\(563\) | 15.2490 | 0.642667 | 0.321333 | − | 0.946966i | \(-0.395869\pi\) | ||||
0.321333 | + | 0.946966i | \(0.395869\pi\) | |||||||
\(564\) | 2.74970 | 0.115783 | ||||||||
\(565\) | 52.3751 | 2.20344 | ||||||||
\(566\) | −25.5327 | −1.07322 | ||||||||
\(567\) | 61.6139 | 2.58754 | ||||||||
\(568\) | 7.85175 | 0.329452 | ||||||||
\(569\) | 24.6859 | 1.03489 | 0.517444 | − | 0.855717i | \(-0.326884\pi\) | ||||
0.517444 | + | 0.855717i | \(0.326884\pi\) | |||||||
\(570\) | 75.7024 | 3.17082 | ||||||||
\(571\) | −26.7686 | −1.12023 | −0.560115 | − | 0.828415i | \(-0.689243\pi\) | ||||
−0.560115 | + | 0.828415i | \(0.689243\pi\) | |||||||
\(572\) | −3.99459 | −0.167022 | ||||||||
\(573\) | −84.6309 | −3.53551 | ||||||||
\(574\) | 7.76008 | 0.323900 | ||||||||
\(575\) | 49.4523 | 2.06230 | ||||||||
\(576\) | 8.25439 | 0.343933 | ||||||||
\(577\) | 9.74406 | 0.405650 | 0.202825 | − | 0.979215i | \(-0.434988\pi\) | ||||
0.202825 | + | 0.979215i | \(0.434988\pi\) | |||||||
\(578\) | 47.2646 | 1.96595 | ||||||||
\(579\) | 36.0520 | 1.49827 | ||||||||
\(580\) | 16.7931 | 0.697294 | ||||||||
\(581\) | 0.00268323 | 0.000111319 0 | ||||||||
\(582\) | −44.1838 | −1.83148 | ||||||||
\(583\) | −10.1192 | −0.419093 | ||||||||
\(584\) | −4.15959 | −0.172125 | ||||||||
\(585\) | −108.072 | −4.46824 | ||||||||
\(586\) | 20.2283 | 0.835624 | ||||||||
\(587\) | 10.1759 | 0.420005 | 0.210002 | − | 0.977701i | \(-0.432653\pi\) | ||||
0.210002 | + | 0.977701i | \(0.432653\pi\) | |||||||
\(588\) | 12.7034 | 0.523878 | ||||||||
\(589\) | 22.5828 | 0.930508 | ||||||||
\(590\) | −25.9883 | −1.06992 | ||||||||
\(591\) | 0.599109 | 0.0246440 | ||||||||
\(592\) | −7.64723 | −0.314299 | ||||||||
\(593\) | −5.11337 | −0.209981 | −0.104990 | − | 0.994473i | \(-0.533481\pi\) | ||||
−0.104990 | + | 0.994473i | \(0.533481\pi\) | |||||||
\(594\) | 19.2477 | 0.789744 | ||||||||
\(595\) | −51.4301 | −2.10843 | ||||||||
\(596\) | −15.3432 | −0.628483 | ||||||||
\(597\) | −24.2226 | −0.991365 | ||||||||
\(598\) | 23.1675 | 0.947388 | ||||||||
\(599\) | −46.5323 | −1.90126 | −0.950629 | − | 0.310331i | \(-0.899560\pi\) | ||||
−0.950629 | + | 0.310331i | \(0.899560\pi\) | |||||||
\(600\) | −26.1966 | −1.06947 | ||||||||
\(601\) | 19.4266 | 0.792430 | 0.396215 | − | 0.918158i | \(-0.370324\pi\) | ||||
0.396215 | + | 0.918158i | \(0.370324\pi\) | |||||||
\(602\) | −7.46594 | −0.304289 | ||||||||
\(603\) | 10.0667 | 0.409949 | ||||||||
\(604\) | 5.99985 | 0.244130 | ||||||||
\(605\) | 35.1011 | 1.42706 | ||||||||
\(606\) | −0.0298471 | −0.00121246 | ||||||||
\(607\) | −1.07284 | −0.0435453 | −0.0217727 | − | 0.999763i | \(-0.506931\pi\) | ||||
−0.0217727 | + | 0.999763i | \(0.506931\pi\) | |||||||
\(608\) | 6.30514 | 0.255707 | ||||||||
\(609\) | 28.2172 | 1.14342 | ||||||||
\(610\) | 14.6460 | 0.592999 | ||||||||
\(611\) | −2.99847 | −0.121305 | ||||||||
\(612\) | 66.1715 | 2.67482 | ||||||||
\(613\) | 16.8203 | 0.679365 | 0.339683 | − | 0.940540i | \(-0.389680\pi\) | ||||
0.339683 | + | 0.940540i | \(0.389680\pi\) | |||||||
\(614\) | 25.0653 | 1.01155 | ||||||||
\(615\) | 51.9761 | 2.09588 | ||||||||
\(616\) | −1.95737 | −0.0788649 | ||||||||
\(617\) | 4.90973 | 0.197658 | 0.0988291 | − | 0.995104i | \(-0.468490\pi\) | ||||
0.0988291 | + | 0.995104i | \(0.468490\pi\) | |||||||
\(618\) | 19.1506 | 0.770349 | ||||||||
\(619\) | −32.2378 | −1.29574 | −0.647872 | − | 0.761749i | \(-0.724341\pi\) | ||||
−0.647872 | + | 0.761749i | \(0.724341\pi\) | |||||||
\(620\) | −12.8185 | −0.514804 | ||||||||
\(621\) | −111.631 | −4.47961 | ||||||||
\(622\) | −23.4401 | −0.939862 | ||||||||
\(623\) | 0.906118 | 0.0363029 | ||||||||
\(624\) | −12.2726 | −0.491297 | ||||||||
\(625\) | −3.06679 | −0.122672 | ||||||||
\(626\) | −6.05460 | −0.241991 | ||||||||
\(627\) | 23.0968 | 0.922398 | ||||||||
\(628\) | −14.8361 | −0.592023 | ||||||||
\(629\) | −61.3042 | −2.44436 | ||||||||
\(630\) | −52.9561 | −2.10982 | ||||||||
\(631\) | −41.6581 | −1.65838 | −0.829192 | − | 0.558964i | \(-0.811199\pi\) | ||||
−0.829192 | + | 0.558964i | \(0.811199\pi\) | |||||||
\(632\) | −3.31384 | −0.131818 | ||||||||
\(633\) | 76.8137 | 3.05307 | ||||||||
\(634\) | −15.0739 | −0.598662 | ||||||||
\(635\) | 24.0822 | 0.955675 | ||||||||
\(636\) | −31.0891 | −1.23276 | ||||||||
\(637\) | −13.8527 | −0.548863 | ||||||||
\(638\) | 5.12357 | 0.202844 | ||||||||
\(639\) | 64.8114 | 2.56390 | ||||||||
\(640\) | −3.57894 | −0.141470 | ||||||||
\(641\) | 39.5295 | 1.56132 | 0.780660 | − | 0.624956i | \(-0.214883\pi\) | ||||
0.780660 | + | 0.624956i | \(0.214883\pi\) | |||||||
\(642\) | −34.9870 | −1.38083 | ||||||||
\(643\) | 7.44453 | 0.293584 | 0.146792 | − | 0.989167i | \(-0.453105\pi\) | ||||
0.146792 | + | 0.989167i | \(0.453105\pi\) | |||||||
\(644\) | 11.3522 | 0.447340 | ||||||||
\(645\) | −50.0060 | −1.96898 | ||||||||
\(646\) | 50.5453 | 1.98868 | ||||||||
\(647\) | 44.3770 | 1.74464 | 0.872321 | − | 0.488934i | \(-0.162614\pi\) | ||||
0.872321 | + | 0.488934i | \(0.162614\pi\) | |||||||
\(648\) | 34.3718 | 1.35025 | ||||||||
\(649\) | −7.92903 | −0.311242 | ||||||||
\(650\) | 28.5666 | 1.12047 | ||||||||
\(651\) | −21.5388 | −0.844172 | ||||||||
\(652\) | −11.8622 | −0.464560 | ||||||||
\(653\) | 44.4547 | 1.73965 | 0.869823 | − | 0.493364i | \(-0.164233\pi\) | ||||
0.869823 | + | 0.493364i | \(0.164233\pi\) | |||||||
\(654\) | −37.3159 | −1.45917 | ||||||||
\(655\) | −49.7161 | −1.94257 | ||||||||
\(656\) | 4.32902 | 0.169020 | ||||||||
\(657\) | −34.3349 | −1.33953 | ||||||||
\(658\) | −1.46927 | −0.0572782 | ||||||||
\(659\) | −27.2924 | −1.06316 | −0.531580 | − | 0.847008i | \(-0.678401\pi\) | ||||
−0.531580 | + | 0.847008i | \(0.678401\pi\) | |||||||
\(660\) | −13.1103 | −0.510317 | ||||||||
\(661\) | 11.0815 | 0.431020 | 0.215510 | − | 0.976502i | \(-0.430859\pi\) | ||||
0.215510 | + | 0.976502i | \(0.430859\pi\) | |||||||
\(662\) | −13.3559 | −0.519093 | ||||||||
\(663\) | −98.3835 | −3.82090 | ||||||||
\(664\) | 0.00149686 | 5.80893e−5 0 | ||||||||
\(665\) | −40.4507 | −1.56861 | ||||||||
\(666\) | −63.1232 | −2.44598 | ||||||||
\(667\) | −29.7152 | −1.15058 | ||||||||
\(668\) | −2.37796 | −0.0920060 | ||||||||
\(669\) | −60.2650 | −2.32998 | ||||||||
\(670\) | −4.36473 | −0.168624 | ||||||||
\(671\) | 4.46850 | 0.172504 | ||||||||
\(672\) | −6.01365 | −0.231982 | ||||||||
\(673\) | 9.89588 | 0.381458 | 0.190729 | − | 0.981643i | \(-0.438915\pi\) | ||||
0.190729 | + | 0.981643i | \(0.438915\pi\) | |||||||
\(674\) | 6.84980 | 0.263844 | ||||||||
\(675\) | −137.647 | −5.29803 | ||||||||
\(676\) | 0.382907 | 0.0147272 | ||||||||
\(677\) | 32.2116 | 1.23799 | 0.618995 | − | 0.785395i | \(-0.287540\pi\) | ||||
0.618995 | + | 0.785395i | \(0.287540\pi\) | |||||||
\(678\) | 49.0944 | 1.88546 | ||||||||
\(679\) | 23.6091 | 0.906034 | ||||||||
\(680\) | −28.6906 | −1.10024 | ||||||||
\(681\) | −92.7657 | −3.55479 | ||||||||
\(682\) | −3.91093 | −0.149757 | ||||||||
\(683\) | −21.1526 | −0.809384 | −0.404692 | − | 0.914453i | \(-0.632621\pi\) | ||||
−0.404692 | + | 0.914453i | \(0.632621\pi\) | |||||||
\(684\) | 52.0450 | 1.98999 | ||||||||
\(685\) | −47.8984 | −1.83010 | ||||||||
\(686\) | −19.3359 | −0.738249 | ||||||||
\(687\) | −61.8267 | −2.35884 | ||||||||
\(688\) | −4.16493 | −0.158786 | ||||||||
\(689\) | 33.9018 | 1.29156 | ||||||||
\(690\) | 76.0358 | 2.89463 | ||||||||
\(691\) | 44.7002 | 1.70047 | 0.850237 | − | 0.526399i | \(-0.176458\pi\) | ||||
0.850237 | + | 0.526399i | \(0.176458\pi\) | |||||||
\(692\) | 6.73048 | 0.255854 | ||||||||
\(693\) | −16.1569 | −0.613751 | ||||||||
\(694\) | −11.8184 | −0.448621 | ||||||||
\(695\) | −10.6470 | −0.403864 | ||||||||
\(696\) | 15.7412 | 0.596667 | ||||||||
\(697\) | 34.7036 | 1.31449 | ||||||||
\(698\) | −11.7736 | −0.445637 | ||||||||
\(699\) | 57.9017 | 2.19004 | ||||||||
\(700\) | 13.9978 | 0.529068 | ||||||||
\(701\) | −39.2007 | −1.48059 | −0.740295 | − | 0.672282i | \(-0.765314\pi\) | ||||
−0.740295 | + | 0.672282i | \(0.765314\pi\) | |||||||
\(702\) | −64.4849 | −2.43383 | ||||||||
\(703\) | −48.2169 | −1.81853 | ||||||||
\(704\) | −1.09193 | −0.0411538 | ||||||||
\(705\) | −9.84102 | −0.370634 | ||||||||
\(706\) | −15.9335 | −0.599664 | ||||||||
\(707\) | 0.0159485 | 0.000599804 0 | ||||||||
\(708\) | −24.3604 | −0.915520 | ||||||||
\(709\) | −33.3399 | −1.25211 | −0.626053 | − | 0.779780i | \(-0.715331\pi\) | ||||
−0.626053 | + | 0.779780i | \(0.715331\pi\) | |||||||
\(710\) | −28.1009 | −1.05461 | ||||||||
\(711\) | −27.3537 | −1.02585 | ||||||||
\(712\) | 0.505484 | 0.0189438 | ||||||||
\(713\) | 22.6823 | 0.849458 | ||||||||
\(714\) | −48.2086 | −1.80416 | ||||||||
\(715\) | 14.2964 | 0.534654 | ||||||||
\(716\) | 7.86388 | 0.293887 | ||||||||
\(717\) | 79.7699 | 2.97906 | ||||||||
\(718\) | −26.9345 | −1.00519 | ||||||||
\(719\) | −22.5955 | −0.842671 | −0.421335 | − | 0.906905i | \(-0.638438\pi\) | ||||
−0.421335 | + | 0.906905i | \(0.638438\pi\) | |||||||
\(720\) | −29.5419 | −1.10096 | ||||||||
\(721\) | −10.2329 | −0.381093 | ||||||||
\(722\) | 20.7548 | 0.772412 | ||||||||
\(723\) | 98.7246 | 3.67161 | ||||||||
\(724\) | −16.1105 | −0.598743 | ||||||||
\(725\) | −36.6403 | −1.36079 | ||||||||
\(726\) | 32.9024 | 1.22112 | ||||||||
\(727\) | −21.2009 | −0.786299 | −0.393150 | − | 0.919474i | \(-0.628615\pi\) | ||||
−0.393150 | + | 0.919474i | \(0.628615\pi\) | |||||||
\(728\) | 6.55771 | 0.243045 | ||||||||
\(729\) | 106.313 | 3.93752 | ||||||||
\(730\) | 14.8869 | 0.550990 | ||||||||
\(731\) | −33.3882 | −1.23491 | ||||||||
\(732\) | 13.7286 | 0.507423 | ||||||||
\(733\) | −28.1566 | −1.03999 | −0.519994 | − | 0.854170i | \(-0.674066\pi\) | ||||
−0.519994 | + | 0.854170i | \(0.674066\pi\) | |||||||
\(734\) | −13.8265 | −0.510345 | ||||||||
\(735\) | −45.4646 | −1.67699 | ||||||||
\(736\) | 6.33291 | 0.233434 | ||||||||
\(737\) | −1.33168 | −0.0490531 | ||||||||
\(738\) | 35.7334 | 1.31536 | ||||||||
\(739\) | 5.41197 | 0.199083 | 0.0995413 | − | 0.995033i | \(-0.468262\pi\) | ||||
0.0995413 | + | 0.995033i | \(0.468262\pi\) | |||||||
\(740\) | 27.3690 | 1.00610 | ||||||||
\(741\) | −77.3804 | −2.84264 | ||||||||
\(742\) | 16.6121 | 0.609850 | ||||||||
\(743\) | 37.2075 | 1.36501 | 0.682506 | − | 0.730880i | \(-0.260890\pi\) | ||||
0.682506 | + | 0.730880i | \(0.260890\pi\) | |||||||
\(744\) | −12.0156 | −0.440512 | ||||||||
\(745\) | 54.9125 | 2.01184 | ||||||||
\(746\) | −10.4072 | −0.381036 | ||||||||
\(747\) | 0.0123556 | 0.000452069 0 | ||||||||
\(748\) | −8.75352 | −0.320060 | ||||||||
\(749\) | 18.6949 | 0.683096 | ||||||||
\(750\) | 33.7236 | 1.23141 | ||||||||
\(751\) | 11.9385 | 0.435642 | 0.217821 | − | 0.975989i | \(-0.430105\pi\) | ||||
0.217821 | + | 0.975989i | \(0.430105\pi\) | |||||||
\(752\) | −0.819644 | −0.0298893 | ||||||||
\(753\) | −100.552 | −3.66431 | ||||||||
\(754\) | −17.1653 | −0.625123 | ||||||||
\(755\) | −21.4731 | −0.781486 | ||||||||
\(756\) | −31.5981 | −1.14921 | ||||||||
\(757\) | −24.6086 | −0.894413 | −0.447206 | − | 0.894431i | \(-0.647581\pi\) | ||||
−0.447206 | + | 0.894431i | \(0.647581\pi\) | |||||||
\(758\) | −7.07875 | −0.257112 | ||||||||
\(759\) | 23.1986 | 0.842054 | ||||||||
\(760\) | −22.5657 | −0.818543 | ||||||||
\(761\) | −41.2530 | −1.49542 | −0.747710 | − | 0.664026i | \(-0.768846\pi\) | ||||
−0.747710 | + | 0.664026i | \(0.768846\pi\) | |||||||
\(762\) | 22.5738 | 0.817761 | ||||||||
\(763\) | 19.9393 | 0.721851 | ||||||||
\(764\) | 25.2272 | 0.912686 | ||||||||
\(765\) | −236.824 | −8.56237 | ||||||||
\(766\) | −8.21579 | −0.296849 | ||||||||
\(767\) | 26.5643 | 0.959182 | ||||||||
\(768\) | −3.35476 | −0.121054 | ||||||||
\(769\) | −35.6929 | −1.28712 | −0.643559 | − | 0.765396i | \(-0.722543\pi\) | ||||
−0.643559 | + | 0.765396i | \(0.722543\pi\) | |||||||
\(770\) | 7.00532 | 0.252454 | ||||||||
\(771\) | −29.1896 | −1.05124 | ||||||||
\(772\) | −10.7465 | −0.386776 | ||||||||
\(773\) | 4.37312 | 0.157290 | 0.0786452 | − | 0.996903i | \(-0.474941\pi\) | ||||
0.0786452 | + | 0.996903i | \(0.474941\pi\) | |||||||
\(774\) | −34.3789 | −1.23572 | ||||||||
\(775\) | 27.9684 | 1.00465 | ||||||||
\(776\) | 13.1705 | 0.472793 | ||||||||
\(777\) | 45.9878 | 1.64980 | ||||||||
\(778\) | −6.36587 | −0.228227 | ||||||||
\(779\) | 27.2950 | 0.977946 | ||||||||
\(780\) | 43.9228 | 1.57269 | ||||||||
\(781\) | −8.57360 | −0.306788 | ||||||||
\(782\) | 50.7679 | 1.81546 | ||||||||
\(783\) | 82.7102 | 2.95582 | ||||||||
\(784\) | −3.78668 | −0.135238 | ||||||||
\(785\) | 53.0973 | 1.89512 | ||||||||
\(786\) | −46.6019 | −1.66224 | ||||||||
\(787\) | −23.6548 | −0.843201 | −0.421601 | − | 0.906782i | \(-0.638532\pi\) | ||||
−0.421601 | + | 0.906782i | \(0.638532\pi\) | |||||||
\(788\) | −0.178585 | −0.00636182 | ||||||||
\(789\) | 65.6375 | 2.33676 | ||||||||
\(790\) | 11.8600 | 0.421961 | ||||||||
\(791\) | −26.2330 | −0.932738 | ||||||||
\(792\) | −9.01325 | −0.320272 | ||||||||
\(793\) | −14.9706 | −0.531623 | ||||||||
\(794\) | −6.79701 | −0.241217 | ||||||||
\(795\) | 111.266 | 3.94620 | ||||||||
\(796\) | 7.22038 | 0.255919 | ||||||||
\(797\) | −30.9024 | −1.09462 | −0.547309 | − | 0.836930i | \(-0.684348\pi\) | ||||
−0.547309 | + | 0.836930i | \(0.684348\pi\) | |||||||
\(798\) | −37.9169 | −1.34224 | ||||||||
\(799\) | −6.57069 | −0.232454 | ||||||||
\(800\) | 7.80879 | 0.276082 | ||||||||
\(801\) | 4.17246 | 0.147427 | ||||||||
\(802\) | 36.0616 | 1.27338 | ||||||||
\(803\) | 4.54201 | 0.160284 | ||||||||
\(804\) | −4.09133 | −0.144290 | ||||||||
\(805\) | −40.6288 | −1.43198 | ||||||||
\(806\) | 13.1026 | 0.461521 | ||||||||
\(807\) | −31.3553 | −1.10376 | ||||||||
\(808\) | 0.00889696 | 0.000312994 0 | ||||||||
\(809\) | −37.2697 | −1.31033 | −0.655167 | − | 0.755484i | \(-0.727402\pi\) | ||||
−0.655167 | + | 0.755484i | \(0.727402\pi\) | |||||||
\(810\) | −123.014 | −4.32228 | ||||||||
\(811\) | −6.47371 | −0.227323 | −0.113661 | − | 0.993520i | \(-0.536258\pi\) | ||||
−0.113661 | + | 0.993520i | \(0.536258\pi\) | |||||||
\(812\) | −8.41111 | −0.295172 | ||||||||
\(813\) | −44.4162 | −1.55774 | ||||||||
\(814\) | 8.35028 | 0.292677 | ||||||||
\(815\) | 42.4541 | 1.48710 | ||||||||
\(816\) | −26.8935 | −0.941460 | ||||||||
\(817\) | −26.2604 | −0.918736 | ||||||||
\(818\) | −31.9276 | −1.11632 | ||||||||
\(819\) | 54.1299 | 1.89145 | ||||||||
\(820\) | −15.4933 | −0.541048 | ||||||||
\(821\) | −27.0955 | −0.945640 | −0.472820 | − | 0.881159i | \(-0.656764\pi\) | ||||
−0.472820 | + | 0.881159i | \(0.656764\pi\) | |||||||
\(822\) | −44.8981 | −1.56600 | ||||||||
\(823\) | 15.8182 | 0.551388 | 0.275694 | − | 0.961245i | \(-0.411092\pi\) | ||||
0.275694 | + | 0.961245i | \(0.411092\pi\) | |||||||
\(824\) | −5.70849 | −0.198865 | ||||||||
\(825\) | 28.6049 | 0.995896 | ||||||||
\(826\) | 13.0167 | 0.452909 | ||||||||
\(827\) | 47.7220 | 1.65945 | 0.829727 | − | 0.558169i | \(-0.188496\pi\) | ||||
0.829727 | + | 0.558169i | \(0.188496\pi\) | |||||||
\(828\) | 52.2743 | 1.81666 | ||||||||
\(829\) | 11.3202 | 0.393168 | 0.196584 | − | 0.980487i | \(-0.437015\pi\) | ||||
0.196584 | + | 0.980487i | \(0.437015\pi\) | |||||||
\(830\) | −0.00535715 | −0.000185949 0 | ||||||||
\(831\) | −38.8774 | −1.34864 | ||||||||
\(832\) | 3.65827 | 0.126828 | ||||||||
\(833\) | −30.3560 | −1.05177 | ||||||||
\(834\) | −9.98008 | −0.345582 | ||||||||
\(835\) | 8.51057 | 0.294520 | ||||||||
\(836\) | −6.88480 | −0.238116 | ||||||||
\(837\) | −63.1345 | −2.18225 | ||||||||
\(838\) | 2.92692 | 0.101109 | ||||||||
\(839\) | 42.5039 | 1.46740 | 0.733698 | − | 0.679475i | \(-0.237793\pi\) | ||||
0.733698 | + | 0.679475i | \(0.237793\pi\) | |||||||
\(840\) | 21.5225 | 0.742596 | ||||||||
\(841\) | −6.98331 | −0.240804 | ||||||||
\(842\) | −2.31229 | −0.0796866 | ||||||||
\(843\) | 33.6971 | 1.16059 | ||||||||
\(844\) | −22.8969 | −0.788145 | ||||||||
\(845\) | −1.37040 | −0.0471432 | ||||||||
\(846\) | −6.76566 | −0.232608 | ||||||||
\(847\) | −17.5810 | −0.604090 | ||||||||
\(848\) | 9.26718 | 0.318236 | ||||||||
\(849\) | 85.6558 | 2.93970 | ||||||||
\(850\) | 62.5993 | 2.14714 | ||||||||
\(851\) | −48.4292 | −1.66013 | ||||||||
\(852\) | −26.3407 | −0.902418 | ||||||||
\(853\) | −2.98116 | −0.102073 | −0.0510364 | − | 0.998697i | \(-0.516252\pi\) | ||||
−0.0510364 | + | 0.998697i | \(0.516252\pi\) | |||||||
\(854\) | −7.33571 | −0.251023 | ||||||||
\(855\) | −186.266 | −6.37016 | ||||||||
\(856\) | 10.4291 | 0.356458 | ||||||||
\(857\) | −50.5479 | −1.72668 | −0.863341 | − | 0.504621i | \(-0.831632\pi\) | ||||
−0.863341 | + | 0.504621i | \(0.831632\pi\) | |||||||
\(858\) | 13.4009 | 0.457498 | ||||||||
\(859\) | 16.4483 | 0.561209 | 0.280604 | − | 0.959824i | \(-0.409465\pi\) | ||||
0.280604 | + | 0.959824i | \(0.409465\pi\) | |||||||
\(860\) | 14.9060 | 0.508291 | ||||||||
\(861\) | −26.0332 | −0.887209 | ||||||||
\(862\) | −27.3341 | −0.931002 | ||||||||
\(863\) | −22.5662 | −0.768162 | −0.384081 | − | 0.923299i | \(-0.625482\pi\) | ||||
−0.384081 | + | 0.923299i | \(0.625482\pi\) | |||||||
\(864\) | −17.6272 | −0.599689 | ||||||||
\(865\) | −24.0880 | −0.819015 | ||||||||
\(866\) | 38.7803 | 1.31781 | ||||||||
\(867\) | −158.561 | −5.38502 | ||||||||
\(868\) | 6.42038 | 0.217922 | ||||||||
\(869\) | 3.61850 | 0.122749 | ||||||||
\(870\) | −56.3366 | −1.90999 | ||||||||
\(871\) | 4.46148 | 0.151172 | ||||||||
\(872\) | 11.1233 | 0.376682 | ||||||||
\(873\) | 108.714 | 3.67942 | ||||||||
\(874\) | 39.9299 | 1.35065 | ||||||||
\(875\) | −18.0198 | −0.609180 | ||||||||
\(876\) | 13.9544 | 0.471476 | ||||||||
\(877\) | −29.4453 | −0.994297 | −0.497149 | − | 0.867665i | \(-0.665620\pi\) | ||||
−0.497149 | + | 0.867665i | \(0.665620\pi\) | |||||||
\(878\) | 3.11143 | 0.105006 | ||||||||
\(879\) | −67.8611 | −2.28890 | ||||||||
\(880\) | 3.90797 | 0.131737 | ||||||||
\(881\) | −32.7795 | −1.10437 | −0.552184 | − | 0.833722i | \(-0.686205\pi\) | ||||
−0.552184 | + | 0.833722i | \(0.686205\pi\) | |||||||
\(882\) | −31.2567 | −1.05247 | ||||||||
\(883\) | 18.7679 | 0.631589 | 0.315794 | − | 0.948828i | \(-0.397729\pi\) | ||||
0.315794 | + | 0.948828i | \(0.397729\pi\) | |||||||
\(884\) | 29.3266 | 0.986359 | ||||||||
\(885\) | 87.1843 | 2.93067 | ||||||||
\(886\) | −8.04748 | −0.270360 | ||||||||
\(887\) | 14.9446 | 0.501791 | 0.250895 | − | 0.968014i | \(-0.419275\pi\) | ||||
0.250895 | + | 0.968014i | \(0.419275\pi\) | |||||||
\(888\) | 25.6546 | 0.860912 | ||||||||
\(889\) | −12.0620 | −0.404547 | ||||||||
\(890\) | −1.80910 | −0.0606410 | ||||||||
\(891\) | −37.5317 | −1.25736 | ||||||||
\(892\) | 17.9641 | 0.601481 | ||||||||
\(893\) | −5.16796 | −0.172939 | ||||||||
\(894\) | 51.4728 | 1.72151 | ||||||||
\(895\) | −28.1443 | −0.940761 | ||||||||
\(896\) | 1.79257 | 0.0598857 | ||||||||
\(897\) | −77.7212 | −2.59503 | ||||||||
\(898\) | −18.1602 | −0.606012 | ||||||||
\(899\) | −16.8058 | −0.560505 | ||||||||
\(900\) | 64.4567 | 2.14856 | ||||||||
\(901\) | 74.2906 | 2.47498 | ||||||||
\(902\) | −4.72700 | −0.157392 | ||||||||
\(903\) | 25.0464 | 0.833492 | ||||||||
\(904\) | −14.6343 | −0.486728 | ||||||||
\(905\) | 57.6586 | 1.91664 | ||||||||
\(906\) | −20.1280 | −0.668709 | ||||||||
\(907\) | 33.8155 | 1.12282 | 0.561412 | − | 0.827536i | \(-0.310258\pi\) | ||||
0.561412 | + | 0.827536i | \(0.310258\pi\) | |||||||
\(908\) | 27.6520 | 0.917664 | ||||||||
\(909\) | 0.0734390 | 0.00243582 | ||||||||
\(910\) | −23.4696 | −0.778011 | ||||||||
\(911\) | −16.1929 | −0.536495 | −0.268248 | − | 0.963350i | \(-0.586444\pi\) | ||||
−0.268248 | + | 0.963350i | \(0.586444\pi\) | |||||||
\(912\) | −21.1522 | −0.700419 | ||||||||
\(913\) | −0.00163447 | −5.40930e−5 0 | ||||||||
\(914\) | 15.1244 | 0.500271 | ||||||||
\(915\) | −49.1337 | −1.62431 | ||||||||
\(916\) | 18.4296 | 0.608930 | ||||||||
\(917\) | 24.9012 | 0.822310 | ||||||||
\(918\) | −141.309 | −4.66388 | ||||||||
\(919\) | 58.8771 | 1.94218 | 0.971089 | − | 0.238719i | \(-0.0767274\pi\) | ||||
0.971089 | + | 0.238719i | \(0.0767274\pi\) | |||||||
\(920\) | −22.6651 | −0.747245 | ||||||||
\(921\) | −84.0878 | −2.77079 | ||||||||
\(922\) | 17.6429 | 0.581037 | ||||||||
\(923\) | 28.7238 | 0.945455 | ||||||||
\(924\) | 6.56651 | 0.216022 | ||||||||
\(925\) | −59.7156 | −1.96344 | ||||||||
\(926\) | 34.6719 | 1.13939 | ||||||||
\(927\) | −47.1201 | −1.54763 | ||||||||
\(928\) | −4.69220 | −0.154029 | ||||||||
\(929\) | −24.4774 | −0.803077 | −0.401538 | − | 0.915842i | \(-0.631524\pi\) | ||||
−0.401538 | + | 0.915842i | \(0.631524\pi\) | |||||||
\(930\) | 43.0030 | 1.41012 | ||||||||
\(931\) | −23.8755 | −0.782488 | ||||||||
\(932\) | −17.2596 | −0.565357 | ||||||||
\(933\) | 78.6358 | 2.57442 | ||||||||
\(934\) | 18.1834 | 0.594978 | ||||||||
\(935\) | 31.3283 | 1.02454 | ||||||||
\(936\) | 30.1967 | 0.987011 | ||||||||
\(937\) | −41.7380 | −1.36352 | −0.681761 | − | 0.731575i | \(-0.738786\pi\) | ||||
−0.681761 | + | 0.731575i | \(0.738786\pi\) | |||||||
\(938\) | 2.18616 | 0.0713805 | ||||||||
\(939\) | 20.3117 | 0.662848 | ||||||||
\(940\) | 2.93345 | 0.0956787 | ||||||||
\(941\) | −25.6956 | −0.837653 | −0.418826 | − | 0.908066i | \(-0.637558\pi\) | ||||
−0.418826 | + | 0.908066i | \(0.637558\pi\) | |||||||
\(942\) | 49.7714 | 1.62164 | ||||||||
\(943\) | 27.4153 | 0.892764 | ||||||||
\(944\) | 7.26145 | 0.236340 | ||||||||
\(945\) | 113.087 | 3.67873 | ||||||||
\(946\) | 4.54783 | 0.147863 | ||||||||
\(947\) | 46.7596 | 1.51948 | 0.759742 | − | 0.650225i | \(-0.225325\pi\) | ||||
0.759742 | + | 0.650225i | \(0.225325\pi\) | |||||||
\(948\) | 11.1171 | 0.361068 | ||||||||
\(949\) | −15.2169 | −0.493962 | ||||||||
\(950\) | 49.2355 | 1.59741 | ||||||||
\(951\) | 50.5694 | 1.63982 | ||||||||
\(952\) | 14.3702 | 0.465741 | ||||||||
\(953\) | 16.1464 | 0.523035 | 0.261517 | − | 0.965199i | \(-0.415777\pi\) | ||||
0.261517 | + | 0.965199i | \(0.415777\pi\) | |||||||
\(954\) | 76.4949 | 2.47661 | ||||||||
\(955\) | −90.2864 | −2.92160 | ||||||||
\(956\) | −23.7782 | −0.769041 | ||||||||
\(957\) | −17.1883 | −0.555620 | ||||||||
\(958\) | 31.7302 | 1.02515 | ||||||||
\(959\) | 23.9908 | 0.774703 | ||||||||
\(960\) | 12.0065 | 0.387507 | ||||||||
\(961\) | −18.1718 | −0.586186 | ||||||||
\(962\) | −27.9756 | −0.901970 | ||||||||
\(963\) | 86.0856 | 2.77407 | ||||||||
\(964\) | −29.4282 | −0.947820 | ||||||||
\(965\) | 38.4612 | 1.23811 | ||||||||
\(966\) | −38.0839 | −1.22533 | ||||||||
\(967\) | 53.0340 | 1.70546 | 0.852729 | − | 0.522354i | \(-0.174946\pi\) | ||||
0.852729 | + | 0.522354i | \(0.174946\pi\) | |||||||
\(968\) | −9.80768 | −0.315231 | ||||||||
\(969\) | −169.567 | −5.44728 | ||||||||
\(970\) | −47.1364 | −1.51346 | ||||||||
\(971\) | 25.9193 | 0.831791 | 0.415896 | − | 0.909412i | \(-0.363468\pi\) | ||||
0.415896 | + | 0.909412i | \(0.363468\pi\) | |||||||
\(972\) | −62.4273 | −2.00236 | ||||||||
\(973\) | 5.33274 | 0.170960 | ||||||||
\(974\) | 29.8048 | 0.955006 | ||||||||
\(975\) | −95.8340 | −3.06914 | ||||||||
\(976\) | −4.09228 | −0.130991 | ||||||||
\(977\) | −36.3226 | −1.16206 | −0.581032 | − | 0.813881i | \(-0.697351\pi\) | ||||
−0.581032 | + | 0.813881i | \(0.697351\pi\) | |||||||
\(978\) | 39.7948 | 1.27250 | ||||||||
\(979\) | −0.551956 | −0.0176406 | ||||||||
\(980\) | 13.5523 | 0.432911 | ||||||||
\(981\) | 91.8158 | 2.93145 | ||||||||
\(982\) | 41.6480 | 1.32904 | ||||||||
\(983\) | −11.0279 | −0.351735 | −0.175867 | − | 0.984414i | \(-0.556273\pi\) | ||||
−0.175867 | + | 0.984414i | \(0.556273\pi\) | |||||||
\(984\) | −14.5228 | −0.462970 | ||||||||
\(985\) | 0.639144 | 0.0203648 | ||||||||
\(986\) | −37.6151 | −1.19791 | ||||||||
\(987\) | 4.92905 | 0.156893 | ||||||||
\(988\) | 23.0659 | 0.733823 | ||||||||
\(989\) | −26.3761 | −0.838711 | ||||||||
\(990\) | 32.2579 | 1.02522 | ||||||||
\(991\) | −58.0320 | −1.84345 | −0.921724 | − | 0.387847i | \(-0.873219\pi\) | ||||
−0.921724 | + | 0.387847i | \(0.873219\pi\) | |||||||
\(992\) | 3.58165 | 0.113718 | ||||||||
\(993\) | 44.8059 | 1.42187 | ||||||||
\(994\) | 14.0749 | 0.446427 | ||||||||
\(995\) | −25.8413 | −0.819223 | ||||||||
\(996\) | −0.00502158 | −0.000159115 0 | ||||||||
\(997\) | −40.5670 | −1.28477 | −0.642385 | − | 0.766382i | \(-0.722055\pi\) | ||||
−0.642385 | + | 0.766382i | \(0.722055\pi\) | |||||||
\(998\) | 33.2866 | 1.05367 | ||||||||
\(999\) | 134.799 | 4.26486 |
(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 | 6022.2.a.e.1.1 | ✓ | 68 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6022.2.a.e.1.1 | ✓ | 68 | 1.1 | even | 1 | trivial |