Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,6,Mod(176,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.176");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.d (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(28.3879361069\) |
Analytic rank: | \(0\) |
Dimension: | \(92\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 176.10 | ||
Character | \(\chi\) | \(=\) | 177.176 |
Dual form | 177.6.d.b.176.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −9.63720 | −1.70363 | −0.851817 | − | 0.523840i | \(-0.824499\pi\) | ||||
−0.851817 | + | 0.523840i | \(0.824499\pi\) | |||||||
\(3\) | 15.3454 | + | 2.74211i | 0.984407 | + | 0.175907i | ||||
\(4\) | 60.8757 | 1.90237 | ||||||||
\(5\) | 48.0995i | 0.860431i | 0.902726 | + | 0.430215i | \(0.141562\pi\) | ||||
−0.902726 | + | 0.430215i | \(0.858438\pi\) | |||||||
\(6\) | −147.887 | − | 26.4263i | −1.67707 | − | 0.299680i | ||||
\(7\) | 55.2643 | 0.426285 | 0.213142 | − | 0.977021i | \(-0.431630\pi\) | ||||
0.213142 | + | 0.977021i | \(0.431630\pi\) | |||||||
\(8\) | −278.281 | −1.53730 | ||||||||
\(9\) | 227.962 | + | 84.1575i | 0.938114 | + | 0.346327i | ||||
\(10\) | − | 463.545i | − | 1.46586i | ||||||
\(11\) | −33.0223 | −0.0822859 | −0.0411430 | − | 0.999153i | \(-0.513100\pi\) | ||||
−0.0411430 | + | 0.999153i | \(0.513100\pi\) | |||||||
\(12\) | 934.161 | + | 166.928i | 1.87270 | + | 0.334638i | ||||
\(13\) | 847.868i | 1.39146i | 0.718305 | + | 0.695729i | \(0.244918\pi\) | ||||
−0.718305 | + | 0.695729i | \(0.755082\pi\) | |||||||
\(14\) | −532.594 | −0.726233 | ||||||||
\(15\) | −131.894 | + | 738.106i | −0.151355 | + | 0.847014i | ||||
\(16\) | 733.828 | 0.716629 | ||||||||
\(17\) | 1128.87i | 0.947371i | 0.880694 | + | 0.473686i | \(0.157077\pi\) | ||||
−0.880694 | + | 0.473686i | \(0.842923\pi\) | |||||||
\(18\) | −2196.91 | − | 811.043i | −1.59820 | − | 0.590014i | ||||
\(19\) | −1381.08 | −0.877678 | −0.438839 | − | 0.898566i | \(-0.644610\pi\) | ||||
−0.438839 | + | 0.898566i | \(0.644610\pi\) | |||||||
\(20\) | 2928.09i | 1.63685i | ||||||||
\(21\) | 848.052 | + | 151.541i | 0.419638 | + | 0.0749863i | ||||
\(22\) | 318.243 | 0.140185 | ||||||||
\(23\) | 468.321 | 0.184597 | 0.0922984 | − | 0.995731i | \(-0.470579\pi\) | ||||
0.0922984 | + | 0.995731i | \(0.470579\pi\) | |||||||
\(24\) | −4270.33 | − | 763.077i | −1.51333 | − | 0.270421i | ||||
\(25\) | 811.434 | 0.259659 | ||||||||
\(26\) | − | 8171.08i | − | 2.37053i | ||||||
\(27\) | 3267.39 | + | 1916.53i | 0.862564 | + | 0.505947i | ||||
\(28\) | 3364.25 | 0.810949 | ||||||||
\(29\) | − | 408.390i | − | 0.0901737i | −0.998983 | − | 0.0450868i | \(-0.985644\pi\) | ||
0.998983 | − | 0.0450868i | \(-0.0143565\pi\) | |||||||
\(30\) | 1271.09 | − | 7113.28i | 0.257854 | − | 1.44300i | ||||
\(31\) | − | 5084.86i | − | 0.950330i | −0.879897 | − | 0.475165i | \(-0.842388\pi\) | ||
0.879897 | − | 0.475165i | \(-0.157612\pi\) | |||||||
\(32\) | 1832.94 | 0.316427 | ||||||||
\(33\) | −506.740 | − | 90.5508i | −0.0810028 | − | 0.0144746i | ||||
\(34\) | − | 10879.1i | − | 1.61397i | ||||||
\(35\) | 2658.19i | 0.366789i | ||||||||
\(36\) | 13877.3 | + | 5123.15i | 1.78464 | + | 0.658841i | ||||
\(37\) | 1578.30i | 0.189533i | 0.995500 | + | 0.0947666i | \(0.0302105\pi\) | ||||
−0.995500 | + | 0.0947666i | \(0.969790\pi\) | |||||||
\(38\) | 13309.8 | 1.49524 | ||||||||
\(39\) | −2324.95 | + | 13010.9i | −0.244766 | + | 1.36976i | ||||
\(40\) | − | 13385.2i | − | 1.32274i | ||||||
\(41\) | − | 16986.4i | − | 1.57813i | −0.614312 | − | 0.789063i | \(-0.710566\pi\) | ||
0.614312 | − | 0.789063i | \(-0.289434\pi\) | |||||||
\(42\) | −8172.85 | − | 1460.43i | −0.714909 | − | 0.127749i | ||||
\(43\) | 11165.2i | 0.920863i | 0.887695 | + | 0.460431i | \(0.152305\pi\) | ||||
−0.887695 | + | 0.460431i | \(0.847695\pi\) | |||||||
\(44\) | −2010.26 | −0.156538 | ||||||||
\(45\) | −4047.94 | + | 10964.9i | −0.297991 | + | 0.807182i | ||||
\(46\) | −4513.30 | −0.314485 | ||||||||
\(47\) | −12073.6 | −0.797249 | −0.398624 | − | 0.917114i | \(-0.630512\pi\) | ||||
−0.398624 | + | 0.917114i | \(0.630512\pi\) | |||||||
\(48\) | 11260.9 | + | 2012.24i | 0.705455 | + | 0.126060i | ||||
\(49\) | −13752.9 | −0.818281 | ||||||||
\(50\) | −7819.96 | −0.442364 | ||||||||
\(51\) | −3095.48 | + | 17322.9i | −0.166649 | + | 0.932599i | ||||
\(52\) | 51614.6i | 2.64706i | ||||||||
\(53\) | − | 9984.02i | − | 0.488220i | −0.969748 | − | 0.244110i | \(-0.921504\pi\) | ||
0.969748 | − | 0.244110i | \(-0.0784958\pi\) | |||||||
\(54\) | −31488.5 | − | 18469.9i | −1.46949 | − | 0.861948i | ||||
\(55\) | − | 1588.36i | − | 0.0708013i | ||||||
\(56\) | −15379.0 | −0.655327 | ||||||||
\(57\) | −21193.2 | − | 3787.08i | −0.863992 | − | 0.154389i | ||||
\(58\) | 3935.73i | 0.153623i | ||||||||
\(59\) | 19800.7 | + | 17968.2i | 0.740543 | + | 0.672009i | ||||
\(60\) | −8029.16 | + | 44932.7i | −0.287933 | + | 1.61133i | ||||
\(61\) | 50439.9i | 1.73560i | 0.496914 | + | 0.867800i | \(0.334466\pi\) | ||||
−0.496914 | + | 0.867800i | \(0.665534\pi\) | |||||||
\(62\) | 49003.8i | 1.61901i | ||||||||
\(63\) | 12598.1 | + | 4650.91i | 0.399904 | + | 0.147634i | ||||
\(64\) | −41146.9 | −1.25570 | ||||||||
\(65\) | −40782.1 | −1.19725 | ||||||||
\(66\) | 4883.55 | + | 872.656i | 0.137999 | + | 0.0246595i | ||||
\(67\) | 34064.3i | 0.927070i | 0.886079 | + | 0.463535i | \(0.153419\pi\) | ||||
−0.886079 | + | 0.463535i | \(0.846581\pi\) | |||||||
\(68\) | 68720.5i | 1.80225i | ||||||||
\(69\) | 7186.57 | + | 1284.19i | 0.181718 | + | 0.0324718i | ||||
\(70\) | − | 25617.5i | − | 0.624873i | ||||||
\(71\) | 18917.3i | 0.445363i | 0.974891 | + | 0.222682i | \(0.0714810\pi\) | ||||
−0.974891 | + | 0.222682i | \(0.928519\pi\) | |||||||
\(72\) | −63437.4 | − | 23419.4i | −1.44216 | − | 0.532409i | ||||
\(73\) | − | 23663.0i | − | 0.519711i | −0.965647 | − | 0.259856i | \(-0.916325\pi\) | ||
0.965647 | − | 0.259856i | \(-0.0836750\pi\) | |||||||
\(74\) | − | 15210.4i | − | 0.322895i | ||||||
\(75\) | 12451.8 | + | 2225.04i | 0.255610 | + | 0.0456757i | ||||
\(76\) | −84074.3 | −1.66966 | ||||||||
\(77\) | −1824.95 | −0.0350772 | ||||||||
\(78\) | 22406.0 | − | 125388.i | 0.416992 | − | 2.33357i | ||||
\(79\) | −61929.7 | −1.11643 | −0.558214 | − | 0.829697i | \(-0.688513\pi\) | ||||
−0.558214 | + | 0.829697i | \(0.688513\pi\) | |||||||
\(80\) | 35296.8i | 0.616610i | ||||||||
\(81\) | 44884.0 | + | 38369.4i | 0.760115 | + | 0.649789i | ||||
\(82\) | 163701.i | 2.68855i | ||||||||
\(83\) | −31566.8 | −0.502962 | −0.251481 | − | 0.967862i | \(-0.580918\pi\) | ||||
−0.251481 | + | 0.967862i | \(0.580918\pi\) | |||||||
\(84\) | 51625.8 | + | 9225.16i | 0.798304 | + | 0.142651i | ||||
\(85\) | −54297.9 | −0.815147 | ||||||||
\(86\) | − | 107601.i | − | 1.56881i | ||||||
\(87\) | 1119.85 | − | 6266.90i | 0.0158621 | − | 0.0887676i | ||||
\(88\) | 9189.48 | 0.126498 | ||||||||
\(89\) | 52358.2 | 0.700664 | 0.350332 | − | 0.936626i | \(-0.386069\pi\) | ||||
0.350332 | + | 0.936626i | \(0.386069\pi\) | |||||||
\(90\) | 39010.8 | − | 105671.i | 0.507667 | − | 1.37514i | ||||
\(91\) | 46856.9i | 0.593157i | ||||||||
\(92\) | 28509.4 | 0.351170 | ||||||||
\(93\) | 13943.2 | − | 78029.1i | 0.167169 | − | 0.935512i | ||||
\(94\) | 116356. | 1.35822 | ||||||||
\(95\) | − | 66429.4i | − | 0.755181i | ||||||
\(96\) | 28127.2 | + | 5026.12i | 0.311493 | + | 0.0556615i | ||||
\(97\) | − | 25026.4i | − | 0.270066i | −0.990841 | − | 0.135033i | \(-0.956886\pi\) | ||
0.990841 | − | 0.135033i | \(-0.0431140\pi\) | |||||||
\(98\) | 132539. | 1.39405 | ||||||||
\(99\) | −7527.82 | − | 2779.07i | −0.0771936 | − | 0.0284978i | ||||
\(100\) | 49396.6 | 0.493966 | ||||||||
\(101\) | −43891.2 | −0.428128 | −0.214064 | − | 0.976820i | \(-0.568670\pi\) | ||||
−0.214064 | + | 0.976820i | \(0.568670\pi\) | |||||||
\(102\) | 29831.7 | − | 166944.i | 0.283908 | − | 1.58881i | ||||
\(103\) | − | 13348.4i | − | 0.123976i | −0.998077 | − | 0.0619880i | \(-0.980256\pi\) | ||
0.998077 | − | 0.0619880i | \(-0.0197440\pi\) | |||||||
\(104\) | − | 235946.i | − | 2.13909i | ||||||
\(105\) | −7289.05 | + | 40790.9i | −0.0645205 | + | 0.361069i | ||||
\(106\) | 96218.0i | 0.831748i | ||||||||
\(107\) | 202715.i | 1.71170i | 0.517226 | + | 0.855849i | \(0.326965\pi\) | ||||
−0.517226 | + | 0.855849i | \(0.673035\pi\) | |||||||
\(108\) | 198905. | + | 116670.i | 1.64091 | + | 0.962496i | ||||
\(109\) | − | 25308.3i | − | 0.204031i | −0.994783 | − | 0.102016i | \(-0.967471\pi\) | ||
0.994783 | − | 0.102016i | \(-0.0325292\pi\) | |||||||
\(110\) | 15307.3i | 0.120619i | ||||||||
\(111\) | −4327.87 | + | 24219.6i | −0.0333401 | + | 0.186578i | ||||
\(112\) | 40554.5 | 0.305488 | ||||||||
\(113\) | −158888. | −1.17056 | −0.585281 | − | 0.810831i | \(-0.699016\pi\) | ||||
−0.585281 | + | 0.810831i | \(0.699016\pi\) | |||||||
\(114\) | 204243. | + | 36496.8i | 1.47193 | + | 0.263023i | ||||
\(115\) | 22526.0i | 0.158833i | ||||||||
\(116\) | − | 24861.0i | − | 0.171543i | ||||||
\(117\) | −71354.5 | + | 193281.i | −0.481899 | + | 1.30535i | ||||
\(118\) | −190823. | − | 173163.i | −1.26161 | − | 1.14486i | ||||
\(119\) | 62386.0i | 0.403850i | ||||||||
\(120\) | 36703.7 | − | 205401.i | 0.232679 | − | 1.30211i | ||||
\(121\) | −159961. | −0.993229 | ||||||||
\(122\) | − | 486099.i | − | 2.95682i | ||||||
\(123\) | 46578.6 | − | 260663.i | 0.277603 | − | 1.55352i | ||||
\(124\) | − | 309544.i | − | 1.80788i | ||||||
\(125\) | 189341.i | 1.08385i | ||||||||
\(126\) | −121411. | − | 44821.7i | −0.681289 | − | 0.251514i | ||||
\(127\) | 22410.3 | 0.123293 | 0.0616464 | − | 0.998098i | \(-0.480365\pi\) | ||||
0.0616464 | + | 0.998098i | \(0.480365\pi\) | |||||||
\(128\) | 337887. | 1.82283 | ||||||||
\(129\) | −30616.2 | + | 171334.i | −0.161986 | + | 0.906504i | ||||
\(130\) | 393025. | 2.03968 | ||||||||
\(131\) | 21644.2 | 0.110195 | 0.0550976 | − | 0.998481i | \(-0.482453\pi\) | ||||
0.0550976 | + | 0.998481i | \(0.482453\pi\) | |||||||
\(132\) | −30848.1 | − | 5512.34i | −0.154097 | − | 0.0275360i | ||||
\(133\) | −76324.5 | −0.374141 | ||||||||
\(134\) | − | 328285.i | − | 1.57939i | ||||||
\(135\) | −92184.0 | + | 157160.i | −0.435333 | + | 0.742177i | ||||
\(136\) | − | 314142.i | − | 1.45639i | ||||||
\(137\) | − | 79532.7i | − | 0.362030i | −0.983480 | − | 0.181015i | \(-0.942062\pi\) | ||
0.983480 | − | 0.181015i | \(-0.0579382\pi\) | |||||||
\(138\) | −69258.4 | − | 12376.0i | −0.309581 | − | 0.0553200i | ||||
\(139\) | 102245. | 0.448852 | 0.224426 | − | 0.974491i | \(-0.427949\pi\) | ||||
0.224426 | + | 0.974491i | \(0.427949\pi\) | |||||||
\(140\) | 161819.i | 0.697766i | ||||||||
\(141\) | −185275. | − | 33107.3i | −0.784817 | − | 0.140241i | ||||
\(142\) | − | 182310.i | − | 0.758735i | ||||||
\(143\) | − | 27998.5i | − | 0.114497i | ||||||
\(144\) | 167285. | + | 61757.1i | 0.672280 | + | 0.248188i | ||||
\(145\) | 19643.4 | 0.0775882 | ||||||||
\(146\) | 228045.i | 0.885398i | ||||||||
\(147\) | −211043. | − | 37711.9i | −0.805522 | − | 0.143941i | ||||
\(148\) | 96080.1i | 0.360561i | ||||||||
\(149\) | 73849.9 | 0.272511 | 0.136256 | − | 0.990674i | \(-0.456493\pi\) | ||||
0.136256 | + | 0.990674i | \(0.456493\pi\) | |||||||
\(150\) | −120000. | − | 21443.2i | −0.435466 | − | 0.0778146i | ||||
\(151\) | 396440.i | 1.41493i | 0.706748 | + | 0.707465i | \(0.250161\pi\) | ||||
−0.706748 | + | 0.707465i | \(0.749839\pi\) | |||||||
\(152\) | 384329. | 1.34925 | ||||||||
\(153\) | −95002.5 | + | 257338.i | −0.328100 | + | 0.888742i | ||||
\(154\) | 17587.5 | 0.0597587 | ||||||||
\(155\) | 244579. | 0.817694 | ||||||||
\(156\) | −141533. | + | 792045.i | −0.465635 | + | 2.60578i | ||||
\(157\) | − | 318654.i | − | 1.03174i | −0.856667 | − | 0.515870i | \(-0.827469\pi\) | ||
0.856667 | − | 0.515870i | \(-0.172531\pi\) | |||||||
\(158\) | 596829. | 1.90198 | ||||||||
\(159\) | 27377.3 | − | 153209.i | 0.0858811 | − | 0.480607i | ||||
\(160\) | 88163.5i | 0.272263i | ||||||||
\(161\) | 25881.4 | 0.0786908 | ||||||||
\(162\) | −432557. | − | 369773.i | −1.29496 | − | 1.10700i | ||||
\(163\) | −44552.9 | −0.131343 | −0.0656715 | − | 0.997841i | \(-0.520919\pi\) | ||||
−0.0656715 | + | 0.997841i | \(0.520919\pi\) | |||||||
\(164\) | − | 1.03406e6i | − | 3.00217i | ||||||
\(165\) | 4355.45 | − | 24373.9i | 0.0124544 | − | 0.0696973i | ||||
\(166\) | 304216. | 0.856863 | ||||||||
\(167\) | − | 217795.i | − | 0.604305i | −0.953260 | − | 0.302152i | \(-0.902295\pi\) | ||
0.953260 | − | 0.302152i | \(-0.0977052\pi\) | |||||||
\(168\) | −235997. | − | 42171.0i | −0.645109 | − | 0.115276i | ||||
\(169\) | −347587. | −0.936153 | ||||||||
\(170\) | 523280. | 1.38871 | ||||||||
\(171\) | −314834. | − | 116228.i | −0.823362 | − | 0.303964i | ||||
\(172\) | 679689.i | 1.75182i | ||||||||
\(173\) | 320693. | 0.814657 | 0.407328 | − | 0.913282i | \(-0.366460\pi\) | ||||
0.407328 | + | 0.913282i | \(0.366460\pi\) | |||||||
\(174\) | −10792.2 | + | 60395.4i | −0.0270233 | + | 0.151227i | ||||
\(175\) | 44843.4 | 0.110689 | ||||||||
\(176\) | −24232.7 | −0.0589685 | ||||||||
\(177\) | 254579. | + | 330025.i | 0.610785 | + | 0.791796i | ||||
\(178\) | −504587. | −1.19367 | ||||||||
\(179\) | 309289. | 0.721492 | 0.360746 | − | 0.932664i | \(-0.382522\pi\) | ||||
0.360746 | + | 0.932664i | \(0.382522\pi\) | |||||||
\(180\) | −246421. | + | 667493.i | −0.566887 | + | 1.53556i | ||||
\(181\) | −519260. | −1.17812 | −0.589058 | − | 0.808090i | \(-0.700501\pi\) | ||||
−0.589058 | + | 0.808090i | \(0.700501\pi\) | |||||||
\(182\) | − | 451569.i | − | 1.01052i | ||||||
\(183\) | −138312. | + | 774019.i | −0.305303 | + | 1.70854i | ||||
\(184\) | −130325. | −0.283781 | ||||||||
\(185\) | −75915.5 | −0.163080 | ||||||||
\(186\) | −134374. | + | 751982.i | −0.284795 | + | 1.59377i | ||||
\(187\) | − | 37277.7i | − | 0.0779553i | ||||||
\(188\) | −734992. | −1.51666 | ||||||||
\(189\) | 180570. | + | 105915.i | 0.367698 | + | 0.215678i | ||||
\(190\) | 640193.i | 1.28655i | ||||||||
\(191\) | −381662. | −0.757000 | −0.378500 | − | 0.925601i | \(-0.623560\pi\) | ||||
−0.378500 | + | 0.925601i | \(0.623560\pi\) | |||||||
\(192\) | −631415. | − | 112829.i | −1.23612 | − | 0.220887i | ||||
\(193\) | 383123. | 0.740364 | 0.370182 | − | 0.928959i | \(-0.379295\pi\) | ||||
0.370182 | + | 0.928959i | \(0.379295\pi\) | |||||||
\(194\) | 241185.i | 0.460093i | ||||||||
\(195\) | −625816. | − | 111829.i | −1.17858 | − | 0.210605i | ||||
\(196\) | −837215. | −1.55667 | ||||||||
\(197\) | 536432.i | 0.984802i | 0.870368 | + | 0.492401i | \(0.163881\pi\) | ||||
−0.870368 | + | 0.492401i | \(0.836119\pi\) | |||||||
\(198\) | 72547.1 | + | 26782.5i | 0.131509 | + | 0.0485499i | ||||
\(199\) | 694003. | 1.24231 | 0.621153 | − | 0.783689i | \(-0.286665\pi\) | ||||
0.621153 | + | 0.783689i | \(0.286665\pi\) | |||||||
\(200\) | −225807. | −0.399174 | ||||||||
\(201\) | −93408.1 | + | 522730.i | −0.163078 | + | 0.912614i | ||||
\(202\) | 422988. | 0.729373 | ||||||||
\(203\) | − | 22569.4i | − | 0.0384397i | ||||||
\(204\) | −188439. | + | 1.05454e6i | −0.317027 | + | 1.77414i | ||||
\(205\) | 817038. | 1.35787 | ||||||||
\(206\) | 128642.i | 0.211210i | ||||||||
\(207\) | 106759. | + | 39412.7i | 0.173173 | + | 0.0639309i | ||||
\(208\) | 622189.i | 0.997159i | ||||||||
\(209\) | 45606.5 | 0.0722205 | ||||||||
\(210\) | 70246.1 | − | 393111.i | 0.109919 | − | 0.615129i | ||||
\(211\) | − | 328315.i | − | 0.507673i | −0.967247 | − | 0.253836i | \(-0.918307\pi\) | ||
0.967247 | − | 0.253836i | \(-0.0816925\pi\) | |||||||
\(212\) | − | 607784.i | − | 0.928773i | ||||||
\(213\) | −51873.5 | + | 290294.i | −0.0783423 | + | 0.438419i | ||||
\(214\) | − | 1.95361e6i | − | 2.91611i | ||||||
\(215\) | −537040. | −0.792339 | ||||||||
\(216\) | −909252. | − | 533333.i | −1.32602 | − | 0.777792i | ||||
\(217\) | − | 281011.i | − | 0.405111i | ||||||
\(218\) | 243901.i | 0.347594i | ||||||||
\(219\) | 64886.5 | − | 363118.i | 0.0914206 | − | 0.511608i | ||||
\(220\) | − | 96692.3i | − | 0.134690i | ||||||
\(221\) | −957129. | −1.31823 | ||||||||
\(222\) | 41708.6 | − | 233409.i | 0.0567993 | − | 0.317860i | ||||
\(223\) | 1.15178e6 | 1.55098 | 0.775492 | − | 0.631358i | \(-0.217502\pi\) | ||||
0.775492 | + | 0.631358i | \(0.217502\pi\) | |||||||
\(224\) | 101296. | 0.134888 | ||||||||
\(225\) | 184976. | + | 68288.3i | 0.243590 | + | 0.0899269i | ||||
\(226\) | 1.53123e6 | 1.99421 | ||||||||
\(227\) | 1.07066e6 | 1.37907 | 0.689535 | − | 0.724252i | \(-0.257815\pi\) | ||||
0.689535 | + | 0.724252i | \(0.257815\pi\) | |||||||
\(228\) | −1.29015e6 | − | 230541.i | −1.64363 | − | 0.293705i | ||||
\(229\) | − | 1.32871e6i | − | 1.67433i | −0.546950 | − | 0.837165i | \(-0.684211\pi\) | ||
0.546950 | − | 0.837165i | \(-0.315789\pi\) | |||||||
\(230\) | − | 217088.i | − | 0.270593i | ||||||
\(231\) | −28004.6 | − | 5004.23i | −0.0345303 | − | 0.00617031i | ||||
\(232\) | 113647.i | 0.138624i | ||||||||
\(233\) | −1.58830e6 | −1.91664 | −0.958322 | − | 0.285690i | \(-0.907777\pi\) | ||||
−0.958322 | + | 0.285690i | \(0.907777\pi\) | |||||||
\(234\) | 687657. | − | 1.86269e6i | 0.820980 | − | 2.22383i | ||||
\(235\) | − | 580737.i | − | 0.685977i | ||||||
\(236\) | 1.20538e6 | + | 1.09383e6i | 1.40878 | + | 1.27841i | ||||
\(237\) | −950334. | − | 169818.i | −1.09902 | − | 0.196387i | ||||
\(238\) | − | 601227.i | − | 0.688012i | ||||||
\(239\) | − | 820213.i | − | 0.928821i | −0.885620 | − | 0.464410i | \(-0.846266\pi\) | ||
0.885620 | − | 0.464410i | \(-0.153734\pi\) | |||||||
\(240\) | −96787.7 | + | 541643.i | −0.108466 | + | 0.606995i | ||||
\(241\) | 1.58114e6 | 1.75359 | 0.876794 | − | 0.480867i | \(-0.159678\pi\) | ||||
0.876794 | + | 0.480867i | \(0.159678\pi\) | |||||||
\(242\) | 1.54157e6 | 1.69210 | ||||||||
\(243\) | 583550. | + | 711870.i | 0.633960 | + | 0.773366i | ||||
\(244\) | 3.07056e6i | 3.30174i | ||||||||
\(245\) | − | 661506.i | − | 0.704074i | ||||||
\(246\) | −448888. | + | 2.51206e6i | −0.472933 | + | 2.64663i | ||||
\(247\) | − | 1.17097e6i | − | 1.22125i | ||||||
\(248\) | 1.41502e6i | 1.46094i | ||||||||
\(249\) | −484405. | − | 86559.7i | −0.495120 | − | 0.0884743i | ||||
\(250\) | − | 1.82471e6i | − | 1.84648i | ||||||
\(251\) | 1.28330e6i | 1.28572i | 0.765985 | + | 0.642858i | \(0.222252\pi\) | ||||
−0.765985 | + | 0.642858i | \(0.777748\pi\) | |||||||
\(252\) | 766921. | + | 283127.i | 0.760763 | + | 0.280854i | ||||
\(253\) | −15465.0 | −0.0151897 | ||||||||
\(254\) | −215972. | −0.210046 | ||||||||
\(255\) | −833223. | − | 148891.i | −0.802436 | − | 0.143390i | ||||
\(256\) | −1.93959e6 | −1.84973 | ||||||||
\(257\) | 369551.i | 0.349013i | 0.984656 | + | 0.174507i | \(0.0558330\pi\) | ||||
−0.984656 | + | 0.174507i | \(0.944167\pi\) | |||||||
\(258\) | 295054. | − | 1.65118e6i | 0.275964 | − | 1.54435i | ||||
\(259\) | 87223.7i | 0.0807951i | ||||||||
\(260\) | −2.48264e6 | −2.27761 | ||||||||
\(261\) | 34369.1 | − | 93097.2i | 0.0312296 | − | 0.0845932i | ||||
\(262\) | −208589. | −0.187732 | ||||||||
\(263\) | − | 408145.i | − | 0.363852i | −0.983312 | − | 0.181926i | \(-0.941767\pi\) | ||
0.983312 | − | 0.181926i | \(-0.0582332\pi\) | |||||||
\(264\) | 141016. | + | 25198.6i | 0.124526 | + | 0.0222518i | ||||
\(265\) | 480227. | 0.420080 | ||||||||
\(266\) | 735555. | 0.637399 | ||||||||
\(267\) | 803457. | + | 143572.i | 0.689738 | + | 0.123251i | ||||
\(268\) | 2.07369e6i | 1.76363i | ||||||||
\(269\) | −1.05990e6 | −0.893070 | −0.446535 | − | 0.894766i | \(-0.647342\pi\) | ||||
−0.446535 | + | 0.894766i | \(0.647342\pi\) | |||||||
\(270\) | 888396. | − | 1.51458e6i | 0.741647 | − | 1.26440i | ||||
\(271\) | 477246. | 0.394747 | 0.197373 | − | 0.980328i | \(-0.436759\pi\) | ||||
0.197373 | + | 0.980328i | \(0.436759\pi\) | |||||||
\(272\) | 828394.i | 0.678914i | ||||||||
\(273\) | −128487. | + | 719037.i | −0.104340 | + | 0.583908i | ||||
\(274\) | 766472.i | 0.616766i | ||||||||
\(275\) | −26795.4 | −0.0213663 | ||||||||
\(276\) | 437487. | + | 78175.9i | 0.345695 | + | 0.0617732i | ||||
\(277\) | 924308. | 0.723798 | 0.361899 | − | 0.932217i | \(-0.382129\pi\) | ||||
0.361899 | + | 0.932217i | \(0.382129\pi\) | |||||||
\(278\) | −985352. | −0.764679 | ||||||||
\(279\) | 427929. | − | 1.15915e6i | 0.329125 | − | 0.891518i | ||||
\(280\) | − | 739723.i | − | 0.563864i | ||||||
\(281\) | 621749.i | 0.469731i | 0.972028 | + | 0.234865i | \(0.0754649\pi\) | ||||
−0.972028 | + | 0.234865i | \(0.924535\pi\) | |||||||
\(282\) | 1.78553e6 | + | 319062.i | 1.33704 | + | 0.238920i | ||||
\(283\) | − | 325081.i | − | 0.241282i | −0.992696 | − | 0.120641i | \(-0.961505\pi\) | ||
0.992696 | − | 0.120641i | \(-0.0384950\pi\) | |||||||
\(284\) | 1.15161e6i | 0.847244i | ||||||||
\(285\) | 182157. | − | 1.01938e6i | 0.132841 | − | 0.743406i | ||||
\(286\) | 269828.i | 0.195061i | ||||||||
\(287\) | − | 938742.i | − | 0.672731i | ||||||
\(288\) | 417840. | + | 154256.i | 0.296844 | + | 0.109587i | ||||
\(289\) | 145519. | 0.102488 | ||||||||
\(290\) | −189307. | −0.132182 | ||||||||
\(291\) | 68625.2 | − | 384040.i | 0.0475063 | − | 0.265854i | ||||
\(292\) | − | 1.44050e6i | − | 0.988681i | ||||||
\(293\) | 2.07939e6i | 1.41503i | 0.706697 | + | 0.707517i | \(0.250185\pi\) | ||||
−0.706697 | + | 0.707517i | \(0.749815\pi\) | |||||||
\(294\) | 2.03386e6 | + | 363437.i | 1.37231 | + | 0.245223i | ||||
\(295\) | −864263. | + | 952405.i | −0.578217 | + | 0.637186i | ||||
\(296\) | − | 439211.i | − | 0.291369i | ||||||
\(297\) | −107897. | − | 63288.1i | −0.0709769 | − | 0.0416323i | ||||
\(298\) | −711707. | −0.464259 | ||||||||
\(299\) | 397074.i | 0.256858i | ||||||||
\(300\) | 758010. | + | 135451.i | 0.486264 | + | 0.0868919i | ||||
\(301\) | 617037.i | 0.392550i | ||||||||
\(302\) | − | 3.82057e6i | − | 2.41052i | ||||||
\(303\) | −673527. | − | 120354.i | −0.421452 | − | 0.0753105i | ||||
\(304\) | −1.01348e6 | −0.628970 | ||||||||
\(305\) | −2.42614e6 | −1.49336 | ||||||||
\(306\) | 915559. | − | 2.48002e6i | 0.558963 | − | 1.51409i | ||||
\(307\) | −394536. | −0.238913 | −0.119457 | − | 0.992839i | \(-0.538115\pi\) | ||||
−0.119457 | + | 0.992839i | \(0.538115\pi\) | |||||||
\(308\) | −111095. | −0.0667297 | ||||||||
\(309\) | 36602.9 | − | 204837.i | 0.0218082 | − | 0.122043i | ||||
\(310\) | −2.35706e6 | −1.39305 | ||||||||
\(311\) | 1.25601e6i | 0.736362i | 0.929754 | + | 0.368181i | \(0.120019\pi\) | ||||
−0.929754 | + | 0.368181i | \(0.879981\pi\) | |||||||
\(312\) | 646989. | − | 3.62068e6i | 0.376279 | − | 2.10573i | ||||
\(313\) | − | 2.31075e6i | − | 1.33319i | −0.745421 | − | 0.666594i | \(-0.767752\pi\) | ||
0.745421 | − | 0.666594i | \(-0.232248\pi\) | |||||||
\(314\) | 3.07093e6i | 1.75771i | ||||||||
\(315\) | −223707. | + | 605965.i | −0.127029 | + | 0.344089i | ||||
\(316\) | −3.77001e6 | −2.12386 | ||||||||
\(317\) | − | 1.10004e6i | − | 0.614839i | −0.951574 | − | 0.307419i | \(-0.900535\pi\) | ||
0.951574 | − | 0.307419i | \(-0.0994654\pi\) | |||||||
\(318\) | −263840. | + | 1.47650e6i | −0.146310 | + | 0.818778i | ||||
\(319\) | 13486.0i | 0.00742002i | ||||||||
\(320\) | − | 1.97915e6i | − | 1.08045i | ||||||
\(321\) | −555868. | + | 3.11074e6i | −0.301099 | + | 1.68501i | ||||
\(322\) | −249425. | −0.134060 | ||||||||
\(323\) | − | 1.55906e6i | − | 0.831487i | ||||||
\(324\) | 2.73235e6 | + | 2.33576e6i | 1.44602 | + | 1.23614i | ||||
\(325\) | 687989.i | 0.361304i | ||||||||
\(326\) | 429365. | 0.223760 | ||||||||
\(327\) | 69398.2 | − | 388366.i | 0.0358904 | − | 0.200850i | ||||
\(328\) | 4.72699e6i | 2.42605i | ||||||||
\(329\) | −667242. | −0.339855 | ||||||||
\(330\) | −41974.4 | + | 234897.i | −0.0212178 | + | 0.118739i | ||||
\(331\) | 1.71679e6 | 0.861288 | 0.430644 | − | 0.902522i | \(-0.358287\pi\) | ||||
0.430644 | + | 0.902522i | \(0.358287\pi\) | |||||||
\(332\) | −1.92165e6 | −0.956818 | ||||||||
\(333\) | −132826. | + | 359792.i | −0.0656405 | + | 0.177804i | ||||
\(334\) | 2.09893e6i | 1.02951i | ||||||||
\(335\) | −1.63848e6 | −0.797680 | ||||||||
\(336\) | 622325. | + | 111205.i | 0.300725 | + | 0.0537373i | ||||
\(337\) | 2.23142e6i | 1.07030i | 0.844757 | + | 0.535151i | \(0.179745\pi\) | ||||
−0.844757 | + | 0.535151i | \(0.820255\pi\) | |||||||
\(338\) | 3.34977e6 | 1.59486 | ||||||||
\(339\) | −2.43819e6 | − | 435688.i | −1.15231 | − | 0.205909i | ||||
\(340\) | −3.30542e6 | −1.55071 | ||||||||
\(341\) | 167914.i | 0.0781988i | ||||||||
\(342\) | 3.03412e6 | + | 1.12012e6i | 1.40271 | + | 0.517843i | ||||
\(343\) | −1.68887e6 | −0.775106 | ||||||||
\(344\) | − | 3.10706e6i | − | 1.41564i | ||||||
\(345\) | −61768.9 | + | 345671.i | −0.0279397 | + | 0.156356i | ||||
\(346\) | −3.09059e6 | −1.38788 | ||||||||
\(347\) | 4.17683e6 | 1.86219 | 0.931093 | − | 0.364781i | \(-0.118856\pi\) | ||||
0.931093 | + | 0.364781i | \(0.118856\pi\) | |||||||
\(348\) | 68171.6 | − | 381502.i | 0.0301756 | − | 0.168868i | ||||
\(349\) | 3.68822e6i | 1.62089i | 0.585816 | + | 0.810444i | \(0.300774\pi\) | ||||
−0.585816 | + | 0.810444i | \(0.699226\pi\) | |||||||
\(350\) | −432165. | −0.188573 | ||||||||
\(351\) | −1.62496e6 | + | 2.77032e6i | −0.704004 | + | 1.20022i | ||||
\(352\) | −60527.9 | −0.0260375 | ||||||||
\(353\) | 4.38448e6 | 1.87276 | 0.936378 | − | 0.350993i | \(-0.114156\pi\) | ||||
0.936378 | + | 0.350993i | \(0.114156\pi\) | |||||||
\(354\) | −2.45343e6 | − | 3.18052e6i | −1.04055 | − | 1.34893i | ||||
\(355\) | −909916. | −0.383204 | ||||||||
\(356\) | 3.18734e6 | 1.33292 | ||||||||
\(357\) | −171069. | + | 957338.i | −0.0710398 | + | 0.397553i | ||||
\(358\) | −2.98068e6 | −1.22916 | ||||||||
\(359\) | 4.69179e6i | 1.92133i | 0.277704 | + | 0.960667i | \(0.410427\pi\) | ||||
−0.277704 | + | 0.960667i | \(0.589573\pi\) | |||||||
\(360\) | 1.12646e6 | − | 3.05131e6i | 0.458101 | − | 1.24088i | ||||
\(361\) | −568714. | −0.229681 | ||||||||
\(362\) | 5.00421e6 | 2.00708 | ||||||||
\(363\) | −2.45466e6 | − | 438630.i | −0.977741 | − | 0.174715i | ||||
\(364\) | 2.85244e6i | 1.12840i | ||||||||
\(365\) | 1.13818e6 | 0.447176 | ||||||||
\(366\) | 1.33294e6 | − | 7.45938e6i | 0.520125 | − | 2.91072i | ||||
\(367\) | − | 2.42409e6i | − | 0.939471i | −0.882807 | − | 0.469736i | \(-0.844349\pi\) | ||
0.882807 | − | 0.469736i | \(-0.155651\pi\) | |||||||
\(368\) | 343667. | 0.132287 | ||||||||
\(369\) | 1.42953e6 | − | 3.87225e6i | 0.546548 | − | 1.48046i | ||||
\(370\) | 731613. | 0.277829 | ||||||||
\(371\) | − | 551760.i | − | 0.208121i | ||||||
\(372\) | 848805. | − | 4.75008e6i | 0.318017 | − | 1.77969i | ||||
\(373\) | −182981. | −0.0680978 | −0.0340489 | − | 0.999420i | \(-0.510840\pi\) | ||||
−0.0340489 | + | 0.999420i | \(0.510840\pi\) | |||||||
\(374\) | 359253.i | 0.132807i | ||||||||
\(375\) | −519193. | + | 2.90551e6i | −0.190656 | + | 1.06695i | ||||
\(376\) | 3.35987e6 | 1.22561 | ||||||||
\(377\) | 346261. | 0.125473 | ||||||||
\(378\) | −1.74019e6 | − | 1.02073e6i | −0.626423 | − | 0.367435i | ||||
\(379\) | 2.41234e6 | 0.862661 | 0.431330 | − | 0.902194i | \(-0.358044\pi\) | ||||
0.431330 | + | 0.902194i | \(0.358044\pi\) | |||||||
\(380\) | − | 4.04393e6i | − | 1.43663i | ||||||
\(381\) | 343894. | + | 61451.4i | 0.121370 | + | 0.0216880i | ||||
\(382\) | 3.67816e6 | 1.28965 | ||||||||
\(383\) | − | 2.53581e6i | − | 0.883324i | −0.897181 | − | 0.441662i | \(-0.854389\pi\) | ||
0.897181 | − | 0.441662i | \(-0.145611\pi\) | |||||||
\(384\) | 5.18501e6 | + | 926524.i | 1.79441 | + | 0.320648i | ||||
\(385\) | − | 87779.5i | − | 0.0301815i | ||||||
\(386\) | −3.69224e6 | −1.26131 | ||||||||
\(387\) | −939634. | + | 2.54523e6i | −0.318920 | + | 0.863874i | ||||
\(388\) | − | 1.52350e6i | − | 0.513764i | ||||||
\(389\) | − | 4.74262e6i | − | 1.58908i | −0.607214 | − | 0.794538i | \(-0.707713\pi\) | ||
0.607214 | − | 0.794538i | \(-0.292287\pi\) | |||||||
\(390\) | 6.03112e6 | + | 1.07772e6i | 2.00787 | + | 0.358793i | ||||
\(391\) | 528672.i | 0.174882i | ||||||||
\(392\) | 3.82716e6 | 1.25794 | ||||||||
\(393\) | 332138. | + | 59350.7i | 0.108477 | + | 0.0193840i | ||||
\(394\) | − | 5.16970e6i | − | 1.67774i | ||||||
\(395\) | − | 2.97879e6i | − | 0.960610i | ||||||
\(396\) | −458261. | − | 169178.i | −0.146850 | − | 0.0542133i | ||||
\(397\) | − | 5.12390e6i | − | 1.63164i | −0.578306 | − | 0.815820i | \(-0.696286\pi\) | ||
0.578306 | − | 0.815820i | \(-0.303714\pi\) | |||||||
\(398\) | −6.68825e6 | −2.11643 | ||||||||
\(399\) | −1.17123e6 | − | 209290.i | −0.368307 | − | 0.0658138i | ||||
\(400\) | 595453. | 0.186079 | ||||||||
\(401\) | 4.04090e6 | 1.25492 | 0.627461 | − | 0.778648i | \(-0.284094\pi\) | ||||
0.627461 | + | 0.778648i | \(0.284094\pi\) | |||||||
\(402\) | 900193. | − | 5.03765e6i | 0.277824 | − | 1.55476i | ||||
\(403\) | 4.31129e6 | 1.32234 | ||||||||
\(404\) | −2.67190e6 | −0.814456 | ||||||||
\(405\) | −1.84555e6 | + | 2.15890e6i | −0.559098 | + | 0.654026i | ||||
\(406\) | 217506.i | 0.0654871i | ||||||||
\(407\) | − | 52119.1i | − | 0.0155959i | ||||||
\(408\) | 861412. | − | 4.82063e6i | 0.256189 | − | 1.43368i | ||||
\(409\) | 3.45461e6i | 1.02115i | 0.859832 | + | 0.510577i | \(0.170568\pi\) | ||||
−0.859832 | + | 0.510577i | \(0.829432\pi\) | |||||||
\(410\) | −7.87397e6 | −2.31331 | ||||||||
\(411\) | 218087. | − | 1.22046e6i | 0.0636834 | − | 0.356384i | ||||
\(412\) | − | 812596.i | − | 0.235848i | ||||||
\(413\) | 1.09427e6 | + | 993001.i | 0.315682 | + | 0.286467i | ||||
\(414\) | −1.02886e6 | − | 379828.i | −0.295023 | − | 0.108915i | ||||
\(415\) | − | 1.51835e6i | − | 0.432764i | ||||||
\(416\) | 1.55409e6i | 0.440294i | ||||||||
\(417\) | 1.56898e6 | + | 280366.i | 0.441853 | + | 0.0789560i | ||||
\(418\) | −439519. | −0.123037 | ||||||||
\(419\) | 905432. | 0.251954 | 0.125977 | − | 0.992033i | \(-0.459793\pi\) | ||||
0.125977 | + | 0.992033i | \(0.459793\pi\) | |||||||
\(420\) | −443726. | + | 2.48318e6i | −0.122742 | + | 0.686885i | ||||
\(421\) | − | 6.97621e6i | − | 1.91829i | −0.282914 | − | 0.959145i | \(-0.591301\pi\) | ||
0.282914 | − | 0.959145i | \(-0.408699\pi\) | |||||||
\(422\) | 3.16403e6i | 0.864888i | ||||||||
\(423\) | −2.75233e6 | − | 1.01609e6i | −0.747910 | − | 0.276109i | ||||
\(424\) | 2.77836e6i | 0.750541i | ||||||||
\(425\) | 916000.i | 0.245993i | ||||||||
\(426\) | 499915. | − | 2.79762e6i | 0.133467 | − | 0.746904i | ||||
\(427\) | 2.78753e6i | 0.739860i | ||||||||
\(428\) | 1.23404e7i | 3.25628i | ||||||||
\(429\) | 76775.1 | − | 429648.i | 0.0201408 | − | 0.112712i | ||||
\(430\) | 5.17557e6 | 1.34985 | ||||||||
\(431\) | −5.22450e6 | −1.35473 | −0.677363 | − | 0.735649i | \(-0.736877\pi\) | ||||
−0.677363 | + | 0.735649i | \(0.736877\pi\) | |||||||
\(432\) | 2.39770e6 | + | 1.40640e6i | 0.618139 | + | 0.362576i | ||||
\(433\) | 530639. | 0.136013 | 0.0680064 | − | 0.997685i | \(-0.478336\pi\) | ||||
0.0680064 | + | 0.997685i | \(0.478336\pi\) | |||||||
\(434\) | 2.70816e6i | 0.690161i | ||||||||
\(435\) | 301435. | + | 53864.3i | 0.0763784 | + | 0.0136483i | ||||
\(436\) | − | 1.54066e6i | − | 0.388142i | ||||||
\(437\) | −646789. | −0.162017 | ||||||||
\(438\) | −625325. | + | 3.49944e6i | −0.155747 | + | 0.871591i | ||||
\(439\) | −2.98179e6 | −0.738441 | −0.369221 | − | 0.929342i | \(-0.620375\pi\) | ||||
−0.369221 | + | 0.929342i | \(0.620375\pi\) | |||||||
\(440\) | 442010.i | 0.108843i | ||||||||
\(441\) | −3.13512e6 | − | 1.15741e6i | −0.767641 | − | 0.283393i | ||||
\(442\) | 9.22405e6 | 2.24577 | ||||||||
\(443\) | 6.64975e6 | 1.60989 | 0.804944 | − | 0.593350i | \(-0.202195\pi\) | ||||
0.804944 | + | 0.593350i | \(0.202195\pi\) | |||||||
\(444\) | −263462. | + | 1.47439e6i | −0.0634251 | + | 0.354939i | ||||
\(445\) | 2.51840e6i | 0.602873i | ||||||||
\(446\) | −1.10999e7 | −2.64231 | ||||||||
\(447\) | 1.13326e6 | + | 202505.i | 0.268262 | + | 0.0479365i | ||||
\(448\) | −2.27396e6 | −0.535288 | ||||||||
\(449\) | − | 8.28821e6i | − | 1.94019i | −0.242722 | − | 0.970096i | \(-0.578040\pi\) | ||
0.242722 | − | 0.970096i | \(-0.421960\pi\) | |||||||
\(450\) | −1.78265e6 | − | 658108.i | −0.414987 | − | 0.153203i | ||||
\(451\) | 560930.i | 0.129858i | ||||||||
\(452\) | −9.67240e6 | −2.22684 | ||||||||
\(453\) | −1.08708e6 | + | 6.08352e6i | −0.248895 | + | 1.39287i | ||||
\(454\) | −1.03182e7 | −2.34943 | ||||||||
\(455\) | −2.25379e6 | −0.510371 | ||||||||
\(456\) | 5.89767e6 | + | 1.05387e6i | 1.32822 | + | 0.237343i | ||||
\(457\) | − | 3.74700e6i | − | 0.839253i | −0.907697 | − | 0.419626i | \(-0.862161\pi\) | ||
0.907697 | − | 0.419626i | \(-0.137839\pi\) | |||||||
\(458\) | 1.28050e7i | 2.85245i | ||||||||
\(459\) | −2.16350e6 | + | 3.68845e6i | −0.479320 | + | 0.817169i | ||||
\(460\) | 1.37129e6i | 0.302158i | ||||||||
\(461\) | 3.49127e6i | 0.765122i | 0.923930 | + | 0.382561i | \(0.124958\pi\) | ||||
−0.923930 | + | 0.382561i | \(0.875042\pi\) | |||||||
\(462\) | 269886. | + | 48226.8i | 0.0588269 | + | 0.0105120i | ||||
\(463\) | 2.88066e6i | 0.624511i | 0.949998 | + | 0.312255i | \(0.101084\pi\) | ||||
−0.949998 | + | 0.312255i | \(0.898916\pi\) | |||||||
\(464\) | − | 299688.i | − | 0.0646211i | ||||||
\(465\) | 3.75316e6 | + | 670664.i | 0.804943 | + | 0.143838i | ||||
\(466\) | 1.53067e7 | 3.26526 | ||||||||
\(467\) | −1.99736e6 | −0.423803 | −0.211901 | − | 0.977291i | \(-0.567966\pi\) | ||||
−0.211901 | + | 0.977291i | \(0.567966\pi\) | |||||||
\(468\) | −4.34375e6 | + | 1.17661e7i | −0.916749 | + | 2.48324i | ||||
\(469\) | 1.88254e6i | 0.395196i | ||||||||
\(470\) | 5.59668e6i | 1.16865i | ||||||||
\(471\) | 873785. | − | 4.88987e6i | 0.181490 | − | 1.01565i | ||||
\(472\) | −5.51016e6 | − | 5.00021e6i | −1.13844 | − | 1.03308i | ||||
\(473\) | − | 368700.i | − | 0.0757740i | ||||||
\(474\) | 9.15857e6 | + | 1.63657e6i | 1.87233 | + | 0.334572i | ||||
\(475\) | −1.12066e6 | −0.227897 | ||||||||
\(476\) | 3.79779e6i | 0.768270i | ||||||||
\(477\) | 840230. | − | 2.27597e6i | 0.169084 | − | 0.458006i | ||||
\(478\) | 7.90456e6i | 1.58237i | ||||||||
\(479\) | − | 2.25462e6i | − | 0.448988i | −0.974475 | − | 0.224494i | \(-0.927927\pi\) | ||
0.974475 | − | 0.224494i | \(-0.0720729\pi\) | |||||||
\(480\) | −241754. | + | 1.35290e6i | −0.0478929 | + | 0.268018i | ||||
\(481\) | −1.33819e6 | −0.263727 | ||||||||
\(482\) | −1.52378e7 | −2.98747 | ||||||||
\(483\) | 397161. | + | 70969.8i | 0.0774637 | + | 0.0138422i | ||||
\(484\) | −9.73771e6 | −1.88948 | ||||||||
\(485\) | 1.20376e6 | 0.232373 | ||||||||
\(486\) | −5.62379e6 | − | 6.86043e6i | −1.08004 | − | 1.31753i | ||||
\(487\) | 7.50521e6 | 1.43397 | 0.716985 | − | 0.697088i | \(-0.245522\pi\) | ||||
0.716985 | + | 0.697088i | \(0.245522\pi\) | |||||||
\(488\) | − | 1.40365e7i | − | 2.66814i | ||||||
\(489\) | −683681. | − | 122169.i | −0.129295 | − | 0.0231041i | ||||
\(490\) | 6.37507e6i | 1.19948i | ||||||||
\(491\) | − | 5.42009e6i | − | 1.01462i | −0.861764 | − | 0.507309i | \(-0.830640\pi\) | ||
0.861764 | − | 0.507309i | \(-0.169360\pi\) | |||||||
\(492\) | 2.83551e6 | − | 1.58680e7i | 0.528102 | − | 2.95536i | ||||
\(493\) | 461017. | 0.0854279 | ||||||||
\(494\) | 1.12849e7i | 2.08056i | ||||||||
\(495\) | 133672. | − | 362084.i | 0.0245204 | − | 0.0664197i | ||||
\(496\) | − | 3.73141e6i | − | 0.681034i | ||||||
\(497\) | 1.04545e6i | 0.189852i | ||||||||
\(498\) | 4.66831e6 | + | 834193.i | 0.843502 | + | 0.150728i | ||||
\(499\) | −7.03295e6 | −1.26441 | −0.632203 | − | 0.774803i | \(-0.717849\pi\) | ||||
−0.632203 | + | 0.774803i | \(0.717849\pi\) | |||||||
\(500\) | 1.15262e7i | 2.06188i | ||||||||
\(501\) | 597217. | − | 3.34214e6i | 0.106301 | − | 0.594882i | ||||
\(502\) | − | 1.23675e7i | − | 2.19039i | ||||||
\(503\) | −3.22241e6 | −0.567885 | −0.283942 | − | 0.958841i | \(-0.591642\pi\) | ||||
−0.283942 | + | 0.958841i | \(0.591642\pi\) | |||||||
\(504\) | −3.50583e6 | − | 1.29426e6i | −0.614772 | − | 0.226958i | ||||
\(505\) | − | 2.11114e6i | − | 0.368374i | ||||||
\(506\) | 149040. | 0.0258777 | ||||||||
\(507\) | −5.33386e6 | − | 953123.i | −0.921556 | − | 0.164675i | ||||
\(508\) | 1.36424e6 | 0.234548 | ||||||||
\(509\) | 7.78339e6 | 1.33160 | 0.665800 | − | 0.746130i | \(-0.268090\pi\) | ||||
0.665800 | + | 0.746130i | \(0.268090\pi\) | |||||||
\(510\) | 8.02994e6 | + | 1.43489e6i | 1.36706 | + | 0.244283i | ||||
\(511\) | − | 1.30772e6i | − | 0.221545i | ||||||
\(512\) | 7.87980e6 | 1.32843 | ||||||||
\(513\) | −4.51253e6 | − | 2.64688e6i | −0.757054 | − | 0.444059i | ||||
\(514\) | − | 3.56144e6i | − | 0.594590i | ||||||
\(515\) | 642054. | 0.106673 | ||||||||
\(516\) | −1.86378e6 | + | 1.04301e7i | −0.308156 | + | 1.72450i | ||||
\(517\) | 398699. | 0.0656023 | ||||||||
\(518\) | − | 840593.i | − | 0.137645i | ||||||
\(519\) | 4.92116e6 | + | 879377.i | 0.801954 | + | 0.143303i | ||||
\(520\) | 1.13489e7 | 1.84054 | ||||||||
\(521\) | 3.75797e6i | 0.606539i | 0.952905 | + | 0.303270i | \(0.0980783\pi\) | ||||
−0.952905 | + | 0.303270i | \(0.901922\pi\) | |||||||
\(522\) | −331222. | + | 897197.i | −0.0532038 | + | 0.144116i | ||||
\(523\) | −1.66971e6 | −0.266923 | −0.133462 | − | 0.991054i | \(-0.542609\pi\) | ||||
−0.133462 | + | 0.991054i | \(0.542609\pi\) | |||||||
\(524\) | 1.31760e6 | 0.209631 | ||||||||
\(525\) | 688139. | + | 122965.i | 0.108963 | + | 0.0194709i | ||||
\(526\) | 3.93338e6i | 0.619871i | ||||||||
\(527\) | 5.74012e6 | 0.900316 | ||||||||
\(528\) | −371860. | − | 66448.7i | −0.0580490 | − | 0.0103729i | ||||
\(529\) | −6.21702e6 | −0.965924 | ||||||||
\(530\) | −4.62804e6 | −0.715661 | ||||||||
\(531\) | 3.00164e6 | + | 5.76244e6i | 0.461979 | + | 0.886891i | ||||
\(532\) | −4.64631e6 | −0.711753 | ||||||||
\(533\) | 1.44022e7 | 2.19590 | ||||||||
\(534\) | −7.74307e6 | − | 1.38363e6i | −1.17506 | − | 0.209975i | ||||
\(535\) | −9.75051e6 | −1.47280 | ||||||||
\(536\) | − | 9.47945e6i | − | 1.42518i | ||||||
\(537\) | 4.74615e6 | + | 848104.i | 0.710241 | + | 0.126915i | ||||
\(538\) | 1.02145e7 | 1.52146 | ||||||||
\(539\) | 454151. | 0.0673330 | ||||||||
\(540\) | −5.61176e6 | + | 9.56722e6i | −0.828162 | + | 1.41189i | ||||
\(541\) | 9.67521e6i | 1.42124i | 0.703576 | + | 0.710620i | \(0.251585\pi\) | ||||
−0.703576 | + | 0.710620i | \(0.748415\pi\) | |||||||
\(542\) | −4.59931e6 | −0.672504 | ||||||||
\(543\) | −7.96824e6 | − | 1.42387e6i | −1.15975 | − | 0.207238i | ||||
\(544\) | 2.06914e6i | 0.299774i | ||||||||
\(545\) | 1.21732e6 | 0.175555 | ||||||||
\(546\) | 1.23825e6 | − | 6.92950e6i | 0.177757 | − | 0.994765i | ||||
\(547\) | 5.44757e6 | 0.778456 | 0.389228 | − | 0.921141i | \(-0.372742\pi\) | ||||
0.389228 | + | 0.921141i | \(0.372742\pi\) | |||||||
\(548\) | − | 4.84161e6i | − | 0.688713i | ||||||
\(549\) | −4.24490e6 | + | 1.14984e7i | −0.601085 | + | 1.62819i | ||||
\(550\) | 258233. | 0.0364003 | ||||||||
\(551\) | 564019.i | 0.0791435i | ||||||||
\(552\) | −1.99988e6 | − | 357365.i | −0.279355 | − | 0.0499188i | ||||
\(553\) | −3.42250e6 | −0.475917 | ||||||||
\(554\) | −8.90775e6 | −1.23309 | ||||||||
\(555\) | −1.16495e6 | − | 208169.i | −0.160537 | − | 0.0286869i | ||||
\(556\) | 6.22421e6 | 0.853881 | ||||||||
\(557\) | 1.58568e6i | 0.216560i | 0.994120 | + | 0.108280i | \(0.0345343\pi\) | ||||
−0.994120 | + | 0.108280i | \(0.965466\pi\) | |||||||
\(558\) | −4.12404e6 | + | 1.11710e7i | −0.560709 | + | 1.51882i | ||||
\(559\) | −9.46661e6 | −1.28134 | ||||||||
\(560\) | 1.95065e6i | 0.262851i | ||||||||
\(561\) | 102220. | − | 572041.i | 0.0137128 | − | 0.0767397i | ||||
\(562\) | − | 5.99192e6i | − | 0.800249i | ||||||
\(563\) | −9.24513e6 | −1.22925 | −0.614627 | − | 0.788818i | \(-0.710694\pi\) | ||||
−0.614627 | + | 0.788818i | \(0.710694\pi\) | |||||||
\(564\) | −1.12787e7 | − | 2.01543e6i | −1.49301 | − | 0.266790i | ||||
\(565\) | − | 7.64242e6i | − | 1.00719i | ||||||
\(566\) | 3.13287e6i | 0.411057i | ||||||||
\(567\) | 2.48049e6 | + | 2.12046e6i | 0.324025 | + | 0.276995i | ||||
\(568\) | − | 5.26434e6i | − | 0.684657i | ||||||
\(569\) | 5.61709e6 | 0.727328 | 0.363664 | − | 0.931530i | \(-0.381526\pi\) | ||||
0.363664 | + | 0.931530i | \(0.381526\pi\) | |||||||
\(570\) | −1.75548e6 | + | 9.82401e6i | −0.226313 | + | 1.26649i | ||||
\(571\) | − | 4.82900e6i | − | 0.619822i | −0.950766 | − | 0.309911i | \(-0.899701\pi\) | ||
0.950766 | − | 0.309911i | \(-0.100299\pi\) | |||||||
\(572\) | − | 1.70443e6i | − | 0.217816i | ||||||
\(573\) | −5.85676e6 | − | 1.04656e6i | −0.745196 | − | 0.133161i | ||||
\(574\) | 9.04685e6i | 1.14609i | ||||||||
\(575\) | 380012. | 0.0479322 | ||||||||
\(576\) | −9.37992e6 | − | 3.46282e6i | −1.17799 | − | 0.434884i | ||||
\(577\) | 3.89350e6 | 0.486856 | 0.243428 | − | 0.969919i | \(-0.421728\pi\) | ||||
0.243428 | + | 0.969919i | \(0.421728\pi\) | |||||||
\(578\) | −1.40239e6 | −0.174602 | ||||||||
\(579\) | 5.87917e6 | + | 1.05057e6i | 0.728819 | + | 0.130235i | ||||
\(580\) | 1.19580e6 | 0.147601 | ||||||||
\(581\) | −1.74452e6 | −0.214405 | ||||||||
\(582\) | −661355. | + | 3.70107e6i | −0.0809333 | + | 0.452918i | ||||
\(583\) | 329695.i | 0.0401736i | ||||||||
\(584\) | 6.58496e6i | 0.798952i | ||||||||
\(585\) | −9.29675e6 | − | 3.43212e6i | −1.12316 | − | 0.414641i | ||||
\(586\) | − | 2.00395e7i | − | 2.41070i | ||||||
\(587\) | −4.16847e6 | −0.499323 | −0.249661 | − | 0.968333i | \(-0.580319\pi\) | ||||
−0.249661 | + | 0.968333i | \(0.580319\pi\) | |||||||
\(588\) | −1.28474e7 | − | 2.29574e6i | −1.53240 | − | 0.273828i | ||||
\(589\) | 7.02260e6i | 0.834084i | ||||||||
\(590\) | 8.32907e6 | − | 9.17852e6i | 0.985069 | − | 1.08553i | ||||
\(591\) | −1.47096e6 | + | 8.23175e6i | −0.173233 | + | 0.969446i | ||||
\(592\) | 1.15820e6i | 0.135825i | ||||||||
\(593\) | − | 4.87840e6i | − | 0.569692i | −0.958573 | − | 0.284846i | \(-0.908057\pi\) | ||
0.958573 | − | 0.284846i | \(-0.0919425\pi\) | |||||||
\(594\) | 1.03982e6 | + | 609920.i | 0.120919 | + | 0.0709262i | ||||
\(595\) | −3.00074e6 | −0.347485 | ||||||||
\(596\) | 4.49566e6 | 0.518416 | ||||||||
\(597\) | 1.06497e7 | + | 1.90303e6i | 1.22293 | + | 0.218530i | ||||
\(598\) | − | 3.82669e6i | − | 0.437593i | ||||||
\(599\) | 1.20293e7i | 1.36985i | 0.728613 | + | 0.684925i | \(0.240165\pi\) | ||||
−0.728613 | + | 0.684925i | \(0.759835\pi\) | |||||||
\(600\) | −3.46509e6 | − | 619187.i | −0.392949 | − | 0.0702172i | ||||
\(601\) | − | 1.12790e6i | − | 0.127375i | −0.997970 | − | 0.0636874i | \(-0.979714\pi\) | ||
0.997970 | − | 0.0636874i | \(-0.0202861\pi\) | |||||||
\(602\) | − | 5.94651e6i | − | 0.668761i | ||||||
\(603\) | −2.86677e6 | + | 7.76536e6i | −0.321070 | + | 0.869697i | ||||
\(604\) | 2.41336e7i | 2.69171i | ||||||||
\(605\) | − | 7.69403e6i | − | 0.854605i | ||||||
\(606\) | 6.49091e6 | + | 1.15988e6i | 0.718000 | + | 0.128301i | ||||
\(607\) | 1.48593e7 | 1.63691 | 0.818457 | − | 0.574568i | \(-0.194830\pi\) | ||||
0.818457 | + | 0.574568i | \(0.194830\pi\) | |||||||
\(608\) | −2.53144e6 | −0.277721 | ||||||||
\(609\) | 61887.8 | − | 346336.i | 0.00676179 | − | 0.0378403i | ||||
\(610\) | 2.33812e7 | 2.54414 | ||||||||
\(611\) | − | 1.02369e7i | − | 1.10934i | ||||||
\(612\) | −5.78335e6 | + | 1.56656e7i | −0.624167 | + | 1.69071i | ||||
\(613\) | − | 8.32649e6i | − | 0.894975i | −0.894290 | − | 0.447488i | \(-0.852319\pi\) | ||
0.894290 | − | 0.447488i | \(-0.147681\pi\) | |||||||
\(614\) | 3.80222e6 | 0.407021 | ||||||||
\(615\) | 1.25378e7 | + | 2.24041e6i | 1.33670 | + | 0.238858i | ||||
\(616\) | 507850. | 0.0539242 | ||||||||
\(617\) | − | 1.68119e7i | − | 1.77789i | −0.458016 | − | 0.888944i | \(-0.651440\pi\) | ||
0.458016 | − | 0.888944i | \(-0.348560\pi\) | |||||||
\(618\) | −352750. | + | 1.97406e6i | −0.0371531 | + | 0.207916i | ||||
\(619\) | 1.19071e7 | 1.24905 | 0.624525 | − | 0.781005i | \(-0.285293\pi\) | ||||
0.624525 | + | 0.781005i | \(0.285293\pi\) | |||||||
\(620\) | 1.48889e7 | 1.55555 | ||||||||
\(621\) | 1.53019e6 | + | 897549.i | 0.159227 | + | 0.0933962i | ||||
\(622\) | − | 1.21044e7i | − | 1.25449i | ||||||
\(623\) | 2.89354e6 | 0.298682 | ||||||||
\(624\) | −1.70611e6 | + | 9.54774e6i | −0.175407 | + | 0.981610i | ||||
\(625\) | −6.57147e6 | −0.672918 | ||||||||
\(626\) | 2.22691e7i | 2.27126i | ||||||||
\(627\) | 699849. | + | 125058.i | 0.0710944 | + | 0.0127041i | ||||
\(628\) | − | 1.93983e7i | − | 1.96275i | ||||||
\(629\) | −1.78169e6 | −0.179558 | ||||||||
\(630\) | 2.15591e6 | − | 5.83981e6i | 0.216411 | − | 0.586202i | ||||
\(631\) | −3.12556e6 | −0.312503 | −0.156251 | − | 0.987717i | \(-0.549941\pi\) | ||||
−0.156251 | + | 0.987717i | \(0.549941\pi\) | |||||||
\(632\) | 1.72338e7 | 1.71629 | ||||||||
\(633\) | 900275. | − | 5.03811e6i | 0.0893030 | − | 0.499757i | ||||
\(634\) | 1.06013e7i | 1.04746i | ||||||||
\(635\) | 1.07792e6i | 0.106085i | ||||||||
\(636\) | 1.66661e6 | − | 9.32668e6i | 0.163377 | − | 0.914291i | ||||
\(637\) | − | 1.16606e7i | − | 1.13860i | ||||||
\(638\) | − | 129967.i | − | 0.0126410i | ||||||
\(639\) | −1.59204e6 | + | 4.31243e6i | −0.154241 | + | 0.417801i | ||||
\(640\) | 1.62522e7i | 1.56842i | ||||||||
\(641\) | − | 9.31161e6i | − | 0.895116i | −0.894255 | − | 0.447558i | \(-0.852294\pi\) | ||
0.894255 | − | 0.447558i | \(-0.147706\pi\) | |||||||
\(642\) | 5.35701e6 | − | 2.99789e7i | 0.512962 | − | 2.87063i | ||||
\(643\) | 1.32930e7 | 1.26793 | 0.633965 | − | 0.773362i | \(-0.281426\pi\) | ||||
0.633965 | + | 0.773362i | \(0.281426\pi\) | |||||||
\(644\) | 1.57555e6 | 0.149699 | ||||||||
\(645\) | −8.24109e6 | − | 1.47262e6i | −0.779984 | − | 0.139378i | ||||
\(646\) | 1.50249e7i | 1.41655i | ||||||||
\(647\) | 9.08894e6i | 0.853597i | 0.904347 | + | 0.426798i | \(0.140359\pi\) | ||||
−0.904347 | + | 0.426798i | \(0.859641\pi\) | |||||||
\(648\) | −1.24904e7 | − | 1.06775e7i | −1.16852 | − | 0.998920i | ||||
\(649\) | −653865. | − | 593351.i | −0.0609363 | − | 0.0552968i | ||||
\(650\) | − | 6.63029e6i | − | 0.615530i | ||||||
\(651\) | 770564. | − | 4.31223e6i | 0.0712617 | − | 0.398794i | ||||
\(652\) | −2.71219e6 | −0.249862 | ||||||||
\(653\) | − | 1.83478e7i | − | 1.68384i | −0.539605 | − | 0.841919i | \(-0.681426\pi\) | ||
0.539605 | − | 0.841919i | \(-0.318574\pi\) | |||||||
\(654\) | −668804. | + | 3.74276e6i | −0.0611441 | + | 0.342174i | ||||
\(655\) | 1.04107e6i | 0.0948153i | ||||||||
\(656\) | − | 1.24651e7i | − | 1.13093i | ||||||
\(657\) | 1.99142e6 | − | 5.39425e6i | 0.179990 | − | 0.487548i | ||||
\(658\) | 6.43035e6 | 0.578988 | ||||||||
\(659\) | −5.04508e6 | −0.452537 | −0.226269 | − | 0.974065i | \(-0.572653\pi\) | ||||
−0.226269 | + | 0.974065i | \(0.572653\pi\) | |||||||
\(660\) | 265141. | − | 1.48378e6i | 0.0236929 | − | 0.132590i | ||||
\(661\) | −1.92331e7 | −1.71216 | −0.856081 | − | 0.516842i | \(-0.827108\pi\) | ||||
−0.856081 | + | 0.516842i | \(0.827108\pi\) | |||||||
\(662\) | −1.65451e7 | −1.46732 | ||||||||
\(663\) | −1.46875e7 | − | 2.62456e6i | −1.29767 | − | 0.231885i | ||||
\(664\) | 8.78444e6 | 0.773204 | ||||||||
\(665\) | − | 3.67117e6i | − | 0.321922i | ||||||
\(666\) | 1.28007e6 | − | 3.46739e6i | 0.111827 | − | 0.302912i | ||||
\(667\) | − | 191257.i | − | 0.0166458i | ||||||
\(668\) | − | 1.32584e7i | − | 1.14961i | ||||||
\(669\) | 1.76745e7 | + | 3.15831e6i | 1.52680 | + | 0.272828i | ||||
\(670\) | 1.57903e7 | 1.35895 | ||||||||
\(671\) | − | 1.66564e6i | − | 0.142815i | ||||||
\(672\) | 1.55443e6 | + | 277765.i | 0.132785 | + | 0.0237277i | ||||
\(673\) | − | 3.51575e6i | − | 0.299213i | −0.988746 | − | 0.149607i | \(-0.952199\pi\) | ||
0.988746 | − | 0.149607i | \(-0.0478007\pi\) | |||||||
\(674\) | − | 2.15046e7i | − | 1.82340i | ||||||
\(675\) | 2.65127e6 | + | 1.55513e6i | 0.223973 | + | 0.131374i | ||||
\(676\) | −2.11596e7 | −1.78091 | ||||||||
\(677\) | 4.86746e6i | 0.408160i | 0.978954 | + | 0.204080i | \(0.0654203\pi\) | ||||
−0.978954 | + | 0.204080i | \(0.934580\pi\) | |||||||
\(678\) | 2.34974e7 | + | 4.19881e6i | 1.96311 | + | 0.350794i | ||||
\(679\) | − | 1.38307e6i | − | 0.115125i | ||||||
\(680\) | 1.51101e7 | 1.25313 | ||||||||
\(681\) | 1.64297e7 | + | 2.93587e6i | 1.35757 | + | 0.242587i | ||||
\(682\) | − | 1.61822e6i | − | 0.133222i | ||||||
\(683\) | 1.34481e7 | 1.10308 | 0.551541 | − | 0.834148i | \(-0.314040\pi\) | ||||
0.551541 | + | 0.834148i | \(0.314040\pi\) | |||||||
\(684\) | −1.91657e7 | − | 7.07548e6i | −1.56634 | − | 0.578250i | ||||
\(685\) | 3.82548e6 | 0.311501 | ||||||||
\(686\) | 1.62760e7 | 1.32050 | ||||||||
\(687\) | 3.64347e6 | − | 2.03896e7i | 0.294526 | − | 1.64822i | ||||
\(688\) | 8.19333e6i | 0.659917i | ||||||||
\(689\) | 8.46513e6 | 0.679337 | ||||||||
\(690\) | 595279. | − | 3.33130e6i | 0.0475990 | − | 0.266373i | ||||
\(691\) | 2.19353e7i | 1.74763i | 0.486262 | + | 0.873813i | \(0.338360\pi\) | ||||
−0.486262 | + | 0.873813i | \(0.661640\pi\) | |||||||
\(692\) | 1.95224e7 | 1.54978 | ||||||||
\(693\) | −416020. | − | 153584.i | −0.0329064 | − | 0.0121482i | ||||
\(694\) | −4.02530e7 | −3.17248 | ||||||||
\(695\) | 4.91792e6i | 0.386206i | ||||||||
\(696\) | −311633. | + | 1.74396e6i | −0.0243849 | + | 0.136462i | ||||
\(697\) | 1.91754e7 | 1.49507 | ||||||||
\(698\) | − | 3.55441e7i | − | 2.76140i | ||||||
\(699\) | −2.43730e7 | − | 4.35528e6i | −1.88676 | − | 0.337150i | ||||
\(700\) | 2.72987e6 | 0.210570 | ||||||||
\(701\) | 2.35117e7 | 1.80713 | 0.903565 | − | 0.428452i | \(-0.140941\pi\) | ||||
0.903565 | + | 0.428452i | \(0.140941\pi\) | |||||||
\(702\) | 1.56601e7 | − | 2.66981e7i | 1.19936 | − | 2.04474i | ||||
\(703\) | − | 2.17976e6i | − | 0.166349i | ||||||
\(704\) | 1.35877e6 | 0.103327 | ||||||||
\(705\) | 1.59245e6 | − | 8.91163e6i | 0.120668 | − | 0.675281i | ||||
\(706\) | −4.22541e7 | −3.19049 | ||||||||
\(707\) | −2.42562e6 | −0.182504 | ||||||||
\(708\) | 1.54976e7 | + | 2.00905e7i | 1.16194 | + | 1.50629i | ||||
\(709\) | −1.29200e7 | −0.965263 | −0.482632 | − | 0.875823i | \(-0.660319\pi\) | ||||
−0.482632 | + | 0.875823i | \(0.660319\pi\) | |||||||
\(710\) | 8.76904e6 | 0.652839 | ||||||||
\(711\) | −1.41176e7 | − | 5.21185e6i | −1.04734 | − | 0.386650i | ||||
\(712\) | −1.45703e7 | −1.07713 | ||||||||
\(713\) | − | 2.38135e6i | − | 0.175428i | ||||||
\(714\) | 1.64863e6 | − | 9.22606e6i | 0.121026 | − | 0.677284i | ||||
\(715\) | 1.34672e6 | 0.0985170 | ||||||||
\(716\) | 1.88282e7 | 1.37254 | ||||||||
\(717\) | 2.24912e6 | − | 1.25865e7i | 0.163386 | − | 0.914338i | ||||
\(718\) | − | 4.52158e7i | − | 3.27325i | ||||||
\(719\) | 3.00043e6 | 0.216452 | 0.108226 | − | 0.994126i | \(-0.465483\pi\) | ||||
0.108226 | + | 0.994126i | \(0.465483\pi\) | |||||||
\(720\) | −2.97049e6 | + | 8.04632e6i | −0.213549 | + | 0.578450i | ||||
\(721\) | − | 737693.i | − | 0.0528491i | ||||||
\(722\) | 5.48081e6 | 0.391293 | ||||||||
\(723\) | 2.42632e7 | + | 4.33566e6i | 1.72624 | + | 0.308467i | ||||
\(724\) | −3.16103e7 | −2.24121 | ||||||||
\(725\) | − | 331381.i | − | 0.0234144i | ||||||
\(726\) | 2.36560e7 | + | 4.22716e6i | 1.66571 | + | 0.297651i | ||||
\(727\) | 1.45696e7 | 1.02238 | 0.511191 | − | 0.859467i | \(-0.329205\pi\) | ||||
0.511191 | + | 0.859467i | \(0.329205\pi\) | |||||||
\(728\) | − | 1.30394e7i | − | 0.911860i | ||||||
\(729\) | 7.00277e6 | + | 1.25241e7i | 0.488035 | + | 0.872824i | ||||
\(730\) | −1.09689e7 | −0.761823 | ||||||||
\(731\) | −1.26040e7 | −0.872399 | ||||||||
\(732\) | −8.41983e6 | + | 4.71190e7i | −0.580798 | + | 3.25026i | ||||
\(733\) | 3.65619e6 | 0.251344 | 0.125672 | − | 0.992072i | \(-0.459891\pi\) | ||||
0.125672 | + | 0.992072i | \(0.459891\pi\) | |||||||
\(734\) | 2.33614e7i | 1.60051i | ||||||||
\(735\) | 1.81392e6 | − | 1.01511e7i | 0.123851 | − | 0.693096i | ||||
\(736\) | 858404. | 0.0584113 | ||||||||
\(737\) | − | 1.12488e6i | − | 0.0762848i | ||||||
\(738\) | −1.37767e7 | + | 3.73177e7i | −0.931118 | + | 2.52216i | ||||
\(739\) | 1.91970e7i | 1.29307i | 0.762885 | + | 0.646535i | \(0.223782\pi\) | ||||
−0.762885 | + | 0.646535i | \(0.776218\pi\) | |||||||
\(740\) | −4.62141e6 | −0.310238 | ||||||||
\(741\) | 3.21094e6 | − | 1.79691e7i | 0.214826 | − | 1.20221i | ||||
\(742\) | 5.31742e6i | 0.354561i | ||||||||
\(743\) | 2.03356e7i | 1.35140i | 0.737175 | + | 0.675702i | \(0.236159\pi\) | ||||
−0.737175 | + | 0.675702i | \(0.763841\pi\) | |||||||
\(744\) | −3.88014e6 | + | 2.17140e7i | −0.256989 | + | 1.43816i | ||||
\(745\) | 3.55215e6i | 0.234477i | ||||||||
\(746\) | 1.76342e6 | 0.116014 | ||||||||
\(747\) | −7.19602e6 | − | 2.65658e6i | −0.471836 | − | 0.174190i | ||||
\(748\) | − | 2.26931e6i | − | 0.148299i | ||||||
\(749\) | 1.12029e7i | 0.729671i | ||||||||
\(750\) | 5.00357e6 | − | 2.80009e7i | 0.324808 | − | 1.81769i | ||||
\(751\) | 1.95164e7i | 1.26270i | 0.775500 | + | 0.631348i | \(0.217498\pi\) | ||||
−0.775500 | + | 0.631348i | \(0.782502\pi\) | |||||||
\(752\) | −8.85998e6 | −0.571332 | ||||||||
\(753\) | −3.51896e6 | + | 1.96928e7i | −0.226166 | + | 1.26567i | ||||
\(754\) | −3.33698e6 | −0.213760 | ||||||||
\(755\) | −1.90686e7 | −1.21745 | ||||||||
\(756\) | 1.09923e7 | + | 6.44768e6i | 0.699496 | + | 0.410298i | ||||
\(757\) | 1.06126e7 | 0.673103 | 0.336551 | − | 0.941665i | \(-0.390739\pi\) | ||||
0.336551 | + | 0.941665i | \(0.390739\pi\) | |||||||
\(758\) | −2.32482e7 | −1.46966 | ||||||||
\(759\) | −237317. | − | 42406.8i | −0.0149529 | − | 0.00267197i | ||||
\(760\) | 1.84860e7i | 1.16094i | ||||||||
\(761\) | − | 2.01406e7i | − | 1.26070i | −0.776313 | − | 0.630348i | \(-0.782912\pi\) | ||
0.776313 | − | 0.630348i | \(-0.217088\pi\) | |||||||
\(762\) | −3.31418e6 | − | 592220.i | −0.206770 | − | 0.0369484i | ||||
\(763\) | − | 1.39865e6i | − | 0.0869754i | ||||||
\(764\) | −2.32340e7 | −1.44009 | ||||||||
\(765\) | −1.23778e7 | − | 4.56958e6i | −0.764701 | − | 0.282308i | ||||
\(766\) | 2.44381e7i | 1.50486i | ||||||||
\(767\) | −1.52347e7 | + | 1.67884e7i | −0.935071 | + | 1.03043i | ||||
\(768\) | −2.97637e7 | − | 5.31856e6i | −1.82089 | − | 0.325380i | ||||
\(769\) | − | 1.52355e7i | − | 0.929053i | −0.885559 | − | 0.464526i | \(-0.846225\pi\) | ||
0.885559 | − | 0.464526i | \(-0.153775\pi\) | |||||||
\(770\) | 845949.i | 0.0514182i | ||||||||
\(771\) | −1.01335e6 | + | 5.67090e6i | −0.0613937 | + | 0.343571i | ||||
\(772\) | 2.33229e7 | 1.40844 | ||||||||
\(773\) | 8.57975e6 | 0.516447 | 0.258224 | − | 0.966085i | \(-0.416863\pi\) | ||||
0.258224 | + | 0.966085i | \(0.416863\pi\) | |||||||
\(774\) | 9.05545e6 | − | 2.45289e7i | 0.543322 | − | 1.47172i | ||||
\(775\) | − | 4.12603e6i | − | 0.246762i | ||||||
\(776\) | 6.96438e6i | 0.415172i | ||||||||
\(777\) | −239177. | + | 1.33848e6i | −0.0142124 | + | 0.0795353i | ||||
\(778\) | 4.57056e7i | 2.70720i | ||||||||
\(779\) | 2.34596e7i | 1.38509i | ||||||||
\(780\) | −3.80970e7 | − | 6.80767e6i | −2.24210 | − | 0.400647i | ||||
\(781\) | − | 624694.i | − | 0.0366471i | ||||||
\(782\) | − | 5.09492e6i | − | 0.297934i | ||||||
\(783\) | 782689. | − | 1.33437e6i | 0.0456231 | − | 0.0777806i | ||||
\(784\) | −1.00922e7 | −0.586404 | ||||||||
\(785\) | 1.53271e7 | 0.887741 | ||||||||
\(786\) | −3.20088e6 | − | 571975.i | −0.184805 | − | 0.0330233i | ||||
\(787\) | −3.09986e6 | −0.178404 | −0.0892022 | − | 0.996014i | \(-0.528432\pi\) | ||||
−0.0892022 | + | 0.996014i | \(0.528432\pi\) | |||||||
\(788\) | 3.26557e7i | 1.87345i | ||||||||
\(789\) | 1.11918e6 | − | 6.26314e6i | 0.0640040 | − | 0.358179i | ||||
\(790\) | 2.87072e7i | 1.63653i | ||||||||
\(791\) | −8.78082e6 | −0.498992 | ||||||||
\(792\) | 2.09485e6 | + | 773363.i | 0.118670 | + | 0.0438097i | ||||
\(793\) | −4.27664e7 | −2.41501 | ||||||||
\(794\) | 4.93801e7i | 2.77972i | ||||||||
\(795\) | 7.36926e6 | + | 1.31683e6i | 0.413529 | + | 0.0738947i | ||||
\(796\) | 4.22479e7 | 2.36332 | ||||||||
\(797\) | −2.92005e7 | −1.62834 | −0.814169 | − | 0.580628i | \(-0.802807\pi\) | ||||
−0.814169 | + | 0.580628i | \(0.802807\pi\) | |||||||
\(798\) | 1.12874e7 | + | 2.01697e6i | 0.627460 | + | 0.112123i | ||||
\(799\) | − | 1.36295e7i | − | 0.755290i | ||||||
\(800\) | 1.48731e6 | 0.0821630 | ||||||||
\(801\) | 1.19357e7 | + | 4.40633e6i | 0.657302 | + | 0.242659i | ||||
\(802\) | −3.89429e7 | −2.13793 | ||||||||
\(803\) | 781406.i | 0.0427649i | ||||||||
\(804\) | −5.68628e6 | + | 3.18215e7i | −0.310233 | + | 1.73613i | ||||
\(805\) | 1.24489e6i | 0.0677080i | ||||||||
\(806\) | −4.15488e7 | −2.25279 | ||||||||
\(807\) | −1.62646e7 | − | 2.90637e6i | −0.879144 | − | 0.157097i | ||||
\(808\) | 1.22141e7 | 0.658161 | ||||||||
\(809\) | 2.32021e6 | 0.124640 | 0.0623199 | − | 0.998056i | \(-0.480150\pi\) | ||||
0.0623199 | + | 0.998056i | \(0.480150\pi\) | |||||||
\(810\) | 1.77859e7 | − | 2.08058e7i | 0.952498 | − | 1.11422i | ||||
\(811\) | 2.10962e7i | 1.12630i | 0.826356 | + | 0.563148i | \(0.190410\pi\) | ||||
−0.826356 | + | 0.563148i | \(0.809590\pi\) | |||||||
\(812\) | − | 1.37393e6i | − | 0.0731263i | ||||||
\(813\) | 7.32352e6 | + | 1.30866e6i | 0.388592 | + | 0.0694386i | ||||
\(814\) | 502282.i | 0.0265697i | ||||||||
\(815\) | − | 2.14297e6i | − | 0.113012i | ||||||
\(816\) | −2.27155e6 | + | 1.27120e7i | −0.119425 | + | 0.668327i | ||||
\(817\) | − | 1.54200e7i | − | 0.808221i | ||||||
\(818\) | − | 3.32928e7i | − | 1.73967i | ||||||
\(819\) | −3.94336e6 | + | 1.06816e7i | −0.205426 | + | 0.556449i | ||||
\(820\) | 4.97378e7 | 2.58316 | ||||||||
\(821\) | 2.51023e7 | 1.29974 | 0.649869 | − | 0.760047i | \(-0.274824\pi\) | ||||
0.649869 | + | 0.760047i | \(0.274824\pi\) | |||||||
\(822\) | −2.10175e6 | + | 1.17618e7i | −0.108493 | + | 0.607148i | ||||
\(823\) | − | 132060.i | − | 0.00679630i | −0.999994 | − | 0.00339815i | \(-0.998918\pi\) | ||
0.999994 | − | 0.00339815i | \(-0.00108167\pi\) | |||||||
\(824\) | 3.71462e6i | 0.190588i | ||||||||
\(825\) | −411186. | − | 73476.0i | −0.0210331 | − | 0.00375847i | ||||
\(826\) | −1.05457e7 | − | 9.56975e6i | −0.537807 | − | 0.488035i | ||||
\(827\) | − | 1.75072e7i | − | 0.890129i | −0.895498 | − | 0.445065i | \(-0.853181\pi\) | ||
0.895498 | − | 0.445065i | \(-0.146819\pi\) | |||||||
\(828\) | 6.49904e6 | + | 2.39928e6i | 0.329438 | + | 0.121620i | ||||
\(829\) | −2.42099e7 | −1.22351 | −0.611753 | − | 0.791049i | \(-0.709535\pi\) | ||||
−0.611753 | + | 0.791049i | \(0.709535\pi\) | |||||||
\(830\) | 1.46326e7i | 0.737271i | ||||||||
\(831\) | 1.41839e7 | + | 2.53456e6i | 0.712512 | + | 0.127321i | ||||
\(832\) | − | 3.48872e7i | − | 1.74726i | ||||||
\(833\) | − | 1.55251e7i | − | 0.775216i | ||||||
\(834\) | −1.51206e7 | − | 2.70194e6i | −0.752756 | − | 0.134512i | ||||
\(835\) | 1.04758e7 | 0.519962 | ||||||||
\(836\) | 2.77633e6 | 0.137390 | ||||||||
\(837\) | 9.74526e6 | − | 1.66142e7i | 0.480817 | − | 0.819721i | ||||
\(838\) | −8.72584e6 | −0.429237 | ||||||||
\(839\) | −3.71411e7 | −1.82159 | −0.910793 | − | 0.412862i | \(-0.864529\pi\) | ||||
−0.910793 | + | 0.412862i | \(0.864529\pi\) | |||||||
\(840\) | 2.02840e6 | − | 1.13513e7i | 0.0991873 | − | 0.555072i | ||||
\(841\) | 2.03444e7 | 0.991869 | ||||||||
\(842\) | 6.72312e7i | 3.26806i | ||||||||
\(843\) | −1.70490e6 | + | 9.54097e6i | −0.0826287 | + | 0.462406i | ||||
\(844\) | − | 1.99864e7i | − | 0.965779i | ||||||
\(845\) | − | 1.67188e7i | − | 0.805495i | ||||||
\(846\) | 2.65247e7 | + | 9.79225e6i | 1.27416 | + | 0.470388i | ||||
\(847\) | −8.84011e6 | −0.423398 | ||||||||
\(848\) | − | 7.32655e6i | − | 0.349873i | ||||||
\(849\) | 891408. | − | 4.98849e6i | 0.0424431 | − | 0.237520i | ||||
\(850\) | − | 8.82768e6i | − | 0.419082i | ||||||
\(851\) | 739151.i | 0.0349872i | ||||||||
\(852\) | −3.15783e6 | + | 1.76718e7i | −0.149036 | + | 0.834032i | ||||
\(853\) | −5.95680e6 | −0.280311 | −0.140156 | − | 0.990129i | \(-0.544760\pi\) | ||||
−0.140156 | + | 0.990129i | \(0.544760\pi\) | |||||||
\(854\) | − | 2.68640e7i | − | 1.26045i | ||||||
\(855\) | 5.59053e6 | − | 1.51434e7i | 0.261540 | − | 0.708446i | ||||
\(856\) | − | 5.64118e7i | − | 2.63139i | ||||||
\(857\) | −1.24953e7 | −0.581161 | −0.290580 | − | 0.956851i | \(-0.593848\pi\) | ||||
−0.290580 | + | 0.956851i | \(0.593848\pi\) | |||||||
\(858\) | −739898. | + | 4.14061e6i | −0.0343126 | + | 0.192020i | ||||
\(859\) | 2.29853e7i | 1.06284i | 0.847109 | + | 0.531419i | \(0.178341\pi\) | ||||
−0.847109 | + | 0.531419i | \(0.821659\pi\) | |||||||
\(860\) | −3.26927e7 | −1.50732 | ||||||||
\(861\) | 2.57414e6 | − | 1.44054e7i | 0.118338 | − | 0.662241i | ||||
\(862\) | 5.03496e7 | 2.30796 | ||||||||
\(863\) | 2.58072e7 | 1.17955 | 0.589773 | − | 0.807569i | \(-0.299217\pi\) | ||||
0.589773 | + | 0.807569i | \(0.299217\pi\) | |||||||
\(864\) | 5.98893e6 | + | 3.51288e6i | 0.272938 | + | 0.160095i | ||||
\(865\) | 1.54252e7i | 0.700956i | ||||||||
\(866\) | −5.11388e6 | −0.231716 | ||||||||
\(867\) | 2.23304e6 | + | 399028.i | 0.100890 | + | 0.0180283i | ||||
\(868\) | − | 1.71068e7i | − | 0.770670i | ||||||
\(869\) | 2.04506e6 | 0.0918664 | ||||||||
\(870\) | −2.90499e6 | − | 519101.i | −0.130121 | − | 0.0232516i | ||||
\(871\) | −2.88820e7 | −1.28998 | ||||||||
\(872\) | 7.04282e6i | 0.313657i | ||||||||
\(873\) | 2.10616e6 | − | 5.70506e6i | 0.0935311 | − | 0.253352i | ||||
\(874\) | 6.23324e6 | 0.276017 | ||||||||
\(875\) | 1.04638e7i | 0.462028i | ||||||||
\(876\) | 3.95001e6 | − | 2.21050e7i | 0.173915 | − | 0.973265i | ||||
\(877\) | −3.38946e7 | −1.48810 | −0.744049 | − | 0.668126i | \(-0.767097\pi\) | ||||
−0.744049 | + | 0.668126i | \(0.767097\pi\) | |||||||
\(878\) | 2.87361e7 | 1.25803 | ||||||||
\(879\) | −5.70192e6 | + | 3.19090e7i | −0.248914 | + | 1.39297i | ||||
\(880\) | − | 1.16558e6i | − | 0.0507383i | ||||||
\(881\) | 2.03567e7 | 0.883623 | 0.441811 | − | 0.897108i | \(-0.354336\pi\) | ||||
0.441811 | + | 0.897108i | \(0.354336\pi\) | |||||||
\(882\) | 3.02138e7 | + | 1.11542e7i | 1.30778 | + | 0.482798i | ||||
\(883\) | −2.28940e7 | −0.988143 | −0.494071 | − | 0.869421i | \(-0.664492\pi\) | ||||
−0.494071 | + | 0.869421i | \(0.664492\pi\) | |||||||
\(884\) | −5.82659e7 | −2.50775 | ||||||||
\(885\) | −1.58740e7 | + | 1.22451e7i | −0.681286 | + | 0.525539i | ||||
\(886\) | −6.40850e7 | −2.74266 | ||||||||
\(887\) | 1.50112e6 | 0.0640629 | 0.0320315 | − | 0.999487i | \(-0.489802\pi\) | ||||
0.0320315 | + | 0.999487i | \(0.489802\pi\) | |||||||
\(888\) | 1.20437e6 | − | 6.73986e6i | 0.0512538 | − | 0.286826i | ||||
\(889\) | 1.23849e6 | 0.0525578 | ||||||||
\(890\) | − | 2.42704e7i | − | 1.02707i | ||||||
\(891\) | −1.48217e6 | − | 1.26704e6i | −0.0625468 | − | 0.0534684i | ||||
\(892\) | 7.01154e7 | 2.95054 | ||||||||
\(893\) | 1.66747e7 | 0.699728 | ||||||||
\(894\) | −1.09214e7 | − | 1.95158e6i | −0.457020 | − | 0.0816662i | ||||
\(895\) | 1.48766e7i | 0.620794i | ||||||||
\(896\) | 1.86731e7 | 0.777046 | ||||||||
\(897\) | −1.08882e6 | + | 6.09326e6i | −0.0451831 | + | 0.252853i | ||||
\(898\) | 7.98751e7i | 3.30537i | ||||||||
\(899\) | −2.07660e6 | −0.0856948 | ||||||||
\(900\) | 1.12605e7 | + | 4.15710e6i | 0.463397 | + | 0.171074i | ||||
\(901\) | 1.12706e7 | 0.462526 | ||||||||
\(902\) | − | 5.40580e6i | − | 0.221230i | ||||||
\(903\) | −1.69198e6 | + | 9.46867e6i | −0.0690521 | + | 0.386429i | ||||
\(904\) | 4.42154e7 | 1.79950 | ||||||||
\(905\) | − | 2.49762e7i | − | 1.01369i | ||||||
\(906\) | 1.04764e7 | − | 5.86281e7i | 0.424026 | − | 2.37293i | ||||
\(907\) | 1.01396e7 | 0.409263 | 0.204632 | − | 0.978839i | \(-0.434400\pi\) | ||||
0.204632 | + | 0.978839i | \(0.434400\pi\) | |||||||
\(908\) | 6.51771e7 | 2.62350 | ||||||||
\(909\) | −1.00055e7 | − | 3.69377e6i | −0.401633 | − | 0.148272i | ||||
\(910\) | 2.17203e7 | 0.869484 | ||||||||
\(911\) | 5.21083e6i | 0.208023i | 0.994576 | + | 0.104011i | \(0.0331678\pi\) | ||||
−0.994576 | + | 0.104011i | \(0.966832\pi\) | |||||||
\(912\) | −1.55522e7 | − | 2.77906e6i | −0.619162 | − | 0.110640i | ||||
\(913\) | 1.04241e6 | 0.0413867 | ||||||||
\(914\) | 3.61106e7i | 1.42978i | ||||||||
\(915\) | −3.72300e7 | − | 6.65273e6i | −1.47008 | − | 0.262692i | ||||
\(916\) | − | 8.08861e7i | − | 3.18519i | ||||||
\(917\) | 1.19615e6 | 0.0469745 | ||||||||
\(918\) | 2.08501e7 | − | 3.55463e7i | 0.816585 | − | 1.39216i | ||||
\(919\) | 1.47154e7i | 0.574757i | 0.957817 | + | 0.287378i | \(0.0927837\pi\) | ||||
−0.957817 | + | 0.287378i | \(0.907216\pi\) | |||||||
\(920\) | − | 6.26856e6i | − | 0.244173i | ||||||
\(921\) | −6.05430e6 | − | 1.08186e6i | −0.235188 | − | 0.0420264i | ||||
\(922\) | − | 3.36460e7i | − | 1.30349i | ||||||
\(923\) | −1.60394e7 | −0.619704 | ||||||||
\(924\) | −1.70480e6 | − | 304636.i | −0.0656892 | − | 0.0117382i | ||||
\(925\) | 1.28069e6i | 0.0492140i | ||||||||
\(926\) | − | 2.77615e7i | − | 1.06394i | ||||||
\(927\) | 1.12337e6 | − | 3.04293e6i | 0.0429362 | − | 0.116304i | ||||
\(928\) | − | 748554.i | − | 0.0285334i | ||||||
\(929\) | 5.17459e7 | 1.96715 | 0.983573 | − | 0.180512i | \(-0.0577755\pi\) | ||||
0.983573 | + | 0.180512i | \(0.0577755\pi\) | |||||||
\(930\) | −3.61700e7 | − | 6.46332e6i | −1.37133 | − | 0.245047i | ||||
\(931\) | 1.89938e7 | 0.718188 | ||||||||
\(932\) | −9.66886e7 | −3.64616 | ||||||||
\(933\) | −3.44411e6 | + | 1.92739e7i | −0.129531 | + | 0.724880i | ||||
\(934\) | 1.92489e7 | 0.722004 | ||||||||
\(935\) | 1.79304e6 | 0.0670751 | ||||||||
\(936\) | 1.98566e7 | − | 5.37865e7i | 0.740824 | − | 2.00671i | ||||
\(937\) | 3.59782e7i | 1.33872i | 0.742938 | + | 0.669361i | \(0.233432\pi\) | ||||
−0.742938 | + | 0.669361i | \(0.766568\pi\) | |||||||
\(938\) | − | 1.81424e7i | − | 0.673269i | ||||||
\(939\) | 6.33632e6 | − | 3.54593e7i | 0.234516 | − | 1.31240i | ||||
\(940\) | − | 3.53528e7i | − | 1.30498i | ||||||
\(941\) | 9.25929e6 | 0.340882 | 0.170441 | − | 0.985368i | \(-0.445481\pi\) | ||||
0.170441 | + | 0.985368i | \(0.445481\pi\) | |||||||
\(942\) | −8.42084e6 | + | 4.71247e7i | −0.309192 | + | 1.73030i | ||||
\(943\) | − | 7.95509e6i | − | 0.291317i | ||||||
\(944\) | 1.45303e7 | + | 1.31856e7i | 0.530695 | + | 0.481581i | ||||
\(945\) | −5.09449e6 | + | 8.68534e6i | −0.185576 | + | 0.316379i | ||||
\(946\) | 3.55324e6i | 0.129091i | ||||||||
\(947\) | 2.87335e7i | 1.04115i | 0.853816 | + | 0.520575i | \(0.174283\pi\) | ||||
−0.853816 | + | 0.520575i | \(0.825717\pi\) | |||||||
\(948\) | −5.78523e7 | − | 1.03378e7i | −2.09074 | − | 0.373600i | ||||
\(949\) | 2.00631e7 | 0.723156 | ||||||||
\(950\) | 1.08000e7 | 0.388253 | ||||||||
\(951\) | 3.01644e6 | − | 1.68806e7i | 0.108154 | − | 0.605251i | ||||
\(952\) | − | 1.73608e7i | − | 0.620838i | ||||||
\(953\) | − | 2.87660e7i | − | 1.02600i | −0.858388 | − | 0.513001i | \(-0.828534\pi\) | ||
0.858388 | − | 0.513001i | \(-0.171466\pi\) | |||||||
\(954\) | −8.09747e6 | + | 2.19340e7i | −0.288057 | + | 0.780274i | ||||
\(955\) | − | 1.83578e7i | − | 0.651346i | ||||||
\(956\) | − | 4.99310e7i | − | 1.76696i | ||||||
\(957\) | −36980.0 | + | 206947.i | −0.00130523 | + | 0.00730432i | ||||
\(958\) | 2.17282e7i | 0.764911i | ||||||||
\(959\) | − | 4.39532e6i | − | 0.154328i | ||||||
\(960\) | 5.42704e6 | − | 3.03708e7i | 0.190058 | − | 1.06360i | ||||
\(961\) | 2.77336e6 | 0.0968720 | ||||||||
\(962\) | 1.28964e7 | 0.449295 | ||||||||
\(963\) | −1.70600e7 | + | 4.62113e7i | −0.592808 | + | 1.60577i | ||||
\(964\) | 9.62529e7 | 3.33596 | ||||||||
\(965\) | 1.84280e7i | 0.637032i | ||||||||
\(966\) | −3.82752e6 | − | 683950.i | −0.131970 | − | 0.0235821i | ||||
\(967\) | − | 3.90085e7i | − | 1.34151i | −0.741680 | − | 0.670754i | \(-0.765971\pi\) | ||
0.741680 | − | 0.670754i | \(-0.234029\pi\) | |||||||
\(968\) | 4.45140e7 | 1.52689 | ||||||||
\(969\) | 4.27510e6 | − | 2.39243e7i | 0.146264 | − | 0.818521i | ||||
\(970\) | −1.16009e7 | −0.395878 | ||||||||
\(971\) | 4.42731e7i | 1.50692i | 0.657491 | + | 0.753462i | \(0.271618\pi\) | ||||
−0.657491 | + | 0.753462i | \(0.728382\pi\) | |||||||
\(972\) | 3.55240e7 | + | 4.33356e7i | 1.20602 | + | 1.47122i | ||||
\(973\) | 5.65048e6 | 0.191339 | ||||||||
\(974\) | −7.23292e7 | −2.44296 | ||||||||
\(975\) | −1.88654e6 | + | 1.05575e7i | −0.0635558 | + | 0.355670i | ||||
\(976\) | 3.70142e7i | 1.24378i | ||||||||
\(977\) | 352721. | 0.0118221 | 0.00591105 | − | 0.999983i | \(-0.498118\pi\) | ||||
0.00591105 | + | 0.999983i | \(0.498118\pi\) | |||||||
\(978\) | 6.58877e6 | + | 1.17737e6i | 0.220271 | + | 0.0393609i | ||||
\(979\) | −1.72899e6 | −0.0576547 | ||||||||
\(980\) | − | 4.02696e7i | − | 1.33941i | ||||||
\(981\) | 2.12988e6 | − | 5.76932e6i | 0.0706616 | − | 0.191405i | ||||
\(982\) | 5.22345e7i | 1.72854i | ||||||||
\(983\) | −3.99184e7 | −1.31762 | −0.658809 | − | 0.752311i | \(-0.728939\pi\) | ||||
−0.658809 | + | 0.752311i | \(0.728939\pi\) | |||||||
\(984\) | −1.29619e7 | + | 7.25375e7i | −0.426759 | + | 2.38822i | ||||
\(985\) | −2.58021e7 | −0.847354 | ||||||||
\(986\) | −4.44292e6 | −0.145538 | ||||||||
\(987\) | −1.02391e7 | − | 1.82965e6i | −0.334556 | − | 0.0597827i | ||||
\(988\) | − | 7.12839e7i | − | 2.32327i | ||||||
\(989\) | 5.22889e6i | 0.169988i | ||||||||
\(990\) | −1.28823e6 | + | 3.48948e6i | −0.0417738 | + | 0.113155i | ||||
\(991\) | 7.82069e6i | 0.252965i | 0.991969 | + | 0.126483i | \(0.0403688\pi\) | ||||
−0.991969 | + | 0.126483i | \(0.959631\pi\) | |||||||
\(992\) | − | 9.32024e6i | − | 0.300710i | ||||||
\(993\) | 2.63449e7 | + | 4.70764e6i | 0.847858 | + | 0.151506i | ||||
\(994\) | − | 1.00753e7i | − | 0.323437i | ||||||
\(995\) | 3.33812e7i | 1.06892i | ||||||||
\(996\) | −2.94885e7 | − | 5.26938e6i | −0.941898 | − | 0.168311i | ||||
\(997\) | 3.34225e7 | 1.06488 | 0.532441 | − | 0.846467i | \(-0.321275\pi\) | ||||
0.532441 | + | 0.846467i | \(0.321275\pi\) | |||||||
\(998\) | 6.77780e7 | 2.15408 | ||||||||
\(999\) | −3.02485e6 | + | 5.15692e6i | −0.0958938 | + | 0.163485i |
(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 | 177.6.d.b.176.10 | yes | 92 | |
3.2 | odd | 2 | inner | 177.6.d.b.176.83 | yes | 92 | |
59.58 | odd | 2 | inner | 177.6.d.b.176.84 | yes | 92 | |
177.176 | even | 2 | inner | 177.6.d.b.176.9 | ✓ | 92 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.6.d.b.176.9 | ✓ | 92 | 177.176 | even | 2 | inner | |
177.6.d.b.176.10 | yes | 92 | 1.1 | even | 1 | trivial | |
177.6.d.b.176.83 | yes | 92 | 3.2 | odd | 2 | inner | |
177.6.d.b.176.84 | yes | 92 | 59.58 | odd | 2 | inner |