Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,5,Mod(39,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.39");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.b (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: | \(7.85611719437\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 39.14 | ||
Character | \(\chi\) | \(=\) | 76.39 |
Dual form | 76.5.b.a.39.13 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.32688 | + | 3.77351i | −0.331719 | + | 0.943378i | ||||
\(3\) | − | 14.8593i | − | 1.65103i | −0.564381 | − | 0.825514i | \(-0.690885\pi\) | ||
0.564381 | − | 0.825514i | \(-0.309115\pi\) | |||||||
\(4\) | −12.4788 | − | 10.0140i | −0.779925 | − | 0.625873i | ||||
\(5\) | 13.5934 | 0.543738 | 0.271869 | − | 0.962334i | \(-0.412358\pi\) | ||||
0.271869 | + | 0.962334i | \(0.412358\pi\) | |||||||
\(6\) | 56.0716 | + | 19.7164i | 1.55754 | + | 0.547677i | ||||
\(7\) | 39.3950i | 0.803979i | 0.915644 | + | 0.401989i | \(0.131681\pi\) | ||||
−0.915644 | + | 0.401989i | \(0.868319\pi\) | |||||||
\(8\) | 54.3456 | − | 33.8016i | 0.849151 | − | 0.528151i | ||||
\(9\) | −139.798 | −1.72590 | ||||||||
\(10\) | −18.0368 | + | 51.2950i | −0.180368 | + | 0.512950i | ||||
\(11\) | − | 218.566i | − | 1.80633i | −0.429291 | − | 0.903166i | \(-0.641236\pi\) | ||
0.429291 | − | 0.903166i | \(-0.358764\pi\) | |||||||
\(12\) | −148.800 | + | 185.426i | −1.03333 | + | 1.28768i | ||||
\(13\) | −320.039 | −1.89372 | −0.946860 | − | 0.321645i | \(-0.895764\pi\) | ||||
−0.946860 | + | 0.321645i | \(0.895764\pi\) | |||||||
\(14\) | −148.657 | − | 52.2722i | −0.758456 | − | 0.266695i | ||||
\(15\) | − | 201.988i | − | 0.897727i | ||||||
\(16\) | 55.4410 | + | 249.925i | 0.216566 | + | 0.976268i | ||||
\(17\) | −187.447 | −0.648606 | −0.324303 | − | 0.945953i | \(-0.605130\pi\) | ||||
−0.324303 | + | 0.945953i | \(0.605130\pi\) | |||||||
\(18\) | 185.494 | − | 527.528i | 0.572512 | − | 1.62817i | ||||
\(19\) | − | 82.8191i | − | 0.229416i | ||||||
\(20\) | −169.630 | − | 136.124i | −0.424075 | − | 0.340311i | ||||
\(21\) | 585.380 | 1.32739 | ||||||||
\(22\) | 824.763 | + | 290.010i | 1.70406 | + | 0.599195i | ||||
\(23\) | 302.811i | 0.572422i | 0.958167 | + | 0.286211i | \(0.0923959\pi\) | ||||
−0.958167 | + | 0.286211i | \(0.907604\pi\) | |||||||
\(24\) | −502.267 | − | 807.536i | −0.871992 | − | 1.40197i | ||||
\(25\) | −440.218 | −0.704349 | ||||||||
\(26\) | 424.652 | − | 1207.67i | 0.628183 | − | 1.78649i | ||||
\(27\) | 873.688i | 1.19848i | ||||||||
\(28\) | 394.500 | − | 491.602i | 0.503188 | − | 0.627043i | ||||
\(29\) | 178.430 | 0.212164 | 0.106082 | − | 0.994357i | \(-0.466169\pi\) | ||||
0.106082 | + | 0.994357i | \(0.466169\pi\) | |||||||
\(30\) | 762.206 | + | 268.014i | 0.846896 | + | 0.297793i | ||||
\(31\) | − | 747.076i | − | 0.777395i | −0.921365 | − | 0.388697i | \(-0.872925\pi\) | ||
0.921365 | − | 0.388697i | \(-0.127075\pi\) | |||||||
\(32\) | −1016.66 | − | 122.412i | −0.992829 | − | 0.119543i | ||||
\(33\) | −3247.73 | −2.98231 | ||||||||
\(34\) | 248.719 | − | 707.335i | 0.215155 | − | 0.611881i | ||||
\(35\) | 535.513i | 0.437154i | ||||||||
\(36\) | 1744.51 | + | 1399.93i | 1.34607 | + | 1.08019i | ||||
\(37\) | 1399.09 | 1.02198 | 0.510990 | − | 0.859587i | \(-0.329279\pi\) | ||||
0.510990 | + | 0.859587i | \(0.329279\pi\) | |||||||
\(38\) | 312.519 | + | 109.891i | 0.216426 | + | 0.0761015i | ||||
\(39\) | 4755.54i | 3.12659i | ||||||||
\(40\) | 738.744 | − | 459.481i | 0.461715 | − | 0.287175i | ||||
\(41\) | 431.243 | 0.256540 | 0.128270 | − | 0.991739i | \(-0.459058\pi\) | ||||
0.128270 | + | 0.991739i | \(0.459058\pi\) | |||||||
\(42\) | −776.726 | + | 2208.94i | −0.440321 | + | 1.25223i | ||||
\(43\) | − | 2944.17i | − | 1.59230i | −0.605098 | − | 0.796151i | \(-0.706866\pi\) | ||
0.605098 | − | 0.796151i | \(-0.293134\pi\) | |||||||
\(44\) | −2188.72 | + | 2727.45i | −1.13053 | + | 1.40880i | ||||
\(45\) | −1900.33 | −0.938435 | ||||||||
\(46\) | −1142.66 | − | 401.793i | −0.540011 | − | 0.189883i | ||||
\(47\) | 2064.30i | 0.934495i | 0.884127 | + | 0.467247i | \(0.154754\pi\) | ||||
−0.884127 | + | 0.467247i | \(0.845246\pi\) | |||||||
\(48\) | 3713.69 | − | 823.812i | 1.61185 | − | 0.357557i | ||||
\(49\) | 849.037 | 0.353618 | ||||||||
\(50\) | 584.115 | − | 1661.17i | 0.233646 | − | 0.664468i | ||||
\(51\) | 2785.33i | 1.07087i | ||||||||
\(52\) | 3993.70 | + | 3204.86i | 1.47696 | + | 1.18523i | ||||
\(53\) | 738.955 | 0.263067 | 0.131533 | − | 0.991312i | \(-0.458010\pi\) | ||||
0.131533 | + | 0.991312i | \(0.458010\pi\) | |||||||
\(54\) | −3296.87 | − | 1159.28i | −1.13062 | − | 0.397557i | ||||
\(55\) | − | 2971.07i | − | 0.982171i | ||||||
\(56\) | 1331.61 | + | 2140.94i | 0.424622 | + | 0.682699i | ||||
\(57\) | −1230.63 | −0.378772 | ||||||||
\(58\) | −236.755 | + | 673.309i | −0.0703790 | + | 0.200151i | ||||
\(59\) | − | 6049.02i | − | 1.73772i | −0.495055 | − | 0.868862i | \(-0.664852\pi\) | ||
0.495055 | − | 0.868862i | \(-0.335148\pi\) | |||||||
\(60\) | −2022.71 | + | 2520.57i | −0.561863 | + | 0.700160i | ||||
\(61\) | 2144.70 | 0.576377 | 0.288188 | − | 0.957574i | \(-0.406947\pi\) | ||||
0.288188 | + | 0.957574i | \(0.406947\pi\) | |||||||
\(62\) | 2819.10 | + | 991.277i | 0.733377 | + | 0.257877i | ||||
\(63\) | − | 5507.32i | − | 1.38758i | ||||||
\(64\) | 1810.90 | − | 3673.94i | 0.442114 | − | 0.896959i | ||||
\(65\) | −4350.43 | −1.02969 | ||||||||
\(66\) | 4309.34 | − | 12255.4i | 0.989288 | − | 2.81344i | ||||
\(67\) | − | 2473.74i | − | 0.551068i | −0.961291 | − | 0.275534i | \(-0.911145\pi\) | ||
0.961291 | − | 0.275534i | \(-0.0888546\pi\) | |||||||
\(68\) | 2339.12 | + | 1877.09i | 0.505864 | + | 0.405945i | ||||
\(69\) | 4499.55 | 0.945086 | ||||||||
\(70\) | −2020.77 | − | 710.559i | −0.412401 | − | 0.145012i | ||||
\(71\) | − | 1349.39i | − | 0.267684i | −0.991003 | − | 0.133842i | \(-0.957269\pi\) | ||
0.991003 | − | 0.133842i | \(-0.0427314\pi\) | |||||||
\(72\) | −7597.39 | + | 4725.39i | −1.46555 | + | 0.911533i | ||||
\(73\) | 973.840 | 0.182744 | 0.0913718 | − | 0.995817i | \(-0.470875\pi\) | ||||
0.0913718 | + | 0.995817i | \(0.470875\pi\) | |||||||
\(74\) | −1856.42 | + | 5279.49i | −0.339010 | + | 0.964114i | ||||
\(75\) | 6541.32i | 1.16290i | ||||||||
\(76\) | −829.347 | + | 1033.48i | −0.143585 | + | 0.178927i | ||||
\(77\) | 8610.41 | 1.45225 | ||||||||
\(78\) | −17945.1 | − | 6310.01i | −2.94955 | − | 1.03715i | ||||
\(79\) | 4625.32i | 0.741118i | 0.928809 | + | 0.370559i | \(0.120834\pi\) | ||||
−0.928809 | + | 0.370559i | \(0.879166\pi\) | |||||||
\(80\) | 753.634 | + | 3397.34i | 0.117755 | + | 0.530834i | ||||
\(81\) | 1658.76 | 0.252821 | ||||||||
\(82\) | −572.206 | + | 1627.30i | −0.0850991 | + | 0.242014i | ||||
\(83\) | 7693.27i | 1.11675i | 0.829590 | + | 0.558373i | \(0.188574\pi\) | ||||
−0.829590 | + | 0.558373i | \(0.811426\pi\) | |||||||
\(84\) | −7304.84 | − | 5861.97i | −1.03527 | − | 0.830779i | ||||
\(85\) | −2548.05 | −0.352672 | ||||||||
\(86\) | 11109.9 | + | 3906.54i | 1.50214 | + | 0.528197i | ||||
\(87\) | − | 2651.34i | − | 0.350290i | ||||||
\(88\) | −7387.90 | − | 11878.1i | −0.954016 | − | 1.53385i | ||||
\(89\) | −6507.33 | −0.821529 | −0.410765 | − | 0.911741i | \(-0.634738\pi\) | ||||
−0.410765 | + | 0.911741i | \(0.634738\pi\) | |||||||
\(90\) | 2521.50 | − | 7170.92i | 0.311297 | − | 0.885299i | ||||
\(91\) | − | 12607.9i | − | 1.52251i | ||||||
\(92\) | 3032.34 | − | 3778.72i | 0.358264 | − | 0.446447i | ||||
\(93\) | −11101.0 | −1.28350 | ||||||||
\(94\) | −7789.66 | − | 2739.07i | −0.881582 | − | 0.309990i | ||||
\(95\) | − | 1125.80i | − | 0.124742i | ||||||
\(96\) | −1818.94 | + | 15106.8i | −0.197368 | + | 1.63919i | ||||
\(97\) | 8348.37 | 0.887275 | 0.443637 | − | 0.896206i | \(-0.353688\pi\) | ||||
0.443637 | + | 0.896206i | \(0.353688\pi\) | |||||||
\(98\) | −1126.57 | + | 3203.85i | −0.117302 | + | 0.333596i | ||||
\(99\) | 30555.0i | 3.11754i | ||||||||
\(100\) | 5493.40 | + | 4408.33i | 0.549340 | + | 0.440833i | ||||
\(101\) | 10023.6 | 0.982609 | 0.491304 | − | 0.870988i | \(-0.336520\pi\) | ||||
0.491304 | + | 0.870988i | \(0.336520\pi\) | |||||||
\(102\) | −10510.5 | − | 3695.78i | −1.01023 | − | 0.355227i | ||||
\(103\) | − | 13770.8i | − | 1.29803i | −0.760777 | − | 0.649013i | \(-0.775182\pi\) | ||
0.760777 | − | 0.649013i | \(-0.224818\pi\) | |||||||
\(104\) | −17392.7 | + | 10817.8i | −1.60805 | + | 1.00017i | ||||
\(105\) | 7957.33 | 0.721753 | ||||||||
\(106\) | −980.501 | + | 2788.46i | −0.0872643 | + | 0.248172i | ||||
\(107\) | − | 5532.09i | − | 0.483194i | −0.970377 | − | 0.241597i | \(-0.922329\pi\) | ||
0.970377 | − | 0.241597i | \(-0.0776712\pi\) | |||||||
\(108\) | 8749.09 | − | 10902.6i | 0.750093 | − | 0.934721i | ||||
\(109\) | 1738.18 | 0.146299 | 0.0731497 | − | 0.997321i | \(-0.476695\pi\) | ||||
0.0731497 | + | 0.997321i | \(0.476695\pi\) | |||||||
\(110\) | 11211.4 | + | 3942.24i | 0.926559 | + | 0.325805i | ||||
\(111\) | − | 20789.5i | − | 1.68732i | ||||||
\(112\) | −9845.77 | + | 2184.10i | −0.784899 | + | 0.174115i | ||||
\(113\) | 17381.6 | 1.36123 | 0.680617 | − | 0.732639i | \(-0.261712\pi\) | ||||
0.680617 | + | 0.732639i | \(0.261712\pi\) | |||||||
\(114\) | 1632.89 | − | 4643.80i | 0.125646 | − | 0.357325i | ||||
\(115\) | 4116.25i | 0.311248i | ||||||||
\(116\) | −2226.60 | − | 1786.79i | −0.165472 | − | 0.132788i | ||||
\(117\) | 44740.6 | 3.26836 | ||||||||
\(118\) | 22826.0 | + | 8026.29i | 1.63933 | + | 0.576436i | ||||
\(119\) | − | 7384.48i | − | 0.521466i | ||||||
\(120\) | −6827.54 | − | 10977.2i | −0.474135 | − | 0.762305i | ||||
\(121\) | −33130.2 | −2.26284 | ||||||||
\(122\) | −2845.75 | + | 8093.04i | −0.191195 | + | 0.543741i | ||||
\(123\) | − | 6407.96i | − | 0.423555i | ||||||
\(124\) | −7481.20 | + | 9322.62i | −0.486550 | + | 0.606310i | ||||
\(125\) | −14480.0 | −0.926719 | ||||||||
\(126\) | 20781.9 | + | 7307.53i | 1.30902 | + | 0.460288i | ||||
\(127\) | − | 15346.4i | − | 0.951476i | −0.879587 | − | 0.475738i | \(-0.842181\pi\) | ||
0.879587 | − | 0.475738i | \(-0.157819\pi\) | |||||||
\(128\) | 11460.8 | + | 11708.3i | 0.699514 | + | 0.714619i | ||||
\(129\) | −43748.1 | −2.62894 | ||||||||
\(130\) | 5772.48 | − | 16416.4i | 0.341567 | − | 0.971385i | ||||
\(131\) | − | 2225.24i | − | 0.129668i | −0.997896 | − | 0.0648341i | \(-0.979348\pi\) | ||
0.997896 | − | 0.0648341i | \(-0.0206518\pi\) | |||||||
\(132\) | 40527.8 | + | 32522.7i | 2.32598 | + | 1.86655i | ||||
\(133\) | 3262.65 | 0.184445 | ||||||||
\(134\) | 9334.70 | + | 3282.35i | 0.519865 | + | 0.182800i | ||||
\(135\) | 11876.4i | 0.651656i | ||||||||
\(136\) | −10186.9 | + | 6336.02i | −0.550765 | + | 0.342562i | ||||
\(137\) | −14510.5 | −0.773110 | −0.386555 | − | 0.922266i | \(-0.626335\pi\) | ||||
−0.386555 | + | 0.922266i | \(0.626335\pi\) | |||||||
\(138\) | −5970.35 | + | 16979.1i | −0.313503 | + | 0.891573i | ||||
\(139\) | 16063.4i | 0.831394i | 0.909503 | + | 0.415697i | \(0.136462\pi\) | ||||
−0.909503 | + | 0.415697i | \(0.863538\pi\) | |||||||
\(140\) | 5362.61 | − | 6682.56i | 0.273603 | − | 0.340947i | ||||
\(141\) | 30674.0 | 1.54288 | ||||||||
\(142\) | 5091.95 | + | 1790.48i | 0.252527 | + | 0.0887957i | ||||
\(143\) | 69949.7i | 3.42069i | ||||||||
\(144\) | −7750.52 | − | 34938.9i | −0.373771 | − | 1.68494i | ||||
\(145\) | 2425.48 | 0.115362 | ||||||||
\(146\) | −1292.16 | + | 3674.80i | −0.0606195 | + | 0.172396i | ||||
\(147\) | − | 12616.1i | − | 0.583834i | ||||||
\(148\) | −17459.0 | − | 14010.4i | −0.797068 | − | 0.639630i | ||||
\(149\) | −17577.1 | −0.791725 | −0.395862 | − | 0.918310i | \(-0.629554\pi\) | ||||
−0.395862 | + | 0.918310i | \(0.629554\pi\) | |||||||
\(150\) | −24683.7 | − | 8679.52i | −1.09706 | − | 0.385756i | ||||
\(151\) | − | 2635.20i | − | 0.115574i | −0.998329 | − | 0.0577869i | \(-0.981596\pi\) | ||
0.998329 | − | 0.0577869i | \(-0.0184044\pi\) | |||||||
\(152\) | −2799.42 | − | 4500.86i | −0.121166 | − | 0.194809i | ||||
\(153\) | 26204.7 | 1.11943 | ||||||||
\(154\) | −11424.9 | + | 32491.5i | −0.481740 | + | 1.37002i | ||||
\(155\) | − | 10155.3i | − | 0.422699i | ||||||
\(156\) | 47621.8 | − | 59343.4i | 1.95685 | − | 2.43850i | ||||
\(157\) | −30767.7 | −1.24823 | −0.624116 | − | 0.781332i | \(-0.714541\pi\) | ||||
−0.624116 | + | 0.781332i | \(0.714541\pi\) | |||||||
\(158\) | −17453.7 | − | 6137.22i | −0.699155 | − | 0.245843i | ||||
\(159\) | − | 10980.3i | − | 0.434331i | ||||||
\(160\) | −13819.9 | − | 1663.99i | −0.539839 | − | 0.0649998i | ||||
\(161\) | −11929.2 | −0.460215 | ||||||||
\(162\) | −2200.97 | + | 6259.35i | −0.0838656 | + | 0.238506i | ||||
\(163\) | 8950.17i | 0.336865i | 0.985713 | + | 0.168433i | \(0.0538705\pi\) | ||||
−0.985713 | + | 0.168433i | \(0.946129\pi\) | |||||||
\(164\) | −5381.40 | − | 4318.46i | −0.200082 | − | 0.160561i | ||||
\(165\) | −44147.9 | −1.62159 | ||||||||
\(166\) | −29030.7 | − | 10208.0i | −1.05351 | − | 0.370446i | ||||
\(167\) | 26980.3i | 0.967419i | 0.875229 | + | 0.483709i | \(0.160711\pi\) | ||||
−0.875229 | + | 0.483709i | \(0.839289\pi\) | |||||||
\(168\) | 31812.8 | − | 19786.8i | 1.12716 | − | 0.701063i | ||||
\(169\) | 73863.8 | 2.58618 | ||||||||
\(170\) | 3380.95 | − | 9615.11i | 0.116988 | − | 0.332703i | ||||
\(171\) | 11577.9i | 0.395948i | ||||||||
\(172\) | −29482.8 | + | 36739.7i | −0.996579 | + | 1.24188i | ||||
\(173\) | 14900.3 | 0.497855 | 0.248927 | − | 0.968522i | \(-0.419922\pi\) | ||||
0.248927 | + | 0.968522i | \(0.419922\pi\) | |||||||
\(174\) | 10004.9 | + | 3518.00i | 0.330456 | + | 0.116198i | ||||
\(175\) | − | 17342.4i | − | 0.566282i | ||||||
\(176\) | 54625.1 | − | 12117.5i | 1.76346 | − | 0.391191i | ||||
\(177\) | −89883.9 | −2.86903 | ||||||||
\(178\) | 8634.42 | − | 24555.5i | 0.272517 | − | 0.775013i | ||||
\(179\) | − | 9333.96i | − | 0.291313i | −0.989335 | − | 0.145656i | \(-0.953471\pi\) | ||
0.989335 | − | 0.145656i | \(-0.0465294\pi\) | |||||||
\(180\) | 23713.8 | + | 19029.8i | 0.731909 | + | 0.587341i | ||||
\(181\) | −2080.59 | −0.0635081 | −0.0317541 | − | 0.999496i | \(-0.510109\pi\) | ||||
−0.0317541 | + | 0.999496i | \(0.510109\pi\) | |||||||
\(182\) | 47576.1 | + | 16729.1i | 1.43630 | + | 0.505046i | ||||
\(183\) | − | 31868.6i | − | 0.951614i | ||||||
\(184\) | 10235.5 | + | 16456.5i | 0.302325 | + | 0.486073i | ||||
\(185\) | 19018.5 | 0.555689 | ||||||||
\(186\) | 14729.6 | − | 41889.8i | 0.425762 | − | 1.21083i | ||||
\(187\) | 40969.6i | 1.17160i | ||||||||
\(188\) | 20671.8 | − | 25760.0i | 0.584875 | − | 0.728836i | ||||
\(189\) | −34418.9 | −0.963549 | ||||||||
\(190\) | 4248.21 | + | 1493.79i | 0.117679 | + | 0.0413793i | ||||
\(191\) | − | 18006.0i | − | 0.493571i | −0.969070 | − | 0.246786i | \(-0.920626\pi\) | ||
0.969070 | − | 0.246786i | \(-0.0793744\pi\) | |||||||
\(192\) | −54592.1 | − | 26908.6i | −1.48090 | − | 0.729943i | ||||
\(193\) | 58313.6 | 1.56551 | 0.782754 | − | 0.622331i | \(-0.213814\pi\) | ||||
0.782754 | + | 0.622331i | \(0.213814\pi\) | |||||||
\(194\) | −11077.2 | + | 31502.7i | −0.294326 | + | 0.837036i | ||||
\(195\) | 64644.1i | 1.70004i | ||||||||
\(196\) | −10595.0 | − | 8502.23i | −0.275796 | − | 0.221320i | ||||
\(197\) | −73647.8 | −1.89770 | −0.948850 | − | 0.315727i | \(-0.897752\pi\) | ||||
−0.948850 | + | 0.315727i | \(0.897752\pi\) | |||||||
\(198\) | −115300. | − | 40542.7i | −2.94102 | − | 1.03415i | ||||
\(199\) | − | 73753.3i | − | 1.86241i | −0.364495 | − | 0.931206i | \(-0.618758\pi\) | ||
0.364495 | − | 0.931206i | \(-0.381242\pi\) | |||||||
\(200\) | −23924.0 | + | 14880.1i | −0.598099 | + | 0.372002i | ||||
\(201\) | −36758.0 | −0.909828 | ||||||||
\(202\) | −13300.1 | + | 37824.1i | −0.325950 | + | 0.926972i | ||||
\(203\) | 7029.25i | 0.170576i | ||||||||
\(204\) | 27892.2 | − | 34757.5i | 0.670227 | − | 0.835197i | ||||
\(205\) | 5862.08 | 0.139490 | ||||||||
\(206\) | 51964.2 | + | 18272.1i | 1.22453 | + | 0.430580i | ||||
\(207\) | − | 42332.3i | − | 0.987942i | ||||||
\(208\) | −17743.3 | − | 79985.6i | −0.410116 | − | 1.84878i | ||||
\(209\) | −18101.5 | −0.414401 | ||||||||
\(210\) | −10558.4 | + | 30027.1i | −0.239419 | + | 0.680886i | ||||
\(211\) | − | 23844.5i | − | 0.535578i | −0.963478 | − | 0.267789i | \(-0.913707\pi\) | ||
0.963478 | − | 0.267789i | \(-0.0862930\pi\) | |||||||
\(212\) | −9221.27 | − | 7399.87i | −0.205173 | − | 0.164646i | ||||
\(213\) | −20051.0 | −0.441953 | ||||||||
\(214\) | 20875.4 | + | 7340.40i | 0.455835 | + | 0.160285i | ||||
\(215\) | − | 40021.4i | − | 0.865795i | ||||||
\(216\) | 29532.1 | + | 47481.2i | 0.632975 | + | 1.01769i | ||||
\(217\) | 29431.0 | 0.625009 | ||||||||
\(218\) | −2306.35 | + | 6559.06i | −0.0485303 | + | 0.138016i | ||||
\(219\) | − | 14470.5i | − | 0.301715i | ||||||
\(220\) | −29752.2 | + | 37075.4i | −0.614714 | + | 0.766020i | ||||
\(221\) | 59990.4 | 1.22828 | ||||||||
\(222\) | 78449.3 | + | 27585.0i | 1.59178 | + | 0.559715i | ||||
\(223\) | 31740.4i | 0.638267i | 0.947710 | + | 0.319133i | \(0.103392\pi\) | ||||
−0.947710 | + | 0.319133i | \(0.896608\pi\) | |||||||
\(224\) | 4822.40 | − | 40051.2i | 0.0961096 | − | 0.798213i | ||||
\(225\) | 61541.5 | 1.21563 | ||||||||
\(226\) | −23063.2 | + | 65589.7i | −0.451547 | + | 1.28416i | ||||
\(227\) | 47727.0i | 0.926216i | 0.886302 | + | 0.463108i | \(0.153266\pi\) | ||||
−0.886302 | + | 0.463108i | \(0.846734\pi\) | |||||||
\(228\) | 15356.8 | + | 12323.5i | 0.295414 | + | 0.237063i | ||||
\(229\) | −77213.9 | −1.47240 | −0.736198 | − | 0.676766i | \(-0.763381\pi\) | ||||
−0.736198 | + | 0.676766i | \(0.763381\pi\) | |||||||
\(230\) | −15532.7 | − | 5461.75i | −0.293624 | − | 0.103247i | ||||
\(231\) | − | 127944.i | − | 2.39771i | ||||||
\(232\) | 9696.91 | − | 6031.24i | 0.180160 | − | 0.112055i | ||||
\(233\) | 30370.4 | 0.559420 | 0.279710 | − | 0.960085i | \(-0.409762\pi\) | ||||
0.279710 | + | 0.960085i | \(0.409762\pi\) | |||||||
\(234\) | −59365.3 | + | 168829.i | −1.08418 | + | 3.08330i | ||||
\(235\) | 28060.9i | 0.508120i | ||||||||
\(236\) | −60574.6 | + | 75484.5i | −1.08759 | + | 1.35529i | ||||
\(237\) | 68728.8 | 1.22361 | ||||||||
\(238\) | 27865.4 | + | 9798.28i | 0.491939 | + | 0.172980i | ||||
\(239\) | − | 19580.3i | − | 0.342786i | −0.985203 | − | 0.171393i | \(-0.945173\pi\) | ||
0.985203 | − | 0.171393i | \(-0.0548268\pi\) | |||||||
\(240\) | 50481.9 | − | 11198.4i | 0.876422 | − | 0.194417i | ||||
\(241\) | 28613.4 | 0.492646 | 0.246323 | − | 0.969188i | \(-0.420778\pi\) | ||||
0.246323 | + | 0.969188i | \(0.420778\pi\) | |||||||
\(242\) | 43959.7 | − | 125017.i | 0.750626 | − | 2.13471i | ||||
\(243\) | 46120.8i | 0.781060i | ||||||||
\(244\) | −26763.3 | − | 21476.9i | −0.449531 | − | 0.360738i | ||||
\(245\) | 11541.3 | 0.192276 | ||||||||
\(246\) | 24180.5 | + | 8502.56i | 0.399572 | + | 0.140501i | ||||
\(247\) | 26505.3i | 0.434449i | ||||||||
\(248\) | −25252.4 | − | 40600.3i | −0.410581 | − | 0.660125i | ||||
\(249\) | 114316. | 1.84378 | ||||||||
\(250\) | 19213.1 | − | 54640.4i | 0.307410 | − | 0.874247i | ||||
\(251\) | − | 46940.8i | − | 0.745080i | −0.928016 | − | 0.372540i | \(-0.878487\pi\) | ||
0.928016 | − | 0.372540i | \(-0.121513\pi\) | |||||||
\(252\) | −55150.1 | + | 68724.8i | −0.868451 | + | 1.08221i | ||||
\(253\) | 66184.4 | 1.03399 | ||||||||
\(254\) | 57909.7 | + | 20362.7i | 0.897602 | + | 0.315623i | ||||
\(255\) | 37862.2i | 0.582271i | ||||||||
\(256\) | −59388.6 | + | 27712.1i | −0.906198 | + | 0.422854i | ||||
\(257\) | 19559.5 | 0.296136 | 0.148068 | − | 0.988977i | \(-0.452695\pi\) | ||||
0.148068 | + | 0.988977i | \(0.452695\pi\) | |||||||
\(258\) | 58048.3 | − | 165084.i | 0.872068 | − | 2.48008i | ||||
\(259\) | 55117.1i | 0.821650i | ||||||||
\(260\) | 54288.1 | + | 43565.0i | 0.803079 | + | 0.644453i | ||||
\(261\) | −24944.1 | −0.366174 | ||||||||
\(262\) | 8396.96 | + | 2952.61i | 0.122326 | + | 0.0430134i | ||||
\(263\) | 64658.4i | 0.934789i | 0.884049 | + | 0.467394i | \(0.154807\pi\) | ||||
−0.884049 | + | 0.467394i | \(0.845193\pi\) | |||||||
\(264\) | −176500. | + | 109779.i | −2.53243 | + | 1.57511i | ||||
\(265\) | 10044.9 | 0.143039 | ||||||||
\(266\) | −4329.14 | + | 12311.7i | −0.0611840 | + | 0.174002i | ||||
\(267\) | 96694.1i | 1.35637i | ||||||||
\(268\) | −24772.0 | + | 30869.3i | −0.344898 | + | 0.429791i | ||||
\(269\) | 43854.6 | 0.606053 | 0.303026 | − | 0.952982i | \(-0.402003\pi\) | ||||
0.303026 | + | 0.952982i | \(0.402003\pi\) | |||||||
\(270\) | −44815.9 | − | 15758.6i | −0.614758 | − | 0.216167i | ||||
\(271\) | − | 87000.6i | − | 1.18463i | −0.805706 | − | 0.592316i | \(-0.798214\pi\) | ||
0.805706 | − | 0.592316i | \(-0.201786\pi\) | |||||||
\(272\) | −10392.3 | − | 46847.7i | −0.140466 | − | 0.633214i | ||||
\(273\) | −187344. | −2.51371 | ||||||||
\(274\) | 19253.6 | − | 54755.6i | 0.256455 | − | 0.729335i | ||||
\(275\) | 96216.9i | 1.27229i | ||||||||
\(276\) | −56149.0 | − | 45058.4i | −0.737096 | − | 0.591504i | ||||
\(277\) | −25935.4 | −0.338013 | −0.169006 | − | 0.985615i | \(-0.554056\pi\) | ||||
−0.169006 | + | 0.985615i | \(0.554056\pi\) | |||||||
\(278\) | −60615.3 | − | 21314.1i | −0.784319 | − | 0.275789i | ||||
\(279\) | 104439.i | 1.34170i | ||||||||
\(280\) | 18101.2 | + | 29102.8i | 0.230883 | + | 0.371209i | ||||
\(281\) | 95997.6 | 1.21576 | 0.607880 | − | 0.794029i | \(-0.292020\pi\) | ||||
0.607880 | + | 0.794029i | \(0.292020\pi\) | |||||||
\(282\) | −40700.5 | + | 115749.i | −0.511802 | + | 1.45552i | ||||
\(283\) | 92886.1i | 1.15979i | 0.814693 | + | 0.579893i | \(0.196906\pi\) | ||||
−0.814693 | + | 0.579893i | \(0.803094\pi\) | |||||||
\(284\) | −13512.8 | + | 16838.8i | −0.167536 | + | 0.208773i | ||||
\(285\) | −16728.5 | −0.205953 | ||||||||
\(286\) | −263956. | − | 92814.5i | −3.22700 | − | 1.13471i | ||||
\(287\) | 16988.8i | 0.206253i | ||||||||
\(288\) | 142126. | + | 17112.8i | 1.71352 | + | 0.206318i | ||||
\(289\) | −48384.5 | −0.579310 | ||||||||
\(290\) | −3218.31 | + | 9152.59i | −0.0382677 | + | 0.108830i | ||||
\(291\) | − | 124051.i | − | 1.46492i | ||||||
\(292\) | −12152.4 | − | 9752.00i | −0.142526 | − | 0.114374i | ||||
\(293\) | 37597.9 | 0.437954 | 0.218977 | − | 0.975730i | \(-0.429728\pi\) | ||||
0.218977 | + | 0.975730i | \(0.429728\pi\) | |||||||
\(294\) | 47606.9 | + | 16739.9i | 0.550776 | + | 0.193669i | ||||
\(295\) | − | 82226.9i | − | 0.944866i | ||||||
\(296\) | 76034.5 | − | 47291.6i | 0.867815 | − | 0.539759i | ||||
\(297\) | 190959. | 2.16485 | ||||||||
\(298\) | 23322.6 | − | 66327.3i | 0.262630 | − | 0.746896i | ||||
\(299\) | − | 96911.4i | − | 1.08401i | ||||||
\(300\) | 65504.5 | − | 81627.8i | 0.727828 | − | 0.906976i | ||||
\(301\) | 115985. | 1.28018 | ||||||||
\(302\) | 9943.95 | + | 3496.58i | 0.109030 | + | 0.0383380i | ||||
\(303\) | − | 148943.i | − | 1.62231i | ||||||
\(304\) | 20698.5 | − | 4591.57i | 0.223971 | − | 0.0496837i | ||||
\(305\) | 29153.8 | 0.313398 | ||||||||
\(306\) | −34770.3 | + | 98883.7i | −0.371335 | + | 1.05604i | ||||
\(307\) | − | 86419.0i | − | 0.916922i | −0.888714 | − | 0.458461i | \(-0.848401\pi\) | ||
0.888714 | − | 0.458461i | \(-0.151599\pi\) | |||||||
\(308\) | −107448. | − | 86224.3i | −1.13265 | − | 0.908926i | ||||
\(309\) | −204623. | −2.14308 | ||||||||
\(310\) | 38321.3 | + | 13474.9i | 0.398765 | + | 0.140217i | ||||
\(311\) | 138034.i | 1.42714i | 0.700586 | + | 0.713568i | \(0.252922\pi\) | ||||
−0.700586 | + | 0.713568i | \(0.747078\pi\) | |||||||
\(312\) | 160745. | + | 258443.i | 1.65131 | + | 2.65494i | ||||
\(313\) | 14528.5 | 0.148297 | 0.0741486 | − | 0.997247i | \(-0.476376\pi\) | ||||
0.0741486 | + | 0.997247i | \(0.476376\pi\) | |||||||
\(314\) | 40824.9 | − | 116102.i | 0.414062 | − | 1.17755i | ||||
\(315\) | − | 74863.4i | − | 0.754482i | ||||||
\(316\) | 46317.8 | − | 57718.4i | 0.463846 | − | 0.578017i | ||||
\(317\) | −167183. | −1.66369 | −0.831846 | − | 0.555007i | \(-0.812716\pi\) | ||||
−0.831846 | + | 0.555007i | \(0.812716\pi\) | |||||||
\(318\) | 41434.4 | + | 14569.5i | 0.409739 | + | 0.144076i | ||||
\(319\) | − | 38998.8i | − | 0.383240i | ||||||
\(320\) | 24616.3 | − | 49941.5i | 0.240394 | − | 0.487710i | ||||
\(321\) | −82202.8 | −0.797768 | ||||||||
\(322\) | 15828.6 | − | 45015.2i | 0.152662 | − | 0.434157i | ||||
\(323\) | 15524.2i | 0.148800i | ||||||||
\(324\) | −20699.3 | − | 16610.8i | −0.197182 | − | 0.158234i | ||||
\(325\) | 140887. | 1.33384 | ||||||||
\(326\) | −33773.6 | − | 11875.8i | −0.317791 | − | 0.111745i | ||||
\(327\) | − | 25828.1i | − | 0.241544i | ||||||
\(328\) | 23436.2 | − | 14576.7i | 0.217841 | − | 0.135492i | ||||
\(329\) | −81323.0 | −0.751314 | ||||||||
\(330\) | 58578.7 | − | 166593.i | 0.537913 | − | 1.52978i | ||||
\(331\) | − | 16289.6i | − | 0.148680i | −0.997233 | − | 0.0743401i | \(-0.976315\pi\) | ||
0.997233 | − | 0.0743401i | \(-0.0236850\pi\) | |||||||
\(332\) | 77040.1 | − | 96002.8i | 0.698942 | − | 0.870979i | ||||
\(333\) | −195590. | −1.76383 | ||||||||
\(334\) | −101811. | − | 35799.6i | −0.912642 | − | 0.320911i | ||||
\(335\) | − | 33626.7i | − | 0.299636i | ||||||
\(336\) | 32454.0 | + | 146301.i | 0.287468 | + | 1.29589i | ||||
\(337\) | 78114.3 | 0.687814 | 0.343907 | − | 0.939004i | \(-0.388250\pi\) | ||||
0.343907 | + | 0.939004i | \(0.388250\pi\) | |||||||
\(338\) | −98008.1 | + | 278726.i | −0.857884 | + | 2.43974i | ||||
\(339\) | − | 258278.i | − | 2.24744i | ||||||
\(340\) | 31796.6 | + | 25516.1i | 0.275058 | + | 0.220728i | ||||
\(341\) | −163286. | −1.40423 | ||||||||
\(342\) | −43689.4 | − | 15362.4i | −0.373528 | − | 0.131343i | ||||
\(343\) | 128035.i | 1.08828i | ||||||||
\(344\) | −99517.6 | − | 160003.i | −0.840975 | − | 1.35210i | ||||
\(345\) | 61164.4 | 0.513879 | ||||||||
\(346\) | −19770.8 | + | 56226.5i | −0.165148 | + | 0.469665i | ||||
\(347\) | 10081.3i | 0.0837257i | 0.999123 | + | 0.0418629i | \(0.0133293\pi\) | ||||
−0.999123 | + | 0.0418629i | \(0.986671\pi\) | |||||||
\(348\) | −26550.4 | + | 33085.6i | −0.219237 | + | 0.273200i | ||||
\(349\) | 233924. | 1.92054 | 0.960272 | − | 0.279065i | \(-0.0900246\pi\) | ||||
0.960272 | + | 0.279065i | \(0.0900246\pi\) | |||||||
\(350\) | 65441.7 | + | 23011.2i | 0.534218 | + | 0.187846i | ||||
\(351\) | − | 279614.i | − | 2.26958i | ||||||
\(352\) | −26755.0 | + | 222207.i | −0.215934 | + | 1.79338i | ||||
\(353\) | −246812. | −1.98070 | −0.990348 | − | 0.138605i | \(-0.955738\pi\) | ||||
−0.990348 | + | 0.138605i | \(0.955738\pi\) | |||||||
\(354\) | 119265. | − | 339178.i | 0.951712 | − | 2.70658i | ||||
\(355\) | − | 18342.9i | − | 0.145550i | ||||||
\(356\) | 81203.7 | + | 65164.2i | 0.640731 | + | 0.514173i | ||||
\(357\) | −109728. | −0.860955 | ||||||||
\(358\) | 35221.8 | + | 12385.0i | 0.274818 | + | 0.0966340i | ||||
\(359\) | − | 44985.4i | − | 0.349046i | −0.984653 | − | 0.174523i | \(-0.944162\pi\) | ||
0.984653 | − | 0.174523i | \(-0.0558383\pi\) | |||||||
\(360\) | −103275. | + | 64234.3i | −0.796873 | + | 0.495635i | ||||
\(361\) | −6859.00 | −0.0526316 | ||||||||
\(362\) | 2760.68 | − | 7851.13i | 0.0210668 | − | 0.0599122i | ||||
\(363\) | 492291.i | 3.73601i | ||||||||
\(364\) | −126255. | + | 157332.i | −0.952898 | + | 1.18744i | ||||
\(365\) | 13237.8 | 0.0993645 | ||||||||
\(366\) | 120257. | + | 42285.7i | 0.897732 | + | 0.315668i | ||||
\(367\) | 182523.i | 1.35514i | 0.735456 | + | 0.677572i | \(0.236968\pi\) | ||||
−0.735456 | + | 0.677572i | \(0.763032\pi\) | |||||||
\(368\) | −75680.0 | + | 16788.2i | −0.558838 | + | 0.123967i | ||||
\(369\) | −60286.8 | −0.442761 | ||||||||
\(370\) | −25235.1 | + | 71766.4i | −0.184333 | + | 0.524225i | ||||
\(371\) | 29111.1i | 0.211500i | ||||||||
\(372\) | 138527. | + | 111165.i | 1.00103 | + | 0.803308i | ||||
\(373\) | 29377.1 | 0.211150 | 0.105575 | − | 0.994411i | \(-0.466332\pi\) | ||||
0.105575 | + | 0.994411i | \(0.466332\pi\) | |||||||
\(374\) | −154599. | − | 54361.6i | −1.10526 | − | 0.388642i | ||||
\(375\) | 215162.i | 1.53004i | ||||||||
\(376\) | 69776.7 | + | 112186.i | 0.493554 | + | 0.793527i | ||||
\(377\) | −57104.6 | −0.401780 | ||||||||
\(378\) | 45669.6 | − | 129880.i | 0.319627 | − | 0.908991i | ||||
\(379\) | − | 212788.i | − | 1.48139i | −0.671841 | − | 0.740695i | \(-0.734496\pi\) | ||
0.671841 | − | 0.740695i | \(-0.265504\pi\) | |||||||
\(380\) | −11273.7 | + | 14048.6i | −0.0780726 | + | 0.0972894i | ||||
\(381\) | −228036. | −1.57091 | ||||||||
\(382\) | 67945.8 | + | 23891.7i | 0.465625 | + | 0.163727i | ||||
\(383\) | − | 34207.1i | − | 0.233194i | −0.993179 | − | 0.116597i | \(-0.962801\pi\) | ||
0.993179 | − | 0.116597i | \(-0.0371987\pi\) | |||||||
\(384\) | 173977. | − | 170300.i | 1.17986 | − | 1.15492i | ||||
\(385\) | 117045. | 0.789645 | ||||||||
\(386\) | −77374.9 | + | 220047.i | −0.519309 | + | 1.47687i | ||||
\(387\) | 411587.i | 2.74815i | ||||||||
\(388\) | −104178. | − | 83600.3i | −0.692008 | − | 0.555321i | ||||
\(389\) | −61528.8 | −0.406611 | −0.203305 | − | 0.979115i | \(-0.565168\pi\) | ||||
−0.203305 | + | 0.979115i | \(0.565168\pi\) | |||||||
\(390\) | −243936. | − | 85774.7i | −1.60378 | − | 0.563936i | ||||
\(391\) | − | 56761.2i | − | 0.371277i | ||||||
\(392\) | 46141.5 | − | 28698.8i | 0.300275 | − | 0.186764i | ||||
\(393\) | −33065.4 | −0.214086 | ||||||||
\(394\) | 97721.5 | − | 277911.i | 0.629503 | − | 1.79025i | ||||
\(395\) | 62874.0i | 0.402974i | ||||||||
\(396\) | 305977. | − | 381290.i | 1.95119 | − | 2.43145i | ||||
\(397\) | 193437. | 1.22732 | 0.613661 | − | 0.789570i | \(-0.289696\pi\) | ||||
0.613661 | + | 0.789570i | \(0.289696\pi\) | |||||||
\(398\) | 278309. | + | 97861.5i | 1.75696 | + | 0.617797i | ||||
\(399\) | − | 48480.6i | − | 0.304525i | ||||||
\(400\) | −24406.1 | − | 110021.i | −0.152538 | − | 0.687634i | ||||
\(401\) | −264301. | −1.64365 | −0.821826 | − | 0.569739i | \(-0.807044\pi\) | ||||
−0.821826 | + | 0.569739i | \(0.807044\pi\) | |||||||
\(402\) | 48773.3 | − | 138707.i | 0.301807 | − | 0.858312i | ||||
\(403\) | 239093.i | 1.47217i | ||||||||
\(404\) | −125082. | − | 100376.i | −0.766361 | − | 0.614988i | ||||
\(405\) | 22548.3 | 0.137468 | ||||||||
\(406\) | −26525.0 | − | 9326.95i | −0.160917 | − | 0.0565832i | ||||
\(407\) | − | 305794.i | − | 1.84604i | ||||||
\(408\) | 94148.6 | + | 151370.i | 0.565579 | + | 0.909328i | ||||
\(409\) | −263755. | −1.57672 | −0.788358 | − | 0.615216i | \(-0.789069\pi\) | ||||
−0.788358 | + | 0.615216i | \(0.789069\pi\) | |||||||
\(410\) | −7778.25 | + | 22120.6i | −0.0462716 | + | 0.131592i | ||||
\(411\) | 215615.i | 1.27643i | ||||||||
\(412\) | −137900. | + | 171843.i | −0.812400 | + | 1.01236i | ||||
\(413\) | 238301. | 1.39709 | ||||||||
\(414\) | 159742. | + | 56169.7i | 0.932003 | + | 0.327719i | ||||
\(415\) | 104578.i | 0.607217i | ||||||||
\(416\) | 325370. | + | 39176.4i | 1.88014 | + | 0.226380i | ||||
\(417\) | 238690. | 1.37266 | ||||||||
\(418\) | 24018.4 | − | 68306.1i | 0.137465 | − | 0.390937i | ||||
\(419\) | 61608.5i | 0.350924i | 0.984486 | + | 0.175462i | \(0.0561419\pi\) | ||||
−0.984486 | + | 0.175462i | \(0.943858\pi\) | |||||||
\(420\) | −99297.9 | − | 79684.4i | −0.562913 | − | 0.451726i | ||||
\(421\) | −109849. | −0.619773 | −0.309886 | − | 0.950774i | \(-0.600291\pi\) | ||||
−0.309886 | + | 0.950774i | \(0.600291\pi\) | |||||||
\(422\) | 89977.4 | + | 31638.7i | 0.505253 | + | 0.177661i | ||||
\(423\) | − | 288584.i | − | 1.61284i | ||||||
\(424\) | 40159.0 | − | 24977.9i | 0.223383 | − | 0.138939i | ||||
\(425\) | 82517.7 | 0.456845 | ||||||||
\(426\) | 26605.2 | − | 75662.7i | 0.146604 | − | 0.416929i | ||||
\(427\) | 84490.3i | 0.463394i | ||||||||
\(428\) | −55398.2 | + | 69033.9i | −0.302418 | + | 0.376855i | ||||
\(429\) | 1.03940e6 | 5.64766 | ||||||||
\(430\) | 151021. | + | 53103.4i | 0.816772 | + | 0.287200i | ||||
\(431\) | − | 53327.9i | − | 0.287078i | −0.989645 | − | 0.143539i | \(-0.954152\pi\) | ||
0.989645 | − | 0.143539i | \(-0.0458482\pi\) | |||||||
\(432\) | −218356. | + | 48438.2i | −1.17003 | + | 0.259549i | ||||
\(433\) | −9322.52 | −0.0497230 | −0.0248615 | − | 0.999691i | \(-0.507914\pi\) | ||||
−0.0248615 | + | 0.999691i | \(0.507914\pi\) | |||||||
\(434\) | −39051.3 | + | 111058.i | −0.207327 | + | 0.589620i | ||||
\(435\) | − | 36040.9i | − | 0.190466i | ||||||
\(436\) | −21690.4 | − | 17406.1i | −0.114103 | − | 0.0915648i | ||||
\(437\) | 25078.6 | 0.131323 | ||||||||
\(438\) | 54604.8 | + | 19200.6i | 0.284631 | + | 0.100085i | ||||
\(439\) | − | 93236.2i | − | 0.483788i | −0.970303 | − | 0.241894i | \(-0.922231\pi\) | ||
0.970303 | − | 0.241894i | \(-0.0777687\pi\) | |||||||
\(440\) | −100427. | − | 161465.i | −0.518734 | − | 0.834011i | ||||
\(441\) | −118693. | −0.610308 | ||||||||
\(442\) | −79599.8 | + | 226374.i | −0.407443 | + | 1.15873i | ||||
\(443\) | − | 240412.i | − | 1.22503i | −0.790457 | − | 0.612517i | \(-0.790157\pi\) | ||
0.790457 | − | 0.612517i | \(-0.209843\pi\) | |||||||
\(444\) | −208185. | + | 259427.i | −1.05605 | + | 1.31598i | ||||
\(445\) | −88457.0 | −0.446696 | ||||||||
\(446\) | −119773. | − | 42115.5i | −0.602127 | − | 0.211725i | ||||
\(447\) | 261182.i | 1.30716i | ||||||||
\(448\) | 144735. | + | 71340.3i | 0.721136 | + | 0.355450i | ||||
\(449\) | −16724.7 | −0.0829595 | −0.0414797 | − | 0.999139i | \(-0.513207\pi\) | ||||
−0.0414797 | + | 0.999139i | \(0.513207\pi\) | |||||||
\(450\) | −81657.9 | + | 232227.i | −0.403249 | + | 1.14680i | ||||
\(451\) | − | 94255.3i | − | 0.463396i | ||||||
\(452\) | −216902. | − | 174059.i | −1.06166 | − | 0.851960i | ||||
\(453\) | −39157.1 | −0.190816 | ||||||||
\(454\) | −180098. | − | 63327.8i | −0.873772 | − | 0.307243i | ||||
\(455\) | − | 171385.i | − | 0.827847i | ||||||
\(456\) | −66879.4 | + | 41597.3i | −0.321635 | + | 0.200049i | ||||
\(457\) | 196032. | 0.938630 | 0.469315 | − | 0.883031i | \(-0.344501\pi\) | ||||
0.469315 | + | 0.883031i | \(0.344501\pi\) | |||||||
\(458\) | 102453. | − | 291368.i | 0.488422 | − | 1.38903i | ||||
\(459\) | − | 163770.i | − | 0.777339i | ||||||
\(460\) | 41220.0 | − | 51365.9i | 0.194801 | − | 0.242750i | ||||
\(461\) | −185469. | −0.872710 | −0.436355 | − | 0.899774i | \(-0.643731\pi\) | ||||
−0.436355 | + | 0.899774i | \(0.643731\pi\) | |||||||
\(462\) | 482800. | + | 169766.i | 2.26195 | + | 0.795366i | ||||
\(463\) | − | 423839.i | − | 1.97715i | −0.150743 | − | 0.988573i | \(-0.548167\pi\) | ||
0.150743 | − | 0.988573i | \(-0.451833\pi\) | |||||||
\(464\) | 9892.35 | + | 44594.1i | 0.0459477 | + | 0.207129i | ||||
\(465\) | −150901. | −0.697888 | ||||||||
\(466\) | −40297.7 | + | 114603.i | −0.185570 | + | 0.527745i | ||||
\(467\) | 287771.i | 1.31951i | 0.751480 | + | 0.659756i | \(0.229340\pi\) | ||||
−0.751480 | + | 0.659756i | \(0.770660\pi\) | |||||||
\(468\) | −558310. | − | 448031.i | −2.54908 | − | 2.04558i | ||||
\(469\) | 97453.0 | 0.443047 | ||||||||
\(470\) | −105888. | − | 37233.4i | −0.479349 | − | 0.168553i | ||||
\(471\) | 457185.i | 2.06087i | ||||||||
\(472\) | −204467. | − | 328738.i | −0.917780 | − | 1.47559i | ||||
\(473\) | −643496. | −2.87623 | ||||||||
\(474\) | −91194.6 | + | 259349.i | −0.405894 | + | 1.15432i | ||||
\(475\) | 36458.5i | 0.161589i | ||||||||
\(476\) | −73947.9 | + | 92149.4i | −0.326371 | + | 0.406704i | ||||
\(477\) | −103304. | −0.454026 | ||||||||
\(478\) | 73886.5 | + | 25980.6i | 0.323377 | + | 0.113709i | ||||
\(479\) | 112548.i | 0.490531i | 0.969456 | + | 0.245265i | \(0.0788751\pi\) | ||||
−0.969456 | + | 0.245265i | \(0.921125\pi\) | |||||||
\(480\) | −24725.7 | + | 205353.i | −0.107316 | + | 0.891289i | ||||
\(481\) | −447763. | −1.93534 | ||||||||
\(482\) | −37966.4 | + | 107973.i | −0.163420 | + | 0.464752i | ||||
\(483\) | 177260.i | 0.759829i | ||||||||
\(484\) | 413425. | + | 331765.i | 1.76484 | + | 1.41625i | ||||
\(485\) | 113483. | 0.482445 | ||||||||
\(486\) | −174038. | − | 61196.6i | −0.736835 | − | 0.259092i | ||||
\(487\) | − | 310805.i | − | 1.31048i | −0.755422 | − | 0.655239i | \(-0.772568\pi\) | ||
0.755422 | − | 0.655239i | \(-0.227432\pi\) | |||||||
\(488\) | 116555. | − | 72494.3i | 0.489431 | − | 0.304414i | ||||
\(489\) | 132993. | 0.556174 | ||||||||
\(490\) | −15313.9 | + | 43551.4i | −0.0637814 | + | 0.181389i | ||||
\(491\) | − | 150980.i | − | 0.626261i | −0.949710 | − | 0.313130i | \(-0.898622\pi\) | ||
0.949710 | − | 0.313130i | \(-0.101378\pi\) | |||||||
\(492\) | −64169.1 | + | 79963.6i | −0.265091 | + | 0.330341i | ||||
\(493\) | −33446.3 | −0.137611 | ||||||||
\(494\) | −100018. | − | 35169.3i | −0.409850 | − | 0.144115i | ||||
\(495\) | 415348.i | 1.69513i | ||||||||
\(496\) | 186713. | − | 41418.7i | 0.758945 | − | 0.168358i | ||||
\(497\) | 53159.3 | 0.215212 | ||||||||
\(498\) | −151683. | + | 431374.i | −0.611617 | + | 1.73938i | ||||
\(499\) | − | 338996.i | − | 1.36142i | −0.732552 | − | 0.680711i | \(-0.761671\pi\) | ||
0.732552 | − | 0.680711i | \(-0.238329\pi\) | |||||||
\(500\) | 180693. | + | 145002.i | 0.722771 | + | 0.580008i | ||||
\(501\) | 400908. | 1.59724 | ||||||||
\(502\) | 177132. | + | 62284.6i | 0.702892 | + | 0.247157i | ||||
\(503\) | − | 143798.i | − | 0.568353i | −0.958772 | − | 0.284177i | \(-0.908280\pi\) | ||
0.958772 | − | 0.284177i | \(-0.0917202\pi\) | |||||||
\(504\) | −186156. | − | 299299.i | −0.732853 | − | 1.17827i | ||||
\(505\) | 136255. | 0.534281 | ||||||||
\(506\) | −87818.4 | + | 249748.i | −0.342993 | + | 0.975439i | ||||
\(507\) | − | 1.09756e6i | − | 4.26985i | ||||||
\(508\) | −153678. | + | 191504.i | −0.595503 | + | 0.742080i | ||||
\(509\) | 100838. | 0.389215 | 0.194608 | − | 0.980881i | \(-0.437657\pi\) | ||||
0.194608 | + | 0.980881i | \(0.437657\pi\) | |||||||
\(510\) | −142873. | − | 50238.4i | −0.549302 | − | 0.193150i | ||||
\(511\) | 38364.4i | 0.146922i | ||||||||
\(512\) | −25770.8 | − | 260874.i | −0.0983079 | − | 0.995156i | ||||
\(513\) | 72358.1 | 0.274949 | ||||||||
\(514\) | −25953.0 | + | 73807.9i | −0.0982338 | + | 0.279368i | ||||
\(515\) | − | 187192.i | − | 0.705786i | ||||||
\(516\) | 545924. | + | 438092.i | 2.05037 | + | 1.64538i | ||||
\(517\) | 451186. | 1.68801 | ||||||||
\(518\) | −207985. | − | 73133.6i | −0.775127 | − | 0.272557i | ||||
\(519\) | − | 221407.i | − | 0.821973i | ||||||
\(520\) | −236427. | + | 147052.i | −0.874360 | + | 0.543830i | ||||
\(521\) | 303656. | 1.11868 | 0.559340 | − | 0.828938i | \(-0.311055\pi\) | ||||
0.559340 | + | 0.828938i | \(0.311055\pi\) | |||||||
\(522\) | 33097.8 | − | 94127.0i | 0.121467 | − | 0.345440i | ||||
\(523\) | − | 68929.8i | − | 0.252002i | −0.992030 | − | 0.126001i | \(-0.959786\pi\) | ||
0.992030 | − | 0.126001i | \(-0.0402142\pi\) | |||||||
\(524\) | −22283.4 | + | 27768.3i | −0.0811558 | + | 0.101132i | ||||
\(525\) | −257695. | −0.934948 | ||||||||
\(526\) | −243989. | − | 85793.6i | −0.881859 | − | 0.310087i | ||||
\(527\) | 140037.i | 0.504223i | ||||||||
\(528\) | −180058. | − | 811688.i | −0.645868 | − | 2.91153i | ||||
\(529\) | 188146. | 0.672333 | ||||||||
\(530\) | −13328.4 | + | 37904.7i | −0.0474489 | + | 0.134940i | ||||
\(531\) | 845638.i | 2.99913i | ||||||||
\(532\) | −40714.0 | − | 32672.1i | −0.143854 | − | 0.115439i | ||||
\(533\) | −138015. | −0.485815 | ||||||||
\(534\) | −364877. | − | 128301.i | −1.27957 | − | 0.449933i | ||||
\(535\) | − | 75200.2i | − | 0.262731i | ||||||
\(536\) | −83616.5 | − | 134437.i | −0.291047 | − | 0.467939i | ||||
\(537\) | −138696. | −0.480966 | ||||||||
\(538\) | −58189.6 | + | 165486.i | −0.201039 | + | 0.571737i | ||||
\(539\) | − | 185571.i | − | 0.638752i | ||||||
\(540\) | 118930. | − | 148204.i | 0.407854 | − | 0.508243i | ||||
\(541\) | −230190. | −0.786488 | −0.393244 | − | 0.919434i | \(-0.628647\pi\) | ||||
−0.393244 | + | 0.919434i | \(0.628647\pi\) | |||||||
\(542\) | 328298. | + | 115439.i | 1.11756 | + | 0.392965i | ||||
\(543\) | 30916.0i | 0.104854i | ||||||||
\(544\) | 190570. | + | 22945.7i | 0.643955 | + | 0.0775360i | ||||
\(545\) | 23627.9 | 0.0795485 | ||||||||
\(546\) | 248583. | − | 706946.i | 0.833845 | − | 2.37138i | ||||
\(547\) | − | 144821.i | − | 0.484013i | −0.970275 | − | 0.242007i | \(-0.922194\pi\) | ||
0.970275 | − | 0.242007i | \(-0.0778056\pi\) | |||||||
\(548\) | 181074. | + | 145308.i | 0.602968 | + | 0.483869i | ||||
\(549\) | −299823. | −0.994766 | ||||||||
\(550\) | −363076. | − | 127668.i | −1.20025 | − | 0.422042i | ||||
\(551\) | − | 14777.4i | − | 0.0486739i | ||||||
\(552\) | 244531. | − | 152092.i | 0.802520 | − | 0.499148i | ||||
\(553\) | −182214. | −0.595843 | ||||||||
\(554\) | 34413.0 | − | 97867.5i | 0.112125 | − | 0.318874i | ||||
\(555\) | − | 282600.i | − | 0.917459i | ||||||
\(556\) | 160858. | − | 200452.i | 0.520347 | − | 0.648425i | ||||
\(557\) | 434744. | 1.40128 | 0.700638 | − | 0.713517i | \(-0.252899\pi\) | ||||
0.700638 | + | 0.713517i | \(0.252899\pi\) | |||||||
\(558\) | −394104. | − | 138578.i | −1.26573 | − | 0.445068i | ||||
\(559\) | 942247.i | 3.01537i | ||||||||
\(560\) | −133838. | + | 29689.4i | −0.426779 | + | 0.0946728i | ||||
\(561\) | 608779. | 1.93434 | ||||||||
\(562\) | −127377. | + | 362248.i | −0.403291 | + | 1.14692i | ||||
\(563\) | 321746.i | 1.01507i | 0.861631 | + | 0.507536i | \(0.169444\pi\) | ||||
−0.861631 | + | 0.507536i | \(0.830556\pi\) | |||||||
\(564\) | −382774. | − | 307168.i | −1.20333 | − | 0.965645i | ||||
\(565\) | 236276. | 0.740155 | ||||||||
\(566\) | −350507. | − | 123248.i | −1.09412 | − | 0.384723i | ||||
\(567\) | 65346.8i | 0.203263i | ||||||||
\(568\) | −45611.7 | − | 73333.7i | −0.141377 | − | 0.227304i | ||||
\(569\) | 371599. | 1.14776 | 0.573879 | − | 0.818940i | \(-0.305438\pi\) | ||||
0.573879 | + | 0.818940i | \(0.305438\pi\) | |||||||
\(570\) | 22196.6 | − | 63125.2i | 0.0683184 | − | 0.194291i | ||||
\(571\) | 383652.i | 1.17670i | 0.808606 | + | 0.588350i | \(0.200222\pi\) | ||||
−0.808606 | + | 0.588350i | \(0.799778\pi\) | |||||||
\(572\) | 700474. | − | 872888.i | 2.14092 | − | 2.66788i | ||||
\(573\) | −267555. | −0.814901 | ||||||||
\(574\) | −64107.5 | − | 22542.0i | −0.194574 | − | 0.0684179i | ||||
\(575\) | − | 133303.i | − | 0.403185i | ||||||
\(576\) | −253159. | + | 513608.i | −0.763043 | + | 1.54806i | ||||
\(577\) | −285078. | −0.856273 | −0.428136 | − | 0.903714i | \(-0.640830\pi\) | ||||
−0.428136 | + | 0.903714i | \(0.640830\pi\) | |||||||
\(578\) | 64200.3 | − | 182580.i | 0.192168 | − | 0.546508i | ||||
\(579\) | − | 866497.i | − | 2.58470i | ||||||
\(580\) | −30267.1 | − | 24288.7i | −0.0899736 | − | 0.0722018i | ||||
\(581\) | −303076. | −0.897841 | ||||||||
\(582\) | 468107. | + | 164600.i | 1.38197 | + | 0.485940i | ||||
\(583\) | − | 161511.i | − | 0.475186i | ||||||
\(584\) | 52924.0 | − | 32917.4i | 0.155177 | − | 0.0965161i | ||||
\(585\) | 608179. | 1.77713 | ||||||||
\(586\) | −49887.8 | + | 141876.i | −0.145278 | + | 0.413157i | ||||
\(587\) | 297282.i | 0.862766i | 0.902169 | + | 0.431383i | \(0.141974\pi\) | ||||
−0.902169 | + | 0.431383i | \(0.858026\pi\) | |||||||
\(588\) | −126337. | + | 157433.i | −0.365406 | + | 0.455347i | ||||
\(589\) | −61872.2 | −0.178347 | ||||||||
\(590\) | 310284. | + | 109105.i | 0.891366 | + | 0.313430i | ||||
\(591\) | 1.09435e6i | 3.13316i | ||||||||
\(592\) | 77567.0 | + | 349667.i | 0.221327 | + | 0.997726i | ||||
\(593\) | 523771. | 1.48947 | 0.744736 | − | 0.667360i | \(-0.232576\pi\) | ||||
0.744736 | + | 0.667360i | \(0.232576\pi\) | |||||||
\(594\) | −253379. | + | 720586.i | −0.718120 | + | 2.04227i | ||||
\(595\) | − | 100380.i | − | 0.283541i | ||||||
\(596\) | 219341. | + | 176016.i | 0.617486 | + | 0.495519i | ||||
\(597\) | −1.09592e6 | −3.07489 | ||||||||
\(598\) | 365696. | + | 128589.i | 1.02263 | + | 0.359586i | ||||
\(599\) | 446927.i | 1.24561i | 0.782376 | + | 0.622806i | \(0.214007\pi\) | ||||
−0.782376 | + | 0.622806i | \(0.785993\pi\) | |||||||
\(600\) | 221107. | + | 355492.i | 0.614187 | + | 0.987478i | ||||
\(601\) | −192111. | −0.531868 | −0.265934 | − | 0.963991i | \(-0.585680\pi\) | ||||
−0.265934 | + | 0.963991i | \(0.585680\pi\) | |||||||
\(602\) | −153898. | + | 437672.i | −0.424659 | + | 1.20769i | ||||
\(603\) | 345823.i | 0.951085i | ||||||||
\(604\) | −26388.8 | + | 32884.1i | −0.0723344 | + | 0.0901388i | ||||
\(605\) | −450354. | −1.23039 | ||||||||
\(606\) | 562039. | + | 197629.i | 1.53046 | + | 0.538153i | ||||
\(607\) | − | 151586.i | − | 0.411416i | −0.978613 | − | 0.205708i | \(-0.934050\pi\) | ||
0.978613 | − | 0.205708i | \(-0.0659497\pi\) | |||||||
\(608\) | −10138.0 | + | 84198.6i | −0.0274249 | + | 0.227771i | ||||
\(609\) | 104450. | 0.281625 | ||||||||
\(610\) | −38683.5 | + | 110012.i | −0.103960 | + | 0.295653i | ||||
\(611\) | − | 660656.i | − | 1.76967i | ||||||
\(612\) | −327003. | − | 262413.i | −0.873069 | − | 0.700619i | ||||
\(613\) | 458529. | 1.22024 | 0.610121 | − | 0.792308i | \(-0.291121\pi\) | ||||
0.610121 | + | 0.792308i | \(0.291121\pi\) | |||||||
\(614\) | 326103. | + | 114667.i | 0.865004 | + | 0.304160i | ||||
\(615\) | − | 87106.2i | − | 0.230303i | ||||||
\(616\) | 467938. | − | 291046.i | 1.23318 | − | 0.767008i | ||||
\(617\) | 555722. | 1.45978 | 0.729890 | − | 0.683565i | \(-0.239571\pi\) | ||||
0.729890 | + | 0.683565i | \(0.239571\pi\) | |||||||
\(618\) | 271510. | − | 772149.i | 0.710900 | − | 2.02173i | ||||
\(619\) | − | 25609.4i | − | 0.0668373i | −0.999441 | − | 0.0334186i | \(-0.989361\pi\) | ||
0.999441 | − | 0.0334186i | \(-0.0106395\pi\) | |||||||
\(620\) | −101695. | + | 126726.i | −0.264556 | + | 0.329673i | ||||
\(621\) | −264563. | −0.686034 | ||||||||
\(622\) | −520873. | − | 183154.i | −1.34633 | − | 0.473408i | ||||
\(623\) | − | 256356.i | − | 0.660492i | ||||||
\(624\) | −1.18853e6 | + | 263652.i | −3.05239 | + | 0.677114i | ||||
\(625\) | 78303.6 | 0.200457 | ||||||||
\(626\) | −19277.6 | + | 54823.6i | −0.0491930 | + | 0.139900i | ||||
\(627\) | 268974.i | 0.684188i | ||||||||
\(628\) | 383944. | + | 308106.i | 0.973527 | + | 0.781234i | ||||
\(629\) | −262256. | −0.662863 | ||||||||
\(630\) | 282498. | + | 99334.5i | 0.711762 | + | 0.250276i | ||||
\(631\) | 142715.i | 0.358435i | 0.983809 | + | 0.179218i | \(0.0573567\pi\) | ||||
−0.983809 | + | 0.179218i | \(0.942643\pi\) | |||||||
\(632\) | 156343. | + | 251366.i | 0.391422 | + | 0.629321i | ||||
\(633\) | −354311. | −0.884255 | ||||||||
\(634\) | 221831. | − | 630866.i | 0.551878 | − | 1.56949i | ||||
\(635\) | − | 208610.i | − | 0.517353i | ||||||
\(636\) | −109957. | + | 137021.i | −0.271836 | + | 0.338746i | ||||
\(637\) | −271725. | −0.669654 | ||||||||
\(638\) | 147163. | + | 51746.6i | 0.361540 | + | 0.127128i | ||||
\(639\) | 188642.i | 0.461994i | ||||||||
\(640\) | 155792. | + | 159156.i | 0.380352 | + | 0.388565i | ||||
\(641\) | −212139. | −0.516304 | −0.258152 | − | 0.966104i | \(-0.583113\pi\) | ||||
−0.258152 | + | 0.966104i | \(0.583113\pi\) | |||||||
\(642\) | 109073. | − | 310193.i | 0.264635 | − | 0.752597i | ||||
\(643\) | 559342.i | 1.35287i | 0.736503 | + | 0.676434i | \(0.236476\pi\) | ||||
−0.736503 | + | 0.676434i | \(0.763524\pi\) | |||||||
\(644\) | 148863. | + | 119459.i | 0.358934 | + | 0.288036i | ||||
\(645\) | −594688. | −1.42945 | ||||||||
\(646\) | −58580.8 | − | 20598.7i | −0.140375 | − | 0.0493599i | ||||
\(647\) | 49429.5i | 0.118080i | 0.998256 | + | 0.0590402i | \(0.0188040\pi\) | ||||
−0.998256 | + | 0.0590402i | \(0.981196\pi\) | |||||||
\(648\) | 90146.4 | − | 56068.8i | 0.214683 | − | 0.133528i | ||||
\(649\) | −1.32211e6 | −3.13891 | ||||||||
\(650\) | −186939. | + | 531639.i | −0.442460 | + | 1.25832i | ||||
\(651\) | − | 437323.i | − | 1.03191i | ||||||
\(652\) | 89626.7 | − | 111687.i | 0.210835 | − | 0.262730i | ||||
\(653\) | 559429. | 1.31195 | 0.655976 | − | 0.754781i | \(-0.272257\pi\) | ||||
0.655976 | + | 0.754781i | \(0.272257\pi\) | |||||||
\(654\) | 97462.7 | + | 34270.7i | 0.227868 | + | 0.0801249i | ||||
\(655\) | − | 30248.6i | − | 0.0705055i | ||||||
\(656\) | 23908.6 | + | 107778.i | 0.0555579 | + | 0.250452i | ||||
\(657\) | −136141. | −0.315396 | ||||||||
\(658\) | 107905. | − | 306873.i | 0.249225 | − | 0.708773i | ||||
\(659\) | 101898.i | 0.234636i | 0.993094 | + | 0.117318i | \(0.0374297\pi\) | ||||
−0.993094 | + | 0.117318i | \(0.962570\pi\) | |||||||
\(660\) | 550913. | + | 442095.i | 1.26472 | + | 1.01491i | ||||
\(661\) | 298743. | 0.683746 | 0.341873 | − | 0.939746i | \(-0.388939\pi\) | ||||
0.341873 | + | 0.939746i | \(0.388939\pi\) | |||||||
\(662\) | 61468.9 | + | 21614.2i | 0.140262 | + | 0.0493201i | ||||
\(663\) | − | 891413.i | − | 2.02792i | ||||||
\(664\) | 260045. | + | 418096.i | 0.589810 | + | 0.948286i | ||||
\(665\) | 44350.7 | 0.100290 | ||||||||
\(666\) | 259523. | − | 738060.i | 0.585096 | − | 1.66396i | ||||
\(667\) | 54030.7i | 0.121448i | ||||||||
\(668\) | 270180. | − | 336682.i | 0.605481 | − | 0.754514i | ||||
\(669\) | 471638. | 1.05380 | ||||||||
\(670\) | 126891. | + | 44618.4i | 0.282670 | + | 0.0993950i | ||||
\(671\) | − | 468758.i | − | 1.04113i | ||||||
\(672\) | −595131. | − | 71657.2i | −1.31787 | − | 0.158680i | ||||
\(673\) | −537612. | −1.18697 | −0.593484 | − | 0.804846i | \(-0.702248\pi\) | ||||
−0.593484 | + | 0.804846i | \(0.702248\pi\) | |||||||
\(674\) | −103648. | + | 294765.i | −0.228161 | + | 0.648869i | ||||
\(675\) | − | 384614.i | − | 0.844145i | ||||||
\(676\) | −921732. | − | 739670.i | −2.01702 | − | 1.61862i | ||||
\(677\) | 676411. | 1.47582 | 0.737909 | − | 0.674900i | \(-0.235813\pi\) | ||||
0.737909 | + | 0.674900i | \(0.235813\pi\) | |||||||
\(678\) | 974615. | + | 342703.i | 2.12018 | + | 0.745518i | ||||
\(679\) | 328884.i | 0.713350i | ||||||||
\(680\) | −138476. | + | 86128.4i | −0.299471 | + | 0.186264i | ||||
\(681\) | 709188. | 1.52921 | ||||||||
\(682\) | 216660. | − | 616161.i | 0.465811 | − | 1.32472i | ||||
\(683\) | − | 482710.i | − | 1.03477i | −0.855752 | − | 0.517386i | \(-0.826905\pi\) | ||
0.855752 | − | 0.517386i | \(-0.173095\pi\) | |||||||
\(684\) | 115941. | − | 144478.i | 0.247813 | − | 0.308810i | ||||
\(685\) | −197248. | −0.420369 | ||||||||
\(686\) | −483142. | − | 169887.i | −1.02666 | − | 0.361003i | ||||
\(687\) | 1.14734e6i | 2.43097i | ||||||||
\(688\) | 735820. | − | 163228.i | 1.55451 | − | 0.344839i | ||||
\(689\) | −236494. | −0.498175 | ||||||||
\(690\) | −81157.6 | + | 230805.i | −0.170463 | + | 0.484782i | ||||
\(691\) | − | 250289.i | − | 0.524186i | −0.965043 | − | 0.262093i | \(-0.915587\pi\) | ||
0.965043 | − | 0.262093i | \(-0.0844127\pi\) | |||||||
\(692\) | −185938. | − | 149211.i | −0.388289 | − | 0.311594i | ||||
\(693\) | −1.20371e6 | −2.50644 | ||||||||
\(694\) | −38042.0 | − | 13376.7i | −0.0789850 | − | 0.0277734i | ||||
\(695\) | 218357.i | 0.452061i | ||||||||
\(696\) | −89619.7 | − | 144089.i | −0.185006 | − | 0.297449i | ||||
\(697\) | −80835.4 | −0.166393 | ||||||||
\(698\) | −310388. | + | 882716.i | −0.637081 | + | 1.81180i | ||||
\(699\) | − | 451281.i | − | 0.923619i | ||||||
\(700\) | −173666. | + | 216412.i | −0.354420 | + | 0.441657i | ||||
\(701\) | −160428. | −0.326472 | −0.163236 | − | 0.986587i | \(-0.552193\pi\) | ||||
−0.163236 | + | 0.986587i | \(0.552193\pi\) | |||||||
\(702\) | 1.05513e6 | + | 371013.i | 2.14107 | + | 0.752862i | ||||
\(703\) | − | 115871.i | − | 0.234458i | ||||||
\(704\) | −803000. | − | 395801.i | −1.62021 | − | 0.798605i | ||||
\(705\) | 416965. | 0.838921 | ||||||||
\(706\) | 327489. | − | 931350.i | 0.657034 | − | 1.86855i | ||||
\(707\) | 394879.i | 0.789996i | ||||||||
\(708\) | 1.12164e6 | + | 900094.i | 2.23763 | + | 1.79565i | ||||
\(709\) | −283273. | −0.563524 | −0.281762 | − | 0.959484i | \(-0.590919\pi\) | ||||
−0.281762 | + | 0.959484i | \(0.590919\pi\) | |||||||
\(710\) | 69217.2 | + | 24338.7i | 0.137308 | + | 0.0482816i | ||||
\(711\) | − | 646608.i | − | 1.27909i | ||||||
\(712\) | −353645. | + | 219958.i | −0.697602 | + | 0.433891i | ||||
\(713\) | 226223. | 0.444998 | ||||||||
\(714\) | 145595. | − | 414059.i | 0.285595 | − | 0.812206i | ||||
\(715\) | 950857.i | 1.85996i | ||||||||
\(716\) | −93469.9 | + | 116477.i | −0.182325 | + | 0.227202i | ||||
\(717\) | −290949. | −0.565950 | ||||||||
\(718\) | 169753. | + | 59690.0i | 0.329282 | + | 0.115785i | ||||
\(719\) | 227848.i | 0.440746i | 0.975416 | + | 0.220373i | \(0.0707274\pi\) | ||||
−0.975416 | + | 0.220373i | \(0.929273\pi\) | |||||||
\(720\) | −105356. | − | 474939.i | −0.203233 | − | 0.916164i | ||||
\(721\) | 542499. | 1.04359 | ||||||||
\(722\) | 9101.04 | − | 25882.5i | 0.0174589 | − | 0.0496515i | ||||
\(723\) | − | 425174.i | − | 0.813373i | ||||||
\(724\) | 25963.3 | + | 20835.0i | 0.0495316 | + | 0.0397480i | ||||
\(725\) | −78548.3 | −0.149438 | ||||||||
\(726\) | −1.85766e6 | − | 653208.i | −3.52447 | − | 1.23931i | ||||
\(727\) | − | 292904.i | − | 0.554187i | −0.960843 | − | 0.277094i | \(-0.910629\pi\) | ||
0.960843 | − | 0.277094i | \(-0.0893712\pi\) | |||||||
\(728\) | −426168. | − | 685185.i | −0.804115 | − | 1.29284i | ||||
\(729\) | 819681. | 1.54237 | ||||||||
\(730\) | −17565.0 | + | 49953.2i | −0.0329611 | + | 0.0937383i | ||||
\(731\) | 551876.i | 1.03278i | ||||||||
\(732\) | −319131. | + | 397682.i | −0.595590 | + | 0.742188i | ||||
\(733\) | −601703. | −1.11989 | −0.559944 | − | 0.828530i | \(-0.689177\pi\) | ||||
−0.559944 | + | 0.828530i | \(0.689177\pi\) | |||||||
\(734\) | −688753. | − | 242185.i | −1.27841 | − | 0.449527i | ||||
\(735\) | − | 171496.i | − | 0.317452i | ||||||
\(736\) | 37067.6 | − | 307855.i | 0.0684288 | − | 0.568318i | ||||
\(737\) | −540677. | −0.995412 | ||||||||
\(738\) | 79993.1 | − | 227493.i | 0.146872 | − | 0.417691i | ||||
\(739\) | − | 187426.i | − | 0.343194i | −0.985167 | − | 0.171597i | \(-0.945107\pi\) | ||
0.985167 | − | 0.171597i | \(-0.0548928\pi\) | |||||||
\(740\) | −237328. | − | 190450.i | −0.433396 | − | 0.347791i | ||||
\(741\) | 393849. | 0.717288 | ||||||||
\(742\) | −109851. | − | 38626.8i | −0.199525 | − | 0.0701586i | ||||
\(743\) | 366710.i | 0.664270i | 0.943232 | + | 0.332135i | \(0.107769\pi\) | ||||
−0.943232 | + | 0.332135i | \(0.892231\pi\) | |||||||
\(744\) | −603291. | + | 375232.i | −1.08989 | + | 0.677882i | ||||
\(745\) | −238933. | −0.430490 | ||||||||
\(746\) | −38979.7 | + | 110855.i | −0.0700424 | + | 0.199194i | ||||
\(747\) | − | 1.07550e6i | − | 1.92739i | ||||||
\(748\) | 410269. | − | 511252.i | 0.733272 | − | 0.913759i | ||||
\(749\) | 217936. | 0.388478 | ||||||||
\(750\) | −811916. | − | 285493.i | −1.44341 | − | 0.507543i | ||||
\(751\) | 489072.i | 0.867147i | 0.901118 | + | 0.433573i | \(0.142747\pi\) | ||||
−0.901118 | + | 0.433573i | \(0.857253\pi\) | |||||||
\(752\) | −515919. | + | 114447.i | −0.912317 | + | 0.202380i | ||||
\(753\) | −697505. | −1.23015 | ||||||||
\(754\) | 75770.7 | − | 215485.i | 0.133278 | − | 0.379031i | ||||
\(755\) | − | 35821.4i | − | 0.0628418i | ||||||
\(756\) | 429507. | + | 344670.i | 0.751496 | + | 0.603059i | ||||
\(757\) | 295975. | 0.516492 | 0.258246 | − | 0.966079i | \(-0.416856\pi\) | ||||
0.258246 | + | 0.966079i | \(0.416856\pi\) | |||||||
\(758\) | 802960. | + | 282344.i | 1.39751 | + | 0.491405i | ||||
\(759\) | − | 983451.i | − | 1.70714i | ||||||
\(760\) | −38053.8 | − | 61182.1i | −0.0658825 | − | 0.105925i | ||||
\(761\) | 189082. | 0.326499 | 0.163250 | − | 0.986585i | \(-0.447802\pi\) | ||||
0.163250 | + | 0.986585i | \(0.447802\pi\) | |||||||
\(762\) | 302575. | − | 860495.i | 0.521102 | − | 1.48197i | ||||
\(763\) | 68475.6i | 0.117622i | ||||||||
\(764\) | −180311. | + | 224693.i | −0.308913 | + | 0.384949i | ||||
\(765\) | 356212. | 0.608675 | ||||||||
\(766\) | 129081. | + | 45388.5i | 0.219991 | + | 0.0773550i | ||||
\(767\) | 1.93592e6i | 3.29076i | ||||||||
\(768\) | 411782. | + | 882470.i | 0.698143 | + | 1.49616i | ||||
\(769\) | 202656. | 0.342694 | 0.171347 | − | 0.985211i | \(-0.445188\pi\) | ||||
0.171347 | + | 0.985211i | \(0.445188\pi\) | |||||||
\(770\) | −155304. | + | 441671.i | −0.261940 | + | 0.744934i | ||||
\(771\) | − | 290639.i | − | 0.488929i | ||||||
\(772\) | −727684. | − | 583951.i | −1.22098 | − | 0.979809i | ||||
\(773\) | 1.00638e6 | 1.68423 | 0.842117 | − | 0.539295i | \(-0.181309\pi\) | ||||
0.842117 | + | 0.539295i | \(0.181309\pi\) | |||||||
\(774\) | −1.55313e6 | − | 546125.i | −2.59254 | − | 0.911613i | ||||
\(775\) | 328877.i | 0.547557i | ||||||||
\(776\) | 453698. | − | 282189.i | 0.753430 | − | 0.468615i | ||||
\(777\) | 819000. | 1.35657 | ||||||||
\(778\) | 81641.0 | − | 232180.i | 0.134881 | − | 0.383588i | ||||
\(779\) | − | 35715.2i | − | 0.0588543i | ||||||
\(780\) | 647344. | − | 806681.i | 1.06401 | − | 1.32591i | ||||
\(781\) | −294932. | −0.483526 | ||||||||
\(782\) | 214189. | + | 75315.0i | 0.350254 | + | 0.123160i | ||||
\(783\) | 155893.i | 0.254274i | ||||||||
\(784\) | 47071.5 | + | 212195.i | 0.0765818 | + | 0.345226i | ||||
\(785\) | −418238. | −0.678711 | ||||||||
\(786\) | 43873.6 | − | 124773.i | 0.0710164 | − | 0.201964i | ||||
\(787\) | − | 588035.i | − | 0.949409i | −0.880145 | − | 0.474705i | \(-0.842555\pi\) | ||
0.880145 | − | 0.474705i | \(-0.157445\pi\) | |||||||
\(788\) | 919037. | + | 737507.i | 1.48006 | + | 1.18772i | ||||
\(789\) | 960776. | 1.54336 | ||||||||
\(790\) | −237256. | − | 83426.0i | −0.380157 | − | 0.133674i | ||||
\(791\) | 684748.i | 1.09440i | ||||||||
\(792\) | 1.03281e6 | + | 1.66053e6i | 1.64653 | + | 2.64726i | ||||
\(793\) | −686386. | −1.09150 | ||||||||
\(794\) | −256667. | + | 729937.i | −0.407126 | + | 1.15783i | ||||
\(795\) | − | 149260.i | − | 0.236162i | ||||||
\(796\) | −738563. | + | 920353.i | −1.16563 | + | 1.45254i | ||||
\(797\) | −275500. | −0.433716 | −0.216858 | − | 0.976203i | \(-0.569581\pi\) | ||||
−0.216858 | + | 0.976203i | \(0.569581\pi\) | |||||||
\(798\) | 182942. | + | 64327.8i | 0.287282 | + | 0.101017i | ||||
\(799\) | − | 386947.i | − | 0.606119i | ||||||
\(800\) | 447551. | + | 53887.8i | 0.699298 | + | 0.0841997i | ||||
\(801\) | 909709. | 1.41787 | ||||||||
\(802\) | 350694. | − | 997342.i | 0.545230 | − | 1.55058i | ||||
\(803\) | − | 212849.i | − | 0.330096i | ||||||
\(804\) | 458696. | + | 368093.i | 0.709598 | + | 0.569437i | ||||
\(805\) | −162159. | −0.250236 | ||||||||
\(806\) | −902222. | − | 317247.i | −1.38881 | − | 0.488346i | ||||
\(807\) | − | 651646.i | − | 1.00061i | ||||||
\(808\) | 544738. | − | 338814.i | 0.834383 | − | 0.518965i | ||||
\(809\) | −321791. | −0.491673 | −0.245837 | − | 0.969311i | \(-0.579063\pi\) | ||||
−0.245837 | + | 0.969311i | \(0.579063\pi\) | |||||||
\(810\) | −29918.7 | + | 85086.1i | −0.0456009 | + | 0.129685i | ||||
\(811\) | − | 86452.4i | − | 0.131442i | −0.997838 | − | 0.0657212i | \(-0.979065\pi\) | ||
0.997838 | − | 0.0657212i | \(-0.0209348\pi\) | |||||||
\(812\) | 70390.7 | − | 87716.7i | 0.106759 | − | 0.133036i | ||||
\(813\) | −1.29276e6 | −1.95586 | ||||||||
\(814\) | 1.15392e6 | + | 405751.i | 1.74151 | + | 0.612365i | ||||
\(815\) | 121664.i | 0.183166i | ||||||||
\(816\) | −696122. | + | 154421.i | −1.04545 | + | 0.231914i | ||||
\(817\) | −243833. | −0.365299 | ||||||||
\(818\) | 349970. | − | 995282.i | 0.523027 | − | 1.48744i | ||||
\(819\) | 1.76256e6i | 2.62770i | ||||||||
\(820\) | −73151.8 | − | 58702.7i | −0.108792 | − | 0.0873032i | ||||
\(821\) | −428678. | −0.635982 | −0.317991 | − | 0.948094i | \(-0.603008\pi\) | ||||
−0.317991 | + | 0.948094i | \(0.603008\pi\) | |||||||
\(822\) | −813627. | − | 286095.i | −1.20415 | − | 0.423415i | ||||
\(823\) | − | 785216.i | − | 1.15928i | −0.814872 | − | 0.579642i | \(-0.803193\pi\) | ||
0.814872 | − | 0.579642i | \(-0.196807\pi\) | |||||||
\(824\) | −465474. | − | 748381.i | −0.685554 | − | 1.10222i | ||||
\(825\) | 1.42971e6 | 2.10059 | ||||||||
\(826\) | −316195. | + | 899231.i | −0.463442 | + | 1.31799i | ||||
\(827\) | − | 328258.i | − | 0.479959i | −0.970778 | − | 0.239980i | \(-0.922859\pi\) | ||
0.970778 | − | 0.239980i | \(-0.0771408\pi\) | |||||||
\(828\) | −423914. | + | 528256.i | −0.618326 | + | 0.770520i | ||||
\(829\) | 443475. | 0.645298 | 0.322649 | − | 0.946519i | \(-0.395427\pi\) | ||||
0.322649 | + | 0.946519i | \(0.395427\pi\) | |||||||
\(830\) | −394626. | − | 138762.i | −0.572836 | − | 0.201425i | ||||
\(831\) | 385381.i | 0.558069i | ||||||||
\(832\) | −579558. | + | 1.17580e6i | −0.837240 | + | 1.69859i | ||||
\(833\) | −159150. | −0.229359 | ||||||||
\(834\) | −316712. | + | 900699.i | −0.455336 | + | 1.29493i | ||||
\(835\) | 366756.i | 0.526022i | ||||||||
\(836\) | 225885. | + | 181267.i | 0.323202 | + | 0.259362i | ||||
\(837\) | 652712. | 0.931688 | ||||||||
\(838\) | −232481. | − | 81746.9i | −0.331054 | − | 0.116408i | ||||
\(839\) | 247253.i | 0.351251i | 0.984457 | + | 0.175626i | \(0.0561949\pi\) | ||||
−0.984457 | + | 0.175626i | \(0.943805\pi\) | |||||||
\(840\) | 432446. | − | 268971.i | 0.612877 | − | 0.381194i | ||||
\(841\) | −675444. | −0.954986 | ||||||||
\(842\) | 145756. | − | 414517.i | 0.205590 | − | 0.584680i | ||||
\(843\) | − | 1.42645e6i | − | 2.00725i | ||||||
\(844\) | −238778. | + | 297550.i | −0.335204 | + | 0.417711i | ||||
\(845\) | 1.00406e6 | 1.40620 | ||||||||
\(846\) | 1.08898e6 | + | 382915.i | 1.52152 | + | 0.535010i | ||||
\(847\) | − | 1.30516e6i | − | 1.81927i | ||||||
\(848\) | 40968.4 | + | 184683.i | 0.0569715 | + | 0.256824i | ||||
\(849\) | 1.38022e6 | 1.91484 | ||||||||
\(850\) | −109491. | + | 311382.i | −0.151544 | + | 0.430978i | ||||
\(851\) | 423661.i | 0.585004i | ||||||||
\(852\) | 250212. | + | 200790.i | 0.344691 | + | 0.276607i | ||||
\(853\) | 518402. | 0.712473 | 0.356237 | − | 0.934396i | \(-0.384060\pi\) | ||||
0.356237 | + | 0.934396i | \(0.384060\pi\) | |||||||
\(854\) | −318825. | − | 112108.i | −0.437156 | − | 0.153717i | ||||
\(855\) | 157384.i | 0.215292i | ||||||||
\(856\) | −186994. | − | 300645.i | −0.255199 | − | 0.410305i | ||||
\(857\) | 1.01908e6 | 1.38754 | 0.693769 | − | 0.720197i | \(-0.255949\pi\) | ||||
0.693769 | + | 0.720197i | \(0.255949\pi\) | |||||||
\(858\) | −1.37916e6 | + | 3.92219e6i | −1.87343 | + | 5.32788i | ||||
\(859\) | − | 393422.i | − | 0.533178i | −0.963810 | − | 0.266589i | \(-0.914103\pi\) | ||
0.963810 | − | 0.266589i | \(-0.0858966\pi\) | |||||||
\(860\) | −400772. | + | 499419.i | −0.541877 | + | 0.675255i | ||||
\(861\) | 252441. | 0.340529 | ||||||||
\(862\) | 201234. | + | 70759.5i | 0.270823 | + | 0.0952292i | ||||
\(863\) | − | 411934.i | − | 0.553103i | −0.960999 | − | 0.276552i | \(-0.910808\pi\) | ||
0.960999 | − | 0.276552i | \(-0.0891917\pi\) | |||||||
\(864\) | 106950. | − | 888241.i | 0.143269 | − | 1.18988i | ||||
\(865\) | 202546. | 0.270702 | ||||||||
\(866\) | 12369.8 | − | 35178.7i | 0.0164941 | − | 0.0469076i | ||||
\(867\) | 718958.i | 0.956457i | ||||||||
\(868\) | −367264. | − | 294721.i | −0.487460 | − | 0.391176i | ||||
\(869\) | 1.01094e6 | 1.33871 | ||||||||
\(870\) | 136001. | + | 47821.7i | 0.179681 | + | 0.0631811i | ||||
\(871\) | 791693.i | 1.04357i | ||||||||
\(872\) | 94462.7 | − | 58753.4i | 0.124230 | − | 0.0772681i | ||||
\(873\) | −1.16708e6 | −1.53134 | ||||||||
\(874\) | −33276.1 | + | 94634.3i | −0.0435622 | + | 0.123887i | ||||
\(875\) | − | 570438.i | − | 0.745062i | ||||||
\(876\) | −144908. | + | 180575.i | −0.188835 | + | 0.235315i | ||||
\(877\) | −415845. | −0.540670 | −0.270335 | − | 0.962766i | \(-0.587134\pi\) | ||||
−0.270335 | + | 0.962766i | \(0.587134\pi\) | |||||||
\(878\) | 351828. | + | 123713.i | 0.456396 | + | 0.160482i | ||||
\(879\) | − | 558677.i | − | 0.723075i | ||||||
\(880\) | 742543. | − | 164719.i | 0.958862 | − | 0.212705i | ||||
\(881\) | −851690. | −1.09731 | −0.548655 | − | 0.836049i | \(-0.684860\pi\) | ||||
−0.548655 | + | 0.836049i | \(0.684860\pi\) | |||||||
\(882\) | 157491. | − | 447891.i | 0.202451 | − | 0.575752i | ||||
\(883\) | 471098.i | 0.604213i | 0.953274 | + | 0.302106i | \(0.0976898\pi\) | ||||
−0.953274 | + | 0.302106i | \(0.902310\pi\) | |||||||
\(884\) | −748608. | − | 600742.i | −0.957966 | − | 0.768747i | ||||
\(885\) | −1.22183e6 | −1.56000 | ||||||||
\(886\) | 907197. | + | 318996.i | 1.15567 | + | 0.406367i | ||||
\(887\) | 681049.i | 0.865627i | 0.901483 | + | 0.432814i | \(0.142479\pi\) | ||||
−0.901483 | + | 0.432814i | \(0.857521\pi\) | |||||||
\(888\) | −702717. | − | 1.12982e6i | −0.891158 | − | 1.43279i | ||||
\(889\) | 604569. | 0.764967 | ||||||||
\(890\) | 117371. | − | 333794.i | 0.148178 | − | 0.421404i | ||||
\(891\) | − | 362549.i | − | 0.456679i | ||||||
\(892\) | 317847. | − | 396082.i | 0.399474 | − | 0.497800i | ||||
\(893\) | 170963. | 0.214388 | ||||||||
\(894\) | −985575. | − | 346556.i | −1.23315 | − | 0.433610i | ||||
\(895\) | − | 126881.i | − | 0.158398i | ||||||
\(896\) | −461249. | + | 451499.i | −0.574538 | + | 0.562394i | ||||
\(897\) | −1.44003e6 | −1.78973 | ||||||||
\(898\) | 22191.6 | − | 63110.9i | 0.0275192 | − | 0.0782622i | ||||
\(899\) | − | 133301.i | − | 0.164936i | ||||||
\(900\) | −767964. | − | 616274.i | −0.948103 | − | 0.760832i | ||||
\(901\) | −138515. | −0.170627 | ||||||||
\(902\) | 355673. | + | 125065.i | 0.437158 | + | 0.153717i | ||||
\(903\) | − | 1.72346e6i | − | 2.11361i | ||||||
\(904\) | 944615. | − | 587527.i | 1.15589 | − | 0.718937i | ||||
\(905\) | −28282.4 | −0.0345318 | ||||||||
\(906\) | 51956.6 | − | 147760.i | 0.0632971 | − | 0.180011i | ||||
\(907\) | − | 521240.i | − | 0.633612i | −0.948490 | − | 0.316806i | \(-0.897390\pi\) | ||
0.948490 | − | 0.316806i | \(-0.102610\pi\) | |||||||
\(908\) | 477936. | − | 595576.i | 0.579693 | − | 0.722379i | ||||
\(909\) | −1.40127e6 | −1.69588 | ||||||||
\(910\) | 646723. | + | 227407.i | 0.780973 | + | 0.274612i | ||||
\(911\) | − | 37792.3i | − | 0.0455372i | −0.999741 | − | 0.0227686i | \(-0.992752\pi\) | ||
0.999741 | − | 0.0227686i | \(-0.00724810\pi\) | |||||||
\(912\) | −68227.4 | − | 307565.i | −0.0820293 | − | 0.369783i | ||||
\(913\) | 1.68149e6 | 2.01722 | ||||||||
\(914\) | −260110. | + | 739729.i | −0.311361 | + | 0.885483i | ||||
\(915\) | − | 433204.i | − | 0.517429i | ||||||
\(916\) | 963537. | + | 773218.i | 1.14836 | + | 0.921533i | ||||
\(917\) | 87663.1 | 0.104251 | ||||||||
\(918\) | 617990. | + | 217303.i | 0.733324 | + | 0.257858i | ||||
\(919\) | 458767.i | 0.543202i | 0.962410 | + | 0.271601i | \(0.0875531\pi\) | ||||
−0.962410 | + | 0.271601i | \(0.912447\pi\) | |||||||
\(920\) | 139136. | + | 223700.i | 0.164386 | + | 0.264296i | ||||
\(921\) | −1.28412e6 | −1.51386 | ||||||||
\(922\) | 246095. | − | 699871.i | 0.289495 | − | 0.823296i | ||||
\(923\) | 431858.i | 0.506918i | ||||||||
\(924\) | −1.28123e6 | + | 1.59659e6i | −1.50066 | + | 1.87004i | ||||
\(925\) | −615905. | −0.719831 | ||||||||
\(926\) | 1.59936e6 | + | 562381.i | 1.86520 | + | 0.655857i | ||||
\(927\) | 1.92512e6i | 2.24026i | ||||||||
\(928\) | −181402. | − | 21841.9i | −0.210643 | − | 0.0253627i | ||||
\(929\) | 583638. | 0.676258 | 0.338129 | − | 0.941100i | \(-0.390206\pi\) | ||||
0.338129 | + | 0.941100i | \(0.390206\pi\) | |||||||
\(930\) | 200227. | − | 569426.i | 0.231503 | − | 0.658372i | ||||
\(931\) | − | 70316.5i | − | 0.0811256i | ||||||
\(932\) | −378986. | − | 304128.i | −0.436306 | − | 0.350126i | ||||
\(933\) | 2.05108e6 | 2.35624 | ||||||||
\(934\) | −1.08591e6 | − | 381836.i | −1.24480 | − | 0.437707i | ||||
\(935\) | 556918.i | 0.637043i | ||||||||
\(936\) | 2.43146e6 | − | 1.51231e6i | 2.77533 | − | 1.72619i | ||||
\(937\) | −132263. | −0.150647 | −0.0753236 | − | 0.997159i | \(-0.523999\pi\) | ||||
−0.0753236 | + | 0.997159i | \(0.523999\pi\) | |||||||
\(938\) | −129308. | + | 367740.i | −0.146967 | + | 0.417961i | ||||
\(939\) | − | 215883.i | − | 0.244843i | ||||||
\(940\) | 281001. | − | 350167.i | 0.318019 | − | 0.396296i | ||||
\(941\) | 664538. | 0.750483 | 0.375241 | − | 0.926927i | \(-0.377560\pi\) | ||||
0.375241 | + | 0.926927i | \(0.377560\pi\) | |||||||
\(942\) | −1.72519e6 | − | 606627.i | −1.94418 | − | 0.683628i | ||||
\(943\) | 130585.i | 0.146849i | ||||||||
\(944\) | 1.51180e6 | − | 335363.i | 1.69648 | − | 0.376332i | ||||
\(945\) | −467872. | −0.523918 | ||||||||
\(946\) | 853839. | − | 2.42824e6i | 0.954099 | − | 2.71337i | ||||
\(947\) | − | 410129.i | − | 0.457321i | −0.973506 | − | 0.228660i | \(-0.926565\pi\) | ||
0.973506 | − | 0.228660i | \(-0.0734345\pi\) | |||||||
\(948\) | −857653. | − | 688248.i | −0.954322 | − | 0.765823i | ||||
\(949\) | −311667. | −0.346065 | ||||||||
\(950\) | −137577. | − | 48375.9i | −0.152439 | − | 0.0536021i | ||||
\(951\) | 2.48421e6i | 2.74680i | ||||||||
\(952\) | −249607. | − | 401314.i | −0.275412 | − | 0.442803i | ||||
\(953\) | −800753. | −0.881683 | −0.440842 | − | 0.897585i | \(-0.645320\pi\) | ||||
−0.440842 | + | 0.897585i | \(0.645320\pi\) | |||||||
\(954\) | 137072. | − | 389819.i | 0.150609 | − | 0.428318i | ||||
\(955\) | − | 244763.i | − | 0.268373i | ||||||
\(956\) | −196076. | + | 244339.i | −0.214541 | + | 0.267347i | ||||
\(957\) | −579494. | −0.632740 | ||||||||
\(958\) | −424701. | − | 149337.i | −0.462756 | − | 0.162718i | ||||
\(959\) | − | 571641.i | − | 0.621564i | ||||||
\(960\) | −742094. | − | 365781.i | −0.805224 | − | 0.396897i | ||||
\(961\) | 365398. | 0.395658 | ||||||||
\(962\) | 594126. | − | 1.68964e6i | 0.641990 | − | 1.82576i | ||||
\(963\) | 773373.i | 0.833943i | ||||||||
\(964\) | −357061. | − | 286533.i | −0.384227 | − | 0.308334i | ||||
\(965\) | 792683. | 0.851226 | ||||||||
\(966\) | −668892. | − | 235202.i | −0.716806 | − | 0.252050i | ||||
\(967\) | 1.11203e6i | 1.18922i | 0.804015 | + | 0.594609i | \(0.202693\pi\) | ||||
−0.804015 | + | 0.594609i | \(0.797307\pi\) | |||||||
\(968\) | −1.80048e6 | + | 1.11986e6i | −1.92149 | + | 1.19512i | ||||
\(969\) | 230678. | 0.245674 | ||||||||
\(970\) | −150578. | + | 428230.i | −0.160036 | + | 0.455128i | ||||
\(971\) | − | 1.51970e6i | − | 1.61183i | −0.592029 | − | 0.805916i | \(-0.701673\pi\) | ||
0.592029 | − | 0.805916i | \(-0.298327\pi\) | |||||||
\(972\) | 461852. | − | 575533.i | 0.488844 | − | 0.609169i | ||||
\(973\) | −632816. | −0.668423 | ||||||||
\(974\) | 1.17283e6 | + | 412399.i | 1.23628 | + | 0.434710i | ||||
\(975\) | − | 2.09348e6i | − | 2.20221i | ||||||
\(976\) | 118904. | + | 536013.i | 0.124824 | + | 0.562698i | ||||
\(977\) | 1.15377e6 | 1.20873 | 0.604364 | − | 0.796708i | \(-0.293427\pi\) | ||||
0.604364 | + | 0.796708i | \(0.293427\pi\) | |||||||
\(978\) | −176465. | + | 501850.i | −0.184493 | + | 0.524682i | ||||
\(979\) | 1.42228e6i | 1.48395i | ||||||||
\(980\) | −144022. | − | 115575.i | −0.149961 | − | 0.120340i | ||||
\(981\) | −242994. | −0.252497 | ||||||||
\(982\) | 569723. | + | 200331.i | 0.590801 | + | 0.207743i | ||||
\(983\) | 565543.i | 0.585273i | 0.956224 | + | 0.292637i | \(0.0945326\pi\) | ||||
−0.956224 | + | 0.292637i | \(0.905467\pi\) | |||||||
\(984\) | −216599. | − | 348245.i | −0.223701 | − | 0.359662i | ||||
\(985\) | −1.00113e6 | −1.03185 | ||||||||
\(986\) | 44379.0 | − | 126210.i | 0.0456482 | − | 0.129819i | ||||
\(987\) | 1.20840e6i | 1.24044i | ||||||||
\(988\) | 265423. | − | 330755.i | 0.271910 | − | 0.338838i | ||||
\(989\) | 891527. | 0.911469 | ||||||||
\(990\) | −1.56732e6 | − | 551115.i | −1.59914 | − | 0.562305i | ||||
\(991\) | − | 748434.i | − | 0.762090i | −0.924557 | − | 0.381045i | \(-0.875564\pi\) | ||
0.924557 | − | 0.381045i | \(-0.124436\pi\) | |||||||
\(992\) | −91450.7 | + | 759520.i | −0.0929317 | + | 0.771820i | ||||
\(993\) | −242051. | −0.245475 | ||||||||
\(994\) | −70535.8 | + | 200597.i | −0.0713899 | + | 0.203026i | ||||
\(995\) | − | 1.00256e6i | − | 1.01266i | ||||||
\(996\) | −1.42653e6 | − | 1.14476e6i | −1.43801 | − | 1.15397i | ||||
\(997\) | −162138. | −0.163115 | −0.0815575 | − | 0.996669i | \(-0.525989\pi\) | ||||
−0.0815575 | + | 0.996669i | \(0.525989\pi\) | |||||||
\(998\) | 1.27920e6 | + | 449805.i | 1.28434 | + | 0.451610i | ||||
\(999\) | 1.22237e6i | 1.22482i |
(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 | 76.5.b.a.39.14 | yes | 36 | |
4.3 | odd | 2 | inner | 76.5.b.a.39.13 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.5.b.a.39.13 | ✓ | 36 | 4.3 | odd | 2 | inner | |
76.5.b.a.39.14 | yes | 36 | 1.1 | even | 1 | trivial |