Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [69,6,Mod(68,69)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(69, 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("69.68");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 69 = 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 69.c (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: | \(11.0664835671\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 68.26 | ||
Character | \(\chi\) | \(=\) | 69.68 |
Dual form | 69.6.c.b.68.8 |
$q$-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 \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(47\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 7.06404i | 1.24876i | 0.781121 | + | 0.624379i | \(0.214648\pi\) | ||||
−0.781121 | + | 0.624379i | \(0.785352\pi\) | |||||||
\(3\) | −15.4896 | − | 1.75248i | −0.993661 | − | 0.112422i | ||||
\(4\) | −17.9007 | −0.559397 | ||||||||
\(5\) | 82.3579 | 1.47326 | 0.736631 | − | 0.676295i | \(-0.236415\pi\) | ||||
0.736631 | + | 0.676295i | \(0.236415\pi\) | |||||||
\(6\) | 12.3796 | − | 109.419i | 0.140387 | − | 1.24084i | ||||
\(7\) | 96.3127i | 0.742914i | 0.928450 | + | 0.371457i | \(0.121142\pi\) | ||||
−0.928450 | + | 0.371457i | \(0.878858\pi\) | |||||||
\(8\) | 99.5980i | 0.550207i | ||||||||
\(9\) | 236.858 | + | 54.2905i | 0.974723 | + | 0.223418i | ||||
\(10\) | 581.779i | 1.83975i | ||||||||
\(11\) | −87.8590 | −0.218930 | −0.109465 | − | 0.993991i | \(-0.534914\pi\) | ||||
−0.109465 | + | 0.993991i | \(0.534914\pi\) | |||||||
\(12\) | 277.275 | + | 31.3706i | 0.555851 | + | 0.0628883i | ||||
\(13\) | 303.810 | 0.498591 | 0.249295 | − | 0.968428i | \(-0.419801\pi\) | ||||
0.249295 | + | 0.968428i | \(0.419801\pi\) | |||||||
\(14\) | −680.357 | −0.927720 | ||||||||
\(15\) | −1275.69 | − | 144.330i | −1.46392 | − | 0.165626i | ||||
\(16\) | −1276.39 | −1.24647 | ||||||||
\(17\) | −460.998 | −0.386881 | −0.193440 | − | 0.981112i | \(-0.561965\pi\) | ||||
−0.193440 | + | 0.981112i | \(0.561965\pi\) | |||||||
\(18\) | −383.510 | + | 1673.17i | −0.278995 | + | 1.21719i | ||||
\(19\) | 1560.29i | 0.991563i | 0.868447 | + | 0.495781i | \(0.165118\pi\) | ||||
−0.868447 | + | 0.495781i | \(0.834882\pi\) | |||||||
\(20\) | −1474.26 | −0.824138 | ||||||||
\(21\) | 168.786 | − | 1491.85i | 0.0835195 | − | 0.738205i | ||||
\(22\) | − | 620.640i | − | 0.273390i | ||||||
\(23\) | −2440.41 | − | 693.361i | −0.961929 | − | 0.273300i | ||||
\(24\) | 174.543 | − | 1542.74i | 0.0618551 | − | 0.546719i | ||||
\(25\) | 3657.82 | 1.17050 | ||||||||
\(26\) | 2146.13i | 0.622619i | ||||||||
\(27\) | −3573.70 | − | 1256.03i | −0.943427 | − | 0.331581i | ||||
\(28\) | − | 1724.07i | − | 0.415584i | ||||||
\(29\) | 4091.99i | 0.903525i | 0.892138 | + | 0.451762i | \(0.149204\pi\) | ||||
−0.892138 | + | 0.451762i | \(0.850796\pi\) | |||||||
\(30\) | 1019.56 | − | 9011.55i | 0.206827 | − | 1.82809i | ||||
\(31\) | 1861.74 | 0.347947 | 0.173974 | − | 0.984750i | \(-0.444339\pi\) | ||||
0.173974 | + | 0.984750i | \(0.444339\pi\) | |||||||
\(32\) | − | 5829.32i | − | 1.00634i | ||||||
\(33\) | 1360.90 | + | 153.971i | 0.217542 | + | 0.0246124i | ||||
\(34\) | − | 3256.51i | − | 0.483120i | ||||||
\(35\) | 7932.11i | 1.09451i | ||||||||
\(36\) | −4239.92 | − | 971.838i | −0.545257 | − | 0.124979i | ||||
\(37\) | 11817.5i | 1.41913i | 0.704640 | + | 0.709565i | \(0.251109\pi\) | ||||
−0.704640 | + | 0.709565i | \(0.748891\pi\) | |||||||
\(38\) | −11021.9 | −1.23822 | ||||||||
\(39\) | −4705.91 | − | 532.421i | −0.495430 | − | 0.0560523i | ||||
\(40\) | 8202.68i | 0.810599i | ||||||||
\(41\) | − | 12179.1i | − | 1.13151i | −0.824574 | − | 0.565754i | \(-0.808585\pi\) | ||
0.824574 | − | 0.565754i | \(-0.191415\pi\) | |||||||
\(42\) | 10538.5 | + | 1192.31i | 0.921839 | + | 0.104296i | ||||
\(43\) | 22461.2i | 1.85252i | 0.376888 | + | 0.926259i | \(0.376994\pi\) | ||||
−0.376888 | + | 0.926259i | \(0.623006\pi\) | |||||||
\(44\) | 1572.74 | 0.122469 | ||||||||
\(45\) | 19507.1 | + | 4471.25i | 1.43602 | + | 0.329153i | ||||
\(46\) | 4897.93 | − | 17239.2i | 0.341286 | − | 1.20122i | ||||
\(47\) | − | 2743.55i | − | 0.181162i | −0.995889 | − | 0.0905811i | \(-0.971128\pi\) | ||
0.995889 | − | 0.0905811i | \(-0.0288724\pi\) | |||||||
\(48\) | 19770.8 | + | 2236.84i | 1.23857 | + | 0.140130i | ||||
\(49\) | 7530.86 | 0.448079 | ||||||||
\(50\) | 25839.0i | 1.46167i | ||||||||
\(51\) | 7140.70 | + | 807.889i | 0.384428 | + | 0.0434937i | ||||
\(52\) | −5438.42 | −0.278910 | ||||||||
\(53\) | 11551.9 | 0.564891 | 0.282445 | − | 0.959283i | \(-0.408854\pi\) | ||||
0.282445 | + | 0.959283i | \(0.408854\pi\) | |||||||
\(54\) | 8872.63 | − | 25244.7i | 0.414065 | − | 1.17811i | ||||
\(55\) | −7235.88 | −0.322541 | ||||||||
\(56\) | −9592.56 | −0.408756 | ||||||||
\(57\) | 2734.37 | − | 24168.3i | 0.111473 | − | 0.985277i | ||||
\(58\) | −28906.0 | −1.12828 | ||||||||
\(59\) | − | 39947.0i | − | 1.49401i | −0.664817 | − | 0.747006i | \(-0.731491\pi\) | ||
0.664817 | − | 0.747006i | \(-0.268509\pi\) | |||||||
\(60\) | 22835.8 | + | 2583.61i | 0.818914 | + | 0.0926509i | ||||
\(61\) | − | 24443.4i | − | 0.841079i | −0.907274 | − | 0.420540i | \(-0.861841\pi\) | ||
0.907274 | − | 0.420540i | \(-0.138159\pi\) | |||||||
\(62\) | 13151.4i | 0.434502i | ||||||||
\(63\) | −5228.87 | + | 22812.4i | −0.165980 | + | 0.724135i | ||||
\(64\) | 334.155 | 0.0101976 | ||||||||
\(65\) | 25021.2 | 0.734555 | ||||||||
\(66\) | −1087.66 | + | 9613.48i | −0.0307349 | + | 0.271657i | ||||
\(67\) | − | 41740.7i | − | 1.13598i | −0.823034 | − | 0.567992i | \(-0.807720\pi\) | ||
0.823034 | − | 0.567992i | \(-0.192280\pi\) | |||||||
\(68\) | 8252.20 | 0.216420 | ||||||||
\(69\) | 36585.9 | + | 15016.7i | 0.925106 | + | 0.379709i | ||||
\(70\) | −56032.8 | −1.36677 | ||||||||
\(71\) | 33816.0i | 0.796115i | 0.917360 | + | 0.398058i | \(0.130316\pi\) | ||||
−0.917360 | + | 0.398058i | \(0.869684\pi\) | |||||||
\(72\) | −5407.23 | + | 23590.6i | −0.122926 | + | 0.536299i | ||||
\(73\) | 63699.0 | 1.39902 | 0.699512 | − | 0.714621i | \(-0.253401\pi\) | ||||
0.699512 | + | 0.714621i | \(0.253401\pi\) | |||||||
\(74\) | −83479.5 | −1.77215 | ||||||||
\(75\) | −56658.2 | − | 6410.24i | −1.16308 | − | 0.131589i | ||||
\(76\) | − | 27930.2i | − | 0.554677i | ||||||
\(77\) | − | 8461.94i | − | 0.162646i | ||||||
\(78\) | 3761.04 | − | 33242.8i | 0.0699958 | − | 0.618672i | ||||
\(79\) | − | 41670.6i | − | 0.751210i | −0.926780 | − | 0.375605i | \(-0.877435\pi\) | ||
0.926780 | − | 0.375605i | \(-0.122565\pi\) | |||||||
\(80\) | −105121. | −1.83638 | ||||||||
\(81\) | 53154.1 | + | 25718.2i | 0.900169 | + | 0.435541i | ||||
\(82\) | 86034.0 | 1.41298 | ||||||||
\(83\) | 72364.0 | 1.15299 | 0.576497 | − | 0.817099i | \(-0.304419\pi\) | ||||
0.576497 | + | 0.817099i | \(0.304419\pi\) | |||||||
\(84\) | −3021.39 | + | 26705.2i | −0.0467206 | + | 0.412949i | ||||
\(85\) | −37966.8 | −0.569977 | ||||||||
\(86\) | −158667. | −2.31335 | ||||||||
\(87\) | 7171.13 | − | 63383.5i | 0.101576 | − | 0.897797i | ||||
\(88\) | − | 8750.58i | − | 0.120457i | ||||||
\(89\) | −9268.15 | −0.124027 | −0.0620137 | − | 0.998075i | \(-0.519752\pi\) | ||||
−0.0620137 | + | 0.998075i | \(0.519752\pi\) | |||||||
\(90\) | −31585.1 | + | 137799.i | −0.411032 | + | 1.79324i | ||||
\(91\) | 29260.8i | 0.370410i | ||||||||
\(92\) | 43685.0 | + | 12411.6i | 0.538100 | + | 0.152883i | ||||
\(93\) | −28837.6 | − | 3262.65i | −0.345742 | − | 0.0391168i | ||||
\(94\) | 19380.5 | 0.226228 | ||||||||
\(95\) | 128502.i | 1.46083i | ||||||||
\(96\) | −10215.8 | + | 90294.0i | −0.113134 | + | 0.999956i | ||||
\(97\) | 28465.2i | 0.307174i | 0.988135 | + | 0.153587i | \(0.0490825\pi\) | ||||
−0.988135 | + | 0.153587i | \(0.950918\pi\) | |||||||
\(98\) | 53198.3i | 0.559542i | ||||||||
\(99\) | −20810.1 | − | 4769.91i | −0.213396 | − | 0.0489127i | ||||
\(100\) | −65477.5 | −0.654775 | ||||||||
\(101\) | − | 105391.i | − | 1.02802i | −0.857785 | − | 0.514008i | \(-0.828160\pi\) | ||
0.857785 | − | 0.514008i | \(-0.171840\pi\) | |||||||
\(102\) | −5706.97 | + | 50442.2i | −0.0543131 | + | 0.480058i | ||||
\(103\) | 208125.i | 1.93300i | 0.256673 | + | 0.966498i | \(0.417374\pi\) | ||||
−0.256673 | + | 0.966498i | \(0.582626\pi\) | |||||||
\(104\) | 30258.9i | 0.274328i | ||||||||
\(105\) | 13900.8 | − | 122866.i | 0.123046 | − | 1.08757i | ||||
\(106\) | 81603.3i | 0.705412i | ||||||||
\(107\) | −183616. | −1.55043 | −0.775215 | − | 0.631698i | \(-0.782358\pi\) | ||||
−0.775215 | + | 0.631698i | \(0.782358\pi\) | |||||||
\(108\) | 63971.7 | + | 22483.8i | 0.527750 | + | 0.185485i | ||||
\(109\) | − | 114970.i | − | 0.926868i | −0.886131 | − | 0.463434i | \(-0.846617\pi\) | ||
0.886131 | − | 0.463434i | \(-0.153383\pi\) | |||||||
\(110\) | − | 51114.6i | − | 0.402775i | ||||||
\(111\) | 20710.0 | − | 183049.i | 0.159541 | − | 1.41013i | ||||
\(112\) | − | 122932.i | − | 0.926022i | ||||||
\(113\) | 186197. | 1.37175 | 0.685876 | − | 0.727719i | \(-0.259419\pi\) | ||||
0.685876 | + | 0.727719i | \(0.259419\pi\) | |||||||
\(114\) | 170726. | + | 19315.7i | 1.23037 | + | 0.139203i | ||||
\(115\) | −200987. | − | 57103.7i | −1.41717 | − | 0.402643i | ||||
\(116\) | − | 73249.6i | − | 0.505429i | ||||||
\(117\) | 71959.8 | + | 16494.0i | 0.485988 | + | 0.111394i | ||||
\(118\) | 282187. | 1.86566 | ||||||||
\(119\) | − | 44400.0i | − | 0.287419i | ||||||
\(120\) | 14375.0 | − | 127057.i | 0.0911287 | − | 0.805460i | ||||
\(121\) | −153332. | −0.952070 | ||||||||
\(122\) | 172669. | 1.05030 | ||||||||
\(123\) | −21343.7 | + | 188651.i | −0.127206 | + | 1.12433i | ||||
\(124\) | −33326.4 | −0.194641 | ||||||||
\(125\) | 43881.6 | 0.251193 | ||||||||
\(126\) | −161148. | − | 36936.9i | −0.904270 | − | 0.207269i | ||||
\(127\) | 130830. | 0.719777 | 0.359888 | − | 0.932995i | \(-0.382815\pi\) | ||||
0.359888 | + | 0.932995i | \(0.382815\pi\) | |||||||
\(128\) | − | 184178.i | − | 0.993601i | ||||||
\(129\) | 39362.8 | − | 347916.i | 0.208263 | − | 1.84077i | ||||
\(130\) | 176751.i | 0.917281i | ||||||||
\(131\) | 54027.3i | 0.275065i | 0.990497 | + | 0.137532i | \(0.0439171\pi\) | ||||
−0.990497 | + | 0.137532i | \(0.956083\pi\) | |||||||
\(132\) | −24361.1 | − | 2756.19i | −0.121692 | − | 0.0137681i | ||||
\(133\) | −150275. | −0.736646 | ||||||||
\(134\) | 294858. | 1.41857 | ||||||||
\(135\) | −294322. | − | 103444.i | −1.38991 | − | 0.488506i | ||||
\(136\) | − | 45914.5i | − | 0.212864i | ||||||
\(137\) | 162442. | 0.739428 | 0.369714 | − | 0.929146i | \(-0.379456\pi\) | ||||
0.369714 | + | 0.929146i | \(0.379456\pi\) | |||||||
\(138\) | −106078. | + | 258445.i | −0.474165 | + | 1.15523i | ||||
\(139\) | 142959. | 0.627587 | 0.313794 | − | 0.949491i | \(-0.398400\pi\) | ||||
0.313794 | + | 0.949491i | \(0.398400\pi\) | |||||||
\(140\) | − | 141990.i | − | 0.612264i | ||||||
\(141\) | −4808.00 | + | 42496.5i | −0.0203665 | + | 0.180014i | ||||
\(142\) | −238877. | −0.994156 | ||||||||
\(143\) | −26692.5 | −0.109156 | ||||||||
\(144\) | −302322. | − | 69295.7i | −1.21496 | − | 0.278484i | ||||
\(145\) | 337008.i | 1.33113i | ||||||||
\(146\) | 449972.i | 1.74704i | ||||||||
\(147\) | −116650. | − | 13197.7i | −0.445238 | − | 0.0503737i | ||||
\(148\) | − | 211542.i | − | 0.793857i | ||||||
\(149\) | 333252. | 1.22972 | 0.614862 | − | 0.788635i | \(-0.289212\pi\) | ||||
0.614862 | + | 0.788635i | \(0.289212\pi\) | |||||||
\(150\) | 45282.2 | − | 400236.i | 0.164323 | − | 1.45241i | ||||
\(151\) | 510659. | 1.82259 | 0.911295 | − | 0.411755i | \(-0.135084\pi\) | ||||
0.911295 | + | 0.411755i | \(0.135084\pi\) | |||||||
\(152\) | −155401. | −0.545564 | ||||||||
\(153\) | −109191. | − | 25027.8i | −0.377101 | − | 0.0864360i | ||||
\(154\) | 59775.5 | 0.203105 | ||||||||
\(155\) | 153329. | 0.512618 | ||||||||
\(156\) | 84239.1 | + | 9530.71i | 0.277142 | + | 0.0313555i | ||||
\(157\) | 335833.i | 1.08736i | 0.839292 | + | 0.543680i | \(0.182970\pi\) | ||||
−0.839292 | + | 0.543680i | \(0.817030\pi\) | |||||||
\(158\) | 294363. | 0.938080 | ||||||||
\(159\) | −178935. | − | 20244.5i | −0.561310 | − | 0.0635059i | ||||
\(160\) | − | 480090.i | − | 1.48260i | ||||||
\(161\) | 66779.5 | − | 235042.i | 0.203039 | − | 0.714631i | ||||
\(162\) | −181675. | + | 375483.i | −0.543885 | + | 1.12409i | ||||
\(163\) | 371286. | 1.09456 | 0.547279 | − | 0.836950i | \(-0.315664\pi\) | ||||
0.547279 | + | 0.836950i | \(0.315664\pi\) | |||||||
\(164\) | 218015.i | 0.632962i | ||||||||
\(165\) | 112081. | + | 12680.7i | 0.320496 | + | 0.0362605i | ||||
\(166\) | 511182.i | 1.43981i | ||||||||
\(167\) | − | 352931.i | − | 0.979262i | −0.871930 | − | 0.489631i | \(-0.837131\pi\) | ||
0.871930 | − | 0.489631i | \(-0.162869\pi\) | |||||||
\(168\) | 148585. | + | 16810.7i | 0.406165 | + | 0.0459530i | ||||
\(169\) | −278992. | −0.751407 | ||||||||
\(170\) | − | 268199.i | − | 0.711763i | ||||||
\(171\) | −84708.7 | + | 369566.i | −0.221533 | + | 0.966499i | ||||
\(172\) | − | 402072.i | − | 1.03629i | ||||||
\(173\) | − | 522540.i | − | 1.32741i | −0.747995 | − | 0.663704i | \(-0.768983\pi\) | ||
0.747995 | − | 0.663704i | \(-0.231017\pi\) | |||||||
\(174\) | 447744. | + | 50657.2i | 1.12113 | + | 0.126843i | ||||
\(175\) | 352294.i | 0.869582i | ||||||||
\(176\) | 112142. | 0.272890 | ||||||||
\(177\) | −70006.2 | + | 618765.i | −0.167959 | + | 1.48454i | ||||
\(178\) | − | 65470.6i | − | 0.154880i | ||||||
\(179\) | 45906.4i | 0.107088i | 0.998565 | + | 0.0535440i | \(0.0170517\pi\) | ||||
−0.998565 | + | 0.0535440i | \(0.982948\pi\) | |||||||
\(180\) | −349191. | − | 80038.5i | −0.803306 | − | 0.184127i | ||||
\(181\) | 401676.i | 0.911337i | 0.890149 | + | 0.455669i | \(0.150600\pi\) | ||||
−0.890149 | + | 0.455669i | \(0.849400\pi\) | |||||||
\(182\) | −206700. | −0.462553 | ||||||||
\(183\) | −42836.5 | + | 378619.i | −0.0945554 | + | 0.835747i | ||||
\(184\) | 69057.4 | − | 243060.i | 0.150372 | − | 0.529260i | ||||
\(185\) | 973266.i | 2.09075i | ||||||||
\(186\) | 23047.5 | − | 203710.i | 0.0488474 | − | 0.431748i | ||||
\(187\) | 40502.9 | 0.0846997 | ||||||||
\(188\) | 49111.4i | 0.101342i | ||||||||
\(189\) | 120971. | − | 344192.i | 0.246336 | − | 0.700885i | ||||
\(190\) | −907742. | −1.82423 | ||||||||
\(191\) | −598178. | −1.18644 | −0.593222 | − | 0.805039i | \(-0.702144\pi\) | ||||
−0.593222 | + | 0.805039i | \(0.702144\pi\) | |||||||
\(192\) | −5175.95 | − | 585.600i | −0.0101330 | − | 0.00114643i | ||||
\(193\) | −535462. | −1.03475 | −0.517375 | − | 0.855759i | \(-0.673091\pi\) | ||||
−0.517375 | + | 0.855759i | \(0.673091\pi\) | |||||||
\(194\) | −201079. | −0.383586 | ||||||||
\(195\) | −387569. | − | 43849.0i | −0.729898 | − | 0.0825797i | ||||
\(196\) | −134808. | −0.250654 | ||||||||
\(197\) | − | 620923.i | − | 1.13991i | −0.821675 | − | 0.569957i | \(-0.806960\pi\) | ||
0.821675 | − | 0.569957i | \(-0.193040\pi\) | |||||||
\(198\) | 33694.8 | − | 147003.i | 0.0610802 | − | 0.266480i | ||||
\(199\) | − | 679618.i | − | 1.21656i | −0.793724 | − | 0.608278i | \(-0.791861\pi\) | ||
0.793724 | − | 0.608278i | \(-0.208139\pi\) | |||||||
\(200\) | 364311.i | 0.644017i | ||||||||
\(201\) | −73149.6 | + | 646548.i | −0.127709 | + | 1.12878i | ||||
\(202\) | 744486. | 1.28374 | ||||||||
\(203\) | −394111. | −0.671241 | ||||||||
\(204\) | −127823. | − | 14461.8i | −0.215048 | − | 0.0243303i | ||||
\(205\) | − | 1.00305e6i | − | 1.66701i | ||||||
\(206\) | −1.47020e6 | −2.41385 | ||||||||
\(207\) | −540386. | − | 296719.i | −0.876554 | − | 0.481304i | ||||
\(208\) | −387780. | −0.621479 | ||||||||
\(209\) | − | 137085.i | − | 0.217083i | ||||||
\(210\) | 867927. | + | 98196.2i | 1.35811 | + | 0.153655i | ||||
\(211\) | −99148.1 | −0.153313 | −0.0766564 | − | 0.997058i | \(-0.524424\pi\) | ||||
−0.0766564 | + | 0.997058i | \(0.524424\pi\) | |||||||
\(212\) | −206788. | −0.315998 | ||||||||
\(213\) | 59261.7 | − | 523797.i | 0.0895005 | − | 0.791069i | ||||
\(214\) | − | 1.29707e6i | − | 1.93611i | ||||||
\(215\) | 1.84986e6i | 2.72924i | ||||||||
\(216\) | 125098. | − | 355933.i | 0.182438 | − | 0.519080i | ||||
\(217\) | 179309.i | 0.258495i | ||||||||
\(218\) | 812152. | 1.15743 | ||||||||
\(219\) | −986674. | − | 111631.i | −1.39016 | − | 0.157280i | ||||
\(220\) | 129527. | 0.180428 | ||||||||
\(221\) | −140056. | −0.192895 | ||||||||
\(222\) | 1.29307e6 | + | 146296.i | 1.76092 | + | 0.199228i | ||||
\(223\) | 434908. | 0.585646 | 0.292823 | − | 0.956167i | \(-0.405405\pi\) | ||||
0.292823 | + | 0.956167i | \(0.405405\pi\) | |||||||
\(224\) | 561438. | 0.747621 | ||||||||
\(225\) | 866382. | + | 198585.i | 1.14091 | + | 0.261511i | ||||
\(226\) | 1.31530e6i | 1.71299i | ||||||||
\(227\) | 947182. | 1.22003 | 0.610013 | − | 0.792392i | \(-0.291164\pi\) | ||||
0.610013 | + | 0.792392i | \(0.291164\pi\) | |||||||
\(228\) | −48947.1 | + | 432629.i | −0.0623577 | + | 0.551161i | ||||
\(229\) | − | 47648.3i | − | 0.0600425i | −0.999549 | − | 0.0300213i | \(-0.990443\pi\) | ||
0.999549 | − | 0.0300213i | \(-0.00955750\pi\) | |||||||
\(230\) | 403383. | − | 1.41978e6i | 0.502803 | − | 1.76971i | ||||
\(231\) | −14829.4 | + | 131072.i | −0.0182849 | + | 0.161615i | ||||
\(232\) | −407555. | −0.497125 | ||||||||
\(233\) | 292242.i | 0.352657i | 0.984331 | + | 0.176328i | \(0.0564221\pi\) | ||||
−0.984331 | + | 0.176328i | \(0.943578\pi\) | |||||||
\(234\) | −116514. | + | 508327.i | −0.139104 | + | 0.606881i | ||||
\(235\) | − | 225953.i | − | 0.266899i | ||||||
\(236\) | 715079.i | 0.835746i | ||||||||
\(237\) | −73026.7 | + | 645462.i | −0.0844522 | + | 0.746448i | ||||
\(238\) | 313644. | 0.358917 | ||||||||
\(239\) | − | 1.53813e6i | − | 1.74180i | −0.491459 | − | 0.870901i | \(-0.663536\pi\) | ||
0.491459 | − | 0.870901i | \(-0.336464\pi\) | |||||||
\(240\) | 1.62828e6 | + | 184221.i | 1.82474 | + | 0.206449i | ||||
\(241\) | − | 370725.i | − | 0.411158i | −0.978641 | − | 0.205579i | \(-0.934092\pi\) | ||
0.978641 | − | 0.205579i | \(-0.0659078\pi\) | |||||||
\(242\) | − | 1.08314e6i | − | 1.18890i | ||||||
\(243\) | −778267. | − | 491517.i | −0.845498 | − | 0.533978i | ||||
\(244\) | 437554.i | 0.470497i | ||||||||
\(245\) | 620225. | 0.660137 | ||||||||
\(246\) | −1.33264e6 | − | 150773.i | −1.40402 | − | 0.158849i | ||||
\(247\) | 474031.i | 0.494384i | ||||||||
\(248\) | 185425.i | 0.191443i | ||||||||
\(249\) | −1.12089e6 | − | 126816.i | −1.14569 | − | 0.129621i | ||||
\(250\) | 309981.i | 0.313679i | ||||||||
\(251\) | 209024. | 0.209417 | 0.104709 | − | 0.994503i | \(-0.466609\pi\) | ||||
0.104709 | + | 0.994503i | \(0.466609\pi\) | |||||||
\(252\) | 93600.4 | − | 408358.i | 0.0928488 | − | 0.405079i | ||||
\(253\) | 214412. | + | 60918.0i | 0.210595 | + | 0.0598335i | ||||
\(254\) | 924189.i | 0.898827i | ||||||||
\(255\) | 588092. | + | 66536.0i | 0.566363 | + | 0.0640776i | ||||
\(256\) | 1.31173e6 | 1.25097 | ||||||||
\(257\) | − | 580419.i | − | 0.548162i | −0.961707 | − | 0.274081i | \(-0.911626\pi\) | ||
0.961707 | − | 0.274081i | \(-0.0883736\pi\) | |||||||
\(258\) | 2.45770e6 | + | 278061.i | 2.29868 | + | 0.260070i | ||||
\(259\) | −1.13818e6 | −1.05429 | ||||||||
\(260\) | −447896. | −0.410908 | ||||||||
\(261\) | −222156. | + | 969220.i | −0.201863 | + | 0.880686i | ||||
\(262\) | −381651. | −0.343490 | ||||||||
\(263\) | −1.58407e6 | −1.41216 | −0.706080 | − | 0.708132i | \(-0.749538\pi\) | ||||
−0.706080 | + | 0.708132i | \(0.749538\pi\) | |||||||
\(264\) | −15335.2 | + | 135543.i | −0.0135419 | + | 0.119693i | ||||
\(265\) | 951391. | 0.832232 | ||||||||
\(266\) | − | 1.06155e6i | − | 0.919893i | ||||||
\(267\) | 143560. | + | 16242.2i | 0.123241 | + | 0.0139434i | ||||
\(268\) | 747188.i | 0.635466i | ||||||||
\(269\) | 1.99855e6i | 1.68397i | 0.539500 | + | 0.841986i | \(0.318613\pi\) | ||||
−0.539500 | + | 0.841986i | \(0.681387\pi\) | |||||||
\(270\) | 730731. | − | 2.07910e6i | 0.610026 | − | 1.73567i | ||||
\(271\) | 1.37973e6 | 1.14122 | 0.570612 | − | 0.821220i | \(-0.306706\pi\) | ||||
0.570612 | + | 0.821220i | \(0.306706\pi\) | |||||||
\(272\) | 588412. | 0.482236 | ||||||||
\(273\) | 51278.9 | − | 453239.i | 0.0416421 | − | 0.368062i | ||||
\(274\) | 1.14749e6i | 0.923367i | ||||||||
\(275\) | −321372. | −0.256257 | ||||||||
\(276\) | −654914. | − | 268809.i | −0.517501 | − | 0.212408i | ||||
\(277\) | 1.43497e6 | 1.12369 | 0.561843 | − | 0.827244i | \(-0.310093\pi\) | ||||
0.561843 | + | 0.827244i | \(0.310093\pi\) | |||||||
\(278\) | 1.00987e6i | 0.783705i | ||||||||
\(279\) | 440966. | + | 101075.i | 0.339152 | + | 0.0777376i | ||||
\(280\) | −790023. | −0.602205 | ||||||||
\(281\) | −1.17003e6 | −0.883954 | −0.441977 | − | 0.897026i | \(-0.645723\pi\) | ||||
−0.441977 | + | 0.897026i | \(0.645723\pi\) | |||||||
\(282\) | −300197. | − | 33963.9i | −0.224794 | − | 0.0254329i | ||||
\(283\) | 1.19800e6i | 0.889179i | 0.895734 | + | 0.444589i | \(0.146650\pi\) | ||||
−0.895734 | + | 0.444589i | \(0.853350\pi\) | |||||||
\(284\) | − | 605330.i | − | 0.445345i | ||||||
\(285\) | 225197. | − | 1.99045e6i | 0.164229 | − | 1.45157i | ||||
\(286\) | − | 188557.i | − | 0.136310i | ||||||
\(287\) | 1.17301e6 | 0.840613 | ||||||||
\(288\) | 316477. | − | 1.38072e6i | 0.224833 | − | 0.980898i | ||||
\(289\) | −1.20734e6 | −0.850323 | ||||||||
\(290\) | −2.38064e6 | −1.66226 | ||||||||
\(291\) | 49884.5 | − | 440915.i | 0.0345329 | − | 0.305226i | ||||
\(292\) | −1.14026e6 | −0.782610 | ||||||||
\(293\) | 2.23825e6 | 1.52314 | 0.761568 | − | 0.648085i | \(-0.224430\pi\) | ||||
0.761568 | + | 0.648085i | \(0.224430\pi\) | |||||||
\(294\) | 93228.8 | − | 824022.i | 0.0629045 | − | 0.555995i | ||||
\(295\) | − | 3.28995e6i | − | 2.20107i | ||||||
\(296\) | −1.17700e6 | −0.780815 | ||||||||
\(297\) | 313981. | + | 110353.i | 0.206544 | + | 0.0725929i | ||||
\(298\) | 2.35411e6i | 1.53563i | ||||||||
\(299\) | −741421. | − | 210650.i | −0.479609 | − | 0.136265i | ||||
\(300\) | 1.01422e6 | + | 114748.i | 0.650624 | + | 0.0736108i | ||||
\(301\) | −2.16330e6 | −1.37626 | ||||||||
\(302\) | 3.60732e6i | 2.27597i | ||||||||
\(303\) | −184695. | + | 1.63247e6i | −0.115571 | + | 1.02150i | ||||
\(304\) | − | 1.99153e6i | − | 1.23596i | ||||||
\(305\) | − | 2.01310e6i | − | 1.23913i | ||||||
\(306\) | 176798. | − | 771330.i | 0.107938 | − | 0.470909i | ||||
\(307\) | −2.25941e6 | −1.36820 | −0.684100 | − | 0.729388i | \(-0.739805\pi\) | ||||
−0.684100 | + | 0.729388i | \(0.739805\pi\) | |||||||
\(308\) | 151475.i | 0.0909836i | ||||||||
\(309\) | 364734. | − | 3.22378e6i | 0.217310 | − | 1.92074i | ||||
\(310\) | 1.08312e6i | 0.640136i | ||||||||
\(311\) | 1.35140e6i | 0.792285i | 0.918189 | + | 0.396142i | \(0.129651\pi\) | ||||
−0.918189 | + | 0.396142i | \(0.870349\pi\) | |||||||
\(312\) | 53028.1 | − | 468700.i | 0.0308404 | − | 0.272589i | ||||
\(313\) | − | 913176.i | − | 0.526858i | −0.964679 | − | 0.263429i | \(-0.915147\pi\) | ||
0.964679 | − | 0.263429i | \(-0.0848535\pi\) | |||||||
\(314\) | −2.37234e6 | −1.35785 | ||||||||
\(315\) | −430638. | + | 1.87878e6i | −0.244532 | + | 1.06684i | ||||
\(316\) | 745932.i | 0.420225i | ||||||||
\(317\) | − | 2.07585e6i | − | 1.16024i | −0.814532 | − | 0.580119i | \(-0.803006\pi\) | ||
0.814532 | − | 0.580119i | \(-0.196994\pi\) | |||||||
\(318\) | 143008. | − | 1.26400e6i | 0.0793035 | − | 0.700940i | ||||
\(319\) | − | 359518.i | − | 0.197808i | ||||||
\(320\) | 27520.3 | 0.0150238 | ||||||||
\(321\) | 2.84415e6 | + | 321784.i | 1.54060 | + | 0.174302i | ||||
\(322\) | 1.66035e6 | + | 471733.i | 0.892401 | + | 0.253546i | ||||
\(323\) | − | 719289.i | − | 0.383617i | ||||||
\(324\) | −951495. | − | 460374.i | −0.503552 | − | 0.243640i | ||||
\(325\) | 1.11128e6 | 0.583601 | ||||||||
\(326\) | 2.62278e6i | 1.36684i | ||||||||
\(327\) | −201482. | + | 1.78084e6i | −0.104200 | + | 0.920992i | ||||
\(328\) | 1.21302e6 | 0.622563 | ||||||||
\(329\) | 264238. | 0.134588 | ||||||||
\(330\) | −89577.1 | + | 791746.i | −0.0452806 | + | 0.400222i | ||||
\(331\) | −1.93557e6 | −0.971043 | −0.485522 | − | 0.874225i | \(-0.661370\pi\) | ||||
−0.485522 | + | 0.874225i | \(0.661370\pi\) | |||||||
\(332\) | −1.29537e6 | −0.644982 | ||||||||
\(333\) | −641579. | + | 2.79907e6i | −0.317059 | + | 1.38326i | ||||
\(334\) | 2.49312e6 | 1.22286 | ||||||||
\(335\) | − | 3.43767e6i | − | 1.67360i | ||||||
\(336\) | −215436. | + | 1.90418e6i | −0.104105 | + | 0.920151i | ||||
\(337\) | − | 294207.i | − | 0.141117i | −0.997508 | − | 0.0705583i | \(-0.977522\pi\) | ||
0.997508 | − | 0.0705583i | \(-0.0224781\pi\) | |||||||
\(338\) | − | 1.97081e6i | − | 0.938326i | ||||||
\(339\) | −2.88412e6 | − | 326305.i | −1.36306 | − | 0.154214i | ||||
\(340\) | 679633. | 0.318843 | ||||||||
\(341\) | −163570. | −0.0761760 | ||||||||
\(342\) | −2.61063e6 | − | 598386.i | −1.20692 | − | 0.276641i | ||||
\(343\) | 2.34405e6i | 1.07580i | ||||||||
\(344\) | −2.23709e6 | −1.01927 | ||||||||
\(345\) | 3.01314e6 | + | 1.23674e6i | 1.36292 | + | 0.559411i | ||||
\(346\) | 3.69125e6 | 1.65761 | ||||||||
\(347\) | 3.21410e6i | 1.43296i | 0.697606 | + | 0.716482i | \(0.254249\pi\) | ||||
−0.697606 | + | 0.716482i | \(0.745751\pi\) | |||||||
\(348\) | −128368. | + | 1.13461e6i | −0.0568211 | + | 0.502225i | ||||
\(349\) | 464451. | 0.204116 | 0.102058 | − | 0.994778i | \(-0.467457\pi\) | ||||
0.102058 | + | 0.994778i | \(0.467457\pi\) | |||||||
\(350\) | −2.48862e6 | −1.08590 | ||||||||
\(351\) | −1.08573e6 | − | 381594.i | −0.470384 | − | 0.165323i | ||||
\(352\) | 512158.i | 0.220317i | ||||||||
\(353\) | 923698.i | 0.394542i | 0.980349 | + | 0.197271i | \(0.0632079\pi\) | ||||
−0.980349 | + | 0.197271i | \(0.936792\pi\) | |||||||
\(354\) | −4.37098e6 | − | 494527.i | −1.85383 | − | 0.209740i | ||||
\(355\) | 2.78501e6i | 1.17289i | ||||||||
\(356\) | 165906. | 0.0693806 | ||||||||
\(357\) | −77810.0 | + | 687740.i | −0.0323121 | + | 0.285597i | ||||
\(358\) | −324285. | −0.133727 | ||||||||
\(359\) | 2.76429e6 | 1.13200 | 0.566002 | − | 0.824404i | \(-0.308489\pi\) | ||||
0.566002 | + | 0.824404i | \(0.308489\pi\) | |||||||
\(360\) | −445328. | + | 1.94287e6i | −0.181102 | + | 0.790109i | ||||
\(361\) | 41606.1 | 0.0168031 | ||||||||
\(362\) | −2.83746e6 | −1.13804 | ||||||||
\(363\) | 2.37505e6 | + | 268711.i | 0.946034 | + | 0.107033i | ||||
\(364\) | − | 523789.i | − | 0.207206i | ||||||
\(365\) | 5.24611e6 | 2.06113 | ||||||||
\(366\) | −2.67458e6 | − | 302599.i | −1.04365 | − | 0.118077i | ||||
\(367\) | − | 1.67359e6i | − | 0.648610i | −0.945953 | − | 0.324305i | \(-0.894870\pi\) | ||
0.945953 | − | 0.324305i | \(-0.105130\pi\) | |||||||
\(368\) | 3.11491e6 | + | 884997.i | 1.19902 | + | 0.340661i | ||||
\(369\) | 661212. | − | 2.88472e6i | 0.252799 | − | 1.10291i | ||||
\(370\) | −6.87520e6 | −2.61084 | ||||||||
\(371\) | 1.11260e6i | 0.419665i | ||||||||
\(372\) | 516213. | + | 58403.7i | 0.193407 | + | 0.0218818i | ||||
\(373\) | 496559.i | 0.184799i | 0.995722 | + | 0.0923993i | \(0.0294536\pi\) | ||||
−0.995722 | + | 0.0923993i | \(0.970546\pi\) | |||||||
\(374\) | 286114.i | 0.105769i | ||||||||
\(375\) | −679709. | − | 76901.5i | −0.249600 | − | 0.0282395i | ||||
\(376\) | 273252. | 0.0996766 | ||||||||
\(377\) | 1.24319e6i | 0.450489i | ||||||||
\(378\) | 2.43139e6 | + | 854548.i | 0.875236 | + | 0.307614i | ||||
\(379\) | − | 3.34566e6i | − | 1.19642i | −0.801340 | − | 0.598209i | \(-0.795879\pi\) | ||
0.801340 | − | 0.598209i | \(-0.204121\pi\) | |||||||
\(380\) | − | 2.30027e6i | − | 0.817185i | ||||||
\(381\) | −2.02651e6 | − | 229277.i | −0.715214 | − | 0.0809184i | ||||
\(382\) | − | 4.22556e6i | − | 1.48158i | ||||||
\(383\) | 338695. | 0.117981 | 0.0589904 | − | 0.998259i | \(-0.481212\pi\) | ||||
0.0589904 | + | 0.998259i | \(0.481212\pi\) | |||||||
\(384\) | −322767. | + | 2.85285e6i | −0.111702 | + | 0.987302i | ||||
\(385\) | − | 696907.i | − | 0.239620i | ||||||
\(386\) | − | 3.78252e6i | − | 1.29215i | ||||||
\(387\) | −1.21943e6 | + | 5.32011e6i | −0.413885 | + | 1.80569i | ||||
\(388\) | − | 509546.i | − | 0.171832i | ||||||
\(389\) | 3.12606e6 | 1.04743 | 0.523714 | − | 0.851894i | \(-0.324546\pi\) | ||||
0.523714 | + | 0.851894i | \(0.324546\pi\) | |||||||
\(390\) | 309751. | − | 2.73780e6i | 0.103122 | − | 0.911466i | ||||
\(391\) | 1.12502e6 | + | 319638.i | 0.372152 | + | 0.105735i | ||||
\(392\) | 750059.i | 0.246536i | ||||||||
\(393\) | 94681.7 | − | 836864.i | 0.0309232 | − | 0.273321i | ||||
\(394\) | 4.38622e6 | 1.42348 | ||||||||
\(395\) | − | 3.43190e6i | − | 1.10673i | ||||||
\(396\) | 372515. | + | 85384.7i | 0.119373 | + | 0.0273616i | ||||
\(397\) | −1.16181e6 | −0.369964 | −0.184982 | − | 0.982742i | \(-0.559223\pi\) | ||||
−0.184982 | + | 0.982742i | \(0.559223\pi\) | |||||||
\(398\) | 4.80085e6 | 1.51918 | ||||||||
\(399\) | 2.32771e6 | + | 263354.i | 0.731976 | + | 0.0828149i | ||||
\(400\) | −4.66879e6 | −1.45900 | ||||||||
\(401\) | 821803. | 0.255215 | 0.127608 | − | 0.991825i | \(-0.459270\pi\) | ||||
0.127608 | + | 0.991825i | \(0.459270\pi\) | |||||||
\(402\) | −4.56724e6 | − | 516732.i | −1.40958 | − | 0.159478i | ||||
\(403\) | 565614. | 0.173483 | ||||||||
\(404\) | 1.88657e6i | 0.575069i | ||||||||
\(405\) | 4.37766e6 | + | 2.11810e6i | 1.32618 | + | 0.641665i | ||||
\(406\) | − | 2.78402e6i | − | 0.838218i | ||||||
\(407\) | − | 1.03828e6i | − | 0.310690i | ||||||
\(408\) | −80464.2 | + | 711199.i | −0.0239305 | + | 0.211515i | ||||
\(409\) | −2.29307e6 | −0.677810 | −0.338905 | − | 0.940821i | \(-0.610057\pi\) | ||||
−0.338905 | + | 0.940821i | \(0.610057\pi\) | |||||||
\(410\) | 7.08558e6 | 2.08169 | ||||||||
\(411\) | −2.51616e6 | − | 284675.i | −0.734741 | − | 0.0831276i | ||||
\(412\) | − | 3.72558e6i | − | 1.08131i | ||||||
\(413\) | 3.84741e6 | 1.10992 | ||||||||
\(414\) | 2.09603e6 | − | 3.81731e6i | 0.601032 | − | 1.09460i | ||||
\(415\) | 5.95974e6 | 1.69866 | ||||||||
\(416\) | − | 1.77101e6i | − | 0.501749i | ||||||
\(417\) | −2.21438e6 | − | 250532.i | −0.623609 | − | 0.0705543i | ||||
\(418\) | 968376. | 0.271084 | ||||||||
\(419\) | −449527. | −0.125090 | −0.0625448 | − | 0.998042i | \(-0.519922\pi\) | ||||
−0.0625448 | + | 0.998042i | \(0.519922\pi\) | |||||||
\(420\) | −248835. | + | 2.19938e6i | −0.0688316 | + | 0.608383i | ||||
\(421\) | − | 4.57385e6i | − | 1.25770i | −0.777527 | − | 0.628850i | \(-0.783526\pi\) | ||
0.777527 | − | 0.628850i | \(-0.216474\pi\) | |||||||
\(422\) | − | 700387.i | − | 0.191451i | ||||||
\(423\) | 148948. | − | 649830.i | 0.0404748 | − | 0.176583i | ||||
\(424\) | 1.15055e6i | 0.310807i | ||||||||
\(425\) | −1.68625e6 | −0.452844 | ||||||||
\(426\) | 3.70013e6 | + | 418628.i | 0.987853 | + | 0.111764i | ||||
\(427\) | 2.35421e6 | 0.624849 | ||||||||
\(428\) | 3.28686e6 | 0.867306 | ||||||||
\(429\) | 413457. | + | 46778.0i | 0.108464 | + | 0.0122715i | ||||
\(430\) | −1.30675e7 | −3.40817 | ||||||||
\(431\) | −4.58849e6 | −1.18981 | −0.594904 | − | 0.803797i | \(-0.702810\pi\) | ||||
−0.594904 | + | 0.803797i | \(0.702810\pi\) | |||||||
\(432\) | 4.56142e6 | + | 1.60318e6i | 1.17595 | + | 0.413307i | ||||
\(433\) | 2.65527e6i | 0.680596i | 0.940318 | + | 0.340298i | \(0.110528\pi\) | ||||
−0.940318 | + | 0.340298i | \(0.889472\pi\) | |||||||
\(434\) | −1.26665e6 | −0.322798 | ||||||||
\(435\) | 590599. | − | 5.22013e6i | 0.149647 | − | 1.32269i | ||||
\(436\) | 2.05804e6i | 0.518487i | ||||||||
\(437\) | 1.08184e6 | − | 3.80774e6i | 0.270994 | − | 0.953813i | ||||
\(438\) | 788566. | − | 6.96991e6i | 0.196405 | − | 1.73597i | ||||
\(439\) | −3.66951e6 | −0.908754 | −0.454377 | − | 0.890810i | \(-0.650138\pi\) | ||||
−0.454377 | + | 0.890810i | \(0.650138\pi\) | |||||||
\(440\) | − | 720679.i | − | 0.177464i | ||||||
\(441\) | 1.78374e6 | + | 408854.i | 0.436752 | + | 0.100109i | ||||
\(442\) | − | 989362.i | − | 0.240879i | ||||||
\(443\) | − | 670900.i | − | 0.162423i | −0.996697 | − | 0.0812117i | \(-0.974121\pi\) | ||
0.996697 | − | 0.0812117i | \(-0.0258790\pi\) | |||||||
\(444\) | −370723. | + | 3.27671e6i | −0.0892466 | + | 0.788825i | ||||
\(445\) | −763305. | −0.182725 | ||||||||
\(446\) | 3.07221e6i | 0.731330i | ||||||||
\(447\) | −5.16196e6 | − | 584017.i | −1.22193 | − | 0.138247i | ||||
\(448\) | 32183.4i | 0.00757595i | ||||||||
\(449\) | 5.53849e6i | 1.29651i | 0.761423 | + | 0.648255i | \(0.224501\pi\) | ||||
−0.761423 | + | 0.648255i | \(0.775499\pi\) | |||||||
\(450\) | −1.40281e6 | + | 6.12016e6i | −0.326563 | + | 1.42473i | ||||
\(451\) | 1.07005e6i | 0.247720i | ||||||||
\(452\) | −3.33305e6 | −0.767354 | ||||||||
\(453\) | −7.90993e6 | − | 894919.i | −1.81104 | − | 0.204898i | ||||
\(454\) | 6.69094e6i | 1.52352i | ||||||||
\(455\) | 2.40986e6i | 0.545711i | ||||||||
\(456\) | 2.40711e6 | + | 272338.i | 0.542106 | + | 0.0613332i | ||||
\(457\) | 4.58966e6i | 1.02799i | 0.857792 | + | 0.513996i | \(0.171836\pi\) | ||||
−0.857792 | + | 0.513996i | \(0.828164\pi\) | |||||||
\(458\) | 336590. | 0.0749786 | ||||||||
\(459\) | 1.64747e6 | + | 579027.i | 0.364994 | + | 0.128282i | ||||
\(460\) | 3.59781e6 | + | 1.02220e6i | 0.792762 | + | 0.225237i | ||||
\(461\) | 4.47210e6i | 0.980074i | 0.871702 | + | 0.490037i | \(0.163017\pi\) | ||||
−0.871702 | + | 0.490037i | \(0.836983\pi\) | |||||||
\(462\) | −925901. | − | 104755.i | −0.201818 | − | 0.0228334i | ||||
\(463\) | 1.82230e6 | 0.395065 | 0.197532 | − | 0.980296i | \(-0.436707\pi\) | ||||
0.197532 | + | 0.980296i | \(0.436707\pi\) | |||||||
\(464\) | − | 5.22297e6i | − | 1.12622i | ||||||
\(465\) | −2.37500e6 | − | 268705.i | −0.509368 | − | 0.0576293i | ||||
\(466\) | −2.06441e6 | −0.440383 | ||||||||
\(467\) | −4.99097e6 | −1.05899 | −0.529496 | − | 0.848312i | \(-0.677619\pi\) | ||||
−0.529496 | + | 0.848312i | \(0.677619\pi\) | |||||||
\(468\) | −1.28813e6 | − | 295254.i | −0.271860 | − | 0.0623134i | ||||
\(469\) | 4.02016e6 | 0.843939 | ||||||||
\(470\) | 1.59614e6 | 0.333293 | ||||||||
\(471\) | 588539. | − | 5.20192e6i | 0.122243 | − | 1.08047i | ||||
\(472\) | 3.97864e6 | 0.822015 | ||||||||
\(473\) | − | 1.97342e6i | − | 0.405571i | ||||||
\(474\) | −4.55957e6 | − | 515864.i | −0.932133 | − | 0.105460i | ||||
\(475\) | 5.70724e6i | 1.16063i | ||||||||
\(476\) | 794792.i | 0.160781i | ||||||||
\(477\) | 2.73616e6 | + | 627159.i | 0.550612 | + | 0.126207i | ||||
\(478\) | 1.08654e7 | 2.17509 | ||||||||
\(479\) | −2.26574e6 | −0.451202 | −0.225601 | − | 0.974220i | \(-0.572435\pi\) | ||||
−0.225601 | + | 0.974220i | \(0.572435\pi\) | |||||||
\(480\) | −841347. | + | 7.43642e6i | −0.166676 | + | 1.47320i | ||||
\(481\) | 3.59029e6i | 0.707565i | ||||||||
\(482\) | 2.61881e6 | 0.513437 | ||||||||
\(483\) | −1.44630e6 | + | 3.52369e6i | −0.282091 | + | 0.687274i | ||||
\(484\) | 2.74475e6 | 0.532585 | ||||||||
\(485\) | 2.34433e6i | 0.452547i | ||||||||
\(486\) | 3.47210e6 | − | 5.49771e6i | 0.666809 | − | 1.05582i | ||||
\(487\) | 919704. | 0.175722 | 0.0878609 | − | 0.996133i | \(-0.471997\pi\) | ||||
0.0878609 | + | 0.996133i | \(0.471997\pi\) | |||||||
\(488\) | 2.43451e6 | 0.462767 | ||||||||
\(489\) | −5.75108e6 | − | 650670.i | −1.08762 | − | 0.123052i | ||||
\(490\) | 4.38130e6i | 0.824352i | ||||||||
\(491\) | − | 6.77346e6i | − | 1.26796i | −0.773348 | − | 0.633982i | \(-0.781420\pi\) | ||
0.773348 | − | 0.633982i | \(-0.218580\pi\) | |||||||
\(492\) | 382067. | − | 3.37698e6i | 0.0711585 | − | 0.628949i | ||||
\(493\) | − | 1.88640e6i | − | 0.349556i | ||||||
\(494\) | −3.34858e6 | −0.617366 | ||||||||
\(495\) | −1.71387e6 | − | 392839.i | −0.314388 | − | 0.0720613i | ||||
\(496\) | −2.37630e6 | −0.433707 | ||||||||
\(497\) | −3.25691e6 | −0.591445 | ||||||||
\(498\) | 895836. | − | 7.91803e6i | 0.161866 | − | 1.43068i | ||||
\(499\) | −2.57927e6 | −0.463709 | −0.231855 | − | 0.972750i | \(-0.574479\pi\) | ||||
−0.231855 | + | 0.972750i | \(0.574479\pi\) | |||||||
\(500\) | −785511. | −0.140516 | ||||||||
\(501\) | −618504. | + | 5.46678e6i | −0.110090 | + | 0.973054i | ||||
\(502\) | 1.47656e6i | 0.261512i | ||||||||
\(503\) | −2.59926e6 | −0.458068 | −0.229034 | − | 0.973418i | \(-0.573557\pi\) | ||||
−0.229034 | + | 0.973418i | \(0.573557\pi\) | |||||||
\(504\) | −2.27207e6 | − | 520785.i | −0.398424 | − | 0.0913234i | ||||
\(505\) | − | 8.67977e6i | − | 1.51454i | ||||||
\(506\) | −430327. | + | 1.51461e6i | −0.0747176 | + | 0.262982i | ||||
\(507\) | 4.32149e6 | + | 488928.i | 0.746644 | + | 0.0844744i | ||||
\(508\) | −2.34195e6 | −0.402641 | ||||||||
\(509\) | − | 7.89088e6i | − | 1.34999i | −0.737822 | − | 0.674996i | \(-0.764146\pi\) | ||
0.737822 | − | 0.674996i | \(-0.235854\pi\) | |||||||
\(510\) | −470013. | + | 4.15431e6i | −0.0800175 | + | 0.707251i | ||||
\(511\) | 6.13502e6i | 1.03935i | ||||||||
\(512\) | 3.37245e6i | 0.568552i | ||||||||
\(513\) | 1.95976e6 | − | 5.57599e6i | 0.328784 | − | 0.935467i | ||||
\(514\) | 4.10011e6 | 0.684522 | ||||||||
\(515\) | 1.71407e7i | 2.84781i | ||||||||
\(516\) | −704622. | + | 6.22795e6i | −0.116502 | + | 1.02972i | ||||
\(517\) | 241045.i | 0.0396618i | ||||||||
\(518\) | − | 8.04014e6i | − | 1.31656i | ||||||
\(519\) | −915740. | + | 8.09396e6i | −0.149229 | + | 1.31899i | ||||
\(520\) | 2.49206e6i | 0.404157i | ||||||||
\(521\) | −9.26811e6 | −1.49588 | −0.747940 | − | 0.663766i | \(-0.768957\pi\) | ||||
−0.747940 | + | 0.663766i | \(0.768957\pi\) | |||||||
\(522\) | −6.84661e6 | − | 1.56932e6i | −1.09976 | − | 0.252078i | ||||
\(523\) | − | 7.44892e6i | − | 1.19080i | −0.803429 | − | 0.595401i | \(-0.796993\pi\) | ||
0.803429 | − | 0.595401i | \(-0.203007\pi\) | |||||||
\(524\) | − | 967127.i | − | 0.153871i | ||||||
\(525\) | 617388. | − | 5.45691e6i | 0.0977597 | − | 0.864069i | ||||
\(526\) | − | 1.11899e7i | − | 1.76345i | ||||||
\(527\) | −858257. | −0.134614 | ||||||||
\(528\) | −1.73704e6 | − | 196527.i | −0.271160 | − | 0.0306787i | ||||
\(529\) | 5.47484e6 | + | 3.38417e6i | 0.850614 | + | 0.525790i | ||||
\(530\) | 6.72067e6i | 1.03926i | ||||||||
\(531\) | 2.16874e6 | − | 9.46175e6i | 0.333789 | − | 1.45625i | ||||
\(532\) | 2.69004e6 | 0.412078 | ||||||||
\(533\) | − | 3.70015e6i | − | 0.564159i | ||||||
\(534\) | −114736. | + | 1.01412e6i | −0.0174119 | + | 0.153898i | ||||
\(535\) | −1.51223e7 | −2.28419 | ||||||||
\(536\) | 4.15729e6 | 0.625026 | ||||||||
\(537\) | 80450.0 | − | 711074.i | 0.0120390 | − | 0.106409i | ||||
\(538\) | −1.41179e7 | −2.10287 | ||||||||
\(539\) | −661654. | −0.0980977 | ||||||||
\(540\) | 5.26857e6 | + | 1.85172e6i | 0.777514 | + | 0.273269i | ||||
\(541\) | 1.12804e6 | 0.165703 | 0.0828517 | − | 0.996562i | \(-0.473597\pi\) | ||||
0.0828517 | + | 0.996562i | \(0.473597\pi\) | |||||||
\(542\) | 9.74648e6i | 1.42511i | ||||||||
\(543\) | 703928. | − | 6.22181e6i | 0.102454 | − | 0.905560i | ||||
\(544\) | 2.68731e6i | 0.389332i | ||||||||
\(545\) | − | 9.46867e6i | − | 1.36552i | ||||||
\(546\) | 3.20170e6 | + | 362236.i | 0.459620 | + | 0.0520009i | ||||
\(547\) | −816790. | −0.116719 | −0.0583596 | − | 0.998296i | \(-0.518587\pi\) | ||||
−0.0583596 | + | 0.998296i | \(0.518587\pi\) | |||||||
\(548\) | −2.90782e6 | −0.413634 | ||||||||
\(549\) | 1.32704e6 | − | 5.78960e6i | 0.187912 | − | 0.819819i | ||||
\(550\) | − | 2.27019e6i | − | 0.320003i | ||||||
\(551\) | −6.38468e6 | −0.895901 | ||||||||
\(552\) | −1.49563e6 | + | 3.64389e6i | −0.208918 | + | 0.508999i | ||||
\(553\) | 4.01341e6 | 0.558085 | ||||||||
\(554\) | 1.01367e7i | 1.40321i | ||||||||
\(555\) | 1.70563e6 | − | 1.50755e7i | 0.235045 | − | 2.07750i | ||||
\(556\) | −2.55906e6 | −0.351070 | ||||||||
\(557\) | −62846.8 | −0.00858311 | −0.00429156 | − | 0.999991i | \(-0.501366\pi\) | ||||
−0.00429156 | + | 0.999991i | \(0.501366\pi\) | |||||||
\(558\) | −713995. | + | 3.11500e6i | −0.0970755 | + | 0.423519i | ||||
\(559\) | 6.82395e6i | 0.923648i | ||||||||
\(560\) | − | 1.01244e7i | − | 1.36427i | ||||||
\(561\) | −627375. | − | 70980.4i | −0.0841627 | − | 0.00952206i | ||||
\(562\) | − | 8.26512e6i | − | 1.10385i | ||||||
\(563\) | 6.57966e6 | 0.874848 | 0.437424 | − | 0.899255i | \(-0.355891\pi\) | ||||
0.437424 | + | 0.899255i | \(0.355891\pi\) | |||||||
\(564\) | 86066.6 | − | 760718.i | 0.0113930 | − | 0.100699i | ||||
\(565\) | 1.53347e7 | 2.02095 | ||||||||
\(566\) | −8.46269e6 | −1.11037 | ||||||||
\(567\) | −2.47699e6 | + | 5.11942e6i | −0.323569 | + | 0.668748i | ||||
\(568\) | −3.36800e6 | −0.438028 | ||||||||
\(569\) | 8.19458e6 | 1.06108 | 0.530538 | − | 0.847661i | \(-0.321990\pi\) | ||||
0.530538 | + | 0.847661i | \(0.321990\pi\) | |||||||
\(570\) | 1.40606e7 | + | 1.59080e6i | 1.81266 | + | 0.205082i | ||||
\(571\) | − | 3.95838e6i | − | 0.508074i | −0.967195 | − | 0.254037i | \(-0.918242\pi\) | ||
0.967195 | − | 0.254037i | \(-0.0817585\pi\) | |||||||
\(572\) | 477814. | 0.0610617 | ||||||||
\(573\) | 9.26556e6 | + | 1.04829e6i | 1.17892 | + | 0.133382i | ||||
\(574\) | 8.28617e6i | 1.04972i | ||||||||
\(575\) | −8.92656e6 | − | 2.53619e6i | −1.12594 | − | 0.319898i | ||||
\(576\) | 79147.3 | + | 18141.5i | 0.00993985 | + | 0.00227833i | ||||
\(577\) | −5.93437e6 | −0.742053 | −0.371027 | − | 0.928622i | \(-0.620994\pi\) | ||||
−0.371027 | + | 0.928622i | \(0.620994\pi\) | |||||||
\(578\) | − | 8.52868e6i | − | 1.06185i | ||||||
\(579\) | 8.29411e6 | + | 938385.i | 1.02819 | + | 0.116328i | ||||
\(580\) | − | 6.03268e6i | − | 0.744629i | ||||||
\(581\) | 6.96958e6i | 0.856576i | ||||||||
\(582\) | 3.11464e6 | + | 352387.i | 0.381154 | + | 0.0431233i | ||||
\(583\) | −1.01494e6 | −0.123671 | ||||||||
\(584\) | 6.34429e6i | 0.769752i | ||||||||
\(585\) | 5.92645e6 | + | 1.35841e6i | 0.715987 | + | 0.164112i | ||||
\(586\) | 1.58111e7i | 1.90203i | ||||||||
\(587\) | 1.32192e7i | 1.58347i | 0.610866 | + | 0.791734i | \(0.290821\pi\) | ||||
−0.610866 | + | 0.791734i | \(0.709179\pi\) | |||||||
\(588\) | 2.08812e6 | + | 236247.i | 0.249065 | + | 0.0281789i | ||||
\(589\) | 2.90484e6i | 0.345012i | ||||||||
\(590\) | 2.32403e7 | 2.74861 | ||||||||
\(591\) | −1.08815e6 | + | 9.61787e6i | −0.128151 | + | 1.13269i | ||||
\(592\) | − | 1.50837e7i | − | 1.76891i | ||||||
\(593\) | 7.51285e6i | 0.877340i | 0.898648 | + | 0.438670i | \(0.144550\pi\) | ||||
−0.898648 | + | 0.438670i | \(0.855450\pi\) | |||||||
\(594\) | −779541. | + | 2.21798e6i | −0.0906510 | + | 0.257924i | ||||
\(595\) | − | 3.65669e6i | − | 0.423444i | ||||||
\(596\) | −5.96545e6 | −0.687904 | ||||||||
\(597\) | −1.19101e6 | + | 1.05270e7i | −0.136767 | + | 1.20884i | ||||
\(598\) | 1.48804e6 | − | 5.23743e6i | 0.170162 | − | 0.598915i | ||||
\(599\) | − | 7.65322e6i | − | 0.871519i | −0.900063 | − | 0.435760i | \(-0.856480\pi\) | ||
0.900063 | − | 0.435760i | \(-0.143520\pi\) | |||||||
\(600\) | 638447. | − | 5.64305e6i | 0.0724014 | − | 0.639935i | ||||
\(601\) | −462278. | −0.0522056 | −0.0261028 | − | 0.999659i | \(-0.508310\pi\) | ||||
−0.0261028 | + | 0.999659i | \(0.508310\pi\) | |||||||
\(602\) | − | 1.52817e7i | − | 1.71862i | ||||||
\(603\) | 2.26612e6 | − | 9.88660e6i | 0.253799 | − | 1.10727i | ||||
\(604\) | −9.14116e6 | −1.01955 | ||||||||
\(605\) | −1.26281e7 | −1.40265 | ||||||||
\(606\) | −1.15318e7 | − | 1.30470e6i | −1.27561 | − | 0.144320i | ||||
\(607\) | −4.48728e6 | −0.494323 | −0.247162 | − | 0.968974i | \(-0.579498\pi\) | ||||
−0.247162 | + | 0.968974i | \(0.579498\pi\) | |||||||
\(608\) | 9.09540e6 | 0.997845 | ||||||||
\(609\) | 6.10464e6 | + | 690671.i | 0.666986 | + | 0.0754619i | ||||
\(610\) | 1.42207e7 | 1.54737 | ||||||||
\(611\) | − | 833517.i | − | 0.0903258i | ||||||
\(612\) | 1.95460e6 | + | 448016.i | 0.210949 | + | 0.0483520i | ||||
\(613\) | − | 3.41404e6i | − | 0.366959i | −0.983024 | − | 0.183479i | \(-0.941264\pi\) | ||
0.983024 | − | 0.183479i | \(-0.0587361\pi\) | |||||||
\(614\) | − | 1.59606e7i | − | 1.70855i | ||||||
\(615\) | −1.75782e6 | + | 1.55369e7i | −0.187407 | + | 1.65644i | ||||
\(616\) | 842793. | 0.0894889 | ||||||||
\(617\) | −1.60232e7 | −1.69448 | −0.847238 | − | 0.531214i | \(-0.821736\pi\) | ||||
−0.847238 | + | 0.531214i | \(0.821736\pi\) | |||||||
\(618\) | 2.27729e7 | + | 2.57650e6i | 2.39854 | + | 0.271368i | ||||
\(619\) | 1.72859e7i | 1.81328i | 0.421901 | + | 0.906642i | \(0.361363\pi\) | ||||
−0.421901 | + | 0.906642i | \(0.638637\pi\) | |||||||
\(620\) | −2.74469e6 | −0.286757 | ||||||||
\(621\) | 7.85040e6 | + | 5.54308e6i | 0.816888 | + | 0.576796i | ||||
\(622\) | −9.54631e6 | −0.989372 | ||||||||
\(623\) | − | 892640.i | − | 0.0921418i | ||||||
\(624\) | 6.00657e6 | + | 679575.i | 0.617539 | + | 0.0698676i | ||||
\(625\) | −7.81668e6 | −0.800428 | ||||||||
\(626\) | 6.45071e6 | 0.657918 | ||||||||
\(627\) | −240239. | + | 2.12340e6i | −0.0244047 | + | 0.215706i | ||||
\(628\) | − | 6.01164e6i | − | 0.608266i | ||||||
\(629\) | − | 5.44786e6i | − | 0.549034i | ||||||
\(630\) | −1.32718e7 | − | 3.04205e6i | −1.33223 | − | 0.305362i | ||||
\(631\) | − | 4.13451e6i | − | 0.413382i | −0.978406 | − | 0.206691i | \(-0.933731\pi\) | ||
0.978406 | − | 0.206691i | \(-0.0662694\pi\) | |||||||
\(632\) | 4.15031e6 | 0.413321 | ||||||||
\(633\) | 1.53577e6 | + | 173755.i | 0.152341 | + | 0.0172357i | ||||
\(634\) | 1.46639e7 | 1.44886 | ||||||||
\(635\) | 1.07749e7 | 1.06042 | ||||||||
\(636\) | 3.20306e6 | + | 362391.i | 0.313995 | + | 0.0355250i | ||||
\(637\) | 2.28795e6 | 0.223408 | ||||||||
\(638\) | 2.53965e6 | 0.247015 | ||||||||
\(639\) | −1.83589e6 | + | 8.00957e6i | −0.177866 | + | 0.775992i | ||||
\(640\) | − | 1.51685e7i | − | 1.46383i | ||||||
\(641\) | −8.64292e6 | −0.830836 | −0.415418 | − | 0.909631i | \(-0.636365\pi\) | ||||
−0.415418 | + | 0.909631i | \(0.636365\pi\) | |||||||
\(642\) | −2.27309e6 | + | 2.00912e7i | −0.217661 | + | 1.92384i | ||||
\(643\) | 1.25671e6i | 0.119870i | 0.998202 | + | 0.0599348i | \(0.0190893\pi\) | ||||
−0.998202 | + | 0.0599348i | \(0.980911\pi\) | |||||||
\(644\) | −1.19540e6 | + | 4.20742e6i | −0.113579 | + | 0.399762i | ||||
\(645\) | 3.24184e6 | − | 2.86536e7i | 0.306826 | − | 2.71194i | ||||
\(646\) | 5.08109e6 | 0.479044 | ||||||||
\(647\) | 3.40198e6i | 0.319500i | 0.987157 | + | 0.159750i | \(0.0510689\pi\) | ||||
−0.987157 | + | 0.159750i | \(0.948931\pi\) | |||||||
\(648\) | −2.56149e6 | + | 5.29404e6i | −0.239637 | + | 0.495279i | ||||
\(649\) | 3.50970e6i | 0.327084i | ||||||||
\(650\) | 7.85014e6i | 0.728776i | ||||||||
\(651\) | 314235. | − | 2.77743e6i | 0.0290604 | − | 0.256856i | ||||
\(652\) | −6.64627e6 | −0.612293 | ||||||||
\(653\) | 2.05797e7i | 1.88867i | 0.328990 | + | 0.944333i | \(0.393292\pi\) | ||||
−0.328990 | + | 0.944333i | \(0.606708\pi\) | |||||||
\(654\) | −1.25799e7 | − | 1.42328e6i | −1.15010 | − | 0.130120i | ||||
\(655\) | 4.44958e6i | 0.405243i | ||||||||
\(656\) | 1.55453e7i | 1.41039i | ||||||||
\(657\) | 1.50876e7 | + | 3.45825e6i | 1.36366 | + | 0.312567i | ||||
\(658\) | 1.86659e6i | 0.168068i | ||||||||
\(659\) | 1.51070e7 | 1.35508 | 0.677539 | − | 0.735486i | \(-0.263046\pi\) | ||||
0.677539 | + | 0.735486i | \(0.263046\pi\) | |||||||
\(660\) | −2.00633e6 | − | 226994.i | −0.179284 | − | 0.0202840i | ||||
\(661\) | − | 1.12641e7i | − | 1.00275i | −0.865229 | − | 0.501376i | \(-0.832827\pi\) | ||
0.865229 | − | 0.501376i | \(-0.167173\pi\) | |||||||
\(662\) | − | 1.36729e7i | − | 1.21260i | ||||||
\(663\) | 2.16942e6 | + | 245445.i | 0.191672 | + | 0.0216856i | ||||
\(664\) | 7.20731e6i | 0.634385i | ||||||||
\(665\) | −1.23764e7 | −1.08527 | ||||||||
\(666\) | −1.97728e7 | − | 4.53214e6i | −1.72736 | − | 0.395930i | ||||
\(667\) | 2.83723e6 | − | 9.98614e6i | 0.246933 | − | 0.869126i | ||||
\(668\) | 6.31772e6i | 0.547796i | ||||||||
\(669\) | −6.73656e6 | − | 762166.i | −0.581933 | − | 0.0658392i | ||||
\(670\) | 2.42839e7 | 2.08993 | ||||||||
\(671\) | 2.14757e6i | 0.184137i | ||||||||
\(672\) | −8.69646e6 | − | 983907.i | −0.742881 | − | 0.0840487i | ||||
\(673\) | −1.33396e7 | −1.13528 | −0.567642 | − | 0.823276i | \(-0.692144\pi\) | ||||
−0.567642 | + | 0.823276i | \(0.692144\pi\) | |||||||
\(674\) | 2.07829e6 | 0.176221 | ||||||||
\(675\) | −1.30719e7 | − | 4.59432e6i | −1.10428 | − | 0.388116i | ||||
\(676\) | 4.99416e6 | 0.420335 | ||||||||
\(677\) | −5.60773e6 | −0.470236 | −0.235118 | − | 0.971967i | \(-0.575548\pi\) | ||||
−0.235118 | + | 0.971967i | \(0.575548\pi\) | |||||||
\(678\) | 2.30503e6 | − | 2.03735e7i | 0.192576 | − | 1.70213i | ||||
\(679\) | −2.74156e6 | −0.228204 | ||||||||
\(680\) | − | 3.78142e6i | − | 0.313605i | ||||||
\(681\) | −1.46715e7 | − | 1.65992e6i | −1.21229 | − | 0.137157i | ||||
\(682\) | − | 1.15547e6i | − | 0.0951254i | ||||||
\(683\) | − | 2.32238e7i | − | 1.90494i | −0.304637 | − | 0.952469i | \(-0.598535\pi\) | ||
0.304637 | − | 0.952469i | \(-0.401465\pi\) | |||||||
\(684\) | 1.51635e6 | − | 6.61549e6i | 0.123925 | − | 0.540657i | ||||
\(685\) | 1.33783e7 | 1.08937 | ||||||||
\(686\) | −1.65584e7 | −1.34341 | ||||||||
\(687\) | −83502.6 | + | 738055.i | −0.00675007 | + | 0.0596619i | ||||
\(688\) | − | 2.86692e7i | − | 2.30911i | ||||||
\(689\) | 3.50959e6 | 0.281649 | ||||||||
\(690\) | −8.73639e6 | + | 2.12849e7i | −0.698569 | + | 1.70196i | ||||
\(691\) | 1.09068e7 | 0.868964 | 0.434482 | − | 0.900681i | \(-0.356932\pi\) | ||||
0.434482 | + | 0.900681i | \(0.356932\pi\) | |||||||
\(692\) | 9.35384e6i | 0.742548i | ||||||||
\(693\) | 459403. | − | 2.00428e6i | 0.0363380 | − | 0.158535i | ||||
\(694\) | −2.27045e7 | −1.78943 | ||||||||
\(695\) | 1.17738e7 | 0.924601 | ||||||||
\(696\) | 6.31287e6 | + | 714230.i | 0.493974 | + | 0.0558876i | ||||
\(697\) | 5.61457e6i | 0.437758i | ||||||||
\(698\) | 3.28090e6i | 0.254891i | ||||||||
\(699\) | 512147. | − | 4.52672e6i | 0.0396462 | − | 0.350421i | ||||
\(700\) | − | 6.30631e6i | − | 0.486441i | ||||||
\(701\) | −2.24487e7 | −1.72543 | −0.862713 | − | 0.505695i | \(-0.831236\pi\) | ||||
−0.862713 | + | 0.505695i | \(0.831236\pi\) | |||||||
\(702\) | 2.69560e6 | − | 7.66961e6i | 0.206449 | − | 0.587396i | ||||
\(703\) | −1.84387e7 | −1.40716 | ||||||||
\(704\) | −29358.6 | −0.00223256 | ||||||||
\(705\) | −395977. | + | 3.49992e6i | −0.0300052 | + | 0.265207i | ||||
\(706\) | −6.52504e6 | −0.492687 | ||||||||
\(707\) | 1.01505e7 | 0.763728 | ||||||||
\(708\) | 1.25316e6 | − | 1.10763e7i | 0.0939558 | − | 0.830448i | ||||
\(709\) | 2.21859e7i | 1.65753i | 0.559596 | + | 0.828766i | \(0.310956\pi\) | ||||
−0.559596 | + | 0.828766i | \(0.689044\pi\) | |||||||
\(710\) | −1.96734e7 | −1.46465 | ||||||||
\(711\) | 2.26231e6 | − | 9.86999e6i | 0.167834 | − | 0.732222i | ||||
\(712\) | − | 923089.i | − | 0.0682407i | ||||||
\(713\) | −4.54339e6 | − | 1.29085e6i | −0.334701 | − | 0.0950941i | ||||
\(714\) | −4.85823e6 | − | 549654.i | −0.356642 | − | 0.0403500i | ||||
\(715\) | −2.19833e6 | −0.160816 | ||||||||
\(716\) | − | 821757.i | − | 0.0599047i | ||||||
\(717\) | −2.69554e6 | + | 2.38251e7i | −0.195816 | + | 1.73076i | ||||
\(718\) | 1.95271e7i | 1.41360i | ||||||||
\(719\) | − | 471342.i | − | 0.0340028i | −0.999855 | − | 0.0170014i | \(-0.994588\pi\) | ||
0.999855 | − | 0.0170014i | \(-0.00541197\pi\) | |||||||
\(720\) | −2.48986e7 | − | 5.70704e6i | −1.78996 | − | 0.410280i | ||||
\(721\) | −2.00451e7 | −1.43605 | ||||||||
\(722\) | 293907.i | 0.0209830i | ||||||||
\(723\) | −649687. | + | 5.74239e6i | −0.0462230 | + | 0.408552i | ||||
\(724\) | − | 7.19028e6i | − | 0.509799i | ||||||
\(725\) | 1.49678e7i | 1.05758i | ||||||||
\(726\) | −1.89818e6 | + | 1.67775e7i | −0.133658 | + | 1.18137i | ||||
\(727\) | 1.10840e7i | 0.777784i | 0.921283 | + | 0.388892i | \(0.127142\pi\) | ||||
−0.921283 | + | 0.388892i | \(0.872858\pi\) | |||||||
\(728\) | −2.91432e6 | −0.203802 | ||||||||
\(729\) | 1.11937e7 | + | 8.97732e6i | 0.780108 | + | 0.625645i | ||||
\(730\) | 3.70587e7i | 2.57385i | ||||||||
\(731\) | − | 1.03546e7i | − | 0.716703i | ||||||
\(732\) | 766803. | − | 6.77755e6i | 0.0528940 | − | 0.467514i | ||||
\(733\) | 7.54820e6i | 0.518900i | 0.965757 | + | 0.259450i | \(0.0835413\pi\) | ||||
−0.965757 | + | 0.259450i | \(0.916459\pi\) | |||||||
\(734\) | 1.18223e7 | 0.809957 | ||||||||
\(735\) | −9.60706e6 | − | 1.08693e6i | −0.655952 | − | 0.0742136i | ||||
\(736\) | −4.04182e6 | + | 1.42259e7i | −0.275032 | + | 0.968023i | ||||
\(737\) | 3.66729e6i | 0.248701i | ||||||||
\(738\) | 2.03778e7 | + | 4.67083e6i | 1.37726 | + | 0.315684i | ||||
\(739\) | 2.33132e7 | 1.57033 | 0.785164 | − | 0.619287i | \(-0.212578\pi\) | ||||
0.785164 | + | 0.619287i | \(0.212578\pi\) | |||||||
\(740\) | − | 1.74222e7i | − | 1.16956i | ||||||
\(741\) | 830729. | − | 7.34257e6i | 0.0555794 | − | 0.491250i | ||||
\(742\) | −7.85943e6 | −0.524061 | ||||||||
\(743\) | 5.07752e6 | 0.337427 | 0.168713 | − | 0.985665i | \(-0.446039\pi\) | ||||
0.168713 | + | 0.985665i | \(0.446039\pi\) | |||||||
\(744\) | 324954. | − | 2.87217e6i | 0.0215223 | − | 0.190229i | ||||
\(745\) | 2.74459e7 | 1.81171 | ||||||||
\(746\) | −3.50771e6 | −0.230769 | ||||||||
\(747\) | 1.71400e7 | + | 3.92868e6i | 1.12385 | + | 0.257599i | ||||
\(748\) | −725030. | −0.0473807 | ||||||||
\(749\) | − | 1.76846e7i | − | 1.15184i | ||||||
\(750\) | 543235. | − | 4.80150e6i | 0.0352643 | − | 0.311690i | ||||
\(751\) | − | 1.75809e7i | − | 1.13747i | −0.822519 | − | 0.568737i | \(-0.807432\pi\) | ||
0.822519 | − | 0.568737i | \(-0.192568\pi\) | |||||||
\(752\) | 3.50183e6i | 0.225814i | ||||||||
\(753\) | −3.23771e6 | − | 366311.i | −0.208090 | − | 0.0235430i | ||||
\(754\) | −8.78195e6 | −0.562552 | ||||||||
\(755\) | 4.20568e7 | 2.68515 | ||||||||
\(756\) | −2.16547e6 | + | 6.16129e6i | −0.137800 | + | 0.392073i | ||||
\(757\) | − | 1.79381e7i | − | 1.13772i | −0.822433 | − | 0.568862i | \(-0.807384\pi\) | ||
0.822433 | − | 0.568862i | \(-0.192616\pi\) | |||||||
\(758\) | 2.36339e7 | 1.49404 | ||||||||
\(759\) | −3.21440e6 | − | 1.31935e6i | −0.202533 | − | 0.0831296i | ||||
\(760\) | −1.27985e7 | −0.803759 | ||||||||
\(761\) | − | 1.50206e7i | − | 0.940214i | −0.882609 | − | 0.470107i | \(-0.844215\pi\) | ||
0.882609 | − | 0.470107i | \(-0.155785\pi\) | |||||||
\(762\) | 1.61962e6 | − | 1.43153e7i | 0.101048 | − | 0.893129i | ||||
\(763\) | 1.10731e7 | 0.688583 | ||||||||
\(764\) | 1.07078e7 | 0.663693 | ||||||||
\(765\) | −8.99274e6 | − | 2.06124e6i | −0.555569 | − | 0.127343i | ||||
\(766\) | 2.39255e6i | 0.147329i | ||||||||
\(767\) | − | 1.21363e7i | − | 0.744901i | ||||||
\(768\) | −2.03183e7 | − | 2.29878e6i | −1.24303 | − | 0.140635i | ||||
\(769\) | 2.25008e7i | 1.37209i | 0.727559 | + | 0.686045i | \(0.240655\pi\) | ||||
−0.727559 | + | 0.686045i | \(0.759345\pi\) | |||||||
\(770\) | 4.92298e6 | 0.299228 | ||||||||
\(771\) | −1.01717e6 | + | 8.99048e6i | −0.0616252 | + | 0.544687i | ||||
\(772\) | 9.58514e6 | 0.578836 | ||||||||
\(773\) | −8.67404e6 | −0.522123 | −0.261061 | − | 0.965322i | \(-0.584073\pi\) | ||||
−0.261061 | + | 0.965322i | \(0.584073\pi\) | |||||||
\(774\) | −3.75815e7 | − | 8.61411e6i | −2.25487 | − | 0.516842i | ||||
\(775\) | 6.80988e6 | 0.407273 | ||||||||
\(776\) | −2.83507e6 | −0.169009 | ||||||||
\(777\) | 1.76300e7 | + | 1.99463e6i | 1.04761 | + | 0.118525i | ||||
\(778\) | 2.20827e7i | 1.30798i | ||||||||
\(779\) | 1.90030e7 | 1.12196 | ||||||||
\(780\) | 6.93775e6 | + | 784929.i | 0.408303 | + | 0.0461949i | ||||
\(781\) | − | 2.97104e6i | − | 0.174293i | ||||||
\(782\) | −2.25794e6 | + | 7.94722e6i | −0.132037 | + | 0.464728i | ||||
\(783\) | 5.13966e6 | − | 1.46235e7i | 0.299592 | − | 0.852409i | ||||
\(784\) | −9.61229e6 | −0.558517 | ||||||||
\(785\) | 2.76584e7i | 1.60197i | ||||||||
\(786\) | 5.91164e6 | + | 668836.i | 0.341312 | + | 0.0386156i | ||||
\(787\) | − | 2.50677e7i | − | 1.44271i | −0.692568 | − | 0.721353i | \(-0.743521\pi\) | ||
0.692568 | − | 0.721353i | \(-0.256479\pi\) | |||||||
\(788\) | 1.11150e7i | 0.637664i | ||||||||
\(789\) | 2.45366e7 | + | 2.77604e6i | 1.40321 | + | 0.158757i | ||||
\(790\) | 2.42431e7 | 1.38204 | ||||||||
\(791\) | 1.79331e7i | 1.01909i | ||||||||
\(792\) | 475074. | − | 2.07264e6i | 0.0269121 | − | 0.117412i | ||||
\(793\) | − | 7.42615e6i | − | 0.419354i | ||||||
\(794\) | − | 8.20710e6i | − | 0.461996i | ||||||
\(795\) | −1.47367e7 | − | 1.66729e6i | −0.826956 | − | 0.0935608i | ||||
\(796\) | 1.21656e7i | 0.680538i | ||||||||
\(797\) | −8.45754e6 | −0.471626 | −0.235813 | − | 0.971798i | \(-0.575775\pi\) | ||||
−0.235813 | + | 0.971798i | \(0.575775\pi\) | |||||||
\(798\) | −1.86035e6 | + | 1.64431e7i | −0.103416 | + | 0.914061i | ||||
\(799\) | 1.26477e6i | 0.0700882i | ||||||||
\(800\) | − | 2.13226e7i | − | 1.17792i | ||||||
\(801\) | −2.19523e6 | − | 503172.i | −0.120892 | − | 0.0277099i | ||||
\(802\) | 5.80525e6i | 0.318702i | ||||||||
\(803\) | −5.59653e6 | −0.306288 | ||||||||
\(804\) | 1.30943e6 | − | 1.15737e7i | 0.0714401 | − | 0.631438i | ||||
\(805\) | 5.49982e6 | − | 1.93576e7i | 0.299129 | − | 1.05284i | ||||
\(806\) | 3.99552e6i | 0.216639i | ||||||||
\(807\) | 3.50242e6 | − | 3.09568e7i | 0.189315 | − | 1.67330i | ||||
\(808\) | 1.04967e7 | 0.565621 | ||||||||
\(809\) | 792665.i | 0.0425812i | 0.999773 | + | 0.0212906i | \(0.00677753\pi\) | ||||
−0.999773 | + | 0.0212906i | \(0.993222\pi\) | |||||||
\(810\) | −1.49623e7 | + | 3.09240e7i | −0.801285 | + | 1.65608i | ||||
\(811\) | −5.20675e6 | −0.277981 | −0.138990 | − | 0.990294i | \(-0.544386\pi\) | ||||
−0.138990 | + | 0.990294i | \(0.544386\pi\) | |||||||
\(812\) | 7.05487e6 | 0.375490 | ||||||||
\(813\) | −2.13715e7 | − | 2.41795e6i | −1.13399 | − | 0.128298i | ||||
\(814\) | 7.33443e6 | 0.387976 | ||||||||
\(815\) | 3.05783e7 | 1.61257 | ||||||||
\(816\) | −9.11430e6 | − | 1.03118e6i | −0.479179 | − | 0.0542137i | ||||
\(817\) | −3.50459e7 | −1.83689 | ||||||||
\(818\) | − | 1.61983e7i | − | 0.846421i | ||||||
\(819\) | −1.58858e6 | + | 6.93064e6i | −0.0827561 | + | 0.361047i | ||||
\(820\) | 1.79553e7i | 0.932518i | ||||||||
\(821\) | − | 4.93224e6i | − | 0.255380i | −0.991814 | − | 0.127690i | \(-0.959244\pi\) | ||
0.991814 | − | 0.127690i | \(-0.0407562\pi\) | |||||||
\(822\) | 2.01096e6 | − | 1.77743e7i | 0.103806 | − | 0.917513i | ||||
\(823\) | 9.20715e6 | 0.473833 | 0.236917 | − | 0.971530i | \(-0.423863\pi\) | ||||
0.236917 | + | 0.971530i | \(0.423863\pi\) | |||||||
\(824\) | −2.07288e7 | −1.06355 | ||||||||
\(825\) | 4.97794e6 | + | 563197.i | 0.254633 | + | 0.0288088i | ||||
\(826\) | 2.71782e7i | 1.38603i | ||||||||
\(827\) | 2.00455e7 | 1.01919 | 0.509593 | − | 0.860415i | \(-0.329796\pi\) | ||||
0.509593 | + | 0.860415i | \(0.329796\pi\) | |||||||
\(828\) | 9.67330e6 | + | 5.31148e6i | 0.490342 | + | 0.269240i | ||||
\(829\) | −2.99048e7 | −1.51131 | −0.755657 | − | 0.654968i | \(-0.772682\pi\) | ||||
−0.755657 | + | 0.654968i | \(0.772682\pi\) | |||||||
\(830\) | 4.20999e7i | 2.12122i | ||||||||
\(831\) | −2.22272e7 | − | 2.51476e6i | −1.11656 | − | 0.126326i | ||||
\(832\) | 101520. | 0.00508443 | ||||||||
\(833\) | −3.47171e6 | −0.173353 | ||||||||
\(834\) | 1.76977e6 | − | 1.56425e7i | 0.0881053 | − | 0.778737i | ||||
\(835\) | − | 2.90667e7i | − | 1.44271i | ||||||
\(836\) | 2.45392e6i | 0.121435i | ||||||||
\(837\) | −6.65328e6 | − | 2.33839e6i | −0.328263 | − | 0.115373i | ||||
\(838\) | − | 3.17548e6i | − | 0.156207i | ||||||
\(839\) | −9.08698e6 | −0.445671 | −0.222836 | − | 0.974856i | \(-0.571531\pi\) | ||||
−0.222836 | + | 0.974856i | \(0.571531\pi\) | |||||||
\(840\) | 1.22372e7 | + | 1.38450e6i | 0.598388 | + | 0.0677008i | ||||
\(841\) | 3.76674e6 | 0.183643 | ||||||||
\(842\) | 3.23099e7 | 1.57056 | ||||||||
\(843\) | 1.81233e7 | + | 2.05045e6i | 0.878351 | + | 0.0993755i | ||||
\(844\) | 1.77482e6 | 0.0857627 | ||||||||
\(845\) | −2.29772e7 | −1.10702 | ||||||||
\(846\) | 4.59043e6 | + | 1.05218e6i | 0.220509 | + | 0.0505433i | ||||
\(847\) | − | 1.47678e7i | − | 0.707306i | ||||||
\(848\) | −1.47447e7 | −0.704121 | ||||||||
\(849\) | 2.09946e6 | − | 1.85565e7i | 0.0999628 | − | 0.883542i | ||||
\(850\) | − | 1.19117e7i | − | 0.565493i | ||||||
\(851\) | 8.19381e6 | − | 2.88396e7i | 0.387849 | − | 1.36510i | ||||
\(852\) | −1.06083e6 | + | 9.37634e6i | −0.0500663 | + | 0.442521i | ||||
\(853\) | 6.90592e6 | 0.324974 | 0.162487 | − | 0.986711i | \(-0.448048\pi\) | ||||
0.162487 | + | 0.986711i | \(0.448048\pi\) | |||||||
\(854\) | 1.66302e7i | 0.780286i | ||||||||
\(855\) | −6.97643e6 | + | 3.04366e7i | −0.326376 | + | 1.42391i | ||||
\(856\) | − | 1.82878e7i | − | 0.853057i | ||||||
\(857\) | − | 1.09221e7i | − | 0.507989i | −0.967206 | − | 0.253994i | \(-0.918256\pi\) | ||
0.967206 | − | 0.253994i | \(-0.0817444\pi\) | |||||||
\(858\) | −330442. | + | 2.92068e6i | −0.0153242 | + | 0.135446i | ||||
\(859\) | 2.15152e7 | 0.994860 | 0.497430 | − | 0.867504i | \(-0.334277\pi\) | ||||
0.497430 | + | 0.867504i | \(0.334277\pi\) | |||||||
\(860\) | − | 3.31138e7i | − | 1.52673i | ||||||
\(861\) | −1.81695e7 | − | 2.05567e6i | −0.835284 | − | 0.0945029i | ||||
\(862\) | − | 3.24133e7i | − | 1.48578i | ||||||
\(863\) | − | 1.63382e6i | − | 0.0746755i | −0.999303 | − | 0.0373377i | \(-0.988112\pi\) | ||
0.999303 | − | 0.0373377i | \(-0.0118877\pi\) | |||||||
\(864\) | −7.32178e6 | + | 2.08322e7i | −0.333682 | + | 0.949404i | ||||
\(865\) | − | 4.30353e7i | − | 1.95562i | ||||||
\(866\) | −1.87570e7 | −0.849900 | ||||||||
\(867\) | 1.87012e7 | + | 2.11583e6i | 0.844933 | + | 0.0955946i | ||||
\(868\) | − | 3.20975e6i | − | 0.144601i | ||||||
\(869\) | 3.66113e6i | 0.164462i | ||||||||
\(870\) | 3.68752e7 | + | 4.17201e6i | 1.65172 | + | 0.186874i | ||||
\(871\) | − | 1.26812e7i | − | 0.566391i | ||||||
\(872\) | 1.14508e7 | 0.509969 | ||||||||
\(873\) | −1.54539e6 | + | 6.74219e6i | −0.0686280 | + | 0.299409i | ||||
\(874\) | 2.68980e7 | + | 7.64217e6i | 1.19108 | + | 0.338406i | ||||
\(875\) | 4.22635e6i | 0.186615i | ||||||||
\(876\) | 1.76622e7 | + | 1.99827e6i | 0.777649 | + | 0.0879822i | ||||
\(877\) | −3.43998e7 | −1.51028 | −0.755139 | − | 0.655564i | \(-0.772431\pi\) | ||||
−0.755139 | + | 0.655564i | \(0.772431\pi\) | |||||||
\(878\) | − | 2.59215e7i | − | 1.13481i | ||||||
\(879\) | −3.46696e7 | − | 3.92248e6i | −1.51348 | − | 0.171233i | ||||
\(880\) | 9.23578e6 | 0.402038 | ||||||||
\(881\) | 3.08894e7 | 1.34082 | 0.670409 | − | 0.741992i | \(-0.266119\pi\) | ||||
0.670409 | + | 0.741992i | \(0.266119\pi\) | |||||||
\(882\) | −2.88816e6 | + | 1.26004e7i | −0.125012 | + | 0.545398i | ||||
\(883\) | 9.24667e6 | 0.399102 | 0.199551 | − | 0.979887i | \(-0.436052\pi\) | ||||
0.199551 | + | 0.979887i | \(0.436052\pi\) | |||||||
\(884\) | 2.50710e6 | 0.107905 | ||||||||
\(885\) | −5.76556e6 | + | 5.09601e7i | −0.247448 | + | 2.18712i | ||||
\(886\) | 4.73926e6 | 0.202827 | ||||||||
\(887\) | − | 1.89393e7i | − | 0.808266i | −0.914700 | − | 0.404133i | \(-0.867573\pi\) | ||
0.914700 | − | 0.404133i | \(-0.132427\pi\) | |||||||
\(888\) | 1.82313e7 | + | 2.06267e6i | 0.775865 | + | 0.0877804i | ||||
\(889\) | 1.26006e7i | 0.534732i | ||||||||
\(890\) | − | 5.39202e6i | − | 0.228179i | ||||||
\(891\) | −4.67007e6 | − | 2.25958e6i | −0.197074 | − | 0.0953527i | ||||
\(892\) | −7.78515e6 | −0.327608 | ||||||||
\(893\) | 4.28072e6 | 0.179634 | ||||||||
\(894\) | 4.12552e6 | − | 3.64643e7i | 0.172638 | − | 1.52589i | ||||
\(895\) | 3.78076e6i | 0.157769i | ||||||||
\(896\) | 1.77387e7 | 0.738160 | ||||||||
\(897\) | 1.11152e7 | + | 4.56222e6i | 0.461249 | + | 0.189319i | ||||
\(898\) | −3.91242e7 | −1.61903 | ||||||||
\(899\) | 7.61821e6i | 0.314379i | ||||||||
\(900\) | −1.55088e7 | − | 3.55480e6i | −0.638224 | − | 0.146288i | ||||
\(901\) | −5.32542e6 | −0.218545 | ||||||||
\(902\) | −7.55886e6 | −0.309343 | ||||||||
\(903\) | 3.35088e7 | + | 3.79114e6i | 1.36754 | + | 0.154721i | ||||
\(904\) | 1.85448e7i | 0.754747i | ||||||||
\(905\) | 3.30812e7i | 1.34264i | ||||||||
\(906\) | 6.32175e6 | − | 5.58761e7i | 0.255868 | − | 2.26154i | ||||
\(907\) | 4.42182e6i | 0.178477i | 0.996010 | + | 0.0892387i | \(0.0284434\pi\) | ||||
−0.996010 | + | 0.0892387i | \(0.971557\pi\) | |||||||
\(908\) | −1.69552e7 | −0.682479 | ||||||||
\(909\) | 5.72173e6 | − | 2.49627e7i | 0.229677 | − | 1.00203i | ||||
\(910\) | −1.70233e7 | −0.681461 | ||||||||
\(911\) | −8.58070e6 | −0.342552 | −0.171276 | − | 0.985223i | \(-0.554789\pi\) | ||||
−0.171276 | + | 0.985223i | \(0.554789\pi\) | |||||||
\(912\) | −3.49011e6 | + | 3.08481e7i | −0.138948 | + | 1.22812i | ||||
\(913\) | −6.35783e6 | −0.252425 | ||||||||
\(914\) | −3.24216e7 | −1.28371 | ||||||||
\(915\) | −3.52792e6 | + | 3.11823e7i | −0.139305 | + | 1.23127i | ||||
\(916\) | 852938.i | 0.0335876i | ||||||||
\(917\) | −5.20352e6 | −0.204350 | ||||||||
\(918\) | −4.09027e6 | + | 1.16378e7i | −0.160194 | + | 0.455789i | ||||
\(919\) | 3.91773e6i | 0.153019i | 0.997069 | + | 0.0765095i | \(0.0243776\pi\) | ||||
−0.997069 | + | 0.0765095i | \(0.975622\pi\) | |||||||
\(920\) | 5.68742e6 | − | 2.00179e7i | 0.221537 | − | 0.779738i | ||||
\(921\) | 3.49975e7 | + | 3.95957e6i | 1.35953 | + | 0.153815i | ||||
\(922\) | −3.15911e7 | −1.22388 | ||||||||
\(923\) | 1.02736e7i | 0.396936i | ||||||||
\(924\) | 265456. | − | 2.34629e6i | 0.0102285 | − | 0.0904069i | ||||
\(925\) | 4.32263e7i | 1.66109i | ||||||||
\(926\) | 1.28728e7i | 0.493341i | ||||||||
\(927\) | −1.12992e7 | + | 4.92960e7i | −0.431866 | + | 1.88414i | ||||
\(928\) | 2.38535e7 | 0.909249 | ||||||||
\(929\) | 2.27456e7i | 0.864684i | 0.901710 | + | 0.432342i | \(0.142313\pi\) | ||||
−0.901710 | + | 0.432342i | \(0.857687\pi\) | |||||||
\(930\) | 1.89814e6 | − | 1.67771e7i | 0.0719650 | − | 0.636078i | ||||
\(931\) | 1.17503e7i | 0.444298i | ||||||||
\(932\) | − | 5.23133e6i | − | 0.197275i | ||||||
\(933\) | 2.36829e6 | − | 2.09326e7i | 0.0890699 | − | 0.787262i | ||||
\(934\) | − | 3.52564e7i | − | 1.32243i | ||||||
\(935\) | 3.33573e6 | 0.124785 | ||||||||
\(936\) | −1.64277e6 | + | 7.16705e6i | −0.0612897 | + | 0.267394i | ||||
\(937\) | 1.14888e6i | 0.0427489i | 0.999772 | + | 0.0213744i | \(0.00680421\pi\) | ||||
−0.999772 | + | 0.0213744i | \(0.993196\pi\) | |||||||
\(938\) | 2.83986e7i | 1.05388i | ||||||||
\(939\) | −1.60032e6 | + | 1.41448e7i | −0.0592302 | + | 0.523518i | ||||
\(940\) | 4.04471e6i | 0.149303i | ||||||||
\(941\) | −4.70391e7 | −1.73175 | −0.865874 | − | 0.500261i | \(-0.833237\pi\) | ||||
−0.865874 | + | 0.500261i | \(0.833237\pi\) | |||||||
\(942\) | 3.67466e7 | + | 4.15747e6i | 1.34924 | + | 0.152652i | ||||
\(943\) | −8.44455e6 | + | 2.97221e7i | −0.309241 | + | 1.08843i | ||||
\(944\) | 5.09878e7i | 1.86224i | ||||||||
\(945\) | 9.96295e6 | − | 2.83469e7i | 0.362918 | − | 1.03259i | ||||
\(946\) | 1.39403e7 | 0.506460 | ||||||||
\(947\) | − | 8.69406e6i | − | 0.315027i | −0.987517 | − | 0.157513i | \(-0.949652\pi\) | ||
0.987517 | − | 0.157513i | \(-0.0503478\pi\) | |||||||
\(948\) | 1.30723e6 | − | 1.15542e7i | 0.0472423 | − | 0.417561i | ||||
\(949\) | 1.93524e7 | 0.697540 | ||||||||
\(950\) | −4.03162e7 | −1.44934 | ||||||||
\(951\) | −3.63787e6 | + | 3.21541e7i | −0.130436 | + | 1.15288i | ||||
\(952\) | 4.42215e6 | 0.158140 | ||||||||
\(953\) | −1.28078e7 | −0.456815 | −0.228408 | − | 0.973566i | \(-0.573352\pi\) | ||||
−0.228408 | + | 0.973566i | \(0.573352\pi\) | |||||||
\(954\) | −4.43028e6 | + | 1.93284e7i | −0.157602 | + | 0.687581i | ||||
\(955\) | −4.92647e7 | −1.74794 | ||||||||
\(956\) | 2.75336e7i | 0.974359i | ||||||||
\(957\) | −630048. | + | 5.56881e6i | −0.0222379 | + | 0.196554i | ||||
\(958\) | − | 1.60053e7i | − | 0.563442i | ||||||
\(959\) | 1.56452e7i | 0.549332i | ||||||||
\(960\) | −426280. | − | 48228.8i | −0.0149285 | − | 0.00168899i | ||||
\(961\) | −2.51631e7 | −0.878933 | ||||||||
\(962\) | −2.53619e7 | −0.883578 | ||||||||
\(963\) | −4.34909e7 | − | 9.96862e6i | −1.51124 | − | 0.346393i | ||||
\(964\) | 6.63623e6i | 0.230001i | ||||||||
\(965\) | −4.40995e7 | −1.52446 | ||||||||
\(966\) | −2.48915e7 | − | 1.02167e7i | −0.858239 | − | 0.352264i | ||||
\(967\) | 5.03888e7 | 1.73288 | 0.866439 | − | 0.499283i | \(-0.166403\pi\) | ||||
0.866439 | + | 0.499283i | \(0.166403\pi\) | |||||||
\(968\) | − | 1.52715e7i | − | 0.523835i | ||||||
\(969\) | −1.26054e6 | + | 1.11415e7i | −0.0431268 | + | 0.381185i | ||||
\(970\) | −1.65604e7 | −0.565122 | ||||||||
\(971\) | 670405. | 0.0228186 | 0.0114093 | − | 0.999935i | \(-0.496368\pi\) | ||||
0.0114093 | + | 0.999935i | \(0.496368\pi\) | |||||||
\(972\) | 1.39315e7 | + | 8.79851e6i | 0.472969 | + | 0.298706i | ||||
\(973\) | 1.37688e7i | 0.466243i | ||||||||
\(974\) | 6.49683e6i | 0.219434i | ||||||||
\(975\) | −1.72134e7 | − | 1.94750e6i | −0.579901 | − | 0.0656093i | ||||
\(976\) | 3.11992e7i | 1.04838i | ||||||||
\(977\) | −3.59434e7 | −1.20471 | −0.602355 | − | 0.798228i | \(-0.705771\pi\) | ||||
−0.602355 | + | 0.798228i | \(0.705771\pi\) | |||||||
\(978\) | 4.59636e6 | − | 4.06259e7i | 0.153662 | − | 1.35817i | ||||
\(979\) | 814290. | 0.0271533 | ||||||||
\(980\) | −1.11025e7 | −0.369279 | ||||||||
\(981\) | 6.24177e6 | − | 2.72315e7i | 0.207079 | − | 0.903439i | ||||
\(982\) | 4.78480e7 | 1.58338 | ||||||||
\(983\) | −1.84333e7 | −0.608443 | −0.304222 | − | 0.952601i | \(-0.598396\pi\) | ||||
−0.304222 | + | 0.952601i | \(0.598396\pi\) | |||||||
\(984\) | −1.87892e7 | − | 2.12579e6i | −0.618616 | − | 0.0699894i | ||||
\(985\) | − | 5.11379e7i | − | 1.67939i | ||||||
\(986\) | 1.33256e7 | 0.436511 | ||||||||
\(987\) | −4.09296e6 | − | 463072.i | −0.133735 | − | 0.0151306i | ||||
\(988\) | − | 8.48549e6i | − | 0.276557i | ||||||
\(989\) | 1.55737e7 | − | 5.48146e7i | 0.506293 | − | 1.78199i | ||||
\(990\) | 2.77503e6 | − | 1.21069e7i | 0.0899871 | − | 0.392594i | ||||
\(991\) | 9.89527e6 | 0.320069 | 0.160034 | − | 0.987111i | \(-0.448839\pi\) | ||||
0.160034 | + | 0.987111i | \(0.448839\pi\) | |||||||
\(992\) | − | 1.08526e7i | − | 0.350152i | ||||||
\(993\) | 2.99813e7 | + | 3.39204e6i | 0.964888 | + | 0.109166i | ||||
\(994\) | − | 2.30069e7i | − | 0.738572i | ||||||
\(995\) | − | 5.59719e7i | − | 1.79231i | ||||||
\(996\) | 2.00648e7 | + | 2.27010e6i | 0.640893 | + | 0.0725098i | ||||
\(997\) | 5.64735e7 | 1.79931 | 0.899657 | − | 0.436598i | \(-0.143817\pi\) | ||||
0.899657 | + | 0.436598i | \(0.143817\pi\) | |||||||
\(998\) | − | 1.82201e7i | − | 0.579061i | ||||||
\(999\) | 1.48431e7 | − | 4.22323e7i | 0.470557 | − | 1.33885i |
(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 | 69.6.c.b.68.26 | yes | 32 | |
3.2 | odd | 2 | inner | 69.6.c.b.68.7 | ✓ | 32 | |
23.22 | odd | 2 | inner | 69.6.c.b.68.25 | yes | 32 | |
69.68 | even | 2 | inner | 69.6.c.b.68.8 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.6.c.b.68.7 | ✓ | 32 | 3.2 | odd | 2 | inner | |
69.6.c.b.68.8 | yes | 32 | 69.68 | even | 2 | inner | |
69.6.c.b.68.25 | yes | 32 | 23.22 | odd | 2 | inner | |
69.6.c.b.68.26 | yes | 32 | 1.1 | even | 1 | trivial |