Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,6,Mod(1,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1045.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(167.601091705\) |
Analytic rank: | \(0\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 1045.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.27957 | −0.756528 | −0.378264 | − | 0.925698i | \(-0.623479\pi\) | ||||
−0.378264 | + | 0.925698i | \(0.623479\pi\) | |||||||
\(3\) | 13.2431 | 0.849545 | 0.424773 | − | 0.905300i | \(-0.360354\pi\) | ||||
0.424773 | + | 0.905300i | \(0.360354\pi\) | |||||||
\(4\) | −13.6853 | −0.427665 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | −56.6748 | −0.642705 | ||||||||
\(7\) | 11.8777 | 0.0916191 | 0.0458095 | − | 0.998950i | \(-0.485413\pi\) | ||||
0.0458095 | + | 0.998950i | \(0.485413\pi\) | |||||||
\(8\) | 195.513 | 1.08007 | ||||||||
\(9\) | −67.6203 | −0.278273 | ||||||||
\(10\) | −106.989 | −0.338330 | ||||||||
\(11\) | −121.000 | −0.301511 | ||||||||
\(12\) | −181.236 | −0.363321 | ||||||||
\(13\) | −608.806 | −0.999126 | −0.499563 | − | 0.866277i | \(-0.666506\pi\) | ||||
−0.499563 | + | 0.866277i | \(0.666506\pi\) | |||||||
\(14\) | −50.8313 | −0.0693124 | ||||||||
\(15\) | 331.078 | 0.379928 | ||||||||
\(16\) | −398.784 | −0.389437 | ||||||||
\(17\) | 2170.89 | 1.82186 | 0.910931 | − | 0.412558i | \(-0.135365\pi\) | ||||
0.910931 | + | 0.412558i | \(0.135365\pi\) | |||||||
\(18\) | 289.386 | 0.210521 | ||||||||
\(19\) | −361.000 | −0.229416 | ||||||||
\(20\) | −342.132 | −0.191258 | ||||||||
\(21\) | 157.297 | 0.0778346 | ||||||||
\(22\) | 517.828 | 0.228102 | ||||||||
\(23\) | 986.989 | 0.389039 | 0.194519 | − | 0.980899i | \(-0.437685\pi\) | ||||
0.194519 | + | 0.980899i | \(0.437685\pi\) | |||||||
\(24\) | 2589.20 | 0.917567 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 2605.43 | 0.755867 | ||||||||
\(27\) | −4113.58 | −1.08595 | ||||||||
\(28\) | −162.549 | −0.0391823 | ||||||||
\(29\) | 1117.15 | 0.246669 | 0.123335 | − | 0.992365i | \(-0.460641\pi\) | ||||
0.123335 | + | 0.992365i | \(0.460641\pi\) | |||||||
\(30\) | −1416.87 | −0.287426 | ||||||||
\(31\) | 145.291 | 0.0271541 | 0.0135771 | − | 0.999908i | \(-0.495678\pi\) | ||||
0.0135771 | + | 0.999908i | \(0.495678\pi\) | |||||||
\(32\) | −4549.80 | −0.785448 | ||||||||
\(33\) | −1602.42 | −0.256148 | ||||||||
\(34\) | −9290.48 | −1.37829 | ||||||||
\(35\) | 296.942 | 0.0409733 | ||||||||
\(36\) | 925.403 | 0.119008 | ||||||||
\(37\) | −6997.18 | −0.840270 | −0.420135 | − | 0.907462i | \(-0.638017\pi\) | ||||
−0.420135 | + | 0.907462i | \(0.638017\pi\) | |||||||
\(38\) | 1544.92 | 0.173559 | ||||||||
\(39\) | −8062.48 | −0.848803 | ||||||||
\(40\) | 4887.83 | 0.483021 | ||||||||
\(41\) | −14203.9 | −1.31962 | −0.659811 | − | 0.751432i | \(-0.729364\pi\) | ||||
−0.659811 | + | 0.751432i | \(0.729364\pi\) | |||||||
\(42\) | −673.164 | −0.0588840 | ||||||||
\(43\) | 12513.9 | 1.03210 | 0.516052 | − | 0.856557i | \(-0.327401\pi\) | ||||
0.516052 | + | 0.856557i | \(0.327401\pi\) | |||||||
\(44\) | 1655.92 | 0.128946 | ||||||||
\(45\) | −1690.51 | −0.124447 | ||||||||
\(46\) | −4223.89 | −0.294319 | ||||||||
\(47\) | 4843.43 | 0.319822 | 0.159911 | − | 0.987131i | \(-0.448879\pi\) | ||||
0.159911 | + | 0.987131i | \(0.448879\pi\) | |||||||
\(48\) | −5281.14 | −0.330845 | ||||||||
\(49\) | −16665.9 | −0.991606 | ||||||||
\(50\) | −2674.73 | −0.151306 | ||||||||
\(51\) | 28749.3 | 1.54775 | ||||||||
\(52\) | 8331.68 | 0.427292 | ||||||||
\(53\) | 19835.3 | 0.969948 | 0.484974 | − | 0.874529i | \(-0.338829\pi\) | ||||
0.484974 | + | 0.874529i | \(0.338829\pi\) | |||||||
\(54\) | 17604.3 | 0.821552 | ||||||||
\(55\) | −3025.00 | −0.134840 | ||||||||
\(56\) | 2322.24 | 0.0989549 | ||||||||
\(57\) | −4780.76 | −0.194899 | ||||||||
\(58\) | −4780.91 | −0.186612 | ||||||||
\(59\) | 20069.4 | 0.750592 | 0.375296 | − | 0.926905i | \(-0.377541\pi\) | ||||
0.375296 | + | 0.926905i | \(0.377541\pi\) | |||||||
\(60\) | −4530.89 | −0.162482 | ||||||||
\(61\) | 39595.8 | 1.36246 | 0.681231 | − | 0.732068i | \(-0.261445\pi\) | ||||
0.681231 | + | 0.732068i | \(0.261445\pi\) | |||||||
\(62\) | −621.785 | −0.0205429 | ||||||||
\(63\) | −803.171 | −0.0254951 | ||||||||
\(64\) | 32232.3 | 0.983651 | ||||||||
\(65\) | −15220.1 | −0.446823 | ||||||||
\(66\) | 6857.65 | 0.193783 | ||||||||
\(67\) | −12028.7 | −0.327365 | −0.163683 | − | 0.986513i | \(-0.552337\pi\) | ||||
−0.163683 | + | 0.986513i | \(0.552337\pi\) | |||||||
\(68\) | −29709.3 | −0.779147 | ||||||||
\(69\) | 13070.8 | 0.330506 | ||||||||
\(70\) | −1270.78 | −0.0309975 | ||||||||
\(71\) | −3232.49 | −0.0761011 | −0.0380505 | − | 0.999276i | \(-0.512115\pi\) | ||||
−0.0380505 | + | 0.999276i | \(0.512115\pi\) | |||||||
\(72\) | −13220.7 | −0.300554 | ||||||||
\(73\) | 2779.96 | 0.0610565 | 0.0305282 | − | 0.999534i | \(-0.490281\pi\) | ||||
0.0305282 | + | 0.999534i | \(0.490281\pi\) | |||||||
\(74\) | 29944.9 | 0.635688 | ||||||||
\(75\) | 8276.94 | 0.169909 | ||||||||
\(76\) | 4940.39 | 0.0981131 | ||||||||
\(77\) | −1437.20 | −0.0276242 | ||||||||
\(78\) | 34503.9 | 0.642144 | ||||||||
\(79\) | 22928.1 | 0.413332 | 0.206666 | − | 0.978412i | \(-0.433739\pi\) | ||||
0.206666 | + | 0.978412i | \(0.433739\pi\) | |||||||
\(80\) | −9969.60 | −0.174162 | ||||||||
\(81\) | −38044.8 | −0.644292 | ||||||||
\(82\) | 60786.8 | 0.998331 | ||||||||
\(83\) | −103440. | −1.64814 | −0.824070 | − | 0.566487i | \(-0.808302\pi\) | ||||
−0.824070 | + | 0.566487i | \(0.808302\pi\) | |||||||
\(84\) | −2152.66 | −0.0332871 | ||||||||
\(85\) | 54272.3 | 0.814762 | ||||||||
\(86\) | −53554.3 | −0.780815 | ||||||||
\(87\) | 14794.5 | 0.209557 | ||||||||
\(88\) | −23657.1 | −0.325653 | ||||||||
\(89\) | −61233.4 | −0.819433 | −0.409716 | − | 0.912213i | \(-0.634372\pi\) | ||||
−0.409716 | + | 0.912213i | \(0.634372\pi\) | |||||||
\(90\) | 7234.64 | 0.0941479 | ||||||||
\(91\) | −7231.19 | −0.0915390 | ||||||||
\(92\) | −13507.2 | −0.166378 | ||||||||
\(93\) | 1924.11 | 0.0230687 | ||||||||
\(94\) | −20727.8 | −0.241954 | ||||||||
\(95\) | −9025.00 | −0.102598 | ||||||||
\(96\) | −60253.5 | −0.667274 | ||||||||
\(97\) | 155760. | 1.68084 | 0.840420 | − | 0.541935i | \(-0.182308\pi\) | ||||
0.840420 | + | 0.541935i | \(0.182308\pi\) | |||||||
\(98\) | 71323.0 | 0.750178 | ||||||||
\(99\) | 8182.05 | 0.0839024 | ||||||||
\(100\) | −8553.30 | −0.0855330 | ||||||||
\(101\) | 116411. | 1.13551 | 0.567754 | − | 0.823198i | \(-0.307813\pi\) | ||||
0.567754 | + | 0.823198i | \(0.307813\pi\) | |||||||
\(102\) | −123035. | −1.17092 | ||||||||
\(103\) | −77913.2 | −0.723632 | −0.361816 | − | 0.932249i | \(-0.617843\pi\) | ||||
−0.361816 | + | 0.932249i | \(0.617843\pi\) | |||||||
\(104\) | −119030. | −1.07913 | ||||||||
\(105\) | 3932.43 | 0.0348087 | ||||||||
\(106\) | −84886.4 | −0.733793 | ||||||||
\(107\) | 81538.6 | 0.688500 | 0.344250 | − | 0.938878i | \(-0.388133\pi\) | ||||
0.344250 | + | 0.938878i | \(0.388133\pi\) | |||||||
\(108\) | 56295.5 | 0.464423 | ||||||||
\(109\) | 55981.5 | 0.451313 | 0.225657 | − | 0.974207i | \(-0.427547\pi\) | ||||
0.225657 | + | 0.974207i | \(0.427547\pi\) | |||||||
\(110\) | 12945.7 | 0.102010 | ||||||||
\(111\) | −92664.4 | −0.713847 | ||||||||
\(112\) | −4736.62 | −0.0356799 | ||||||||
\(113\) | −48284.2 | −0.355720 | −0.177860 | − | 0.984056i | \(-0.556917\pi\) | ||||
−0.177860 | + | 0.984056i | \(0.556917\pi\) | |||||||
\(114\) | 20459.6 | 0.147447 | ||||||||
\(115\) | 24674.7 | 0.173983 | ||||||||
\(116\) | −15288.5 | −0.105492 | ||||||||
\(117\) | 41167.6 | 0.278030 | ||||||||
\(118\) | −85888.3 | −0.567844 | ||||||||
\(119\) | 25785.1 | 0.166917 | ||||||||
\(120\) | 64730.1 | 0.410349 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | −169453. | −1.03074 | ||||||||
\(123\) | −188104. | −1.12108 | ||||||||
\(124\) | −1988.35 | −0.0116129 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 3437.23 | 0.0192878 | ||||||||
\(127\) | 137758. | 0.757892 | 0.378946 | − | 0.925419i | \(-0.376287\pi\) | ||||
0.378946 | + | 0.925419i | \(0.376287\pi\) | |||||||
\(128\) | 7653.40 | 0.0412885 | ||||||||
\(129\) | 165723. | 0.876819 | ||||||||
\(130\) | 65135.7 | 0.338034 | ||||||||
\(131\) | −183015. | −0.931769 | −0.465884 | − | 0.884846i | \(-0.654264\pi\) | ||||
−0.465884 | + | 0.884846i | \(0.654264\pi\) | |||||||
\(132\) | 21929.5 | 0.109545 | ||||||||
\(133\) | −4287.84 | −0.0210189 | ||||||||
\(134\) | 51477.8 | 0.247661 | ||||||||
\(135\) | −102839. | −0.485652 | ||||||||
\(136\) | 424438. | 1.96774 | ||||||||
\(137\) | −284891. | −1.29681 | −0.648406 | − | 0.761295i | \(-0.724564\pi\) | ||||
−0.648406 | + | 0.761295i | \(0.724564\pi\) | |||||||
\(138\) | −55937.4 | −0.250037 | ||||||||
\(139\) | 26645.6 | 0.116974 | 0.0584868 | − | 0.998288i | \(-0.481372\pi\) | ||||
0.0584868 | + | 0.998288i | \(0.481372\pi\) | |||||||
\(140\) | −4063.73 | −0.0175228 | ||||||||
\(141\) | 64142.0 | 0.271703 | ||||||||
\(142\) | 13833.7 | 0.0575726 | ||||||||
\(143\) | 73665.5 | 0.301248 | ||||||||
\(144\) | 26965.9 | 0.108370 | ||||||||
\(145\) | 27928.7 | 0.110314 | ||||||||
\(146\) | −11897.0 | −0.0461909 | ||||||||
\(147\) | −220708. | −0.842414 | ||||||||
\(148\) | 95758.4 | 0.359354 | ||||||||
\(149\) | 303506. | 1.11996 | 0.559978 | − | 0.828507i | \(-0.310810\pi\) | ||||
0.559978 | + | 0.828507i | \(0.310810\pi\) | |||||||
\(150\) | −35421.7 | −0.128541 | ||||||||
\(151\) | 91029.9 | 0.324894 | 0.162447 | − | 0.986717i | \(-0.448061\pi\) | ||||
0.162447 | + | 0.986717i | \(0.448061\pi\) | |||||||
\(152\) | −70580.3 | −0.247785 | ||||||||
\(153\) | −146796. | −0.506975 | ||||||||
\(154\) | 6150.59 | 0.0208985 | ||||||||
\(155\) | 3632.29 | 0.0121437 | ||||||||
\(156\) | 110337. | 0.363004 | ||||||||
\(157\) | −294041. | −0.952049 | −0.476024 | − | 0.879432i | \(-0.657923\pi\) | ||||
−0.476024 | + | 0.879432i | \(0.657923\pi\) | |||||||
\(158\) | −98122.2 | −0.312698 | ||||||||
\(159\) | 262680. | 0.824014 | ||||||||
\(160\) | −113745. | −0.351263 | ||||||||
\(161\) | 11723.1 | 0.0356433 | ||||||||
\(162\) | 162815. | 0.487425 | ||||||||
\(163\) | −216759. | −0.639010 | −0.319505 | − | 0.947585i | \(-0.603517\pi\) | ||||
−0.319505 | + | 0.947585i | \(0.603517\pi\) | |||||||
\(164\) | 194385. | 0.564356 | ||||||||
\(165\) | −40060.4 | −0.114553 | ||||||||
\(166\) | 442680. | 1.24686 | ||||||||
\(167\) | 115741. | 0.321141 | 0.160570 | − | 0.987024i | \(-0.448667\pi\) | ||||
0.160570 | + | 0.987024i | \(0.448667\pi\) | |||||||
\(168\) | 30753.7 | 0.0840667 | ||||||||
\(169\) | −648.409 | −0.00174635 | ||||||||
\(170\) | −232262. | −0.616390 | ||||||||
\(171\) | 24410.9 | 0.0638402 | ||||||||
\(172\) | −171257. | −0.441395 | ||||||||
\(173\) | −217742. | −0.553130 | −0.276565 | − | 0.960995i | \(-0.589196\pi\) | ||||
−0.276565 | + | 0.960995i | \(0.589196\pi\) | |||||||
\(174\) | −63314.0 | −0.158536 | ||||||||
\(175\) | 7423.54 | 0.0183238 | ||||||||
\(176\) | 48252.9 | 0.117420 | ||||||||
\(177\) | 265781. | 0.637662 | ||||||||
\(178\) | 262053. | 0.619924 | ||||||||
\(179\) | 132007. | 0.307940 | 0.153970 | − | 0.988076i | \(-0.450794\pi\) | ||||
0.153970 | + | 0.988076i | \(0.450794\pi\) | |||||||
\(180\) | 23135.1 | 0.0532218 | ||||||||
\(181\) | 677944. | 1.53815 | 0.769073 | − | 0.639161i | \(-0.220718\pi\) | ||||
0.769073 | + | 0.639161i | \(0.220718\pi\) | |||||||
\(182\) | 30946.4 | 0.0692519 | ||||||||
\(183\) | 524371. | 1.15747 | ||||||||
\(184\) | 192969. | 0.420188 | ||||||||
\(185\) | −174929. | −0.375780 | ||||||||
\(186\) | −8234.36 | −0.0174521 | ||||||||
\(187\) | −262678. | −0.549312 | ||||||||
\(188\) | −66283.7 | −0.136777 | ||||||||
\(189\) | −48859.7 | −0.0994938 | ||||||||
\(190\) | 38623.1 | 0.0776182 | ||||||||
\(191\) | 756704. | 1.50087 | 0.750434 | − | 0.660946i | \(-0.229845\pi\) | ||||
0.750434 | + | 0.660946i | \(0.229845\pi\) | |||||||
\(192\) | 426855. | 0.835656 | ||||||||
\(193\) | 221018. | 0.427105 | 0.213552 | − | 0.976932i | \(-0.431497\pi\) | ||||
0.213552 | + | 0.976932i | \(0.431497\pi\) | |||||||
\(194\) | −666586. | −1.27160 | ||||||||
\(195\) | −201562. | −0.379596 | ||||||||
\(196\) | 228078. | 0.424075 | ||||||||
\(197\) | 480123. | 0.881428 | 0.440714 | − | 0.897647i | \(-0.354725\pi\) | ||||
0.440714 | + | 0.897647i | \(0.354725\pi\) | |||||||
\(198\) | −35015.7 | −0.0634745 | ||||||||
\(199\) | 43013.5 | 0.0769967 | 0.0384983 | − | 0.999259i | \(-0.487743\pi\) | ||||
0.0384983 | + | 0.999259i | \(0.487743\pi\) | |||||||
\(200\) | 122196. | 0.216014 | ||||||||
\(201\) | −159298. | −0.278112 | ||||||||
\(202\) | −498188. | −0.859043 | ||||||||
\(203\) | 13269.1 | 0.0225996 | ||||||||
\(204\) | −393443. | −0.661921 | ||||||||
\(205\) | −355099. | −0.590153 | ||||||||
\(206\) | 333435. | 0.547448 | ||||||||
\(207\) | −66740.5 | −0.108259 | ||||||||
\(208\) | 242782. | 0.389097 | ||||||||
\(209\) | 43681.0 | 0.0691714 | ||||||||
\(210\) | −16829.1 | −0.0263337 | ||||||||
\(211\) | 393510. | 0.608484 | 0.304242 | − | 0.952595i | \(-0.401597\pi\) | ||||
0.304242 | + | 0.952595i | \(0.401597\pi\) | |||||||
\(212\) | −271451. | −0.414813 | ||||||||
\(213\) | −42808.1 | −0.0646513 | ||||||||
\(214\) | −348950. | −0.520870 | ||||||||
\(215\) | 312849. | 0.461571 | ||||||||
\(216\) | −804259. | −1.17290 | ||||||||
\(217\) | 1725.72 | 0.00248784 | ||||||||
\(218\) | −239577. | −0.341431 | ||||||||
\(219\) | 36815.3 | 0.0518702 | ||||||||
\(220\) | 41398.0 | 0.0576664 | ||||||||
\(221\) | −1.32165e6 | −1.82027 | ||||||||
\(222\) | 396564. | 0.540045 | ||||||||
\(223\) | 1.30521e6 | 1.75760 | 0.878798 | − | 0.477195i | \(-0.158346\pi\) | ||||
0.878798 | + | 0.477195i | \(0.158346\pi\) | |||||||
\(224\) | −54041.0 | −0.0719621 | ||||||||
\(225\) | −42262.7 | −0.0556546 | ||||||||
\(226\) | 206635. | 0.269112 | ||||||||
\(227\) | −1.31152e6 | −1.68931 | −0.844655 | − | 0.535311i | \(-0.820195\pi\) | ||||
−0.844655 | + | 0.535311i | \(0.820195\pi\) | |||||||
\(228\) | 65426.0 | 0.0833515 | ||||||||
\(229\) | −495209. | −0.624022 | −0.312011 | − | 0.950078i | \(-0.601003\pi\) | ||||
−0.312011 | + | 0.950078i | \(0.601003\pi\) | |||||||
\(230\) | −105597. | −0.131623 | ||||||||
\(231\) | −19032.9 | −0.0234680 | ||||||||
\(232\) | 218417. | 0.266420 | ||||||||
\(233\) | −407725. | −0.492015 | −0.246007 | − | 0.969268i | \(-0.579119\pi\) | ||||
−0.246007 | + | 0.969268i | \(0.579119\pi\) | |||||||
\(234\) | −176180. | −0.210337 | ||||||||
\(235\) | 121086. | 0.143029 | ||||||||
\(236\) | −274655. | −0.321002 | ||||||||
\(237\) | 303638. | 0.351145 | ||||||||
\(238\) | −110349. | −0.126278 | ||||||||
\(239\) | −959369. | −1.08640 | −0.543201 | − | 0.839603i | \(-0.682788\pi\) | ||||
−0.543201 | + | 0.839603i | \(0.682788\pi\) | |||||||
\(240\) | −132028. | −0.147958 | ||||||||
\(241\) | 1.40519e6 | 1.55845 | 0.779223 | − | 0.626747i | \(-0.215614\pi\) | ||||
0.779223 | + | 0.626747i | \(0.215614\pi\) | |||||||
\(242\) | −62657.2 | −0.0687753 | ||||||||
\(243\) | 495768. | 0.538596 | ||||||||
\(244\) | −541880. | −0.582678 | ||||||||
\(245\) | −416648. | −0.443460 | ||||||||
\(246\) | 805005. | 0.848127 | ||||||||
\(247\) | 219779. | 0.229215 | ||||||||
\(248\) | 28406.4 | 0.0293283 | ||||||||
\(249\) | −1.36987e6 | −1.40017 | ||||||||
\(250\) | −66868.3 | −0.0676659 | ||||||||
\(251\) | 1.16660e6 | 1.16879 | 0.584397 | − | 0.811468i | \(-0.301331\pi\) | ||||
0.584397 | + | 0.811468i | \(0.301331\pi\) | |||||||
\(252\) | 10991.6 | 0.0109034 | ||||||||
\(253\) | −119426. | −0.117300 | ||||||||
\(254\) | −589544. | −0.573366 | ||||||||
\(255\) | 718733. | 0.692177 | ||||||||
\(256\) | −1.06419e6 | −1.01489 | ||||||||
\(257\) | −1.04400e6 | −0.985976 | −0.492988 | − | 0.870036i | \(-0.664095\pi\) | ||||
−0.492988 | + | 0.870036i | \(0.664095\pi\) | |||||||
\(258\) | −709225. | −0.663338 | ||||||||
\(259\) | −83110.1 | −0.0769847 | ||||||||
\(260\) | 208292. | 0.191091 | ||||||||
\(261\) | −75541.8 | −0.0686414 | ||||||||
\(262\) | 783225. | 0.704909 | ||||||||
\(263\) | 1.52744e6 | 1.36168 | 0.680839 | − | 0.732433i | \(-0.261615\pi\) | ||||
0.680839 | + | 0.732433i | \(0.261615\pi\) | |||||||
\(264\) | −313294. | −0.276657 | ||||||||
\(265\) | 495882. | 0.433774 | ||||||||
\(266\) | 18350.1 | 0.0159014 | ||||||||
\(267\) | −810920. | −0.696145 | ||||||||
\(268\) | 164616. | 0.140003 | ||||||||
\(269\) | −757695. | −0.638431 | −0.319215 | − | 0.947682i | \(-0.603419\pi\) | ||||
−0.319215 | + | 0.947682i | \(0.603419\pi\) | |||||||
\(270\) | 440108. | 0.367409 | ||||||||
\(271\) | −488209. | −0.403815 | −0.201908 | − | 0.979405i | \(-0.564714\pi\) | ||||
−0.201908 | + | 0.979405i | \(0.564714\pi\) | |||||||
\(272\) | −865716. | −0.709501 | ||||||||
\(273\) | −95763.4 | −0.0777666 | ||||||||
\(274\) | 1.21921e6 | 0.981075 | ||||||||
\(275\) | −75625.0 | −0.0603023 | ||||||||
\(276\) | −178877. | −0.141346 | ||||||||
\(277\) | −876260. | −0.686173 | −0.343086 | − | 0.939304i | \(-0.611472\pi\) | ||||
−0.343086 | + | 0.939304i | \(0.611472\pi\) | |||||||
\(278\) | −114032. | −0.0884939 | ||||||||
\(279\) | −9824.65 | −0.00755625 | ||||||||
\(280\) | 58056.0 | 0.0442540 | ||||||||
\(281\) | 829031. | 0.626333 | 0.313166 | − | 0.949698i | \(-0.398610\pi\) | ||||
0.313166 | + | 0.949698i | \(0.398610\pi\) | |||||||
\(282\) | −274500. | −0.205551 | ||||||||
\(283\) | −197711. | −0.146745 | −0.0733726 | − | 0.997305i | \(-0.523376\pi\) | ||||
−0.0733726 | + | 0.997305i | \(0.523376\pi\) | |||||||
\(284\) | 44237.5 | 0.0325458 | ||||||||
\(285\) | −119519. | −0.0871615 | ||||||||
\(286\) | −315257. | −0.227903 | ||||||||
\(287\) | −168710. | −0.120902 | ||||||||
\(288\) | 307659. | 0.218569 | ||||||||
\(289\) | 3.29291e6 | 2.31918 | ||||||||
\(290\) | −119523. | −0.0834556 | ||||||||
\(291\) | 2.06275e6 | 1.42795 | ||||||||
\(292\) | −38044.6 | −0.0261117 | ||||||||
\(293\) | 1.83759e6 | 1.25049 | 0.625244 | − | 0.780429i | \(-0.284999\pi\) | ||||
0.625244 | + | 0.780429i | \(0.284999\pi\) | |||||||
\(294\) | 944537. | 0.637310 | ||||||||
\(295\) | 501734. | 0.335675 | ||||||||
\(296\) | −1.36804e6 | −0.907549 | ||||||||
\(297\) | 497743. | 0.327426 | ||||||||
\(298\) | −1.29887e6 | −0.847278 | ||||||||
\(299\) | −600885. | −0.388699 | ||||||||
\(300\) | −113272. | −0.0726642 | ||||||||
\(301\) | 148636. | 0.0945604 | ||||||||
\(302\) | −389569. | −0.245791 | ||||||||
\(303\) | 1.54164e6 | 0.964665 | ||||||||
\(304\) | 143961. | 0.0893431 | ||||||||
\(305\) | 989895. | 0.609312 | ||||||||
\(306\) | 628225. | 0.383541 | ||||||||
\(307\) | 2.58579e6 | 1.56584 | 0.782921 | − | 0.622121i | \(-0.213729\pi\) | ||||
0.782921 | + | 0.622121i | \(0.213729\pi\) | |||||||
\(308\) | 19668.5 | 0.0118139 | ||||||||
\(309\) | −1.03181e6 | −0.614758 | ||||||||
\(310\) | −15544.6 | −0.00918705 | ||||||||
\(311\) | 3.12725e6 | 1.83342 | 0.916710 | − | 0.399552i | \(-0.130834\pi\) | ||||
0.916710 | + | 0.399552i | \(0.130834\pi\) | |||||||
\(312\) | −1.57632e6 | −0.916766 | ||||||||
\(313\) | −1.79490e6 | −1.03557 | −0.517784 | − | 0.855511i | \(-0.673243\pi\) | ||||
−0.517784 | + | 0.855511i | \(0.673243\pi\) | |||||||
\(314\) | 1.25837e6 | 0.720252 | ||||||||
\(315\) | −20079.3 | −0.0114018 | ||||||||
\(316\) | −313777. | −0.176768 | ||||||||
\(317\) | 713831. | 0.398977 | 0.199488 | − | 0.979900i | \(-0.436072\pi\) | ||||
0.199488 | + | 0.979900i | \(0.436072\pi\) | |||||||
\(318\) | −1.12416e6 | −0.623390 | ||||||||
\(319\) | −135175. | −0.0743736 | ||||||||
\(320\) | 805807. | 0.439902 | ||||||||
\(321\) | 1.07982e6 | 0.584912 | ||||||||
\(322\) | −50169.9 | −0.0269652 | ||||||||
\(323\) | −783691. | −0.417964 | ||||||||
\(324\) | 520653. | 0.275541 | ||||||||
\(325\) | −380504. | −0.199825 | ||||||||
\(326\) | 927634. | 0.483429 | ||||||||
\(327\) | 741368. | 0.383411 | ||||||||
\(328\) | −2.77706e6 | −1.42528 | ||||||||
\(329\) | 57528.6 | 0.0293018 | ||||||||
\(330\) | 171441. | 0.0866623 | ||||||||
\(331\) | 2.96536e6 | 1.48767 | 0.743836 | − | 0.668362i | \(-0.233004\pi\) | ||||
0.743836 | + | 0.668362i | \(0.233004\pi\) | |||||||
\(332\) | 1.41561e6 | 0.704852 | ||||||||
\(333\) | 473151. | 0.233824 | ||||||||
\(334\) | −495321. | −0.242952 | ||||||||
\(335\) | −300718. | −0.146402 | ||||||||
\(336\) | −62727.5 | −0.0303117 | ||||||||
\(337\) | 2.33783e6 | 1.12134 | 0.560670 | − | 0.828039i | \(-0.310543\pi\) | ||||
0.560670 | + | 0.828039i | \(0.310543\pi\) | |||||||
\(338\) | 2774.91 | 0.00132117 | ||||||||
\(339\) | −639432. | −0.302200 | ||||||||
\(340\) | −742731. | −0.348445 | ||||||||
\(341\) | −17580.3 | −0.00818728 | ||||||||
\(342\) | −104468. | −0.0482969 | ||||||||
\(343\) | −397580. | −0.182469 | ||||||||
\(344\) | 2.44664e6 | 1.11474 | ||||||||
\(345\) | 326770. | 0.147807 | ||||||||
\(346\) | 931843. | 0.418459 | ||||||||
\(347\) | −2.55615e6 | −1.13963 | −0.569814 | − | 0.821774i | \(-0.692985\pi\) | ||||
−0.569814 | + | 0.821774i | \(0.692985\pi\) | |||||||
\(348\) | −202467. | −0.0896201 | ||||||||
\(349\) | 97407.5 | 0.0428084 | 0.0214042 | − | 0.999771i | \(-0.493186\pi\) | ||||
0.0214042 | + | 0.999771i | \(0.493186\pi\) | |||||||
\(350\) | −31769.6 | −0.0138625 | ||||||||
\(351\) | 2.50437e6 | 1.08500 | ||||||||
\(352\) | 550526. | 0.236822 | ||||||||
\(353\) | 4.35548e6 | 1.86037 | 0.930184 | − | 0.367094i | \(-0.119647\pi\) | ||||
0.930184 | + | 0.367094i | \(0.119647\pi\) | |||||||
\(354\) | −1.13743e6 | −0.482409 | ||||||||
\(355\) | −80812.2 | −0.0340334 | ||||||||
\(356\) | 837996. | 0.350443 | ||||||||
\(357\) | 341475. | 0.141804 | ||||||||
\(358\) | −564935. | −0.232965 | ||||||||
\(359\) | 4.02320e6 | 1.64754 | 0.823769 | − | 0.566926i | \(-0.191867\pi\) | ||||
0.823769 | + | 0.566926i | \(0.191867\pi\) | |||||||
\(360\) | −330517. | −0.134412 | ||||||||
\(361\) | 130321. | 0.0526316 | ||||||||
\(362\) | −2.90131e6 | −1.16365 | ||||||||
\(363\) | 193892. | 0.0772314 | ||||||||
\(364\) | 98960.9 | 0.0391481 | ||||||||
\(365\) | 69499.0 | 0.0273053 | ||||||||
\(366\) | −2.24408e6 | −0.875662 | ||||||||
\(367\) | −427192. | −0.165561 | −0.0827805 | − | 0.996568i | \(-0.526380\pi\) | ||||
−0.0827805 | + | 0.996568i | \(0.526380\pi\) | |||||||
\(368\) | −393595. | −0.151506 | ||||||||
\(369\) | 960475. | 0.367215 | ||||||||
\(370\) | 748623. | 0.284288 | ||||||||
\(371\) | 235597. | 0.0888657 | ||||||||
\(372\) | −26332.0 | −0.00986566 | ||||||||
\(373\) | 3.08228e6 | 1.14710 | 0.573548 | − | 0.819172i | \(-0.305567\pi\) | ||||
0.573548 | + | 0.819172i | \(0.305567\pi\) | |||||||
\(374\) | 1.12415e6 | 0.415570 | ||||||||
\(375\) | 206923. | 0.0759856 | ||||||||
\(376\) | 946955. | 0.345430 | ||||||||
\(377\) | −680126. | −0.246454 | ||||||||
\(378\) | 209098. | 0.0752699 | ||||||||
\(379\) | 3.00884e6 | 1.07597 | 0.537987 | − | 0.842953i | \(-0.319185\pi\) | ||||
0.537987 | + | 0.842953i | \(0.319185\pi\) | |||||||
\(380\) | 123510. | 0.0438775 | ||||||||
\(381\) | 1.82434e6 | 0.643863 | ||||||||
\(382\) | −3.23837e6 | −1.13545 | ||||||||
\(383\) | −155731. | −0.0542472 | −0.0271236 | − | 0.999632i | \(-0.508635\pi\) | ||||
−0.0271236 | + | 0.999632i | \(0.508635\pi\) | |||||||
\(384\) | 101355. | 0.0350765 | ||||||||
\(385\) | −35929.9 | −0.0123539 | ||||||||
\(386\) | −945862. | −0.323117 | ||||||||
\(387\) | −846197. | −0.287206 | ||||||||
\(388\) | −2.13162e6 | −0.718837 | ||||||||
\(389\) | −3.16932e6 | −1.06192 | −0.530960 | − | 0.847397i | \(-0.678169\pi\) | ||||
−0.530960 | + | 0.847397i | \(0.678169\pi\) | |||||||
\(390\) | 862598. | 0.287175 | ||||||||
\(391\) | 2.14264e6 | 0.708775 | ||||||||
\(392\) | −3.25841e6 | −1.07100 | ||||||||
\(393\) | −2.42368e6 | −0.791580 | ||||||||
\(394\) | −2.05472e6 | −0.666825 | ||||||||
\(395\) | 573201. | 0.184848 | ||||||||
\(396\) | −111974. | −0.0358821 | ||||||||
\(397\) | 4.88674e6 | 1.55612 | 0.778060 | − | 0.628191i | \(-0.216204\pi\) | ||||
0.778060 | + | 0.628191i | \(0.216204\pi\) | |||||||
\(398\) | −184079. | −0.0582502 | ||||||||
\(399\) | −56784.2 | −0.0178565 | ||||||||
\(400\) | −249240. | −0.0778875 | ||||||||
\(401\) | 227783. | 0.0707391 | 0.0353696 | − | 0.999374i | \(-0.488739\pi\) | ||||
0.0353696 | + | 0.999374i | \(0.488739\pi\) | |||||||
\(402\) | 681725. | 0.210399 | ||||||||
\(403\) | −88454.3 | −0.0271304 | ||||||||
\(404\) | −1.59312e6 | −0.485617 | ||||||||
\(405\) | −951119. | −0.288136 | ||||||||
\(406\) | −56786.0 | −0.0170973 | ||||||||
\(407\) | 846659. | 0.253351 | ||||||||
\(408\) | 5.62088e6 | 1.67168 | ||||||||
\(409\) | 1.30452e6 | 0.385605 | 0.192803 | − | 0.981238i | \(-0.438242\pi\) | ||||
0.192803 | + | 0.981238i | \(0.438242\pi\) | |||||||
\(410\) | 1.51967e6 | 0.446467 | ||||||||
\(411\) | −3.77284e6 | −1.10170 | ||||||||
\(412\) | 1.06626e6 | 0.309472 | ||||||||
\(413\) | 238377. | 0.0687685 | ||||||||
\(414\) | 285620. | 0.0819009 | ||||||||
\(415\) | −2.58601e6 | −0.737071 | ||||||||
\(416\) | 2.76995e6 | 0.784762 | ||||||||
\(417\) | 352870. | 0.0993745 | ||||||||
\(418\) | −186936. | −0.0523301 | ||||||||
\(419\) | 5.68370e6 | 1.58160 | 0.790799 | − | 0.612076i | \(-0.209665\pi\) | ||||
0.790799 | + | 0.612076i | \(0.209665\pi\) | |||||||
\(420\) | −53816.4 | −0.0148865 | ||||||||
\(421\) | 2.49111e6 | 0.684996 | 0.342498 | − | 0.939519i | \(-0.388727\pi\) | ||||
0.342498 | + | 0.939519i | \(0.388727\pi\) | |||||||
\(422\) | −1.68405e6 | −0.460335 | ||||||||
\(423\) | −327514. | −0.0889978 | ||||||||
\(424\) | 3.87806e6 | 1.04761 | ||||||||
\(425\) | 1.35681e6 | 0.364373 | ||||||||
\(426\) | 183200. | 0.0489105 | ||||||||
\(427\) | 470306. | 0.124828 | ||||||||
\(428\) | −1.11588e6 | −0.294447 | ||||||||
\(429\) | 975560. | 0.255924 | ||||||||
\(430\) | −1.33886e6 | −0.349191 | ||||||||
\(431\) | 1.62364e6 | 0.421015 | 0.210508 | − | 0.977592i | \(-0.432488\pi\) | ||||
0.210508 | + | 0.977592i | \(0.432488\pi\) | |||||||
\(432\) | 1.64043e6 | 0.422910 | ||||||||
\(433\) | 4.11880e6 | 1.05573 | 0.527863 | − | 0.849330i | \(-0.322994\pi\) | ||||
0.527863 | + | 0.849330i | \(0.322994\pi\) | |||||||
\(434\) | −7385.35 | −0.00188212 | ||||||||
\(435\) | 369862. | 0.0937167 | ||||||||
\(436\) | −766122. | −0.193011 | ||||||||
\(437\) | −356303. | −0.0892516 | ||||||||
\(438\) | −157554. | −0.0392413 | ||||||||
\(439\) | −498345. | −0.123415 | −0.0617076 | − | 0.998094i | \(-0.519655\pi\) | ||||
−0.0617076 | + | 0.998094i | \(0.519655\pi\) | |||||||
\(440\) | −591428. | −0.145636 | ||||||||
\(441\) | 1.12695e6 | 0.275937 | ||||||||
\(442\) | 5.65610e6 | 1.37709 | ||||||||
\(443\) | −497639. | −0.120477 | −0.0602386 | − | 0.998184i | \(-0.519186\pi\) | ||||
−0.0602386 | + | 0.998184i | \(0.519186\pi\) | |||||||
\(444\) | 1.26814e6 | 0.305288 | ||||||||
\(445\) | −1.53083e6 | −0.366461 | ||||||||
\(446\) | −5.58575e6 | −1.32967 | ||||||||
\(447\) | 4.01935e6 | 0.951453 | ||||||||
\(448\) | 382844. | 0.0901212 | ||||||||
\(449\) | 7.53957e6 | 1.76494 | 0.882471 | − | 0.470367i | \(-0.155878\pi\) | ||||
0.882471 | + | 0.470367i | \(0.155878\pi\) | |||||||
\(450\) | 180866. | 0.0421042 | ||||||||
\(451\) | 1.71868e6 | 0.397881 | ||||||||
\(452\) | 660782. | 0.152129 | ||||||||
\(453\) | 1.20552e6 | 0.276012 | ||||||||
\(454\) | 5.61273e6 | 1.27801 | ||||||||
\(455\) | −180780. | −0.0409375 | ||||||||
\(456\) | −934702. | −0.210504 | ||||||||
\(457\) | −4.56957e6 | −1.02349 | −0.511747 | − | 0.859136i | \(-0.671001\pi\) | ||||
−0.511747 | + | 0.859136i | \(0.671001\pi\) | |||||||
\(458\) | 2.11928e6 | 0.472091 | ||||||||
\(459\) | −8.93012e6 | −1.97845 | ||||||||
\(460\) | −337681. | −0.0744066 | ||||||||
\(461\) | −2.01890e6 | −0.442448 | −0.221224 | − | 0.975223i | \(-0.571005\pi\) | ||||
−0.221224 | + | 0.975223i | \(0.571005\pi\) | |||||||
\(462\) | 81452.8 | 0.0177542 | ||||||||
\(463\) | 4.61836e6 | 1.00123 | 0.500617 | − | 0.865669i | \(-0.333107\pi\) | ||||
0.500617 | + | 0.865669i | \(0.333107\pi\) | |||||||
\(464\) | −445500. | −0.0960623 | ||||||||
\(465\) | 48102.7 | 0.0103166 | ||||||||
\(466\) | 1.74489e6 | 0.372223 | ||||||||
\(467\) | 4.66977e6 | 0.990839 | 0.495420 | − | 0.868654i | \(-0.335014\pi\) | ||||
0.495420 | + | 0.868654i | \(0.335014\pi\) | |||||||
\(468\) | −563391. | −0.118904 | ||||||||
\(469\) | −142873. | −0.0299929 | ||||||||
\(470\) | −518195. | −0.108205 | ||||||||
\(471\) | −3.89402e6 | −0.808809 | ||||||||
\(472\) | 3.92383e6 | 0.810691 | ||||||||
\(473\) | −1.51419e6 | −0.311191 | ||||||||
\(474\) | −1.29944e6 | −0.265651 | ||||||||
\(475\) | −225625. | −0.0458831 | ||||||||
\(476\) | −352876. | −0.0713847 | ||||||||
\(477\) | −1.34127e6 | −0.269910 | ||||||||
\(478\) | 4.10568e6 | 0.821894 | ||||||||
\(479\) | 3.46392e6 | 0.689810 | 0.344905 | − | 0.938638i | \(-0.387911\pi\) | ||||
0.344905 | + | 0.938638i | \(0.387911\pi\) | |||||||
\(480\) | −1.50634e6 | −0.298414 | ||||||||
\(481\) | 4.25992e6 | 0.839536 | ||||||||
\(482\) | −6.01360e6 | −1.17901 | ||||||||
\(483\) | 155250. | 0.0302806 | ||||||||
\(484\) | −200366. | −0.0388786 | ||||||||
\(485\) | 3.89400e6 | 0.751695 | ||||||||
\(486\) | −2.12167e6 | −0.407463 | ||||||||
\(487\) | −6.76913e6 | −1.29333 | −0.646667 | − | 0.762773i | \(-0.723838\pi\) | ||||
−0.646667 | + | 0.762773i | \(0.723838\pi\) | |||||||
\(488\) | 7.74151e6 | 1.47155 | ||||||||
\(489\) | −2.87056e6 | −0.542868 | ||||||||
\(490\) | 1.78307e6 | 0.335490 | ||||||||
\(491\) | −184736. | −0.0345819 | −0.0172910 | − | 0.999851i | \(-0.505504\pi\) | ||||
−0.0172910 | + | 0.999851i | \(0.505504\pi\) | |||||||
\(492\) | 2.57426e6 | 0.479446 | ||||||||
\(493\) | 2.42520e6 | 0.449398 | ||||||||
\(494\) | −940559. | −0.173408 | ||||||||
\(495\) | 204551. | 0.0375223 | ||||||||
\(496\) | −57939.9 | −0.0105748 | ||||||||
\(497\) | −38394.4 | −0.00697231 | ||||||||
\(498\) | 5.86245e6 | 1.05927 | ||||||||
\(499\) | −5.96534e6 | −1.07247 | −0.536233 | − | 0.844070i | \(-0.680153\pi\) | ||||
−0.536233 | + | 0.844070i | \(0.680153\pi\) | |||||||
\(500\) | −213833. | −0.0382515 | ||||||||
\(501\) | 1.53277e6 | 0.272824 | ||||||||
\(502\) | −4.99255e6 | −0.884225 | ||||||||
\(503\) | −1.10592e7 | −1.94896 | −0.974478 | − | 0.224483i | \(-0.927931\pi\) | ||||
−0.974478 | + | 0.224483i | \(0.927931\pi\) | |||||||
\(504\) | −157031. | −0.0275365 | ||||||||
\(505\) | 2.91027e6 | 0.507814 | ||||||||
\(506\) | 511090. | 0.0887404 | ||||||||
\(507\) | −8586.94 | −0.00148361 | ||||||||
\(508\) | −1.88526e6 | −0.324124 | ||||||||
\(509\) | −9.46412e6 | −1.61915 | −0.809573 | − | 0.587019i | \(-0.800301\pi\) | ||||
−0.809573 | + | 0.587019i | \(0.800301\pi\) | |||||||
\(510\) | −3.07587e6 | −0.523651 | ||||||||
\(511\) | 33019.4 | 0.00559394 | ||||||||
\(512\) | 4.30935e6 | 0.726502 | ||||||||
\(513\) | 1.48500e6 | 0.249134 | ||||||||
\(514\) | 4.46786e6 | 0.745919 | ||||||||
\(515\) | −1.94783e6 | −0.323618 | ||||||||
\(516\) | −2.26797e6 | −0.374985 | ||||||||
\(517\) | −586055. | −0.0964300 | ||||||||
\(518\) | 355676. | 0.0582411 | ||||||||
\(519\) | −2.88358e6 | −0.469909 | ||||||||
\(520\) | −2.97574e6 | −0.482600 | ||||||||
\(521\) | 4.23835e6 | 0.684073 | 0.342036 | − | 0.939687i | \(-0.388883\pi\) | ||||
0.342036 | + | 0.939687i | \(0.388883\pi\) | |||||||
\(522\) | 323286. | 0.0519291 | ||||||||
\(523\) | −6.57389e6 | −1.05092 | −0.525458 | − | 0.850820i | \(-0.676106\pi\) | ||||
−0.525458 | + | 0.850820i | \(0.676106\pi\) | |||||||
\(524\) | 2.50461e6 | 0.398485 | ||||||||
\(525\) | 98310.7 | 0.0155669 | ||||||||
\(526\) | −6.53678e6 | −1.03015 | ||||||||
\(527\) | 315412. | 0.0494711 | ||||||||
\(528\) | 639017. | 0.0997534 | ||||||||
\(529\) | −5.46220e6 | −0.848649 | ||||||||
\(530\) | −2.12216e6 | −0.328162 | ||||||||
\(531\) | −1.35710e6 | −0.208869 | ||||||||
\(532\) | 58680.3 | 0.00898903 | ||||||||
\(533\) | 8.64744e6 | 1.31847 | ||||||||
\(534\) | 3.47039e6 | 0.526653 | ||||||||
\(535\) | 2.03847e6 | 0.307907 | ||||||||
\(536\) | −2.35178e6 | −0.353577 | ||||||||
\(537\) | 1.74819e6 | 0.261609 | ||||||||
\(538\) | 3.24261e6 | 0.482991 | ||||||||
\(539\) | 2.01658e6 | 0.298980 | ||||||||
\(540\) | 1.40739e6 | 0.207696 | ||||||||
\(541\) | 7.89424e6 | 1.15962 | 0.579812 | − | 0.814750i | \(-0.303126\pi\) | ||||
0.579812 | + | 0.814750i | \(0.303126\pi\) | |||||||
\(542\) | 2.08933e6 | 0.305498 | ||||||||
\(543\) | 8.97808e6 | 1.30672 | ||||||||
\(544\) | −9.87713e6 | −1.43098 | ||||||||
\(545\) | 1.39954e6 | 0.201833 | ||||||||
\(546\) | 409826. | 0.0588326 | ||||||||
\(547\) | −3.40867e6 | −0.487099 | −0.243549 | − | 0.969888i | \(-0.578312\pi\) | ||||
−0.243549 | + | 0.969888i | \(0.578312\pi\) | |||||||
\(548\) | 3.89881e6 | 0.554601 | ||||||||
\(549\) | −2.67748e6 | −0.379136 | ||||||||
\(550\) | 323642. | 0.0456204 | ||||||||
\(551\) | −403290. | −0.0565898 | ||||||||
\(552\) | 2.55551e6 | 0.356969 | ||||||||
\(553\) | 272332. | 0.0378691 | ||||||||
\(554\) | 3.75002e6 | 0.519109 | ||||||||
\(555\) | −2.31661e6 | −0.319242 | ||||||||
\(556\) | −364652. | −0.0500256 | ||||||||
\(557\) | 8.69872e6 | 1.18800 | 0.594001 | − | 0.804464i | \(-0.297547\pi\) | ||||
0.594001 | + | 0.804464i | \(0.297547\pi\) | |||||||
\(558\) | 42045.3 | 0.00571652 | ||||||||
\(559\) | −7.61856e6 | −1.03120 | ||||||||
\(560\) | −118416. | −0.0159565 | ||||||||
\(561\) | −3.47867e6 | −0.466666 | ||||||||
\(562\) | −3.54790e6 | −0.473838 | ||||||||
\(563\) | −3.05136e6 | −0.405717 | −0.202858 | − | 0.979208i | \(-0.565023\pi\) | ||||
−0.202858 | + | 0.979208i | \(0.565023\pi\) | |||||||
\(564\) | −877802. | −0.116198 | ||||||||
\(565\) | −1.20710e6 | −0.159083 | ||||||||
\(566\) | 846116. | 0.111017 | ||||||||
\(567\) | −451883. | −0.0590294 | ||||||||
\(568\) | −631994. | −0.0821944 | ||||||||
\(569\) | −8.67457e6 | −1.12323 | −0.561613 | − | 0.827400i | \(-0.689819\pi\) | ||||
−0.561613 | + | 0.827400i | \(0.689819\pi\) | |||||||
\(570\) | 511490. | 0.0659401 | ||||||||
\(571\) | 963909. | 0.123722 | 0.0618608 | − | 0.998085i | \(-0.480297\pi\) | ||||
0.0618608 | + | 0.998085i | \(0.480297\pi\) | |||||||
\(572\) | −1.00813e6 | −0.128833 | ||||||||
\(573\) | 1.00211e7 | 1.27506 | ||||||||
\(574\) | 722005. | 0.0914661 | ||||||||
\(575\) | 616868. | 0.0778077 | ||||||||
\(576\) | −2.17956e6 | −0.273723 | ||||||||
\(577\) | −6.94281e6 | −0.868152 | −0.434076 | − | 0.900876i | \(-0.642925\pi\) | ||||
−0.434076 | + | 0.900876i | \(0.642925\pi\) | |||||||
\(578\) | −1.40922e7 | −1.75453 | ||||||||
\(579\) | 2.92696e6 | 0.362845 | ||||||||
\(580\) | −382212. | −0.0471774 | ||||||||
\(581\) | −1.22863e6 | −0.151001 | ||||||||
\(582\) | −8.82766e6 | −1.08028 | ||||||||
\(583\) | −2.40007e6 | −0.292450 | ||||||||
\(584\) | 543520. | 0.0659452 | ||||||||
\(585\) | 1.02919e6 | 0.124339 | ||||||||
\(586\) | −7.86409e6 | −0.946029 | ||||||||
\(587\) | 2.88979e6 | 0.346155 | 0.173077 | − | 0.984908i | \(-0.444629\pi\) | ||||
0.173077 | + | 0.984908i | \(0.444629\pi\) | |||||||
\(588\) | 3.02046e6 | 0.360271 | ||||||||
\(589\) | −52450.2 | −0.00622958 | ||||||||
\(590\) | −2.14721e6 | −0.253947 | ||||||||
\(591\) | 6.35832e6 | 0.748813 | ||||||||
\(592\) | 2.79036e6 | 0.327232 | ||||||||
\(593\) | 4.76414e6 | 0.556349 | 0.278175 | − | 0.960531i | \(-0.410271\pi\) | ||||
0.278175 | + | 0.960531i | \(0.410271\pi\) | |||||||
\(594\) | −2.13012e6 | −0.247707 | ||||||||
\(595\) | 644628. | 0.0746477 | ||||||||
\(596\) | −4.15356e6 | −0.478966 | ||||||||
\(597\) | 569632. | 0.0654122 | ||||||||
\(598\) | 2.57153e6 | 0.294061 | ||||||||
\(599\) | −7.22809e6 | −0.823108 | −0.411554 | − | 0.911385i | \(-0.635014\pi\) | ||||
−0.411554 | + | 0.911385i | \(0.635014\pi\) | |||||||
\(600\) | 1.61825e6 | 0.183513 | ||||||||
\(601\) | 3.81027e6 | 0.430299 | 0.215149 | − | 0.976581i | \(-0.430976\pi\) | ||||
0.215149 | + | 0.976581i | \(0.430976\pi\) | |||||||
\(602\) | −636100. | −0.0715376 | ||||||||
\(603\) | 813386. | 0.0910968 | ||||||||
\(604\) | −1.24577e6 | −0.138946 | ||||||||
\(605\) | 366025. | 0.0406558 | ||||||||
\(606\) | −6.59756e6 | −0.729796 | ||||||||
\(607\) | 1.64080e7 | 1.80752 | 0.903762 | − | 0.428034i | \(-0.140794\pi\) | ||||
0.903762 | + | 0.428034i | \(0.140794\pi\) | |||||||
\(608\) | 1.64248e6 | 0.180194 | ||||||||
\(609\) | 175724. | 0.0191994 | ||||||||
\(610\) | −4.23633e6 | −0.460962 | ||||||||
\(611\) | −2.94871e6 | −0.319543 | ||||||||
\(612\) | 2.00895e6 | 0.216815 | ||||||||
\(613\) | 2.02821e6 | 0.218002 | 0.109001 | − | 0.994042i | \(-0.465235\pi\) | ||||
0.109001 | + | 0.994042i | \(0.465235\pi\) | |||||||
\(614\) | −1.10661e7 | −1.18460 | ||||||||
\(615\) | −4.70261e6 | −0.501361 | ||||||||
\(616\) | −280991. | −0.0298360 | ||||||||
\(617\) | 9.37403e6 | 0.991320 | 0.495660 | − | 0.868517i | \(-0.334926\pi\) | ||||
0.495660 | + | 0.868517i | \(0.334926\pi\) | |||||||
\(618\) | 4.41571e6 | 0.465082 | ||||||||
\(619\) | 7.59697e6 | 0.796918 | 0.398459 | − | 0.917186i | \(-0.369545\pi\) | ||||
0.398459 | + | 0.917186i | \(0.369545\pi\) | |||||||
\(620\) | −49708.9 | −0.00519343 | ||||||||
\(621\) | −4.06005e6 | −0.422477 | ||||||||
\(622\) | −1.33833e7 | −1.38703 | ||||||||
\(623\) | −727309. | −0.0750757 | ||||||||
\(624\) | 3.21519e6 | 0.330556 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 7.68139e6 | 0.783437 | ||||||||
\(627\) | 578472. | 0.0587643 | ||||||||
\(628\) | 4.02404e6 | 0.407158 | ||||||||
\(629\) | −1.51901e7 | −1.53086 | ||||||||
\(630\) | 85930.6 | 0.00862575 | ||||||||
\(631\) | 1.50154e7 | 1.50128 | 0.750642 | − | 0.660709i | \(-0.229744\pi\) | ||||
0.750642 | + | 0.660709i | \(0.229744\pi\) | |||||||
\(632\) | 4.48274e6 | 0.446427 | ||||||||
\(633\) | 5.21129e6 | 0.516935 | ||||||||
\(634\) | −3.05489e6 | −0.301837 | ||||||||
\(635\) | 3.44395e6 | 0.338939 | ||||||||
\(636\) | −3.59486e6 | −0.352402 | ||||||||
\(637\) | 1.01463e7 | 0.990740 | ||||||||
\(638\) | 578490. | 0.0562657 | ||||||||
\(639\) | 218582. | 0.0211769 | ||||||||
\(640\) | 191335. | 0.0184648 | ||||||||
\(641\) | 1.96960e7 | 1.89336 | 0.946679 | − | 0.322180i | \(-0.104415\pi\) | ||||
0.946679 | + | 0.322180i | \(0.104415\pi\) | |||||||
\(642\) | −4.62118e6 | −0.442502 | ||||||||
\(643\) | 1.52750e7 | 1.45698 | 0.728492 | − | 0.685055i | \(-0.240222\pi\) | ||||
0.728492 | + | 0.685055i | \(0.240222\pi\) | |||||||
\(644\) | −160434. | −0.0152434 | ||||||||
\(645\) | 4.14309e6 | 0.392125 | ||||||||
\(646\) | 3.35386e6 | 0.316201 | ||||||||
\(647\) | −1.37109e7 | −1.28767 | −0.643836 | − | 0.765164i | \(-0.722658\pi\) | ||||
−0.643836 | + | 0.765164i | \(0.722658\pi\) | |||||||
\(648\) | −7.43826e6 | −0.695879 | ||||||||
\(649\) | −2.42839e6 | −0.226312 | ||||||||
\(650\) | 1.62839e6 | 0.151173 | ||||||||
\(651\) | 22853.9 | 0.00211353 | ||||||||
\(652\) | 2.96640e6 | 0.273282 | ||||||||
\(653\) | −3.26845e6 | −0.299957 | −0.149979 | − | 0.988689i | \(-0.547920\pi\) | ||||
−0.149979 | + | 0.988689i | \(0.547920\pi\) | |||||||
\(654\) | −3.17274e6 | −0.290061 | ||||||||
\(655\) | −4.57537e6 | −0.416700 | ||||||||
\(656\) | 5.66430e6 | 0.513910 | ||||||||
\(657\) | −187982. | −0.0169904 | ||||||||
\(658\) | −246198. | −0.0221676 | ||||||||
\(659\) | −2.79749e6 | −0.250931 | −0.125466 | − | 0.992098i | \(-0.540042\pi\) | ||||
−0.125466 | + | 0.992098i | \(0.540042\pi\) | |||||||
\(660\) | 548238. | 0.0489902 | ||||||||
\(661\) | 8.71937e6 | 0.776214 | 0.388107 | − | 0.921614i | \(-0.373129\pi\) | ||||
0.388107 | + | 0.921614i | \(0.373129\pi\) | |||||||
\(662\) | −1.26905e7 | −1.12547 | ||||||||
\(663\) | −1.75028e7 | −1.54640 | ||||||||
\(664\) | −2.02239e7 | −1.78011 | ||||||||
\(665\) | −107196. | −0.00939992 | ||||||||
\(666\) | −2.02488e6 | −0.176895 | ||||||||
\(667\) | 1.10261e6 | 0.0959639 | ||||||||
\(668\) | −1.58395e6 | −0.137341 | ||||||||
\(669\) | 1.72851e7 | 1.49316 | ||||||||
\(670\) | 1.28694e6 | 0.110757 | ||||||||
\(671\) | −4.79109e6 | −0.410798 | ||||||||
\(672\) | −715671. | −0.0611350 | ||||||||
\(673\) | 9.68767e6 | 0.824483 | 0.412242 | − | 0.911075i | \(-0.364746\pi\) | ||||
0.412242 | + | 0.911075i | \(0.364746\pi\) | |||||||
\(674\) | −1.00049e7 | −0.848326 | ||||||||
\(675\) | −2.57098e6 | −0.217190 | ||||||||
\(676\) | 8873.66 | 0.000746855 0 | ||||||||
\(677\) | −1.68290e7 | −1.41119 | −0.705596 | − | 0.708614i | \(-0.749321\pi\) | ||||
−0.705596 | + | 0.708614i | \(0.749321\pi\) | |||||||
\(678\) | 2.73649e6 | 0.228623 | ||||||||
\(679\) | 1.85006e6 | 0.153997 | ||||||||
\(680\) | 1.06110e7 | 0.879999 | ||||||||
\(681\) | −1.73686e7 | −1.43515 | ||||||||
\(682\) | 75236.0 | 0.00619391 | ||||||||
\(683\) | 1.26965e7 | 1.04143 | 0.520717 | − | 0.853729i | \(-0.325665\pi\) | ||||
0.520717 | + | 0.853729i | \(0.325665\pi\) | |||||||
\(684\) | −334070. | −0.0273022 | ||||||||
\(685\) | −7.12227e6 | −0.579952 | ||||||||
\(686\) | 1.70147e6 | 0.138043 | ||||||||
\(687\) | −6.55811e6 | −0.530135 | ||||||||
\(688\) | −4.99036e6 | −0.401940 | ||||||||
\(689\) | −1.20758e7 | −0.969100 | ||||||||
\(690\) | −1.39843e6 | −0.111820 | ||||||||
\(691\) | −1.72598e7 | −1.37512 | −0.687560 | − | 0.726127i | \(-0.741318\pi\) | ||||
−0.687560 | + | 0.726127i | \(0.741318\pi\) | |||||||
\(692\) | 2.97986e6 | 0.236554 | ||||||||
\(693\) | 97183.7 | 0.00768706 | ||||||||
\(694\) | 1.09392e7 | 0.862160 | ||||||||
\(695\) | 666140. | 0.0523122 | ||||||||
\(696\) | 2.89252e6 | 0.226336 | ||||||||
\(697\) | −3.08352e7 | −2.40417 | ||||||||
\(698\) | −416862. | −0.0323857 | ||||||||
\(699\) | −5.39955e6 | −0.417989 | ||||||||
\(700\) | −101593. | −0.00783646 | ||||||||
\(701\) | −1.78321e7 | −1.37059 | −0.685294 | − | 0.728266i | \(-0.740326\pi\) | ||||
−0.685294 | + | 0.728266i | \(0.740326\pi\) | |||||||
\(702\) | −1.07176e7 | −0.820835 | ||||||||
\(703\) | 2.52598e6 | 0.192771 | ||||||||
\(704\) | −3.90011e6 | −0.296582 | ||||||||
\(705\) | 1.60355e6 | 0.121509 | ||||||||
\(706\) | −1.86396e7 | −1.40742 | ||||||||
\(707\) | 1.38269e6 | 0.104034 | ||||||||
\(708\) | −3.63728e6 | −0.272706 | ||||||||
\(709\) | −2.03015e7 | −1.51675 | −0.758373 | − | 0.651821i | \(-0.774005\pi\) | ||||
−0.758373 | + | 0.651821i | \(0.774005\pi\) | |||||||
\(710\) | 345841. | 0.0257473 | ||||||||
\(711\) | −1.55040e6 | −0.115019 | ||||||||
\(712\) | −1.19719e7 | −0.885044 | ||||||||
\(713\) | 143401. | 0.0105640 | ||||||||
\(714\) | −1.46136e6 | −0.107279 | ||||||||
\(715\) | 1.84164e6 | 0.134722 | ||||||||
\(716\) | −1.80656e6 | −0.131695 | ||||||||
\(717\) | −1.27050e7 | −0.922948 | ||||||||
\(718\) | −1.72176e7 | −1.24641 | ||||||||
\(719\) | −4.58061e6 | −0.330446 | −0.165223 | − | 0.986256i | \(-0.552834\pi\) | ||||
−0.165223 | + | 0.986256i | \(0.552834\pi\) | |||||||
\(720\) | 674147. | 0.0484645 | ||||||||
\(721\) | −925427. | −0.0662985 | ||||||||
\(722\) | −557718. | −0.0398173 | ||||||||
\(723\) | 1.86090e7 | 1.32397 | ||||||||
\(724\) | −9.27786e6 | −0.657811 | ||||||||
\(725\) | 698217. | 0.0493339 | ||||||||
\(726\) | −829775. | −0.0584277 | ||||||||
\(727\) | −3.12165e6 | −0.219053 | −0.109526 | − | 0.993984i | \(-0.534933\pi\) | ||||
−0.109526 | + | 0.993984i | \(0.534933\pi\) | |||||||
\(728\) | −1.41379e6 | −0.0988685 | ||||||||
\(729\) | 1.58104e7 | 1.10185 | ||||||||
\(730\) | −297426. | −0.0206572 | ||||||||
\(731\) | 2.71664e7 | 1.88035 | ||||||||
\(732\) | −7.17617e6 | −0.495011 | ||||||||
\(733\) | 1.64680e7 | 1.13209 | 0.566046 | − | 0.824374i | \(-0.308473\pi\) | ||||
0.566046 | + | 0.824374i | \(0.308473\pi\) | |||||||
\(734\) | 1.82820e6 | 0.125252 | ||||||||
\(735\) | −5.51771e6 | −0.376739 | ||||||||
\(736\) | −4.49060e6 | −0.305570 | ||||||||
\(737\) | 1.45548e6 | 0.0987043 | ||||||||
\(738\) | −4.11042e6 | −0.277808 | ||||||||
\(739\) | −2.24853e7 | −1.51456 | −0.757281 | − | 0.653089i | \(-0.773473\pi\) | ||||
−0.757281 | + | 0.653089i | \(0.773473\pi\) | |||||||
\(740\) | 2.39396e6 | 0.160708 | ||||||||
\(741\) | 2.91055e6 | 0.194729 | ||||||||
\(742\) | −1.00825e6 | −0.0672294 | ||||||||
\(743\) | −2.11668e7 | −1.40664 | −0.703321 | − | 0.710873i | \(-0.748300\pi\) | ||||
−0.703321 | + | 0.710873i | \(0.748300\pi\) | |||||||
\(744\) | 376189. | 0.0249157 | ||||||||
\(745\) | 7.58764e6 | 0.500860 | ||||||||
\(746\) | −1.31908e7 | −0.867810 | ||||||||
\(747\) | 6.99466e6 | 0.458633 | ||||||||
\(748\) | 3.59482e6 | 0.234922 | ||||||||
\(749\) | 968488. | 0.0630797 | ||||||||
\(750\) | −885543. | −0.0574853 | ||||||||
\(751\) | −6.33885e6 | −0.410119 | −0.205060 | − | 0.978749i | \(-0.565739\pi\) | ||||
−0.205060 | + | 0.978749i | \(0.565739\pi\) | |||||||
\(752\) | −1.93148e6 | −0.124551 | ||||||||
\(753\) | 1.54494e7 | 0.992943 | ||||||||
\(754\) | 2.91064e6 | 0.186449 | ||||||||
\(755\) | 2.27575e6 | 0.145297 | ||||||||
\(756\) | 668658. | 0.0425500 | ||||||||
\(757\) | −2.14477e7 | −1.36032 | −0.680160 | − | 0.733064i | \(-0.738090\pi\) | ||||
−0.680160 | + | 0.733064i | \(0.738090\pi\) | |||||||
\(758\) | −1.28766e7 | −0.814004 | ||||||||
\(759\) | −1.58157e6 | −0.0996513 | ||||||||
\(760\) | −1.76451e6 | −0.110813 | ||||||||
\(761\) | −1.27796e6 | −0.0799939 | −0.0399970 | − | 0.999200i | \(-0.512735\pi\) | ||||
−0.0399970 | + | 0.999200i | \(0.512735\pi\) | |||||||
\(762\) | −7.80739e6 | −0.487101 | ||||||||
\(763\) | 664929. | 0.0413489 | ||||||||
\(764\) | −1.03557e7 | −0.641869 | ||||||||
\(765\) | −3.66991e6 | −0.226726 | ||||||||
\(766\) | 666461. | 0.0410395 | ||||||||
\(767\) | −1.22183e7 | −0.749936 | ||||||||
\(768\) | −1.40931e7 | −0.862193 | ||||||||
\(769\) | −1.25278e7 | −0.763937 | −0.381969 | − | 0.924175i | \(-0.624754\pi\) | ||||
−0.381969 | + | 0.924175i | \(0.624754\pi\) | |||||||
\(770\) | 153765. | 0.00934608 | ||||||||
\(771\) | −1.38258e7 | −0.837631 | ||||||||
\(772\) | −3.02469e6 | −0.182658 | ||||||||
\(773\) | 1.37232e7 | 0.826053 | 0.413027 | − | 0.910719i | \(-0.364472\pi\) | ||||
0.413027 | + | 0.910719i | \(0.364472\pi\) | |||||||
\(774\) | 3.62136e6 | 0.217280 | ||||||||
\(775\) | 90807.1 | 0.00543082 | ||||||||
\(776\) | 3.04532e7 | 1.81542 | ||||||||
\(777\) | −1.10064e6 | −0.0654020 | ||||||||
\(778\) | 1.35633e7 | 0.803373 | ||||||||
\(779\) | 5.12762e6 | 0.302742 | ||||||||
\(780\) | 2.75843e6 | 0.162340 | ||||||||
\(781\) | 391131. | 0.0229453 | ||||||||
\(782\) | −9.16960e6 | −0.536208 | ||||||||
\(783\) | −4.59547e6 | −0.267871 | ||||||||
\(784\) | 6.64610e6 | 0.386168 | ||||||||
\(785\) | −7.35103e6 | −0.425769 | ||||||||
\(786\) | 1.03723e7 | 0.598853 | ||||||||
\(787\) | 4.20499e6 | 0.242007 | 0.121004 | − | 0.992652i | \(-0.461389\pi\) | ||||
0.121004 | + | 0.992652i | \(0.461389\pi\) | |||||||
\(788\) | −6.57062e6 | −0.376956 | ||||||||
\(789\) | 2.02280e7 | 1.15681 | ||||||||
\(790\) | −2.45305e6 | −0.139843 | ||||||||
\(791\) | −573503. | −0.0325908 | ||||||||
\(792\) | 1.59970e6 | 0.0906204 | ||||||||
\(793\) | −2.41062e7 | −1.36127 | ||||||||
\(794\) | −2.09131e7 | −1.17725 | ||||||||
\(795\) | 6.56701e6 | 0.368510 | ||||||||
\(796\) | −588652. | −0.0329288 | ||||||||
\(797\) | −2.00669e7 | −1.11901 | −0.559507 | − | 0.828826i | \(-0.689009\pi\) | ||||
−0.559507 | + | 0.828826i | \(0.689009\pi\) | |||||||
\(798\) | 243012. | 0.0135089 | ||||||||
\(799\) | 1.05146e7 | 0.582672 | ||||||||
\(800\) | −2.84363e6 | −0.157090 | ||||||||
\(801\) | 4.14062e6 | 0.228026 | ||||||||
\(802\) | −974812. | −0.0535161 | ||||||||
\(803\) | −336375. | −0.0184092 | ||||||||
\(804\) | 2.18003e6 | 0.118939 | ||||||||
\(805\) | 293078. | 0.0159402 | ||||||||
\(806\) | 378546. | 0.0205249 | ||||||||
\(807\) | −1.00342e7 | −0.542376 | ||||||||
\(808\) | 2.27599e7 | 1.22643 | ||||||||
\(809\) | −5.43542e6 | −0.291986 | −0.145993 | − | 0.989286i | \(-0.546638\pi\) | ||||
−0.145993 | + | 0.989286i | \(0.546638\pi\) | |||||||
\(810\) | 4.07038e6 | 0.217983 | ||||||||
\(811\) | −1.68868e7 | −0.901563 | −0.450782 | − | 0.892634i | \(-0.648855\pi\) | ||||
−0.450782 | + | 0.892634i | \(0.648855\pi\) | |||||||
\(812\) | −181591. | −0.00966507 | ||||||||
\(813\) | −6.46541e6 | −0.343059 | ||||||||
\(814\) | −3.62333e6 | −0.191667 | ||||||||
\(815\) | −5.41897e6 | −0.285774 | ||||||||
\(816\) | −1.14648e7 | −0.602754 | ||||||||
\(817\) | −4.51753e6 | −0.236781 | ||||||||
\(818\) | −5.58279e6 | −0.291721 | ||||||||
\(819\) | 488975. | 0.0254728 | ||||||||
\(820\) | 4.85962e6 | 0.252388 | ||||||||
\(821\) | −1.99548e7 | −1.03321 | −0.516606 | − | 0.856223i | \(-0.672805\pi\) | ||||
−0.516606 | + | 0.856223i | \(0.672805\pi\) | |||||||
\(822\) | 1.61461e7 | 0.833467 | ||||||||
\(823\) | 3.06729e7 | 1.57854 | 0.789270 | − | 0.614046i | \(-0.210459\pi\) | ||||
0.789270 | + | 0.614046i | \(0.210459\pi\) | |||||||
\(824\) | −1.52331e7 | −0.781573 | ||||||||
\(825\) | −1.00151e6 | −0.0512295 | ||||||||
\(826\) | −1.02015e6 | −0.0520253 | ||||||||
\(827\) | 647257. | 0.0329088 | 0.0164544 | − | 0.999865i | \(-0.494762\pi\) | ||||
0.0164544 | + | 0.999865i | \(0.494762\pi\) | |||||||
\(828\) | 913362. | 0.0462985 | ||||||||
\(829\) | 5.31655e6 | 0.268685 | 0.134343 | − | 0.990935i | \(-0.457108\pi\) | ||||
0.134343 | + | 0.990935i | \(0.457108\pi\) | |||||||
\(830\) | 1.10670e7 | 0.557615 | ||||||||
\(831\) | −1.16044e7 | −0.582935 | ||||||||
\(832\) | −1.96232e7 | −0.982792 | ||||||||
\(833\) | −3.61799e7 | −1.80657 | ||||||||
\(834\) | −1.51013e6 | −0.0751796 | ||||||||
\(835\) | 2.89352e6 | 0.143619 | ||||||||
\(836\) | −597787. | −0.0295822 | ||||||||
\(837\) | −597667. | −0.0294880 | ||||||||
\(838\) | −2.43238e7 | −1.19652 | ||||||||
\(839\) | −2.26426e7 | −1.11051 | −0.555254 | − | 0.831681i | \(-0.687379\pi\) | ||||
−0.555254 | + | 0.831681i | \(0.687379\pi\) | |||||||
\(840\) | 768842. | 0.0375958 | ||||||||
\(841\) | −1.92631e7 | −0.939154 | ||||||||
\(842\) | −1.06609e7 | −0.518219 | ||||||||
\(843\) | 1.09789e7 | 0.532098 | ||||||||
\(844\) | −5.38529e6 | −0.260227 | ||||||||
\(845\) | −16210.2 | −0.000780993 0 | ||||||||
\(846\) | 1.40162e6 | 0.0673293 | ||||||||
\(847\) | 173901. | 0.00832901 | ||||||||
\(848\) | −7.90998e6 | −0.377734 | ||||||||
\(849\) | −2.61830e6 | −0.124667 | ||||||||
\(850\) | −5.80655e6 | −0.275658 | ||||||||
\(851\) | −6.90614e6 | −0.326897 | ||||||||
\(852\) | 585842. | 0.0276491 | ||||||||
\(853\) | 1.55183e7 | 0.730251 | 0.365125 | − | 0.930958i | \(-0.381026\pi\) | ||||
0.365125 | + | 0.930958i | \(0.381026\pi\) | |||||||
\(854\) | −2.01271e6 | −0.0944356 | ||||||||
\(855\) | 610273. | 0.0285502 | ||||||||
\(856\) | 1.59419e7 | 0.743628 | ||||||||
\(857\) | −2.74647e7 | −1.27739 | −0.638695 | − | 0.769460i | \(-0.720525\pi\) | ||||
−0.638695 | + | 0.769460i | \(0.720525\pi\) | |||||||
\(858\) | −4.17498e6 | −0.193614 | ||||||||
\(859\) | −2.81821e7 | −1.30314 | −0.651569 | − | 0.758589i | \(-0.725889\pi\) | ||||
−0.651569 | + | 0.758589i | \(0.725889\pi\) | |||||||
\(860\) | −4.28142e6 | −0.197398 | ||||||||
\(861\) | −2.23424e6 | −0.102712 | ||||||||
\(862\) | −6.94850e6 | −0.318510 | ||||||||
\(863\) | 1.36345e7 | 0.623180 | 0.311590 | − | 0.950217i | \(-0.399139\pi\) | ||||
0.311590 | + | 0.950217i | \(0.399139\pi\) | |||||||
\(864\) | 1.87160e7 | 0.852958 | ||||||||
\(865\) | −5.44355e6 | −0.247367 | ||||||||
\(866\) | −1.76267e7 | −0.798686 | ||||||||
\(867\) | 4.36083e7 | 1.97025 | ||||||||
\(868\) | −23617.0 | −0.00106396 | ||||||||
\(869\) | −2.77429e6 | −0.124624 | ||||||||
\(870\) | −1.58285e6 | −0.0708993 | ||||||||
\(871\) | 7.32316e6 | 0.327079 | ||||||||
\(872\) | 1.09451e7 | 0.487449 | ||||||||
\(873\) | −1.05325e7 | −0.467732 | ||||||||
\(874\) | 1.52482e6 | 0.0675213 | ||||||||
\(875\) | 185588. | 0.00819466 | ||||||||
\(876\) | −503828. | −0.0221831 | ||||||||
\(877\) | 2.04955e7 | 0.899826 | 0.449913 | − | 0.893072i | \(-0.351455\pi\) | ||||
0.449913 | + | 0.893072i | \(0.351455\pi\) | |||||||
\(878\) | 2.13270e6 | 0.0933671 | ||||||||
\(879\) | 2.43354e7 | 1.06235 | ||||||||
\(880\) | 1.20632e6 | 0.0525117 | ||||||||
\(881\) | 2.63579e7 | 1.14412 | 0.572060 | − | 0.820212i | \(-0.306145\pi\) | ||||
0.572060 | + | 0.820212i | \(0.306145\pi\) | |||||||
\(882\) | −4.82288e6 | −0.208754 | ||||||||
\(883\) | −3.38025e6 | −0.145897 | −0.0729486 | − | 0.997336i | \(-0.523241\pi\) | ||||
−0.0729486 | + | 0.997336i | \(0.523241\pi\) | |||||||
\(884\) | 1.80872e7 | 0.778466 | ||||||||
\(885\) | 6.64452e6 | 0.285171 | ||||||||
\(886\) | 2.12968e6 | 0.0911444 | ||||||||
\(887\) | −1.56679e7 | −0.668655 | −0.334327 | − | 0.942457i | \(-0.608509\pi\) | ||||
−0.334327 | + | 0.942457i | \(0.608509\pi\) | |||||||
\(888\) | −1.81171e7 | −0.771004 | ||||||||
\(889\) | 1.63624e6 | 0.0694373 | ||||||||
\(890\) | 6.55131e6 | 0.277238 | ||||||||
\(891\) | 4.60342e6 | 0.194261 | ||||||||
\(892\) | −1.78622e7 | −0.751662 | ||||||||
\(893\) | −1.74848e6 | −0.0733722 | ||||||||
\(894\) | −1.72011e7 | −0.719801 | ||||||||
\(895\) | 3.30018e6 | 0.137715 | ||||||||
\(896\) | 90904.5 | 0.00378282 | ||||||||
\(897\) | −7.95757e6 | −0.330217 | ||||||||
\(898\) | −3.22661e7 | −1.33523 | ||||||||
\(899\) | 162312. | 0.00669809 | ||||||||
\(900\) | 578377. | 0.0238015 | ||||||||
\(901\) | 4.30602e7 | 1.76711 | ||||||||
\(902\) | −7.35520e6 | −0.301008 | ||||||||
\(903\) | 1.96841e6 | 0.0803333 | ||||||||
\(904\) | −9.44020e6 | −0.384202 | ||||||||
\(905\) | 1.69486e7 | 0.687880 | ||||||||
\(906\) | −5.15910e6 | −0.208811 | ||||||||
\(907\) | 3.97386e7 | 1.60396 | 0.801981 | − | 0.597349i | \(-0.203779\pi\) | ||||
0.801981 | + | 0.597349i | \(0.203779\pi\) | |||||||
\(908\) | 1.79485e7 | 0.722459 | ||||||||
\(909\) | −7.87173e6 | −0.315981 | ||||||||
\(910\) | 773660. | 0.0309704 | ||||||||
\(911\) | −8.60111e6 | −0.343367 | −0.171684 | − | 0.985152i | \(-0.554921\pi\) | ||||
−0.171684 | + | 0.985152i | \(0.554921\pi\) | |||||||
\(912\) | 1.90649e6 | 0.0759010 | ||||||||
\(913\) | 1.25163e7 | 0.496933 | ||||||||
\(914\) | 1.95558e7 | 0.774302 | ||||||||
\(915\) | 1.31093e7 | 0.517638 | ||||||||
\(916\) | 6.77708e6 | 0.266873 | ||||||||
\(917\) | −2.17379e6 | −0.0853678 | ||||||||
\(918\) | 3.82171e7 | 1.49676 | ||||||||
\(919\) | −2.53760e7 | −0.991140 | −0.495570 | − | 0.868568i | \(-0.665041\pi\) | ||||
−0.495570 | + | 0.868568i | \(0.665041\pi\) | |||||||
\(920\) | 4.82424e6 | 0.187914 | ||||||||
\(921\) | 3.42439e7 | 1.33025 | ||||||||
\(922\) | 8.64001e6 | 0.334724 | ||||||||
\(923\) | 1.96796e6 | 0.0760346 | ||||||||
\(924\) | 260471. | 0.0100364 | ||||||||
\(925\) | −4.37324e6 | −0.168054 | ||||||||
\(926\) | −1.97646e7 | −0.757462 | ||||||||
\(927\) | 5.26851e6 | 0.201367 | ||||||||
\(928\) | −5.08280e6 | −0.193746 | ||||||||
\(929\) | 1.42066e7 | 0.540073 | 0.270036 | − | 0.962850i | \(-0.412964\pi\) | ||||
0.270036 | + | 0.962850i | \(0.412964\pi\) | |||||||
\(930\) | −205859. | −0.00780481 | ||||||||
\(931\) | 6.01640e6 | 0.227490 | ||||||||
\(932\) | 5.57984e6 | 0.210417 | ||||||||
\(933\) | 4.14145e7 | 1.55757 | ||||||||
\(934\) | −1.99846e7 | −0.749598 | ||||||||
\(935\) | −6.56694e6 | −0.245660 | ||||||||
\(936\) | 8.04882e6 | 0.300291 | ||||||||
\(937\) | 5.58399e6 | 0.207776 | 0.103888 | − | 0.994589i | \(-0.466872\pi\) | ||||
0.103888 | + | 0.994589i | \(0.466872\pi\) | |||||||
\(938\) | 611435. | 0.0226905 | ||||||||
\(939\) | −2.37700e7 | −0.879763 | ||||||||
\(940\) | −1.65709e6 | −0.0611684 | ||||||||
\(941\) | 2.63319e7 | 0.969411 | 0.484706 | − | 0.874677i | \(-0.338927\pi\) | ||||
0.484706 | + | 0.874677i | \(0.338927\pi\) | |||||||
\(942\) | 1.66647e7 | 0.611887 | ||||||||
\(943\) | −1.40191e7 | −0.513383 | ||||||||
\(944\) | −8.00334e6 | −0.292308 | ||||||||
\(945\) | −1.22149e6 | −0.0444950 | ||||||||
\(946\) | 6.48007e6 | 0.235425 | ||||||||
\(947\) | 5.13035e7 | 1.85897 | 0.929484 | − | 0.368863i | \(-0.120253\pi\) | ||||
0.929484 | + | 0.368863i | \(0.120253\pi\) | |||||||
\(948\) | −4.15538e6 | −0.150172 | ||||||||
\(949\) | −1.69246e6 | −0.0610031 | ||||||||
\(950\) | 965578. | 0.0347119 | ||||||||
\(951\) | 9.45334e6 | 0.338949 | ||||||||
\(952\) | 5.04133e6 | 0.180282 | ||||||||
\(953\) | 1.28686e7 | 0.458986 | 0.229493 | − | 0.973310i | \(-0.426293\pi\) | ||||
0.229493 | + | 0.973310i | \(0.426293\pi\) | |||||||
\(954\) | 5.74004e6 | 0.204195 | ||||||||
\(955\) | 1.89176e7 | 0.671208 | ||||||||
\(956\) | 1.31292e7 | 0.464616 | ||||||||
\(957\) | −1.79013e6 | −0.0631838 | ||||||||
\(958\) | −1.48241e7 | −0.521861 | ||||||||
\(959\) | −3.38384e6 | −0.118813 | ||||||||
\(960\) | 1.06714e7 | 0.373717 | ||||||||
\(961\) | −2.86080e7 | −0.999263 | ||||||||
\(962\) | −1.82306e7 | −0.635132 | ||||||||
\(963\) | −5.51367e6 | −0.191591 | ||||||||
\(964\) | −1.92304e7 | −0.666493 | ||||||||
\(965\) | 5.52545e6 | 0.191007 | ||||||||
\(966\) | −664405. | −0.0229082 | ||||||||
\(967\) | −1.21851e6 | −0.0419047 | −0.0209524 | − | 0.999780i | \(-0.506670\pi\) | ||||
−0.0209524 | + | 0.999780i | \(0.506670\pi\) | |||||||
\(968\) | 2.86251e6 | 0.0981881 | ||||||||
\(969\) | −1.03785e7 | −0.355079 | ||||||||
\(970\) | −1.66646e7 | −0.568678 | ||||||||
\(971\) | −1.46249e7 | −0.497789 | −0.248895 | − | 0.968531i | \(-0.580067\pi\) | ||||
−0.248895 | + | 0.968531i | \(0.580067\pi\) | |||||||
\(972\) | −6.78473e6 | −0.230339 | ||||||||
\(973\) | 316487. | 0.0107170 | ||||||||
\(974\) | 2.89690e7 | 0.978443 | ||||||||
\(975\) | −5.03905e6 | −0.169761 | ||||||||
\(976\) | −1.57902e7 | −0.530594 | ||||||||
\(977\) | −3.17616e7 | −1.06455 | −0.532274 | − | 0.846572i | \(-0.678662\pi\) | ||||
−0.532274 | + | 0.846572i | \(0.678662\pi\) | |||||||
\(978\) | 1.22848e7 | 0.410695 | ||||||||
\(979\) | 7.40924e6 | 0.247068 | ||||||||
\(980\) | 5.70195e6 | 0.189652 | ||||||||
\(981\) | −3.78548e6 | −0.125588 | ||||||||
\(982\) | 790593. | 0.0261622 | ||||||||
\(983\) | 2.31472e7 | 0.764039 | 0.382019 | − | 0.924154i | \(-0.375229\pi\) | ||||
0.382019 | + | 0.924154i | \(0.375229\pi\) | |||||||
\(984\) | −3.67769e7 | −1.21084 | ||||||||
\(985\) | 1.20031e7 | 0.394187 | ||||||||
\(986\) | −1.03788e7 | −0.339982 | ||||||||
\(987\) | 761857. | 0.0248932 | ||||||||
\(988\) | −3.00774e6 | −0.0980274 | ||||||||
\(989\) | 1.23511e7 | 0.401528 | ||||||||
\(990\) | −875392. | −0.0283867 | ||||||||
\(991\) | −3.16204e7 | −1.02278 | −0.511392 | − | 0.859348i | \(-0.670870\pi\) | ||||
−0.511392 | + | 0.859348i | \(0.670870\pi\) | |||||||
\(992\) | −661048. | −0.0213282 | ||||||||
\(993\) | 3.92705e7 | 1.26384 | ||||||||
\(994\) | 164311. | 0.00527475 | ||||||||
\(995\) | 1.07534e6 | 0.0344340 | ||||||||
\(996\) | 1.87471e7 | 0.598804 | ||||||||
\(997\) | 4.01493e7 | 1.27921 | 0.639603 | − | 0.768706i | \(-0.279099\pi\) | ||||
0.639603 | + | 0.768706i | \(0.279099\pi\) | |||||||
\(998\) | 2.55291e7 | 0.811351 | ||||||||
\(999\) | 2.87834e7 | 0.912491 |
(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 | 1045.6.a.f.1.13 | ✓ | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.6.a.f.1.13 | ✓ | 38 | 1.1 | even | 1 | trivial |