Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [29,6,Mod(1,29)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(29, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("29.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.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: | \(4.65113077458\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.3257317.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 34x^{2} - 27x + 10 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.275208\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 29.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.91663 | 1.04592 | 0.522961 | − | 0.852357i | \(-0.324827\pi\) | ||||
0.522961 | + | 0.852357i | \(0.324827\pi\) | |||||||
\(3\) | −18.2828 | −1.17284 | −0.586422 | − | 0.810005i | \(-0.699464\pi\) | ||||
−0.586422 | + | 0.810005i | \(0.699464\pi\) | |||||||
\(4\) | 3.00648 | 0.0939526 | ||||||||
\(5\) | −97.7313 | −1.74827 | −0.874135 | − | 0.485683i | \(-0.838571\pi\) | ||||
−0.874135 | + | 0.485683i | \(0.838571\pi\) | |||||||
\(6\) | −108.173 | −1.22670 | ||||||||
\(7\) | 139.558 | 1.07649 | 0.538246 | − | 0.842788i | \(-0.319087\pi\) | ||||
0.538246 | + | 0.842788i | \(0.319087\pi\) | |||||||
\(8\) | −171.544 | −0.947655 | ||||||||
\(9\) | 91.2623 | 0.375565 | ||||||||
\(10\) | −578.240 | −1.82855 | ||||||||
\(11\) | 533.092 | 1.32838 | 0.664188 | − | 0.747566i | \(-0.268778\pi\) | ||||
0.664188 | + | 0.747566i | \(0.268778\pi\) | |||||||
\(12\) | −54.9671 | −0.110192 | ||||||||
\(13\) | −675.965 | −1.10934 | −0.554672 | − | 0.832069i | \(-0.687156\pi\) | ||||
−0.554672 | + | 0.832069i | \(0.687156\pi\) | |||||||
\(14\) | 825.715 | 1.12593 | ||||||||
\(15\) | 1786.81 | 2.05045 | ||||||||
\(16\) | −1111.17 | −1.08513 | ||||||||
\(17\) | −268.994 | −0.225746 | −0.112873 | − | 0.993609i | \(-0.536005\pi\) | ||||
−0.112873 | + | 0.993609i | \(0.536005\pi\) | |||||||
\(18\) | 539.965 | 0.392812 | ||||||||
\(19\) | −2649.15 | −1.68354 | −0.841768 | − | 0.539840i | \(-0.818485\pi\) | ||||
−0.841768 | + | 0.539840i | \(0.818485\pi\) | |||||||
\(20\) | −293.828 | −0.164255 | ||||||||
\(21\) | −2551.52 | −1.26256 | ||||||||
\(22\) | 3154.11 | 1.38938 | ||||||||
\(23\) | 794.438 | 0.313141 | 0.156571 | − | 0.987667i | \(-0.449956\pi\) | ||||
0.156571 | + | 0.987667i | \(0.449956\pi\) | |||||||
\(24\) | 3136.31 | 1.11145 | ||||||||
\(25\) | 6426.40 | 2.05645 | ||||||||
\(26\) | −3999.43 | −1.16029 | ||||||||
\(27\) | 2774.20 | 0.732366 | ||||||||
\(28\) | 419.580 | 0.101139 | ||||||||
\(29\) | −841.000 | −0.185695 | ||||||||
\(30\) | 10571.9 | 2.14461 | ||||||||
\(31\) | −4231.04 | −0.790756 | −0.395378 | − | 0.918518i | \(-0.629386\pi\) | ||||
−0.395378 | + | 0.918518i | \(0.629386\pi\) | |||||||
\(32\) | −1084.97 | −0.187302 | ||||||||
\(33\) | −9746.44 | −1.55798 | ||||||||
\(34\) | −1591.54 | −0.236113 | ||||||||
\(35\) | −13639.2 | −1.88200 | ||||||||
\(36\) | 274.379 | 0.0352853 | ||||||||
\(37\) | −2689.54 | −0.322979 | −0.161489 | − | 0.986874i | \(-0.551630\pi\) | ||||
−0.161489 | + | 0.986874i | \(0.551630\pi\) | |||||||
\(38\) | −15674.0 | −1.76085 | ||||||||
\(39\) | 12358.6 | 1.30109 | ||||||||
\(40\) | 16765.2 | 1.65676 | ||||||||
\(41\) | 1395.36 | 0.129636 | 0.0648182 | − | 0.997897i | \(-0.479353\pi\) | ||||
0.0648182 | + | 0.997897i | \(0.479353\pi\) | |||||||
\(42\) | −15096.4 | −1.32054 | ||||||||
\(43\) | −23810.5 | −1.96380 | −0.981901 | − | 0.189395i | \(-0.939347\pi\) | ||||
−0.981901 | + | 0.189395i | \(0.939347\pi\) | |||||||
\(44\) | 1602.73 | 0.124804 | ||||||||
\(45\) | −8919.18 | −0.656589 | ||||||||
\(46\) | 4700.39 | 0.327521 | ||||||||
\(47\) | 11267.5 | 0.744016 | 0.372008 | − | 0.928229i | \(-0.378669\pi\) | ||||
0.372008 | + | 0.928229i | \(0.378669\pi\) | |||||||
\(48\) | 20315.3 | 1.27268 | ||||||||
\(49\) | 2669.53 | 0.158834 | ||||||||
\(50\) | 38022.6 | 2.15089 | ||||||||
\(51\) | 4917.98 | 0.264766 | ||||||||
\(52\) | −2032.28 | −0.104226 | ||||||||
\(53\) | −3396.67 | −0.166097 | −0.0830487 | − | 0.996545i | \(-0.526466\pi\) | ||||
−0.0830487 | + | 0.996545i | \(0.526466\pi\) | |||||||
\(54\) | 16413.9 | 0.765997 | ||||||||
\(55\) | −52099.8 | −2.32236 | ||||||||
\(56\) | −23940.4 | −1.02014 | ||||||||
\(57\) | 48433.9 | 1.97453 | ||||||||
\(58\) | −4975.88 | −0.194223 | ||||||||
\(59\) | −2785.38 | −0.104173 | −0.0520865 | − | 0.998643i | \(-0.516587\pi\) | ||||
−0.0520865 | + | 0.998643i | \(0.516587\pi\) | |||||||
\(60\) | 5372.00 | 0.192645 | ||||||||
\(61\) | 41551.7 | 1.42976 | 0.714881 | − | 0.699246i | \(-0.246481\pi\) | ||||
0.714881 | + | 0.699246i | \(0.246481\pi\) | |||||||
\(62\) | −25033.5 | −0.827069 | ||||||||
\(63\) | 12736.4 | 0.404292 | ||||||||
\(64\) | 29138.0 | 0.889222 | ||||||||
\(65\) | 66062.9 | 1.93943 | ||||||||
\(66\) | −57666.1 | −1.62952 | ||||||||
\(67\) | 8574.14 | 0.233348 | 0.116674 | − | 0.993170i | \(-0.462777\pi\) | ||||
0.116674 | + | 0.993170i | \(0.462777\pi\) | |||||||
\(68\) | −808.728 | −0.0212095 | ||||||||
\(69\) | −14524.6 | −0.367266 | ||||||||
\(70\) | −80698.2 | −1.96842 | ||||||||
\(71\) | −6995.03 | −0.164681 | −0.0823405 | − | 0.996604i | \(-0.526240\pi\) | ||||
−0.0823405 | + | 0.996604i | \(0.526240\pi\) | |||||||
\(72\) | −15655.5 | −0.355906 | ||||||||
\(73\) | −4994.73 | −0.109699 | −0.0548497 | − | 0.998495i | \(-0.517468\pi\) | ||||
−0.0548497 | + | 0.998495i | \(0.517468\pi\) | |||||||
\(74\) | −15913.0 | −0.337811 | ||||||||
\(75\) | −117493. | −2.41190 | ||||||||
\(76\) | −7964.62 | −0.158173 | ||||||||
\(77\) | 74397.5 | 1.42998 | ||||||||
\(78\) | 73121.0 | 1.36084 | ||||||||
\(79\) | −23856.6 | −0.430071 | −0.215036 | − | 0.976606i | \(-0.568987\pi\) | ||||
−0.215036 | + | 0.976606i | \(0.568987\pi\) | |||||||
\(80\) | 108596. | 1.89709 | ||||||||
\(81\) | −72896.9 | −1.23452 | ||||||||
\(82\) | 8255.84 | 0.135590 | ||||||||
\(83\) | 43076.9 | 0.686356 | 0.343178 | − | 0.939270i | \(-0.388497\pi\) | ||||
0.343178 | + | 0.939270i | \(0.388497\pi\) | |||||||
\(84\) | −7671.11 | −0.118621 | ||||||||
\(85\) | 26289.2 | 0.394666 | ||||||||
\(86\) | −140878. | −2.05398 | ||||||||
\(87\) | 15375.9 | 0.217792 | ||||||||
\(88\) | −91448.7 | −1.25884 | ||||||||
\(89\) | 13806.4 | 0.184759 | 0.0923793 | − | 0.995724i | \(-0.470553\pi\) | ||||
0.0923793 | + | 0.995724i | \(0.470553\pi\) | |||||||
\(90\) | −52771.5 | −0.686741 | ||||||||
\(91\) | −94336.6 | −1.19420 | ||||||||
\(92\) | 2388.47 | 0.0294205 | ||||||||
\(93\) | 77355.4 | 0.927435 | ||||||||
\(94\) | 66665.5 | 0.778183 | ||||||||
\(95\) | 258905. | 2.94327 | ||||||||
\(96\) | 19836.3 | 0.219676 | ||||||||
\(97\) | −176400. | −1.90357 | −0.951786 | − | 0.306762i | \(-0.900755\pi\) | ||||
−0.951786 | + | 0.306762i | \(0.900755\pi\) | |||||||
\(98\) | 15794.6 | 0.166128 | ||||||||
\(99\) | 48651.2 | 0.498891 | ||||||||
\(100\) | 19320.9 | 0.193209 | ||||||||
\(101\) | −112043. | −1.09290 | −0.546452 | − | 0.837490i | \(-0.684022\pi\) | ||||
−0.546452 | + | 0.837490i | \(0.684022\pi\) | |||||||
\(102\) | 29097.9 | 0.276924 | ||||||||
\(103\) | 38255.6 | 0.355305 | 0.177653 | − | 0.984093i | \(-0.443150\pi\) | ||||
0.177653 | + | 0.984093i | \(0.443150\pi\) | |||||||
\(104\) | 115958. | 1.05127 | ||||||||
\(105\) | 249364. | 2.20729 | ||||||||
\(106\) | −20096.8 | −0.173725 | ||||||||
\(107\) | −19410.6 | −0.163900 | −0.0819499 | − | 0.996636i | \(-0.526115\pi\) | ||||
−0.0819499 | + | 0.996636i | \(0.526115\pi\) | |||||||
\(108\) | 8340.58 | 0.0688077 | ||||||||
\(109\) | −51029.2 | −0.411389 | −0.205694 | − | 0.978616i | \(-0.565945\pi\) | ||||
−0.205694 | + | 0.978616i | \(0.565945\pi\) | |||||||
\(110\) | −308255. | −2.42901 | ||||||||
\(111\) | 49172.5 | 0.378804 | ||||||||
\(112\) | −155073. | −1.16813 | ||||||||
\(113\) | 45687.3 | 0.336588 | 0.168294 | − | 0.985737i | \(-0.446174\pi\) | ||||
0.168294 | + | 0.985737i | \(0.446174\pi\) | |||||||
\(114\) | 286566. | 2.06520 | ||||||||
\(115\) | −77641.5 | −0.547456 | ||||||||
\(116\) | −2528.45 | −0.0174466 | ||||||||
\(117\) | −61690.1 | −0.416630 | ||||||||
\(118\) | −16480.1 | −0.108957 | ||||||||
\(119\) | −37540.4 | −0.243014 | ||||||||
\(120\) | −306515. | −1.94312 | ||||||||
\(121\) | 123136. | 0.764581 | ||||||||
\(122\) | 245846. | 1.49542 | ||||||||
\(123\) | −25511.2 | −0.152043 | ||||||||
\(124\) | −12720.6 | −0.0742937 | ||||||||
\(125\) | −322650. | −1.84696 | ||||||||
\(126\) | 75356.6 | 0.422858 | ||||||||
\(127\) | 267210. | 1.47009 | 0.735044 | − | 0.678019i | \(-0.237161\pi\) | ||||
0.735044 | + | 0.678019i | \(0.237161\pi\) | |||||||
\(128\) | 207118. | 1.11736 | ||||||||
\(129\) | 435324. | 2.30323 | ||||||||
\(130\) | 390870. | 2.02849 | ||||||||
\(131\) | −165523. | −0.842713 | −0.421356 | − | 0.906895i | \(-0.638446\pi\) | ||||
−0.421356 | + | 0.906895i | \(0.638446\pi\) | |||||||
\(132\) | −29302.5 | −0.146376 | ||||||||
\(133\) | −369711. | −1.81231 | ||||||||
\(134\) | 50730.0 | 0.244063 | ||||||||
\(135\) | −271126. | −1.28037 | ||||||||
\(136\) | 46144.3 | 0.213930 | ||||||||
\(137\) | 91000.4 | 0.414230 | 0.207115 | − | 0.978317i | \(-0.433593\pi\) | ||||
0.207115 | + | 0.978317i | \(0.433593\pi\) | |||||||
\(138\) | −85936.6 | −0.384132 | ||||||||
\(139\) | −400431. | −1.75788 | −0.878942 | − | 0.476928i | \(-0.841750\pi\) | ||||
−0.878942 | + | 0.476928i | \(0.841750\pi\) | |||||||
\(140\) | −41006.1 | −0.176819 | ||||||||
\(141\) | −206002. | −0.872616 | ||||||||
\(142\) | −41387.0 | −0.172244 | ||||||||
\(143\) | −360352. | −1.47362 | ||||||||
\(144\) | −101408. | −0.407535 | ||||||||
\(145\) | 82192.0 | 0.324646 | ||||||||
\(146\) | −29551.9 | −0.114737 | ||||||||
\(147\) | −48806.6 | −0.186288 | ||||||||
\(148\) | −8086.07 | −0.0303447 | ||||||||
\(149\) | −18312.8 | −0.0675756 | −0.0337878 | − | 0.999429i | \(-0.510757\pi\) | ||||
−0.0337878 | + | 0.999429i | \(0.510757\pi\) | |||||||
\(150\) | −695162. | −2.52265 | ||||||||
\(151\) | −17899.8 | −0.0638859 | −0.0319430 | − | 0.999490i | \(-0.510169\pi\) | ||||
−0.0319430 | + | 0.999490i | \(0.510169\pi\) | |||||||
\(152\) | 454445. | 1.59541 | ||||||||
\(153\) | −24549.0 | −0.0847824 | ||||||||
\(154\) | 440182. | 1.49565 | ||||||||
\(155\) | 413505. | 1.38246 | ||||||||
\(156\) | 37155.8 | 0.122241 | ||||||||
\(157\) | −413598. | −1.33915 | −0.669576 | − | 0.742744i | \(-0.733524\pi\) | ||||
−0.669576 | + | 0.742744i | \(0.733524\pi\) | |||||||
\(158\) | −141151. | −0.449821 | ||||||||
\(159\) | 62100.7 | 0.194807 | ||||||||
\(160\) | 106035. | 0.327454 | ||||||||
\(161\) | 110870. | 0.337094 | ||||||||
\(162\) | −431304. | −1.29121 | ||||||||
\(163\) | 178276. | 0.525562 | 0.262781 | − | 0.964856i | \(-0.415360\pi\) | ||||
0.262781 | + | 0.964856i | \(0.415360\pi\) | |||||||
\(164\) | 4195.13 | 0.0121797 | ||||||||
\(165\) | 952532. | 2.72377 | ||||||||
\(166\) | 254870. | 0.717875 | ||||||||
\(167\) | −452143. | −1.25454 | −0.627269 | − | 0.778802i | \(-0.715828\pi\) | ||||
−0.627269 | + | 0.778802i | \(0.715828\pi\) | |||||||
\(168\) | 437698. | 1.19647 | ||||||||
\(169\) | 85635.9 | 0.230642 | ||||||||
\(170\) | 155543. | 0.412790 | ||||||||
\(171\) | −241767. | −0.632277 | ||||||||
\(172\) | −71586.0 | −0.184504 | ||||||||
\(173\) | 754374. | 1.91634 | 0.958168 | − | 0.286206i | \(-0.0923943\pi\) | ||||
0.958168 | + | 0.286206i | \(0.0923943\pi\) | |||||||
\(174\) | 90973.3 | 0.227793 | ||||||||
\(175\) | 896858. | 2.21375 | ||||||||
\(176\) | −592356. | −1.44145 | ||||||||
\(177\) | 50924.7 | 0.122179 | ||||||||
\(178\) | 81687.2 | 0.193243 | ||||||||
\(179\) | −352813. | −0.823024 | −0.411512 | − | 0.911404i | \(-0.634999\pi\) | ||||
−0.411512 | + | 0.911404i | \(0.634999\pi\) | |||||||
\(180\) | −26815.4 | −0.0616883 | ||||||||
\(181\) | 227087. | 0.515224 | 0.257612 | − | 0.966248i | \(-0.417064\pi\) | ||||
0.257612 | + | 0.966248i | \(0.417064\pi\) | |||||||
\(182\) | −558154. | −1.24904 | ||||||||
\(183\) | −759683. | −1.67689 | ||||||||
\(184\) | −136281. | −0.296750 | ||||||||
\(185\) | 262852. | 0.564654 | ||||||||
\(186\) | 457683. | 0.970024 | ||||||||
\(187\) | −143399. | −0.299876 | ||||||||
\(188\) | 33875.5 | 0.0699023 | ||||||||
\(189\) | 387162. | 0.788385 | ||||||||
\(190\) | 1.53184e6 | 3.07844 | ||||||||
\(191\) | 183415. | 0.363790 | 0.181895 | − | 0.983318i | \(-0.441777\pi\) | ||||
0.181895 | + | 0.983318i | \(0.441777\pi\) | |||||||
\(192\) | −532726. | −1.04292 | ||||||||
\(193\) | 997005. | 1.92665 | 0.963327 | − | 0.268329i | \(-0.0864714\pi\) | ||||
0.963327 | + | 0.268329i | \(0.0864714\pi\) | |||||||
\(194\) | −1.04369e6 | −1.99099 | ||||||||
\(195\) | −1.20782e6 | −2.27465 | ||||||||
\(196\) | 8025.90 | 0.0149229 | ||||||||
\(197\) | −861288. | −1.58119 | −0.790593 | − | 0.612342i | \(-0.790227\pi\) | ||||
−0.790593 | + | 0.612342i | \(0.790227\pi\) | |||||||
\(198\) | 287851. | 0.521801 | ||||||||
\(199\) | −837743. | −1.49961 | −0.749805 | − | 0.661659i | \(-0.769853\pi\) | ||||
−0.749805 | + | 0.661659i | \(0.769853\pi\) | |||||||
\(200\) | −1.10241e6 | −1.94880 | ||||||||
\(201\) | −156760. | −0.273681 | ||||||||
\(202\) | −662918. | −1.14309 | ||||||||
\(203\) | −117369. | −0.199899 | ||||||||
\(204\) | 14785.8 | 0.0248754 | ||||||||
\(205\) | −136371. | −0.226640 | ||||||||
\(206\) | 226344. | 0.371621 | ||||||||
\(207\) | 72502.2 | 0.117605 | ||||||||
\(208\) | 751111. | 1.20378 | ||||||||
\(209\) | −1.41224e6 | −2.23637 | ||||||||
\(210\) | 1.47539e6 | 2.30866 | ||||||||
\(211\) | −637594. | −0.985912 | −0.492956 | − | 0.870054i | \(-0.664084\pi\) | ||||
−0.492956 | + | 0.870054i | \(0.664084\pi\) | |||||||
\(212\) | −10212.0 | −0.0156053 | ||||||||
\(213\) | 127889. | 0.193145 | ||||||||
\(214\) | −114845. | −0.171426 | ||||||||
\(215\) | 2.32703e6 | 3.43326 | ||||||||
\(216\) | −475896. | −0.694030 | ||||||||
\(217\) | −590477. | −0.851243 | ||||||||
\(218\) | −301921. | −0.430281 | ||||||||
\(219\) | 91317.8 | 0.128660 | ||||||||
\(220\) | −156637. | −0.218192 | ||||||||
\(221\) | 181831. | 0.250430 | ||||||||
\(222\) | 290935. | 0.396199 | ||||||||
\(223\) | 45526.9 | 0.0613064 | 0.0306532 | − | 0.999530i | \(-0.490241\pi\) | ||||
0.0306532 | + | 0.999530i | \(0.490241\pi\) | |||||||
\(224\) | −151416. | −0.201629 | ||||||||
\(225\) | 586488. | 0.772330 | ||||||||
\(226\) | 270315. | 0.352045 | ||||||||
\(227\) | 1.33313e6 | 1.71715 | 0.858575 | − | 0.512688i | \(-0.171350\pi\) | ||||
0.858575 | + | 0.512688i | \(0.171350\pi\) | |||||||
\(228\) | 145616. | 0.185512 | ||||||||
\(229\) | 830883. | 1.04701 | 0.523506 | − | 0.852022i | \(-0.324624\pi\) | ||||
0.523506 | + | 0.852022i | \(0.324624\pi\) | |||||||
\(230\) | −459376. | −0.572596 | ||||||||
\(231\) | −1.36020e6 | −1.67715 | ||||||||
\(232\) | 144268. | 0.175975 | ||||||||
\(233\) | 767627. | 0.926319 | 0.463159 | − | 0.886275i | \(-0.346716\pi\) | ||||
0.463159 | + | 0.886275i | \(0.346716\pi\) | |||||||
\(234\) | −364997. | −0.435763 | ||||||||
\(235\) | −1.10119e6 | −1.30074 | ||||||||
\(236\) | −8374.22 | −0.00978733 | ||||||||
\(237\) | 436166. | 0.504407 | ||||||||
\(238\) | −222113. | −0.254174 | ||||||||
\(239\) | −1.22858e6 | −1.39126 | −0.695631 | − | 0.718399i | \(-0.744875\pi\) | ||||
−0.695631 | + | 0.718399i | \(0.744875\pi\) | |||||||
\(240\) | −1.98544e6 | −2.22500 | ||||||||
\(241\) | 304030. | 0.337190 | 0.168595 | − | 0.985685i | \(-0.446077\pi\) | ||||
0.168595 | + | 0.985685i | \(0.446077\pi\) | |||||||
\(242\) | 728553. | 0.799692 | ||||||||
\(243\) | 658633. | 0.715530 | ||||||||
\(244\) | 124924. | 0.134330 | ||||||||
\(245\) | −260897. | −0.277685 | ||||||||
\(246\) | −150940. | −0.159026 | ||||||||
\(247\) | 1.79073e6 | 1.86762 | ||||||||
\(248\) | 725809. | 0.749364 | ||||||||
\(249\) | −787569. | −0.804989 | ||||||||
\(250\) | −1.90900e6 | −1.93177 | ||||||||
\(251\) | 850953. | 0.852553 | 0.426276 | − | 0.904593i | \(-0.359825\pi\) | ||||
0.426276 | + | 0.904593i | \(0.359825\pi\) | |||||||
\(252\) | 38291.8 | 0.0379843 | ||||||||
\(253\) | 423509. | 0.415969 | ||||||||
\(254\) | 1.58098e6 | 1.53760 | ||||||||
\(255\) | −480641. | −0.462882 | ||||||||
\(256\) | 293022. | 0.279448 | ||||||||
\(257\) | 28252.8 | 0.0266826 | 0.0133413 | − | 0.999911i | \(-0.495753\pi\) | ||||
0.0133413 | + | 0.999911i | \(0.495753\pi\) | |||||||
\(258\) | 2.57565e6 | 2.40900 | ||||||||
\(259\) | −375348. | −0.347684 | ||||||||
\(260\) | 198617. | 0.182215 | ||||||||
\(261\) | −76751.6 | −0.0697406 | ||||||||
\(262\) | −979337. | −0.881412 | ||||||||
\(263\) | 393978. | 0.351223 | 0.175611 | − | 0.984460i | \(-0.443810\pi\) | ||||
0.175611 | + | 0.984460i | \(0.443810\pi\) | |||||||
\(264\) | 1.67194e6 | 1.47643 | ||||||||
\(265\) | 331960. | 0.290383 | ||||||||
\(266\) | −2.18744e6 | −1.89554 | ||||||||
\(267\) | −252420. | −0.216693 | ||||||||
\(268\) | 25778.0 | 0.0219236 | ||||||||
\(269\) | 453727. | 0.382309 | 0.191154 | − | 0.981560i | \(-0.438777\pi\) | ||||
0.191154 | + | 0.981560i | \(0.438777\pi\) | |||||||
\(270\) | −1.60415e6 | −1.33917 | ||||||||
\(271\) | −1.54312e6 | −1.27637 | −0.638186 | − | 0.769882i | \(-0.720315\pi\) | ||||
−0.638186 | + | 0.769882i | \(0.720315\pi\) | |||||||
\(272\) | 298898. | 0.244963 | ||||||||
\(273\) | 1.72474e6 | 1.40061 | ||||||||
\(274\) | 538416. | 0.433253 | ||||||||
\(275\) | 3.42587e6 | 2.73174 | ||||||||
\(276\) | −43667.9 | −0.0345056 | ||||||||
\(277\) | −1.13023e6 | −0.885050 | −0.442525 | − | 0.896756i | \(-0.645917\pi\) | ||||
−0.442525 | + | 0.896756i | \(0.645917\pi\) | |||||||
\(278\) | −2.36920e6 | −1.83861 | ||||||||
\(279\) | −386134. | −0.296980 | ||||||||
\(280\) | 2.33972e6 | 1.78348 | ||||||||
\(281\) | −1.17984e6 | −0.891371 | −0.445685 | − | 0.895190i | \(-0.647040\pi\) | ||||
−0.445685 | + | 0.895190i | \(0.647040\pi\) | |||||||
\(282\) | −1.21884e6 | −0.912688 | ||||||||
\(283\) | 345340. | 0.256319 | 0.128160 | − | 0.991754i | \(-0.459093\pi\) | ||||
0.128160 | + | 0.991754i | \(0.459093\pi\) | |||||||
\(284\) | −21030.5 | −0.0154722 | ||||||||
\(285\) | −4.73351e6 | −3.45200 | ||||||||
\(286\) | −2.13207e6 | −1.54130 | ||||||||
\(287\) | 194734. | 0.139553 | ||||||||
\(288\) | −99016.6 | −0.0703440 | ||||||||
\(289\) | −1.34750e6 | −0.949039 | ||||||||
\(290\) | 486300. | 0.339554 | ||||||||
\(291\) | 3.22509e6 | 2.23260 | ||||||||
\(292\) | −15016.6 | −0.0103066 | ||||||||
\(293\) | 2.40825e6 | 1.63883 | 0.819414 | − | 0.573202i | \(-0.194299\pi\) | ||||
0.819414 | + | 0.573202i | \(0.194299\pi\) | |||||||
\(294\) | −288770. | −0.194843 | ||||||||
\(295\) | 272219. | 0.182123 | ||||||||
\(296\) | 461374. | 0.306072 | ||||||||
\(297\) | 1.47890e6 | 0.972856 | ||||||||
\(298\) | −108350. | −0.0706788 | ||||||||
\(299\) | −537013. | −0.347381 | ||||||||
\(300\) | −353241. | −0.226604 | ||||||||
\(301\) | −3.32296e6 | −2.11402 | ||||||||
\(302\) | −105906. | −0.0668197 | ||||||||
\(303\) | 2.04847e6 | 1.28181 | ||||||||
\(304\) | 2.94365e6 | 1.82685 | ||||||||
\(305\) | −4.06090e6 | −2.49961 | ||||||||
\(306\) | −145248. | −0.0886758 | ||||||||
\(307\) | 595416. | 0.360558 | 0.180279 | − | 0.983616i | \(-0.442300\pi\) | ||||
0.180279 | + | 0.983616i | \(0.442300\pi\) | |||||||
\(308\) | 223675. | 0.134351 | ||||||||
\(309\) | −699420. | −0.416718 | ||||||||
\(310\) | 2.44655e6 | 1.44594 | ||||||||
\(311\) | 999900. | 0.586213 | 0.293107 | − | 0.956080i | \(-0.405311\pi\) | ||||
0.293107 | + | 0.956080i | \(0.405311\pi\) | |||||||
\(312\) | −2.12004e6 | −1.23298 | ||||||||
\(313\) | −365270. | −0.210743 | −0.105371 | − | 0.994433i | \(-0.533603\pi\) | ||||
−0.105371 | + | 0.994433i | \(0.533603\pi\) | |||||||
\(314\) | −2.44711e6 | −1.40065 | ||||||||
\(315\) | −1.24475e6 | −0.706813 | ||||||||
\(316\) | −71724.5 | −0.0404064 | ||||||||
\(317\) | 1.60635e6 | 0.897823 | 0.448912 | − | 0.893576i | \(-0.351812\pi\) | ||||
0.448912 | + | 0.893576i | \(0.351812\pi\) | |||||||
\(318\) | 367427. | 0.203752 | ||||||||
\(319\) | −448331. | −0.246673 | ||||||||
\(320\) | −2.84770e6 | −1.55460 | ||||||||
\(321\) | 354880. | 0.192229 | ||||||||
\(322\) | 655979. | 0.352574 | ||||||||
\(323\) | 712606. | 0.380052 | ||||||||
\(324\) | −219164. | −0.115986 | ||||||||
\(325\) | −4.34403e6 | −2.28131 | ||||||||
\(326\) | 1.05479e6 | 0.549697 | ||||||||
\(327\) | 932959. | 0.482495 | ||||||||
\(328\) | −239366. | −0.122851 | ||||||||
\(329\) | 1.57247e6 | 0.800928 | ||||||||
\(330\) | 5.63578e6 | 2.84885 | ||||||||
\(331\) | −535124. | −0.268463 | −0.134232 | − | 0.990950i | \(-0.542857\pi\) | ||||
−0.134232 | + | 0.990950i | \(0.542857\pi\) | |||||||
\(332\) | 129510. | 0.0644850 | ||||||||
\(333\) | −245454. | −0.121299 | ||||||||
\(334\) | −2.67516e6 | −1.31215 | ||||||||
\(335\) | −837961. | −0.407955 | ||||||||
\(336\) | 2.83517e6 | 1.37003 | ||||||||
\(337\) | 1.93303e6 | 0.927178 | 0.463589 | − | 0.886050i | \(-0.346561\pi\) | ||||
0.463589 | + | 0.886050i | \(0.346561\pi\) | |||||||
\(338\) | 506676. | 0.241234 | ||||||||
\(339\) | −835293. | −0.394766 | ||||||||
\(340\) | 79038.0 | 0.0370799 | ||||||||
\(341\) | −2.25553e6 | −1.05042 | ||||||||
\(342\) | −1.43045e6 | −0.661312 | ||||||||
\(343\) | −1.97300e6 | −0.905508 | ||||||||
\(344\) | 4.08455e6 | 1.86101 | ||||||||
\(345\) | 1.41951e6 | 0.642081 | ||||||||
\(346\) | 4.46335e6 | 2.00434 | ||||||||
\(347\) | −2.83701e6 | −1.26485 | −0.632423 | − | 0.774623i | \(-0.717940\pi\) | ||||
−0.632423 | + | 0.774623i | \(0.717940\pi\) | |||||||
\(348\) | 46227.3 | 0.0204621 | ||||||||
\(349\) | 1.11395e6 | 0.489555 | 0.244778 | − | 0.969579i | \(-0.421285\pi\) | ||||
0.244778 | + | 0.969579i | \(0.421285\pi\) | |||||||
\(350\) | 5.30638e6 | 2.31541 | ||||||||
\(351\) | −1.87526e6 | −0.812445 | ||||||||
\(352\) | −578388. | −0.248807 | ||||||||
\(353\) | −3.49053e6 | −1.49092 | −0.745461 | − | 0.666549i | \(-0.767771\pi\) | ||||
−0.745461 | + | 0.666549i | \(0.767771\pi\) | |||||||
\(354\) | 301303. | 0.127789 | ||||||||
\(355\) | 683633. | 0.287907 | ||||||||
\(356\) | 41508.7 | 0.0173586 | ||||||||
\(357\) | 686345. | 0.285018 | ||||||||
\(358\) | −2.08746e6 | −0.860819 | ||||||||
\(359\) | 469676. | 0.192337 | 0.0961684 | − | 0.995365i | \(-0.469341\pi\) | ||||
0.0961684 | + | 0.995365i | \(0.469341\pi\) | |||||||
\(360\) | 1.53003e6 | 0.622220 | ||||||||
\(361\) | 4.54189e6 | 1.83429 | ||||||||
\(362\) | 1.34359e6 | 0.538884 | ||||||||
\(363\) | −2.25128e6 | −0.896735 | ||||||||
\(364\) | −283621. | −0.112198 | ||||||||
\(365\) | 488141. | 0.191784 | ||||||||
\(366\) | −4.49476e6 | −1.75390 | ||||||||
\(367\) | 2.70229e6 | 1.04729 | 0.523645 | − | 0.851936i | \(-0.324572\pi\) | ||||
0.523645 | + | 0.851936i | \(0.324572\pi\) | |||||||
\(368\) | −882755. | −0.339798 | ||||||||
\(369\) | 127344. | 0.0486869 | ||||||||
\(370\) | 1.55520e6 | 0.590584 | ||||||||
\(371\) | −474033. | −0.178803 | ||||||||
\(372\) | 232568. | 0.0871349 | ||||||||
\(373\) | 2.77666e6 | 1.03336 | 0.516678 | − | 0.856180i | \(-0.327168\pi\) | ||||
0.516678 | + | 0.856180i | \(0.327168\pi\) | |||||||
\(374\) | −848438. | −0.313647 | ||||||||
\(375\) | 5.89897e6 | 2.16620 | ||||||||
\(376\) | −1.93287e6 | −0.705071 | ||||||||
\(377\) | 568487. | 0.206000 | ||||||||
\(378\) | 2.29070e6 | 0.824590 | ||||||||
\(379\) | −4.41837e6 | −1.58002 | −0.790012 | − | 0.613091i | \(-0.789926\pi\) | ||||
−0.790012 | + | 0.613091i | \(0.789926\pi\) | |||||||
\(380\) | 778393. | 0.276528 | ||||||||
\(381\) | −4.88536e6 | −1.72419 | ||||||||
\(382\) | 1.08520e6 | 0.380496 | ||||||||
\(383\) | 1.37796e6 | 0.479999 | 0.239999 | − | 0.970773i | \(-0.422853\pi\) | ||||
0.239999 | + | 0.970773i | \(0.422853\pi\) | |||||||
\(384\) | −3.78670e6 | −1.31049 | ||||||||
\(385\) | −7.27096e6 | −2.50000 | ||||||||
\(386\) | 5.89891e6 | 2.01513 | ||||||||
\(387\) | −2.17300e6 | −0.737535 | ||||||||
\(388\) | −530344. | −0.178846 | ||||||||
\(389\) | 649334. | 0.217568 | 0.108784 | − | 0.994065i | \(-0.465304\pi\) | ||||
0.108784 | + | 0.994065i | \(0.465304\pi\) | |||||||
\(390\) | −7.14621e6 | −2.37911 | ||||||||
\(391\) | −213699. | −0.0706906 | ||||||||
\(392\) | −457941. | −0.150520 | ||||||||
\(393\) | 3.02623e6 | 0.988371 | ||||||||
\(394\) | −5.09592e6 | −1.65380 | ||||||||
\(395\) | 2.33154e6 | 0.751881 | ||||||||
\(396\) | 146269. | 0.0468721 | ||||||||
\(397\) | −2.52909e6 | −0.805356 | −0.402678 | − | 0.915342i | \(-0.631921\pi\) | ||||
−0.402678 | + | 0.915342i | \(0.631921\pi\) | |||||||
\(398\) | −4.95661e6 | −1.56847 | ||||||||
\(399\) | 6.75936e6 | 2.12556 | ||||||||
\(400\) | −7.14082e6 | −2.23151 | ||||||||
\(401\) | −3.64231e6 | −1.13114 | −0.565569 | − | 0.824701i | \(-0.691344\pi\) | ||||
−0.565569 | + | 0.824701i | \(0.691344\pi\) | |||||||
\(402\) | −927488. | −0.286248 | ||||||||
\(403\) | 2.86003e6 | 0.877220 | ||||||||
\(404\) | −336856. | −0.102681 | ||||||||
\(405\) | 7.12431e6 | 2.15827 | ||||||||
\(406\) | −694426. | −0.209079 | ||||||||
\(407\) | −1.43377e6 | −0.429037 | ||||||||
\(408\) | −843650. | −0.250906 | ||||||||
\(409\) | 2.68522e6 | 0.793729 | 0.396865 | − | 0.917877i | \(-0.370098\pi\) | ||||
0.396865 | + | 0.917877i | \(0.370098\pi\) | |||||||
\(410\) | −806854. | −0.237047 | ||||||||
\(411\) | −1.66375e6 | −0.485828 | ||||||||
\(412\) | 115015. | 0.0333819 | ||||||||
\(413\) | −388724. | −0.112141 | ||||||||
\(414\) | 428969. | 0.123006 | ||||||||
\(415\) | −4.20996e6 | −1.19994 | ||||||||
\(416\) | 733401. | 0.207782 | ||||||||
\(417\) | 7.32101e6 | 2.06173 | ||||||||
\(418\) | −8.35570e6 | −2.33906 | ||||||||
\(419\) | −4.33500e6 | −1.20630 | −0.603148 | − | 0.797629i | \(-0.706087\pi\) | ||||
−0.603148 | + | 0.797629i | \(0.706087\pi\) | |||||||
\(420\) | 749708. | 0.207381 | ||||||||
\(421\) | 3.38962e6 | 0.932063 | 0.466032 | − | 0.884768i | \(-0.345683\pi\) | ||||
0.466032 | + | 0.884768i | \(0.345683\pi\) | |||||||
\(422\) | −3.77241e6 | −1.03119 | ||||||||
\(423\) | 1.02830e6 | 0.279426 | ||||||||
\(424\) | 582677. | 0.157403 | ||||||||
\(425\) | −1.72867e6 | −0.464236 | ||||||||
\(426\) | 756672. | 0.202015 | ||||||||
\(427\) | 5.79888e6 | 1.53913 | ||||||||
\(428\) | −58357.6 | −0.0153988 | ||||||||
\(429\) | 6.58826e6 | 1.72833 | ||||||||
\(430\) | 1.37682e7 | 3.59092 | ||||||||
\(431\) | 290831. | 0.0754132 | 0.0377066 | − | 0.999289i | \(-0.487995\pi\) | ||||
0.0377066 | + | 0.999289i | \(0.487995\pi\) | |||||||
\(432\) | −3.08260e6 | −0.794709 | ||||||||
\(433\) | −2.64162e6 | −0.677097 | −0.338549 | − | 0.940949i | \(-0.609936\pi\) | ||||
−0.338549 | + | 0.940949i | \(0.609936\pi\) | |||||||
\(434\) | −3.49363e6 | −0.890333 | ||||||||
\(435\) | −1.50270e6 | −0.380759 | ||||||||
\(436\) | −153418. | −0.0386511 | ||||||||
\(437\) | −2.10458e6 | −0.527185 | ||||||||
\(438\) | 540293. | 0.134569 | ||||||||
\(439\) | 5.65486e6 | 1.40043 | 0.700214 | − | 0.713933i | \(-0.253088\pi\) | ||||
0.700214 | + | 0.713933i | \(0.253088\pi\) | |||||||
\(440\) | 8.93740e6 | 2.20079 | ||||||||
\(441\) | 243627. | 0.0596526 | ||||||||
\(442\) | 1.07583e6 | 0.261931 | ||||||||
\(443\) | 1.31778e6 | 0.319031 | 0.159515 | − | 0.987195i | \(-0.449007\pi\) | ||||
0.159515 | + | 0.987195i | \(0.449007\pi\) | |||||||
\(444\) | 147836. | 0.0355896 | ||||||||
\(445\) | −1.34932e6 | −0.323008 | ||||||||
\(446\) | 269366. | 0.0641217 | ||||||||
\(447\) | 334810. | 0.0792556 | ||||||||
\(448\) | 4.06646e6 | 0.957241 | ||||||||
\(449\) | −6.50617e6 | −1.52303 | −0.761517 | − | 0.648145i | \(-0.775545\pi\) | ||||
−0.761517 | + | 0.648145i | \(0.775545\pi\) | |||||||
\(450\) | 3.47003e6 | 0.807797 | ||||||||
\(451\) | 743857. | 0.172206 | ||||||||
\(452\) | 137358. | 0.0316234 | ||||||||
\(453\) | 327259. | 0.0749283 | ||||||||
\(454\) | 7.88764e6 | 1.79601 | ||||||||
\(455\) | 9.21963e6 | 2.08778 | ||||||||
\(456\) | −8.30855e6 | −1.87117 | ||||||||
\(457\) | −3.50691e6 | −0.785477 | −0.392739 | − | 0.919650i | \(-0.628472\pi\) | ||||
−0.392739 | + | 0.919650i | \(0.628472\pi\) | |||||||
\(458\) | 4.91603e6 | 1.09509 | ||||||||
\(459\) | −746244. | −0.165329 | ||||||||
\(460\) | −233428. | −0.0514349 | ||||||||
\(461\) | −1.22247e6 | −0.267908 | −0.133954 | − | 0.990988i | \(-0.542767\pi\) | ||||
−0.133954 | + | 0.990988i | \(0.542767\pi\) | |||||||
\(462\) | −8.04778e6 | −1.75417 | ||||||||
\(463\) | 382178. | 0.0828540 | 0.0414270 | − | 0.999142i | \(-0.486810\pi\) | ||||
0.0414270 | + | 0.999142i | \(0.486810\pi\) | |||||||
\(464\) | 934493. | 0.201503 | ||||||||
\(465\) | −7.56004e6 | −1.62141 | ||||||||
\(466\) | 4.54176e6 | 0.968857 | ||||||||
\(467\) | −1.81409e6 | −0.384916 | −0.192458 | − | 0.981305i | \(-0.561646\pi\) | ||||
−0.192458 | + | 0.981305i | \(0.561646\pi\) | |||||||
\(468\) | −185470. | −0.0391435 | ||||||||
\(469\) | 1.19659e6 | 0.251197 | ||||||||
\(470\) | −6.51531e6 | −1.36047 | ||||||||
\(471\) | 7.56175e6 | 1.57062 | ||||||||
\(472\) | 477816. | 0.0987200 | ||||||||
\(473\) | −1.26932e7 | −2.60867 | ||||||||
\(474\) | 2.58063e6 | 0.527570 | ||||||||
\(475\) | −1.70245e7 | −3.46210 | ||||||||
\(476\) | −112865. | −0.0228318 | ||||||||
\(477\) | −309987. | −0.0623804 | ||||||||
\(478\) | −7.26906e6 | −1.45515 | ||||||||
\(479\) | 4.87397e6 | 0.970609 | 0.485304 | − | 0.874345i | \(-0.338709\pi\) | ||||
0.485304 | + | 0.874345i | \(0.338709\pi\) | |||||||
\(480\) | −1.93863e6 | −0.384053 | ||||||||
\(481\) | 1.81804e6 | 0.358294 | ||||||||
\(482\) | 1.79883e6 | 0.352674 | ||||||||
\(483\) | −2.02703e6 | −0.395359 | ||||||||
\(484\) | 370208. | 0.0718344 | ||||||||
\(485\) | 1.72398e7 | 3.32796 | ||||||||
\(486\) | 3.89689e6 | 0.748389 | ||||||||
\(487\) | −1.84954e6 | −0.353379 | −0.176690 | − | 0.984267i | \(-0.556539\pi\) | ||||
−0.176690 | + | 0.984267i | \(0.556539\pi\) | |||||||
\(488\) | −7.12793e6 | −1.35492 | ||||||||
\(489\) | −3.25939e6 | −0.616403 | ||||||||
\(490\) | −1.54363e6 | −0.290437 | ||||||||
\(491\) | −5.47088e6 | −1.02413 | −0.512063 | − | 0.858948i | \(-0.671119\pi\) | ||||
−0.512063 | + | 0.858948i | \(0.671119\pi\) | |||||||
\(492\) | −76699.0 | −0.0142849 | ||||||||
\(493\) | 226224. | 0.0419201 | ||||||||
\(494\) | 1.05951e7 | 1.95338 | ||||||||
\(495\) | −4.75475e6 | −0.872196 | ||||||||
\(496\) | 4.70140e6 | 0.858070 | ||||||||
\(497\) | −976215. | −0.177278 | ||||||||
\(498\) | −4.65975e6 | −0.841956 | ||||||||
\(499\) | 5.27760e6 | 0.948823 | 0.474411 | − | 0.880303i | \(-0.342661\pi\) | ||||
0.474411 | + | 0.880303i | \(0.342661\pi\) | |||||||
\(500\) | −970044. | −0.173527 | ||||||||
\(501\) | 8.26645e6 | 1.47138 | ||||||||
\(502\) | 5.03477e6 | 0.891703 | ||||||||
\(503\) | 6.07721e6 | 1.07099 | 0.535494 | − | 0.844539i | \(-0.320125\pi\) | ||||
0.535494 | + | 0.844539i | \(0.320125\pi\) | |||||||
\(504\) | −2.18485e6 | −0.383130 | ||||||||
\(505\) | 1.09501e7 | 1.91069 | ||||||||
\(506\) | 2.50574e6 | 0.435071 | ||||||||
\(507\) | −1.56567e6 | −0.270508 | ||||||||
\(508\) | 803363. | 0.138119 | ||||||||
\(509\) | 4.28972e6 | 0.733896 | 0.366948 | − | 0.930242i | \(-0.380403\pi\) | ||||
0.366948 | + | 0.930242i | \(0.380403\pi\) | |||||||
\(510\) | −2.84377e6 | −0.484138 | ||||||||
\(511\) | −697056. | −0.118091 | ||||||||
\(512\) | −4.89407e6 | −0.825078 | ||||||||
\(513\) | −7.34926e6 | −1.23296 | ||||||||
\(514\) | 167161. | 0.0279079 | ||||||||
\(515\) | −3.73876e6 | −0.621169 | ||||||||
\(516\) | 1.30879e6 | 0.216395 | ||||||||
\(517\) | 6.00661e6 | 0.988333 | ||||||||
\(518\) | −2.22079e6 | −0.363650 | ||||||||
\(519\) | −1.37921e7 | −2.24756 | ||||||||
\(520\) | −1.13327e7 | −1.83791 | ||||||||
\(521\) | 3.12541e6 | 0.504444 | 0.252222 | − | 0.967669i | \(-0.418839\pi\) | ||||
0.252222 | + | 0.967669i | \(0.418839\pi\) | |||||||
\(522\) | −454110. | −0.0729433 | ||||||||
\(523\) | −6.57035e6 | −1.05035 | −0.525176 | − | 0.850994i | \(-0.676000\pi\) | ||||
−0.525176 | + | 0.850994i | \(0.676000\pi\) | |||||||
\(524\) | −497642. | −0.0791751 | ||||||||
\(525\) | −1.63971e7 | −2.59639 | ||||||||
\(526\) | 2.33102e6 | 0.367352 | ||||||||
\(527\) | 1.13813e6 | 0.178510 | ||||||||
\(528\) | 1.08299e7 | 1.69060 | ||||||||
\(529\) | −5.80521e6 | −0.901942 | ||||||||
\(530\) | 1.96409e6 | 0.303718 | ||||||||
\(531\) | −254201. | −0.0391237 | ||||||||
\(532\) | −1.11153e6 | −0.170271 | ||||||||
\(533\) | −943216. | −0.143811 | ||||||||
\(534\) | −1.49347e6 | −0.226644 | ||||||||
\(535\) | 1.89702e6 | 0.286541 | ||||||||
\(536\) | −1.47084e6 | −0.221133 | ||||||||
\(537\) | 6.45043e6 | 0.965279 | ||||||||
\(538\) | 2.68453e6 | 0.399865 | ||||||||
\(539\) | 1.42311e6 | 0.210992 | ||||||||
\(540\) | −815136. | −0.120294 | ||||||||
\(541\) | −6.72381e6 | −0.987694 | −0.493847 | − | 0.869549i | \(-0.664410\pi\) | ||||
−0.493847 | + | 0.869549i | \(0.664410\pi\) | |||||||
\(542\) | −9.13008e6 | −1.33499 | ||||||||
\(543\) | −4.15180e6 | −0.604278 | ||||||||
\(544\) | 291850. | 0.0422827 | ||||||||
\(545\) | 4.98715e6 | 0.719219 | ||||||||
\(546\) | 1.02046e7 | 1.46493 | ||||||||
\(547\) | 1.19150e6 | 0.170264 | 0.0851322 | − | 0.996370i | \(-0.472869\pi\) | ||||
0.0851322 | + | 0.996370i | \(0.472869\pi\) | |||||||
\(548\) | 273591. | 0.0389180 | ||||||||
\(549\) | 3.79210e6 | 0.536969 | ||||||||
\(550\) | 2.02696e7 | 2.85718 | ||||||||
\(551\) | 2.22793e6 | 0.312625 | ||||||||
\(552\) | 2.49160e6 | 0.348042 | ||||||||
\(553\) | −3.32939e6 | −0.462968 | ||||||||
\(554\) | −6.68716e6 | −0.925693 | ||||||||
\(555\) | −4.80569e6 | −0.662252 | ||||||||
\(556\) | −1.20389e6 | −0.165158 | ||||||||
\(557\) | 2.43064e6 | 0.331958 | 0.165979 | − | 0.986129i | \(-0.446922\pi\) | ||||
0.165979 | + | 0.986129i | \(0.446922\pi\) | |||||||
\(558\) | −2.28461e6 | −0.310618 | ||||||||
\(559\) | 1.60951e7 | 2.17853 | ||||||||
\(560\) | 1.51555e7 | 2.04220 | ||||||||
\(561\) | 2.62174e6 | 0.351708 | ||||||||
\(562\) | −6.98069e6 | −0.932304 | ||||||||
\(563\) | −1.05702e7 | −1.40544 | −0.702721 | − | 0.711466i | \(-0.748032\pi\) | ||||
−0.702721 | + | 0.711466i | \(0.748032\pi\) | |||||||
\(564\) | −619341. | −0.0819846 | ||||||||
\(565\) | −4.46508e6 | −0.588447 | ||||||||
\(566\) | 2.04325e6 | 0.268090 | ||||||||
\(567\) | −1.01734e7 | −1.32895 | ||||||||
\(568\) | 1.19995e6 | 0.156061 | ||||||||
\(569\) | 5.17877e6 | 0.670573 | 0.335286 | − | 0.942116i | \(-0.391167\pi\) | ||||
0.335286 | + | 0.942116i | \(0.391167\pi\) | |||||||
\(570\) | −2.80064e7 | −3.61053 | ||||||||
\(571\) | −3.92258e6 | −0.503479 | −0.251739 | − | 0.967795i | \(-0.581003\pi\) | ||||
−0.251739 | + | 0.967795i | \(0.581003\pi\) | |||||||
\(572\) | −1.08339e6 | −0.138451 | ||||||||
\(573\) | −3.35335e6 | −0.426670 | ||||||||
\(574\) | 1.15217e6 | 0.145961 | ||||||||
\(575\) | 5.10538e6 | 0.643959 | ||||||||
\(576\) | 2.65920e6 | 0.333961 | ||||||||
\(577\) | 1.12133e7 | 1.40215 | 0.701074 | − | 0.713089i | \(-0.252704\pi\) | ||||
0.701074 | + | 0.713089i | \(0.252704\pi\) | |||||||
\(578\) | −7.97265e6 | −0.992620 | ||||||||
\(579\) | −1.82281e7 | −2.25967 | ||||||||
\(580\) | 247109. | 0.0305013 | ||||||||
\(581\) | 6.01174e6 | 0.738857 | ||||||||
\(582\) | 1.90817e7 | 2.33512 | ||||||||
\(583\) | −1.81074e6 | −0.220640 | ||||||||
\(584\) | 856814. | 0.103957 | ||||||||
\(585\) | 6.02905e6 | 0.728382 | ||||||||
\(586\) | 1.42487e7 | 1.71409 | ||||||||
\(587\) | 1.03337e7 | 1.23783 | 0.618915 | − | 0.785458i | \(-0.287573\pi\) | ||||
0.618915 | + | 0.785458i | \(0.287573\pi\) | |||||||
\(588\) | −146736. | −0.0175023 | ||||||||
\(589\) | 1.12086e7 | 1.33127 | ||||||||
\(590\) | 1.61062e6 | 0.190486 | ||||||||
\(591\) | 1.57468e7 | 1.85448 | ||||||||
\(592\) | 2.98853e6 | 0.350472 | ||||||||
\(593\) | −1.58653e7 | −1.85272 | −0.926362 | − | 0.376634i | \(-0.877081\pi\) | ||||
−0.926362 | + | 0.376634i | \(0.877081\pi\) | |||||||
\(594\) | 8.75012e6 | 1.01753 | ||||||||
\(595\) | 3.66887e6 | 0.424855 | ||||||||
\(596\) | −55057.2 | −0.00634890 | ||||||||
\(597\) | 1.53163e7 | 1.75881 | ||||||||
\(598\) | −3.17730e6 | −0.363334 | ||||||||
\(599\) | −9.66314e6 | −1.10040 | −0.550201 | − | 0.835032i | \(-0.685449\pi\) | ||||
−0.550201 | + | 0.835032i | \(0.685449\pi\) | |||||||
\(600\) | 2.01552e7 | 2.28564 | ||||||||
\(601\) | −1.07881e7 | −1.21831 | −0.609155 | − | 0.793051i | \(-0.708491\pi\) | ||||
−0.609155 | + | 0.793051i | \(0.708491\pi\) | |||||||
\(602\) | −1.96607e7 | −2.21110 | ||||||||
\(603\) | 782495. | 0.0876372 | ||||||||
\(604\) | −53815.4 | −0.00600225 | ||||||||
\(605\) | −1.20343e7 | −1.33669 | ||||||||
\(606\) | 1.21200e7 | 1.34067 | ||||||||
\(607\) | 6.76786e6 | 0.745555 | 0.372778 | − | 0.927921i | \(-0.378405\pi\) | ||||
0.372778 | + | 0.927921i | \(0.378405\pi\) | |||||||
\(608\) | 2.87424e6 | 0.315329 | ||||||||
\(609\) | 2.14583e6 | 0.234451 | ||||||||
\(610\) | −2.40268e7 | −2.61440 | ||||||||
\(611\) | −7.61643e6 | −0.825370 | ||||||||
\(612\) | −73806.3 | −0.00796553 | ||||||||
\(613\) | 2.91439e6 | 0.313253 | 0.156627 | − | 0.987658i | \(-0.449938\pi\) | ||||
0.156627 | + | 0.987658i | \(0.449938\pi\) | |||||||
\(614\) | 3.52286e6 | 0.377115 | ||||||||
\(615\) | 2.49324e6 | 0.265813 | ||||||||
\(616\) | −1.27624e7 | −1.35513 | ||||||||
\(617\) | −1.01418e7 | −1.07251 | −0.536254 | − | 0.844056i | \(-0.680161\pi\) | ||||
−0.536254 | + | 0.844056i | \(0.680161\pi\) | |||||||
\(618\) | −4.13821e6 | −0.435854 | ||||||||
\(619\) | −6.89280e6 | −0.723051 | −0.361526 | − | 0.932362i | \(-0.617744\pi\) | ||||
−0.361526 | + | 0.932362i | \(0.617744\pi\) | |||||||
\(620\) | 1.24320e6 | 0.129885 | ||||||||
\(621\) | 2.20393e6 | 0.229334 | ||||||||
\(622\) | 5.91603e6 | 0.613133 | ||||||||
\(623\) | 1.92680e6 | 0.198891 | ||||||||
\(624\) | −1.37324e7 | −1.41184 | ||||||||
\(625\) | 1.14505e7 | 1.17253 | ||||||||
\(626\) | −2.16116e6 | −0.220420 | ||||||||
\(627\) | 2.58198e7 | 2.62291 | ||||||||
\(628\) | −1.24348e6 | −0.125817 | ||||||||
\(629\) | 723472. | 0.0729113 | ||||||||
\(630\) | −7.36470e6 | −0.739271 | ||||||||
\(631\) | −7.52515e6 | −0.752388 | −0.376194 | − | 0.926541i | \(-0.622767\pi\) | ||||
−0.376194 | + | 0.926541i | \(0.622767\pi\) | |||||||
\(632\) | 4.09245e6 | 0.407559 | ||||||||
\(633\) | 1.16570e7 | 1.15632 | ||||||||
\(634\) | 9.50415e6 | 0.939053 | ||||||||
\(635\) | −2.61148e7 | −2.57011 | ||||||||
\(636\) | 186705. | 0.0183026 | ||||||||
\(637\) | −1.80451e6 | −0.176202 | ||||||||
\(638\) | −2.65261e6 | −0.258001 | ||||||||
\(639\) | −638382. | −0.0618484 | ||||||||
\(640\) | −2.02419e7 | −1.95345 | ||||||||
\(641\) | −278549. | −0.0267767 | −0.0133883 | − | 0.999910i | \(-0.504262\pi\) | ||||
−0.0133883 | + | 0.999910i | \(0.504262\pi\) | |||||||
\(642\) | 2.09969e6 | 0.201057 | ||||||||
\(643\) | −3.63623e6 | −0.346836 | −0.173418 | − | 0.984848i | \(-0.555481\pi\) | ||||
−0.173418 | + | 0.984848i | \(0.555481\pi\) | |||||||
\(644\) | 333330. | 0.0316709 | ||||||||
\(645\) | −4.25448e7 | −4.02668 | ||||||||
\(646\) | 4.21622e6 | 0.397505 | ||||||||
\(647\) | −1.08234e7 | −1.01649 | −0.508243 | − | 0.861214i | \(-0.669705\pi\) | ||||
−0.508243 | + | 0.861214i | \(0.669705\pi\) | |||||||
\(648\) | 1.25050e7 | 1.16989 | ||||||||
\(649\) | −1.48487e6 | −0.138381 | ||||||||
\(650\) | −2.57020e7 | −2.38607 | ||||||||
\(651\) | 1.07956e7 | 0.998376 | ||||||||
\(652\) | 535984. | 0.0493779 | ||||||||
\(653\) | 8.86232e6 | 0.813326 | 0.406663 | − | 0.913578i | \(-0.366692\pi\) | ||||
0.406663 | + | 0.913578i | \(0.366692\pi\) | |||||||
\(654\) | 5.51997e6 | 0.504652 | ||||||||
\(655\) | 1.61768e7 | 1.47329 | ||||||||
\(656\) | −1.55048e6 | −0.140672 | ||||||||
\(657\) | −455830. | −0.0411993 | ||||||||
\(658\) | 9.30373e6 | 0.837708 | ||||||||
\(659\) | −4.94619e6 | −0.443667 | −0.221833 | − | 0.975085i | \(-0.571204\pi\) | ||||
−0.221833 | + | 0.975085i | \(0.571204\pi\) | |||||||
\(660\) | 2.86377e6 | 0.255905 | ||||||||
\(661\) | −6.34440e6 | −0.564790 | −0.282395 | − | 0.959298i | \(-0.591129\pi\) | ||||
−0.282395 | + | 0.959298i | \(0.591129\pi\) | |||||||
\(662\) | −3.16613e6 | −0.280791 | ||||||||
\(663\) | −3.32438e6 | −0.293716 | ||||||||
\(664\) | −7.38958e6 | −0.650429 | ||||||||
\(665\) | 3.61323e7 | 3.16841 | ||||||||
\(666\) | −1.45226e6 | −0.126870 | ||||||||
\(667\) | −668122. | −0.0581489 | ||||||||
\(668\) | −1.35936e6 | −0.117867 | ||||||||
\(669\) | −832361. | −0.0719029 | ||||||||
\(670\) | −4.95790e6 | −0.426689 | ||||||||
\(671\) | 2.21509e7 | 1.89926 | ||||||||
\(672\) | 2.76832e6 | 0.236479 | ||||||||
\(673\) | 1.00239e7 | 0.853095 | 0.426548 | − | 0.904465i | \(-0.359730\pi\) | ||||
0.426548 | + | 0.904465i | \(0.359730\pi\) | |||||||
\(674\) | 1.14370e7 | 0.969756 | ||||||||
\(675\) | 1.78281e7 | 1.50607 | ||||||||
\(676\) | 257463. | 0.0216695 | ||||||||
\(677\) | 3.44231e6 | 0.288654 | 0.144327 | − | 0.989530i | \(-0.453898\pi\) | ||||
0.144327 | + | 0.989530i | \(0.453898\pi\) | |||||||
\(678\) | −4.94212e6 | −0.412894 | ||||||||
\(679\) | −2.46181e7 | −2.04918 | ||||||||
\(680\) | −4.50975e6 | −0.374007 | ||||||||
\(681\) | −2.43734e7 | −2.01395 | ||||||||
\(682\) | −1.33452e7 | −1.09866 | ||||||||
\(683\) | 2.51352e6 | 0.206172 | 0.103086 | − | 0.994672i | \(-0.467128\pi\) | ||||
0.103086 | + | 0.994672i | \(0.467128\pi\) | |||||||
\(684\) | −726869. | −0.0594041 | ||||||||
\(685\) | −8.89359e6 | −0.724187 | ||||||||
\(686\) | −1.16735e7 | −0.947090 | ||||||||
\(687\) | −1.51909e7 | −1.22798 | ||||||||
\(688\) | 2.64575e7 | 2.13097 | ||||||||
\(689\) | 2.29603e6 | 0.184259 | ||||||||
\(690\) | 8.39869e6 | 0.671566 | ||||||||
\(691\) | −2.01696e7 | −1.60695 | −0.803474 | − | 0.595340i | \(-0.797017\pi\) | ||||
−0.803474 | + | 0.595340i | \(0.797017\pi\) | |||||||
\(692\) | 2.26802e6 | 0.180045 | ||||||||
\(693\) | 6.78968e6 | 0.537052 | ||||||||
\(694\) | −1.67856e7 | −1.32293 | ||||||||
\(695\) | 3.91346e7 | 3.07326 | ||||||||
\(696\) | −2.63764e6 | −0.206391 | ||||||||
\(697\) | −375345. | −0.0292650 | ||||||||
\(698\) | 6.59082e6 | 0.512037 | ||||||||
\(699\) | −1.40344e7 | −1.08643 | ||||||||
\(700\) | 2.69639e6 | 0.207988 | ||||||||
\(701\) | 1.67322e6 | 0.128605 | 0.0643025 | − | 0.997930i | \(-0.479518\pi\) | ||||
0.0643025 | + | 0.997930i | \(0.479518\pi\) | |||||||
\(702\) | −1.10952e7 | −0.849754 | ||||||||
\(703\) | 7.12499e6 | 0.543746 | ||||||||
\(704\) | 1.55333e7 | 1.18122 | ||||||||
\(705\) | 2.01328e7 | 1.52557 | ||||||||
\(706\) | −2.06522e7 | −1.55939 | ||||||||
\(707\) | −1.56366e7 | −1.17650 | ||||||||
\(708\) | 153104. | 0.0114790 | ||||||||
\(709\) | 6.28913e6 | 0.469867 | 0.234933 | − | 0.972011i | \(-0.424513\pi\) | ||||
0.234933 | + | 0.972011i | \(0.424513\pi\) | |||||||
\(710\) | 4.04480e6 | 0.301128 | ||||||||
\(711\) | −2.17721e6 | −0.161520 | ||||||||
\(712\) | −2.36840e6 | −0.175087 | ||||||||
\(713\) | −3.36130e6 | −0.247619 | ||||||||
\(714\) | 4.06085e6 | 0.298107 | ||||||||
\(715\) | 3.52177e7 | 2.57629 | ||||||||
\(716\) | −1.06073e6 | −0.0773253 | ||||||||
\(717\) | 2.24620e7 | 1.63173 | ||||||||
\(718\) | 2.77890e6 | 0.201169 | ||||||||
\(719\) | 2.87519e6 | 0.207417 | 0.103709 | − | 0.994608i | \(-0.466929\pi\) | ||||
0.103709 | + | 0.994608i | \(0.466929\pi\) | |||||||
\(720\) | 9.91071e6 | 0.712481 | ||||||||
\(721\) | 5.33888e6 | 0.382483 | ||||||||
\(722\) | 2.68726e7 | 1.91852 | ||||||||
\(723\) | −5.55854e6 | −0.395471 | ||||||||
\(724\) | 682734. | 0.0484067 | ||||||||
\(725\) | −5.40461e6 | −0.381873 | ||||||||
\(726\) | −1.33200e7 | −0.937914 | ||||||||
\(727\) | 2.76368e6 | 0.193933 | 0.0969665 | − | 0.995288i | \(-0.469086\pi\) | ||||
0.0969665 | + | 0.995288i | \(0.469086\pi\) | |||||||
\(728\) | 1.61829e7 | 1.13169 | ||||||||
\(729\) | 5.67227e6 | 0.395310 | ||||||||
\(730\) | 2.88815e6 | 0.200591 | ||||||||
\(731\) | 6.40490e6 | 0.443321 | ||||||||
\(732\) | −2.28397e6 | −0.157548 | ||||||||
\(733\) | −1.06643e7 | −0.733115 | −0.366557 | − | 0.930395i | \(-0.619464\pi\) | ||||
−0.366557 | + | 0.930395i | \(0.619464\pi\) | |||||||
\(734\) | 1.59885e7 | 1.09538 | ||||||||
\(735\) | 4.76993e6 | 0.325682 | ||||||||
\(736\) | −861940. | −0.0586520 | ||||||||
\(737\) | 4.57081e6 | 0.309973 | ||||||||
\(738\) | 753446. | 0.0509227 | ||||||||
\(739\) | −3.98603e6 | −0.268491 | −0.134245 | − | 0.990948i | \(-0.542861\pi\) | ||||
−0.134245 | + | 0.990948i | \(0.542861\pi\) | |||||||
\(740\) | 790262. | 0.0530508 | ||||||||
\(741\) | −3.27397e7 | −2.19043 | ||||||||
\(742\) | −2.80468e6 | −0.187014 | ||||||||
\(743\) | −2.19748e7 | −1.46034 | −0.730170 | − | 0.683266i | \(-0.760559\pi\) | ||||
−0.730170 | + | 0.683266i | \(0.760559\pi\) | |||||||
\(744\) | −1.32698e7 | −0.878888 | ||||||||
\(745\) | 1.78974e6 | 0.118140 | ||||||||
\(746\) | 1.64285e7 | 1.08081 | ||||||||
\(747\) | 3.93130e6 | 0.257771 | ||||||||
\(748\) | −431127. | −0.0281741 | ||||||||
\(749\) | −2.70891e6 | −0.176437 | ||||||||
\(750\) | 3.49020e7 | 2.26567 | ||||||||
\(751\) | −1.84068e7 | −1.19091 | −0.595456 | − | 0.803388i | \(-0.703028\pi\) | ||||
−0.595456 | + | 0.803388i | \(0.703028\pi\) | |||||||
\(752\) | −1.25201e7 | −0.807351 | ||||||||
\(753\) | −1.55578e7 | −0.999912 | ||||||||
\(754\) | 3.36352e6 | 0.215460 | ||||||||
\(755\) | 1.74937e6 | 0.111690 | ||||||||
\(756\) | 1.16400e6 | 0.0740709 | ||||||||
\(757\) | 2.78199e7 | 1.76447 | 0.882237 | − | 0.470805i | \(-0.156037\pi\) | ||||
0.882237 | + | 0.470805i | \(0.156037\pi\) | |||||||
\(758\) | −2.61418e7 | −1.65258 | ||||||||
\(759\) | −7.74295e6 | −0.487867 | ||||||||
\(760\) | −4.44135e7 | −2.78921 | ||||||||
\(761\) | 1.96481e6 | 0.122987 | 0.0614935 | − | 0.998107i | \(-0.480414\pi\) | ||||
0.0614935 | + | 0.998107i | \(0.480414\pi\) | |||||||
\(762\) | −2.89048e7 | −1.80336 | ||||||||
\(763\) | −7.12155e6 | −0.442857 | ||||||||
\(764\) | 551434. | 0.0341791 | ||||||||
\(765\) | 2.39921e6 | 0.148223 | ||||||||
\(766\) | 8.15288e6 | 0.502041 | ||||||||
\(767\) | 1.88282e6 | 0.115564 | ||||||||
\(768\) | −5.35728e6 | −0.327749 | ||||||||
\(769\) | −1.16064e7 | −0.707754 | −0.353877 | − | 0.935292i | \(-0.615137\pi\) | ||||
−0.353877 | + | 0.935292i | \(0.615137\pi\) | |||||||
\(770\) | −4.30196e7 | −2.61481 | ||||||||
\(771\) | −516541. | −0.0312946 | ||||||||
\(772\) | 2.99748e6 | 0.181014 | ||||||||
\(773\) | 2.10057e7 | 1.26441 | 0.632207 | − | 0.774800i | \(-0.282149\pi\) | ||||
0.632207 | + | 0.774800i | \(0.282149\pi\) | |||||||
\(774\) | −1.28568e7 | −0.771404 | ||||||||
\(775\) | −2.71904e7 | −1.62615 | ||||||||
\(776\) | 3.02604e7 | 1.80393 | ||||||||
\(777\) | 6.86243e6 | 0.407779 | ||||||||
\(778\) | 3.84187e6 | 0.227559 | ||||||||
\(779\) | −3.69652e6 | −0.218248 | ||||||||
\(780\) | −3.63129e6 | −0.213710 | ||||||||
\(781\) | −3.72900e6 | −0.218758 | ||||||||
\(782\) | −1.26438e6 | −0.0739368 | ||||||||
\(783\) | −2.33310e6 | −0.135997 | ||||||||
\(784\) | −2.96630e6 | −0.172355 | ||||||||
\(785\) | 4.04215e7 | 2.34120 | ||||||||
\(786\) | 1.79051e7 | 1.03376 | ||||||||
\(787\) | −8.11927e6 | −0.467283 | −0.233642 | − | 0.972323i | \(-0.575064\pi\) | ||||
−0.233642 | + | 0.972323i | \(0.575064\pi\) | |||||||
\(788\) | −2.58945e6 | −0.148557 | ||||||||
\(789\) | −7.20304e6 | −0.411930 | ||||||||
\(790\) | 1.37948e7 | 0.786409 | ||||||||
\(791\) | 6.37604e6 | 0.362335 | ||||||||
\(792\) | −8.34582e6 | −0.472776 | ||||||||
\(793\) | −2.80875e7 | −1.58610 | ||||||||
\(794\) | −1.49637e7 | −0.842340 | ||||||||
\(795\) | −6.06918e6 | −0.340575 | ||||||||
\(796\) | −2.51866e6 | −0.140892 | ||||||||
\(797\) | −1.42204e7 | −0.792985 | −0.396493 | − | 0.918038i | \(-0.629773\pi\) | ||||
−0.396493 | + | 0.918038i | \(0.629773\pi\) | |||||||
\(798\) | 3.99926e7 | 2.22317 | ||||||||
\(799\) | −3.03089e6 | −0.167959 | ||||||||
\(800\) | −6.97244e6 | −0.385177 | ||||||||
\(801\) | 1.26000e6 | 0.0693889 | ||||||||
\(802\) | −2.15502e7 | −1.18308 | ||||||||
\(803\) | −2.66265e6 | −0.145722 | ||||||||
\(804\) | −471295. | −0.0257130 | ||||||||
\(805\) | −1.08355e7 | −0.589332 | ||||||||
\(806\) | 1.69218e7 | 0.917504 | ||||||||
\(807\) | −8.29542e6 | −0.448389 | ||||||||
\(808\) | 1.92203e7 | 1.03570 | ||||||||
\(809\) | 2.40784e7 | 1.29347 | 0.646736 | − | 0.762714i | \(-0.276134\pi\) | ||||
0.646736 | + | 0.762714i | \(0.276134\pi\) | |||||||
\(810\) | 4.21519e7 | 2.25738 | ||||||||
\(811\) | 2.71158e7 | 1.44767 | 0.723836 | − | 0.689972i | \(-0.242377\pi\) | ||||
0.723836 | + | 0.689972i | \(0.242377\pi\) | |||||||
\(812\) | −352867. | −0.0187811 | ||||||||
\(813\) | 2.82127e7 | 1.49699 | ||||||||
\(814\) | −8.48311e6 | −0.448739 | ||||||||
\(815\) | −1.74231e7 | −0.918824 | ||||||||
\(816\) | −5.46471e6 | −0.287304 | ||||||||
\(817\) | 6.30776e7 | 3.30613 | ||||||||
\(818\) | 1.58875e7 | 0.830179 | ||||||||
\(819\) | −8.60937e6 | −0.448499 | ||||||||
\(820\) | −409996. | −0.0212934 | ||||||||
\(821\) | −1.57023e7 | −0.813025 | −0.406513 | − | 0.913645i | \(-0.633255\pi\) | ||||
−0.406513 | + | 0.913645i | \(0.633255\pi\) | |||||||
\(822\) | −9.84377e6 | −0.508138 | ||||||||
\(823\) | −1.52411e7 | −0.784364 | −0.392182 | − | 0.919888i | \(-0.628280\pi\) | ||||
−0.392182 | + | 0.919888i | \(0.628280\pi\) | |||||||
\(824\) | −6.56250e6 | −0.336707 | ||||||||
\(825\) | −6.26346e7 | −3.20390 | ||||||||
\(826\) | −2.29993e6 | −0.117291 | ||||||||
\(827\) | −2.27417e7 | −1.15627 | −0.578136 | − | 0.815940i | \(-0.696220\pi\) | ||||
−0.578136 | + | 0.815940i | \(0.696220\pi\) | |||||||
\(828\) | 217977. | 0.0110493 | ||||||||
\(829\) | 1.10029e7 | 0.556060 | 0.278030 | − | 0.960572i | \(-0.410319\pi\) | ||||
0.278030 | + | 0.960572i | \(0.410319\pi\) | |||||||
\(830\) | −2.49088e7 | −1.25504 | ||||||||
\(831\) | 2.06638e7 | 1.03803 | ||||||||
\(832\) | −1.96963e7 | −0.986453 | ||||||||
\(833\) | −718089. | −0.0358563 | ||||||||
\(834\) | 4.33157e7 | 2.15640 | ||||||||
\(835\) | 4.41885e7 | 2.19327 | ||||||||
\(836\) | −4.24588e6 | −0.210113 | ||||||||
\(837\) | −1.17377e7 | −0.579123 | ||||||||
\(838\) | −2.56486e7 | −1.26169 | ||||||||
\(839\) | −2.33372e7 | −1.14458 | −0.572288 | − | 0.820053i | \(-0.693944\pi\) | ||||
−0.572288 | + | 0.820053i | \(0.693944\pi\) | |||||||
\(840\) | −4.27768e7 | −2.09175 | ||||||||
\(841\) | 707281. | 0.0344828 | ||||||||
\(842\) | 2.00551e7 | 0.974866 | ||||||||
\(843\) | 2.15709e7 | 1.04544 | ||||||||
\(844\) | −1.91692e6 | −0.0926291 | ||||||||
\(845\) | −8.36931e6 | −0.403225 | ||||||||
\(846\) | 6.08405e6 | 0.292258 | ||||||||
\(847\) | 1.71847e7 | 0.823065 | ||||||||
\(848\) | 3.77427e6 | 0.180237 | ||||||||
\(849\) | −6.31380e6 | −0.300622 | ||||||||
\(850\) | −1.02279e7 | −0.485555 | ||||||||
\(851\) | −2.13667e6 | −0.101138 | ||||||||
\(852\) | 384496. | 0.0181465 | ||||||||
\(853\) | 1.63119e7 | 0.767595 | 0.383797 | − | 0.923417i | \(-0.374616\pi\) | ||||
0.383797 | + | 0.923417i | \(0.374616\pi\) | |||||||
\(854\) | 3.43098e7 | 1.60981 | ||||||||
\(855\) | 2.36282e7 | 1.10539 | ||||||||
\(856\) | 3.32976e6 | 0.155321 | ||||||||
\(857\) | −1.11103e7 | −0.516743 | −0.258372 | − | 0.966046i | \(-0.583186\pi\) | ||||
−0.258372 | + | 0.966046i | \(0.583186\pi\) | |||||||
\(858\) | 3.89803e7 | 1.80770 | ||||||||
\(859\) | 2.94971e7 | 1.36394 | 0.681971 | − | 0.731379i | \(-0.261123\pi\) | ||||
0.681971 | + | 0.731379i | \(0.261123\pi\) | |||||||
\(860\) | 6.99619e6 | 0.322564 | ||||||||
\(861\) | −3.56030e6 | −0.163674 | ||||||||
\(862\) | 1.72074e6 | 0.0788764 | ||||||||
\(863\) | 2.33489e7 | 1.06718 | 0.533592 | − | 0.845742i | \(-0.320842\pi\) | ||||
0.533592 | + | 0.845742i | \(0.320842\pi\) | |||||||
\(864\) | −3.00991e6 | −0.137173 | ||||||||
\(865\) | −7.37260e7 | −3.35027 | ||||||||
\(866\) | −1.56295e7 | −0.708191 | ||||||||
\(867\) | 2.46361e7 | 1.11307 | ||||||||
\(868\) | −1.77526e6 | −0.0799765 | ||||||||
\(869\) | −1.27178e7 | −0.571296 | ||||||||
\(870\) | −8.89094e6 | −0.398244 | ||||||||
\(871\) | −5.79582e6 | −0.258863 | ||||||||
\(872\) | 8.75374e6 | 0.389855 | ||||||||
\(873\) | −1.60987e7 | −0.714915 | ||||||||
\(874\) | −1.24520e7 | −0.551394 | ||||||||
\(875\) | −4.50286e7 | −1.98824 | ||||||||
\(876\) | 274545. | 0.0120880 | ||||||||
\(877\) | −3.29425e7 | −1.44630 | −0.723149 | − | 0.690692i | \(-0.757306\pi\) | ||||
−0.723149 | + | 0.690692i | \(0.757306\pi\) | |||||||
\(878\) | 3.34577e7 | 1.46474 | ||||||||
\(879\) | −4.40297e7 | −1.92209 | ||||||||
\(880\) | 5.78917e7 | 2.52005 | ||||||||
\(881\) | 3.22782e7 | 1.40110 | 0.700550 | − | 0.713603i | \(-0.252938\pi\) | ||||
0.700550 | + | 0.713603i | \(0.252938\pi\) | |||||||
\(882\) | 1.44145e6 | 0.0623920 | ||||||||
\(883\) | −1.31542e7 | −0.567758 | −0.283879 | − | 0.958860i | \(-0.591621\pi\) | ||||
−0.283879 | + | 0.958860i | \(0.591621\pi\) | |||||||
\(884\) | 546672. | 0.0235286 | ||||||||
\(885\) | −4.97694e6 | −0.213602 | ||||||||
\(886\) | 7.79679e6 | 0.333681 | ||||||||
\(887\) | −5.84285e6 | −0.249354 | −0.124677 | − | 0.992197i | \(-0.539789\pi\) | ||||
−0.124677 | + | 0.992197i | \(0.539789\pi\) | |||||||
\(888\) | −8.43523e6 | −0.358975 | ||||||||
\(889\) | 3.72914e7 | 1.58254 | ||||||||
\(890\) | −7.98340e6 | −0.337841 | ||||||||
\(891\) | −3.88608e7 | −1.63990 | ||||||||
\(892\) | 136876. | 0.00575990 | ||||||||
\(893\) | −2.98492e7 | −1.25258 | ||||||||
\(894\) | 1.98095e6 | 0.0828952 | ||||||||
\(895\) | 3.44809e7 | 1.43887 | ||||||||
\(896\) | 2.89050e7 | 1.20283 | ||||||||
\(897\) | 9.81811e6 | 0.407424 | ||||||||
\(898\) | −3.84946e7 | −1.59297 | ||||||||
\(899\) | 3.55830e6 | 0.146840 | ||||||||
\(900\) | 1.76327e6 | 0.0725625 | ||||||||
\(901\) | 913684. | 0.0374959 | ||||||||
\(902\) | 4.40112e6 | 0.180114 | ||||||||
\(903\) | 6.07531e7 | 2.47941 | ||||||||
\(904\) | −7.83737e6 | −0.318970 | ||||||||
\(905\) | −2.21935e7 | −0.900751 | ||||||||
\(906\) | 1.93627e6 | 0.0783691 | ||||||||
\(907\) | −2.27296e7 | −0.917431 | −0.458716 | − | 0.888583i | \(-0.651690\pi\) | ||||
−0.458716 | + | 0.888583i | \(0.651690\pi\) | |||||||
\(908\) | 4.00804e6 | 0.161331 | ||||||||
\(909\) | −1.02253e7 | −0.410457 | ||||||||
\(910\) | 5.45491e7 | 2.18366 | ||||||||
\(911\) | 2.85916e7 | 1.14141 | 0.570706 | − | 0.821154i | \(-0.306670\pi\) | ||||
0.570706 | + | 0.821154i | \(0.306670\pi\) | |||||||
\(912\) | −5.38183e7 | −2.14261 | ||||||||
\(913\) | 2.29640e7 | 0.911738 | ||||||||
\(914\) | −2.07491e7 | −0.821548 | ||||||||
\(915\) | 7.42448e7 | 2.93166 | ||||||||
\(916\) | 2.49804e6 | 0.0983695 | ||||||||
\(917\) | −2.31001e7 | −0.907173 | ||||||||
\(918\) | −4.41525e6 | −0.172921 | ||||||||
\(919\) | 4.07727e7 | 1.59250 | 0.796252 | − | 0.604966i | \(-0.206813\pi\) | ||||
0.796252 | + | 0.604966i | \(0.206813\pi\) | |||||||
\(920\) | 1.33189e7 | 0.518799 | ||||||||
\(921\) | −1.08859e7 | −0.422878 | ||||||||
\(922\) | −7.23289e6 | −0.280210 | ||||||||
\(923\) | 4.72840e6 | 0.182688 | ||||||||
\(924\) | −4.08941e6 | −0.157573 | ||||||||
\(925\) | −1.72841e7 | −0.664189 | ||||||||
\(926\) | 2.26121e6 | 0.0866588 | ||||||||
\(927\) | 3.49129e6 | 0.133440 | ||||||||
\(928\) | 912458. | 0.0347811 | ||||||||
\(929\) | −4.12838e7 | −1.56943 | −0.784713 | − | 0.619860i | \(-0.787190\pi\) | ||||
−0.784713 | + | 0.619860i | \(0.787190\pi\) | |||||||
\(930\) | −4.47300e7 | −1.69586 | ||||||||
\(931\) | −7.07198e6 | −0.267403 | ||||||||
\(932\) | 2.30786e6 | 0.0870301 | ||||||||
\(933\) | −1.82810e7 | −0.687537 | ||||||||
\(934\) | −1.07333e7 | −0.402592 | ||||||||
\(935\) | 1.40146e7 | 0.524264 | ||||||||
\(936\) | 1.05826e7 | 0.394822 | ||||||||
\(937\) | 4.54057e7 | 1.68951 | 0.844755 | − | 0.535153i | \(-0.179746\pi\) | ||||
0.844755 | + | 0.535153i | \(0.179746\pi\) | |||||||
\(938\) | 7.07979e6 | 0.262732 | ||||||||
\(939\) | 6.67817e6 | 0.247169 | ||||||||
\(940\) | −3.31070e6 | −0.122208 | ||||||||
\(941\) | 4.70900e7 | 1.73362 | 0.866812 | − | 0.498635i | \(-0.166165\pi\) | ||||
0.866812 | + | 0.498635i | \(0.166165\pi\) | |||||||
\(942\) | 4.47401e7 | 1.64274 | ||||||||
\(943\) | 1.10853e6 | 0.0405946 | ||||||||
\(944\) | 3.09503e6 | 0.113041 | ||||||||
\(945\) | −3.78379e7 | −1.37831 | ||||||||
\(946\) | −7.51010e7 | −2.72846 | ||||||||
\(947\) | 2.49040e6 | 0.0902390 | 0.0451195 | − | 0.998982i | \(-0.485633\pi\) | ||||
0.0451195 | + | 0.998982i | \(0.485633\pi\) | |||||||
\(948\) | 1.31133e6 | 0.0473904 | ||||||||
\(949\) | 3.37626e6 | 0.121694 | ||||||||
\(950\) | −1.00728e8 | −3.62109 | ||||||||
\(951\) | −2.93686e7 | −1.05301 | ||||||||
\(952\) | 6.43983e6 | 0.230294 | ||||||||
\(953\) | −1.43265e7 | −0.510985 | −0.255493 | − | 0.966811i | \(-0.582238\pi\) | ||||
−0.255493 | + | 0.966811i | \(0.582238\pi\) | |||||||
\(954\) | −1.83408e6 | −0.0652450 | ||||||||
\(955\) | −1.79254e7 | −0.636004 | ||||||||
\(956\) | −3.69371e6 | −0.130713 | ||||||||
\(957\) | 8.19676e6 | 0.289309 | ||||||||
\(958\) | 2.88375e7 | 1.01518 | ||||||||
\(959\) | 1.26999e7 | 0.445916 | ||||||||
\(960\) | 5.20640e7 | 1.82331 | ||||||||
\(961\) | −1.07275e7 | −0.374704 | ||||||||
\(962\) | 1.07566e7 | 0.374748 | ||||||||
\(963\) | −1.77145e6 | −0.0615550 | ||||||||
\(964\) | 914063. | 0.0316799 | ||||||||
\(965\) | −9.74385e7 | −3.36831 | ||||||||
\(966\) | −1.19932e7 | −0.413515 | ||||||||
\(967\) | −1.92616e7 | −0.662407 | −0.331204 | − | 0.943559i | \(-0.607455\pi\) | ||||
−0.331204 | + | 0.943559i | \(0.607455\pi\) | |||||||
\(968\) | −2.11233e7 | −0.724559 | ||||||||
\(969\) | −1.30285e7 | −0.445742 | ||||||||
\(970\) | 1.02002e8 | 3.48079 | ||||||||
\(971\) | −3.31255e7 | −1.12749 | −0.563747 | − | 0.825948i | \(-0.690641\pi\) | ||||
−0.563747 | + | 0.825948i | \(0.690641\pi\) | |||||||
\(972\) | 1.98017e6 | 0.0672259 | ||||||||
\(973\) | −5.58834e7 | −1.89235 | ||||||||
\(974\) | −1.09430e7 | −0.369607 | ||||||||
\(975\) | 7.94211e7 | 2.67562 | ||||||||
\(976\) | −4.61709e7 | −1.55147 | ||||||||
\(977\) | −5.00959e7 | −1.67906 | −0.839529 | − | 0.543314i | \(-0.817169\pi\) | ||||
−0.839529 | + | 0.543314i | \(0.817169\pi\) | |||||||
\(978\) | −1.92846e7 | −0.644709 | ||||||||
\(979\) | 7.36008e6 | 0.245429 | ||||||||
\(980\) | −784382. | −0.0260893 | ||||||||
\(981\) | −4.65704e6 | −0.154503 | ||||||||
\(982\) | −3.23692e7 | −1.07116 | ||||||||
\(983\) | −6.69976e6 | −0.221144 | −0.110572 | − | 0.993868i | \(-0.535268\pi\) | ||||
−0.110572 | + | 0.993868i | \(0.535268\pi\) | |||||||
\(984\) | 4.37629e6 | 0.144085 | ||||||||
\(985\) | 8.41748e7 | 2.76434 | ||||||||
\(986\) | 1.33849e6 | 0.0438451 | ||||||||
\(987\) | −2.87493e7 | −0.939364 | ||||||||
\(988\) | 5.38381e6 | 0.175468 | ||||||||
\(989\) | −1.89160e7 | −0.614948 | ||||||||
\(990\) | −2.81321e7 | −0.912249 | ||||||||
\(991\) | −3.54819e7 | −1.14768 | −0.573842 | − | 0.818966i | \(-0.694548\pi\) | ||||
−0.573842 | + | 0.818966i | \(0.694548\pi\) | |||||||
\(992\) | 4.59054e6 | 0.148110 | ||||||||
\(993\) | 9.78359e6 | 0.314866 | ||||||||
\(994\) | −5.77590e6 | −0.185419 | ||||||||
\(995\) | 8.18737e7 | 2.62172 | ||||||||
\(996\) | −2.36781e6 | −0.0756309 | ||||||||
\(997\) | −2.99768e7 | −0.955097 | −0.477549 | − | 0.878605i | \(-0.658475\pi\) | ||||
−0.477549 | + | 0.878605i | \(0.658475\pi\) | |||||||
\(998\) | 3.12256e7 | 0.992395 | ||||||||
\(999\) | −7.46132e6 | −0.236538 |
(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 | 29.6.a.a.1.4 | ✓ | 4 | |
3.2 | odd | 2 | 261.6.a.a.1.1 | 4 | |||
4.3 | odd | 2 | 464.6.a.i.1.4 | 4 | |||
5.4 | even | 2 | 725.6.a.a.1.1 | 4 | |||
29.28 | even | 2 | 841.6.a.a.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.6.a.a.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial | |
261.6.a.a.1.1 | 4 | 3.2 | odd | 2 | |||
464.6.a.i.1.4 | 4 | 4.3 | odd | 2 | |||
725.6.a.a.1.1 | 4 | 5.4 | even | 2 | |||
841.6.a.a.1.1 | 4 | 29.28 | even | 2 |