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: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 184x^{5} + 584x^{4} + 10145x^{3} - 34491x^{2} - 149754x + 524902 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(7.83842\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −6.83842 | −1.20887 | −0.604436 | − | 0.796653i | \(-0.706602\pi\) | ||||
−0.604436 | + | 0.796653i | \(0.706602\pi\) | |||||||
\(3\) | −24.5656 | −1.57588 | −0.787942 | − | 0.615750i | \(-0.788853\pi\) | ||||
−0.787942 | + | 0.615750i | \(0.788853\pi\) | |||||||
\(4\) | 14.7640 | 0.461374 | ||||||||
\(5\) | −54.3066 | −0.971467 | −0.485733 | − | 0.874107i | \(-0.661447\pi\) | ||||
−0.485733 | + | 0.874107i | \(0.661447\pi\) | |||||||
\(6\) | 167.990 | 1.90504 | ||||||||
\(7\) | −37.6697 | −0.290567 | −0.145284 | − | 0.989390i | \(-0.546409\pi\) | ||||
−0.145284 | + | 0.989390i | \(0.546409\pi\) | |||||||
\(8\) | 117.867 | 0.651131 | ||||||||
\(9\) | 360.469 | 1.48341 | ||||||||
\(10\) | 371.372 | 1.17438 | ||||||||
\(11\) | −146.903 | −0.366058 | −0.183029 | − | 0.983107i | \(-0.558590\pi\) | ||||
−0.183029 | + | 0.983107i | \(0.558590\pi\) | |||||||
\(12\) | −362.686 | −0.727072 | ||||||||
\(13\) | 162.581 | 0.266815 | 0.133408 | − | 0.991061i | \(-0.457408\pi\) | ||||
0.133408 | + | 0.991061i | \(0.457408\pi\) | |||||||
\(14\) | 257.601 | 0.351259 | ||||||||
\(15\) | 1334.08 | 1.53092 | ||||||||
\(16\) | −1278.47 | −1.24851 | ||||||||
\(17\) | −2162.70 | −1.81499 | −0.907493 | − | 0.420068i | \(-0.862006\pi\) | ||||
−0.907493 | + | 0.420068i | \(0.862006\pi\) | |||||||
\(18\) | −2465.04 | −1.79325 | ||||||||
\(19\) | 2494.06 | 1.58498 | 0.792489 | − | 0.609886i | \(-0.208785\pi\) | ||||
0.792489 | + | 0.609886i | \(0.208785\pi\) | |||||||
\(20\) | −801.781 | −0.448209 | ||||||||
\(21\) | 925.378 | 0.457900 | ||||||||
\(22\) | 1004.59 | 0.442518 | ||||||||
\(23\) | −122.601 | −0.0483251 | −0.0241626 | − | 0.999708i | \(-0.507692\pi\) | ||||
−0.0241626 | + | 0.999708i | \(0.507692\pi\) | |||||||
\(24\) | −2895.48 | −1.02611 | ||||||||
\(25\) | −175.788 | −0.0562522 | ||||||||
\(26\) | −1111.79 | −0.322546 | ||||||||
\(27\) | −2885.69 | −0.761798 | ||||||||
\(28\) | −556.154 | −0.134060 | ||||||||
\(29\) | 841.000 | 0.185695 | ||||||||
\(30\) | −9122.96 | −1.85069 | ||||||||
\(31\) | 8674.26 | 1.62117 | 0.810584 | − | 0.585622i | \(-0.199150\pi\) | ||||
0.810584 | + | 0.585622i | \(0.199150\pi\) | |||||||
\(32\) | 4970.98 | 0.858157 | ||||||||
\(33\) | 3608.77 | 0.576865 | ||||||||
\(34\) | 14789.4 | 2.19409 | ||||||||
\(35\) | 2045.71 | 0.282276 | ||||||||
\(36\) | 5321.95 | 0.684407 | ||||||||
\(37\) | 11752.8 | 1.41136 | 0.705679 | − | 0.708532i | \(-0.250642\pi\) | ||||
0.705679 | + | 0.708532i | \(0.250642\pi\) | |||||||
\(38\) | −17055.4 | −1.91604 | ||||||||
\(39\) | −3993.89 | −0.420470 | ||||||||
\(40\) | −6400.97 | −0.632552 | ||||||||
\(41\) | 9519.28 | 0.884391 | 0.442195 | − | 0.896919i | \(-0.354200\pi\) | ||||
0.442195 | + | 0.896919i | \(0.354200\pi\) | |||||||
\(42\) | −6328.12 | −0.553543 | ||||||||
\(43\) | −14834.7 | −1.22351 | −0.611756 | − | 0.791046i | \(-0.709537\pi\) | ||||
−0.611756 | + | 0.791046i | \(0.709537\pi\) | |||||||
\(44\) | −2168.88 | −0.168890 | ||||||||
\(45\) | −19575.8 | −1.44108 | ||||||||
\(46\) | 838.394 | 0.0584189 | ||||||||
\(47\) | −3827.35 | −0.252728 | −0.126364 | − | 0.991984i | \(-0.540331\pi\) | ||||
−0.126364 | + | 0.991984i | \(0.540331\pi\) | |||||||
\(48\) | 31406.4 | 1.96750 | ||||||||
\(49\) | −15388.0 | −0.915571 | ||||||||
\(50\) | 1202.11 | 0.0680017 | ||||||||
\(51\) | 53127.9 | 2.86021 | ||||||||
\(52\) | 2400.34 | 0.123102 | ||||||||
\(53\) | −33207.9 | −1.62387 | −0.811936 | − | 0.583746i | \(-0.801586\pi\) | ||||
−0.811936 | + | 0.583746i | \(0.801586\pi\) | |||||||
\(54\) | 19733.5 | 0.920917 | ||||||||
\(55\) | 7977.83 | 0.355613 | ||||||||
\(56\) | −4440.02 | −0.189197 | ||||||||
\(57\) | −61268.2 | −2.49774 | ||||||||
\(58\) | −5751.11 | −0.224482 | ||||||||
\(59\) | 19608.0 | 0.733336 | 0.366668 | − | 0.930352i | \(-0.380498\pi\) | ||||
0.366668 | + | 0.930352i | \(0.380498\pi\) | |||||||
\(60\) | 19696.2 | 0.706326 | ||||||||
\(61\) | 24024.9 | 0.826679 | 0.413340 | − | 0.910577i | \(-0.364362\pi\) | ||||
0.413340 | + | 0.910577i | \(0.364362\pi\) | |||||||
\(62\) | −59318.2 | −1.95979 | ||||||||
\(63\) | −13578.7 | −0.431030 | ||||||||
\(64\) | 6917.49 | 0.211105 | ||||||||
\(65\) | −8829.21 | −0.259202 | ||||||||
\(66\) | −24678.3 | −0.697357 | ||||||||
\(67\) | 55181.2 | 1.50177 | 0.750886 | − | 0.660432i | \(-0.229627\pi\) | ||||
0.750886 | + | 0.660432i | \(0.229627\pi\) | |||||||
\(68\) | −31930.0 | −0.837387 | ||||||||
\(69\) | 3011.76 | 0.0761548 | ||||||||
\(70\) | −13989.4 | −0.341236 | ||||||||
\(71\) | −41626.8 | −0.980002 | −0.490001 | − | 0.871722i | \(-0.663004\pi\) | ||||
−0.490001 | + | 0.871722i | \(0.663004\pi\) | |||||||
\(72\) | 42487.4 | 0.965894 | ||||||||
\(73\) | −15707.6 | −0.344987 | −0.172493 | − | 0.985011i | \(-0.555182\pi\) | ||||
−0.172493 | + | 0.985011i | \(0.555182\pi\) | |||||||
\(74\) | −80370.5 | −1.70615 | ||||||||
\(75\) | 4318.34 | 0.0886469 | ||||||||
\(76\) | 36822.3 | 0.731268 | ||||||||
\(77\) | 5533.80 | 0.106365 | ||||||||
\(78\) | 27311.9 | 0.508295 | ||||||||
\(79\) | 56772.8 | 1.02346 | 0.511732 | − | 0.859145i | \(-0.329004\pi\) | ||||
0.511732 | + | 0.859145i | \(0.329004\pi\) | |||||||
\(80\) | 69429.5 | 1.21288 | ||||||||
\(81\) | −16705.2 | −0.282905 | ||||||||
\(82\) | −65096.8 | −1.06912 | ||||||||
\(83\) | 107406. | 1.71133 | 0.855664 | − | 0.517532i | \(-0.173149\pi\) | ||||
0.855664 | + | 0.517532i | \(0.173149\pi\) | |||||||
\(84\) | 13662.2 | 0.211263 | ||||||||
\(85\) | 117449. | 1.76320 | ||||||||
\(86\) | 101446. | 1.47907 | ||||||||
\(87\) | −20659.7 | −0.292634 | ||||||||
\(88\) | −17315.1 | −0.238352 | ||||||||
\(89\) | 37615.4 | 0.503374 | 0.251687 | − | 0.967809i | \(-0.419015\pi\) | ||||
0.251687 | + | 0.967809i | \(0.419015\pi\) | |||||||
\(90\) | 133868. | 1.74209 | ||||||||
\(91\) | −6124.36 | −0.0775278 | ||||||||
\(92\) | −1810.07 | −0.0222960 | ||||||||
\(93\) | −213088. | −2.55477 | ||||||||
\(94\) | 26173.0 | 0.305516 | ||||||||
\(95\) | −135444. | −1.53975 | ||||||||
\(96\) | −122115. | −1.35236 | ||||||||
\(97\) | −43944.4 | −0.474214 | −0.237107 | − | 0.971484i | \(-0.576199\pi\) | ||||
−0.237107 | + | 0.971484i | \(0.576199\pi\) | |||||||
\(98\) | 105230. | 1.10681 | ||||||||
\(99\) | −52954.1 | −0.543014 | ||||||||
\(100\) | −2595.33 | −0.0259533 | ||||||||
\(101\) | 71165.6 | 0.694171 | 0.347086 | − | 0.937833i | \(-0.387171\pi\) | ||||
0.347086 | + | 0.937833i | \(0.387171\pi\) | |||||||
\(102\) | −363311. | −3.45763 | ||||||||
\(103\) | −36173.8 | −0.335970 | −0.167985 | − | 0.985790i | \(-0.553726\pi\) | ||||
−0.167985 | + | 0.985790i | \(0.553726\pi\) | |||||||
\(104\) | 19162.9 | 0.173732 | ||||||||
\(105\) | −50254.2 | −0.444835 | ||||||||
\(106\) | 227090. | 1.96306 | ||||||||
\(107\) | 44407.3 | 0.374969 | 0.187484 | − | 0.982268i | \(-0.439967\pi\) | ||||
0.187484 | + | 0.982268i | \(0.439967\pi\) | |||||||
\(108\) | −42604.2 | −0.351474 | ||||||||
\(109\) | −142245. | −1.14676 | −0.573379 | − | 0.819290i | \(-0.694368\pi\) | ||||
−0.573379 | + | 0.819290i | \(0.694368\pi\) | |||||||
\(110\) | −54555.8 | −0.429891 | ||||||||
\(111\) | −288715. | −2.22414 | ||||||||
\(112\) | 48159.6 | 0.362776 | ||||||||
\(113\) | 29934.7 | 0.220536 | 0.110268 | − | 0.993902i | \(-0.464829\pi\) | ||||
0.110268 | + | 0.993902i | \(0.464829\pi\) | |||||||
\(114\) | 418977. | 3.01945 | ||||||||
\(115\) | 6658.03 | 0.0469463 | ||||||||
\(116\) | 12416.5 | 0.0856750 | ||||||||
\(117\) | 58605.2 | 0.395796 | ||||||||
\(118\) | −134088. | −0.886510 | ||||||||
\(119\) | 81468.0 | 0.527375 | ||||||||
\(120\) | 157244. | 0.996828 | ||||||||
\(121\) | −139470. | −0.866001 | ||||||||
\(122\) | −164292. | −0.999350 | ||||||||
\(123\) | −233847. | −1.39370 | ||||||||
\(124\) | 128066. | 0.747965 | ||||||||
\(125\) | 179255. | 1.02611 | ||||||||
\(126\) | 92857.1 | 0.521061 | ||||||||
\(127\) | 219282. | 1.20641 | 0.603204 | − | 0.797587i | \(-0.293890\pi\) | ||||
0.603204 | + | 0.797587i | \(0.293890\pi\) | |||||||
\(128\) | −206376. | −1.11336 | ||||||||
\(129\) | 364424. | 1.92811 | ||||||||
\(130\) | 60377.8 | 0.313342 | ||||||||
\(131\) | 207170. | 1.05475 | 0.527374 | − | 0.849633i | \(-0.323177\pi\) | ||||
0.527374 | + | 0.849633i | \(0.323177\pi\) | |||||||
\(132\) | 53279.8 | 0.266151 | ||||||||
\(133\) | −93950.5 | −0.460543 | ||||||||
\(134\) | −377352. | −1.81545 | ||||||||
\(135\) | 156712. | 0.740062 | ||||||||
\(136\) | −254911. | −1.18179 | ||||||||
\(137\) | 11815.8 | 0.0537852 | 0.0268926 | − | 0.999638i | \(-0.491439\pi\) | ||||
0.0268926 | + | 0.999638i | \(0.491439\pi\) | |||||||
\(138\) | −20595.7 | −0.0920615 | ||||||||
\(139\) | −51342.5 | −0.225393 | −0.112696 | − | 0.993629i | \(-0.535949\pi\) | ||||
−0.112696 | + | 0.993629i | \(0.535949\pi\) | |||||||
\(140\) | 30202.8 | 0.130235 | ||||||||
\(141\) | 94021.2 | 0.398270 | ||||||||
\(142\) | 284661. | 1.18470 | ||||||||
\(143\) | −23883.7 | −0.0976699 | ||||||||
\(144\) | −460849. | −1.85205 | ||||||||
\(145\) | −45671.9 | −0.180397 | ||||||||
\(146\) | 107415. | 0.417045 | ||||||||
\(147\) | 378015. | 1.44283 | ||||||||
\(148\) | 173518. | 0.651163 | ||||||||
\(149\) | 159538. | 0.588707 | 0.294353 | − | 0.955697i | \(-0.404896\pi\) | ||||
0.294353 | + | 0.955697i | \(0.404896\pi\) | |||||||
\(150\) | −29530.6 | −0.107163 | ||||||||
\(151\) | 64145.0 | 0.228939 | 0.114470 | − | 0.993427i | \(-0.463483\pi\) | ||||
0.114470 | + | 0.993427i | \(0.463483\pi\) | |||||||
\(152\) | 293968. | 1.03203 | ||||||||
\(153\) | −779584. | −2.69237 | ||||||||
\(154\) | −37842.5 | −0.128581 | ||||||||
\(155\) | −471070. | −1.57491 | ||||||||
\(156\) | −58965.7 | −0.193994 | ||||||||
\(157\) | 556965. | 1.80335 | 0.901673 | − | 0.432419i | \(-0.142340\pi\) | ||||
0.901673 | + | 0.432419i | \(0.142340\pi\) | |||||||
\(158\) | −388236. | −1.23724 | ||||||||
\(159\) | 815772. | 2.55903 | ||||||||
\(160\) | −269957. | −0.833671 | ||||||||
\(161\) | 4618.32 | 0.0140417 | ||||||||
\(162\) | 114237. | 0.341996 | ||||||||
\(163\) | −175236. | −0.516599 | −0.258299 | − | 0.966065i | \(-0.583162\pi\) | ||||
−0.258299 | + | 0.966065i | \(0.583162\pi\) | |||||||
\(164\) | 140542. | 0.408035 | ||||||||
\(165\) | −195980. | −0.560406 | ||||||||
\(166\) | −734487. | −2.06878 | ||||||||
\(167\) | 464707. | 1.28940 | 0.644700 | − | 0.764436i | \(-0.276982\pi\) | ||||
0.644700 | + | 0.764436i | \(0.276982\pi\) | |||||||
\(168\) | 109072. | 0.298153 | ||||||||
\(169\) | −344861. | −0.928810 | ||||||||
\(170\) | −803164. | −2.13148 | ||||||||
\(171\) | 899031. | 2.35117 | ||||||||
\(172\) | −219019. | −0.564497 | ||||||||
\(173\) | −92110.9 | −0.233989 | −0.116995 | − | 0.993133i | \(-0.537326\pi\) | ||||
−0.116995 | + | 0.993133i | \(0.537326\pi\) | |||||||
\(174\) | 141279. | 0.353758 | ||||||||
\(175\) | 6621.88 | 0.0163450 | ||||||||
\(176\) | 187812. | 0.457027 | ||||||||
\(177\) | −481682. | −1.15565 | ||||||||
\(178\) | −257230. | −0.608516 | ||||||||
\(179\) | 46322.2 | 0.108058 | 0.0540290 | − | 0.998539i | \(-0.482794\pi\) | ||||
0.0540290 | + | 0.998539i | \(0.482794\pi\) | |||||||
\(180\) | −289017. | −0.664878 | ||||||||
\(181\) | 118183. | 0.268139 | 0.134069 | − | 0.990972i | \(-0.457196\pi\) | ||||
0.134069 | + | 0.990972i | \(0.457196\pi\) | |||||||
\(182\) | 41880.9 | 0.0937212 | ||||||||
\(183\) | −590186. | −1.30275 | ||||||||
\(184\) | −14450.6 | −0.0314660 | ||||||||
\(185\) | −638255. | −1.37109 | ||||||||
\(186\) | 1.45719e6 | 3.08840 | ||||||||
\(187\) | 317707. | 0.664390 | ||||||||
\(188\) | −56506.9 | −0.116602 | ||||||||
\(189\) | 108703. | 0.221354 | ||||||||
\(190\) | 926224. | 1.86137 | ||||||||
\(191\) | −349094. | −0.692404 | −0.346202 | − | 0.938160i | \(-0.612529\pi\) | ||||
−0.346202 | + | 0.938160i | \(0.612529\pi\) | |||||||
\(192\) | −169932. | −0.332677 | ||||||||
\(193\) | −128726. | −0.248756 | −0.124378 | − | 0.992235i | \(-0.539694\pi\) | ||||
−0.124378 | + | 0.992235i | \(0.539694\pi\) | |||||||
\(194\) | 300510. | 0.573264 | ||||||||
\(195\) | 216895. | 0.408472 | ||||||||
\(196\) | −227188. | −0.422420 | ||||||||
\(197\) | 615954. | 1.13079 | 0.565396 | − | 0.824820i | \(-0.308724\pi\) | ||||
0.565396 | + | 0.824820i | \(0.308724\pi\) | |||||||
\(198\) | 362122. | 0.656436 | ||||||||
\(199\) | −333500. | −0.596985 | −0.298492 | − | 0.954412i | \(-0.596484\pi\) | ||||
−0.298492 | + | 0.954412i | \(0.596484\pi\) | |||||||
\(200\) | −20719.7 | −0.0366275 | ||||||||
\(201\) | −1.35556e6 | −2.36662 | ||||||||
\(202\) | −486660. | −0.839165 | ||||||||
\(203\) | −31680.2 | −0.0539570 | ||||||||
\(204\) | 784379. | 1.31962 | ||||||||
\(205\) | −516960. | −0.859156 | ||||||||
\(206\) | 247371. | 0.406145 | ||||||||
\(207\) | −44193.7 | −0.0716860 | ||||||||
\(208\) | −207855. | −0.333121 | ||||||||
\(209\) | −366386. | −0.580195 | ||||||||
\(210\) | 343659. | 0.537749 | ||||||||
\(211\) | 246416. | 0.381033 | 0.190516 | − | 0.981684i | \(-0.438984\pi\) | ||||
0.190516 | + | 0.981684i | \(0.438984\pi\) | |||||||
\(212\) | −490280. | −0.749212 | ||||||||
\(213\) | 1.02259e6 | 1.54437 | ||||||||
\(214\) | −303676. | −0.453290 | ||||||||
\(215\) | 805624. | 1.18860 | ||||||||
\(216\) | −340128. | −0.496030 | ||||||||
\(217\) | −326756. | −0.471058 | ||||||||
\(218\) | 972733. | 1.38628 | ||||||||
\(219\) | 385866. | 0.543659 | ||||||||
\(220\) | 117784. | 0.164071 | ||||||||
\(221\) | −351613. | −0.484266 | ||||||||
\(222\) | 1.97435e6 | 2.68870 | ||||||||
\(223\) | −275147. | −0.370512 | −0.185256 | − | 0.982690i | \(-0.559311\pi\) | ||||
−0.185256 | + | 0.982690i | \(0.559311\pi\) | |||||||
\(224\) | −187255. | −0.249352 | ||||||||
\(225\) | −63366.1 | −0.0834451 | ||||||||
\(226\) | −204706. | −0.266600 | ||||||||
\(227\) | −461856. | −0.594897 | −0.297448 | − | 0.954738i | \(-0.596136\pi\) | ||||
−0.297448 | + | 0.954738i | \(0.596136\pi\) | |||||||
\(228\) | −904561. | −1.15239 | ||||||||
\(229\) | −311105. | −0.392029 | −0.196015 | − | 0.980601i | \(-0.562800\pi\) | ||||
−0.196015 | + | 0.980601i | \(0.562800\pi\) | |||||||
\(230\) | −45530.4 | −0.0567521 | ||||||||
\(231\) | −135941. | −0.167618 | ||||||||
\(232\) | 99126.3 | 0.120912 | ||||||||
\(233\) | 1.52969e6 | 1.84592 | 0.922962 | − | 0.384891i | \(-0.125761\pi\) | ||||
0.922962 | + | 0.384891i | \(0.125761\pi\) | |||||||
\(234\) | −400767. | −0.478467 | ||||||||
\(235\) | 207851. | 0.245517 | ||||||||
\(236\) | 289492. | 0.338342 | ||||||||
\(237\) | −1.39466e6 | −1.61286 | ||||||||
\(238\) | −557113. | −0.637530 | ||||||||
\(239\) | 1.21977e6 | 1.38129 | 0.690644 | − | 0.723195i | \(-0.257327\pi\) | ||||
0.690644 | + | 0.723195i | \(0.257327\pi\) | |||||||
\(240\) | −1.70558e6 | −1.91136 | ||||||||
\(241\) | 563284. | 0.624719 | 0.312360 | − | 0.949964i | \(-0.398881\pi\) | ||||
0.312360 | + | 0.949964i | \(0.398881\pi\) | |||||||
\(242\) | 953757. | 1.04689 | ||||||||
\(243\) | 1.11160e6 | 1.20762 | ||||||||
\(244\) | 354703. | 0.381408 | ||||||||
\(245\) | 835670. | 0.889447 | ||||||||
\(246\) | 1.59914e6 | 1.68480 | ||||||||
\(247\) | 405486. | 0.422896 | ||||||||
\(248\) | 1.02241e6 | 1.05559 | ||||||||
\(249\) | −2.63849e6 | −2.69685 | ||||||||
\(250\) | −1.22582e6 | −1.24044 | ||||||||
\(251\) | −1.52639e6 | −1.52926 | −0.764629 | − | 0.644470i | \(-0.777078\pi\) | ||||
−0.764629 | + | 0.644470i | \(0.777078\pi\) | |||||||
\(252\) | −200476. | −0.198866 | ||||||||
\(253\) | 18010.4 | 0.0176898 | ||||||||
\(254\) | −1.49954e6 | −1.45839 | ||||||||
\(255\) | −2.88520e6 | −2.77860 | ||||||||
\(256\) | 1.18993e6 | 1.13480 | ||||||||
\(257\) | 197606. | 0.186624 | 0.0933121 | − | 0.995637i | \(-0.470255\pi\) | ||||
0.0933121 | + | 0.995637i | \(0.470255\pi\) | |||||||
\(258\) | −2.49208e6 | −2.33084 | ||||||||
\(259\) | −442724. | −0.410094 | ||||||||
\(260\) | −130354. | −0.119589 | ||||||||
\(261\) | 303154. | 0.275462 | ||||||||
\(262\) | −1.41671e6 | −1.27506 | ||||||||
\(263\) | −2.03558e6 | −1.81468 | −0.907339 | − | 0.420400i | \(-0.861890\pi\) | ||||
−0.907339 | + | 0.420400i | \(0.861890\pi\) | |||||||
\(264\) | 425356. | 0.375615 | ||||||||
\(265\) | 1.80341e6 | 1.57754 | ||||||||
\(266\) | 642473. | 0.556738 | ||||||||
\(267\) | −924046. | −0.793260 | ||||||||
\(268\) | 814693. | 0.692878 | ||||||||
\(269\) | −728283. | −0.613648 | −0.306824 | − | 0.951766i | \(-0.599266\pi\) | ||||
−0.306824 | + | 0.951766i | \(0.599266\pi\) | |||||||
\(270\) | −1.07166e6 | −0.894640 | ||||||||
\(271\) | −878997. | −0.727049 | −0.363525 | − | 0.931585i | \(-0.618427\pi\) | ||||
−0.363525 | + | 0.931585i | \(0.618427\pi\) | |||||||
\(272\) | 2.76495e6 | 2.26602 | ||||||||
\(273\) | 150449. | 0.122175 | ||||||||
\(274\) | −80801.6 | −0.0650195 | ||||||||
\(275\) | 25823.9 | 0.0205916 | ||||||||
\(276\) | 44465.5 | 0.0351358 | ||||||||
\(277\) | −981143. | −0.768304 | −0.384152 | − | 0.923270i | \(-0.625506\pi\) | ||||
−0.384152 | + | 0.923270i | \(0.625506\pi\) | |||||||
\(278\) | 351102. | 0.272471 | ||||||||
\(279\) | 3.12680e6 | 2.40486 | ||||||||
\(280\) | 241123. | 0.183799 | ||||||||
\(281\) | 1.45423e6 | 1.09867 | 0.549333 | − | 0.835603i | \(-0.314882\pi\) | ||||
0.549333 | + | 0.835603i | \(0.314882\pi\) | |||||||
\(282\) | −642956. | −0.481458 | ||||||||
\(283\) | 1.81952e6 | 1.35049 | 0.675243 | − | 0.737595i | \(-0.264039\pi\) | ||||
0.675243 | + | 0.737595i | \(0.264039\pi\) | |||||||
\(284\) | −614576. | −0.452147 | ||||||||
\(285\) | 3.32727e6 | 2.42647 | ||||||||
\(286\) | 163326. | 0.118070 | ||||||||
\(287\) | −358588. | −0.256975 | ||||||||
\(288\) | 1.79188e6 | 1.27300 | ||||||||
\(289\) | 3.25740e6 | 2.29417 | ||||||||
\(290\) | 312323. | 0.218077 | ||||||||
\(291\) | 1.07952e6 | 0.747306 | ||||||||
\(292\) | −231906. | −0.159168 | ||||||||
\(293\) | 279641. | 0.190297 | 0.0951484 | − | 0.995463i | \(-0.469667\pi\) | ||||
0.0951484 | + | 0.995463i | \(0.469667\pi\) | |||||||
\(294\) | −2.58503e6 | −1.74420 | ||||||||
\(295\) | −1.06484e6 | −0.712412 | ||||||||
\(296\) | 1.38527e6 | 0.918978 | ||||||||
\(297\) | 423917. | 0.278862 | ||||||||
\(298\) | −1.09099e6 | −0.711672 | ||||||||
\(299\) | −19932.5 | −0.0128939 | ||||||||
\(300\) | 63755.8 | 0.0408994 | ||||||||
\(301\) | 558819. | 0.355513 | ||||||||
\(302\) | −438650. | −0.276759 | ||||||||
\(303\) | −1.74823e6 | −1.09393 | ||||||||
\(304\) | −3.18859e6 | −1.97886 | ||||||||
\(305\) | −1.30471e6 | −0.803091 | ||||||||
\(306\) | 5.33112e6 | 3.25473 | ||||||||
\(307\) | −1.65629e6 | −1.00297 | −0.501487 | − | 0.865165i | \(-0.667214\pi\) | ||||
−0.501487 | + | 0.865165i | \(0.667214\pi\) | |||||||
\(308\) | 81700.9 | 0.0490738 | ||||||||
\(309\) | 888630. | 0.529450 | ||||||||
\(310\) | 3.22137e6 | 1.90387 | ||||||||
\(311\) | −1.33517e6 | −0.782771 | −0.391386 | − | 0.920227i | \(-0.628004\pi\) | ||||
−0.391386 | + | 0.920227i | \(0.628004\pi\) | |||||||
\(312\) | −470749. | −0.273781 | ||||||||
\(313\) | −2.25773e6 | −1.30260 | −0.651300 | − | 0.758821i | \(-0.725776\pi\) | ||||
−0.651300 | + | 0.758821i | \(0.725776\pi\) | |||||||
\(314\) | −3.80876e6 | −2.18002 | ||||||||
\(315\) | 737416. | 0.418732 | ||||||||
\(316\) | 838191. | 0.472199 | ||||||||
\(317\) | 2.76702e6 | 1.54655 | 0.773274 | − | 0.634072i | \(-0.218618\pi\) | ||||
0.773274 | + | 0.634072i | \(0.218618\pi\) | |||||||
\(318\) | −5.57859e6 | −3.09355 | ||||||||
\(319\) | −123546. | −0.0679753 | ||||||||
\(320\) | −375666. | −0.205082 | ||||||||
\(321\) | −1.09089e6 | −0.590907 | ||||||||
\(322\) | −31582.0 | −0.0169746 | ||||||||
\(323\) | −5.39390e6 | −2.87671 | ||||||||
\(324\) | −246636. | −0.130525 | ||||||||
\(325\) | −28579.7 | −0.0150089 | ||||||||
\(326\) | 1.19833e6 | 0.624503 | ||||||||
\(327\) | 3.49434e6 | 1.80716 | ||||||||
\(328\) | 1.12201e6 | 0.575854 | ||||||||
\(329\) | 144175. | 0.0734346 | ||||||||
\(330\) | 1.34019e6 | 0.677459 | ||||||||
\(331\) | 1.50762e6 | 0.756350 | 0.378175 | − | 0.925734i | \(-0.376552\pi\) | ||||
0.378175 | + | 0.925734i | \(0.376552\pi\) | |||||||
\(332\) | 1.58574e6 | 0.789562 | ||||||||
\(333\) | 4.23652e6 | 2.09362 | ||||||||
\(334\) | −3.17786e6 | −1.55872 | ||||||||
\(335\) | −2.99670e6 | −1.45892 | ||||||||
\(336\) | −1.18307e6 | −0.571692 | ||||||||
\(337\) | 2.65301e6 | 1.27252 | 0.636259 | − | 0.771476i | \(-0.280481\pi\) | ||||
0.636259 | + | 0.771476i | \(0.280481\pi\) | |||||||
\(338\) | 2.35830e6 | 1.12281 | ||||||||
\(339\) | −735364. | −0.347539 | ||||||||
\(340\) | 1.73401e6 | 0.813493 | ||||||||
\(341\) | −1.27428e6 | −0.593442 | ||||||||
\(342\) | −6.14795e6 | −2.84227 | ||||||||
\(343\) | 1.21277e6 | 0.556602 | ||||||||
\(344\) | −1.74853e6 | −0.796666 | ||||||||
\(345\) | −163558. | −0.0739818 | ||||||||
\(346\) | 629893. | 0.282863 | ||||||||
\(347\) | −1.30221e6 | −0.580574 | −0.290287 | − | 0.956940i | \(-0.593751\pi\) | ||||
−0.290287 | + | 0.956940i | \(0.593751\pi\) | |||||||
\(348\) | −305019. | −0.135014 | ||||||||
\(349\) | −1.20351e6 | −0.528914 | −0.264457 | − | 0.964397i | \(-0.585193\pi\) | ||||
−0.264457 | + | 0.964397i | \(0.585193\pi\) | |||||||
\(350\) | −45283.2 | −0.0197591 | ||||||||
\(351\) | −469157. | −0.203259 | ||||||||
\(352\) | −730253. | −0.314135 | ||||||||
\(353\) | −1.97691e6 | −0.844404 | −0.422202 | − | 0.906502i | \(-0.638743\pi\) | ||||
−0.422202 | + | 0.906502i | \(0.638743\pi\) | |||||||
\(354\) | 3.29394e6 | 1.39704 | ||||||||
\(355\) | 2.26061e6 | 0.952039 | ||||||||
\(356\) | 555353. | 0.232244 | ||||||||
\(357\) | −2.00131e6 | −0.831082 | ||||||||
\(358\) | −316771. | −0.130628 | ||||||||
\(359\) | −2.29106e6 | −0.938209 | −0.469105 | − | 0.883143i | \(-0.655423\pi\) | ||||
−0.469105 | + | 0.883143i | \(0.655423\pi\) | |||||||
\(360\) | −2.30735e6 | −0.938334 | ||||||||
\(361\) | 3.74425e6 | 1.51216 | ||||||||
\(362\) | −808187. | −0.324146 | ||||||||
\(363\) | 3.42617e6 | 1.36472 | ||||||||
\(364\) | −90419.8 | −0.0357693 | ||||||||
\(365\) | 853027. | 0.335143 | ||||||||
\(366\) | 4.03594e6 | 1.57486 | ||||||||
\(367\) | 755682. | 0.292869 | 0.146435 | − | 0.989220i | \(-0.453220\pi\) | ||||
0.146435 | + | 0.989220i | \(0.453220\pi\) | |||||||
\(368\) | 156741. | 0.0603343 | ||||||||
\(369\) | 3.43140e6 | 1.31191 | ||||||||
\(370\) | 4.36466e6 | 1.65747 | ||||||||
\(371\) | 1.25093e6 | 0.471844 | ||||||||
\(372\) | −3.14603e6 | −1.17871 | ||||||||
\(373\) | −4.45947e6 | −1.65963 | −0.829815 | − | 0.558038i | \(-0.811554\pi\) | ||||
−0.829815 | + | 0.558038i | \(0.811554\pi\) | |||||||
\(374\) | −2.17262e6 | −0.803164 | ||||||||
\(375\) | −4.40350e6 | −1.61704 | ||||||||
\(376\) | −451119. | −0.164559 | ||||||||
\(377\) | 136730. | 0.0495463 | ||||||||
\(378\) | −743356. | −0.267588 | ||||||||
\(379\) | 4.02987e6 | 1.44109 | 0.720547 | − | 0.693406i | \(-0.243891\pi\) | ||||
0.720547 | + | 0.693406i | \(0.243891\pi\) | |||||||
\(380\) | −1.99969e6 | −0.710402 | ||||||||
\(381\) | −5.38680e6 | −1.90116 | ||||||||
\(382\) | 2.38725e6 | 0.837028 | ||||||||
\(383\) | 4.12660e6 | 1.43746 | 0.718729 | − | 0.695291i | \(-0.244724\pi\) | ||||
0.718729 | + | 0.695291i | \(0.244724\pi\) | |||||||
\(384\) | 5.06975e6 | 1.75452 | ||||||||
\(385\) | −300522. | −0.103330 | ||||||||
\(386\) | 880284. | 0.300715 | ||||||||
\(387\) | −5.34745e6 | −1.81497 | ||||||||
\(388\) | −648793. | −0.218790 | ||||||||
\(389\) | −1.37522e6 | −0.460784 | −0.230392 | − | 0.973098i | \(-0.574001\pi\) | ||||
−0.230392 | + | 0.973098i | \(0.574001\pi\) | |||||||
\(390\) | −1.48322e6 | −0.493791 | ||||||||
\(391\) | 265148. | 0.0877094 | ||||||||
\(392\) | −1.81374e6 | −0.596156 | ||||||||
\(393\) | −5.08925e6 | −1.66216 | ||||||||
\(394\) | −4.21215e6 | −1.36698 | ||||||||
\(395\) | −3.08314e6 | −0.994261 | ||||||||
\(396\) | −781812. | −0.250533 | ||||||||
\(397\) | 3.95058e6 | 1.25801 | 0.629006 | − | 0.777400i | \(-0.283462\pi\) | ||||
0.629006 | + | 0.777400i | \(0.283462\pi\) | |||||||
\(398\) | 2.28061e6 | 0.721679 | ||||||||
\(399\) | 2.30795e6 | 0.725762 | ||||||||
\(400\) | 224740. | 0.0702313 | ||||||||
\(401\) | 601236. | 0.186717 | 0.0933585 | − | 0.995633i | \(-0.470240\pi\) | ||||
0.0933585 | + | 0.995633i | \(0.470240\pi\) | |||||||
\(402\) | 9.26988e6 | 2.86094 | ||||||||
\(403\) | 1.41027e6 | 0.432552 | ||||||||
\(404\) | 1.05069e6 | 0.320272 | ||||||||
\(405\) | 907205. | 0.274832 | ||||||||
\(406\) | 216642. | 0.0652272 | ||||||||
\(407\) | −1.72653e6 | −0.516639 | ||||||||
\(408\) | 6.26204e6 | 1.86237 | ||||||||
\(409\) | 6.38666e6 | 1.88784 | 0.943921 | − | 0.330171i | \(-0.107106\pi\) | ||||
0.943921 | + | 0.330171i | \(0.107106\pi\) | |||||||
\(410\) | 3.53519e6 | 1.03861 | ||||||||
\(411\) | −290263. | −0.0847593 | ||||||||
\(412\) | −534068. | −0.155008 | ||||||||
\(413\) | −738627. | −0.213084 | ||||||||
\(414\) | 302215. | 0.0866592 | ||||||||
\(415\) | −5.83286e6 | −1.66250 | ||||||||
\(416\) | 808185. | 0.228969 | ||||||||
\(417\) | 1.26126e6 | 0.355193 | ||||||||
\(418\) | 2.50550e6 | 0.701381 | ||||||||
\(419\) | 4.44705e6 | 1.23748 | 0.618738 | − | 0.785597i | \(-0.287644\pi\) | ||||
0.618738 | + | 0.785597i | \(0.287644\pi\) | |||||||
\(420\) | −741951. | −0.205235 | ||||||||
\(421\) | 413525. | 0.113710 | 0.0568548 | − | 0.998382i | \(-0.481893\pi\) | ||||
0.0568548 | + | 0.998382i | \(0.481893\pi\) | |||||||
\(422\) | −1.68509e6 | −0.460620 | ||||||||
\(423\) | −1.37964e6 | −0.374900 | ||||||||
\(424\) | −3.91412e6 | −1.05735 | ||||||||
\(425\) | 380176. | 0.102097 | ||||||||
\(426\) | −6.99288e6 | −1.86695 | ||||||||
\(427\) | −905010. | −0.240206 | ||||||||
\(428\) | 655628. | 0.173001 | ||||||||
\(429\) | 586716. | 0.153916 | ||||||||
\(430\) | −5.50920e6 | −1.43687 | ||||||||
\(431\) | −3.32051e6 | −0.861016 | −0.430508 | − | 0.902587i | \(-0.641666\pi\) | ||||
−0.430508 | + | 0.902587i | \(0.641666\pi\) | |||||||
\(432\) | 3.68927e6 | 0.951111 | ||||||||
\(433\) | 1.14444e6 | 0.293341 | 0.146670 | − | 0.989185i | \(-0.453144\pi\) | ||||
0.146670 | + | 0.989185i | \(0.453144\pi\) | |||||||
\(434\) | 2.23450e6 | 0.569450 | ||||||||
\(435\) | 1.12196e6 | 0.284285 | ||||||||
\(436\) | −2.10011e6 | −0.529084 | ||||||||
\(437\) | −305774. | −0.0765943 | ||||||||
\(438\) | −2.63872e6 | −0.657215 | ||||||||
\(439\) | 900181. | 0.222930 | 0.111465 | − | 0.993768i | \(-0.464446\pi\) | ||||
0.111465 | + | 0.993768i | \(0.464446\pi\) | |||||||
\(440\) | 940325. | 0.231551 | ||||||||
\(441\) | −5.54689e6 | −1.35817 | ||||||||
\(442\) | 2.40447e6 | 0.585416 | ||||||||
\(443\) | 3.62823e6 | 0.878386 | 0.439193 | − | 0.898393i | \(-0.355264\pi\) | ||||
0.439193 | + | 0.898393i | \(0.355264\pi\) | |||||||
\(444\) | −4.26257e6 | −1.02616 | ||||||||
\(445\) | −2.04277e6 | −0.489012 | ||||||||
\(446\) | 1.88157e6 | 0.447902 | ||||||||
\(447\) | −3.91915e6 | −0.927733 | ||||||||
\(448\) | −260580. | −0.0613403 | ||||||||
\(449\) | −2.10851e6 | −0.493583 | −0.246791 | − | 0.969069i | \(-0.579376\pi\) | ||||
−0.246791 | + | 0.969069i | \(0.579376\pi\) | |||||||
\(450\) | 433324. | 0.100874 | ||||||||
\(451\) | −1.39841e6 | −0.323739 | ||||||||
\(452\) | 441955. | 0.101749 | ||||||||
\(453\) | −1.57576e6 | −0.360782 | ||||||||
\(454\) | 3.15836e6 | 0.719155 | ||||||||
\(455\) | 332593. | 0.0753157 | ||||||||
\(456\) | −7.22151e6 | −1.62636 | ||||||||
\(457\) | 157338. | 0.0352407 | 0.0176203 | − | 0.999845i | \(-0.494391\pi\) | ||||
0.0176203 | + | 0.999845i | \(0.494391\pi\) | |||||||
\(458\) | 2.12747e6 | 0.473914 | ||||||||
\(459\) | 6.24086e6 | 1.38265 | ||||||||
\(460\) | 98298.9 | 0.0216598 | ||||||||
\(461\) | −79527.0 | −0.0174286 | −0.00871429 | − | 0.999962i | \(-0.502774\pi\) | ||||
−0.00871429 | + | 0.999962i | \(0.502774\pi\) | |||||||
\(462\) | 929623. | 0.202629 | ||||||||
\(463\) | 421922. | 0.0914703 | 0.0457352 | − | 0.998954i | \(-0.485437\pi\) | ||||
0.0457352 | + | 0.998954i | \(0.485437\pi\) | |||||||
\(464\) | −1.07520e6 | −0.231842 | ||||||||
\(465\) | 1.15721e7 | 2.48188 | ||||||||
\(466\) | −1.04607e7 | −2.23149 | ||||||||
\(467\) | 3.56062e6 | 0.755498 | 0.377749 | − | 0.925908i | \(-0.376698\pi\) | ||||
0.377749 | + | 0.925908i | \(0.376698\pi\) | |||||||
\(468\) | 865246. | 0.182610 | ||||||||
\(469\) | −2.07866e6 | −0.436366 | ||||||||
\(470\) | −1.42137e6 | −0.296799 | ||||||||
\(471\) | −1.36822e7 | −2.84186 | ||||||||
\(472\) | 2.31114e6 | 0.477498 | ||||||||
\(473\) | 2.17927e6 | 0.447877 | ||||||||
\(474\) | 9.53725e6 | 1.94974 | ||||||||
\(475\) | −438427. | −0.0891585 | ||||||||
\(476\) | 1.20279e6 | 0.243317 | ||||||||
\(477\) | −1.19704e7 | −2.40887 | ||||||||
\(478\) | −8.34132e6 | −1.66980 | ||||||||
\(479\) | 3.58247e6 | 0.713417 | 0.356708 | − | 0.934216i | \(-0.383899\pi\) | ||||
0.356708 | + | 0.934216i | \(0.383899\pi\) | |||||||
\(480\) | 6.63166e6 | 1.31377 | ||||||||
\(481\) | 1.91078e6 | 0.376572 | ||||||||
\(482\) | −3.85197e6 | −0.755206 | ||||||||
\(483\) | −113452. | −0.0221281 | ||||||||
\(484\) | −2.05914e6 | −0.399550 | ||||||||
\(485\) | 2.38647e6 | 0.460683 | ||||||||
\(486\) | −7.60156e6 | −1.45986 | ||||||||
\(487\) | 8.65020e6 | 1.65274 | 0.826368 | − | 0.563130i | \(-0.190403\pi\) | ||||
0.826368 | + | 0.563130i | \(0.190403\pi\) | |||||||
\(488\) | 2.83175e6 | 0.538276 | ||||||||
\(489\) | 4.30477e6 | 0.814100 | ||||||||
\(490\) | −5.71466e6 | −1.07523 | ||||||||
\(491\) | 146402. | 0.0274059 | 0.0137030 | − | 0.999906i | \(-0.495638\pi\) | ||||
0.0137030 | + | 0.999906i | \(0.495638\pi\) | |||||||
\(492\) | −3.45250e6 | −0.643016 | ||||||||
\(493\) | −1.81883e6 | −0.337034 | ||||||||
\(494\) | −2.77289e6 | −0.511228 | ||||||||
\(495\) | 2.87576e6 | 0.527521 | ||||||||
\(496\) | −1.10898e7 | −2.02404 | ||||||||
\(497\) | 1.56807e6 | 0.284756 | ||||||||
\(498\) | 1.80431e7 | 3.26015 | ||||||||
\(499\) | −4.24620e6 | −0.763394 | −0.381697 | − | 0.924287i | \(-0.624660\pi\) | ||||
−0.381697 | + | 0.924287i | \(0.624660\pi\) | |||||||
\(500\) | 2.64651e6 | 0.473422 | ||||||||
\(501\) | −1.14158e7 | −2.03194 | ||||||||
\(502\) | 1.04381e7 | 1.84868 | ||||||||
\(503\) | 2.20106e6 | 0.387892 | 0.193946 | − | 0.981012i | \(-0.437871\pi\) | ||||
0.193946 | + | 0.981012i | \(0.437871\pi\) | |||||||
\(504\) | −1.60049e6 | −0.280657 | ||||||||
\(505\) | −3.86476e6 | −0.674364 | ||||||||
\(506\) | −123163. | −0.0213847 | ||||||||
\(507\) | 8.47171e6 | 1.46370 | ||||||||
\(508\) | 3.23748e6 | 0.556605 | ||||||||
\(509\) | −1.03089e6 | −0.176367 | −0.0881834 | − | 0.996104i | \(-0.528106\pi\) | ||||
−0.0881834 | + | 0.996104i | \(0.528106\pi\) | |||||||
\(510\) | 1.97302e7 | 3.35897 | ||||||||
\(511\) | 591700. | 0.100242 | ||||||||
\(512\) | −1.53318e6 | −0.258474 | ||||||||
\(513\) | −7.19709e6 | −1.20743 | ||||||||
\(514\) | −1.35131e6 | −0.225605 | ||||||||
\(515\) | 1.96448e6 | 0.326384 | ||||||||
\(516\) | 5.38034e6 | 0.889581 | ||||||||
\(517\) | 562251. | 0.0925133 | ||||||||
\(518\) | 3.02753e6 | 0.495752 | ||||||||
\(519\) | 2.26276e6 | 0.368740 | ||||||||
\(520\) | −1.04067e6 | −0.168774 | ||||||||
\(521\) | 1.09737e7 | 1.77117 | 0.885583 | − | 0.464480i | \(-0.153759\pi\) | ||||
0.885583 | + | 0.464480i | \(0.153759\pi\) | |||||||
\(522\) | −2.07309e6 | −0.332999 | ||||||||
\(523\) | −1.91358e6 | −0.305909 | −0.152954 | − | 0.988233i | \(-0.548879\pi\) | ||||
−0.152954 | + | 0.988233i | \(0.548879\pi\) | |||||||
\(524\) | 3.05865e6 | 0.486633 | ||||||||
\(525\) | −162670. | −0.0257579 | ||||||||
\(526\) | 1.39202e7 | 2.19372 | ||||||||
\(527\) | −1.87598e7 | −2.94240 | ||||||||
\(528\) | −4.61371e6 | −0.720221 | ||||||||
\(529\) | −6.42131e6 | −0.997665 | ||||||||
\(530\) | −1.23325e7 | −1.90704 | ||||||||
\(531\) | 7.06807e6 | 1.08784 | ||||||||
\(532\) | −1.38708e6 | −0.212482 | ||||||||
\(533\) | 1.54765e6 | 0.235969 | ||||||||
\(534\) | 6.31901e6 | 0.958950 | ||||||||
\(535\) | −2.41161e6 | −0.364270 | ||||||||
\(536\) | 6.50405e6 | 0.977849 | ||||||||
\(537\) | −1.13793e6 | −0.170287 | ||||||||
\(538\) | 4.98030e6 | 0.741822 | ||||||||
\(539\) | 2.26055e6 | 0.335152 | ||||||||
\(540\) | 2.31369e6 | 0.341445 | ||||||||
\(541\) | −3.63173e6 | −0.533483 | −0.266741 | − | 0.963768i | \(-0.585947\pi\) | ||||
−0.266741 | + | 0.963768i | \(0.585947\pi\) | |||||||
\(542\) | 6.01095e6 | 0.878910 | ||||||||
\(543\) | −2.90324e6 | −0.422556 | ||||||||
\(544\) | −1.07507e7 | −1.55754 | ||||||||
\(545\) | 7.72487e6 | 1.11404 | ||||||||
\(546\) | −1.02883e6 | −0.147694 | ||||||||
\(547\) | −7.98387e6 | −1.14089 | −0.570447 | − | 0.821335i | \(-0.693230\pi\) | ||||
−0.570447 | + | 0.821335i | \(0.693230\pi\) | |||||||
\(548\) | 174449. | 0.0248151 | ||||||||
\(549\) | 8.66022e6 | 1.22630 | ||||||||
\(550\) | −176594. | −0.0248926 | ||||||||
\(551\) | 2.09751e6 | 0.294323 | ||||||||
\(552\) | 354987. | 0.0495867 | ||||||||
\(553\) | −2.13861e6 | −0.297385 | ||||||||
\(554\) | 6.70947e6 | 0.928782 | ||||||||
\(555\) | 1.56791e7 | 2.16067 | ||||||||
\(556\) | −758019. | −0.103990 | ||||||||
\(557\) | −4.40511e6 | −0.601614 | −0.300807 | − | 0.953685i | \(-0.597256\pi\) | ||||
−0.300807 | + | 0.953685i | \(0.597256\pi\) | |||||||
\(558\) | −2.13823e7 | −2.90717 | ||||||||
\(559\) | −2.41184e6 | −0.326452 | ||||||||
\(560\) | −2.61539e6 | −0.352424 | ||||||||
\(561\) | −7.80467e6 | −1.04700 | ||||||||
\(562\) | −9.94460e6 | −1.32815 | ||||||||
\(563\) | 8.26618e6 | 1.09909 | 0.549545 | − | 0.835464i | \(-0.314801\pi\) | ||||
0.549545 | + | 0.835464i | \(0.314801\pi\) | |||||||
\(564\) | 1.38813e6 | 0.183752 | ||||||||
\(565\) | −1.62565e6 | −0.214243 | ||||||||
\(566\) | −1.24426e7 | −1.63257 | ||||||||
\(567\) | 629281. | 0.0822028 | ||||||||
\(568\) | −4.90643e6 | −0.638109 | ||||||||
\(569\) | −1.12505e7 | −1.45677 | −0.728385 | − | 0.685168i | \(-0.759729\pi\) | ||||
−0.728385 | + | 0.685168i | \(0.759729\pi\) | |||||||
\(570\) | −2.27532e7 | −2.93330 | ||||||||
\(571\) | 2.47253e6 | 0.317360 | 0.158680 | − | 0.987330i | \(-0.449276\pi\) | ||||
0.158680 | + | 0.987330i | \(0.449276\pi\) | |||||||
\(572\) | −352617. | −0.0450623 | ||||||||
\(573\) | 8.57571e6 | 1.09115 | ||||||||
\(574\) | 2.45217e6 | 0.310650 | ||||||||
\(575\) | 21551.7 | 0.00271839 | ||||||||
\(576\) | 2.49354e6 | 0.313156 | ||||||||
\(577\) | 1.24000e7 | 1.55054 | 0.775270 | − | 0.631630i | \(-0.217614\pi\) | ||||
0.775270 | + | 0.631630i | \(0.217614\pi\) | |||||||
\(578\) | −2.22754e7 | −2.77336 | ||||||||
\(579\) | 3.16224e6 | 0.392011 | ||||||||
\(580\) | −674298. | −0.0832304 | ||||||||
\(581\) | −4.04595e6 | −0.497256 | ||||||||
\(582\) | −7.38221e6 | −0.903398 | ||||||||
\(583\) | 4.87836e6 | 0.594432 | ||||||||
\(584\) | −1.85141e6 | −0.224631 | ||||||||
\(585\) | −3.18265e6 | −0.384503 | ||||||||
\(586\) | −1.91230e6 | −0.230045 | ||||||||
\(587\) | 5.73588e6 | 0.687076 | 0.343538 | − | 0.939139i | \(-0.388375\pi\) | ||||
0.343538 | + | 0.939139i | \(0.388375\pi\) | |||||||
\(588\) | 5.58100e6 | 0.665685 | ||||||||
\(589\) | 2.16341e7 | 2.56952 | ||||||||
\(590\) | 7.28185e6 | 0.861215 | ||||||||
\(591\) | −1.51313e7 | −1.78200 | ||||||||
\(592\) | −1.50256e7 | −1.76209 | ||||||||
\(593\) | −8.23346e6 | −0.961492 | −0.480746 | − | 0.876860i | \(-0.659634\pi\) | ||||
−0.480746 | + | 0.876860i | \(0.659634\pi\) | |||||||
\(594\) | −2.89892e6 | −0.337109 | ||||||||
\(595\) | −4.42426e6 | −0.512328 | ||||||||
\(596\) | 2.35542e6 | 0.271614 | ||||||||
\(597\) | 8.19263e6 | 0.940779 | ||||||||
\(598\) | 136307. | 0.0155871 | ||||||||
\(599\) | −2.06935e6 | −0.235650 | −0.117825 | − | 0.993034i | \(-0.537592\pi\) | ||||
−0.117825 | + | 0.993034i | \(0.537592\pi\) | |||||||
\(600\) | 508991. | 0.0577207 | ||||||||
\(601\) | 2.18287e6 | 0.246514 | 0.123257 | − | 0.992375i | \(-0.460666\pi\) | ||||
0.123257 | + | 0.992375i | \(0.460666\pi\) | |||||||
\(602\) | −3.82144e6 | −0.429770 | ||||||||
\(603\) | 1.98911e7 | 2.22774 | ||||||||
\(604\) | 947034. | 0.105627 | ||||||||
\(605\) | 7.57417e6 | 0.841292 | ||||||||
\(606\) | 1.19551e7 | 1.32243 | ||||||||
\(607\) | −7.87116e6 | −0.867095 | −0.433548 | − | 0.901131i | \(-0.642738\pi\) | ||||
−0.433548 | + | 0.901131i | \(0.642738\pi\) | |||||||
\(608\) | 1.23979e7 | 1.36016 | ||||||||
\(609\) | 778243. | 0.0850300 | ||||||||
\(610\) | 8.92217e6 | 0.970836 | ||||||||
\(611\) | −622253. | −0.0674317 | ||||||||
\(612\) | −1.15097e7 | −1.24219 | ||||||||
\(613\) | 1.01857e7 | 1.09481 | 0.547406 | − | 0.836867i | \(-0.315615\pi\) | ||||
0.547406 | + | 0.836867i | \(0.315615\pi\) | |||||||
\(614\) | 1.13264e7 | 1.21247 | ||||||||
\(615\) | 1.26994e7 | 1.35393 | ||||||||
\(616\) | 652254. | 0.0692572 | ||||||||
\(617\) | 1.28805e7 | 1.36213 | 0.681067 | − | 0.732221i | \(-0.261516\pi\) | ||||
0.681067 | + | 0.732221i | \(0.261516\pi\) | |||||||
\(618\) | −6.07682e6 | −0.640038 | ||||||||
\(619\) | 2.22093e6 | 0.232974 | 0.116487 | − | 0.993192i | \(-0.462837\pi\) | ||||
0.116487 | + | 0.993192i | \(0.462837\pi\) | |||||||
\(620\) | −6.95486e6 | −0.726623 | ||||||||
\(621\) | 353787. | 0.0368140 | ||||||||
\(622\) | 9.13043e6 | 0.946271 | ||||||||
\(623\) | −1.41696e6 | −0.146264 | ||||||||
\(624\) | 5.10608e6 | 0.524960 | ||||||||
\(625\) | −9.18539e6 | −0.940584 | ||||||||
\(626\) | 1.54393e7 | 1.57468 | ||||||||
\(627\) | 9.00050e6 | 0.914319 | ||||||||
\(628\) | 8.22301e6 | 0.832017 | ||||||||
\(629\) | −2.54177e7 | −2.56159 | ||||||||
\(630\) | −5.04276e6 | −0.506194 | ||||||||
\(631\) | −1.12269e7 | −1.12250 | −0.561252 | − | 0.827645i | \(-0.689680\pi\) | ||||
−0.561252 | + | 0.827645i | \(0.689680\pi\) | |||||||
\(632\) | 6.69165e6 | 0.666408 | ||||||||
\(633\) | −6.05335e6 | −0.600464 | ||||||||
\(634\) | −1.89220e7 | −1.86958 | ||||||||
\(635\) | −1.19085e7 | −1.17199 | ||||||||
\(636\) | 1.20440e7 | 1.18067 | ||||||||
\(637\) | −2.50179e6 | −0.244288 | ||||||||
\(638\) | 844858. | 0.0821735 | ||||||||
\(639\) | −1.50051e7 | −1.45374 | ||||||||
\(640\) | 1.12076e7 | 1.08159 | ||||||||
\(641\) | 1.73945e6 | 0.167212 | 0.0836060 | − | 0.996499i | \(-0.473356\pi\) | ||||
0.0836060 | + | 0.996499i | \(0.473356\pi\) | |||||||
\(642\) | 7.45998e6 | 0.714332 | ||||||||
\(643\) | 6.08165e6 | 0.580088 | 0.290044 | − | 0.957013i | \(-0.406330\pi\) | ||||
0.290044 | + | 0.957013i | \(0.406330\pi\) | |||||||
\(644\) | 68184.8 | 0.00647847 | ||||||||
\(645\) | −1.97906e7 | −1.87310 | ||||||||
\(646\) | 3.68857e7 | 3.47758 | ||||||||
\(647\) | −2.01823e6 | −0.189544 | −0.0947721 | − | 0.995499i | \(-0.530212\pi\) | ||||
−0.0947721 | + | 0.995499i | \(0.530212\pi\) | |||||||
\(648\) | −1.96900e6 | −0.184208 | ||||||||
\(649\) | −2.88048e6 | −0.268444 | ||||||||
\(650\) | 195440. | 0.0181439 | ||||||||
\(651\) | 8.02697e6 | 0.742333 | ||||||||
\(652\) | −2.58717e6 | −0.238345 | ||||||||
\(653\) | 5.21279e6 | 0.478396 | 0.239198 | − | 0.970971i | \(-0.423116\pi\) | ||||
0.239198 | + | 0.970971i | \(0.423116\pi\) | |||||||
\(654\) | −2.38958e7 | −2.18462 | ||||||||
\(655\) | −1.12507e7 | −1.02465 | ||||||||
\(656\) | −1.21701e7 | −1.10417 | ||||||||
\(657\) | −5.66209e6 | −0.511757 | ||||||||
\(658\) | −985930. | −0.0887731 | ||||||||
\(659\) | 7.29296e6 | 0.654170 | 0.327085 | − | 0.944995i | \(-0.393934\pi\) | ||||
0.327085 | + | 0.944995i | \(0.393934\pi\) | |||||||
\(660\) | −2.89344e6 | −0.258556 | ||||||||
\(661\) | −1.08067e7 | −0.962034 | −0.481017 | − | 0.876711i | \(-0.659732\pi\) | ||||
−0.481017 | + | 0.876711i | \(0.659732\pi\) | |||||||
\(662\) | −1.03098e7 | −0.914331 | ||||||||
\(663\) | 8.63757e6 | 0.763146 | ||||||||
\(664\) | 1.26596e7 | 1.11430 | ||||||||
\(665\) | 5.10214e6 | 0.447402 | ||||||||
\(666\) | −2.89711e7 | −2.53092 | ||||||||
\(667\) | −103107. | −0.00897375 | ||||||||
\(668\) | 6.86091e6 | 0.594895 | ||||||||
\(669\) | 6.75915e6 | 0.583884 | ||||||||
\(670\) | 2.04927e7 | 1.76365 | ||||||||
\(671\) | −3.52934e6 | −0.302613 | ||||||||
\(672\) | 4.60003e6 | 0.392950 | ||||||||
\(673\) | 3.23697e6 | 0.275487 | 0.137743 | − | 0.990468i | \(-0.456015\pi\) | ||||
0.137743 | + | 0.990468i | \(0.456015\pi\) | |||||||
\(674\) | −1.81424e7 | −1.53831 | ||||||||
\(675\) | 507269. | 0.0428528 | ||||||||
\(676\) | −5.09151e6 | −0.428529 | ||||||||
\(677\) | −6.00931e6 | −0.503910 | −0.251955 | − | 0.967739i | \(-0.581073\pi\) | ||||
−0.251955 | + | 0.967739i | \(0.581073\pi\) | |||||||
\(678\) | 5.02873e6 | 0.420130 | ||||||||
\(679\) | 1.65537e6 | 0.137791 | ||||||||
\(680\) | 1.38434e7 | 1.14807 | ||||||||
\(681\) | 1.13458e7 | 0.937488 | ||||||||
\(682\) | 8.71405e6 | 0.717396 | ||||||||
\(683\) | −7.39622e6 | −0.606678 | −0.303339 | − | 0.952883i | \(-0.598101\pi\) | ||||
−0.303339 | + | 0.952883i | \(0.598101\pi\) | |||||||
\(684\) | 1.32733e7 | 1.08477 | ||||||||
\(685\) | −641678. | −0.0522506 | ||||||||
\(686\) | −8.29346e6 | −0.672861 | ||||||||
\(687\) | 7.64249e6 | 0.617793 | ||||||||
\(688\) | 1.89658e7 | 1.52757 | ||||||||
\(689\) | −5.39896e6 | −0.433274 | ||||||||
\(690\) | 1.11848e6 | 0.0894347 | ||||||||
\(691\) | −1.10125e7 | −0.877383 | −0.438692 | − | 0.898638i | \(-0.644558\pi\) | ||||
−0.438692 | + | 0.898638i | \(0.644558\pi\) | |||||||
\(692\) | −1.35992e6 | −0.107956 | ||||||||
\(693\) | 1.99476e6 | 0.157782 | ||||||||
\(694\) | 8.90506e6 | 0.701840 | ||||||||
\(695\) | 2.78824e6 | 0.218962 | ||||||||
\(696\) | −2.43510e6 | −0.190543 | ||||||||
\(697\) | −2.05873e7 | −1.60516 | ||||||||
\(698\) | 8.23008e6 | 0.639390 | ||||||||
\(699\) | −3.75778e7 | −2.90896 | ||||||||
\(700\) | 97765.2 | 0.00754118 | ||||||||
\(701\) | 1.97899e7 | 1.52106 | 0.760532 | − | 0.649300i | \(-0.224938\pi\) | ||||
0.760532 | + | 0.649300i | \(0.224938\pi\) | |||||||
\(702\) | 3.20829e6 | 0.245715 | ||||||||
\(703\) | 2.93122e7 | 2.23697 | ||||||||
\(704\) | −1.01620e6 | −0.0772768 | ||||||||
\(705\) | −5.10598e6 | −0.386906 | ||||||||
\(706\) | 1.35189e7 | 1.02078 | ||||||||
\(707\) | −2.68078e6 | −0.201703 | ||||||||
\(708\) | −7.11154e6 | −0.533188 | ||||||||
\(709\) | −1.20373e7 | −0.899317 | −0.449658 | − | 0.893201i | \(-0.648454\pi\) | ||||
−0.449658 | + | 0.893201i | \(0.648454\pi\) | |||||||
\(710\) | −1.54590e7 | −1.15089 | ||||||||
\(711\) | 2.04648e7 | 1.51822 | ||||||||
\(712\) | 4.43363e6 | 0.327762 | ||||||||
\(713\) | −1.06347e6 | −0.0783431 | ||||||||
\(714\) | 1.36858e7 | 1.00467 | ||||||||
\(715\) | 1.29704e6 | 0.0948831 | ||||||||
\(716\) | 683900. | 0.0498551 | ||||||||
\(717\) | −2.99645e7 | −2.17675 | ||||||||
\(718\) | 1.56672e7 | 1.13418 | ||||||||
\(719\) | −1.01004e7 | −0.728643 | −0.364322 | − | 0.931273i | \(-0.618699\pi\) | ||||
−0.364322 | + | 0.931273i | \(0.618699\pi\) | |||||||
\(720\) | 2.50272e7 | 1.79920 | ||||||||
\(721\) | 1.36265e6 | 0.0976219 | ||||||||
\(722\) | −2.56048e7 | −1.82801 | ||||||||
\(723\) | −1.38374e7 | −0.984485 | ||||||||
\(724\) | 1.74485e6 | 0.123712 | ||||||||
\(725\) | −147838. | −0.0104458 | ||||||||
\(726\) | −2.34296e7 | −1.64977 | ||||||||
\(727\) | 2.01441e7 | 1.41356 | 0.706778 | − | 0.707436i | \(-0.250148\pi\) | ||||
0.706778 | + | 0.707436i | \(0.250148\pi\) | |||||||
\(728\) | −721861. | −0.0504807 | ||||||||
\(729\) | −2.32477e7 | −1.62017 | ||||||||
\(730\) | −5.83335e6 | −0.405146 | ||||||||
\(731\) | 3.20830e7 | 2.22066 | ||||||||
\(732\) | −8.71349e6 | −0.601055 | ||||||||
\(733\) | −2.42377e7 | −1.66622 | −0.833110 | − | 0.553108i | \(-0.813442\pi\) | ||||
−0.833110 | + | 0.553108i | \(0.813442\pi\) | |||||||
\(734\) | −5.16767e6 | −0.354042 | ||||||||
\(735\) | −2.05287e7 | −1.40166 | ||||||||
\(736\) | −609445. | −0.0414705 | ||||||||
\(737\) | −8.10630e6 | −0.549736 | ||||||||
\(738\) | −2.34654e7 | −1.58594 | ||||||||
\(739\) | −6.78569e6 | −0.457070 | −0.228535 | − | 0.973536i | \(-0.573394\pi\) | ||||
−0.228535 | + | 0.973536i | \(0.573394\pi\) | |||||||
\(740\) | −9.42317e6 | −0.632584 | ||||||||
\(741\) | −9.96102e6 | −0.666436 | ||||||||
\(742\) | −8.55439e6 | −0.570400 | ||||||||
\(743\) | 4.71605e6 | 0.313406 | 0.156703 | − | 0.987646i | \(-0.449914\pi\) | ||||
0.156703 | + | 0.987646i | \(0.449914\pi\) | |||||||
\(744\) | −2.51161e7 | −1.66349 | ||||||||
\(745\) | −8.66398e6 | −0.571909 | ||||||||
\(746\) | 3.04957e7 | 2.00628 | ||||||||
\(747\) | 3.87165e7 | 2.53860 | ||||||||
\(748\) | 4.69062e6 | 0.306532 | ||||||||
\(749\) | −1.67281e6 | −0.108954 | ||||||||
\(750\) | 3.01130e7 | 1.95479 | ||||||||
\(751\) | −1.69859e7 | −1.09898 | −0.549490 | − | 0.835501i | \(-0.685178\pi\) | ||||
−0.549490 | + | 0.835501i | \(0.685178\pi\) | |||||||
\(752\) | 4.89316e6 | 0.315533 | ||||||||
\(753\) | 3.74967e7 | 2.40993 | ||||||||
\(754\) | −935019. | −0.0598952 | ||||||||
\(755\) | −3.48350e6 | −0.222407 | ||||||||
\(756\) | 1.60489e6 | 0.102127 | ||||||||
\(757\) | −2.07327e7 | −1.31497 | −0.657486 | − | 0.753467i | \(-0.728380\pi\) | ||||
−0.657486 | + | 0.753467i | \(0.728380\pi\) | |||||||
\(758\) | −2.75579e7 | −1.74210 | ||||||||
\(759\) | −442437. | −0.0278771 | ||||||||
\(760\) | −1.59644e7 | −1.00258 | ||||||||
\(761\) | −52400.3 | −0.00327999 | −0.00163999 | − | 0.999999i | \(-0.500522\pi\) | ||||
−0.00163999 | + | 0.999999i | \(0.500522\pi\) | |||||||
\(762\) | 3.68372e7 | 2.29826 | ||||||||
\(763\) | 5.35834e6 | 0.333210 | ||||||||
\(764\) | −5.15402e6 | −0.319457 | ||||||||
\(765\) | 4.23366e7 | 2.61555 | ||||||||
\(766\) | −2.82194e7 | −1.73770 | ||||||||
\(767\) | 3.18788e6 | 0.195665 | ||||||||
\(768\) | −2.92312e7 | −1.78832 | ||||||||
\(769\) | −2.09357e7 | −1.27665 | −0.638325 | − | 0.769767i | \(-0.720373\pi\) | ||||
−0.638325 | + | 0.769767i | \(0.720373\pi\) | |||||||
\(770\) | 2.05510e6 | 0.124912 | ||||||||
\(771\) | −4.85432e6 | −0.294098 | ||||||||
\(772\) | −1.90051e6 | −0.114770 | ||||||||
\(773\) | 2.78692e7 | 1.67755 | 0.838777 | − | 0.544476i | \(-0.183271\pi\) | ||||
0.838777 | + | 0.544476i | \(0.183271\pi\) | |||||||
\(774\) | 3.65681e7 | 2.19407 | ||||||||
\(775\) | −1.52483e6 | −0.0911942 | ||||||||
\(776\) | −5.17960e6 | −0.308775 | ||||||||
\(777\) | 1.08758e7 | 0.646261 | ||||||||
\(778\) | 9.40431e6 | 0.557029 | ||||||||
\(779\) | 2.37417e7 | 1.40174 | ||||||||
\(780\) | 3.20223e6 | 0.188459 | ||||||||
\(781\) | 6.11512e6 | 0.358738 | ||||||||
\(782\) | −1.81319e6 | −0.106030 | ||||||||
\(783\) | −2.42686e6 | −0.141462 | ||||||||
\(784\) | 1.96731e7 | 1.14310 | ||||||||
\(785\) | −3.02469e7 | −1.75189 | ||||||||
\(786\) | 3.48024e7 | 2.00934 | ||||||||
\(787\) | 1.87393e7 | 1.07849 | 0.539245 | − | 0.842149i | \(-0.318710\pi\) | ||||
0.539245 | + | 0.842149i | \(0.318710\pi\) | |||||||
\(788\) | 9.09392e6 | 0.521717 | ||||||||
\(789\) | 5.00053e7 | 2.85972 | ||||||||
\(790\) | 2.10838e7 | 1.20194 | ||||||||
\(791\) | −1.12763e6 | −0.0640805 | ||||||||
\(792\) | −6.24155e6 | −0.353573 | ||||||||
\(793\) | 3.90598e6 | 0.220571 | ||||||||
\(794\) | −2.70157e7 | −1.52078 | ||||||||
\(795\) | −4.43019e7 | −2.48602 | ||||||||
\(796\) | −4.92378e6 | −0.275433 | ||||||||
\(797\) | −2.79661e6 | −0.155950 | −0.0779751 | − | 0.996955i | \(-0.524845\pi\) | ||||
−0.0779751 | + | 0.996955i | \(0.524845\pi\) | |||||||
\(798\) | −1.57827e7 | −0.877354 | ||||||||
\(799\) | 8.27740e6 | 0.458698 | ||||||||
\(800\) | −873838. | −0.0482732 | ||||||||
\(801\) | 1.35592e7 | 0.746711 | ||||||||
\(802\) | −4.11150e6 | −0.225717 | ||||||||
\(803\) | 2.30750e6 | 0.126285 | ||||||||
\(804\) | −2.00134e7 | −1.09190 | ||||||||
\(805\) | −250806. | −0.0136410 | ||||||||
\(806\) | −9.64399e6 | −0.522901 | ||||||||
\(807\) | 1.78907e7 | 0.967038 | ||||||||
\(808\) | 8.38809e6 | 0.451996 | ||||||||
\(809\) | 2.31444e7 | 1.24330 | 0.621648 | − | 0.783296i | \(-0.286463\pi\) | ||||
0.621648 | + | 0.783296i | \(0.286463\pi\) | |||||||
\(810\) | −6.20385e6 | −0.332238 | ||||||||
\(811\) | 1.44543e7 | 0.771694 | 0.385847 | − | 0.922563i | \(-0.373909\pi\) | ||||
0.385847 | + | 0.922563i | \(0.373909\pi\) | |||||||
\(812\) | −467725. | −0.0248943 | ||||||||
\(813\) | 2.15931e7 | 1.14575 | ||||||||
\(814\) | 1.18067e7 | 0.624551 | ||||||||
\(815\) | 9.51646e6 | 0.501859 | ||||||||
\(816\) | −6.79226e7 | −3.57099 | ||||||||
\(817\) | −3.69987e7 | −1.93924 | ||||||||
\(818\) | −4.36747e7 | −2.28216 | ||||||||
\(819\) | −2.20764e6 | −0.115005 | ||||||||
\(820\) | −7.63238e6 | −0.396392 | ||||||||
\(821\) | 1.80178e7 | 0.932920 | 0.466460 | − | 0.884542i | \(-0.345529\pi\) | ||||
0.466460 | + | 0.884542i | \(0.345529\pi\) | |||||||
\(822\) | 1.98494e6 | 0.102463 | ||||||||
\(823\) | 6.65519e6 | 0.342500 | 0.171250 | − | 0.985228i | \(-0.445219\pi\) | ||||
0.171250 | + | 0.985228i | \(0.445219\pi\) | |||||||
\(824\) | −4.26370e6 | −0.218760 | ||||||||
\(825\) | −634379. | −0.0324499 | ||||||||
\(826\) | 5.05104e6 | 0.257591 | ||||||||
\(827\) | 5.27683e6 | 0.268293 | 0.134146 | − | 0.990962i | \(-0.457171\pi\) | ||||
0.134146 | + | 0.990962i | \(0.457171\pi\) | |||||||
\(828\) | −652474. | −0.0330740 | ||||||||
\(829\) | −724962. | −0.0366378 | −0.0183189 | − | 0.999832i | \(-0.505831\pi\) | ||||
−0.0183189 | + | 0.999832i | \(0.505831\pi\) | |||||||
\(830\) | 3.98875e7 | 2.00975 | ||||||||
\(831\) | 2.41024e7 | 1.21076 | ||||||||
\(832\) | 1.12465e6 | 0.0563261 | ||||||||
\(833\) | 3.32796e7 | 1.66175 | ||||||||
\(834\) | −8.62503e6 | −0.429383 | ||||||||
\(835\) | −2.52367e7 | −1.25261 | ||||||||
\(836\) | −5.40932e6 | −0.267687 | ||||||||
\(837\) | −2.50312e7 | −1.23500 | ||||||||
\(838\) | −3.04108e7 | −1.49595 | ||||||||
\(839\) | 1.71120e7 | 0.839256 | 0.419628 | − | 0.907696i | \(-0.362160\pi\) | ||||
0.419628 | + | 0.907696i | \(0.362160\pi\) | |||||||
\(840\) | −5.92332e6 | −0.289646 | ||||||||
\(841\) | 707281. | 0.0344828 | ||||||||
\(842\) | −2.82786e6 | −0.137460 | ||||||||
\(843\) | −3.57239e7 | −1.73137 | ||||||||
\(844\) | 3.63808e6 | 0.175799 | ||||||||
\(845\) | 1.87282e7 | 0.902308 | ||||||||
\(846\) | 9.43456e6 | 0.453206 | ||||||||
\(847\) | 5.25380e6 | 0.251632 | ||||||||
\(848\) | 4.24554e7 | 2.02742 | ||||||||
\(849\) | −4.46975e7 | −2.12821 | ||||||||
\(850\) | −2.59980e6 | −0.123422 | ||||||||
\(851\) | −1.44090e6 | −0.0682040 | ||||||||
\(852\) | 1.50974e7 | 0.712532 | ||||||||
\(853\) | −3.96032e6 | −0.186362 | −0.0931810 | − | 0.995649i | \(-0.529704\pi\) | ||||
−0.0931810 | + | 0.995649i | \(0.529704\pi\) | |||||||
\(854\) | 6.18884e6 | 0.290378 | ||||||||
\(855\) | −4.88234e7 | −2.28409 | ||||||||
\(856\) | 5.23417e6 | 0.244154 | ||||||||
\(857\) | 1.78958e7 | 0.832338 | 0.416169 | − | 0.909287i | \(-0.363373\pi\) | ||||
0.416169 | + | 0.909287i | \(0.363373\pi\) | |||||||
\(858\) | −4.01221e6 | −0.186065 | ||||||||
\(859\) | 3.52591e7 | 1.63038 | 0.815188 | − | 0.579197i | \(-0.196634\pi\) | ||||
0.815188 | + | 0.579197i | \(0.196634\pi\) | |||||||
\(860\) | 1.18942e7 | 0.548390 | ||||||||
\(861\) | 8.80893e6 | 0.404963 | ||||||||
\(862\) | 2.27070e7 | 1.04086 | ||||||||
\(863\) | −4.23888e7 | −1.93742 | −0.968711 | − | 0.248192i | \(-0.920163\pi\) | ||||
−0.968711 | + | 0.248192i | \(0.920163\pi\) | |||||||
\(864\) | −1.43447e7 | −0.653742 | ||||||||
\(865\) | 5.00223e6 | 0.227313 | ||||||||
\(866\) | −7.82614e6 | −0.354612 | ||||||||
\(867\) | −8.00199e7 | −3.61535 | ||||||||
\(868\) | −4.82422e6 | −0.217334 | ||||||||
\(869\) | −8.34011e6 | −0.374647 | ||||||||
\(870\) | −7.67241e6 | −0.343664 | ||||||||
\(871\) | 8.97139e6 | 0.400695 | ||||||||
\(872\) | −1.67661e7 | −0.746689 | ||||||||
\(873\) | −1.58406e7 | −0.703453 | ||||||||
\(874\) | 2.09101e6 | 0.0925928 | ||||||||
\(875\) | −6.75247e6 | −0.298155 | ||||||||
\(876\) | 5.69692e6 | 0.250830 | ||||||||
\(877\) | 3.53937e6 | 0.155391 | 0.0776956 | − | 0.996977i | \(-0.475244\pi\) | ||||
0.0776956 | + | 0.996977i | \(0.475244\pi\) | |||||||
\(878\) | −6.15582e6 | −0.269494 | ||||||||
\(879\) | −6.86954e6 | −0.299886 | ||||||||
\(880\) | −1.01994e7 | −0.443986 | ||||||||
\(881\) | −1.82655e7 | −0.792851 | −0.396426 | − | 0.918067i | \(-0.629750\pi\) | ||||
−0.396426 | + | 0.918067i | \(0.629750\pi\) | |||||||
\(882\) | 3.79320e7 | 1.64185 | ||||||||
\(883\) | −2.56061e7 | −1.10520 | −0.552602 | − | 0.833446i | \(-0.686365\pi\) | ||||
−0.552602 | + | 0.833446i | \(0.686365\pi\) | |||||||
\(884\) | −5.19119e6 | −0.223428 | ||||||||
\(885\) | 2.61585e7 | 1.12268 | ||||||||
\(886\) | −2.48114e7 | −1.06186 | ||||||||
\(887\) | −4.46206e6 | −0.190426 | −0.0952130 | − | 0.995457i | \(-0.530353\pi\) | ||||
−0.0952130 | + | 0.995457i | \(0.530353\pi\) | |||||||
\(888\) | −3.40300e7 | −1.44820 | ||||||||
\(889\) | −8.26030e6 | −0.350543 | ||||||||
\(890\) | 1.39693e7 | 0.591153 | ||||||||
\(891\) | 2.45406e6 | 0.103560 | ||||||||
\(892\) | −4.06226e6 | −0.170945 | ||||||||
\(893\) | −9.54566e6 | −0.400569 | ||||||||
\(894\) | 2.68008e7 | 1.12151 | ||||||||
\(895\) | −2.51561e6 | −0.104975 | ||||||||
\(896\) | 7.77412e6 | 0.323505 | ||||||||
\(897\) | 489653. | 0.0203193 | ||||||||
\(898\) | 1.44189e7 | 0.596679 | ||||||||
\(899\) | 7.29505e6 | 0.301043 | ||||||||
\(900\) | −935535. | −0.0384994 | ||||||||
\(901\) | 7.18186e7 | 2.94730 | ||||||||
\(902\) | 9.56294e6 | 0.391359 | ||||||||
\(903\) | −1.37277e7 | −0.560247 | ||||||||
\(904\) | 3.52832e6 | 0.143598 | ||||||||
\(905\) | −6.41814e6 | −0.260488 | ||||||||
\(906\) | 1.07757e7 | 0.436139 | ||||||||
\(907\) | 4.62490e7 | 1.86674 | 0.933371 | − | 0.358914i | \(-0.116853\pi\) | ||||
0.933371 | + | 0.358914i | \(0.116853\pi\) | |||||||
\(908\) | −6.81882e6 | −0.274470 | ||||||||
\(909\) | 2.56530e7 | 1.02974 | ||||||||
\(910\) | −2.27441e6 | −0.0910471 | ||||||||
\(911\) | −3.42662e7 | −1.36795 | −0.683974 | − | 0.729507i | \(-0.739750\pi\) | ||||
−0.683974 | + | 0.729507i | \(0.739750\pi\) | |||||||
\(912\) | 7.83296e7 | 3.11845 | ||||||||
\(913\) | −1.57783e7 | −0.626446 | ||||||||
\(914\) | −1.07595e6 | −0.0426015 | ||||||||
\(915\) | 3.20510e7 | 1.26558 | ||||||||
\(916\) | −4.59315e6 | −0.180872 | ||||||||
\(917\) | −7.80402e6 | −0.306475 | ||||||||
\(918\) | −4.26776e7 | −1.67145 | ||||||||
\(919\) | 1.31785e7 | 0.514728 | 0.257364 | − | 0.966315i | \(-0.417146\pi\) | ||||
0.257364 | + | 0.966315i | \(0.417146\pi\) | |||||||
\(920\) | 784763. | 0.0305681 | ||||||||
\(921\) | 4.06877e7 | 1.58057 | ||||||||
\(922\) | 543839. | 0.0210690 | ||||||||
\(923\) | −6.76771e6 | −0.261479 | ||||||||
\(924\) | −2.00703e6 | −0.0773347 | ||||||||
\(925\) | −2.06600e6 | −0.0793919 | ||||||||
\(926\) | −2.88528e6 | −0.110576 | ||||||||
\(927\) | −1.30395e7 | −0.498381 | ||||||||
\(928\) | 4.18059e6 | 0.159356 | ||||||||
\(929\) | −1.62539e7 | −0.617899 | −0.308949 | − | 0.951078i | \(-0.599977\pi\) | ||||
−0.308949 | + | 0.951078i | \(0.599977\pi\) | |||||||
\(930\) | −7.91349e7 | −3.00027 | ||||||||
\(931\) | −3.83786e7 | −1.45116 | ||||||||
\(932\) | 2.25843e7 | 0.851661 | ||||||||
\(933\) | 3.27992e7 | 1.23356 | ||||||||
\(934\) | −2.43490e7 | −0.913301 | ||||||||
\(935\) | −1.72536e7 | −0.645433 | ||||||||
\(936\) | 6.90764e6 | 0.257715 | ||||||||
\(937\) | −2.53494e7 | −0.943233 | −0.471617 | − | 0.881804i | \(-0.656329\pi\) | ||||
−0.471617 | + | 0.881804i | \(0.656329\pi\) | |||||||
\(938\) | 1.42147e7 | 0.527511 | ||||||||
\(939\) | 5.54625e7 | 2.05275 | ||||||||
\(940\) | 3.06870e6 | 0.113275 | ||||||||
\(941\) | 9.02296e6 | 0.332181 | 0.166091 | − | 0.986110i | \(-0.446886\pi\) | ||||
0.166091 | + | 0.986110i | \(0.446886\pi\) | |||||||
\(942\) | 9.35645e7 | 3.43545 | ||||||||
\(943\) | −1.16707e6 | −0.0427383 | ||||||||
\(944\) | −2.50683e7 | −0.915576 | ||||||||
\(945\) | −5.90329e6 | −0.215038 | ||||||||
\(946\) | −1.49028e7 | −0.541426 | ||||||||
\(947\) | −338514. | −0.0122660 | −0.00613298 | − | 0.999981i | \(-0.501952\pi\) | ||||
−0.00613298 | + | 0.999981i | \(0.501952\pi\) | |||||||
\(948\) | −2.05907e7 | −0.744131 | ||||||||
\(949\) | −2.55375e6 | −0.0920477 | ||||||||
\(950\) | 2.99814e6 | 0.107781 | ||||||||
\(951\) | −6.79734e7 | −2.43718 | ||||||||
\(952\) | 9.60241e6 | 0.343390 | ||||||||
\(953\) | −1.25549e7 | −0.447797 | −0.223899 | − | 0.974612i | \(-0.571878\pi\) | ||||
−0.223899 | + | 0.974612i | \(0.571878\pi\) | |||||||
\(954\) | 8.18587e7 | 2.91202 | ||||||||
\(955\) | 1.89581e7 | 0.672647 | ||||||||
\(956\) | 1.80087e7 | 0.637291 | ||||||||
\(957\) | 3.03498e6 | 0.107121 | ||||||||
\(958\) | −2.44984e7 | −0.862430 | ||||||||
\(959\) | −445099. | −0.0156282 | ||||||||
\(960\) | 9.22846e6 | 0.323185 | ||||||||
\(961\) | 4.66136e7 | 1.62819 | ||||||||
\(962\) | −1.30667e7 | −0.455227 | ||||||||
\(963\) | 1.60074e7 | 0.556232 | ||||||||
\(964\) | 8.31630e6 | 0.288229 | ||||||||
\(965\) | 6.99069e6 | 0.241658 | ||||||||
\(966\) | 775832. | 0.0267501 | ||||||||
\(967\) | −1.51562e6 | −0.0521224 | −0.0260612 | − | 0.999660i | \(-0.508296\pi\) | ||||
−0.0260612 | + | 0.999660i | \(0.508296\pi\) | |||||||
\(968\) | −1.64390e7 | −0.563880 | ||||||||
\(969\) | 1.32504e8 | 4.53337 | ||||||||
\(970\) | −1.63197e7 | −0.556907 | ||||||||
\(971\) | 3.97841e7 | 1.35413 | 0.677067 | − | 0.735921i | \(-0.263251\pi\) | ||||
0.677067 | + | 0.735921i | \(0.263251\pi\) | |||||||
\(972\) | 1.64116e7 | 0.557166 | ||||||||
\(973\) | 1.93406e6 | 0.0654918 | ||||||||
\(974\) | −5.91537e7 | −1.99795 | ||||||||
\(975\) | 702079. | 0.0236523 | ||||||||
\(976\) | −3.07152e7 | −1.03212 | ||||||||
\(977\) | −1.08895e7 | −0.364982 | −0.182491 | − | 0.983208i | \(-0.558416\pi\) | ||||
−0.182491 | + | 0.983208i | \(0.558416\pi\) | |||||||
\(978\) | −2.94378e7 | −0.984143 | ||||||||
\(979\) | −5.52584e6 | −0.184264 | ||||||||
\(980\) | 1.23378e7 | 0.410367 | ||||||||
\(981\) | −5.12750e7 | −1.70111 | ||||||||
\(982\) | −1.00116e6 | −0.0331303 | ||||||||
\(983\) | 1.51586e7 | 0.500353 | 0.250177 | − | 0.968200i | \(-0.419511\pi\) | ||||
0.250177 | + | 0.968200i | \(0.419511\pi\) | |||||||
\(984\) | −2.75629e7 | −0.907479 | ||||||||
\(985\) | −3.34504e7 | −1.09853 | ||||||||
\(986\) | 1.24379e7 | 0.407432 | ||||||||
\(987\) | −3.54175e6 | −0.115724 | ||||||||
\(988\) | 5.98659e6 | 0.195113 | ||||||||
\(989\) | 1.81875e6 | 0.0591264 | ||||||||
\(990\) | −1.96656e7 | −0.637705 | ||||||||
\(991\) | −4.43710e7 | −1.43521 | −0.717605 | − | 0.696451i | \(-0.754762\pi\) | ||||
−0.717605 | + | 0.696451i | \(0.754762\pi\) | |||||||
\(992\) | 4.31195e7 | 1.39122 | ||||||||
\(993\) | −3.70357e7 | −1.19192 | ||||||||
\(994\) | −1.07231e7 | −0.344234 | ||||||||
\(995\) | 1.81113e7 | 0.579951 | ||||||||
\(996\) | −3.89546e7 | −1.24426 | ||||||||
\(997\) | −4.48040e7 | −1.42751 | −0.713754 | − | 0.700397i | \(-0.753006\pi\) | ||||
−0.713754 | + | 0.700397i | \(0.753006\pi\) | |||||||
\(998\) | 2.90373e7 | 0.922847 | ||||||||
\(999\) | −3.39149e7 | −1.07517 |
(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.b.1.2 | ✓ | 7 | |
3.2 | odd | 2 | 261.6.a.e.1.6 | 7 | |||
4.3 | odd | 2 | 464.6.a.k.1.7 | 7 | |||
5.4 | even | 2 | 725.6.a.b.1.6 | 7 | |||
29.28 | even | 2 | 841.6.a.b.1.6 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.6.a.b.1.2 | ✓ | 7 | 1.1 | even | 1 | trivial | |
261.6.a.e.1.6 | 7 | 3.2 | odd | 2 | |||
464.6.a.k.1.7 | 7 | 4.3 | odd | 2 | |||
725.6.a.b.1.6 | 7 | 5.4 | even | 2 | |||
841.6.a.b.1.6 | 7 | 29.28 | even | 2 |