Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,6,Mod(1,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("448.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.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: | \(71.8519512762\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 56) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 448.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −30.0000 | −1.92450 | −0.962250 | − | 0.272166i | \(-0.912260\pi\) | ||||
−0.962250 | + | 0.272166i | \(0.912260\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −32.0000 | −0.572433 | −0.286217 | − | 0.958165i | \(-0.592398\pi\) | ||||
−0.286217 | + | 0.958165i | \(0.592398\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 49.0000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 657.000 | 2.70370 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 624.000 | 1.55490 | 0.777451 | − | 0.628944i | \(-0.216512\pi\) | ||||
0.777451 | + | 0.628944i | \(0.216512\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 708.000 | 1.16192 | 0.580958 | − | 0.813933i | \(-0.302678\pi\) | ||||
0.580958 | + | 0.813933i | \(0.302678\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 960.000 | 1.10165 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 934.000 | 0.783835 | 0.391917 | − | 0.920000i | \(-0.371812\pi\) | ||||
0.391917 | + | 0.920000i | \(0.371812\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1858.00 | −1.18076 | −0.590380 | − | 0.807125i | \(-0.701022\pi\) | ||||
−0.590380 | + | 0.807125i | \(0.701022\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1470.00 | −0.727393 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1120.00 | −0.441467 | −0.220734 | − | 0.975334i | \(-0.570845\pi\) | ||||
−0.220734 | + | 0.975334i | \(0.570845\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2101.00 | −0.672320 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −12420.0 | −3.27878 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1174.00 | 0.259223 | 0.129611 | − | 0.991565i | \(-0.458627\pi\) | ||||
0.129611 | + | 0.991565i | \(0.458627\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2908.00 | 0.543488 | 0.271744 | − | 0.962370i | \(-0.412400\pi\) | ||||
0.271744 | + | 0.962370i | \(0.412400\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −18720.0 | −2.99241 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1568.00 | −0.216359 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 12462.0 | 1.49652 | 0.748262 | − | 0.663404i | \(-0.230889\pi\) | ||||
0.748262 | + | 0.663404i | \(0.230889\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −21240.0 | −2.23611 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2662.00 | 0.247314 | 0.123657 | − | 0.992325i | \(-0.460538\pi\) | ||||
0.123657 | + | 0.992325i | \(0.460538\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7144.00 | 0.589210 | 0.294605 | − | 0.955619i | \(-0.404812\pi\) | ||||
0.294605 | + | 0.955619i | \(0.404812\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −21024.0 | −1.54769 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7468.00 | −0.493128 | −0.246564 | − | 0.969127i | \(-0.579302\pi\) | ||||
−0.246564 | + | 0.969127i | \(0.579302\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −28020.0 | −1.50849 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 27274.0 | 1.33370 | 0.666852 | − | 0.745191i | \(-0.267642\pi\) | ||||
0.666852 | + | 0.745191i | \(0.267642\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −19968.0 | −0.890078 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 55740.0 | 2.27237 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2490.00 | −0.0931257 | −0.0465628 | − | 0.998915i | \(-0.514827\pi\) | ||||
−0.0465628 | + | 0.998915i | \(0.514827\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11096.0 | 0.381805 | 0.190903 | − | 0.981609i | \(-0.438859\pi\) | ||||
0.190903 | + | 0.981609i | \(0.438859\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 32193.0 | 1.02190 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −22656.0 | −0.665120 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −39756.0 | −1.08197 | −0.540986 | − | 0.841032i | \(-0.681949\pi\) | ||||
−0.540986 | + | 0.841032i | \(0.681949\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 33600.0 | 0.849604 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −69888.0 | −1.64534 | −0.822672 | − | 0.568516i | \(-0.807518\pi\) | ||||
−0.822672 | + | 0.568516i | \(0.807518\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16450.0 | 0.361292 | 0.180646 | − | 0.983548i | \(-0.442181\pi\) | ||||
0.180646 | + | 0.983548i | \(0.442181\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 63030.0 | 1.29388 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 30576.0 | 0.587698 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 78376.0 | 1.41291 | 0.706456 | − | 0.707757i | \(-0.250293\pi\) | ||||
0.706456 | + | 0.707757i | \(0.250293\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 212949. | 3.60631 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −109818. | −1.74976 | −0.874880 | − | 0.484340i | \(-0.839060\pi\) | ||||
−0.874880 | + | 0.484340i | \(0.839060\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −29888.0 | −0.448693 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −35220.0 | −0.498874 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −56966.0 | −0.762326 | −0.381163 | − | 0.924508i | \(-0.624476\pi\) | ||||
−0.381163 | + | 0.924508i | \(0.624476\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 34692.0 | 0.439163 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −87240.0 | −1.04594 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 59456.0 | 0.675907 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −115946. | −1.25120 | −0.625600 | − | 0.780144i | \(-0.715146\pi\) | ||||
−0.625600 | + | 0.780144i | \(0.715146\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 409968. | 4.20399 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8352.00 | −0.0814680 | −0.0407340 | − | 0.999170i | \(-0.512970\pi\) | ||||
−0.0407340 | + | 0.999170i | \(0.512970\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 179484. | 1.66699 | 0.833494 | − | 0.552528i | \(-0.186337\pi\) | ||||
0.833494 | + | 0.552528i | \(0.186337\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 47040.0 | 0.416384 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 53892.0 | 0.455056 | 0.227528 | − | 0.973772i | \(-0.426936\pi\) | ||||
0.227528 | + | 0.973772i | \(0.426936\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −105970. | −0.854312 | −0.427156 | − | 0.904178i | \(-0.640485\pi\) | ||||
−0.427156 | + | 0.904178i | \(0.640485\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −373860. | −2.88006 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2502.00 | 0.0184328 | 0.00921640 | − | 0.999958i | \(-0.497066\pi\) | ||||
0.00921640 | + | 0.999958i | \(0.497066\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 35840.0 | 0.252711 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 465156. | 3.14148 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 45766.0 | 0.296262 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 228325. | 1.41772 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −79860.0 | −0.475956 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 167232. | 0.957292 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 287792. | 1.58332 | 0.791661 | − | 0.610960i | \(-0.209216\pi\) | ||||
0.791661 | + | 0.610960i | \(0.209216\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −214320. | −1.13394 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 47662.0 | 0.242658 | 0.121329 | − | 0.992612i | \(-0.461284\pi\) | ||||
0.121329 | + | 0.992612i | \(0.461284\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −91042.0 | −0.446285 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 397440. | 1.87688 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 223154. | 1.01579 | 0.507894 | − | 0.861419i | \(-0.330424\pi\) | ||||
0.507894 | + | 0.861419i | \(0.330424\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −250542. | −1.09988 | −0.549938 | − | 0.835206i | \(-0.685349\pi\) | ||||
−0.549938 | + | 0.835206i | \(0.685349\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 224040. | 0.949025 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 441792. | 1.80667 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −37568.0 | −0.148388 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −72030.0 | −0.274929 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 487394. | 1.79852 | 0.899258 | − | 0.437418i | \(-0.144107\pi\) | ||||
0.899258 | + | 0.437418i | \(0.144107\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −54680.0 | −0.195158 | −0.0975790 | − | 0.995228i | \(-0.531110\pi\) | ||||
−0.0975790 | + | 0.995228i | \(0.531110\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 613638. | 2.11926 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −93056.0 | −0.311111 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −211068. | −0.683397 | −0.341699 | − | 0.939810i | \(-0.611002\pi\) | ||||
−0.341699 | + | 0.939810i | \(0.611002\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −818220. | −2.56671 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −54880.0 | −0.166859 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20192.0 | 0.0595265 | 0.0297632 | − | 0.999557i | \(-0.490525\pi\) | ||||
0.0297632 | + | 0.999557i | \(0.490525\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 599040. | 1.71296 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4524.00 | −0.0125525 | −0.00627627 | − | 0.999980i | \(-0.501998\pi\) | ||||
−0.00627627 | + | 0.999980i | \(0.501998\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 129971. | 0.350050 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.22071e6 | −3.19243 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 104332. | 0.265034 | 0.132517 | − | 0.991181i | \(-0.457694\pi\) | ||||
0.132517 | + | 0.991181i | \(0.457694\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −102949. | −0.254113 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 74700.0 | 0.179220 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 201724. | 0.470571 | 0.235285 | − | 0.971926i | \(-0.424398\pi\) | ||||
0.235285 | + | 0.971926i | \(0.424398\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −655700. | −1.48768 | −0.743839 | − | 0.668359i | \(-0.766997\pi\) | ||||
−0.743839 | + | 0.668359i | \(0.766997\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −332880. | −0.734784 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −398784. | −0.856660 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 582816. | 1.21879 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −608580. | −1.23926 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −151496. | −0.300482 | −0.150241 | − | 0.988649i | \(-0.548005\pi\) | ||||
−0.150241 | + | 0.988649i | \(0.548005\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 229326. | 0.443159 | 0.221580 | − | 0.975142i | \(-0.428879\pi\) | ||||
0.221580 | + | 0.975142i | \(0.428879\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 679680. | 1.28002 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −421086. | −0.773046 | −0.386523 | − | 0.922280i | \(-0.626324\pi\) | ||||
−0.386523 | + | 0.922280i | \(0.626324\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 197300. | 0.353179 | 0.176589 | − | 0.984285i | \(-0.443494\pi\) | ||||
0.176589 | + | 0.984285i | \(0.443494\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.19268e6 | 2.08225 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 57526.0 | 0.0979770 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −85184.0 | −0.141571 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −735840. | −1.19360 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.15939e6 | −1.83597 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −679052. | −1.05002 | −0.525009 | − | 0.851097i | \(-0.675938\pi\) | ||||
−0.525009 | + | 0.851097i | \(0.675938\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.09664e6 | 3.16647 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −228608. | −0.337284 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 142492. | 0.205419 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −493500. | −0.695307 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 661272. | 0.910751 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −184440. | −0.248366 | −0.124183 | − | 0.992259i | \(-0.539631\pi\) | ||||
−0.124183 | + | 0.992259i | \(0.539631\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.38036e6 | −1.81775 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 868078. | 1.11813 | 0.559067 | − | 0.829122i | \(-0.311159\pi\) | ||||
0.559067 | + | 0.829122i | \(0.311159\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 593860. | 0.748334 | 0.374167 | − | 0.927361i | \(-0.377929\pi\) | ||||
0.374167 | + | 0.927361i | \(0.377929\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −917280. | −1.13102 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 48218.0 | 0.0581861 | 0.0290931 | − | 0.999577i | \(-0.490738\pi\) | ||||
0.0290931 | + | 0.999577i | \(0.490738\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 238976. | 0.282283 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.35128e6 | −2.71915 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 241688. | 0.273691 | 0.136845 | − | 0.990592i | \(-0.456304\pi\) | ||||
0.136845 | + | 0.990592i | \(0.456304\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 565270. | 0.626922 | 0.313461 | − | 0.949601i | \(-0.398512\pi\) | ||||
0.313461 | + | 0.949601i | \(0.398512\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.37041e6 | −3.66157 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −76832.0 | −0.0817762 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.31546e6 | −1.37194 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.29454e6 | 3.36741 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.43775e6 | 1.44045 | 0.720224 | − | 0.693741i | \(-0.244039\pi\) | ||||
0.720224 | + | 0.693741i | \(0.244039\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −698880. | −0.686438 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 896640. | 0.863511 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 494802. | 0.467303 | 0.233652 | − | 0.972320i | \(-0.424933\pi\) | ||||
0.233652 | + | 0.972320i | \(0.424933\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 610638. | 0.565633 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 771318. | 0.700861 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.55654e6 | 1.38762 | 0.693812 | − | 0.720156i | \(-0.255930\pi\) | ||||
0.693812 | + | 0.720156i | \(0.255930\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −872768. | −0.763456 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.70898e6 | 1.46710 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.36204e6 | −1.14765 | −0.573823 | − | 0.818979i | \(-0.694540\pi\) | ||||
−0.573823 | + | 0.818979i | \(0.694540\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 558320. | 0.461806 | 0.230903 | − | 0.972977i | \(-0.425832\pi\) | ||||
0.230903 | + | 0.972977i | \(0.425832\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.04076e6 | −0.845170 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.31102e6 | −1.04539 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −586342. | −0.459147 | −0.229573 | − | 0.973291i | \(-0.573733\pi\) | ||||
−0.229573 | + | 0.973291i | \(0.573733\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.91056e6 | 1.46943 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 606234. | 0.458010 | 0.229005 | − | 0.973425i | \(-0.426453\pi\) | ||||
0.229005 | + | 0.973425i | \(0.426453\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 865174. | 0.642151 | 0.321076 | − | 0.947054i | \(-0.395956\pi\) | ||||
0.321076 | + | 0.947054i | \(0.395956\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.78368e6 | −1.30078 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 130438. | 0.0934758 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −547501. | −0.385603 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.47838e6 | 2.40793 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 353352. | 0.240458 | 0.120229 | − | 0.992746i | \(-0.461637\pi\) | ||||
0.120229 | + | 0.992746i | \(0.461637\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 79680.0 | 0.0533082 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.75008e6 | −5.09818 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −792960. | −0.512948 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 350056. | 0.222701 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 250560. | 0.156785 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −355072. | −0.218558 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.95904e6 | 1.18631 | 0.593153 | − | 0.805090i | \(-0.297883\pi\) | ||||
0.593153 | + | 0.805090i | \(0.297883\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.38452e6 | −3.20812 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.06257e6 | 1.79550 | 0.897749 | − | 0.440508i | \(-0.145202\pi\) | ||||
0.897749 | + | 0.440508i | \(0.145202\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −582634. | −0.336151 | −0.168076 | − | 0.985774i | \(-0.553755\pi\) | ||||
−0.168076 | + | 0.985774i | \(0.553755\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.03018e6 | −0.584972 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.09585e6 | 1.73034 | 0.865171 | − | 0.501478i | \(-0.167210\pi\) | ||||
0.865171 | + | 0.501478i | \(0.167210\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 732576. | 0.403066 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.61676e6 | −0.875756 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.73537e6 | −0.925521 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.48751e6 | −0.781180 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.17910e6 | 1.64412 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −365932. | −0.186385 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −625496. | −0.313801 | −0.156901 | − | 0.987614i | \(-0.550150\pi\) | ||||
−0.156901 | + | 0.987614i | \(0.550150\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.18753e6 | 4.04616 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.27219e6 | 0.619356 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.32494e6 | 1.11516 | 0.557580 | − | 0.830123i | \(-0.311730\pi\) | ||||
0.557580 | + | 0.830123i | \(0.311730\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −75060.0 | −0.0354739 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.81459e6 | 0.845071 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 117649. | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.07520e6 | −0.486342 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 781128. | 0.348256 | 0.174128 | − | 0.984723i | \(-0.444289\pi\) | ||||
0.174128 | + | 0.984723i | \(0.444289\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.48586e6 | −0.653002 | −0.326501 | − | 0.945197i | \(-0.605870\pi\) | ||||
−0.326501 | + | 0.945197i | \(0.605870\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.79336e6 | −3.80967 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.44463e6 | 0.617048 | 0.308524 | − | 0.951217i | \(-0.400165\pi\) | ||||
0.308524 | + | 0.951217i | \(0.400165\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.23642e6 | 0.941850 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.37298e6 | −0.570156 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 404040. | 0.165458 | 0.0827291 | − | 0.996572i | \(-0.473636\pi\) | ||||
0.0827291 | + | 0.996572i | \(0.473636\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 976065. | 0.394195 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.84975e6 | −2.72840 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −526400. | −0.206816 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.71698e6 | −1.05298 | −0.526492 | − | 0.850180i | \(-0.676493\pi\) | ||||
−0.526492 | + | 0.850180i | \(0.676493\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.74893e6 | 0.668663 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.33643e6 | 0.504092 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.79399e6 | 0.667647 | 0.333824 | − | 0.942636i | \(-0.391661\pi\) | ||||
0.333824 | + | 0.942636i | \(0.391661\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.01696e6 | −1.84231 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 831192. | 0.301195 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18624.0 | 0.00666001 | 0.00333001 | − | 0.999994i | \(-0.498940\pi\) | ||||
0.00333001 | + | 0.999994i | \(0.498940\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.63376e6 | −3.04711 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.33004e6 | −0.463307 | −0.231654 | − | 0.972798i | \(-0.574414\pi\) | ||||
−0.231654 | + | 0.972798i | \(0.574414\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −978432. | −0.336418 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.69361e6 | 1.59305 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.26506e6 | −0.758936 | −0.379468 | − | 0.925205i | \(-0.623893\pi\) | ||||
−0.379468 | + | 0.925205i | \(0.623893\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.04608e6 | −0.346037 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.42986e6 | −0.466995 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.50803e6 | −0.808798 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.48900e6 | 1.42947 | 0.714733 | − | 0.699398i | \(-0.246548\pi\) | ||||
0.714733 | + | 0.699398i | \(0.246548\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.73126e6 | 0.858877 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −95442.0 | −0.0296400 | −0.0148200 | − | 0.999890i | \(-0.504718\pi\) | ||||
−0.0148200 | + | 0.999890i | \(0.504718\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.05886e6 | 0.631488 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.81437e6 | −2.06437 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.77629e6 | 2.32695 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.99003e6 | −0.883828 | −0.441914 | − | 0.897057i | \(-0.645700\pi\) | ||||
−0.441914 | + | 0.897057i | \(0.645700\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.69462e6 | −1.95489 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −122010. | −0.0351982 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.51418e6 | 1.00162 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.51626e6 | 2.11671 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.39037e6 | −0.943436 | −0.471718 | − | 0.881749i | \(-0.656366\pi\) | ||||
−0.471718 | + | 0.881749i | \(0.656366\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.38397e6 | −0.930512 | −0.465256 | − | 0.885176i | \(-0.654038\pi\) | ||||
−0.465256 | + | 0.885176i | \(0.654038\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.90648e6 | −1.33327 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.96233e6 | −0.526988 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 543704. | 0.144309 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.32538e7 | −3.47693 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.98353e6 | −0.514334 | −0.257167 | − | 0.966367i | \(-0.582789\pi\) | ||||
−0.257167 | + | 0.966367i | \(0.582789\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.17581e6 | −1.83929 | −0.919647 | − | 0.392746i | \(-0.871525\pi\) | ||||
−0.919647 | + | 0.392746i | \(0.871525\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.12704e6 | 0.285572 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.08096e6 | 0.521267 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.44390e6 | −0.605231 | −0.302616 | − | 0.953113i | \(-0.597860\pi\) | ||||
−0.302616 | + | 0.953113i | \(0.597860\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.57746e6 | 0.386243 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −231716. | −0.0560979 | −0.0280490 | − | 0.999607i | \(-0.508929\pi\) | ||||
−0.0280490 | + | 0.999607i | \(0.508929\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.82291e6 | 0.436381 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.46218e7 | −3.46125 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.73637e6 | −1.10874 | −0.554370 | − | 0.832271i | \(-0.687041\pi\) | ||||
−0.554370 | + | 0.832271i | \(0.687041\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.66109e6 | 0.384549 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.64040e6 | 0.375582 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.11014e6 | −0.251392 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.87486e6 | −1.76381 | −0.881906 | − | 0.471426i | \(-0.843740\pi\) | ||||
−0.881906 | + | 0.471426i | \(0.843740\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.16003e7 | −2.57002 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.23218e6 | 1.80411 | 0.902054 | − | 0.431623i | \(-0.142059\pi\) | ||||
0.902054 | + | 0.431623i | \(0.142059\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.36038e6 | 0.511717 | 0.255859 | − | 0.966714i | \(-0.417642\pi\) | ||||
0.255859 | + | 0.966714i | \(0.417642\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.79168e6 | 0.598733 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.31700e6 | 1.34035 | 0.670175 | − | 0.742203i | \(-0.266219\pi\) | ||||
0.670175 | + | 0.742203i | \(0.266219\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.94804e6 | −0.408947 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.33204e6 | 1.31520 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.45786e6 | 0.916164 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.90366e6 | 0.793849 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.79190e7 | 3.60594 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.45856e6 | 0.290459 | 0.145229 | − | 0.989398i | \(-0.453608\pi\) | ||||
0.145229 | + | 0.989398i | \(0.453608\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.82310e6 | 1.73883 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.64640e6 | 0.321120 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.71027e6 | 0.716228 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.28782e6 | 1.77456 | 0.887282 | − | 0.461228i | \(-0.152591\pi\) | ||||
0.887282 | + | 0.461228i | \(0.152591\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −605760. | −0.114559 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 234972. | 0.0439858 | 0.0219929 | − | 0.999758i | \(-0.492999\pi\) | ||||
0.0219929 | + | 0.999758i | \(0.492999\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.09652e6 | 0.203188 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.31190e7 | −2.40651 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.42451e6 | −0.621882 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.00792e6 | 1.25991 | 0.629953 | − | 0.776633i | \(-0.283074\pi\) | ||||
0.629953 | + | 0.776633i | \(0.283074\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 135720. | 0.0241574 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.94752e6 | 0.871902 | 0.435951 | − | 0.899970i | \(-0.356412\pi\) | ||||
0.435951 | + | 0.899970i | \(0.356412\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 267264. | 0.0466350 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.89913e6 | −0.673671 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.50640e6 | −0.942049 | −0.471025 | − | 0.882120i | \(-0.656116\pi\) | ||||
−0.471025 | + | 0.882120i | \(0.656116\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 806050. | 0.136556 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.30764e7 | 3.87145 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.74349e6 | −0.954240 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.66003e6 | −0.766765 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.12996e6 | −0.510059 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.63076e6 | 0.263206 | 0.131603 | − | 0.991303i | \(-0.457988\pi\) | ||||
0.131603 | + | 0.991303i | \(0.457988\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.00765e7 | 1.61086 | 0.805429 | − | 0.592692i | \(-0.201935\pi\) | ||||
0.805429 | + | 0.592692i | \(0.201935\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.08847e6 | 0.489041 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.71607e6 | 0.426005 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.18194e6 | −0.805107 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.63593e6 | −0.251784 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.88470e6 | 0.287358 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.72454e6 | −0.260489 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.05172e6 | −0.905614 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.49822e6 | 0.222129 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.25225e7 | 1.83949 | 0.919746 | − | 0.392513i | \(-0.128394\pi\) | ||||
0.919746 | + | 0.392513i | \(0.128394\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.96710e7 | 2.86304 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.39104e6 | 0.489037 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.67430e6 | −0.953756 | −0.476878 | − | 0.878970i | \(-0.658232\pi\) | ||||
−0.476878 | + | 0.878970i | \(0.658232\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.29007e6 | 1.03229 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.18129e6 | −0.306080 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.84042e6 | 0.534031 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.19635e7 | 1.64864 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.61643e6 | 0.630475 | 0.315238 | − | 0.949013i | \(-0.397916\pi\) | ||||
0.315238 | + | 0.949013i | \(0.397916\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.05795e6 | 0.684613 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.74845e7 | −2.34555 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.84218e6 | 1.17568 | 0.587839 | − | 0.808978i | \(-0.299979\pi\) | ||||
0.587839 | + | 0.808978i | \(0.299979\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −80064.0 | −0.0105515 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.04345e7 | 1.36306 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.15771e7 | 1.49906 | 0.749532 | − | 0.661968i | \(-0.230279\pi\) | ||||
0.749532 | + | 0.661968i | \(0.230279\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.48069e6 | −0.575115 | −0.287557 | − | 0.957763i | \(-0.592843\pi\) | ||||
−0.287557 | + | 0.957763i | \(0.592843\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.54488e6 | 0.578277 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.35312e6 | 0.296807 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.32788e7 | 1.66042 | 0.830212 | − | 0.557448i | \(-0.188220\pi\) | ||||
0.830212 | + | 0.557448i | \(0.188220\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.87978e6 | −0.852861 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.38108e6 | −0.661347 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.70190e7 | 2.07378 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.48850e7 | −1.79829 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.11188e7 | 1.33187 | 0.665936 | − | 0.746009i | \(-0.268032\pi\) | ||||
0.665936 | + | 0.746009i | \(0.268032\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.40306e6 | −0.641729 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.26326e7 | 1.48773 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.92737e6 | −0.458632 | −0.229316 | − | 0.973352i | \(-0.573649\pi\) | ||||
−0.229316 | + | 0.973352i | \(0.573649\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.46451e6 | −0.169590 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.91900e6 | −0.679693 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.74099e7 | −1.98258 | −0.991289 | − | 0.131704i | \(-0.957955\pi\) | ||||
−0.991289 | + | 0.131704i | \(0.957955\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.46243e6 | 0.842740 | 0.421370 | − | 0.906889i | \(-0.361549\pi\) | ||||
0.421370 | + | 0.906889i | \(0.361549\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.61197e7 | −2.92533 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.30640e6 | −0.811549 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 701152. | 0.0772397 | 0.0386198 | − | 0.999254i | \(-0.487704\pi\) | ||||
0.0386198 | + | 0.999254i | \(0.487704\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.72578e6 | −0.188557 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.28734e6 | −0.572974 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.09575e7 | −1.17777 | −0.588886 | − | 0.808216i | \(-0.700433\pi\) | ||||
−0.588886 | + | 0.808216i | \(0.700433\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.55552e6 | 0.272453 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.90666e6 | 0.201633 | 0.100816 | − | 0.994905i | \(-0.467855\pi\) | ||||
0.100816 | + | 0.994905i | \(0.467855\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.22346e6 | 0.233240 | 0.116620 | − | 0.993177i | \(-0.462794\pi\) | ||||
0.116620 | + | 0.993177i | \(0.462794\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.39104e7 | 1.44747 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.79133e6 | −0.288132 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.21420e6 | 0.124334 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.47818e7 | 3.53332 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.16395e7 | 1.17303 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 752624. | 0.0752497 | 0.0376248 | − | 0.999292i | \(-0.488021\pi\) | ||||
0.0376248 | + | 0.999292i | \(0.488021\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.03716e7 | 2.02076 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.20934e6 | −0.906347 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.69991e6 | 0.165988 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.59164e7 | −4.44852 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.45429e6 | −0.235929 | −0.117964 | − | 0.993018i | \(-0.537637\pi\) | ||||
−0.117964 | + | 0.993018i | \(0.537637\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.58237e7 | −1.50932 | −0.754660 | − | 0.656116i | \(-0.772198\pi\) | ||||
−0.754660 | + | 0.656116i | \(0.772198\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.85824e6 | 0.649103 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.65489e6 | −0.249337 | −0.124668 | − | 0.992198i | \(-0.539787\pi\) | ||||
−0.124668 | + | 0.992198i | \(0.539787\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.55376e6 | −0.144801 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.27476e6 | −0.395330 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.26899e6 | −0.850648 | −0.425324 | − | 0.905041i | \(-0.639840\pi\) | ||||
−0.425324 | + | 0.905041i | \(0.639840\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.52518e6 | −0.138905 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.08076e7 | 0.976827 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.68242e7 | 1.50911 | 0.754556 | − | 0.656235i | \(-0.227852\pi\) | ||||
0.754556 | + | 0.656235i | \(0.227852\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.77217e6 | 0.602871 | 0.301435 | − | 0.953487i | \(-0.402534\pi\) | ||||
0.301435 | + | 0.953487i | \(0.402534\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.98382e7 | −1.75274 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.91334e6 | 0.255469 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.31488e6 | −0.114438 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.53320e6 | 0.477981 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.92390e6 | 0.593669 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.61315e6 | 0.647928 | 0.323964 | − | 0.946069i | \(-0.394984\pi\) | ||||
0.323964 | + | 0.946069i | \(0.394984\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.60944e7 | 2.20439 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.11672e6 | −0.512917 | −0.256459 | − | 0.966555i | \(-0.582556\pi\) | ||||
−0.256459 | + | 0.966555i | \(0.582556\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.68135e6 | −0.472909 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.60423e7 | −2.15185 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.12588e7 | 0.923511 | 0.461755 | − | 0.887007i | \(-0.347220\pi\) | ||||
0.461755 | + | 0.887007i | \(0.347220\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.14093e6 | −0.581471 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.78158e7 | −1.44017 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.93100e7 | 1.54965 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.50952e6 | −0.757641 | −0.378821 | − | 0.925470i | \(-0.623670\pi\) | ||||
−0.378821 | + | 0.925470i | \(0.623670\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.00884e7 | 1.58896 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.01734e6 | 0.629605 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.48631e6 | 0.193853 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.44654e6 | −0.111979 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.53868e7 | −1.18264 | −0.591322 | − | 0.806436i | \(-0.701394\pi\) | ||||
−0.591322 | + | 0.806436i | \(0.701394\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.31544e7 | −1.76703 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.16928e6 | −0.543254 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −409248. | −0.0307920 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.21379e6 | 0.0906834 | 0.0453417 | − | 0.998972i | \(-0.485562\pi\) | ||||
0.0453417 | + | 0.998972i | \(0.485562\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.14930e7 | 3.82010 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.25696e6 | −0.239932 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.41373e7 | −1.03420 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.25064e6 | −0.526718 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.00002e7 | −0.721418 | −0.360709 | − | 0.932678i | \(-0.617465\pi\) | ||||
−0.360709 | + | 0.932678i | \(0.617465\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.79472e6 | 0.630063 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.69581e7 | −1.20651 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.46657e6 | −0.174281 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.33745e7 | 0.938514 | 0.469257 | − | 0.883062i | \(-0.344522\pi\) | ||||
0.469257 | + | 0.883062i | \(0.344522\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.93657e7 | 3.44038 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.67250e6 | 0.461844 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.61380e7 | −1.10940 | −0.554701 | − | 0.832050i | \(-0.687167\pi\) | ||||
−0.554701 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.30496e6 | 0.157378 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.48077e7 | −1.68236 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.61059e6 | −0.579992 | −0.289996 | − | 0.957028i | \(-0.593654\pi\) | ||||
−0.289996 | + | 0.957028i | \(0.593654\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.94639e7 | 2.64031 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.85027e7 | −1.89415 | −0.947075 | − | 0.321012i | \(-0.895977\pi\) | ||||
−0.947075 | + | 0.321012i | \(0.895977\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.55966e7 | −1.02953 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.21504e7 | −4.73083 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.64071e6 | 0.171995 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.28721e6 | −0.471478 | −0.235739 | − | 0.971816i | \(-0.575751\pi\) | ||||
−0.235739 | + | 0.971816i | \(0.575751\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.31324e7 | −2.77215 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.74976e6 | 0.111715 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.77165e7 | 1.75792 | 0.878958 | − | 0.476899i | \(-0.158239\pi\) | ||||
0.878958 | + | 0.476899i | \(0.158239\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.09664e7 | 1.32105 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.07625e7 | 1.92557 | 0.962787 | − | 0.270262i | \(-0.0871103\pi\) | ||||
0.962787 | + | 0.270262i | \(0.0871103\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.19253e6 | −0.322900 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.96364e7 | −1.21313 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.76292e6 | −0.108204 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.83665e7 | −1.11998 | −0.559990 | − | 0.828499i | \(-0.689195\pi\) | ||||
−0.559990 | + | 0.828499i | \(0.689195\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.48441e7 | −0.899325 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.01397e7 | 0.610348 | 0.305174 | − | 0.952297i | \(-0.401285\pi\) | ||||
0.305174 | + | 0.952297i | \(0.401285\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.10971e6 | −0.365398 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.83191e7 | −1.08856 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.94600e6 | −0.292018 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.36101e7 | −2.55835 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.45811e7 | −0.849934 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.75418e6 | 0.391199 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.89442e7 | 1.09028 | 0.545140 | − | 0.838345i | \(-0.316476\pi\) | ||||
0.545140 | + | 0.838345i | \(0.316476\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.66963e7 | −2.67049 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 122598. | 0.00696694 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.85597e6 | 0.443626 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.61830e7 | 1.46927 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.19835e7 | 0.668248 | 0.334124 | − | 0.942529i | \(-0.391560\pi\) | ||||
0.334124 | + | 0.942529i | \(0.391560\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.97511e6 | −0.386531 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.74267e7 | −2.06110 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.02648e7 | 0.561774 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.75616e6 | 0.0955156 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.08611e7 | 2.20865 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.31823e6 | −0.339410 | −0.169705 | − | 0.985495i | \(-0.554281\pi\) | ||||
−0.169705 | + | 0.985495i | \(0.554281\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.47079e6 | −0.0785231 | −0.0392615 | − | 0.999229i | \(-0.512501\pi\) | ||||
−0.0392615 | + | 0.999229i | \(0.512501\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.67496e7 | −0.888747 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −646144. | −0.0340750 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.32736e7 | −0.695716 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.27926e7 | 1.18737 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.10138e7 | 1.08804 | 0.544022 | − | 0.839071i | \(-0.316901\pi\) | ||||
0.544022 | + | 0.839071i | \(0.316901\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.35856e7 | −0.699163 | −0.349582 | − | 0.936906i | \(-0.613676\pi\) | ||||
−0.349582 | + | 0.936906i | \(0.613676\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.93307e7 | 2.01186 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.62070e7 | 1.33246 | 0.666230 | − | 0.745747i | \(-0.267907\pi\) | ||||
0.666230 | + | 0.745747i | \(0.267907\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.17710e7 | 0.594876 | 0.297438 | − | 0.954741i | \(-0.403868\pi\) | ||||
0.297438 | + | 0.954741i | \(0.403868\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.75903e7 | 0.883628 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.24253e6 | 0.111976 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 144768. | 0.00718549 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.61174e7 | −1.78198 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.44898e7 | 0.710651 | 0.355326 | − | 0.934743i | \(-0.384370\pi\) | ||||
0.355326 | + | 0.934743i | \(0.384370\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.91329e7 | −0.932804 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.81870e7 | −0.881440 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.15907e6 | −0.200380 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.11879e7 | 0.535847 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.59552e7 | −1.23582 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.39574e7 | −0.660666 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.77865e7 | −0.836984 | −0.418492 | − | 0.908220i | \(-0.637441\pi\) | ||||
−0.418492 | + | 0.908220i | \(0.637441\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.90626e7 | 1.82745 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.79124e7 | 1.76331 | 0.881656 | − | 0.471893i | \(-0.156429\pi\) | ||||
0.881656 | + | 0.471893i | \(0.156429\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.32376e7 | −1.53690 | −0.768451 | − | 0.639909i | \(-0.778972\pi\) | ||||
−0.768451 | + | 0.639909i | \(0.778972\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.91314e6 | −0.179894 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.33166e6 | 0.106571 | 0.0532853 | − | 0.998579i | \(-0.483031\pi\) | ||||
0.0532853 | + | 0.998579i | \(0.483031\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.33862e6 | −0.151715 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.64250e7 | 0.742093 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.89066e7 | 2.19694 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.81472e7 | −1.25716 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.61765e7 | −3.38287 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.19437e6 | 0.361822 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.38189e7 | 1.48477 | 0.742386 | − | 0.669972i | \(-0.233694\pi\) | ||||
0.742386 | + | 0.669972i | \(0.233694\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.06006e7 | −0.462761 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.65707e7 | 1.15336 | 0.576678 | − | 0.816972i | \(-0.304349\pi\) | ||||
0.576678 | + | 0.816972i | \(0.304349\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.74913e7 | −0.754954 | −0.377477 | − | 0.926019i | \(-0.623208\pi\) | ||||
−0.377477 | + | 0.926019i | \(0.623208\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.39040e6 | −0.102592 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.77452e7 | −0.757305 | −0.378652 | − | 0.925539i | \(-0.623612\pi\) | ||||
−0.378652 | + | 0.925539i | \(0.623612\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.41018e7 | 0.598440 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.32880e8 | 5.60746 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.38755e7 | 0.582266 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.45517e6 | −0.269370 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.37888e7 | 0.987169 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.41399e6 | 0.140885 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.54739e7 | 1.04540 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.05017e7 | −0.428587 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.09824e7 | 0.851596 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.82335e7 | 1.13958 | 0.569792 | − | 0.821789i | \(-0.307024\pi\) | ||||
0.569792 | + | 0.821789i | \(0.307024\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.48726e6 | −0.220265 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.71757e7 | 0.685674 | 0.342837 | − | 0.939395i | \(-0.388612\pi\) | ||||
0.342837 | + | 0.939395i | \(0.388612\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.85264e7 | −2.72070 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.06522e7 | 0.420615 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.33544e6 | 0.0917160 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.42273e7 | 0.946273 | 0.473137 | − | 0.880989i | \(-0.343122\pi\) | ||||
0.473137 | + | 0.880989i | \(0.343122\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.87711e7 | −2.28305 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.94807e7 | −1.91175 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.61827e7 | −1.00614 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.17921e8 | 4.50704 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.45919e7 | 0.934874 | 0.467437 | − | 0.884026i | \(-0.345178\pi\) | ||||
0.467437 | + | 0.884026i | \(0.345178\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.46106e6 | −0.168680 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.18770e7 | −3.45544 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.86501e7 | −0.697674 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.31199e7 | −0.488181 | −0.244090 | − | 0.969753i | \(-0.578489\pi\) | ||||
−0.244090 | + | 0.969753i | \(0.578489\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.74790e7 | 0.646924 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −640776. | −0.0235902 | −0.0117951 | − | 0.999930i | \(-0.503755\pi\) | ||||
−0.0117951 | + | 0.999930i | \(0.503755\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.98144e6 | −0.109181 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.94746e7 | 0.709395 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.01502e7 | −0.730135 | −0.365068 | − | 0.930981i | \(-0.618954\pi\) | ||||
−0.365068 | + | 0.930981i | \(0.618954\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.16466e7 | 0.419791 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.28755e7 | −3.33004 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.33217e7 | −1.18849 | −0.594244 | − | 0.804285i | \(-0.702549\pi\) | ||||
−0.594244 | + | 0.804285i | \(0.702549\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.84787e6 | 0.172006 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.19773e7 | −0.775701 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.09345e7 | 0.383932 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.01727e7 | −0.704621 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.54070e7 | 1.23034 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.33843e6 | −0.253679 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.51857e7 | 1.55394 | 0.776970 | − | 0.629537i | \(-0.216755\pi\) | ||||
0.776970 | + | 0.629537i | \(0.216755\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.20612e7 | 1.78117 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.62935e7 | −0.894953 | −0.447477 | − | 0.894296i | \(-0.647677\pi\) | ||||
−0.447477 | + | 0.894296i | \(0.647677\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.22766e7 | −0.415714 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.46252e7 | 1.50338 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.02548e7 | 0.678879 | 0.339440 | − | 0.940628i | \(-0.389763\pi\) | ||||
0.339440 | + | 0.940628i | \(0.389763\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.55468e7 | −1.18534 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.96223e7 | −2.30981 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.43782e6 | 0.311521 | 0.155761 | − | 0.987795i | \(-0.450217\pi\) | ||||
0.155761 | + | 0.987795i | \(0.450217\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.34748e7 | 0.442517 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.09780e7 | 0.358698 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.00128e6 | −0.260117 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.53265e7 | 0.495747 | 0.247874 | − | 0.968792i | \(-0.420268\pi\) | ||||
0.247874 | + | 0.968792i | \(0.420268\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.87649e7 | 0.603911 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.31360e6 | −0.202171 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.16514e6 | 0.0689841 | 0.0344920 | − | 0.999405i | \(-0.489019\pi\) | ||||
0.0344920 | + | 0.999405i | \(0.489019\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.54778e8 | −4.90677 |
(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 | 448.6.a.a.1.1 | 1 | ||
4.3 | odd | 2 | 448.6.a.p.1.1 | 1 | |||
8.3 | odd | 2 | 112.6.a.a.1.1 | 1 | |||
8.5 | even | 2 | 56.6.a.b.1.1 | ✓ | 1 | ||
24.5 | odd | 2 | 504.6.a.b.1.1 | 1 | |||
24.11 | even | 2 | 1008.6.a.h.1.1 | 1 | |||
56.5 | odd | 6 | 392.6.i.f.361.1 | 2 | |||
56.13 | odd | 2 | 392.6.a.a.1.1 | 1 | |||
56.27 | even | 2 | 784.6.a.n.1.1 | 1 | |||
56.37 | even | 6 | 392.6.i.a.361.1 | 2 | |||
56.45 | odd | 6 | 392.6.i.f.177.1 | 2 | |||
56.53 | even | 6 | 392.6.i.a.177.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.6.a.b.1.1 | ✓ | 1 | 8.5 | even | 2 | ||
112.6.a.a.1.1 | 1 | 8.3 | odd | 2 | |||
392.6.a.a.1.1 | 1 | 56.13 | odd | 2 | |||
392.6.i.a.177.1 | 2 | 56.53 | even | 6 | |||
392.6.i.a.361.1 | 2 | 56.37 | even | 6 | |||
392.6.i.f.177.1 | 2 | 56.45 | odd | 6 | |||
392.6.i.f.361.1 | 2 | 56.5 | odd | 6 | |||
448.6.a.a.1.1 | 1 | 1.1 | even | 1 | trivial | ||
448.6.a.p.1.1 | 1 | 4.3 | odd | 2 | |||
504.6.a.b.1.1 | 1 | 24.5 | odd | 2 | |||
784.6.a.n.1.1 | 1 | 56.27 | even | 2 | |||
1008.6.a.h.1.1 | 1 | 24.11 | even | 2 |