Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1078,6,Mod(1,1078)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1078, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1078.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1078 = 2 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1078.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: | \(172.893757758\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 22) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1078.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000 | 0.707107 | ||||||||
\(3\) | 29.0000 | 1.86035 | 0.930175 | − | 0.367115i | \(-0.119655\pi\) | ||||
0.930175 | + | 0.367115i | \(0.119655\pi\) | |||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 31.0000 | 0.554545 | 0.277272 | − | 0.960791i | \(-0.410570\pi\) | ||||
0.277272 | + | 0.960791i | \(0.410570\pi\) | |||||||
\(6\) | 116.000 | 1.31547 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 64.0000 | 0.353553 | ||||||||
\(9\) | 598.000 | 2.46091 | ||||||||
\(10\) | 124.000 | 0.392122 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | 464.000 | 0.930175 | ||||||||
\(13\) | −112.000 | −0.183806 | −0.0919030 | − | 0.995768i | \(-0.529295\pi\) | ||||
−0.0919030 | + | 0.995768i | \(0.529295\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 899.000 | 1.03165 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 1142.00 | 0.958393 | 0.479197 | − | 0.877708i | \(-0.340928\pi\) | ||||
0.479197 | + | 0.877708i | \(0.340928\pi\) | |||||||
\(18\) | 2392.00 | 1.74012 | ||||||||
\(19\) | 612.000 | 0.388926 | 0.194463 | − | 0.980910i | \(-0.437704\pi\) | ||||
0.194463 | + | 0.980910i | \(0.437704\pi\) | |||||||
\(20\) | 496.000 | 0.277272 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 484.000 | 0.213201 | ||||||||
\(23\) | −1941.00 | −0.765078 | −0.382539 | − | 0.923939i | \(-0.624950\pi\) | ||||
−0.382539 | + | 0.923939i | \(0.624950\pi\) | |||||||
\(24\) | 1856.00 | 0.657733 | ||||||||
\(25\) | −2164.00 | −0.692480 | ||||||||
\(26\) | −448.000 | −0.129970 | ||||||||
\(27\) | 10295.0 | 2.71780 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1192.00 | 0.263197 | 0.131599 | − | 0.991303i | \(-0.457989\pi\) | ||||
0.131599 | + | 0.991303i | \(0.457989\pi\) | |||||||
\(30\) | 3596.00 | 0.729485 | ||||||||
\(31\) | 1037.00 | 0.193809 | 0.0969046 | − | 0.995294i | \(-0.469106\pi\) | ||||
0.0969046 | + | 0.995294i | \(0.469106\pi\) | |||||||
\(32\) | 1024.00 | 0.176777 | ||||||||
\(33\) | 3509.00 | 0.560917 | ||||||||
\(34\) | 4568.00 | 0.677686 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 9568.00 | 1.23045 | ||||||||
\(37\) | 8083.00 | 0.970663 | 0.485331 | − | 0.874330i | \(-0.338699\pi\) | ||||
0.485331 | + | 0.874330i | \(0.338699\pi\) | |||||||
\(38\) | 2448.00 | 0.275012 | ||||||||
\(39\) | −3248.00 | −0.341944 | ||||||||
\(40\) | 1984.00 | 0.196061 | ||||||||
\(41\) | 10444.0 | 0.970303 | 0.485151 | − | 0.874430i | \(-0.338765\pi\) | ||||
0.485151 | + | 0.874430i | \(0.338765\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 58.0000 | 0.00478362 | 0.00239181 | − | 0.999997i | \(-0.499239\pi\) | ||||
0.00239181 | + | 0.999997i | \(0.499239\pi\) | |||||||
\(44\) | 1936.00 | 0.150756 | ||||||||
\(45\) | 18538.0 | 1.36468 | ||||||||
\(46\) | −7764.00 | −0.540992 | ||||||||
\(47\) | −8656.00 | −0.571574 | −0.285787 | − | 0.958293i | \(-0.592255\pi\) | ||||
−0.285787 | + | 0.958293i | \(0.592255\pi\) | |||||||
\(48\) | 7424.00 | 0.465088 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −8656.00 | −0.489657 | ||||||||
\(51\) | 33118.0 | 1.78295 | ||||||||
\(52\) | −1792.00 | −0.0919030 | ||||||||
\(53\) | −20318.0 | −0.993554 | −0.496777 | − | 0.867878i | \(-0.665483\pi\) | ||||
−0.496777 | + | 0.867878i | \(0.665483\pi\) | |||||||
\(54\) | 41180.0 | 1.92177 | ||||||||
\(55\) | 3751.00 | 0.167202 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 17748.0 | 0.723540 | ||||||||
\(58\) | 4768.00 | 0.186109 | ||||||||
\(59\) | 21351.0 | 0.798524 | 0.399262 | − | 0.916837i | \(-0.369266\pi\) | ||||
0.399262 | + | 0.916837i | \(0.369266\pi\) | |||||||
\(60\) | 14384.0 | 0.515824 | ||||||||
\(61\) | −47044.0 | −1.61875 | −0.809375 | − | 0.587293i | \(-0.800194\pi\) | ||||
−0.809375 | + | 0.587293i | \(0.800194\pi\) | |||||||
\(62\) | 4148.00 | 0.137044 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | −3472.00 | −0.101929 | ||||||||
\(66\) | 14036.0 | 0.396628 | ||||||||
\(67\) | 48093.0 | 1.30887 | 0.654433 | − | 0.756120i | \(-0.272908\pi\) | ||||
0.654433 | + | 0.756120i | \(0.272908\pi\) | |||||||
\(68\) | 18272.0 | 0.479197 | ||||||||
\(69\) | −56289.0 | −1.42331 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −24967.0 | −0.587788 | −0.293894 | − | 0.955838i | \(-0.594951\pi\) | ||||
−0.293894 | + | 0.955838i | \(0.594951\pi\) | |||||||
\(72\) | 38272.0 | 0.870061 | ||||||||
\(73\) | 42288.0 | 0.928774 | 0.464387 | − | 0.885632i | \(-0.346275\pi\) | ||||
0.464387 | + | 0.885632i | \(0.346275\pi\) | |||||||
\(74\) | 32332.0 | 0.686362 | ||||||||
\(75\) | −62756.0 | −1.28826 | ||||||||
\(76\) | 9792.00 | 0.194463 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −12992.0 | −0.241791 | ||||||||
\(79\) | −72410.0 | −1.30536 | −0.652681 | − | 0.757633i | \(-0.726356\pi\) | ||||
−0.652681 | + | 0.757633i | \(0.726356\pi\) | |||||||
\(80\) | 7936.00 | 0.138636 | ||||||||
\(81\) | 153241. | 2.59515 | ||||||||
\(82\) | 41776.0 | 0.686108 | ||||||||
\(83\) | 15806.0 | 0.251841 | 0.125921 | − | 0.992040i | \(-0.459812\pi\) | ||||
0.125921 | + | 0.992040i | \(0.459812\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 35402.0 | 0.531472 | ||||||||
\(86\) | 232.000 | 0.00338253 | ||||||||
\(87\) | 34568.0 | 0.489639 | ||||||||
\(88\) | 7744.00 | 0.106600 | ||||||||
\(89\) | 114761. | 1.53575 | 0.767873 | − | 0.640602i | \(-0.221315\pi\) | ||||
0.767873 | + | 0.640602i | \(0.221315\pi\) | |||||||
\(90\) | 74152.0 | 0.964976 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −31056.0 | −0.382539 | ||||||||
\(93\) | 30073.0 | 0.360553 | ||||||||
\(94\) | −34624.0 | −0.404164 | ||||||||
\(95\) | 18972.0 | 0.215677 | ||||||||
\(96\) | 29696.0 | 0.328867 | ||||||||
\(97\) | 5159.00 | 0.0556719 | 0.0278360 | − | 0.999613i | \(-0.491138\pi\) | ||||
0.0278360 | + | 0.999613i | \(0.491138\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 72358.0 | 0.741991 | ||||||||
\(100\) | −34624.0 | −0.346240 | ||||||||
\(101\) | 61426.0 | 0.599168 | 0.299584 | − | 0.954070i | \(-0.403152\pi\) | ||||
0.299584 | + | 0.954070i | \(0.403152\pi\) | |||||||
\(102\) | 132472. | 1.26073 | ||||||||
\(103\) | −185896. | −1.72654 | −0.863271 | − | 0.504741i | \(-0.831588\pi\) | ||||
−0.863271 | + | 0.504741i | \(0.831588\pi\) | |||||||
\(104\) | −7168.00 | −0.0649852 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −81272.0 | −0.702548 | ||||||||
\(107\) | −23970.0 | −0.202399 | −0.101200 | − | 0.994866i | \(-0.532268\pi\) | ||||
−0.101200 | + | 0.994866i | \(0.532268\pi\) | |||||||
\(108\) | 164720. | 1.35890 | ||||||||
\(109\) | −56326.0 | −0.454091 | −0.227045 | − | 0.973884i | \(-0.572907\pi\) | ||||
−0.227045 | + | 0.973884i | \(0.572907\pi\) | |||||||
\(110\) | 15004.0 | 0.118229 | ||||||||
\(111\) | 234407. | 1.80577 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −261903. | −1.92950 | −0.964749 | − | 0.263171i | \(-0.915231\pi\) | ||||
−0.964749 | + | 0.263171i | \(0.915231\pi\) | |||||||
\(114\) | 70992.0 | 0.511620 | ||||||||
\(115\) | −60171.0 | −0.424270 | ||||||||
\(116\) | 19072.0 | 0.131599 | ||||||||
\(117\) | −66976.0 | −0.452329 | ||||||||
\(118\) | 85404.0 | 0.564642 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 57536.0 | 0.364743 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | −188176. | −1.14463 | ||||||||
\(123\) | 302876. | 1.80510 | ||||||||
\(124\) | 16592.0 | 0.0969046 | ||||||||
\(125\) | −163959. | −0.938556 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 87404.0 | 0.480864 | 0.240432 | − | 0.970666i | \(-0.422711\pi\) | ||||
0.240432 | + | 0.970666i | \(0.422711\pi\) | |||||||
\(128\) | 16384.0 | 0.0883883 | ||||||||
\(129\) | 1682.00 | 0.00889922 | ||||||||
\(130\) | −13888.0 | −0.0720744 | ||||||||
\(131\) | −265122. | −1.34979 | −0.674897 | − | 0.737912i | \(-0.735812\pi\) | ||||
−0.674897 | + | 0.737912i | \(0.735812\pi\) | |||||||
\(132\) | 56144.0 | 0.280458 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 192372. | 0.925507 | ||||||||
\(135\) | 319145. | 1.50714 | ||||||||
\(136\) | 73088.0 | 0.338843 | ||||||||
\(137\) | 245857. | 1.11913 | 0.559566 | − | 0.828786i | \(-0.310968\pi\) | ||||
0.559566 | + | 0.828786i | \(0.310968\pi\) | |||||||
\(138\) | −225156. | −1.00644 | ||||||||
\(139\) | 363594. | 1.59617 | 0.798086 | − | 0.602544i | \(-0.205846\pi\) | ||||
0.798086 | + | 0.602544i | \(0.205846\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −251024. | −1.06333 | ||||||||
\(142\) | −99868.0 | −0.415629 | ||||||||
\(143\) | −13552.0 | −0.0554196 | ||||||||
\(144\) | 153088. | 0.615226 | ||||||||
\(145\) | 36952.0 | 0.145955 | ||||||||
\(146\) | 169152. | 0.656742 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 129328. | 0.485331 | ||||||||
\(149\) | −55750.0 | −0.205721 | −0.102861 | − | 0.994696i | \(-0.532800\pi\) | ||||
−0.102861 | + | 0.994696i | \(0.532800\pi\) | |||||||
\(150\) | −251024. | −0.910934 | ||||||||
\(151\) | 65642.0 | 0.234282 | 0.117141 | − | 0.993115i | \(-0.462627\pi\) | ||||
0.117141 | + | 0.993115i | \(0.462627\pi\) | |||||||
\(152\) | 39168.0 | 0.137506 | ||||||||
\(153\) | 682916. | 2.35852 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 32147.0 | 0.107476 | ||||||||
\(156\) | −51968.0 | −0.170972 | ||||||||
\(157\) | 275367. | 0.891585 | 0.445793 | − | 0.895136i | \(-0.352922\pi\) | ||||
0.445793 | + | 0.895136i | \(0.352922\pi\) | |||||||
\(158\) | −289640. | −0.923030 | ||||||||
\(159\) | −589222. | −1.84836 | ||||||||
\(160\) | 31744.0 | 0.0980306 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 612964. | 1.83505 | ||||||||
\(163\) | 291940. | 0.860646 | 0.430323 | − | 0.902675i | \(-0.358400\pi\) | ||||
0.430323 | + | 0.902675i | \(0.358400\pi\) | |||||||
\(164\) | 167104. | 0.485151 | ||||||||
\(165\) | 108779. | 0.311054 | ||||||||
\(166\) | 63224.0 | 0.178079 | ||||||||
\(167\) | 337344. | 0.936013 | 0.468006 | − | 0.883725i | \(-0.344972\pi\) | ||||
0.468006 | + | 0.883725i | \(0.344972\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −358749. | −0.966215 | ||||||||
\(170\) | 141608. | 0.375808 | ||||||||
\(171\) | 365976. | 0.957111 | ||||||||
\(172\) | 928.000 | 0.00239181 | ||||||||
\(173\) | 116742. | 0.296560 | 0.148280 | − | 0.988945i | \(-0.452626\pi\) | ||||
0.148280 | + | 0.988945i | \(0.452626\pi\) | |||||||
\(174\) | 138272. | 0.346227 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 30976.0 | 0.0753778 | ||||||||
\(177\) | 619179. | 1.48554 | ||||||||
\(178\) | 459044. | 1.08594 | ||||||||
\(179\) | −19107.0 | −0.0445718 | −0.0222859 | − | 0.999752i | \(-0.507094\pi\) | ||||
−0.0222859 | + | 0.999752i | \(0.507094\pi\) | |||||||
\(180\) | 296608. | 0.682341 | ||||||||
\(181\) | 16177.0 | 0.0367030 | 0.0183515 | − | 0.999832i | \(-0.494158\pi\) | ||||
0.0183515 | + | 0.999832i | \(0.494158\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.36428e6 | −3.01144 | ||||||||
\(184\) | −124224. | −0.270496 | ||||||||
\(185\) | 250573. | 0.538276 | ||||||||
\(186\) | 120292. | 0.254950 | ||||||||
\(187\) | 138182. | 0.288966 | ||||||||
\(188\) | −138496. | −0.285787 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 75888.0 | 0.152507 | ||||||||
\(191\) | 685333. | 1.35931 | 0.679655 | − | 0.733532i | \(-0.262130\pi\) | ||||
0.679655 | + | 0.733532i | \(0.262130\pi\) | |||||||
\(192\) | 118784. | 0.232544 | ||||||||
\(193\) | −309292. | −0.597689 | −0.298845 | − | 0.954302i | \(-0.596601\pi\) | ||||
−0.298845 | + | 0.954302i | \(0.596601\pi\) | |||||||
\(194\) | 20636.0 | 0.0393660 | ||||||||
\(195\) | −100688. | −0.189623 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −120930. | −0.222008 | −0.111004 | − | 0.993820i | \(-0.535407\pi\) | ||||
−0.111004 | + | 0.993820i | \(0.535407\pi\) | |||||||
\(198\) | 289432. | 0.524667 | ||||||||
\(199\) | −915536. | −1.63886 | −0.819432 | − | 0.573177i | \(-0.805711\pi\) | ||||
−0.819432 | + | 0.573177i | \(0.805711\pi\) | |||||||
\(200\) | −138496. | −0.244829 | ||||||||
\(201\) | 1.39470e6 | 2.43495 | ||||||||
\(202\) | 245704. | 0.423676 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 529888. | 0.891474 | ||||||||
\(205\) | 323764. | 0.538076 | ||||||||
\(206\) | −743584. | −1.22085 | ||||||||
\(207\) | −1.16072e6 | −1.88279 | ||||||||
\(208\) | −28672.0 | −0.0459515 | ||||||||
\(209\) | 74052.0 | 0.117266 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −134580. | −0.208101 | −0.104051 | − | 0.994572i | \(-0.533180\pi\) | ||||
−0.104051 | + | 0.994572i | \(0.533180\pi\) | |||||||
\(212\) | −325088. | −0.496777 | ||||||||
\(213\) | −724043. | −1.09349 | ||||||||
\(214\) | −95880.0 | −0.143118 | ||||||||
\(215\) | 1798.00 | 0.00265273 | ||||||||
\(216\) | 658880. | 0.960886 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −225304. | −0.321091 | ||||||||
\(219\) | 1.22635e6 | 1.72785 | ||||||||
\(220\) | 60016.0 | 0.0836008 | ||||||||
\(221\) | −127904. | −0.176158 | ||||||||
\(222\) | 937628. | 1.27687 | ||||||||
\(223\) | −468839. | −0.631337 | −0.315669 | − | 0.948869i | \(-0.602229\pi\) | ||||
−0.315669 | + | 0.948869i | \(0.602229\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.29407e6 | −1.70413 | ||||||||
\(226\) | −1.04761e6 | −1.36436 | ||||||||
\(227\) | −275022. | −0.354244 | −0.177122 | − | 0.984189i | \(-0.556679\pi\) | ||||
−0.177122 | + | 0.984189i | \(0.556679\pi\) | |||||||
\(228\) | 283968. | 0.361770 | ||||||||
\(229\) | 642281. | 0.809350 | 0.404675 | − | 0.914461i | \(-0.367385\pi\) | ||||
0.404675 | + | 0.914461i | \(0.367385\pi\) | |||||||
\(230\) | −240684. | −0.300004 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 76288.0 | 0.0930543 | ||||||||
\(233\) | −1.50485e6 | −1.81595 | −0.907973 | − | 0.419029i | \(-0.862371\pi\) | ||||
−0.907973 | + | 0.419029i | \(0.862371\pi\) | |||||||
\(234\) | −267904. | −0.319845 | ||||||||
\(235\) | −268336. | −0.316964 | ||||||||
\(236\) | 341616. | 0.399262 | ||||||||
\(237\) | −2.09989e6 | −2.42843 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −304694. | −0.345040 | −0.172520 | − | 0.985006i | \(-0.555191\pi\) | ||||
−0.172520 | + | 0.985006i | \(0.555191\pi\) | |||||||
\(240\) | 230144. | 0.257912 | ||||||||
\(241\) | −1.27181e6 | −1.41052 | −0.705260 | − | 0.708949i | \(-0.749170\pi\) | ||||
−0.705260 | + | 0.708949i | \(0.749170\pi\) | |||||||
\(242\) | 58564.0 | 0.0642824 | ||||||||
\(243\) | 1.94230e6 | 2.11009 | ||||||||
\(244\) | −752704. | −0.809375 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.21150e6 | 1.27640 | ||||||||
\(247\) | −68544.0 | −0.0714870 | ||||||||
\(248\) | 66368.0 | 0.0685219 | ||||||||
\(249\) | 458374. | 0.468513 | ||||||||
\(250\) | −655836. | −0.663659 | ||||||||
\(251\) | −629965. | −0.631149 | −0.315575 | − | 0.948901i | \(-0.602197\pi\) | ||||
−0.315575 | + | 0.948901i | \(0.602197\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −234861. | −0.230680 | ||||||||
\(254\) | 349616. | 0.340022 | ||||||||
\(255\) | 1.02666e6 | 0.988725 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −544086. | −0.513848 | −0.256924 | − | 0.966432i | \(-0.582709\pi\) | ||||
−0.256924 | + | 0.966432i | \(0.582709\pi\) | |||||||
\(258\) | 6728.00 | 0.00629270 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −55552.0 | −0.0509643 | ||||||||
\(261\) | 712816. | 0.647703 | ||||||||
\(262\) | −1.06049e6 | −0.954449 | ||||||||
\(263\) | −1.98933e6 | −1.77345 | −0.886724 | − | 0.462300i | \(-0.847024\pi\) | ||||
−0.886724 | + | 0.462300i | \(0.847024\pi\) | |||||||
\(264\) | 224576. | 0.198314 | ||||||||
\(265\) | −629858. | −0.550970 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.32807e6 | 2.85703 | ||||||||
\(268\) | 769488. | 0.654433 | ||||||||
\(269\) | −1.75446e6 | −1.47830 | −0.739149 | − | 0.673541i | \(-0.764772\pi\) | ||||
−0.739149 | + | 0.673541i | \(0.764772\pi\) | |||||||
\(270\) | 1.27658e6 | 1.06571 | ||||||||
\(271\) | 1.65824e6 | 1.37159 | 0.685795 | − | 0.727795i | \(-0.259455\pi\) | ||||
0.685795 | + | 0.727795i | \(0.259455\pi\) | |||||||
\(272\) | 292352. | 0.239598 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 983428. | 0.791346 | ||||||||
\(275\) | −261844. | −0.208791 | ||||||||
\(276\) | −900624. | −0.711657 | ||||||||
\(277\) | −42634.0 | −0.0333854 | −0.0166927 | − | 0.999861i | \(-0.505314\pi\) | ||||
−0.0166927 | + | 0.999861i | \(0.505314\pi\) | |||||||
\(278\) | 1.45438e6 | 1.12866 | ||||||||
\(279\) | 620126. | 0.476946 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 319510. | 0.241390 | 0.120695 | − | 0.992690i | \(-0.461488\pi\) | ||||
0.120695 | + | 0.992690i | \(0.461488\pi\) | |||||||
\(282\) | −1.00410e6 | −0.751887 | ||||||||
\(283\) | 2.02735e6 | 1.50474 | 0.752371 | − | 0.658739i | \(-0.228910\pi\) | ||||
0.752371 | + | 0.658739i | \(0.228910\pi\) | |||||||
\(284\) | −399472. | −0.293894 | ||||||||
\(285\) | 550188. | 0.401235 | ||||||||
\(286\) | −54208.0 | −0.0391876 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 612352. | 0.435031 | ||||||||
\(289\) | −115693. | −0.0814821 | ||||||||
\(290\) | 147808. | 0.103206 | ||||||||
\(291\) | 149611. | 0.103569 | ||||||||
\(292\) | 676608. | 0.464387 | ||||||||
\(293\) | −718844. | −0.489177 | −0.244588 | − | 0.969627i | \(-0.578653\pi\) | ||||
−0.244588 | + | 0.969627i | \(0.578653\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 661881. | 0.442818 | ||||||||
\(296\) | 517312. | 0.343181 | ||||||||
\(297\) | 1.24570e6 | 0.819446 | ||||||||
\(298\) | −223000. | −0.145467 | ||||||||
\(299\) | 217392. | 0.140626 | ||||||||
\(300\) | −1.00410e6 | −0.644128 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 262568. | 0.165663 | ||||||||
\(303\) | 1.78135e6 | 1.11466 | ||||||||
\(304\) | 156672. | 0.0972316 | ||||||||
\(305\) | −1.45836e6 | −0.897669 | ||||||||
\(306\) | 2.73166e6 | 1.66772 | ||||||||
\(307\) | 1.98142e6 | 1.19986 | 0.599930 | − | 0.800052i | \(-0.295195\pi\) | ||||
0.599930 | + | 0.800052i | \(0.295195\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.39098e6 | −3.21197 | ||||||||
\(310\) | 128588. | 0.0759970 | ||||||||
\(311\) | 1.51030e6 | 0.885446 | 0.442723 | − | 0.896658i | \(-0.354012\pi\) | ||||
0.442723 | + | 0.896658i | \(0.354012\pi\) | |||||||
\(312\) | −207872. | −0.120895 | ||||||||
\(313\) | −2.00092e6 | −1.15443 | −0.577216 | − | 0.816591i | \(-0.695861\pi\) | ||||
−0.577216 | + | 0.816591i | \(0.695861\pi\) | |||||||
\(314\) | 1.10147e6 | 0.630446 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.15856e6 | −0.652681 | ||||||||
\(317\) | −259331. | −0.144946 | −0.0724730 | − | 0.997370i | \(-0.523089\pi\) | ||||
−0.0724730 | + | 0.997370i | \(0.523089\pi\) | |||||||
\(318\) | −2.35689e6 | −1.30699 | ||||||||
\(319\) | 144232. | 0.0793569 | ||||||||
\(320\) | 126976. | 0.0693181 | ||||||||
\(321\) | −695130. | −0.376533 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 698904. | 0.372744 | ||||||||
\(324\) | 2.45186e6 | 1.29757 | ||||||||
\(325\) | 242368. | 0.127282 | ||||||||
\(326\) | 1.16776e6 | 0.608569 | ||||||||
\(327\) | −1.63345e6 | −0.844768 | ||||||||
\(328\) | 668416. | 0.343054 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 435116. | 0.219948 | ||||||||
\(331\) | 51203.0 | 0.0256877 | 0.0128439 | − | 0.999918i | \(-0.495912\pi\) | ||||
0.0128439 | + | 0.999918i | \(0.495912\pi\) | |||||||
\(332\) | 252896. | 0.125921 | ||||||||
\(333\) | 4.83363e6 | 2.38871 | ||||||||
\(334\) | 1.34938e6 | 0.661861 | ||||||||
\(335\) | 1.49088e6 | 0.725824 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 266870. | 0.128004 | 0.0640022 | − | 0.997950i | \(-0.479614\pi\) | ||||
0.0640022 | + | 0.997950i | \(0.479614\pi\) | |||||||
\(338\) | −1.43500e6 | −0.683217 | ||||||||
\(339\) | −7.59519e6 | −3.58954 | ||||||||
\(340\) | 566432. | 0.265736 | ||||||||
\(341\) | 125477. | 0.0584357 | ||||||||
\(342\) | 1.46390e6 | 0.676780 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3712.00 | 0.00169127 | ||||||||
\(345\) | −1.74496e6 | −0.789292 | ||||||||
\(346\) | 466968. | 0.209699 | ||||||||
\(347\) | 622800. | 0.277667 | 0.138834 | − | 0.990316i | \(-0.455665\pi\) | ||||
0.138834 | + | 0.990316i | \(0.455665\pi\) | |||||||
\(348\) | 553088. | 0.244820 | ||||||||
\(349\) | −2.43649e6 | −1.07078 | −0.535391 | − | 0.844604i | \(-0.679836\pi\) | ||||
−0.535391 | + | 0.844604i | \(0.679836\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.15304e6 | −0.499547 | ||||||||
\(352\) | 123904. | 0.0533002 | ||||||||
\(353\) | −1.55957e6 | −0.666144 | −0.333072 | − | 0.942901i | \(-0.608085\pi\) | ||||
−0.333072 | + | 0.942901i | \(0.608085\pi\) | |||||||
\(354\) | 2.47672e6 | 1.05043 | ||||||||
\(355\) | −773977. | −0.325955 | ||||||||
\(356\) | 1.83618e6 | 0.767873 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −76428.0 | −0.0315170 | ||||||||
\(359\) | 1.91961e6 | 0.786098 | 0.393049 | − | 0.919518i | \(-0.371420\pi\) | ||||
0.393049 | + | 0.919518i | \(0.371420\pi\) | |||||||
\(360\) | 1.18643e6 | 0.482488 | ||||||||
\(361\) | −2.10156e6 | −0.848736 | ||||||||
\(362\) | 64708.0 | 0.0259529 | ||||||||
\(363\) | 424589. | 0.169123 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.31093e6 | 0.515047 | ||||||||
\(366\) | −5.45710e6 | −2.12941 | ||||||||
\(367\) | −3.61225e6 | −1.39995 | −0.699975 | − | 0.714167i | \(-0.746806\pi\) | ||||
−0.699975 | + | 0.714167i | \(0.746806\pi\) | |||||||
\(368\) | −496896. | −0.191270 | ||||||||
\(369\) | 6.24551e6 | 2.38782 | ||||||||
\(370\) | 1.00229e6 | 0.380619 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 481168. | 0.180277 | ||||||||
\(373\) | 3.93968e6 | 1.46619 | 0.733093 | − | 0.680128i | \(-0.238076\pi\) | ||||
0.733093 | + | 0.680128i | \(0.238076\pi\) | |||||||
\(374\) | 552728. | 0.204330 | ||||||||
\(375\) | −4.75481e6 | −1.74604 | ||||||||
\(376\) | −553984. | −0.202082 | ||||||||
\(377\) | −133504. | −0.0483772 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.18829e6 | −0.782540 | −0.391270 | − | 0.920276i | \(-0.627964\pi\) | ||||
−0.391270 | + | 0.920276i | \(0.627964\pi\) | |||||||
\(380\) | 303552. | 0.107839 | ||||||||
\(381\) | 2.53472e6 | 0.894575 | ||||||||
\(382\) | 2.74133e6 | 0.961177 | ||||||||
\(383\) | −768387. | −0.267660 | −0.133830 | − | 0.991004i | \(-0.542728\pi\) | ||||
−0.133830 | + | 0.991004i | \(0.542728\pi\) | |||||||
\(384\) | 475136. | 0.164433 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.23717e6 | −0.422630 | ||||||||
\(387\) | 34684.0 | 0.0117720 | ||||||||
\(388\) | 82544.0 | 0.0278360 | ||||||||
\(389\) | 324313. | 0.108665 | 0.0543326 | − | 0.998523i | \(-0.482697\pi\) | ||||
0.0543326 | + | 0.998523i | \(0.482697\pi\) | |||||||
\(390\) | −402752. | −0.134084 | ||||||||
\(391\) | −2.21662e6 | −0.733246 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.68854e6 | −2.51109 | ||||||||
\(394\) | −483720. | −0.156983 | ||||||||
\(395\) | −2.24471e6 | −0.723882 | ||||||||
\(396\) | 1.15773e6 | 0.370995 | ||||||||
\(397\) | −334758. | −0.106599 | −0.0532997 | − | 0.998579i | \(-0.516974\pi\) | ||||
−0.0532997 | + | 0.998579i | \(0.516974\pi\) | |||||||
\(398\) | −3.66214e6 | −1.15885 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −553984. | −0.173120 | ||||||||
\(401\) | −902022. | −0.280128 | −0.140064 | − | 0.990142i | \(-0.544731\pi\) | ||||
−0.140064 | + | 0.990142i | \(0.544731\pi\) | |||||||
\(402\) | 5.57879e6 | 1.72177 | ||||||||
\(403\) | −116144. | −0.0356233 | ||||||||
\(404\) | 982816. | 0.299584 | ||||||||
\(405\) | 4.75047e6 | 1.43913 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 978043. | 0.292666 | ||||||||
\(408\) | 2.11955e6 | 0.630367 | ||||||||
\(409\) | 5.00457e6 | 1.47931 | 0.739654 | − | 0.672987i | \(-0.234989\pi\) | ||||
0.739654 | + | 0.672987i | \(0.234989\pi\) | |||||||
\(410\) | 1.29506e6 | 0.380477 | ||||||||
\(411\) | 7.12985e6 | 2.08198 | ||||||||
\(412\) | −2.97434e6 | −0.863271 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −4.64287e6 | −1.33133 | ||||||||
\(415\) | 489986. | 0.139657 | ||||||||
\(416\) | −114688. | −0.0324926 | ||||||||
\(417\) | 1.05442e7 | 2.96944 | ||||||||
\(418\) | 296208. | 0.0829194 | ||||||||
\(419\) | 3.00124e6 | 0.835151 | 0.417576 | − | 0.908642i | \(-0.362880\pi\) | ||||
0.417576 | + | 0.908642i | \(0.362880\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.56224e6 | 1.25451 | 0.627253 | − | 0.778816i | \(-0.284179\pi\) | ||||
0.627253 | + | 0.778816i | \(0.284179\pi\) | |||||||
\(422\) | −538320. | −0.147150 | ||||||||
\(423\) | −5.17629e6 | −1.40659 | ||||||||
\(424\) | −1.30035e6 | −0.351274 | ||||||||
\(425\) | −2.47129e6 | −0.663668 | ||||||||
\(426\) | −2.89617e6 | −0.773215 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −383520. | −0.101200 | ||||||||
\(429\) | −393008. | −0.103100 | ||||||||
\(430\) | 7192.00 | 0.00187577 | ||||||||
\(431\) | 4.89783e6 | 1.27002 | 0.635009 | − | 0.772504i | \(-0.280996\pi\) | ||||
0.635009 | + | 0.772504i | \(0.280996\pi\) | |||||||
\(432\) | 2.63552e6 | 0.679449 | ||||||||
\(433\) | −6.72876e6 | −1.72471 | −0.862353 | − | 0.506307i | \(-0.831010\pi\) | ||||
−0.862353 | + | 0.506307i | \(0.831010\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.07161e6 | 0.271527 | ||||||||
\(436\) | −901216. | −0.227045 | ||||||||
\(437\) | −1.18789e6 | −0.297559 | ||||||||
\(438\) | 4.90541e6 | 1.22177 | ||||||||
\(439\) | 3.35034e6 | 0.829711 | 0.414856 | − | 0.909887i | \(-0.363832\pi\) | ||||
0.414856 | + | 0.909887i | \(0.363832\pi\) | |||||||
\(440\) | 240064. | 0.0591147 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −511616. | −0.124563 | ||||||||
\(443\) | −7.12434e6 | −1.72479 | −0.862394 | − | 0.506238i | \(-0.831036\pi\) | ||||
−0.862394 | + | 0.506238i | \(0.831036\pi\) | |||||||
\(444\) | 3.75051e6 | 0.902886 | ||||||||
\(445\) | 3.55759e6 | 0.851640 | ||||||||
\(446\) | −1.87536e6 | −0.446423 | ||||||||
\(447\) | −1.61675e6 | −0.382714 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.70928e6 | −0.634218 | −0.317109 | − | 0.948389i | \(-0.602712\pi\) | ||||
−0.317109 | + | 0.948389i | \(0.602712\pi\) | |||||||
\(450\) | −5.17629e6 | −1.20500 | ||||||||
\(451\) | 1.26372e6 | 0.292557 | ||||||||
\(452\) | −4.19045e6 | −0.964749 | ||||||||
\(453\) | 1.90362e6 | 0.435847 | ||||||||
\(454\) | −1.10009e6 | −0.250489 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.13587e6 | 0.255810 | ||||||||
\(457\) | 2.41361e6 | 0.540601 | 0.270301 | − | 0.962776i | \(-0.412877\pi\) | ||||
0.270301 | + | 0.962776i | \(0.412877\pi\) | |||||||
\(458\) | 2.56912e6 | 0.572297 | ||||||||
\(459\) | 1.17569e7 | 2.60472 | ||||||||
\(460\) | −962736. | −0.212135 | ||||||||
\(461\) | 6.56065e6 | 1.43779 | 0.718894 | − | 0.695120i | \(-0.244649\pi\) | ||||
0.718894 | + | 0.695120i | \(0.244649\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.72421e6 | −1.02418 | −0.512090 | − | 0.858932i | \(-0.671129\pi\) | ||||
−0.512090 | + | 0.858932i | \(0.671129\pi\) | |||||||
\(464\) | 305152. | 0.0657993 | ||||||||
\(465\) | 932263. | 0.199943 | ||||||||
\(466\) | −6.01939e6 | −1.28407 | ||||||||
\(467\) | 2.28444e6 | 0.484716 | 0.242358 | − | 0.970187i | \(-0.422079\pi\) | ||||
0.242358 | + | 0.970187i | \(0.422079\pi\) | |||||||
\(468\) | −1.07162e6 | −0.226165 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.07334e6 | −0.224127 | ||||||||
\(471\) | 7.98564e6 | 1.65866 | ||||||||
\(472\) | 1.36646e6 | 0.282321 | ||||||||
\(473\) | 7018.00 | 0.00144232 | ||||||||
\(474\) | −8.39956e6 | −1.71716 | ||||||||
\(475\) | −1.32437e6 | −0.269324 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.21502e7 | −2.44504 | ||||||||
\(478\) | −1.21878e6 | −0.243980 | ||||||||
\(479\) | −951544. | −0.189492 | −0.0947458 | − | 0.995501i | \(-0.530204\pi\) | ||||
−0.0947458 | + | 0.995501i | \(0.530204\pi\) | |||||||
\(480\) | 920576. | 0.182371 | ||||||||
\(481\) | −905296. | −0.178414 | ||||||||
\(482\) | −5.08723e6 | −0.997388 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 234256. | 0.0454545 | ||||||||
\(485\) | 159929. | 0.0308726 | ||||||||
\(486\) | 7.76922e6 | 1.49206 | ||||||||
\(487\) | 3.51484e6 | 0.671558 | 0.335779 | − | 0.941941i | \(-0.391000\pi\) | ||||
0.335779 | + | 0.941941i | \(0.391000\pi\) | |||||||
\(488\) | −3.01082e6 | −0.572314 | ||||||||
\(489\) | 8.46626e6 | 1.60110 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.78719e6 | −1.08334 | −0.541669 | − | 0.840592i | \(-0.682207\pi\) | ||||
−0.541669 | + | 0.840592i | \(0.682207\pi\) | |||||||
\(492\) | 4.84602e6 | 0.902552 | ||||||||
\(493\) | 1.36126e6 | 0.252246 | ||||||||
\(494\) | −274176. | −0.0505489 | ||||||||
\(495\) | 2.24310e6 | 0.411467 | ||||||||
\(496\) | 265472. | 0.0484523 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.83350e6 | 0.331289 | ||||||||
\(499\) | 1.02912e6 | 0.185019 | 0.0925095 | − | 0.995712i | \(-0.470511\pi\) | ||||
0.0925095 | + | 0.995712i | \(0.470511\pi\) | |||||||
\(500\) | −2.62334e6 | −0.469278 | ||||||||
\(501\) | 9.78298e6 | 1.74131 | ||||||||
\(502\) | −2.51986e6 | −0.446290 | ||||||||
\(503\) | 727370. | 0.128184 | 0.0640922 | − | 0.997944i | \(-0.479585\pi\) | ||||
0.0640922 | + | 0.997944i | \(0.479585\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.90421e6 | 0.332266 | ||||||||
\(506\) | −939444. | −0.163115 | ||||||||
\(507\) | −1.04037e7 | −1.79750 | ||||||||
\(508\) | 1.39846e6 | 0.240432 | ||||||||
\(509\) | 1.94630e6 | 0.332977 | 0.166489 | − | 0.986043i | \(-0.446757\pi\) | ||||
0.166489 | + | 0.986043i | \(0.446757\pi\) | |||||||
\(510\) | 4.10663e6 | 0.699134 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 262144. | 0.0441942 | ||||||||
\(513\) | 6.30054e6 | 1.05702 | ||||||||
\(514\) | −2.17634e6 | −0.363345 | ||||||||
\(515\) | −5.76278e6 | −0.957445 | ||||||||
\(516\) | 26912.0 | 0.00444961 | ||||||||
\(517\) | −1.04738e6 | −0.172336 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.38552e6 | 0.551705 | ||||||||
\(520\) | −222208. | −0.0360372 | ||||||||
\(521\) | 1.03133e7 | 1.66457 | 0.832286 | − | 0.554346i | \(-0.187032\pi\) | ||||
0.832286 | + | 0.554346i | \(0.187032\pi\) | |||||||
\(522\) | 2.85126e6 | 0.457995 | ||||||||
\(523\) | 6.86840e6 | 1.09800 | 0.548998 | − | 0.835823i | \(-0.315009\pi\) | ||||
0.548998 | + | 0.835823i | \(0.315009\pi\) | |||||||
\(524\) | −4.24195e6 | −0.674897 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.95734e6 | −1.25402 | ||||||||
\(527\) | 1.18425e6 | 0.185746 | ||||||||
\(528\) | 898304. | 0.140229 | ||||||||
\(529\) | −2.66886e6 | −0.414655 | ||||||||
\(530\) | −2.51943e6 | −0.389595 | ||||||||
\(531\) | 1.27679e7 | 1.96509 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.16973e6 | −0.178347 | ||||||||
\(534\) | 1.33123e7 | 2.02022 | ||||||||
\(535\) | −743070. | −0.112239 | ||||||||
\(536\) | 3.07795e6 | 0.462754 | ||||||||
\(537\) | −554103. | −0.0829191 | ||||||||
\(538\) | −7.01783e6 | −1.04532 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 5.10632e6 | 0.753570 | ||||||||
\(541\) | 1.00545e7 | 1.47695 | 0.738476 | − | 0.674280i | \(-0.235546\pi\) | ||||
0.738476 | + | 0.674280i | \(0.235546\pi\) | |||||||
\(542\) | 6.63296e6 | 0.969860 | ||||||||
\(543\) | 469133. | 0.0682805 | ||||||||
\(544\) | 1.16941e6 | 0.169422 | ||||||||
\(545\) | −1.74611e6 | −0.251814 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.85725e6 | 1.40860 | 0.704299 | − | 0.709903i | \(-0.251261\pi\) | ||||
0.704299 | + | 0.709903i | \(0.251261\pi\) | |||||||
\(548\) | 3.93371e6 | 0.559566 | ||||||||
\(549\) | −2.81323e7 | −3.98359 | ||||||||
\(550\) | −1.04738e6 | −0.147637 | ||||||||
\(551\) | 729504. | 0.102364 | ||||||||
\(552\) | −3.60250e6 | −0.503218 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −170536. | −0.0236070 | ||||||||
\(555\) | 7.26662e6 | 1.00138 | ||||||||
\(556\) | 5.81750e6 | 0.798086 | ||||||||
\(557\) | −1.45892e7 | −1.99247 | −0.996237 | − | 0.0866757i | \(-0.972376\pi\) | ||||
−0.996237 | + | 0.0866757i | \(0.972376\pi\) | |||||||
\(558\) | 2.48050e6 | 0.337252 | ||||||||
\(559\) | −6496.00 | −0.000879258 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.00728e6 | 0.537579 | ||||||||
\(562\) | 1.27804e6 | 0.170688 | ||||||||
\(563\) | 1.02413e7 | 1.36171 | 0.680855 | − | 0.732418i | \(-0.261608\pi\) | ||||
0.680855 | + | 0.732418i | \(0.261608\pi\) | |||||||
\(564\) | −4.01638e6 | −0.531664 | ||||||||
\(565\) | −8.11899e6 | −1.06999 | ||||||||
\(566\) | 8.10939e6 | 1.06401 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.59789e6 | −0.207814 | ||||||||
\(569\) | −751816. | −0.0973489 | −0.0486744 | − | 0.998815i | \(-0.515500\pi\) | ||||
−0.0486744 | + | 0.998815i | \(0.515500\pi\) | |||||||
\(570\) | 2.20075e6 | 0.283716 | ||||||||
\(571\) | −7.01854e6 | −0.900858 | −0.450429 | − | 0.892812i | \(-0.648729\pi\) | ||||
−0.450429 | + | 0.892812i | \(0.648729\pi\) | |||||||
\(572\) | −216832. | −0.0277098 | ||||||||
\(573\) | 1.98747e7 | 2.52879 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.20032e6 | 0.529801 | ||||||||
\(576\) | 2.44941e6 | 0.307613 | ||||||||
\(577\) | 3.36377e6 | 0.420617 | 0.210308 | − | 0.977635i | \(-0.432553\pi\) | ||||
0.210308 | + | 0.977635i | \(0.432553\pi\) | |||||||
\(578\) | −462772. | −0.0576166 | ||||||||
\(579\) | −8.96947e6 | −1.11191 | ||||||||
\(580\) | 591232. | 0.0729773 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 598444. | 0.0732346 | ||||||||
\(583\) | −2.45848e6 | −0.299568 | ||||||||
\(584\) | 2.70643e6 | 0.328371 | ||||||||
\(585\) | −2.07626e6 | −0.250837 | ||||||||
\(586\) | −2.87538e6 | −0.345900 | ||||||||
\(587\) | −1.40585e7 | −1.68401 | −0.842006 | − | 0.539468i | \(-0.818625\pi\) | ||||
−0.842006 | + | 0.539468i | \(0.818625\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 634644. | 0.0753775 | ||||||||
\(590\) | 2.64752e6 | 0.313119 | ||||||||
\(591\) | −3.50697e6 | −0.413013 | ||||||||
\(592\) | 2.06925e6 | 0.242666 | ||||||||
\(593\) | 5.39420e6 | 0.629927 | 0.314963 | − | 0.949104i | \(-0.398008\pi\) | ||||
0.314963 | + | 0.949104i | \(0.398008\pi\) | |||||||
\(594\) | 4.98278e6 | 0.579436 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −892000. | −0.102861 | ||||||||
\(597\) | −2.65505e7 | −3.04886 | ||||||||
\(598\) | 869568. | 0.0994376 | ||||||||
\(599\) | −1.20204e7 | −1.36883 | −0.684417 | − | 0.729090i | \(-0.739943\pi\) | ||||
−0.684417 | + | 0.729090i | \(0.739943\pi\) | |||||||
\(600\) | −4.01638e6 | −0.455467 | ||||||||
\(601\) | −1.64636e6 | −0.185925 | −0.0929626 | − | 0.995670i | \(-0.529634\pi\) | ||||
−0.0929626 | + | 0.995670i | \(0.529634\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.87596e7 | 3.22099 | ||||||||
\(604\) | 1.05027e6 | 0.117141 | ||||||||
\(605\) | 453871. | 0.0504132 | ||||||||
\(606\) | 7.12542e6 | 0.788186 | ||||||||
\(607\) | −4.88451e6 | −0.538083 | −0.269041 | − | 0.963129i | \(-0.586707\pi\) | ||||
−0.269041 | + | 0.963129i | \(0.586707\pi\) | |||||||
\(608\) | 626688. | 0.0687531 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.83346e6 | −0.634748 | ||||||||
\(611\) | 969472. | 0.105059 | ||||||||
\(612\) | 1.09267e7 | 1.17926 | ||||||||
\(613\) | 3.49011e6 | 0.375136 | 0.187568 | − | 0.982252i | \(-0.439940\pi\) | ||||
0.187568 | + | 0.982252i | \(0.439940\pi\) | |||||||
\(614\) | 7.92568e6 | 0.848429 | ||||||||
\(615\) | 9.38916e6 | 1.00101 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.12072e6 | 0.964531 | 0.482266 | − | 0.876025i | \(-0.339814\pi\) | ||||
0.482266 | + | 0.876025i | \(0.339814\pi\) | |||||||
\(618\) | −2.15639e7 | −2.27121 | ||||||||
\(619\) | −1.46635e7 | −1.53820 | −0.769098 | − | 0.639131i | \(-0.779294\pi\) | ||||
−0.769098 | + | 0.639131i | \(0.779294\pi\) | |||||||
\(620\) | 514352. | 0.0537380 | ||||||||
\(621\) | −1.99826e7 | −2.07933 | ||||||||
\(622\) | 6.04120e6 | 0.626105 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −831488. | −0.0854859 | ||||||||
\(625\) | 1.67977e6 | 0.172009 | ||||||||
\(626\) | −8.00368e6 | −0.816307 | ||||||||
\(627\) | 2.14751e6 | 0.218155 | ||||||||
\(628\) | 4.40587e6 | 0.445793 | ||||||||
\(629\) | 9.23079e6 | 0.930277 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.63870e7 | −1.63842 | −0.819212 | − | 0.573491i | \(-0.805589\pi\) | ||||
−0.819212 | + | 0.573491i | \(0.805589\pi\) | |||||||
\(632\) | −4.63424e6 | −0.461515 | ||||||||
\(633\) | −3.90282e6 | −0.387141 | ||||||||
\(634\) | −1.03732e6 | −0.102492 | ||||||||
\(635\) | 2.70952e6 | 0.266660 | ||||||||
\(636\) | −9.42755e6 | −0.924179 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 576928. | 0.0561138 | ||||||||
\(639\) | −1.49303e7 | −1.44649 | ||||||||
\(640\) | 507904. | 0.0490153 | ||||||||
\(641\) | −3.26835e6 | −0.314184 | −0.157092 | − | 0.987584i | \(-0.550212\pi\) | ||||
−0.157092 | + | 0.987584i | \(0.550212\pi\) | |||||||
\(642\) | −2.78052e6 | −0.266249 | ||||||||
\(643\) | −8.32842e6 | −0.794393 | −0.397197 | − | 0.917734i | \(-0.630017\pi\) | ||||
−0.397197 | + | 0.917734i | \(0.630017\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 52142.0 | 0.00493501 | ||||||||
\(646\) | 2.79562e6 | 0.263570 | ||||||||
\(647\) | −2.49694e6 | −0.234503 | −0.117251 | − | 0.993102i | \(-0.537408\pi\) | ||||
−0.117251 | + | 0.993102i | \(0.537408\pi\) | |||||||
\(648\) | 9.80742e6 | 0.917524 | ||||||||
\(649\) | 2.58347e6 | 0.240764 | ||||||||
\(650\) | 969472. | 0.0900019 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.67104e6 | 0.430323 | ||||||||
\(653\) | −789105. | −0.0724189 | −0.0362094 | − | 0.999344i | \(-0.511528\pi\) | ||||
−0.0362094 | + | 0.999344i | \(0.511528\pi\) | |||||||
\(654\) | −6.53382e6 | −0.597341 | ||||||||
\(655\) | −8.21878e6 | −0.748521 | ||||||||
\(656\) | 2.67366e6 | 0.242576 | ||||||||
\(657\) | 2.52882e7 | 2.28562 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.31393e6 | −0.745749 | −0.372874 | − | 0.927882i | \(-0.621628\pi\) | ||||
−0.372874 | + | 0.927882i | \(0.621628\pi\) | |||||||
\(660\) | 1.74046e6 | 0.155527 | ||||||||
\(661\) | 4.33517e6 | 0.385925 | 0.192962 | − | 0.981206i | \(-0.438190\pi\) | ||||
0.192962 | + | 0.981206i | \(0.438190\pi\) | |||||||
\(662\) | 204812. | 0.0181640 | ||||||||
\(663\) | −3.70922e6 | −0.327716 | ||||||||
\(664\) | 1.01158e6 | 0.0890393 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.93345e7 | 1.68907 | ||||||||
\(667\) | −2.31367e6 | −0.201366 | ||||||||
\(668\) | 5.39750e6 | 0.468006 | ||||||||
\(669\) | −1.35963e7 | −1.17451 | ||||||||
\(670\) | 5.96353e6 | 0.513235 | ||||||||
\(671\) | −5.69232e6 | −0.488071 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.29313e6 | 0.620693 | 0.310346 | − | 0.950624i | \(-0.399555\pi\) | ||||
0.310346 | + | 0.950624i | \(0.399555\pi\) | |||||||
\(674\) | 1.06748e6 | 0.0905128 | ||||||||
\(675\) | −2.22784e7 | −1.88202 | ||||||||
\(676\) | −5.73998e6 | −0.483108 | ||||||||
\(677\) | −1.55814e7 | −1.30658 | −0.653288 | − | 0.757109i | \(-0.726611\pi\) | ||||
−0.653288 | + | 0.757109i | \(0.726611\pi\) | |||||||
\(678\) | −3.03807e7 | −2.53819 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2.26573e6 | 0.187904 | ||||||||
\(681\) | −7.97564e6 | −0.659019 | ||||||||
\(682\) | 501908. | 0.0413203 | ||||||||
\(683\) | −2.16930e6 | −0.177938 | −0.0889690 | − | 0.996034i | \(-0.528357\pi\) | ||||
−0.0889690 | + | 0.996034i | \(0.528357\pi\) | |||||||
\(684\) | 5.85562e6 | 0.478556 | ||||||||
\(685\) | 7.62157e6 | 0.620609 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.86261e7 | 1.50567 | ||||||||
\(688\) | 14848.0 | 0.00119591 | ||||||||
\(689\) | 2.27562e6 | 0.182621 | ||||||||
\(690\) | −6.97984e6 | −0.558113 | ||||||||
\(691\) | 1.32195e7 | 1.05322 | 0.526610 | − | 0.850107i | \(-0.323463\pi\) | ||||
0.526610 | + | 0.850107i | \(0.323463\pi\) | |||||||
\(692\) | 1.86787e6 | 0.148280 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.49120e6 | 0.196341 | ||||||||
\(695\) | 1.12714e7 | 0.885149 | ||||||||
\(696\) | 2.21235e6 | 0.173114 | ||||||||
\(697\) | 1.19270e7 | 0.929932 | ||||||||
\(698\) | −9.74596e6 | −0.757157 | ||||||||
\(699\) | −4.36406e7 | −3.37830 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.59395e7 | −1.99373 | −0.996866 | − | 0.0791122i | \(-0.974791\pi\) | ||||
−0.996866 | + | 0.0791122i | \(0.974791\pi\) | |||||||
\(702\) | −4.61216e6 | −0.353233 | ||||||||
\(703\) | 4.94680e6 | 0.377516 | ||||||||
\(704\) | 495616. | 0.0376889 | ||||||||
\(705\) | −7.78174e6 | −0.589663 | ||||||||
\(706\) | −6.23828e6 | −0.471035 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 9.90686e6 | 0.742768 | ||||||||
\(709\) | 3.57531e6 | 0.267115 | 0.133557 | − | 0.991041i | \(-0.457360\pi\) | ||||
0.133557 | + | 0.991041i | \(0.457360\pi\) | |||||||
\(710\) | −3.09591e6 | −0.230485 | ||||||||
\(711\) | −4.33012e7 | −3.21237 | ||||||||
\(712\) | 7.34470e6 | 0.542968 | ||||||||
\(713\) | −2.01282e6 | −0.148279 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −420112. | −0.0307326 | ||||||||
\(716\) | −305712. | −0.0222859 | ||||||||
\(717\) | −8.83613e6 | −0.641895 | ||||||||
\(718\) | 7.67843e6 | 0.555855 | ||||||||
\(719\) | 1.95814e6 | 0.141261 | 0.0706304 | − | 0.997503i | \(-0.477499\pi\) | ||||
0.0706304 | + | 0.997503i | \(0.477499\pi\) | |||||||
\(720\) | 4.74573e6 | 0.341171 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −8.40622e6 | −0.600147 | ||||||||
\(723\) | −3.68824e7 | −2.62406 | ||||||||
\(724\) | 258832. | 0.0183515 | ||||||||
\(725\) | −2.57949e6 | −0.182259 | ||||||||
\(726\) | 1.69836e6 | 0.119588 | ||||||||
\(727\) | −1.55360e7 | −1.09019 | −0.545095 | − | 0.838374i | \(-0.683507\pi\) | ||||
−0.545095 | + | 0.838374i | \(0.683507\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.90893e7 | 1.33036 | ||||||||
\(730\) | 5.24371e6 | 0.364193 | ||||||||
\(731\) | 66236.0 | 0.00458459 | ||||||||
\(732\) | −2.18284e7 | −1.50572 | ||||||||
\(733\) | 1.46002e7 | 1.00369 | 0.501844 | − | 0.864958i | \(-0.332655\pi\) | ||||
0.501844 | + | 0.864958i | \(0.332655\pi\) | |||||||
\(734\) | −1.44490e7 | −0.989915 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.98758e6 | −0.135248 | ||||||||
\(737\) | 5.81925e6 | 0.394638 | ||||||||
\(738\) | 2.49820e7 | 1.68845 | ||||||||
\(739\) | −2.06682e7 | −1.39217 | −0.696085 | − | 0.717959i | \(-0.745077\pi\) | ||||
−0.696085 | + | 0.717959i | \(0.745077\pi\) | |||||||
\(740\) | 4.00917e6 | 0.269138 | ||||||||
\(741\) | −1.98778e6 | −0.132991 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.17065e7 | 0.777953 | 0.388976 | − | 0.921248i | \(-0.372829\pi\) | ||||
0.388976 | + | 0.921248i | \(0.372829\pi\) | |||||||
\(744\) | 1.92467e6 | 0.127475 | ||||||||
\(745\) | −1.72825e6 | −0.114082 | ||||||||
\(746\) | 1.57587e7 | 1.03675 | ||||||||
\(747\) | 9.45199e6 | 0.619757 | ||||||||
\(748\) | 2.21091e6 | 0.144483 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.90192e7 | −1.23464 | ||||||||
\(751\) | −1.27607e7 | −0.825610 | −0.412805 | − | 0.910819i | \(-0.635451\pi\) | ||||
−0.412805 | + | 0.910819i | \(0.635451\pi\) | |||||||
\(752\) | −2.21594e6 | −0.142894 | ||||||||
\(753\) | −1.82690e7 | −1.17416 | ||||||||
\(754\) | −534016. | −0.0342079 | ||||||||
\(755\) | 2.03490e6 | 0.129920 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.40869e7 | −0.893458 | −0.446729 | − | 0.894669i | \(-0.647411\pi\) | ||||
−0.446729 | + | 0.894669i | \(0.647411\pi\) | |||||||
\(758\) | −8.75316e6 | −0.553339 | ||||||||
\(759\) | −6.81097e6 | −0.429145 | ||||||||
\(760\) | 1.21421e6 | 0.0762534 | ||||||||
\(761\) | −2.33822e7 | −1.46360 | −0.731801 | − | 0.681518i | \(-0.761320\pi\) | ||||
−0.731801 | + | 0.681518i | \(0.761320\pi\) | |||||||
\(762\) | 1.01389e7 | 0.632560 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.09653e7 | 0.679655 | ||||||||
\(765\) | 2.11704e7 | 1.30790 | ||||||||
\(766\) | −3.07355e6 | −0.189264 | ||||||||
\(767\) | −2.39131e6 | −0.146774 | ||||||||
\(768\) | 1.90054e6 | 0.116272 | ||||||||
\(769\) | 1.09575e7 | 0.668185 | 0.334092 | − | 0.942540i | \(-0.391570\pi\) | ||||
0.334092 | + | 0.942540i | \(0.391570\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.57785e7 | −0.955938 | ||||||||
\(772\) | −4.94867e6 | −0.298845 | ||||||||
\(773\) | −1.69336e7 | −1.01930 | −0.509648 | − | 0.860383i | \(-0.670224\pi\) | ||||
−0.509648 | + | 0.860383i | \(0.670224\pi\) | |||||||
\(774\) | 138736. | 0.00832409 | ||||||||
\(775\) | −2.24407e6 | −0.134209 | ||||||||
\(776\) | 330176. | 0.0196830 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.29725e6 | 0.0768379 | ||||||||
\(779\) | 6.39173e6 | 0.377376 | ||||||||
\(780\) | −1.61101e6 | −0.0948115 | ||||||||
\(781\) | −3.02101e6 | −0.177225 | ||||||||
\(782\) | −8.86649e6 | −0.518483 | ||||||||
\(783\) | 1.22716e7 | 0.715316 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.53638e6 | 0.494424 | ||||||||
\(786\) | −3.07542e7 | −1.77561 | ||||||||
\(787\) | 7.51655e6 | 0.432595 | 0.216298 | − | 0.976327i | \(-0.430602\pi\) | ||||
0.216298 | + | 0.976327i | \(0.430602\pi\) | |||||||
\(788\) | −1.93488e6 | −0.111004 | ||||||||
\(789\) | −5.76907e7 | −3.29923 | ||||||||
\(790\) | −8.97884e6 | −0.511862 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 4.63091e6 | 0.262333 | ||||||||
\(793\) | 5.26893e6 | 0.297536 | ||||||||
\(794\) | −1.33903e6 | −0.0753771 | ||||||||
\(795\) | −1.82659e7 | −1.02500 | ||||||||
\(796\) | −1.46486e7 | −0.819432 | ||||||||
\(797\) | −3.93788e6 | −0.219592 | −0.109796 | − | 0.993954i | \(-0.535020\pi\) | ||||
−0.109796 | + | 0.993954i | \(0.535020\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.88515e6 | −0.547793 | ||||||||
\(800\) | −2.21594e6 | −0.122414 | ||||||||
\(801\) | 6.86271e7 | 3.77932 | ||||||||
\(802\) | −3.60809e6 | −0.198080 | ||||||||
\(803\) | 5.11685e6 | 0.280036 | ||||||||
\(804\) | 2.23152e7 | 1.21747 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −464576. | −0.0251895 | ||||||||
\(807\) | −5.08793e7 | −2.75015 | ||||||||
\(808\) | 3.93126e6 | 0.211838 | ||||||||
\(809\) | −1.73609e7 | −0.932612 | −0.466306 | − | 0.884624i | \(-0.654415\pi\) | ||||
−0.466306 | + | 0.884624i | \(0.654415\pi\) | |||||||
\(810\) | 1.90019e7 | 1.01762 | ||||||||
\(811\) | −2.70850e7 | −1.44603 | −0.723014 | − | 0.690833i | \(-0.757244\pi\) | ||||
−0.723014 | + | 0.690833i | \(0.757244\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.80890e7 | 2.55164 | ||||||||
\(814\) | 3.91217e6 | 0.206946 | ||||||||
\(815\) | 9.05014e6 | 0.477267 | ||||||||
\(816\) | 8.47821e6 | 0.445737 | ||||||||
\(817\) | 35496.0 | 0.00186048 | ||||||||
\(818\) | 2.00183e7 | 1.04603 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.18022e6 | 0.269038 | ||||||||
\(821\) | 3.59384e7 | 1.86080 | 0.930402 | − | 0.366540i | \(-0.119458\pi\) | ||||
0.930402 | + | 0.366540i | \(0.119458\pi\) | |||||||
\(822\) | 2.85194e7 | 1.47218 | ||||||||
\(823\) | −505509. | −0.0260153 | −0.0130077 | − | 0.999915i | \(-0.504141\pi\) | ||||
−0.0130077 | + | 0.999915i | \(0.504141\pi\) | |||||||
\(824\) | −1.18973e7 | −0.610425 | ||||||||
\(825\) | −7.59348e6 | −0.388424 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.99955e7 | −1.52508 | −0.762539 | − | 0.646942i | \(-0.776048\pi\) | ||||
−0.762539 | + | 0.646942i | \(0.776048\pi\) | |||||||
\(828\) | −1.85715e7 | −0.941393 | ||||||||
\(829\) | −2.96942e7 | −1.50067 | −0.750334 | − | 0.661059i | \(-0.770107\pi\) | ||||
−0.750334 | + | 0.661059i | \(0.770107\pi\) | |||||||
\(830\) | 1.95994e6 | 0.0987526 | ||||||||
\(831\) | −1.23639e6 | −0.0621086 | ||||||||
\(832\) | −458752. | −0.0229757 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 4.21769e7 | 2.09971 | ||||||||
\(835\) | 1.04577e7 | 0.519061 | ||||||||
\(836\) | 1.18483e6 | 0.0586329 | ||||||||
\(837\) | 1.06759e7 | 0.526734 | ||||||||
\(838\) | 1.20049e7 | 0.590541 | ||||||||
\(839\) | 1.41371e7 | 0.693356 | 0.346678 | − | 0.937984i | \(-0.387310\pi\) | ||||
0.346678 | + | 0.937984i | \(0.387310\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.90903e7 | −0.930727 | ||||||||
\(842\) | 1.82490e7 | 0.887070 | ||||||||
\(843\) | 9.26579e6 | 0.449069 | ||||||||
\(844\) | −2.15328e6 | −0.104051 | ||||||||
\(845\) | −1.11212e7 | −0.535810 | ||||||||
\(846\) | −2.07052e7 | −0.994609 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5.20141e6 | −0.248388 | ||||||||
\(849\) | 5.87931e7 | 2.79935 | ||||||||
\(850\) | −9.88515e6 | −0.469284 | ||||||||
\(851\) | −1.56891e7 | −0.742633 | ||||||||
\(852\) | −1.15847e7 | −0.546746 | ||||||||
\(853\) | 4.68539e6 | 0.220482 | 0.110241 | − | 0.993905i | \(-0.464838\pi\) | ||||
0.110241 | + | 0.993905i | \(0.464838\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.13453e7 | 0.530761 | ||||||||
\(856\) | −1.53408e6 | −0.0715589 | ||||||||
\(857\) | 4.12846e7 | 1.92015 | 0.960076 | − | 0.279740i | \(-0.0902483\pi\) | ||||
0.960076 | + | 0.279740i | \(0.0902483\pi\) | |||||||
\(858\) | −1.57203e6 | −0.0729026 | ||||||||
\(859\) | 3.54805e6 | 0.164062 | 0.0820308 | − | 0.996630i | \(-0.473859\pi\) | ||||
0.0820308 | + | 0.996630i | \(0.473859\pi\) | |||||||
\(860\) | 28768.0 | 0.00132637 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.95913e7 | 0.898039 | ||||||||
\(863\) | −3.07605e7 | −1.40594 | −0.702970 | − | 0.711219i | \(-0.748143\pi\) | ||||
−0.702970 | + | 0.711219i | \(0.748143\pi\) | |||||||
\(864\) | 1.05421e7 | 0.480443 | ||||||||
\(865\) | 3.61900e6 | 0.164456 | ||||||||
\(866\) | −2.69150e7 | −1.21955 | ||||||||
\(867\) | −3.35510e6 | −0.151585 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.76161e6 | −0.393581 | ||||||||
\(870\) | 4.28643e6 | 0.191998 | ||||||||
\(871\) | −5.38642e6 | −0.240577 | ||||||||
\(872\) | −3.60486e6 | −0.160545 | ||||||||
\(873\) | 3.08508e6 | 0.137003 | ||||||||
\(874\) | −4.75157e6 | −0.210406 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.96216e7 | 0.863923 | ||||||||
\(877\) | 3.05535e7 | 1.34141 | 0.670706 | − | 0.741723i | \(-0.265991\pi\) | ||||
0.670706 | + | 0.741723i | \(0.265991\pi\) | |||||||
\(878\) | 1.34013e7 | 0.586695 | ||||||||
\(879\) | −2.08465e7 | −0.910040 | ||||||||
\(880\) | 960256. | 0.0418004 | ||||||||
\(881\) | −4.21018e7 | −1.82751 | −0.913757 | − | 0.406262i | \(-0.866832\pi\) | ||||
−0.913757 | + | 0.406262i | \(0.866832\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 57164.0 | 0.00246729 | 0.00123365 | − | 0.999999i | \(-0.499607\pi\) | ||||
0.00123365 | + | 0.999999i | \(0.499607\pi\) | |||||||
\(884\) | −2.04646e6 | −0.0880792 | ||||||||
\(885\) | 1.91945e7 | 0.823796 | ||||||||
\(886\) | −2.84974e7 | −1.21961 | ||||||||
\(887\) | 1.16106e7 | 0.495504 | 0.247752 | − | 0.968824i | \(-0.420308\pi\) | ||||
0.247752 | + | 0.968824i | \(0.420308\pi\) | |||||||
\(888\) | 1.50020e7 | 0.638437 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.42304e7 | 0.602200 | ||||||||
\(891\) | 1.85422e7 | 0.782467 | ||||||||
\(892\) | −7.50142e6 | −0.315669 | ||||||||
\(893\) | −5.29747e6 | −0.222300 | ||||||||
\(894\) | −6.46700e6 | −0.270619 | ||||||||
\(895\) | −592317. | −0.0247170 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.30437e6 | 0.261614 | ||||||||
\(898\) | −1.08371e7 | −0.448460 | ||||||||
\(899\) | 1.23610e6 | 0.0510101 | ||||||||
\(900\) | −2.07052e7 | −0.852064 | ||||||||
\(901\) | −2.32032e7 | −0.952215 | ||||||||
\(902\) | 5.05490e6 | 0.206869 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.67618e7 | −0.682181 | ||||||||
\(905\) | 501487. | 0.0203535 | ||||||||
\(906\) | 7.61447e6 | 0.308191 | ||||||||
\(907\) | 2.09855e7 | 0.847034 | 0.423517 | − | 0.905888i | \(-0.360795\pi\) | ||||
0.423517 | + | 0.905888i | \(0.360795\pi\) | |||||||
\(908\) | −4.40035e6 | −0.177122 | ||||||||
\(909\) | 3.67327e7 | 1.47450 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.74125e7 | 1.89277 | 0.946383 | − | 0.323047i | \(-0.104707\pi\) | ||||
0.946383 | + | 0.323047i | \(0.104707\pi\) | |||||||
\(912\) | 4.54349e6 | 0.180885 | ||||||||
\(913\) | 1.91253e6 | 0.0759330 | ||||||||
\(914\) | 9.65445e6 | 0.382263 | ||||||||
\(915\) | −4.22926e7 | −1.66998 | ||||||||
\(916\) | 1.02765e7 | 0.404675 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 4.70276e7 | 1.84181 | ||||||||
\(919\) | 4.04326e7 | 1.57922 | 0.789610 | − | 0.613609i | \(-0.210283\pi\) | ||||
0.789610 | + | 0.613609i | \(0.210283\pi\) | |||||||
\(920\) | −3.85094e6 | −0.150002 | ||||||||
\(921\) | 5.74612e7 | 2.23216 | ||||||||
\(922\) | 2.62426e7 | 1.01667 | ||||||||
\(923\) | 2.79630e6 | 0.108039 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.74916e7 | −0.672164 | ||||||||
\(926\) | −1.88968e7 | −0.724205 | ||||||||
\(927\) | −1.11166e8 | −4.24885 | ||||||||
\(928\) | 1.22061e6 | 0.0465271 | ||||||||
\(929\) | −3.30757e7 | −1.25739 | −0.628694 | − | 0.777652i | \(-0.716410\pi\) | ||||
−0.628694 | + | 0.777652i | \(0.716410\pi\) | |||||||
\(930\) | 3.72905e6 | 0.141381 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.40776e7 | −0.907973 | ||||||||
\(933\) | 4.37987e7 | 1.64724 | ||||||||
\(934\) | 9.13776e6 | 0.342746 | ||||||||
\(935\) | 4.28364e6 | 0.160245 | ||||||||
\(936\) | −4.28646e6 | −0.159922 | ||||||||
\(937\) | 3.15132e7 | 1.17258 | 0.586292 | − | 0.810100i | \(-0.300587\pi\) | ||||
0.586292 | + | 0.810100i | \(0.300587\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.80267e7 | −2.14765 | ||||||||
\(940\) | −4.29338e6 | −0.158482 | ||||||||
\(941\) | 9.54147e6 | 0.351270 | 0.175635 | − | 0.984455i | \(-0.443802\pi\) | ||||
0.175635 | + | 0.984455i | \(0.443802\pi\) | |||||||
\(942\) | 3.19426e7 | 1.17285 | ||||||||
\(943\) | −2.02718e7 | −0.742358 | ||||||||
\(944\) | 5.46586e6 | 0.199631 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 28072.0 | 0.00101987 | ||||||||
\(947\) | 2.24208e7 | 0.812410 | 0.406205 | − | 0.913782i | \(-0.366852\pi\) | ||||
0.406205 | + | 0.913782i | \(0.366852\pi\) | |||||||
\(948\) | −3.35982e7 | −1.21422 | ||||||||
\(949\) | −4.73626e6 | −0.170714 | ||||||||
\(950\) | −5.29747e6 | −0.190441 | ||||||||
\(951\) | −7.52060e6 | −0.269650 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.68985e7 | 0.602720 | 0.301360 | − | 0.953510i | \(-0.402559\pi\) | ||||
0.301360 | + | 0.953510i | \(0.402559\pi\) | |||||||
\(954\) | −4.86007e7 | −1.72891 | ||||||||
\(955\) | 2.12453e7 | 0.753798 | ||||||||
\(956\) | −4.87510e6 | −0.172520 | ||||||||
\(957\) | 4.18273e6 | 0.147632 | ||||||||
\(958\) | −3.80618e6 | −0.133991 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 3.68230e6 | 0.128956 | ||||||||
\(961\) | −2.75538e7 | −0.962438 | ||||||||
\(962\) | −3.62118e6 | −0.126157 | ||||||||
\(963\) | −1.43341e7 | −0.498085 | ||||||||
\(964\) | −2.03489e7 | −0.705260 | ||||||||
\(965\) | −9.58805e6 | −0.331445 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.06946e7 | −1.05559 | −0.527796 | − | 0.849371i | \(-0.676982\pi\) | ||||
−0.527796 | + | 0.849371i | \(0.676982\pi\) | |||||||
\(968\) | 937024. | 0.0321412 | ||||||||
\(969\) | 2.02682e7 | 0.693436 | ||||||||
\(970\) | 639716. | 0.0218302 | ||||||||
\(971\) | −3.35664e7 | −1.14250 | −0.571251 | − | 0.820776i | \(-0.693542\pi\) | ||||
−0.571251 | + | 0.820776i | \(0.693542\pi\) | |||||||
\(972\) | 3.10769e7 | 1.05505 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1.40594e7 | 0.474863 | ||||||||
\(975\) | 7.02867e6 | 0.236789 | ||||||||
\(976\) | −1.20433e7 | −0.404687 | ||||||||
\(977\) | 2.47897e7 | 0.830873 | 0.415436 | − | 0.909622i | \(-0.363629\pi\) | ||||
0.415436 | + | 0.909622i | \(0.363629\pi\) | |||||||
\(978\) | 3.38650e7 | 1.13215 | ||||||||
\(979\) | 1.38861e7 | 0.463045 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.36829e7 | −1.11747 | ||||||||
\(982\) | −2.31488e7 | −0.766036 | ||||||||
\(983\) | −5.22606e6 | −0.172501 | −0.0862503 | − | 0.996274i | \(-0.527488\pi\) | ||||
−0.0862503 | + | 0.996274i | \(0.527488\pi\) | |||||||
\(984\) | 1.93841e7 | 0.638200 | ||||||||
\(985\) | −3.74883e6 | −0.123113 | ||||||||
\(986\) | 5.44506e6 | 0.178365 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.09670e6 | −0.0357435 | ||||||||
\(989\) | −112578. | −0.00365985 | ||||||||
\(990\) | 8.97239e6 | 0.290951 | ||||||||
\(991\) | 2.40826e7 | 0.778967 | 0.389484 | − | 0.921033i | \(-0.372653\pi\) | ||||
0.389484 | + | 0.921033i | \(0.372653\pi\) | |||||||
\(992\) | 1.06189e6 | 0.0342610 | ||||||||
\(993\) | 1.48489e6 | 0.0477882 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.83816e7 | −0.908823 | ||||||||
\(996\) | 7.33398e6 | 0.234256 | ||||||||
\(997\) | 1.32606e7 | 0.422499 | 0.211249 | − | 0.977432i | \(-0.432247\pi\) | ||||
0.211249 | + | 0.977432i | \(0.432247\pi\) | |||||||
\(998\) | 4.11650e6 | 0.130828 | ||||||||
\(999\) | 8.32145e7 | 2.63806 |
(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 | 1078.6.a.f.1.1 | 1 | ||
7.6 | odd | 2 | 22.6.a.c.1.1 | ✓ | 1 | ||
21.20 | even | 2 | 198.6.a.b.1.1 | 1 | |||
28.27 | even | 2 | 176.6.a.e.1.1 | 1 | |||
35.13 | even | 4 | 550.6.b.a.199.1 | 2 | |||
35.27 | even | 4 | 550.6.b.a.199.2 | 2 | |||
35.34 | odd | 2 | 550.6.a.c.1.1 | 1 | |||
56.13 | odd | 2 | 704.6.a.j.1.1 | 1 | |||
56.27 | even | 2 | 704.6.a.a.1.1 | 1 | |||
77.76 | even | 2 | 242.6.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
22.6.a.c.1.1 | ✓ | 1 | 7.6 | odd | 2 | ||
176.6.a.e.1.1 | 1 | 28.27 | even | 2 | |||
198.6.a.b.1.1 | 1 | 21.20 | even | 2 | |||
242.6.a.a.1.1 | 1 | 77.76 | even | 2 | |||
550.6.a.c.1.1 | 1 | 35.34 | odd | 2 | |||
550.6.b.a.199.1 | 2 | 35.13 | even | 4 | |||
550.6.b.a.199.2 | 2 | 35.27 | even | 4 | |||
704.6.a.a.1.1 | 1 | 56.27 | even | 2 | |||
704.6.a.j.1.1 | 1 | 56.13 | odd | 2 | |||
1078.6.a.f.1.1 | 1 | 1.1 | even | 1 | trivial |