Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [160,6,Mod(1,160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(160, 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("160.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 160 = 2^{5} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 160.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: | \(25.6614111701\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.81998080.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 100x^{2} - 376x - 367 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{11} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.92659\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 160.1 |
$q$-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 | ||||||||
\(3\) | 27.0971 | 1.73828 | 0.869139 | − | 0.494568i | \(-0.164674\pi\) | ||||
0.869139 | + | 0.494568i | \(0.164674\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 250.932 | 1.93558 | 0.967789 | − | 0.251762i | \(-0.0810099\pi\) | ||||
0.967789 | + | 0.251762i | \(0.0810099\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 491.252 | 2.02161 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 318.107 | 0.792668 | 0.396334 | − | 0.918107i | \(-0.370282\pi\) | ||||
0.396334 | + | 0.918107i | \(0.370282\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1076.75 | −1.76709 | −0.883544 | − | 0.468348i | \(-0.844850\pi\) | ||||
−0.883544 | + | 0.468348i | \(0.844850\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 677.427 | 0.777382 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1120.75 | −0.940564 | −0.470282 | − | 0.882516i | \(-0.655848\pi\) | ||||
−0.470282 | + | 0.882516i | \(0.655848\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 749.388 | 0.476237 | 0.238118 | − | 0.971236i | \(-0.423469\pi\) | ||||
0.238118 | + | 0.971236i | \(0.423469\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6799.52 | 3.36457 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −250.932 | −0.0989091 | −0.0494546 | − | 0.998776i | \(-0.515748\pi\) | ||||
−0.0494546 | + | 0.998776i | \(0.515748\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 6726.89 | 1.77584 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5626.53 | −1.24235 | −0.621177 | − | 0.783670i | \(-0.713345\pi\) | ||||
−0.621177 | + | 0.783670i | \(0.713345\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7570.79 | −1.41494 | −0.707469 | − | 0.706745i | \(-0.750163\pi\) | ||||
−0.707469 | + | 0.706745i | \(0.750163\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8619.76 | 1.37788 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6273.30 | 0.865617 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3072.49 | 0.368966 | 0.184483 | − | 0.982836i | \(-0.440939\pi\) | ||||
0.184483 | + | 0.982836i | \(0.440939\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −29176.9 | −3.07169 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5390.72 | 0.500826 | 0.250413 | − | 0.968139i | \(-0.419434\pi\) | ||||
0.250413 | + | 0.968139i | \(0.419434\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2088.26 | −0.172232 | −0.0861159 | − | 0.996285i | \(-0.527446\pi\) | ||||
−0.0861159 | + | 0.996285i | \(0.527446\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 12281.3 | 0.904092 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4076.00 | −0.269147 | −0.134573 | − | 0.990904i | \(-0.542966\pi\) | ||||
−0.134573 | + | 0.990904i | \(0.542966\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 46159.8 | 2.74646 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −30369.2 | −1.63496 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9027.77 | 0.441460 | 0.220730 | − | 0.975335i | \(-0.429156\pi\) | ||||
0.220730 | + | 0.975335i | \(0.429156\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7952.67 | 0.354492 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 20306.2 | 0.827832 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 27481.5 | 1.02781 | 0.513903 | − | 0.857848i | \(-0.328199\pi\) | ||||
0.513903 | + | 0.857848i | \(0.328199\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −41567.1 | −1.43029 | −0.715147 | − | 0.698974i | \(-0.753640\pi\) | ||||
−0.715147 | + | 0.698974i | \(0.753640\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 123271. | 3.91299 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −26918.9 | −0.790266 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −27782.1 | −0.756099 | −0.378049 | − | 0.925785i | \(-0.623405\pi\) | ||||
−0.378049 | + | 0.925785i | \(0.623405\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6799.52 | −0.171932 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14284.9 | 0.336303 | 0.168151 | − | 0.985761i | \(-0.446220\pi\) | ||||
0.168151 | + | 0.985761i | \(0.446220\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 32642.3 | 0.716924 | 0.358462 | − | 0.933544i | \(-0.383301\pi\) | ||||
0.358462 | + | 0.933544i | \(0.383301\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 16935.7 | 0.347656 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 79823.1 | 1.53427 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 19864.3 | 0.358100 | 0.179050 | − | 0.983840i | \(-0.442698\pi\) | ||||
0.179050 | + | 0.983840i | \(0.442698\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 62904.9 | 1.06530 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 76615.8 | 1.22074 | 0.610370 | − | 0.792117i | \(-0.291021\pi\) | ||||
0.610370 | + | 0.792117i | \(0.291021\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −28018.9 | −0.420633 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −152462. | −2.15956 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 24407.4 | 0.326622 | 0.163311 | − | 0.986575i | \(-0.447783\pi\) | ||||
0.163311 | + | 0.986575i | \(0.447783\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −270192. | −3.42034 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −205146. | −2.45955 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 18734.7 | 0.212980 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −65973.5 | −0.711935 | −0.355967 | − | 0.934498i | \(-0.615849\pi\) | ||||
−0.355967 | + | 0.934498i | \(0.615849\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 156270. | 1.60247 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −89919.4 | −0.877101 | −0.438551 | − | 0.898706i | \(-0.644508\pi\) | ||||
−0.438551 | + | 0.898706i | \(0.644508\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 64846.3 | 0.602271 | 0.301136 | − | 0.953581i | \(-0.402634\pi\) | ||||
0.301136 | + | 0.953581i | \(0.402634\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 169988. | 1.50468 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −127808. | −1.07919 | −0.539595 | − | 0.841925i | \(-0.681423\pi\) | ||||
−0.539595 | + | 0.841925i | \(0.681423\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 23209.8 | 0.187114 | 0.0935569 | − | 0.995614i | \(-0.470176\pi\) | ||||
0.0935569 | + | 0.995614i | \(0.470176\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 83255.5 | 0.641365 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −106124. | −0.781842 | −0.390921 | − | 0.920424i | \(-0.627844\pi\) | ||||
−0.390921 | + | 0.920424i | \(0.627844\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6273.30 | −0.0442335 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −528957. | −3.57237 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −281233. | −1.82053 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −59859.1 | −0.371678 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 146073. | 0.870575 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −55034.4 | −0.302778 | −0.151389 | − | 0.988474i | \(-0.548375\pi\) | ||||
−0.151389 | + | 0.988474i | \(0.548375\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −56585.8 | −0.299387 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −123085. | −0.626655 | −0.313327 | − | 0.949645i | \(-0.601444\pi\) | ||||
−0.313327 | + | 0.949645i | \(0.601444\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 188045. | 0.921793 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 168172. | 0.794182 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 227197. | 1.03419 | 0.517095 | − | 0.855928i | \(-0.327013\pi\) | ||||
0.517095 | + | 0.855928i | \(0.327013\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −223187. | −0.979786 | −0.489893 | − | 0.871783i | \(-0.662964\pi\) | ||||
−0.489893 | + | 0.871783i | \(0.662964\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −110448. | −0.467852 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −342523. | −1.40071 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −140663. | −0.555598 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.25080e6 | 4.77412 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 31091.8 | 0.114731 | 0.0573655 | − | 0.998353i | \(-0.481730\pi\) | ||||
0.0573655 | + | 0.998353i | \(0.481730\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 325683. | 1.16239 | 0.581196 | − | 0.813764i | \(-0.302585\pi\) | ||||
0.581196 | + | 0.813764i | \(0.302585\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −550572. | −1.90145 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −189270. | −0.632779 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −67159.8 | −0.217450 | −0.108725 | − | 0.994072i | \(-0.534677\pi\) | ||||
−0.108725 | + | 0.994072i | \(0.534677\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 244626. | 0.767380 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −62966.8 | −0.191446 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 138531. | 0.408394 | 0.204197 | − | 0.978930i | \(-0.434542\pi\) | ||||
0.204197 | + | 0.978930i | \(0.434542\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 215494. | 0.616205 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −314527. | −0.872704 | −0.436352 | − | 0.899776i | \(-0.643730\pi\) | ||||
−0.436352 | + | 0.899776i | \(0.643730\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 788107. | 2.12260 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 368138. | 0.962765 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −578808. | −1.47035 | −0.735173 | − | 0.677880i | \(-0.762899\pi\) | ||||
−0.735173 | + | 0.677880i | \(0.762899\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 156832. | 0.387116 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 744670. | 1.78661 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −279606. | −0.652250 | −0.326125 | − | 0.945327i | \(-0.605743\pi\) | ||||
−0.326125 | + | 0.945327i | \(0.605743\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −474917. | −1.07751 | −0.538755 | − | 0.842463i | \(-0.681105\pi\) | ||||
−0.538755 | + | 0.842463i | \(0.681105\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.12635e6 | −2.48625 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 76812.3 | 0.165007 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −356519. | −0.745554 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.68799e6 | 3.43729 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 680793. | 1.35030 | 0.675152 | − | 0.737679i | \(-0.264078\pi\) | ||||
0.675152 | + | 0.737679i | \(0.264078\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −480051. | −0.927671 | −0.463835 | − | 0.885921i | \(-0.653527\pi\) | ||||
−0.463835 | + | 0.885921i | \(0.653527\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −729422. | −1.37370 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 928980. | 1.70546 | 0.852728 | − | 0.522355i | \(-0.174946\pi\) | ||||
0.852728 | + | 0.522355i | \(0.174946\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 141359. | 0.253040 | 0.126520 | − | 0.991964i | \(-0.459619\pi\) | ||||
0.126520 | + | 0.991964i | \(0.459619\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −752815. | −1.31431 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.41188e6 | −2.40467 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 134768. | 0.223976 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −123271. | −0.199956 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 238385. | 0.377497 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.08461e6 | −1.67713 | −0.838567 | − | 0.544799i | \(-0.816606\pi\) | ||||
−0.838567 | + | 0.544799i | \(0.816606\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 387078. | 0.584588 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −52206.5 | −0.0770244 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.89975e6 | −2.73872 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 884510. | 1.24621 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.20678e6 | 1.66206 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 430800. | 0.580114 | 0.290057 | − | 0.957009i | \(-0.406326\pi\) | ||||
0.290057 | + | 0.957009i | \(0.406326\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 307032. | 0.404322 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 524.734 | 0.000675888 0 | 0.000337944 | − | 1.00000i | \(-0.499892\pi\) | ||||
0.000337944 | 1.00000i | \(0.499892\pi\) | ||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −563646. | −0.710260 | −0.355130 | − | 0.934817i | \(-0.615563\pi\) | ||||
−0.355130 | + | 0.934817i | \(0.615563\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.16297e6 | 2.66699 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.17201e6 | 1.41431 | 0.707153 | − | 0.707061i | \(-0.249979\pi\) | ||||
0.707153 | + | 0.707061i | \(0.249979\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −101900. | −0.120366 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 538263. | 0.622478 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.34048e6 | 1.51798 | 0.758990 | − | 0.651102i | \(-0.225693\pi\) | ||||
0.758990 | + | 0.651102i | \(0.225693\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.44553e6 | 1.60318 | 0.801592 | − | 0.597871i | \(-0.203987\pi\) | ||||
0.801592 | + | 0.597871i | \(0.203987\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 69905.4 | 0.0759443 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.15400e6 | 1.22826 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −806907. | −0.841552 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.07606e6 | 2.12198 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.73066e6 | 1.73391 | 0.866957 | − | 0.498383i | \(-0.166073\pi\) | ||||
0.866957 | + | 0.498383i | \(0.166073\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −79823.1 | −0.0784020 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −759229. | −0.731177 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.46437e6 | −1.38298 | −0.691492 | − | 0.722384i | \(-0.743046\pi\) | ||||
−0.691492 | + | 0.722384i | \(0.743046\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 770986. | 0.714163 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.76404e6 | −2.51156 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.06316e6 | 0.947787 | 0.473894 | − | 0.880582i | \(-0.342848\pi\) | ||||
0.473894 | + | 0.880582i | \(0.342848\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 225694. | 0.197427 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 661368. | 0.567760 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.46767e6 | 1.23665 | 0.618327 | − | 0.785921i | \(-0.287811\pi\) | ||||
0.618327 | + | 0.785921i | \(0.287811\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.27316e6 | −1.88021 | −0.940104 | − | 0.340887i | \(-0.889273\pi\) | ||||
−0.940104 | + | 0.340887i | \(0.889273\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.32142e6 | −5.94550 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 198817. | 0.158534 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −499874. | −0.391436 | −0.195718 | − | 0.980660i | \(-0.562704\pi\) | ||||
−0.195718 | + | 0.980660i | \(0.562704\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.71916e6 | −2.86045 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 782548. | 0.591215 | 0.295607 | − | 0.955310i | \(-0.404478\pi\) | ||||
0.295607 | + | 0.955310i | \(0.404478\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.77627e6 | 1.31839 | 0.659194 | − | 0.751973i | \(-0.270897\pi\) | ||||
0.659194 | + | 0.751973i | \(0.270897\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 507656. | 0.370218 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.35270e6 | 0.969388 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −163766. | −0.115340 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.78769e6 | −1.23754 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −37135.6 | −0.0252709 | −0.0126355 | − | 0.999920i | \(-0.504022\pi\) | ||||
−0.0126355 | + | 0.999920i | \(0.504022\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 687039. | 0.459649 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.13987e6 | 1.40765 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 270192. | 0.174781 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −524011. | −0.333368 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.43655e6 | −1.52465 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.03918e6 | −0.639647 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −442910. | −0.268206 | −0.134103 | − | 0.990967i | \(-0.542815\pi\) | ||||
−0.134103 | + | 0.990967i | \(0.542815\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.75715e6 | 1.04692 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 261003. | 0.153019 | 0.0765095 | − | 0.997069i | \(-0.475622\pi\) | ||||
0.0765095 | + | 0.997069i | \(0.475622\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −673617. | −0.388644 | −0.194322 | − | 0.980938i | \(-0.562251\pi\) | ||||
−0.194322 | + | 0.980938i | \(0.562251\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.08177e6 | 1.74994 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −965919. | −0.539874 | −0.269937 | − | 0.962878i | \(-0.587003\pi\) | ||||
−0.269937 | + | 0.962878i | \(0.587003\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.78984e6 | −0.984774 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.46322e6 | −1.87593 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −839880. | −0.447931 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −672972. | −0.353418 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 628919. | 0.325256 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.02280e6 | −0.520955 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.93523e6 | −0.970875 | −0.485438 | − | 0.874271i | \(-0.661340\pi\) | ||||
−0.485438 | + | 0.874271i | \(0.661340\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.50937e6 | 0.745906 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −694553. | −0.338138 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.83525e6 | 0.880279 | 0.440139 | − | 0.897930i | \(-0.354929\pi\) | ||||
0.440139 | + | 0.897930i | \(0.354929\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.87566e6 | −1.35906 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.40832e6 | −1.12157 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.36556e6 | 3.38042 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −169988. | −0.0768901 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.82770e6 | −1.26069 | −0.630346 | − | 0.776314i | \(-0.717087\pi\) | ||||
−0.630346 | + | 0.776314i | \(0.717087\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.02951e6 | −0.452445 | −0.226223 | − | 0.974076i | \(-0.572638\pi\) | ||||
−0.226223 | + | 0.974076i | \(0.572638\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.24321e6 | −3.13807 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.36405e6 | 1.00977 | 0.504883 | − | 0.863188i | \(-0.331536\pi\) | ||||
0.504883 | + | 0.863188i | \(0.331536\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 357122. | 0.150399 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.62059e6 | −3.16460 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.56931e6 | 1.05216 | 0.526078 | − | 0.850436i | \(-0.323662\pi\) | ||||
0.526078 | + | 0.850436i | \(0.323662\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.91452e6 | −0.773199 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.62201e6 | −0.646080 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 816057. | 0.320618 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.66700e6 | 0.646055 | 0.323027 | − | 0.946390i | \(-0.395299\pi\) | ||||
0.323027 | + | 0.946390i | \(0.395299\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.64820e6 | 1.01248 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.26536e6 | 0.854480 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.20579e6 | −1.56522 | −0.782611 | − | 0.622511i | \(-0.786113\pi\) | ||||
−0.782611 | + | 0.622511i | \(0.786113\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 423392. | 0.155476 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.05839e6 | 2.19535 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.96494e6 | 1.06027 | 0.530136 | − | 0.847913i | \(-0.322141\pi\) | ||||
0.530136 | + | 0.847913i | \(0.322141\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.49127e6 | −0.526313 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.78837e6 | 0.971301 | 0.485650 | − | 0.874153i | \(-0.338583\pi\) | ||||
0.485650 | + | 0.874153i | \(0.338583\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.99558e6 | 0.686147 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.02586e6 | −0.348186 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.84640e6 | 1.62385 | 0.811924 | − | 0.583763i | \(-0.198420\pi\) | ||||
0.811924 | + | 0.583763i | \(0.198420\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 281233. | 0.0930303 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.33525e6 | −1.08930 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 496607. | 0.160147 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.08924e6 | 0.665291 | 0.332646 | − | 0.943052i | \(-0.392059\pi\) | ||||
0.332646 | + | 0.943052i | \(0.392059\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.09548e6 | 1.60233 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.72071e6 | 1.77660 | 0.888298 | − | 0.459268i | \(-0.151888\pi\) | ||||
0.888298 | + | 0.459268i | \(0.151888\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.15189e6 | 2.50032 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.57262e6 | 0.476417 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 977380. | 0.292467 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −437627. | −0.129359 | −0.0646794 | − | 0.997906i | \(-0.520602\pi\) | ||||
−0.0646794 | + | 0.997906i | \(0.520602\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.15637e6 | 1.79771 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.89600e6 | 1.98940 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.91539e6 | 0.545931 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.04770e6 | −1.70314 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.01226e6 | −1.39476 | −0.697379 | − | 0.716703i | \(-0.745651\pi\) | ||||
−0.697379 | + | 0.716703i | \(0.745651\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −948769. | −0.260889 | −0.130444 | − | 0.991456i | \(-0.541640\pi\) | ||||
−0.130444 | + | 0.991456i | \(0.541640\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.00234e6 | −0.544110 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −700472. | −0.188113 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.04305e7 | −2.76845 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.28137e6 | −2.43483 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.33719e6 | −1.38395 | −0.691974 | − | 0.721923i | \(-0.743259\pi\) | ||||
−0.691974 | + | 0.721923i | \(0.743259\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.68308e6 | −0.944041 | −0.472021 | − | 0.881588i | \(-0.656475\pi\) | ||||
−0.472021 | + | 0.881588i | \(0.656475\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.81156e6 | −0.965783 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −188045. | −0.0471041 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.20149e6 | 0.792849 | 0.396424 | − | 0.918067i | \(-0.370251\pi\) | ||||
0.396424 | + | 0.918067i | \(0.370251\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.26761e7 | 5.55228 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.19675e6 | −0.531828 | −0.265914 | − | 0.963997i | \(-0.585674\pi\) | ||||
−0.265914 | + | 0.963997i | \(0.585674\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 610184. | 0.146070 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 842498. | 0.199434 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.79059e6 | 0.653251 | 0.326626 | − | 0.945154i | \(-0.394088\pi\) | ||||
0.326626 | + | 0.945154i | \(0.394088\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.71482e6 | 0.396989 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.82505e6 | 2.02056 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.75480e6 | −1.52962 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.73567e6 | 1.06070 | 0.530348 | − | 0.847780i | \(-0.322061\pi\) | ||||
0.530348 | + | 0.847780i | \(0.322061\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.53919e6 | −1.67029 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.07704e6 | −0.455190 | −0.227595 | − | 0.973756i | \(-0.573086\pi\) | ||||
−0.227595 | + | 0.973756i | \(0.573086\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.07901e6 | −1.53469 | −0.767344 | − | 0.641236i | \(-0.778422\pi\) | ||||
−0.767344 | + | 0.641236i | \(0.778422\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.12866e6 | −1.09995 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.56203e6 | −0.543615 | −0.271808 | − | 0.962352i | \(-0.587621\pi\) | ||||
−0.271808 | + | 0.962352i | \(0.587621\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.97142e6 | −1.46349 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.81983e6 | −0.377989 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −664290. | −0.136523 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 468368. | 0.0952473 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.43491e6 | 0.892460 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.23584e6 | 1.83924 | 0.919619 | − | 0.392812i | \(-0.128498\pi\) | ||||
0.919619 | + | 0.392812i | \(0.128498\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.30832e6 | −0.651996 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.70622e6 | −0.332787 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.64934e6 | −0.318387 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.58613e6 | −0.685178 | −0.342589 | − | 0.939485i | \(-0.611304\pi\) | ||||
−0.342589 | + | 0.939485i | \(0.611304\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.75380e6 | 0.709903 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.76716e6 | 0.892393 | 0.446197 | − | 0.894935i | \(-0.352778\pi\) | ||||
0.446197 | + | 0.894935i | \(0.352778\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.30596e6 | 1.16851 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.90676e6 | 0.716644 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.58453e6 | 0.650940 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.13248e6 | 0.203601 | 0.101801 | − | 0.994805i | \(-0.467540\pi\) | ||||
0.101801 | + | 0.994805i | \(0.467540\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.52277e6 | −1.51700 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.63918e6 | −1.17002 | −0.585012 | − | 0.811025i | \(-0.698910\pi\) | ||||
−0.585012 | + | 0.811025i | \(0.698910\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.24798e6 | −0.392252 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.13554e7 | 3.68967 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.86315e6 | 1.68741 | 0.843706 | − | 0.536805i | \(-0.180369\pi\) | ||||
0.843706 | + | 0.536805i | \(0.180369\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.19099e6 | 1.38766 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.04105e6 | 0.845722 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.62116e6 | 0.269344 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.29660e6 | −0.213344 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.56840e7 | −2.55587 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.38917e6 | −0.869817 | −0.434908 | − | 0.900475i | \(-0.643219\pi\) | ||||
−0.434908 | + | 0.900475i | \(0.643219\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.18840e7 | −1.89981 | −0.949905 | − | 0.312539i | \(-0.898821\pi\) | ||||
−0.949905 | + | 0.312539i | \(0.898821\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.24970e6 | 0.672915 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.48500e6 | 1.33084 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.37338e6 | −0.990217 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.35004e7 | 2.07782 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.80448e6 | −0.885004 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.19520e6 | −0.482629 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.57651e6 | −1.13379 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.46837e7 | 2.17703 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.38145e6 | −1.23119 | −0.615596 | − | 0.788062i | \(-0.711085\pi\) | ||||
−0.615596 | + | 0.788062i | \(0.711085\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.28689e7 | −1.87301 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 580246. | 0.0836798 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.58605e6 | 0.798246 | 0.399123 | − | 0.916897i | \(-0.369315\pi\) | ||||
0.399123 | + | 0.916897i | \(0.369315\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.04199e7 | −2.89150 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.21645e6 | −0.591655 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.98458e6 | 0.693131 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.08139e6 | 0.286827 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.08231e6 | 0.830674 | 0.415337 | − | 0.909668i | \(-0.363664\pi\) | ||||
0.415337 | + | 0.909668i | \(0.363664\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.24854e6 | 0.304349 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.66064e6 | −1.29598 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.97762e6 | 1.06072 | 0.530362 | − | 0.847771i | \(-0.322056\pi\) | ||||
0.530362 | + | 0.847771i | \(0.322056\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.65311e6 | −0.349651 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.57849e7 | 2.06197 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.20355e6 | −0.414812 | −0.207406 | − | 0.978255i | \(-0.566502\pi\) | ||||
−0.207406 | + | 0.978255i | \(0.566502\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.44485e7 | −1.85453 | −0.927264 | − | 0.374408i | \(-0.877846\pi\) | ||||
−0.927264 | + | 0.374408i | \(0.877846\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.84475e7 | 2.34720 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −156832. | −0.0197818 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.96262e6 | 0.620542 | 0.310271 | − | 0.950648i | \(-0.399580\pi\) | ||||
0.310271 | + | 0.950648i | \(0.399580\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.30080e7 | −1.61255 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.92253e7 | 2.36284 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.87179e6 | 0.349931 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.32239e7 | −1.59761 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.25528e7 | −1.50365 | −0.751824 | − | 0.659363i | \(-0.770826\pi\) | ||||
−0.751824 | + | 0.659363i | \(0.770826\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.67346e6 | −0.673845 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.51726e7 | 2.96456 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −871194. | −0.101737 | −0.0508684 | − | 0.998705i | \(-0.516199\pi\) | ||||
−0.0508684 | + | 0.998705i | \(0.516199\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.03083e6 | −0.814168 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.83041e6 | 0.439854 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.77951e6 | −1.11365 | −0.556827 | − | 0.830629i | \(-0.687981\pi\) | ||||
−0.556827 | + | 0.830629i | \(0.687981\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.24588e7 | 1.40698 | 0.703492 | − | 0.710704i | \(-0.251623\pi\) | ||||
0.703492 | + | 0.710704i | \(0.251623\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.36480e7 | −1.52854 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.49648e6 | −0.166220 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.66989e7 | −1.83957 | −0.919783 | − | 0.392427i | \(-0.871635\pi\) | ||||
−0.919783 | + | 0.392427i | \(0.871635\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.82577e7 | −4.17999 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.38885e6 | 0.475607 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.26676e6 | 0.136159 | 0.0680793 | − | 0.997680i | \(-0.478313\pi\) | ||||
0.0680793 | + | 0.997680i | \(0.478313\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.65182e6 | 0.389333 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.70474e6 | −0.180279 | −0.0901393 | − | 0.995929i | \(-0.528731\pi\) | ||||
−0.0901393 | + | 0.995929i | \(0.528731\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.01627e7 | 1.06606 | 0.533029 | − | 0.846097i | \(-0.321054\pi\) | ||||
0.533029 | + | 0.846097i | \(0.321054\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.68799e6 | −0.175647 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.12459e6 | 0.632203 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.45955e6 | 0.656195 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.44351e6 | −0.347036 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.02073e7 | 1.02056 | 0.510279 | − | 0.860009i | \(-0.329542\pi\) | ||||
0.510279 | + | 0.860009i | \(0.329542\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.93898e7 | −2.91533 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.37586e6 | −0.135407 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.97028e7 | −4.85325 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.01746e6 | 0.679873 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.45144e7 | 1.39526 | 0.697630 | − | 0.716458i | \(-0.254238\pi\) | ||||
0.697630 | + | 0.716458i | \(0.254238\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.90150e6 | −0.658288 | −0.329144 | − | 0.944280i | \(-0.606760\pi\) | ||||
−0.329144 | + | 0.944280i | \(0.606760\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.41464e6 | −0.133890 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.22382e7 | −1.14937 | −0.574683 | − | 0.818376i | \(-0.694875\pi\) | ||||
−0.574683 | + | 0.818376i | \(0.694875\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.74206e6 | 0.814708 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.14778e7 | −4.76066 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.96282e7 | 1.80134 | 0.900672 | − | 0.434499i | \(-0.143074\pi\) | ||||
0.900672 | + | 0.434499i | \(0.143074\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.07713e6 | −0.280248 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.60356e7 | 1.44934 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.18259e6 | −0.195776 | −0.0978880 | − | 0.995197i | \(-0.531209\pi\) | ||||
−0.0978880 | + | 0.995197i | \(0.531209\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.44654e6 | 0.662904 | 0.331452 | − | 0.943472i | \(-0.392462\pi\) | ||||
0.331452 | + | 0.943472i | \(0.392462\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.27001e7 | 2.88912 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.70114e6 | 0.412239 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.41188e6 | 0.122880 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.16734e7 | 1.00840 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.32228e7 | −1.13375 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.34404e7 | −1.14387 | −0.571933 | − | 0.820300i | \(-0.693806\pi\) | ||||
−0.571933 | + | 0.820300i | \(0.693806\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.20431e6 | 0.355169 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.23014e6 | 0.522428 | 0.261214 | − | 0.965281i | \(-0.415877\pi\) | ||||
0.261214 | + | 0.965281i | \(0.415877\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.65549e7 | −1.37801 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14218.8 | 0.00117488 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.02607e6 | 0.0841635 | 0.0420817 | − | 0.999114i | \(-0.486601\pi\) | ||||
0.0420817 | + | 0.999114i | \(0.486601\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.67992e6 | 0.462504 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.52732e7 | −1.23463 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.72070e6 | −0.780098 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.46823e7 | 1.16976 | 0.584881 | − | 0.811119i | \(-0.301141\pi\) | ||||
0.584881 | + | 0.811119i | \(0.301141\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.92132e7 | 3.10170 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.57966e6 | −0.438173 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.04167e6 | −0.471059 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.17582e7 | 2.45846 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.25346e6 | −0.326924 | −0.163462 | − | 0.986550i | \(-0.552266\pi\) | ||||
−0.163462 | + | 0.986550i | \(0.552266\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.30249e6 | 0.175715 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.76119e6 | −0.209230 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.25636e7 | −1.69770 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.46830e6 | 0.632675 | 0.316337 | − | 0.948647i | \(-0.397547\pi\) | ||||
0.316337 | + | 0.948647i | \(0.397547\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.75835e6 | 0.723940 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.89975e6 | 0.139950 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.56307e6 | −0.626418 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.63231e7 | 2.63867 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −245933. | −0.0177417 | −0.00887083 | − | 0.999961i | \(-0.502824\pi\) | ||||
−0.00887083 | + | 0.999961i | \(0.502824\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.62720e7 | 1.16574 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.91695e7 | 2.78678 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.51658e6 | −0.248471 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.48936e7 | −1.04511 | −0.522556 | − | 0.852605i | \(-0.675021\pi\) | ||||
−0.522556 | + | 0.852605i | \(0.675021\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.33917e7 | −0.933288 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.34043e6 | 0.161995 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.11220e7 | −0.764580 | −0.382290 | − | 0.924042i | \(-0.624864\pi\) | ||||
−0.382290 | + | 0.924042i | \(0.624864\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.12699e7 | 2.13505 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.83768e6 | −0.599335 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.15121e7 | 1.44901 | 0.724505 | − | 0.689270i | \(-0.242069\pi\) | ||||
0.724505 | + | 0.689270i | \(0.242069\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.18648e7 | −1.46285 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.59551e7 | 1.72485 | 0.862424 | − | 0.506187i | \(-0.168945\pi\) | ||||
0.862424 | + | 0.506187i | \(0.168945\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 777296. | 0.0513093 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.76376e7 | 2.46786 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.20711e7 | −2.08886 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37924.6 | 0.00245370 | 0.00122685 | − | 0.999999i | \(-0.499609\pi\) | ||||
0.00122685 | + | 0.999999i | \(0.499609\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.68958e7 | 3.01402 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.14207e6 | 0.519837 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.38963e7 | 0.881374 | 0.440687 | − | 0.897661i | \(-0.354735\pi\) | ||||
0.440687 | + | 0.897661i | \(0.354735\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.16297e6 | −0.136285 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.34668e7 | −1.46890 | −0.734449 | − | 0.678664i | \(-0.762559\pi\) | ||||
−0.734449 | + | 0.678664i | \(0.762559\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.82409e6 | 0.362173 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.37643e7 | −0.850356 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.95909e7 | −1.81622 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.71429e7 | 1.04537 | 0.522683 | − | 0.852527i | \(-0.324931\pi\) | ||||
0.522683 | + | 0.852527i | \(0.324931\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.96801e7 | −2.40401 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.29619e7 | 0.780224 | 0.390112 | − | 0.920767i | \(-0.372436\pi\) | ||||
0.390112 | + | 0.920767i | \(0.372436\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.73175e6 | −0.282987 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.08915e7 | 1.24141 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.03974e6 | 0.238512 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.54411e6 | 0.266576 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.78490e7 | −2.20623 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.67899e6 | −0.0972468 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.28899e7 | 1.31737 | 0.658683 | − | 0.752420i | \(-0.271114\pi\) | ||||
0.658683 | + | 0.752420i | \(0.271114\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.88086e7 | 1.64752 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.66300e7 | −1.51332 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.47576e7 | 2.52746 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.11566e6 | 0.343183 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.72212e7 | 1.51796 | 0.758981 | − | 0.651113i | \(-0.225698\pi\) | ||||
0.758981 | + | 0.651113i | \(0.225698\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.56819e6 | 0.253150 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.19902e7 | 0.660303 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.03837e7 | 0.568282 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.57417e6 | −0.0856174 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.97696e7 | 2.14965 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.71507e7 | 0.921323 | 0.460661 | − | 0.887576i | \(-0.347612\pi\) | ||||
0.460661 | + | 0.887576i | \(0.347612\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.85530e6 | 0.0990515 | 0.0495258 | − | 0.998773i | \(-0.484229\pi\) | ||||
0.0495258 | + | 0.998773i | \(0.484229\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.15959e7 | −3.26833 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.46329e6 | 0.182639 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.56492e6 | −0.0820231 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.32732e8 | −6.91460 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.55795e6 | −0.236000 | −0.118000 | − | 0.993014i | \(-0.537648\pi\) | ||||
−0.118000 | + | 0.993014i | \(0.537648\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.53222e7 | −1.30317 | −0.651586 | − | 0.758575i | \(-0.725896\pi\) | ||||
−0.651586 | + | 0.758575i | \(0.725896\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.38735e6 | 0.275575 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.37327e7 | −0.698219 | −0.349110 | − | 0.937082i | \(-0.613516\pi\) | ||||
−0.349110 | + | 0.937082i | \(0.613516\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.94031e6 | −0.199133 | −0.0995667 | − | 0.995031i | \(-0.531746\pi\) | ||||
−0.0995667 | + | 0.995031i | \(0.531746\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.35451e7 | −0.680425 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.17338e7 | −2.58322 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.86318e6 | −0.390285 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.09279e7 | −2.51271 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 635610. | 0.0311735 | 0.0155868 | − | 0.999879i | \(-0.495038\pi\) | ||||
0.0155868 | + | 0.999879i | \(0.495038\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.11467e7 | 0.543444 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.12048e7 | 1.02770 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.97027e7 | 0.949257 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.50206e7 | −0.719412 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.81318e7 | 2.29173 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −770986. | −0.0364941 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.49876e7 | −0.705275 | −0.352638 | − | 0.935760i | \(-0.614715\pi\) | ||||
−0.352638 | + | 0.935760i | \(0.614715\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.20345e6 | 0.430562 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.93680e7 | −0.900811 | −0.450405 | − | 0.892824i | \(-0.648721\pi\) | ||||
−0.450405 | + | 0.892824i | \(0.648721\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.26651e7 | 1.51043 | 0.755215 | − | 0.655477i | \(-0.227532\pi\) | ||||
0.755215 | + | 0.655477i | \(0.227532\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.66543e7 | 1.68507 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.58577e6 | 0.0724790 | 0.0362395 | − | 0.999343i | \(-0.488462\pi\) | ||||
0.0362395 | + | 0.999343i | \(0.488462\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.44702e7 | −0.657559 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.43759e6 | −0.200493 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.31896e6 | 0.283855 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.99145e7 | 1.33609 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.24096e7 | −1.43926 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.92081e6 | 0.173123 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.76484e7 | 0.774828 | 0.387414 | − | 0.921906i | \(-0.373368\pi\) | ||||
0.387414 | + | 0.921906i | \(0.373368\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.00627e6 | −0.0439279 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.89390e6 | −0.386058 | −0.193029 | − | 0.981193i | \(-0.561831\pi\) | ||||
−0.193029 | + | 0.981193i | \(0.561831\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.37374e6 | −0.275101 | −0.137551 | − | 0.990495i | \(-0.543923\pi\) | ||||
−0.137551 | + | 0.990495i | \(0.543923\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.86167e7 | 0.798998 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.99742e7 | 1.27920 | 0.639601 | − | 0.768707i | \(-0.279100\pi\) | ||||
0.639601 | + | 0.768707i | \(0.279100\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.38099e7 | −0.586051 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.00105e7 | 0.844429 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.05451e6 | −0.128178 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.99015e6 | −0.291695 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.32142e6 | 0.303818 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.25973e7 | 1.75785 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.01179e7 | −0.415221 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.41992e7 | −0.579487 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.18729e7 | −0.481877 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.99329e6 | −0.0804547 | −0.0402273 | − | 0.999191i | \(-0.512808\pi\) | ||||
−0.0402273 | + | 0.999191i | \(0.512808\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.41730e7 | −1.77316 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.64815e7 | 0.657963 | 0.328982 | − | 0.944336i | \(-0.393295\pi\) | ||||
0.328982 | + | 0.944336i | \(0.393295\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.43720e7 | 0.967640 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.81587e7 | −1.11188 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.08861e7 | −1.21294 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.45655e6 | 0.330297 | 0.165148 | − | 0.986269i | \(-0.447190\pi\) | ||||
0.165148 | + | 0.986269i | \(0.447190\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.20016e7 | −0.466217 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.53813e7 | −0.594277 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.92031e6 | 0.0737932 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.18558e7 | 1.21756 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.70844e7 | 0.649472 | 0.324736 | − | 0.945805i | \(-0.394725\pi\) | ||||
0.324736 | + | 0.945805i | \(0.394725\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.45916e7 | 1.30797 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.07243e6 | 0.265989 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.91299e6 | −0.333422 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.35711e7 | −0.877064 | −0.438532 | − | 0.898716i | \(-0.644501\pi\) | ||||
−0.438532 | + | 0.898716i | \(0.644501\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.82530e7 | −0.675572 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.44798e7 | −1.63753 | −0.818763 | − | 0.574131i | \(-0.805340\pi\) | ||||
−0.818763 | + | 0.574131i | \(0.805340\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.35270e6 | −0.0495363 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.21998e7 | 1.53720 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.90955e7 | −0.691921 | −0.345961 | − | 0.938249i | \(-0.612447\pi\) | ||||
−0.345961 | + | 0.938249i | \(0.612447\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.51477e7 | −1.26687 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.61736e7 | −0.938452 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.90401e7 | 1.03578 | 0.517888 | − | 0.855448i | \(-0.326718\pi\) | ||||
0.517888 | + | 0.855448i | \(0.326718\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.70198e7 | 0.603874 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.84993e7 | −1.71181 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.70109e7 | 2.00176 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.86878e7 | 1.00205 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.27858e7 | −2.18170 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.20013e7 | −0.414867 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.46040e6 | −0.119004 | −0.0595018 | − | 0.998228i | \(-0.518951\pi\) | ||||
−0.0595018 | + | 0.998228i | \(0.518951\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.27583e7 | −0.778629 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.43875e7 | 1.51082 | 0.755410 | − | 0.655252i | \(-0.227438\pi\) | ||||
0.755410 | + | 0.655252i | \(0.227438\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.60046e7 | −1.89645 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.82356e7 | −0.614338 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.55597e7 | 0.521512 | 0.260756 | − | 0.965405i | \(-0.416028\pi\) | ||||
0.260756 | + | 0.965405i | \(0.416028\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.76415e6 | 0.258903 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.14019e7 | 0.378271 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.93263e7 | 1.29807 | 0.649036 | − | 0.760758i | \(-0.275172\pi\) | ||||
0.649036 | + | 0.760758i | \(0.275172\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.32245e7 | 0.762703 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.77148e7 | −0.905565 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 524011. | 0.0170353 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.63955e7 | 0.853780 | 0.426890 | − | 0.904303i | \(-0.359609\pi\) | ||||
0.426890 | + | 0.904303i | \(0.359609\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.24392e7 | −1.68765 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.53397e6 | 0.113163 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.49308e6 | 0.111294 | 0.0556468 | − | 0.998451i | \(-0.482278\pi\) | ||||
0.0556468 | + | 0.998451i | \(0.482278\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.06683e7 | 0.655226 |
(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 | 160.6.a.h.1.4 | yes | 4 | |
4.3 | odd | 2 | inner | 160.6.a.h.1.1 | ✓ | 4 | |
5.2 | odd | 4 | 800.6.c.l.449.2 | 8 | |||
5.3 | odd | 4 | 800.6.c.l.449.8 | 8 | |||
5.4 | even | 2 | 800.6.a.r.1.1 | 4 | |||
8.3 | odd | 2 | 320.6.a.z.1.4 | 4 | |||
8.5 | even | 2 | 320.6.a.z.1.1 | 4 | |||
20.3 | even | 4 | 800.6.c.l.449.1 | 8 | |||
20.7 | even | 4 | 800.6.c.l.449.7 | 8 | |||
20.19 | odd | 2 | 800.6.a.r.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.6.a.h.1.1 | ✓ | 4 | 4.3 | odd | 2 | inner | |
160.6.a.h.1.4 | yes | 4 | 1.1 | even | 1 | trivial | |
320.6.a.z.1.1 | 4 | 8.5 | even | 2 | |||
320.6.a.z.1.4 | 4 | 8.3 | odd | 2 | |||
800.6.a.r.1.1 | 4 | 5.4 | even | 2 | |||
800.6.a.r.1.4 | 4 | 20.19 | odd | 2 | |||
800.6.c.l.449.1 | 8 | 20.3 | even | 4 | |||
800.6.c.l.449.2 | 8 | 5.2 | odd | 4 | |||
800.6.c.l.449.7 | 8 | 20.7 | even | 4 | |||
800.6.c.l.449.8 | 8 | 5.3 | odd | 4 |