Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,6,Mod(1,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, 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("531.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.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: | \(85.1638083207\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 283 x^{10} + 1045 x^{9} + 27968 x^{8} - 94393 x^{7} - 1130486 x^{6} + \cdots - 50564480 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 177) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(8.80731\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 531.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.80731 | 1.55693 | 0.778463 | − | 0.627690i | \(-0.215999\pi\) | ||||
0.778463 | + | 0.627690i | \(0.215999\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 45.5687 | 1.42402 | ||||||||
\(5\) | 88.4760 | 1.58271 | 0.791354 | − | 0.611359i | \(-0.209377\pi\) | ||||
0.791354 | + | 0.611359i | \(0.209377\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −134.279 | −1.03577 | −0.517884 | − | 0.855451i | \(-0.673280\pi\) | ||||
−0.517884 | + | 0.855451i | \(0.673280\pi\) | |||||||
\(8\) | 119.504 | 0.660170 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 779.236 | 2.46416 | ||||||||
\(11\) | −423.269 | −1.05471 | −0.527357 | − | 0.849644i | \(-0.676817\pi\) | ||||
−0.527357 | + | 0.849644i | \(0.676817\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −713.936 | −1.17166 | −0.585829 | − | 0.810434i | \(-0.699231\pi\) | ||||
−0.585829 | + | 0.810434i | \(0.699231\pi\) | |||||||
\(14\) | −1182.64 | −1.61262 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −405.693 | −0.396184 | ||||||||
\(17\) | −924.109 | −0.775534 | −0.387767 | − | 0.921757i | \(-0.626754\pi\) | ||||
−0.387767 | + | 0.921757i | \(0.626754\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −64.3204 | −0.0408756 | −0.0204378 | − | 0.999791i | \(-0.506506\pi\) | ||||
−0.0204378 | + | 0.999791i | \(0.506506\pi\) | |||||||
\(20\) | 4031.74 | 2.25381 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3727.86 | −1.64211 | ||||||||
\(23\) | −3703.37 | −1.45975 | −0.729873 | − | 0.683583i | \(-0.760421\pi\) | ||||
−0.729873 | + | 0.683583i | \(0.760421\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4703.01 | 1.50496 | ||||||||
\(26\) | −6287.86 | −1.82419 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −6118.92 | −1.47496 | ||||||||
\(29\) | −4990.17 | −1.10185 | −0.550923 | − | 0.834556i | \(-0.685724\pi\) | ||||
−0.550923 | + | 0.834556i | \(0.685724\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3097.37 | 0.578880 | 0.289440 | − | 0.957196i | \(-0.406531\pi\) | ||||
0.289440 | + | 0.957196i | \(0.406531\pi\) | |||||||
\(32\) | −7397.18 | −1.27700 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8138.92 | −1.20745 | ||||||||
\(35\) | −11880.5 | −1.63932 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4978.34 | −0.597834 | −0.298917 | − | 0.954279i | \(-0.596625\pi\) | ||||
−0.298917 | + | 0.954279i | \(0.596625\pi\) | |||||||
\(38\) | −566.489 | −0.0636404 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 10573.2 | 1.04486 | ||||||||
\(41\) | −996.199 | −0.0925522 | −0.0462761 | − | 0.998929i | \(-0.514735\pi\) | ||||
−0.0462761 | + | 0.998929i | \(0.514735\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7715.17 | 0.636318 | 0.318159 | − | 0.948037i | \(-0.396935\pi\) | ||||
0.318159 | + | 0.948037i | \(0.396935\pi\) | |||||||
\(44\) | −19287.8 | −1.50193 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −32616.7 | −2.27272 | ||||||||
\(47\) | 17274.4 | 1.14067 | 0.570333 | − | 0.821414i | \(-0.306814\pi\) | ||||
0.570333 | + | 0.821414i | \(0.306814\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1223.84 | 0.0728171 | ||||||||
\(50\) | 41420.8 | 2.34312 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −32533.1 | −1.66847 | ||||||||
\(53\) | 34756.3 | 1.69959 | 0.849796 | − | 0.527112i | \(-0.176725\pi\) | ||||
0.849796 | + | 0.527112i | \(0.176725\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −37449.1 | −1.66930 | ||||||||
\(56\) | −16046.8 | −0.683784 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −43950.0 | −1.71549 | ||||||||
\(59\) | 3481.00 | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 33316.0 | 1.14638 | 0.573190 | − | 0.819422i | \(-0.305706\pi\) | ||||
0.573190 | + | 0.819422i | \(0.305706\pi\) | |||||||
\(62\) | 27279.5 | 0.901274 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −52167.1 | −1.59201 | ||||||||
\(65\) | −63166.3 | −1.85439 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 50498.8 | 1.37434 | 0.687169 | − | 0.726497i | \(-0.258853\pi\) | ||||
0.687169 | + | 0.726497i | \(0.258853\pi\) | |||||||
\(68\) | −42110.4 | −1.10438 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −104635. | −2.55230 | ||||||||
\(71\) | 16903.5 | 0.397951 | 0.198975 | − | 0.980004i | \(-0.436239\pi\) | ||||
0.198975 | + | 0.980004i | \(0.436239\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −84572.2 | −1.85746 | −0.928732 | − | 0.370752i | \(-0.879100\pi\) | ||||
−0.928732 | + | 0.370752i | \(0.879100\pi\) | |||||||
\(74\) | −43845.8 | −0.930783 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2930.99 | −0.0582078 | ||||||||
\(77\) | 56836.1 | 1.09244 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9984.38 | 0.179992 | 0.0899960 | − | 0.995942i | \(-0.471315\pi\) | ||||
0.0899960 | + | 0.995942i | \(0.471315\pi\) | |||||||
\(80\) | −35894.1 | −0.627044 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8773.83 | −0.144097 | ||||||||
\(83\) | −11880.4 | −0.189293 | −0.0946467 | − | 0.995511i | \(-0.530172\pi\) | ||||
−0.0946467 | + | 0.995511i | \(0.530172\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −81761.5 | −1.22744 | ||||||||
\(86\) | 67949.9 | 0.990701 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −50582.1 | −0.696290 | ||||||||
\(89\) | 8140.62 | 0.108939 | 0.0544694 | − | 0.998515i | \(-0.482653\pi\) | ||||
0.0544694 | + | 0.998515i | \(0.482653\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 95866.6 | 1.21357 | ||||||||
\(92\) | −168758. | −2.07871 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 152141. | 1.77593 | ||||||||
\(95\) | −5690.81 | −0.0646942 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −137348. | −1.48215 | −0.741077 | − | 0.671420i | \(-0.765685\pi\) | ||||
−0.741077 | + | 0.671420i | \(0.765685\pi\) | |||||||
\(98\) | 10778.7 | 0.113371 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 214310. | 2.14310 | ||||||||
\(101\) | 32965.3 | 0.321553 | 0.160777 | − | 0.986991i | \(-0.448600\pi\) | ||||
0.160777 | + | 0.986991i | \(0.448600\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 168560. | 1.56553 | 0.782764 | − | 0.622319i | \(-0.213809\pi\) | ||||
0.782764 | + | 0.622319i | \(0.213809\pi\) | |||||||
\(104\) | −85318.0 | −0.773494 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 306110. | 2.64614 | ||||||||
\(107\) | 36729.3 | 0.310137 | 0.155069 | − | 0.987904i | \(-0.450440\pi\) | ||||
0.155069 | + | 0.987904i | \(0.450440\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 171480. | 1.38244 | 0.691222 | − | 0.722642i | \(-0.257073\pi\) | ||||
0.691222 | + | 0.722642i | \(0.257073\pi\) | |||||||
\(110\) | −329826. | −2.59898 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 54476.0 | 0.410356 | ||||||||
\(113\) | −10840.2 | −0.0798624 | −0.0399312 | − | 0.999202i | \(-0.512714\pi\) | ||||
−0.0399312 | + | 0.999202i | \(0.512714\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −327659. | −2.31035 | ||||||||
\(116\) | −227396. | −1.56905 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 30658.2 | 0.202695 | ||||||||
\(119\) | 124088. | 0.803274 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18105.3 | 0.112420 | ||||||||
\(122\) | 293425. | 1.78483 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 141143. | 0.824337 | ||||||||
\(125\) | 139616. | 0.799208 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −266071. | −1.46382 | −0.731911 | − | 0.681400i | \(-0.761371\pi\) | ||||
−0.731911 | + | 0.681400i | \(0.761371\pi\) | |||||||
\(128\) | −222742. | −1.20165 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −556325. | −2.88715 | ||||||||
\(131\) | −344872. | −1.75582 | −0.877910 | − | 0.478826i | \(-0.841062\pi\) | ||||
−0.877910 | + | 0.478826i | \(0.841062\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8636.87 | 0.0423377 | ||||||||
\(134\) | 444758. | 2.13975 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −110434. | −0.511985 | ||||||||
\(137\) | −299475. | −1.36320 | −0.681600 | − | 0.731725i | \(-0.738716\pi\) | ||||
−0.681600 | + | 0.731725i | \(0.738716\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −279442. | −1.22675 | −0.613373 | − | 0.789793i | \(-0.710188\pi\) | ||||
−0.613373 | + | 0.789793i | \(0.710188\pi\) | |||||||
\(140\) | −541377. | −2.33443 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 148874. | 0.619581 | ||||||||
\(143\) | 302187. | 1.23576 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −441511. | −1.74390 | ||||||||
\(146\) | −744853. | −2.89193 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −226856. | −0.851328 | ||||||||
\(149\) | −522957. | −1.92974 | −0.964872 | − | 0.262719i | \(-0.915381\pi\) | ||||
−0.964872 | + | 0.262719i | \(0.915381\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −225544. | −0.804988 | −0.402494 | − | 0.915423i | \(-0.631857\pi\) | ||||
−0.402494 | + | 0.915423i | \(0.631857\pi\) | |||||||
\(152\) | −7686.52 | −0.0269849 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 500573. | 1.70085 | ||||||||
\(155\) | 274043. | 0.916197 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 169574. | 0.549047 | 0.274524 | − | 0.961580i | \(-0.411480\pi\) | ||||
0.274524 | + | 0.961580i | \(0.411480\pi\) | |||||||
\(158\) | 87935.5 | 0.280234 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −654473. | −2.02112 | ||||||||
\(161\) | 497284. | 1.51196 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 247010. | 0.728192 | 0.364096 | − | 0.931361i | \(-0.381378\pi\) | ||||
0.364096 | + | 0.931361i | \(0.381378\pi\) | |||||||
\(164\) | −45395.5 | −0.131796 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −104634. | −0.294716 | ||||||||
\(167\) | 37137.6 | 0.103044 | 0.0515220 | − | 0.998672i | \(-0.483593\pi\) | ||||
0.0515220 | + | 0.998672i | \(0.483593\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 138412. | 0.372785 | ||||||||
\(170\) | −720099. | −1.91104 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 351570. | 0.906131 | ||||||||
\(173\) | 49966.1 | 0.126929 | 0.0634644 | − | 0.997984i | \(-0.479785\pi\) | ||||
0.0634644 | + | 0.997984i | \(0.479785\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −631515. | −1.55879 | ||||||||
\(176\) | 171717. | 0.417861 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 71697.0 | 0.169610 | ||||||||
\(179\) | 53182.0 | 0.124060 | 0.0620300 | − | 0.998074i | \(-0.480243\pi\) | ||||
0.0620300 | + | 0.998074i | \(0.480243\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −228956. | −0.519463 | −0.259732 | − | 0.965681i | \(-0.583634\pi\) | ||||
−0.259732 | + | 0.965681i | \(0.583634\pi\) | |||||||
\(182\) | 844327. | 1.88944 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −442566. | −0.963681 | ||||||||
\(185\) | −440464. | −0.946195 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 391146. | 0.817966 | ||||||||
\(188\) | 787171. | 1.62433 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −50120.7 | −0.100724 | ||||||||
\(191\) | −383018. | −0.759689 | −0.379845 | − | 0.925050i | \(-0.624023\pi\) | ||||
−0.379845 | + | 0.925050i | \(0.624023\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −671956. | −1.29852 | −0.649258 | − | 0.760568i | \(-0.724921\pi\) | ||||
−0.649258 | + | 0.760568i | \(0.724921\pi\) | |||||||
\(194\) | −1.20967e6 | −2.30761 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 55768.6 | 0.103693 | ||||||||
\(197\) | 517980. | 0.950927 | 0.475464 | − | 0.879735i | \(-0.342280\pi\) | ||||
0.475464 | + | 0.879735i | \(0.342280\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 437764. | 0.783624 | 0.391812 | − | 0.920045i | \(-0.371848\pi\) | ||||
0.391812 | + | 0.920045i | \(0.371848\pi\) | |||||||
\(200\) | 562026. | 0.993531 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 290335. | 0.500635 | ||||||||
\(203\) | 670075. | 1.14126 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −88139.8 | −0.146483 | ||||||||
\(206\) | 1.48456e6 | 2.43741 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 289639. | 0.464193 | ||||||||
\(209\) | 27224.8 | 0.0431121 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 795724. | 1.23043 | 0.615214 | − | 0.788360i | \(-0.289070\pi\) | ||||
0.615214 | + | 0.788360i | \(0.289070\pi\) | |||||||
\(212\) | 1.58380e6 | 2.42025 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 323487. | 0.482861 | ||||||||
\(215\) | 682608. | 1.00711 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −415911. | −0.599586 | ||||||||
\(218\) | 1.51028e6 | 2.15237 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.70651e6 | −2.37712 | ||||||||
\(221\) | 659755. | 0.908662 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.44232e6 | −1.94222 | −0.971110 | − | 0.238632i | \(-0.923301\pi\) | ||||
−0.971110 | + | 0.238632i | \(0.923301\pi\) | |||||||
\(224\) | 993285. | 1.32268 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −95473.3 | −0.124340 | ||||||||
\(227\) | 421642. | 0.543099 | 0.271549 | − | 0.962425i | \(-0.412464\pi\) | ||||
0.271549 | + | 0.962425i | \(0.412464\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.41705e6 | −1.78565 | −0.892823 | − | 0.450407i | \(-0.851279\pi\) | ||||
−0.892823 | + | 0.450407i | \(0.851279\pi\) | |||||||
\(230\) | −2.88580e6 | −3.59705 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −596344. | −0.727406 | ||||||||
\(233\) | −673154. | −0.812315 | −0.406158 | − | 0.913803i | \(-0.633132\pi\) | ||||
−0.406158 | + | 0.913803i | \(0.633132\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.52837e6 | 1.80534 | ||||||||
\(236\) | 158625. | 0.185392 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.09289e6 | 1.25064 | ||||||||
\(239\) | 760337. | 0.861016 | 0.430508 | − | 0.902587i | \(-0.358334\pi\) | ||||
0.430508 | + | 0.902587i | \(0.358334\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 470539. | 0.521859 | 0.260929 | − | 0.965358i | \(-0.415971\pi\) | ||||
0.260929 | + | 0.965358i | \(0.415971\pi\) | |||||||
\(242\) | 159459. | 0.175029 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.51817e6 | 1.63247 | ||||||||
\(245\) | 108280. | 0.115248 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 45920.7 | 0.0478923 | ||||||||
\(248\) | 370147. | 0.382159 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.22964e6 | 1.24431 | ||||||||
\(251\) | −962815. | −0.964625 | −0.482313 | − | 0.875999i | \(-0.660203\pi\) | ||||
−0.482313 | + | 0.875999i | \(0.660203\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.56752e6 | 1.53961 | ||||||||
\(254\) | −2.34337e6 | −2.27906 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −292409. | −0.278863 | ||||||||
\(257\) | 931917. | 0.880125 | 0.440062 | − | 0.897967i | \(-0.354956\pi\) | ||||
0.440062 | + | 0.897967i | \(0.354956\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 668486. | 0.619217 | ||||||||
\(260\) | −2.87840e6 | −2.64070 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.03740e6 | −2.73368 | ||||||||
\(263\) | 1.26124e6 | 1.12437 | 0.562184 | − | 0.827012i | \(-0.309961\pi\) | ||||
0.562184 | + | 0.827012i | \(0.309961\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.07510e6 | 2.68996 | ||||||||
\(266\) | 76067.6 | 0.0659167 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.30116e6 | 1.95709 | ||||||||
\(269\) | 688569. | 0.580185 | 0.290093 | − | 0.956999i | \(-0.406314\pi\) | ||||
0.290093 | + | 0.956999i | \(0.406314\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −733019. | −0.606306 | −0.303153 | − | 0.952942i | \(-0.598039\pi\) | ||||
−0.303153 | + | 0.952942i | \(0.598039\pi\) | |||||||
\(272\) | 374905. | 0.307255 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.63757e6 | −2.12240 | ||||||||
\(275\) | −1.99064e6 | −1.58730 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −176065. | −0.137871 | −0.0689356 | − | 0.997621i | \(-0.521960\pi\) | ||||
−0.0689356 | + | 0.997621i | \(0.521960\pi\) | |||||||
\(278\) | −2.46113e6 | −1.90995 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.41976e6 | −1.08223 | ||||||||
\(281\) | 1.04068e6 | 0.786232 | 0.393116 | − | 0.919489i | \(-0.371397\pi\) | ||||
0.393116 | + | 0.919489i | \(0.371397\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 715219. | 0.530851 | 0.265426 | − | 0.964131i | \(-0.414488\pi\) | ||||
0.265426 | + | 0.964131i | \(0.414488\pi\) | |||||||
\(284\) | 770268. | 0.566691 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.66145e6 | 1.92399 | ||||||||
\(287\) | 133769. | 0.0958626 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −565879. | −0.398546 | ||||||||
\(290\) | −3.88852e6 | −2.71512 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.85384e6 | −2.64507 | ||||||||
\(293\) | −2.03867e6 | −1.38732 | −0.693662 | − | 0.720301i | \(-0.744004\pi\) | ||||
−0.693662 | + | 0.720301i | \(0.744004\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 307985. | 0.206051 | ||||||||
\(296\) | −594930. | −0.394672 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.60584e6 | −3.00447 | ||||||||
\(299\) | 2.64397e6 | 1.71032 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.03599e6 | −0.659079 | ||||||||
\(302\) | −1.98644e6 | −1.25331 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 26094.3 | 0.0161943 | ||||||||
\(305\) | 2.94767e6 | 1.81439 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.35132e6 | −0.818301 | −0.409151 | − | 0.912467i | \(-0.634175\pi\) | ||||
−0.409151 | + | 0.912467i | \(0.634175\pi\) | |||||||
\(308\) | 2.58994e6 | 1.55566 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.41358e6 | 1.42645 | ||||||||
\(311\) | 1.87621e6 | 1.09997 | 0.549985 | − | 0.835175i | \(-0.314633\pi\) | ||||
0.549985 | + | 0.835175i | \(0.314633\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.45653e6 | 1.41730 | 0.708649 | − | 0.705561i | \(-0.249305\pi\) | ||||
0.708649 | + | 0.705561i | \(0.249305\pi\) | |||||||
\(314\) | 1.49349e6 | 0.854826 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 454975. | 0.256312 | ||||||||
\(317\) | 1.75984e6 | 0.983615 | 0.491808 | − | 0.870704i | \(-0.336336\pi\) | ||||
0.491808 | + | 0.870704i | \(0.336336\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.11218e6 | 1.16213 | ||||||||
\(320\) | −4.61553e6 | −2.51969 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.37974e6 | 2.35401 | ||||||||
\(323\) | 59439.1 | 0.0317005 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.35765e6 | −1.76330 | ||||||||
\(326\) | 2.17549e6 | 1.13374 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −119049. | −0.0611002 | ||||||||
\(329\) | −2.31959e6 | −1.18147 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.62035e6 | −1.31459 | −0.657293 | − | 0.753635i | \(-0.728299\pi\) | ||||
−0.657293 | + | 0.753635i | \(0.728299\pi\) | |||||||
\(332\) | −541374. | −0.269558 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 327082. | 0.160432 | ||||||||
\(335\) | 4.46793e6 | 2.17518 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.56955e6 | 1.23249 | 0.616244 | − | 0.787555i | \(-0.288653\pi\) | ||||
0.616244 | + | 0.787555i | \(0.288653\pi\) | |||||||
\(338\) | 1.21904e6 | 0.580398 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.72577e6 | −1.74791 | ||||||||
\(341\) | −1.31102e6 | −0.610552 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.09249e6 | 0.960347 | ||||||||
\(344\) | 921991. | 0.420079 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 440067. | 0.197619 | ||||||||
\(347\) | −1.69640e6 | −0.756318 | −0.378159 | − | 0.925741i | \(-0.623443\pi\) | ||||
−0.378159 | + | 0.925741i | \(0.623443\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.36923e6 | −1.04122 | −0.520612 | − | 0.853794i | \(-0.674296\pi\) | ||||
−0.520612 | + | 0.853794i | \(0.674296\pi\) | |||||||
\(350\) | −5.56195e6 | −2.42693 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.13099e6 | 1.34687 | ||||||||
\(353\) | −4.33080e6 | −1.84983 | −0.924914 | − | 0.380175i | \(-0.875864\pi\) | ||||
−0.924914 | + | 0.380175i | \(0.875864\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.49555e6 | 0.629840 | ||||||||
\(356\) | 370957. | 0.155131 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 468390. | 0.193152 | ||||||||
\(359\) | 1.01517e6 | 0.415723 | 0.207862 | − | 0.978158i | \(-0.433350\pi\) | ||||
0.207862 | + | 0.978158i | \(0.433350\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.47196e6 | −0.998329 | ||||||||
\(362\) | −2.01648e6 | −0.808766 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.36852e6 | 1.72815 | ||||||||
\(365\) | −7.48261e6 | −2.93982 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.21426e6 | −0.858151 | −0.429076 | − | 0.903269i | \(-0.641161\pi\) | ||||
−0.429076 | + | 0.903269i | \(0.641161\pi\) | |||||||
\(368\) | 1.50243e6 | 0.578328 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.87930e6 | −1.47316 | ||||||||
\(371\) | −4.66705e6 | −1.76038 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.01840e6 | −0.751166 | −0.375583 | − | 0.926789i | \(-0.622557\pi\) | ||||
−0.375583 | + | 0.926789i | \(0.622557\pi\) | |||||||
\(374\) | 3.44495e6 | 1.27351 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.06435e6 | 0.753033 | ||||||||
\(377\) | 3.56267e6 | 1.29099 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.76169e6 | 1.70280 | 0.851398 | − | 0.524520i | \(-0.175755\pi\) | ||||
0.851398 | + | 0.524520i | \(0.175755\pi\) | |||||||
\(380\) | −259323. | −0.0921259 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.37336e6 | −1.18278 | ||||||||
\(383\) | −1.00203e6 | −0.349046 | −0.174523 | − | 0.984653i | \(-0.555838\pi\) | ||||
−0.174523 | + | 0.984653i | \(0.555838\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.02863e6 | 1.72901 | ||||||||
\(386\) | −5.91812e6 | −2.02170 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6.25877e6 | −2.11062 | ||||||||
\(389\) | 5.08858e6 | 1.70499 | 0.852496 | − | 0.522734i | \(-0.175088\pi\) | ||||
0.852496 | + | 0.522734i | \(0.175088\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.42232e6 | 1.13208 | ||||||||
\(392\) | 146253. | 0.0480717 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.56201e6 | 1.48052 | ||||||||
\(395\) | 883378. | 0.284875 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.16172e6 | −1.32525 | −0.662624 | − | 0.748953i | \(-0.730557\pi\) | ||||
−0.662624 | + | 0.748953i | \(0.730557\pi\) | |||||||
\(398\) | 3.85552e6 | 1.22004 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.90798e6 | −0.596243 | ||||||||
\(401\) | −6.12721e6 | −1.90284 | −0.951420 | − | 0.307897i | \(-0.900375\pi\) | ||||
−0.951420 | + | 0.307897i | \(0.900375\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.21132e6 | −0.678250 | ||||||||
\(404\) | 1.50218e6 | 0.457899 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.90156e6 | 1.77685 | ||||||||
\(407\) | 2.10718e6 | 0.630543 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.39272e6 | −0.411675 | −0.205837 | − | 0.978586i | \(-0.565992\pi\) | ||||
−0.205837 | + | 0.978586i | \(0.565992\pi\) | |||||||
\(410\) | −776274. | −0.228063 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.68104e6 | 2.22934 | ||||||||
\(413\) | −467425. | −0.134846 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.05113e6 | −0.299596 | ||||||||
\(416\) | 5.28111e6 | 1.49621 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 239777. | 0.0671223 | ||||||||
\(419\) | 4.89970e6 | 1.36343 | 0.681717 | − | 0.731616i | \(-0.261233\pi\) | ||||
0.681717 | + | 0.731616i | \(0.261233\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.47517e6 | −0.405637 | −0.202818 | − | 0.979216i | \(-0.565010\pi\) | ||||
−0.202818 | + | 0.979216i | \(0.565010\pi\) | |||||||
\(422\) | 7.00819e6 | 1.91569 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.15351e6 | 1.12202 | ||||||||
\(425\) | −4.34609e6 | −1.16715 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.47364e6 | −1.18739 | ||||||||
\(428\) | 1.67371e6 | 0.441642 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.01194e6 | 1.56799 | ||||||||
\(431\) | 6.48538e6 | 1.68168 | 0.840838 | − | 0.541286i | \(-0.182063\pi\) | ||||
0.840838 | + | 0.541286i | \(0.182063\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.86229e6 | 1.50262 | 0.751308 | − | 0.659952i | \(-0.229423\pi\) | ||||
0.751308 | + | 0.659952i | \(0.229423\pi\) | |||||||
\(434\) | −3.66306e6 | −0.933511 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.81413e6 | 1.96863 | ||||||||
\(437\) | 238202. | 0.0596680 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.42815e6 | −1.09663 | −0.548316 | − | 0.836271i | \(-0.684731\pi\) | ||||
−0.548316 | + | 0.836271i | \(0.684731\pi\) | |||||||
\(440\) | −4.47530e6 | −1.10202 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.81067e6 | 1.41472 | ||||||||
\(443\) | 7.50913e6 | 1.81794 | 0.908971 | − | 0.416859i | \(-0.136869\pi\) | ||||
0.908971 | + | 0.416859i | \(0.136869\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 720250. | 0.172418 | ||||||||
\(446\) | −1.27029e7 | −3.02389 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 7.00494e6 | 1.64896 | ||||||||
\(449\) | −1.95240e6 | −0.457040 | −0.228520 | − | 0.973539i | \(-0.573389\pi\) | ||||
−0.228520 | + | 0.973539i | \(0.573389\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 421660. | 0.0976160 | ||||||||
\(452\) | −493975. | −0.113726 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.71353e6 | 0.845565 | ||||||||
\(455\) | 8.48190e6 | 1.92072 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.94530e6 | −1.33163 | −0.665814 | − | 0.746118i | \(-0.731916\pi\) | ||||
−0.665814 | + | 0.746118i | \(0.731916\pi\) | |||||||
\(458\) | −1.24804e7 | −2.78012 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.49310e7 | −3.28999 | ||||||||
\(461\) | −6.52618e6 | −1.43023 | −0.715116 | − | 0.699006i | \(-0.753626\pi\) | ||||
−0.715116 | + | 0.699006i | \(0.753626\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.21024e6 | −0.262373 | −0.131187 | − | 0.991358i | \(-0.541879\pi\) | ||||
−0.131187 | + | 0.991358i | \(0.541879\pi\) | |||||||
\(464\) | 2.02448e6 | 0.436534 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.92868e6 | −1.26472 | ||||||||
\(467\) | 3.93565e6 | 0.835073 | 0.417536 | − | 0.908660i | \(-0.362894\pi\) | ||||
0.417536 | + | 0.908660i | \(0.362894\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.78092e6 | −1.42350 | ||||||||
\(470\) | 1.34608e7 | 2.81078 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 415992. | 0.0859469 | ||||||||
\(473\) | −3.26559e6 | −0.671133 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −302499. | −0.0615163 | ||||||||
\(476\) | 5.65455e6 | 1.14388 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6.69652e6 | 1.34054 | ||||||||
\(479\) | 242633. | 0.0483183 | 0.0241592 | − | 0.999708i | \(-0.492309\pi\) | ||||
0.0241592 | + | 0.999708i | \(0.492309\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.55422e6 | 0.700457 | ||||||||
\(482\) | 4.14418e6 | 0.812496 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 825035. | 0.160088 | ||||||||
\(485\) | −1.21520e7 | −2.34582 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.57797e6 | −0.492556 | −0.246278 | − | 0.969199i | \(-0.579208\pi\) | ||||
−0.246278 | + | 0.969199i | \(0.579208\pi\) | |||||||
\(488\) | 3.98139e6 | 0.756807 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 953657. | 0.179433 | ||||||||
\(491\) | 287405. | 0.0538010 | 0.0269005 | − | 0.999638i | \(-0.491436\pi\) | ||||
0.0269005 | + | 0.999638i | \(0.491436\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.61147e6 | 0.854519 | ||||||||
\(494\) | 404437. | 0.0745648 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.25658e6 | −0.229343 | ||||||||
\(497\) | −2.26978e6 | −0.412185 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.52048e6 | 0.812706 | 0.406353 | − | 0.913716i | \(-0.366800\pi\) | ||||
0.406353 | + | 0.913716i | \(0.366800\pi\) | |||||||
\(500\) | 6.36211e6 | 1.13809 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8.47981e6 | −1.50185 | ||||||||
\(503\) | 2.75026e6 | 0.484679 | 0.242339 | − | 0.970192i | \(-0.422085\pi\) | ||||
0.242339 | + | 0.970192i | \(0.422085\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.91664e6 | 0.508925 | ||||||||
\(506\) | 1.38056e7 | 2.39706 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.21245e7 | −2.08451 | ||||||||
\(509\) | −2.32843e6 | −0.398354 | −0.199177 | − | 0.979964i | \(-0.563827\pi\) | ||||
−0.199177 | + | 0.979964i | \(0.563827\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.13563e7 | 1.92390 | ||||||||
\(512\) | 4.55240e6 | 0.767477 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8.20768e6 | 1.37029 | ||||||||
\(515\) | 1.49135e7 | 2.47777 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.31171e6 | −1.20307 | ||||||||
\(518\) | 5.88757e6 | 0.964076 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −7.54860e6 | −1.22422 | ||||||||
\(521\) | −1.70375e6 | −0.274986 | −0.137493 | − | 0.990503i | \(-0.543904\pi\) | ||||
−0.137493 | + | 0.990503i | \(0.543904\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.39690e6 | −0.702898 | −0.351449 | − | 0.936207i | \(-0.614311\pi\) | ||||
−0.351449 | + | 0.936207i | \(0.614311\pi\) | |||||||
\(524\) | −1.57154e7 | −2.50032 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.11081e7 | 1.75056 | ||||||||
\(527\) | −2.86231e6 | −0.448941 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.27858e6 | 1.13086 | ||||||||
\(530\) | 2.70834e7 | 4.18806 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 393571. | 0.0602898 | ||||||||
\(533\) | 711223. | 0.108440 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.24967e6 | 0.490856 | ||||||||
\(536\) | 6.03478e6 | 0.907298 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.06444e6 | 0.903306 | ||||||||
\(539\) | −518012. | −0.0768011 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.96004e6 | −0.434815 | −0.217407 | − | 0.976081i | \(-0.569760\pi\) | ||||
−0.217407 | + | 0.976081i | \(0.569760\pi\) | |||||||
\(542\) | −6.45593e6 | −0.943975 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.83580e6 | 0.990358 | ||||||||
\(545\) | 1.51719e7 | 2.18801 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.64363e6 | −0.520673 | −0.260337 | − | 0.965518i | \(-0.583834\pi\) | ||||
−0.260337 | + | 0.965518i | \(0.583834\pi\) | |||||||
\(548\) | −1.36467e7 | −1.94123 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.75321e7 | −2.47132 | ||||||||
\(551\) | 320970. | 0.0450386 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.34069e6 | −0.186430 | ||||||||
\(554\) | −1.55066e6 | −0.214655 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.27338e7 | −1.74691 | ||||||||
\(557\) | 5.39423e6 | 0.736701 | 0.368350 | − | 0.929687i | \(-0.379923\pi\) | ||||
0.368350 | + | 0.929687i | \(0.379923\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.50814e6 | −0.745548 | ||||||||
\(560\) | 4.81982e6 | 0.649473 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.16558e6 | 1.22411 | ||||||||
\(563\) | 8.18538e6 | 1.08835 | 0.544174 | − | 0.838973i | \(-0.316843\pi\) | ||||
0.544174 | + | 0.838973i | \(0.316843\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −959101. | −0.126399 | ||||||||
\(566\) | 6.29915e6 | 0.826496 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.02002e6 | 0.262715 | ||||||||
\(569\) | −1.23194e7 | −1.59518 | −0.797590 | − | 0.603201i | \(-0.793892\pi\) | ||||
−0.797590 | + | 0.603201i | \(0.793892\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.09533e7 | 1.40590 | 0.702948 | − | 0.711241i | \(-0.251866\pi\) | ||||
0.702948 | + | 0.711241i | \(0.251866\pi\) | |||||||
\(572\) | 1.37703e7 | 1.75975 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.17814e6 | 0.149251 | ||||||||
\(575\) | −1.74170e7 | −2.19686 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −803138. | −0.100427 | −0.0502135 | − | 0.998739i | \(-0.515990\pi\) | ||||
−0.0502135 | + | 0.998739i | \(0.515990\pi\) | |||||||
\(578\) | −4.98387e6 | −0.620508 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.01191e7 | −2.48335 | ||||||||
\(581\) | 1.59529e6 | 0.196064 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.47113e7 | −1.79258 | ||||||||
\(584\) | −1.01067e7 | −1.22624 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.79552e7 | −2.15996 | ||||||||
\(587\) | −6.51982e6 | −0.780980 | −0.390490 | − | 0.920607i | \(-0.627694\pi\) | ||||
−0.390490 | + | 0.920607i | \(0.627694\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −199224. | −0.0236621 | ||||||||
\(590\) | 2.71252e6 | 0.320806 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.01968e6 | 0.236852 | ||||||||
\(593\) | 2.02927e6 | 0.236975 | 0.118488 | − | 0.992956i | \(-0.462195\pi\) | ||||
0.118488 | + | 0.992956i | \(0.462195\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.09789e7 | 1.27135 | ||||||||
\(596\) | −2.38304e7 | −2.74800 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.32862e7 | 2.66285 | ||||||||
\(599\) | −667254. | −0.0759843 | −0.0379922 | − | 0.999278i | \(-0.512096\pi\) | ||||
−0.0379922 | + | 0.999278i | \(0.512096\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.42028e6 | −0.837981 | −0.418991 | − | 0.907991i | \(-0.637616\pi\) | ||||
−0.418991 | + | 0.907991i | \(0.637616\pi\) | |||||||
\(602\) | −9.12424e6 | −1.02614 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.02778e7 | −1.14632 | ||||||||
\(605\) | 1.60189e6 | 0.177927 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.14891e6 | −0.236727 | −0.118363 | − | 0.992970i | \(-0.537765\pi\) | ||||
−0.118363 | + | 0.992970i | \(0.537765\pi\) | |||||||
\(608\) | 475789. | 0.0521982 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.59611e7 | 2.82487 | ||||||||
\(611\) | −1.23328e7 | −1.33647 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.69964e7 | 1.82686 | 0.913429 | − | 0.406999i | \(-0.133425\pi\) | ||||
0.913429 | + | 0.406999i | \(0.133425\pi\) | |||||||
\(614\) | −1.19015e7 | −1.27404 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.79211e6 | 0.721196 | ||||||||
\(617\) | 3.94765e6 | 0.417470 | 0.208735 | − | 0.977972i | \(-0.433065\pi\) | ||||
0.208735 | + | 0.977972i | \(0.433065\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.73731e6 | −0.496942 | −0.248471 | − | 0.968639i | \(-0.579928\pi\) | ||||
−0.248471 | + | 0.968639i | \(0.579928\pi\) | |||||||
\(620\) | 1.24878e7 | 1.30468 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.65244e7 | 1.71257 | ||||||||
\(623\) | −1.09311e6 | −0.112835 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.34425e6 | −0.240051 | ||||||||
\(626\) | 2.16354e7 | 2.20663 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.72726e6 | 0.781855 | ||||||||
\(629\) | 4.60053e6 | 0.463640 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.34194e7 | −1.34172 | −0.670859 | − | 0.741585i | \(-0.734074\pi\) | ||||
−0.670859 | + | 0.741585i | \(0.734074\pi\) | |||||||
\(632\) | 1.19317e6 | 0.118825 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.54995e7 | 1.53142 | ||||||||
\(635\) | −2.35409e7 | −2.31680 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −873742. | −0.0853168 | ||||||||
\(638\) | 1.86027e7 | 1.80935 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.97073e7 | −1.90185 | ||||||||
\(641\) | −1.36524e7 | −1.31239 | −0.656196 | − | 0.754591i | \(-0.727835\pi\) | ||||
−0.656196 | + | 0.754591i | \(0.727835\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −918910. | −0.0876487 | −0.0438244 | − | 0.999039i | \(-0.513954\pi\) | ||||
−0.0438244 | + | 0.999039i | \(0.513954\pi\) | |||||||
\(644\) | 2.26606e7 | 2.15306 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 523498. | 0.0493553 | ||||||||
\(647\) | 1.68376e7 | 1.58132 | 0.790658 | − | 0.612258i | \(-0.209738\pi\) | ||||
0.790658 | + | 0.612258i | \(0.209738\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.47340e6 | −0.137312 | ||||||||
\(650\) | −2.95718e7 | −2.74533 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.12559e7 | 1.03696 | ||||||||
\(653\) | −7.85260e6 | −0.720661 | −0.360330 | − | 0.932825i | \(-0.617336\pi\) | ||||
−0.360330 | + | 0.932825i | \(0.617336\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.05129e7 | −2.77895 | ||||||||
\(656\) | 404151. | 0.0366677 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.04293e7 | −1.83946 | ||||||||
\(659\) | −1.37264e7 | −1.23124 | −0.615622 | − | 0.788042i | \(-0.711095\pi\) | ||||
−0.615622 | + | 0.788042i | \(0.711095\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.55788e7 | −1.38686 | −0.693428 | − | 0.720526i | \(-0.743901\pi\) | ||||
−0.693428 | + | 0.720526i | \(0.743901\pi\) | |||||||
\(662\) | −2.30782e7 | −2.04672 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.41975e6 | −0.124966 | ||||||||
\(665\) | 764156. | 0.0670082 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.84804e7 | 1.60841 | ||||||||
\(668\) | 1.69231e6 | 0.146737 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.93504e7 | 3.38659 | ||||||||
\(671\) | −1.41016e7 | −1.20910 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.65010e6 | 0.821285 | 0.410643 | − | 0.911796i | \(-0.365304\pi\) | ||||
0.410643 | + | 0.911796i | \(0.365304\pi\) | |||||||
\(674\) | 2.26308e7 | 1.91889 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.30727e6 | 0.530853 | ||||||||
\(677\) | −2.85548e6 | −0.239446 | −0.119723 | − | 0.992807i | \(-0.538201\pi\) | ||||
−0.119723 | + | 0.992807i | \(0.538201\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.84430e7 | 1.53517 | ||||||||
\(680\) | −9.77080e6 | −0.810322 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.15465e7 | −0.950585 | ||||||||
\(683\) | 4.39043e6 | 0.360127 | 0.180063 | − | 0.983655i | \(-0.442370\pi\) | ||||
0.180063 | + | 0.983655i | \(0.442370\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.64964e7 | −2.15755 | ||||||||
\(686\) | 1.84292e7 | 1.49519 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.12999e6 | −0.252099 | ||||||||
\(689\) | −2.48138e7 | −1.99134 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.79380e6 | −0.700618 | −0.350309 | − | 0.936634i | \(-0.613923\pi\) | ||||
−0.350309 | + | 0.936634i | \(0.613923\pi\) | |||||||
\(692\) | 2.27689e6 | 0.180749 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.49407e7 | −1.17753 | ||||||||
\(695\) | −2.47239e7 | −1.94158 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 920597. | 0.0717774 | ||||||||
\(698\) | −2.08666e7 | −1.62111 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.87773e7 | −2.21975 | ||||||||
\(701\) | −1.57360e7 | −1.20948 | −0.604742 | − | 0.796421i | \(-0.706724\pi\) | ||||
−0.604742 | + | 0.796421i | \(0.706724\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 320209. | 0.0244368 | ||||||||
\(704\) | 2.20807e7 | 1.67912 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.81427e7 | −2.88005 | ||||||||
\(707\) | −4.42654e6 | −0.333055 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.11378e7 | 1.57922 | 0.789611 | − | 0.613607i | \(-0.210282\pi\) | ||||
0.789611 | + | 0.613607i | \(0.210282\pi\) | |||||||
\(710\) | 1.31718e7 | 0.980615 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 972834. | 0.0719182 | ||||||||
\(713\) | −1.14707e7 | −0.845017 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.67363e7 | 1.95585 | ||||||||
\(716\) | 2.42343e6 | 0.176664 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.94095e6 | 0.647250 | ||||||||
\(719\) | 2.29229e7 | 1.65366 | 0.826831 | − | 0.562451i | \(-0.190141\pi\) | ||||
0.826831 | + | 0.562451i | \(0.190141\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.26340e7 | −1.62152 | ||||||||
\(722\) | −2.17713e7 | −1.55433 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.04332e7 | −0.739727 | ||||||||
\(725\) | −2.34688e7 | −1.65824 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.81555e6 | 0.478261 | 0.239130 | − | 0.970987i | \(-0.423138\pi\) | ||||
0.239130 | + | 0.970987i | \(0.423138\pi\) | |||||||
\(728\) | 1.14564e7 | 0.801161 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.59016e7 | −4.57709 | ||||||||
\(731\) | −7.12966e6 | −0.493487 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.68755e7 | 1.16011 | 0.580053 | − | 0.814578i | \(-0.303032\pi\) | ||||
0.580053 | + | 0.814578i | \(0.303032\pi\) | |||||||
\(734\) | −1.95017e7 | −1.33608 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.73945e7 | 1.86410 | ||||||||
\(737\) | −2.13745e7 | −1.44953 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.09722e6 | 0.410696 | 0.205348 | − | 0.978689i | \(-0.434167\pi\) | ||||
0.205348 | + | 0.978689i | \(0.434167\pi\) | |||||||
\(740\) | −2.00714e7 | −1.34740 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.11041e7 | −2.74079 | ||||||||
\(743\) | −5.82391e6 | −0.387028 | −0.193514 | − | 0.981097i | \(-0.561989\pi\) | ||||
−0.193514 | + | 0.981097i | \(0.561989\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.62691e7 | −3.05422 | ||||||||
\(746\) | −1.77767e7 | −1.16951 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.78240e7 | 1.16480 | ||||||||
\(749\) | −4.93198e6 | −0.321230 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.45028e7 | −0.938321 | −0.469160 | − | 0.883113i | \(-0.655443\pi\) | ||||
−0.469160 | + | 0.883113i | \(0.655443\pi\) | |||||||
\(752\) | −7.00810e6 | −0.451914 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.13775e7 | 2.00997 | ||||||||
\(755\) | −1.99553e7 | −1.27406 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.63506e7 | 1.67128 | 0.835642 | − | 0.549274i | \(-0.185096\pi\) | ||||
0.835642 | + | 0.549274i | \(0.185096\pi\) | |||||||
\(758\) | 4.19376e7 | 2.65113 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −680072. | −0.0427092 | ||||||||
\(761\) | 8.31384e6 | 0.520403 | 0.260202 | − | 0.965554i | \(-0.416211\pi\) | ||||
0.260202 | + | 0.965554i | \(0.416211\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.30262e7 | −1.43189 | ||||||||
\(764\) | −1.74536e7 | −1.08181 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.82517e6 | −0.543439 | ||||||||
\(767\) | −2.48521e6 | −0.152537 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.06046e7 | 0.646666 | 0.323333 | − | 0.946285i | \(-0.395197\pi\) | ||||
0.323333 | + | 0.946285i | \(0.395197\pi\) | |||||||
\(770\) | 4.42887e7 | 2.69194 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.06202e7 | −1.84912 | ||||||||
\(773\) | 2.65938e7 | 1.60078 | 0.800390 | − | 0.599479i | \(-0.204626\pi\) | ||||
0.800390 | + | 0.599479i | \(0.204626\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.45669e7 | 0.871192 | ||||||||
\(776\) | −1.64136e7 | −0.978474 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.48167e7 | 2.65455 | ||||||||
\(779\) | 64075.9 | 0.00378313 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.15470e6 | −0.419724 | ||||||||
\(782\) | 3.01414e7 | 1.76257 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −496502. | −0.0288490 | ||||||||
\(785\) | 1.50032e7 | 0.868981 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.05442e7 | −1.75789 | −0.878945 | − | 0.476923i | \(-0.841752\pi\) | ||||
−0.878945 | + | 0.476923i | \(0.841752\pi\) | |||||||
\(788\) | 2.36037e7 | 1.35414 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7.78018e6 | 0.443529 | ||||||||
\(791\) | 1.45562e6 | 0.0827190 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.37855e7 | −1.34317 | ||||||||
\(794\) | −3.66536e7 | −2.06331 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.99483e7 | 1.11590 | ||||||||
\(797\) | 2.58869e7 | 1.44356 | 0.721779 | − | 0.692123i | \(-0.243325\pi\) | ||||
0.721779 | + | 0.692123i | \(0.243325\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.59634e7 | −0.884625 | ||||||||
\(800\) | −3.47890e7 | −1.92184 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −5.39643e7 | −2.96258 | ||||||||
\(803\) | 3.57967e7 | 1.95909 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.39977e7 | 2.39299 | ||||||||
\(806\) | −1.94758e7 | −1.05599 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.93947e6 | 0.212280 | ||||||||
\(809\) | −6.74823e6 | −0.362509 | −0.181254 | − | 0.983436i | \(-0.558016\pi\) | ||||
−0.181254 | + | 0.983436i | \(0.558016\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.22287e7 | −1.18676 | −0.593378 | − | 0.804924i | \(-0.702206\pi\) | ||||
−0.593378 | + | 0.804924i | \(0.702206\pi\) | |||||||
\(812\) | 3.05345e7 | 1.62517 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.85585e7 | 0.981709 | ||||||||
\(815\) | 2.18545e7 | 1.15251 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −496243. | −0.0260099 | ||||||||
\(818\) | −1.22661e7 | −0.640947 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.01641e6 | −0.208595 | ||||||||
\(821\) | 1.57133e7 | 0.813599 | 0.406799 | − | 0.913517i | \(-0.366645\pi\) | ||||
0.406799 | + | 0.913517i | \(0.366645\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.22414e7 | −1.14462 | −0.572311 | − | 0.820036i | \(-0.693953\pi\) | ||||
−0.572311 | + | 0.820036i | \(0.693953\pi\) | |||||||
\(824\) | 2.01435e7 | 1.03351 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.11676e6 | −0.209945 | ||||||||
\(827\) | −1.20770e7 | −0.614038 | −0.307019 | − | 0.951703i | \(-0.599332\pi\) | ||||
−0.307019 | + | 0.951703i | \(0.599332\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.91099e6 | −0.0965765 | −0.0482882 | − | 0.998833i | \(-0.515377\pi\) | ||||
−0.0482882 | + | 0.998833i | \(0.515377\pi\) | |||||||
\(830\) | −9.25762e6 | −0.466449 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.72440e7 | 1.86530 | ||||||||
\(833\) | −1.13096e6 | −0.0564722 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.28579e6 | 0.163088 | ||||||||
\(836\) | 1.24060e6 | 0.0613925 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.31532e7 | 2.12277 | ||||||||
\(839\) | −3.50301e7 | −1.71805 | −0.859025 | − | 0.511933i | \(-0.828930\pi\) | ||||
−0.859025 | + | 0.511933i | \(0.828930\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.39070e6 | 0.214064 | ||||||||
\(842\) | −1.29923e7 | −0.631547 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.62601e7 | 1.75216 | ||||||||
\(845\) | 1.22462e7 | 0.590009 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.43116e6 | −0.116441 | ||||||||
\(848\) | −1.41004e7 | −0.673352 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.82774e7 | −1.81717 | ||||||||
\(851\) | 1.84366e7 | 0.872685 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.10044e7 | −0.988412 | −0.494206 | − | 0.869345i | \(-0.664541\pi\) | ||||
−0.494206 | + | 0.869345i | \(0.664541\pi\) | |||||||
\(854\) | −3.94008e7 | −1.84867 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.38929e6 | 0.204743 | ||||||||
\(857\) | −2.13586e7 | −0.993390 | −0.496695 | − | 0.867925i | \(-0.665453\pi\) | ||||
−0.496695 | + | 0.867925i | \(0.665453\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.37853e7 | 1.09983 | 0.549915 | − | 0.835221i | \(-0.314660\pi\) | ||||
0.549915 | + | 0.835221i | \(0.314660\pi\) | |||||||
\(860\) | 3.11055e7 | 1.43414 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.71188e7 | 2.61825 | ||||||||
\(863\) | 345138. | 0.0157749 | 0.00788744 | − | 0.999969i | \(-0.497489\pi\) | ||||
0.00788744 | + | 0.999969i | \(0.497489\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.42080e6 | 0.200891 | ||||||||
\(866\) | 5.16310e7 | 2.33946 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.89525e7 | −0.853823 | ||||||||
\(869\) | −4.22607e6 | −0.189840 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.60529e7 | −1.61026 | ||||||||
\(872\) | 2.04925e7 | 0.912649 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.09792e6 | 0.0928988 | ||||||||
\(875\) | −1.87475e7 | −0.827794 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.10330e7 | −0.923425 | −0.461712 | − | 0.887030i | \(-0.652765\pi\) | ||||
−0.461712 | + | 0.887030i | \(0.652765\pi\) | |||||||
\(878\) | −3.90001e7 | −1.70738 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.51928e7 | 0.661352 | ||||||||
\(881\) | 3.40176e7 | 1.47660 | 0.738302 | − | 0.674470i | \(-0.235628\pi\) | ||||
0.738302 | + | 0.674470i | \(0.235628\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.95646e6 | 0.429737 | 0.214869 | − | 0.976643i | \(-0.431068\pi\) | ||||
0.214869 | + | 0.976643i | \(0.431068\pi\) | |||||||
\(884\) | 3.00642e7 | 1.29395 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.61352e7 | 2.83040 | ||||||||
\(887\) | 1.73362e7 | 0.739850 | 0.369925 | − | 0.929062i | \(-0.379383\pi\) | ||||
0.369925 | + | 0.929062i | \(0.379383\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.57277e7 | 1.51618 | ||||||||
\(890\) | 6.34346e6 | 0.268443 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6.57245e7 | −2.76576 | ||||||||
\(893\) | −1.11110e6 | −0.0466254 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.70533e6 | 0.196351 | ||||||||
\(896\) | 2.99095e7 | 1.24463 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.71954e7 | −0.711577 | ||||||||
\(899\) | −1.54564e7 | −0.637836 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.21187e7 | −1.31809 | ||||||||
\(902\) | 3.71369e6 | 0.151981 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.29545e6 | −0.0527228 | ||||||||
\(905\) | −2.02571e7 | −0.822158 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.69488e6 | 0.310587 | 0.155294 | − | 0.987868i | \(-0.450368\pi\) | ||||
0.155294 | + | 0.987868i | \(0.450368\pi\) | |||||||
\(908\) | 1.92137e7 | 0.773384 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 7.47027e7 | 2.99042 | ||||||||
\(911\) | 1.61662e7 | 0.645376 | 0.322688 | − | 0.946505i | \(-0.395413\pi\) | ||||
0.322688 | + | 0.946505i | \(0.395413\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.02859e6 | 0.199650 | ||||||||
\(914\) | −5.23621e7 | −2.07325 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.45730e7 | −2.54280 | ||||||||
\(917\) | 4.63091e7 | 1.81862 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.62199e7 | −1.41468 | −0.707341 | − | 0.706873i | \(-0.750105\pi\) | ||||
−0.707341 | + | 0.706873i | \(0.750105\pi\) | |||||||
\(920\) | −3.91564e7 | −1.52522 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5.74780e7 | −2.22677 | ||||||||
\(923\) | −1.20680e7 | −0.466263 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.34132e7 | −0.899717 | ||||||||
\(926\) | −1.06590e7 | −0.408496 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.69132e7 | 1.40706 | ||||||||
\(929\) | 2.11322e6 | 0.0803350 | 0.0401675 | − | 0.999193i | \(-0.487211\pi\) | ||||
0.0401675 | + | 0.999193i | \(0.487211\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −78717.6 | −0.00297644 | ||||||||
\(932\) | −3.06747e7 | −1.15675 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.46625e7 | 1.30015 | ||||||||
\(935\) | 3.46071e7 | 1.29460 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.46913e6 | −0.0546652 | −0.0273326 | − | 0.999626i | \(-0.508701\pi\) | ||||
−0.0273326 | + | 0.999626i | \(0.508701\pi\) | |||||||
\(938\) | −5.97217e7 | −2.21628 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.96458e7 | 2.57084 | ||||||||
\(941\) | 3.58757e7 | 1.32077 | 0.660384 | − | 0.750928i | \(-0.270393\pi\) | ||||
0.660384 | + | 0.750928i | \(0.270393\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.68929e6 | 0.135103 | ||||||||
\(944\) | −1.41222e6 | −0.0515788 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.87611e7 | −1.04491 | ||||||||
\(947\) | 2.42642e7 | 0.879208 | 0.439604 | − | 0.898192i | \(-0.355119\pi\) | ||||
0.439604 | + | 0.898192i | \(0.355119\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.03792e7 | 2.17631 | ||||||||
\(950\) | −2.66420e6 | −0.0957764 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.48290e7 | 0.530298 | ||||||||
\(953\) | 3.58333e7 | 1.27807 | 0.639036 | − | 0.769177i | \(-0.279334\pi\) | ||||
0.639036 | + | 0.769177i | \(0.279334\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.38879e7 | −1.20237 | ||||||||
\(956\) | 3.46475e7 | 1.22611 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.13695e6 | 0.0752281 | ||||||||
\(959\) | 4.02132e7 | 1.41196 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.90355e7 | −0.664898 | ||||||||
\(962\) | 3.13031e7 | 1.09056 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.14418e7 | 0.743138 | ||||||||
\(965\) | −5.94520e7 | −2.05517 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.27974e7 | −1.12791 | −0.563953 | − | 0.825807i | \(-0.690720\pi\) | ||||
−0.563953 | + | 0.825807i | \(0.690720\pi\) | |||||||
\(968\) | 2.16365e6 | 0.0742161 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.07027e8 | −3.65226 | ||||||||
\(971\) | −5.64198e7 | −1.92036 | −0.960182 | − | 0.279376i | \(-0.909872\pi\) | ||||
−0.960182 | + | 0.279376i | \(0.909872\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.75232e7 | 1.27063 | ||||||||
\(974\) | −2.27050e7 | −0.766874 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.35161e7 | −0.454178 | ||||||||
\(977\) | 3.59696e7 | 1.20559 | 0.602794 | − | 0.797897i | \(-0.294054\pi\) | ||||
0.602794 | + | 0.797897i | \(0.294054\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.44567e6 | −0.114899 | ||||||||
\(980\) | 4.93419e6 | 0.164116 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.53126e6 | 0.0837642 | ||||||||
\(983\) | 119682. | 0.00395044 | 0.00197522 | − | 0.999998i | \(-0.499371\pi\) | ||||
0.00197522 | + | 0.999998i | \(0.499371\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.58288e7 | 1.50504 | ||||||||
\(986\) | 4.06146e7 | 1.33042 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.09254e6 | 0.0681997 | ||||||||
\(989\) | −2.85721e7 | −0.928863 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.51751e6 | −0.243159 | −0.121579 | − | 0.992582i | \(-0.538796\pi\) | ||||
−0.121579 | + | 0.992582i | \(0.538796\pi\) | |||||||
\(992\) | −2.29118e7 | −0.739230 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.99906e7 | −0.641742 | ||||||||
\(995\) | 3.87316e7 | 1.24025 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.03530e7 | 0.967084 | 0.483542 | − | 0.875321i | \(-0.339350\pi\) | ||||
0.483542 | + | 0.875321i | \(0.339350\pi\) | |||||||
\(998\) | 3.98133e7 | 1.26532 | ||||||||
\(999\) | 0 | 0 |
(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 | 531.6.a.d.1.10 | 12 | ||
3.2 | odd | 2 | 177.6.a.b.1.3 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.6.a.b.1.3 | ✓ | 12 | 3.2 | odd | 2 | ||
531.6.a.d.1.10 | 12 | 1.1 | even | 1 | trivial |