Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,6,Mod(1,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, 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("588.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.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: | \(94.3056860500\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 699x^{2} - 686x + 59664 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{2}\cdot 7 \) |
Twist minimal: | no (minimal twist has level 84) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(26.2941\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 588.1 |
$q$-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 | ||||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −31.9616 | −0.571746 | −0.285873 | − | 0.958267i | \(-0.592284\pi\) | ||||
−0.285873 | + | 0.958267i | \(0.592284\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 260.884 | 0.650077 | 0.325039 | − | 0.945701i | \(-0.394623\pi\) | ||||
0.325039 | + | 0.945701i | \(0.394623\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 769.735 | 1.26323 | 0.631616 | − | 0.775281i | \(-0.282392\pi\) | ||||
0.631616 | + | 0.775281i | \(0.282392\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 287.654 | 0.330098 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1553.32 | −1.30358 | −0.651791 | − | 0.758399i | \(-0.725982\pi\) | ||||
−0.651791 | + | 0.758399i | \(0.725982\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 750.049 | 0.476656 | 0.238328 | − | 0.971185i | \(-0.423401\pi\) | ||||
0.238328 | + | 0.971185i | \(0.423401\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 754.854 | 0.297539 | 0.148769 | − | 0.988872i | \(-0.452469\pi\) | ||||
0.148769 | + | 0.988872i | \(0.452469\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2103.46 | −0.673106 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6008.93 | 1.32679 | 0.663395 | − | 0.748269i | \(-0.269115\pi\) | ||||
0.663395 | + | 0.748269i | \(0.269115\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6420.04 | −1.19987 | −0.599934 | − | 0.800049i | \(-0.704807\pi\) | ||||
−0.599934 | + | 0.800049i | \(0.704807\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2347.95 | −0.375322 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4775.73 | −0.573502 | −0.286751 | − | 0.958005i | \(-0.592575\pi\) | ||||
−0.286751 | + | 0.958005i | \(0.592575\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6927.62 | −0.729327 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5423.27 | −0.503850 | −0.251925 | − | 0.967747i | \(-0.581064\pi\) | ||||
−0.251925 | + | 0.967747i | \(0.581064\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11896.4 | −0.981171 | −0.490585 | − | 0.871393i | \(-0.663217\pi\) | ||||
−0.490585 | + | 0.871393i | \(0.663217\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2588.89 | −0.190582 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −17428.0 | −1.15081 | −0.575404 | − | 0.817869i | \(-0.695155\pi\) | ||||
−0.575404 | + | 0.817869i | \(0.695155\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 13979.9 | 0.752623 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 37650.6 | 1.84112 | 0.920561 | − | 0.390599i | \(-0.127732\pi\) | ||||
0.920561 | + | 0.390599i | \(0.127732\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8338.26 | −0.371679 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6750.44 | −0.275198 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 22078.1 | 0.825717 | 0.412859 | − | 0.910795i | \(-0.364530\pi\) | ||||
0.412859 | + | 0.910795i | \(0.364530\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8173.38 | −0.281240 | −0.140620 | − | 0.990064i | \(-0.544910\pi\) | ||||
−0.140620 | + | 0.990064i | \(0.544910\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −24602.0 | −0.722248 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13001.7 | 0.353846 | 0.176923 | − | 0.984225i | \(-0.443386\pi\) | ||||
0.176923 | + | 0.984225i | \(0.443386\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6793.69 | −0.171784 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12349.6 | −0.290742 | −0.145371 | − | 0.989377i | \(-0.546438\pi\) | ||||
−0.145371 | + | 0.989377i | \(0.546438\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 43600.3 | 0.957596 | 0.478798 | − | 0.877925i | \(-0.341073\pi\) | ||||
0.478798 | + | 0.877925i | \(0.341073\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 18931.1 | 0.388618 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 76749.5 | 1.38359 | 0.691796 | − | 0.722093i | \(-0.256820\pi\) | ||||
0.691796 | + | 0.722093i | \(0.256820\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 21893.6 | 0.348836 | 0.174418 | − | 0.984672i | \(-0.444196\pi\) | ||||
0.174418 | + | 0.984672i | \(0.444196\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 49646.5 | 0.745318 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −54080.4 | −0.766023 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −136967. | −1.83291 | −0.916454 | − | 0.400139i | \(-0.868962\pi\) | ||||
−0.916454 | + | 0.400139i | \(0.868962\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 57780.4 | 0.692744 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −23972.8 | −0.272527 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −93050.1 | −1.00412 | −0.502062 | − | 0.864832i | \(-0.667425\pi\) | ||||
−0.502062 | + | 0.864832i | \(0.667425\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 21131.6 | 0.216692 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 122302. | 1.19297 | 0.596484 | − | 0.802625i | \(-0.296564\pi\) | ||||
0.596484 | + | 0.802625i | \(0.296564\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 74801.3 | 0.694730 | 0.347365 | − | 0.937730i | \(-0.387076\pi\) | ||||
0.347365 | + | 0.937730i | \(0.387076\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 70772.4 | 0.597592 | 0.298796 | − | 0.954317i | \(-0.403415\pi\) | ||||
0.298796 | + | 0.954317i | \(0.403415\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −142262. | −1.14689 | −0.573446 | − | 0.819243i | \(-0.694394\pi\) | ||||
−0.573446 | + | 0.819243i | \(0.694394\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 42981.5 | 0.331112 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 198899. | 1.46533 | 0.732667 | − | 0.680588i | \(-0.238275\pi\) | ||||
0.732667 | + | 0.680588i | \(0.238275\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −24126.3 | −0.170117 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 62348.6 | 0.421077 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −92990.7 | −0.577399 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 48809.4 | 0.290898 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 167110. | 0.956592 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 219619. | 1.20826 | 0.604131 | − | 0.796885i | \(-0.293521\pi\) | ||||
0.604131 | + | 0.796885i | \(0.293521\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 107068. | 0.566479 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 54622.1 | 0.278093 | 0.139047 | − | 0.990286i | \(-0.455596\pi\) | ||||
0.139047 | + | 0.990286i | \(0.455596\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 23300.0 | 0.110033 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 72942.8 | 0.332033 | 0.166017 | − | 0.986123i | \(-0.446909\pi\) | ||||
0.166017 | + | 0.986123i | \(0.446909\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −110668. | −0.485831 | −0.242915 | − | 0.970047i | \(-0.578104\pi\) | ||||
−0.242915 | + | 0.970047i | \(0.578104\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 156852. | 0.664419 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 200811. | 0.821199 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −192055. | −0.758587 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 327025. | 1.20675 | 0.603373 | − | 0.797459i | \(-0.293823\pi\) | ||||
0.603373 | + | 0.797459i | \(0.293823\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 174490. | 0.622771 | 0.311386 | − | 0.950284i | \(-0.399207\pi\) | ||||
0.311386 | + | 0.950284i | \(0.399207\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −125819. | −0.434527 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 205195. | 0.686020 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 440292. | 1.42558 | 0.712790 | − | 0.701377i | \(-0.247431\pi\) | ||||
0.712790 | + | 0.701377i | \(0.247431\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −338856. | −1.06297 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 56491.9 | 0.166540 | 0.0832698 | − | 0.996527i | \(-0.473464\pi\) | ||||
0.0832698 | + | 0.996527i | \(0.473464\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 75044.3 | 0.214589 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −688014. | −1.90900 | −0.954501 | − | 0.298209i | \(-0.903611\pi\) | ||||
−0.954501 | + | 0.298209i | \(0.903611\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 221200. | 0.595755 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 60754.0 | 0.158885 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 282558. | 0.717782 | 0.358891 | − | 0.933379i | \(-0.383155\pi\) | ||||
0.358891 | + | 0.933379i | \(0.383155\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −198703. | −0.476728 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 151782. | 0.354069 | 0.177034 | − | 0.984205i | \(-0.443350\pi\) | ||||
0.177034 | + | 0.984205i | \(0.443350\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −322258. | −0.731151 | −0.365575 | − | 0.930782i | \(-0.619128\pi\) | ||||
−0.365575 | + | 0.930782i | \(0.619128\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 73560.4 | 0.162374 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 152640. | 0.327898 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −405235. | −0.847429 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 538521. | 1.06812 | 0.534059 | − | 0.845447i | \(-0.320666\pi\) | ||||
0.534059 | + | 0.845447i | \(0.320666\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 303440. | 0.586380 | 0.293190 | − | 0.956054i | \(-0.405283\pi\) | ||||
0.293190 | + | 0.956054i | \(0.405283\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 221418. | 0.416990 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 656475. | 1.20518 | 0.602591 | − | 0.798050i | \(-0.294135\pi\) | ||||
0.602591 | + | 0.798050i | \(0.294135\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 842204. | 1.50759 | 0.753797 | − | 0.657107i | \(-0.228220\pi\) | ||||
0.753797 | + | 0.657107i | \(0.228220\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −117016. | −0.204293 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 173336. | 0.288074 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 61143.2 | 0.0991796 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 195675. | 0.309864 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.01133e6 | 1.56382 | 0.781908 | − | 0.623394i | \(-0.214247\pi\) | ||||
0.781908 | + | 0.623394i | \(0.214247\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 111147. | 0.167860 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 380228. | 0.560981 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −392403. | −0.552869 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.19564e6 | −1.64673 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 957124. | 1.28886 | 0.644431 | − | 0.764663i | \(-0.277094\pi\) | ||||
0.644431 | + | 0.764663i | \(0.277094\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −170380. | −0.224369 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 471480. | 0.607293 | 0.303647 | − | 0.952785i | \(-0.401796\pi\) | ||||
0.303647 | + | 0.952785i | \(0.401796\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −268196. | −0.337959 | −0.168980 | − | 0.985620i | \(-0.554047\pi\) | ||||
−0.168980 | + | 0.985620i | \(0.554047\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.54722e6 | 1.86708 | 0.933538 | − | 0.358478i | \(-0.116704\pi\) | ||||
0.933538 | + | 0.358478i | \(0.116704\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 557027. | 0.657970 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −690745. | −0.798817 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −937542. | −1.06169 | −0.530843 | − | 0.847470i | \(-0.678125\pi\) | ||||
−0.530843 | + | 0.847470i | \(0.678125\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.28486e6 | −1.42499 | −0.712497 | − | 0.701675i | \(-0.752436\pi\) | ||||
−0.712497 | + | 0.701675i | \(0.752436\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 577339. | 0.602128 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −197042. | −0.201401 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 709769. | 0.711103 | 0.355552 | − | 0.934657i | \(-0.384293\pi\) | ||||
0.355552 | + | 0.934657i | \(0.384293\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 196929. | 0.193423 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −446819. | −0.430309 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.82016e6 | −1.71900 | −0.859502 | − | 0.511132i | \(-0.829226\pi\) | ||||
−0.859502 | + | 0.511132i | \(0.829226\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 486723. | 0.442263 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 359187. | 0.320208 | 0.160104 | − | 0.987100i | \(-0.448817\pi\) | ||||
0.160104 | + | 0.987100i | \(0.448817\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.20337e6 | −1.05265 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.23270e6 | 1.05823 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.15767e6 | 0.975446 | 0.487723 | − | 0.872998i | \(-0.337828\pi\) | ||||
0.487723 | + | 0.872998i | \(0.337828\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −780175. | −0.645311 | −0.322655 | − | 0.946516i | \(-0.604576\pi\) | ||||
−0.322655 | + | 0.946516i | \(0.604576\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −548757. | −0.437571 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −326331. | −0.255540 | −0.127770 | − | 0.991804i | \(-0.540782\pi\) | ||||
−0.127770 | + | 0.991804i | \(0.540782\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −520023. | −0.399956 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 364094. | 0.275073 | 0.137536 | − | 0.990497i | \(-0.456082\pi\) | ||||
0.137536 | + | 0.990497i | \(0.456082\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −64019.2 | −0.0475165 | −0.0237582 | − | 0.999718i | \(-0.507563\pi\) | ||||
−0.0237582 | + | 0.999718i | \(0.507563\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 215755. | 0.157343 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 992939. | 0.699324 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 837451. | 0.579731 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 398020. | 0.270855 | 0.135427 | − | 0.990787i | \(-0.456759\pi\) | ||||
0.135427 | + | 0.990787i | \(0.456759\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −705651. | −0.472101 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −190184. | −0.125107 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 581038. | 0.375860 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.10071e6 | −0.688760 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 261234. | 0.160798 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −638841. | −0.386854 | −0.193427 | − | 0.981115i | \(-0.561960\pi\) | ||||
−0.193427 | + | 0.981115i | \(0.561960\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −673212. | −0.401103 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.48188e6 | 1.45506 | 0.727529 | − | 0.686077i | \(-0.240669\pi\) | ||||
0.727529 | + | 0.686077i | \(0.240669\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.47653e6 | 0.851889 | 0.425944 | − | 0.904749i | \(-0.359942\pi\) | ||||
0.425944 | + | 0.904749i | \(0.359942\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.23126e6 | −1.24710 | −0.623551 | − | 0.781783i | \(-0.714310\pi\) | ||||
−0.623551 | + | 0.781783i | \(0.714310\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.56763e6 | 0.862516 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −636952. | −0.345020 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.16506e6 | −0.621360 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.61910e6 | −0.850289 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.28036e6 | 0.662159 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.41122e6 | −1.20967 | −0.604836 | − | 0.796350i | \(-0.706761\pi\) | ||||
−0.604836 | + | 0.796350i | \(0.706761\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −386834. | −0.191167 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −415556. | −0.202310 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.79586e6 | −0.861388 | −0.430694 | − | 0.902498i | \(-0.641731\pi\) | ||||
−0.430694 | + | 0.902498i | \(0.641731\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.79009e6 | −0.846011 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.67488e6 | −0.780007 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 217137. | 0.0982169 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.20731e6 | 0.984103 | 0.492051 | − | 0.870566i | \(-0.336247\pi\) | ||||
0.492051 | + | 0.870566i | \(0.336247\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 148188. | 0.0651252 | 0.0325626 | − | 0.999470i | \(-0.489633\pi\) | ||||
0.0325626 | + | 0.999470i | \(0.489633\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −561137. | −0.243109 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.97040e6 | 0.841623 | 0.420811 | − | 0.907148i | \(-0.361745\pi\) | ||||
0.420811 | + | 0.907148i | \(0.361745\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 394714. | 0.166231 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.43395e6 | 0.996723 | 0.498362 | − | 0.866969i | \(-0.333935\pi\) | ||||
0.498362 | + | 0.866969i | \(0.333935\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.91353e6 | −0.772799 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 836917. | 0.333362 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.39354e6 | −0.547502 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.30348e6 | −1.66784 | −0.833920 | − | 0.551886i | \(-0.813908\pi\) | ||||
−0.833920 | + | 0.551886i | \(0.813908\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −439285. | −0.167950 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.20305e6 | −0.447726 | −0.223863 | − | 0.974621i | \(-0.571867\pi\) | ||||
−0.223863 | + | 0.974621i | \(0.571867\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.50399e6 | −0.552289 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.62529e6 | 1.67604 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.11488e6 | 1.82910 | 0.914550 | − | 0.404473i | \(-0.132545\pi\) | ||||
0.914550 | + | 0.404473i | \(0.132545\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.97657e6 | −0.697590 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.01055e6 | 1.74537 | 0.872687 | − | 0.488280i | \(-0.162375\pi\) | ||||
0.872687 | + | 0.488280i | \(0.162375\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −963609. | −0.327057 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.08326e6 | −1.36815 | −0.684073 | − | 0.729413i | \(-0.739793\pi\) | ||||
−0.684073 | + | 0.729413i | \(0.739793\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.17253e6 | −0.387866 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −491599. | −0.160557 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.45304e6 | −0.791063 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.07300e6 | −0.341682 | −0.170841 | − | 0.985299i | \(-0.554648\pi\) | ||||
−0.170841 | + | 0.985299i | \(0.554648\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.89948e6 | −0.589894 | −0.294947 | − | 0.955514i | \(-0.595302\pi\) | ||||
−0.294947 | + | 0.955514i | \(0.595302\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.94173e6 | −1.51571 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −209700. | −0.0635274 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.24591e6 | −0.372821 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.93577e6 | 0.572198 | 0.286099 | − | 0.958200i | \(-0.407641\pi\) | ||||
0.286099 | + | 0.958200i | \(0.407641\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −656486. | −0.191699 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −699754. | −0.199446 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 996012. | 0.280495 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.93448e6 | 1.09484 | 0.547422 | − | 0.836856i | \(-0.315609\pi\) | ||||
0.547422 | + | 0.836856i | \(0.315609\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.16927e6 | −1.42142 | −0.710712 | − | 0.703483i | \(-0.751627\pi\) | ||||
−0.710712 | + | 0.703483i | \(0.751627\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.41167e6 | −0.383603 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.26734e6 | 0.877448 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.80730e6 | −0.474119 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.12951e6 | −0.552187 | −0.276093 | − | 0.961131i | \(-0.589040\pi\) | ||||
−0.276093 | + | 0.961131i | \(0.589040\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.20879e6 | 0.822473 | 0.411237 | − | 0.911529i | \(-0.365097\pi\) | ||||
0.411237 | + | 0.911529i | \(0.365097\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.72849e6 | 0.437971 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 566177. | 0.141824 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.99077e6 | 1.73126 | 0.865632 | − | 0.500680i | \(-0.166917\pi\) | ||||
0.865632 | + | 0.500680i | \(0.166917\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.46008e6 | 1.80607 | 0.903034 | − | 0.429568i | \(-0.141334\pi\) | ||||
0.903034 | + | 0.429568i | \(0.141334\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.37768e6 | 1.04796 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.94323e6 | −0.696715 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.61620e6 | −1.31470 | −0.657350 | − | 0.753586i | \(-0.728323\pi\) | ||||
−0.657350 | + | 0.753586i | \(0.728323\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.41484e6 | −0.327542 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.57041e6 | −0.359557 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.81271e6 | −1.97387 | −0.986936 | − | 0.161111i | \(-0.948492\pi\) | ||||
−0.986936 | + | 0.161111i | \(0.948492\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.13237e6 | 0.250874 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.24339e6 | 0.710798 | 0.355399 | − | 0.934715i | \(-0.384345\pi\) | ||||
0.355399 | + | 0.934715i | \(0.384345\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.70039e6 | −1.23581 | −0.617906 | − | 0.786252i | \(-0.712019\pi\) | ||||
−0.617906 | + | 0.786252i | \(0.712019\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.84675e6 | −0.396074 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.18014e6 | 0.462585 | 0.231292 | − | 0.972884i | \(-0.425705\pi\) | ||||
0.231292 | + | 0.972884i | \(0.425705\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.96263e6 | −0.823059 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.10358e6 | −0.637837 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.57770e6 | −0.320840 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.04970e6 | 0.613707 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.93616e6 | 0.783852 | 0.391926 | − | 0.919997i | \(-0.371809\pi\) | ||||
0.391926 | + | 0.919997i | \(0.371809\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.67605e6 | −0.724466 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.97403e6 | 0.574104 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.00176e6 | 1.33778 | 0.668890 | − | 0.743361i | \(-0.266770\pi\) | ||||
0.668890 | + | 0.743361i | \(0.266770\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −508428. | −0.0961517 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.37114e6 | −1.75424 | −0.877119 | − | 0.480273i | \(-0.840537\pi\) | ||||
−0.877119 | + | 0.480273i | \(0.840537\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.33378e6 | −1.72958 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −675399. | −0.123893 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.75932e6 | −1.75456 | −0.877280 | − | 0.479978i | \(-0.840645\pi\) | ||||
−0.877280 | + | 0.479978i | \(0.840645\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.19213e6 | 1.10216 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.69667e6 | −0.299004 | −0.149502 | − | 0.988761i | \(-0.547767\pi\) | ||||
−0.149502 | + | 0.988761i | \(0.547767\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.90895e6 | −0.682075 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.99080e6 | −0.343959 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.73566e6 | −0.639106 | −0.319553 | − | 0.947568i | \(-0.603533\pi\) | ||||
−0.319553 | + | 0.947568i | \(0.603533\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −546786. | −0.0917326 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.39077e6 | −0.397209 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.54668e6 | −0.748114 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.54302e6 | −0.414412 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.32718e6 | 1.18261 | 0.591306 | − | 0.806447i | \(-0.298612\pi\) | ||||
0.591306 | + | 0.806447i | \(0.298612\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9591.43 | −0.00153331 | −0.000766653 | − | 1.00000i | \(-0.500244\pi\) | ||||
−0.000766653 | 1.00000i | \(0.500244\pi\) | ||||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.97236e6 | 1.56413 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.86654e6 | −0.911471 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.78832e6 | 0.275239 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.17448e6 | −0.636479 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.26200e6 | −0.341671 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.36604e6 | −0.204422 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.75692e6 | −0.551872 | −0.275936 | − | 0.961176i | \(-0.588988\pi\) | ||||
−0.275936 | + | 0.961176i | \(0.588988\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.90032e6 | 0.422130 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.54692e6 | 0.655731 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.03391e7 | 1.47746 | 0.738729 | − | 0.674002i | \(-0.235426\pi\) | ||||
0.738729 | + | 0.674002i | \(0.235426\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −662044. | −0.0937467 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.50699e6 | 0.632423 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.37376e6 | −0.189312 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.00476e7 | −1.37222 | −0.686108 | − | 0.727500i | \(-0.740682\pi\) | ||||
−0.686108 | + | 0.727500i | \(0.740682\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.15708e6 | −1.23945 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.64712e6 | 0.489263 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.49380e6 | −1.12936 | −0.564678 | − | 0.825311i | \(-0.691000\pi\) | ||||
−0.564678 | + | 0.825311i | \(0.691000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.35713e6 | −0.837799 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.81531e6 | 0.494025 | 0.247012 | − | 0.969012i | \(-0.420551\pi\) | ||||
0.247012 | + | 0.969012i | \(0.420551\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.22133e7 | 1.56762 | 0.783812 | − | 0.620998i | \(-0.213272\pi\) | ||||
0.783812 | + | 0.620998i | \(0.213272\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.84669e6 | −0.616678 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.58780e6 | −0.200275 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.29471e6 | −0.286938 | −0.143469 | − | 0.989655i | \(-0.545826\pi\) | ||||
−0.143469 | + | 0.989655i | \(0.545826\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.73096e6 | −0.338547 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.82243e6 | 1.19687 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.99276e6 | −0.240749 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.53391e6 | 0.902454 | 0.451227 | − | 0.892409i | \(-0.350986\pi\) | ||||
0.451227 | + | 0.892409i | \(0.350986\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.81534e6 | −0.571925 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.90827e6 | −0.695812 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.23521e6 | 0.844918 | 0.422459 | − | 0.906382i | \(-0.361167\pi\) | ||||
0.422459 | + | 0.906382i | \(0.361167\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.57984e6 | −0.870410 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.33856e6 | 0.380182 | 0.190091 | − | 0.981766i | \(-0.439122\pi\) | ||||
0.190091 | + | 0.981766i | \(0.439122\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.48297e7 | 1.67474 | 0.837370 | − | 0.546636i | \(-0.184092\pi\) | ||||
0.837370 | + | 0.546636i | \(0.184092\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.05314e6 | 0.117949 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.97213e6 | 0.330126 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.37473e6 | −0.702247 | −0.351124 | − | 0.936329i | \(-0.614200\pi\) | ||||
−0.351124 | + | 0.936329i | \(0.614200\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.34149e7 | −1.45374 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.54869e7 | −1.66461 | −0.832306 | − | 0.554317i | \(-0.812980\pi\) | ||||
−0.832306 | + | 0.554317i | \(0.812980\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.56003e6 | −0.166320 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.55324e6 | −0.481513 | −0.240756 | − | 0.970586i | \(-0.577396\pi\) | ||||
−0.240756 | + | 0.970586i | \(0.577396\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.16422e7 | −1.22126 | −0.610628 | − | 0.791918i | \(-0.709083\pi\) | ||||
−0.610628 | + | 0.791918i | \(0.709083\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −550289. | −0.0572613 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.23221e6 | 0.126178 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.76108e6 | −0.178900 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.41822e6 | 0.747607 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.07436e7 | 1.07417 | 0.537087 | − | 0.843527i | \(-0.319525\pi\) | ||||
0.537087 | + | 0.843527i | \(0.319525\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.10195e6 | −0.902870 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.01938e6 | −0.690819 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.00032e6 | −0.0969140 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.23138e7 | 1.18371 | 0.591857 | − | 0.806043i | \(-0.298395\pi\) | ||||
0.591857 | + | 0.806043i | \(0.298395\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.67944e7 | −1.60191 | −0.800955 | − | 0.598724i | \(-0.795675\pi\) | ||||
−0.800955 | + | 0.598724i | \(0.795675\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.42205e6 | −0.323882 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.99108e7 | 1.86994 | 0.934970 | − | 0.354726i | \(-0.115426\pi\) | ||||
0.934970 | + | 0.354726i | \(0.115426\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.75981e6 | 0.536780 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.10990e7 | 1.93633 | 0.968163 | − | 0.250319i | \(-0.0805355\pi\) | ||||
0.968163 | + | 0.250319i | \(0.0805355\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.74581e6 | −0.158999 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.53163e6 | 0.319199 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.75070e7 | 1.57035 | 0.785177 | − | 0.619271i | \(-0.212572\pi\) | ||||
0.785177 | + | 0.619271i | \(0.212572\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.80169e7 | 1.60389 | 0.801947 | − | 0.597395i | \(-0.203797\pi\) | ||||
0.801947 | + | 0.597395i | \(0.203797\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.07608e7 | 0.950737 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.53587e6 | 0.394771 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.61412e6 | −0.744124 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.13230e6 | −0.182828 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.48593e7 | 1.26462 | 0.632312 | − | 0.774714i | \(-0.282106\pi\) | ||||
0.632312 | + | 0.774714i | \(0.282106\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.53342e6 | 0.129539 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.18320e6 | 0.602347 | 0.301173 | − | 0.953569i | \(-0.402622\pi\) | ||||
0.301173 | + | 0.953569i | \(0.402622\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.24332e6 | −0.350621 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.65092e6 | 0.135417 | 0.0677087 | − | 0.997705i | \(-0.478431\pi\) | ||||
0.0677087 | + | 0.997705i | \(0.478431\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.33137e6 | −0.189839 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.41377e6 | 0.195121 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.89810e7 | 2.32576 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 777444. | 0.0619404 | 0.0309702 | − | 0.999520i | \(-0.490140\pi\) | ||||
0.0309702 | + | 0.999520i | \(0.490140\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.53713e6 | 0.277772 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.42406e6 | 0.656809 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.39250e7 | −1.07796 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.65671e6 | 0.127336 | 0.0636681 | − | 0.997971i | \(-0.479720\pi\) | ||||
0.0636681 | + | 0.997971i | \(0.479720\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.58203e6 | −0.273364 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.01324e6 | −0.379879 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.99901e6 | 0.373481 | 0.186740 | − | 0.982409i | \(-0.440208\pi\) | ||||
0.186740 | + | 0.982409i | \(0.440208\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.21671e6 | 0.461197 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.84619e6 | −0.357007 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.41825e6 | −0.469517 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.43788e6 | 0.612965 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.81384e7 | −1.30851 | −0.654253 | − | 0.756276i | \(-0.727017\pi\) | ||||
−0.654253 | + | 0.756276i | \(0.727017\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.15637e7 | 0.822721 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.26395e7 | −0.893070 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.17918e7 | 0.827454 | 0.413727 | − | 0.910401i | \(-0.364227\pi\) | ||||
0.413727 | + | 0.910401i | \(0.364227\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.84789e7 | 1.27904 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.96469e6 | −0.341297 | −0.170648 | − | 0.985332i | \(-0.554586\pi\) | ||||
−0.170648 | + | 0.985332i | \(0.554586\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.39194e6 | 0.230027 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.86292e7 | 1.25483 | 0.627413 | − | 0.778686i | \(-0.284114\pi\) | ||||
0.627413 | + | 0.778686i | \(0.284114\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.19605e6 | −0.347639 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.77727e7 | 1.18109 | 0.590544 | − | 0.807006i | \(-0.298913\pi\) | ||||
0.590544 | + | 0.807006i | \(0.298913\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.04523e7 | −0.689953 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.77338e6 | 0.116279 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.66059e6 | 0.301537 | 0.150769 | − | 0.988569i | \(-0.451825\pi\) | ||||
0.150769 | + | 0.988569i | \(0.451825\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.38792e6 | −0.410556 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.57699e6 | −0.356067 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.36520e6 | −0.150013 | −0.0750064 | − | 0.997183i | \(-0.523898\pi\) | ||||
−0.0750064 | + | 0.997183i | \(0.523898\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.77236e6 | −0.111673 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.76946e7 | −1.10759 | −0.553794 | − | 0.832654i | \(-0.686820\pi\) | ||||
−0.553794 | + | 0.832654i | \(0.686820\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.02137e6 | 0.248439 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.69943e7 | 1.04307 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.90324e6 | −0.481936 | −0.240968 | − | 0.970533i | \(-0.577465\pi\) | ||||
−0.240968 | + | 0.970533i | \(0.577465\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.63814e7 | 0.992468 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.22460e7 | 1.33907 | 0.669534 | − | 0.742782i | \(-0.266494\pi\) | ||||
0.669534 | + | 0.742782i | \(0.266494\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.35043e7 | 0.807639 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.06771e6 | −0.240163 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.22181e6 | −0.189005 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.38051e6 | −0.255341 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.40724e7 | −0.815070 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.49897e7 | 1.43822 | 0.719108 | − | 0.694898i | \(-0.244551\pi\) | ||||
0.719108 | + | 0.694898i | \(0.244551\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.23269e6 | −0.184872 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.29134e6 | −0.355271 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.08304e7 | 0.607750 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.40897e7 | 0.785696 | 0.392848 | − | 0.919603i | \(-0.371490\pi\) | ||||
0.392848 | + | 0.919603i | \(0.371490\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.70712e7 | 1.50017 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.10943e7 | −0.610970 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.13746e7 | 0.622512 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.04190e7 | −0.563174 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.54305e7 | −1.36611 | −0.683053 | − | 0.730369i | \(-0.739348\pi\) | ||||
−0.683053 | + | 0.730369i | \(0.739348\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.97155e6 | 0.105258 | 0.0526291 | − | 0.998614i | \(-0.483240\pi\) | ||||
0.0526291 | + | 0.998614i | \(0.483240\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.02158e6 | 0.372570 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.80557e6 | −0.0952184 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.92288e6 | −0.467681 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.11451e6 | −0.0577067 | −0.0288534 | − | 0.999584i | \(-0.509186\pi\) | ||||
−0.0288534 | + | 0.999584i | \(0.509186\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.79838e6 | 0.144015 | 0.0720073 | − | 0.997404i | \(-0.477060\pi\) | ||||
0.0720073 | + | 0.997404i | \(0.477060\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.93882e6 | 0.252632 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.56547e6 | 0.0795940 | 0.0397970 | − | 0.999208i | \(-0.487329\pi\) | ||||
0.0397970 | + | 0.999208i | \(0.487329\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.33721e7 | −0.675791 | −0.337895 | − | 0.941184i | \(-0.609715\pi\) | ||||
−0.337895 | + | 0.941184i | \(0.609715\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.93698e6 | 0.147536 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.19900e7 | 1.09146 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.68021e6 | 0.230915 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.37187e6 | 0.214418 | 0.107209 | − | 0.994236i | \(-0.465809\pi\) | ||||
0.107209 | + | 0.994236i | \(0.465809\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.55961e7 | 0.760372 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.27685e6 | −0.158813 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.06989e6 | −0.340621 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 576173. | 0.0274336 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.60498e6 | −0.170639 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.45910e7 | −0.686612 | −0.343306 | − | 0.939224i | \(-0.611547\pi\) | ||||
−0.343306 | + | 0.939224i | \(0.611547\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.94179e6 | −0.0908422 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.31276e7 | −0.610565 | −0.305283 | − | 0.952262i | \(-0.598751\pi\) | ||||
−0.305283 | + | 0.952262i | \(0.598751\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.42131e7 | 0.657211 | 0.328605 | − | 0.944467i | \(-0.393421\pi\) | ||||
0.328605 | + | 0.944467i | \(0.393421\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.66170e7 | 1.21656 | 0.608278 | − | 0.793724i | \(-0.291861\pi\) | ||||
0.608278 | + | 0.793724i | \(0.291861\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.03101e6 | −0.410389 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.93646e6 | −0.403755 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.00227e7 | 0.899441 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.00079e7 | 0.446990 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.53706e6 | −0.334708 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.42383e7 | −0.625114 | −0.312557 | − | 0.949899i | \(-0.601186\pi\) | ||||
−0.312557 | + | 0.949899i | \(0.601186\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.58218e6 | −0.156378 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.51921e7 | −0.659445 | −0.329722 | − | 0.944078i | \(-0.606955\pi\) | ||||
−0.329722 | + | 0.944078i | \(0.606955\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.03997e7 | 0.448868 | 0.224434 | − | 0.974489i | \(-0.427947\pi\) | ||||
0.224434 | + | 0.974489i | \(0.427947\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.35086e6 | 0.272567 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.02129e7 | 0.862618 | 0.431309 | − | 0.902204i | \(-0.358052\pi\) | ||||
0.431309 | + | 0.902204i | \(0.358052\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.71166e6 | 0.0722308 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.30718e7 | −0.548540 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.85119e6 | −0.202437 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.22934e6 | −0.217003 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.85776e7 | −1.59197 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.84834e7 | −2.40005 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.02999e7 | 0.418033 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.35643e6 | −0.175838 | −0.0879189 | − | 0.996128i | \(-0.528022\pi\) | ||||
−0.0879189 | + | 0.996128i | \(0.528022\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.90643e6 | 0.397656 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.99500e7 | 0.796427 | 0.398214 | − | 0.917293i | \(-0.369630\pi\) | ||||
0.398214 | + | 0.917293i | \(0.369630\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.71168e6 | 0.226771 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.35111e6 | −0.0928368 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.55172e6 | −0.373072 | −0.186536 | − | 0.982448i | \(-0.559726\pi\) | ||||
−0.186536 | + | 0.982448i | \(0.559726\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.74957e6 | 0.223350 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.50594e6 | −0.367275 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.00455e7 | 0.386028 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.05891e6 | 0.231577 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.26025e7 | −0.479090 | −0.239545 | − | 0.970885i | \(-0.576998\pi\) | ||||
−0.239545 | + | 0.970885i | \(0.576998\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.23370e7 | −0.840078 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.29520e7 | 0.484514 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.00216e7 | 0.372897 | 0.186448 | − | 0.982465i | \(-0.440302\pi\) | ||||
0.186448 | + | 0.982465i | \(0.440302\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.32888e7 | −0.491838 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.54113e6 | −0.0567369 | −0.0283684 | − | 0.999598i | \(-0.509031\pi\) | ||||
−0.0283684 | + | 0.999598i | \(0.509031\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.09377e6 | −0.149915 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.07046e7 | 1.11257 | 0.556287 | − | 0.830990i | \(-0.312226\pi\) | ||||
0.556287 | + | 0.830990i | \(0.312226\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.35607e7 | 1.20967 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.00813e7 | 0.720014 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.39769e7 | −1.56853 | −0.784263 | − | 0.620428i | \(-0.786959\pi\) | ||||
−0.784263 | + | 0.620428i | \(0.786959\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.72120e7 | −0.610692 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.41087e7 | −0.497974 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.25878e7 | 0.439684 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.73257e6 | 0.199197 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.69841e6 | −0.335261 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.20732e7 | −1.44690 | −0.723452 | − | 0.690375i | \(-0.757445\pi\) | ||||
−0.723452 | + | 0.690375i | \(0.757445\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.04856e7 | 0.358743 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.08006e7 | 0.707992 | 0.353996 | − | 0.935247i | \(-0.384823\pi\) | ||||
0.353996 | + | 0.935247i | \(0.384823\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.45719e7 | 0.490915 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.74338e7 | 1.25466 | 0.627332 | − | 0.778752i | \(-0.284147\pi\) | ||||
0.627332 | + | 0.778752i | \(0.284147\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.57324e7 | −1.19153 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.15232e7 | −0.382297 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.41962e7 | −0.798664 | −0.399332 | − | 0.916806i | \(-0.630758\pi\) | ||||
−0.399332 | + | 0.916806i | \(0.630758\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.09820e7 | −0.689058 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.98005e6 | −0.291936 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.52080e7 | −0.815369 | −0.407684 | − | 0.913123i | \(-0.633664\pi\) | ||||
−0.407684 | + | 0.913123i | \(0.633664\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.17010e7 | 0.698404 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.69182e7 | −0.861962 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.95511e7 | 1.57876 | 0.789379 | − | 0.613907i | \(-0.210403\pi\) | ||||
0.789379 | + | 0.613907i | \(0.210403\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.48150e6 | 0.110371 |
(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 | 588.6.a.n.1.2 | 4 | ||
7.2 | even | 3 | 84.6.i.c.25.3 | ✓ | 8 | ||
7.3 | odd | 6 | 588.6.i.o.373.2 | 8 | |||
7.4 | even | 3 | 84.6.i.c.37.3 | yes | 8 | ||
7.5 | odd | 6 | 588.6.i.o.361.2 | 8 | |||
7.6 | odd | 2 | 588.6.a.p.1.3 | 4 | |||
21.2 | odd | 6 | 252.6.k.f.109.2 | 8 | |||
21.11 | odd | 6 | 252.6.k.f.37.2 | 8 | |||
28.11 | odd | 6 | 336.6.q.i.289.3 | 8 | |||
28.23 | odd | 6 | 336.6.q.i.193.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.6.i.c.25.3 | ✓ | 8 | 7.2 | even | 3 | ||
84.6.i.c.37.3 | yes | 8 | 7.4 | even | 3 | ||
252.6.k.f.37.2 | 8 | 21.11 | odd | 6 | |||
252.6.k.f.109.2 | 8 | 21.2 | odd | 6 | |||
336.6.q.i.193.3 | 8 | 28.23 | odd | 6 | |||
336.6.q.i.289.3 | 8 | 28.11 | odd | 6 | |||
588.6.a.n.1.2 | 4 | 1.1 | even | 1 | trivial | ||
588.6.a.p.1.3 | 4 | 7.6 | odd | 2 | |||
588.6.i.o.361.2 | 8 | 7.5 | odd | 6 | |||
588.6.i.o.373.2 | 8 | 7.3 | odd | 6 |