Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,6,Mod(1,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("448.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(71.8519512762\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 229x^{3} - 272x^{2} + 7973x - 13998 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | no (minimal twist has level 224) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-8.98949\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 448.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −19.9790 | −1.28165 | −0.640826 | − | 0.767686i | \(-0.721408\pi\) | ||||
−0.640826 | + | 0.767686i | \(0.721408\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −106.158 | −1.89901 | −0.949504 | − | 0.313754i | \(-0.898413\pi\) | ||||
−0.949504 | + | 0.313754i | \(0.898413\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −49.0000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 156.159 | 0.642631 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 452.252 | 1.12693 | 0.563467 | − | 0.826138i | \(-0.309467\pi\) | ||||
0.563467 | + | 0.826138i | \(0.309467\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −886.820 | −1.45538 | −0.727691 | − | 0.685905i | \(-0.759407\pi\) | ||||
−0.727691 | + | 0.685905i | \(0.759407\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2120.92 | 2.43387 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 297.950 | 0.250047 | 0.125023 | − | 0.992154i | \(-0.460099\pi\) | ||||
0.125023 | + | 0.992154i | \(0.460099\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2286.25 | −1.45291 | −0.726457 | − | 0.687212i | \(-0.758834\pi\) | ||||
−0.726457 | + | 0.687212i | \(0.758834\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 978.970 | 0.484419 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 555.550 | 0.218979 | 0.109490 | − | 0.993988i | \(-0.465078\pi\) | ||||
0.109490 | + | 0.993988i | \(0.465078\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8144.48 | 2.60623 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1734.99 | 0.458022 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8267.13 | 1.82541 | 0.912704 | − | 0.408621i | \(-0.133990\pi\) | ||||
0.912704 | + | 0.408621i | \(0.133990\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4247.14 | 0.793765 | 0.396883 | − | 0.917869i | \(-0.370092\pi\) | ||||
0.396883 | + | 0.917869i | \(0.370092\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −9035.53 | −1.44434 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5201.73 | 0.717758 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 758.789 | 0.0911206 | 0.0455603 | − | 0.998962i | \(-0.485493\pi\) | ||||
0.0455603 | + | 0.998962i | \(0.485493\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 17717.8 | 1.86529 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 17202.5 | 1.59820 | 0.799100 | − | 0.601198i | \(-0.205310\pi\) | ||||
0.799100 | + | 0.601198i | \(0.205310\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5371.38 | 0.443011 | 0.221505 | − | 0.975159i | \(-0.428903\pi\) | ||||
0.221505 | + | 0.975159i | \(0.428903\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −16577.5 | −1.22036 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −25656.0 | −1.69412 | −0.847060 | − | 0.531497i | \(-0.821630\pi\) | ||||
−0.847060 | + | 0.531497i | \(0.821630\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5952.74 | −0.320473 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10834.4 | −0.529806 | −0.264903 | − | 0.964275i | \(-0.585340\pi\) | ||||
−0.264903 | + | 0.964275i | \(0.585340\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −48010.1 | −2.14006 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 45677.0 | 1.86213 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2794.28 | 0.104506 | 0.0522528 | − | 0.998634i | \(-0.483360\pi\) | ||||
0.0522528 | + | 0.998634i | \(0.483360\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8464.18 | −0.291246 | −0.145623 | − | 0.989340i | \(-0.546519\pi\) | ||||
−0.145623 | + | 0.989340i | \(0.546519\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7651.81 | −0.242892 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 94142.9 | 2.76378 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14334.1 | −0.390106 | −0.195053 | − | 0.980793i | \(-0.562488\pi\) | ||||
−0.195053 | + | 0.980793i | \(0.562488\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −11099.3 | −0.280655 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −61130.9 | −1.43918 | −0.719589 | − | 0.694400i | \(-0.755670\pi\) | ||||
−0.719589 | + | 0.694400i | \(0.755670\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6008.30 | −0.131961 | −0.0659803 | − | 0.997821i | \(-0.521017\pi\) | ||||
−0.0659803 | + | 0.997821i | \(0.521017\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −162718. | −3.34029 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −22160.3 | −0.425941 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 25300.2 | 0.456096 | 0.228048 | − | 0.973650i | \(-0.426766\pi\) | ||||
0.228048 | + | 0.973650i | \(0.426766\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −72610.0 | −1.22966 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5432.19 | 0.0865526 | 0.0432763 | − | 0.999063i | \(-0.486220\pi\) | ||||
0.0432763 | + | 0.999063i | \(0.486220\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −31629.7 | −0.474841 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −165169. | −2.33954 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 30312.7 | 0.405649 | 0.202824 | − | 0.979215i | \(-0.434988\pi\) | ||||
0.202824 | + | 0.979215i | \(0.434988\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 43454.2 | 0.550083 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −84853.5 | −1.01733 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 242703. | 2.75910 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −83046.9 | −0.896177 | −0.448089 | − | 0.893989i | \(-0.647895\pi\) | ||||
−0.448089 | + | 0.893989i | \(0.647895\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 70623.4 | 0.724203 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 136029. | 1.32687 | 0.663433 | − | 0.748235i | \(-0.269099\pi\) | ||||
0.663433 | + | 0.748235i | \(0.269099\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 65195.4 | 0.605514 | 0.302757 | − | 0.953068i | \(-0.402093\pi\) | ||||
0.302757 | + | 0.953068i | \(0.402093\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −103925. | −0.919916 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −121743. | −1.02798 | −0.513988 | − | 0.857797i | \(-0.671833\pi\) | ||||
−0.513988 | + | 0.857797i | \(0.671833\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −35552.4 | −0.286617 | −0.143309 | − | 0.989678i | \(-0.545774\pi\) | ||||
−0.143309 | + | 0.989678i | \(0.545774\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −15159.8 | −0.116785 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 186103. | 1.37106 | 0.685530 | − | 0.728045i | \(-0.259571\pi\) | ||||
0.685530 | + | 0.728045i | \(0.259571\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −58975.9 | −0.415844 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −138485. | −0.935274 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14599.6 | −0.0945088 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 43480.8 | 0.269981 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −343688. | −2.04834 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −532857. | −3.05025 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −171332. | −0.942601 | −0.471301 | − | 0.881973i | \(-0.656215\pi\) | ||||
−0.471301 | + | 0.881973i | \(0.656215\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −107315. | −0.567786 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 328559. | 1.67277 | 0.836383 | − | 0.548145i | \(-0.184666\pi\) | ||||
0.836383 | + | 0.548145i | \(0.184666\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 112026. | 0.549150 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −184182. | −0.869788 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 32938.6 | 0.149935 | 0.0749675 | − | 0.997186i | \(-0.476115\pi\) | ||||
0.0749675 | + | 0.997186i | \(0.476115\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 129231. | 0.567324 | 0.283662 | − | 0.958924i | \(-0.408451\pi\) | ||||
0.283662 | + | 0.958924i | \(0.408451\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 512580. | 2.17127 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −401066. | −1.64012 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −877621. | −3.46647 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −47969.5 | −0.183093 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −306271. | −1.13016 | −0.565081 | − | 0.825035i | \(-0.691155\pi\) | ||||
−0.565081 | + | 0.825035i | \(0.691155\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −263579. | −0.940736 | −0.470368 | − | 0.882470i | \(-0.655879\pi\) | ||||
−0.470368 | + | 0.882470i | \(0.655879\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 46527.7 | 0.160688 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −450867. | −1.50737 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 386226. | 1.25053 | 0.625263 | − | 0.780414i | \(-0.284992\pi\) | ||||
0.625263 | + | 0.780414i | \(0.284992\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 216461. | 0.679027 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −27221.9 | −0.0827664 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 107342. | 0.316448 | 0.158224 | − | 0.987403i | \(-0.449423\pi\) | ||||
0.158224 | + | 0.987403i | \(0.449423\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 959192. | 2.74281 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −378368. | −1.04984 | −0.524919 | − | 0.851152i | \(-0.675905\pi\) | ||||
−0.524919 | + | 0.851152i | \(0.675905\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 415157. | 1.11814 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −357020. | −0.933688 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 568280. | 1.44360 | 0.721801 | − | 0.692101i | \(-0.243315\pi\) | ||||
0.721801 | + | 0.692101i | \(0.243315\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −399080. | −0.985064 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −55826.8 | −0.133940 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 102649. | 0.239454 | 0.119727 | − | 0.992807i | \(-0.461798\pi\) | ||||
0.119727 | + | 0.992807i | \(0.461798\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 214817. | 0.487386 | 0.243693 | − | 0.969852i | \(-0.421641\pi\) | ||||
0.243693 | + | 0.969852i | \(0.421641\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 169106. | 0.373276 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −80551.4 | −0.173039 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 134748. | 0.281786 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −85014.3 | −0.173116 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −693025. | −1.37457 | −0.687283 | − | 0.726390i | \(-0.741197\pi\) | ||||
−0.687283 | + | 0.726390i | \(0.741197\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 169011. | 0.326604 | 0.163302 | − | 0.986576i | \(-0.447786\pi\) | ||||
0.163302 | + | 0.986576i | \(0.447786\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.88088e6 | −3.54221 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 461835. | 0.847855 | 0.423927 | − | 0.905696i | \(-0.360651\pi\) | ||||
0.423927 | + | 0.905696i | \(0.360651\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 844976. | 1.51256 | 0.756278 | − | 0.654250i | \(-0.227016\pi\) | ||||
0.756278 | + | 0.654250i | \(0.227016\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 286380. | 0.499980 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −405090. | −0.689939 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.82618e6 | −3.03500 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 86754.3 | 0.140723 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.03396e6 | −1.63734 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 497886. | 0.769882 | 0.384941 | − | 0.922941i | \(-0.374222\pi\) | ||||
0.384941 | + | 0.922941i | \(0.374222\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.22133e6 | 1.84453 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −570214. | −0.841282 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −208110. | −0.300015 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 120040. | 0.169127 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −264228. | −0.363914 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 976639. | 1.31514 | 0.657570 | − | 0.753394i | \(-0.271584\pi\) | ||||
0.657570 | + | 0.753394i | \(0.271584\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.27184e6 | 1.67485 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.01893e6 | −1.31244 | −0.656222 | − | 0.754568i | \(-0.727846\pi\) | ||||
−0.656222 | + | 0.754568i | \(0.727846\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −172096. | −0.216862 | −0.108431 | − | 0.994104i | \(-0.534583\pi\) | ||||
−0.108431 | + | 0.994104i | \(0.534583\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 442741. | 0.545908 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 569270. | 0.686955 | 0.343478 | − | 0.939161i | \(-0.388395\pi\) | ||||
0.343478 | + | 0.939161i | \(0.388395\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.72358e6 | 3.21715 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −505472. | −0.584556 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.39868e6 | −1.58389 | −0.791943 | − | 0.610595i | \(-0.790930\pi\) | ||||
−0.791943 | + | 0.610595i | \(0.790930\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.18533e6 | 1.31461 | 0.657307 | − | 0.753623i | \(-0.271695\pi\) | ||||
0.657307 | + | 0.753623i | \(0.271695\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.02907e6 | 1.11797 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −254885. | −0.271287 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.02749e6 | 2.11455 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −108530. | −0.110930 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −781131. | −0.782599 | −0.391300 | − | 0.920263i | \(-0.627974\pi\) | ||||
−0.391300 | + | 0.920263i | \(0.627974\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 251248. | 0.246775 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 631930. | 0.608581 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.52738e6 | −1.44249 | −0.721247 | − | 0.692678i | \(-0.756431\pi\) | ||||
−0.721247 | + | 0.692678i | \(0.756431\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −37180.7 | −0.0344404 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.29099e6 | 1.17306 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 728038. | 0.649030 | 0.324515 | − | 0.945881i | \(-0.394799\pi\) | ||||
0.324515 | + | 0.945881i | \(0.394799\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.15016e6 | 1.00611 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −605617. | −0.519901 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.05070e6 | 0.885313 | 0.442656 | − | 0.896691i | \(-0.354036\pi\) | ||||
0.442656 | + | 0.896691i | \(0.354036\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −688732. | −0.569675 | −0.284837 | − | 0.958576i | \(-0.591940\pi\) | ||||
−0.284837 | + | 0.958576i | \(0.591940\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −868170. | −0.705015 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.68336e6 | 2.93706 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −317611. | −0.248711 | −0.124356 | − | 0.992238i | \(-0.539686\pi\) | ||||
−0.124356 | + | 0.992238i | \(0.539686\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 663231. | 0.510098 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.01321e6 | −0.765478 | −0.382739 | − | 0.923856i | \(-0.625019\pi\) | ||||
−0.382739 | + | 0.923856i | \(0.625019\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.28474e6 | 0.953561 | 0.476781 | − | 0.879022i | \(-0.341804\pi\) | ||||
0.476781 | + | 0.879022i | \(0.341804\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.84897e6 | −3.53620 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −842921. | −0.604063 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.33108e6 | −0.937477 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.65919e6 | 1.14859 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.37245e6 | −1.61446 | −0.807230 | − | 0.590237i | \(-0.799034\pi\) | ||||
−0.807230 | + | 0.590237i | \(0.799034\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −296634. | −0.198457 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 784651. | 0.516161 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −492673. | −0.318699 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −263197. | −0.167442 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.71772e6 | −1.70058 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 898539. | 0.553079 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.00154e6 | −1.81760 | −0.908800 | − | 0.417231i | \(-0.863000\pi\) | ||||
−0.908800 | + | 0.417231i | \(0.863000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.30254e6 | −0.776058 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 378276. | 0.221773 | 0.110886 | − | 0.993833i | \(-0.464631\pi\) | ||||
0.110886 | + | 0.993833i | \(0.464631\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −306373. | −0.176763 | −0.0883813 | − | 0.996087i | \(-0.528169\pi\) | ||||
−0.0883813 | + | 0.996087i | \(0.528169\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 812299. | 0.461254 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.43596e6 | 1.36152 | 0.680758 | − | 0.732509i | \(-0.261651\pi\) | ||||
0.680758 | + | 0.732509i | \(0.261651\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.73883e6 | 2.05712 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.43229e6 | 1.31751 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −681189. | −0.363297 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.22269e6 | −3.79307 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 710299. | 0.367343 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.25714e6 | 0.640317 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 217384. | 0.109058 | 0.0545291 | − | 0.998512i | \(-0.482634\pi\) | ||||
0.0545291 | + | 0.998512i | \(0.482634\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 118492. | 0.0585569 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.52167e6 | 0.740815 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.34165e6 | 0.643522 | 0.321761 | − | 0.946821i | \(-0.395725\pi\) | ||||
0.321761 | + | 0.946821i | \(0.395725\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.71814e6 | −1.75722 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.92078e6 | 0.894522 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −117649. | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.17828e6 | 0.532967 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.47196e6 | −0.656253 | −0.328127 | − | 0.944634i | \(-0.606417\pi\) | ||||
−0.328127 | + | 0.944634i | \(0.606417\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.15482e6 | 1.82595 | 0.912975 | − | 0.408016i | \(-0.133779\pi\) | ||||
0.912975 | + | 0.408016i | \(0.133779\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.53862e6 | −0.666598 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.41522e6 | −1.03162 | −0.515810 | − | 0.856703i | \(-0.672509\pi\) | ||||
−0.515810 | + | 0.856703i | \(0.672509\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.48952e6 | 2.73301 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 291684. | 0.121127 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 803886. | 0.329199 | 0.164599 | − | 0.986361i | \(-0.447367\pi\) | ||||
0.164599 | + | 0.986361i | \(0.447367\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.75085e6 | 1.11096 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −868701. | −0.346022 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 637828. | 0.250594 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.03890e6 | −1.95286 | −0.976428 | − | 0.215842i | \(-0.930750\pi\) | ||||
−0.976428 | + | 0.215842i | \(0.930750\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.68633e6 | 1.02705 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 530888. | 0.200248 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 86405.3 | 0.0321565 | 0.0160782 | − | 0.999871i | \(-0.494882\pi\) | ||||
0.0160782 | + | 0.999871i | \(0.494882\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.06459e7 | 3.90936 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.33146e6 | −2.65667 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.60986e6 | 0.575691 | 0.287845 | − | 0.957677i | \(-0.407061\pi\) | ||||
0.287845 | + | 0.957677i | \(0.407061\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.42303e6 | 1.20809 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.09358e6 | 1.07762 | 0.538808 | − | 0.842429i | \(-0.318875\pi\) | ||||
0.538808 | + | 0.842429i | \(0.318875\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.35249e6 | 0.808866 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 838791. | 0.284693 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −331993. | −0.111238 | −0.0556191 | − | 0.998452i | \(-0.517713\pi\) | ||||
−0.0556191 | + | 0.998452i | \(0.517713\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 165526. | 0.0547551 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.56427e6 | −2.14390 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.68581e6 | −0.866130 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −797824. | −0.254057 | −0.127028 | − | 0.991899i | \(-0.540544\pi\) | ||||
−0.127028 | + | 0.991899i | \(0.540544\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.23817e6 | −0.703819 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.22782e6 | −0.691862 | −0.345931 | − | 0.938260i | \(-0.612437\pi\) | ||||
−0.345931 | + | 0.938260i | \(0.612437\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.76645e6 | −1.15523 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.70812e6 | 2.33513 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 343164. | 0.102687 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.00358e6 | 0.296650 | 0.148325 | − | 0.988939i | \(-0.452612\pi\) | ||||
0.148325 | + | 0.988939i | \(0.452612\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −658079. | −0.192165 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −136920. | −0.0394994 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −576670. | −0.164364 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.58191e6 | −0.727111 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.56464e6 | 0.991929 | 0.495965 | − | 0.868343i | \(-0.334815\pi\) | ||||
0.495965 | + | 0.868343i | \(0.334815\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.39330e6 | −0.658100 | −0.329050 | − | 0.944312i | \(-0.606729\pi\) | ||||
−0.329050 | + | 0.944312i | \(0.606729\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.00642e6 | −1.08869 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.42665e6 | 0.651681 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 414745. | 0.110081 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.01289e6 | 2.10206 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −130925. | −0.0339491 | −0.0169745 | − | 0.999856i | \(-0.505403\pi\) | ||||
−0.0169745 | + | 0.999856i | \(0.505403\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.70732e6 | 0.693937 | 0.346969 | − | 0.937877i | \(-0.387211\pi\) | ||||
0.346969 | + | 0.937877i | \(0.387211\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.75340e7 | 4.44280 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.27013e6 | −0.318158 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.04646e6 | 1.74506 | 0.872529 | − | 0.488562i | \(-0.162478\pi\) | ||||
0.872529 | + | 0.488562i | \(0.162478\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 374939. | 0.0918045 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.17797e6 | 0.527281 | 0.263641 | − | 0.964621i | \(-0.415077\pi\) | ||||
0.263641 | + | 0.964621i | \(0.415077\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.21793e6 | −0.770331 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.11899e6 | 1.44847 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.52327e6 | −0.590674 | −0.295337 | − | 0.955393i | \(-0.595432\pi\) | ||||
−0.295337 | + | 0.955393i | \(0.595432\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.77985e6 | 1.80107 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.26603e6 | 1.20570 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.61300e6 | −1.04461 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.08980e6 | 0.244094 | 0.122047 | − | 0.992524i | \(-0.461054\pi\) | ||||
0.122047 | + | 0.992524i | \(0.461054\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 516939. | 0.114527 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.14703e6 | −1.12799 | −0.563994 | − | 0.825779i | \(-0.690736\pi\) | ||||
−0.563994 | + | 0.825779i | \(0.690736\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.03321e6 | −1.09117 | −0.545585 | − | 0.838055i | \(-0.683693\pi\) | ||||
−0.545585 | + | 0.838055i | \(0.683693\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9.00786e6 | 1.93192 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.07086e6 | 0.227216 | 0.113608 | − | 0.993526i | \(-0.463759\pi\) | ||||
0.113608 | + | 0.993526i | \(0.463759\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 702370. | 0.147446 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.71640e6 | −1.60274 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.42921e6 | 0.499244 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.86203e7 | −3.78664 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.69190e6 | −0.340470 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.30339e6 | 1.05612 | 0.528062 | − | 0.849206i | \(-0.322919\pi\) | ||||
0.528062 | + | 0.849206i | \(0.322919\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −672909. | −0.132615 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 543866. | 0.106078 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.81607e6 | 1.70185 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.00137e6 | 0.573453 | 0.286726 | − | 0.958013i | \(-0.407433\pi\) | ||||
0.286726 | + | 0.958013i | \(0.407433\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.14459e6 | −0.405576 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.37046e6 | −1.37972 | −0.689860 | − | 0.723943i | \(-0.742328\pi\) | ||||
−0.689860 | + | 0.723943i | \(0.742328\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.46319e6 | 0.456437 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.49722e6 | −1.37527 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.99541e6 | 0.543958 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8624.58 | −0.00155055 | −0.000775276 | − | 1.00000i | \(-0.500247\pi\) | ||||
−0.000775276 | 1.00000i | \(0.500247\pi\) | ||||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.55939e6 | 1.34553 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −124603. | −0.0219587 | −0.0109794 | − | 0.999940i | \(-0.503495\pi\) | ||||
−0.0109794 | + | 0.999940i | \(0.503495\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.44405e7 | −2.51973 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.29441e6 | −1.43306 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.12727e6 | 0.192856 | 0.0964279 | − | 0.995340i | \(-0.469258\pi\) | ||||
0.0964279 | + | 0.995340i | \(0.469258\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 294406. | 0.0498764 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.96662e6 | −0.665467 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.92101e6 | −1.14988 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.16030e7 | −1.90916 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.13537e7 | −1.85019 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.96035e6 | −1.28481 | −0.642404 | − | 0.766367i | \(-0.722063\pi\) | ||||
−0.642404 | + | 0.766367i | \(0.722063\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.19765e6 | −0.351321 | −0.175661 | − | 0.984451i | \(-0.556206\pi\) | ||||
−0.175661 | + | 0.984451i | \(0.556206\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7.97320e6 | 1.26251 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.26544e6 | 0.198478 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.12771e6 | −0.952048 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 436352. | 0.0671585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.52555e7 | −2.32599 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.29239e7 | 1.95214 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.05082e6 | −0.306897 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.08586e6 | 0.160991 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.57555e6 | −0.231440 | −0.115720 | − | 0.993282i | \(-0.536918\pi\) | ||||
−0.115720 | + | 0.993282i | \(0.536918\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.29183e6 | −0.624659 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.77416e6 | 0.544288 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.04857e7 | −1.49840 | −0.749201 | − | 0.662343i | \(-0.769562\pi\) | ||||
−0.749201 | + | 0.662343i | \(0.769562\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.32176e6 | −0.187164 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.89007e7 | −2.65216 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.23971e6 | −0.172388 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.60933e6 | 0.221776 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.88209e6 | −0.393613 | −0.196807 | − | 0.980442i | \(-0.563057\pi\) | ||||
−0.196807 | + | 0.980442i | \(0.563057\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.76344e6 | −0.644750 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.69214e6 | −0.361152 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.31106e6 | −0.972096 | −0.486048 | − | 0.873932i | \(-0.661562\pi\) | ||||
−0.486048 | + | 0.873932i | \(0.661562\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.97562e7 | −2.60365 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.55789e6 | 0.464766 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.30620e6 | 0.428103 | 0.214052 | − | 0.976822i | \(-0.431334\pi\) | ||||
0.214052 | + | 0.976822i | \(0.431334\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.22306e6 | −0.542047 | −0.271024 | − | 0.962573i | \(-0.587362\pi\) | ||||
−0.271024 | + | 0.962573i | \(0.587362\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.38459e7 | 1.76171 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.52467e6 | 0.570712 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.28814e6 | −0.536203 | −0.268102 | − | 0.963391i | \(-0.586396\pi\) | ||||
−0.268102 | + | 0.963391i | \(0.586396\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.37666e6 | −0.418592 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −266177. | −0.0327138 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.89990e6 | −0.597057 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.47013e7 | 1.77609 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.56309e7 | −1.87236 | −0.936180 | − | 0.351521i | \(-0.885665\pi\) | ||||
−0.936180 | + | 0.351521i | \(0.885665\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.71003e6 | −1.15327 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.22699e6 | −1.08665 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.78346e6 | −0.792163 | −0.396081 | − | 0.918215i | \(-0.629630\pi\) | ||||
−0.396081 | + | 0.918215i | \(0.629630\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.54986e6 | 0.179473 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.68817e7 | −1.93857 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.41543e6 | 0.161184 | 0.0805919 | − | 0.996747i | \(-0.474319\pi\) | ||||
0.0805919 | + | 0.996747i | \(0.474319\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.71218e6 | 0.645083 | 0.322542 | − | 0.946555i | \(-0.395463\pi\) | ||||
0.322542 | + | 0.946555i | \(0.395463\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.23840e6 | −0.250694 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.61582e6 | −0.512697 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.41559e6 | −0.816910 | −0.408455 | − | 0.912779i | \(-0.633932\pi\) | ||||
−0.408455 | + | 0.912779i | \(0.633932\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.09327e6 | 0.884262 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.27522e7 | 2.46559 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.00094e7 | 1.07587 | 0.537933 | − | 0.842988i | \(-0.319205\pi\) | ||||
0.537933 | + | 0.842988i | \(0.319205\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.64851e7 | 3.88981 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.32953e7 | 1.40600 | 0.702999 | − | 0.711190i | \(-0.251844\pi\) | ||||
0.702999 | + | 0.711190i | \(0.251844\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −785629. | −0.0824121 | −0.0412060 | − | 0.999151i | \(-0.513120\pi\) | ||||
−0.0412060 | + | 0.999151i | \(0.513120\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 963871. | 0.100297 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.48532e6 | −0.153321 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.11155e7 | 3.18622 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.06575e7 | 2.09850 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 226081. | 0.0227844 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.13220e7 | −1.13201 | −0.566005 | − | 0.824402i | \(-0.691512\pi\) | ||||
−0.566005 | + | 0.824402i | \(0.691512\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.94726e6 | −0.986720 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.81882e7 | 1.79001 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.12926e6 | −0.207912 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.54616e6 | −0.924861 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.12306e6 | −0.492475 | −0.246237 | − | 0.969210i | \(-0.579194\pi\) | ||||
−0.246237 | + | 0.969210i | \(0.579194\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.74313e6 | −0.643182 | −0.321591 | − | 0.946879i | \(-0.604218\pi\) | ||||
−0.321591 | + | 0.946879i | \(0.604218\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.13923e7 | 1.07823 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.93239e7 | 1.81482 | 0.907410 | − | 0.420247i | \(-0.138057\pi\) | ||||
0.907410 | + | 0.420247i | \(0.138057\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.26372e6 | 0.117771 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.15782e6 | 0.384515 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.59779e6 | −0.880823 | −0.440411 | − | 0.897796i | \(-0.645167\pi\) | ||||
−0.440411 | + | 0.897796i | \(0.645167\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.48791e7 | −3.17660 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −938252. | −0.0848020 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.51712e7 | −1.36084 | −0.680419 | − | 0.732824i | \(-0.738202\pi\) | ||||
−0.680419 | + | 0.732824i | \(0.738202\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.17829e6 | 0.104894 | 0.0524468 | − | 0.998624i | \(-0.483298\pi\) | ||||
0.0524468 | + | 0.998624i | \(0.483298\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.27901e6 | 0.466411 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.18925e7 | −1.04284 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.59280e6 | 0.399727 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.95122e7 | −1.68555 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.82794e6 | −0.328215 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.34216e7 | 1.14226 | 0.571131 | − | 0.820859i | \(-0.306505\pi\) | ||||
0.571131 | + | 0.820859i | \(0.306505\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.41306e7 | 1.19371 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.24042e6 | 0.271725 | 0.135862 | − | 0.990728i | \(-0.456620\pi\) | ||||
0.135862 | + | 0.990728i | \(0.456620\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.06930e6 | 0.338723 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.03572e7 | 1.68210 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.97746e7 | −1.62202 | −0.811011 | − | 0.585031i | \(-0.801082\pi\) | ||||
−0.811011 | + | 0.585031i | \(0.801082\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.49669e6 | −0.284728 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.43831e6 | 0.277941 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.60821e6 | 0.771071 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.59677e7 | −1.27217 | −0.636086 | − | 0.771618i | \(-0.719448\pi\) | ||||
−0.636086 | + | 0.771618i | \(0.719448\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.46055e6 | −0.273723 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.37189e7 | −1.07735 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.12548e6 | 0.399625 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.13734e7 | −0.880438 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.38418e6 | 0.183250 | 0.0916251 | − | 0.995794i | \(-0.470794\pi\) | ||||
0.0916251 | + | 0.995794i | \(0.470794\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.73478e6 | −0.132390 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.44144e7 | −4.12326 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.66541e6 | −0.501509 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.13193e7 | 1.59278 | 0.796391 | − | 0.604782i | \(-0.206740\pi\) | ||||
0.796391 | + | 0.604782i | \(0.206740\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.95086e6 | 0.293102 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.35950e6 | 0.173818 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.25763e7 | 3.11460 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.79442e7 | 2.02999 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.57018e7 | −1.85413 | −0.927067 | − | 0.374897i | \(-0.877678\pi\) | ||||
−0.927067 | + | 0.374897i | \(0.877678\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.19458e6 | −0.228863 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.36818e7 | −1.68488 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.73315e7 | 4.75744 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.23186e7 | 0.864423 | 0.432211 | − | 0.901772i | \(-0.357733\pi\) | ||||
0.432211 | + | 0.901772i | \(0.357733\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.91556e6 | −0.203190 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.60040e6 | 0.110773 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.74378e7 | −1.19876 | −0.599379 | − | 0.800466i | \(-0.704586\pi\) | ||||
−0.599379 | + | 0.800466i | \(0.704586\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.09234e6 | 0.347695 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.48261e6 | −0.439624 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.50344e7 | −1.68627 | −0.843134 | − | 0.537704i | \(-0.819292\pi\) | ||||
−0.843134 | + | 0.537704i | \(0.819292\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.05072e7 | −2.71011 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.31077e7 | 1.53562 | 0.767811 | − | 0.640676i | \(-0.221346\pi\) | ||||
0.767811 | + | 0.640676i | \(0.221346\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.25131e7 | 2.14619 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 848288. | 0.0556214 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.96539e6 | 0.388539 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.74588e7 | 1.12957 | 0.564786 | − | 0.825238i | \(-0.308959\pi\) | ||||
0.564786 | + | 0.825238i | \(0.308959\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.56062e7 | 1.00302 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.79809e7 | 1.78647 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.63158e6 | −0.420608 | −0.210304 | − | 0.977636i | \(-0.567445\pi\) | ||||
−0.210304 | + | 0.977636i | \(0.567445\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.01968e6 | −0.316280 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.74131e7 | −1.08997 | −0.544985 | − | 0.838446i | \(-0.683465\pi\) | ||||
−0.544985 | + | 0.838446i | \(0.683465\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.74207e6 | 0.108331 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.93928e6 | −0.305148 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.47802e6 | −0.152095 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.83850e7 | 1.73090 | 0.865452 | − | 0.500991i | \(-0.167031\pi\) | ||||
0.865452 | + | 0.500991i | \(0.167031\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.05154e7 | 1.84877 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.59767e7 | 1.56363 | 0.781816 | − | 0.623509i | \(-0.214294\pi\) | ||||
0.781816 | + | 0.623509i | \(0.214294\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.45907e7 | 2.06874 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 742831. | 0.0441405 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.93292e7 | −2.32205 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.76465e7 | −1.62186 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.43434e7 | 0.836078 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.10009e7 | −2.37476 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.68085e7 | −1.54290 | −0.771448 | − | 0.636293i | \(-0.780467\pi\) | ||||
−0.771448 | + | 0.636293i | \(0.780467\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.45455e7 | −0.831830 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.11903e6 | −0.518212 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.50621e6 | 0.423875 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.29790e7 | −1.28948 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.93026e6 | 0.163403 | 0.0817014 | − | 0.996657i | \(-0.473965\pi\) | ||||
0.0817014 | + | 0.996657i | \(0.473965\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.64421e6 | −0.423609 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.73362e6 | 0.260683 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.71726e6 | −0.148711 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.88982e6 | 0.157174 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.09918e7 | −1.13466 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.98402e7 | 1.60299 | 0.801494 | − | 0.598003i | \(-0.204039\pi\) | ||||
0.801494 | + | 0.598003i | \(0.204039\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.53235e7 | 1.35199 | 0.675993 | − | 0.736908i | \(-0.263715\pi\) | ||||
0.675993 | + | 0.736908i | \(0.263715\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.37602e7 | 0.730124 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.13952e7 | −0.600937 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.22803e7 | −0.643657 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.78578e6 | 0.353500 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.86859e6 | 0.303862 | 0.151931 | − | 0.988391i | \(-0.451451\pi\) | ||||
0.151931 | + | 0.988391i | \(0.451451\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.81684e6 | −0.505210 | −0.252605 | − | 0.967569i | \(-0.581287\pi\) | ||||
−0.252605 | + | 0.967569i | \(0.581287\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.35897e7 | −3.76428 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.76584e7 | −1.40625 | −0.703127 | − | 0.711065i | \(-0.748213\pi\) | ||||
−0.703127 | + | 0.711065i | \(0.748213\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.06302e7 | 1.04260 | 0.521298 | − | 0.853374i | \(-0.325448\pi\) | ||||
0.521298 | + | 0.853374i | \(0.325448\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.34553e6 | 0.318761 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 715378. | 0.0357210 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.01667e7 | 1.99365 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.36873e6 | 0.363562 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.55068e7 | −0.760533 | −0.380266 | − | 0.924877i | \(-0.624168\pi\) | ||||
−0.380266 | + | 0.924877i | \(0.624168\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.78343e7 | 2.33211 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.02429e7 | 0.981076 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.40721e7 | −2.12335 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.13056e6 | −0.102043 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.56678e7 | −1.22213 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 421545. | 0.0199535 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.07567e6 | −0.285905 | −0.142952 | − | 0.989730i | \(-0.545660\pi\) | ||||
−0.142952 | + | 0.989730i | \(0.545660\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.79004e7 | 1.77308 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.60713e7 | −1.21258 | −0.606291 | − | 0.795243i | \(-0.707343\pi\) | ||||
−0.606291 | + | 0.795243i | \(0.707343\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.89265e6 | −0.179996 | −0.0899980 | − | 0.995942i | \(-0.528686\pi\) | ||||
−0.0899980 | + | 0.995942i | \(0.528686\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.68407e7 | 0.774198 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.73425e7 | −0.792657 | −0.396329 | − | 0.918109i | \(-0.629716\pi\) | ||||
−0.396329 | + | 0.918109i | \(0.629716\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.03274e7 | −2.74141 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.65937e7 | 1.20152 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.14421e7 | 0.513990 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.27117e7 | 0.567754 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.29685e7 | −0.575911 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.61100e7 | 1.15289 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.40336e6 | −0.105516 | −0.0527582 | − | 0.998607i | \(-0.516801\pi\) | ||||
−0.0527582 | + | 0.998607i | \(0.516801\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.73990e7 | 2.06918 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.40789e7 | −0.611125 | −0.305563 | − | 0.952172i | \(-0.598845\pi\) | ||||
−0.305563 | + | 0.952172i | \(0.598845\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.30002e7 | 1.85596 | 0.927979 | − | 0.372632i | \(-0.121545\pi\) | ||||
0.927979 | + | 0.372632i | \(0.121545\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.92645e6 | 0.254353 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 136209. | 0.00581297 | 0.00290648 | − | 0.999996i | \(-0.499075\pi\) | ||||
0.00290648 | + | 0.999996i | \(0.499075\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.39524e6 | 0.356270 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.28380e7 | −1.38574 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.86561e7 | 2.46141 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.08970e7 | −0.454725 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.84309e6 | 0.408461 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.51117e7 | 1.44895 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.22813e6 | −0.132476 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.25841e6 | 0.214603 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.28045e7 | −0.925550 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.23331e6 | 0.332320 | 0.166160 | − | 0.986099i | \(-0.446863\pi\) | ||||
0.166160 | + | 0.986099i | \(0.446863\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.12422e7 | 0.852686 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.15065e6 | 0.365306 | 0.182653 | − | 0.983177i | \(-0.441532\pi\) | ||||
0.182653 | + | 0.983177i | \(0.441532\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.45672e6 | 0.0975391 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.79519e7 | −0.708855 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.60994e7 | −0.632246 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.27063e7 | 0.886865 | 0.443433 | − | 0.896308i | \(-0.353761\pi\) | ||||
0.443433 | + | 0.896308i | \(0.353761\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.99677e7 | 2.32953 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.42121e7 | 2.09456 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.17994e6 | 0.237482 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.01809e7 | 0.389122 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.95825e6 | −0.0744439 | −0.0372220 | − | 0.999307i | \(-0.511851\pi\) | ||||
−0.0372220 | + | 0.999307i | \(0.511851\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.48929e6 | −0.207559 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.55757e6 | −0.284235 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.43046e7 | −0.535115 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.49113e7 | −1.29902 | −0.649512 | − | 0.760351i | \(-0.725027\pi\) | ||||
−0.649512 | + | 0.760351i | \(0.725027\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.12103e6 | 0.226548 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.99605e7 | −1.10300 | −0.551500 | − | 0.834175i | \(-0.685944\pi\) | ||||
−0.551500 | + | 0.834175i | \(0.685944\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.55683e6 | 0.349973 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.02494e6 | 0.328749 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.74875e7 | 0.633655 | 0.316827 | − | 0.948483i | \(-0.397382\pi\) | ||||
0.316827 | + | 0.948483i | \(0.397382\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.32828e6 | 0.192053 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.86681e7 | −1.74499 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.25389e7 | −0.447226 | −0.223613 | − | 0.974678i | \(-0.571785\pi\) | ||||
−0.223613 | + | 0.974678i | \(0.571785\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.35700e7 | 2.61031 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.46979e7 | −2.63651 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.61399e6 | −0.0566701 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.05910e7 | −0.369936 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.90113e7 | −0.660610 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.79418e7 | −0.620223 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.28111e7 | −0.784477 | −0.392238 | − | 0.919864i | \(-0.628299\pi\) | ||||
−0.392238 | + | 0.919864i | \(0.628299\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.36095e7 | 0.465620 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −190729. | −0.00649186 | −0.00324593 | − | 0.999995i | \(-0.501033\pi\) | ||||
−0.00324593 | + | 0.999995i | \(0.501033\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.33234e6 | −0.214428 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.44302e8 | 4.86139 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.92970e7 | 0.646775 | 0.323388 | − | 0.946267i | \(-0.395178\pi\) | ||||
0.323388 | + | 0.946267i | \(0.395178\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.37090e7 | 0.457140 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.55183e6 | −0.184189 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.60890e7 | 0.531062 | 0.265531 | − | 0.964102i | \(-0.414453\pi\) | ||||
0.265531 | + | 0.964102i | \(0.414453\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.90274e7 | −1.61008 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.51164e7 | −0.820664 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.98407e6 | 0.0970103 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.90847e7 | 0.940762 | 0.470381 | − | 0.882463i | \(-0.344117\pi\) | ||||
0.470381 | + | 0.882463i | \(0.344117\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.34311e6 | −0.139775 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.97008e7 | −2.87236 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.48593e7 | −1.42927 | −0.714636 | − | 0.699497i | \(-0.753408\pi\) | ||||
−0.714636 | + | 0.699497i | \(0.753408\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.31649e6 | 0.0417353 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 448.6.a.be.1.2 | 5 | ||
4.3 | odd | 2 | 448.6.a.bf.1.4 | 5 | |||
8.3 | odd | 2 | 224.6.a.i.1.2 | ✓ | 5 | ||
8.5 | even | 2 | 224.6.a.j.1.4 | yes | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.6.a.i.1.2 | ✓ | 5 | 8.3 | odd | 2 | ||
224.6.a.j.1.4 | yes | 5 | 8.5 | even | 2 | ||
448.6.a.be.1.2 | 5 | 1.1 | even | 1 | trivial | ||
448.6.a.bf.1.4 | 5 | 4.3 | odd | 2 |