Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [32,6,Mod(1,32)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(32, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("32.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 32 = 2^{5} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 32.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: | \(5.13228223402\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 32.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 27.7128 | 1.77778 | 0.888889 | − | 0.458123i | \(-0.151478\pi\) | ||||
0.888889 | + | 0.458123i | \(0.151478\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 46.0000 | 0.822873 | 0.411437 | − | 0.911438i | \(-0.365027\pi\) | ||||
0.411437 | + | 0.911438i | \(0.365027\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −166.277 | −1.28259 | −0.641293 | − | 0.767296i | \(-0.721602\pi\) | ||||
−0.641293 | + | 0.767296i | \(0.721602\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 525.000 | 2.16049 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 83.1384 | 0.207167 | 0.103583 | − | 0.994621i | \(-0.466969\pi\) | ||||
0.103583 | + | 0.994621i | \(0.466969\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −42.0000 | −0.0689272 | −0.0344636 | − | 0.999406i | \(-0.510972\pi\) | ||||
−0.0344636 | + | 0.999406i | \(0.510972\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1274.79 | 1.46289 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 962.000 | 0.807333 | 0.403667 | − | 0.914906i | \(-0.367736\pi\) | ||||
0.403667 | + | 0.914906i | \(0.367736\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2078.46 | −1.32086 | −0.660432 | − | 0.750886i | \(-0.729627\pi\) | ||||
−0.660432 | + | 0.750886i | \(0.729627\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4608.00 | −2.28015 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3159.26 | −1.24528 | −0.622638 | − | 0.782510i | \(-0.713939\pi\) | ||||
−0.622638 | + | 0.782510i | \(0.713939\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1009.00 | −0.322880 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 7815.01 | 2.06310 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2554.00 | −0.563931 | −0.281965 | − | 0.959425i | \(-0.590986\pi\) | ||||
−0.281965 | + | 0.959425i | \(0.590986\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1995.32 | 0.372914 | 0.186457 | − | 0.982463i | \(-0.440299\pi\) | ||||
0.186457 | + | 0.982463i | \(0.440299\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2304.00 | 0.368297 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7648.74 | −1.05541 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11950.0 | 1.43504 | 0.717519 | − | 0.696539i | \(-0.245278\pi\) | ||||
0.717519 | + | 0.696539i | \(0.245278\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1163.94 | −0.122537 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5078.00 | −0.471773 | −0.235886 | − | 0.971781i | \(-0.575799\pi\) | ||||
−0.235886 | + | 0.971781i | \(0.575799\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12553.9 | −1.03540 | −0.517699 | − | 0.855563i | \(-0.673211\pi\) | ||||
−0.517699 | + | 0.855563i | \(0.673211\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 24150.0 | 1.77781 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12304.5 | 0.812492 | 0.406246 | − | 0.913764i | \(-0.366838\pi\) | ||||
0.406246 | + | 0.913764i | \(0.366838\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10841.0 | 0.645029 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 26659.7 | 1.43526 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −19714.0 | −0.964018 | −0.482009 | − | 0.876166i | \(-0.660093\pi\) | ||||
−0.482009 | + | 0.876166i | \(0.660093\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3824.37 | 0.170472 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −57600.0 | −2.34820 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8895.81 | −0.332702 | −0.166351 | − | 0.986067i | \(-0.553199\pi\) | ||||
−0.166351 | + | 0.986067i | \(0.553199\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 29318.0 | 1.00881 | 0.504405 | − | 0.863467i | \(-0.331712\pi\) | ||||
0.504405 | + | 0.863467i | \(0.331712\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −87295.4 | −2.77102 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1932.00 | −0.0567184 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 16877.1 | 0.459315 | 0.229658 | − | 0.973271i | \(-0.426239\pi\) | ||||
0.229658 | + | 0.973271i | \(0.426239\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −87552.0 | −2.21383 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 80976.8 | 1.90640 | 0.953202 | − | 0.302334i | \(-0.0977658\pi\) | ||||
0.953202 | + | 0.302334i | \(0.0977658\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 37914.0 | 0.832707 | 0.416354 | − | 0.909203i | \(-0.363308\pi\) | ||||
0.416354 | + | 0.909203i | \(0.363308\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −27962.2 | −0.574009 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −13824.0 | −0.265709 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 88791.9 | 1.60068 | 0.800342 | − | 0.599544i | \(-0.204651\pi\) | ||||
0.800342 | + | 0.599544i | \(0.204651\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 89001.0 | 1.50724 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −39324.5 | −0.626567 | −0.313284 | − | 0.949660i | \(-0.601429\pi\) | ||||
−0.313284 | + | 0.949660i | \(0.601429\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 44252.0 | 0.664333 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −70778.5 | −1.00254 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13930.0 | 0.186413 | 0.0932065 | − | 0.995647i | \(-0.470288\pi\) | ||||
0.0932065 | + | 0.995647i | \(0.470288\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6983.63 | 0.0884052 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 55296.0 | 0.662959 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −95609.2 | −1.08690 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 163602. | 1.76547 | 0.882733 | − | 0.469875i | \(-0.155701\pi\) | ||||
0.882733 | + | 0.469875i | \(0.155701\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 43647.7 | 0.447583 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −148562. | −1.44912 | −0.724560 | − | 0.689212i | \(-0.757957\pi\) | ||||
−0.724560 | + | 0.689212i | \(0.757957\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −100598. | −0.934317 | −0.467158 | − | 0.884174i | \(-0.654722\pi\) | ||||
−0.467158 | + | 0.884174i | \(0.654722\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −211968. | −1.87628 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 194960. | 1.64621 | 0.823105 | − | 0.567889i | \(-0.192240\pi\) | ||||
0.823105 | + | 0.567889i | \(0.192240\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 123222. | 0.993395 | 0.496698 | − | 0.867924i | \(-0.334546\pi\) | ||||
0.496698 | + | 0.867924i | \(0.334546\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 331168. | 2.55118 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −51278.0 | −0.377777 | −0.188888 | − | 0.981999i | \(-0.560488\pi\) | ||||
−0.188888 | + | 0.981999i | \(0.560488\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −145326. | −1.02470 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −22050.0 | −0.148917 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −159958. | −1.03547 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −154139. | −0.957082 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −140726. | −0.838708 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −190164. | −1.08856 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −148984. | −0.819654 | −0.409827 | − | 0.912163i | \(-0.634411\pi\) | ||||
−0.409827 | + | 0.912163i | \(0.634411\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −347904. | −1.84071 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −221231. | −1.12634 | −0.563169 | − | 0.826342i | \(-0.690418\pi\) | ||||
−0.563169 | + | 0.826342i | \(0.690418\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 345600. | 1.69412 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 359491. | 1.69767 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 241034. | 1.09718 | 0.548589 | − | 0.836092i | \(-0.315165\pi\) | ||||
0.548589 | + | 0.836092i | \(0.315165\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 169020. | 0.741997 | 0.370999 | − | 0.928633i | \(-0.379015\pi\) | ||||
0.370999 | + | 0.928633i | \(0.379015\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 340992. | 1.44443 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3491.81 | −0.0142794 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −117484. | −0.464044 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 300435. | 1.14672 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −103810. | −0.383066 | −0.191533 | − | 0.981486i | \(-0.561346\pi\) | ||||
−0.191533 | + | 0.981486i | \(0.561346\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −101595. | −0.362602 | −0.181301 | − | 0.983428i | \(-0.558031\pi\) | ||||
−0.181301 | + | 0.983428i | \(0.558031\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 505050. | 1.74424 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 91784.8 | 0.306861 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −234458. | −0.759130 | −0.379565 | − | 0.925165i | \(-0.623926\pi\) | ||||
−0.379565 | + | 0.925165i | \(0.623926\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −546330. | −1.71381 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 525312. | 1.59718 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 388672. | 1.14581 | 0.572907 | − | 0.819620i | \(-0.305815\pi\) | ||||
0.572907 | + | 0.819620i | \(0.305815\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 105984. | 0.303061 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −67342.1 | −0.186851 | −0.0934256 | − | 0.995626i | \(-0.529782\pi\) | ||||
−0.0934256 | + | 0.995626i | \(0.529782\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −369529. | −0.995249 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.09119e6 | −2.85372 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −206282. | −0.524018 | −0.262009 | − | 0.965065i | \(-0.584385\pi\) | ||||
−0.262009 | + | 0.965065i | \(0.584385\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 167773. | 0.414122 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −246528. | −0.591470 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 198119. | 0.462161 | 0.231081 | − | 0.972935i | \(-0.425774\pi\) | ||||
0.231081 | + | 0.972935i | \(0.425774\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19746.0 | −0.0448005 | −0.0224002 | − | 0.999749i | \(-0.507131\pi\) | ||||
−0.0224002 | + | 0.999749i | \(0.507131\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 812484. | 1.79344 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 549700. | 1.18085 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 79979.2 | 0.167253 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.29946e6 | −2.64610 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 701023. | 1.39043 | 0.695215 | − | 0.718802i | \(-0.255309\pi\) | ||||
0.695215 | + | 0.718802i | \(0.255309\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −628622. | −1.21478 | −0.607388 | − | 0.794405i | \(-0.707783\pi\) | ||||
−0.607388 | + | 0.794405i | \(0.707783\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −53541.2 | −0.100833 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −334034. | −0.613232 | −0.306616 | − | 0.951833i | \(-0.599197\pi\) | ||||
−0.306616 | + | 0.951833i | \(0.599197\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −318088. | −0.569396 | −0.284698 | − | 0.958617i | \(-0.591893\pi\) | ||||
−0.284698 | + | 0.958617i | \(0.591893\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 467712. | 0.816561 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 424671. | 0.723290 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −233588. | −0.388209 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.65861e6 | −2.69041 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −172800. | −0.273639 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −736357. | −1.13863 | −0.569315 | − | 0.822120i | \(-0.692791\pi\) | ||||
−0.569315 | + | 0.822120i | \(0.692791\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.24410e6 | 3.38916 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −577480. | −0.852002 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −331776. | −0.478295 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.05070e6 | 1.48037 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −40404.0 | −0.0556472 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.31226e6 | 1.76708 | 0.883541 | − | 0.468354i | \(-0.155153\pi\) | ||||
0.883541 | + | 0.468354i | \(0.155153\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −529725. | −0.697580 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −344276. | −0.443448 | −0.221724 | − | 0.975109i | \(-0.571168\pi\) | ||||
−0.221724 | + | 0.975109i | \(0.571168\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −664626. | −0.837507 | −0.418754 | − | 0.908100i | \(-0.637533\pi\) | ||||
−0.418754 | + | 0.908100i | \(0.637533\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −383102. | −0.472372 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.09433e6 | 1.32056 | 0.660281 | − | 0.751019i | \(-0.270437\pi\) | ||||
0.660281 | + | 0.751019i | \(0.270437\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 566006. | 0.668577 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.46067e6 | 2.84566 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 596269. | 0.675223 | 0.337612 | − | 0.941285i | \(-0.390381\pi\) | ||||
0.337612 | + | 0.941285i | \(0.390381\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −64734.0 | −0.0717943 | −0.0358971 | − | 0.999355i | \(-0.511429\pi\) | ||||
−0.0358971 | + | 0.999355i | \(0.511429\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 567420. | 0.616437 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 498686. | 0.530777 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 87295.4 | 0.0910435 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.08979e6 | −1.11390 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.29521e6 | −1.29765 | −0.648824 | − | 0.760938i | \(-0.724739\pi\) | ||||
−0.648824 | + | 0.760938i | \(0.724739\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −262656. | −0.257980 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.22635e6 | 1.18104 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 52226.0 | 0.0493235 | 0.0246618 | − | 0.999696i | \(-0.492149\pi\) | ||||
0.0246618 | + | 0.999696i | \(0.492149\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.98701e6 | −1.84056 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.34085e6 | −1.21837 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.17342e6 | −1.04607 | −0.523037 | − | 0.852310i | \(-0.675201\pi\) | ||||
−0.523037 | + | 0.852310i | \(0.675201\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −906844. | −0.793264 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 386039. | 0.331401 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −359498. | −0.302912 | −0.151456 | − | 0.988464i | \(-0.548396\pi\) | ||||
−0.151456 | + | 0.988464i | \(0.548396\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.00331e6 | −0.829877 | −0.414939 | − | 0.909849i | \(-0.636197\pi\) | ||||
−0.414939 | + | 0.909849i | \(0.636197\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 193536. | 0.157165 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −83886.7 | −0.0668900 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −638370. | −0.499888 | −0.249944 | − | 0.968260i | \(-0.580412\pi\) | ||||
−0.249944 | + | 0.968260i | \(0.580412\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.04754e6 | 0.805679 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −112790. | −0.0852128 | −0.0426064 | − | 0.999092i | \(-0.513566\pi\) | ||||
−0.0426064 | + | 0.999092i | \(0.513566\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 487939. | 0.362160 | 0.181080 | − | 0.983468i | \(-0.442041\pi\) | ||||
0.181080 | + | 0.983468i | \(0.442041\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.64960e6 | −1.93227 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 844354. | 0.605090 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −494413. | −0.348213 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.53387e6 | 3.13861 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 990350. | 0.673938 | 0.336969 | − | 0.941516i | \(-0.390598\pi\) | ||||
0.336969 | + | 0.941516i | \(0.390598\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −409207. | −0.273772 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 649728. | 0.427406 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 132689. | 0.0858335 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.08742e6 | 1.32799 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.11707e6 | −2.57621 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.34863e6 | 0.830123 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −340618. | −0.206263 | −0.103132 | − | 0.994668i | \(-0.532886\pi\) | ||||
−0.103132 | + | 0.994668i | \(0.532886\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.78784e6 | −1.66101 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.41418e6 | 0.829097 | 0.414548 | − | 0.910027i | \(-0.363940\pi\) | ||||
0.414548 | + | 0.910027i | \(0.363940\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 940154. | 0.542423 | 0.271212 | − | 0.962520i | \(-0.412576\pi\) | ||||
0.271212 | + | 0.962520i | \(0.412576\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.01559e6 | −2.28020 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.42825e6 | −1.35720 | −0.678602 | − | 0.734506i | \(-0.737414\pi\) | ||||
−0.678602 | + | 0.734506i | \(0.737414\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −212336. | −0.116828 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.40288e6 | 2.92660 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.99948e6 | −1.06638 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 42378.0 | 0.0222552 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.41483e6 | 1.76604 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.04595e6 | −1.04209 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 762296. | 0.382432 | 0.191216 | − | 0.981548i | \(-0.438757\pi\) | ||||
0.191216 | + | 0.981548i | \(0.438757\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.27375e6 | 3.10039 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 776347. | 0.377958 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.97506e6 | 1.42699 | 0.713495 | − | 0.700661i | \(-0.247111\pi\) | ||||
0.713495 | + | 0.700661i | \(0.247111\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.42106e6 | −0.671603 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 165888. | 0.0772554 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 992008. | 0.455281 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.02739e6 | −1.82170 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.91159e6 | 1.29810 | 0.649048 | − | 0.760748i | \(-0.275167\pi\) | ||||
0.649048 | + | 0.760748i | \(0.275167\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.60641e6 | 0.705979 | 0.352989 | − | 0.935627i | \(-0.385165\pi\) | ||||
0.352989 | + | 0.935627i | \(0.385165\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −328231. | −0.142204 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.22819e6 | −1.80600 | −0.903000 | − | 0.429641i | \(-0.858640\pi\) | ||||
−0.903000 | + | 0.429641i | \(0.858640\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.72493e6 | 1.56873 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.43290e6 | −1.84084 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.07464e6 | −0.849583 | −0.424792 | − | 0.905291i | \(-0.639653\pi\) | ||||
−0.424792 | + | 0.905291i | \(0.639653\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.84390e6 | 0.744680 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.27163e6 | −1.70148 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.74404e6 | 0.685212 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.33087e6 | 0.903343 | 0.451672 | − | 0.892184i | \(-0.350828\pi\) | ||||
0.451672 | + | 0.892184i | \(0.350828\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.66595e6 | −1.01926 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.27798e6 | 1.23644 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.50630e6 | 0.560583 | 0.280292 | − | 0.959915i | \(-0.409569\pi\) | ||||
0.280292 | + | 0.959915i | \(0.409569\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.26998e6 | −1.93522 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 107268. | 0.0388702 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 843772. | 0.301736 | 0.150868 | − | 0.988554i | \(-0.451793\pi\) | ||||
0.150868 | + | 0.988554i | \(0.451793\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.12877e6 | −1.45716 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.58360e6 | −1.24831 | −0.624155 | − | 0.781300i | \(-0.714557\pi\) | ||||
−0.624155 | + | 0.781300i | \(0.714557\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −635904. | −0.218645 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.59080e6 | −2.23697 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 786446. | 0.263509 | 0.131754 | − | 0.991282i | \(-0.457939\pi\) | ||||
0.131754 | + | 0.991282i | \(0.457939\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.03921e6 | −1.00535 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.13094e6 | −2.00238 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.08443e6 | 1.31716 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.16889e6 | 0.372217 | 0.186108 | − | 0.982529i | \(-0.440412\pi\) | ||||
0.186108 | + | 0.982529i | \(0.440412\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.57755e6 | 3.01177 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.58400e6 | −1.42359 | −0.711793 | − | 0.702390i | \(-0.752116\pi\) | ||||
−0.711793 | + | 0.702390i | \(0.752116\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −83803.5 | −0.0257039 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.09405e6 | 1.24027 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 993504. | 0.297292 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.31356e6 | 1.27505 | 0.637526 | − | 0.770429i | \(-0.279958\pi\) | ||||
0.637526 | + | 0.770429i | \(0.279958\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.67973e6 | 1.95054 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.47917e6 | 0.426719 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.80893e6 | −0.515585 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.68403e6 | 1.31911 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.63257e6 | −1.01083 | −0.505416 | − | 0.862876i | \(-0.668661\pi\) | ||||
−0.505416 | + | 0.862876i | \(0.668661\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.01688e6 | −1.37952 | −0.689761 | − | 0.724037i | \(-0.742284\pi\) | ||||
−0.689761 | + | 0.724037i | \(0.742284\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.45986e6 | 1.75538 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −970658. | −0.260672 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.87491e6 | −1.29389 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −96768.0 | −0.0253857 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −189888. | −0.0492385 | −0.0246192 | − | 0.999697i | \(-0.507837\pi\) | ||||
−0.0246192 | + | 0.999697i | \(0.507837\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.21687e6 | 1.33718 | 0.668590 | − | 0.743631i | \(-0.266898\pi\) | ||||
0.668590 | + | 0.743631i | \(0.266898\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.25581e6 | −0.824966 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.56640e6 | 1.64484 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.36661e6 | −0.833741 | −0.416871 | − | 0.908966i | \(-0.636873\pi\) | ||||
−0.416871 | + | 0.908966i | \(0.636873\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.69152e6 | 1.39358 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.42654e6 | −1.07166 | −0.535828 | − | 0.844327i | \(-0.680000\pi\) | ||||
−0.535828 | + | 0.844327i | \(0.680000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 640780. | 0.153394 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.87687e6 | −0.681006 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 443506. | 0.103821 | 0.0519103 | − | 0.998652i | \(-0.483469\pi\) | ||||
0.0519103 | + | 0.998652i | \(0.483469\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −422177. | −0.0977357 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.81549e6 | −0.644627 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 321247. | 0.0727462 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 590538. | 0.132269 | 0.0661344 | − | 0.997811i | \(-0.478933\pi\) | ||||
0.0661344 | + | 0.997811i | \(0.478933\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.51804e6 | 1.66561 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.79463e6 | −1.05076 | −0.525380 | − | 0.850868i | \(-0.676077\pi\) | ||||
−0.525380 | + | 0.850868i | \(0.676077\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.40038e6 | 0.303595 | 0.151798 | − | 0.988412i | \(-0.451494\pi\) | ||||
0.151798 | + | 0.988412i | \(0.451494\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.54362e6 | 0.545531 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.31681e6 | 0.703766 | 0.351883 | − | 0.936044i | \(-0.385542\pi\) | ||||
0.351883 | + | 0.936044i | \(0.385542\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.80627e6 | −0.589112 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.49749e6 | −1.34956 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.04371e6 | −0.214500 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.09717e6 | 0.426480 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.03498e7 | −2.08275 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.00360e6 | −0.996424 | −0.498212 | − | 0.867055i | \(-0.666010\pi\) | ||||
−0.498212 | + | 0.867055i | \(0.666010\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −501900. | −0.0989133 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.45579e7 | 2.83942 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.52569e6 | 1.45275 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.90133e6 | 1.12753 | 0.563764 | − | 0.825936i | \(-0.309353\pi\) | ||||
0.563764 | + | 0.825936i | \(0.309353\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.07712e7 | 2.03700 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.15480e6 | −1.52654 | −0.763272 | − | 0.646077i | \(-0.776409\pi\) | ||||
−0.763272 | + | 0.646077i | \(0.776409\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.45695e6 | −0.455280 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.00779e6 | 0.368304 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.34646e7 | −2.44513 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −470979. | −0.0846741 | −0.0423370 | − | 0.999103i | \(-0.513480\pi\) | ||||
−0.0423370 | + | 0.999103i | \(0.513480\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.86624e6 | −0.332180 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.23452e6 | 1.62740 | 0.813700 | − | 0.581285i | \(-0.197450\pi\) | ||||
0.813700 | + | 0.581285i | \(0.197450\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.83385e6 | −1.19244 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.02407e7 | −1.76933 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.95283e6 | −0.505177 | −0.252588 | − | 0.967574i | \(-0.581282\pi\) | ||||
−0.252588 | + | 0.967574i | \(0.581282\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.30422e6 | −1.06802 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.62432e7 | −2.72507 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.62749e6 | −0.768824 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.02298e6 | 0.168321 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.71665e6 | −0.931587 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.04570e7 | 1.68776 | 0.843882 | − | 0.536529i | \(-0.180265\pi\) | ||||
0.843882 | + | 0.536529i | \(0.180265\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.77571e6 | −0.923318 | −0.461659 | − | 0.887058i | \(-0.652746\pi\) | ||||
−0.461659 | + | 0.887058i | \(0.652746\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.64947e6 | 0.736216 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.91950e6 | 0.301066 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.54459e6 | 0.550714 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.67030e6 | −0.718801 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 213276. | 0.0325180 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.96814e6 | 1.35462 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.49043e6 | 0.821620 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 901304. | 0.133629 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.86409e6 | −0.567615 | −0.283808 | − | 0.958881i | \(-0.591598\pi\) | ||||
−0.283808 | + | 0.958881i | \(0.591598\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −547217. | −0.0796453 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.66821e6 | 0.817438 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.49633e6 | 1.21412 | 0.607062 | − | 0.794654i | \(-0.292348\pi\) | ||||
0.607062 | + | 0.794654i | \(0.292348\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.53920e7 | 2.17953 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.30839e6 | 0.744876 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.47640e7 | −2.05302 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.52337e7 | 2.09930 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.33253e6 | 0.864848 | 0.432424 | − | 0.901671i | \(-0.357658\pi\) | ||||
0.432424 | + | 0.901671i | \(0.357658\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 527264. | 0.0713672 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.21645e6 | 0.297338 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.47605e6 | 1.12700 | 0.563498 | − | 0.826117i | \(-0.309455\pi\) | ||||
0.563498 | + | 0.826117i | \(0.309455\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.35879e6 | −0.310862 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.47988e7 | −1.93317 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.69279e6 | 0.219191 | 0.109596 | − | 0.993976i | \(-0.465044\pi\) | ||||
0.109596 | + | 0.993976i | \(0.465044\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.50901e6 | −0.578750 | −0.289375 | − | 0.957216i | \(-0.593448\pi\) | ||||
−0.289375 | + | 0.957216i | \(0.593448\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.94273e7 | 2.47188 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.18769e6 | 0.402075 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.07577e6 | −0.509648 | −0.254824 | − | 0.966987i | \(-0.582018\pi\) | ||||
−0.254824 | + | 0.966987i | \(0.582018\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.74209e7 | −2.15960 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.53875e6 | 0.803627 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.63899e6 | −0.199712 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.01430e6 | −0.122540 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.15563e6 | 0.976928 | 0.488464 | − | 0.872584i | \(-0.337557\pi\) | ||||
0.488464 | + | 0.872584i | \(0.337557\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.14720e6 | −0.492569 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.25702e6 | −1.09019 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −528622. | −0.0617317 | −0.0308659 | − | 0.999524i | \(-0.509826\pi\) | ||||
−0.0308659 | + | 0.999524i | \(0.509826\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.35808e6 | −0.852064 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.81510e6 | −1.01226 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.84381e6 | −0.551595 | −0.275797 | − | 0.961216i | \(-0.588942\pi\) | ||||
−0.275797 | + | 0.961216i | \(0.588942\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.11804e6 | −0.239193 | −0.119596 | − | 0.992823i | \(-0.538160\pi\) | ||||
−0.119596 | + | 0.992823i | \(0.538160\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.86048e6 | 0.992348 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.09039e6 | −0.787557 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.93109e6 | 0.763536 | 0.381768 | − | 0.924258i | \(-0.375315\pi\) | ||||
0.381768 | + | 0.924258i | \(0.375315\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.17688e7 | 1.28585 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −516789. | −0.0560028 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.21599e6 | −0.345671 | −0.172836 | − | 0.984951i | \(-0.555293\pi\) | ||||
−0.172836 | + | 0.984951i | \(0.555293\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.47338e6 | −0.690150 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.46326e7 | 1.54742 | 0.773709 | − | 0.633541i | \(-0.218399\pi\) | ||||
0.773709 | + | 0.633541i | \(0.218399\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.42706e6 | 0.254597 | 0.127299 | − | 0.991864i | \(-0.459369\pi\) | ||||
0.127299 | + | 0.991864i | \(0.459369\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.46897e7 | −2.56913 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.31624e6 | −0.239091 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.59442e6 | −0.572869 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.78877e6 | −0.486469 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.14959e7 | 1.15855 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.62235e7 | 1.62207 | 0.811036 | − | 0.584996i | \(-0.198904\pi\) | ||||
0.811036 | + | 0.584996i | \(0.198904\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.04065e7 | −2.02423 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.85327e6 | −0.674471 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −455322. | −0.0444601 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.25128e7 | 4.11877 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.22399e7 | −1.17662 | −0.588308 | − | 0.808637i | \(-0.700206\pi\) | ||||
−0.588308 | + | 0.808637i | \(0.700206\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.40461e6 | 0.229360 | 0.114680 | − | 0.993402i | \(-0.463416\pi\) | ||||
0.114680 | + | 0.993402i | \(0.463416\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.60036e7 | −1.51467 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.39515e7 | −1.31026 | −0.655132 | − | 0.755514i | \(-0.727387\pi\) | ||||
−0.655132 | + | 0.755514i | \(0.727387\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −739584. | −0.0689248 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.19445e6 | −0.850302 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.59391e7 | −1.46279 | −0.731395 | − | 0.681954i | \(-0.761130\pi\) | ||||
−0.731395 | + | 0.681954i | \(0.761130\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.01766e7 | −0.926833 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.99048e7 | 1.79906 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.36470e6 | 0.301809 | 0.150905 | − | 0.988548i | \(-0.451781\pi\) | ||||
0.150905 | + | 0.988548i | \(0.451781\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.51194e6 | −0.757748 | −0.378874 | − | 0.925448i | \(-0.623689\pi\) | ||||
−0.378874 | + | 0.925448i | \(0.623689\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.11971e6 | −0.0989284 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.58976e7 | 1.39405 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.06875e6 | 0.702250 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.63663e7 | 3.14148 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.43745e6 | 0.208992 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.15169e7 | 0.980161 | 0.490080 | − | 0.871677i | \(-0.336967\pi\) | ||||
0.490080 | + | 0.871677i | \(0.336967\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.88535e6 | −0.666134 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.32692e7 | −1.95124 | −0.975618 | − | 0.219475i | \(-0.929565\pi\) | ||||
−0.975618 | + | 0.219475i | \(0.929565\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.72032e7 | −2.26436 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.54086e6 | −0.788352 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.90399e7 | −1.56176 | −0.780880 | − | 0.624682i | \(-0.785229\pi\) | ||||
−0.780880 | + | 0.624682i | \(0.785229\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.10876e7 | 0.902838 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.84187e7 | −1.48890 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 827988. | 0.0664471 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.15780e6 | 0.570275 | 0.285138 | − | 0.958487i | \(-0.407961\pi\) | ||||
0.285138 | + | 0.958487i | \(0.407961\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.25760e6 | −0.574064 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.77494e6 | 0.610569 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.88504e6 | −0.380878 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.03270e7 | 2.34766 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.77684e6 | 0.674595 | 0.337297 | − | 0.941398i | \(-0.390487\pi\) | ||||
0.337297 | + | 0.941398i | \(0.390487\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.48376e7 | −1.89549 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.56856e7 | 1.18858 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.47024e7 | 1.85862 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.08481e6 | 0.604024 | 0.302012 | − | 0.953304i | \(-0.402342\pi\) | ||||
0.302012 | + | 0.953304i | \(0.402342\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.66157e7 | 3.45827 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.30374e6 | −0.464381 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −160623. | −0.0117502 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.65243e7 | 1.20040 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.42855e7 | −1.03056 | −0.515280 | − | 0.857022i | \(-0.672312\pi\) | ||||
−0.515280 | + | 0.857022i | \(0.672312\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.67270e7 | 1.19834 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.79396e6 | −0.127634 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.57699e6 | 0.182082 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.17227e7 | 0.822605 | 0.411302 | − | 0.911499i | \(-0.365074\pi\) | ||||
0.411302 | + | 0.911499i | \(0.365074\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5.90244e6 | −0.411351 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.20769e7 | −0.835912 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.81661e7 | 1.24882 | 0.624412 | − | 0.781095i | \(-0.285339\pi\) | ||||
0.624412 | + | 0.781095i | \(0.285339\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.38200e7 | 0.943603 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.40314e6 | 0.0951549 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.27312e7 | −0.857550 | −0.428775 | − | 0.903411i | \(-0.641055\pi\) | ||||
−0.428775 | + | 0.903411i | \(0.641055\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.41920e6 | 0.161855 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.82988e6 | −0.121605 | −0.0608023 | − | 0.998150i | \(-0.519366\pi\) | ||||
−0.0608023 | + | 0.998150i | \(0.519366\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.77526e6 | −0.315215 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.06454e7 | −1.35369 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.24173e7 | −2.11141 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.64577e6 | 0.365278 | 0.182639 | − | 0.983180i | \(-0.441536\pi\) | ||||
0.182639 | + | 0.983180i | \(0.441536\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.58940e7 | −2.30693 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.67338e6 | −0.298376 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 139230. | 0.00883066 | 0.00441533 | − | 0.999990i | \(-0.498595\pi\) | ||||
0.00441533 | + | 0.999990i | \(0.498595\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.27894e6 | −0.458631 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.36251e7 | 0.852863 | 0.426432 | − | 0.904520i | \(-0.359770\pi\) | ||||
0.426432 | + | 0.904520i | \(0.359770\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.04890e7 | −1.27412 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.32323e7 | 1.43529 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 373624. | 0.0229322 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.06840e7 | −0.651504 | −0.325752 | − | 0.945455i | \(-0.605618\pi\) | ||||
−0.325752 | + | 0.945455i | \(0.605618\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.44733e6 | 0.0876862 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.22367e7 | 1.33851 | 0.669255 | − | 0.743033i | \(-0.266614\pi\) | ||||
0.669255 | + | 0.743033i | \(0.266614\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.01328e6 | −0.120407 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.50656e7 | −3.27211 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.05544e7 | 0.623148 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.73229e6 | 0.394944 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.99595e7 | −1.16345 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.07851e7 | −0.624667 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.81333e7 | 1.61914 | 0.809569 | − | 0.587025i | \(-0.199701\pi\) | ||||
0.809569 | + | 0.587025i | \(0.199701\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.25187e7 | −1.85969 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.52635e6 | 0.484531 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.23136e6 | −0.0695346 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.51312e7 | −1.41025 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.43450e7 | −1.35758 | −0.678789 | − | 0.734333i | \(-0.737495\pi\) | ||||
−0.678789 | + | 0.734333i | \(0.737495\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.18369e7 | 0.655951 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.31325e6 | 0.402744 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.15211e6 | 0.172509 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.41644e7 | 1.31427 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.96270e6 | −0.538509 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.30810e7 | 1.23989 | 0.619945 | − | 0.784645i | \(-0.287155\pi\) | ||||
0.619945 | + | 0.784645i | \(0.287155\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.33586e7 | 1.78096 | 0.890482 | − | 0.455019i | \(-0.150368\pi\) | ||||
0.890482 | + | 0.455019i | \(0.150368\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.78047e7 | −1.47534 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.78789e7 | 0.942860 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.60928e7 | 1.36762 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.66641e6 | 0.190999 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.03134e7 | −1.05178 | −0.525890 | − | 0.850553i | \(-0.676268\pi\) | ||||
−0.525890 | + | 0.850553i | \(0.676268\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.90531e6 | 0.355372 | 0.177686 | − | 0.984087i | \(-0.443139\pi\) | ||||
0.177686 | + | 0.984087i | \(0.443139\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.32474e6 | −0.118916 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.12498e7 | 1.58885 | 0.794427 | − | 0.607360i | \(-0.207771\pi\) | ||||
0.794427 | + | 0.607360i | \(0.207771\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.32015e7 | 1.17254 | 0.586272 | − | 0.810114i | \(-0.300595\pi\) | ||||
0.586272 | + | 0.810114i | \(0.300595\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.76910e7 | −0.888690 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.04290e7 | 0.520753 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.09774e6 | −0.153755 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.55935e7 | 0.769359 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.91651e7 | −1.43041 | −0.715203 | − | 0.698917i | \(-0.753666\pi\) | ||||
−0.715203 | + | 0.698917i | \(0.753666\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.39882e7 | −0.681982 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.12573e6 | −0.151489 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.69983e7 | −0.818964 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.56298e7 | 1.22754 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.35222e7 | 0.643839 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.77532e7 | −1.78702 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.23146e6 | −0.434408 | −0.217204 | − | 0.976126i | \(-0.569694\pi\) | ||||
−0.217204 | + | 0.976126i | \(0.569694\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.01948e7 | −2.34825 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.34077e6 | −0.341421 | −0.170710 | − | 0.985321i | \(-0.554606\pi\) | ||||
−0.170710 | + | 0.985321i | \(0.554606\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.57274e7 | −0.727233 | −0.363616 | − | 0.931549i | \(-0.618458\pi\) | ||||
−0.363616 | + | 0.931549i | \(0.618458\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.33994e7 | 1.07572 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.72990e6 | −0.261891 | −0.130945 | − | 0.991390i | \(-0.541801\pi\) | ||||
−0.130945 | + | 0.991390i | \(0.541801\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.48897e6 | −0.431200 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.37016e7 | −0.619046 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.38202e6 | 0.331608 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −708838. | −0.0316593 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.58910e7 | 3.81428 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.16199e7 | 1.39618 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.57123e7 | 1.56790 | 0.783950 | − | 0.620823i | \(-0.213202\pi\) | ||||
0.783950 | + | 0.620823i | \(0.213202\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.74454e7 | 1.19811 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.77000e6 | −0.0768304 | −0.0384152 | − | 0.999262i | \(-0.512231\pi\) | ||||
−0.0384152 | + | 0.999262i | \(0.512231\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.70394e7 | −1.16706 | −0.583532 | − | 0.812090i | \(-0.698330\pi\) | ||||
−0.583532 | + | 0.812090i | \(0.698330\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.13403e7 | −0.486705 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.07893e7 | 1.31399 | 0.656994 | − | 0.753896i | \(-0.271828\pi\) | ||||
0.656994 | + | 0.753896i | \(0.271828\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.47726e7 | 1.05128 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.39940e6 | 0.312250 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.55744e7 | −1.07319 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.11347e6 | 0.380300 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.67718e6 | 0.152593 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.09605e6 | −0.210298 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.89649e7 | −0.778284 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.78484e7 | 2.36087 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −908316. | −0.0368651 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.94729e7 | −0.785983 | −0.392992 | − | 0.919542i | \(-0.628560\pi\) | ||||
−0.392992 | + | 0.919542i | \(0.628560\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.79950e7 | −3.13081 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.44863e7 | 0.977522 | 0.488761 | − | 0.872418i | \(-0.337449\pi\) | ||||
0.488761 | + | 0.872418i | \(0.337449\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.26938e6 | −0.129804 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.73743e7 | 1.47577 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.67857e7 | 1.44463 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.05656e7 | −0.803254 | −0.401627 | − | 0.915803i | \(-0.631555\pi\) | ||||
−0.401627 | + | 0.915803i | \(0.631555\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.43949e6 | −0.366690 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.40103e6 | −0.131403 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.20576e7 | −0.463345 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.28137e7 | −2.01859 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.50171e7 | −1.71135 | −0.855674 | − | 0.517514i | \(-0.826857\pi\) | ||||
−0.855674 | + | 0.517514i | \(0.826857\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.25326e7 | −0.851995 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.91910e7 | 1.47395 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.67904e6 | 0.137628 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.31151e7 | 0.860097 | 0.430048 | − | 0.902806i | \(-0.358496\pi\) | ||||
0.430048 | + | 0.902806i | \(0.358496\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.60543e7 | 0.964308 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −664042. | −0.0244468 | −0.0122234 | − | 0.999925i | \(-0.503891\pi\) | ||||
−0.0122234 | + | 0.999925i | \(0.503891\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.60427e7 | 0.587488 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.97750e7 | −2.17741 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.17375e7 | −1.87469 | −0.937347 | − | 0.348398i | \(-0.886726\pi\) | ||||
−0.937347 | + | 0.348398i | \(0.886726\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.59239e6 | −0.0573962 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.72936e7 | −2.41281 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.89030e7 | 1.03089 | 0.515444 | − | 0.856923i | \(-0.327627\pi\) | ||||
0.515444 | + | 0.856923i | \(0.327627\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.22471e7 | 1.14415 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.88442e6 | −0.207694 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.00784e7 | −1.40723 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.46478e7 | −0.860935 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.02354e8 | 3.55663 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.89166e7 | −0.999607 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.36554e7 | −0.813512 | −0.406756 | − | 0.913537i | \(-0.633340\pi\) | ||||
−0.406756 | + | 0.913537i | \(0.633340\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.54112e7 | −1.89578 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.15207e7 | −1.07287 | −0.536436 | − | 0.843941i | \(-0.680230\pi\) | ||||
−0.536436 | + | 0.843941i | \(0.680230\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.81042e7 | −0.951676 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.17441e6 | 0.0395649 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.82778e6 | 0.161812 | 0.0809060 | − | 0.996722i | \(-0.474219\pi\) | ||||
0.0809060 | + | 0.996722i | \(0.474219\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.15812e6 | 0.0386186 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.46916e7 | 2.14622 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.81641e7 | 0.929636 | 0.464818 | − | 0.885406i | \(-0.346120\pi\) | ||||
0.464818 | + | 0.885406i | \(0.346120\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.53656e7 | −0.504612 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.66991e7 | −1.85261 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.96611e7 | 1.28936 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.95301e7 | −0.955171 | −0.477585 | − | 0.878585i | \(-0.658488\pi\) | ||||
−0.477585 | + | 0.878585i | \(0.658488\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.11254e7 | 0.679879 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.46320e7 | −0.468540 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.16306e7 | −1.64501 | −0.822507 | − | 0.568756i | \(-0.807425\pi\) | ||||
−0.822507 | + | 0.568756i | \(0.807425\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.33894e7 | 2.96063 |
(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 | 32.6.a.d.1.2 | yes | 2 | |
3.2 | odd | 2 | 288.6.a.l.1.1 | 2 | |||
4.3 | odd | 2 | inner | 32.6.a.d.1.1 | ✓ | 2 | |
5.2 | odd | 4 | 800.6.c.d.449.2 | 4 | |||
5.3 | odd | 4 | 800.6.c.d.449.4 | 4 | |||
5.4 | even | 2 | 800.6.a.k.1.1 | 2 | |||
8.3 | odd | 2 | 64.6.a.h.1.2 | 2 | |||
8.5 | even | 2 | 64.6.a.h.1.1 | 2 | |||
12.11 | even | 2 | 288.6.a.l.1.2 | 2 | |||
16.3 | odd | 4 | 256.6.b.l.129.1 | 4 | |||
16.5 | even | 4 | 256.6.b.l.129.2 | 4 | |||
16.11 | odd | 4 | 256.6.b.l.129.4 | 4 | |||
16.13 | even | 4 | 256.6.b.l.129.3 | 4 | |||
20.3 | even | 4 | 800.6.c.d.449.1 | 4 | |||
20.7 | even | 4 | 800.6.c.d.449.3 | 4 | |||
20.19 | odd | 2 | 800.6.a.k.1.2 | 2 | |||
24.5 | odd | 2 | 576.6.a.bp.1.1 | 2 | |||
24.11 | even | 2 | 576.6.a.bp.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.6.a.d.1.1 | ✓ | 2 | 4.3 | odd | 2 | inner | |
32.6.a.d.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
64.6.a.h.1.1 | 2 | 8.5 | even | 2 | |||
64.6.a.h.1.2 | 2 | 8.3 | odd | 2 | |||
256.6.b.l.129.1 | 4 | 16.3 | odd | 4 | |||
256.6.b.l.129.2 | 4 | 16.5 | even | 4 | |||
256.6.b.l.129.3 | 4 | 16.13 | even | 4 | |||
256.6.b.l.129.4 | 4 | 16.11 | odd | 4 | |||
288.6.a.l.1.1 | 2 | 3.2 | odd | 2 | |||
288.6.a.l.1.2 | 2 | 12.11 | even | 2 | |||
576.6.a.bp.1.1 | 2 | 24.5 | odd | 2 | |||
576.6.a.bp.1.2 | 2 | 24.11 | even | 2 | |||
800.6.a.k.1.1 | 2 | 5.4 | even | 2 | |||
800.6.a.k.1.2 | 2 | 20.19 | odd | 2 | |||
800.6.c.d.449.1 | 4 | 20.3 | even | 4 | |||
800.6.c.d.449.2 | 4 | 5.2 | odd | 4 | |||
800.6.c.d.449.3 | 4 | 20.7 | even | 4 | |||
800.6.c.d.449.4 | 4 | 5.3 | odd | 4 |