Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,6,Mod(1,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, 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("441.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.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: | \(70.7292645375\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 59x^{4} + 122x^{3} + 941x^{2} - 1856x - 2338 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4}\cdot 7^{3} \) |
Twist minimal: | no (minimal twist has level 147) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.75353\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.20863 | −1.45109 | −0.725547 | − | 0.688172i | \(-0.758413\pi\) | ||||
−0.725547 | + | 0.688172i | \(0.758413\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 35.3816 | 1.10568 | ||||||||
\(5\) | 29.2259 | 0.522809 | 0.261405 | − | 0.965229i | \(-0.415814\pi\) | ||||
0.261405 | + | 0.965229i | \(0.415814\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −27.7583 | −0.153344 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −239.905 | −0.758646 | ||||||||
\(11\) | −377.338 | −0.940262 | −0.470131 | − | 0.882597i | \(-0.655793\pi\) | ||||
−0.470131 | + | 0.882597i | \(0.655793\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −509.772 | −0.836600 | −0.418300 | − | 0.908309i | \(-0.637374\pi\) | ||||
−0.418300 | + | 0.908309i | \(0.637374\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −904.354 | −0.883158 | ||||||||
\(17\) | 1605.98 | 1.34778 | 0.673889 | − | 0.738833i | \(-0.264623\pi\) | ||||
0.673889 | + | 0.738833i | \(0.264623\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2156.74 | −1.37061 | −0.685306 | − | 0.728256i | \(-0.740331\pi\) | ||||
−0.685306 | + | 0.728256i | \(0.740331\pi\) | |||||||
\(20\) | 1034.06 | 0.578057 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3097.43 | 1.36441 | ||||||||
\(23\) | 4434.38 | 1.74789 | 0.873944 | − | 0.486027i | \(-0.161554\pi\) | ||||
0.873944 | + | 0.486027i | \(0.161554\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2270.85 | −0.726671 | ||||||||
\(26\) | 4184.53 | 1.21399 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4772.55 | −1.05379 | −0.526897 | − | 0.849929i | \(-0.676645\pi\) | ||||
−0.526897 | + | 0.849929i | \(0.676645\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7155.93 | 1.33740 | 0.668701 | − | 0.743532i | \(-0.266851\pi\) | ||||
0.668701 | + | 0.743532i | \(0.266851\pi\) | |||||||
\(32\) | 8311.77 | 1.43489 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −13182.9 | −1.95575 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5574.32 | 0.669402 | 0.334701 | − | 0.942324i | \(-0.391365\pi\) | ||||
0.334701 | + | 0.942324i | \(0.391365\pi\) | |||||||
\(38\) | 17703.9 | 1.98889 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −811.262 | −0.0801699 | ||||||||
\(41\) | −9911.64 | −0.920844 | −0.460422 | − | 0.887700i | \(-0.652302\pi\) | ||||
−0.460422 | + | 0.887700i | \(0.652302\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4886.16 | −0.402992 | −0.201496 | − | 0.979489i | \(-0.564580\pi\) | ||||
−0.201496 | + | 0.979489i | \(0.564580\pi\) | |||||||
\(44\) | −13350.8 | −1.03962 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −36400.2 | −2.53635 | ||||||||
\(47\) | 9266.09 | 0.611859 | 0.305930 | − | 0.952054i | \(-0.401033\pi\) | ||||
0.305930 | + | 0.952054i | \(0.401033\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 18640.5 | 1.05447 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −18036.6 | −0.925007 | ||||||||
\(53\) | 9246.11 | 0.452136 | 0.226068 | − | 0.974111i | \(-0.427413\pi\) | ||||
0.226068 | + | 0.974111i | \(0.427413\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11028.1 | −0.491578 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 39176.1 | 1.52915 | ||||||||
\(59\) | −14120.7 | −0.528114 | −0.264057 | − | 0.964507i | \(-0.585061\pi\) | ||||
−0.264057 | + | 0.964507i | \(0.585061\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 18030.9 | 0.620431 | 0.310216 | − | 0.950666i | \(-0.399599\pi\) | ||||
0.310216 | + | 0.950666i | \(0.399599\pi\) | |||||||
\(62\) | −58740.4 | −1.94070 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −39288.9 | −1.19900 | ||||||||
\(65\) | −14898.6 | −0.437382 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −46514.1 | −1.26589 | −0.632947 | − | 0.774195i | \(-0.718155\pi\) | ||||
−0.632947 | + | 0.774195i | \(0.718155\pi\) | |||||||
\(68\) | 56822.2 | 1.49020 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −64269.9 | −1.51308 | −0.756540 | − | 0.653948i | \(-0.773112\pi\) | ||||
−0.756540 | + | 0.653948i | \(0.773112\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 60921.0 | 1.33801 | 0.669005 | − | 0.743258i | \(-0.266720\pi\) | ||||
0.669005 | + | 0.743258i | \(0.266720\pi\) | |||||||
\(74\) | −45757.5 | −0.971366 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −76309.0 | −1.51545 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −71464.7 | −1.28832 | −0.644160 | − | 0.764891i | \(-0.722793\pi\) | ||||
−0.644160 | + | 0.764891i | \(0.722793\pi\) | |||||||
\(80\) | −26430.6 | −0.461723 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 81361.0 | 1.33623 | ||||||||
\(83\) | 11597.5 | 0.184785 | 0.0923926 | − | 0.995723i | \(-0.470549\pi\) | ||||
0.0923926 | + | 0.995723i | \(0.470549\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 46936.3 | 0.704630 | ||||||||
\(86\) | 40108.7 | 0.584780 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 10474.3 | 0.144184 | ||||||||
\(89\) | 78238.9 | 1.04700 | 0.523502 | − | 0.852025i | \(-0.324625\pi\) | ||||
0.523502 | + | 0.852025i | \(0.324625\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 156896. | 1.93260 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −76061.9 | −0.887866 | ||||||||
\(95\) | −63032.8 | −0.716568 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −151480. | −1.63466 | −0.817330 | − | 0.576170i | \(-0.804546\pi\) | ||||
−0.817330 | + | 0.576170i | \(0.804546\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −80346.1 | −0.803461 | ||||||||
\(101\) | −91407.2 | −0.891614 | −0.445807 | − | 0.895129i | \(-0.647083\pi\) | ||||
−0.445807 | + | 0.895129i | \(0.647083\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 56930.8 | 0.528754 | 0.264377 | − | 0.964419i | \(-0.414834\pi\) | ||||
0.264377 | + | 0.964419i | \(0.414834\pi\) | |||||||
\(104\) | 14150.4 | 0.128288 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −75897.9 | −0.656093 | ||||||||
\(107\) | 196209. | 1.65676 | 0.828380 | − | 0.560166i | \(-0.189263\pi\) | ||||
0.828380 | + | 0.560166i | \(0.189263\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 105853. | 0.853368 | 0.426684 | − | 0.904401i | \(-0.359682\pi\) | ||||
0.426684 | + | 0.904401i | \(0.359682\pi\) | |||||||
\(110\) | 90525.2 | 0.713326 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 67589.3 | 0.497945 | 0.248973 | − | 0.968511i | \(-0.419907\pi\) | ||||
0.248973 | + | 0.968511i | \(0.419907\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 129599. | 0.913812 | ||||||||
\(116\) | −168861. | −1.16515 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 115912. | 0.766343 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −18667.0 | −0.115907 | ||||||||
\(122\) | −148009. | −0.900304 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 253188. | 1.47873 | ||||||||
\(125\) | −157699. | −0.902719 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 281805. | 1.55039 | 0.775193 | − | 0.631724i | \(-0.217653\pi\) | ||||
0.775193 | + | 0.631724i | \(0.217653\pi\) | |||||||
\(128\) | 56531.6 | 0.304977 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 122297. | 0.634683 | ||||||||
\(131\) | −88576.7 | −0.450964 | −0.225482 | − | 0.974247i | \(-0.572396\pi\) | ||||
−0.225482 | + | 0.974247i | \(0.572396\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 381817. | 1.83693 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −44579.3 | −0.206674 | ||||||||
\(137\) | 286830. | 1.30564 | 0.652820 | − | 0.757513i | \(-0.273586\pi\) | ||||
0.652820 | + | 0.757513i | \(0.273586\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 345909. | 1.51853 | 0.759267 | − | 0.650779i | \(-0.225558\pi\) | ||||
0.759267 | + | 0.650779i | \(0.225558\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 527568. | 2.19562 | ||||||||
\(143\) | 192356. | 0.786623 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −139482. | −0.550933 | ||||||||
\(146\) | −500078. | −1.94158 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 197228. | 0.740142 | ||||||||
\(149\) | 304757. | 1.12458 | 0.562288 | − | 0.826942i | \(-0.309921\pi\) | ||||
0.562288 | + | 0.826942i | \(0.309921\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 348313. | 1.24316 | 0.621581 | − | 0.783350i | \(-0.286491\pi\) | ||||
0.621581 | + | 0.783350i | \(0.286491\pi\) | |||||||
\(152\) | 59867.5 | 0.210176 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 209139. | 0.699206 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −188561. | −0.610523 | −0.305262 | − | 0.952269i | \(-0.598744\pi\) | ||||
−0.305262 | + | 0.952269i | \(0.598744\pi\) | |||||||
\(158\) | 586627. | 1.86947 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 242919. | 0.750174 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 271248. | 0.799645 | 0.399823 | − | 0.916593i | \(-0.369072\pi\) | ||||
0.399823 | + | 0.916593i | \(0.369072\pi\) | |||||||
\(164\) | −350690. | −1.01815 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −95199.2 | −0.268141 | ||||||||
\(167\) | 422260. | 1.17163 | 0.585813 | − | 0.810446i | \(-0.300775\pi\) | ||||
0.585813 | + | 0.810446i | \(0.300775\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −111425. | −0.300101 | ||||||||
\(170\) | −385283. | −1.02249 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −172880. | −0.445578 | ||||||||
\(173\) | 301288. | 0.765361 | 0.382681 | − | 0.923881i | \(-0.375001\pi\) | ||||
0.382681 | + | 0.923881i | \(0.375001\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 341247. | 0.830400 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −642235. | −1.51930 | ||||||||
\(179\) | 285557. | 0.666131 | 0.333065 | − | 0.942904i | \(-0.391917\pi\) | ||||
0.333065 | + | 0.942904i | \(0.391917\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −536753. | −1.21781 | −0.608903 | − | 0.793244i | \(-0.708390\pi\) | ||||
−0.608903 | + | 0.793244i | \(0.708390\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −123091. | −0.268029 | ||||||||
\(185\) | 162915. | 0.349970 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −605998. | −1.26726 | ||||||||
\(188\) | 327849. | 0.676518 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 517413. | 1.03981 | ||||||||
\(191\) | 356684. | 0.707457 | 0.353729 | − | 0.935348i | \(-0.384914\pi\) | ||||
0.353729 | + | 0.935348i | \(0.384914\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 750853. | 1.45098 | 0.725490 | − | 0.688233i | \(-0.241613\pi\) | ||||
0.725490 | + | 0.688233i | \(0.241613\pi\) | |||||||
\(194\) | 1.24345e6 | 2.37205 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −296470. | −0.544272 | −0.272136 | − | 0.962259i | \(-0.587730\pi\) | ||||
−0.272136 | + | 0.962259i | \(0.587730\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −484572. | −0.867412 | −0.433706 | − | 0.901055i | \(-0.642794\pi\) | ||||
−0.433706 | + | 0.901055i | \(0.642794\pi\) | |||||||
\(200\) | 63034.9 | 0.111431 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 750328. | 1.29382 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −289677. | −0.481426 | ||||||||
\(206\) | −467323. | −0.767272 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 461014. | 0.738849 | ||||||||
\(209\) | 813821. | 1.28873 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 849306. | 1.31328 | 0.656641 | − | 0.754203i | \(-0.271977\pi\) | ||||
0.656641 | + | 0.754203i | \(0.271977\pi\) | |||||||
\(212\) | 327142. | 0.499916 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.61061e6 | −2.40412 | ||||||||
\(215\) | −142803. | −0.210688 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −868906. | −1.23832 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −390190. | −0.543525 | ||||||||
\(221\) | −818684. | −1.12755 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.06822e6 | −1.43847 | −0.719233 | − | 0.694769i | \(-0.755506\pi\) | ||||
−0.719233 | + | 0.694769i | \(0.755506\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −554815. | −0.722566 | ||||||||
\(227\) | 32350.8 | 0.0416698 | 0.0208349 | − | 0.999783i | \(-0.493368\pi\) | ||||
0.0208349 | + | 0.999783i | \(0.493368\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.18287e6 | −1.49056 | −0.745280 | − | 0.666752i | \(-0.767684\pi\) | ||||
−0.745280 | + | 0.666752i | \(0.767684\pi\) | |||||||
\(230\) | −1.06383e6 | −1.32603 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 132478. | 0.161593 | ||||||||
\(233\) | −329750. | −0.397919 | −0.198960 | − | 0.980008i | \(-0.563756\pi\) | ||||
−0.198960 | + | 0.980008i | \(0.563756\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 270810. | 0.319886 | ||||||||
\(236\) | −499614. | −0.583922 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 459379. | 0.520207 | 0.260104 | − | 0.965581i | \(-0.416243\pi\) | ||||
0.260104 | + | 0.965581i | \(0.416243\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.45979e6 | 1.61900 | 0.809499 | − | 0.587121i | \(-0.199739\pi\) | ||||
0.809499 | + | 0.587121i | \(0.199739\pi\) | |||||||
\(242\) | 153230. | 0.168192 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 637963. | 0.685995 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.09945e6 | 1.14665 | ||||||||
\(248\) | −198636. | −0.205083 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.29449e6 | 1.30993 | ||||||||
\(251\) | 523090. | 0.524074 | 0.262037 | − | 0.965058i | \(-0.415606\pi\) | ||||
0.262037 | + | 0.965058i | \(0.415606\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.67326e6 | −1.64347 | ||||||||
\(254\) | −2.31324e6 | −2.24976 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 793198. | 0.756453 | ||||||||
\(257\) | 465448. | 0.439580 | 0.219790 | − | 0.975547i | \(-0.429463\pi\) | ||||
0.219790 | + | 0.975547i | \(0.429463\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −527135. | −0.483602 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 727094. | 0.654391 | ||||||||
\(263\) | −129621. | −0.115555 | −0.0577773 | − | 0.998329i | \(-0.518401\pi\) | ||||
−0.0577773 | + | 0.998329i | \(0.518401\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 270226. | 0.236381 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.64574e6 | −1.39967 | ||||||||
\(269\) | 1.40436e6 | 1.18331 | 0.591653 | − | 0.806193i | \(-0.298476\pi\) | ||||
0.591653 | + | 0.806193i | \(0.298476\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 885085. | 0.732086 | 0.366043 | − | 0.930598i | \(-0.380712\pi\) | ||||
0.366043 | + | 0.930598i | \(0.380712\pi\) | |||||||
\(272\) | −1.45237e6 | −1.19030 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.35448e6 | −1.89461 | ||||||||
\(275\) | 856876. | 0.683261 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.33714e6 | −1.04707 | −0.523535 | − | 0.852004i | \(-0.675387\pi\) | ||||
−0.523535 | + | 0.852004i | \(0.675387\pi\) | |||||||
\(278\) | −2.83944e6 | −2.20354 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.80115e6 | 1.36077 | 0.680383 | − | 0.732857i | \(-0.261813\pi\) | ||||
0.680383 | + | 0.732857i | \(0.261813\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 971887. | 0.721356 | 0.360678 | − | 0.932690i | \(-0.382545\pi\) | ||||
0.360678 | + | 0.932690i | \(0.382545\pi\) | |||||||
\(284\) | −2.27397e6 | −1.67297 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.57898e6 | −1.14146 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.15932e6 | 0.816503 | ||||||||
\(290\) | 1.14496e6 | 0.799456 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.15548e6 | 1.47941 | ||||||||
\(293\) | −675064. | −0.459384 | −0.229692 | − | 0.973263i | \(-0.573772\pi\) | ||||
−0.229692 | + | 0.973263i | \(0.573772\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −412692. | −0.276103 | ||||||||
\(296\) | −154734. | −0.102649 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.50164e6 | −1.63186 | ||||||||
\(299\) | −2.26052e6 | −1.46228 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.85918e6 | −1.80395 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.95046e6 | 1.21047 | ||||||||
\(305\) | 526971. | 0.324367 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −894063. | −0.541405 | −0.270702 | − | 0.962663i | \(-0.587256\pi\) | ||||
−0.270702 | + | 0.962663i | \(0.587256\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.71674e6 | −1.01461 | ||||||||
\(311\) | −974011. | −0.571035 | −0.285518 | − | 0.958373i | \(-0.592166\pi\) | ||||
−0.285518 | + | 0.958373i | \(0.592166\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −705256. | −0.406899 | −0.203449 | − | 0.979085i | \(-0.565215\pi\) | ||||
−0.203449 | + | 0.979085i | \(0.565215\pi\) | |||||||
\(314\) | 1.54783e6 | 0.885927 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.52854e6 | −1.42446 | ||||||||
\(317\) | 1.88491e6 | 1.05352 | 0.526761 | − | 0.850014i | \(-0.323406\pi\) | ||||
0.526761 | + | 0.850014i | \(0.323406\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.80087e6 | 0.990842 | ||||||||
\(320\) | −1.14826e6 | −0.626850 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.46369e6 | −1.84728 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.15761e6 | 0.607932 | ||||||||
\(326\) | −2.22657e6 | −1.16036 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 275131. | 0.141206 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 605333. | 0.303686 | 0.151843 | − | 0.988405i | \(-0.451479\pi\) | ||||
0.151843 | + | 0.988405i | \(0.451479\pi\) | |||||||
\(332\) | 410336. | 0.204312 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.46618e6 | −1.70014 | ||||||||
\(335\) | −1.35942e6 | −0.661821 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.50499e6 | 1.68117 | 0.840586 | − | 0.541677i | \(-0.182211\pi\) | ||||
0.840586 | + | 0.541677i | \(0.182211\pi\) | |||||||
\(338\) | 914650. | 0.435475 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.66068e6 | 0.779092 | ||||||||
\(341\) | −2.70020e6 | −1.25751 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 135632. | 0.0617966 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.47316e6 | −1.11061 | ||||||||
\(347\) | 2.66338e6 | 1.18743 | 0.593717 | − | 0.804674i | \(-0.297660\pi\) | ||||
0.593717 | + | 0.804674i | \(0.297660\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.02690e6 | −0.890778 | −0.445389 | − | 0.895337i | \(-0.646935\pi\) | ||||
−0.445389 | + | 0.895337i | \(0.646935\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.13635e6 | −1.34917 | ||||||||
\(353\) | 1.50563e6 | 0.643103 | 0.321551 | − | 0.946892i | \(-0.395796\pi\) | ||||
0.321551 | + | 0.946892i | \(0.395796\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.87835e6 | −0.791052 | ||||||||
\(356\) | 2.76822e6 | 1.15765 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.34403e6 | −0.966619 | ||||||||
\(359\) | −2.08268e6 | −0.852877 | −0.426438 | − | 0.904517i | \(-0.640232\pi\) | ||||
−0.426438 | + | 0.904517i | \(0.640232\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.17544e6 | 0.878575 | ||||||||
\(362\) | 4.40601e6 | 1.76715 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.78047e6 | 0.699524 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.93430e6 | 1.13721 | 0.568603 | − | 0.822612i | \(-0.307484\pi\) | ||||
0.568603 | + | 0.822612i | \(0.307484\pi\) | |||||||
\(368\) | −4.01025e6 | −1.54366 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.33731e6 | −0.507839 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −407769. | −0.151755 | −0.0758774 | − | 0.997117i | \(-0.524176\pi\) | ||||
−0.0758774 | + | 0.997117i | \(0.524176\pi\) | |||||||
\(374\) | 4.97441e6 | 1.83892 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −257211. | −0.0938253 | ||||||||
\(377\) | 2.43291e6 | 0.881604 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 326165. | 0.116638 | 0.0583188 | − | 0.998298i | \(-0.481426\pi\) | ||||
0.0583188 | + | 0.998298i | \(0.481426\pi\) | |||||||
\(380\) | −2.23020e6 | −0.792292 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.92789e6 | −1.02659 | ||||||||
\(383\) | 1.76218e6 | 0.613838 | 0.306919 | − | 0.951736i | \(-0.400702\pi\) | ||||
0.306919 | + | 0.951736i | \(0.400702\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.16347e6 | −2.10551 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.35962e6 | −1.80740 | ||||||||
\(389\) | 3.55950e6 | 1.19266 | 0.596328 | − | 0.802741i | \(-0.296626\pi\) | ||||
0.596328 | + | 0.802741i | \(0.296626\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.12153e6 | 2.35576 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.43362e6 | 0.789790 | ||||||||
\(395\) | −2.08862e6 | −0.673546 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 635379. | 0.202328 | 0.101164 | − | 0.994870i | \(-0.467743\pi\) | ||||
0.101164 | + | 0.994870i | \(0.467743\pi\) | |||||||
\(398\) | 3.97767e6 | 1.25870 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.05365e6 | 0.641765 | ||||||||
\(401\) | −1.97947e6 | −0.614734 | −0.307367 | − | 0.951591i | \(-0.599448\pi\) | ||||
−0.307367 | + | 0.951591i | \(0.599448\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.64789e6 | −1.11887 | ||||||||
\(404\) | −3.23413e6 | −0.985836 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.10340e6 | −0.629414 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.28287e6 | −1.56157 | −0.780785 | − | 0.624799i | \(-0.785181\pi\) | ||||
−0.780785 | + | 0.624799i | \(0.785181\pi\) | |||||||
\(410\) | 2.37785e6 | 0.698594 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.01430e6 | 0.584630 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 338946. | 0.0966074 | ||||||||
\(416\) | −4.23711e6 | −1.20043 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.68036e6 | −1.87007 | ||||||||
\(419\) | −318626. | −0.0886639 | −0.0443319 | − | 0.999017i | \(-0.514116\pi\) | ||||
−0.0443319 | + | 0.999017i | \(0.514116\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −46024.4 | −0.0126556 | −0.00632780 | − | 0.999980i | \(-0.502014\pi\) | ||||
−0.00632780 | + | 0.999980i | \(0.502014\pi\) | |||||||
\(422\) | −6.97164e6 | −1.90570 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −256656. | −0.0693326 | ||||||||
\(425\) | −3.64693e6 | −0.979390 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 6.94219e6 | 1.83184 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.17221e6 | 0.305728 | ||||||||
\(431\) | 4.55645e6 | 1.18150 | 0.590749 | − | 0.806855i | \(-0.298832\pi\) | ||||
0.590749 | + | 0.806855i | \(0.298832\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.98232e6 | 1.78970 | 0.894850 | − | 0.446368i | \(-0.147283\pi\) | ||||
0.894850 | + | 0.446368i | \(0.147283\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.74524e6 | 0.943547 | ||||||||
\(437\) | −9.56382e6 | −2.39567 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.66904e6 | 0.413338 | 0.206669 | − | 0.978411i | \(-0.433738\pi\) | ||||
0.206669 | + | 0.978411i | \(0.433738\pi\) | |||||||
\(440\) | 306120. | 0.0753807 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.72028e6 | 1.63618 | ||||||||
\(443\) | 561410. | 0.135916 | 0.0679580 | − | 0.997688i | \(-0.478352\pi\) | ||||
0.0679580 | + | 0.997688i | \(0.478352\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.28661e6 | 0.547383 | ||||||||
\(446\) | 8.76864e6 | 2.08735 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.64485e6 | 0.853225 | 0.426613 | − | 0.904434i | \(-0.359707\pi\) | ||||
0.426613 | + | 0.904434i | \(0.359707\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.74004e6 | 0.865835 | ||||||||
\(452\) | 2.39142e6 | 0.550566 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −265556. | −0.0604667 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.81947e6 | 0.631506 | 0.315753 | − | 0.948841i | \(-0.397743\pi\) | ||||
0.315753 | + | 0.948841i | \(0.397743\pi\) | |||||||
\(458\) | 9.70976e6 | 2.16294 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.58542e6 | 1.01038 | ||||||||
\(461\) | 803065. | 0.175994 | 0.0879971 | − | 0.996121i | \(-0.471953\pi\) | ||||
0.0879971 | + | 0.996121i | \(0.471953\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −114276. | −0.0247745 | −0.0123872 | − | 0.999923i | \(-0.503943\pi\) | ||||
−0.0123872 | + | 0.999923i | \(0.503943\pi\) | |||||||
\(464\) | 4.31607e6 | 0.930666 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.70680e6 | 0.577418 | ||||||||
\(467\) | −6.17863e6 | −1.31099 | −0.655496 | − | 0.755199i | \(-0.727540\pi\) | ||||
−0.655496 | + | 0.755199i | \(0.727540\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −2.22298e6 | −0.464184 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 391968. | 0.0809833 | ||||||||
\(473\) | 1.84373e6 | 0.378918 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.89763e6 | 0.995983 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.77087e6 | −0.754869 | ||||||||
\(479\) | 1.38581e6 | 0.275972 | 0.137986 | − | 0.990434i | \(-0.455937\pi\) | ||||
0.137986 | + | 0.990434i | \(0.455937\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.84163e6 | −0.560022 | ||||||||
\(482\) | −1.19828e7 | −2.34932 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −660467. | −0.128156 | ||||||||
\(485\) | −4.42716e6 | −0.854615 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 218793. | 0.0418033 | 0.0209017 | − | 0.999782i | \(-0.493346\pi\) | ||||
0.0209017 | + | 0.999782i | \(0.493346\pi\) | |||||||
\(488\) | −500508. | −0.0951397 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.85181e6 | 1.65702 | 0.828511 | − | 0.559973i | \(-0.189188\pi\) | ||||
0.828511 | + | 0.559973i | \(0.189188\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.66463e6 | −1.42028 | ||||||||
\(494\) | −9.02495e6 | −1.66390 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.47149e6 | −1.18114 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.66757e6 | 0.659367 | 0.329684 | − | 0.944091i | \(-0.393058\pi\) | ||||
0.329684 | + | 0.944091i | \(0.393058\pi\) | |||||||
\(500\) | −5.57963e6 | −0.998114 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.29385e6 | −0.760480 | ||||||||
\(503\) | 8.87701e6 | 1.56440 | 0.782198 | − | 0.623029i | \(-0.214098\pi\) | ||||
0.782198 | + | 0.623029i | \(0.214098\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.67146e6 | −0.466144 | ||||||||
\(506\) | 1.37352e7 | 2.38483 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.97072e6 | 1.71422 | ||||||||
\(509\) | 5.29056e6 | 0.905121 | 0.452561 | − | 0.891734i | \(-0.350511\pi\) | ||||
0.452561 | + | 0.891734i | \(0.350511\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −8.32008e6 | −1.40266 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.82069e6 | −0.637873 | ||||||||
\(515\) | 1.66385e6 | 0.276438 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.49645e6 | −0.575308 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 413559. | 0.0670701 | ||||||||
\(521\) | 8.79675e6 | 1.41980 | 0.709901 | − | 0.704301i | \(-0.248740\pi\) | ||||
0.709901 | + | 0.704301i | \(0.248740\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.03365e6 | 0.484966 | 0.242483 | − | 0.970156i | \(-0.422038\pi\) | ||||
0.242483 | + | 0.970156i | \(0.422038\pi\) | |||||||
\(524\) | −3.13399e6 | −0.498619 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.06401e6 | 0.167681 | ||||||||
\(527\) | 1.14923e7 | 1.80252 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.32274e7 | 2.05511 | ||||||||
\(530\) | −2.21819e6 | −0.343011 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.05268e6 | 0.770378 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.73439e6 | 0.866170 | ||||||||
\(536\) | 1.29115e6 | 0.194118 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.15279e7 | −1.71709 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.43726e6 | −0.211126 | −0.105563 | − | 0.994413i | \(-0.533665\pi\) | ||||
−0.105563 | + | 0.994413i | \(0.533665\pi\) | |||||||
\(542\) | −7.26534e6 | −1.06233 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.33485e7 | 1.93391 | ||||||||
\(545\) | 3.09365e6 | 0.446148 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.93548e6 | 0.848179 | 0.424089 | − | 0.905620i | \(-0.360594\pi\) | ||||
0.424089 | + | 0.905620i | \(0.360594\pi\) | |||||||
\(548\) | 1.01485e7 | 1.44361 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −7.03378e6 | −0.991476 | ||||||||
\(551\) | 1.02932e7 | 1.44434 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.09761e7 | 1.51940 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.22388e7 | 1.67901 | ||||||||
\(557\) | −4.39523e6 | −0.600266 | −0.300133 | − | 0.953897i | \(-0.597031\pi\) | ||||
−0.300133 | + | 0.953897i | \(0.597031\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.49083e6 | 0.337143 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.47850e7 | −1.97460 | ||||||||
\(563\) | −6.46414e6 | −0.859487 | −0.429744 | − | 0.902951i | \(-0.641396\pi\) | ||||
−0.429744 | + | 0.902951i | \(0.641396\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.97536e6 | 0.260330 | ||||||||
\(566\) | −7.97786e6 | −1.04676 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.78402e6 | 0.232022 | ||||||||
\(569\) | −7.30225e6 | −0.945531 | −0.472766 | − | 0.881188i | \(-0.656744\pi\) | ||||
−0.472766 | + | 0.881188i | \(0.656744\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.15896e6 | −1.17559 | −0.587795 | − | 0.809010i | \(-0.700004\pi\) | ||||
−0.587795 | + | 0.809010i | \(0.700004\pi\) | |||||||
\(572\) | 6.80588e6 | 0.869749 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.00698e7 | −1.27014 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.14739e6 | −0.768690 | −0.384345 | − | 0.923190i | \(-0.625573\pi\) | ||||
−0.384345 | + | 0.923190i | \(0.625573\pi\) | |||||||
\(578\) | −9.51641e6 | −1.18482 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.93510e6 | −0.609153 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.48891e6 | −0.425127 | ||||||||
\(584\) | −1.69106e6 | −0.205177 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.54135e6 | 0.666610 | ||||||||
\(587\) | −8.30740e6 | −0.995107 | −0.497554 | − | 0.867433i | \(-0.665768\pi\) | ||||
−0.497554 | + | 0.867433i | \(0.665768\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.54335e7 | −1.83306 | ||||||||
\(590\) | 3.38763e6 | 0.400651 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.04115e6 | −0.591188 | ||||||||
\(593\) | −1.36669e7 | −1.59600 | −0.797999 | − | 0.602658i | \(-0.794108\pi\) | ||||
−0.797999 | + | 0.602658i | \(0.794108\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.07828e7 | 1.24341 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.85558e7 | 2.12191 | ||||||||
\(599\) | 3.01585e6 | 0.343433 | 0.171717 | − | 0.985146i | \(-0.445069\pi\) | ||||
0.171717 | + | 0.985146i | \(0.445069\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.31661e7 | −1.48686 | −0.743429 | − | 0.668815i | \(-0.766802\pi\) | ||||
−0.743429 | + | 0.668815i | \(0.766802\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.23239e7 | 1.37453 | ||||||||
\(605\) | −545559. | −0.0605974 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.26550e7 | 1.39409 | 0.697044 | − | 0.717028i | \(-0.254498\pi\) | ||||
0.697044 | + | 0.717028i | \(0.254498\pi\) | |||||||
\(608\) | −1.79263e7 | −1.96668 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.32571e6 | −0.470687 | ||||||||
\(611\) | −4.72359e6 | −0.511881 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.03470e6 | −0.433671 | −0.216835 | − | 0.976208i | \(-0.569573\pi\) | ||||
−0.216835 | + | 0.976208i | \(0.569573\pi\) | |||||||
\(614\) | 7.33903e6 | 0.785630 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.52192e7 | 1.60946 | 0.804728 | − | 0.593644i | \(-0.202311\pi\) | ||||
0.804728 | + | 0.593644i | \(0.202311\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.04642e7 | −1.09769 | −0.548843 | − | 0.835925i | \(-0.684932\pi\) | ||||
−0.548843 | + | 0.835925i | \(0.684932\pi\) | |||||||
\(620\) | 7.39966e6 | 0.773094 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7.99530e6 | 0.828626 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.48751e6 | 0.254721 | ||||||||
\(626\) | 5.78919e6 | 0.590448 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.67158e6 | −0.675040 | ||||||||
\(629\) | 8.95225e6 | 0.902205 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.41229e6 | 0.541138 | 0.270569 | − | 0.962701i | \(-0.412788\pi\) | ||||
0.270569 | + | 0.962701i | \(0.412788\pi\) | |||||||
\(632\) | 1.98374e6 | 0.197557 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.54726e7 | −1.52876 | ||||||||
\(635\) | 8.23602e6 | 0.810556 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.47826e7 | −1.43781 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.65219e6 | 0.159445 | ||||||||
\(641\) | −9.82808e6 | −0.944765 | −0.472382 | − | 0.881394i | \(-0.656606\pi\) | ||||
−0.472382 | + | 0.881394i | \(0.656606\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.06067e6 | −0.768854 | −0.384427 | − | 0.923155i | \(-0.625601\pi\) | ||||
−0.384427 | + | 0.923155i | \(0.625601\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.84321e7 | 2.68058 | ||||||||
\(647\) | −1.70359e7 | −1.59994 | −0.799971 | − | 0.600038i | \(-0.795152\pi\) | ||||
−0.799971 | + | 0.600038i | \(0.795152\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.32829e6 | 0.496565 | ||||||||
\(650\) | −9.50242e6 | −0.882167 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.59718e6 | 0.884148 | ||||||||
\(653\) | −1.54447e7 | −1.41741 | −0.708707 | − | 0.705503i | \(-0.750721\pi\) | ||||
−0.708707 | + | 0.705503i | \(0.750721\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.58874e6 | −0.235768 | ||||||||
\(656\) | 8.96363e6 | 0.813251 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.28485e7 | 1.15250 | 0.576248 | − | 0.817275i | \(-0.304516\pi\) | ||||
0.576248 | + | 0.817275i | \(0.304516\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.88793e7 | −1.68067 | −0.840337 | − | 0.542065i | \(-0.817643\pi\) | ||||
−0.840337 | + | 0.542065i | \(0.817643\pi\) | |||||||
\(662\) | −4.96896e6 | −0.440677 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −321926. | −0.0283358 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.11633e7 | −1.84191 | ||||||||
\(668\) | 1.49402e7 | 1.29544 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.11589e7 | 0.960365 | ||||||||
\(671\) | −6.80376e6 | −0.583368 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.42483e6 | 0.121262 | 0.0606311 | − | 0.998160i | \(-0.480689\pi\) | ||||
0.0606311 | + | 0.998160i | \(0.480689\pi\) | |||||||
\(674\) | −2.87712e7 | −2.43954 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.94241e6 | −0.331814 | ||||||||
\(677\) | 1.83981e7 | 1.54277 | 0.771386 | − | 0.636368i | \(-0.219564\pi\) | ||||
0.771386 | + | 0.636368i | \(0.219564\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.30287e6 | −0.108051 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.21650e7 | 1.82476 | ||||||||
\(683\) | 3.69137e6 | 0.302786 | 0.151393 | − | 0.988474i | \(-0.451624\pi\) | ||||
0.151393 | + | 0.988474i | \(0.451624\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.38288e6 | 0.682600 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.41882e6 | 0.355906 | ||||||||
\(689\) | −4.71341e6 | −0.378257 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.42711e7 | −1.13700 | −0.568502 | − | 0.822682i | \(-0.692477\pi\) | ||||
−0.568502 | + | 0.822682i | \(0.692477\pi\) | |||||||
\(692\) | 1.06600e7 | 0.846241 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.18627e7 | −1.72308 | ||||||||
\(695\) | 1.01095e7 | 0.793904 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.59179e7 | −1.24109 | ||||||||
\(698\) | 1.66381e7 | 1.29260 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.09094e7 | −0.838507 | −0.419254 | − | 0.907869i | \(-0.637708\pi\) | ||||
−0.419254 | + | 0.907869i | \(0.637708\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.20224e7 | −0.917490 | ||||||||
\(704\) | 1.48252e7 | 1.12738 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.23591e7 | −0.933203 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.62686e6 | −0.196255 | −0.0981277 | − | 0.995174i | \(-0.531285\pi\) | ||||
−0.0981277 | + | 0.995174i | \(0.531285\pi\) | |||||||
\(710\) | 1.54187e7 | 1.14789 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.17178e6 | −0.160552 | ||||||||
\(713\) | 3.17321e7 | 2.33763 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.62179e6 | 0.411254 | ||||||||
\(716\) | 1.01035e7 | 0.736524 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.70959e7 | 1.23760 | ||||||||
\(719\) | −2.38777e7 | −1.72254 | −0.861272 | − | 0.508144i | \(-0.830332\pi\) | ||||
−0.861272 | + | 0.508144i | \(0.830332\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.78574e7 | −1.27490 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.89912e7 | −1.34650 | ||||||||
\(725\) | 1.08377e7 | 0.765761 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.62895e7 | 1.84479 | 0.922393 | − | 0.386253i | \(-0.126231\pi\) | ||||
0.922393 | + | 0.386253i | \(0.126231\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.46152e7 | −1.01508 | ||||||||
\(731\) | −7.84708e6 | −0.543144 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.13470e7 | −0.780051 | −0.390025 | − | 0.920804i | \(-0.627534\pi\) | ||||
−0.390025 | + | 0.920804i | \(0.627534\pi\) | |||||||
\(734\) | −2.40866e7 | −1.65019 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.68576e7 | 2.50803 | ||||||||
\(737\) | 1.75515e7 | 1.19027 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.89668e6 | −0.329830 | −0.164915 | − | 0.986308i | \(-0.552735\pi\) | ||||
−0.164915 | + | 0.986308i | \(0.552735\pi\) | |||||||
\(740\) | 5.76418e6 | 0.386953 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.56896e7 | −1.04265 | −0.521326 | − | 0.853357i | \(-0.674563\pi\) | ||||
−0.521326 | + | 0.853357i | \(0.674563\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.90681e6 | 0.587938 | ||||||||
\(746\) | 3.34723e6 | 0.220211 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.14412e7 | −1.40118 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.36120e7 | −0.880687 | −0.440344 | − | 0.897829i | \(-0.645143\pi\) | ||||
−0.440344 | + | 0.897829i | \(0.645143\pi\) | |||||||
\(752\) | −8.37982e6 | −0.540368 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.99709e7 | −1.27929 | ||||||||
\(755\) | 1.01798e7 | 0.649937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.65571e6 | 0.358713 | 0.179357 | − | 0.983784i | \(-0.442598\pi\) | ||||
0.179357 | + | 0.983784i | \(0.442598\pi\) | |||||||
\(758\) | −2.67737e6 | −0.169252 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.74968e6 | 0.109882 | ||||||||
\(761\) | 1.74718e7 | 1.09364 | 0.546822 | − | 0.837249i | \(-0.315837\pi\) | ||||
0.546822 | + | 0.837249i | \(0.315837\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.26200e7 | 0.782218 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.44651e7 | −0.890737 | ||||||||
\(767\) | 7.19836e6 | 0.441820 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.34195e7 | −0.818316 | −0.409158 | − | 0.912464i | \(-0.634177\pi\) | ||||
−0.409158 | + | 0.912464i | \(0.634177\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.65664e7 | 1.60431 | ||||||||
\(773\) | 1.72891e7 | 1.04069 | 0.520347 | − | 0.853955i | \(-0.325802\pi\) | ||||
0.520347 | + | 0.853955i | \(0.325802\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.62500e7 | −0.971850 | ||||||||
\(776\) | 4.20484e6 | 0.250666 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.92186e7 | −1.73066 | ||||||||
\(779\) | 2.13769e7 | 1.26212 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.42515e7 | 1.42269 | ||||||||
\(782\) | −5.84580e7 | −3.41843 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.51086e6 | −0.319187 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.45247e7 | 0.835932 | 0.417966 | − | 0.908463i | \(-0.362743\pi\) | ||||
0.417966 | + | 0.908463i | \(0.362743\pi\) | |||||||
\(788\) | −1.04896e7 | −0.601788 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.71447e7 | 0.977378 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.19167e6 | −0.519053 | ||||||||
\(794\) | −5.21559e6 | −0.293597 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.71449e7 | −0.959075 | ||||||||
\(797\) | 1.33304e7 | 0.743354 | 0.371677 | − | 0.928362i | \(-0.378783\pi\) | ||||
0.371677 | + | 0.928362i | \(0.378783\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.48812e7 | 0.824650 | ||||||||
\(800\) | −1.88747e7 | −1.04269 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.62487e7 | 0.892038 | ||||||||
\(803\) | −2.29878e7 | −1.25808 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.99442e7 | 1.62358 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.53731e6 | 0.136724 | ||||||||
\(809\) | −8.29655e6 | −0.445683 | −0.222842 | − | 0.974855i | \(-0.571533\pi\) | ||||
−0.222842 | + | 0.974855i | \(0.571533\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.73910e6 | 0.253013 | 0.126507 | − | 0.991966i | \(-0.459623\pi\) | ||||
0.126507 | + | 0.991966i | \(0.459623\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.72660e7 | 0.913339 | ||||||||
\(815\) | 7.92747e6 | 0.418062 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.05382e7 | 0.552346 | ||||||||
\(818\) | 4.33651e7 | 2.26599 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.02492e7 | −0.532300 | ||||||||
\(821\) | 7.73294e6 | 0.400393 | 0.200197 | − | 0.979756i | \(-0.435842\pi\) | ||||
0.200197 | + | 0.979756i | \(0.435842\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.52365e7 | 0.784123 | 0.392062 | − | 0.919939i | \(-0.371762\pi\) | ||||
0.392062 | + | 0.919939i | \(0.371762\pi\) | |||||||
\(824\) | −1.58030e6 | −0.0810816 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.56525e7 | −1.30427 | −0.652133 | − | 0.758105i | \(-0.726126\pi\) | ||||
−0.652133 | + | 0.758105i | \(0.726126\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.26069e7 | −1.14250 | −0.571248 | − | 0.820778i | \(-0.693541\pi\) | ||||
−0.571248 | + | 0.820778i | \(0.693541\pi\) | |||||||
\(830\) | −2.78228e6 | −0.140187 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.00284e7 | 1.00309 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.23409e7 | 0.612537 | ||||||||
\(836\) | 2.87943e7 | 1.42492 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.61549e6 | 0.128660 | ||||||||
\(839\) | −1.59455e7 | −0.782049 | −0.391024 | − | 0.920380i | \(-0.627879\pi\) | ||||
−0.391024 | + | 0.920380i | \(0.627879\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.26610e6 | 0.110481 | ||||||||
\(842\) | 377797. | 0.0183645 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.00498e7 | 1.45206 | ||||||||
\(845\) | −3.25651e6 | −0.156896 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −8.36175e6 | −0.399308 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.99363e7 | 1.42119 | ||||||||
\(851\) | 2.47186e7 | 1.17004 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.44060e7 | 1.61906 | 0.809528 | − | 0.587082i | \(-0.199723\pi\) | ||||
0.809528 | + | 0.587082i | \(0.199723\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.44644e6 | −0.254055 | ||||||||
\(857\) | −5.53039e6 | −0.257219 | −0.128610 | − | 0.991695i | \(-0.541051\pi\) | ||||
−0.128610 | + | 0.991695i | \(0.541051\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.39566e7 | 0.645351 | 0.322676 | − | 0.946510i | \(-0.395418\pi\) | ||||
0.322676 | + | 0.946510i | \(0.395418\pi\) | |||||||
\(860\) | −5.05258e6 | −0.232953 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.74022e7 | −1.71447 | ||||||||
\(863\) | −1.38532e7 | −0.633173 | −0.316586 | − | 0.948564i | \(-0.602537\pi\) | ||||
−0.316586 | + | 0.948564i | \(0.602537\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.80542e6 | 0.400138 | ||||||||
\(866\) | −5.73153e7 | −2.59702 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.69663e7 | 1.21136 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.37116e7 | 1.05905 | ||||||||
\(872\) | −2.93830e6 | −0.130859 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 7.85058e7 | 3.47635 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.42739e7 | −1.06571 | −0.532856 | − | 0.846206i | \(-0.678881\pi\) | ||||
−0.532856 | + | 0.846206i | \(0.678881\pi\) | |||||||
\(878\) | −1.37005e7 | −0.599792 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 9.97326e6 | 0.434141 | ||||||||
\(881\) | −1.86802e7 | −0.810854 | −0.405427 | − | 0.914127i | \(-0.632877\pi\) | ||||
−0.405427 | + | 0.914127i | \(0.632877\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.91586e7 | 1.25854 | 0.629268 | − | 0.777188i | \(-0.283355\pi\) | ||||
0.629268 | + | 0.777188i | \(0.283355\pi\) | |||||||
\(884\) | −2.89664e7 | −1.24670 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.60841e6 | −0.197227 | ||||||||
\(887\) | 625102. | 0.0266773 | 0.0133387 | − | 0.999911i | \(-0.495754\pi\) | ||||
0.0133387 | + | 0.999911i | \(0.495754\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1.87699e7 | −0.794304 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.77954e7 | −1.59048 | ||||||||
\(893\) | −1.99846e7 | −0.838621 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.34566e6 | 0.348259 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.99192e7 | −1.23811 | ||||||||
\(899\) | −3.41520e7 | −1.40934 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.48491e7 | 0.609379 | ||||||||
\(902\) | −3.07006e7 | −1.25641 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.87616e6 | −0.0763572 | ||||||||
\(905\) | −1.56871e7 | −0.636681 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.81672e6 | −0.154054 | −0.0770268 | − | 0.997029i | \(-0.524543\pi\) | ||||
−0.0770268 | + | 0.997029i | \(0.524543\pi\) | |||||||
\(908\) | 1.14462e6 | 0.0460732 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.41226e6 | −0.375749 | −0.187875 | − | 0.982193i | \(-0.560160\pi\) | ||||
−0.187875 | + | 0.982193i | \(0.560160\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.37616e6 | −0.173747 | ||||||||
\(914\) | −2.31440e7 | −0.916374 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.18519e7 | −1.64807 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.81092e6 | 0.266022 | 0.133011 | − | 0.991115i | \(-0.457535\pi\) | ||||
0.133011 | + | 0.991115i | \(0.457535\pi\) | |||||||
\(920\) | −3.59745e6 | −0.140128 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −6.59207e6 | −0.255384 | ||||||||
\(923\) | 3.27630e7 | 1.26584 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.26584e7 | −0.486435 | ||||||||
\(926\) | 938053. | 0.0359501 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.96683e7 | −1.51208 | ||||||||
\(929\) | −6.97913e6 | −0.265315 | −0.132658 | − | 0.991162i | \(-0.542351\pi\) | ||||
−0.132658 | + | 0.991162i | \(0.542351\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.16671e7 | −0.439969 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5.07181e7 | 1.90237 | ||||||||
\(935\) | −1.77108e7 | −0.662537 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.31557e7 | −0.861606 | −0.430803 | − | 0.902446i | \(-0.641770\pi\) | ||||
−0.430803 | + | 0.902446i | \(0.641770\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9.58169e6 | 0.353690 | ||||||||
\(941\) | −1.82489e7 | −0.671835 | −0.335918 | − | 0.941891i | \(-0.609046\pi\) | ||||
−0.335918 | + | 0.941891i | \(0.609046\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.39520e7 | −1.60953 | ||||||||
\(944\) | 1.27701e7 | 0.466408 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.51345e7 | −0.549846 | ||||||||
\(947\) | −1.46102e7 | −0.529395 | −0.264698 | − | 0.964331i | \(-0.585272\pi\) | ||||
−0.264698 | + | 0.964331i | \(0.585272\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.10558e7 | −1.11938 | ||||||||
\(950\) | −4.02028e7 | −1.44527 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.49338e7 | −0.532645 | −0.266322 | − | 0.963884i | \(-0.585809\pi\) | ||||
−0.266322 | + | 0.963884i | \(0.585809\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.04244e7 | 0.369865 | ||||||||
\(956\) | 1.62536e7 | 0.575180 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.13756e7 | −0.400462 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.25781e7 | 0.788641 | ||||||||
\(962\) | 2.33259e7 | 0.812645 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5.16495e7 | 1.79009 | ||||||||
\(965\) | 2.19444e7 | 0.758586 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.73806e6 | −0.162942 | −0.0814712 | − | 0.996676i | \(-0.525962\pi\) | ||||
−0.0814712 | + | 0.996676i | \(0.525962\pi\) | |||||||
\(968\) | 518164. | 0.0177737 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.63409e7 | 1.24013 | ||||||||
\(971\) | 1.34756e7 | 0.458670 | 0.229335 | − | 0.973348i | \(-0.426345\pi\) | ||||
0.229335 | + | 0.973348i | \(0.426345\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.79599e6 | −0.0606606 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.63063e7 | −0.547939 | ||||||||
\(977\) | −2.33437e7 | −0.782410 | −0.391205 | − | 0.920304i | \(-0.627942\pi\) | ||||
−0.391205 | + | 0.920304i | \(0.627942\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.95225e7 | −0.984457 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.26612e7 | −2.40450 | ||||||||
\(983\) | 2.01946e7 | 0.666578 | 0.333289 | − | 0.942825i | \(-0.391842\pi\) | ||||
0.333289 | + | 0.942825i | \(0.391842\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.66462e6 | −0.284550 | ||||||||
\(986\) | 6.29161e7 | 2.06096 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.89002e7 | 1.26783 | ||||||||
\(989\) | −2.16671e7 | −0.704385 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.42175e7 | 0.783330 | 0.391665 | − | 0.920108i | \(-0.371899\pi\) | ||||
0.391665 | + | 0.920108i | \(0.371899\pi\) | |||||||
\(992\) | 5.94784e7 | 1.91902 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.41621e7 | −0.453491 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.84270e6 | −0.186155 | −0.0930776 | − | 0.995659i | \(-0.529670\pi\) | ||||
−0.0930776 | + | 0.995659i | \(0.529670\pi\) | |||||||
\(998\) | −3.01057e7 | −0.956804 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 441.6.a.bb.1.2 | 6 | ||
3.2 | odd | 2 | 147.6.a.n.1.5 | ✓ | 6 | ||
7.6 | odd | 2 | 441.6.a.ba.1.2 | 6 | |||
21.2 | odd | 6 | 147.6.e.q.67.2 | 12 | |||
21.5 | even | 6 | 147.6.e.p.67.2 | 12 | |||
21.11 | odd | 6 | 147.6.e.q.79.2 | 12 | |||
21.17 | even | 6 | 147.6.e.p.79.2 | 12 | |||
21.20 | even | 2 | 147.6.a.o.1.5 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
147.6.a.n.1.5 | ✓ | 6 | 3.2 | odd | 2 | ||
147.6.a.o.1.5 | yes | 6 | 21.20 | even | 2 | ||
147.6.e.p.67.2 | 12 | 21.5 | even | 6 | |||
147.6.e.p.79.2 | 12 | 21.17 | even | 6 | |||
147.6.e.q.67.2 | 12 | 21.2 | odd | 6 | |||
147.6.e.q.79.2 | 12 | 21.11 | odd | 6 | |||
441.6.a.ba.1.2 | 6 | 7.6 | odd | 2 | |||
441.6.a.bb.1.2 | 6 | 1.1 | even | 1 | trivial |